TSTP Solution File: ITP261^3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP261^3 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 03:27:51 EDT 2023
% Result : Timeout 299.83s 300.14s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 2.30/2.34 % Problem : ITP261^3 : TPTP v8.1.2. Released v8.1.0.
% 2.30/2.35 % Command : do_cvc5 %s %d
% 2.35/2.57 % Computer : n013.cluster.edu
% 2.35/2.57 % Model : x86_64 x86_64
% 2.35/2.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 2.35/2.57 % Memory : 8042.1875MB
% 2.35/2.57 % OS : Linux 3.10.0-693.el7.x86_64
% 2.35/2.57 % CPULimit : 300
% 2.35/2.57 % WCLimit : 300
% 2.35/2.57 % DateTime : Sun Aug 27 14:30:49 EDT 2023
% 2.35/2.57 % CPUTime :
% 4.71/4.98 %----Proving TH0
% 4.71/4.98 %------------------------------------------------------------------------------
% 4.71/4.98 % File : ITP261^3 : TPTP v8.1.2. Released v8.1.0.
% 4.71/4.98 % Domain : Interactive Theorem Proving
% 4.71/4.98 % Problem : Sledgehammer problem VEBT_DeleteCorrectness 00010_000214
% 4.71/4.98 % Version : [Des22] axioms.
% 4.71/4.98 % English :
% 4.71/4.98
% 4.71/4.98 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 4.71/4.98 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 4.71/4.98 % Source : [Des22]
% 4.71/4.98 % Names : 0073_VEBT_DeleteCorrectness_00010_000214 [Des22]
% 4.71/4.98
% 4.71/4.98 % Status : Theorem
% 4.71/4.98 % Rating : 1.00 v8.1.0
% 4.71/4.98 % Syntax : Number of formulae : 10531 (4574 unt;1183 typ; 0 def)
% 4.71/4.98 % Number of atoms : 29156 (11175 equ; 0 cnn)
% 4.71/4.98 % Maximal formula atoms : 71 ( 3 avg)
% 4.71/4.98 % Number of connectives : 107864 (3005 ~; 454 |;2337 &;90159 @)
% 4.71/4.98 % ( 0 <=>;11909 =>; 0 <=; 0 <~>)
% 4.71/4.98 % Maximal formula depth : 39 ( 6 avg)
% 4.71/4.98 % Number of types : 92 ( 91 usr)
% 4.71/4.98 % Number of type conns : 4609 (4609 >; 0 *; 0 +; 0 <<)
% 4.71/4.98 % Number of symbols : 1095 (1092 usr; 77 con; 0-8 aty)
% 4.71/4.98 % Number of variables : 24075 (1986 ^;21164 !; 925 ?;24075 :)
% 4.71/4.98 % SPC : TH0_THM_EQU_NAR
% 4.71/4.98
% 4.71/4.98 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 4.71/4.98 % from the van Emde Boas Trees session in the Archive of Formal
% 4.71/4.98 % proofs -
% 4.71/4.98 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 4.71/4.98 % 2022-02-18 07:25:35.497
% 4.71/4.98 %------------------------------------------------------------------------------
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Ocount__list_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
% 4.71/4.99 count_6735058137522573441at_rat: list_set_nat_rat > set_nat_rat > nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Ocount__list_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.71/4.99 count_list_set_nat: list_set_nat > set_nat > nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Ocount__list_001t__VEBT____Definitions__OVEBT,type,
% 4.71/4.99 count_list_VEBT_VEBT: list_VEBT_VEBT > vEBT_VEBT > nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Odistinct_001t__Complex__Ocomplex,type,
% 4.71/4.99 distinct_complex: list_complex > $o ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Odistinct_001t__Extended____Nat__Oenat,type,
% 4.71/4.99 distin4523846830085650399d_enat: list_Extended_enat > $o ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Odistinct_001t__Int__Oint,type,
% 4.71/4.99 distinct_int: list_int > $o ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Odistinct_001t__List__Olist_It__Nat__Onat_J,type,
% 4.71/4.99 distinct_list_nat: list_list_nat > $o ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Odistinct_001t__Nat__Onat,type,
% 4.71/4.99 distinct_nat: list_nat > $o ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Odistinct_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.71/4.99 distin6923225563576452346at_nat: list_P6011104703257516679at_nat > $o ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Odistinct_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.71/4.99 distinct_set_nat: list_set_nat > $o ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Odistinct_001t__VEBT____Definitions__OVEBT,type,
% 4.71/4.99 distinct_VEBT_VEBT: list_VEBT_VEBT > $o ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Oenumerate_001t__Int__Oint,type,
% 4.71/4.99 enumerate_int: nat > list_int > list_P3521021558325789923at_int ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Oenumerate_001t__Nat__Onat,type,
% 4.71/4.99 enumerate_nat: nat > list_nat > list_P6011104703257516679at_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Oenumerate_001t__VEBT____Definitions__OVEBT,type,
% 4.71/4.99 enumerate_VEBT_VEBT: nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Ofind_001t__Int__Oint,type,
% 4.71/4.99 find_int: ( int > $o ) > list_int > option_int ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Ofind_001t__Nat__Onat,type,
% 4.71/4.99 find_nat: ( nat > $o ) > list_nat > option_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Ofind_001t__Num__Onum,type,
% 4.71/4.99 find_num: ( num > $o ) > list_num > option_num ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Ofind_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.71/4.99 find_P8199882355184865565at_nat: ( product_prod_nat_nat > $o ) > list_P6011104703257516679at_nat > option4927543243414619207at_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Ofind_001t__VEBT____Definitions__OVEBT,type,
% 4.71/4.99 find_VEBT_VEBT: ( vEBT_VEBT > $o ) > list_VEBT_VEBT > option_VEBT_VEBT ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Ofold_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.71/4.99 fold_nat_nat: ( nat > nat > nat ) > list_nat > nat > nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olast_001t__Nat__Onat,type,
% 4.71/4.99 last_nat: list_nat > nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 4.71/4.99 linord2614967742042102400et_nat: set_nat > list_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist_OCons_001_Eo,type,
% 4.71/4.99 cons_o: $o > list_o > list_o ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 4.71/4.99 cons_int: int > list_int > list_int ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 4.71/4.99 cons_nat: nat > list_nat > list_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist_OCons_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
% 4.71/4.99 cons_set_nat_rat: set_nat_rat > list_set_nat_rat > list_set_nat_rat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist_OCons_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.71/4.99 cons_set_nat: set_nat > list_set_nat > list_set_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist_OCons_001t__VEBT____Definitions__OVEBT,type,
% 4.71/4.99 cons_VEBT_VEBT: vEBT_VEBT > list_VEBT_VEBT > list_VEBT_VEBT ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 4.71/4.99 nil_int: list_int ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 4.71/4.99 nil_nat: list_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist_Ohd_001t__Nat__Onat,type,
% 4.71/4.99 hd_nat: list_nat > nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.71/4.99 map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist_Omap_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 4.71/4.99 map_VE8901447254227204932T_VEBT: ( vEBT_VEBT > vEBT_VEBT ) > list_VEBT_VEBT > list_VEBT_VEBT ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist_Oset_001_Eo,type,
% 4.71/4.99 set_o2: list_o > set_o ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 4.71/4.99 set_complex2: list_complex > set_complex ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist_Oset_001t__Extended____Nat__Oenat,type,
% 4.71/4.99 set_Extended_enat2: list_Extended_enat > set_Extended_enat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 4.71/4.99 set_int2: list_int > set_int ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Nat__Onat_J,type,
% 4.71/4.99 set_list_nat2: list_list_nat > set_list_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 4.71/4.99 set_list_VEBT_VEBT2: list_list_VEBT_VEBT > set_list_VEBT_VEBT ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 4.71/4.99 set_nat2: list_nat > set_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.71/4.99 set_Pr5648618587558075414at_nat: list_P6011104703257516679at_nat > set_Pr1261947904930325089at_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
% 4.71/4.99 set_real2: list_real > set_real ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist_Oset_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
% 4.71/4.99 set_set_nat_rat2: list_set_nat_rat > set_set_nat_rat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist_Oset_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.71/4.99 set_set_nat2: list_set_nat > set_set_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
% 4.71/4.99 set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
% 4.71/4.99 size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist__update_001_Eo,type,
% 4.71/4.99 list_update_o: list_o > nat > $o > list_o ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist__update_001t__Int__Oint,type,
% 4.71/4.99 list_update_int: list_int > nat > int > list_int ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist__update_001t__Nat__Onat,type,
% 4.71/4.99 list_update_nat: list_nat > nat > nat > list_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist__update_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.71/4.99 list_u6180841689913720943at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat > list_P6011104703257516679at_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist__update_001t__Real__Oreal,type,
% 4.71/4.99 list_update_real: list_real > nat > real > list_real ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist__update_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
% 4.71/4.99 list_u886106648575569423at_rat: list_set_nat_rat > nat > set_nat_rat > list_set_nat_rat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist__update_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.71/4.99 list_update_set_nat: list_set_nat > nat > set_nat > list_set_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Olist__update_001t__VEBT____Definitions__OVEBT,type,
% 4.71/4.99 list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Onth_001_Eo,type,
% 4.71/4.99 nth_o: list_o > nat > $o ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Onth_001t__Int__Oint,type,
% 4.71/4.99 nth_int: list_int > nat > int ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 4.71/4.99 nth_nat: list_nat > nat > nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Onth_001t__Num__Onum,type,
% 4.71/4.99 nth_num: list_num > nat > num ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 4.71/4.99 nth_Pr4439495888332055232nt_int: list_P5707943133018811711nt_int > nat > product_prod_int_int ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
% 4.71/4.99 nth_Pr8617346907841251940nt_nat: list_P8198026277950538467nt_nat > nat > product_prod_int_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Int__Oint_Mt__VEBT____Definitions__OVEBT_J,type,
% 4.71/4.99 nth_Pr3474266648193625910T_VEBT: list_P7524865323317820941T_VEBT > nat > produc1531783533982839933T_VEBT ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
% 4.71/4.99 nth_Pr3440142176431000676at_int: list_P3521021558325789923at_int > nat > product_prod_nat_int ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.71/4.99 nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J,type,
% 4.71/4.99 nth_Pr744662078594809490T_VEBT: list_P5647936690300460905T_VEBT > nat > produc8025551001238799321T_VEBT ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 4.71/4.99 nth_Pr6744343527793145070at_nat: list_P8469869581646625389at_nat > nat > produc859450856879609959at_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 4.71/4.99 nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 4.71/4.99 nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 4.71/4.99 nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Onth_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
% 4.71/4.99 nth_set_nat_rat: list_set_nat_rat > nat > set_nat_rat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Onth_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.71/4.99 nth_set_nat: list_set_nat > nat > set_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 4.71/4.99 nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Oproduct_001t__Int__Oint_001t__Int__Oint,type,
% 4.71/4.99 product_int_int: list_int > list_int > list_P5707943133018811711nt_int ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Oproduct_001t__Int__Oint_001t__Nat__Onat,type,
% 4.71/4.99 product_int_nat: list_int > list_nat > list_P8198026277950538467nt_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Oproduct_001t__Int__Oint_001t__VEBT____Definitions__OVEBT,type,
% 4.71/4.99 produc662631939642741121T_VEBT: list_int > list_VEBT_VEBT > list_P7524865323317820941T_VEBT ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__Int__Oint,type,
% 4.71/4.99 product_nat_int: list_nat > list_int > list_P3521021558325789923at_int ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.71/4.99 product_nat_nat: list_nat > list_nat > list_P6011104703257516679at_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 4.71/4.99 produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Oproduct_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.71/4.99 produc3544356994491977349at_nat: list_P6011104703257516679at_nat > list_P6011104703257516679at_nat > list_P8469869581646625389at_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 4.71/4.99 produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 4.71/4.99 produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 4.71/4.99 produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_OremoveAll_001_Eo,type,
% 4.71/4.99 removeAll_o: $o > list_o > list_o ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_OremoveAll_001t__Int__Oint,type,
% 4.71/4.99 removeAll_int: int > list_int > list_int ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_OremoveAll_001t__Nat__Onat,type,
% 4.71/4.99 removeAll_nat: nat > list_nat > list_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_OremoveAll_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.71/4.99 remove3673390508374433037at_nat: product_prod_nat_nat > list_P6011104703257516679at_nat > list_P6011104703257516679at_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_OremoveAll_001t__Real__Oreal,type,
% 4.71/4.99 removeAll_real: real > list_real > list_real ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_OremoveAll_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
% 4.71/4.99 remove939820145577552881at_rat: set_nat_rat > list_set_nat_rat > list_set_nat_rat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_OremoveAll_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.71/4.99 removeAll_set_nat: set_nat > list_set_nat > list_set_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_OremoveAll_001t__VEBT____Definitions__OVEBT,type,
% 4.71/4.99 removeAll_VEBT_VEBT: vEBT_VEBT > list_VEBT_VEBT > list_VEBT_VEBT ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 4.71/4.99 replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Orotate1_001t__Int__Oint,type,
% 4.71/4.99 rotate1_int: list_int > list_int ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Orotate1_001t__Nat__Onat,type,
% 4.71/4.99 rotate1_nat: list_nat > list_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Orotate1_001t__VEBT____Definitions__OVEBT,type,
% 4.71/4.99 rotate1_VEBT_VEBT: list_VEBT_VEBT > list_VEBT_VEBT ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 4.71/4.99 sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 4.71/4.99 sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 4.71/4.99 take_nat: nat > list_nat > list_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Otake_001t__VEBT____Definitions__OVEBT,type,
% 4.71/4.99 take_VEBT_VEBT: nat > list_VEBT_VEBT > list_VEBT_VEBT ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Oupt,type,
% 4.71/4.99 upt: nat > nat > list_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Oupto,type,
% 4.71/4.99 upto: int > int > list_int ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Oupto__rel,type,
% 4.71/4.99 upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Ozip_001t__Int__Oint_001t__Int__Oint,type,
% 4.71/4.99 zip_int_int: list_int > list_int > list_P5707943133018811711nt_int ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Ozip_001t__Int__Oint_001t__Nat__Onat,type,
% 4.71/4.99 zip_int_nat: list_int > list_nat > list_P8198026277950538467nt_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Ozip_001t__Int__Oint_001t__VEBT____Definitions__OVEBT,type,
% 4.71/4.99 zip_int_VEBT_VEBT: list_int > list_VEBT_VEBT > list_P7524865323317820941T_VEBT ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Ozip_001t__Nat__Onat_001t__Int__Oint,type,
% 4.71/4.99 zip_nat_int: list_nat > list_int > list_P3521021558325789923at_int ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Ozip_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.71/4.99 zip_nat_nat: list_nat > list_nat > list_P6011104703257516679at_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Ozip_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 4.71/4.99 zip_nat_VEBT_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Ozip_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.71/4.99 zip_Pr4664179122662387191at_nat: list_P6011104703257516679at_nat > list_P6011104703257516679at_nat > list_P8469869581646625389at_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 4.71/4.99 zip_VEBT_VEBT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 4.71/4.99 zip_VEBT_VEBT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 4.71/4.99 zip_VE537291747668921783T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_OSuc,type,
% 4.71/4.99 suc: nat > nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.71/4.99 compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 4.71/4.99 case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 4.71/4.99 case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Onat_Opred,type,
% 4.71/4.99 pred: nat > nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 4.71/4.99 semiri4939895301339042750nteger: nat > code_integer ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 4.71/4.99 semiri8010041392384452111omplex: nat > complex ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Extended____Nat__Oenat,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Extended____Nat__Oenat_J,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
% 4.71/4.99 size_s3023201423986296836st_nat: list_list_nat > nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__VEBT____Definitions__OVEBT_J_J,type,
% 4.71/4.99 size_s8217280938318005548T_VEBT: list_list_VEBT_VEBT > nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Num__Onum_J,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_I_062_It__Nat__Onat_Mt__Rat__Orat_J_J_J,type,
% 4.71/4.99 size_s3959913991096427681at_rat: list_set_nat_rat > nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 4.71/4.99 size_s3254054031482475050et_nat: list_set_nat > nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 4.71/4.99 size_size_num: num > nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Nat__Onat_J,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Num__Onum_J,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Osize__class_Osize_001t__String__Ochar,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat__Bijection_Olist__decode,type,
% 4.71/4.99 nat_list_decode: nat > list_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat__Bijection_Olist__decode__rel,type,
% 4.71/4.99 nat_list_decode_rel: nat > nat > $o ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat__Bijection_Olist__encode,type,
% 4.71/4.99 nat_list_encode: list_nat > nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 4.71/4.99 nat_list_encode_rel: list_nat > list_nat > $o ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat__Bijection_Oprod__decode,type,
% 4.71/4.99 nat_prod_decode: nat > product_prod_nat_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 4.71/4.99 nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 4.71/4.99 nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 4.71/4.99 nat_prod_encode: product_prod_nat_nat > nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat__Bijection_Oset__decode,type,
% 4.71/4.99 nat_set_decode: nat > set_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Nat__Bijection_Oset__encode,type,
% 4.71/4.99 nat_set_encode: set_nat > nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_NthRoot_Oroot,type,
% 4.71/4.99 root: nat > real > real ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_NthRoot_Osqrt,type,
% 4.71/4.99 sqrt: real > real ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Num_OBitM,type,
% 4.71/4.99 bitM: num > num ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Num_Oinc,type,
% 4.71/4.99 inc: num > num ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Num_Onat__of__num,type,
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% 4.71/4.99
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% 4.71/4.99 neg_nu8804712462038260780nteger: code_integer > code_integer ).
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% 4.71/4.99 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
% 4.71/4.99 neg_numeral_dbl_rat: rat > rat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
% 4.71/4.99 neg_nu7757733837767384882nteger: code_integer > code_integer ).
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% 4.71/4.99 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Complex__Ocomplex,type,
% 4.71/4.99 neg_nu6511756317524482435omplex: complex > complex ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Code____Numeral__Ointeger,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Complex__Ocomplex,type,
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% 4.71/4.99 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
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% 4.71/4.99 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
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% 4.71/4.99 thf(sy_c_Num_Onum_OBit0,type,
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% 4.71/4.99 thf(sy_c_Num_Onum_OBit1,type,
% 4.71/4.99 bit1: num > num ).
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% 4.71/4.99 thf(sy_c_Num_Onum_Osize__num,type,
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% 4.71/4.99 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex,type,
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% 4.71/4.99 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Rat__Orat,type,
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% 4.71/4.99 thf(sy_c_Option_Ooption_OSome_001t__Nat__Onat,type,
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% 4.71/4.99 thf(sy_c_Option_Ooption_OSome_001t__Num__Onum,type,
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% 4.71/4.99 thf(sy_c_Option_Ooption_Osize__option_001t__Nat__Onat,type,
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% 4.71/4.99 thf(sy_c_Option_Ooption_Osize__option_001t__Num__Onum,type,
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% 4.71/4.99 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 4.71/4.99 produc9060074326276436823at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > produc1319942482725812455at_nat ).
% 4.71/4.99
% 4.71/4.99 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Extended____Nat__Oenat,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__Nat__Onat,type,
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% 4.71/4.99
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
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% 4.71/4.99
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% 4.71/4.99
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Product__Type_Ounit_OAbs__unit,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Product__Type_Ounit_ORep__unit,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Quotient_Oquot__type_Oabs_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Quotient_Oquot__type_Orep_001t__Real__Oreal_001_062_It__Nat__Onat_Mt__Rat__Orat_J,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Rat_OFract,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Rat_Ofield__char__0__class_ORats_001t__Real__Oreal,type,
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% 4.71/4.99
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Real_Ocauchy,type,
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% 4.71/4.99
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Real_Opcr__real,type,
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% 4.71/4.99
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% 4.71/4.99
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Real_Oreal_ORep__real,type,
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Real_Orealrel,type,
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% 4.71/4.99 thf(sy_c_Real_Orep__real,type,
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% 4.71/4.99
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% 4.71/4.99
% 4.71/4.99 thf(sy_c_Relation_Otransp_001_062_It__Nat__Onat_Mt__Rat__Orat_J,type,
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% 4.71/4.99 thf(sy_c_Rings_Oalgebraic__semidom__class_Ocoprime_001t__Nat__Onat,type,
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% 4.71/4.99 thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint,type,
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% 4.71/4.99 thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
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% 4.71/4.99 thf(sy_c_Rings_Odvd__class_Odvd_001t__Int__Oint,type,
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% 4.71/4.99 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Nat__Onat,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Series_Osuminf_001t__Complex__Ocomplex,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Series_Osuminf_001t__Int__Oint,type,
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% 4.71/5.00 thf(sy_c_Series_Osuminf_001t__Nat__Onat,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Series_Osuminf_001t__Real__Oreal,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Series_Osummable_001t__Complex__Ocomplex,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Series_Osummable_001t__Int__Oint,type,
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% 4.71/5.00
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% 4.71/5.00 thf(sy_c_Series_Osummable_001t__Real__Oreal,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Complex__Ocomplex_J,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Extended____Nat__Oenat_J,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Int__Oint_J,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_OCollect_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Nat__Onat_J,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_OPow_001t__Nat__Onat,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oimage_001t__Extended____Nat__Oenat_001t__Extended____Nat__Oenat,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Int__Oint,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Nat__Onat,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Int__Oint,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Real__Oreal,type,
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% 4.71/5.00
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__String__Ochar,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Real__Oreal,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oimage_001t__String__Ochar_001t__Nat__Onat,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oinsert_001_062_It__Nat__Onat_Mt__Rat__Orat_J,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oinsert_001_Eo,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oinsert_001t__Complex__Ocomplex,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oinsert_001t__Extended____Nat__Oenat,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oinsert_001t__Int__Oint,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oinsert_001t__List__Olist_It__Nat__Onat_J,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oinsert_001t__Num__Onum,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 4.71/5.00 insert9069300056098147895at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oinsert_001t__Rat__Orat,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oinsert_001t__Real__Oreal,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oinsert_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oinsert_001t__Set__Oset_It__Nat__Onat_J,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oinsert_001t__VEBT____Definitions__OVEBT,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Ois__empty_001_Eo,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Ois__empty_001t__Nat__Onat,type,
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% 4.71/5.00
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Ois__singleton_001_Eo,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Ois__singleton_001t__Complex__Ocomplex,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Ois__singleton_001t__Int__Oint,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Ois__singleton_001t__List__Olist_It__Nat__Onat_J,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Ois__singleton_001t__Nat__Onat,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Ois__singleton_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Ois__singleton_001t__Real__Oreal,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Ois__singleton_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Ois__singleton_001t__Set__Oset_It__Nat__Onat_J,type,
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% 4.71/5.00
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oremove_001t__Int__Oint,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oremove_001t__Nat__Onat,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oremove_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oremove_001t__Real__Oreal,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oremove_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Oremove_001t__Set__Oset_It__Nat__Onat_J,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Othe__elem_001_Eo,type,
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% 4.71/5.00
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Othe__elem_001t__Nat__Onat,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Othe__elem_001t__Real__Oreal,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set_Ovimage_001t__Nat__Onat_001t__Nat__Onat,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Complex__Ocomplex,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Int__Oint,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Nat__Onat,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Rat__Orat,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Real__Oreal,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001_Eo,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Int__Oint,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Nat__Onat,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Num__Onum,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Rat__Orat,type,
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% 4.71/5.00 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Real__Oreal,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Int__Oint,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Nat__Onat,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Nat__Onat,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Real__Oreal,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Int__Oint,type,
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% 4.71/5.00 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Nat__Onat,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Int__Oint,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Nat__Onat,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Int__Oint,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Nat__Onat,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Real__Oreal,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Nat__Onat,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Int__Oint,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_String_OCode_Oabort_001t__Real__Oreal,type,
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% 4.71/5.00 thf(sy_c_String_Ochar_OChar,type,
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% 4.71/5.00 thf(sy_c_String_Ochar_Osize__char,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_String_Ounique__euclidean__semiring__with__bit__operations__class_Ochar__of_001t__Nat__Onat,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Topological__Spaces_Ocontinuous_001t__Real__Oreal_001t__Real__Oreal,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Real__Oreal_001t__Real__Oreal,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal,type,
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% 4.71/5.00
% 4.71/5.00 thf(sy_c_Topological__Spaces_Otopological__space__class_Oat__within_001t__Real__Oreal,type,
% 4.71/5.00 topolo2177554685111907308n_real: real > set_real > filter_real ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Topological__Spaces_Otopological__space__class_Oconvergent_001t__Real__Oreal,type,
% 4.71/5.00 topolo7531315842566124627t_real: ( nat > real ) > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
% 4.71/5.00 topolo2815343760600316023s_real: real > filter_real ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Complex__Ocomplex,type,
% 4.71/5.00 topolo6517432010174082258omplex: ( nat > complex ) > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
% 4.71/5.00 topolo4055970368930404560y_real: ( nat > real ) > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Transcendental_Oarccos,type,
% 4.71/5.00 arccos: real > real ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 4.71/5.00 arcosh_real: real > real ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Transcendental_Oarcsin,type,
% 4.71/5.00 arcsin: real > real ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Transcendental_Oarctan,type,
% 4.71/5.00 arctan: real > real ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
% 4.71/5.00 arsinh_real: real > real ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
% 4.71/5.00 artanh_real: real > real ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
% 4.71/5.00 cos_real: real > real ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Transcendental_Ocos__coeff,type,
% 4.71/5.00 cos_coeff: nat > real ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
% 4.71/5.00 cosh_real: real > real ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
% 4.71/5.00 exp_complex: complex > complex ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
% 4.71/5.00 exp_real: real > real ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
% 4.71/5.00 ln_ln_real: real > real ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Transcendental_Olog,type,
% 4.71/5.00 log: real > real > real ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Transcendental_Opi,type,
% 4.71/5.00 pi: real ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 4.71/5.00 powr_real: real > real > real ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Transcendental_Opowr__real,type,
% 4.71/5.00 powr_real2: real > real > real ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
% 4.71/5.00 sin_real: real > real ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Transcendental_Osin__coeff,type,
% 4.71/5.00 sin_coeff: nat > real ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Transcendental_Osinh_001t__Complex__Ocomplex,type,
% 4.71/5.00 sinh_complex: complex > complex ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
% 4.71/5.00 sinh_real: real > real ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 4.71/5.00 tan_real: real > real ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 4.71/5.00 tanh_real: real > real ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Transfer_Oleft__total_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_It__Nat__Onat_Mt__Rat__Orat_J,type,
% 4.71/5.00 left_t2768085380646472630at_rat: ( ( nat > rat ) > ( nat > rat ) > $o ) > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Transitive__Closure_Ortrancl_001t__Nat__Onat,type,
% 4.71/5.00 transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Transitive__Closure_Otrancl_001t__Nat__Onat,type,
% 4.71/5.00 transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Typedef_Otype__definition_001t__Product____Type__Ounit_001_Eo,type,
% 4.71/5.00 type_d6188575255521822967unit_o: ( product_unit > $o ) > ( $o > product_unit ) > set_o > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Typedef_Otype__definition_001t__Real__Oreal_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
% 4.71/5.00 type_d8072115097938612567at_rat: ( real > set_nat_rat ) > ( set_nat_rat > real ) > set_set_nat_rat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 4.71/5.00 vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 4.71/5.00 vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 4.71/5.00 vEBT_size_VEBT: vEBT_VEBT > nat ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 4.71/5.00 vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oelim__dead,type,
% 4.71/5.00 vEBT_VEBT_elim_dead: vEBT_VEBT > extended_enat > vEBT_VEBT ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oelim__dead__rel,type,
% 4.71/5.00 vEBT_V312737461966249ad_rel: produc7272778201969148633d_enat > produc7272778201969148633d_enat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 4.71/5.00 vEBT_VEBT_high: nat > nat > nat ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 4.71/5.00 vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 4.71/5.00 vEBT_VEBT_low: nat > nat > nat ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 4.71/5.00 vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 4.71/5.00 vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 4.71/5.00 vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 4.71/5.00 vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 4.71/5.00 vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 4.71/5.00 vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 4.71/5.00 vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 4.71/5.00 vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 4.71/5.00 vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 4.71/5.00 vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Delete_Ovebt__delete,type,
% 4.71/5.00 vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Delete_Ovebt__delete__rel,type,
% 4.71/5.00 vEBT_vebt_delete_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 4.71/5.00 vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 4.71/5.00 vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 4.71/5.00 vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 4.71/5.00 vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull__rel,type,
% 4.71/5.00 vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 4.71/5.00 vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Member_Ovebt__member,type,
% 4.71/5.00 vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 4.71/5.00 vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oadd,type,
% 4.71/5.00 vEBT_VEBT_add: option_nat > option_nat > option_nat ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ogreater,type,
% 4.71/5.00 vEBT_VEBT_greater: option_nat > option_nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oless,type,
% 4.71/5.00 vEBT_VEBT_less: option_nat > option_nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__MinMax_OVEBT__internal_Olesseq,type,
% 4.71/5.00 vEBT_VEBT_lesseq: option_nat > option_nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omax__in__set,type,
% 4.71/5.00 vEBT_VEBT_max_in_set: set_nat > nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omin__in__set,type,
% 4.71/5.00 vEBT_VEBT_min_in_set: set_nat > nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omul,type,
% 4.71/5.00 vEBT_VEBT_mul: option_nat > option_nat > option_nat ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Nat__Onat,type,
% 4.71/5.00 vEBT_V4262088993061758097ft_nat: ( nat > nat > nat ) > option_nat > option_nat > option_nat ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__MinMax_OVEBT__internal_Opower,type,
% 4.71/5.00 vEBT_VEBT_power: option_nat > option_nat > option_nat ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__MinMax_Ovebt__maxt,type,
% 4.71/5.00 vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__MinMax_Ovebt__maxt__rel,type,
% 4.71/5.00 vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__MinMax_Ovebt__mint,type,
% 4.71/5.00 vEBT_vebt_mint: vEBT_VEBT > option_nat ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__MinMax_Ovebt__mint__rel,type,
% 4.71/5.00 vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Pred_Ois__pred__in__set,type,
% 4.71/5.00 vEBT_is_pred_in_set: set_nat > nat > nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Pred_Ovebt__pred,type,
% 4.71/5.00 vEBT_vebt_pred: vEBT_VEBT > nat > option_nat ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Pred_Ovebt__pred__rel,type,
% 4.71/5.00 vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Succ_Ois__succ__in__set,type,
% 4.71/5.00 vEBT_is_succ_in_set: set_nat > nat > nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Succ_Ovebt__succ,type,
% 4.71/5.00 vEBT_vebt_succ: vEBT_VEBT > nat > option_nat ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_VEBT__Succ_Ovebt__succ__rel,type,
% 4.71/5.00 vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 4.71/5.00 accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 4.71/5.00 accp_nat: ( nat > nat > $o ) > nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 4.71/5.00 accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.71/5.00 accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Extended____Nat__Oenat_J,type,
% 4.71/5.00 accp_P6183159247885693666d_enat: ( produc7272778201969148633d_enat > produc7272778201969148633d_enat > $o ) > produc7272778201969148633d_enat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 4.71/5.00 accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Wellfounded_Oaccp_001t__VEBT____Definitions__OVEBT,type,
% 4.71/5.00 accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Wellfounded_Oless__than,type,
% 4.71/5.00 less_than: set_Pr1261947904930325089at_nat ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Wellfounded_Olex__prod_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.71/5.00 lex_prod_nat_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Wellfounded_Omax__ext_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.71/5.00 max_ex8135407076693332796at_nat: set_Pr8693737435421807431at_nat > set_Pr4329608150637261639at_nat ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Wellfounded_Omin__ext_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.71/5.00 min_ex6901939911449802026at_nat: set_Pr8693737435421807431at_nat > set_Pr4329608150637261639at_nat ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Wellfounded_Opred__nat,type,
% 4.71/5.00 pred_nat: set_Pr1261947904930325089at_nat ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Wellfounded_Owf_001t__Nat__Onat,type,
% 4.71/5.00 wf_nat: set_Pr1261947904930325089at_nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_Wellfounded_Owf_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.71/5.00 wf_Pro7803398752247294826at_nat: set_Pr8693737435421807431at_nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_fChoice_001t__Real__Oreal,type,
% 4.71/5.00 fChoice_real: ( real > $o ) > real ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_member_001_062_It__Nat__Onat_Mt__Rat__Orat_J,type,
% 4.71/5.00 member_nat_rat: ( nat > rat ) > set_nat_rat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_member_001_Eo,type,
% 4.71/5.00 member_o: $o > set_o > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_member_001t__Complex__Ocomplex,type,
% 4.71/5.00 member_complex: complex > set_complex > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_member_001t__Extended____Nat__Oenat,type,
% 4.71/5.00 member_Extended_enat: extended_enat > set_Extended_enat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_member_001t__Int__Oint,type,
% 4.71/5.00 member_int: int > set_int > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 4.71/5.00 member_list_nat: list_nat > set_list_nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_member_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 4.71/5.00 member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_member_001t__Nat__Onat,type,
% 4.71/5.00 member_nat: nat > set_nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_member_001t__Num__Onum,type,
% 4.71/5.00 member_num: num > set_num > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_member_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 4.71/5.00 member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.71/5.00 member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 4.71/5.00 member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 4.71/5.00 member8757157785044589968at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
% 4.71/5.00 member1466754251312161552at_nat: produc1319942482725812455at_nat > set_Pr7459493094073627847at_nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_member_001t__Rat__Orat,type,
% 4.71/5.00 member_rat: rat > set_rat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_member_001t__Real__Oreal,type,
% 4.71/5.00 member_real: real > set_real > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_member_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
% 4.71/5.00 member_set_nat_rat: set_nat_rat > set_set_nat_rat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_member_001t__Set__Oset_It__Int__Oint_J,type,
% 4.71/5.00 member_set_int: set_int > set_set_int > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.71/5.00 member_set_nat: set_nat > set_set_nat > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 4.71/5.00 member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 4.71/5.00
% 4.71/5.00 thf(sy_v_n,type,
% 4.71/5.00 n: nat ).
% 4.71/5.00
% 4.71/5.00 thf(sy_v_t,type,
% 4.71/5.00 t: vEBT_VEBT ).
% 4.71/5.00
% 4.71/5.00 thf(sy_v_x,type,
% 4.71/5.00 x: nat ).
% 4.71/5.00
% 4.71/5.00 % Relevant facts (9308)
% 4.71/5.00 thf(fact_0_valid__eq,axiom,
% 4.71/5.00 vEBT_VEBT_valid = vEBT_invar_vebt ).
% 4.71/5.00
% 4.71/5.00 % valid_eq
% 4.71/5.00 thf(fact_1_valid__eq1,axiom,
% 4.71/5.00 ! [T: vEBT_VEBT,D: nat] :
% 4.71/5.00 ( ( vEBT_invar_vebt @ T @ D )
% 4.71/5.00 => ( vEBT_VEBT_valid @ T @ D ) ) ).
% 4.71/5.00
% 4.71/5.00 % valid_eq1
% 4.71/5.00 thf(fact_2_valid__eq2,axiom,
% 4.71/5.00 ! [T: vEBT_VEBT,D: nat] :
% 4.71/5.00 ( ( vEBT_VEBT_valid @ T @ D )
% 4.71/5.00 => ( vEBT_invar_vebt @ T @ D ) ) ).
% 4.71/5.00
% 4.71/5.00 % valid_eq2
% 4.71/5.00 thf(fact_3_dele__bmo__cont__corr,axiom,
% 4.71/5.00 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 4.71/5.00 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.00 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ T @ X ) @ Y )
% 4.71/5.00 = ( ( X != Y )
% 4.71/5.00 & ( vEBT_V8194947554948674370ptions @ T @ Y ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % dele_bmo_cont_corr
% 4.71/5.00 thf(fact_4_valid__0__not,axiom,
% 4.71/5.00 ! [T: vEBT_VEBT] :
% 4.71/5.00 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 4.71/5.00
% 4.71/5.00 % valid_0_not
% 4.71/5.00 thf(fact_5_valid__tree__deg__neq__0,axiom,
% 4.71/5.00 ! [T: vEBT_VEBT] :
% 4.71/5.00 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 4.71/5.00
% 4.71/5.00 % valid_tree_deg_neq_0
% 4.71/5.00 thf(fact_6_deg__deg__n,axiom,
% 4.71/5.00 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 4.71/5.00 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 4.71/5.00 => ( Deg = N ) ) ).
% 4.71/5.00
% 4.71/5.00 % deg_deg_n
% 4.71/5.00 thf(fact_7_set__vebt__set__vebt_H__valid,axiom,
% 4.71/5.00 ! [T: vEBT_VEBT,N: nat] :
% 4.71/5.00 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.00 => ( ( vEBT_set_vebt @ T )
% 4.71/5.00 = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % set_vebt_set_vebt'_valid
% 4.71/5.00 thf(fact_8_member__correct,axiom,
% 4.71/5.00 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 4.71/5.00 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.00 => ( ( vEBT_vebt_member @ T @ X )
% 4.71/5.00 = ( member_nat @ X @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % member_correct
% 4.71/5.00 thf(fact_9_set__vebt__finite,axiom,
% 4.71/5.00 ! [T: vEBT_VEBT,N: nat] :
% 4.71/5.00 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.00 => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % set_vebt_finite
% 4.71/5.00 thf(fact_10_deg__not__0,axiom,
% 4.71/5.00 ! [T: vEBT_VEBT,N: nat] :
% 4.71/5.00 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.00 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 4.71/5.00
% 4.71/5.00 % deg_not_0
% 4.71/5.00 thf(fact_11_Leaf__0__not,axiom,
% 4.71/5.00 ! [A: $o,B: $o] :
% 4.71/5.00 ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 4.71/5.00
% 4.71/5.00 % Leaf_0_not
% 4.71/5.00 thf(fact_12_valid__member__both__member__options,axiom,
% 4.71/5.00 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 4.71/5.00 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.00 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 4.71/5.00 => ( vEBT_vebt_member @ T @ X ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % valid_member_both_member_options
% 4.71/5.00 thf(fact_13_both__member__options__equiv__member,axiom,
% 4.71/5.00 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 4.71/5.00 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.00 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 4.71/5.00 = ( vEBT_vebt_member @ T @ X ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % both_member_options_equiv_member
% 4.71/5.00 thf(fact_14_pred__none__empty,axiom,
% 4.71/5.00 ! [Xs: set_nat,A: nat] :
% 4.71/5.00 ( ~ ? [X_1: nat] : ( vEBT_is_pred_in_set @ Xs @ A @ X_1 )
% 4.71/5.00 => ( ( finite_finite_nat @ Xs )
% 4.71/5.00 => ~ ? [X2: nat] :
% 4.71/5.00 ( ( member_nat @ X2 @ Xs )
% 4.71/5.00 & ( ord_less_nat @ X2 @ A ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % pred_none_empty
% 4.71/5.00 thf(fact_15_succ__none__empty,axiom,
% 4.71/5.00 ! [Xs: set_nat,A: nat] :
% 4.71/5.00 ( ~ ? [X_1: nat] : ( vEBT_is_succ_in_set @ Xs @ A @ X_1 )
% 4.71/5.00 => ( ( finite_finite_nat @ Xs )
% 4.71/5.00 => ~ ? [X2: nat] :
% 4.71/5.00 ( ( member_nat @ X2 @ Xs )
% 4.71/5.00 & ( ord_less_nat @ A @ X2 ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % succ_none_empty
% 4.71/5.00 thf(fact_16_buildup__gives__valid,axiom,
% 4.71/5.00 ! [N: nat] :
% 4.71/5.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.00 => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N ) ) ).
% 4.71/5.00
% 4.71/5.00 % buildup_gives_valid
% 4.71/5.00 thf(fact_17_bot__nat__0_Onot__eq__extremum,axiom,
% 4.71/5.00 ! [A: nat] :
% 4.71/5.00 ( ( A != zero_zero_nat )
% 4.71/5.00 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 4.71/5.00
% 4.71/5.00 % bot_nat_0.not_eq_extremum
% 4.71/5.00 thf(fact_18_neq0__conv,axiom,
% 4.71/5.00 ! [N: nat] :
% 4.71/5.00 ( ( N != zero_zero_nat )
% 4.71/5.00 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 4.71/5.00
% 4.71/5.00 % neq0_conv
% 4.71/5.00 thf(fact_19_less__nat__zero__code,axiom,
% 4.71/5.00 ! [N: nat] :
% 4.71/5.00 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 4.71/5.00
% 4.71/5.00 % less_nat_zero_code
% 4.71/5.00 thf(fact_20_not__gr__zero,axiom,
% 4.71/5.00 ! [N: nat] :
% 4.71/5.00 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 4.71/5.00 = ( N = zero_zero_nat ) ) ).
% 4.71/5.00
% 4.71/5.00 % not_gr_zero
% 4.71/5.00 thf(fact_21_vebt__delete_Osimps_I1_J,axiom,
% 4.71/5.00 ! [A: $o,B: $o] :
% 4.71/5.00 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat )
% 4.71/5.00 = ( vEBT_Leaf @ $false @ B ) ) ).
% 4.71/5.00
% 4.71/5.00 % vebt_delete.simps(1)
% 4.71/5.00 thf(fact_22_obtain__set__pred,axiom,
% 4.71/5.00 ! [Z: nat,X: nat,A2: set_nat] :
% 4.71/5.00 ( ( ord_less_nat @ Z @ X )
% 4.71/5.00 => ( ( vEBT_VEBT_min_in_set @ A2 @ Z )
% 4.71/5.00 => ( ( finite_finite_nat @ A2 )
% 4.71/5.00 => ? [X_1: nat] : ( vEBT_is_pred_in_set @ A2 @ X @ X_1 ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % obtain_set_pred
% 4.71/5.00 thf(fact_23_obtain__set__succ,axiom,
% 4.71/5.00 ! [X: nat,Z: nat,A2: set_nat,B2: set_nat] :
% 4.71/5.00 ( ( ord_less_nat @ X @ Z )
% 4.71/5.00 => ( ( vEBT_VEBT_max_in_set @ A2 @ Z )
% 4.71/5.00 => ( ( finite_finite_nat @ B2 )
% 4.71/5.00 => ( ( A2 = B2 )
% 4.71/5.00 => ? [X_1: nat] : ( vEBT_is_succ_in_set @ A2 @ X @ X_1 ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % obtain_set_succ
% 4.71/5.00 thf(fact_24_VEBT_Oinject_I2_J,axiom,
% 4.71/5.00 ! [X21: $o,X22: $o,Y21: $o,Y22: $o] :
% 4.71/5.00 ( ( ( vEBT_Leaf @ X21 @ X22 )
% 4.71/5.00 = ( vEBT_Leaf @ Y21 @ Y22 ) )
% 4.71/5.00 = ( ( X21 = Y21 )
% 4.71/5.00 & ( X22 = Y22 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % VEBT.inject(2)
% 4.71/5.00 thf(fact_25_VEBT_Oinject_I1_J,axiom,
% 4.71/5.00 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 4.71/5.00 ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 4.71/5.00 = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 4.71/5.00 = ( ( X11 = Y11 )
% 4.71/5.00 & ( X12 = Y12 )
% 4.71/5.00 & ( X13 = Y13 )
% 4.71/5.00 & ( X14 = Y14 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % VEBT.inject(1)
% 4.71/5.00 thf(fact_26_finite__psubset__induct,axiom,
% 4.71/5.00 ! [A2: set_nat,P: set_nat > $o] :
% 4.71/5.00 ( ( finite_finite_nat @ A2 )
% 4.71/5.00 => ( ! [A3: set_nat] :
% 4.71/5.00 ( ( finite_finite_nat @ A3 )
% 4.71/5.00 => ( ! [B3: set_nat] :
% 4.71/5.00 ( ( ord_less_set_nat @ B3 @ A3 )
% 4.71/5.00 => ( P @ B3 ) )
% 4.71/5.00 => ( P @ A3 ) ) )
% 4.71/5.00 => ( P @ A2 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_psubset_induct
% 4.71/5.00 thf(fact_27_finite__psubset__induct,axiom,
% 4.71/5.00 ! [A2: set_int,P: set_int > $o] :
% 4.71/5.00 ( ( finite_finite_int @ A2 )
% 4.71/5.00 => ( ! [A3: set_int] :
% 4.71/5.00 ( ( finite_finite_int @ A3 )
% 4.71/5.00 => ( ! [B3: set_int] :
% 4.71/5.00 ( ( ord_less_set_int @ B3 @ A3 )
% 4.71/5.00 => ( P @ B3 ) )
% 4.71/5.00 => ( P @ A3 ) ) )
% 4.71/5.00 => ( P @ A2 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_psubset_induct
% 4.71/5.00 thf(fact_28_finite__psubset__induct,axiom,
% 4.71/5.00 ! [A2: set_complex,P: set_complex > $o] :
% 4.71/5.00 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.00 => ( ! [A3: set_complex] :
% 4.71/5.00 ( ( finite3207457112153483333omplex @ A3 )
% 4.71/5.00 => ( ! [B3: set_complex] :
% 4.71/5.00 ( ( ord_less_set_complex @ B3 @ A3 )
% 4.71/5.00 => ( P @ B3 ) )
% 4.71/5.00 => ( P @ A3 ) ) )
% 4.71/5.00 => ( P @ A2 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_psubset_induct
% 4.71/5.00 thf(fact_29_finite__psubset__induct,axiom,
% 4.71/5.00 ! [A2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 4.71/5.00 ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.00 => ( ! [A3: set_Pr1261947904930325089at_nat] :
% 4.71/5.00 ( ( finite6177210948735845034at_nat @ A3 )
% 4.71/5.00 => ( ! [B3: set_Pr1261947904930325089at_nat] :
% 4.71/5.00 ( ( ord_le7866589430770878221at_nat @ B3 @ A3 )
% 4.71/5.00 => ( P @ B3 ) )
% 4.71/5.00 => ( P @ A3 ) ) )
% 4.71/5.00 => ( P @ A2 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_psubset_induct
% 4.71/5.00 thf(fact_30_finite__psubset__induct,axiom,
% 4.71/5.00 ! [A2: set_Extended_enat,P: set_Extended_enat > $o] :
% 4.71/5.00 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.00 => ( ! [A3: set_Extended_enat] :
% 4.71/5.00 ( ( finite4001608067531595151d_enat @ A3 )
% 4.71/5.00 => ( ! [B3: set_Extended_enat] :
% 4.71/5.00 ( ( ord_le2529575680413868914d_enat @ B3 @ A3 )
% 4.71/5.00 => ( P @ B3 ) )
% 4.71/5.00 => ( P @ A3 ) ) )
% 4.71/5.00 => ( P @ A2 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_psubset_induct
% 4.71/5.00 thf(fact_31_vebt__buildup_Osimps_I1_J,axiom,
% 4.71/5.00 ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 4.71/5.00 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 4.71/5.00
% 4.71/5.00 % vebt_buildup.simps(1)
% 4.71/5.00 thf(fact_32_zero__reorient,axiom,
% 4.71/5.00 ! [X: literal] :
% 4.71/5.00 ( ( zero_zero_literal = X )
% 4.71/5.00 = ( X = zero_zero_literal ) ) ).
% 4.71/5.00
% 4.71/5.00 % zero_reorient
% 4.71/5.00 thf(fact_33_zero__reorient,axiom,
% 4.71/5.00 ! [X: real] :
% 4.71/5.00 ( ( zero_zero_real = X )
% 4.71/5.00 = ( X = zero_zero_real ) ) ).
% 4.71/5.00
% 4.71/5.00 % zero_reorient
% 4.71/5.00 thf(fact_34_zero__reorient,axiom,
% 4.71/5.00 ! [X: rat] :
% 4.71/5.00 ( ( zero_zero_rat = X )
% 4.71/5.00 = ( X = zero_zero_rat ) ) ).
% 4.71/5.00
% 4.71/5.00 % zero_reorient
% 4.71/5.00 thf(fact_35_zero__reorient,axiom,
% 4.71/5.00 ! [X: nat] :
% 4.71/5.00 ( ( zero_zero_nat = X )
% 4.71/5.00 = ( X = zero_zero_nat ) ) ).
% 4.71/5.00
% 4.71/5.00 % zero_reorient
% 4.71/5.00 thf(fact_36_zero__reorient,axiom,
% 4.71/5.00 ! [X: int] :
% 4.71/5.00 ( ( zero_zero_int = X )
% 4.71/5.00 = ( X = zero_zero_int ) ) ).
% 4.71/5.00
% 4.71/5.00 % zero_reorient
% 4.71/5.00 thf(fact_37_linorder__neqE__nat,axiom,
% 4.71/5.00 ! [X: nat,Y: nat] :
% 4.71/5.00 ( ( X != Y )
% 4.71/5.00 => ( ~ ( ord_less_nat @ X @ Y )
% 4.71/5.00 => ( ord_less_nat @ Y @ X ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % linorder_neqE_nat
% 4.71/5.00 thf(fact_38_infinite__descent,axiom,
% 4.71/5.00 ! [P: nat > $o,N: nat] :
% 4.71/5.00 ( ! [N2: nat] :
% 4.71/5.00 ( ~ ( P @ N2 )
% 4.71/5.00 => ? [M: nat] :
% 4.71/5.00 ( ( ord_less_nat @ M @ N2 )
% 4.71/5.00 & ~ ( P @ M ) ) )
% 4.71/5.00 => ( P @ N ) ) ).
% 4.71/5.00
% 4.71/5.00 % infinite_descent
% 4.71/5.00 thf(fact_39_nat__less__induct,axiom,
% 4.71/5.00 ! [P: nat > $o,N: nat] :
% 4.71/5.00 ( ! [N2: nat] :
% 4.71/5.00 ( ! [M: nat] :
% 4.71/5.00 ( ( ord_less_nat @ M @ N2 )
% 4.71/5.00 => ( P @ M ) )
% 4.71/5.00 => ( P @ N2 ) )
% 4.71/5.00 => ( P @ N ) ) ).
% 4.71/5.00
% 4.71/5.00 % nat_less_induct
% 4.71/5.00 thf(fact_40_less__irrefl__nat,axiom,
% 4.71/5.00 ! [N: nat] :
% 4.71/5.00 ~ ( ord_less_nat @ N @ N ) ).
% 4.71/5.00
% 4.71/5.00 % less_irrefl_nat
% 4.71/5.00 thf(fact_41_less__not__refl3,axiom,
% 4.71/5.00 ! [S: nat,T: nat] :
% 4.71/5.00 ( ( ord_less_nat @ S @ T )
% 4.71/5.00 => ( S != T ) ) ).
% 4.71/5.00
% 4.71/5.00 % less_not_refl3
% 4.71/5.00 thf(fact_42_less__not__refl2,axiom,
% 4.71/5.00 ! [N: nat,M2: nat] :
% 4.71/5.00 ( ( ord_less_nat @ N @ M2 )
% 4.71/5.00 => ( M2 != N ) ) ).
% 4.71/5.00
% 4.71/5.00 % less_not_refl2
% 4.71/5.00 thf(fact_43_less__not__refl,axiom,
% 4.71/5.00 ! [N: nat] :
% 4.71/5.00 ~ ( ord_less_nat @ N @ N ) ).
% 4.71/5.00
% 4.71/5.00 % less_not_refl
% 4.71/5.00 thf(fact_44_nat__neq__iff,axiom,
% 4.71/5.00 ! [M2: nat,N: nat] :
% 4.71/5.00 ( ( M2 != N )
% 4.71/5.00 = ( ( ord_less_nat @ M2 @ N )
% 4.71/5.00 | ( ord_less_nat @ N @ M2 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % nat_neq_iff
% 4.71/5.00 thf(fact_45_mem__Collect__eq,axiom,
% 4.71/5.00 ! [A: $o,P: $o > $o] :
% 4.71/5.00 ( ( member_o @ A @ ( collect_o @ P ) )
% 4.71/5.00 = ( P @ A ) ) ).
% 4.71/5.00
% 4.71/5.00 % mem_Collect_eq
% 4.71/5.00 thf(fact_46_mem__Collect__eq,axiom,
% 4.71/5.00 ! [A: set_nat,P: set_nat > $o] :
% 4.71/5.00 ( ( member_set_nat @ A @ ( collect_set_nat @ P ) )
% 4.71/5.00 = ( P @ A ) ) ).
% 4.71/5.00
% 4.71/5.00 % mem_Collect_eq
% 4.71/5.00 thf(fact_47_mem__Collect__eq,axiom,
% 4.71/5.00 ! [A: set_nat_rat,P: set_nat_rat > $o] :
% 4.71/5.00 ( ( member_set_nat_rat @ A @ ( collect_set_nat_rat @ P ) )
% 4.71/5.00 = ( P @ A ) ) ).
% 4.71/5.00
% 4.71/5.00 % mem_Collect_eq
% 4.71/5.00 thf(fact_48_mem__Collect__eq,axiom,
% 4.71/5.00 ! [A: nat,P: nat > $o] :
% 4.71/5.00 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 4.71/5.00 = ( P @ A ) ) ).
% 4.71/5.00
% 4.71/5.00 % mem_Collect_eq
% 4.71/5.00 thf(fact_49_mem__Collect__eq,axiom,
% 4.71/5.00 ! [A: int,P: int > $o] :
% 4.71/5.00 ( ( member_int @ A @ ( collect_int @ P ) )
% 4.71/5.00 = ( P @ A ) ) ).
% 4.71/5.00
% 4.71/5.00 % mem_Collect_eq
% 4.71/5.00 thf(fact_50_mem__Collect__eq,axiom,
% 4.71/5.00 ! [A: nat > rat,P: ( nat > rat ) > $o] :
% 4.71/5.00 ( ( member_nat_rat @ A @ ( collect_nat_rat @ P ) )
% 4.71/5.00 = ( P @ A ) ) ).
% 4.71/5.00
% 4.71/5.00 % mem_Collect_eq
% 4.71/5.00 thf(fact_51_Collect__mem__eq,axiom,
% 4.71/5.00 ! [A2: set_o] :
% 4.71/5.00 ( ( collect_o
% 4.71/5.00 @ ^ [X3: $o] : ( member_o @ X3 @ A2 ) )
% 4.71/5.00 = A2 ) ).
% 4.71/5.00
% 4.71/5.00 % Collect_mem_eq
% 4.71/5.00 thf(fact_52_Collect__mem__eq,axiom,
% 4.71/5.00 ! [A2: set_set_nat] :
% 4.71/5.00 ( ( collect_set_nat
% 4.71/5.00 @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A2 ) )
% 4.71/5.00 = A2 ) ).
% 4.71/5.00
% 4.71/5.00 % Collect_mem_eq
% 4.71/5.00 thf(fact_53_Collect__mem__eq,axiom,
% 4.71/5.00 ! [A2: set_set_nat_rat] :
% 4.71/5.00 ( ( collect_set_nat_rat
% 4.71/5.00 @ ^ [X3: set_nat_rat] : ( member_set_nat_rat @ X3 @ A2 ) )
% 4.71/5.00 = A2 ) ).
% 4.71/5.00
% 4.71/5.00 % Collect_mem_eq
% 4.71/5.00 thf(fact_54_Collect__mem__eq,axiom,
% 4.71/5.00 ! [A2: set_nat] :
% 4.71/5.00 ( ( collect_nat
% 4.71/5.00 @ ^ [X3: nat] : ( member_nat @ X3 @ A2 ) )
% 4.71/5.00 = A2 ) ).
% 4.71/5.00
% 4.71/5.00 % Collect_mem_eq
% 4.71/5.00 thf(fact_55_Collect__mem__eq,axiom,
% 4.71/5.00 ! [A2: set_int] :
% 4.71/5.00 ( ( collect_int
% 4.71/5.00 @ ^ [X3: int] : ( member_int @ X3 @ A2 ) )
% 4.71/5.00 = A2 ) ).
% 4.71/5.00
% 4.71/5.00 % Collect_mem_eq
% 4.71/5.00 thf(fact_56_Collect__mem__eq,axiom,
% 4.71/5.00 ! [A2: set_nat_rat] :
% 4.71/5.00 ( ( collect_nat_rat
% 4.71/5.00 @ ^ [X3: nat > rat] : ( member_nat_rat @ X3 @ A2 ) )
% 4.71/5.00 = A2 ) ).
% 4.71/5.00
% 4.71/5.00 % Collect_mem_eq
% 4.71/5.00 thf(fact_57_Collect__cong,axiom,
% 4.71/5.00 ! [P: set_nat > $o,Q: set_nat > $o] :
% 4.71/5.00 ( ! [X4: set_nat] :
% 4.71/5.00 ( ( P @ X4 )
% 4.71/5.00 = ( Q @ X4 ) )
% 4.71/5.00 => ( ( collect_set_nat @ P )
% 4.71/5.00 = ( collect_set_nat @ Q ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % Collect_cong
% 4.71/5.00 thf(fact_58_Collect__cong,axiom,
% 4.71/5.00 ! [P: set_nat_rat > $o,Q: set_nat_rat > $o] :
% 4.71/5.00 ( ! [X4: set_nat_rat] :
% 4.71/5.00 ( ( P @ X4 )
% 4.71/5.00 = ( Q @ X4 ) )
% 4.71/5.00 => ( ( collect_set_nat_rat @ P )
% 4.71/5.00 = ( collect_set_nat_rat @ Q ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % Collect_cong
% 4.71/5.00 thf(fact_59_Collect__cong,axiom,
% 4.71/5.00 ! [P: nat > $o,Q: nat > $o] :
% 4.71/5.00 ( ! [X4: nat] :
% 4.71/5.00 ( ( P @ X4 )
% 4.71/5.00 = ( Q @ X4 ) )
% 4.71/5.00 => ( ( collect_nat @ P )
% 4.71/5.00 = ( collect_nat @ Q ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % Collect_cong
% 4.71/5.00 thf(fact_60_Collect__cong,axiom,
% 4.71/5.00 ! [P: int > $o,Q: int > $o] :
% 4.71/5.00 ( ! [X4: int] :
% 4.71/5.00 ( ( P @ X4 )
% 4.71/5.00 = ( Q @ X4 ) )
% 4.71/5.00 => ( ( collect_int @ P )
% 4.71/5.00 = ( collect_int @ Q ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % Collect_cong
% 4.71/5.00 thf(fact_61_Collect__cong,axiom,
% 4.71/5.00 ! [P: ( nat > rat ) > $o,Q: ( nat > rat ) > $o] :
% 4.71/5.00 ( ! [X4: nat > rat] :
% 4.71/5.00 ( ( P @ X4 )
% 4.71/5.00 = ( Q @ X4 ) )
% 4.71/5.00 => ( ( collect_nat_rat @ P )
% 4.71/5.00 = ( collect_nat_rat @ Q ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % Collect_cong
% 4.71/5.00 thf(fact_62_zero__less__iff__neq__zero,axiom,
% 4.71/5.00 ! [N: nat] :
% 4.71/5.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.00 = ( N != zero_zero_nat ) ) ).
% 4.71/5.00
% 4.71/5.00 % zero_less_iff_neq_zero
% 4.71/5.00 thf(fact_63_gr__implies__not__zero,axiom,
% 4.71/5.00 ! [M2: nat,N: nat] :
% 4.71/5.00 ( ( ord_less_nat @ M2 @ N )
% 4.71/5.00 => ( N != zero_zero_nat ) ) ).
% 4.71/5.00
% 4.71/5.00 % gr_implies_not_zero
% 4.71/5.00 thf(fact_64_not__less__zero,axiom,
% 4.71/5.00 ! [N: nat] :
% 4.71/5.00 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 4.71/5.00
% 4.71/5.00 % not_less_zero
% 4.71/5.00 thf(fact_65_gr__zeroI,axiom,
% 4.71/5.00 ! [N: nat] :
% 4.71/5.00 ( ( N != zero_zero_nat )
% 4.71/5.00 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 4.71/5.00
% 4.71/5.00 % gr_zeroI
% 4.71/5.00 thf(fact_66_infinite__descent0,axiom,
% 4.71/5.00 ! [P: nat > $o,N: nat] :
% 4.71/5.00 ( ( P @ zero_zero_nat )
% 4.71/5.00 => ( ! [N2: nat] :
% 4.71/5.00 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.71/5.00 => ( ~ ( P @ N2 )
% 4.71/5.00 => ? [M: nat] :
% 4.71/5.00 ( ( ord_less_nat @ M @ N2 )
% 4.71/5.00 & ~ ( P @ M ) ) ) )
% 4.71/5.00 => ( P @ N ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % infinite_descent0
% 4.71/5.00 thf(fact_67_gr__implies__not0,axiom,
% 4.71/5.00 ! [M2: nat,N: nat] :
% 4.71/5.00 ( ( ord_less_nat @ M2 @ N )
% 4.71/5.00 => ( N != zero_zero_nat ) ) ).
% 4.71/5.00
% 4.71/5.00 % gr_implies_not0
% 4.71/5.00 thf(fact_68_less__zeroE,axiom,
% 4.71/5.00 ! [N: nat] :
% 4.71/5.00 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 4.71/5.00
% 4.71/5.00 % less_zeroE
% 4.71/5.00 thf(fact_69_not__less0,axiom,
% 4.71/5.00 ! [N: nat] :
% 4.71/5.00 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 4.71/5.00
% 4.71/5.00 % not_less0
% 4.71/5.00 thf(fact_70_not__gr0,axiom,
% 4.71/5.00 ! [N: nat] :
% 4.71/5.00 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 4.71/5.00 = ( N = zero_zero_nat ) ) ).
% 4.71/5.00
% 4.71/5.00 % not_gr0
% 4.71/5.00 thf(fact_71_gr0I,axiom,
% 4.71/5.00 ! [N: nat] :
% 4.71/5.00 ( ( N != zero_zero_nat )
% 4.71/5.00 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 4.71/5.00
% 4.71/5.00 % gr0I
% 4.71/5.00 thf(fact_72_bot__nat__0_Oextremum__strict,axiom,
% 4.71/5.00 ! [A: nat] :
% 4.71/5.00 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 4.71/5.00
% 4.71/5.00 % bot_nat_0.extremum_strict
% 4.71/5.00 thf(fact_73_VEBT_Oexhaust,axiom,
% 4.71/5.00 ! [Y: vEBT_VEBT] :
% 4.71/5.00 ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 4.71/5.00 ( Y
% 4.71/5.00 != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 4.71/5.00 => ~ ! [X212: $o,X222: $o] :
% 4.71/5.00 ( Y
% 4.71/5.00 != ( vEBT_Leaf @ X212 @ X222 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % VEBT.exhaust
% 4.71/5.00 thf(fact_74_VEBT_Odistinct_I1_J,axiom,
% 4.71/5.00 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X22: $o] :
% 4.71/5.00 ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 4.71/5.00 != ( vEBT_Leaf @ X21 @ X22 ) ) ).
% 4.71/5.00
% 4.71/5.00 % VEBT.distinct(1)
% 4.71/5.00 thf(fact_75_succ__member,axiom,
% 4.71/5.00 ! [T: vEBT_VEBT,X: nat,Y: nat] :
% 4.71/5.00 ( ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y )
% 4.71/5.00 = ( ( vEBT_vebt_member @ T @ Y )
% 4.71/5.00 & ( ord_less_nat @ X @ Y )
% 4.71/5.00 & ! [Z2: nat] :
% 4.71/5.00 ( ( ( vEBT_vebt_member @ T @ Z2 )
% 4.71/5.00 & ( ord_less_nat @ X @ Z2 ) )
% 4.71/5.00 => ( ord_less_eq_nat @ Y @ Z2 ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % succ_member
% 4.71/5.00 thf(fact_76_pred__member,axiom,
% 4.71/5.00 ! [T: vEBT_VEBT,X: nat,Y: nat] :
% 4.71/5.00 ( ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y )
% 4.71/5.00 = ( ( vEBT_vebt_member @ T @ Y )
% 4.71/5.00 & ( ord_less_nat @ Y @ X )
% 4.71/5.00 & ! [Z2: nat] :
% 4.71/5.00 ( ( ( vEBT_vebt_member @ T @ Z2 )
% 4.71/5.00 & ( ord_less_nat @ Z2 @ X ) )
% 4.71/5.00 => ( ord_less_eq_nat @ Z2 @ Y ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % pred_member
% 4.71/5.00 thf(fact_77_buildup__nothing__in__leaf,axiom,
% 4.71/5.00 ! [N: nat,X: nat] :
% 4.71/5.00 ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 4.71/5.00
% 4.71/5.00 % buildup_nothing_in_leaf
% 4.71/5.00 thf(fact_78_buildup__gives__empty,axiom,
% 4.71/5.00 ! [N: nat] :
% 4.71/5.00 ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N ) )
% 4.71/5.00 = bot_bot_set_nat ) ).
% 4.71/5.00
% 4.71/5.00 % buildup_gives_empty
% 4.71/5.00 thf(fact_79_buildup__nothing__in__min__max,axiom,
% 4.71/5.00 ! [N: nat,X: nat] :
% 4.71/5.00 ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 4.71/5.00
% 4.71/5.00 % buildup_nothing_in_min_max
% 4.71/5.00 thf(fact_80_deg1Leaf,axiom,
% 4.71/5.00 ! [T: vEBT_VEBT] :
% 4.71/5.00 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 4.71/5.00 = ( ? [A4: $o,B4: $o] :
% 4.71/5.00 ( T
% 4.71/5.00 = ( vEBT_Leaf @ A4 @ B4 ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % deg1Leaf
% 4.71/5.00 thf(fact_81_deg__1__Leaf,axiom,
% 4.71/5.00 ! [T: vEBT_VEBT] :
% 4.71/5.00 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 4.71/5.00 => ? [A5: $o,B5: $o] :
% 4.71/5.00 ( T
% 4.71/5.00 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % deg_1_Leaf
% 4.71/5.00 thf(fact_82_deg__1__Leafy,axiom,
% 4.71/5.00 ! [T: vEBT_VEBT,N: nat] :
% 4.71/5.00 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.00 => ( ( N = one_one_nat )
% 4.71/5.00 => ? [A5: $o,B5: $o] :
% 4.71/5.00 ( T
% 4.71/5.00 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % deg_1_Leafy
% 4.71/5.00 thf(fact_83_finite__nat__set__iff__bounded,axiom,
% 4.71/5.00 ( finite_finite_nat
% 4.71/5.00 = ( ^ [N3: set_nat] :
% 4.71/5.00 ? [M3: nat] :
% 4.71/5.00 ! [X3: nat] :
% 4.71/5.00 ( ( member_nat @ X3 @ N3 )
% 4.71/5.00 => ( ord_less_nat @ X3 @ M3 ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_nat_set_iff_bounded
% 4.71/5.00 thf(fact_84_infinite__nat__iff__unbounded,axiom,
% 4.71/5.00 ! [S2: set_nat] :
% 4.71/5.00 ( ( ~ ( finite_finite_nat @ S2 ) )
% 4.71/5.00 = ( ! [M3: nat] :
% 4.71/5.00 ? [N4: nat] :
% 4.71/5.00 ( ( ord_less_nat @ M3 @ N4 )
% 4.71/5.00 & ( member_nat @ N4 @ S2 ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % infinite_nat_iff_unbounded
% 4.71/5.00 thf(fact_85_bounded__nat__set__is__finite,axiom,
% 4.71/5.00 ! [N5: set_nat,N: nat] :
% 4.71/5.00 ( ! [X4: nat] :
% 4.71/5.00 ( ( member_nat @ X4 @ N5 )
% 4.71/5.00 => ( ord_less_nat @ X4 @ N ) )
% 4.71/5.00 => ( finite_finite_nat @ N5 ) ) ).
% 4.71/5.00
% 4.71/5.00 % bounded_nat_set_is_finite
% 4.71/5.00 thf(fact_86_unbounded__k__infinite,axiom,
% 4.71/5.00 ! [K: nat,S2: set_nat] :
% 4.71/5.00 ( ! [M4: nat] :
% 4.71/5.00 ( ( ord_less_nat @ K @ M4 )
% 4.71/5.00 => ? [N6: nat] :
% 4.71/5.00 ( ( ord_less_nat @ M4 @ N6 )
% 4.71/5.00 & ( member_nat @ N6 @ S2 ) ) )
% 4.71/5.00 => ~ ( finite_finite_nat @ S2 ) ) ).
% 4.71/5.00
% 4.71/5.00 % unbounded_k_infinite
% 4.71/5.00 thf(fact_87_max__in__set__def,axiom,
% 4.71/5.00 ( vEBT_VEBT_max_in_set
% 4.71/5.00 = ( ^ [Xs2: set_nat,X3: nat] :
% 4.71/5.00 ( ( member_nat @ X3 @ Xs2 )
% 4.71/5.00 & ! [Y2: nat] :
% 4.71/5.00 ( ( member_nat @ Y2 @ Xs2 )
% 4.71/5.00 => ( ord_less_eq_nat @ Y2 @ X3 ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % max_in_set_def
% 4.71/5.00 thf(fact_88_min__in__set__def,axiom,
% 4.71/5.00 ( vEBT_VEBT_min_in_set
% 4.71/5.00 = ( ^ [Xs2: set_nat,X3: nat] :
% 4.71/5.00 ( ( member_nat @ X3 @ Xs2 )
% 4.71/5.00 & ! [Y2: nat] :
% 4.71/5.00 ( ( member_nat @ Y2 @ Xs2 )
% 4.71/5.00 => ( ord_less_eq_nat @ X3 @ Y2 ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % min_in_set_def
% 4.71/5.00 thf(fact_89_both__member__options__def,axiom,
% 4.71/5.00 ( vEBT_V8194947554948674370ptions
% 4.71/5.00 = ( ^ [T2: vEBT_VEBT,X3: nat] :
% 4.71/5.00 ( ( vEBT_V5719532721284313246member @ T2 @ X3 )
% 4.71/5.00 | ( vEBT_VEBT_membermima @ T2 @ X3 ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % both_member_options_def
% 4.71/5.00 thf(fact_90_member__valid__both__member__options,axiom,
% 4.71/5.00 ! [Tree: vEBT_VEBT,N: nat,X: nat] :
% 4.71/5.00 ( ( vEBT_invar_vebt @ Tree @ N )
% 4.71/5.00 => ( ( vEBT_vebt_member @ Tree @ X )
% 4.71/5.00 => ( ( vEBT_V5719532721284313246member @ Tree @ X )
% 4.71/5.00 | ( vEBT_VEBT_membermima @ Tree @ X ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % member_valid_both_member_options
% 4.71/5.00 thf(fact_91_le__zero__eq,axiom,
% 4.71/5.00 ! [N: nat] :
% 4.71/5.00 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 4.71/5.00 = ( N = zero_zero_nat ) ) ).
% 4.71/5.00
% 4.71/5.00 % le_zero_eq
% 4.71/5.00 thf(fact_92_bot__nat__0_Oextremum,axiom,
% 4.71/5.00 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 4.71/5.00
% 4.71/5.00 % bot_nat_0.extremum
% 4.71/5.00 thf(fact_93_le0,axiom,
% 4.71/5.00 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 4.71/5.00
% 4.71/5.00 % le0
% 4.71/5.00 thf(fact_94_less__one,axiom,
% 4.71/5.00 ! [N: nat] :
% 4.71/5.00 ( ( ord_less_nat @ N @ one_one_nat )
% 4.71/5.00 = ( N = zero_zero_nat ) ) ).
% 4.71/5.00
% 4.71/5.00 % less_one
% 4.71/5.00 thf(fact_95_Nat_Oex__has__greatest__nat,axiom,
% 4.71/5.00 ! [P: nat > $o,K: nat,B: nat] :
% 4.71/5.00 ( ( P @ K )
% 4.71/5.00 => ( ! [Y3: nat] :
% 4.71/5.00 ( ( P @ Y3 )
% 4.71/5.00 => ( ord_less_eq_nat @ Y3 @ B ) )
% 4.71/5.00 => ? [X4: nat] :
% 4.71/5.00 ( ( P @ X4 )
% 4.71/5.00 & ! [Y4: nat] :
% 4.71/5.00 ( ( P @ Y4 )
% 4.71/5.00 => ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % Nat.ex_has_greatest_nat
% 4.71/5.00 thf(fact_96_one__reorient,axiom,
% 4.71/5.00 ! [X: complex] :
% 4.71/5.00 ( ( one_one_complex = X )
% 4.71/5.00 = ( X = one_one_complex ) ) ).
% 4.71/5.00
% 4.71/5.00 % one_reorient
% 4.71/5.00 thf(fact_97_one__reorient,axiom,
% 4.71/5.00 ! [X: real] :
% 4.71/5.00 ( ( one_one_real = X )
% 4.71/5.00 = ( X = one_one_real ) ) ).
% 4.71/5.00
% 4.71/5.00 % one_reorient
% 4.71/5.00 thf(fact_98_one__reorient,axiom,
% 4.71/5.00 ! [X: rat] :
% 4.71/5.00 ( ( one_one_rat = X )
% 4.71/5.00 = ( X = one_one_rat ) ) ).
% 4.71/5.00
% 4.71/5.00 % one_reorient
% 4.71/5.00 thf(fact_99_one__reorient,axiom,
% 4.71/5.00 ! [X: nat] :
% 4.71/5.00 ( ( one_one_nat = X )
% 4.71/5.00 = ( X = one_one_nat ) ) ).
% 4.71/5.00
% 4.71/5.00 % one_reorient
% 4.71/5.00 thf(fact_100_one__reorient,axiom,
% 4.71/5.00 ! [X: int] :
% 4.71/5.00 ( ( one_one_int = X )
% 4.71/5.00 = ( X = one_one_int ) ) ).
% 4.71/5.00
% 4.71/5.00 % one_reorient
% 4.71/5.00 thf(fact_101_nat__le__linear,axiom,
% 4.71/5.00 ! [M2: nat,N: nat] :
% 4.71/5.00 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.00 | ( ord_less_eq_nat @ N @ M2 ) ) ).
% 4.71/5.00
% 4.71/5.00 % nat_le_linear
% 4.71/5.00 thf(fact_102_le__antisym,axiom,
% 4.71/5.00 ! [M2: nat,N: nat] :
% 4.71/5.00 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.00 => ( ( ord_less_eq_nat @ N @ M2 )
% 4.71/5.00 => ( M2 = N ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % le_antisym
% 4.71/5.00 thf(fact_103_eq__imp__le,axiom,
% 4.71/5.00 ! [M2: nat,N: nat] :
% 4.71/5.00 ( ( M2 = N )
% 4.71/5.00 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 4.71/5.00
% 4.71/5.00 % eq_imp_le
% 4.71/5.00 thf(fact_104_le__trans,axiom,
% 4.71/5.00 ! [I: nat,J: nat,K: nat] :
% 4.71/5.00 ( ( ord_less_eq_nat @ I @ J )
% 4.71/5.00 => ( ( ord_less_eq_nat @ J @ K )
% 4.71/5.00 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % le_trans
% 4.71/5.00 thf(fact_105_le__refl,axiom,
% 4.71/5.00 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 4.71/5.00
% 4.71/5.00 % le_refl
% 4.71/5.00 thf(fact_106_bounded__Max__nat,axiom,
% 4.71/5.00 ! [P: nat > $o,X: nat,M5: nat] :
% 4.71/5.00 ( ( P @ X )
% 4.71/5.00 => ( ! [X4: nat] :
% 4.71/5.00 ( ( P @ X4 )
% 4.71/5.00 => ( ord_less_eq_nat @ X4 @ M5 ) )
% 4.71/5.00 => ~ ! [M4: nat] :
% 4.71/5.00 ( ( P @ M4 )
% 4.71/5.00 => ~ ! [X2: nat] :
% 4.71/5.00 ( ( P @ X2 )
% 4.71/5.00 => ( ord_less_eq_nat @ X2 @ M4 ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % bounded_Max_nat
% 4.71/5.00 thf(fact_107_finite__has__minimal,axiom,
% 4.71/5.00 ! [A2: set_Extended_enat] :
% 4.71/5.00 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.00 => ( ( A2 != bot_bo7653980558646680370d_enat )
% 4.71/5.00 => ? [X4: extended_enat] :
% 4.71/5.00 ( ( member_Extended_enat @ X4 @ A2 )
% 4.71/5.00 & ! [Xa: extended_enat] :
% 4.71/5.00 ( ( member_Extended_enat @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_le2932123472753598470d_enat @ Xa @ X4 )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_minimal
% 4.71/5.00 thf(fact_108_finite__has__minimal,axiom,
% 4.71/5.00 ! [A2: set_real] :
% 4.71/5.00 ( ( finite_finite_real @ A2 )
% 4.71/5.00 => ( ( A2 != bot_bot_set_real )
% 4.71/5.00 => ? [X4: real] :
% 4.71/5.00 ( ( member_real @ X4 @ A2 )
% 4.71/5.00 & ! [Xa: real] :
% 4.71/5.00 ( ( member_real @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_real @ Xa @ X4 )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_minimal
% 4.71/5.00 thf(fact_109_finite__has__minimal,axiom,
% 4.71/5.00 ! [A2: set_o] :
% 4.71/5.00 ( ( finite_finite_o @ A2 )
% 4.71/5.00 => ( ( A2 != bot_bot_set_o )
% 4.71/5.00 => ? [X4: $o] :
% 4.71/5.00 ( ( member_o @ X4 @ A2 )
% 4.71/5.00 & ! [Xa: $o] :
% 4.71/5.00 ( ( member_o @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_o @ Xa @ X4 )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_minimal
% 4.71/5.00 thf(fact_110_finite__has__minimal,axiom,
% 4.71/5.00 ! [A2: set_set_int] :
% 4.71/5.00 ( ( finite6197958912794628473et_int @ A2 )
% 4.71/5.00 => ( ( A2 != bot_bot_set_set_int )
% 4.71/5.00 => ? [X4: set_int] :
% 4.71/5.00 ( ( member_set_int @ X4 @ A2 )
% 4.71/5.00 & ! [Xa: set_int] :
% 4.71/5.00 ( ( member_set_int @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_set_int @ Xa @ X4 )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_minimal
% 4.71/5.00 thf(fact_111_finite__has__minimal,axiom,
% 4.71/5.00 ! [A2: set_rat] :
% 4.71/5.00 ( ( finite_finite_rat @ A2 )
% 4.71/5.00 => ( ( A2 != bot_bot_set_rat )
% 4.71/5.00 => ? [X4: rat] :
% 4.71/5.00 ( ( member_rat @ X4 @ A2 )
% 4.71/5.00 & ! [Xa: rat] :
% 4.71/5.00 ( ( member_rat @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_rat @ Xa @ X4 )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_minimal
% 4.71/5.00 thf(fact_112_finite__has__minimal,axiom,
% 4.71/5.00 ! [A2: set_num] :
% 4.71/5.00 ( ( finite_finite_num @ A2 )
% 4.71/5.00 => ( ( A2 != bot_bot_set_num )
% 4.71/5.00 => ? [X4: num] :
% 4.71/5.00 ( ( member_num @ X4 @ A2 )
% 4.71/5.00 & ! [Xa: num] :
% 4.71/5.00 ( ( member_num @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_num @ Xa @ X4 )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_minimal
% 4.71/5.00 thf(fact_113_finite__has__minimal,axiom,
% 4.71/5.00 ! [A2: set_nat] :
% 4.71/5.00 ( ( finite_finite_nat @ A2 )
% 4.71/5.00 => ( ( A2 != bot_bot_set_nat )
% 4.71/5.00 => ? [X4: nat] :
% 4.71/5.00 ( ( member_nat @ X4 @ A2 )
% 4.71/5.00 & ! [Xa: nat] :
% 4.71/5.00 ( ( member_nat @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_nat @ Xa @ X4 )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_minimal
% 4.71/5.00 thf(fact_114_finite__has__minimal,axiom,
% 4.71/5.00 ! [A2: set_int] :
% 4.71/5.00 ( ( finite_finite_int @ A2 )
% 4.71/5.00 => ( ( A2 != bot_bot_set_int )
% 4.71/5.00 => ? [X4: int] :
% 4.71/5.00 ( ( member_int @ X4 @ A2 )
% 4.71/5.00 & ! [Xa: int] :
% 4.71/5.00 ( ( member_int @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_int @ Xa @ X4 )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_minimal
% 4.71/5.00 thf(fact_115_finite__has__maximal,axiom,
% 4.71/5.00 ! [A2: set_Extended_enat] :
% 4.71/5.00 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.00 => ( ( A2 != bot_bo7653980558646680370d_enat )
% 4.71/5.00 => ? [X4: extended_enat] :
% 4.71/5.00 ( ( member_Extended_enat @ X4 @ A2 )
% 4.71/5.00 & ! [Xa: extended_enat] :
% 4.71/5.00 ( ( member_Extended_enat @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_le2932123472753598470d_enat @ X4 @ Xa )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_maximal
% 4.71/5.00 thf(fact_116_finite__has__maximal,axiom,
% 4.71/5.00 ! [A2: set_real] :
% 4.71/5.00 ( ( finite_finite_real @ A2 )
% 4.71/5.00 => ( ( A2 != bot_bot_set_real )
% 4.71/5.00 => ? [X4: real] :
% 4.71/5.00 ( ( member_real @ X4 @ A2 )
% 4.71/5.00 & ! [Xa: real] :
% 4.71/5.00 ( ( member_real @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_real @ X4 @ Xa )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_maximal
% 4.71/5.00 thf(fact_117_finite__has__maximal,axiom,
% 4.71/5.00 ! [A2: set_o] :
% 4.71/5.00 ( ( finite_finite_o @ A2 )
% 4.71/5.00 => ( ( A2 != bot_bot_set_o )
% 4.71/5.00 => ? [X4: $o] :
% 4.71/5.00 ( ( member_o @ X4 @ A2 )
% 4.71/5.00 & ! [Xa: $o] :
% 4.71/5.00 ( ( member_o @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_o @ X4 @ Xa )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_maximal
% 4.71/5.00 thf(fact_118_finite__has__maximal,axiom,
% 4.71/5.00 ! [A2: set_set_int] :
% 4.71/5.00 ( ( finite6197958912794628473et_int @ A2 )
% 4.71/5.00 => ( ( A2 != bot_bot_set_set_int )
% 4.71/5.00 => ? [X4: set_int] :
% 4.71/5.00 ( ( member_set_int @ X4 @ A2 )
% 4.71/5.00 & ! [Xa: set_int] :
% 4.71/5.00 ( ( member_set_int @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_set_int @ X4 @ Xa )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_maximal
% 4.71/5.00 thf(fact_119_finite__has__maximal,axiom,
% 4.71/5.00 ! [A2: set_rat] :
% 4.71/5.00 ( ( finite_finite_rat @ A2 )
% 4.71/5.00 => ( ( A2 != bot_bot_set_rat )
% 4.71/5.00 => ? [X4: rat] :
% 4.71/5.00 ( ( member_rat @ X4 @ A2 )
% 4.71/5.00 & ! [Xa: rat] :
% 4.71/5.00 ( ( member_rat @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_rat @ X4 @ Xa )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_maximal
% 4.71/5.00 thf(fact_120_finite__has__maximal,axiom,
% 4.71/5.00 ! [A2: set_num] :
% 4.71/5.00 ( ( finite_finite_num @ A2 )
% 4.71/5.00 => ( ( A2 != bot_bot_set_num )
% 4.71/5.00 => ? [X4: num] :
% 4.71/5.00 ( ( member_num @ X4 @ A2 )
% 4.71/5.00 & ! [Xa: num] :
% 4.71/5.00 ( ( member_num @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_num @ X4 @ Xa )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_maximal
% 4.71/5.00 thf(fact_121_finite__has__maximal,axiom,
% 4.71/5.00 ! [A2: set_nat] :
% 4.71/5.00 ( ( finite_finite_nat @ A2 )
% 4.71/5.00 => ( ( A2 != bot_bot_set_nat )
% 4.71/5.00 => ? [X4: nat] :
% 4.71/5.00 ( ( member_nat @ X4 @ A2 )
% 4.71/5.00 & ! [Xa: nat] :
% 4.71/5.00 ( ( member_nat @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_nat @ X4 @ Xa )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_maximal
% 4.71/5.00 thf(fact_122_finite__has__maximal,axiom,
% 4.71/5.00 ! [A2: set_int] :
% 4.71/5.00 ( ( finite_finite_int @ A2 )
% 4.71/5.00 => ( ( A2 != bot_bot_set_int )
% 4.71/5.00 => ? [X4: int] :
% 4.71/5.00 ( ( member_int @ X4 @ A2 )
% 4.71/5.00 & ! [Xa: int] :
% 4.71/5.00 ( ( member_int @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_int @ X4 @ Xa )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_maximal
% 4.71/5.00 thf(fact_123_finite__transitivity__chain,axiom,
% 4.71/5.00 ! [A2: set_set_nat,R: set_nat > set_nat > $o] :
% 4.71/5.00 ( ( finite1152437895449049373et_nat @ A2 )
% 4.71/5.00 => ( ! [X4: set_nat] :
% 4.71/5.00 ~ ( R @ X4 @ X4 )
% 4.71/5.00 => ( ! [X4: set_nat,Y3: set_nat,Z3: set_nat] :
% 4.71/5.00 ( ( R @ X4 @ Y3 )
% 4.71/5.00 => ( ( R @ Y3 @ Z3 )
% 4.71/5.00 => ( R @ X4 @ Z3 ) ) )
% 4.71/5.00 => ( ! [X4: set_nat] :
% 4.71/5.00 ( ( member_set_nat @ X4 @ A2 )
% 4.71/5.00 => ? [Y4: set_nat] :
% 4.71/5.00 ( ( member_set_nat @ Y4 @ A2 )
% 4.71/5.00 & ( R @ X4 @ Y4 ) ) )
% 4.71/5.00 => ( A2 = bot_bot_set_set_nat ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_transitivity_chain
% 4.71/5.00 thf(fact_124_finite__transitivity__chain,axiom,
% 4.71/5.00 ! [A2: set_set_nat_rat,R: set_nat_rat > set_nat_rat > $o] :
% 4.71/5.00 ( ( finite6430367030675640852at_rat @ A2 )
% 4.71/5.00 => ( ! [X4: set_nat_rat] :
% 4.71/5.00 ~ ( R @ X4 @ X4 )
% 4.71/5.00 => ( ! [X4: set_nat_rat,Y3: set_nat_rat,Z3: set_nat_rat] :
% 4.71/5.00 ( ( R @ X4 @ Y3 )
% 4.71/5.00 => ( ( R @ Y3 @ Z3 )
% 4.71/5.00 => ( R @ X4 @ Z3 ) ) )
% 4.71/5.00 => ( ! [X4: set_nat_rat] :
% 4.71/5.00 ( ( member_set_nat_rat @ X4 @ A2 )
% 4.71/5.00 => ? [Y4: set_nat_rat] :
% 4.71/5.00 ( ( member_set_nat_rat @ Y4 @ A2 )
% 4.71/5.00 & ( R @ X4 @ Y4 ) ) )
% 4.71/5.00 => ( A2 = bot_bo6797373522285170759at_rat ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_transitivity_chain
% 4.71/5.00 thf(fact_125_finite__transitivity__chain,axiom,
% 4.71/5.00 ! [A2: set_complex,R: complex > complex > $o] :
% 4.71/5.00 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.00 => ( ! [X4: complex] :
% 4.71/5.00 ~ ( R @ X4 @ X4 )
% 4.71/5.00 => ( ! [X4: complex,Y3: complex,Z3: complex] :
% 4.71/5.00 ( ( R @ X4 @ Y3 )
% 4.71/5.00 => ( ( R @ Y3 @ Z3 )
% 4.71/5.00 => ( R @ X4 @ Z3 ) ) )
% 4.71/5.00 => ( ! [X4: complex] :
% 4.71/5.00 ( ( member_complex @ X4 @ A2 )
% 4.71/5.00 => ? [Y4: complex] :
% 4.71/5.00 ( ( member_complex @ Y4 @ A2 )
% 4.71/5.00 & ( R @ X4 @ Y4 ) ) )
% 4.71/5.00 => ( A2 = bot_bot_set_complex ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_transitivity_chain
% 4.71/5.00 thf(fact_126_finite__transitivity__chain,axiom,
% 4.71/5.00 ! [A2: set_Pr1261947904930325089at_nat,R: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 4.71/5.00 ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.00 => ( ! [X4: product_prod_nat_nat] :
% 4.71/5.00 ~ ( R @ X4 @ X4 )
% 4.71/5.00 => ( ! [X4: product_prod_nat_nat,Y3: product_prod_nat_nat,Z3: product_prod_nat_nat] :
% 4.71/5.00 ( ( R @ X4 @ Y3 )
% 4.71/5.00 => ( ( R @ Y3 @ Z3 )
% 4.71/5.00 => ( R @ X4 @ Z3 ) ) )
% 4.71/5.00 => ( ! [X4: product_prod_nat_nat] :
% 4.71/5.00 ( ( member8440522571783428010at_nat @ X4 @ A2 )
% 4.71/5.00 => ? [Y4: product_prod_nat_nat] :
% 4.71/5.00 ( ( member8440522571783428010at_nat @ Y4 @ A2 )
% 4.71/5.00 & ( R @ X4 @ Y4 ) ) )
% 4.71/5.00 => ( A2 = bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_transitivity_chain
% 4.71/5.00 thf(fact_127_finite__transitivity__chain,axiom,
% 4.71/5.00 ! [A2: set_Extended_enat,R: extended_enat > extended_enat > $o] :
% 4.71/5.00 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.00 => ( ! [X4: extended_enat] :
% 4.71/5.00 ~ ( R @ X4 @ X4 )
% 4.71/5.00 => ( ! [X4: extended_enat,Y3: extended_enat,Z3: extended_enat] :
% 4.71/5.00 ( ( R @ X4 @ Y3 )
% 4.71/5.00 => ( ( R @ Y3 @ Z3 )
% 4.71/5.00 => ( R @ X4 @ Z3 ) ) )
% 4.71/5.00 => ( ! [X4: extended_enat] :
% 4.71/5.00 ( ( member_Extended_enat @ X4 @ A2 )
% 4.71/5.00 => ? [Y4: extended_enat] :
% 4.71/5.00 ( ( member_Extended_enat @ Y4 @ A2 )
% 4.71/5.00 & ( R @ X4 @ Y4 ) ) )
% 4.71/5.00 => ( A2 = bot_bo7653980558646680370d_enat ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_transitivity_chain
% 4.71/5.00 thf(fact_128_finite__transitivity__chain,axiom,
% 4.71/5.00 ! [A2: set_real,R: real > real > $o] :
% 4.71/5.00 ( ( finite_finite_real @ A2 )
% 4.71/5.00 => ( ! [X4: real] :
% 4.71/5.00 ~ ( R @ X4 @ X4 )
% 4.71/5.00 => ( ! [X4: real,Y3: real,Z3: real] :
% 4.71/5.00 ( ( R @ X4 @ Y3 )
% 4.71/5.00 => ( ( R @ Y3 @ Z3 )
% 4.71/5.00 => ( R @ X4 @ Z3 ) ) )
% 4.71/5.00 => ( ! [X4: real] :
% 4.71/5.00 ( ( member_real @ X4 @ A2 )
% 4.71/5.00 => ? [Y4: real] :
% 4.71/5.00 ( ( member_real @ Y4 @ A2 )
% 4.71/5.00 & ( R @ X4 @ Y4 ) ) )
% 4.71/5.00 => ( A2 = bot_bot_set_real ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_transitivity_chain
% 4.71/5.00 thf(fact_129_finite__transitivity__chain,axiom,
% 4.71/5.00 ! [A2: set_o,R: $o > $o > $o] :
% 4.71/5.00 ( ( finite_finite_o @ A2 )
% 4.71/5.00 => ( ! [X4: $o] :
% 4.71/5.00 ~ ( R @ X4 @ X4 )
% 4.71/5.00 => ( ! [X4: $o,Y3: $o,Z3: $o] :
% 4.71/5.00 ( ( R @ X4 @ Y3 )
% 4.71/5.00 => ( ( R @ Y3 @ Z3 )
% 4.71/5.00 => ( R @ X4 @ Z3 ) ) )
% 4.71/5.00 => ( ! [X4: $o] :
% 4.71/5.00 ( ( member_o @ X4 @ A2 )
% 4.71/5.00 => ? [Y4: $o] :
% 4.71/5.00 ( ( member_o @ Y4 @ A2 )
% 4.71/5.00 & ( R @ X4 @ Y4 ) ) )
% 4.71/5.00 => ( A2 = bot_bot_set_o ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_transitivity_chain
% 4.71/5.00 thf(fact_130_finite__transitivity__chain,axiom,
% 4.71/5.00 ! [A2: set_nat,R: nat > nat > $o] :
% 4.71/5.00 ( ( finite_finite_nat @ A2 )
% 4.71/5.00 => ( ! [X4: nat] :
% 4.71/5.00 ~ ( R @ X4 @ X4 )
% 4.71/5.00 => ( ! [X4: nat,Y3: nat,Z3: nat] :
% 4.71/5.00 ( ( R @ X4 @ Y3 )
% 4.71/5.00 => ( ( R @ Y3 @ Z3 )
% 4.71/5.00 => ( R @ X4 @ Z3 ) ) )
% 4.71/5.00 => ( ! [X4: nat] :
% 4.71/5.00 ( ( member_nat @ X4 @ A2 )
% 4.71/5.00 => ? [Y4: nat] :
% 4.71/5.00 ( ( member_nat @ Y4 @ A2 )
% 4.71/5.00 & ( R @ X4 @ Y4 ) ) )
% 4.71/5.00 => ( A2 = bot_bot_set_nat ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_transitivity_chain
% 4.71/5.00 thf(fact_131_finite__transitivity__chain,axiom,
% 4.71/5.00 ! [A2: set_int,R: int > int > $o] :
% 4.71/5.00 ( ( finite_finite_int @ A2 )
% 4.71/5.00 => ( ! [X4: int] :
% 4.71/5.00 ~ ( R @ X4 @ X4 )
% 4.71/5.00 => ( ! [X4: int,Y3: int,Z3: int] :
% 4.71/5.00 ( ( R @ X4 @ Y3 )
% 4.71/5.00 => ( ( R @ Y3 @ Z3 )
% 4.71/5.00 => ( R @ X4 @ Z3 ) ) )
% 4.71/5.00 => ( ! [X4: int] :
% 4.71/5.00 ( ( member_int @ X4 @ A2 )
% 4.71/5.00 => ? [Y4: int] :
% 4.71/5.00 ( ( member_int @ Y4 @ A2 )
% 4.71/5.00 & ( R @ X4 @ Y4 ) ) )
% 4.71/5.00 => ( A2 = bot_bot_set_int ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_transitivity_chain
% 4.71/5.00 thf(fact_132_infinite__nat__iff__unbounded__le,axiom,
% 4.71/5.00 ! [S2: set_nat] :
% 4.71/5.00 ( ( ~ ( finite_finite_nat @ S2 ) )
% 4.71/5.00 = ( ! [M3: nat] :
% 4.71/5.00 ? [N4: nat] :
% 4.71/5.00 ( ( ord_less_eq_nat @ M3 @ N4 )
% 4.71/5.00 & ( member_nat @ N4 @ S2 ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % infinite_nat_iff_unbounded_le
% 4.71/5.00 thf(fact_133_finite__nat__set__iff__bounded__le,axiom,
% 4.71/5.00 ( finite_finite_nat
% 4.71/5.00 = ( ^ [N3: set_nat] :
% 4.71/5.00 ? [M3: nat] :
% 4.71/5.00 ! [X3: nat] :
% 4.71/5.00 ( ( member_nat @ X3 @ N3 )
% 4.71/5.00 => ( ord_less_eq_nat @ X3 @ M3 ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_nat_set_iff_bounded_le
% 4.71/5.00 thf(fact_134_zero__le,axiom,
% 4.71/5.00 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 4.71/5.00
% 4.71/5.00 % zero_le
% 4.71/5.00 thf(fact_135_finite__has__maximal2,axiom,
% 4.71/5.00 ! [A2: set_o,A: $o] :
% 4.71/5.00 ( ( finite_finite_o @ A2 )
% 4.71/5.00 => ( ( member_o @ A @ A2 )
% 4.71/5.00 => ? [X4: $o] :
% 4.71/5.00 ( ( member_o @ X4 @ A2 )
% 4.71/5.00 & ( ord_less_eq_o @ A @ X4 )
% 4.71/5.00 & ! [Xa: $o] :
% 4.71/5.00 ( ( member_o @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_o @ X4 @ Xa )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_maximal2
% 4.71/5.00 thf(fact_136_finite__has__maximal2,axiom,
% 4.71/5.00 ! [A2: set_set_nat,A: set_nat] :
% 4.71/5.00 ( ( finite1152437895449049373et_nat @ A2 )
% 4.71/5.00 => ( ( member_set_nat @ A @ A2 )
% 4.71/5.00 => ? [X4: set_nat] :
% 4.71/5.00 ( ( member_set_nat @ X4 @ A2 )
% 4.71/5.00 & ( ord_less_eq_set_nat @ A @ X4 )
% 4.71/5.00 & ! [Xa: set_nat] :
% 4.71/5.00 ( ( member_set_nat @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_set_nat @ X4 @ Xa )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_maximal2
% 4.71/5.00 thf(fact_137_finite__has__maximal2,axiom,
% 4.71/5.00 ! [A2: set_set_nat_rat,A: set_nat_rat] :
% 4.71/5.00 ( ( finite6430367030675640852at_rat @ A2 )
% 4.71/5.00 => ( ( member_set_nat_rat @ A @ A2 )
% 4.71/5.00 => ? [X4: set_nat_rat] :
% 4.71/5.00 ( ( member_set_nat_rat @ X4 @ A2 )
% 4.71/5.00 & ( ord_le2679597024174929757at_rat @ A @ X4 )
% 4.71/5.00 & ! [Xa: set_nat_rat] :
% 4.71/5.00 ( ( member_set_nat_rat @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_le2679597024174929757at_rat @ X4 @ Xa )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_maximal2
% 4.71/5.00 thf(fact_138_finite__has__maximal2,axiom,
% 4.71/5.00 ! [A2: set_Extended_enat,A: extended_enat] :
% 4.71/5.00 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.00 => ( ( member_Extended_enat @ A @ A2 )
% 4.71/5.00 => ? [X4: extended_enat] :
% 4.71/5.00 ( ( member_Extended_enat @ X4 @ A2 )
% 4.71/5.00 & ( ord_le2932123472753598470d_enat @ A @ X4 )
% 4.71/5.00 & ! [Xa: extended_enat] :
% 4.71/5.00 ( ( member_Extended_enat @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_le2932123472753598470d_enat @ X4 @ Xa )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_maximal2
% 4.71/5.00 thf(fact_139_finite__has__maximal2,axiom,
% 4.71/5.00 ! [A2: set_set_int,A: set_int] :
% 4.71/5.00 ( ( finite6197958912794628473et_int @ A2 )
% 4.71/5.00 => ( ( member_set_int @ A @ A2 )
% 4.71/5.00 => ? [X4: set_int] :
% 4.71/5.00 ( ( member_set_int @ X4 @ A2 )
% 4.71/5.00 & ( ord_less_eq_set_int @ A @ X4 )
% 4.71/5.00 & ! [Xa: set_int] :
% 4.71/5.00 ( ( member_set_int @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_set_int @ X4 @ Xa )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_maximal2
% 4.71/5.00 thf(fact_140_finite__has__maximal2,axiom,
% 4.71/5.00 ! [A2: set_rat,A: rat] :
% 4.71/5.00 ( ( finite_finite_rat @ A2 )
% 4.71/5.00 => ( ( member_rat @ A @ A2 )
% 4.71/5.00 => ? [X4: rat] :
% 4.71/5.00 ( ( member_rat @ X4 @ A2 )
% 4.71/5.00 & ( ord_less_eq_rat @ A @ X4 )
% 4.71/5.00 & ! [Xa: rat] :
% 4.71/5.00 ( ( member_rat @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_rat @ X4 @ Xa )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_maximal2
% 4.71/5.00 thf(fact_141_finite__has__maximal2,axiom,
% 4.71/5.00 ! [A2: set_num,A: num] :
% 4.71/5.00 ( ( finite_finite_num @ A2 )
% 4.71/5.00 => ( ( member_num @ A @ A2 )
% 4.71/5.00 => ? [X4: num] :
% 4.71/5.00 ( ( member_num @ X4 @ A2 )
% 4.71/5.00 & ( ord_less_eq_num @ A @ X4 )
% 4.71/5.00 & ! [Xa: num] :
% 4.71/5.00 ( ( member_num @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_num @ X4 @ Xa )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_maximal2
% 4.71/5.00 thf(fact_142_finite__has__maximal2,axiom,
% 4.71/5.00 ! [A2: set_nat,A: nat] :
% 4.71/5.00 ( ( finite_finite_nat @ A2 )
% 4.71/5.00 => ( ( member_nat @ A @ A2 )
% 4.71/5.00 => ? [X4: nat] :
% 4.71/5.00 ( ( member_nat @ X4 @ A2 )
% 4.71/5.00 & ( ord_less_eq_nat @ A @ X4 )
% 4.71/5.00 & ! [Xa: nat] :
% 4.71/5.00 ( ( member_nat @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_nat @ X4 @ Xa )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_maximal2
% 4.71/5.00 thf(fact_143_finite__has__maximal2,axiom,
% 4.71/5.00 ! [A2: set_int,A: int] :
% 4.71/5.00 ( ( finite_finite_int @ A2 )
% 4.71/5.00 => ( ( member_int @ A @ A2 )
% 4.71/5.00 => ? [X4: int] :
% 4.71/5.00 ( ( member_int @ X4 @ A2 )
% 4.71/5.00 & ( ord_less_eq_int @ A @ X4 )
% 4.71/5.00 & ! [Xa: int] :
% 4.71/5.00 ( ( member_int @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_int @ X4 @ Xa )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_maximal2
% 4.71/5.00 thf(fact_144_finite__has__minimal2,axiom,
% 4.71/5.00 ! [A2: set_o,A: $o] :
% 4.71/5.00 ( ( finite_finite_o @ A2 )
% 4.71/5.00 => ( ( member_o @ A @ A2 )
% 4.71/5.00 => ? [X4: $o] :
% 4.71/5.00 ( ( member_o @ X4 @ A2 )
% 4.71/5.00 & ( ord_less_eq_o @ X4 @ A )
% 4.71/5.00 & ! [Xa: $o] :
% 4.71/5.00 ( ( member_o @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_o @ Xa @ X4 )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_minimal2
% 4.71/5.00 thf(fact_145_finite__has__minimal2,axiom,
% 4.71/5.00 ! [A2: set_set_nat,A: set_nat] :
% 4.71/5.00 ( ( finite1152437895449049373et_nat @ A2 )
% 4.71/5.00 => ( ( member_set_nat @ A @ A2 )
% 4.71/5.00 => ? [X4: set_nat] :
% 4.71/5.00 ( ( member_set_nat @ X4 @ A2 )
% 4.71/5.00 & ( ord_less_eq_set_nat @ X4 @ A )
% 4.71/5.00 & ! [Xa: set_nat] :
% 4.71/5.00 ( ( member_set_nat @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_set_nat @ Xa @ X4 )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_minimal2
% 4.71/5.00 thf(fact_146_finite__has__minimal2,axiom,
% 4.71/5.00 ! [A2: set_set_nat_rat,A: set_nat_rat] :
% 4.71/5.00 ( ( finite6430367030675640852at_rat @ A2 )
% 4.71/5.00 => ( ( member_set_nat_rat @ A @ A2 )
% 4.71/5.00 => ? [X4: set_nat_rat] :
% 4.71/5.00 ( ( member_set_nat_rat @ X4 @ A2 )
% 4.71/5.00 & ( ord_le2679597024174929757at_rat @ X4 @ A )
% 4.71/5.00 & ! [Xa: set_nat_rat] :
% 4.71/5.00 ( ( member_set_nat_rat @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_le2679597024174929757at_rat @ Xa @ X4 )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_minimal2
% 4.71/5.00 thf(fact_147_finite__has__minimal2,axiom,
% 4.71/5.00 ! [A2: set_Extended_enat,A: extended_enat] :
% 4.71/5.00 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.00 => ( ( member_Extended_enat @ A @ A2 )
% 4.71/5.00 => ? [X4: extended_enat] :
% 4.71/5.00 ( ( member_Extended_enat @ X4 @ A2 )
% 4.71/5.00 & ( ord_le2932123472753598470d_enat @ X4 @ A )
% 4.71/5.00 & ! [Xa: extended_enat] :
% 4.71/5.00 ( ( member_Extended_enat @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_le2932123472753598470d_enat @ Xa @ X4 )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_minimal2
% 4.71/5.00 thf(fact_148_finite__has__minimal2,axiom,
% 4.71/5.00 ! [A2: set_set_int,A: set_int] :
% 4.71/5.00 ( ( finite6197958912794628473et_int @ A2 )
% 4.71/5.00 => ( ( member_set_int @ A @ A2 )
% 4.71/5.00 => ? [X4: set_int] :
% 4.71/5.00 ( ( member_set_int @ X4 @ A2 )
% 4.71/5.00 & ( ord_less_eq_set_int @ X4 @ A )
% 4.71/5.00 & ! [Xa: set_int] :
% 4.71/5.00 ( ( member_set_int @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_set_int @ Xa @ X4 )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_minimal2
% 4.71/5.00 thf(fact_149_finite__has__minimal2,axiom,
% 4.71/5.00 ! [A2: set_rat,A: rat] :
% 4.71/5.00 ( ( finite_finite_rat @ A2 )
% 4.71/5.00 => ( ( member_rat @ A @ A2 )
% 4.71/5.00 => ? [X4: rat] :
% 4.71/5.00 ( ( member_rat @ X4 @ A2 )
% 4.71/5.00 & ( ord_less_eq_rat @ X4 @ A )
% 4.71/5.00 & ! [Xa: rat] :
% 4.71/5.00 ( ( member_rat @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_rat @ Xa @ X4 )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_minimal2
% 4.71/5.00 thf(fact_150_finite__has__minimal2,axiom,
% 4.71/5.00 ! [A2: set_num,A: num] :
% 4.71/5.00 ( ( finite_finite_num @ A2 )
% 4.71/5.00 => ( ( member_num @ A @ A2 )
% 4.71/5.00 => ? [X4: num] :
% 4.71/5.00 ( ( member_num @ X4 @ A2 )
% 4.71/5.00 & ( ord_less_eq_num @ X4 @ A )
% 4.71/5.00 & ! [Xa: num] :
% 4.71/5.00 ( ( member_num @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_num @ Xa @ X4 )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_minimal2
% 4.71/5.00 thf(fact_151_finite__has__minimal2,axiom,
% 4.71/5.00 ! [A2: set_nat,A: nat] :
% 4.71/5.00 ( ( finite_finite_nat @ A2 )
% 4.71/5.00 => ( ( member_nat @ A @ A2 )
% 4.71/5.00 => ? [X4: nat] :
% 4.71/5.00 ( ( member_nat @ X4 @ A2 )
% 4.71/5.00 & ( ord_less_eq_nat @ X4 @ A )
% 4.71/5.00 & ! [Xa: nat] :
% 4.71/5.00 ( ( member_nat @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_nat @ Xa @ X4 )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_minimal2
% 4.71/5.00 thf(fact_152_finite__has__minimal2,axiom,
% 4.71/5.00 ! [A2: set_int,A: int] :
% 4.71/5.00 ( ( finite_finite_int @ A2 )
% 4.71/5.00 => ( ( member_int @ A @ A2 )
% 4.71/5.00 => ? [X4: int] :
% 4.71/5.00 ( ( member_int @ X4 @ A2 )
% 4.71/5.00 & ( ord_less_eq_int @ X4 @ A )
% 4.71/5.00 & ! [Xa: int] :
% 4.71/5.00 ( ( member_int @ Xa @ A2 )
% 4.71/5.00 => ( ( ord_less_eq_int @ Xa @ X4 )
% 4.71/5.00 => ( X4 = Xa ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_has_minimal2
% 4.71/5.00 thf(fact_153_less__eq__nat_Osimps_I1_J,axiom,
% 4.71/5.00 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 4.71/5.00
% 4.71/5.00 % less_eq_nat.simps(1)
% 4.71/5.00 thf(fact_154_bot__nat__0_Oextremum__unique,axiom,
% 4.71/5.00 ! [A: nat] :
% 4.71/5.00 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 4.71/5.00 = ( A = zero_zero_nat ) ) ).
% 4.71/5.00
% 4.71/5.00 % bot_nat_0.extremum_unique
% 4.71/5.00 thf(fact_155_bot__nat__0_Oextremum__uniqueI,axiom,
% 4.71/5.00 ! [A: nat] :
% 4.71/5.00 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 4.71/5.00 => ( A = zero_zero_nat ) ) ).
% 4.71/5.00
% 4.71/5.00 % bot_nat_0.extremum_uniqueI
% 4.71/5.00 thf(fact_156_le__0__eq,axiom,
% 4.71/5.00 ! [N: nat] :
% 4.71/5.00 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 4.71/5.00 = ( N = zero_zero_nat ) ) ).
% 4.71/5.00
% 4.71/5.00 % le_0_eq
% 4.71/5.00 thf(fact_157_nat__less__le,axiom,
% 4.71/5.00 ( ord_less_nat
% 4.71/5.00 = ( ^ [M3: nat,N4: nat] :
% 4.71/5.00 ( ( ord_less_eq_nat @ M3 @ N4 )
% 4.71/5.00 & ( M3 != N4 ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % nat_less_le
% 4.71/5.00 thf(fact_158_less__imp__le__nat,axiom,
% 4.71/5.00 ! [M2: nat,N: nat] :
% 4.71/5.00 ( ( ord_less_nat @ M2 @ N )
% 4.71/5.00 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 4.71/5.00
% 4.71/5.00 % less_imp_le_nat
% 4.71/5.00 thf(fact_159_le__eq__less__or__eq,axiom,
% 4.71/5.00 ( ord_less_eq_nat
% 4.71/5.00 = ( ^ [M3: nat,N4: nat] :
% 4.71/5.00 ( ( ord_less_nat @ M3 @ N4 )
% 4.71/5.00 | ( M3 = N4 ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % le_eq_less_or_eq
% 4.71/5.00 thf(fact_160_less__or__eq__imp__le,axiom,
% 4.71/5.00 ! [M2: nat,N: nat] :
% 4.71/5.00 ( ( ( ord_less_nat @ M2 @ N )
% 4.71/5.00 | ( M2 = N ) )
% 4.71/5.00 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 4.71/5.00
% 4.71/5.00 % less_or_eq_imp_le
% 4.71/5.00 thf(fact_161_le__neq__implies__less,axiom,
% 4.71/5.00 ! [M2: nat,N: nat] :
% 4.71/5.00 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.00 => ( ( M2 != N )
% 4.71/5.00 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % le_neq_implies_less
% 4.71/5.00 thf(fact_162_less__mono__imp__le__mono,axiom,
% 4.71/5.00 ! [F: nat > nat,I: nat,J: nat] :
% 4.71/5.00 ( ! [I2: nat,J2: nat] :
% 4.71/5.00 ( ( ord_less_nat @ I2 @ J2 )
% 4.71/5.00 => ( ord_less_nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
% 4.71/5.00 => ( ( ord_less_eq_nat @ I @ J )
% 4.71/5.00 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % less_mono_imp_le_mono
% 4.71/5.00 thf(fact_163_finite_OemptyI,axiom,
% 4.71/5.00 finite3207457112153483333omplex @ bot_bot_set_complex ).
% 4.71/5.00
% 4.71/5.00 % finite.emptyI
% 4.71/5.00 thf(fact_164_finite_OemptyI,axiom,
% 4.71/5.00 finite6177210948735845034at_nat @ bot_bo2099793752762293965at_nat ).
% 4.71/5.00
% 4.71/5.00 % finite.emptyI
% 4.71/5.00 thf(fact_165_finite_OemptyI,axiom,
% 4.71/5.00 finite4001608067531595151d_enat @ bot_bo7653980558646680370d_enat ).
% 4.71/5.00
% 4.71/5.00 % finite.emptyI
% 4.71/5.00 thf(fact_166_finite_OemptyI,axiom,
% 4.71/5.00 finite_finite_real @ bot_bot_set_real ).
% 4.71/5.00
% 4.71/5.00 % finite.emptyI
% 4.71/5.00 thf(fact_167_finite_OemptyI,axiom,
% 4.71/5.00 finite_finite_o @ bot_bot_set_o ).
% 4.71/5.00
% 4.71/5.00 % finite.emptyI
% 4.71/5.00 thf(fact_168_finite_OemptyI,axiom,
% 4.71/5.00 finite_finite_nat @ bot_bot_set_nat ).
% 4.71/5.00
% 4.71/5.00 % finite.emptyI
% 4.71/5.00 thf(fact_169_finite_OemptyI,axiom,
% 4.71/5.00 finite_finite_int @ bot_bot_set_int ).
% 4.71/5.00
% 4.71/5.00 % finite.emptyI
% 4.71/5.00 thf(fact_170_infinite__imp__nonempty,axiom,
% 4.71/5.00 ! [S2: set_complex] :
% 4.71/5.00 ( ~ ( finite3207457112153483333omplex @ S2 )
% 4.71/5.00 => ( S2 != bot_bot_set_complex ) ) ).
% 4.71/5.00
% 4.71/5.00 % infinite_imp_nonempty
% 4.71/5.00 thf(fact_171_infinite__imp__nonempty,axiom,
% 4.71/5.00 ! [S2: set_Pr1261947904930325089at_nat] :
% 4.71/5.00 ( ~ ( finite6177210948735845034at_nat @ S2 )
% 4.71/5.00 => ( S2 != bot_bo2099793752762293965at_nat ) ) ).
% 4.71/5.00
% 4.71/5.00 % infinite_imp_nonempty
% 4.71/5.00 thf(fact_172_infinite__imp__nonempty,axiom,
% 4.71/5.00 ! [S2: set_Extended_enat] :
% 4.71/5.00 ( ~ ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.00 => ( S2 != bot_bo7653980558646680370d_enat ) ) ).
% 4.71/5.00
% 4.71/5.00 % infinite_imp_nonempty
% 4.71/5.00 thf(fact_173_infinite__imp__nonempty,axiom,
% 4.71/5.00 ! [S2: set_real] :
% 4.71/5.00 ( ~ ( finite_finite_real @ S2 )
% 4.71/5.00 => ( S2 != bot_bot_set_real ) ) ).
% 4.71/5.00
% 4.71/5.00 % infinite_imp_nonempty
% 4.71/5.00 thf(fact_174_infinite__imp__nonempty,axiom,
% 4.71/5.00 ! [S2: set_o] :
% 4.71/5.00 ( ~ ( finite_finite_o @ S2 )
% 4.71/5.00 => ( S2 != bot_bot_set_o ) ) ).
% 4.71/5.00
% 4.71/5.00 % infinite_imp_nonempty
% 4.71/5.00 thf(fact_175_infinite__imp__nonempty,axiom,
% 4.71/5.00 ! [S2: set_nat] :
% 4.71/5.00 ( ~ ( finite_finite_nat @ S2 )
% 4.71/5.00 => ( S2 != bot_bot_set_nat ) ) ).
% 4.71/5.00
% 4.71/5.00 % infinite_imp_nonempty
% 4.71/5.00 thf(fact_176_infinite__imp__nonempty,axiom,
% 4.71/5.00 ! [S2: set_int] :
% 4.71/5.00 ( ~ ( finite_finite_int @ S2 )
% 4.71/5.00 => ( S2 != bot_bot_set_int ) ) ).
% 4.71/5.00
% 4.71/5.00 % infinite_imp_nonempty
% 4.71/5.00 thf(fact_177_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 4.71/5.00 ! [A: $o,B: $o,X: nat] :
% 4.71/5.00 ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X )
% 4.71/5.00 = ( ( ( X = zero_zero_nat )
% 4.71/5.00 => A )
% 4.71/5.00 & ( ( X != zero_zero_nat )
% 4.71/5.00 => ( ( ( X = one_one_nat )
% 4.71/5.00 => B )
% 4.71/5.00 & ( X = one_one_nat ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % VEBT_internal.naive_member.simps(1)
% 4.71/5.00 thf(fact_178_VEBT__internal_Omembermima_Osimps_I1_J,axiom,
% 4.71/5.00 ! [Uu: $o,Uv: $o,Uw: nat] :
% 4.71/5.00 ~ ( vEBT_VEBT_membermima @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw ) ).
% 4.71/5.00
% 4.71/5.00 % VEBT_internal.membermima.simps(1)
% 4.71/5.00 thf(fact_179_ex__least__nat__le,axiom,
% 4.71/5.00 ! [P: nat > $o,N: nat] :
% 4.71/5.00 ( ( P @ N )
% 4.71/5.00 => ( ~ ( P @ zero_zero_nat )
% 4.71/5.00 => ? [K2: nat] :
% 4.71/5.00 ( ( ord_less_eq_nat @ K2 @ N )
% 4.71/5.00 & ! [I3: nat] :
% 4.71/5.00 ( ( ord_less_nat @ I3 @ K2 )
% 4.71/5.00 => ~ ( P @ I3 ) )
% 4.71/5.00 & ( P @ K2 ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % ex_least_nat_le
% 4.71/5.00 thf(fact_180_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 4.71/5.00 ! [Uu: $o,Uv: $o,D: nat] :
% 4.71/5.00 ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu @ Uv ) @ D )
% 4.71/5.00 = ( D = one_one_nat ) ) ).
% 4.71/5.00
% 4.71/5.00 % VEBT_internal.valid'.simps(1)
% 4.71/5.00 thf(fact_181_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 4.71/5.00 ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 4.71/5.00 ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) ).
% 4.71/5.00
% 4.71/5.00 % VEBT_internal.naive_member.simps(2)
% 4.71/5.00 thf(fact_182_vebt__member_Osimps_I1_J,axiom,
% 4.71/5.00 ! [A: $o,B: $o,X: nat] :
% 4.71/5.00 ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X )
% 4.71/5.00 = ( ( ( X = zero_zero_nat )
% 4.71/5.00 => A )
% 4.71/5.00 & ( ( X != zero_zero_nat )
% 4.71/5.00 => ( ( ( X = one_one_nat )
% 4.71/5.00 => B )
% 4.71/5.00 & ( X = one_one_nat ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % vebt_member.simps(1)
% 4.71/5.00 thf(fact_183_is__pred__in__set__def,axiom,
% 4.71/5.00 ( vEBT_is_pred_in_set
% 4.71/5.00 = ( ^ [Xs2: set_nat,X3: nat,Y2: nat] :
% 4.71/5.00 ( ( member_nat @ Y2 @ Xs2 )
% 4.71/5.00 & ( ord_less_nat @ Y2 @ X3 )
% 4.71/5.00 & ! [Z2: nat] :
% 4.71/5.00 ( ( member_nat @ Z2 @ Xs2 )
% 4.71/5.00 => ( ( ord_less_nat @ Z2 @ X3 )
% 4.71/5.00 => ( ord_less_eq_nat @ Z2 @ Y2 ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % is_pred_in_set_def
% 4.71/5.00 thf(fact_184_is__succ__in__set__def,axiom,
% 4.71/5.00 ( vEBT_is_succ_in_set
% 4.71/5.00 = ( ^ [Xs2: set_nat,X3: nat,Y2: nat] :
% 4.71/5.00 ( ( member_nat @ Y2 @ Xs2 )
% 4.71/5.00 & ( ord_less_nat @ X3 @ Y2 )
% 4.71/5.00 & ! [Z2: nat] :
% 4.71/5.00 ( ( member_nat @ Z2 @ Xs2 )
% 4.71/5.00 => ( ( ord_less_nat @ X3 @ Z2 )
% 4.71/5.00 => ( ord_less_eq_nat @ Y2 @ Z2 ) ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % is_succ_in_set_def
% 4.71/5.00 thf(fact_185_infinite__growing,axiom,
% 4.71/5.00 ! [X5: set_Extended_enat] :
% 4.71/5.00 ( ( X5 != bot_bo7653980558646680370d_enat )
% 4.71/5.00 => ( ! [X4: extended_enat] :
% 4.71/5.00 ( ( member_Extended_enat @ X4 @ X5 )
% 4.71/5.00 => ? [Xa: extended_enat] :
% 4.71/5.00 ( ( member_Extended_enat @ Xa @ X5 )
% 4.71/5.00 & ( ord_le72135733267957522d_enat @ X4 @ Xa ) ) )
% 4.71/5.00 => ~ ( finite4001608067531595151d_enat @ X5 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % infinite_growing
% 4.71/5.00 thf(fact_186_infinite__growing,axiom,
% 4.71/5.00 ! [X5: set_o] :
% 4.71/5.00 ( ( X5 != bot_bot_set_o )
% 4.71/5.00 => ( ! [X4: $o] :
% 4.71/5.00 ( ( member_o @ X4 @ X5 )
% 4.71/5.00 => ? [Xa: $o] :
% 4.71/5.00 ( ( member_o @ Xa @ X5 )
% 4.71/5.00 & ( ord_less_o @ X4 @ Xa ) ) )
% 4.71/5.00 => ~ ( finite_finite_o @ X5 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % infinite_growing
% 4.71/5.00 thf(fact_187_infinite__growing,axiom,
% 4.71/5.00 ! [X5: set_real] :
% 4.71/5.00 ( ( X5 != bot_bot_set_real )
% 4.71/5.00 => ( ! [X4: real] :
% 4.71/5.00 ( ( member_real @ X4 @ X5 )
% 4.71/5.00 => ? [Xa: real] :
% 4.71/5.00 ( ( member_real @ Xa @ X5 )
% 4.71/5.00 & ( ord_less_real @ X4 @ Xa ) ) )
% 4.71/5.00 => ~ ( finite_finite_real @ X5 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % infinite_growing
% 4.71/5.00 thf(fact_188_infinite__growing,axiom,
% 4.71/5.00 ! [X5: set_rat] :
% 4.71/5.00 ( ( X5 != bot_bot_set_rat )
% 4.71/5.00 => ( ! [X4: rat] :
% 4.71/5.00 ( ( member_rat @ X4 @ X5 )
% 4.71/5.00 => ? [Xa: rat] :
% 4.71/5.00 ( ( member_rat @ Xa @ X5 )
% 4.71/5.00 & ( ord_less_rat @ X4 @ Xa ) ) )
% 4.71/5.00 => ~ ( finite_finite_rat @ X5 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % infinite_growing
% 4.71/5.00 thf(fact_189_infinite__growing,axiom,
% 4.71/5.00 ! [X5: set_num] :
% 4.71/5.00 ( ( X5 != bot_bot_set_num )
% 4.71/5.00 => ( ! [X4: num] :
% 4.71/5.00 ( ( member_num @ X4 @ X5 )
% 4.71/5.00 => ? [Xa: num] :
% 4.71/5.00 ( ( member_num @ Xa @ X5 )
% 4.71/5.00 & ( ord_less_num @ X4 @ Xa ) ) )
% 4.71/5.00 => ~ ( finite_finite_num @ X5 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % infinite_growing
% 4.71/5.00 thf(fact_190_infinite__growing,axiom,
% 4.71/5.00 ! [X5: set_nat] :
% 4.71/5.00 ( ( X5 != bot_bot_set_nat )
% 4.71/5.00 => ( ! [X4: nat] :
% 4.71/5.00 ( ( member_nat @ X4 @ X5 )
% 4.71/5.00 => ? [Xa: nat] :
% 4.71/5.00 ( ( member_nat @ Xa @ X5 )
% 4.71/5.00 & ( ord_less_nat @ X4 @ Xa ) ) )
% 4.71/5.00 => ~ ( finite_finite_nat @ X5 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % infinite_growing
% 4.71/5.00 thf(fact_191_infinite__growing,axiom,
% 4.71/5.00 ! [X5: set_int] :
% 4.71/5.00 ( ( X5 != bot_bot_set_int )
% 4.71/5.00 => ( ! [X4: int] :
% 4.71/5.00 ( ( member_int @ X4 @ X5 )
% 4.71/5.00 => ? [Xa: int] :
% 4.71/5.00 ( ( member_int @ Xa @ X5 )
% 4.71/5.00 & ( ord_less_int @ X4 @ Xa ) ) )
% 4.71/5.00 => ~ ( finite_finite_int @ X5 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % infinite_growing
% 4.71/5.00 thf(fact_192_ex__min__if__finite,axiom,
% 4.71/5.00 ! [S2: set_Extended_enat] :
% 4.71/5.00 ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.00 => ( ( S2 != bot_bo7653980558646680370d_enat )
% 4.71/5.00 => ? [X4: extended_enat] :
% 4.71/5.00 ( ( member_Extended_enat @ X4 @ S2 )
% 4.71/5.00 & ~ ? [Xa: extended_enat] :
% 4.71/5.00 ( ( member_Extended_enat @ Xa @ S2 )
% 4.71/5.00 & ( ord_le72135733267957522d_enat @ Xa @ X4 ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % ex_min_if_finite
% 4.71/5.00 thf(fact_193_ex__min__if__finite,axiom,
% 4.71/5.00 ! [S2: set_o] :
% 4.71/5.00 ( ( finite_finite_o @ S2 )
% 4.71/5.00 => ( ( S2 != bot_bot_set_o )
% 4.71/5.00 => ? [X4: $o] :
% 4.71/5.00 ( ( member_o @ X4 @ S2 )
% 4.71/5.00 & ~ ? [Xa: $o] :
% 4.71/5.00 ( ( member_o @ Xa @ S2 )
% 4.71/5.00 & ( ord_less_o @ Xa @ X4 ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % ex_min_if_finite
% 4.71/5.00 thf(fact_194_ex__min__if__finite,axiom,
% 4.71/5.00 ! [S2: set_real] :
% 4.71/5.00 ( ( finite_finite_real @ S2 )
% 4.71/5.00 => ( ( S2 != bot_bot_set_real )
% 4.71/5.00 => ? [X4: real] :
% 4.71/5.00 ( ( member_real @ X4 @ S2 )
% 4.71/5.00 & ~ ? [Xa: real] :
% 4.71/5.00 ( ( member_real @ Xa @ S2 )
% 4.71/5.00 & ( ord_less_real @ Xa @ X4 ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % ex_min_if_finite
% 4.71/5.00 thf(fact_195_ex__min__if__finite,axiom,
% 4.71/5.00 ! [S2: set_rat] :
% 4.71/5.00 ( ( finite_finite_rat @ S2 )
% 4.71/5.00 => ( ( S2 != bot_bot_set_rat )
% 4.71/5.00 => ? [X4: rat] :
% 4.71/5.00 ( ( member_rat @ X4 @ S2 )
% 4.71/5.00 & ~ ? [Xa: rat] :
% 4.71/5.00 ( ( member_rat @ Xa @ S2 )
% 4.71/5.00 & ( ord_less_rat @ Xa @ X4 ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % ex_min_if_finite
% 4.71/5.00 thf(fact_196_ex__min__if__finite,axiom,
% 4.71/5.00 ! [S2: set_num] :
% 4.71/5.00 ( ( finite_finite_num @ S2 )
% 4.71/5.00 => ( ( S2 != bot_bot_set_num )
% 4.71/5.00 => ? [X4: num] :
% 4.71/5.00 ( ( member_num @ X4 @ S2 )
% 4.71/5.00 & ~ ? [Xa: num] :
% 4.71/5.00 ( ( member_num @ Xa @ S2 )
% 4.71/5.00 & ( ord_less_num @ Xa @ X4 ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % ex_min_if_finite
% 4.71/5.00 thf(fact_197_ex__min__if__finite,axiom,
% 4.71/5.00 ! [S2: set_nat] :
% 4.71/5.00 ( ( finite_finite_nat @ S2 )
% 4.71/5.00 => ( ( S2 != bot_bot_set_nat )
% 4.71/5.00 => ? [X4: nat] :
% 4.71/5.00 ( ( member_nat @ X4 @ S2 )
% 4.71/5.00 & ~ ? [Xa: nat] :
% 4.71/5.00 ( ( member_nat @ Xa @ S2 )
% 4.71/5.00 & ( ord_less_nat @ Xa @ X4 ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % ex_min_if_finite
% 4.71/5.00 thf(fact_198_ex__min__if__finite,axiom,
% 4.71/5.00 ! [S2: set_int] :
% 4.71/5.00 ( ( finite_finite_int @ S2 )
% 4.71/5.00 => ( ( S2 != bot_bot_set_int )
% 4.71/5.00 => ? [X4: int] :
% 4.71/5.00 ( ( member_int @ X4 @ S2 )
% 4.71/5.00 & ~ ? [Xa: int] :
% 4.71/5.00 ( ( member_int @ Xa @ S2 )
% 4.71/5.00 & ( ord_less_int @ Xa @ X4 ) ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % ex_min_if_finite
% 4.71/5.00 thf(fact_199_less__numeral__extra_I1_J,axiom,
% 4.71/5.00 ord_less_real @ zero_zero_real @ one_one_real ).
% 4.71/5.00
% 4.71/5.00 % less_numeral_extra(1)
% 4.71/5.00 thf(fact_200_less__numeral__extra_I1_J,axiom,
% 4.71/5.00 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 4.71/5.00
% 4.71/5.00 % less_numeral_extra(1)
% 4.71/5.00 thf(fact_201_less__numeral__extra_I1_J,axiom,
% 4.71/5.00 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 4.71/5.00
% 4.71/5.00 % less_numeral_extra(1)
% 4.71/5.00 thf(fact_202_less__numeral__extra_I1_J,axiom,
% 4.71/5.00 ord_less_int @ zero_zero_int @ one_one_int ).
% 4.71/5.00
% 4.71/5.00 % less_numeral_extra(1)
% 4.71/5.00 thf(fact_203_zero__less__one,axiom,
% 4.71/5.00 ord_less_real @ zero_zero_real @ one_one_real ).
% 4.71/5.00
% 4.71/5.00 % zero_less_one
% 4.71/5.00 thf(fact_204_zero__less__one,axiom,
% 4.71/5.00 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 4.71/5.00
% 4.71/5.00 % zero_less_one
% 4.71/5.00 thf(fact_205_zero__less__one,axiom,
% 4.71/5.00 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 4.71/5.00
% 4.71/5.00 % zero_less_one
% 4.71/5.00 thf(fact_206_zero__less__one,axiom,
% 4.71/5.00 ord_less_int @ zero_zero_int @ one_one_int ).
% 4.71/5.00
% 4.71/5.00 % zero_less_one
% 4.71/5.00 thf(fact_207_not__one__less__zero,axiom,
% 4.71/5.00 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 4.71/5.00
% 4.71/5.00 % not_one_less_zero
% 4.71/5.00 thf(fact_208_not__one__less__zero,axiom,
% 4.71/5.00 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 4.71/5.00
% 4.71/5.00 % not_one_less_zero
% 4.71/5.00 thf(fact_209_not__one__less__zero,axiom,
% 4.71/5.00 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 4.71/5.00
% 4.71/5.00 % not_one_less_zero
% 4.71/5.00 thf(fact_210_not__one__less__zero,axiom,
% 4.71/5.00 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 4.71/5.00
% 4.71/5.00 % not_one_less_zero
% 4.71/5.00 thf(fact_211_zero__less__one__class_Ozero__le__one,axiom,
% 4.71/5.00 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 4.71/5.00
% 4.71/5.00 % zero_less_one_class.zero_le_one
% 4.71/5.00 thf(fact_212_zero__less__one__class_Ozero__le__one,axiom,
% 4.71/5.00 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 4.71/5.00
% 4.71/5.00 % zero_less_one_class.zero_le_one
% 4.71/5.00 thf(fact_213_zero__less__one__class_Ozero__le__one,axiom,
% 4.71/5.00 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 4.71/5.00
% 4.71/5.00 % zero_less_one_class.zero_le_one
% 4.71/5.00 thf(fact_214_zero__less__one__class_Ozero__le__one,axiom,
% 4.71/5.00 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 4.71/5.00
% 4.71/5.00 % zero_less_one_class.zero_le_one
% 4.71/5.00 thf(fact_215_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 4.71/5.00 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 4.71/5.00
% 4.71/5.00 % linordered_nonzero_semiring_class.zero_le_one
% 4.71/5.00 thf(fact_216_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 4.71/5.00 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 4.71/5.00
% 4.71/5.00 % linordered_nonzero_semiring_class.zero_le_one
% 4.71/5.00 thf(fact_217_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 4.71/5.00 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 4.71/5.00
% 4.71/5.00 % linordered_nonzero_semiring_class.zero_le_one
% 4.71/5.00 thf(fact_218_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 4.71/5.00 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 4.71/5.00
% 4.71/5.00 % linordered_nonzero_semiring_class.zero_le_one
% 4.71/5.00 thf(fact_219_not__one__le__zero,axiom,
% 4.71/5.00 ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 4.71/5.00
% 4.71/5.00 % not_one_le_zero
% 4.71/5.00 thf(fact_220_not__one__le__zero,axiom,
% 4.71/5.00 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 4.71/5.00
% 4.71/5.00 % not_one_le_zero
% 4.71/5.00 thf(fact_221_not__one__le__zero,axiom,
% 4.71/5.00 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 4.71/5.00
% 4.71/5.00 % not_one_le_zero
% 4.71/5.00 thf(fact_222_not__one__le__zero,axiom,
% 4.71/5.00 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 4.71/5.00
% 4.71/5.00 % not_one_le_zero
% 4.71/5.00 thf(fact_223_empty__iff,axiom,
% 4.71/5.00 ! [C: set_nat] :
% 4.71/5.00 ~ ( member_set_nat @ C @ bot_bot_set_set_nat ) ).
% 4.71/5.00
% 4.71/5.00 % empty_iff
% 4.71/5.00 thf(fact_224_empty__iff,axiom,
% 4.71/5.00 ! [C: set_nat_rat] :
% 4.71/5.00 ~ ( member_set_nat_rat @ C @ bot_bo6797373522285170759at_rat ) ).
% 4.71/5.00
% 4.71/5.00 % empty_iff
% 4.71/5.00 thf(fact_225_empty__iff,axiom,
% 4.71/5.00 ! [C: real] :
% 4.71/5.00 ~ ( member_real @ C @ bot_bot_set_real ) ).
% 4.71/5.00
% 4.71/5.00 % empty_iff
% 4.71/5.00 thf(fact_226_empty__iff,axiom,
% 4.71/5.00 ! [C: $o] :
% 4.71/5.00 ~ ( member_o @ C @ bot_bot_set_o ) ).
% 4.71/5.00
% 4.71/5.00 % empty_iff
% 4.71/5.00 thf(fact_227_empty__iff,axiom,
% 4.71/5.00 ! [C: nat] :
% 4.71/5.00 ~ ( member_nat @ C @ bot_bot_set_nat ) ).
% 4.71/5.00
% 4.71/5.00 % empty_iff
% 4.71/5.00 thf(fact_228_empty__iff,axiom,
% 4.71/5.00 ! [C: int] :
% 4.71/5.00 ~ ( member_int @ C @ bot_bot_set_int ) ).
% 4.71/5.00
% 4.71/5.00 % empty_iff
% 4.71/5.00 thf(fact_229_empty__subsetI,axiom,
% 4.71/5.00 ! [A2: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A2 ) ).
% 4.71/5.00
% 4.71/5.00 % empty_subsetI
% 4.71/5.00 thf(fact_230_empty__subsetI,axiom,
% 4.71/5.00 ! [A2: set_o] : ( ord_less_eq_set_o @ bot_bot_set_o @ A2 ) ).
% 4.71/5.00
% 4.71/5.00 % empty_subsetI
% 4.71/5.00 thf(fact_231_empty__subsetI,axiom,
% 4.71/5.00 ! [A2: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A2 ) ).
% 4.71/5.00
% 4.71/5.00 % empty_subsetI
% 4.71/5.00 thf(fact_232_empty__subsetI,axiom,
% 4.71/5.00 ! [A2: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A2 ) ).
% 4.71/5.00
% 4.71/5.00 % empty_subsetI
% 4.71/5.00 thf(fact_233_subset__empty,axiom,
% 4.71/5.00 ! [A2: set_real] :
% 4.71/5.00 ( ( ord_less_eq_set_real @ A2 @ bot_bot_set_real )
% 4.71/5.00 = ( A2 = bot_bot_set_real ) ) ).
% 4.71/5.00
% 4.71/5.00 % subset_empty
% 4.71/5.00 thf(fact_234_subset__empty,axiom,
% 4.71/5.00 ! [A2: set_o] :
% 4.71/5.00 ( ( ord_less_eq_set_o @ A2 @ bot_bot_set_o )
% 4.71/5.00 = ( A2 = bot_bot_set_o ) ) ).
% 4.71/5.00
% 4.71/5.00 % subset_empty
% 4.71/5.00 thf(fact_235_subset__empty,axiom,
% 4.71/5.00 ! [A2: set_nat] :
% 4.71/5.00 ( ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat )
% 4.71/5.00 = ( A2 = bot_bot_set_nat ) ) ).
% 4.71/5.00
% 4.71/5.00 % subset_empty
% 4.71/5.00 thf(fact_236_subset__empty,axiom,
% 4.71/5.00 ! [A2: set_int] :
% 4.71/5.00 ( ( ord_less_eq_set_int @ A2 @ bot_bot_set_int )
% 4.71/5.00 = ( A2 = bot_bot_set_int ) ) ).
% 4.71/5.00
% 4.71/5.00 % subset_empty
% 4.71/5.00 thf(fact_237_empty__Collect__eq,axiom,
% 4.71/5.00 ! [P: set_nat > $o] :
% 4.71/5.00 ( ( bot_bot_set_set_nat
% 4.71/5.00 = ( collect_set_nat @ P ) )
% 4.71/5.00 = ( ! [X3: set_nat] :
% 4.71/5.00 ~ ( P @ X3 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % empty_Collect_eq
% 4.71/5.00 thf(fact_238_empty__Collect__eq,axiom,
% 4.71/5.00 ! [P: set_nat_rat > $o] :
% 4.71/5.00 ( ( bot_bo6797373522285170759at_rat
% 4.71/5.00 = ( collect_set_nat_rat @ P ) )
% 4.71/5.00 = ( ! [X3: set_nat_rat] :
% 4.71/5.00 ~ ( P @ X3 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % empty_Collect_eq
% 4.71/5.00 thf(fact_239_empty__Collect__eq,axiom,
% 4.71/5.00 ! [P: ( nat > rat ) > $o] :
% 4.71/5.00 ( ( bot_bot_set_nat_rat
% 4.71/5.00 = ( collect_nat_rat @ P ) )
% 4.71/5.00 = ( ! [X3: nat > rat] :
% 4.71/5.00 ~ ( P @ X3 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % empty_Collect_eq
% 4.71/5.00 thf(fact_240_empty__Collect__eq,axiom,
% 4.71/5.00 ! [P: real > $o] :
% 4.71/5.00 ( ( bot_bot_set_real
% 4.71/5.00 = ( collect_real @ P ) )
% 4.71/5.00 = ( ! [X3: real] :
% 4.71/5.00 ~ ( P @ X3 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % empty_Collect_eq
% 4.71/5.00 thf(fact_241_empty__Collect__eq,axiom,
% 4.71/5.00 ! [P: $o > $o] :
% 4.71/5.00 ( ( bot_bot_set_o
% 4.71/5.00 = ( collect_o @ P ) )
% 4.71/5.00 = ( ! [X3: $o] :
% 4.71/5.00 ~ ( P @ X3 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % empty_Collect_eq
% 4.71/5.00 thf(fact_242_empty__Collect__eq,axiom,
% 4.71/5.00 ! [P: nat > $o] :
% 4.71/5.00 ( ( bot_bot_set_nat
% 4.71/5.00 = ( collect_nat @ P ) )
% 4.71/5.00 = ( ! [X3: nat] :
% 4.71/5.00 ~ ( P @ X3 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % empty_Collect_eq
% 4.71/5.00 thf(fact_243_empty__Collect__eq,axiom,
% 4.71/5.00 ! [P: int > $o] :
% 4.71/5.00 ( ( bot_bot_set_int
% 4.71/5.00 = ( collect_int @ P ) )
% 4.71/5.00 = ( ! [X3: int] :
% 4.71/5.00 ~ ( P @ X3 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % empty_Collect_eq
% 4.71/5.00 thf(fact_244_Collect__empty__eq,axiom,
% 4.71/5.00 ! [P: set_nat > $o] :
% 4.71/5.00 ( ( ( collect_set_nat @ P )
% 4.71/5.00 = bot_bot_set_set_nat )
% 4.71/5.00 = ( ! [X3: set_nat] :
% 4.71/5.00 ~ ( P @ X3 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % Collect_empty_eq
% 4.71/5.00 thf(fact_245_Collect__empty__eq,axiom,
% 4.71/5.00 ! [P: set_nat_rat > $o] :
% 4.71/5.00 ( ( ( collect_set_nat_rat @ P )
% 4.71/5.00 = bot_bo6797373522285170759at_rat )
% 4.71/5.00 = ( ! [X3: set_nat_rat] :
% 4.71/5.00 ~ ( P @ X3 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % Collect_empty_eq
% 4.71/5.00 thf(fact_246_Collect__empty__eq,axiom,
% 4.71/5.00 ! [P: ( nat > rat ) > $o] :
% 4.71/5.00 ( ( ( collect_nat_rat @ P )
% 4.71/5.00 = bot_bot_set_nat_rat )
% 4.71/5.00 = ( ! [X3: nat > rat] :
% 4.71/5.00 ~ ( P @ X3 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % Collect_empty_eq
% 4.71/5.00 thf(fact_247_Collect__empty__eq,axiom,
% 4.71/5.00 ! [P: real > $o] :
% 4.71/5.00 ( ( ( collect_real @ P )
% 4.71/5.00 = bot_bot_set_real )
% 4.71/5.00 = ( ! [X3: real] :
% 4.71/5.00 ~ ( P @ X3 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % Collect_empty_eq
% 4.71/5.00 thf(fact_248_Collect__empty__eq,axiom,
% 4.71/5.00 ! [P: $o > $o] :
% 4.71/5.00 ( ( ( collect_o @ P )
% 4.71/5.00 = bot_bot_set_o )
% 4.71/5.00 = ( ! [X3: $o] :
% 4.71/5.00 ~ ( P @ X3 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % Collect_empty_eq
% 4.71/5.00 thf(fact_249_Collect__empty__eq,axiom,
% 4.71/5.00 ! [P: nat > $o] :
% 4.71/5.00 ( ( ( collect_nat @ P )
% 4.71/5.00 = bot_bot_set_nat )
% 4.71/5.00 = ( ! [X3: nat] :
% 4.71/5.00 ~ ( P @ X3 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % Collect_empty_eq
% 4.71/5.00 thf(fact_250_Collect__empty__eq,axiom,
% 4.71/5.00 ! [P: int > $o] :
% 4.71/5.00 ( ( ( collect_int @ P )
% 4.71/5.00 = bot_bot_set_int )
% 4.71/5.00 = ( ! [X3: int] :
% 4.71/5.00 ~ ( P @ X3 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % Collect_empty_eq
% 4.71/5.00 thf(fact_251_all__not__in__conv,axiom,
% 4.71/5.00 ! [A2: set_set_nat] :
% 4.71/5.00 ( ( ! [X3: set_nat] :
% 4.71/5.00 ~ ( member_set_nat @ X3 @ A2 ) )
% 4.71/5.00 = ( A2 = bot_bot_set_set_nat ) ) ).
% 4.71/5.00
% 4.71/5.00 % all_not_in_conv
% 4.71/5.00 thf(fact_252_all__not__in__conv,axiom,
% 4.71/5.00 ! [A2: set_set_nat_rat] :
% 4.71/5.00 ( ( ! [X3: set_nat_rat] :
% 4.71/5.00 ~ ( member_set_nat_rat @ X3 @ A2 ) )
% 4.71/5.00 = ( A2 = bot_bo6797373522285170759at_rat ) ) ).
% 4.71/5.00
% 4.71/5.00 % all_not_in_conv
% 4.71/5.00 thf(fact_253_all__not__in__conv,axiom,
% 4.71/5.00 ! [A2: set_real] :
% 4.71/5.00 ( ( ! [X3: real] :
% 4.71/5.00 ~ ( member_real @ X3 @ A2 ) )
% 4.71/5.00 = ( A2 = bot_bot_set_real ) ) ).
% 4.71/5.00
% 4.71/5.00 % all_not_in_conv
% 4.71/5.00 thf(fact_254_all__not__in__conv,axiom,
% 4.71/5.00 ! [A2: set_o] :
% 4.71/5.00 ( ( ! [X3: $o] :
% 4.71/5.00 ~ ( member_o @ X3 @ A2 ) )
% 4.71/5.00 = ( A2 = bot_bot_set_o ) ) ).
% 4.71/5.00
% 4.71/5.00 % all_not_in_conv
% 4.71/5.00 thf(fact_255_all__not__in__conv,axiom,
% 4.71/5.00 ! [A2: set_nat] :
% 4.71/5.00 ( ( ! [X3: nat] :
% 4.71/5.00 ~ ( member_nat @ X3 @ A2 ) )
% 4.71/5.00 = ( A2 = bot_bot_set_nat ) ) ).
% 4.71/5.00
% 4.71/5.00 % all_not_in_conv
% 4.71/5.00 thf(fact_256_all__not__in__conv,axiom,
% 4.71/5.00 ! [A2: set_int] :
% 4.71/5.00 ( ( ! [X3: int] :
% 4.71/5.00 ~ ( member_int @ X3 @ A2 ) )
% 4.71/5.00 = ( A2 = bot_bot_set_int ) ) ).
% 4.71/5.00
% 4.71/5.00 % all_not_in_conv
% 4.71/5.00 thf(fact_257_psubsetI,axiom,
% 4.71/5.00 ! [A2: set_int,B2: set_int] :
% 4.71/5.00 ( ( ord_less_eq_set_int @ A2 @ B2 )
% 4.71/5.00 => ( ( A2 != B2 )
% 4.71/5.00 => ( ord_less_set_int @ A2 @ B2 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % psubsetI
% 4.71/5.00 thf(fact_258_subset__iff__psubset__eq,axiom,
% 4.71/5.00 ( ord_less_eq_set_int
% 4.71/5.00 = ( ^ [A6: set_int,B6: set_int] :
% 4.71/5.00 ( ( ord_less_set_int @ A6 @ B6 )
% 4.71/5.00 | ( A6 = B6 ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % subset_iff_psubset_eq
% 4.71/5.00 thf(fact_259_subset__psubset__trans,axiom,
% 4.71/5.00 ! [A2: set_int,B2: set_int,C2: set_int] :
% 4.71/5.00 ( ( ord_less_eq_set_int @ A2 @ B2 )
% 4.71/5.00 => ( ( ord_less_set_int @ B2 @ C2 )
% 4.71/5.00 => ( ord_less_set_int @ A2 @ C2 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % subset_psubset_trans
% 4.71/5.00 thf(fact_260_subset__not__subset__eq,axiom,
% 4.71/5.00 ( ord_less_set_int
% 4.71/5.00 = ( ^ [A6: set_int,B6: set_int] :
% 4.71/5.00 ( ( ord_less_eq_set_int @ A6 @ B6 )
% 4.71/5.00 & ~ ( ord_less_eq_set_int @ B6 @ A6 ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % subset_not_subset_eq
% 4.71/5.00 thf(fact_261_psubset__subset__trans,axiom,
% 4.71/5.00 ! [A2: set_int,B2: set_int,C2: set_int] :
% 4.71/5.00 ( ( ord_less_set_int @ A2 @ B2 )
% 4.71/5.00 => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 4.71/5.00 => ( ord_less_set_int @ A2 @ C2 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % psubset_subset_trans
% 4.71/5.00 thf(fact_262_psubset__imp__subset,axiom,
% 4.71/5.00 ! [A2: set_int,B2: set_int] :
% 4.71/5.00 ( ( ord_less_set_int @ A2 @ B2 )
% 4.71/5.00 => ( ord_less_eq_set_int @ A2 @ B2 ) ) ).
% 4.71/5.00
% 4.71/5.00 % psubset_imp_subset
% 4.71/5.00 thf(fact_263_psubset__eq,axiom,
% 4.71/5.00 ( ord_less_set_int
% 4.71/5.00 = ( ^ [A6: set_int,B6: set_int] :
% 4.71/5.00 ( ( ord_less_eq_set_int @ A6 @ B6 )
% 4.71/5.00 & ( A6 != B6 ) ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % psubset_eq
% 4.71/5.00 thf(fact_264_psubsetE,axiom,
% 4.71/5.00 ! [A2: set_int,B2: set_int] :
% 4.71/5.00 ( ( ord_less_set_int @ A2 @ B2 )
% 4.71/5.00 => ~ ( ( ord_less_eq_set_int @ A2 @ B2 )
% 4.71/5.00 => ( ord_less_eq_set_int @ B2 @ A2 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % psubsetE
% 4.71/5.00 thf(fact_265_rev__finite__subset,axiom,
% 4.71/5.00 ! [B2: set_nat,A2: set_nat] :
% 4.71/5.00 ( ( finite_finite_nat @ B2 )
% 4.71/5.00 => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 4.71/5.00 => ( finite_finite_nat @ A2 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % rev_finite_subset
% 4.71/5.00 thf(fact_266_rev__finite__subset,axiom,
% 4.71/5.00 ! [B2: set_complex,A2: set_complex] :
% 4.71/5.00 ( ( finite3207457112153483333omplex @ B2 )
% 4.71/5.00 => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 4.71/5.00 => ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % rev_finite_subset
% 4.71/5.00 thf(fact_267_rev__finite__subset,axiom,
% 4.71/5.00 ! [B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.00 ( ( finite6177210948735845034at_nat @ B2 )
% 4.71/5.00 => ( ( ord_le3146513528884898305at_nat @ A2 @ B2 )
% 4.71/5.00 => ( finite6177210948735845034at_nat @ A2 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % rev_finite_subset
% 4.71/5.00 thf(fact_268_rev__finite__subset,axiom,
% 4.71/5.00 ! [B2: set_Extended_enat,A2: set_Extended_enat] :
% 4.71/5.00 ( ( finite4001608067531595151d_enat @ B2 )
% 4.71/5.00 => ( ( ord_le7203529160286727270d_enat @ A2 @ B2 )
% 4.71/5.00 => ( finite4001608067531595151d_enat @ A2 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % rev_finite_subset
% 4.71/5.00 thf(fact_269_rev__finite__subset,axiom,
% 4.71/5.00 ! [B2: set_int,A2: set_int] :
% 4.71/5.00 ( ( finite_finite_int @ B2 )
% 4.71/5.00 => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 4.71/5.00 => ( finite_finite_int @ A2 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % rev_finite_subset
% 4.71/5.00 thf(fact_270_infinite__super,axiom,
% 4.71/5.00 ! [S2: set_nat,T3: set_nat] :
% 4.71/5.00 ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 4.71/5.00 => ( ~ ( finite_finite_nat @ S2 )
% 4.71/5.00 => ~ ( finite_finite_nat @ T3 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % infinite_super
% 4.71/5.00 thf(fact_271_infinite__super,axiom,
% 4.71/5.00 ! [S2: set_complex,T3: set_complex] :
% 4.71/5.00 ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 4.71/5.00 => ( ~ ( finite3207457112153483333omplex @ S2 )
% 4.71/5.00 => ~ ( finite3207457112153483333omplex @ T3 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % infinite_super
% 4.71/5.00 thf(fact_272_infinite__super,axiom,
% 4.71/5.00 ! [S2: set_Pr1261947904930325089at_nat,T3: set_Pr1261947904930325089at_nat] :
% 4.71/5.00 ( ( ord_le3146513528884898305at_nat @ S2 @ T3 )
% 4.71/5.00 => ( ~ ( finite6177210948735845034at_nat @ S2 )
% 4.71/5.00 => ~ ( finite6177210948735845034at_nat @ T3 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % infinite_super
% 4.71/5.00 thf(fact_273_infinite__super,axiom,
% 4.71/5.00 ! [S2: set_Extended_enat,T3: set_Extended_enat] :
% 4.71/5.00 ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 4.71/5.00 => ( ~ ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.00 => ~ ( finite4001608067531595151d_enat @ T3 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % infinite_super
% 4.71/5.00 thf(fact_274_infinite__super,axiom,
% 4.71/5.00 ! [S2: set_int,T3: set_int] :
% 4.71/5.00 ( ( ord_less_eq_set_int @ S2 @ T3 )
% 4.71/5.00 => ( ~ ( finite_finite_int @ S2 )
% 4.71/5.00 => ~ ( finite_finite_int @ T3 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % infinite_super
% 4.71/5.00 thf(fact_275_finite__subset,axiom,
% 4.71/5.00 ! [A2: set_nat,B2: set_nat] :
% 4.71/5.00 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 4.71/5.00 => ( ( finite_finite_nat @ B2 )
% 4.71/5.00 => ( finite_finite_nat @ A2 ) ) ) ).
% 4.71/5.00
% 4.71/5.00 % finite_subset
% 4.71/5.00 thf(fact_276_finite__subset,axiom,
% 4.71/5.00 ! [A2: set_complex,B2: set_complex] :
% 4.71/5.00 ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 4.71/5.00 => ( ( finite3207457112153483333omplex @ B2 )
% 4.71/5.01 => ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % finite_subset
% 4.71/5.01 thf(fact_277_finite__subset,axiom,
% 4.71/5.01 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 4.71/5.01 ( ( ord_le3146513528884898305at_nat @ A2 @ B2 )
% 4.71/5.01 => ( ( finite6177210948735845034at_nat @ B2 )
% 4.71/5.01 => ( finite6177210948735845034at_nat @ A2 ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % finite_subset
% 4.71/5.01 thf(fact_278_finite__subset,axiom,
% 4.71/5.01 ! [A2: set_Extended_enat,B2: set_Extended_enat] :
% 4.71/5.01 ( ( ord_le7203529160286727270d_enat @ A2 @ B2 )
% 4.71/5.01 => ( ( finite4001608067531595151d_enat @ B2 )
% 4.71/5.01 => ( finite4001608067531595151d_enat @ A2 ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % finite_subset
% 4.71/5.01 thf(fact_279_finite__subset,axiom,
% 4.71/5.01 ! [A2: set_int,B2: set_int] :
% 4.71/5.01 ( ( ord_less_eq_set_int @ A2 @ B2 )
% 4.71/5.01 => ( ( finite_finite_int @ B2 )
% 4.71/5.01 => ( finite_finite_int @ A2 ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % finite_subset
% 4.71/5.01 thf(fact_280_linorder__neqE__linordered__idom,axiom,
% 4.71/5.01 ! [X: real,Y: real] :
% 4.71/5.01 ( ( X != Y )
% 4.71/5.01 => ( ~ ( ord_less_real @ X @ Y )
% 4.71/5.01 => ( ord_less_real @ Y @ X ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_neqE_linordered_idom
% 4.71/5.01 thf(fact_281_linorder__neqE__linordered__idom,axiom,
% 4.71/5.01 ! [X: rat,Y: rat] :
% 4.71/5.01 ( ( X != Y )
% 4.71/5.01 => ( ~ ( ord_less_rat @ X @ Y )
% 4.71/5.01 => ( ord_less_rat @ Y @ X ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_neqE_linordered_idom
% 4.71/5.01 thf(fact_282_linorder__neqE__linordered__idom,axiom,
% 4.71/5.01 ! [X: int,Y: int] :
% 4.71/5.01 ( ( X != Y )
% 4.71/5.01 => ( ~ ( ord_less_int @ X @ Y )
% 4.71/5.01 => ( ord_less_int @ Y @ X ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_neqE_linordered_idom
% 4.71/5.01 thf(fact_283_ex__in__conv,axiom,
% 4.71/5.01 ! [A2: set_set_nat] :
% 4.71/5.01 ( ( ? [X3: set_nat] : ( member_set_nat @ X3 @ A2 ) )
% 4.71/5.01 = ( A2 != bot_bot_set_set_nat ) ) ).
% 4.71/5.01
% 4.71/5.01 % ex_in_conv
% 4.71/5.01 thf(fact_284_ex__in__conv,axiom,
% 4.71/5.01 ! [A2: set_set_nat_rat] :
% 4.71/5.01 ( ( ? [X3: set_nat_rat] : ( member_set_nat_rat @ X3 @ A2 ) )
% 4.71/5.01 = ( A2 != bot_bo6797373522285170759at_rat ) ) ).
% 4.71/5.01
% 4.71/5.01 % ex_in_conv
% 4.71/5.01 thf(fact_285_ex__in__conv,axiom,
% 4.71/5.01 ! [A2: set_real] :
% 4.71/5.01 ( ( ? [X3: real] : ( member_real @ X3 @ A2 ) )
% 4.71/5.01 = ( A2 != bot_bot_set_real ) ) ).
% 4.71/5.01
% 4.71/5.01 % ex_in_conv
% 4.71/5.01 thf(fact_286_ex__in__conv,axiom,
% 4.71/5.01 ! [A2: set_o] :
% 4.71/5.01 ( ( ? [X3: $o] : ( member_o @ X3 @ A2 ) )
% 4.71/5.01 = ( A2 != bot_bot_set_o ) ) ).
% 4.71/5.01
% 4.71/5.01 % ex_in_conv
% 4.71/5.01 thf(fact_287_ex__in__conv,axiom,
% 4.71/5.01 ! [A2: set_nat] :
% 4.71/5.01 ( ( ? [X3: nat] : ( member_nat @ X3 @ A2 ) )
% 4.71/5.01 = ( A2 != bot_bot_set_nat ) ) ).
% 4.71/5.01
% 4.71/5.01 % ex_in_conv
% 4.71/5.01 thf(fact_288_ex__in__conv,axiom,
% 4.71/5.01 ! [A2: set_int] :
% 4.71/5.01 ( ( ? [X3: int] : ( member_int @ X3 @ A2 ) )
% 4.71/5.01 = ( A2 != bot_bot_set_int ) ) ).
% 4.71/5.01
% 4.71/5.01 % ex_in_conv
% 4.71/5.01 thf(fact_289_equals0I,axiom,
% 4.71/5.01 ! [A2: set_set_nat] :
% 4.71/5.01 ( ! [Y3: set_nat] :
% 4.71/5.01 ~ ( member_set_nat @ Y3 @ A2 )
% 4.71/5.01 => ( A2 = bot_bot_set_set_nat ) ) ).
% 4.71/5.01
% 4.71/5.01 % equals0I
% 4.71/5.01 thf(fact_290_equals0I,axiom,
% 4.71/5.01 ! [A2: set_set_nat_rat] :
% 4.71/5.01 ( ! [Y3: set_nat_rat] :
% 4.71/5.01 ~ ( member_set_nat_rat @ Y3 @ A2 )
% 4.71/5.01 => ( A2 = bot_bo6797373522285170759at_rat ) ) ).
% 4.71/5.01
% 4.71/5.01 % equals0I
% 4.71/5.01 thf(fact_291_equals0I,axiom,
% 4.71/5.01 ! [A2: set_real] :
% 4.71/5.01 ( ! [Y3: real] :
% 4.71/5.01 ~ ( member_real @ Y3 @ A2 )
% 4.71/5.01 => ( A2 = bot_bot_set_real ) ) ).
% 4.71/5.01
% 4.71/5.01 % equals0I
% 4.71/5.01 thf(fact_292_equals0I,axiom,
% 4.71/5.01 ! [A2: set_o] :
% 4.71/5.01 ( ! [Y3: $o] :
% 4.71/5.01 ~ ( member_o @ Y3 @ A2 )
% 4.71/5.01 => ( A2 = bot_bot_set_o ) ) ).
% 4.71/5.01
% 4.71/5.01 % equals0I
% 4.71/5.01 thf(fact_293_equals0I,axiom,
% 4.71/5.01 ! [A2: set_nat] :
% 4.71/5.01 ( ! [Y3: nat] :
% 4.71/5.01 ~ ( member_nat @ Y3 @ A2 )
% 4.71/5.01 => ( A2 = bot_bot_set_nat ) ) ).
% 4.71/5.01
% 4.71/5.01 % equals0I
% 4.71/5.01 thf(fact_294_equals0I,axiom,
% 4.71/5.01 ! [A2: set_int] :
% 4.71/5.01 ( ! [Y3: int] :
% 4.71/5.01 ~ ( member_int @ Y3 @ A2 )
% 4.71/5.01 => ( A2 = bot_bot_set_int ) ) ).
% 4.71/5.01
% 4.71/5.01 % equals0I
% 4.71/5.01 thf(fact_295_equals0D,axiom,
% 4.71/5.01 ! [A2: set_set_nat,A: set_nat] :
% 4.71/5.01 ( ( A2 = bot_bot_set_set_nat )
% 4.71/5.01 => ~ ( member_set_nat @ A @ A2 ) ) ).
% 4.71/5.01
% 4.71/5.01 % equals0D
% 4.71/5.01 thf(fact_296_equals0D,axiom,
% 4.71/5.01 ! [A2: set_set_nat_rat,A: set_nat_rat] :
% 4.71/5.01 ( ( A2 = bot_bo6797373522285170759at_rat )
% 4.71/5.01 => ~ ( member_set_nat_rat @ A @ A2 ) ) ).
% 4.71/5.01
% 4.71/5.01 % equals0D
% 4.71/5.01 thf(fact_297_equals0D,axiom,
% 4.71/5.01 ! [A2: set_real,A: real] :
% 4.71/5.01 ( ( A2 = bot_bot_set_real )
% 4.71/5.01 => ~ ( member_real @ A @ A2 ) ) ).
% 4.71/5.01
% 4.71/5.01 % equals0D
% 4.71/5.01 thf(fact_298_equals0D,axiom,
% 4.71/5.01 ! [A2: set_o,A: $o] :
% 4.71/5.01 ( ( A2 = bot_bot_set_o )
% 4.71/5.01 => ~ ( member_o @ A @ A2 ) ) ).
% 4.71/5.01
% 4.71/5.01 % equals0D
% 4.71/5.01 thf(fact_299_equals0D,axiom,
% 4.71/5.01 ! [A2: set_nat,A: nat] :
% 4.71/5.01 ( ( A2 = bot_bot_set_nat )
% 4.71/5.01 => ~ ( member_nat @ A @ A2 ) ) ).
% 4.71/5.01
% 4.71/5.01 % equals0D
% 4.71/5.01 thf(fact_300_equals0D,axiom,
% 4.71/5.01 ! [A2: set_int,A: int] :
% 4.71/5.01 ( ( A2 = bot_bot_set_int )
% 4.71/5.01 => ~ ( member_int @ A @ A2 ) ) ).
% 4.71/5.01
% 4.71/5.01 % equals0D
% 4.71/5.01 thf(fact_301_emptyE,axiom,
% 4.71/5.01 ! [A: set_nat] :
% 4.71/5.01 ~ ( member_set_nat @ A @ bot_bot_set_set_nat ) ).
% 4.71/5.01
% 4.71/5.01 % emptyE
% 4.71/5.01 thf(fact_302_emptyE,axiom,
% 4.71/5.01 ! [A: set_nat_rat] :
% 4.71/5.01 ~ ( member_set_nat_rat @ A @ bot_bo6797373522285170759at_rat ) ).
% 4.71/5.01
% 4.71/5.01 % emptyE
% 4.71/5.01 thf(fact_303_emptyE,axiom,
% 4.71/5.01 ! [A: real] :
% 4.71/5.01 ~ ( member_real @ A @ bot_bot_set_real ) ).
% 4.71/5.01
% 4.71/5.01 % emptyE
% 4.71/5.01 thf(fact_304_emptyE,axiom,
% 4.71/5.01 ! [A: $o] :
% 4.71/5.01 ~ ( member_o @ A @ bot_bot_set_o ) ).
% 4.71/5.01
% 4.71/5.01 % emptyE
% 4.71/5.01 thf(fact_305_emptyE,axiom,
% 4.71/5.01 ! [A: nat] :
% 4.71/5.01 ~ ( member_nat @ A @ bot_bot_set_nat ) ).
% 4.71/5.01
% 4.71/5.01 % emptyE
% 4.71/5.01 thf(fact_306_emptyE,axiom,
% 4.71/5.01 ! [A: int] :
% 4.71/5.01 ~ ( member_int @ A @ bot_bot_set_int ) ).
% 4.71/5.01
% 4.71/5.01 % emptyE
% 4.71/5.01 thf(fact_307_psubsetD,axiom,
% 4.71/5.01 ! [A2: set_o,B2: set_o,C: $o] :
% 4.71/5.01 ( ( ord_less_set_o @ A2 @ B2 )
% 4.71/5.01 => ( ( member_o @ C @ A2 )
% 4.71/5.01 => ( member_o @ C @ B2 ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % psubsetD
% 4.71/5.01 thf(fact_308_psubsetD,axiom,
% 4.71/5.01 ! [A2: set_set_nat,B2: set_set_nat,C: set_nat] :
% 4.71/5.01 ( ( ord_less_set_set_nat @ A2 @ B2 )
% 4.71/5.01 => ( ( member_set_nat @ C @ A2 )
% 4.71/5.01 => ( member_set_nat @ C @ B2 ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % psubsetD
% 4.71/5.01 thf(fact_309_psubsetD,axiom,
% 4.71/5.01 ! [A2: set_set_nat_rat,B2: set_set_nat_rat,C: set_nat_rat] :
% 4.71/5.01 ( ( ord_le1311537459589289991at_rat @ A2 @ B2 )
% 4.71/5.01 => ( ( member_set_nat_rat @ C @ A2 )
% 4.71/5.01 => ( member_set_nat_rat @ C @ B2 ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % psubsetD
% 4.71/5.01 thf(fact_310_psubsetD,axiom,
% 4.71/5.01 ! [A2: set_nat,B2: set_nat,C: nat] :
% 4.71/5.01 ( ( ord_less_set_nat @ A2 @ B2 )
% 4.71/5.01 => ( ( member_nat @ C @ A2 )
% 4.71/5.01 => ( member_nat @ C @ B2 ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % psubsetD
% 4.71/5.01 thf(fact_311_psubsetD,axiom,
% 4.71/5.01 ! [A2: set_int,B2: set_int,C: int] :
% 4.71/5.01 ( ( ord_less_set_int @ A2 @ B2 )
% 4.71/5.01 => ( ( member_int @ C @ A2 )
% 4.71/5.01 => ( member_int @ C @ B2 ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % psubsetD
% 4.71/5.01 thf(fact_312_le__numeral__extra_I3_J,axiom,
% 4.71/5.01 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 4.71/5.01
% 4.71/5.01 % le_numeral_extra(3)
% 4.71/5.01 thf(fact_313_le__numeral__extra_I3_J,axiom,
% 4.71/5.01 ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 4.71/5.01
% 4.71/5.01 % le_numeral_extra(3)
% 4.71/5.01 thf(fact_314_le__numeral__extra_I3_J,axiom,
% 4.71/5.01 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 4.71/5.01
% 4.71/5.01 % le_numeral_extra(3)
% 4.71/5.01 thf(fact_315_le__numeral__extra_I3_J,axiom,
% 4.71/5.01 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 4.71/5.01
% 4.71/5.01 % le_numeral_extra(3)
% 4.71/5.01 thf(fact_316_less__numeral__extra_I3_J,axiom,
% 4.71/5.01 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 4.71/5.01
% 4.71/5.01 % less_numeral_extra(3)
% 4.71/5.01 thf(fact_317_less__numeral__extra_I3_J,axiom,
% 4.71/5.01 ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 4.71/5.01
% 4.71/5.01 % less_numeral_extra(3)
% 4.71/5.01 thf(fact_318_less__numeral__extra_I3_J,axiom,
% 4.71/5.01 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 4.71/5.01
% 4.71/5.01 % less_numeral_extra(3)
% 4.71/5.01 thf(fact_319_less__numeral__extra_I3_J,axiom,
% 4.71/5.01 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 4.71/5.01
% 4.71/5.01 % less_numeral_extra(3)
% 4.71/5.01 thf(fact_320_le__numeral__extra_I4_J,axiom,
% 4.71/5.01 ord_less_eq_real @ one_one_real @ one_one_real ).
% 4.71/5.01
% 4.71/5.01 % le_numeral_extra(4)
% 4.71/5.01 thf(fact_321_le__numeral__extra_I4_J,axiom,
% 4.71/5.01 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 4.71/5.01
% 4.71/5.01 % le_numeral_extra(4)
% 4.71/5.01 thf(fact_322_le__numeral__extra_I4_J,axiom,
% 4.71/5.01 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 4.71/5.01
% 4.71/5.01 % le_numeral_extra(4)
% 4.71/5.01 thf(fact_323_le__numeral__extra_I4_J,axiom,
% 4.71/5.01 ord_less_eq_int @ one_one_int @ one_one_int ).
% 4.71/5.01
% 4.71/5.01 % le_numeral_extra(4)
% 4.71/5.01 thf(fact_324_zero__neq__one,axiom,
% 4.71/5.01 zero_zero_complex != one_one_complex ).
% 4.71/5.01
% 4.71/5.01 % zero_neq_one
% 4.71/5.01 thf(fact_325_zero__neq__one,axiom,
% 4.71/5.01 zero_zero_real != one_one_real ).
% 4.71/5.01
% 4.71/5.01 % zero_neq_one
% 4.71/5.01 thf(fact_326_zero__neq__one,axiom,
% 4.71/5.01 zero_zero_rat != one_one_rat ).
% 4.71/5.01
% 4.71/5.01 % zero_neq_one
% 4.71/5.01 thf(fact_327_zero__neq__one,axiom,
% 4.71/5.01 zero_zero_nat != one_one_nat ).
% 4.71/5.01
% 4.71/5.01 % zero_neq_one
% 4.71/5.01 thf(fact_328_zero__neq__one,axiom,
% 4.71/5.01 zero_zero_int != one_one_int ).
% 4.71/5.01
% 4.71/5.01 % zero_neq_one
% 4.71/5.01 thf(fact_329_less__numeral__extra_I4_J,axiom,
% 4.71/5.01 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 4.71/5.01
% 4.71/5.01 % less_numeral_extra(4)
% 4.71/5.01 thf(fact_330_less__numeral__extra_I4_J,axiom,
% 4.71/5.01 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 4.71/5.01
% 4.71/5.01 % less_numeral_extra(4)
% 4.71/5.01 thf(fact_331_less__numeral__extra_I4_J,axiom,
% 4.71/5.01 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 4.71/5.01
% 4.71/5.01 % less_numeral_extra(4)
% 4.71/5.01 thf(fact_332_less__numeral__extra_I4_J,axiom,
% 4.71/5.01 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 4.71/5.01
% 4.71/5.01 % less_numeral_extra(4)
% 4.71/5.01 thf(fact_333_not__psubset__empty,axiom,
% 4.71/5.01 ! [A2: set_real] :
% 4.71/5.01 ~ ( ord_less_set_real @ A2 @ bot_bot_set_real ) ).
% 4.71/5.01
% 4.71/5.01 % not_psubset_empty
% 4.71/5.01 thf(fact_334_not__psubset__empty,axiom,
% 4.71/5.01 ! [A2: set_o] :
% 4.71/5.01 ~ ( ord_less_set_o @ A2 @ bot_bot_set_o ) ).
% 4.71/5.01
% 4.71/5.01 % not_psubset_empty
% 4.71/5.01 thf(fact_335_not__psubset__empty,axiom,
% 4.71/5.01 ! [A2: set_nat] :
% 4.71/5.01 ~ ( ord_less_set_nat @ A2 @ bot_bot_set_nat ) ).
% 4.71/5.01
% 4.71/5.01 % not_psubset_empty
% 4.71/5.01 thf(fact_336_not__psubset__empty,axiom,
% 4.71/5.01 ! [A2: set_int] :
% 4.71/5.01 ~ ( ord_less_set_int @ A2 @ bot_bot_set_int ) ).
% 4.71/5.01
% 4.71/5.01 % not_psubset_empty
% 4.71/5.01 thf(fact_337_dual__order_Orefl,axiom,
% 4.71/5.01 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.refl
% 4.71/5.01 thf(fact_338_dual__order_Orefl,axiom,
% 4.71/5.01 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.refl
% 4.71/5.01 thf(fact_339_dual__order_Orefl,axiom,
% 4.71/5.01 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.refl
% 4.71/5.01 thf(fact_340_dual__order_Orefl,axiom,
% 4.71/5.01 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.refl
% 4.71/5.01 thf(fact_341_dual__order_Orefl,axiom,
% 4.71/5.01 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.refl
% 4.71/5.01 thf(fact_342_order__refl,axiom,
% 4.71/5.01 ! [X: set_int] : ( ord_less_eq_set_int @ X @ X ) ).
% 4.71/5.01
% 4.71/5.01 % order_refl
% 4.71/5.01 thf(fact_343_order__refl,axiom,
% 4.71/5.01 ! [X: rat] : ( ord_less_eq_rat @ X @ X ) ).
% 4.71/5.01
% 4.71/5.01 % order_refl
% 4.71/5.01 thf(fact_344_order__refl,axiom,
% 4.71/5.01 ! [X: num] : ( ord_less_eq_num @ X @ X ) ).
% 4.71/5.01
% 4.71/5.01 % order_refl
% 4.71/5.01 thf(fact_345_order__refl,axiom,
% 4.71/5.01 ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 4.71/5.01
% 4.71/5.01 % order_refl
% 4.71/5.01 thf(fact_346_order__refl,axiom,
% 4.71/5.01 ! [X: int] : ( ord_less_eq_int @ X @ X ) ).
% 4.71/5.01
% 4.71/5.01 % order_refl
% 4.71/5.01 thf(fact_347_arg__min__if__finite_I2_J,axiom,
% 4.71/5.01 ! [S2: set_complex,F: complex > real] :
% 4.71/5.01 ( ( finite3207457112153483333omplex @ S2 )
% 4.71/5.01 => ( ( S2 != bot_bot_set_complex )
% 4.71/5.01 => ~ ? [X2: complex] :
% 4.71/5.01 ( ( member_complex @ X2 @ S2 )
% 4.71/5.01 & ( ord_less_real @ ( F @ X2 ) @ ( F @ ( lattic8794016678065449205x_real @ F @ S2 ) ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % arg_min_if_finite(2)
% 4.71/5.01 thf(fact_348_arg__min__if__finite_I2_J,axiom,
% 4.71/5.01 ! [S2: set_Extended_enat,F: extended_enat > real] :
% 4.71/5.01 ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.01 => ( ( S2 != bot_bo7653980558646680370d_enat )
% 4.71/5.01 => ~ ? [X2: extended_enat] :
% 4.71/5.01 ( ( member_Extended_enat @ X2 @ S2 )
% 4.71/5.01 & ( ord_less_real @ ( F @ X2 ) @ ( F @ ( lattic1189837152898106425t_real @ F @ S2 ) ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % arg_min_if_finite(2)
% 4.71/5.01 thf(fact_349_arg__min__if__finite_I2_J,axiom,
% 4.71/5.01 ! [S2: set_real,F: real > real] :
% 4.71/5.01 ( ( finite_finite_real @ S2 )
% 4.71/5.01 => ( ( S2 != bot_bot_set_real )
% 4.71/5.01 => ~ ? [X2: real] :
% 4.71/5.01 ( ( member_real @ X2 @ S2 )
% 4.71/5.01 & ( ord_less_real @ ( F @ X2 ) @ ( F @ ( lattic8440615504127631091l_real @ F @ S2 ) ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % arg_min_if_finite(2)
% 4.71/5.01 thf(fact_350_arg__min__if__finite_I2_J,axiom,
% 4.71/5.01 ! [S2: set_o,F: $o > real] :
% 4.71/5.01 ( ( finite_finite_o @ S2 )
% 4.71/5.01 => ( ( S2 != bot_bot_set_o )
% 4.71/5.01 => ~ ? [X2: $o] :
% 4.71/5.01 ( ( member_o @ X2 @ S2 )
% 4.71/5.01 & ( ord_less_real @ ( F @ X2 ) @ ( F @ ( lattic8697145971487455083o_real @ F @ S2 ) ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % arg_min_if_finite(2)
% 4.71/5.01 thf(fact_351_arg__min__if__finite_I2_J,axiom,
% 4.71/5.01 ! [S2: set_nat,F: nat > real] :
% 4.71/5.01 ( ( finite_finite_nat @ S2 )
% 4.71/5.01 => ( ( S2 != bot_bot_set_nat )
% 4.71/5.01 => ~ ? [X2: nat] :
% 4.71/5.01 ( ( member_nat @ X2 @ S2 )
% 4.71/5.01 & ( ord_less_real @ ( F @ X2 ) @ ( F @ ( lattic488527866317076247t_real @ F @ S2 ) ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % arg_min_if_finite(2)
% 4.71/5.01 thf(fact_352_arg__min__if__finite_I2_J,axiom,
% 4.71/5.01 ! [S2: set_int,F: int > real] :
% 4.71/5.01 ( ( finite_finite_int @ S2 )
% 4.71/5.01 => ( ( S2 != bot_bot_set_int )
% 4.71/5.01 => ~ ? [X2: int] :
% 4.71/5.01 ( ( member_int @ X2 @ S2 )
% 4.71/5.01 & ( ord_less_real @ ( F @ X2 ) @ ( F @ ( lattic2675449441010098035t_real @ F @ S2 ) ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % arg_min_if_finite(2)
% 4.71/5.01 thf(fact_353_arg__min__if__finite_I2_J,axiom,
% 4.71/5.01 ! [S2: set_complex,F: complex > rat] :
% 4.71/5.01 ( ( finite3207457112153483333omplex @ S2 )
% 4.71/5.01 => ( ( S2 != bot_bot_set_complex )
% 4.71/5.01 => ~ ? [X2: complex] :
% 4.71/5.01 ( ( member_complex @ X2 @ S2 )
% 4.71/5.01 & ( ord_less_rat @ ( F @ X2 ) @ ( F @ ( lattic4729654577720512673ex_rat @ F @ S2 ) ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % arg_min_if_finite(2)
% 4.71/5.01 thf(fact_354_arg__min__if__finite_I2_J,axiom,
% 4.71/5.01 ! [S2: set_Extended_enat,F: extended_enat > rat] :
% 4.71/5.01 ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.01 => ( ( S2 != bot_bo7653980558646680370d_enat )
% 4.71/5.01 => ~ ? [X2: extended_enat] :
% 4.71/5.01 ( ( member_Extended_enat @ X2 @ S2 )
% 4.71/5.01 & ( ord_less_rat @ ( F @ X2 ) @ ( F @ ( lattic3210252021154270693at_rat @ F @ S2 ) ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % arg_min_if_finite(2)
% 4.71/5.01 thf(fact_355_arg__min__if__finite_I2_J,axiom,
% 4.71/5.01 ! [S2: set_real,F: real > rat] :
% 4.71/5.01 ( ( finite_finite_real @ S2 )
% 4.71/5.01 => ( ( S2 != bot_bot_set_real )
% 4.71/5.01 => ~ ? [X2: real] :
% 4.71/5.01 ( ( member_real @ X2 @ S2 )
% 4.71/5.01 & ( ord_less_rat @ ( F @ X2 ) @ ( F @ ( lattic4420706379359479199al_rat @ F @ S2 ) ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % arg_min_if_finite(2)
% 4.71/5.01 thf(fact_356_arg__min__if__finite_I2_J,axiom,
% 4.71/5.01 ! [S2: set_o,F: $o > rat] :
% 4.71/5.01 ( ( finite_finite_o @ S2 )
% 4.71/5.01 => ( ( S2 != bot_bot_set_o )
% 4.71/5.01 => ~ ? [X2: $o] :
% 4.71/5.01 ( ( member_o @ X2 @ S2 )
% 4.71/5.01 & ( ord_less_rat @ ( F @ X2 ) @ ( F @ ( lattic2140725968369957399_o_rat @ F @ S2 ) ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % arg_min_if_finite(2)
% 4.71/5.01 thf(fact_357_arg__min__least,axiom,
% 4.71/5.01 ! [S2: set_complex,Y: complex,F: complex > rat] :
% 4.71/5.01 ( ( finite3207457112153483333omplex @ S2 )
% 4.71/5.01 => ( ( S2 != bot_bot_set_complex )
% 4.71/5.01 => ( ( member_complex @ Y @ S2 )
% 4.71/5.01 => ( ord_less_eq_rat @ ( F @ ( lattic4729654577720512673ex_rat @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % arg_min_least
% 4.71/5.01 thf(fact_358_arg__min__least,axiom,
% 4.71/5.01 ! [S2: set_Extended_enat,Y: extended_enat,F: extended_enat > rat] :
% 4.71/5.01 ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.01 => ( ( S2 != bot_bo7653980558646680370d_enat )
% 4.71/5.01 => ( ( member_Extended_enat @ Y @ S2 )
% 4.71/5.01 => ( ord_less_eq_rat @ ( F @ ( lattic3210252021154270693at_rat @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % arg_min_least
% 4.71/5.01 thf(fact_359_arg__min__least,axiom,
% 4.71/5.01 ! [S2: set_real,Y: real,F: real > rat] :
% 4.71/5.01 ( ( finite_finite_real @ S2 )
% 4.71/5.01 => ( ( S2 != bot_bot_set_real )
% 4.71/5.01 => ( ( member_real @ Y @ S2 )
% 4.71/5.01 => ( ord_less_eq_rat @ ( F @ ( lattic4420706379359479199al_rat @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % arg_min_least
% 4.71/5.01 thf(fact_360_arg__min__least,axiom,
% 4.71/5.01 ! [S2: set_o,Y: $o,F: $o > rat] :
% 4.71/5.01 ( ( finite_finite_o @ S2 )
% 4.71/5.01 => ( ( S2 != bot_bot_set_o )
% 4.71/5.01 => ( ( member_o @ Y @ S2 )
% 4.71/5.01 => ( ord_less_eq_rat @ ( F @ ( lattic2140725968369957399_o_rat @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % arg_min_least
% 4.71/5.01 thf(fact_361_arg__min__least,axiom,
% 4.71/5.01 ! [S2: set_nat,Y: nat,F: nat > rat] :
% 4.71/5.01 ( ( finite_finite_nat @ S2 )
% 4.71/5.01 => ( ( S2 != bot_bot_set_nat )
% 4.71/5.01 => ( ( member_nat @ Y @ S2 )
% 4.71/5.01 => ( ord_less_eq_rat @ ( F @ ( lattic6811802900495863747at_rat @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % arg_min_least
% 4.71/5.01 thf(fact_362_arg__min__least,axiom,
% 4.71/5.01 ! [S2: set_int,Y: int,F: int > rat] :
% 4.71/5.01 ( ( finite_finite_int @ S2 )
% 4.71/5.01 => ( ( S2 != bot_bot_set_int )
% 4.71/5.01 => ( ( member_int @ Y @ S2 )
% 4.71/5.01 => ( ord_less_eq_rat @ ( F @ ( lattic7811156612396918303nt_rat @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % arg_min_least
% 4.71/5.01 thf(fact_363_arg__min__least,axiom,
% 4.71/5.01 ! [S2: set_complex,Y: complex,F: complex > num] :
% 4.71/5.01 ( ( finite3207457112153483333omplex @ S2 )
% 4.71/5.01 => ( ( S2 != bot_bot_set_complex )
% 4.71/5.01 => ( ( member_complex @ Y @ S2 )
% 4.71/5.01 => ( ord_less_eq_num @ ( F @ ( lattic1922116423962787043ex_num @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % arg_min_least
% 4.71/5.01 thf(fact_364_arg__min__least,axiom,
% 4.71/5.01 ! [S2: set_Extended_enat,Y: extended_enat,F: extended_enat > num] :
% 4.71/5.01 ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.01 => ( ( S2 != bot_bo7653980558646680370d_enat )
% 4.71/5.01 => ( ( member_Extended_enat @ Y @ S2 )
% 4.71/5.01 => ( ord_less_eq_num @ ( F @ ( lattic402713867396545063at_num @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % arg_min_least
% 4.71/5.01 thf(fact_365_arg__min__least,axiom,
% 4.71/5.01 ! [S2: set_real,Y: real,F: real > num] :
% 4.71/5.01 ( ( finite_finite_real @ S2 )
% 4.71/5.01 => ( ( S2 != bot_bot_set_real )
% 4.71/5.01 => ( ( member_real @ Y @ S2 )
% 4.71/5.01 => ( ord_less_eq_num @ ( F @ ( lattic1613168225601753569al_num @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % arg_min_least
% 4.71/5.01 thf(fact_366_arg__min__least,axiom,
% 4.71/5.01 ! [S2: set_o,Y: $o,F: $o > num] :
% 4.71/5.01 ( ( finite_finite_o @ S2 )
% 4.71/5.01 => ( ( S2 != bot_bot_set_o )
% 4.71/5.01 => ( ( member_o @ Y @ S2 )
% 4.71/5.01 => ( ord_less_eq_num @ ( F @ ( lattic8556559851467007577_o_num @ F @ S2 ) ) @ ( F @ Y ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % arg_min_least
% 4.71/5.01 thf(fact_367_nat__descend__induct,axiom,
% 4.71/5.01 ! [N: nat,P: nat > $o,M2: nat] :
% 4.71/5.01 ( ! [K2: nat] :
% 4.71/5.01 ( ( ord_less_nat @ N @ K2 )
% 4.71/5.01 => ( P @ K2 ) )
% 4.71/5.01 => ( ! [K2: nat] :
% 4.71/5.01 ( ( ord_less_eq_nat @ K2 @ N )
% 4.71/5.01 => ( ! [I3: nat] :
% 4.71/5.01 ( ( ord_less_nat @ K2 @ I3 )
% 4.71/5.01 => ( P @ I3 ) )
% 4.71/5.01 => ( P @ K2 ) ) )
% 4.71/5.01 => ( P @ M2 ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % nat_descend_induct
% 4.71/5.01 thf(fact_368_bot_Onot__eq__extremum,axiom,
% 4.71/5.01 ! [A: set_real] :
% 4.71/5.01 ( ( A != bot_bot_set_real )
% 4.71/5.01 = ( ord_less_set_real @ bot_bot_set_real @ A ) ) ).
% 4.71/5.01
% 4.71/5.01 % bot.not_eq_extremum
% 4.71/5.01 thf(fact_369_bot_Onot__eq__extremum,axiom,
% 4.71/5.01 ! [A: set_o] :
% 4.71/5.01 ( ( A != bot_bot_set_o )
% 4.71/5.01 = ( ord_less_set_o @ bot_bot_set_o @ A ) ) ).
% 4.71/5.01
% 4.71/5.01 % bot.not_eq_extremum
% 4.71/5.01 thf(fact_370_bot_Onot__eq__extremum,axiom,
% 4.71/5.01 ! [A: set_nat] :
% 4.71/5.01 ( ( A != bot_bot_set_nat )
% 4.71/5.01 = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 4.71/5.01
% 4.71/5.01 % bot.not_eq_extremum
% 4.71/5.01 thf(fact_371_bot_Onot__eq__extremum,axiom,
% 4.71/5.01 ! [A: set_int] :
% 4.71/5.01 ( ( A != bot_bot_set_int )
% 4.71/5.01 = ( ord_less_set_int @ bot_bot_set_int @ A ) ) ).
% 4.71/5.01
% 4.71/5.01 % bot.not_eq_extremum
% 4.71/5.01 thf(fact_372_bot_Onot__eq__extremum,axiom,
% 4.71/5.01 ! [A: nat] :
% 4.71/5.01 ( ( A != bot_bot_nat )
% 4.71/5.01 = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 4.71/5.01
% 4.71/5.01 % bot.not_eq_extremum
% 4.71/5.01 thf(fact_373_bot_Oextremum__strict,axiom,
% 4.71/5.01 ! [A: set_real] :
% 4.71/5.01 ~ ( ord_less_set_real @ A @ bot_bot_set_real ) ).
% 4.71/5.01
% 4.71/5.01 % bot.extremum_strict
% 4.71/5.01 thf(fact_374_bot_Oextremum__strict,axiom,
% 4.71/5.01 ! [A: set_o] :
% 4.71/5.01 ~ ( ord_less_set_o @ A @ bot_bot_set_o ) ).
% 4.71/5.01
% 4.71/5.01 % bot.extremum_strict
% 4.71/5.01 thf(fact_375_bot_Oextremum__strict,axiom,
% 4.71/5.01 ! [A: set_nat] :
% 4.71/5.01 ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 4.71/5.01
% 4.71/5.01 % bot.extremum_strict
% 4.71/5.01 thf(fact_376_bot_Oextremum__strict,axiom,
% 4.71/5.01 ! [A: set_int] :
% 4.71/5.01 ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 4.71/5.01
% 4.71/5.01 % bot.extremum_strict
% 4.71/5.01 thf(fact_377_bot_Oextremum__strict,axiom,
% 4.71/5.01 ! [A: nat] :
% 4.71/5.01 ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 4.71/5.01
% 4.71/5.01 % bot.extremum_strict
% 4.71/5.01 thf(fact_378_bot_Oextremum__uniqueI,axiom,
% 4.71/5.01 ! [A: set_real] :
% 4.71/5.01 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 4.71/5.01 => ( A = bot_bot_set_real ) ) ).
% 4.71/5.01
% 4.71/5.01 % bot.extremum_uniqueI
% 4.71/5.01 thf(fact_379_bot_Oextremum__uniqueI,axiom,
% 4.71/5.01 ! [A: set_o] :
% 4.71/5.01 ( ( ord_less_eq_set_o @ A @ bot_bot_set_o )
% 4.71/5.01 => ( A = bot_bot_set_o ) ) ).
% 4.71/5.01
% 4.71/5.01 % bot.extremum_uniqueI
% 4.71/5.01 thf(fact_380_bot_Oextremum__uniqueI,axiom,
% 4.71/5.01 ! [A: set_nat] :
% 4.71/5.01 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 4.71/5.01 => ( A = bot_bot_set_nat ) ) ).
% 4.71/5.01
% 4.71/5.01 % bot.extremum_uniqueI
% 4.71/5.01 thf(fact_381_bot_Oextremum__uniqueI,axiom,
% 4.71/5.01 ! [A: set_int] :
% 4.71/5.01 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 4.71/5.01 => ( A = bot_bot_set_int ) ) ).
% 4.71/5.01
% 4.71/5.01 % bot.extremum_uniqueI
% 4.71/5.01 thf(fact_382_bot_Oextremum__uniqueI,axiom,
% 4.71/5.01 ! [A: nat] :
% 4.71/5.01 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 4.71/5.01 => ( A = bot_bot_nat ) ) ).
% 4.71/5.01
% 4.71/5.01 % bot.extremum_uniqueI
% 4.71/5.01 thf(fact_383_bot_Oextremum__unique,axiom,
% 4.71/5.01 ! [A: set_real] :
% 4.71/5.01 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 4.71/5.01 = ( A = bot_bot_set_real ) ) ).
% 4.71/5.01
% 4.71/5.01 % bot.extremum_unique
% 4.71/5.01 thf(fact_384_bot_Oextremum__unique,axiom,
% 4.71/5.01 ! [A: set_o] :
% 4.71/5.01 ( ( ord_less_eq_set_o @ A @ bot_bot_set_o )
% 4.71/5.01 = ( A = bot_bot_set_o ) ) ).
% 4.71/5.01
% 4.71/5.01 % bot.extremum_unique
% 4.71/5.01 thf(fact_385_bot_Oextremum__unique,axiom,
% 4.71/5.01 ! [A: set_nat] :
% 4.71/5.01 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 4.71/5.01 = ( A = bot_bot_set_nat ) ) ).
% 4.71/5.01
% 4.71/5.01 % bot.extremum_unique
% 4.71/5.01 thf(fact_386_bot_Oextremum__unique,axiom,
% 4.71/5.01 ! [A: set_int] :
% 4.71/5.01 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 4.71/5.01 = ( A = bot_bot_set_int ) ) ).
% 4.71/5.01
% 4.71/5.01 % bot.extremum_unique
% 4.71/5.01 thf(fact_387_bot_Oextremum__unique,axiom,
% 4.71/5.01 ! [A: nat] :
% 4.71/5.01 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 4.71/5.01 = ( A = bot_bot_nat ) ) ).
% 4.71/5.01
% 4.71/5.01 % bot.extremum_unique
% 4.71/5.01 thf(fact_388_bot_Oextremum,axiom,
% 4.71/5.01 ! [A: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A ) ).
% 4.71/5.01
% 4.71/5.01 % bot.extremum
% 4.71/5.01 thf(fact_389_bot_Oextremum,axiom,
% 4.71/5.01 ! [A: set_o] : ( ord_less_eq_set_o @ bot_bot_set_o @ A ) ).
% 4.71/5.01
% 4.71/5.01 % bot.extremum
% 4.71/5.01 thf(fact_390_bot_Oextremum,axiom,
% 4.71/5.01 ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 4.71/5.01
% 4.71/5.01 % bot.extremum
% 4.71/5.01 thf(fact_391_bot_Oextremum,axiom,
% 4.71/5.01 ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 4.71/5.01
% 4.71/5.01 % bot.extremum
% 4.71/5.01 thf(fact_392_bot_Oextremum,axiom,
% 4.71/5.01 ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 4.71/5.01
% 4.71/5.01 % bot.extremum
% 4.71/5.01 thf(fact_393_field__lbound__gt__zero,axiom,
% 4.71/5.01 ! [D1: real,D2: real] :
% 4.71/5.01 ( ( ord_less_real @ zero_zero_real @ D1 )
% 4.71/5.01 => ( ( ord_less_real @ zero_zero_real @ D2 )
% 4.71/5.01 => ? [E: real] :
% 4.71/5.01 ( ( ord_less_real @ zero_zero_real @ E )
% 4.71/5.01 & ( ord_less_real @ E @ D1 )
% 4.71/5.01 & ( ord_less_real @ E @ D2 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % field_lbound_gt_zero
% 4.71/5.01 thf(fact_394_field__lbound__gt__zero,axiom,
% 4.71/5.01 ! [D1: rat,D2: rat] :
% 4.71/5.01 ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 4.71/5.01 => ( ( ord_less_rat @ zero_zero_rat @ D2 )
% 4.71/5.01 => ? [E: rat] :
% 4.71/5.01 ( ( ord_less_rat @ zero_zero_rat @ E )
% 4.71/5.01 & ( ord_less_rat @ E @ D1 )
% 4.71/5.01 & ( ord_less_rat @ E @ D2 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % field_lbound_gt_zero
% 4.71/5.01 thf(fact_395_subsetI,axiom,
% 4.71/5.01 ! [A2: set_o,B2: set_o] :
% 4.71/5.01 ( ! [X4: $o] :
% 4.71/5.01 ( ( member_o @ X4 @ A2 )
% 4.71/5.01 => ( member_o @ X4 @ B2 ) )
% 4.71/5.01 => ( ord_less_eq_set_o @ A2 @ B2 ) ) ).
% 4.71/5.01
% 4.71/5.01 % subsetI
% 4.71/5.01 thf(fact_396_subsetI,axiom,
% 4.71/5.01 ! [A2: set_set_nat,B2: set_set_nat] :
% 4.71/5.01 ( ! [X4: set_nat] :
% 4.71/5.01 ( ( member_set_nat @ X4 @ A2 )
% 4.71/5.01 => ( member_set_nat @ X4 @ B2 ) )
% 4.71/5.01 => ( ord_le6893508408891458716et_nat @ A2 @ B2 ) ) ).
% 4.71/5.01
% 4.71/5.01 % subsetI
% 4.71/5.01 thf(fact_397_subsetI,axiom,
% 4.71/5.01 ! [A2: set_set_nat_rat,B2: set_set_nat_rat] :
% 4.71/5.01 ( ! [X4: set_nat_rat] :
% 4.71/5.01 ( ( member_set_nat_rat @ X4 @ A2 )
% 4.71/5.01 => ( member_set_nat_rat @ X4 @ B2 ) )
% 4.71/5.01 => ( ord_le4375437777232675859at_rat @ A2 @ B2 ) ) ).
% 4.71/5.01
% 4.71/5.01 % subsetI
% 4.71/5.01 thf(fact_398_subsetI,axiom,
% 4.71/5.01 ! [A2: set_nat,B2: set_nat] :
% 4.71/5.01 ( ! [X4: nat] :
% 4.71/5.01 ( ( member_nat @ X4 @ A2 )
% 4.71/5.01 => ( member_nat @ X4 @ B2 ) )
% 4.71/5.01 => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ).
% 4.71/5.01
% 4.71/5.01 % subsetI
% 4.71/5.01 thf(fact_399_subsetI,axiom,
% 4.71/5.01 ! [A2: set_int,B2: set_int] :
% 4.71/5.01 ( ! [X4: int] :
% 4.71/5.01 ( ( member_int @ X4 @ A2 )
% 4.71/5.01 => ( member_int @ X4 @ B2 ) )
% 4.71/5.01 => ( ord_less_eq_set_int @ A2 @ B2 ) ) ).
% 4.71/5.01
% 4.71/5.01 % subsetI
% 4.71/5.01 thf(fact_400_subset__antisym,axiom,
% 4.71/5.01 ! [A2: set_int,B2: set_int] :
% 4.71/5.01 ( ( ord_less_eq_set_int @ A2 @ B2 )
% 4.71/5.01 => ( ( ord_less_eq_set_int @ B2 @ A2 )
% 4.71/5.01 => ( A2 = B2 ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % subset_antisym
% 4.71/5.01 thf(fact_401_in__mono,axiom,
% 4.71/5.01 ! [A2: set_o,B2: set_o,X: $o] :
% 4.71/5.01 ( ( ord_less_eq_set_o @ A2 @ B2 )
% 4.71/5.01 => ( ( member_o @ X @ A2 )
% 4.71/5.01 => ( member_o @ X @ B2 ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % in_mono
% 4.71/5.01 thf(fact_402_in__mono,axiom,
% 4.71/5.01 ! [A2: set_set_nat,B2: set_set_nat,X: set_nat] :
% 4.71/5.01 ( ( ord_le6893508408891458716et_nat @ A2 @ B2 )
% 4.71/5.01 => ( ( member_set_nat @ X @ A2 )
% 4.71/5.01 => ( member_set_nat @ X @ B2 ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % in_mono
% 4.71/5.01 thf(fact_403_in__mono,axiom,
% 4.71/5.01 ! [A2: set_set_nat_rat,B2: set_set_nat_rat,X: set_nat_rat] :
% 4.71/5.01 ( ( ord_le4375437777232675859at_rat @ A2 @ B2 )
% 4.71/5.01 => ( ( member_set_nat_rat @ X @ A2 )
% 4.71/5.01 => ( member_set_nat_rat @ X @ B2 ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % in_mono
% 4.71/5.01 thf(fact_404_in__mono,axiom,
% 4.71/5.01 ! [A2: set_nat,B2: set_nat,X: nat] :
% 4.71/5.01 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 4.71/5.01 => ( ( member_nat @ X @ A2 )
% 4.71/5.01 => ( member_nat @ X @ B2 ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % in_mono
% 4.71/5.01 thf(fact_405_in__mono,axiom,
% 4.71/5.01 ! [A2: set_int,B2: set_int,X: int] :
% 4.71/5.01 ( ( ord_less_eq_set_int @ A2 @ B2 )
% 4.71/5.01 => ( ( member_int @ X @ A2 )
% 4.71/5.01 => ( member_int @ X @ B2 ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % in_mono
% 4.71/5.01 thf(fact_406_subsetD,axiom,
% 4.71/5.01 ! [A2: set_o,B2: set_o,C: $o] :
% 4.71/5.01 ( ( ord_less_eq_set_o @ A2 @ B2 )
% 4.71/5.01 => ( ( member_o @ C @ A2 )
% 4.71/5.01 => ( member_o @ C @ B2 ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % subsetD
% 4.71/5.01 thf(fact_407_subsetD,axiom,
% 4.71/5.01 ! [A2: set_set_nat,B2: set_set_nat,C: set_nat] :
% 4.71/5.01 ( ( ord_le6893508408891458716et_nat @ A2 @ B2 )
% 4.71/5.01 => ( ( member_set_nat @ C @ A2 )
% 4.71/5.01 => ( member_set_nat @ C @ B2 ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % subsetD
% 4.71/5.01 thf(fact_408_subsetD,axiom,
% 4.71/5.01 ! [A2: set_set_nat_rat,B2: set_set_nat_rat,C: set_nat_rat] :
% 4.71/5.01 ( ( ord_le4375437777232675859at_rat @ A2 @ B2 )
% 4.71/5.01 => ( ( member_set_nat_rat @ C @ A2 )
% 4.71/5.01 => ( member_set_nat_rat @ C @ B2 ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % subsetD
% 4.71/5.01 thf(fact_409_subsetD,axiom,
% 4.71/5.01 ! [A2: set_nat,B2: set_nat,C: nat] :
% 4.71/5.01 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 4.71/5.01 => ( ( member_nat @ C @ A2 )
% 4.71/5.01 => ( member_nat @ C @ B2 ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % subsetD
% 4.71/5.01 thf(fact_410_subsetD,axiom,
% 4.71/5.01 ! [A2: set_int,B2: set_int,C: int] :
% 4.71/5.01 ( ( ord_less_eq_set_int @ A2 @ B2 )
% 4.71/5.01 => ( ( member_int @ C @ A2 )
% 4.71/5.01 => ( member_int @ C @ B2 ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % subsetD
% 4.71/5.01 thf(fact_411_equalityE,axiom,
% 4.71/5.01 ! [A2: set_int,B2: set_int] :
% 4.71/5.01 ( ( A2 = B2 )
% 4.71/5.01 => ~ ( ( ord_less_eq_set_int @ A2 @ B2 )
% 4.71/5.01 => ~ ( ord_less_eq_set_int @ B2 @ A2 ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % equalityE
% 4.71/5.01 thf(fact_412_subset__eq,axiom,
% 4.71/5.01 ( ord_less_eq_set_o
% 4.71/5.01 = ( ^ [A6: set_o,B6: set_o] :
% 4.71/5.01 ! [X3: $o] :
% 4.71/5.01 ( ( member_o @ X3 @ A6 )
% 4.71/5.01 => ( member_o @ X3 @ B6 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % subset_eq
% 4.71/5.01 thf(fact_413_subset__eq,axiom,
% 4.71/5.01 ( ord_le6893508408891458716et_nat
% 4.71/5.01 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 4.71/5.01 ! [X3: set_nat] :
% 4.71/5.01 ( ( member_set_nat @ X3 @ A6 )
% 4.71/5.01 => ( member_set_nat @ X3 @ B6 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % subset_eq
% 4.71/5.01 thf(fact_414_subset__eq,axiom,
% 4.71/5.01 ( ord_le4375437777232675859at_rat
% 4.71/5.01 = ( ^ [A6: set_set_nat_rat,B6: set_set_nat_rat] :
% 4.71/5.01 ! [X3: set_nat_rat] :
% 4.71/5.01 ( ( member_set_nat_rat @ X3 @ A6 )
% 4.71/5.01 => ( member_set_nat_rat @ X3 @ B6 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % subset_eq
% 4.71/5.01 thf(fact_415_subset__eq,axiom,
% 4.71/5.01 ( ord_less_eq_set_nat
% 4.71/5.01 = ( ^ [A6: set_nat,B6: set_nat] :
% 4.71/5.01 ! [X3: nat] :
% 4.71/5.01 ( ( member_nat @ X3 @ A6 )
% 4.71/5.01 => ( member_nat @ X3 @ B6 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % subset_eq
% 4.71/5.01 thf(fact_416_subset__eq,axiom,
% 4.71/5.01 ( ord_less_eq_set_int
% 4.71/5.01 = ( ^ [A6: set_int,B6: set_int] :
% 4.71/5.01 ! [X3: int] :
% 4.71/5.01 ( ( member_int @ X3 @ A6 )
% 4.71/5.01 => ( member_int @ X3 @ B6 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % subset_eq
% 4.71/5.01 thf(fact_417_equalityD1,axiom,
% 4.71/5.01 ! [A2: set_int,B2: set_int] :
% 4.71/5.01 ( ( A2 = B2 )
% 4.71/5.01 => ( ord_less_eq_set_int @ A2 @ B2 ) ) ).
% 4.71/5.01
% 4.71/5.01 % equalityD1
% 4.71/5.01 thf(fact_418_equalityD2,axiom,
% 4.71/5.01 ! [A2: set_int,B2: set_int] :
% 4.71/5.01 ( ( A2 = B2 )
% 4.71/5.01 => ( ord_less_eq_set_int @ B2 @ A2 ) ) ).
% 4.71/5.01
% 4.71/5.01 % equalityD2
% 4.71/5.01 thf(fact_419_subset__iff,axiom,
% 4.71/5.01 ( ord_less_eq_set_o
% 4.71/5.01 = ( ^ [A6: set_o,B6: set_o] :
% 4.71/5.01 ! [T2: $o] :
% 4.71/5.01 ( ( member_o @ T2 @ A6 )
% 4.71/5.01 => ( member_o @ T2 @ B6 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % subset_iff
% 4.71/5.01 thf(fact_420_subset__iff,axiom,
% 4.71/5.01 ( ord_le6893508408891458716et_nat
% 4.71/5.01 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 4.71/5.01 ! [T2: set_nat] :
% 4.71/5.01 ( ( member_set_nat @ T2 @ A6 )
% 4.71/5.01 => ( member_set_nat @ T2 @ B6 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % subset_iff
% 4.71/5.01 thf(fact_421_subset__iff,axiom,
% 4.71/5.01 ( ord_le4375437777232675859at_rat
% 4.71/5.01 = ( ^ [A6: set_set_nat_rat,B6: set_set_nat_rat] :
% 4.71/5.01 ! [T2: set_nat_rat] :
% 4.71/5.01 ( ( member_set_nat_rat @ T2 @ A6 )
% 4.71/5.01 => ( member_set_nat_rat @ T2 @ B6 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % subset_iff
% 4.71/5.01 thf(fact_422_subset__iff,axiom,
% 4.71/5.01 ( ord_less_eq_set_nat
% 4.71/5.01 = ( ^ [A6: set_nat,B6: set_nat] :
% 4.71/5.01 ! [T2: nat] :
% 4.71/5.01 ( ( member_nat @ T2 @ A6 )
% 4.71/5.01 => ( member_nat @ T2 @ B6 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % subset_iff
% 4.71/5.01 thf(fact_423_subset__iff,axiom,
% 4.71/5.01 ( ord_less_eq_set_int
% 4.71/5.01 = ( ^ [A6: set_int,B6: set_int] :
% 4.71/5.01 ! [T2: int] :
% 4.71/5.01 ( ( member_int @ T2 @ A6 )
% 4.71/5.01 => ( member_int @ T2 @ B6 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % subset_iff
% 4.71/5.01 thf(fact_424_subset__refl,axiom,
% 4.71/5.01 ! [A2: set_int] : ( ord_less_eq_set_int @ A2 @ A2 ) ).
% 4.71/5.01
% 4.71/5.01 % subset_refl
% 4.71/5.01 thf(fact_425_Collect__mono,axiom,
% 4.71/5.01 ! [P: set_nat > $o,Q: set_nat > $o] :
% 4.71/5.01 ( ! [X4: set_nat] :
% 4.71/5.01 ( ( P @ X4 )
% 4.71/5.01 => ( Q @ X4 ) )
% 4.71/5.01 => ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % Collect_mono
% 4.71/5.01 thf(fact_426_Collect__mono,axiom,
% 4.71/5.01 ! [P: set_nat_rat > $o,Q: set_nat_rat > $o] :
% 4.71/5.01 ( ! [X4: set_nat_rat] :
% 4.71/5.01 ( ( P @ X4 )
% 4.71/5.01 => ( Q @ X4 ) )
% 4.71/5.01 => ( ord_le4375437777232675859at_rat @ ( collect_set_nat_rat @ P ) @ ( collect_set_nat_rat @ Q ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % Collect_mono
% 4.71/5.01 thf(fact_427_Collect__mono,axiom,
% 4.71/5.01 ! [P: nat > $o,Q: nat > $o] :
% 4.71/5.01 ( ! [X4: nat] :
% 4.71/5.01 ( ( P @ X4 )
% 4.71/5.01 => ( Q @ X4 ) )
% 4.71/5.01 => ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % Collect_mono
% 4.71/5.01 thf(fact_428_Collect__mono,axiom,
% 4.71/5.01 ! [P: ( nat > rat ) > $o,Q: ( nat > rat ) > $o] :
% 4.71/5.01 ( ! [X4: nat > rat] :
% 4.71/5.01 ( ( P @ X4 )
% 4.71/5.01 => ( Q @ X4 ) )
% 4.71/5.01 => ( ord_le2679597024174929757at_rat @ ( collect_nat_rat @ P ) @ ( collect_nat_rat @ Q ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % Collect_mono
% 4.71/5.01 thf(fact_429_Collect__mono,axiom,
% 4.71/5.01 ! [P: int > $o,Q: int > $o] :
% 4.71/5.01 ( ! [X4: int] :
% 4.71/5.01 ( ( P @ X4 )
% 4.71/5.01 => ( Q @ X4 ) )
% 4.71/5.01 => ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % Collect_mono
% 4.71/5.01 thf(fact_430_subset__trans,axiom,
% 4.71/5.01 ! [A2: set_int,B2: set_int,C2: set_int] :
% 4.71/5.01 ( ( ord_less_eq_set_int @ A2 @ B2 )
% 4.71/5.01 => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 4.71/5.01 => ( ord_less_eq_set_int @ A2 @ C2 ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % subset_trans
% 4.71/5.01 thf(fact_431_set__eq__subset,axiom,
% 4.71/5.01 ( ( ^ [Y5: set_int,Z4: set_int] : ( Y5 = Z4 ) )
% 4.71/5.01 = ( ^ [A6: set_int,B6: set_int] :
% 4.71/5.01 ( ( ord_less_eq_set_int @ A6 @ B6 )
% 4.71/5.01 & ( ord_less_eq_set_int @ B6 @ A6 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % set_eq_subset
% 4.71/5.01 thf(fact_432_Collect__mono__iff,axiom,
% 4.71/5.01 ! [P: set_nat > $o,Q: set_nat > $o] :
% 4.71/5.01 ( ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) )
% 4.71/5.01 = ( ! [X3: set_nat] :
% 4.71/5.01 ( ( P @ X3 )
% 4.71/5.01 => ( Q @ X3 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % Collect_mono_iff
% 4.71/5.01 thf(fact_433_Collect__mono__iff,axiom,
% 4.71/5.01 ! [P: set_nat_rat > $o,Q: set_nat_rat > $o] :
% 4.71/5.01 ( ( ord_le4375437777232675859at_rat @ ( collect_set_nat_rat @ P ) @ ( collect_set_nat_rat @ Q ) )
% 4.71/5.01 = ( ! [X3: set_nat_rat] :
% 4.71/5.01 ( ( P @ X3 )
% 4.71/5.01 => ( Q @ X3 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % Collect_mono_iff
% 4.71/5.01 thf(fact_434_Collect__mono__iff,axiom,
% 4.71/5.01 ! [P: nat > $o,Q: nat > $o] :
% 4.71/5.01 ( ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) )
% 4.71/5.01 = ( ! [X3: nat] :
% 4.71/5.01 ( ( P @ X3 )
% 4.71/5.01 => ( Q @ X3 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % Collect_mono_iff
% 4.71/5.01 thf(fact_435_Collect__mono__iff,axiom,
% 4.71/5.01 ! [P: ( nat > rat ) > $o,Q: ( nat > rat ) > $o] :
% 4.71/5.01 ( ( ord_le2679597024174929757at_rat @ ( collect_nat_rat @ P ) @ ( collect_nat_rat @ Q ) )
% 4.71/5.01 = ( ! [X3: nat > rat] :
% 4.71/5.01 ( ( P @ X3 )
% 4.71/5.01 => ( Q @ X3 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % Collect_mono_iff
% 4.71/5.01 thf(fact_436_Collect__mono__iff,axiom,
% 4.71/5.01 ! [P: int > $o,Q: int > $o] :
% 4.71/5.01 ( ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) )
% 4.71/5.01 = ( ! [X3: int] :
% 4.71/5.01 ( ( P @ X3 )
% 4.71/5.01 => ( Q @ X3 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % Collect_mono_iff
% 4.71/5.01 thf(fact_437_bot__set__def,axiom,
% 4.71/5.01 ( bot_bot_set_set_nat
% 4.71/5.01 = ( collect_set_nat @ bot_bot_set_nat_o ) ) ).
% 4.71/5.01
% 4.71/5.01 % bot_set_def
% 4.71/5.01 thf(fact_438_bot__set__def,axiom,
% 4.71/5.01 ( bot_bo6797373522285170759at_rat
% 4.71/5.01 = ( collect_set_nat_rat @ bot_bo3445895781125589758_rat_o ) ) ).
% 4.71/5.01
% 4.71/5.01 % bot_set_def
% 4.71/5.01 thf(fact_439_bot__set__def,axiom,
% 4.71/5.01 ( bot_bot_set_nat_rat
% 4.71/5.01 = ( collect_nat_rat @ bot_bot_nat_rat_o ) ) ).
% 4.71/5.01
% 4.71/5.01 % bot_set_def
% 4.71/5.01 thf(fact_440_bot__set__def,axiom,
% 4.71/5.01 ( bot_bot_set_real
% 4.71/5.01 = ( collect_real @ bot_bot_real_o ) ) ).
% 4.71/5.01
% 4.71/5.01 % bot_set_def
% 4.71/5.01 thf(fact_441_bot__set__def,axiom,
% 4.71/5.01 ( bot_bot_set_o
% 4.71/5.01 = ( collect_o @ bot_bot_o_o ) ) ).
% 4.71/5.01
% 4.71/5.01 % bot_set_def
% 4.71/5.01 thf(fact_442_bot__set__def,axiom,
% 4.71/5.01 ( bot_bot_set_nat
% 4.71/5.01 = ( collect_nat @ bot_bot_nat_o ) ) ).
% 4.71/5.01
% 4.71/5.01 % bot_set_def
% 4.71/5.01 thf(fact_443_bot__set__def,axiom,
% 4.71/5.01 ( bot_bot_set_int
% 4.71/5.01 = ( collect_int @ bot_bot_int_o ) ) ).
% 4.71/5.01
% 4.71/5.01 % bot_set_def
% 4.71/5.01 thf(fact_444_bot__nat__def,axiom,
% 4.71/5.01 bot_bot_nat = zero_zero_nat ).
% 4.71/5.01
% 4.71/5.01 % bot_nat_def
% 4.71/5.01 thf(fact_445_nle__le,axiom,
% 4.71/5.01 ! [A: rat,B: rat] :
% 4.71/5.01 ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 4.71/5.01 = ( ( ord_less_eq_rat @ B @ A )
% 4.71/5.01 & ( B != A ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % nle_le
% 4.71/5.01 thf(fact_446_nle__le,axiom,
% 4.71/5.01 ! [A: num,B: num] :
% 4.71/5.01 ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 4.71/5.01 = ( ( ord_less_eq_num @ B @ A )
% 4.71/5.01 & ( B != A ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % nle_le
% 4.71/5.01 thf(fact_447_nle__le,axiom,
% 4.71/5.01 ! [A: nat,B: nat] :
% 4.71/5.01 ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 4.71/5.01 = ( ( ord_less_eq_nat @ B @ A )
% 4.71/5.01 & ( B != A ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % nle_le
% 4.71/5.01 thf(fact_448_nle__le,axiom,
% 4.71/5.01 ! [A: int,B: int] :
% 4.71/5.01 ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 4.71/5.01 = ( ( ord_less_eq_int @ B @ A )
% 4.71/5.01 & ( B != A ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % nle_le
% 4.71/5.01 thf(fact_449_le__cases3,axiom,
% 4.71/5.01 ! [X: rat,Y: rat,Z: rat] :
% 4.71/5.01 ( ( ( ord_less_eq_rat @ X @ Y )
% 4.71/5.01 => ~ ( ord_less_eq_rat @ Y @ Z ) )
% 4.71/5.01 => ( ( ( ord_less_eq_rat @ Y @ X )
% 4.71/5.01 => ~ ( ord_less_eq_rat @ X @ Z ) )
% 4.71/5.01 => ( ( ( ord_less_eq_rat @ X @ Z )
% 4.71/5.01 => ~ ( ord_less_eq_rat @ Z @ Y ) )
% 4.71/5.01 => ( ( ( ord_less_eq_rat @ Z @ Y )
% 4.71/5.01 => ~ ( ord_less_eq_rat @ Y @ X ) )
% 4.71/5.01 => ( ( ( ord_less_eq_rat @ Y @ Z )
% 4.71/5.01 => ~ ( ord_less_eq_rat @ Z @ X ) )
% 4.71/5.01 => ~ ( ( ord_less_eq_rat @ Z @ X )
% 4.71/5.01 => ~ ( ord_less_eq_rat @ X @ Y ) ) ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % le_cases3
% 4.71/5.01 thf(fact_450_le__cases3,axiom,
% 4.71/5.01 ! [X: num,Y: num,Z: num] :
% 4.71/5.01 ( ( ( ord_less_eq_num @ X @ Y )
% 4.71/5.01 => ~ ( ord_less_eq_num @ Y @ Z ) )
% 4.71/5.01 => ( ( ( ord_less_eq_num @ Y @ X )
% 4.71/5.01 => ~ ( ord_less_eq_num @ X @ Z ) )
% 4.71/5.01 => ( ( ( ord_less_eq_num @ X @ Z )
% 4.71/5.01 => ~ ( ord_less_eq_num @ Z @ Y ) )
% 4.71/5.01 => ( ( ( ord_less_eq_num @ Z @ Y )
% 4.71/5.01 => ~ ( ord_less_eq_num @ Y @ X ) )
% 4.71/5.01 => ( ( ( ord_less_eq_num @ Y @ Z )
% 4.71/5.01 => ~ ( ord_less_eq_num @ Z @ X ) )
% 4.71/5.01 => ~ ( ( ord_less_eq_num @ Z @ X )
% 4.71/5.01 => ~ ( ord_less_eq_num @ X @ Y ) ) ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % le_cases3
% 4.71/5.01 thf(fact_451_le__cases3,axiom,
% 4.71/5.01 ! [X: nat,Y: nat,Z: nat] :
% 4.71/5.01 ( ( ( ord_less_eq_nat @ X @ Y )
% 4.71/5.01 => ~ ( ord_less_eq_nat @ Y @ Z ) )
% 4.71/5.01 => ( ( ( ord_less_eq_nat @ Y @ X )
% 4.71/5.01 => ~ ( ord_less_eq_nat @ X @ Z ) )
% 4.71/5.01 => ( ( ( ord_less_eq_nat @ X @ Z )
% 4.71/5.01 => ~ ( ord_less_eq_nat @ Z @ Y ) )
% 4.71/5.01 => ( ( ( ord_less_eq_nat @ Z @ Y )
% 4.71/5.01 => ~ ( ord_less_eq_nat @ Y @ X ) )
% 4.71/5.01 => ( ( ( ord_less_eq_nat @ Y @ Z )
% 4.71/5.01 => ~ ( ord_less_eq_nat @ Z @ X ) )
% 4.71/5.01 => ~ ( ( ord_less_eq_nat @ Z @ X )
% 4.71/5.01 => ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % le_cases3
% 4.71/5.01 thf(fact_452_le__cases3,axiom,
% 4.71/5.01 ! [X: int,Y: int,Z: int] :
% 4.71/5.01 ( ( ( ord_less_eq_int @ X @ Y )
% 4.71/5.01 => ~ ( ord_less_eq_int @ Y @ Z ) )
% 4.71/5.01 => ( ( ( ord_less_eq_int @ Y @ X )
% 4.71/5.01 => ~ ( ord_less_eq_int @ X @ Z ) )
% 4.71/5.01 => ( ( ( ord_less_eq_int @ X @ Z )
% 4.71/5.01 => ~ ( ord_less_eq_int @ Z @ Y ) )
% 4.71/5.01 => ( ( ( ord_less_eq_int @ Z @ Y )
% 4.71/5.01 => ~ ( ord_less_eq_int @ Y @ X ) )
% 4.71/5.01 => ( ( ( ord_less_eq_int @ Y @ Z )
% 4.71/5.01 => ~ ( ord_less_eq_int @ Z @ X ) )
% 4.71/5.01 => ~ ( ( ord_less_eq_int @ Z @ X )
% 4.71/5.01 => ~ ( ord_less_eq_int @ X @ Y ) ) ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % le_cases3
% 4.71/5.01 thf(fact_453_order__class_Oorder__eq__iff,axiom,
% 4.71/5.01 ( ( ^ [Y5: set_int,Z4: set_int] : ( Y5 = Z4 ) )
% 4.71/5.01 = ( ^ [X3: set_int,Y2: set_int] :
% 4.71/5.01 ( ( ord_less_eq_set_int @ X3 @ Y2 )
% 4.71/5.01 & ( ord_less_eq_set_int @ Y2 @ X3 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_class.order_eq_iff
% 4.71/5.01 thf(fact_454_order__class_Oorder__eq__iff,axiom,
% 4.71/5.01 ( ( ^ [Y5: rat,Z4: rat] : ( Y5 = Z4 ) )
% 4.71/5.01 = ( ^ [X3: rat,Y2: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 4.71/5.01 & ( ord_less_eq_rat @ Y2 @ X3 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_class.order_eq_iff
% 4.71/5.01 thf(fact_455_order__class_Oorder__eq__iff,axiom,
% 4.71/5.01 ( ( ^ [Y5: num,Z4: num] : ( Y5 = Z4 ) )
% 4.71/5.01 = ( ^ [X3: num,Y2: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ X3 @ Y2 )
% 4.71/5.01 & ( ord_less_eq_num @ Y2 @ X3 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_class.order_eq_iff
% 4.71/5.01 thf(fact_456_order__class_Oorder__eq__iff,axiom,
% 4.71/5.01 ( ( ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 4.71/5.01 = ( ^ [X3: nat,Y2: nat] :
% 4.71/5.01 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 4.71/5.01 & ( ord_less_eq_nat @ Y2 @ X3 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_class.order_eq_iff
% 4.71/5.01 thf(fact_457_order__class_Oorder__eq__iff,axiom,
% 4.71/5.01 ( ( ^ [Y5: int,Z4: int] : ( Y5 = Z4 ) )
% 4.71/5.01 = ( ^ [X3: int,Y2: int] :
% 4.71/5.01 ( ( ord_less_eq_int @ X3 @ Y2 )
% 4.71/5.01 & ( ord_less_eq_int @ Y2 @ X3 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_class.order_eq_iff
% 4.71/5.01 thf(fact_458_ord__eq__le__trans,axiom,
% 4.71/5.01 ! [A: set_int,B: set_int,C: set_int] :
% 4.71/5.01 ( ( A = B )
% 4.71/5.01 => ( ( ord_less_eq_set_int @ B @ C )
% 4.71/5.01 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_eq_le_trans
% 4.71/5.01 thf(fact_459_ord__eq__le__trans,axiom,
% 4.71/5.01 ! [A: rat,B: rat,C: rat] :
% 4.71/5.01 ( ( A = B )
% 4.71/5.01 => ( ( ord_less_eq_rat @ B @ C )
% 4.71/5.01 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_eq_le_trans
% 4.71/5.01 thf(fact_460_ord__eq__le__trans,axiom,
% 4.71/5.01 ! [A: num,B: num,C: num] :
% 4.71/5.01 ( ( A = B )
% 4.71/5.01 => ( ( ord_less_eq_num @ B @ C )
% 4.71/5.01 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_eq_le_trans
% 4.71/5.01 thf(fact_461_ord__eq__le__trans,axiom,
% 4.71/5.01 ! [A: nat,B: nat,C: nat] :
% 4.71/5.01 ( ( A = B )
% 4.71/5.01 => ( ( ord_less_eq_nat @ B @ C )
% 4.71/5.01 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_eq_le_trans
% 4.71/5.01 thf(fact_462_ord__eq__le__trans,axiom,
% 4.71/5.01 ! [A: int,B: int,C: int] :
% 4.71/5.01 ( ( A = B )
% 4.71/5.01 => ( ( ord_less_eq_int @ B @ C )
% 4.71/5.01 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_eq_le_trans
% 4.71/5.01 thf(fact_463_ord__le__eq__trans,axiom,
% 4.71/5.01 ! [A: set_int,B: set_int,C: set_int] :
% 4.71/5.01 ( ( ord_less_eq_set_int @ A @ B )
% 4.71/5.01 => ( ( B = C )
% 4.71/5.01 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_le_eq_trans
% 4.71/5.01 thf(fact_464_ord__le__eq__trans,axiom,
% 4.71/5.01 ! [A: rat,B: rat,C: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.01 => ( ( B = C )
% 4.71/5.01 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_le_eq_trans
% 4.71/5.01 thf(fact_465_ord__le__eq__trans,axiom,
% 4.71/5.01 ! [A: num,B: num,C: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ A @ B )
% 4.71/5.01 => ( ( B = C )
% 4.71/5.01 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_le_eq_trans
% 4.71/5.01 thf(fact_466_ord__le__eq__trans,axiom,
% 4.71/5.01 ! [A: nat,B: nat,C: nat] :
% 4.71/5.01 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.01 => ( ( B = C )
% 4.71/5.01 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_le_eq_trans
% 4.71/5.01 thf(fact_467_ord__le__eq__trans,axiom,
% 4.71/5.01 ! [A: int,B: int,C: int] :
% 4.71/5.01 ( ( ord_less_eq_int @ A @ B )
% 4.71/5.01 => ( ( B = C )
% 4.71/5.01 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_le_eq_trans
% 4.71/5.01 thf(fact_468_order__antisym,axiom,
% 4.71/5.01 ! [X: set_int,Y: set_int] :
% 4.71/5.01 ( ( ord_less_eq_set_int @ X @ Y )
% 4.71/5.01 => ( ( ord_less_eq_set_int @ Y @ X )
% 4.71/5.01 => ( X = Y ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_antisym
% 4.71/5.01 thf(fact_469_order__antisym,axiom,
% 4.71/5.01 ! [X: rat,Y: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ X @ Y )
% 4.71/5.01 => ( ( ord_less_eq_rat @ Y @ X )
% 4.71/5.01 => ( X = Y ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_antisym
% 4.71/5.01 thf(fact_470_order__antisym,axiom,
% 4.71/5.01 ! [X: num,Y: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ X @ Y )
% 4.71/5.01 => ( ( ord_less_eq_num @ Y @ X )
% 4.71/5.01 => ( X = Y ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_antisym
% 4.71/5.01 thf(fact_471_order__antisym,axiom,
% 4.71/5.01 ! [X: nat,Y: nat] :
% 4.71/5.01 ( ( ord_less_eq_nat @ X @ Y )
% 4.71/5.01 => ( ( ord_less_eq_nat @ Y @ X )
% 4.71/5.01 => ( X = Y ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_antisym
% 4.71/5.01 thf(fact_472_order__antisym,axiom,
% 4.71/5.01 ! [X: int,Y: int] :
% 4.71/5.01 ( ( ord_less_eq_int @ X @ Y )
% 4.71/5.01 => ( ( ord_less_eq_int @ Y @ X )
% 4.71/5.01 => ( X = Y ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_antisym
% 4.71/5.01 thf(fact_473_order_Otrans,axiom,
% 4.71/5.01 ! [A: set_int,B: set_int,C: set_int] :
% 4.71/5.01 ( ( ord_less_eq_set_int @ A @ B )
% 4.71/5.01 => ( ( ord_less_eq_set_int @ B @ C )
% 4.71/5.01 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order.trans
% 4.71/5.01 thf(fact_474_order_Otrans,axiom,
% 4.71/5.01 ! [A: rat,B: rat,C: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.01 => ( ( ord_less_eq_rat @ B @ C )
% 4.71/5.01 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order.trans
% 4.71/5.01 thf(fact_475_order_Otrans,axiom,
% 4.71/5.01 ! [A: num,B: num,C: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ A @ B )
% 4.71/5.01 => ( ( ord_less_eq_num @ B @ C )
% 4.71/5.01 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order.trans
% 4.71/5.01 thf(fact_476_order_Otrans,axiom,
% 4.71/5.01 ! [A: nat,B: nat,C: nat] :
% 4.71/5.01 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.01 => ( ( ord_less_eq_nat @ B @ C )
% 4.71/5.01 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order.trans
% 4.71/5.01 thf(fact_477_order_Otrans,axiom,
% 4.71/5.01 ! [A: int,B: int,C: int] :
% 4.71/5.01 ( ( ord_less_eq_int @ A @ B )
% 4.71/5.01 => ( ( ord_less_eq_int @ B @ C )
% 4.71/5.01 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order.trans
% 4.71/5.01 thf(fact_478_order__trans,axiom,
% 4.71/5.01 ! [X: set_int,Y: set_int,Z: set_int] :
% 4.71/5.01 ( ( ord_less_eq_set_int @ X @ Y )
% 4.71/5.01 => ( ( ord_less_eq_set_int @ Y @ Z )
% 4.71/5.01 => ( ord_less_eq_set_int @ X @ Z ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_trans
% 4.71/5.01 thf(fact_479_order__trans,axiom,
% 4.71/5.01 ! [X: rat,Y: rat,Z: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ X @ Y )
% 4.71/5.01 => ( ( ord_less_eq_rat @ Y @ Z )
% 4.71/5.01 => ( ord_less_eq_rat @ X @ Z ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_trans
% 4.71/5.01 thf(fact_480_order__trans,axiom,
% 4.71/5.01 ! [X: num,Y: num,Z: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ X @ Y )
% 4.71/5.01 => ( ( ord_less_eq_num @ Y @ Z )
% 4.71/5.01 => ( ord_less_eq_num @ X @ Z ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_trans
% 4.71/5.01 thf(fact_481_order__trans,axiom,
% 4.71/5.01 ! [X: nat,Y: nat,Z: nat] :
% 4.71/5.01 ( ( ord_less_eq_nat @ X @ Y )
% 4.71/5.01 => ( ( ord_less_eq_nat @ Y @ Z )
% 4.71/5.01 => ( ord_less_eq_nat @ X @ Z ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_trans
% 4.71/5.01 thf(fact_482_order__trans,axiom,
% 4.71/5.01 ! [X: int,Y: int,Z: int] :
% 4.71/5.01 ( ( ord_less_eq_int @ X @ Y )
% 4.71/5.01 => ( ( ord_less_eq_int @ Y @ Z )
% 4.71/5.01 => ( ord_less_eq_int @ X @ Z ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_trans
% 4.71/5.01 thf(fact_483_linorder__wlog,axiom,
% 4.71/5.01 ! [P: rat > rat > $o,A: rat,B: rat] :
% 4.71/5.01 ( ! [A5: rat,B5: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ A5 @ B5 )
% 4.71/5.01 => ( P @ A5 @ B5 ) )
% 4.71/5.01 => ( ! [A5: rat,B5: rat] :
% 4.71/5.01 ( ( P @ B5 @ A5 )
% 4.71/5.01 => ( P @ A5 @ B5 ) )
% 4.71/5.01 => ( P @ A @ B ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_wlog
% 4.71/5.01 thf(fact_484_linorder__wlog,axiom,
% 4.71/5.01 ! [P: num > num > $o,A: num,B: num] :
% 4.71/5.01 ( ! [A5: num,B5: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ A5 @ B5 )
% 4.71/5.01 => ( P @ A5 @ B5 ) )
% 4.71/5.01 => ( ! [A5: num,B5: num] :
% 4.71/5.01 ( ( P @ B5 @ A5 )
% 4.71/5.01 => ( P @ A5 @ B5 ) )
% 4.71/5.01 => ( P @ A @ B ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_wlog
% 4.71/5.01 thf(fact_485_linorder__wlog,axiom,
% 4.71/5.01 ! [P: nat > nat > $o,A: nat,B: nat] :
% 4.71/5.01 ( ! [A5: nat,B5: nat] :
% 4.71/5.01 ( ( ord_less_eq_nat @ A5 @ B5 )
% 4.71/5.01 => ( P @ A5 @ B5 ) )
% 4.71/5.01 => ( ! [A5: nat,B5: nat] :
% 4.71/5.01 ( ( P @ B5 @ A5 )
% 4.71/5.01 => ( P @ A5 @ B5 ) )
% 4.71/5.01 => ( P @ A @ B ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_wlog
% 4.71/5.01 thf(fact_486_linorder__wlog,axiom,
% 4.71/5.01 ! [P: int > int > $o,A: int,B: int] :
% 4.71/5.01 ( ! [A5: int,B5: int] :
% 4.71/5.01 ( ( ord_less_eq_int @ A5 @ B5 )
% 4.71/5.01 => ( P @ A5 @ B5 ) )
% 4.71/5.01 => ( ! [A5: int,B5: int] :
% 4.71/5.01 ( ( P @ B5 @ A5 )
% 4.71/5.01 => ( P @ A5 @ B5 ) )
% 4.71/5.01 => ( P @ A @ B ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_wlog
% 4.71/5.01 thf(fact_487_dual__order_Oeq__iff,axiom,
% 4.71/5.01 ( ( ^ [Y5: set_int,Z4: set_int] : ( Y5 = Z4 ) )
% 4.71/5.01 = ( ^ [A4: set_int,B4: set_int] :
% 4.71/5.01 ( ( ord_less_eq_set_int @ B4 @ A4 )
% 4.71/5.01 & ( ord_less_eq_set_int @ A4 @ B4 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.eq_iff
% 4.71/5.01 thf(fact_488_dual__order_Oeq__iff,axiom,
% 4.71/5.01 ( ( ^ [Y5: rat,Z4: rat] : ( Y5 = Z4 ) )
% 4.71/5.01 = ( ^ [A4: rat,B4: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ B4 @ A4 )
% 4.71/5.01 & ( ord_less_eq_rat @ A4 @ B4 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.eq_iff
% 4.71/5.01 thf(fact_489_dual__order_Oeq__iff,axiom,
% 4.71/5.01 ( ( ^ [Y5: num,Z4: num] : ( Y5 = Z4 ) )
% 4.71/5.01 = ( ^ [A4: num,B4: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ B4 @ A4 )
% 4.71/5.01 & ( ord_less_eq_num @ A4 @ B4 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.eq_iff
% 4.71/5.01 thf(fact_490_dual__order_Oeq__iff,axiom,
% 4.71/5.01 ( ( ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 4.71/5.01 = ( ^ [A4: nat,B4: nat] :
% 4.71/5.01 ( ( ord_less_eq_nat @ B4 @ A4 )
% 4.71/5.01 & ( ord_less_eq_nat @ A4 @ B4 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.eq_iff
% 4.71/5.01 thf(fact_491_dual__order_Oeq__iff,axiom,
% 4.71/5.01 ( ( ^ [Y5: int,Z4: int] : ( Y5 = Z4 ) )
% 4.71/5.01 = ( ^ [A4: int,B4: int] :
% 4.71/5.01 ( ( ord_less_eq_int @ B4 @ A4 )
% 4.71/5.01 & ( ord_less_eq_int @ A4 @ B4 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.eq_iff
% 4.71/5.01 thf(fact_492_dual__order_Oantisym,axiom,
% 4.71/5.01 ! [B: set_int,A: set_int] :
% 4.71/5.01 ( ( ord_less_eq_set_int @ B @ A )
% 4.71/5.01 => ( ( ord_less_eq_set_int @ A @ B )
% 4.71/5.01 => ( A = B ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.antisym
% 4.71/5.01 thf(fact_493_dual__order_Oantisym,axiom,
% 4.71/5.01 ! [B: rat,A: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ B @ A )
% 4.71/5.01 => ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.01 => ( A = B ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.antisym
% 4.71/5.01 thf(fact_494_dual__order_Oantisym,axiom,
% 4.71/5.01 ! [B: num,A: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ B @ A )
% 4.71/5.01 => ( ( ord_less_eq_num @ A @ B )
% 4.71/5.01 => ( A = B ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.antisym
% 4.71/5.01 thf(fact_495_dual__order_Oantisym,axiom,
% 4.71/5.01 ! [B: nat,A: nat] :
% 4.71/5.01 ( ( ord_less_eq_nat @ B @ A )
% 4.71/5.01 => ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.01 => ( A = B ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.antisym
% 4.71/5.01 thf(fact_496_dual__order_Oantisym,axiom,
% 4.71/5.01 ! [B: int,A: int] :
% 4.71/5.01 ( ( ord_less_eq_int @ B @ A )
% 4.71/5.01 => ( ( ord_less_eq_int @ A @ B )
% 4.71/5.01 => ( A = B ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.antisym
% 4.71/5.01 thf(fact_497_dual__order_Otrans,axiom,
% 4.71/5.01 ! [B: set_int,A: set_int,C: set_int] :
% 4.71/5.01 ( ( ord_less_eq_set_int @ B @ A )
% 4.71/5.01 => ( ( ord_less_eq_set_int @ C @ B )
% 4.71/5.01 => ( ord_less_eq_set_int @ C @ A ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.trans
% 4.71/5.01 thf(fact_498_dual__order_Otrans,axiom,
% 4.71/5.01 ! [B: rat,A: rat,C: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ B @ A )
% 4.71/5.01 => ( ( ord_less_eq_rat @ C @ B )
% 4.71/5.01 => ( ord_less_eq_rat @ C @ A ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.trans
% 4.71/5.01 thf(fact_499_dual__order_Otrans,axiom,
% 4.71/5.01 ! [B: num,A: num,C: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ B @ A )
% 4.71/5.01 => ( ( ord_less_eq_num @ C @ B )
% 4.71/5.01 => ( ord_less_eq_num @ C @ A ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.trans
% 4.71/5.01 thf(fact_500_dual__order_Otrans,axiom,
% 4.71/5.01 ! [B: nat,A: nat,C: nat] :
% 4.71/5.01 ( ( ord_less_eq_nat @ B @ A )
% 4.71/5.01 => ( ( ord_less_eq_nat @ C @ B )
% 4.71/5.01 => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.trans
% 4.71/5.01 thf(fact_501_dual__order_Otrans,axiom,
% 4.71/5.01 ! [B: int,A: int,C: int] :
% 4.71/5.01 ( ( ord_less_eq_int @ B @ A )
% 4.71/5.01 => ( ( ord_less_eq_int @ C @ B )
% 4.71/5.01 => ( ord_less_eq_int @ C @ A ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.trans
% 4.71/5.01 thf(fact_502_antisym,axiom,
% 4.71/5.01 ! [A: set_int,B: set_int] :
% 4.71/5.01 ( ( ord_less_eq_set_int @ A @ B )
% 4.71/5.01 => ( ( ord_less_eq_set_int @ B @ A )
% 4.71/5.01 => ( A = B ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % antisym
% 4.71/5.01 thf(fact_503_antisym,axiom,
% 4.71/5.01 ! [A: rat,B: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.01 => ( ( ord_less_eq_rat @ B @ A )
% 4.71/5.01 => ( A = B ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % antisym
% 4.71/5.01 thf(fact_504_antisym,axiom,
% 4.71/5.01 ! [A: num,B: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ A @ B )
% 4.71/5.01 => ( ( ord_less_eq_num @ B @ A )
% 4.71/5.01 => ( A = B ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % antisym
% 4.71/5.01 thf(fact_505_antisym,axiom,
% 4.71/5.01 ! [A: nat,B: nat] :
% 4.71/5.01 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.01 => ( ( ord_less_eq_nat @ B @ A )
% 4.71/5.01 => ( A = B ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % antisym
% 4.71/5.01 thf(fact_506_antisym,axiom,
% 4.71/5.01 ! [A: int,B: int] :
% 4.71/5.01 ( ( ord_less_eq_int @ A @ B )
% 4.71/5.01 => ( ( ord_less_eq_int @ B @ A )
% 4.71/5.01 => ( A = B ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % antisym
% 4.71/5.01 thf(fact_507_Orderings_Oorder__eq__iff,axiom,
% 4.71/5.01 ( ( ^ [Y5: set_int,Z4: set_int] : ( Y5 = Z4 ) )
% 4.71/5.01 = ( ^ [A4: set_int,B4: set_int] :
% 4.71/5.01 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 4.71/5.01 & ( ord_less_eq_set_int @ B4 @ A4 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % Orderings.order_eq_iff
% 4.71/5.01 thf(fact_508_Orderings_Oorder__eq__iff,axiom,
% 4.71/5.01 ( ( ^ [Y5: rat,Z4: rat] : ( Y5 = Z4 ) )
% 4.71/5.01 = ( ^ [A4: rat,B4: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ A4 @ B4 )
% 4.71/5.01 & ( ord_less_eq_rat @ B4 @ A4 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % Orderings.order_eq_iff
% 4.71/5.01 thf(fact_509_Orderings_Oorder__eq__iff,axiom,
% 4.71/5.01 ( ( ^ [Y5: num,Z4: num] : ( Y5 = Z4 ) )
% 4.71/5.01 = ( ^ [A4: num,B4: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ A4 @ B4 )
% 4.71/5.01 & ( ord_less_eq_num @ B4 @ A4 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % Orderings.order_eq_iff
% 4.71/5.01 thf(fact_510_Orderings_Oorder__eq__iff,axiom,
% 4.71/5.01 ( ( ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 4.71/5.01 = ( ^ [A4: nat,B4: nat] :
% 4.71/5.01 ( ( ord_less_eq_nat @ A4 @ B4 )
% 4.71/5.01 & ( ord_less_eq_nat @ B4 @ A4 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % Orderings.order_eq_iff
% 4.71/5.01 thf(fact_511_Orderings_Oorder__eq__iff,axiom,
% 4.71/5.01 ( ( ^ [Y5: int,Z4: int] : ( Y5 = Z4 ) )
% 4.71/5.01 = ( ^ [A4: int,B4: int] :
% 4.71/5.01 ( ( ord_less_eq_int @ A4 @ B4 )
% 4.71/5.01 & ( ord_less_eq_int @ B4 @ A4 ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % Orderings.order_eq_iff
% 4.71/5.01 thf(fact_512_order__subst1,axiom,
% 4.71/5.01 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 4.71/5.01 => ( ( ord_less_eq_rat @ B @ C )
% 4.71/5.01 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_subst1
% 4.71/5.01 thf(fact_513_order__subst1,axiom,
% 4.71/5.01 ! [A: rat,F: num > rat,B: num,C: num] :
% 4.71/5.01 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 4.71/5.01 => ( ( ord_less_eq_num @ B @ C )
% 4.71/5.01 => ( ! [X4: num,Y3: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_subst1
% 4.71/5.01 thf(fact_514_order__subst1,axiom,
% 4.71/5.01 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 4.71/5.01 => ( ( ord_less_eq_nat @ B @ C )
% 4.71/5.01 => ( ! [X4: nat,Y3: nat] :
% 4.71/5.01 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_subst1
% 4.71/5.01 thf(fact_515_order__subst1,axiom,
% 4.71/5.01 ! [A: rat,F: int > rat,B: int,C: int] :
% 4.71/5.01 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 4.71/5.01 => ( ( ord_less_eq_int @ B @ C )
% 4.71/5.01 => ( ! [X4: int,Y3: int] :
% 4.71/5.01 ( ( ord_less_eq_int @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_subst1
% 4.71/5.01 thf(fact_516_order__subst1,axiom,
% 4.71/5.01 ! [A: num,F: rat > num,B: rat,C: rat] :
% 4.71/5.01 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 4.71/5.01 => ( ( ord_less_eq_rat @ B @ C )
% 4.71/5.01 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_subst1
% 4.71/5.01 thf(fact_517_order__subst1,axiom,
% 4.71/5.01 ! [A: num,F: num > num,B: num,C: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 4.71/5.01 => ( ( ord_less_eq_num @ B @ C )
% 4.71/5.01 => ( ! [X4: num,Y3: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_subst1
% 4.71/5.01 thf(fact_518_order__subst1,axiom,
% 4.71/5.01 ! [A: num,F: nat > num,B: nat,C: nat] :
% 4.71/5.01 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 4.71/5.01 => ( ( ord_less_eq_nat @ B @ C )
% 4.71/5.01 => ( ! [X4: nat,Y3: nat] :
% 4.71/5.01 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_subst1
% 4.71/5.01 thf(fact_519_order__subst1,axiom,
% 4.71/5.01 ! [A: num,F: int > num,B: int,C: int] :
% 4.71/5.01 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 4.71/5.01 => ( ( ord_less_eq_int @ B @ C )
% 4.71/5.01 => ( ! [X4: int,Y3: int] :
% 4.71/5.01 ( ( ord_less_eq_int @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_subst1
% 4.71/5.01 thf(fact_520_order__subst1,axiom,
% 4.71/5.01 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 4.71/5.01 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 4.71/5.01 => ( ( ord_less_eq_rat @ B @ C )
% 4.71/5.01 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_subst1
% 4.71/5.01 thf(fact_521_order__subst1,axiom,
% 4.71/5.01 ! [A: nat,F: num > nat,B: num,C: num] :
% 4.71/5.01 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 4.71/5.01 => ( ( ord_less_eq_num @ B @ C )
% 4.71/5.01 => ( ! [X4: num,Y3: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_subst1
% 4.71/5.01 thf(fact_522_order__subst2,axiom,
% 4.71/5.01 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.01 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 4.71/5.01 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_subst2
% 4.71/5.01 thf(fact_523_order__subst2,axiom,
% 4.71/5.01 ! [A: rat,B: rat,F: rat > num,C: num] :
% 4.71/5.01 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.01 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 4.71/5.01 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_subst2
% 4.71/5.01 thf(fact_524_order__subst2,axiom,
% 4.71/5.01 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.01 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 4.71/5.01 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_subst2
% 4.71/5.01 thf(fact_525_order__subst2,axiom,
% 4.71/5.01 ! [A: rat,B: rat,F: rat > int,C: int] :
% 4.71/5.01 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.01 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 4.71/5.01 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_subst2
% 4.71/5.01 thf(fact_526_order__subst2,axiom,
% 4.71/5.01 ! [A: num,B: num,F: num > rat,C: rat] :
% 4.71/5.01 ( ( ord_less_eq_num @ A @ B )
% 4.71/5.01 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 4.71/5.01 => ( ! [X4: num,Y3: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_subst2
% 4.71/5.01 thf(fact_527_order__subst2,axiom,
% 4.71/5.01 ! [A: num,B: num,F: num > num,C: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ A @ B )
% 4.71/5.01 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 4.71/5.01 => ( ! [X4: num,Y3: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_subst2
% 4.71/5.01 thf(fact_528_order__subst2,axiom,
% 4.71/5.01 ! [A: num,B: num,F: num > nat,C: nat] :
% 4.71/5.01 ( ( ord_less_eq_num @ A @ B )
% 4.71/5.01 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 4.71/5.01 => ( ! [X4: num,Y3: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_subst2
% 4.71/5.01 thf(fact_529_order__subst2,axiom,
% 4.71/5.01 ! [A: num,B: num,F: num > int,C: int] :
% 4.71/5.01 ( ( ord_less_eq_num @ A @ B )
% 4.71/5.01 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 4.71/5.01 => ( ! [X4: num,Y3: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_subst2
% 4.71/5.01 thf(fact_530_order__subst2,axiom,
% 4.71/5.01 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 4.71/5.01 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.01 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 4.71/5.01 => ( ! [X4: nat,Y3: nat] :
% 4.71/5.01 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_subst2
% 4.71/5.01 thf(fact_531_order__subst2,axiom,
% 4.71/5.01 ! [A: nat,B: nat,F: nat > num,C: num] :
% 4.71/5.01 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.01 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 4.71/5.01 => ( ! [X4: nat,Y3: nat] :
% 4.71/5.01 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_subst2
% 4.71/5.01 thf(fact_532_order__eq__refl,axiom,
% 4.71/5.01 ! [X: set_int,Y: set_int] :
% 4.71/5.01 ( ( X = Y )
% 4.71/5.01 => ( ord_less_eq_set_int @ X @ Y ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_eq_refl
% 4.71/5.01 thf(fact_533_order__eq__refl,axiom,
% 4.71/5.01 ! [X: rat,Y: rat] :
% 4.71/5.01 ( ( X = Y )
% 4.71/5.01 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_eq_refl
% 4.71/5.01 thf(fact_534_order__eq__refl,axiom,
% 4.71/5.01 ! [X: num,Y: num] :
% 4.71/5.01 ( ( X = Y )
% 4.71/5.01 => ( ord_less_eq_num @ X @ Y ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_eq_refl
% 4.71/5.01 thf(fact_535_order__eq__refl,axiom,
% 4.71/5.01 ! [X: nat,Y: nat] :
% 4.71/5.01 ( ( X = Y )
% 4.71/5.01 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_eq_refl
% 4.71/5.01 thf(fact_536_order__eq__refl,axiom,
% 4.71/5.01 ! [X: int,Y: int] :
% 4.71/5.01 ( ( X = Y )
% 4.71/5.01 => ( ord_less_eq_int @ X @ Y ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_eq_refl
% 4.71/5.01 thf(fact_537_linorder__linear,axiom,
% 4.71/5.01 ! [X: rat,Y: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ X @ Y )
% 4.71/5.01 | ( ord_less_eq_rat @ Y @ X ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_linear
% 4.71/5.01 thf(fact_538_linorder__linear,axiom,
% 4.71/5.01 ! [X: num,Y: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ X @ Y )
% 4.71/5.01 | ( ord_less_eq_num @ Y @ X ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_linear
% 4.71/5.01 thf(fact_539_linorder__linear,axiom,
% 4.71/5.01 ! [X: nat,Y: nat] :
% 4.71/5.01 ( ( ord_less_eq_nat @ X @ Y )
% 4.71/5.01 | ( ord_less_eq_nat @ Y @ X ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_linear
% 4.71/5.01 thf(fact_540_linorder__linear,axiom,
% 4.71/5.01 ! [X: int,Y: int] :
% 4.71/5.01 ( ( ord_less_eq_int @ X @ Y )
% 4.71/5.01 | ( ord_less_eq_int @ Y @ X ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_linear
% 4.71/5.01 thf(fact_541_ord__eq__le__subst,axiom,
% 4.71/5.01 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 4.71/5.01 ( ( A
% 4.71/5.01 = ( F @ B ) )
% 4.71/5.01 => ( ( ord_less_eq_rat @ B @ C )
% 4.71/5.01 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_eq_le_subst
% 4.71/5.01 thf(fact_542_ord__eq__le__subst,axiom,
% 4.71/5.01 ! [A: num,F: rat > num,B: rat,C: rat] :
% 4.71/5.01 ( ( A
% 4.71/5.01 = ( F @ B ) )
% 4.71/5.01 => ( ( ord_less_eq_rat @ B @ C )
% 4.71/5.01 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_eq_le_subst
% 4.71/5.01 thf(fact_543_ord__eq__le__subst,axiom,
% 4.71/5.01 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 4.71/5.01 ( ( A
% 4.71/5.01 = ( F @ B ) )
% 4.71/5.01 => ( ( ord_less_eq_rat @ B @ C )
% 4.71/5.01 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_eq_le_subst
% 4.71/5.01 thf(fact_544_ord__eq__le__subst,axiom,
% 4.71/5.01 ! [A: int,F: rat > int,B: rat,C: rat] :
% 4.71/5.01 ( ( A
% 4.71/5.01 = ( F @ B ) )
% 4.71/5.01 => ( ( ord_less_eq_rat @ B @ C )
% 4.71/5.01 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_eq_le_subst
% 4.71/5.01 thf(fact_545_ord__eq__le__subst,axiom,
% 4.71/5.01 ! [A: rat,F: num > rat,B: num,C: num] :
% 4.71/5.01 ( ( A
% 4.71/5.01 = ( F @ B ) )
% 4.71/5.01 => ( ( ord_less_eq_num @ B @ C )
% 4.71/5.01 => ( ! [X4: num,Y3: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_eq_le_subst
% 4.71/5.01 thf(fact_546_ord__eq__le__subst,axiom,
% 4.71/5.01 ! [A: num,F: num > num,B: num,C: num] :
% 4.71/5.01 ( ( A
% 4.71/5.01 = ( F @ B ) )
% 4.71/5.01 => ( ( ord_less_eq_num @ B @ C )
% 4.71/5.01 => ( ! [X4: num,Y3: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_eq_le_subst
% 4.71/5.01 thf(fact_547_ord__eq__le__subst,axiom,
% 4.71/5.01 ! [A: nat,F: num > nat,B: num,C: num] :
% 4.71/5.01 ( ( A
% 4.71/5.01 = ( F @ B ) )
% 4.71/5.01 => ( ( ord_less_eq_num @ B @ C )
% 4.71/5.01 => ( ! [X4: num,Y3: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_eq_le_subst
% 4.71/5.01 thf(fact_548_ord__eq__le__subst,axiom,
% 4.71/5.01 ! [A: int,F: num > int,B: num,C: num] :
% 4.71/5.01 ( ( A
% 4.71/5.01 = ( F @ B ) )
% 4.71/5.01 => ( ( ord_less_eq_num @ B @ C )
% 4.71/5.01 => ( ! [X4: num,Y3: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_eq_le_subst
% 4.71/5.01 thf(fact_549_ord__eq__le__subst,axiom,
% 4.71/5.01 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 4.71/5.01 ( ( A
% 4.71/5.01 = ( F @ B ) )
% 4.71/5.01 => ( ( ord_less_eq_nat @ B @ C )
% 4.71/5.01 => ( ! [X4: nat,Y3: nat] :
% 4.71/5.01 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_eq_le_subst
% 4.71/5.01 thf(fact_550_ord__eq__le__subst,axiom,
% 4.71/5.01 ! [A: num,F: nat > num,B: nat,C: nat] :
% 4.71/5.01 ( ( A
% 4.71/5.01 = ( F @ B ) )
% 4.71/5.01 => ( ( ord_less_eq_nat @ B @ C )
% 4.71/5.01 => ( ! [X4: nat,Y3: nat] :
% 4.71/5.01 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_eq_le_subst
% 4.71/5.01 thf(fact_551_ord__le__eq__subst,axiom,
% 4.71/5.01 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.01 => ( ( ( F @ B )
% 4.71/5.01 = C )
% 4.71/5.01 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_le_eq_subst
% 4.71/5.01 thf(fact_552_ord__le__eq__subst,axiom,
% 4.71/5.01 ! [A: rat,B: rat,F: rat > num,C: num] :
% 4.71/5.01 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.01 => ( ( ( F @ B )
% 4.71/5.01 = C )
% 4.71/5.01 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_le_eq_subst
% 4.71/5.01 thf(fact_553_ord__le__eq__subst,axiom,
% 4.71/5.01 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.01 => ( ( ( F @ B )
% 4.71/5.01 = C )
% 4.71/5.01 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_le_eq_subst
% 4.71/5.01 thf(fact_554_ord__le__eq__subst,axiom,
% 4.71/5.01 ! [A: rat,B: rat,F: rat > int,C: int] :
% 4.71/5.01 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.01 => ( ( ( F @ B )
% 4.71/5.01 = C )
% 4.71/5.01 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_le_eq_subst
% 4.71/5.01 thf(fact_555_ord__le__eq__subst,axiom,
% 4.71/5.01 ! [A: num,B: num,F: num > rat,C: rat] :
% 4.71/5.01 ( ( ord_less_eq_num @ A @ B )
% 4.71/5.01 => ( ( ( F @ B )
% 4.71/5.01 = C )
% 4.71/5.01 => ( ! [X4: num,Y3: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_le_eq_subst
% 4.71/5.01 thf(fact_556_ord__le__eq__subst,axiom,
% 4.71/5.01 ! [A: num,B: num,F: num > num,C: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ A @ B )
% 4.71/5.01 => ( ( ( F @ B )
% 4.71/5.01 = C )
% 4.71/5.01 => ( ! [X4: num,Y3: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_le_eq_subst
% 4.71/5.01 thf(fact_557_ord__le__eq__subst,axiom,
% 4.71/5.01 ! [A: num,B: num,F: num > nat,C: nat] :
% 4.71/5.01 ( ( ord_less_eq_num @ A @ B )
% 4.71/5.01 => ( ( ( F @ B )
% 4.71/5.01 = C )
% 4.71/5.01 => ( ! [X4: num,Y3: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_le_eq_subst
% 4.71/5.01 thf(fact_558_ord__le__eq__subst,axiom,
% 4.71/5.01 ! [A: num,B: num,F: num > int,C: int] :
% 4.71/5.01 ( ( ord_less_eq_num @ A @ B )
% 4.71/5.01 => ( ( ( F @ B )
% 4.71/5.01 = C )
% 4.71/5.01 => ( ! [X4: num,Y3: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_le_eq_subst
% 4.71/5.01 thf(fact_559_ord__le__eq__subst,axiom,
% 4.71/5.01 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 4.71/5.01 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.01 => ( ( ( F @ B )
% 4.71/5.01 = C )
% 4.71/5.01 => ( ! [X4: nat,Y3: nat] :
% 4.71/5.01 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_le_eq_subst
% 4.71/5.01 thf(fact_560_ord__le__eq__subst,axiom,
% 4.71/5.01 ! [A: nat,B: nat,F: nat > num,C: num] :
% 4.71/5.01 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.01 => ( ( ( F @ B )
% 4.71/5.01 = C )
% 4.71/5.01 => ( ! [X4: nat,Y3: nat] :
% 4.71/5.01 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_le_eq_subst
% 4.71/5.01 thf(fact_561_linorder__le__cases,axiom,
% 4.71/5.01 ! [X: rat,Y: rat] :
% 4.71/5.01 ( ~ ( ord_less_eq_rat @ X @ Y )
% 4.71/5.01 => ( ord_less_eq_rat @ Y @ X ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_le_cases
% 4.71/5.01 thf(fact_562_linorder__le__cases,axiom,
% 4.71/5.01 ! [X: num,Y: num] :
% 4.71/5.01 ( ~ ( ord_less_eq_num @ X @ Y )
% 4.71/5.01 => ( ord_less_eq_num @ Y @ X ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_le_cases
% 4.71/5.01 thf(fact_563_linorder__le__cases,axiom,
% 4.71/5.01 ! [X: nat,Y: nat] :
% 4.71/5.01 ( ~ ( ord_less_eq_nat @ X @ Y )
% 4.71/5.01 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_le_cases
% 4.71/5.01 thf(fact_564_linorder__le__cases,axiom,
% 4.71/5.01 ! [X: int,Y: int] :
% 4.71/5.01 ( ~ ( ord_less_eq_int @ X @ Y )
% 4.71/5.01 => ( ord_less_eq_int @ Y @ X ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_le_cases
% 4.71/5.01 thf(fact_565_order__antisym__conv,axiom,
% 4.71/5.01 ! [Y: set_int,X: set_int] :
% 4.71/5.01 ( ( ord_less_eq_set_int @ Y @ X )
% 4.71/5.01 => ( ( ord_less_eq_set_int @ X @ Y )
% 4.71/5.01 = ( X = Y ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_antisym_conv
% 4.71/5.01 thf(fact_566_order__antisym__conv,axiom,
% 4.71/5.01 ! [Y: rat,X: rat] :
% 4.71/5.01 ( ( ord_less_eq_rat @ Y @ X )
% 4.71/5.01 => ( ( ord_less_eq_rat @ X @ Y )
% 4.71/5.01 = ( X = Y ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_antisym_conv
% 4.71/5.01 thf(fact_567_order__antisym__conv,axiom,
% 4.71/5.01 ! [Y: num,X: num] :
% 4.71/5.01 ( ( ord_less_eq_num @ Y @ X )
% 4.71/5.01 => ( ( ord_less_eq_num @ X @ Y )
% 4.71/5.01 = ( X = Y ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_antisym_conv
% 4.71/5.01 thf(fact_568_order__antisym__conv,axiom,
% 4.71/5.01 ! [Y: nat,X: nat] :
% 4.71/5.01 ( ( ord_less_eq_nat @ Y @ X )
% 4.71/5.01 => ( ( ord_less_eq_nat @ X @ Y )
% 4.71/5.01 = ( X = Y ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_antisym_conv
% 4.71/5.01 thf(fact_569_order__antisym__conv,axiom,
% 4.71/5.01 ! [Y: int,X: int] :
% 4.71/5.01 ( ( ord_less_eq_int @ Y @ X )
% 4.71/5.01 => ( ( ord_less_eq_int @ X @ Y )
% 4.71/5.01 = ( X = Y ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_antisym_conv
% 4.71/5.01 thf(fact_570_lt__ex,axiom,
% 4.71/5.01 ! [X: real] :
% 4.71/5.01 ? [Y3: real] : ( ord_less_real @ Y3 @ X ) ).
% 4.71/5.01
% 4.71/5.01 % lt_ex
% 4.71/5.01 thf(fact_571_lt__ex,axiom,
% 4.71/5.01 ! [X: rat] :
% 4.71/5.01 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X ) ).
% 4.71/5.01
% 4.71/5.01 % lt_ex
% 4.71/5.01 thf(fact_572_lt__ex,axiom,
% 4.71/5.01 ! [X: int] :
% 4.71/5.01 ? [Y3: int] : ( ord_less_int @ Y3 @ X ) ).
% 4.71/5.01
% 4.71/5.01 % lt_ex
% 4.71/5.01 thf(fact_573_gt__ex,axiom,
% 4.71/5.01 ! [X: real] :
% 4.71/5.01 ? [X_1: real] : ( ord_less_real @ X @ X_1 ) ).
% 4.71/5.01
% 4.71/5.01 % gt_ex
% 4.71/5.01 thf(fact_574_gt__ex,axiom,
% 4.71/5.01 ! [X: rat] :
% 4.71/5.01 ? [X_1: rat] : ( ord_less_rat @ X @ X_1 ) ).
% 4.71/5.01
% 4.71/5.01 % gt_ex
% 4.71/5.01 thf(fact_575_gt__ex,axiom,
% 4.71/5.01 ! [X: nat] :
% 4.71/5.01 ? [X_1: nat] : ( ord_less_nat @ X @ X_1 ) ).
% 4.71/5.01
% 4.71/5.01 % gt_ex
% 4.71/5.01 thf(fact_576_gt__ex,axiom,
% 4.71/5.01 ! [X: int] :
% 4.71/5.01 ? [X_1: int] : ( ord_less_int @ X @ X_1 ) ).
% 4.71/5.01
% 4.71/5.01 % gt_ex
% 4.71/5.01 thf(fact_577_dense,axiom,
% 4.71/5.01 ! [X: real,Y: real] :
% 4.71/5.01 ( ( ord_less_real @ X @ Y )
% 4.71/5.01 => ? [Z3: real] :
% 4.71/5.01 ( ( ord_less_real @ X @ Z3 )
% 4.71/5.01 & ( ord_less_real @ Z3 @ Y ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % dense
% 4.71/5.01 thf(fact_578_dense,axiom,
% 4.71/5.01 ! [X: rat,Y: rat] :
% 4.71/5.01 ( ( ord_less_rat @ X @ Y )
% 4.71/5.01 => ? [Z3: rat] :
% 4.71/5.01 ( ( ord_less_rat @ X @ Z3 )
% 4.71/5.01 & ( ord_less_rat @ Z3 @ Y ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % dense
% 4.71/5.01 thf(fact_579_less__imp__neq,axiom,
% 4.71/5.01 ! [X: real,Y: real] :
% 4.71/5.01 ( ( ord_less_real @ X @ Y )
% 4.71/5.01 => ( X != Y ) ) ).
% 4.71/5.01
% 4.71/5.01 % less_imp_neq
% 4.71/5.01 thf(fact_580_less__imp__neq,axiom,
% 4.71/5.01 ! [X: rat,Y: rat] :
% 4.71/5.01 ( ( ord_less_rat @ X @ Y )
% 4.71/5.01 => ( X != Y ) ) ).
% 4.71/5.01
% 4.71/5.01 % less_imp_neq
% 4.71/5.01 thf(fact_581_less__imp__neq,axiom,
% 4.71/5.01 ! [X: num,Y: num] :
% 4.71/5.01 ( ( ord_less_num @ X @ Y )
% 4.71/5.01 => ( X != Y ) ) ).
% 4.71/5.01
% 4.71/5.01 % less_imp_neq
% 4.71/5.01 thf(fact_582_less__imp__neq,axiom,
% 4.71/5.01 ! [X: nat,Y: nat] :
% 4.71/5.01 ( ( ord_less_nat @ X @ Y )
% 4.71/5.01 => ( X != Y ) ) ).
% 4.71/5.01
% 4.71/5.01 % less_imp_neq
% 4.71/5.01 thf(fact_583_less__imp__neq,axiom,
% 4.71/5.01 ! [X: int,Y: int] :
% 4.71/5.01 ( ( ord_less_int @ X @ Y )
% 4.71/5.01 => ( X != Y ) ) ).
% 4.71/5.01
% 4.71/5.01 % less_imp_neq
% 4.71/5.01 thf(fact_584_order_Oasym,axiom,
% 4.71/5.01 ! [A: real,B: real] :
% 4.71/5.01 ( ( ord_less_real @ A @ B )
% 4.71/5.01 => ~ ( ord_less_real @ B @ A ) ) ).
% 4.71/5.01
% 4.71/5.01 % order.asym
% 4.71/5.01 thf(fact_585_order_Oasym,axiom,
% 4.71/5.01 ! [A: rat,B: rat] :
% 4.71/5.01 ( ( ord_less_rat @ A @ B )
% 4.71/5.01 => ~ ( ord_less_rat @ B @ A ) ) ).
% 4.71/5.01
% 4.71/5.01 % order.asym
% 4.71/5.01 thf(fact_586_order_Oasym,axiom,
% 4.71/5.01 ! [A: num,B: num] :
% 4.71/5.01 ( ( ord_less_num @ A @ B )
% 4.71/5.01 => ~ ( ord_less_num @ B @ A ) ) ).
% 4.71/5.01
% 4.71/5.01 % order.asym
% 4.71/5.01 thf(fact_587_order_Oasym,axiom,
% 4.71/5.01 ! [A: nat,B: nat] :
% 4.71/5.01 ( ( ord_less_nat @ A @ B )
% 4.71/5.01 => ~ ( ord_less_nat @ B @ A ) ) ).
% 4.71/5.01
% 4.71/5.01 % order.asym
% 4.71/5.01 thf(fact_588_order_Oasym,axiom,
% 4.71/5.01 ! [A: int,B: int] :
% 4.71/5.01 ( ( ord_less_int @ A @ B )
% 4.71/5.01 => ~ ( ord_less_int @ B @ A ) ) ).
% 4.71/5.01
% 4.71/5.01 % order.asym
% 4.71/5.01 thf(fact_589_ord__eq__less__trans,axiom,
% 4.71/5.01 ! [A: real,B: real,C: real] :
% 4.71/5.01 ( ( A = B )
% 4.71/5.01 => ( ( ord_less_real @ B @ C )
% 4.71/5.01 => ( ord_less_real @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_eq_less_trans
% 4.71/5.01 thf(fact_590_ord__eq__less__trans,axiom,
% 4.71/5.01 ! [A: rat,B: rat,C: rat] :
% 4.71/5.01 ( ( A = B )
% 4.71/5.01 => ( ( ord_less_rat @ B @ C )
% 4.71/5.01 => ( ord_less_rat @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_eq_less_trans
% 4.71/5.01 thf(fact_591_ord__eq__less__trans,axiom,
% 4.71/5.01 ! [A: num,B: num,C: num] :
% 4.71/5.01 ( ( A = B )
% 4.71/5.01 => ( ( ord_less_num @ B @ C )
% 4.71/5.01 => ( ord_less_num @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_eq_less_trans
% 4.71/5.01 thf(fact_592_ord__eq__less__trans,axiom,
% 4.71/5.01 ! [A: nat,B: nat,C: nat] :
% 4.71/5.01 ( ( A = B )
% 4.71/5.01 => ( ( ord_less_nat @ B @ C )
% 4.71/5.01 => ( ord_less_nat @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_eq_less_trans
% 4.71/5.01 thf(fact_593_ord__eq__less__trans,axiom,
% 4.71/5.01 ! [A: int,B: int,C: int] :
% 4.71/5.01 ( ( A = B )
% 4.71/5.01 => ( ( ord_less_int @ B @ C )
% 4.71/5.01 => ( ord_less_int @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_eq_less_trans
% 4.71/5.01 thf(fact_594_ord__less__eq__trans,axiom,
% 4.71/5.01 ! [A: real,B: real,C: real] :
% 4.71/5.01 ( ( ord_less_real @ A @ B )
% 4.71/5.01 => ( ( B = C )
% 4.71/5.01 => ( ord_less_real @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_less_eq_trans
% 4.71/5.01 thf(fact_595_ord__less__eq__trans,axiom,
% 4.71/5.01 ! [A: rat,B: rat,C: rat] :
% 4.71/5.01 ( ( ord_less_rat @ A @ B )
% 4.71/5.01 => ( ( B = C )
% 4.71/5.01 => ( ord_less_rat @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_less_eq_trans
% 4.71/5.01 thf(fact_596_ord__less__eq__trans,axiom,
% 4.71/5.01 ! [A: num,B: num,C: num] :
% 4.71/5.01 ( ( ord_less_num @ A @ B )
% 4.71/5.01 => ( ( B = C )
% 4.71/5.01 => ( ord_less_num @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_less_eq_trans
% 4.71/5.01 thf(fact_597_ord__less__eq__trans,axiom,
% 4.71/5.01 ! [A: nat,B: nat,C: nat] :
% 4.71/5.01 ( ( ord_less_nat @ A @ B )
% 4.71/5.01 => ( ( B = C )
% 4.71/5.01 => ( ord_less_nat @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_less_eq_trans
% 4.71/5.01 thf(fact_598_ord__less__eq__trans,axiom,
% 4.71/5.01 ! [A: int,B: int,C: int] :
% 4.71/5.01 ( ( ord_less_int @ A @ B )
% 4.71/5.01 => ( ( B = C )
% 4.71/5.01 => ( ord_less_int @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_less_eq_trans
% 4.71/5.01 thf(fact_599_less__induct,axiom,
% 4.71/5.01 ! [P: nat > $o,A: nat] :
% 4.71/5.01 ( ! [X4: nat] :
% 4.71/5.01 ( ! [Y4: nat] :
% 4.71/5.01 ( ( ord_less_nat @ Y4 @ X4 )
% 4.71/5.01 => ( P @ Y4 ) )
% 4.71/5.01 => ( P @ X4 ) )
% 4.71/5.01 => ( P @ A ) ) ).
% 4.71/5.01
% 4.71/5.01 % less_induct
% 4.71/5.01 thf(fact_600_antisym__conv3,axiom,
% 4.71/5.01 ! [Y: real,X: real] :
% 4.71/5.01 ( ~ ( ord_less_real @ Y @ X )
% 4.71/5.01 => ( ( ~ ( ord_less_real @ X @ Y ) )
% 4.71/5.01 = ( X = Y ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % antisym_conv3
% 4.71/5.01 thf(fact_601_antisym__conv3,axiom,
% 4.71/5.01 ! [Y: rat,X: rat] :
% 4.71/5.01 ( ~ ( ord_less_rat @ Y @ X )
% 4.71/5.01 => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 4.71/5.01 = ( X = Y ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % antisym_conv3
% 4.71/5.01 thf(fact_602_antisym__conv3,axiom,
% 4.71/5.01 ! [Y: num,X: num] :
% 4.71/5.01 ( ~ ( ord_less_num @ Y @ X )
% 4.71/5.01 => ( ( ~ ( ord_less_num @ X @ Y ) )
% 4.71/5.01 = ( X = Y ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % antisym_conv3
% 4.71/5.01 thf(fact_603_antisym__conv3,axiom,
% 4.71/5.01 ! [Y: nat,X: nat] :
% 4.71/5.01 ( ~ ( ord_less_nat @ Y @ X )
% 4.71/5.01 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 4.71/5.01 = ( X = Y ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % antisym_conv3
% 4.71/5.01 thf(fact_604_antisym__conv3,axiom,
% 4.71/5.01 ! [Y: int,X: int] :
% 4.71/5.01 ( ~ ( ord_less_int @ Y @ X )
% 4.71/5.01 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 4.71/5.01 = ( X = Y ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % antisym_conv3
% 4.71/5.01 thf(fact_605_linorder__cases,axiom,
% 4.71/5.01 ! [X: real,Y: real] :
% 4.71/5.01 ( ~ ( ord_less_real @ X @ Y )
% 4.71/5.01 => ( ( X != Y )
% 4.71/5.01 => ( ord_less_real @ Y @ X ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_cases
% 4.71/5.01 thf(fact_606_linorder__cases,axiom,
% 4.71/5.01 ! [X: rat,Y: rat] :
% 4.71/5.01 ( ~ ( ord_less_rat @ X @ Y )
% 4.71/5.01 => ( ( X != Y )
% 4.71/5.01 => ( ord_less_rat @ Y @ X ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_cases
% 4.71/5.01 thf(fact_607_linorder__cases,axiom,
% 4.71/5.01 ! [X: num,Y: num] :
% 4.71/5.01 ( ~ ( ord_less_num @ X @ Y )
% 4.71/5.01 => ( ( X != Y )
% 4.71/5.01 => ( ord_less_num @ Y @ X ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_cases
% 4.71/5.01 thf(fact_608_linorder__cases,axiom,
% 4.71/5.01 ! [X: nat,Y: nat] :
% 4.71/5.01 ( ~ ( ord_less_nat @ X @ Y )
% 4.71/5.01 => ( ( X != Y )
% 4.71/5.01 => ( ord_less_nat @ Y @ X ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_cases
% 4.71/5.01 thf(fact_609_linorder__cases,axiom,
% 4.71/5.01 ! [X: int,Y: int] :
% 4.71/5.01 ( ~ ( ord_less_int @ X @ Y )
% 4.71/5.01 => ( ( X != Y )
% 4.71/5.01 => ( ord_less_int @ Y @ X ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_cases
% 4.71/5.01 thf(fact_610_dual__order_Oasym,axiom,
% 4.71/5.01 ! [B: real,A: real] :
% 4.71/5.01 ( ( ord_less_real @ B @ A )
% 4.71/5.01 => ~ ( ord_less_real @ A @ B ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.asym
% 4.71/5.01 thf(fact_611_dual__order_Oasym,axiom,
% 4.71/5.01 ! [B: rat,A: rat] :
% 4.71/5.01 ( ( ord_less_rat @ B @ A )
% 4.71/5.01 => ~ ( ord_less_rat @ A @ B ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.asym
% 4.71/5.01 thf(fact_612_dual__order_Oasym,axiom,
% 4.71/5.01 ! [B: num,A: num] :
% 4.71/5.01 ( ( ord_less_num @ B @ A )
% 4.71/5.01 => ~ ( ord_less_num @ A @ B ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.asym
% 4.71/5.01 thf(fact_613_dual__order_Oasym,axiom,
% 4.71/5.01 ! [B: nat,A: nat] :
% 4.71/5.01 ( ( ord_less_nat @ B @ A )
% 4.71/5.01 => ~ ( ord_less_nat @ A @ B ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.asym
% 4.71/5.01 thf(fact_614_dual__order_Oasym,axiom,
% 4.71/5.01 ! [B: int,A: int] :
% 4.71/5.01 ( ( ord_less_int @ B @ A )
% 4.71/5.01 => ~ ( ord_less_int @ A @ B ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.asym
% 4.71/5.01 thf(fact_615_dual__order_Oirrefl,axiom,
% 4.71/5.01 ! [A: real] :
% 4.71/5.01 ~ ( ord_less_real @ A @ A ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.irrefl
% 4.71/5.01 thf(fact_616_dual__order_Oirrefl,axiom,
% 4.71/5.01 ! [A: rat] :
% 4.71/5.01 ~ ( ord_less_rat @ A @ A ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.irrefl
% 4.71/5.01 thf(fact_617_dual__order_Oirrefl,axiom,
% 4.71/5.01 ! [A: num] :
% 4.71/5.01 ~ ( ord_less_num @ A @ A ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.irrefl
% 4.71/5.01 thf(fact_618_dual__order_Oirrefl,axiom,
% 4.71/5.01 ! [A: nat] :
% 4.71/5.01 ~ ( ord_less_nat @ A @ A ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.irrefl
% 4.71/5.01 thf(fact_619_dual__order_Oirrefl,axiom,
% 4.71/5.01 ! [A: int] :
% 4.71/5.01 ~ ( ord_less_int @ A @ A ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.irrefl
% 4.71/5.01 thf(fact_620_exists__least__iff,axiom,
% 4.71/5.01 ( ( ^ [P2: nat > $o] :
% 4.71/5.01 ? [X6: nat] : ( P2 @ X6 ) )
% 4.71/5.01 = ( ^ [P3: nat > $o] :
% 4.71/5.01 ? [N4: nat] :
% 4.71/5.01 ( ( P3 @ N4 )
% 4.71/5.01 & ! [M3: nat] :
% 4.71/5.01 ( ( ord_less_nat @ M3 @ N4 )
% 4.71/5.01 => ~ ( P3 @ M3 ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % exists_least_iff
% 4.71/5.01 thf(fact_621_linorder__less__wlog,axiom,
% 4.71/5.01 ! [P: real > real > $o,A: real,B: real] :
% 4.71/5.01 ( ! [A5: real,B5: real] :
% 4.71/5.01 ( ( ord_less_real @ A5 @ B5 )
% 4.71/5.01 => ( P @ A5 @ B5 ) )
% 4.71/5.01 => ( ! [A5: real] : ( P @ A5 @ A5 )
% 4.71/5.01 => ( ! [A5: real,B5: real] :
% 4.71/5.01 ( ( P @ B5 @ A5 )
% 4.71/5.01 => ( P @ A5 @ B5 ) )
% 4.71/5.01 => ( P @ A @ B ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_less_wlog
% 4.71/5.01 thf(fact_622_linorder__less__wlog,axiom,
% 4.71/5.01 ! [P: rat > rat > $o,A: rat,B: rat] :
% 4.71/5.01 ( ! [A5: rat,B5: rat] :
% 4.71/5.01 ( ( ord_less_rat @ A5 @ B5 )
% 4.71/5.01 => ( P @ A5 @ B5 ) )
% 4.71/5.01 => ( ! [A5: rat] : ( P @ A5 @ A5 )
% 4.71/5.01 => ( ! [A5: rat,B5: rat] :
% 4.71/5.01 ( ( P @ B5 @ A5 )
% 4.71/5.01 => ( P @ A5 @ B5 ) )
% 4.71/5.01 => ( P @ A @ B ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_less_wlog
% 4.71/5.01 thf(fact_623_linorder__less__wlog,axiom,
% 4.71/5.01 ! [P: num > num > $o,A: num,B: num] :
% 4.71/5.01 ( ! [A5: num,B5: num] :
% 4.71/5.01 ( ( ord_less_num @ A5 @ B5 )
% 4.71/5.01 => ( P @ A5 @ B5 ) )
% 4.71/5.01 => ( ! [A5: num] : ( P @ A5 @ A5 )
% 4.71/5.01 => ( ! [A5: num,B5: num] :
% 4.71/5.01 ( ( P @ B5 @ A5 )
% 4.71/5.01 => ( P @ A5 @ B5 ) )
% 4.71/5.01 => ( P @ A @ B ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_less_wlog
% 4.71/5.01 thf(fact_624_linorder__less__wlog,axiom,
% 4.71/5.01 ! [P: nat > nat > $o,A: nat,B: nat] :
% 4.71/5.01 ( ! [A5: nat,B5: nat] :
% 4.71/5.01 ( ( ord_less_nat @ A5 @ B5 )
% 4.71/5.01 => ( P @ A5 @ B5 ) )
% 4.71/5.01 => ( ! [A5: nat] : ( P @ A5 @ A5 )
% 4.71/5.01 => ( ! [A5: nat,B5: nat] :
% 4.71/5.01 ( ( P @ B5 @ A5 )
% 4.71/5.01 => ( P @ A5 @ B5 ) )
% 4.71/5.01 => ( P @ A @ B ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_less_wlog
% 4.71/5.01 thf(fact_625_linorder__less__wlog,axiom,
% 4.71/5.01 ! [P: int > int > $o,A: int,B: int] :
% 4.71/5.01 ( ! [A5: int,B5: int] :
% 4.71/5.01 ( ( ord_less_int @ A5 @ B5 )
% 4.71/5.01 => ( P @ A5 @ B5 ) )
% 4.71/5.01 => ( ! [A5: int] : ( P @ A5 @ A5 )
% 4.71/5.01 => ( ! [A5: int,B5: int] :
% 4.71/5.01 ( ( P @ B5 @ A5 )
% 4.71/5.01 => ( P @ A5 @ B5 ) )
% 4.71/5.01 => ( P @ A @ B ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_less_wlog
% 4.71/5.01 thf(fact_626_order_Ostrict__trans,axiom,
% 4.71/5.01 ! [A: real,B: real,C: real] :
% 4.71/5.01 ( ( ord_less_real @ A @ B )
% 4.71/5.01 => ( ( ord_less_real @ B @ C )
% 4.71/5.01 => ( ord_less_real @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order.strict_trans
% 4.71/5.01 thf(fact_627_order_Ostrict__trans,axiom,
% 4.71/5.01 ! [A: rat,B: rat,C: rat] :
% 4.71/5.01 ( ( ord_less_rat @ A @ B )
% 4.71/5.01 => ( ( ord_less_rat @ B @ C )
% 4.71/5.01 => ( ord_less_rat @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order.strict_trans
% 4.71/5.01 thf(fact_628_order_Ostrict__trans,axiom,
% 4.71/5.01 ! [A: num,B: num,C: num] :
% 4.71/5.01 ( ( ord_less_num @ A @ B )
% 4.71/5.01 => ( ( ord_less_num @ B @ C )
% 4.71/5.01 => ( ord_less_num @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order.strict_trans
% 4.71/5.01 thf(fact_629_order_Ostrict__trans,axiom,
% 4.71/5.01 ! [A: nat,B: nat,C: nat] :
% 4.71/5.01 ( ( ord_less_nat @ A @ B )
% 4.71/5.01 => ( ( ord_less_nat @ B @ C )
% 4.71/5.01 => ( ord_less_nat @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order.strict_trans
% 4.71/5.01 thf(fact_630_order_Ostrict__trans,axiom,
% 4.71/5.01 ! [A: int,B: int,C: int] :
% 4.71/5.01 ( ( ord_less_int @ A @ B )
% 4.71/5.01 => ( ( ord_less_int @ B @ C )
% 4.71/5.01 => ( ord_less_int @ A @ C ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order.strict_trans
% 4.71/5.01 thf(fact_631_not__less__iff__gr__or__eq,axiom,
% 4.71/5.01 ! [X: real,Y: real] :
% 4.71/5.01 ( ( ~ ( ord_less_real @ X @ Y ) )
% 4.71/5.01 = ( ( ord_less_real @ Y @ X )
% 4.71/5.01 | ( X = Y ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % not_less_iff_gr_or_eq
% 4.71/5.01 thf(fact_632_not__less__iff__gr__or__eq,axiom,
% 4.71/5.01 ! [X: rat,Y: rat] :
% 4.71/5.01 ( ( ~ ( ord_less_rat @ X @ Y ) )
% 4.71/5.01 = ( ( ord_less_rat @ Y @ X )
% 4.71/5.01 | ( X = Y ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % not_less_iff_gr_or_eq
% 4.71/5.01 thf(fact_633_not__less__iff__gr__or__eq,axiom,
% 4.71/5.01 ! [X: num,Y: num] :
% 4.71/5.01 ( ( ~ ( ord_less_num @ X @ Y ) )
% 4.71/5.01 = ( ( ord_less_num @ Y @ X )
% 4.71/5.01 | ( X = Y ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % not_less_iff_gr_or_eq
% 4.71/5.01 thf(fact_634_not__less__iff__gr__or__eq,axiom,
% 4.71/5.01 ! [X: nat,Y: nat] :
% 4.71/5.01 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 4.71/5.01 = ( ( ord_less_nat @ Y @ X )
% 4.71/5.01 | ( X = Y ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % not_less_iff_gr_or_eq
% 4.71/5.01 thf(fact_635_not__less__iff__gr__or__eq,axiom,
% 4.71/5.01 ! [X: int,Y: int] :
% 4.71/5.01 ( ( ~ ( ord_less_int @ X @ Y ) )
% 4.71/5.01 = ( ( ord_less_int @ Y @ X )
% 4.71/5.01 | ( X = Y ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % not_less_iff_gr_or_eq
% 4.71/5.01 thf(fact_636_dual__order_Ostrict__trans,axiom,
% 4.71/5.01 ! [B: real,A: real,C: real] :
% 4.71/5.01 ( ( ord_less_real @ B @ A )
% 4.71/5.01 => ( ( ord_less_real @ C @ B )
% 4.71/5.01 => ( ord_less_real @ C @ A ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.strict_trans
% 4.71/5.01 thf(fact_637_dual__order_Ostrict__trans,axiom,
% 4.71/5.01 ! [B: rat,A: rat,C: rat] :
% 4.71/5.01 ( ( ord_less_rat @ B @ A )
% 4.71/5.01 => ( ( ord_less_rat @ C @ B )
% 4.71/5.01 => ( ord_less_rat @ C @ A ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.strict_trans
% 4.71/5.01 thf(fact_638_dual__order_Ostrict__trans,axiom,
% 4.71/5.01 ! [B: num,A: num,C: num] :
% 4.71/5.01 ( ( ord_less_num @ B @ A )
% 4.71/5.01 => ( ( ord_less_num @ C @ B )
% 4.71/5.01 => ( ord_less_num @ C @ A ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.strict_trans
% 4.71/5.01 thf(fact_639_dual__order_Ostrict__trans,axiom,
% 4.71/5.01 ! [B: nat,A: nat,C: nat] :
% 4.71/5.01 ( ( ord_less_nat @ B @ A )
% 4.71/5.01 => ( ( ord_less_nat @ C @ B )
% 4.71/5.01 => ( ord_less_nat @ C @ A ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.strict_trans
% 4.71/5.01 thf(fact_640_dual__order_Ostrict__trans,axiom,
% 4.71/5.01 ! [B: int,A: int,C: int] :
% 4.71/5.01 ( ( ord_less_int @ B @ A )
% 4.71/5.01 => ( ( ord_less_int @ C @ B )
% 4.71/5.01 => ( ord_less_int @ C @ A ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.strict_trans
% 4.71/5.01 thf(fact_641_order_Ostrict__implies__not__eq,axiom,
% 4.71/5.01 ! [A: real,B: real] :
% 4.71/5.01 ( ( ord_less_real @ A @ B )
% 4.71/5.01 => ( A != B ) ) ).
% 4.71/5.01
% 4.71/5.01 % order.strict_implies_not_eq
% 4.71/5.01 thf(fact_642_order_Ostrict__implies__not__eq,axiom,
% 4.71/5.01 ! [A: rat,B: rat] :
% 4.71/5.01 ( ( ord_less_rat @ A @ B )
% 4.71/5.01 => ( A != B ) ) ).
% 4.71/5.01
% 4.71/5.01 % order.strict_implies_not_eq
% 4.71/5.01 thf(fact_643_order_Ostrict__implies__not__eq,axiom,
% 4.71/5.01 ! [A: num,B: num] :
% 4.71/5.01 ( ( ord_less_num @ A @ B )
% 4.71/5.01 => ( A != B ) ) ).
% 4.71/5.01
% 4.71/5.01 % order.strict_implies_not_eq
% 4.71/5.01 thf(fact_644_order_Ostrict__implies__not__eq,axiom,
% 4.71/5.01 ! [A: nat,B: nat] :
% 4.71/5.01 ( ( ord_less_nat @ A @ B )
% 4.71/5.01 => ( A != B ) ) ).
% 4.71/5.01
% 4.71/5.01 % order.strict_implies_not_eq
% 4.71/5.01 thf(fact_645_order_Ostrict__implies__not__eq,axiom,
% 4.71/5.01 ! [A: int,B: int] :
% 4.71/5.01 ( ( ord_less_int @ A @ B )
% 4.71/5.01 => ( A != B ) ) ).
% 4.71/5.01
% 4.71/5.01 % order.strict_implies_not_eq
% 4.71/5.01 thf(fact_646_dual__order_Ostrict__implies__not__eq,axiom,
% 4.71/5.01 ! [B: real,A: real] :
% 4.71/5.01 ( ( ord_less_real @ B @ A )
% 4.71/5.01 => ( A != B ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.strict_implies_not_eq
% 4.71/5.01 thf(fact_647_dual__order_Ostrict__implies__not__eq,axiom,
% 4.71/5.01 ! [B: rat,A: rat] :
% 4.71/5.01 ( ( ord_less_rat @ B @ A )
% 4.71/5.01 => ( A != B ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.strict_implies_not_eq
% 4.71/5.01 thf(fact_648_dual__order_Ostrict__implies__not__eq,axiom,
% 4.71/5.01 ! [B: num,A: num] :
% 4.71/5.01 ( ( ord_less_num @ B @ A )
% 4.71/5.01 => ( A != B ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.strict_implies_not_eq
% 4.71/5.01 thf(fact_649_dual__order_Ostrict__implies__not__eq,axiom,
% 4.71/5.01 ! [B: nat,A: nat] :
% 4.71/5.01 ( ( ord_less_nat @ B @ A )
% 4.71/5.01 => ( A != B ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.strict_implies_not_eq
% 4.71/5.01 thf(fact_650_dual__order_Ostrict__implies__not__eq,axiom,
% 4.71/5.01 ! [B: int,A: int] :
% 4.71/5.01 ( ( ord_less_int @ B @ A )
% 4.71/5.01 => ( A != B ) ) ).
% 4.71/5.01
% 4.71/5.01 % dual_order.strict_implies_not_eq
% 4.71/5.01 thf(fact_651_linorder__neqE,axiom,
% 4.71/5.01 ! [X: real,Y: real] :
% 4.71/5.01 ( ( X != Y )
% 4.71/5.01 => ( ~ ( ord_less_real @ X @ Y )
% 4.71/5.01 => ( ord_less_real @ Y @ X ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_neqE
% 4.71/5.01 thf(fact_652_linorder__neqE,axiom,
% 4.71/5.01 ! [X: rat,Y: rat] :
% 4.71/5.01 ( ( X != Y )
% 4.71/5.01 => ( ~ ( ord_less_rat @ X @ Y )
% 4.71/5.01 => ( ord_less_rat @ Y @ X ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_neqE
% 4.71/5.01 thf(fact_653_linorder__neqE,axiom,
% 4.71/5.01 ! [X: num,Y: num] :
% 4.71/5.01 ( ( X != Y )
% 4.71/5.01 => ( ~ ( ord_less_num @ X @ Y )
% 4.71/5.01 => ( ord_less_num @ Y @ X ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_neqE
% 4.71/5.01 thf(fact_654_linorder__neqE,axiom,
% 4.71/5.01 ! [X: nat,Y: nat] :
% 4.71/5.01 ( ( X != Y )
% 4.71/5.01 => ( ~ ( ord_less_nat @ X @ Y )
% 4.71/5.01 => ( ord_less_nat @ Y @ X ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_neqE
% 4.71/5.01 thf(fact_655_linorder__neqE,axiom,
% 4.71/5.01 ! [X: int,Y: int] :
% 4.71/5.01 ( ( X != Y )
% 4.71/5.01 => ( ~ ( ord_less_int @ X @ Y )
% 4.71/5.01 => ( ord_less_int @ Y @ X ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_neqE
% 4.71/5.01 thf(fact_656_order__less__asym,axiom,
% 4.71/5.01 ! [X: real,Y: real] :
% 4.71/5.01 ( ( ord_less_real @ X @ Y )
% 4.71/5.01 => ~ ( ord_less_real @ Y @ X ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_less_asym
% 4.71/5.01 thf(fact_657_order__less__asym,axiom,
% 4.71/5.01 ! [X: rat,Y: rat] :
% 4.71/5.01 ( ( ord_less_rat @ X @ Y )
% 4.71/5.01 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_less_asym
% 4.71/5.01 thf(fact_658_order__less__asym,axiom,
% 4.71/5.01 ! [X: num,Y: num] :
% 4.71/5.01 ( ( ord_less_num @ X @ Y )
% 4.71/5.01 => ~ ( ord_less_num @ Y @ X ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_less_asym
% 4.71/5.01 thf(fact_659_order__less__asym,axiom,
% 4.71/5.01 ! [X: nat,Y: nat] :
% 4.71/5.01 ( ( ord_less_nat @ X @ Y )
% 4.71/5.01 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_less_asym
% 4.71/5.01 thf(fact_660_order__less__asym,axiom,
% 4.71/5.01 ! [X: int,Y: int] :
% 4.71/5.01 ( ( ord_less_int @ X @ Y )
% 4.71/5.01 => ~ ( ord_less_int @ Y @ X ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_less_asym
% 4.71/5.01 thf(fact_661_linorder__neq__iff,axiom,
% 4.71/5.01 ! [X: real,Y: real] :
% 4.71/5.01 ( ( X != Y )
% 4.71/5.01 = ( ( ord_less_real @ X @ Y )
% 4.71/5.01 | ( ord_less_real @ Y @ X ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_neq_iff
% 4.71/5.01 thf(fact_662_linorder__neq__iff,axiom,
% 4.71/5.01 ! [X: rat,Y: rat] :
% 4.71/5.01 ( ( X != Y )
% 4.71/5.01 = ( ( ord_less_rat @ X @ Y )
% 4.71/5.01 | ( ord_less_rat @ Y @ X ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_neq_iff
% 4.71/5.01 thf(fact_663_linorder__neq__iff,axiom,
% 4.71/5.01 ! [X: num,Y: num] :
% 4.71/5.01 ( ( X != Y )
% 4.71/5.01 = ( ( ord_less_num @ X @ Y )
% 4.71/5.01 | ( ord_less_num @ Y @ X ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_neq_iff
% 4.71/5.01 thf(fact_664_linorder__neq__iff,axiom,
% 4.71/5.01 ! [X: nat,Y: nat] :
% 4.71/5.01 ( ( X != Y )
% 4.71/5.01 = ( ( ord_less_nat @ X @ Y )
% 4.71/5.01 | ( ord_less_nat @ Y @ X ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_neq_iff
% 4.71/5.01 thf(fact_665_linorder__neq__iff,axiom,
% 4.71/5.01 ! [X: int,Y: int] :
% 4.71/5.01 ( ( X != Y )
% 4.71/5.01 = ( ( ord_less_int @ X @ Y )
% 4.71/5.01 | ( ord_less_int @ Y @ X ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % linorder_neq_iff
% 4.71/5.01 thf(fact_666_order__less__asym_H,axiom,
% 4.71/5.01 ! [A: real,B: real] :
% 4.71/5.01 ( ( ord_less_real @ A @ B )
% 4.71/5.01 => ~ ( ord_less_real @ B @ A ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_less_asym'
% 4.71/5.01 thf(fact_667_order__less__asym_H,axiom,
% 4.71/5.01 ! [A: rat,B: rat] :
% 4.71/5.01 ( ( ord_less_rat @ A @ B )
% 4.71/5.01 => ~ ( ord_less_rat @ B @ A ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_less_asym'
% 4.71/5.01 thf(fact_668_order__less__asym_H,axiom,
% 4.71/5.01 ! [A: num,B: num] :
% 4.71/5.01 ( ( ord_less_num @ A @ B )
% 4.71/5.01 => ~ ( ord_less_num @ B @ A ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_less_asym'
% 4.71/5.01 thf(fact_669_order__less__asym_H,axiom,
% 4.71/5.01 ! [A: nat,B: nat] :
% 4.71/5.01 ( ( ord_less_nat @ A @ B )
% 4.71/5.01 => ~ ( ord_less_nat @ B @ A ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_less_asym'
% 4.71/5.01 thf(fact_670_order__less__asym_H,axiom,
% 4.71/5.01 ! [A: int,B: int] :
% 4.71/5.01 ( ( ord_less_int @ A @ B )
% 4.71/5.01 => ~ ( ord_less_int @ B @ A ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_less_asym'
% 4.71/5.01 thf(fact_671_order__less__trans,axiom,
% 4.71/5.01 ! [X: real,Y: real,Z: real] :
% 4.71/5.01 ( ( ord_less_real @ X @ Y )
% 4.71/5.01 => ( ( ord_less_real @ Y @ Z )
% 4.71/5.01 => ( ord_less_real @ X @ Z ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_less_trans
% 4.71/5.01 thf(fact_672_order__less__trans,axiom,
% 4.71/5.01 ! [X: rat,Y: rat,Z: rat] :
% 4.71/5.01 ( ( ord_less_rat @ X @ Y )
% 4.71/5.01 => ( ( ord_less_rat @ Y @ Z )
% 4.71/5.01 => ( ord_less_rat @ X @ Z ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_less_trans
% 4.71/5.01 thf(fact_673_order__less__trans,axiom,
% 4.71/5.01 ! [X: num,Y: num,Z: num] :
% 4.71/5.01 ( ( ord_less_num @ X @ Y )
% 4.71/5.01 => ( ( ord_less_num @ Y @ Z )
% 4.71/5.01 => ( ord_less_num @ X @ Z ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_less_trans
% 4.71/5.01 thf(fact_674_order__less__trans,axiom,
% 4.71/5.01 ! [X: nat,Y: nat,Z: nat] :
% 4.71/5.01 ( ( ord_less_nat @ X @ Y )
% 4.71/5.01 => ( ( ord_less_nat @ Y @ Z )
% 4.71/5.01 => ( ord_less_nat @ X @ Z ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_less_trans
% 4.71/5.01 thf(fact_675_order__less__trans,axiom,
% 4.71/5.01 ! [X: int,Y: int,Z: int] :
% 4.71/5.01 ( ( ord_less_int @ X @ Y )
% 4.71/5.01 => ( ( ord_less_int @ Y @ Z )
% 4.71/5.01 => ( ord_less_int @ X @ Z ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % order_less_trans
% 4.71/5.01 thf(fact_676_ord__eq__less__subst,axiom,
% 4.71/5.01 ! [A: real,F: real > real,B: real,C: real] :
% 4.71/5.01 ( ( A
% 4.71/5.01 = ( F @ B ) )
% 4.71/5.01 => ( ( ord_less_real @ B @ C )
% 4.71/5.01 => ( ! [X4: real,Y3: real] :
% 4.71/5.01 ( ( ord_less_real @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_eq_less_subst
% 4.71/5.01 thf(fact_677_ord__eq__less__subst,axiom,
% 4.71/5.01 ! [A: rat,F: real > rat,B: real,C: real] :
% 4.71/5.01 ( ( A
% 4.71/5.01 = ( F @ B ) )
% 4.71/5.01 => ( ( ord_less_real @ B @ C )
% 4.71/5.01 => ( ! [X4: real,Y3: real] :
% 4.71/5.01 ( ( ord_less_real @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_eq_less_subst
% 4.71/5.01 thf(fact_678_ord__eq__less__subst,axiom,
% 4.71/5.01 ! [A: num,F: real > num,B: real,C: real] :
% 4.71/5.01 ( ( A
% 4.71/5.01 = ( F @ B ) )
% 4.71/5.01 => ( ( ord_less_real @ B @ C )
% 4.71/5.01 => ( ! [X4: real,Y3: real] :
% 4.71/5.01 ( ( ord_less_real @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_eq_less_subst
% 4.71/5.01 thf(fact_679_ord__eq__less__subst,axiom,
% 4.71/5.01 ! [A: nat,F: real > nat,B: real,C: real] :
% 4.71/5.01 ( ( A
% 4.71/5.01 = ( F @ B ) )
% 4.71/5.01 => ( ( ord_less_real @ B @ C )
% 4.71/5.01 => ( ! [X4: real,Y3: real] :
% 4.71/5.01 ( ( ord_less_real @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_eq_less_subst
% 4.71/5.01 thf(fact_680_ord__eq__less__subst,axiom,
% 4.71/5.01 ! [A: int,F: real > int,B: real,C: real] :
% 4.71/5.01 ( ( A
% 4.71/5.01 = ( F @ B ) )
% 4.71/5.01 => ( ( ord_less_real @ B @ C )
% 4.71/5.01 => ( ! [X4: real,Y3: real] :
% 4.71/5.01 ( ( ord_less_real @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_eq_less_subst
% 4.71/5.01 thf(fact_681_ord__eq__less__subst,axiom,
% 4.71/5.01 ! [A: real,F: rat > real,B: rat,C: rat] :
% 4.71/5.01 ( ( A
% 4.71/5.01 = ( F @ B ) )
% 4.71/5.01 => ( ( ord_less_rat @ B @ C )
% 4.71/5.01 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.01 ( ( ord_less_rat @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.01 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.01
% 4.71/5.01 % ord_eq_less_subst
% 4.71/5.01 thf(fact_682_ord__eq__less__subst,axiom,
% 4.71/5.01 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 4.71/5.01 ( ( A
% 4.71/5.01 = ( F @ B ) )
% 4.71/5.01 => ( ( ord_less_rat @ B @ C )
% 4.71/5.01 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.01 ( ( ord_less_rat @ X4 @ Y3 )
% 4.71/5.01 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % ord_eq_less_subst
% 4.71/5.02 thf(fact_683_ord__eq__less__subst,axiom,
% 4.71/5.02 ! [A: num,F: rat > num,B: rat,C: rat] :
% 4.71/5.02 ( ( A
% 4.71/5.02 = ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_rat @ B @ C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % ord_eq_less_subst
% 4.71/5.02 thf(fact_684_ord__eq__less__subst,axiom,
% 4.71/5.02 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 4.71/5.02 ( ( A
% 4.71/5.02 = ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_rat @ B @ C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % ord_eq_less_subst
% 4.71/5.02 thf(fact_685_ord__eq__less__subst,axiom,
% 4.71/5.02 ! [A: int,F: rat > int,B: rat,C: rat] :
% 4.71/5.02 ( ( A
% 4.71/5.02 = ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_rat @ B @ C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % ord_eq_less_subst
% 4.71/5.02 thf(fact_686_ord__less__eq__subst,axiom,
% 4.71/5.02 ! [A: real,B: real,F: real > real,C: real] :
% 4.71/5.02 ( ( ord_less_real @ A @ B )
% 4.71/5.02 => ( ( ( F @ B )
% 4.71/5.02 = C )
% 4.71/5.02 => ( ! [X4: real,Y3: real] :
% 4.71/5.02 ( ( ord_less_real @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % ord_less_eq_subst
% 4.71/5.02 thf(fact_687_ord__less__eq__subst,axiom,
% 4.71/5.02 ! [A: real,B: real,F: real > rat,C: rat] :
% 4.71/5.02 ( ( ord_less_real @ A @ B )
% 4.71/5.02 => ( ( ( F @ B )
% 4.71/5.02 = C )
% 4.71/5.02 => ( ! [X4: real,Y3: real] :
% 4.71/5.02 ( ( ord_less_real @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % ord_less_eq_subst
% 4.71/5.02 thf(fact_688_ord__less__eq__subst,axiom,
% 4.71/5.02 ! [A: real,B: real,F: real > num,C: num] :
% 4.71/5.02 ( ( ord_less_real @ A @ B )
% 4.71/5.02 => ( ( ( F @ B )
% 4.71/5.02 = C )
% 4.71/5.02 => ( ! [X4: real,Y3: real] :
% 4.71/5.02 ( ( ord_less_real @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % ord_less_eq_subst
% 4.71/5.02 thf(fact_689_ord__less__eq__subst,axiom,
% 4.71/5.02 ! [A: real,B: real,F: real > nat,C: nat] :
% 4.71/5.02 ( ( ord_less_real @ A @ B )
% 4.71/5.02 => ( ( ( F @ B )
% 4.71/5.02 = C )
% 4.71/5.02 => ( ! [X4: real,Y3: real] :
% 4.71/5.02 ( ( ord_less_real @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % ord_less_eq_subst
% 4.71/5.02 thf(fact_690_ord__less__eq__subst,axiom,
% 4.71/5.02 ! [A: real,B: real,F: real > int,C: int] :
% 4.71/5.02 ( ( ord_less_real @ A @ B )
% 4.71/5.02 => ( ( ( F @ B )
% 4.71/5.02 = C )
% 4.71/5.02 => ( ! [X4: real,Y3: real] :
% 4.71/5.02 ( ( ord_less_real @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % ord_less_eq_subst
% 4.71/5.02 thf(fact_691_ord__less__eq__subst,axiom,
% 4.71/5.02 ! [A: rat,B: rat,F: rat > real,C: real] :
% 4.71/5.02 ( ( ord_less_rat @ A @ B )
% 4.71/5.02 => ( ( ( F @ B )
% 4.71/5.02 = C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % ord_less_eq_subst
% 4.71/5.02 thf(fact_692_ord__less__eq__subst,axiom,
% 4.71/5.02 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 4.71/5.02 ( ( ord_less_rat @ A @ B )
% 4.71/5.02 => ( ( ( F @ B )
% 4.71/5.02 = C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % ord_less_eq_subst
% 4.71/5.02 thf(fact_693_ord__less__eq__subst,axiom,
% 4.71/5.02 ! [A: rat,B: rat,F: rat > num,C: num] :
% 4.71/5.02 ( ( ord_less_rat @ A @ B )
% 4.71/5.02 => ( ( ( F @ B )
% 4.71/5.02 = C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % ord_less_eq_subst
% 4.71/5.02 thf(fact_694_ord__less__eq__subst,axiom,
% 4.71/5.02 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 4.71/5.02 ( ( ord_less_rat @ A @ B )
% 4.71/5.02 => ( ( ( F @ B )
% 4.71/5.02 = C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % ord_less_eq_subst
% 4.71/5.02 thf(fact_695_ord__less__eq__subst,axiom,
% 4.71/5.02 ! [A: rat,B: rat,F: rat > int,C: int] :
% 4.71/5.02 ( ( ord_less_rat @ A @ B )
% 4.71/5.02 => ( ( ( F @ B )
% 4.71/5.02 = C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % ord_less_eq_subst
% 4.71/5.02 thf(fact_696_order__less__irrefl,axiom,
% 4.71/5.02 ! [X: real] :
% 4.71/5.02 ~ ( ord_less_real @ X @ X ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_irrefl
% 4.71/5.02 thf(fact_697_order__less__irrefl,axiom,
% 4.71/5.02 ! [X: rat] :
% 4.71/5.02 ~ ( ord_less_rat @ X @ X ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_irrefl
% 4.71/5.02 thf(fact_698_order__less__irrefl,axiom,
% 4.71/5.02 ! [X: num] :
% 4.71/5.02 ~ ( ord_less_num @ X @ X ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_irrefl
% 4.71/5.02 thf(fact_699_order__less__irrefl,axiom,
% 4.71/5.02 ! [X: nat] :
% 4.71/5.02 ~ ( ord_less_nat @ X @ X ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_irrefl
% 4.71/5.02 thf(fact_700_order__less__irrefl,axiom,
% 4.71/5.02 ! [X: int] :
% 4.71/5.02 ~ ( ord_less_int @ X @ X ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_irrefl
% 4.71/5.02 thf(fact_701_order__less__subst1,axiom,
% 4.71/5.02 ! [A: real,F: real > real,B: real,C: real] :
% 4.71/5.02 ( ( ord_less_real @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_real @ B @ C )
% 4.71/5.02 => ( ! [X4: real,Y3: real] :
% 4.71/5.02 ( ( ord_less_real @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_subst1
% 4.71/5.02 thf(fact_702_order__less__subst1,axiom,
% 4.71/5.02 ! [A: real,F: rat > real,B: rat,C: rat] :
% 4.71/5.02 ( ( ord_less_real @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_rat @ B @ C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_subst1
% 4.71/5.02 thf(fact_703_order__less__subst1,axiom,
% 4.71/5.02 ! [A: real,F: num > real,B: num,C: num] :
% 4.71/5.02 ( ( ord_less_real @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_num @ B @ C )
% 4.71/5.02 => ( ! [X4: num,Y3: num] :
% 4.71/5.02 ( ( ord_less_num @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_subst1
% 4.71/5.02 thf(fact_704_order__less__subst1,axiom,
% 4.71/5.02 ! [A: real,F: nat > real,B: nat,C: nat] :
% 4.71/5.02 ( ( ord_less_real @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_nat @ B @ C )
% 4.71/5.02 => ( ! [X4: nat,Y3: nat] :
% 4.71/5.02 ( ( ord_less_nat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_subst1
% 4.71/5.02 thf(fact_705_order__less__subst1,axiom,
% 4.71/5.02 ! [A: real,F: int > real,B: int,C: int] :
% 4.71/5.02 ( ( ord_less_real @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_int @ B @ C )
% 4.71/5.02 => ( ! [X4: int,Y3: int] :
% 4.71/5.02 ( ( ord_less_int @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_subst1
% 4.71/5.02 thf(fact_706_order__less__subst1,axiom,
% 4.71/5.02 ! [A: rat,F: real > rat,B: real,C: real] :
% 4.71/5.02 ( ( ord_less_rat @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_real @ B @ C )
% 4.71/5.02 => ( ! [X4: real,Y3: real] :
% 4.71/5.02 ( ( ord_less_real @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_subst1
% 4.71/5.02 thf(fact_707_order__less__subst1,axiom,
% 4.71/5.02 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 4.71/5.02 ( ( ord_less_rat @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_rat @ B @ C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_subst1
% 4.71/5.02 thf(fact_708_order__less__subst1,axiom,
% 4.71/5.02 ! [A: rat,F: num > rat,B: num,C: num] :
% 4.71/5.02 ( ( ord_less_rat @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_num @ B @ C )
% 4.71/5.02 => ( ! [X4: num,Y3: num] :
% 4.71/5.02 ( ( ord_less_num @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_subst1
% 4.71/5.02 thf(fact_709_order__less__subst1,axiom,
% 4.71/5.02 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 4.71/5.02 ( ( ord_less_rat @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_nat @ B @ C )
% 4.71/5.02 => ( ! [X4: nat,Y3: nat] :
% 4.71/5.02 ( ( ord_less_nat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_subst1
% 4.71/5.02 thf(fact_710_order__less__subst1,axiom,
% 4.71/5.02 ! [A: rat,F: int > rat,B: int,C: int] :
% 4.71/5.02 ( ( ord_less_rat @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_int @ B @ C )
% 4.71/5.02 => ( ! [X4: int,Y3: int] :
% 4.71/5.02 ( ( ord_less_int @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_subst1
% 4.71/5.02 thf(fact_711_order__less__subst2,axiom,
% 4.71/5.02 ! [A: real,B: real,F: real > real,C: real] :
% 4.71/5.02 ( ( ord_less_real @ A @ B )
% 4.71/5.02 => ( ( ord_less_real @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: real,Y3: real] :
% 4.71/5.02 ( ( ord_less_real @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_subst2
% 4.71/5.02 thf(fact_712_order__less__subst2,axiom,
% 4.71/5.02 ! [A: real,B: real,F: real > rat,C: rat] :
% 4.71/5.02 ( ( ord_less_real @ A @ B )
% 4.71/5.02 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: real,Y3: real] :
% 4.71/5.02 ( ( ord_less_real @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_subst2
% 4.71/5.02 thf(fact_713_order__less__subst2,axiom,
% 4.71/5.02 ! [A: real,B: real,F: real > num,C: num] :
% 4.71/5.02 ( ( ord_less_real @ A @ B )
% 4.71/5.02 => ( ( ord_less_num @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: real,Y3: real] :
% 4.71/5.02 ( ( ord_less_real @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_subst2
% 4.71/5.02 thf(fact_714_order__less__subst2,axiom,
% 4.71/5.02 ! [A: real,B: real,F: real > nat,C: nat] :
% 4.71/5.02 ( ( ord_less_real @ A @ B )
% 4.71/5.02 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: real,Y3: real] :
% 4.71/5.02 ( ( ord_less_real @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_subst2
% 4.71/5.02 thf(fact_715_order__less__subst2,axiom,
% 4.71/5.02 ! [A: real,B: real,F: real > int,C: int] :
% 4.71/5.02 ( ( ord_less_real @ A @ B )
% 4.71/5.02 => ( ( ord_less_int @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: real,Y3: real] :
% 4.71/5.02 ( ( ord_less_real @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_subst2
% 4.71/5.02 thf(fact_716_order__less__subst2,axiom,
% 4.71/5.02 ! [A: rat,B: rat,F: rat > real,C: real] :
% 4.71/5.02 ( ( ord_less_rat @ A @ B )
% 4.71/5.02 => ( ( ord_less_real @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_subst2
% 4.71/5.02 thf(fact_717_order__less__subst2,axiom,
% 4.71/5.02 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 4.71/5.02 ( ( ord_less_rat @ A @ B )
% 4.71/5.02 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_subst2
% 4.71/5.02 thf(fact_718_order__less__subst2,axiom,
% 4.71/5.02 ! [A: rat,B: rat,F: rat > num,C: num] :
% 4.71/5.02 ( ( ord_less_rat @ A @ B )
% 4.71/5.02 => ( ( ord_less_num @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_subst2
% 4.71/5.02 thf(fact_719_order__less__subst2,axiom,
% 4.71/5.02 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 4.71/5.02 ( ( ord_less_rat @ A @ B )
% 4.71/5.02 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_subst2
% 4.71/5.02 thf(fact_720_order__less__subst2,axiom,
% 4.71/5.02 ! [A: rat,B: rat,F: rat > int,C: int] :
% 4.71/5.02 ( ( ord_less_rat @ A @ B )
% 4.71/5.02 => ( ( ord_less_int @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_subst2
% 4.71/5.02 thf(fact_721_order__less__not__sym,axiom,
% 4.71/5.02 ! [X: real,Y: real] :
% 4.71/5.02 ( ( ord_less_real @ X @ Y )
% 4.71/5.02 => ~ ( ord_less_real @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_not_sym
% 4.71/5.02 thf(fact_722_order__less__not__sym,axiom,
% 4.71/5.02 ! [X: rat,Y: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X @ Y )
% 4.71/5.02 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_not_sym
% 4.71/5.02 thf(fact_723_order__less__not__sym,axiom,
% 4.71/5.02 ! [X: num,Y: num] :
% 4.71/5.02 ( ( ord_less_num @ X @ Y )
% 4.71/5.02 => ~ ( ord_less_num @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_not_sym
% 4.71/5.02 thf(fact_724_order__less__not__sym,axiom,
% 4.71/5.02 ! [X: nat,Y: nat] :
% 4.71/5.02 ( ( ord_less_nat @ X @ Y )
% 4.71/5.02 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_not_sym
% 4.71/5.02 thf(fact_725_order__less__not__sym,axiom,
% 4.71/5.02 ! [X: int,Y: int] :
% 4.71/5.02 ( ( ord_less_int @ X @ Y )
% 4.71/5.02 => ~ ( ord_less_int @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_not_sym
% 4.71/5.02 thf(fact_726_order__less__imp__triv,axiom,
% 4.71/5.02 ! [X: real,Y: real,P: $o] :
% 4.71/5.02 ( ( ord_less_real @ X @ Y )
% 4.71/5.02 => ( ( ord_less_real @ Y @ X )
% 4.71/5.02 => P ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_imp_triv
% 4.71/5.02 thf(fact_727_order__less__imp__triv,axiom,
% 4.71/5.02 ! [X: rat,Y: rat,P: $o] :
% 4.71/5.02 ( ( ord_less_rat @ X @ Y )
% 4.71/5.02 => ( ( ord_less_rat @ Y @ X )
% 4.71/5.02 => P ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_imp_triv
% 4.71/5.02 thf(fact_728_order__less__imp__triv,axiom,
% 4.71/5.02 ! [X: num,Y: num,P: $o] :
% 4.71/5.02 ( ( ord_less_num @ X @ Y )
% 4.71/5.02 => ( ( ord_less_num @ Y @ X )
% 4.71/5.02 => P ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_imp_triv
% 4.71/5.02 thf(fact_729_order__less__imp__triv,axiom,
% 4.71/5.02 ! [X: nat,Y: nat,P: $o] :
% 4.71/5.02 ( ( ord_less_nat @ X @ Y )
% 4.71/5.02 => ( ( ord_less_nat @ Y @ X )
% 4.71/5.02 => P ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_imp_triv
% 4.71/5.02 thf(fact_730_order__less__imp__triv,axiom,
% 4.71/5.02 ! [X: int,Y: int,P: $o] :
% 4.71/5.02 ( ( ord_less_int @ X @ Y )
% 4.71/5.02 => ( ( ord_less_int @ Y @ X )
% 4.71/5.02 => P ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_imp_triv
% 4.71/5.02 thf(fact_731_linorder__less__linear,axiom,
% 4.71/5.02 ! [X: real,Y: real] :
% 4.71/5.02 ( ( ord_less_real @ X @ Y )
% 4.71/5.02 | ( X = Y )
% 4.71/5.02 | ( ord_less_real @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % linorder_less_linear
% 4.71/5.02 thf(fact_732_linorder__less__linear,axiom,
% 4.71/5.02 ! [X: rat,Y: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X @ Y )
% 4.71/5.02 | ( X = Y )
% 4.71/5.02 | ( ord_less_rat @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % linorder_less_linear
% 4.71/5.02 thf(fact_733_linorder__less__linear,axiom,
% 4.71/5.02 ! [X: num,Y: num] :
% 4.71/5.02 ( ( ord_less_num @ X @ Y )
% 4.71/5.02 | ( X = Y )
% 4.71/5.02 | ( ord_less_num @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % linorder_less_linear
% 4.71/5.02 thf(fact_734_linorder__less__linear,axiom,
% 4.71/5.02 ! [X: nat,Y: nat] :
% 4.71/5.02 ( ( ord_less_nat @ X @ Y )
% 4.71/5.02 | ( X = Y )
% 4.71/5.02 | ( ord_less_nat @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % linorder_less_linear
% 4.71/5.02 thf(fact_735_linorder__less__linear,axiom,
% 4.71/5.02 ! [X: int,Y: int] :
% 4.71/5.02 ( ( ord_less_int @ X @ Y )
% 4.71/5.02 | ( X = Y )
% 4.71/5.02 | ( ord_less_int @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % linorder_less_linear
% 4.71/5.02 thf(fact_736_order__less__imp__not__eq,axiom,
% 4.71/5.02 ! [X: real,Y: real] :
% 4.71/5.02 ( ( ord_less_real @ X @ Y )
% 4.71/5.02 => ( X != Y ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_imp_not_eq
% 4.71/5.02 thf(fact_737_order__less__imp__not__eq,axiom,
% 4.71/5.02 ! [X: rat,Y: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X @ Y )
% 4.71/5.02 => ( X != Y ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_imp_not_eq
% 4.71/5.02 thf(fact_738_order__less__imp__not__eq,axiom,
% 4.71/5.02 ! [X: num,Y: num] :
% 4.71/5.02 ( ( ord_less_num @ X @ Y )
% 4.71/5.02 => ( X != Y ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_imp_not_eq
% 4.71/5.02 thf(fact_739_order__less__imp__not__eq,axiom,
% 4.71/5.02 ! [X: nat,Y: nat] :
% 4.71/5.02 ( ( ord_less_nat @ X @ Y )
% 4.71/5.02 => ( X != Y ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_imp_not_eq
% 4.71/5.02 thf(fact_740_order__less__imp__not__eq,axiom,
% 4.71/5.02 ! [X: int,Y: int] :
% 4.71/5.02 ( ( ord_less_int @ X @ Y )
% 4.71/5.02 => ( X != Y ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_imp_not_eq
% 4.71/5.02 thf(fact_741_order__less__imp__not__eq2,axiom,
% 4.71/5.02 ! [X: real,Y: real] :
% 4.71/5.02 ( ( ord_less_real @ X @ Y )
% 4.71/5.02 => ( Y != X ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_imp_not_eq2
% 4.71/5.02 thf(fact_742_order__less__imp__not__eq2,axiom,
% 4.71/5.02 ! [X: rat,Y: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X @ Y )
% 4.71/5.02 => ( Y != X ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_imp_not_eq2
% 4.71/5.02 thf(fact_743_order__less__imp__not__eq2,axiom,
% 4.71/5.02 ! [X: num,Y: num] :
% 4.71/5.02 ( ( ord_less_num @ X @ Y )
% 4.71/5.02 => ( Y != X ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_imp_not_eq2
% 4.71/5.02 thf(fact_744_order__less__imp__not__eq2,axiom,
% 4.71/5.02 ! [X: nat,Y: nat] :
% 4.71/5.02 ( ( ord_less_nat @ X @ Y )
% 4.71/5.02 => ( Y != X ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_imp_not_eq2
% 4.71/5.02 thf(fact_745_order__less__imp__not__eq2,axiom,
% 4.71/5.02 ! [X: int,Y: int] :
% 4.71/5.02 ( ( ord_less_int @ X @ Y )
% 4.71/5.02 => ( Y != X ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_imp_not_eq2
% 4.71/5.02 thf(fact_746_order__less__imp__not__less,axiom,
% 4.71/5.02 ! [X: real,Y: real] :
% 4.71/5.02 ( ( ord_less_real @ X @ Y )
% 4.71/5.02 => ~ ( ord_less_real @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_imp_not_less
% 4.71/5.02 thf(fact_747_order__less__imp__not__less,axiom,
% 4.71/5.02 ! [X: rat,Y: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X @ Y )
% 4.71/5.02 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_imp_not_less
% 4.71/5.02 thf(fact_748_order__less__imp__not__less,axiom,
% 4.71/5.02 ! [X: num,Y: num] :
% 4.71/5.02 ( ( ord_less_num @ X @ Y )
% 4.71/5.02 => ~ ( ord_less_num @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_imp_not_less
% 4.71/5.02 thf(fact_749_order__less__imp__not__less,axiom,
% 4.71/5.02 ! [X: nat,Y: nat] :
% 4.71/5.02 ( ( ord_less_nat @ X @ Y )
% 4.71/5.02 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_imp_not_less
% 4.71/5.02 thf(fact_750_order__less__imp__not__less,axiom,
% 4.71/5.02 ! [X: int,Y: int] :
% 4.71/5.02 ( ( ord_less_int @ X @ Y )
% 4.71/5.02 => ~ ( ord_less_int @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_imp_not_less
% 4.71/5.02 thf(fact_751_leD,axiom,
% 4.71/5.02 ! [Y: real,X: real] :
% 4.71/5.02 ( ( ord_less_eq_real @ Y @ X )
% 4.71/5.02 => ~ ( ord_less_real @ X @ Y ) ) ).
% 4.71/5.02
% 4.71/5.02 % leD
% 4.71/5.02 thf(fact_752_leD,axiom,
% 4.71/5.02 ! [Y: set_int,X: set_int] :
% 4.71/5.02 ( ( ord_less_eq_set_int @ Y @ X )
% 4.71/5.02 => ~ ( ord_less_set_int @ X @ Y ) ) ).
% 4.71/5.02
% 4.71/5.02 % leD
% 4.71/5.02 thf(fact_753_leD,axiom,
% 4.71/5.02 ! [Y: rat,X: rat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ Y @ X )
% 4.71/5.02 => ~ ( ord_less_rat @ X @ Y ) ) ).
% 4.71/5.02
% 4.71/5.02 % leD
% 4.71/5.02 thf(fact_754_leD,axiom,
% 4.71/5.02 ! [Y: num,X: num] :
% 4.71/5.02 ( ( ord_less_eq_num @ Y @ X )
% 4.71/5.02 => ~ ( ord_less_num @ X @ Y ) ) ).
% 4.71/5.02
% 4.71/5.02 % leD
% 4.71/5.02 thf(fact_755_leD,axiom,
% 4.71/5.02 ! [Y: nat,X: nat] :
% 4.71/5.02 ( ( ord_less_eq_nat @ Y @ X )
% 4.71/5.02 => ~ ( ord_less_nat @ X @ Y ) ) ).
% 4.71/5.02
% 4.71/5.02 % leD
% 4.71/5.02 thf(fact_756_leD,axiom,
% 4.71/5.02 ! [Y: int,X: int] :
% 4.71/5.02 ( ( ord_less_eq_int @ Y @ X )
% 4.71/5.02 => ~ ( ord_less_int @ X @ Y ) ) ).
% 4.71/5.02
% 4.71/5.02 % leD
% 4.71/5.02 thf(fact_757_leI,axiom,
% 4.71/5.02 ! [X: real,Y: real] :
% 4.71/5.02 ( ~ ( ord_less_real @ X @ Y )
% 4.71/5.02 => ( ord_less_eq_real @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % leI
% 4.71/5.02 thf(fact_758_leI,axiom,
% 4.71/5.02 ! [X: rat,Y: rat] :
% 4.71/5.02 ( ~ ( ord_less_rat @ X @ Y )
% 4.71/5.02 => ( ord_less_eq_rat @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % leI
% 4.71/5.02 thf(fact_759_leI,axiom,
% 4.71/5.02 ! [X: num,Y: num] :
% 4.71/5.02 ( ~ ( ord_less_num @ X @ Y )
% 4.71/5.02 => ( ord_less_eq_num @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % leI
% 4.71/5.02 thf(fact_760_leI,axiom,
% 4.71/5.02 ! [X: nat,Y: nat] :
% 4.71/5.02 ( ~ ( ord_less_nat @ X @ Y )
% 4.71/5.02 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % leI
% 4.71/5.02 thf(fact_761_leI,axiom,
% 4.71/5.02 ! [X: int,Y: int] :
% 4.71/5.02 ( ~ ( ord_less_int @ X @ Y )
% 4.71/5.02 => ( ord_less_eq_int @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % leI
% 4.71/5.02 thf(fact_762_nless__le,axiom,
% 4.71/5.02 ! [A: real,B: real] :
% 4.71/5.02 ( ( ~ ( ord_less_real @ A @ B ) )
% 4.71/5.02 = ( ~ ( ord_less_eq_real @ A @ B )
% 4.71/5.02 | ( A = B ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % nless_le
% 4.71/5.02 thf(fact_763_nless__le,axiom,
% 4.71/5.02 ! [A: set_int,B: set_int] :
% 4.71/5.02 ( ( ~ ( ord_less_set_int @ A @ B ) )
% 4.71/5.02 = ( ~ ( ord_less_eq_set_int @ A @ B )
% 4.71/5.02 | ( A = B ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % nless_le
% 4.71/5.02 thf(fact_764_nless__le,axiom,
% 4.71/5.02 ! [A: rat,B: rat] :
% 4.71/5.02 ( ( ~ ( ord_less_rat @ A @ B ) )
% 4.71/5.02 = ( ~ ( ord_less_eq_rat @ A @ B )
% 4.71/5.02 | ( A = B ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % nless_le
% 4.71/5.02 thf(fact_765_nless__le,axiom,
% 4.71/5.02 ! [A: num,B: num] :
% 4.71/5.02 ( ( ~ ( ord_less_num @ A @ B ) )
% 4.71/5.02 = ( ~ ( ord_less_eq_num @ A @ B )
% 4.71/5.02 | ( A = B ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % nless_le
% 4.71/5.02 thf(fact_766_nless__le,axiom,
% 4.71/5.02 ! [A: nat,B: nat] :
% 4.71/5.02 ( ( ~ ( ord_less_nat @ A @ B ) )
% 4.71/5.02 = ( ~ ( ord_less_eq_nat @ A @ B )
% 4.71/5.02 | ( A = B ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % nless_le
% 4.71/5.02 thf(fact_767_nless__le,axiom,
% 4.71/5.02 ! [A: int,B: int] :
% 4.71/5.02 ( ( ~ ( ord_less_int @ A @ B ) )
% 4.71/5.02 = ( ~ ( ord_less_eq_int @ A @ B )
% 4.71/5.02 | ( A = B ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % nless_le
% 4.71/5.02 thf(fact_768_antisym__conv1,axiom,
% 4.71/5.02 ! [X: real,Y: real] :
% 4.71/5.02 ( ~ ( ord_less_real @ X @ Y )
% 4.71/5.02 => ( ( ord_less_eq_real @ X @ Y )
% 4.71/5.02 = ( X = Y ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % antisym_conv1
% 4.71/5.02 thf(fact_769_antisym__conv1,axiom,
% 4.71/5.02 ! [X: set_int,Y: set_int] :
% 4.71/5.02 ( ~ ( ord_less_set_int @ X @ Y )
% 4.71/5.02 => ( ( ord_less_eq_set_int @ X @ Y )
% 4.71/5.02 = ( X = Y ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % antisym_conv1
% 4.71/5.02 thf(fact_770_antisym__conv1,axiom,
% 4.71/5.02 ! [X: rat,Y: rat] :
% 4.71/5.02 ( ~ ( ord_less_rat @ X @ Y )
% 4.71/5.02 => ( ( ord_less_eq_rat @ X @ Y )
% 4.71/5.02 = ( X = Y ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % antisym_conv1
% 4.71/5.02 thf(fact_771_antisym__conv1,axiom,
% 4.71/5.02 ! [X: num,Y: num] :
% 4.71/5.02 ( ~ ( ord_less_num @ X @ Y )
% 4.71/5.02 => ( ( ord_less_eq_num @ X @ Y )
% 4.71/5.02 = ( X = Y ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % antisym_conv1
% 4.71/5.02 thf(fact_772_antisym__conv1,axiom,
% 4.71/5.02 ! [X: nat,Y: nat] :
% 4.71/5.02 ( ~ ( ord_less_nat @ X @ Y )
% 4.71/5.02 => ( ( ord_less_eq_nat @ X @ Y )
% 4.71/5.02 = ( X = Y ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % antisym_conv1
% 4.71/5.02 thf(fact_773_antisym__conv1,axiom,
% 4.71/5.02 ! [X: int,Y: int] :
% 4.71/5.02 ( ~ ( ord_less_int @ X @ Y )
% 4.71/5.02 => ( ( ord_less_eq_int @ X @ Y )
% 4.71/5.02 = ( X = Y ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % antisym_conv1
% 4.71/5.02 thf(fact_774_antisym__conv2,axiom,
% 4.71/5.02 ! [X: real,Y: real] :
% 4.71/5.02 ( ( ord_less_eq_real @ X @ Y )
% 4.71/5.02 => ( ( ~ ( ord_less_real @ X @ Y ) )
% 4.71/5.02 = ( X = Y ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % antisym_conv2
% 4.71/5.02 thf(fact_775_antisym__conv2,axiom,
% 4.71/5.02 ! [X: set_int,Y: set_int] :
% 4.71/5.02 ( ( ord_less_eq_set_int @ X @ Y )
% 4.71/5.02 => ( ( ~ ( ord_less_set_int @ X @ Y ) )
% 4.71/5.02 = ( X = Y ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % antisym_conv2
% 4.71/5.02 thf(fact_776_antisym__conv2,axiom,
% 4.71/5.02 ! [X: rat,Y: rat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ X @ Y )
% 4.71/5.02 => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 4.71/5.02 = ( X = Y ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % antisym_conv2
% 4.71/5.02 thf(fact_777_antisym__conv2,axiom,
% 4.71/5.02 ! [X: num,Y: num] :
% 4.71/5.02 ( ( ord_less_eq_num @ X @ Y )
% 4.71/5.02 => ( ( ~ ( ord_less_num @ X @ Y ) )
% 4.71/5.02 = ( X = Y ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % antisym_conv2
% 4.71/5.02 thf(fact_778_antisym__conv2,axiom,
% 4.71/5.02 ! [X: nat,Y: nat] :
% 4.71/5.02 ( ( ord_less_eq_nat @ X @ Y )
% 4.71/5.02 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 4.71/5.02 = ( X = Y ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % antisym_conv2
% 4.71/5.02 thf(fact_779_antisym__conv2,axiom,
% 4.71/5.02 ! [X: int,Y: int] :
% 4.71/5.02 ( ( ord_less_eq_int @ X @ Y )
% 4.71/5.02 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 4.71/5.02 = ( X = Y ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % antisym_conv2
% 4.71/5.02 thf(fact_780_dense__ge,axiom,
% 4.71/5.02 ! [Z: real,Y: real] :
% 4.71/5.02 ( ! [X4: real] :
% 4.71/5.02 ( ( ord_less_real @ Z @ X4 )
% 4.71/5.02 => ( ord_less_eq_real @ Y @ X4 ) )
% 4.71/5.02 => ( ord_less_eq_real @ Y @ Z ) ) ).
% 4.71/5.02
% 4.71/5.02 % dense_ge
% 4.71/5.02 thf(fact_781_dense__ge,axiom,
% 4.71/5.02 ! [Z: rat,Y: rat] :
% 4.71/5.02 ( ! [X4: rat] :
% 4.71/5.02 ( ( ord_less_rat @ Z @ X4 )
% 4.71/5.02 => ( ord_less_eq_rat @ Y @ X4 ) )
% 4.71/5.02 => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 4.71/5.02
% 4.71/5.02 % dense_ge
% 4.71/5.02 thf(fact_782_dense__le,axiom,
% 4.71/5.02 ! [Y: real,Z: real] :
% 4.71/5.02 ( ! [X4: real] :
% 4.71/5.02 ( ( ord_less_real @ X4 @ Y )
% 4.71/5.02 => ( ord_less_eq_real @ X4 @ Z ) )
% 4.71/5.02 => ( ord_less_eq_real @ Y @ Z ) ) ).
% 4.71/5.02
% 4.71/5.02 % dense_le
% 4.71/5.02 thf(fact_783_dense__le,axiom,
% 4.71/5.02 ! [Y: rat,Z: rat] :
% 4.71/5.02 ( ! [X4: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X4 @ Y )
% 4.71/5.02 => ( ord_less_eq_rat @ X4 @ Z ) )
% 4.71/5.02 => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 4.71/5.02
% 4.71/5.02 % dense_le
% 4.71/5.02 thf(fact_784_less__le__not__le,axiom,
% 4.71/5.02 ( ord_less_real
% 4.71/5.02 = ( ^ [X3: real,Y2: real] :
% 4.71/5.02 ( ( ord_less_eq_real @ X3 @ Y2 )
% 4.71/5.02 & ~ ( ord_less_eq_real @ Y2 @ X3 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % less_le_not_le
% 4.71/5.02 thf(fact_785_less__le__not__le,axiom,
% 4.71/5.02 ( ord_less_set_int
% 4.71/5.02 = ( ^ [X3: set_int,Y2: set_int] :
% 4.71/5.02 ( ( ord_less_eq_set_int @ X3 @ Y2 )
% 4.71/5.02 & ~ ( ord_less_eq_set_int @ Y2 @ X3 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % less_le_not_le
% 4.71/5.02 thf(fact_786_less__le__not__le,axiom,
% 4.71/5.02 ( ord_less_rat
% 4.71/5.02 = ( ^ [X3: rat,Y2: rat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 4.71/5.02 & ~ ( ord_less_eq_rat @ Y2 @ X3 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % less_le_not_le
% 4.71/5.02 thf(fact_787_less__le__not__le,axiom,
% 4.71/5.02 ( ord_less_num
% 4.71/5.02 = ( ^ [X3: num,Y2: num] :
% 4.71/5.02 ( ( ord_less_eq_num @ X3 @ Y2 )
% 4.71/5.02 & ~ ( ord_less_eq_num @ Y2 @ X3 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % less_le_not_le
% 4.71/5.02 thf(fact_788_less__le__not__le,axiom,
% 4.71/5.02 ( ord_less_nat
% 4.71/5.02 = ( ^ [X3: nat,Y2: nat] :
% 4.71/5.02 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 4.71/5.02 & ~ ( ord_less_eq_nat @ Y2 @ X3 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % less_le_not_le
% 4.71/5.02 thf(fact_789_less__le__not__le,axiom,
% 4.71/5.02 ( ord_less_int
% 4.71/5.02 = ( ^ [X3: int,Y2: int] :
% 4.71/5.02 ( ( ord_less_eq_int @ X3 @ Y2 )
% 4.71/5.02 & ~ ( ord_less_eq_int @ Y2 @ X3 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % less_le_not_le
% 4.71/5.02 thf(fact_790_not__le__imp__less,axiom,
% 4.71/5.02 ! [Y: real,X: real] :
% 4.71/5.02 ( ~ ( ord_less_eq_real @ Y @ X )
% 4.71/5.02 => ( ord_less_real @ X @ Y ) ) ).
% 4.71/5.02
% 4.71/5.02 % not_le_imp_less
% 4.71/5.02 thf(fact_791_not__le__imp__less,axiom,
% 4.71/5.02 ! [Y: rat,X: rat] :
% 4.71/5.02 ( ~ ( ord_less_eq_rat @ Y @ X )
% 4.71/5.02 => ( ord_less_rat @ X @ Y ) ) ).
% 4.71/5.02
% 4.71/5.02 % not_le_imp_less
% 4.71/5.02 thf(fact_792_not__le__imp__less,axiom,
% 4.71/5.02 ! [Y: num,X: num] :
% 4.71/5.02 ( ~ ( ord_less_eq_num @ Y @ X )
% 4.71/5.02 => ( ord_less_num @ X @ Y ) ) ).
% 4.71/5.02
% 4.71/5.02 % not_le_imp_less
% 4.71/5.02 thf(fact_793_not__le__imp__less,axiom,
% 4.71/5.02 ! [Y: nat,X: nat] :
% 4.71/5.02 ( ~ ( ord_less_eq_nat @ Y @ X )
% 4.71/5.02 => ( ord_less_nat @ X @ Y ) ) ).
% 4.71/5.02
% 4.71/5.02 % not_le_imp_less
% 4.71/5.02 thf(fact_794_not__le__imp__less,axiom,
% 4.71/5.02 ! [Y: int,X: int] :
% 4.71/5.02 ( ~ ( ord_less_eq_int @ Y @ X )
% 4.71/5.02 => ( ord_less_int @ X @ Y ) ) ).
% 4.71/5.02
% 4.71/5.02 % not_le_imp_less
% 4.71/5.02 thf(fact_795_order_Oorder__iff__strict,axiom,
% 4.71/5.02 ( ord_less_eq_real
% 4.71/5.02 = ( ^ [A4: real,B4: real] :
% 4.71/5.02 ( ( ord_less_real @ A4 @ B4 )
% 4.71/5.02 | ( A4 = B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.order_iff_strict
% 4.71/5.02 thf(fact_796_order_Oorder__iff__strict,axiom,
% 4.71/5.02 ( ord_less_eq_set_int
% 4.71/5.02 = ( ^ [A4: set_int,B4: set_int] :
% 4.71/5.02 ( ( ord_less_set_int @ A4 @ B4 )
% 4.71/5.02 | ( A4 = B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.order_iff_strict
% 4.71/5.02 thf(fact_797_order_Oorder__iff__strict,axiom,
% 4.71/5.02 ( ord_less_eq_rat
% 4.71/5.02 = ( ^ [A4: rat,B4: rat] :
% 4.71/5.02 ( ( ord_less_rat @ A4 @ B4 )
% 4.71/5.02 | ( A4 = B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.order_iff_strict
% 4.71/5.02 thf(fact_798_order_Oorder__iff__strict,axiom,
% 4.71/5.02 ( ord_less_eq_num
% 4.71/5.02 = ( ^ [A4: num,B4: num] :
% 4.71/5.02 ( ( ord_less_num @ A4 @ B4 )
% 4.71/5.02 | ( A4 = B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.order_iff_strict
% 4.71/5.02 thf(fact_799_order_Oorder__iff__strict,axiom,
% 4.71/5.02 ( ord_less_eq_nat
% 4.71/5.02 = ( ^ [A4: nat,B4: nat] :
% 4.71/5.02 ( ( ord_less_nat @ A4 @ B4 )
% 4.71/5.02 | ( A4 = B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.order_iff_strict
% 4.71/5.02 thf(fact_800_order_Oorder__iff__strict,axiom,
% 4.71/5.02 ( ord_less_eq_int
% 4.71/5.02 = ( ^ [A4: int,B4: int] :
% 4.71/5.02 ( ( ord_less_int @ A4 @ B4 )
% 4.71/5.02 | ( A4 = B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.order_iff_strict
% 4.71/5.02 thf(fact_801_order_Ostrict__iff__order,axiom,
% 4.71/5.02 ( ord_less_real
% 4.71/5.02 = ( ^ [A4: real,B4: real] :
% 4.71/5.02 ( ( ord_less_eq_real @ A4 @ B4 )
% 4.71/5.02 & ( A4 != B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_iff_order
% 4.71/5.02 thf(fact_802_order_Ostrict__iff__order,axiom,
% 4.71/5.02 ( ord_less_set_int
% 4.71/5.02 = ( ^ [A4: set_int,B4: set_int] :
% 4.71/5.02 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 4.71/5.02 & ( A4 != B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_iff_order
% 4.71/5.02 thf(fact_803_order_Ostrict__iff__order,axiom,
% 4.71/5.02 ( ord_less_rat
% 4.71/5.02 = ( ^ [A4: rat,B4: rat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ A4 @ B4 )
% 4.71/5.02 & ( A4 != B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_iff_order
% 4.71/5.02 thf(fact_804_order_Ostrict__iff__order,axiom,
% 4.71/5.02 ( ord_less_num
% 4.71/5.02 = ( ^ [A4: num,B4: num] :
% 4.71/5.02 ( ( ord_less_eq_num @ A4 @ B4 )
% 4.71/5.02 & ( A4 != B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_iff_order
% 4.71/5.02 thf(fact_805_order_Ostrict__iff__order,axiom,
% 4.71/5.02 ( ord_less_nat
% 4.71/5.02 = ( ^ [A4: nat,B4: nat] :
% 4.71/5.02 ( ( ord_less_eq_nat @ A4 @ B4 )
% 4.71/5.02 & ( A4 != B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_iff_order
% 4.71/5.02 thf(fact_806_order_Ostrict__iff__order,axiom,
% 4.71/5.02 ( ord_less_int
% 4.71/5.02 = ( ^ [A4: int,B4: int] :
% 4.71/5.02 ( ( ord_less_eq_int @ A4 @ B4 )
% 4.71/5.02 & ( A4 != B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_iff_order
% 4.71/5.02 thf(fact_807_order_Ostrict__trans1,axiom,
% 4.71/5.02 ! [A: real,B: real,C: real] :
% 4.71/5.02 ( ( ord_less_eq_real @ A @ B )
% 4.71/5.02 => ( ( ord_less_real @ B @ C )
% 4.71/5.02 => ( ord_less_real @ A @ C ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_trans1
% 4.71/5.02 thf(fact_808_order_Ostrict__trans1,axiom,
% 4.71/5.02 ! [A: set_int,B: set_int,C: set_int] :
% 4.71/5.02 ( ( ord_less_eq_set_int @ A @ B )
% 4.71/5.02 => ( ( ord_less_set_int @ B @ C )
% 4.71/5.02 => ( ord_less_set_int @ A @ C ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_trans1
% 4.71/5.02 thf(fact_809_order_Ostrict__trans1,axiom,
% 4.71/5.02 ! [A: rat,B: rat,C: rat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.02 => ( ( ord_less_rat @ B @ C )
% 4.71/5.02 => ( ord_less_rat @ A @ C ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_trans1
% 4.71/5.02 thf(fact_810_order_Ostrict__trans1,axiom,
% 4.71/5.02 ! [A: num,B: num,C: num] :
% 4.71/5.02 ( ( ord_less_eq_num @ A @ B )
% 4.71/5.02 => ( ( ord_less_num @ B @ C )
% 4.71/5.02 => ( ord_less_num @ A @ C ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_trans1
% 4.71/5.02 thf(fact_811_order_Ostrict__trans1,axiom,
% 4.71/5.02 ! [A: nat,B: nat,C: nat] :
% 4.71/5.02 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.02 => ( ( ord_less_nat @ B @ C )
% 4.71/5.02 => ( ord_less_nat @ A @ C ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_trans1
% 4.71/5.02 thf(fact_812_order_Ostrict__trans1,axiom,
% 4.71/5.02 ! [A: int,B: int,C: int] :
% 4.71/5.02 ( ( ord_less_eq_int @ A @ B )
% 4.71/5.02 => ( ( ord_less_int @ B @ C )
% 4.71/5.02 => ( ord_less_int @ A @ C ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_trans1
% 4.71/5.02 thf(fact_813_order_Ostrict__trans2,axiom,
% 4.71/5.02 ! [A: real,B: real,C: real] :
% 4.71/5.02 ( ( ord_less_real @ A @ B )
% 4.71/5.02 => ( ( ord_less_eq_real @ B @ C )
% 4.71/5.02 => ( ord_less_real @ A @ C ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_trans2
% 4.71/5.02 thf(fact_814_order_Ostrict__trans2,axiom,
% 4.71/5.02 ! [A: set_int,B: set_int,C: set_int] :
% 4.71/5.02 ( ( ord_less_set_int @ A @ B )
% 4.71/5.02 => ( ( ord_less_eq_set_int @ B @ C )
% 4.71/5.02 => ( ord_less_set_int @ A @ C ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_trans2
% 4.71/5.02 thf(fact_815_order_Ostrict__trans2,axiom,
% 4.71/5.02 ! [A: rat,B: rat,C: rat] :
% 4.71/5.02 ( ( ord_less_rat @ A @ B )
% 4.71/5.02 => ( ( ord_less_eq_rat @ B @ C )
% 4.71/5.02 => ( ord_less_rat @ A @ C ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_trans2
% 4.71/5.02 thf(fact_816_order_Ostrict__trans2,axiom,
% 4.71/5.02 ! [A: num,B: num,C: num] :
% 4.71/5.02 ( ( ord_less_num @ A @ B )
% 4.71/5.02 => ( ( ord_less_eq_num @ B @ C )
% 4.71/5.02 => ( ord_less_num @ A @ C ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_trans2
% 4.71/5.02 thf(fact_817_order_Ostrict__trans2,axiom,
% 4.71/5.02 ! [A: nat,B: nat,C: nat] :
% 4.71/5.02 ( ( ord_less_nat @ A @ B )
% 4.71/5.02 => ( ( ord_less_eq_nat @ B @ C )
% 4.71/5.02 => ( ord_less_nat @ A @ C ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_trans2
% 4.71/5.02 thf(fact_818_order_Ostrict__trans2,axiom,
% 4.71/5.02 ! [A: int,B: int,C: int] :
% 4.71/5.02 ( ( ord_less_int @ A @ B )
% 4.71/5.02 => ( ( ord_less_eq_int @ B @ C )
% 4.71/5.02 => ( ord_less_int @ A @ C ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_trans2
% 4.71/5.02 thf(fact_819_order_Ostrict__iff__not,axiom,
% 4.71/5.02 ( ord_less_real
% 4.71/5.02 = ( ^ [A4: real,B4: real] :
% 4.71/5.02 ( ( ord_less_eq_real @ A4 @ B4 )
% 4.71/5.02 & ~ ( ord_less_eq_real @ B4 @ A4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_iff_not
% 4.71/5.02 thf(fact_820_order_Ostrict__iff__not,axiom,
% 4.71/5.02 ( ord_less_set_int
% 4.71/5.02 = ( ^ [A4: set_int,B4: set_int] :
% 4.71/5.02 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 4.71/5.02 & ~ ( ord_less_eq_set_int @ B4 @ A4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_iff_not
% 4.71/5.02 thf(fact_821_order_Ostrict__iff__not,axiom,
% 4.71/5.02 ( ord_less_rat
% 4.71/5.02 = ( ^ [A4: rat,B4: rat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ A4 @ B4 )
% 4.71/5.02 & ~ ( ord_less_eq_rat @ B4 @ A4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_iff_not
% 4.71/5.02 thf(fact_822_order_Ostrict__iff__not,axiom,
% 4.71/5.02 ( ord_less_num
% 4.71/5.02 = ( ^ [A4: num,B4: num] :
% 4.71/5.02 ( ( ord_less_eq_num @ A4 @ B4 )
% 4.71/5.02 & ~ ( ord_less_eq_num @ B4 @ A4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_iff_not
% 4.71/5.02 thf(fact_823_order_Ostrict__iff__not,axiom,
% 4.71/5.02 ( ord_less_nat
% 4.71/5.02 = ( ^ [A4: nat,B4: nat] :
% 4.71/5.02 ( ( ord_less_eq_nat @ A4 @ B4 )
% 4.71/5.02 & ~ ( ord_less_eq_nat @ B4 @ A4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_iff_not
% 4.71/5.02 thf(fact_824_order_Ostrict__iff__not,axiom,
% 4.71/5.02 ( ord_less_int
% 4.71/5.02 = ( ^ [A4: int,B4: int] :
% 4.71/5.02 ( ( ord_less_eq_int @ A4 @ B4 )
% 4.71/5.02 & ~ ( ord_less_eq_int @ B4 @ A4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_iff_not
% 4.71/5.02 thf(fact_825_dense__ge__bounded,axiom,
% 4.71/5.02 ! [Z: real,X: real,Y: real] :
% 4.71/5.02 ( ( ord_less_real @ Z @ X )
% 4.71/5.02 => ( ! [W: real] :
% 4.71/5.02 ( ( ord_less_real @ Z @ W )
% 4.71/5.02 => ( ( ord_less_real @ W @ X )
% 4.71/5.02 => ( ord_less_eq_real @ Y @ W ) ) )
% 4.71/5.02 => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dense_ge_bounded
% 4.71/5.02 thf(fact_826_dense__ge__bounded,axiom,
% 4.71/5.02 ! [Z: rat,X: rat,Y: rat] :
% 4.71/5.02 ( ( ord_less_rat @ Z @ X )
% 4.71/5.02 => ( ! [W: rat] :
% 4.71/5.02 ( ( ord_less_rat @ Z @ W )
% 4.71/5.02 => ( ( ord_less_rat @ W @ X )
% 4.71/5.02 => ( ord_less_eq_rat @ Y @ W ) ) )
% 4.71/5.02 => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dense_ge_bounded
% 4.71/5.02 thf(fact_827_dense__le__bounded,axiom,
% 4.71/5.02 ! [X: real,Y: real,Z: real] :
% 4.71/5.02 ( ( ord_less_real @ X @ Y )
% 4.71/5.02 => ( ! [W: real] :
% 4.71/5.02 ( ( ord_less_real @ X @ W )
% 4.71/5.02 => ( ( ord_less_real @ W @ Y )
% 4.71/5.02 => ( ord_less_eq_real @ W @ Z ) ) )
% 4.71/5.02 => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dense_le_bounded
% 4.71/5.02 thf(fact_828_dense__le__bounded,axiom,
% 4.71/5.02 ! [X: rat,Y: rat,Z: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X @ Y )
% 4.71/5.02 => ( ! [W: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X @ W )
% 4.71/5.02 => ( ( ord_less_rat @ W @ Y )
% 4.71/5.02 => ( ord_less_eq_rat @ W @ Z ) ) )
% 4.71/5.02 => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dense_le_bounded
% 4.71/5.02 thf(fact_829_dual__order_Oorder__iff__strict,axiom,
% 4.71/5.02 ( ord_less_eq_real
% 4.71/5.02 = ( ^ [B4: real,A4: real] :
% 4.71/5.02 ( ( ord_less_real @ B4 @ A4 )
% 4.71/5.02 | ( A4 = B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.order_iff_strict
% 4.71/5.02 thf(fact_830_dual__order_Oorder__iff__strict,axiom,
% 4.71/5.02 ( ord_less_eq_set_int
% 4.71/5.02 = ( ^ [B4: set_int,A4: set_int] :
% 4.71/5.02 ( ( ord_less_set_int @ B4 @ A4 )
% 4.71/5.02 | ( A4 = B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.order_iff_strict
% 4.71/5.02 thf(fact_831_dual__order_Oorder__iff__strict,axiom,
% 4.71/5.02 ( ord_less_eq_rat
% 4.71/5.02 = ( ^ [B4: rat,A4: rat] :
% 4.71/5.02 ( ( ord_less_rat @ B4 @ A4 )
% 4.71/5.02 | ( A4 = B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.order_iff_strict
% 4.71/5.02 thf(fact_832_dual__order_Oorder__iff__strict,axiom,
% 4.71/5.02 ( ord_less_eq_num
% 4.71/5.02 = ( ^ [B4: num,A4: num] :
% 4.71/5.02 ( ( ord_less_num @ B4 @ A4 )
% 4.71/5.02 | ( A4 = B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.order_iff_strict
% 4.71/5.02 thf(fact_833_dual__order_Oorder__iff__strict,axiom,
% 4.71/5.02 ( ord_less_eq_nat
% 4.71/5.02 = ( ^ [B4: nat,A4: nat] :
% 4.71/5.02 ( ( ord_less_nat @ B4 @ A4 )
% 4.71/5.02 | ( A4 = B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.order_iff_strict
% 4.71/5.02 thf(fact_834_dual__order_Oorder__iff__strict,axiom,
% 4.71/5.02 ( ord_less_eq_int
% 4.71/5.02 = ( ^ [B4: int,A4: int] :
% 4.71/5.02 ( ( ord_less_int @ B4 @ A4 )
% 4.71/5.02 | ( A4 = B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.order_iff_strict
% 4.71/5.02 thf(fact_835_dual__order_Ostrict__iff__order,axiom,
% 4.71/5.02 ( ord_less_real
% 4.71/5.02 = ( ^ [B4: real,A4: real] :
% 4.71/5.02 ( ( ord_less_eq_real @ B4 @ A4 )
% 4.71/5.02 & ( A4 != B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_iff_order
% 4.71/5.02 thf(fact_836_dual__order_Ostrict__iff__order,axiom,
% 4.71/5.02 ( ord_less_set_int
% 4.71/5.02 = ( ^ [B4: set_int,A4: set_int] :
% 4.71/5.02 ( ( ord_less_eq_set_int @ B4 @ A4 )
% 4.71/5.02 & ( A4 != B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_iff_order
% 4.71/5.02 thf(fact_837_dual__order_Ostrict__iff__order,axiom,
% 4.71/5.02 ( ord_less_rat
% 4.71/5.02 = ( ^ [B4: rat,A4: rat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ B4 @ A4 )
% 4.71/5.02 & ( A4 != B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_iff_order
% 4.71/5.02 thf(fact_838_dual__order_Ostrict__iff__order,axiom,
% 4.71/5.02 ( ord_less_num
% 4.71/5.02 = ( ^ [B4: num,A4: num] :
% 4.71/5.02 ( ( ord_less_eq_num @ B4 @ A4 )
% 4.71/5.02 & ( A4 != B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_iff_order
% 4.71/5.02 thf(fact_839_dual__order_Ostrict__iff__order,axiom,
% 4.71/5.02 ( ord_less_nat
% 4.71/5.02 = ( ^ [B4: nat,A4: nat] :
% 4.71/5.02 ( ( ord_less_eq_nat @ B4 @ A4 )
% 4.71/5.02 & ( A4 != B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_iff_order
% 4.71/5.02 thf(fact_840_dual__order_Ostrict__iff__order,axiom,
% 4.71/5.02 ( ord_less_int
% 4.71/5.02 = ( ^ [B4: int,A4: int] :
% 4.71/5.02 ( ( ord_less_eq_int @ B4 @ A4 )
% 4.71/5.02 & ( A4 != B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_iff_order
% 4.71/5.02 thf(fact_841_dual__order_Ostrict__trans1,axiom,
% 4.71/5.02 ! [B: real,A: real,C: real] :
% 4.71/5.02 ( ( ord_less_eq_real @ B @ A )
% 4.71/5.02 => ( ( ord_less_real @ C @ B )
% 4.71/5.02 => ( ord_less_real @ C @ A ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_trans1
% 4.71/5.02 thf(fact_842_dual__order_Ostrict__trans1,axiom,
% 4.71/5.02 ! [B: set_int,A: set_int,C: set_int] :
% 4.71/5.02 ( ( ord_less_eq_set_int @ B @ A )
% 4.71/5.02 => ( ( ord_less_set_int @ C @ B )
% 4.71/5.02 => ( ord_less_set_int @ C @ A ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_trans1
% 4.71/5.02 thf(fact_843_dual__order_Ostrict__trans1,axiom,
% 4.71/5.02 ! [B: rat,A: rat,C: rat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ B @ A )
% 4.71/5.02 => ( ( ord_less_rat @ C @ B )
% 4.71/5.02 => ( ord_less_rat @ C @ A ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_trans1
% 4.71/5.02 thf(fact_844_dual__order_Ostrict__trans1,axiom,
% 4.71/5.02 ! [B: num,A: num,C: num] :
% 4.71/5.02 ( ( ord_less_eq_num @ B @ A )
% 4.71/5.02 => ( ( ord_less_num @ C @ B )
% 4.71/5.02 => ( ord_less_num @ C @ A ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_trans1
% 4.71/5.02 thf(fact_845_dual__order_Ostrict__trans1,axiom,
% 4.71/5.02 ! [B: nat,A: nat,C: nat] :
% 4.71/5.02 ( ( ord_less_eq_nat @ B @ A )
% 4.71/5.02 => ( ( ord_less_nat @ C @ B )
% 4.71/5.02 => ( ord_less_nat @ C @ A ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_trans1
% 4.71/5.02 thf(fact_846_dual__order_Ostrict__trans1,axiom,
% 4.71/5.02 ! [B: int,A: int,C: int] :
% 4.71/5.02 ( ( ord_less_eq_int @ B @ A )
% 4.71/5.02 => ( ( ord_less_int @ C @ B )
% 4.71/5.02 => ( ord_less_int @ C @ A ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_trans1
% 4.71/5.02 thf(fact_847_dual__order_Ostrict__trans2,axiom,
% 4.71/5.02 ! [B: real,A: real,C: real] :
% 4.71/5.02 ( ( ord_less_real @ B @ A )
% 4.71/5.02 => ( ( ord_less_eq_real @ C @ B )
% 4.71/5.02 => ( ord_less_real @ C @ A ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_trans2
% 4.71/5.02 thf(fact_848_dual__order_Ostrict__trans2,axiom,
% 4.71/5.02 ! [B: set_int,A: set_int,C: set_int] :
% 4.71/5.02 ( ( ord_less_set_int @ B @ A )
% 4.71/5.02 => ( ( ord_less_eq_set_int @ C @ B )
% 4.71/5.02 => ( ord_less_set_int @ C @ A ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_trans2
% 4.71/5.02 thf(fact_849_dual__order_Ostrict__trans2,axiom,
% 4.71/5.02 ! [B: rat,A: rat,C: rat] :
% 4.71/5.02 ( ( ord_less_rat @ B @ A )
% 4.71/5.02 => ( ( ord_less_eq_rat @ C @ B )
% 4.71/5.02 => ( ord_less_rat @ C @ A ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_trans2
% 4.71/5.02 thf(fact_850_dual__order_Ostrict__trans2,axiom,
% 4.71/5.02 ! [B: num,A: num,C: num] :
% 4.71/5.02 ( ( ord_less_num @ B @ A )
% 4.71/5.02 => ( ( ord_less_eq_num @ C @ B )
% 4.71/5.02 => ( ord_less_num @ C @ A ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_trans2
% 4.71/5.02 thf(fact_851_dual__order_Ostrict__trans2,axiom,
% 4.71/5.02 ! [B: nat,A: nat,C: nat] :
% 4.71/5.02 ( ( ord_less_nat @ B @ A )
% 4.71/5.02 => ( ( ord_less_eq_nat @ C @ B )
% 4.71/5.02 => ( ord_less_nat @ C @ A ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_trans2
% 4.71/5.02 thf(fact_852_dual__order_Ostrict__trans2,axiom,
% 4.71/5.02 ! [B: int,A: int,C: int] :
% 4.71/5.02 ( ( ord_less_int @ B @ A )
% 4.71/5.02 => ( ( ord_less_eq_int @ C @ B )
% 4.71/5.02 => ( ord_less_int @ C @ A ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_trans2
% 4.71/5.02 thf(fact_853_dual__order_Ostrict__iff__not,axiom,
% 4.71/5.02 ( ord_less_real
% 4.71/5.02 = ( ^ [B4: real,A4: real] :
% 4.71/5.02 ( ( ord_less_eq_real @ B4 @ A4 )
% 4.71/5.02 & ~ ( ord_less_eq_real @ A4 @ B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_iff_not
% 4.71/5.02 thf(fact_854_dual__order_Ostrict__iff__not,axiom,
% 4.71/5.02 ( ord_less_set_int
% 4.71/5.02 = ( ^ [B4: set_int,A4: set_int] :
% 4.71/5.02 ( ( ord_less_eq_set_int @ B4 @ A4 )
% 4.71/5.02 & ~ ( ord_less_eq_set_int @ A4 @ B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_iff_not
% 4.71/5.02 thf(fact_855_dual__order_Ostrict__iff__not,axiom,
% 4.71/5.02 ( ord_less_rat
% 4.71/5.02 = ( ^ [B4: rat,A4: rat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ B4 @ A4 )
% 4.71/5.02 & ~ ( ord_less_eq_rat @ A4 @ B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_iff_not
% 4.71/5.02 thf(fact_856_dual__order_Ostrict__iff__not,axiom,
% 4.71/5.02 ( ord_less_num
% 4.71/5.02 = ( ^ [B4: num,A4: num] :
% 4.71/5.02 ( ( ord_less_eq_num @ B4 @ A4 )
% 4.71/5.02 & ~ ( ord_less_eq_num @ A4 @ B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_iff_not
% 4.71/5.02 thf(fact_857_dual__order_Ostrict__iff__not,axiom,
% 4.71/5.02 ( ord_less_nat
% 4.71/5.02 = ( ^ [B4: nat,A4: nat] :
% 4.71/5.02 ( ( ord_less_eq_nat @ B4 @ A4 )
% 4.71/5.02 & ~ ( ord_less_eq_nat @ A4 @ B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_iff_not
% 4.71/5.02 thf(fact_858_dual__order_Ostrict__iff__not,axiom,
% 4.71/5.02 ( ord_less_int
% 4.71/5.02 = ( ^ [B4: int,A4: int] :
% 4.71/5.02 ( ( ord_less_eq_int @ B4 @ A4 )
% 4.71/5.02 & ~ ( ord_less_eq_int @ A4 @ B4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_iff_not
% 4.71/5.02 thf(fact_859_order_Ostrict__implies__order,axiom,
% 4.71/5.02 ! [A: real,B: real] :
% 4.71/5.02 ( ( ord_less_real @ A @ B )
% 4.71/5.02 => ( ord_less_eq_real @ A @ B ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_implies_order
% 4.71/5.02 thf(fact_860_order_Ostrict__implies__order,axiom,
% 4.71/5.02 ! [A: set_int,B: set_int] :
% 4.71/5.02 ( ( ord_less_set_int @ A @ B )
% 4.71/5.02 => ( ord_less_eq_set_int @ A @ B ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_implies_order
% 4.71/5.02 thf(fact_861_order_Ostrict__implies__order,axiom,
% 4.71/5.02 ! [A: rat,B: rat] :
% 4.71/5.02 ( ( ord_less_rat @ A @ B )
% 4.71/5.02 => ( ord_less_eq_rat @ A @ B ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_implies_order
% 4.71/5.02 thf(fact_862_order_Ostrict__implies__order,axiom,
% 4.71/5.02 ! [A: num,B: num] :
% 4.71/5.02 ( ( ord_less_num @ A @ B )
% 4.71/5.02 => ( ord_less_eq_num @ A @ B ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_implies_order
% 4.71/5.02 thf(fact_863_order_Ostrict__implies__order,axiom,
% 4.71/5.02 ! [A: nat,B: nat] :
% 4.71/5.02 ( ( ord_less_nat @ A @ B )
% 4.71/5.02 => ( ord_less_eq_nat @ A @ B ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_implies_order
% 4.71/5.02 thf(fact_864_order_Ostrict__implies__order,axiom,
% 4.71/5.02 ! [A: int,B: int] :
% 4.71/5.02 ( ( ord_less_int @ A @ B )
% 4.71/5.02 => ( ord_less_eq_int @ A @ B ) ) ).
% 4.71/5.02
% 4.71/5.02 % order.strict_implies_order
% 4.71/5.02 thf(fact_865_dual__order_Ostrict__implies__order,axiom,
% 4.71/5.02 ! [B: real,A: real] :
% 4.71/5.02 ( ( ord_less_real @ B @ A )
% 4.71/5.02 => ( ord_less_eq_real @ B @ A ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_implies_order
% 4.71/5.02 thf(fact_866_dual__order_Ostrict__implies__order,axiom,
% 4.71/5.02 ! [B: set_int,A: set_int] :
% 4.71/5.02 ( ( ord_less_set_int @ B @ A )
% 4.71/5.02 => ( ord_less_eq_set_int @ B @ A ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_implies_order
% 4.71/5.02 thf(fact_867_dual__order_Ostrict__implies__order,axiom,
% 4.71/5.02 ! [B: rat,A: rat] :
% 4.71/5.02 ( ( ord_less_rat @ B @ A )
% 4.71/5.02 => ( ord_less_eq_rat @ B @ A ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_implies_order
% 4.71/5.02 thf(fact_868_dual__order_Ostrict__implies__order,axiom,
% 4.71/5.02 ! [B: num,A: num] :
% 4.71/5.02 ( ( ord_less_num @ B @ A )
% 4.71/5.02 => ( ord_less_eq_num @ B @ A ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_implies_order
% 4.71/5.02 thf(fact_869_dual__order_Ostrict__implies__order,axiom,
% 4.71/5.02 ! [B: nat,A: nat] :
% 4.71/5.02 ( ( ord_less_nat @ B @ A )
% 4.71/5.02 => ( ord_less_eq_nat @ B @ A ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_implies_order
% 4.71/5.02 thf(fact_870_dual__order_Ostrict__implies__order,axiom,
% 4.71/5.02 ! [B: int,A: int] :
% 4.71/5.02 ( ( ord_less_int @ B @ A )
% 4.71/5.02 => ( ord_less_eq_int @ B @ A ) ) ).
% 4.71/5.02
% 4.71/5.02 % dual_order.strict_implies_order
% 4.71/5.02 thf(fact_871_order__le__less,axiom,
% 4.71/5.02 ( ord_less_eq_real
% 4.71/5.02 = ( ^ [X3: real,Y2: real] :
% 4.71/5.02 ( ( ord_less_real @ X3 @ Y2 )
% 4.71/5.02 | ( X3 = Y2 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less
% 4.71/5.02 thf(fact_872_order__le__less,axiom,
% 4.71/5.02 ( ord_less_eq_set_int
% 4.71/5.02 = ( ^ [X3: set_int,Y2: set_int] :
% 4.71/5.02 ( ( ord_less_set_int @ X3 @ Y2 )
% 4.71/5.02 | ( X3 = Y2 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less
% 4.71/5.02 thf(fact_873_order__le__less,axiom,
% 4.71/5.02 ( ord_less_eq_rat
% 4.71/5.02 = ( ^ [X3: rat,Y2: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X3 @ Y2 )
% 4.71/5.02 | ( X3 = Y2 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less
% 4.71/5.02 thf(fact_874_order__le__less,axiom,
% 4.71/5.02 ( ord_less_eq_num
% 4.71/5.02 = ( ^ [X3: num,Y2: num] :
% 4.71/5.02 ( ( ord_less_num @ X3 @ Y2 )
% 4.71/5.02 | ( X3 = Y2 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less
% 4.71/5.02 thf(fact_875_order__le__less,axiom,
% 4.71/5.02 ( ord_less_eq_nat
% 4.71/5.02 = ( ^ [X3: nat,Y2: nat] :
% 4.71/5.02 ( ( ord_less_nat @ X3 @ Y2 )
% 4.71/5.02 | ( X3 = Y2 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less
% 4.71/5.02 thf(fact_876_order__le__less,axiom,
% 4.71/5.02 ( ord_less_eq_int
% 4.71/5.02 = ( ^ [X3: int,Y2: int] :
% 4.71/5.02 ( ( ord_less_int @ X3 @ Y2 )
% 4.71/5.02 | ( X3 = Y2 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less
% 4.71/5.02 thf(fact_877_order__less__le,axiom,
% 4.71/5.02 ( ord_less_real
% 4.71/5.02 = ( ^ [X3: real,Y2: real] :
% 4.71/5.02 ( ( ord_less_eq_real @ X3 @ Y2 )
% 4.71/5.02 & ( X3 != Y2 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le
% 4.71/5.02 thf(fact_878_order__less__le,axiom,
% 4.71/5.02 ( ord_less_set_int
% 4.71/5.02 = ( ^ [X3: set_int,Y2: set_int] :
% 4.71/5.02 ( ( ord_less_eq_set_int @ X3 @ Y2 )
% 4.71/5.02 & ( X3 != Y2 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le
% 4.71/5.02 thf(fact_879_order__less__le,axiom,
% 4.71/5.02 ( ord_less_rat
% 4.71/5.02 = ( ^ [X3: rat,Y2: rat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 4.71/5.02 & ( X3 != Y2 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le
% 4.71/5.02 thf(fact_880_order__less__le,axiom,
% 4.71/5.02 ( ord_less_num
% 4.71/5.02 = ( ^ [X3: num,Y2: num] :
% 4.71/5.02 ( ( ord_less_eq_num @ X3 @ Y2 )
% 4.71/5.02 & ( X3 != Y2 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le
% 4.71/5.02 thf(fact_881_order__less__le,axiom,
% 4.71/5.02 ( ord_less_nat
% 4.71/5.02 = ( ^ [X3: nat,Y2: nat] :
% 4.71/5.02 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 4.71/5.02 & ( X3 != Y2 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le
% 4.71/5.02 thf(fact_882_order__less__le,axiom,
% 4.71/5.02 ( ord_less_int
% 4.71/5.02 = ( ^ [X3: int,Y2: int] :
% 4.71/5.02 ( ( ord_less_eq_int @ X3 @ Y2 )
% 4.71/5.02 & ( X3 != Y2 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le
% 4.71/5.02 thf(fact_883_linorder__not__le,axiom,
% 4.71/5.02 ! [X: real,Y: real] :
% 4.71/5.02 ( ( ~ ( ord_less_eq_real @ X @ Y ) )
% 4.71/5.02 = ( ord_less_real @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % linorder_not_le
% 4.71/5.02 thf(fact_884_linorder__not__le,axiom,
% 4.71/5.02 ! [X: rat,Y: rat] :
% 4.71/5.02 ( ( ~ ( ord_less_eq_rat @ X @ Y ) )
% 4.71/5.02 = ( ord_less_rat @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % linorder_not_le
% 4.71/5.02 thf(fact_885_linorder__not__le,axiom,
% 4.71/5.02 ! [X: num,Y: num] :
% 4.71/5.02 ( ( ~ ( ord_less_eq_num @ X @ Y ) )
% 4.71/5.02 = ( ord_less_num @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % linorder_not_le
% 4.71/5.02 thf(fact_886_linorder__not__le,axiom,
% 4.71/5.02 ! [X: nat,Y: nat] :
% 4.71/5.02 ( ( ~ ( ord_less_eq_nat @ X @ Y ) )
% 4.71/5.02 = ( ord_less_nat @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % linorder_not_le
% 4.71/5.02 thf(fact_887_linorder__not__le,axiom,
% 4.71/5.02 ! [X: int,Y: int] :
% 4.71/5.02 ( ( ~ ( ord_less_eq_int @ X @ Y ) )
% 4.71/5.02 = ( ord_less_int @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % linorder_not_le
% 4.71/5.02 thf(fact_888_linorder__not__less,axiom,
% 4.71/5.02 ! [X: real,Y: real] :
% 4.71/5.02 ( ( ~ ( ord_less_real @ X @ Y ) )
% 4.71/5.02 = ( ord_less_eq_real @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % linorder_not_less
% 4.71/5.02 thf(fact_889_linorder__not__less,axiom,
% 4.71/5.02 ! [X: rat,Y: rat] :
% 4.71/5.02 ( ( ~ ( ord_less_rat @ X @ Y ) )
% 4.71/5.02 = ( ord_less_eq_rat @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % linorder_not_less
% 4.71/5.02 thf(fact_890_linorder__not__less,axiom,
% 4.71/5.02 ! [X: num,Y: num] :
% 4.71/5.02 ( ( ~ ( ord_less_num @ X @ Y ) )
% 4.71/5.02 = ( ord_less_eq_num @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % linorder_not_less
% 4.71/5.02 thf(fact_891_linorder__not__less,axiom,
% 4.71/5.02 ! [X: nat,Y: nat] :
% 4.71/5.02 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 4.71/5.02 = ( ord_less_eq_nat @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % linorder_not_less
% 4.71/5.02 thf(fact_892_linorder__not__less,axiom,
% 4.71/5.02 ! [X: int,Y: int] :
% 4.71/5.02 ( ( ~ ( ord_less_int @ X @ Y ) )
% 4.71/5.02 = ( ord_less_eq_int @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % linorder_not_less
% 4.71/5.02 thf(fact_893_order__less__imp__le,axiom,
% 4.71/5.02 ! [X: real,Y: real] :
% 4.71/5.02 ( ( ord_less_real @ X @ Y )
% 4.71/5.02 => ( ord_less_eq_real @ X @ Y ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_imp_le
% 4.71/5.02 thf(fact_894_order__less__imp__le,axiom,
% 4.71/5.02 ! [X: set_int,Y: set_int] :
% 4.71/5.02 ( ( ord_less_set_int @ X @ Y )
% 4.71/5.02 => ( ord_less_eq_set_int @ X @ Y ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_imp_le
% 4.71/5.02 thf(fact_895_order__less__imp__le,axiom,
% 4.71/5.02 ! [X: rat,Y: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X @ Y )
% 4.71/5.02 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_imp_le
% 4.71/5.02 thf(fact_896_order__less__imp__le,axiom,
% 4.71/5.02 ! [X: num,Y: num] :
% 4.71/5.02 ( ( ord_less_num @ X @ Y )
% 4.71/5.02 => ( ord_less_eq_num @ X @ Y ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_imp_le
% 4.71/5.02 thf(fact_897_order__less__imp__le,axiom,
% 4.71/5.02 ! [X: nat,Y: nat] :
% 4.71/5.02 ( ( ord_less_nat @ X @ Y )
% 4.71/5.02 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_imp_le
% 4.71/5.02 thf(fact_898_order__less__imp__le,axiom,
% 4.71/5.02 ! [X: int,Y: int] :
% 4.71/5.02 ( ( ord_less_int @ X @ Y )
% 4.71/5.02 => ( ord_less_eq_int @ X @ Y ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_imp_le
% 4.71/5.02 thf(fact_899_order__le__neq__trans,axiom,
% 4.71/5.02 ! [A: real,B: real] :
% 4.71/5.02 ( ( ord_less_eq_real @ A @ B )
% 4.71/5.02 => ( ( A != B )
% 4.71/5.02 => ( ord_less_real @ A @ B ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_neq_trans
% 4.71/5.02 thf(fact_900_order__le__neq__trans,axiom,
% 4.71/5.02 ! [A: set_int,B: set_int] :
% 4.71/5.02 ( ( ord_less_eq_set_int @ A @ B )
% 4.71/5.02 => ( ( A != B )
% 4.71/5.02 => ( ord_less_set_int @ A @ B ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_neq_trans
% 4.71/5.02 thf(fact_901_order__le__neq__trans,axiom,
% 4.71/5.02 ! [A: rat,B: rat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.02 => ( ( A != B )
% 4.71/5.02 => ( ord_less_rat @ A @ B ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_neq_trans
% 4.71/5.02 thf(fact_902_order__le__neq__trans,axiom,
% 4.71/5.02 ! [A: num,B: num] :
% 4.71/5.02 ( ( ord_less_eq_num @ A @ B )
% 4.71/5.02 => ( ( A != B )
% 4.71/5.02 => ( ord_less_num @ A @ B ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_neq_trans
% 4.71/5.02 thf(fact_903_order__le__neq__trans,axiom,
% 4.71/5.02 ! [A: nat,B: nat] :
% 4.71/5.02 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.02 => ( ( A != B )
% 4.71/5.02 => ( ord_less_nat @ A @ B ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_neq_trans
% 4.71/5.02 thf(fact_904_order__le__neq__trans,axiom,
% 4.71/5.02 ! [A: int,B: int] :
% 4.71/5.02 ( ( ord_less_eq_int @ A @ B )
% 4.71/5.02 => ( ( A != B )
% 4.71/5.02 => ( ord_less_int @ A @ B ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_neq_trans
% 4.71/5.02 thf(fact_905_order__neq__le__trans,axiom,
% 4.71/5.02 ! [A: real,B: real] :
% 4.71/5.02 ( ( A != B )
% 4.71/5.02 => ( ( ord_less_eq_real @ A @ B )
% 4.71/5.02 => ( ord_less_real @ A @ B ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_neq_le_trans
% 4.71/5.02 thf(fact_906_order__neq__le__trans,axiom,
% 4.71/5.02 ! [A: set_int,B: set_int] :
% 4.71/5.02 ( ( A != B )
% 4.71/5.02 => ( ( ord_less_eq_set_int @ A @ B )
% 4.71/5.02 => ( ord_less_set_int @ A @ B ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_neq_le_trans
% 4.71/5.02 thf(fact_907_order__neq__le__trans,axiom,
% 4.71/5.02 ! [A: rat,B: rat] :
% 4.71/5.02 ( ( A != B )
% 4.71/5.02 => ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.02 => ( ord_less_rat @ A @ B ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_neq_le_trans
% 4.71/5.02 thf(fact_908_order__neq__le__trans,axiom,
% 4.71/5.02 ! [A: num,B: num] :
% 4.71/5.02 ( ( A != B )
% 4.71/5.02 => ( ( ord_less_eq_num @ A @ B )
% 4.71/5.02 => ( ord_less_num @ A @ B ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_neq_le_trans
% 4.71/5.02 thf(fact_909_order__neq__le__trans,axiom,
% 4.71/5.02 ! [A: nat,B: nat] :
% 4.71/5.02 ( ( A != B )
% 4.71/5.02 => ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.02 => ( ord_less_nat @ A @ B ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_neq_le_trans
% 4.71/5.02 thf(fact_910_order__neq__le__trans,axiom,
% 4.71/5.02 ! [A: int,B: int] :
% 4.71/5.02 ( ( A != B )
% 4.71/5.02 => ( ( ord_less_eq_int @ A @ B )
% 4.71/5.02 => ( ord_less_int @ A @ B ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_neq_le_trans
% 4.71/5.02 thf(fact_911_order__le__less__trans,axiom,
% 4.71/5.02 ! [X: real,Y: real,Z: real] :
% 4.71/5.02 ( ( ord_less_eq_real @ X @ Y )
% 4.71/5.02 => ( ( ord_less_real @ Y @ Z )
% 4.71/5.02 => ( ord_less_real @ X @ Z ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less_trans
% 4.71/5.02 thf(fact_912_order__le__less__trans,axiom,
% 4.71/5.02 ! [X: set_int,Y: set_int,Z: set_int] :
% 4.71/5.02 ( ( ord_less_eq_set_int @ X @ Y )
% 4.71/5.02 => ( ( ord_less_set_int @ Y @ Z )
% 4.71/5.02 => ( ord_less_set_int @ X @ Z ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less_trans
% 4.71/5.02 thf(fact_913_order__le__less__trans,axiom,
% 4.71/5.02 ! [X: rat,Y: rat,Z: rat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ X @ Y )
% 4.71/5.02 => ( ( ord_less_rat @ Y @ Z )
% 4.71/5.02 => ( ord_less_rat @ X @ Z ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less_trans
% 4.71/5.02 thf(fact_914_order__le__less__trans,axiom,
% 4.71/5.02 ! [X: num,Y: num,Z: num] :
% 4.71/5.02 ( ( ord_less_eq_num @ X @ Y )
% 4.71/5.02 => ( ( ord_less_num @ Y @ Z )
% 4.71/5.02 => ( ord_less_num @ X @ Z ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less_trans
% 4.71/5.02 thf(fact_915_order__le__less__trans,axiom,
% 4.71/5.02 ! [X: nat,Y: nat,Z: nat] :
% 4.71/5.02 ( ( ord_less_eq_nat @ X @ Y )
% 4.71/5.02 => ( ( ord_less_nat @ Y @ Z )
% 4.71/5.02 => ( ord_less_nat @ X @ Z ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less_trans
% 4.71/5.02 thf(fact_916_order__le__less__trans,axiom,
% 4.71/5.02 ! [X: int,Y: int,Z: int] :
% 4.71/5.02 ( ( ord_less_eq_int @ X @ Y )
% 4.71/5.02 => ( ( ord_less_int @ Y @ Z )
% 4.71/5.02 => ( ord_less_int @ X @ Z ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less_trans
% 4.71/5.02 thf(fact_917_order__less__le__trans,axiom,
% 4.71/5.02 ! [X: real,Y: real,Z: real] :
% 4.71/5.02 ( ( ord_less_real @ X @ Y )
% 4.71/5.02 => ( ( ord_less_eq_real @ Y @ Z )
% 4.71/5.02 => ( ord_less_real @ X @ Z ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le_trans
% 4.71/5.02 thf(fact_918_order__less__le__trans,axiom,
% 4.71/5.02 ! [X: set_int,Y: set_int,Z: set_int] :
% 4.71/5.02 ( ( ord_less_set_int @ X @ Y )
% 4.71/5.02 => ( ( ord_less_eq_set_int @ Y @ Z )
% 4.71/5.02 => ( ord_less_set_int @ X @ Z ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le_trans
% 4.71/5.02 thf(fact_919_order__less__le__trans,axiom,
% 4.71/5.02 ! [X: rat,Y: rat,Z: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X @ Y )
% 4.71/5.02 => ( ( ord_less_eq_rat @ Y @ Z )
% 4.71/5.02 => ( ord_less_rat @ X @ Z ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le_trans
% 4.71/5.02 thf(fact_920_order__less__le__trans,axiom,
% 4.71/5.02 ! [X: num,Y: num,Z: num] :
% 4.71/5.02 ( ( ord_less_num @ X @ Y )
% 4.71/5.02 => ( ( ord_less_eq_num @ Y @ Z )
% 4.71/5.02 => ( ord_less_num @ X @ Z ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le_trans
% 4.71/5.02 thf(fact_921_order__less__le__trans,axiom,
% 4.71/5.02 ! [X: nat,Y: nat,Z: nat] :
% 4.71/5.02 ( ( ord_less_nat @ X @ Y )
% 4.71/5.02 => ( ( ord_less_eq_nat @ Y @ Z )
% 4.71/5.02 => ( ord_less_nat @ X @ Z ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le_trans
% 4.71/5.02 thf(fact_922_order__less__le__trans,axiom,
% 4.71/5.02 ! [X: int,Y: int,Z: int] :
% 4.71/5.02 ( ( ord_less_int @ X @ Y )
% 4.71/5.02 => ( ( ord_less_eq_int @ Y @ Z )
% 4.71/5.02 => ( ord_less_int @ X @ Z ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le_trans
% 4.71/5.02 thf(fact_923_order__le__less__subst1,axiom,
% 4.71/5.02 ! [A: real,F: real > real,B: real,C: real] :
% 4.71/5.02 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_real @ B @ C )
% 4.71/5.02 => ( ! [X4: real,Y3: real] :
% 4.71/5.02 ( ( ord_less_real @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less_subst1
% 4.71/5.02 thf(fact_924_order__le__less__subst1,axiom,
% 4.71/5.02 ! [A: real,F: rat > real,B: rat,C: rat] :
% 4.71/5.02 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_rat @ B @ C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less_subst1
% 4.71/5.02 thf(fact_925_order__le__less__subst1,axiom,
% 4.71/5.02 ! [A: real,F: num > real,B: num,C: num] :
% 4.71/5.02 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_num @ B @ C )
% 4.71/5.02 => ( ! [X4: num,Y3: num] :
% 4.71/5.02 ( ( ord_less_num @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less_subst1
% 4.71/5.02 thf(fact_926_order__le__less__subst1,axiom,
% 4.71/5.02 ! [A: real,F: nat > real,B: nat,C: nat] :
% 4.71/5.02 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_nat @ B @ C )
% 4.71/5.02 => ( ! [X4: nat,Y3: nat] :
% 4.71/5.02 ( ( ord_less_nat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less_subst1
% 4.71/5.02 thf(fact_927_order__le__less__subst1,axiom,
% 4.71/5.02 ! [A: real,F: int > real,B: int,C: int] :
% 4.71/5.02 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_int @ B @ C )
% 4.71/5.02 => ( ! [X4: int,Y3: int] :
% 4.71/5.02 ( ( ord_less_int @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less_subst1
% 4.71/5.02 thf(fact_928_order__le__less__subst1,axiom,
% 4.71/5.02 ! [A: rat,F: real > rat,B: real,C: real] :
% 4.71/5.02 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_real @ B @ C )
% 4.71/5.02 => ( ! [X4: real,Y3: real] :
% 4.71/5.02 ( ( ord_less_real @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less_subst1
% 4.71/5.02 thf(fact_929_order__le__less__subst1,axiom,
% 4.71/5.02 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_rat @ B @ C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less_subst1
% 4.71/5.02 thf(fact_930_order__le__less__subst1,axiom,
% 4.71/5.02 ! [A: rat,F: num > rat,B: num,C: num] :
% 4.71/5.02 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_num @ B @ C )
% 4.71/5.02 => ( ! [X4: num,Y3: num] :
% 4.71/5.02 ( ( ord_less_num @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less_subst1
% 4.71/5.02 thf(fact_931_order__le__less__subst1,axiom,
% 4.71/5.02 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_nat @ B @ C )
% 4.71/5.02 => ( ! [X4: nat,Y3: nat] :
% 4.71/5.02 ( ( ord_less_nat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less_subst1
% 4.71/5.02 thf(fact_932_order__le__less__subst1,axiom,
% 4.71/5.02 ! [A: rat,F: int > rat,B: int,C: int] :
% 4.71/5.02 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_int @ B @ C )
% 4.71/5.02 => ( ! [X4: int,Y3: int] :
% 4.71/5.02 ( ( ord_less_int @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less_subst1
% 4.71/5.02 thf(fact_933_order__le__less__subst2,axiom,
% 4.71/5.02 ! [A: rat,B: rat,F: rat > real,C: real] :
% 4.71/5.02 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.02 => ( ( ord_less_real @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less_subst2
% 4.71/5.02 thf(fact_934_order__le__less__subst2,axiom,
% 4.71/5.02 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.02 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less_subst2
% 4.71/5.02 thf(fact_935_order__le__less__subst2,axiom,
% 4.71/5.02 ! [A: rat,B: rat,F: rat > num,C: num] :
% 4.71/5.02 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.02 => ( ( ord_less_num @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less_subst2
% 4.71/5.02 thf(fact_936_order__le__less__subst2,axiom,
% 4.71/5.02 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.02 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less_subst2
% 4.71/5.02 thf(fact_937_order__le__less__subst2,axiom,
% 4.71/5.02 ! [A: rat,B: rat,F: rat > int,C: int] :
% 4.71/5.02 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.02 => ( ( ord_less_int @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less_subst2
% 4.71/5.02 thf(fact_938_order__le__less__subst2,axiom,
% 4.71/5.02 ! [A: num,B: num,F: num > real,C: real] :
% 4.71/5.02 ( ( ord_less_eq_num @ A @ B )
% 4.71/5.02 => ( ( ord_less_real @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: num,Y3: num] :
% 4.71/5.02 ( ( ord_less_eq_num @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less_subst2
% 4.71/5.02 thf(fact_939_order__le__less__subst2,axiom,
% 4.71/5.02 ! [A: num,B: num,F: num > rat,C: rat] :
% 4.71/5.02 ( ( ord_less_eq_num @ A @ B )
% 4.71/5.02 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: num,Y3: num] :
% 4.71/5.02 ( ( ord_less_eq_num @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less_subst2
% 4.71/5.02 thf(fact_940_order__le__less__subst2,axiom,
% 4.71/5.02 ! [A: num,B: num,F: num > num,C: num] :
% 4.71/5.02 ( ( ord_less_eq_num @ A @ B )
% 4.71/5.02 => ( ( ord_less_num @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: num,Y3: num] :
% 4.71/5.02 ( ( ord_less_eq_num @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less_subst2
% 4.71/5.02 thf(fact_941_order__le__less__subst2,axiom,
% 4.71/5.02 ! [A: num,B: num,F: num > nat,C: nat] :
% 4.71/5.02 ( ( ord_less_eq_num @ A @ B )
% 4.71/5.02 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: num,Y3: num] :
% 4.71/5.02 ( ( ord_less_eq_num @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less_subst2
% 4.71/5.02 thf(fact_942_order__le__less__subst2,axiom,
% 4.71/5.02 ! [A: num,B: num,F: num > int,C: int] :
% 4.71/5.02 ( ( ord_less_eq_num @ A @ B )
% 4.71/5.02 => ( ( ord_less_int @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: num,Y3: num] :
% 4.71/5.02 ( ( ord_less_eq_num @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_less_subst2
% 4.71/5.02 thf(fact_943_order__less__le__subst1,axiom,
% 4.71/5.02 ! [A: real,F: rat > real,B: rat,C: rat] :
% 4.71/5.02 ( ( ord_less_real @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_eq_rat @ B @ C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le_subst1
% 4.71/5.02 thf(fact_944_order__less__le__subst1,axiom,
% 4.71/5.02 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 4.71/5.02 ( ( ord_less_rat @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_eq_rat @ B @ C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le_subst1
% 4.71/5.02 thf(fact_945_order__less__le__subst1,axiom,
% 4.71/5.02 ! [A: num,F: rat > num,B: rat,C: rat] :
% 4.71/5.02 ( ( ord_less_num @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_eq_rat @ B @ C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le_subst1
% 4.71/5.02 thf(fact_946_order__less__le__subst1,axiom,
% 4.71/5.02 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 4.71/5.02 ( ( ord_less_nat @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_eq_rat @ B @ C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le_subst1
% 4.71/5.02 thf(fact_947_order__less__le__subst1,axiom,
% 4.71/5.02 ! [A: int,F: rat > int,B: rat,C: rat] :
% 4.71/5.02 ( ( ord_less_int @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_eq_rat @ B @ C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le_subst1
% 4.71/5.02 thf(fact_948_order__less__le__subst1,axiom,
% 4.71/5.02 ! [A: real,F: num > real,B: num,C: num] :
% 4.71/5.02 ( ( ord_less_real @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_eq_num @ B @ C )
% 4.71/5.02 => ( ! [X4: num,Y3: num] :
% 4.71/5.02 ( ( ord_less_eq_num @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le_subst1
% 4.71/5.02 thf(fact_949_order__less__le__subst1,axiom,
% 4.71/5.02 ! [A: rat,F: num > rat,B: num,C: num] :
% 4.71/5.02 ( ( ord_less_rat @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_eq_num @ B @ C )
% 4.71/5.02 => ( ! [X4: num,Y3: num] :
% 4.71/5.02 ( ( ord_less_eq_num @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le_subst1
% 4.71/5.02 thf(fact_950_order__less__le__subst1,axiom,
% 4.71/5.02 ! [A: num,F: num > num,B: num,C: num] :
% 4.71/5.02 ( ( ord_less_num @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_eq_num @ B @ C )
% 4.71/5.02 => ( ! [X4: num,Y3: num] :
% 4.71/5.02 ( ( ord_less_eq_num @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le_subst1
% 4.71/5.02 thf(fact_951_order__less__le__subst1,axiom,
% 4.71/5.02 ! [A: nat,F: num > nat,B: num,C: num] :
% 4.71/5.02 ( ( ord_less_nat @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_eq_num @ B @ C )
% 4.71/5.02 => ( ! [X4: num,Y3: num] :
% 4.71/5.02 ( ( ord_less_eq_num @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le_subst1
% 4.71/5.02 thf(fact_952_order__less__le__subst1,axiom,
% 4.71/5.02 ! [A: int,F: num > int,B: num,C: num] :
% 4.71/5.02 ( ( ord_less_int @ A @ ( F @ B ) )
% 4.71/5.02 => ( ( ord_less_eq_num @ B @ C )
% 4.71/5.02 => ( ! [X4: num,Y3: num] :
% 4.71/5.02 ( ( ord_less_eq_num @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le_subst1
% 4.71/5.02 thf(fact_953_order__less__le__subst2,axiom,
% 4.71/5.02 ! [A: real,B: real,F: real > real,C: real] :
% 4.71/5.02 ( ( ord_less_real @ A @ B )
% 4.71/5.02 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: real,Y3: real] :
% 4.71/5.02 ( ( ord_less_real @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le_subst2
% 4.71/5.02 thf(fact_954_order__less__le__subst2,axiom,
% 4.71/5.02 ! [A: rat,B: rat,F: rat > real,C: real] :
% 4.71/5.02 ( ( ord_less_rat @ A @ B )
% 4.71/5.02 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le_subst2
% 4.71/5.02 thf(fact_955_order__less__le__subst2,axiom,
% 4.71/5.02 ! [A: num,B: num,F: num > real,C: real] :
% 4.71/5.02 ( ( ord_less_num @ A @ B )
% 4.71/5.02 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: num,Y3: num] :
% 4.71/5.02 ( ( ord_less_num @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le_subst2
% 4.71/5.02 thf(fact_956_order__less__le__subst2,axiom,
% 4.71/5.02 ! [A: nat,B: nat,F: nat > real,C: real] :
% 4.71/5.02 ( ( ord_less_nat @ A @ B )
% 4.71/5.02 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: nat,Y3: nat] :
% 4.71/5.02 ( ( ord_less_nat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le_subst2
% 4.71/5.02 thf(fact_957_order__less__le__subst2,axiom,
% 4.71/5.02 ! [A: int,B: int,F: int > real,C: real] :
% 4.71/5.02 ( ( ord_less_int @ A @ B )
% 4.71/5.02 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: int,Y3: int] :
% 4.71/5.02 ( ( ord_less_int @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le_subst2
% 4.71/5.02 thf(fact_958_order__less__le__subst2,axiom,
% 4.71/5.02 ! [A: real,B: real,F: real > rat,C: rat] :
% 4.71/5.02 ( ( ord_less_real @ A @ B )
% 4.71/5.02 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: real,Y3: real] :
% 4.71/5.02 ( ( ord_less_real @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le_subst2
% 4.71/5.02 thf(fact_959_order__less__le__subst2,axiom,
% 4.71/5.02 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 4.71/5.02 ( ( ord_less_rat @ A @ B )
% 4.71/5.02 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: rat,Y3: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le_subst2
% 4.71/5.02 thf(fact_960_order__less__le__subst2,axiom,
% 4.71/5.02 ! [A: num,B: num,F: num > rat,C: rat] :
% 4.71/5.02 ( ( ord_less_num @ A @ B )
% 4.71/5.02 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: num,Y3: num] :
% 4.71/5.02 ( ( ord_less_num @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le_subst2
% 4.71/5.02 thf(fact_961_order__less__le__subst2,axiom,
% 4.71/5.02 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 4.71/5.02 ( ( ord_less_nat @ A @ B )
% 4.71/5.02 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: nat,Y3: nat] :
% 4.71/5.02 ( ( ord_less_nat @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le_subst2
% 4.71/5.02 thf(fact_962_order__less__le__subst2,axiom,
% 4.71/5.02 ! [A: int,B: int,F: int > rat,C: rat] :
% 4.71/5.02 ( ( ord_less_int @ A @ B )
% 4.71/5.02 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 4.71/5.02 => ( ! [X4: int,Y3: int] :
% 4.71/5.02 ( ( ord_less_int @ X4 @ Y3 )
% 4.71/5.02 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 4.71/5.02 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_less_le_subst2
% 4.71/5.02 thf(fact_963_linorder__le__less__linear,axiom,
% 4.71/5.02 ! [X: real,Y: real] :
% 4.71/5.02 ( ( ord_less_eq_real @ X @ Y )
% 4.71/5.02 | ( ord_less_real @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % linorder_le_less_linear
% 4.71/5.02 thf(fact_964_linorder__le__less__linear,axiom,
% 4.71/5.02 ! [X: rat,Y: rat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ X @ Y )
% 4.71/5.02 | ( ord_less_rat @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % linorder_le_less_linear
% 4.71/5.02 thf(fact_965_linorder__le__less__linear,axiom,
% 4.71/5.02 ! [X: num,Y: num] :
% 4.71/5.02 ( ( ord_less_eq_num @ X @ Y )
% 4.71/5.02 | ( ord_less_num @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % linorder_le_less_linear
% 4.71/5.02 thf(fact_966_linorder__le__less__linear,axiom,
% 4.71/5.02 ! [X: nat,Y: nat] :
% 4.71/5.02 ( ( ord_less_eq_nat @ X @ Y )
% 4.71/5.02 | ( ord_less_nat @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % linorder_le_less_linear
% 4.71/5.02 thf(fact_967_linorder__le__less__linear,axiom,
% 4.71/5.02 ! [X: int,Y: int] :
% 4.71/5.02 ( ( ord_less_eq_int @ X @ Y )
% 4.71/5.02 | ( ord_less_int @ Y @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % linorder_le_less_linear
% 4.71/5.02 thf(fact_968_order__le__imp__less__or__eq,axiom,
% 4.71/5.02 ! [X: real,Y: real] :
% 4.71/5.02 ( ( ord_less_eq_real @ X @ Y )
% 4.71/5.02 => ( ( ord_less_real @ X @ Y )
% 4.71/5.02 | ( X = Y ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_imp_less_or_eq
% 4.71/5.02 thf(fact_969_order__le__imp__less__or__eq,axiom,
% 4.71/5.02 ! [X: set_int,Y: set_int] :
% 4.71/5.02 ( ( ord_less_eq_set_int @ X @ Y )
% 4.71/5.02 => ( ( ord_less_set_int @ X @ Y )
% 4.71/5.02 | ( X = Y ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_imp_less_or_eq
% 4.71/5.02 thf(fact_970_order__le__imp__less__or__eq,axiom,
% 4.71/5.02 ! [X: rat,Y: rat] :
% 4.71/5.02 ( ( ord_less_eq_rat @ X @ Y )
% 4.71/5.02 => ( ( ord_less_rat @ X @ Y )
% 4.71/5.02 | ( X = Y ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_imp_less_or_eq
% 4.71/5.02 thf(fact_971_order__le__imp__less__or__eq,axiom,
% 4.71/5.02 ! [X: num,Y: num] :
% 4.71/5.02 ( ( ord_less_eq_num @ X @ Y )
% 4.71/5.02 => ( ( ord_less_num @ X @ Y )
% 4.71/5.02 | ( X = Y ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_imp_less_or_eq
% 4.71/5.02 thf(fact_972_order__le__imp__less__or__eq,axiom,
% 4.71/5.02 ! [X: nat,Y: nat] :
% 4.71/5.02 ( ( ord_less_eq_nat @ X @ Y )
% 4.71/5.02 => ( ( ord_less_nat @ X @ Y )
% 4.71/5.02 | ( X = Y ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_imp_less_or_eq
% 4.71/5.02 thf(fact_973_order__le__imp__less__or__eq,axiom,
% 4.71/5.02 ! [X: int,Y: int] :
% 4.71/5.02 ( ( ord_less_eq_int @ X @ Y )
% 4.71/5.02 => ( ( ord_less_int @ X @ Y )
% 4.71/5.02 | ( X = Y ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % order_le_imp_less_or_eq
% 4.71/5.02 thf(fact_974_subset__emptyI,axiom,
% 4.71/5.02 ! [A2: set_set_nat] :
% 4.71/5.02 ( ! [X4: set_nat] :
% 4.71/5.02 ~ ( member_set_nat @ X4 @ A2 )
% 4.71/5.02 => ( ord_le6893508408891458716et_nat @ A2 @ bot_bot_set_set_nat ) ) ).
% 4.71/5.02
% 4.71/5.02 % subset_emptyI
% 4.71/5.02 thf(fact_975_subset__emptyI,axiom,
% 4.71/5.02 ! [A2: set_set_nat_rat] :
% 4.71/5.02 ( ! [X4: set_nat_rat] :
% 4.71/5.02 ~ ( member_set_nat_rat @ X4 @ A2 )
% 4.71/5.02 => ( ord_le4375437777232675859at_rat @ A2 @ bot_bo6797373522285170759at_rat ) ) ).
% 4.71/5.02
% 4.71/5.02 % subset_emptyI
% 4.71/5.02 thf(fact_976_subset__emptyI,axiom,
% 4.71/5.02 ! [A2: set_real] :
% 4.71/5.02 ( ! [X4: real] :
% 4.71/5.02 ~ ( member_real @ X4 @ A2 )
% 4.71/5.02 => ( ord_less_eq_set_real @ A2 @ bot_bot_set_real ) ) ).
% 4.71/5.02
% 4.71/5.02 % subset_emptyI
% 4.71/5.02 thf(fact_977_subset__emptyI,axiom,
% 4.71/5.02 ! [A2: set_o] :
% 4.71/5.02 ( ! [X4: $o] :
% 4.71/5.02 ~ ( member_o @ X4 @ A2 )
% 4.71/5.02 => ( ord_less_eq_set_o @ A2 @ bot_bot_set_o ) ) ).
% 4.71/5.02
% 4.71/5.02 % subset_emptyI
% 4.71/5.02 thf(fact_978_subset__emptyI,axiom,
% 4.71/5.02 ! [A2: set_nat] :
% 4.71/5.02 ( ! [X4: nat] :
% 4.71/5.02 ~ ( member_nat @ X4 @ A2 )
% 4.71/5.02 => ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat ) ) ).
% 4.71/5.02
% 4.71/5.02 % subset_emptyI
% 4.71/5.02 thf(fact_979_subset__emptyI,axiom,
% 4.71/5.02 ! [A2: set_int] :
% 4.71/5.02 ( ! [X4: int] :
% 4.71/5.02 ~ ( member_int @ X4 @ A2 )
% 4.71/5.02 => ( ord_less_eq_set_int @ A2 @ bot_bot_set_int ) ) ).
% 4.71/5.02
% 4.71/5.02 % subset_emptyI
% 4.71/5.02 thf(fact_980_minf_I8_J,axiom,
% 4.71/5.02 ! [T: real] :
% 4.71/5.02 ? [Z3: real] :
% 4.71/5.02 ! [X2: real] :
% 4.71/5.02 ( ( ord_less_real @ X2 @ Z3 )
% 4.71/5.02 => ~ ( ord_less_eq_real @ T @ X2 ) ) ).
% 4.71/5.02
% 4.71/5.02 % minf(8)
% 4.71/5.02 thf(fact_981_minf_I8_J,axiom,
% 4.71/5.02 ! [T: rat] :
% 4.71/5.02 ? [Z3: rat] :
% 4.71/5.02 ! [X2: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X2 @ Z3 )
% 4.71/5.02 => ~ ( ord_less_eq_rat @ T @ X2 ) ) ).
% 4.71/5.02
% 4.71/5.02 % minf(8)
% 4.71/5.02 thf(fact_982_minf_I8_J,axiom,
% 4.71/5.02 ! [T: num] :
% 4.71/5.02 ? [Z3: num] :
% 4.71/5.02 ! [X2: num] :
% 4.71/5.02 ( ( ord_less_num @ X2 @ Z3 )
% 4.71/5.02 => ~ ( ord_less_eq_num @ T @ X2 ) ) ).
% 4.71/5.02
% 4.71/5.02 % minf(8)
% 4.71/5.02 thf(fact_983_minf_I8_J,axiom,
% 4.71/5.02 ! [T: nat] :
% 4.71/5.02 ? [Z3: nat] :
% 4.71/5.02 ! [X2: nat] :
% 4.71/5.02 ( ( ord_less_nat @ X2 @ Z3 )
% 4.71/5.02 => ~ ( ord_less_eq_nat @ T @ X2 ) ) ).
% 4.71/5.02
% 4.71/5.02 % minf(8)
% 4.71/5.02 thf(fact_984_minf_I8_J,axiom,
% 4.71/5.02 ! [T: int] :
% 4.71/5.02 ? [Z3: int] :
% 4.71/5.02 ! [X2: int] :
% 4.71/5.02 ( ( ord_less_int @ X2 @ Z3 )
% 4.71/5.02 => ~ ( ord_less_eq_int @ T @ X2 ) ) ).
% 4.71/5.02
% 4.71/5.02 % minf(8)
% 4.71/5.02 thf(fact_985_minf_I6_J,axiom,
% 4.71/5.02 ! [T: real] :
% 4.71/5.02 ? [Z3: real] :
% 4.71/5.02 ! [X2: real] :
% 4.71/5.02 ( ( ord_less_real @ X2 @ Z3 )
% 4.71/5.02 => ( ord_less_eq_real @ X2 @ T ) ) ).
% 4.71/5.02
% 4.71/5.02 % minf(6)
% 4.71/5.02 thf(fact_986_minf_I6_J,axiom,
% 4.71/5.02 ! [T: rat] :
% 4.71/5.02 ? [Z3: rat] :
% 4.71/5.02 ! [X2: rat] :
% 4.71/5.02 ( ( ord_less_rat @ X2 @ Z3 )
% 4.71/5.02 => ( ord_less_eq_rat @ X2 @ T ) ) ).
% 4.71/5.02
% 4.71/5.02 % minf(6)
% 4.71/5.02 thf(fact_987_minf_I6_J,axiom,
% 4.71/5.02 ! [T: num] :
% 4.71/5.02 ? [Z3: num] :
% 4.71/5.02 ! [X2: num] :
% 4.71/5.02 ( ( ord_less_num @ X2 @ Z3 )
% 4.71/5.02 => ( ord_less_eq_num @ X2 @ T ) ) ).
% 4.71/5.02
% 4.71/5.02 % minf(6)
% 4.71/5.02 thf(fact_988_minf_I6_J,axiom,
% 4.71/5.02 ! [T: nat] :
% 4.71/5.02 ? [Z3: nat] :
% 4.71/5.02 ! [X2: nat] :
% 4.71/5.02 ( ( ord_less_nat @ X2 @ Z3 )
% 4.71/5.02 => ( ord_less_eq_nat @ X2 @ T ) ) ).
% 4.71/5.02
% 4.71/5.02 % minf(6)
% 4.71/5.02 thf(fact_989_minf_I6_J,axiom,
% 4.71/5.02 ! [T: int] :
% 4.71/5.02 ? [Z3: int] :
% 4.71/5.02 ! [X2: int] :
% 4.71/5.02 ( ( ord_less_int @ X2 @ Z3 )
% 4.71/5.02 => ( ord_less_eq_int @ X2 @ T ) ) ).
% 4.71/5.02
% 4.71/5.02 % minf(6)
% 4.71/5.02 thf(fact_990_pinf_I8_J,axiom,
% 4.71/5.02 ! [T: real] :
% 4.71/5.02 ? [Z3: real] :
% 4.71/5.02 ! [X2: real] :
% 4.71/5.02 ( ( ord_less_real @ Z3 @ X2 )
% 4.71/5.02 => ( ord_less_eq_real @ T @ X2 ) ) ).
% 4.71/5.02
% 4.71/5.02 % pinf(8)
% 4.71/5.02 thf(fact_991_pinf_I8_J,axiom,
% 4.71/5.02 ! [T: rat] :
% 4.71/5.02 ? [Z3: rat] :
% 4.71/5.02 ! [X2: rat] :
% 4.71/5.02 ( ( ord_less_rat @ Z3 @ X2 )
% 4.71/5.02 => ( ord_less_eq_rat @ T @ X2 ) ) ).
% 4.71/5.02
% 4.71/5.02 % pinf(8)
% 4.71/5.02 thf(fact_992_pinf_I8_J,axiom,
% 4.71/5.02 ! [T: num] :
% 4.71/5.02 ? [Z3: num] :
% 4.71/5.02 ! [X2: num] :
% 4.71/5.02 ( ( ord_less_num @ Z3 @ X2 )
% 4.71/5.02 => ( ord_less_eq_num @ T @ X2 ) ) ).
% 4.71/5.02
% 4.71/5.02 % pinf(8)
% 4.71/5.02 thf(fact_993_pinf_I8_J,axiom,
% 4.71/5.02 ! [T: nat] :
% 4.71/5.02 ? [Z3: nat] :
% 4.71/5.02 ! [X2: nat] :
% 4.71/5.02 ( ( ord_less_nat @ Z3 @ X2 )
% 4.71/5.02 => ( ord_less_eq_nat @ T @ X2 ) ) ).
% 4.71/5.02
% 4.71/5.02 % pinf(8)
% 4.71/5.02 thf(fact_994_pinf_I8_J,axiom,
% 4.71/5.02 ! [T: int] :
% 4.71/5.02 ? [Z3: int] :
% 4.71/5.02 ! [X2: int] :
% 4.71/5.02 ( ( ord_less_int @ Z3 @ X2 )
% 4.71/5.02 => ( ord_less_eq_int @ T @ X2 ) ) ).
% 4.71/5.02
% 4.71/5.02 % pinf(8)
% 4.71/5.02 thf(fact_995_pinf_I6_J,axiom,
% 4.71/5.02 ! [T: real] :
% 4.71/5.02 ? [Z3: real] :
% 4.71/5.02 ! [X2: real] :
% 4.71/5.02 ( ( ord_less_real @ Z3 @ X2 )
% 4.71/5.02 => ~ ( ord_less_eq_real @ X2 @ T ) ) ).
% 4.71/5.02
% 4.71/5.02 % pinf(6)
% 4.71/5.02 thf(fact_996_pinf_I6_J,axiom,
% 4.71/5.02 ! [T: rat] :
% 4.71/5.02 ? [Z3: rat] :
% 4.71/5.02 ! [X2: rat] :
% 4.71/5.02 ( ( ord_less_rat @ Z3 @ X2 )
% 4.71/5.02 => ~ ( ord_less_eq_rat @ X2 @ T ) ) ).
% 4.71/5.02
% 4.71/5.02 % pinf(6)
% 4.71/5.02 thf(fact_997_pinf_I6_J,axiom,
% 4.71/5.02 ! [T: num] :
% 4.71/5.02 ? [Z3: num] :
% 4.71/5.02 ! [X2: num] :
% 4.71/5.02 ( ( ord_less_num @ Z3 @ X2 )
% 4.71/5.02 => ~ ( ord_less_eq_num @ X2 @ T ) ) ).
% 4.71/5.02
% 4.71/5.02 % pinf(6)
% 4.71/5.02 thf(fact_998_pinf_I6_J,axiom,
% 4.71/5.02 ! [T: nat] :
% 4.71/5.02 ? [Z3: nat] :
% 4.71/5.02 ! [X2: nat] :
% 4.71/5.02 ( ( ord_less_nat @ Z3 @ X2 )
% 4.71/5.02 => ~ ( ord_less_eq_nat @ X2 @ T ) ) ).
% 4.71/5.02
% 4.71/5.02 % pinf(6)
% 4.71/5.02 thf(fact_999_pinf_I6_J,axiom,
% 4.71/5.02 ! [T: int] :
% 4.71/5.02 ? [Z3: int] :
% 4.71/5.02 ! [X2: int] :
% 4.71/5.02 ( ( ord_less_int @ Z3 @ X2 )
% 4.71/5.02 => ~ ( ord_less_eq_int @ X2 @ T ) ) ).
% 4.71/5.02
% 4.71/5.02 % pinf(6)
% 4.71/5.02 thf(fact_1000_verit__comp__simplify1_I3_J,axiom,
% 4.71/5.02 ! [B7: real,A7: real] :
% 4.71/5.02 ( ( ~ ( ord_less_eq_real @ B7 @ A7 ) )
% 4.71/5.02 = ( ord_less_real @ A7 @ B7 ) ) ).
% 4.71/5.02
% 4.71/5.02 % verit_comp_simplify1(3)
% 4.71/5.02 thf(fact_1001_verit__comp__simplify1_I3_J,axiom,
% 4.71/5.02 ! [B7: rat,A7: rat] :
% 4.71/5.02 ( ( ~ ( ord_less_eq_rat @ B7 @ A7 ) )
% 4.71/5.02 = ( ord_less_rat @ A7 @ B7 ) ) ).
% 4.71/5.02
% 4.71/5.02 % verit_comp_simplify1(3)
% 4.71/5.02 thf(fact_1002_verit__comp__simplify1_I3_J,axiom,
% 4.71/5.02 ! [B7: num,A7: num] :
% 4.71/5.02 ( ( ~ ( ord_less_eq_num @ B7 @ A7 ) )
% 4.71/5.02 = ( ord_less_num @ A7 @ B7 ) ) ).
% 4.71/5.02
% 4.71/5.02 % verit_comp_simplify1(3)
% 4.71/5.02 thf(fact_1003_verit__comp__simplify1_I3_J,axiom,
% 4.71/5.02 ! [B7: nat,A7: nat] :
% 4.71/5.02 ( ( ~ ( ord_less_eq_nat @ B7 @ A7 ) )
% 4.71/5.02 = ( ord_less_nat @ A7 @ B7 ) ) ).
% 4.71/5.02
% 4.71/5.02 % verit_comp_simplify1(3)
% 4.71/5.02 thf(fact_1004_verit__comp__simplify1_I3_J,axiom,
% 4.71/5.02 ! [B7: int,A7: int] :
% 4.71/5.02 ( ( ~ ( ord_less_eq_int @ B7 @ A7 ) )
% 4.71/5.02 = ( ord_less_int @ A7 @ B7 ) ) ).
% 4.71/5.02
% 4.71/5.02 % verit_comp_simplify1(3)
% 4.71/5.02 thf(fact_1005_complete__interval,axiom,
% 4.71/5.02 ! [A: real,B: real,P: real > $o] :
% 4.71/5.02 ( ( ord_less_real @ A @ B )
% 4.71/5.02 => ( ( P @ A )
% 4.71/5.02 => ( ~ ( P @ B )
% 4.71/5.02 => ? [C3: real] :
% 4.71/5.02 ( ( ord_less_eq_real @ A @ C3 )
% 4.71/5.02 & ( ord_less_eq_real @ C3 @ B )
% 4.71/5.02 & ! [X2: real] :
% 4.71/5.02 ( ( ( ord_less_eq_real @ A @ X2 )
% 4.71/5.02 & ( ord_less_real @ X2 @ C3 ) )
% 4.71/5.02 => ( P @ X2 ) )
% 4.71/5.02 & ! [D3: real] :
% 4.71/5.02 ( ! [X4: real] :
% 4.71/5.02 ( ( ( ord_less_eq_real @ A @ X4 )
% 4.71/5.02 & ( ord_less_real @ X4 @ D3 ) )
% 4.71/5.02 => ( P @ X4 ) )
% 4.71/5.02 => ( ord_less_eq_real @ D3 @ C3 ) ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % complete_interval
% 4.71/5.02 thf(fact_1006_complete__interval,axiom,
% 4.71/5.02 ! [A: nat,B: nat,P: nat > $o] :
% 4.71/5.02 ( ( ord_less_nat @ A @ B )
% 4.71/5.02 => ( ( P @ A )
% 4.71/5.02 => ( ~ ( P @ B )
% 4.71/5.02 => ? [C3: nat] :
% 4.71/5.02 ( ( ord_less_eq_nat @ A @ C3 )
% 4.71/5.02 & ( ord_less_eq_nat @ C3 @ B )
% 4.71/5.02 & ! [X2: nat] :
% 4.71/5.02 ( ( ( ord_less_eq_nat @ A @ X2 )
% 4.71/5.02 & ( ord_less_nat @ X2 @ C3 ) )
% 4.71/5.02 => ( P @ X2 ) )
% 4.71/5.02 & ! [D3: nat] :
% 4.71/5.02 ( ! [X4: nat] :
% 4.71/5.02 ( ( ( ord_less_eq_nat @ A @ X4 )
% 4.71/5.02 & ( ord_less_nat @ X4 @ D3 ) )
% 4.71/5.02 => ( P @ X4 ) )
% 4.71/5.02 => ( ord_less_eq_nat @ D3 @ C3 ) ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % complete_interval
% 4.71/5.02 thf(fact_1007_complete__interval,axiom,
% 4.71/5.02 ! [A: int,B: int,P: int > $o] :
% 4.71/5.02 ( ( ord_less_int @ A @ B )
% 4.71/5.02 => ( ( P @ A )
% 4.71/5.02 => ( ~ ( P @ B )
% 4.71/5.02 => ? [C3: int] :
% 4.71/5.02 ( ( ord_less_eq_int @ A @ C3 )
% 4.71/5.02 & ( ord_less_eq_int @ C3 @ B )
% 4.71/5.02 & ! [X2: int] :
% 4.71/5.02 ( ( ( ord_less_eq_int @ A @ X2 )
% 4.71/5.02 & ( ord_less_int @ X2 @ C3 ) )
% 4.71/5.02 => ( P @ X2 ) )
% 4.71/5.02 & ! [D3: int] :
% 4.71/5.02 ( ! [X4: int] :
% 4.71/5.02 ( ( ( ord_less_eq_int @ A @ X4 )
% 4.71/5.02 & ( ord_less_int @ X4 @ D3 ) )
% 4.71/5.02 => ( P @ X4 ) )
% 4.71/5.02 => ( ord_less_eq_int @ D3 @ C3 ) ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % complete_interval
% 4.71/5.02 thf(fact_1008_deg__SUcn__Node,axiom,
% 4.71/5.02 ! [Tree: vEBT_VEBT,N: nat] :
% 4.71/5.02 ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N ) ) )
% 4.71/5.02 => ? [Info2: option4927543243414619207at_nat,TreeList2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 4.71/5.02 ( Tree
% 4.71/5.02 = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N ) ) @ TreeList2 @ S3 ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % deg_SUcn_Node
% 4.71/5.02 thf(fact_1009_dbl__inc__simps_I2_J,axiom,
% 4.71/5.02 ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 4.71/5.02 = one_one_complex ) ).
% 4.71/5.02
% 4.71/5.02 % dbl_inc_simps(2)
% 4.71/5.02 thf(fact_1010_dbl__inc__simps_I2_J,axiom,
% 4.71/5.02 ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 4.71/5.02 = one_one_real ) ).
% 4.71/5.02
% 4.71/5.02 % dbl_inc_simps(2)
% 4.71/5.02 thf(fact_1011_dbl__inc__simps_I2_J,axiom,
% 4.71/5.02 ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 4.71/5.02 = one_one_rat ) ).
% 4.71/5.02
% 4.71/5.02 % dbl_inc_simps(2)
% 4.71/5.02 thf(fact_1012_dbl__inc__simps_I2_J,axiom,
% 4.71/5.02 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 4.71/5.02 = one_one_int ) ).
% 4.71/5.02
% 4.71/5.02 % dbl_inc_simps(2)
% 4.71/5.02 thf(fact_1013_VEBT_Osize__gen_I2_J,axiom,
% 4.71/5.02 ! [X21: $o,X22: $o] :
% 4.71/5.02 ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X22 ) )
% 4.71/5.02 = zero_zero_nat ) ).
% 4.71/5.02
% 4.71/5.02 % VEBT.size_gen(2)
% 4.71/5.02 thf(fact_1014_min__Null__member,axiom,
% 4.71/5.02 ! [T: vEBT_VEBT,X: nat] :
% 4.71/5.02 ( ( vEBT_VEBT_minNull @ T )
% 4.71/5.02 => ~ ( vEBT_vebt_member @ T @ X ) ) ).
% 4.71/5.02
% 4.71/5.02 % min_Null_member
% 4.71/5.02 thf(fact_1015_not__min__Null__member,axiom,
% 4.71/5.02 ! [T: vEBT_VEBT] :
% 4.71/5.02 ( ~ ( vEBT_VEBT_minNull @ T )
% 4.71/5.02 => ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 ) ) ).
% 4.71/5.02
% 4.71/5.02 % not_min_Null_member
% 4.71/5.02 thf(fact_1016_nat_Oinject,axiom,
% 4.71/5.02 ! [X23: nat,Y23: nat] :
% 4.71/5.02 ( ( ( suc @ X23 )
% 4.71/5.02 = ( suc @ Y23 ) )
% 4.71/5.02 = ( X23 = Y23 ) ) ).
% 4.71/5.02
% 4.71/5.02 % nat.inject
% 4.71/5.02 thf(fact_1017_old_Onat_Oinject,axiom,
% 4.71/5.02 ! [Nat: nat,Nat2: nat] :
% 4.71/5.02 ( ( ( suc @ Nat )
% 4.71/5.02 = ( suc @ Nat2 ) )
% 4.71/5.02 = ( Nat = Nat2 ) ) ).
% 4.71/5.02
% 4.71/5.02 % old.nat.inject
% 4.71/5.02 thf(fact_1018_Suc__less__eq,axiom,
% 4.71/5.02 ! [M2: nat,N: nat] :
% 4.71/5.02 ( ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 4.71/5.02 = ( ord_less_nat @ M2 @ N ) ) ).
% 4.71/5.02
% 4.71/5.02 % Suc_less_eq
% 4.71/5.02 thf(fact_1019_Suc__mono,axiom,
% 4.71/5.02 ! [M2: nat,N: nat] :
% 4.71/5.02 ( ( ord_less_nat @ M2 @ N )
% 4.71/5.02 => ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % Suc_mono
% 4.71/5.02 thf(fact_1020_lessI,axiom,
% 4.71/5.02 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 4.71/5.02
% 4.71/5.02 % lessI
% 4.71/5.02 thf(fact_1021_Suc__le__mono,axiom,
% 4.71/5.02 ! [N: nat,M2: nat] :
% 4.71/5.02 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M2 ) )
% 4.71/5.02 = ( ord_less_eq_nat @ N @ M2 ) ) ).
% 4.71/5.02
% 4.71/5.02 % Suc_le_mono
% 4.71/5.02 thf(fact_1022_zero__less__Suc,axiom,
% 4.71/5.02 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 4.71/5.02
% 4.71/5.02 % zero_less_Suc
% 4.71/5.02 thf(fact_1023_less__Suc0,axiom,
% 4.71/5.02 ! [N: nat] :
% 4.71/5.02 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 4.71/5.02 = ( N = zero_zero_nat ) ) ).
% 4.71/5.02
% 4.71/5.02 % less_Suc0
% 4.71/5.02 thf(fact_1024_Suc__inject,axiom,
% 4.71/5.02 ! [X: nat,Y: nat] :
% 4.71/5.02 ( ( ( suc @ X )
% 4.71/5.02 = ( suc @ Y ) )
% 4.71/5.02 => ( X = Y ) ) ).
% 4.71/5.02
% 4.71/5.02 % Suc_inject
% 4.71/5.02 thf(fact_1025_n__not__Suc__n,axiom,
% 4.71/5.02 ! [N: nat] :
% 4.71/5.02 ( N
% 4.71/5.02 != ( suc @ N ) ) ).
% 4.71/5.02
% 4.71/5.02 % n_not_Suc_n
% 4.71/5.02 thf(fact_1026_not0__implies__Suc,axiom,
% 4.71/5.02 ! [N: nat] :
% 4.71/5.02 ( ( N != zero_zero_nat )
% 4.71/5.02 => ? [M4: nat] :
% 4.71/5.02 ( N
% 4.71/5.02 = ( suc @ M4 ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % not0_implies_Suc
% 4.71/5.02 thf(fact_1027_Zero__not__Suc,axiom,
% 4.71/5.02 ! [M2: nat] :
% 4.71/5.02 ( zero_zero_nat
% 4.71/5.02 != ( suc @ M2 ) ) ).
% 4.71/5.02
% 4.71/5.02 % Zero_not_Suc
% 4.71/5.02 thf(fact_1028_Zero__neq__Suc,axiom,
% 4.71/5.02 ! [M2: nat] :
% 4.71/5.02 ( zero_zero_nat
% 4.71/5.02 != ( suc @ M2 ) ) ).
% 4.71/5.02
% 4.71/5.02 % Zero_neq_Suc
% 4.71/5.02 thf(fact_1029_Suc__neq__Zero,axiom,
% 4.71/5.02 ! [M2: nat] :
% 4.71/5.02 ( ( suc @ M2 )
% 4.71/5.02 != zero_zero_nat ) ).
% 4.71/5.02
% 4.71/5.02 % Suc_neq_Zero
% 4.71/5.02 thf(fact_1030_zero__induct,axiom,
% 4.71/5.02 ! [P: nat > $o,K: nat] :
% 4.71/5.02 ( ( P @ K )
% 4.71/5.02 => ( ! [N2: nat] :
% 4.71/5.02 ( ( P @ ( suc @ N2 ) )
% 4.71/5.02 => ( P @ N2 ) )
% 4.71/5.02 => ( P @ zero_zero_nat ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % zero_induct
% 4.71/5.02 thf(fact_1031_diff__induct,axiom,
% 4.71/5.02 ! [P: nat > nat > $o,M2: nat,N: nat] :
% 4.71/5.02 ( ! [X4: nat] : ( P @ X4 @ zero_zero_nat )
% 4.71/5.02 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 4.71/5.02 => ( ! [X4: nat,Y3: nat] :
% 4.71/5.02 ( ( P @ X4 @ Y3 )
% 4.71/5.02 => ( P @ ( suc @ X4 ) @ ( suc @ Y3 ) ) )
% 4.71/5.02 => ( P @ M2 @ N ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % diff_induct
% 4.71/5.02 thf(fact_1032_nat__induct,axiom,
% 4.71/5.02 ! [P: nat > $o,N: nat] :
% 4.71/5.02 ( ( P @ zero_zero_nat )
% 4.71/5.02 => ( ! [N2: nat] :
% 4.71/5.02 ( ( P @ N2 )
% 4.71/5.02 => ( P @ ( suc @ N2 ) ) )
% 4.71/5.02 => ( P @ N ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % nat_induct
% 4.71/5.02 thf(fact_1033_vebt__buildup_Ocases,axiom,
% 4.71/5.02 ! [X: nat] :
% 4.71/5.02 ( ( X != zero_zero_nat )
% 4.71/5.02 => ( ( X
% 4.71/5.02 != ( suc @ zero_zero_nat ) )
% 4.71/5.02 => ~ ! [Va: nat] :
% 4.71/5.02 ( X
% 4.71/5.02 != ( suc @ ( suc @ Va ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % vebt_buildup.cases
% 4.71/5.02 thf(fact_1034_old_Onat_Oexhaust,axiom,
% 4.71/5.02 ! [Y: nat] :
% 4.71/5.02 ( ( Y != zero_zero_nat )
% 4.71/5.02 => ~ ! [Nat3: nat] :
% 4.71/5.02 ( Y
% 4.71/5.02 != ( suc @ Nat3 ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % old.nat.exhaust
% 4.71/5.02 thf(fact_1035_nat_OdiscI,axiom,
% 4.71/5.02 ! [Nat: nat,X23: nat] :
% 4.71/5.02 ( ( Nat
% 4.71/5.02 = ( suc @ X23 ) )
% 4.71/5.02 => ( Nat != zero_zero_nat ) ) ).
% 4.71/5.02
% 4.71/5.02 % nat.discI
% 4.71/5.02 thf(fact_1036_old_Onat_Odistinct_I1_J,axiom,
% 4.71/5.02 ! [Nat2: nat] :
% 4.71/5.02 ( zero_zero_nat
% 4.71/5.02 != ( suc @ Nat2 ) ) ).
% 4.71/5.02
% 4.71/5.02 % old.nat.distinct(1)
% 4.71/5.02 thf(fact_1037_old_Onat_Odistinct_I2_J,axiom,
% 4.71/5.02 ! [Nat2: nat] :
% 4.71/5.02 ( ( suc @ Nat2 )
% 4.71/5.02 != zero_zero_nat ) ).
% 4.71/5.02
% 4.71/5.02 % old.nat.distinct(2)
% 4.71/5.02 thf(fact_1038_nat_Odistinct_I1_J,axiom,
% 4.71/5.02 ! [X23: nat] :
% 4.71/5.02 ( zero_zero_nat
% 4.71/5.02 != ( suc @ X23 ) ) ).
% 4.71/5.02
% 4.71/5.02 % nat.distinct(1)
% 4.71/5.02 thf(fact_1039_not__less__less__Suc__eq,axiom,
% 4.71/5.02 ! [N: nat,M2: nat] :
% 4.71/5.02 ( ~ ( ord_less_nat @ N @ M2 )
% 4.71/5.02 => ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 4.71/5.02 = ( N = M2 ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % not_less_less_Suc_eq
% 4.71/5.02 thf(fact_1040_strict__inc__induct,axiom,
% 4.71/5.02 ! [I: nat,J: nat,P: nat > $o] :
% 4.71/5.02 ( ( ord_less_nat @ I @ J )
% 4.71/5.02 => ( ! [I2: nat] :
% 4.71/5.02 ( ( J
% 4.71/5.02 = ( suc @ I2 ) )
% 4.71/5.02 => ( P @ I2 ) )
% 4.71/5.02 => ( ! [I2: nat] :
% 4.71/5.02 ( ( ord_less_nat @ I2 @ J )
% 4.71/5.02 => ( ( P @ ( suc @ I2 ) )
% 4.71/5.02 => ( P @ I2 ) ) )
% 4.71/5.02 => ( P @ I ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % strict_inc_induct
% 4.71/5.02 thf(fact_1041_less__Suc__induct,axiom,
% 4.71/5.02 ! [I: nat,J: nat,P: nat > nat > $o] :
% 4.71/5.02 ( ( ord_less_nat @ I @ J )
% 4.71/5.02 => ( ! [I2: nat] : ( P @ I2 @ ( suc @ I2 ) )
% 4.71/5.02 => ( ! [I2: nat,J2: nat,K2: nat] :
% 4.71/5.02 ( ( ord_less_nat @ I2 @ J2 )
% 4.71/5.02 => ( ( ord_less_nat @ J2 @ K2 )
% 4.71/5.02 => ( ( P @ I2 @ J2 )
% 4.71/5.02 => ( ( P @ J2 @ K2 )
% 4.71/5.02 => ( P @ I2 @ K2 ) ) ) ) )
% 4.71/5.02 => ( P @ I @ J ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % less_Suc_induct
% 4.71/5.02 thf(fact_1042_less__trans__Suc,axiom,
% 4.71/5.02 ! [I: nat,J: nat,K: nat] :
% 4.71/5.02 ( ( ord_less_nat @ I @ J )
% 4.71/5.02 => ( ( ord_less_nat @ J @ K )
% 4.71/5.02 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % less_trans_Suc
% 4.71/5.02 thf(fact_1043_Suc__less__SucD,axiom,
% 4.71/5.02 ! [M2: nat,N: nat] :
% 4.71/5.02 ( ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 4.71/5.02 => ( ord_less_nat @ M2 @ N ) ) ).
% 4.71/5.02
% 4.71/5.02 % Suc_less_SucD
% 4.71/5.02 thf(fact_1044_less__antisym,axiom,
% 4.71/5.02 ! [N: nat,M2: nat] :
% 4.71/5.02 ( ~ ( ord_less_nat @ N @ M2 )
% 4.71/5.02 => ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 4.71/5.02 => ( M2 = N ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % less_antisym
% 4.71/5.02 thf(fact_1045_Suc__less__eq2,axiom,
% 4.71/5.02 ! [N: nat,M2: nat] :
% 4.71/5.02 ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 4.71/5.02 = ( ? [M6: nat] :
% 4.71/5.02 ( ( M2
% 4.71/5.02 = ( suc @ M6 ) )
% 4.71/5.02 & ( ord_less_nat @ N @ M6 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % Suc_less_eq2
% 4.71/5.02 thf(fact_1046_All__less__Suc,axiom,
% 4.71/5.02 ! [N: nat,P: nat > $o] :
% 4.71/5.02 ( ( ! [I4: nat] :
% 4.71/5.02 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 4.71/5.02 => ( P @ I4 ) ) )
% 4.71/5.02 = ( ( P @ N )
% 4.71/5.02 & ! [I4: nat] :
% 4.71/5.02 ( ( ord_less_nat @ I4 @ N )
% 4.71/5.02 => ( P @ I4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % All_less_Suc
% 4.71/5.02 thf(fact_1047_not__less__eq,axiom,
% 4.71/5.02 ! [M2: nat,N: nat] :
% 4.71/5.02 ( ( ~ ( ord_less_nat @ M2 @ N ) )
% 4.71/5.02 = ( ord_less_nat @ N @ ( suc @ M2 ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % not_less_eq
% 4.71/5.02 thf(fact_1048_less__Suc__eq,axiom,
% 4.71/5.02 ! [M2: nat,N: nat] :
% 4.71/5.02 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 4.71/5.02 = ( ( ord_less_nat @ M2 @ N )
% 4.71/5.02 | ( M2 = N ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % less_Suc_eq
% 4.71/5.02 thf(fact_1049_Ex__less__Suc,axiom,
% 4.71/5.02 ! [N: nat,P: nat > $o] :
% 4.71/5.02 ( ( ? [I4: nat] :
% 4.71/5.02 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 4.71/5.02 & ( P @ I4 ) ) )
% 4.71/5.02 = ( ( P @ N )
% 4.71/5.02 | ? [I4: nat] :
% 4.71/5.02 ( ( ord_less_nat @ I4 @ N )
% 4.71/5.02 & ( P @ I4 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % Ex_less_Suc
% 4.71/5.02 thf(fact_1050_less__SucI,axiom,
% 4.71/5.02 ! [M2: nat,N: nat] :
% 4.71/5.02 ( ( ord_less_nat @ M2 @ N )
% 4.71/5.02 => ( ord_less_nat @ M2 @ ( suc @ N ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % less_SucI
% 4.71/5.02 thf(fact_1051_less__SucE,axiom,
% 4.71/5.02 ! [M2: nat,N: nat] :
% 4.71/5.02 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 4.71/5.02 => ( ~ ( ord_less_nat @ M2 @ N )
% 4.71/5.02 => ( M2 = N ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % less_SucE
% 4.71/5.02 thf(fact_1052_Suc__lessI,axiom,
% 4.71/5.02 ! [M2: nat,N: nat] :
% 4.71/5.02 ( ( ord_less_nat @ M2 @ N )
% 4.71/5.02 => ( ( ( suc @ M2 )
% 4.71/5.02 != N )
% 4.71/5.02 => ( ord_less_nat @ ( suc @ M2 ) @ N ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % Suc_lessI
% 4.71/5.02 thf(fact_1053_Suc__lessE,axiom,
% 4.71/5.02 ! [I: nat,K: nat] :
% 4.71/5.02 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 4.71/5.02 => ~ ! [J2: nat] :
% 4.71/5.02 ( ( ord_less_nat @ I @ J2 )
% 4.71/5.02 => ( K
% 4.71/5.02 != ( suc @ J2 ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % Suc_lessE
% 4.71/5.02 thf(fact_1054_Suc__lessD,axiom,
% 4.71/5.02 ! [M2: nat,N: nat] :
% 4.71/5.02 ( ( ord_less_nat @ ( suc @ M2 ) @ N )
% 4.71/5.02 => ( ord_less_nat @ M2 @ N ) ) ).
% 4.71/5.02
% 4.71/5.02 % Suc_lessD
% 4.71/5.02 thf(fact_1055_Nat_OlessE,axiom,
% 4.71/5.02 ! [I: nat,K: nat] :
% 4.71/5.02 ( ( ord_less_nat @ I @ K )
% 4.71/5.02 => ( ( K
% 4.71/5.02 != ( suc @ I ) )
% 4.71/5.02 => ~ ! [J2: nat] :
% 4.71/5.02 ( ( ord_less_nat @ I @ J2 )
% 4.71/5.02 => ( K
% 4.71/5.02 != ( suc @ J2 ) ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % Nat.lessE
% 4.71/5.02 thf(fact_1056_Suc__leD,axiom,
% 4.71/5.02 ! [M2: nat,N: nat] :
% 4.71/5.02 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 4.71/5.02 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 4.71/5.02
% 4.71/5.02 % Suc_leD
% 4.71/5.02 thf(fact_1057_le__SucE,axiom,
% 4.71/5.02 ! [M2: nat,N: nat] :
% 4.71/5.02 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 4.71/5.02 => ( ~ ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.02 => ( M2
% 4.71/5.02 = ( suc @ N ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % le_SucE
% 4.71/5.02 thf(fact_1058_le__SucI,axiom,
% 4.71/5.02 ! [M2: nat,N: nat] :
% 4.71/5.02 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.02 => ( ord_less_eq_nat @ M2 @ ( suc @ N ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % le_SucI
% 4.71/5.02 thf(fact_1059_Suc__le__D,axiom,
% 4.71/5.02 ! [N: nat,M7: nat] :
% 4.71/5.02 ( ( ord_less_eq_nat @ ( suc @ N ) @ M7 )
% 4.71/5.02 => ? [M4: nat] :
% 4.71/5.02 ( M7
% 4.71/5.02 = ( suc @ M4 ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % Suc_le_D
% 4.71/5.02 thf(fact_1060_le__Suc__eq,axiom,
% 4.71/5.02 ! [M2: nat,N: nat] :
% 4.71/5.02 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 4.71/5.02 = ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.02 | ( M2
% 4.71/5.02 = ( suc @ N ) ) ) ) ).
% 4.71/5.02
% 4.71/5.02 % le_Suc_eq
% 4.71/5.02 thf(fact_1061_Suc__n__not__le__n,axiom,
% 4.71/5.02 ! [N: nat] :
% 4.71/5.02 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 4.71/5.02
% 4.71/5.02 % Suc_n_not_le_n
% 4.71/5.02 thf(fact_1062_not__less__eq__eq,axiom,
% 4.71/5.02 ! [M2: nat,N: nat] :
% 4.71/5.02 ( ( ~ ( ord_less_eq_nat @ M2 @ N ) )
% 4.71/5.02 = ( ord_less_eq_nat @ ( suc @ N ) @ M2 ) ) ).
% 4.71/5.02
% 4.71/5.02 % not_less_eq_eq
% 4.71/5.02 thf(fact_1063_full__nat__induct,axiom,
% 4.71/5.02 ! [P: nat > $o,N: nat] :
% 4.71/5.02 ( ! [N2: nat] :
% 4.71/5.02 ( ! [M: nat] :
% 4.71/5.02 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 4.71/5.02 => ( P @ M ) )
% 4.71/5.02 => ( P @ N2 ) )
% 4.71/5.02 => ( P @ N ) ) ).
% 4.71/5.02
% 4.71/5.02 % full_nat_induct
% 4.71/5.02 thf(fact_1064_nat__induct__at__least,axiom,
% 4.71/5.02 ! [M2: nat,N: nat,P: nat > $o] :
% 4.71/5.02 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.02 => ( ( P @ M2 )
% 4.71/5.02 => ( ! [N2: nat] :
% 4.71/5.02 ( ( ord_less_eq_nat @ M2 @ N2 )
% 4.71/5.02 => ( ( P @ N2 )
% 4.71/5.03 => ( P @ ( suc @ N2 ) ) ) )
% 4.71/5.03 => ( P @ N ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % nat_induct_at_least
% 4.71/5.03 thf(fact_1065_transitive__stepwise__le,axiom,
% 4.71/5.03 ! [M2: nat,N: nat,R: nat > nat > $o] :
% 4.71/5.03 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.03 => ( ! [X4: nat] : ( R @ X4 @ X4 )
% 4.71/5.03 => ( ! [X4: nat,Y3: nat,Z3: nat] :
% 4.71/5.03 ( ( R @ X4 @ Y3 )
% 4.71/5.03 => ( ( R @ Y3 @ Z3 )
% 4.71/5.03 => ( R @ X4 @ Z3 ) ) )
% 4.71/5.03 => ( ! [N2: nat] : ( R @ N2 @ ( suc @ N2 ) )
% 4.71/5.03 => ( R @ M2 @ N ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % transitive_stepwise_le
% 4.71/5.03 thf(fact_1066_VEBT__internal_OminNull_Osimps_I1_J,axiom,
% 4.71/5.03 vEBT_VEBT_minNull @ ( vEBT_Leaf @ $false @ $false ) ).
% 4.71/5.03
% 4.71/5.03 % VEBT_internal.minNull.simps(1)
% 4.71/5.03 thf(fact_1067_VEBT__internal_OminNull_Osimps_I2_J,axiom,
% 4.71/5.03 ! [Uv: $o] :
% 4.71/5.03 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ $true @ Uv ) ) ).
% 4.71/5.03
% 4.71/5.03 % VEBT_internal.minNull.simps(2)
% 4.71/5.03 thf(fact_1068_VEBT__internal_OminNull_Osimps_I3_J,axiom,
% 4.71/5.03 ! [Uu: $o] :
% 4.71/5.03 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ Uu @ $true ) ) ).
% 4.71/5.03
% 4.71/5.03 % VEBT_internal.minNull.simps(3)
% 4.71/5.03 thf(fact_1069_lift__Suc__mono__less__iff,axiom,
% 4.71/5.03 ! [F: nat > real,N: nat,M2: nat] :
% 4.71/5.03 ( ! [N2: nat] : ( ord_less_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 4.71/5.03 => ( ( ord_less_real @ ( F @ N ) @ ( F @ M2 ) )
% 4.71/5.03 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % lift_Suc_mono_less_iff
% 4.71/5.03 thf(fact_1070_lift__Suc__mono__less__iff,axiom,
% 4.71/5.03 ! [F: nat > rat,N: nat,M2: nat] :
% 4.71/5.03 ( ! [N2: nat] : ( ord_less_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 4.71/5.03 => ( ( ord_less_rat @ ( F @ N ) @ ( F @ M2 ) )
% 4.71/5.03 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % lift_Suc_mono_less_iff
% 4.71/5.03 thf(fact_1071_lift__Suc__mono__less__iff,axiom,
% 4.71/5.03 ! [F: nat > num,N: nat,M2: nat] :
% 4.71/5.03 ( ! [N2: nat] : ( ord_less_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 4.71/5.03 => ( ( ord_less_num @ ( F @ N ) @ ( F @ M2 ) )
% 4.71/5.03 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % lift_Suc_mono_less_iff
% 4.71/5.03 thf(fact_1072_lift__Suc__mono__less__iff,axiom,
% 4.71/5.03 ! [F: nat > nat,N: nat,M2: nat] :
% 4.71/5.03 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 4.71/5.03 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M2 ) )
% 4.71/5.03 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % lift_Suc_mono_less_iff
% 4.71/5.03 thf(fact_1073_lift__Suc__mono__less__iff,axiom,
% 4.71/5.03 ! [F: nat > int,N: nat,M2: nat] :
% 4.71/5.03 ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 4.71/5.03 => ( ( ord_less_int @ ( F @ N ) @ ( F @ M2 ) )
% 4.71/5.03 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % lift_Suc_mono_less_iff
% 4.71/5.03 thf(fact_1074_lift__Suc__mono__less,axiom,
% 4.71/5.03 ! [F: nat > real,N: nat,N7: nat] :
% 4.71/5.03 ( ! [N2: nat] : ( ord_less_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 4.71/5.03 => ( ( ord_less_nat @ N @ N7 )
% 4.71/5.03 => ( ord_less_real @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % lift_Suc_mono_less
% 4.71/5.03 thf(fact_1075_lift__Suc__mono__less,axiom,
% 4.71/5.03 ! [F: nat > rat,N: nat,N7: nat] :
% 4.71/5.03 ( ! [N2: nat] : ( ord_less_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 4.71/5.03 => ( ( ord_less_nat @ N @ N7 )
% 4.71/5.03 => ( ord_less_rat @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % lift_Suc_mono_less
% 4.71/5.03 thf(fact_1076_lift__Suc__mono__less,axiom,
% 4.71/5.03 ! [F: nat > num,N: nat,N7: nat] :
% 4.71/5.03 ( ! [N2: nat] : ( ord_less_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 4.71/5.03 => ( ( ord_less_nat @ N @ N7 )
% 4.71/5.03 => ( ord_less_num @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % lift_Suc_mono_less
% 4.71/5.03 thf(fact_1077_lift__Suc__mono__less,axiom,
% 4.71/5.03 ! [F: nat > nat,N: nat,N7: nat] :
% 4.71/5.03 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 4.71/5.03 => ( ( ord_less_nat @ N @ N7 )
% 4.71/5.03 => ( ord_less_nat @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % lift_Suc_mono_less
% 4.71/5.03 thf(fact_1078_lift__Suc__mono__less,axiom,
% 4.71/5.03 ! [F: nat > int,N: nat,N7: nat] :
% 4.71/5.03 ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 4.71/5.03 => ( ( ord_less_nat @ N @ N7 )
% 4.71/5.03 => ( ord_less_int @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % lift_Suc_mono_less
% 4.71/5.03 thf(fact_1079_lift__Suc__mono__le,axiom,
% 4.71/5.03 ! [F: nat > set_int,N: nat,N7: nat] :
% 4.71/5.03 ( ! [N2: nat] : ( ord_less_eq_set_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 4.71/5.03 => ( ( ord_less_eq_nat @ N @ N7 )
% 4.71/5.03 => ( ord_less_eq_set_int @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % lift_Suc_mono_le
% 4.71/5.03 thf(fact_1080_lift__Suc__mono__le,axiom,
% 4.71/5.03 ! [F: nat > rat,N: nat,N7: nat] :
% 4.71/5.03 ( ! [N2: nat] : ( ord_less_eq_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 4.71/5.03 => ( ( ord_less_eq_nat @ N @ N7 )
% 4.71/5.03 => ( ord_less_eq_rat @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % lift_Suc_mono_le
% 4.71/5.03 thf(fact_1081_lift__Suc__mono__le,axiom,
% 4.71/5.03 ! [F: nat > num,N: nat,N7: nat] :
% 4.71/5.03 ( ! [N2: nat] : ( ord_less_eq_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 4.71/5.03 => ( ( ord_less_eq_nat @ N @ N7 )
% 4.71/5.03 => ( ord_less_eq_num @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % lift_Suc_mono_le
% 4.71/5.03 thf(fact_1082_lift__Suc__mono__le,axiom,
% 4.71/5.03 ! [F: nat > nat,N: nat,N7: nat] :
% 4.71/5.03 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 4.71/5.03 => ( ( ord_less_eq_nat @ N @ N7 )
% 4.71/5.03 => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % lift_Suc_mono_le
% 4.71/5.03 thf(fact_1083_lift__Suc__mono__le,axiom,
% 4.71/5.03 ! [F: nat > int,N: nat,N7: nat] :
% 4.71/5.03 ( ! [N2: nat] : ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 4.71/5.03 => ( ( ord_less_eq_nat @ N @ N7 )
% 4.71/5.03 => ( ord_less_eq_int @ ( F @ N ) @ ( F @ N7 ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % lift_Suc_mono_le
% 4.71/5.03 thf(fact_1084_lift__Suc__antimono__le,axiom,
% 4.71/5.03 ! [F: nat > set_int,N: nat,N7: nat] :
% 4.71/5.03 ( ! [N2: nat] : ( ord_less_eq_set_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 4.71/5.03 => ( ( ord_less_eq_nat @ N @ N7 )
% 4.71/5.03 => ( ord_less_eq_set_int @ ( F @ N7 ) @ ( F @ N ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % lift_Suc_antimono_le
% 4.71/5.03 thf(fact_1085_lift__Suc__antimono__le,axiom,
% 4.71/5.03 ! [F: nat > rat,N: nat,N7: nat] :
% 4.71/5.03 ( ! [N2: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 4.71/5.03 => ( ( ord_less_eq_nat @ N @ N7 )
% 4.71/5.03 => ( ord_less_eq_rat @ ( F @ N7 ) @ ( F @ N ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % lift_Suc_antimono_le
% 4.71/5.03 thf(fact_1086_lift__Suc__antimono__le,axiom,
% 4.71/5.03 ! [F: nat > num,N: nat,N7: nat] :
% 4.71/5.03 ( ! [N2: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 4.71/5.03 => ( ( ord_less_eq_nat @ N @ N7 )
% 4.71/5.03 => ( ord_less_eq_num @ ( F @ N7 ) @ ( F @ N ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % lift_Suc_antimono_le
% 4.71/5.03 thf(fact_1087_lift__Suc__antimono__le,axiom,
% 4.71/5.03 ! [F: nat > nat,N: nat,N7: nat] :
% 4.71/5.03 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 4.71/5.03 => ( ( ord_less_eq_nat @ N @ N7 )
% 4.71/5.03 => ( ord_less_eq_nat @ ( F @ N7 ) @ ( F @ N ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % lift_Suc_antimono_le
% 4.71/5.03 thf(fact_1088_lift__Suc__antimono__le,axiom,
% 4.71/5.03 ! [F: nat > int,N: nat,N7: nat] :
% 4.71/5.03 ( ! [N2: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 4.71/5.03 => ( ( ord_less_eq_nat @ N @ N7 )
% 4.71/5.03 => ( ord_less_eq_int @ ( F @ N7 ) @ ( F @ N ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % lift_Suc_antimono_le
% 4.71/5.03 thf(fact_1089_less__Suc__eq__0__disj,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 4.71/5.03 = ( ( M2 = zero_zero_nat )
% 4.71/5.03 | ? [J3: nat] :
% 4.71/5.03 ( ( M2
% 4.71/5.03 = ( suc @ J3 ) )
% 4.71/5.03 & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % less_Suc_eq_0_disj
% 4.71/5.03 thf(fact_1090_gr0__implies__Suc,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.03 => ? [M4: nat] :
% 4.71/5.03 ( N
% 4.71/5.03 = ( suc @ M4 ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % gr0_implies_Suc
% 4.71/5.03 thf(fact_1091_All__less__Suc2,axiom,
% 4.71/5.03 ! [N: nat,P: nat > $o] :
% 4.71/5.03 ( ( ! [I4: nat] :
% 4.71/5.03 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 4.71/5.03 => ( P @ I4 ) ) )
% 4.71/5.03 = ( ( P @ zero_zero_nat )
% 4.71/5.03 & ! [I4: nat] :
% 4.71/5.03 ( ( ord_less_nat @ I4 @ N )
% 4.71/5.03 => ( P @ ( suc @ I4 ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % All_less_Suc2
% 4.71/5.03 thf(fact_1092_gr0__conv__Suc,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.03 = ( ? [M3: nat] :
% 4.71/5.03 ( N
% 4.71/5.03 = ( suc @ M3 ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % gr0_conv_Suc
% 4.71/5.03 thf(fact_1093_Ex__less__Suc2,axiom,
% 4.71/5.03 ! [N: nat,P: nat > $o] :
% 4.71/5.03 ( ( ? [I4: nat] :
% 4.71/5.03 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 4.71/5.03 & ( P @ I4 ) ) )
% 4.71/5.03 = ( ( P @ zero_zero_nat )
% 4.71/5.03 | ? [I4: nat] :
% 4.71/5.03 ( ( ord_less_nat @ I4 @ N )
% 4.71/5.03 & ( P @ ( suc @ I4 ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % Ex_less_Suc2
% 4.71/5.03 thf(fact_1094_Suc__leI,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_nat @ M2 @ N )
% 4.71/5.03 => ( ord_less_eq_nat @ ( suc @ M2 ) @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % Suc_leI
% 4.71/5.03 thf(fact_1095_Suc__le__eq,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 4.71/5.03 = ( ord_less_nat @ M2 @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % Suc_le_eq
% 4.71/5.03 thf(fact_1096_dec__induct,axiom,
% 4.71/5.03 ! [I: nat,J: nat,P: nat > $o] :
% 4.71/5.03 ( ( ord_less_eq_nat @ I @ J )
% 4.71/5.03 => ( ( P @ I )
% 4.71/5.03 => ( ! [N2: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ I @ N2 )
% 4.71/5.03 => ( ( ord_less_nat @ N2 @ J )
% 4.71/5.03 => ( ( P @ N2 )
% 4.71/5.03 => ( P @ ( suc @ N2 ) ) ) ) )
% 4.71/5.03 => ( P @ J ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % dec_induct
% 4.71/5.03 thf(fact_1097_inc__induct,axiom,
% 4.71/5.03 ! [I: nat,J: nat,P: nat > $o] :
% 4.71/5.03 ( ( ord_less_eq_nat @ I @ J )
% 4.71/5.03 => ( ( P @ J )
% 4.71/5.03 => ( ! [N2: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ I @ N2 )
% 4.71/5.03 => ( ( ord_less_nat @ N2 @ J )
% 4.71/5.03 => ( ( P @ ( suc @ N2 ) )
% 4.71/5.03 => ( P @ N2 ) ) ) )
% 4.71/5.03 => ( P @ I ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % inc_induct
% 4.71/5.03 thf(fact_1098_Suc__le__lessD,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 4.71/5.03 => ( ord_less_nat @ M2 @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % Suc_le_lessD
% 4.71/5.03 thf(fact_1099_le__less__Suc__eq,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.03 => ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 4.71/5.03 = ( N = M2 ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % le_less_Suc_eq
% 4.71/5.03 thf(fact_1100_less__Suc__eq__le,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 4.71/5.03 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % less_Suc_eq_le
% 4.71/5.03 thf(fact_1101_less__eq__Suc__le,axiom,
% 4.71/5.03 ( ord_less_nat
% 4.71/5.03 = ( ^ [N4: nat] : ( ord_less_eq_nat @ ( suc @ N4 ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % less_eq_Suc_le
% 4.71/5.03 thf(fact_1102_le__imp__less__Suc,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.03 => ( ord_less_nat @ M2 @ ( suc @ N ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % le_imp_less_Suc
% 4.71/5.03 thf(fact_1103_One__nat__def,axiom,
% 4.71/5.03 ( one_one_nat
% 4.71/5.03 = ( suc @ zero_zero_nat ) ) ).
% 4.71/5.03
% 4.71/5.03 % One_nat_def
% 4.71/5.03 thf(fact_1104_vebt__delete_Osimps_I3_J,axiom,
% 4.71/5.03 ! [A: $o,B: $o,N: nat] :
% 4.71/5.03 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ N ) ) )
% 4.71/5.03 = ( vEBT_Leaf @ A @ B ) ) ).
% 4.71/5.03
% 4.71/5.03 % vebt_delete.simps(3)
% 4.71/5.03 thf(fact_1105_ex__least__nat__less,axiom,
% 4.71/5.03 ! [P: nat > $o,N: nat] :
% 4.71/5.03 ( ( P @ N )
% 4.71/5.03 => ( ~ ( P @ zero_zero_nat )
% 4.71/5.03 => ? [K2: nat] :
% 4.71/5.03 ( ( ord_less_nat @ K2 @ N )
% 4.71/5.03 & ! [I3: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ I3 @ K2 )
% 4.71/5.03 => ~ ( P @ I3 ) )
% 4.71/5.03 & ( P @ ( suc @ K2 ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % ex_least_nat_less
% 4.71/5.03 thf(fact_1106_verit__la__disequality,axiom,
% 4.71/5.03 ! [A: rat,B: rat] :
% 4.71/5.03 ( ( A = B )
% 4.71/5.03 | ~ ( ord_less_eq_rat @ A @ B )
% 4.71/5.03 | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 4.71/5.03
% 4.71/5.03 % verit_la_disequality
% 4.71/5.03 thf(fact_1107_verit__la__disequality,axiom,
% 4.71/5.03 ! [A: num,B: num] :
% 4.71/5.03 ( ( A = B )
% 4.71/5.03 | ~ ( ord_less_eq_num @ A @ B )
% 4.71/5.03 | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 4.71/5.03
% 4.71/5.03 % verit_la_disequality
% 4.71/5.03 thf(fact_1108_verit__la__disequality,axiom,
% 4.71/5.03 ! [A: nat,B: nat] :
% 4.71/5.03 ( ( A = B )
% 4.71/5.03 | ~ ( ord_less_eq_nat @ A @ B )
% 4.71/5.03 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 4.71/5.03
% 4.71/5.03 % verit_la_disequality
% 4.71/5.03 thf(fact_1109_verit__la__disequality,axiom,
% 4.71/5.03 ! [A: int,B: int] :
% 4.71/5.03 ( ( A = B )
% 4.71/5.03 | ~ ( ord_less_eq_int @ A @ B )
% 4.71/5.03 | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 4.71/5.03
% 4.71/5.03 % verit_la_disequality
% 4.71/5.03 thf(fact_1110_verit__comp__simplify1_I2_J,axiom,
% 4.71/5.03 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 4.71/5.03
% 4.71/5.03 % verit_comp_simplify1(2)
% 4.71/5.03 thf(fact_1111_verit__comp__simplify1_I2_J,axiom,
% 4.71/5.03 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 4.71/5.03
% 4.71/5.03 % verit_comp_simplify1(2)
% 4.71/5.03 thf(fact_1112_verit__comp__simplify1_I2_J,axiom,
% 4.71/5.03 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 4.71/5.03
% 4.71/5.03 % verit_comp_simplify1(2)
% 4.71/5.03 thf(fact_1113_verit__comp__simplify1_I2_J,axiom,
% 4.71/5.03 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 4.71/5.03
% 4.71/5.03 % verit_comp_simplify1(2)
% 4.71/5.03 thf(fact_1114_verit__comp__simplify1_I2_J,axiom,
% 4.71/5.03 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 4.71/5.03
% 4.71/5.03 % verit_comp_simplify1(2)
% 4.71/5.03 thf(fact_1115_ex__gt__or__lt,axiom,
% 4.71/5.03 ! [A: real] :
% 4.71/5.03 ? [B5: real] :
% 4.71/5.03 ( ( ord_less_real @ A @ B5 )
% 4.71/5.03 | ( ord_less_real @ B5 @ A ) ) ).
% 4.71/5.03
% 4.71/5.03 % ex_gt_or_lt
% 4.71/5.03 thf(fact_1116_verit__comp__simplify1_I1_J,axiom,
% 4.71/5.03 ! [A: real] :
% 4.71/5.03 ~ ( ord_less_real @ A @ A ) ).
% 4.71/5.03
% 4.71/5.03 % verit_comp_simplify1(1)
% 4.71/5.03 thf(fact_1117_verit__comp__simplify1_I1_J,axiom,
% 4.71/5.03 ! [A: rat] :
% 4.71/5.03 ~ ( ord_less_rat @ A @ A ) ).
% 4.71/5.03
% 4.71/5.03 % verit_comp_simplify1(1)
% 4.71/5.03 thf(fact_1118_verit__comp__simplify1_I1_J,axiom,
% 4.71/5.03 ! [A: num] :
% 4.71/5.03 ~ ( ord_less_num @ A @ A ) ).
% 4.71/5.03
% 4.71/5.03 % verit_comp_simplify1(1)
% 4.71/5.03 thf(fact_1119_verit__comp__simplify1_I1_J,axiom,
% 4.71/5.03 ! [A: nat] :
% 4.71/5.03 ~ ( ord_less_nat @ A @ A ) ).
% 4.71/5.03
% 4.71/5.03 % verit_comp_simplify1(1)
% 4.71/5.03 thf(fact_1120_verit__comp__simplify1_I1_J,axiom,
% 4.71/5.03 ! [A: int] :
% 4.71/5.03 ~ ( ord_less_int @ A @ A ) ).
% 4.71/5.03
% 4.71/5.03 % verit_comp_simplify1(1)
% 4.71/5.03 thf(fact_1121_pinf_I1_J,axiom,
% 4.71/5.03 ! [P: real > $o,P4: real > $o,Q: real > $o,Q2: real > $o] :
% 4.71/5.03 ( ? [Z5: real] :
% 4.71/5.03 ! [X4: real] :
% 4.71/5.03 ( ( ord_less_real @ Z5 @ X4 )
% 4.71/5.03 => ( ( P @ X4 )
% 4.71/5.03 = ( P4 @ X4 ) ) )
% 4.71/5.03 => ( ? [Z5: real] :
% 4.71/5.03 ! [X4: real] :
% 4.71/5.03 ( ( ord_less_real @ Z5 @ X4 )
% 4.71/5.03 => ( ( Q @ X4 )
% 4.71/5.03 = ( Q2 @ X4 ) ) )
% 4.71/5.03 => ? [Z3: real] :
% 4.71/5.03 ! [X2: real] :
% 4.71/5.03 ( ( ord_less_real @ Z3 @ X2 )
% 4.71/5.03 => ( ( ( P @ X2 )
% 4.71/5.03 & ( Q @ X2 ) )
% 4.71/5.03 = ( ( P4 @ X2 )
% 4.71/5.03 & ( Q2 @ X2 ) ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(1)
% 4.71/5.03 thf(fact_1122_pinf_I1_J,axiom,
% 4.71/5.03 ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q2: rat > $o] :
% 4.71/5.03 ( ? [Z5: rat] :
% 4.71/5.03 ! [X4: rat] :
% 4.71/5.03 ( ( ord_less_rat @ Z5 @ X4 )
% 4.71/5.03 => ( ( P @ X4 )
% 4.71/5.03 = ( P4 @ X4 ) ) )
% 4.71/5.03 => ( ? [Z5: rat] :
% 4.71/5.03 ! [X4: rat] :
% 4.71/5.03 ( ( ord_less_rat @ Z5 @ X4 )
% 4.71/5.03 => ( ( Q @ X4 )
% 4.71/5.03 = ( Q2 @ X4 ) ) )
% 4.71/5.03 => ? [Z3: rat] :
% 4.71/5.03 ! [X2: rat] :
% 4.71/5.03 ( ( ord_less_rat @ Z3 @ X2 )
% 4.71/5.03 => ( ( ( P @ X2 )
% 4.71/5.03 & ( Q @ X2 ) )
% 4.71/5.03 = ( ( P4 @ X2 )
% 4.71/5.03 & ( Q2 @ X2 ) ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(1)
% 4.71/5.03 thf(fact_1123_pinf_I1_J,axiom,
% 4.71/5.03 ! [P: num > $o,P4: num > $o,Q: num > $o,Q2: num > $o] :
% 4.71/5.03 ( ? [Z5: num] :
% 4.71/5.03 ! [X4: num] :
% 4.71/5.03 ( ( ord_less_num @ Z5 @ X4 )
% 4.71/5.03 => ( ( P @ X4 )
% 4.71/5.03 = ( P4 @ X4 ) ) )
% 4.71/5.03 => ( ? [Z5: num] :
% 4.71/5.03 ! [X4: num] :
% 4.71/5.03 ( ( ord_less_num @ Z5 @ X4 )
% 4.71/5.03 => ( ( Q @ X4 )
% 4.71/5.03 = ( Q2 @ X4 ) ) )
% 4.71/5.03 => ? [Z3: num] :
% 4.71/5.03 ! [X2: num] :
% 4.71/5.03 ( ( ord_less_num @ Z3 @ X2 )
% 4.71/5.03 => ( ( ( P @ X2 )
% 4.71/5.03 & ( Q @ X2 ) )
% 4.71/5.03 = ( ( P4 @ X2 )
% 4.71/5.03 & ( Q2 @ X2 ) ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(1)
% 4.71/5.03 thf(fact_1124_pinf_I1_J,axiom,
% 4.71/5.03 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 4.71/5.03 ( ? [Z5: nat] :
% 4.71/5.03 ! [X4: nat] :
% 4.71/5.03 ( ( ord_less_nat @ Z5 @ X4 )
% 4.71/5.03 => ( ( P @ X4 )
% 4.71/5.03 = ( P4 @ X4 ) ) )
% 4.71/5.03 => ( ? [Z5: nat] :
% 4.71/5.03 ! [X4: nat] :
% 4.71/5.03 ( ( ord_less_nat @ Z5 @ X4 )
% 4.71/5.03 => ( ( Q @ X4 )
% 4.71/5.03 = ( Q2 @ X4 ) ) )
% 4.71/5.03 => ? [Z3: nat] :
% 4.71/5.03 ! [X2: nat] :
% 4.71/5.03 ( ( ord_less_nat @ Z3 @ X2 )
% 4.71/5.03 => ( ( ( P @ X2 )
% 4.71/5.03 & ( Q @ X2 ) )
% 4.71/5.03 = ( ( P4 @ X2 )
% 4.71/5.03 & ( Q2 @ X2 ) ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(1)
% 4.71/5.03 thf(fact_1125_pinf_I1_J,axiom,
% 4.71/5.03 ! [P: int > $o,P4: int > $o,Q: int > $o,Q2: int > $o] :
% 4.71/5.03 ( ? [Z5: int] :
% 4.71/5.03 ! [X4: int] :
% 4.71/5.03 ( ( ord_less_int @ Z5 @ X4 )
% 4.71/5.03 => ( ( P @ X4 )
% 4.71/5.03 = ( P4 @ X4 ) ) )
% 4.71/5.03 => ( ? [Z5: int] :
% 4.71/5.03 ! [X4: int] :
% 4.71/5.03 ( ( ord_less_int @ Z5 @ X4 )
% 4.71/5.03 => ( ( Q @ X4 )
% 4.71/5.03 = ( Q2 @ X4 ) ) )
% 4.71/5.03 => ? [Z3: int] :
% 4.71/5.03 ! [X2: int] :
% 4.71/5.03 ( ( ord_less_int @ Z3 @ X2 )
% 4.71/5.03 => ( ( ( P @ X2 )
% 4.71/5.03 & ( Q @ X2 ) )
% 4.71/5.03 = ( ( P4 @ X2 )
% 4.71/5.03 & ( Q2 @ X2 ) ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(1)
% 4.71/5.03 thf(fact_1126_pinf_I2_J,axiom,
% 4.71/5.03 ! [P: real > $o,P4: real > $o,Q: real > $o,Q2: real > $o] :
% 4.71/5.03 ( ? [Z5: real] :
% 4.71/5.03 ! [X4: real] :
% 4.71/5.03 ( ( ord_less_real @ Z5 @ X4 )
% 4.71/5.03 => ( ( P @ X4 )
% 4.71/5.03 = ( P4 @ X4 ) ) )
% 4.71/5.03 => ( ? [Z5: real] :
% 4.71/5.03 ! [X4: real] :
% 4.71/5.03 ( ( ord_less_real @ Z5 @ X4 )
% 4.71/5.03 => ( ( Q @ X4 )
% 4.71/5.03 = ( Q2 @ X4 ) ) )
% 4.71/5.03 => ? [Z3: real] :
% 4.71/5.03 ! [X2: real] :
% 4.71/5.03 ( ( ord_less_real @ Z3 @ X2 )
% 4.71/5.03 => ( ( ( P @ X2 )
% 4.71/5.03 | ( Q @ X2 ) )
% 4.71/5.03 = ( ( P4 @ X2 )
% 4.71/5.03 | ( Q2 @ X2 ) ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(2)
% 4.71/5.03 thf(fact_1127_pinf_I2_J,axiom,
% 4.71/5.03 ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q2: rat > $o] :
% 4.71/5.03 ( ? [Z5: rat] :
% 4.71/5.03 ! [X4: rat] :
% 4.71/5.03 ( ( ord_less_rat @ Z5 @ X4 )
% 4.71/5.03 => ( ( P @ X4 )
% 4.71/5.03 = ( P4 @ X4 ) ) )
% 4.71/5.03 => ( ? [Z5: rat] :
% 4.71/5.03 ! [X4: rat] :
% 4.71/5.03 ( ( ord_less_rat @ Z5 @ X4 )
% 4.71/5.03 => ( ( Q @ X4 )
% 4.71/5.03 = ( Q2 @ X4 ) ) )
% 4.71/5.03 => ? [Z3: rat] :
% 4.71/5.03 ! [X2: rat] :
% 4.71/5.03 ( ( ord_less_rat @ Z3 @ X2 )
% 4.71/5.03 => ( ( ( P @ X2 )
% 4.71/5.03 | ( Q @ X2 ) )
% 4.71/5.03 = ( ( P4 @ X2 )
% 4.71/5.03 | ( Q2 @ X2 ) ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(2)
% 4.71/5.03 thf(fact_1128_pinf_I2_J,axiom,
% 4.71/5.03 ! [P: num > $o,P4: num > $o,Q: num > $o,Q2: num > $o] :
% 4.71/5.03 ( ? [Z5: num] :
% 4.71/5.03 ! [X4: num] :
% 4.71/5.03 ( ( ord_less_num @ Z5 @ X4 )
% 4.71/5.03 => ( ( P @ X4 )
% 4.71/5.03 = ( P4 @ X4 ) ) )
% 4.71/5.03 => ( ? [Z5: num] :
% 4.71/5.03 ! [X4: num] :
% 4.71/5.03 ( ( ord_less_num @ Z5 @ X4 )
% 4.71/5.03 => ( ( Q @ X4 )
% 4.71/5.03 = ( Q2 @ X4 ) ) )
% 4.71/5.03 => ? [Z3: num] :
% 4.71/5.03 ! [X2: num] :
% 4.71/5.03 ( ( ord_less_num @ Z3 @ X2 )
% 4.71/5.03 => ( ( ( P @ X2 )
% 4.71/5.03 | ( Q @ X2 ) )
% 4.71/5.03 = ( ( P4 @ X2 )
% 4.71/5.03 | ( Q2 @ X2 ) ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(2)
% 4.71/5.03 thf(fact_1129_pinf_I2_J,axiom,
% 4.71/5.03 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 4.71/5.03 ( ? [Z5: nat] :
% 4.71/5.03 ! [X4: nat] :
% 4.71/5.03 ( ( ord_less_nat @ Z5 @ X4 )
% 4.71/5.03 => ( ( P @ X4 )
% 4.71/5.03 = ( P4 @ X4 ) ) )
% 4.71/5.03 => ( ? [Z5: nat] :
% 4.71/5.03 ! [X4: nat] :
% 4.71/5.03 ( ( ord_less_nat @ Z5 @ X4 )
% 4.71/5.03 => ( ( Q @ X4 )
% 4.71/5.03 = ( Q2 @ X4 ) ) )
% 4.71/5.03 => ? [Z3: nat] :
% 4.71/5.03 ! [X2: nat] :
% 4.71/5.03 ( ( ord_less_nat @ Z3 @ X2 )
% 4.71/5.03 => ( ( ( P @ X2 )
% 4.71/5.03 | ( Q @ X2 ) )
% 4.71/5.03 = ( ( P4 @ X2 )
% 4.71/5.03 | ( Q2 @ X2 ) ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(2)
% 4.71/5.03 thf(fact_1130_pinf_I2_J,axiom,
% 4.71/5.03 ! [P: int > $o,P4: int > $o,Q: int > $o,Q2: int > $o] :
% 4.71/5.03 ( ? [Z5: int] :
% 4.71/5.03 ! [X4: int] :
% 4.71/5.03 ( ( ord_less_int @ Z5 @ X4 )
% 4.71/5.03 => ( ( P @ X4 )
% 4.71/5.03 = ( P4 @ X4 ) ) )
% 4.71/5.03 => ( ? [Z5: int] :
% 4.71/5.03 ! [X4: int] :
% 4.71/5.03 ( ( ord_less_int @ Z5 @ X4 )
% 4.71/5.03 => ( ( Q @ X4 )
% 4.71/5.03 = ( Q2 @ X4 ) ) )
% 4.71/5.03 => ? [Z3: int] :
% 4.71/5.03 ! [X2: int] :
% 4.71/5.03 ( ( ord_less_int @ Z3 @ X2 )
% 4.71/5.03 => ( ( ( P @ X2 )
% 4.71/5.03 | ( Q @ X2 ) )
% 4.71/5.03 = ( ( P4 @ X2 )
% 4.71/5.03 | ( Q2 @ X2 ) ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(2)
% 4.71/5.03 thf(fact_1131_pinf_I3_J,axiom,
% 4.71/5.03 ! [T: real] :
% 4.71/5.03 ? [Z3: real] :
% 4.71/5.03 ! [X2: real] :
% 4.71/5.03 ( ( ord_less_real @ Z3 @ X2 )
% 4.71/5.03 => ( X2 != T ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(3)
% 4.71/5.03 thf(fact_1132_pinf_I3_J,axiom,
% 4.71/5.03 ! [T: rat] :
% 4.71/5.03 ? [Z3: rat] :
% 4.71/5.03 ! [X2: rat] :
% 4.71/5.03 ( ( ord_less_rat @ Z3 @ X2 )
% 4.71/5.03 => ( X2 != T ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(3)
% 4.71/5.03 thf(fact_1133_pinf_I3_J,axiom,
% 4.71/5.03 ! [T: num] :
% 4.71/5.03 ? [Z3: num] :
% 4.71/5.03 ! [X2: num] :
% 4.71/5.03 ( ( ord_less_num @ Z3 @ X2 )
% 4.71/5.03 => ( X2 != T ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(3)
% 4.71/5.03 thf(fact_1134_pinf_I3_J,axiom,
% 4.71/5.03 ! [T: nat] :
% 4.71/5.03 ? [Z3: nat] :
% 4.71/5.03 ! [X2: nat] :
% 4.71/5.03 ( ( ord_less_nat @ Z3 @ X2 )
% 4.71/5.03 => ( X2 != T ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(3)
% 4.71/5.03 thf(fact_1135_pinf_I3_J,axiom,
% 4.71/5.03 ! [T: int] :
% 4.71/5.03 ? [Z3: int] :
% 4.71/5.03 ! [X2: int] :
% 4.71/5.03 ( ( ord_less_int @ Z3 @ X2 )
% 4.71/5.03 => ( X2 != T ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(3)
% 4.71/5.03 thf(fact_1136_pinf_I4_J,axiom,
% 4.71/5.03 ! [T: real] :
% 4.71/5.03 ? [Z3: real] :
% 4.71/5.03 ! [X2: real] :
% 4.71/5.03 ( ( ord_less_real @ Z3 @ X2 )
% 4.71/5.03 => ( X2 != T ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(4)
% 4.71/5.03 thf(fact_1137_pinf_I4_J,axiom,
% 4.71/5.03 ! [T: rat] :
% 4.71/5.03 ? [Z3: rat] :
% 4.71/5.03 ! [X2: rat] :
% 4.71/5.03 ( ( ord_less_rat @ Z3 @ X2 )
% 4.71/5.03 => ( X2 != T ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(4)
% 4.71/5.03 thf(fact_1138_pinf_I4_J,axiom,
% 4.71/5.03 ! [T: num] :
% 4.71/5.03 ? [Z3: num] :
% 4.71/5.03 ! [X2: num] :
% 4.71/5.03 ( ( ord_less_num @ Z3 @ X2 )
% 4.71/5.03 => ( X2 != T ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(4)
% 4.71/5.03 thf(fact_1139_pinf_I4_J,axiom,
% 4.71/5.03 ! [T: nat] :
% 4.71/5.03 ? [Z3: nat] :
% 4.71/5.03 ! [X2: nat] :
% 4.71/5.03 ( ( ord_less_nat @ Z3 @ X2 )
% 4.71/5.03 => ( X2 != T ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(4)
% 4.71/5.03 thf(fact_1140_pinf_I4_J,axiom,
% 4.71/5.03 ! [T: int] :
% 4.71/5.03 ? [Z3: int] :
% 4.71/5.03 ! [X2: int] :
% 4.71/5.03 ( ( ord_less_int @ Z3 @ X2 )
% 4.71/5.03 => ( X2 != T ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(4)
% 4.71/5.03 thf(fact_1141_pinf_I5_J,axiom,
% 4.71/5.03 ! [T: real] :
% 4.71/5.03 ? [Z3: real] :
% 4.71/5.03 ! [X2: real] :
% 4.71/5.03 ( ( ord_less_real @ Z3 @ X2 )
% 4.71/5.03 => ~ ( ord_less_real @ X2 @ T ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(5)
% 4.71/5.03 thf(fact_1142_pinf_I5_J,axiom,
% 4.71/5.03 ! [T: rat] :
% 4.71/5.03 ? [Z3: rat] :
% 4.71/5.03 ! [X2: rat] :
% 4.71/5.03 ( ( ord_less_rat @ Z3 @ X2 )
% 4.71/5.03 => ~ ( ord_less_rat @ X2 @ T ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(5)
% 4.71/5.03 thf(fact_1143_pinf_I5_J,axiom,
% 4.71/5.03 ! [T: num] :
% 4.71/5.03 ? [Z3: num] :
% 4.71/5.03 ! [X2: num] :
% 4.71/5.03 ( ( ord_less_num @ Z3 @ X2 )
% 4.71/5.03 => ~ ( ord_less_num @ X2 @ T ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(5)
% 4.71/5.03 thf(fact_1144_pinf_I5_J,axiom,
% 4.71/5.03 ! [T: nat] :
% 4.71/5.03 ? [Z3: nat] :
% 4.71/5.03 ! [X2: nat] :
% 4.71/5.03 ( ( ord_less_nat @ Z3 @ X2 )
% 4.71/5.03 => ~ ( ord_less_nat @ X2 @ T ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(5)
% 4.71/5.03 thf(fact_1145_pinf_I5_J,axiom,
% 4.71/5.03 ! [T: int] :
% 4.71/5.03 ? [Z3: int] :
% 4.71/5.03 ! [X2: int] :
% 4.71/5.03 ( ( ord_less_int @ Z3 @ X2 )
% 4.71/5.03 => ~ ( ord_less_int @ X2 @ T ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(5)
% 4.71/5.03 thf(fact_1146_pinf_I7_J,axiom,
% 4.71/5.03 ! [T: real] :
% 4.71/5.03 ? [Z3: real] :
% 4.71/5.03 ! [X2: real] :
% 4.71/5.03 ( ( ord_less_real @ Z3 @ X2 )
% 4.71/5.03 => ( ord_less_real @ T @ X2 ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(7)
% 4.71/5.03 thf(fact_1147_pinf_I7_J,axiom,
% 4.71/5.03 ! [T: rat] :
% 4.71/5.03 ? [Z3: rat] :
% 4.71/5.03 ! [X2: rat] :
% 4.71/5.03 ( ( ord_less_rat @ Z3 @ X2 )
% 4.71/5.03 => ( ord_less_rat @ T @ X2 ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(7)
% 4.71/5.03 thf(fact_1148_pinf_I7_J,axiom,
% 4.71/5.03 ! [T: num] :
% 4.71/5.03 ? [Z3: num] :
% 4.71/5.03 ! [X2: num] :
% 4.71/5.03 ( ( ord_less_num @ Z3 @ X2 )
% 4.71/5.03 => ( ord_less_num @ T @ X2 ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(7)
% 4.71/5.03 thf(fact_1149_pinf_I7_J,axiom,
% 4.71/5.03 ! [T: nat] :
% 4.71/5.03 ? [Z3: nat] :
% 4.71/5.03 ! [X2: nat] :
% 4.71/5.03 ( ( ord_less_nat @ Z3 @ X2 )
% 4.71/5.03 => ( ord_less_nat @ T @ X2 ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(7)
% 4.71/5.03 thf(fact_1150_pinf_I7_J,axiom,
% 4.71/5.03 ! [T: int] :
% 4.71/5.03 ? [Z3: int] :
% 4.71/5.03 ! [X2: int] :
% 4.71/5.03 ( ( ord_less_int @ Z3 @ X2 )
% 4.71/5.03 => ( ord_less_int @ T @ X2 ) ) ).
% 4.71/5.03
% 4.71/5.03 % pinf(7)
% 4.71/5.03 thf(fact_1151_minf_I1_J,axiom,
% 4.71/5.03 ! [P: real > $o,P4: real > $o,Q: real > $o,Q2: real > $o] :
% 4.71/5.03 ( ? [Z5: real] :
% 4.71/5.03 ! [X4: real] :
% 4.71/5.03 ( ( ord_less_real @ X4 @ Z5 )
% 4.71/5.03 => ( ( P @ X4 )
% 4.71/5.03 = ( P4 @ X4 ) ) )
% 4.71/5.03 => ( ? [Z5: real] :
% 4.71/5.03 ! [X4: real] :
% 4.71/5.03 ( ( ord_less_real @ X4 @ Z5 )
% 4.71/5.03 => ( ( Q @ X4 )
% 4.71/5.03 = ( Q2 @ X4 ) ) )
% 4.71/5.03 => ? [Z3: real] :
% 4.71/5.03 ! [X2: real] :
% 4.71/5.03 ( ( ord_less_real @ X2 @ Z3 )
% 4.71/5.03 => ( ( ( P @ X2 )
% 4.71/5.03 & ( Q @ X2 ) )
% 4.71/5.03 = ( ( P4 @ X2 )
% 4.71/5.03 & ( Q2 @ X2 ) ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(1)
% 4.71/5.03 thf(fact_1152_minf_I1_J,axiom,
% 4.71/5.03 ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q2: rat > $o] :
% 4.71/5.03 ( ? [Z5: rat] :
% 4.71/5.03 ! [X4: rat] :
% 4.71/5.03 ( ( ord_less_rat @ X4 @ Z5 )
% 4.71/5.03 => ( ( P @ X4 )
% 4.71/5.03 = ( P4 @ X4 ) ) )
% 4.71/5.03 => ( ? [Z5: rat] :
% 4.71/5.03 ! [X4: rat] :
% 4.71/5.03 ( ( ord_less_rat @ X4 @ Z5 )
% 4.71/5.03 => ( ( Q @ X4 )
% 4.71/5.03 = ( Q2 @ X4 ) ) )
% 4.71/5.03 => ? [Z3: rat] :
% 4.71/5.03 ! [X2: rat] :
% 4.71/5.03 ( ( ord_less_rat @ X2 @ Z3 )
% 4.71/5.03 => ( ( ( P @ X2 )
% 4.71/5.03 & ( Q @ X2 ) )
% 4.71/5.03 = ( ( P4 @ X2 )
% 4.71/5.03 & ( Q2 @ X2 ) ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(1)
% 4.71/5.03 thf(fact_1153_minf_I1_J,axiom,
% 4.71/5.03 ! [P: num > $o,P4: num > $o,Q: num > $o,Q2: num > $o] :
% 4.71/5.03 ( ? [Z5: num] :
% 4.71/5.03 ! [X4: num] :
% 4.71/5.03 ( ( ord_less_num @ X4 @ Z5 )
% 4.71/5.03 => ( ( P @ X4 )
% 4.71/5.03 = ( P4 @ X4 ) ) )
% 4.71/5.03 => ( ? [Z5: num] :
% 4.71/5.03 ! [X4: num] :
% 4.71/5.03 ( ( ord_less_num @ X4 @ Z5 )
% 4.71/5.03 => ( ( Q @ X4 )
% 4.71/5.03 = ( Q2 @ X4 ) ) )
% 4.71/5.03 => ? [Z3: num] :
% 4.71/5.03 ! [X2: num] :
% 4.71/5.03 ( ( ord_less_num @ X2 @ Z3 )
% 4.71/5.03 => ( ( ( P @ X2 )
% 4.71/5.03 & ( Q @ X2 ) )
% 4.71/5.03 = ( ( P4 @ X2 )
% 4.71/5.03 & ( Q2 @ X2 ) ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(1)
% 4.71/5.03 thf(fact_1154_minf_I1_J,axiom,
% 4.71/5.03 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 4.71/5.03 ( ? [Z5: nat] :
% 4.71/5.03 ! [X4: nat] :
% 4.71/5.03 ( ( ord_less_nat @ X4 @ Z5 )
% 4.71/5.03 => ( ( P @ X4 )
% 4.71/5.03 = ( P4 @ X4 ) ) )
% 4.71/5.03 => ( ? [Z5: nat] :
% 4.71/5.03 ! [X4: nat] :
% 4.71/5.03 ( ( ord_less_nat @ X4 @ Z5 )
% 4.71/5.03 => ( ( Q @ X4 )
% 4.71/5.03 = ( Q2 @ X4 ) ) )
% 4.71/5.03 => ? [Z3: nat] :
% 4.71/5.03 ! [X2: nat] :
% 4.71/5.03 ( ( ord_less_nat @ X2 @ Z3 )
% 4.71/5.03 => ( ( ( P @ X2 )
% 4.71/5.03 & ( Q @ X2 ) )
% 4.71/5.03 = ( ( P4 @ X2 )
% 4.71/5.03 & ( Q2 @ X2 ) ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(1)
% 4.71/5.03 thf(fact_1155_minf_I1_J,axiom,
% 4.71/5.03 ! [P: int > $o,P4: int > $o,Q: int > $o,Q2: int > $o] :
% 4.71/5.03 ( ? [Z5: int] :
% 4.71/5.03 ! [X4: int] :
% 4.71/5.03 ( ( ord_less_int @ X4 @ Z5 )
% 4.71/5.03 => ( ( P @ X4 )
% 4.71/5.03 = ( P4 @ X4 ) ) )
% 4.71/5.03 => ( ? [Z5: int] :
% 4.71/5.03 ! [X4: int] :
% 4.71/5.03 ( ( ord_less_int @ X4 @ Z5 )
% 4.71/5.03 => ( ( Q @ X4 )
% 4.71/5.03 = ( Q2 @ X4 ) ) )
% 4.71/5.03 => ? [Z3: int] :
% 4.71/5.03 ! [X2: int] :
% 4.71/5.03 ( ( ord_less_int @ X2 @ Z3 )
% 4.71/5.03 => ( ( ( P @ X2 )
% 4.71/5.03 & ( Q @ X2 ) )
% 4.71/5.03 = ( ( P4 @ X2 )
% 4.71/5.03 & ( Q2 @ X2 ) ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(1)
% 4.71/5.03 thf(fact_1156_minf_I2_J,axiom,
% 4.71/5.03 ! [P: real > $o,P4: real > $o,Q: real > $o,Q2: real > $o] :
% 4.71/5.03 ( ? [Z5: real] :
% 4.71/5.03 ! [X4: real] :
% 4.71/5.03 ( ( ord_less_real @ X4 @ Z5 )
% 4.71/5.03 => ( ( P @ X4 )
% 4.71/5.03 = ( P4 @ X4 ) ) )
% 4.71/5.03 => ( ? [Z5: real] :
% 4.71/5.03 ! [X4: real] :
% 4.71/5.03 ( ( ord_less_real @ X4 @ Z5 )
% 4.71/5.03 => ( ( Q @ X4 )
% 4.71/5.03 = ( Q2 @ X4 ) ) )
% 4.71/5.03 => ? [Z3: real] :
% 4.71/5.03 ! [X2: real] :
% 4.71/5.03 ( ( ord_less_real @ X2 @ Z3 )
% 4.71/5.03 => ( ( ( P @ X2 )
% 4.71/5.03 | ( Q @ X2 ) )
% 4.71/5.03 = ( ( P4 @ X2 )
% 4.71/5.03 | ( Q2 @ X2 ) ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(2)
% 4.71/5.03 thf(fact_1157_minf_I2_J,axiom,
% 4.71/5.03 ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q2: rat > $o] :
% 4.71/5.03 ( ? [Z5: rat] :
% 4.71/5.03 ! [X4: rat] :
% 4.71/5.03 ( ( ord_less_rat @ X4 @ Z5 )
% 4.71/5.03 => ( ( P @ X4 )
% 4.71/5.03 = ( P4 @ X4 ) ) )
% 4.71/5.03 => ( ? [Z5: rat] :
% 4.71/5.03 ! [X4: rat] :
% 4.71/5.03 ( ( ord_less_rat @ X4 @ Z5 )
% 4.71/5.03 => ( ( Q @ X4 )
% 4.71/5.03 = ( Q2 @ X4 ) ) )
% 4.71/5.03 => ? [Z3: rat] :
% 4.71/5.03 ! [X2: rat] :
% 4.71/5.03 ( ( ord_less_rat @ X2 @ Z3 )
% 4.71/5.03 => ( ( ( P @ X2 )
% 4.71/5.03 | ( Q @ X2 ) )
% 4.71/5.03 = ( ( P4 @ X2 )
% 4.71/5.03 | ( Q2 @ X2 ) ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(2)
% 4.71/5.03 thf(fact_1158_minf_I2_J,axiom,
% 4.71/5.03 ! [P: num > $o,P4: num > $o,Q: num > $o,Q2: num > $o] :
% 4.71/5.03 ( ? [Z5: num] :
% 4.71/5.03 ! [X4: num] :
% 4.71/5.03 ( ( ord_less_num @ X4 @ Z5 )
% 4.71/5.03 => ( ( P @ X4 )
% 4.71/5.03 = ( P4 @ X4 ) ) )
% 4.71/5.03 => ( ? [Z5: num] :
% 4.71/5.03 ! [X4: num] :
% 4.71/5.03 ( ( ord_less_num @ X4 @ Z5 )
% 4.71/5.03 => ( ( Q @ X4 )
% 4.71/5.03 = ( Q2 @ X4 ) ) )
% 4.71/5.03 => ? [Z3: num] :
% 4.71/5.03 ! [X2: num] :
% 4.71/5.03 ( ( ord_less_num @ X2 @ Z3 )
% 4.71/5.03 => ( ( ( P @ X2 )
% 4.71/5.03 | ( Q @ X2 ) )
% 4.71/5.03 = ( ( P4 @ X2 )
% 4.71/5.03 | ( Q2 @ X2 ) ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(2)
% 4.71/5.03 thf(fact_1159_minf_I2_J,axiom,
% 4.71/5.03 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 4.71/5.03 ( ? [Z5: nat] :
% 4.71/5.03 ! [X4: nat] :
% 4.71/5.03 ( ( ord_less_nat @ X4 @ Z5 )
% 4.71/5.03 => ( ( P @ X4 )
% 4.71/5.03 = ( P4 @ X4 ) ) )
% 4.71/5.03 => ( ? [Z5: nat] :
% 4.71/5.03 ! [X4: nat] :
% 4.71/5.03 ( ( ord_less_nat @ X4 @ Z5 )
% 4.71/5.03 => ( ( Q @ X4 )
% 4.71/5.03 = ( Q2 @ X4 ) ) )
% 4.71/5.03 => ? [Z3: nat] :
% 4.71/5.03 ! [X2: nat] :
% 4.71/5.03 ( ( ord_less_nat @ X2 @ Z3 )
% 4.71/5.03 => ( ( ( P @ X2 )
% 4.71/5.03 | ( Q @ X2 ) )
% 4.71/5.03 = ( ( P4 @ X2 )
% 4.71/5.03 | ( Q2 @ X2 ) ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(2)
% 4.71/5.03 thf(fact_1160_minf_I2_J,axiom,
% 4.71/5.03 ! [P: int > $o,P4: int > $o,Q: int > $o,Q2: int > $o] :
% 4.71/5.03 ( ? [Z5: int] :
% 4.71/5.03 ! [X4: int] :
% 4.71/5.03 ( ( ord_less_int @ X4 @ Z5 )
% 4.71/5.03 => ( ( P @ X4 )
% 4.71/5.03 = ( P4 @ X4 ) ) )
% 4.71/5.03 => ( ? [Z5: int] :
% 4.71/5.03 ! [X4: int] :
% 4.71/5.03 ( ( ord_less_int @ X4 @ Z5 )
% 4.71/5.03 => ( ( Q @ X4 )
% 4.71/5.03 = ( Q2 @ X4 ) ) )
% 4.71/5.03 => ? [Z3: int] :
% 4.71/5.03 ! [X2: int] :
% 4.71/5.03 ( ( ord_less_int @ X2 @ Z3 )
% 4.71/5.03 => ( ( ( P @ X2 )
% 4.71/5.03 | ( Q @ X2 ) )
% 4.71/5.03 = ( ( P4 @ X2 )
% 4.71/5.03 | ( Q2 @ X2 ) ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(2)
% 4.71/5.03 thf(fact_1161_minf_I3_J,axiom,
% 4.71/5.03 ! [T: real] :
% 4.71/5.03 ? [Z3: real] :
% 4.71/5.03 ! [X2: real] :
% 4.71/5.03 ( ( ord_less_real @ X2 @ Z3 )
% 4.71/5.03 => ( X2 != T ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(3)
% 4.71/5.03 thf(fact_1162_minf_I3_J,axiom,
% 4.71/5.03 ! [T: rat] :
% 4.71/5.03 ? [Z3: rat] :
% 4.71/5.03 ! [X2: rat] :
% 4.71/5.03 ( ( ord_less_rat @ X2 @ Z3 )
% 4.71/5.03 => ( X2 != T ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(3)
% 4.71/5.03 thf(fact_1163_minf_I3_J,axiom,
% 4.71/5.03 ! [T: num] :
% 4.71/5.03 ? [Z3: num] :
% 4.71/5.03 ! [X2: num] :
% 4.71/5.03 ( ( ord_less_num @ X2 @ Z3 )
% 4.71/5.03 => ( X2 != T ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(3)
% 4.71/5.03 thf(fact_1164_minf_I3_J,axiom,
% 4.71/5.03 ! [T: nat] :
% 4.71/5.03 ? [Z3: nat] :
% 4.71/5.03 ! [X2: nat] :
% 4.71/5.03 ( ( ord_less_nat @ X2 @ Z3 )
% 4.71/5.03 => ( X2 != T ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(3)
% 4.71/5.03 thf(fact_1165_minf_I3_J,axiom,
% 4.71/5.03 ! [T: int] :
% 4.71/5.03 ? [Z3: int] :
% 4.71/5.03 ! [X2: int] :
% 4.71/5.03 ( ( ord_less_int @ X2 @ Z3 )
% 4.71/5.03 => ( X2 != T ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(3)
% 4.71/5.03 thf(fact_1166_minf_I4_J,axiom,
% 4.71/5.03 ! [T: real] :
% 4.71/5.03 ? [Z3: real] :
% 4.71/5.03 ! [X2: real] :
% 4.71/5.03 ( ( ord_less_real @ X2 @ Z3 )
% 4.71/5.03 => ( X2 != T ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(4)
% 4.71/5.03 thf(fact_1167_minf_I4_J,axiom,
% 4.71/5.03 ! [T: rat] :
% 4.71/5.03 ? [Z3: rat] :
% 4.71/5.03 ! [X2: rat] :
% 4.71/5.03 ( ( ord_less_rat @ X2 @ Z3 )
% 4.71/5.03 => ( X2 != T ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(4)
% 4.71/5.03 thf(fact_1168_minf_I4_J,axiom,
% 4.71/5.03 ! [T: num] :
% 4.71/5.03 ? [Z3: num] :
% 4.71/5.03 ! [X2: num] :
% 4.71/5.03 ( ( ord_less_num @ X2 @ Z3 )
% 4.71/5.03 => ( X2 != T ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(4)
% 4.71/5.03 thf(fact_1169_minf_I4_J,axiom,
% 4.71/5.03 ! [T: nat] :
% 4.71/5.03 ? [Z3: nat] :
% 4.71/5.03 ! [X2: nat] :
% 4.71/5.03 ( ( ord_less_nat @ X2 @ Z3 )
% 4.71/5.03 => ( X2 != T ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(4)
% 4.71/5.03 thf(fact_1170_minf_I4_J,axiom,
% 4.71/5.03 ! [T: int] :
% 4.71/5.03 ? [Z3: int] :
% 4.71/5.03 ! [X2: int] :
% 4.71/5.03 ( ( ord_less_int @ X2 @ Z3 )
% 4.71/5.03 => ( X2 != T ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(4)
% 4.71/5.03 thf(fact_1171_minf_I5_J,axiom,
% 4.71/5.03 ! [T: real] :
% 4.71/5.03 ? [Z3: real] :
% 4.71/5.03 ! [X2: real] :
% 4.71/5.03 ( ( ord_less_real @ X2 @ Z3 )
% 4.71/5.03 => ( ord_less_real @ X2 @ T ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(5)
% 4.71/5.03 thf(fact_1172_minf_I5_J,axiom,
% 4.71/5.03 ! [T: rat] :
% 4.71/5.03 ? [Z3: rat] :
% 4.71/5.03 ! [X2: rat] :
% 4.71/5.03 ( ( ord_less_rat @ X2 @ Z3 )
% 4.71/5.03 => ( ord_less_rat @ X2 @ T ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(5)
% 4.71/5.03 thf(fact_1173_minf_I5_J,axiom,
% 4.71/5.03 ! [T: num] :
% 4.71/5.03 ? [Z3: num] :
% 4.71/5.03 ! [X2: num] :
% 4.71/5.03 ( ( ord_less_num @ X2 @ Z3 )
% 4.71/5.03 => ( ord_less_num @ X2 @ T ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(5)
% 4.71/5.03 thf(fact_1174_minf_I5_J,axiom,
% 4.71/5.03 ! [T: nat] :
% 4.71/5.03 ? [Z3: nat] :
% 4.71/5.03 ! [X2: nat] :
% 4.71/5.03 ( ( ord_less_nat @ X2 @ Z3 )
% 4.71/5.03 => ( ord_less_nat @ X2 @ T ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(5)
% 4.71/5.03 thf(fact_1175_minf_I5_J,axiom,
% 4.71/5.03 ! [T: int] :
% 4.71/5.03 ? [Z3: int] :
% 4.71/5.03 ! [X2: int] :
% 4.71/5.03 ( ( ord_less_int @ X2 @ Z3 )
% 4.71/5.03 => ( ord_less_int @ X2 @ T ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(5)
% 4.71/5.03 thf(fact_1176_minf_I7_J,axiom,
% 4.71/5.03 ! [T: real] :
% 4.71/5.03 ? [Z3: real] :
% 4.71/5.03 ! [X2: real] :
% 4.71/5.03 ( ( ord_less_real @ X2 @ Z3 )
% 4.71/5.03 => ~ ( ord_less_real @ T @ X2 ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(7)
% 4.71/5.03 thf(fact_1177_minf_I7_J,axiom,
% 4.71/5.03 ! [T: rat] :
% 4.71/5.03 ? [Z3: rat] :
% 4.71/5.03 ! [X2: rat] :
% 4.71/5.03 ( ( ord_less_rat @ X2 @ Z3 )
% 4.71/5.03 => ~ ( ord_less_rat @ T @ X2 ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(7)
% 4.71/5.03 thf(fact_1178_minf_I7_J,axiom,
% 4.71/5.03 ! [T: num] :
% 4.71/5.03 ? [Z3: num] :
% 4.71/5.03 ! [X2: num] :
% 4.71/5.03 ( ( ord_less_num @ X2 @ Z3 )
% 4.71/5.03 => ~ ( ord_less_num @ T @ X2 ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(7)
% 4.71/5.03 thf(fact_1179_minf_I7_J,axiom,
% 4.71/5.03 ! [T: nat] :
% 4.71/5.03 ? [Z3: nat] :
% 4.71/5.03 ! [X2: nat] :
% 4.71/5.03 ( ( ord_less_nat @ X2 @ Z3 )
% 4.71/5.03 => ~ ( ord_less_nat @ T @ X2 ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(7)
% 4.71/5.03 thf(fact_1180_minf_I7_J,axiom,
% 4.71/5.03 ! [T: int] :
% 4.71/5.03 ? [Z3: int] :
% 4.71/5.03 ! [X2: int] :
% 4.71/5.03 ( ( ord_less_int @ X2 @ Z3 )
% 4.71/5.03 => ~ ( ord_less_int @ T @ X2 ) ) ).
% 4.71/5.03
% 4.71/5.03 % minf(7)
% 4.71/5.03 thf(fact_1181_nat__induct__non__zero,axiom,
% 4.71/5.03 ! [N: nat,P: nat > $o] :
% 4.71/5.03 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.03 => ( ( P @ one_one_nat )
% 4.71/5.03 => ( ! [N2: nat] :
% 4.71/5.03 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.71/5.03 => ( ( P @ N2 )
% 4.71/5.03 => ( P @ ( suc @ N2 ) ) ) )
% 4.71/5.03 => ( P @ N ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % nat_induct_non_zero
% 4.71/5.03 thf(fact_1182_invar__vebt_Ointros_I1_J,axiom,
% 4.71/5.03 ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 4.71/5.03
% 4.71/5.03 % invar_vebt.intros(1)
% 4.71/5.03 thf(fact_1183_vebt__delete_Osimps_I2_J,axiom,
% 4.71/5.03 ! [A: $o,B: $o] :
% 4.71/5.03 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) )
% 4.71/5.03 = ( vEBT_Leaf @ A @ $false ) ) ).
% 4.71/5.03
% 4.71/5.03 % vebt_delete.simps(2)
% 4.71/5.03 thf(fact_1184_vebt__buildup_Osimps_I2_J,axiom,
% 4.71/5.03 ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 4.71/5.03 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 4.71/5.03
% 4.71/5.03 % vebt_buildup.simps(2)
% 4.71/5.03 thf(fact_1185_Collect__empty__eq__bot,axiom,
% 4.71/5.03 ! [P: set_nat > $o] :
% 4.71/5.03 ( ( ( collect_set_nat @ P )
% 4.71/5.03 = bot_bot_set_set_nat )
% 4.71/5.03 = ( P = bot_bot_set_nat_o ) ) ).
% 4.71/5.03
% 4.71/5.03 % Collect_empty_eq_bot
% 4.71/5.03 thf(fact_1186_Collect__empty__eq__bot,axiom,
% 4.71/5.03 ! [P: set_nat_rat > $o] :
% 4.71/5.03 ( ( ( collect_set_nat_rat @ P )
% 4.71/5.03 = bot_bo6797373522285170759at_rat )
% 4.71/5.03 = ( P = bot_bo3445895781125589758_rat_o ) ) ).
% 4.71/5.03
% 4.71/5.03 % Collect_empty_eq_bot
% 4.71/5.03 thf(fact_1187_Collect__empty__eq__bot,axiom,
% 4.71/5.03 ! [P: ( nat > rat ) > $o] :
% 4.71/5.03 ( ( ( collect_nat_rat @ P )
% 4.71/5.03 = bot_bot_set_nat_rat )
% 4.71/5.03 = ( P = bot_bot_nat_rat_o ) ) ).
% 4.71/5.03
% 4.71/5.03 % Collect_empty_eq_bot
% 4.71/5.03 thf(fact_1188_Collect__empty__eq__bot,axiom,
% 4.71/5.03 ! [P: real > $o] :
% 4.71/5.03 ( ( ( collect_real @ P )
% 4.71/5.03 = bot_bot_set_real )
% 4.71/5.03 = ( P = bot_bot_real_o ) ) ).
% 4.71/5.03
% 4.71/5.03 % Collect_empty_eq_bot
% 4.71/5.03 thf(fact_1189_Collect__empty__eq__bot,axiom,
% 4.71/5.03 ! [P: $o > $o] :
% 4.71/5.03 ( ( ( collect_o @ P )
% 4.71/5.03 = bot_bot_set_o )
% 4.71/5.03 = ( P = bot_bot_o_o ) ) ).
% 4.71/5.03
% 4.71/5.03 % Collect_empty_eq_bot
% 4.71/5.03 thf(fact_1190_Collect__empty__eq__bot,axiom,
% 4.71/5.03 ! [P: nat > $o] :
% 4.71/5.03 ( ( ( collect_nat @ P )
% 4.71/5.03 = bot_bot_set_nat )
% 4.71/5.03 = ( P = bot_bot_nat_o ) ) ).
% 4.71/5.03
% 4.71/5.03 % Collect_empty_eq_bot
% 4.71/5.03 thf(fact_1191_Collect__empty__eq__bot,axiom,
% 4.71/5.03 ! [P: int > $o] :
% 4.71/5.03 ( ( ( collect_int @ P )
% 4.71/5.03 = bot_bot_set_int )
% 4.71/5.03 = ( P = bot_bot_int_o ) ) ).
% 4.71/5.03
% 4.71/5.03 % Collect_empty_eq_bot
% 4.71/5.03 thf(fact_1192_bot__empty__eq,axiom,
% 4.71/5.03 ( bot_bot_set_nat_o
% 4.71/5.03 = ( ^ [X3: set_nat] : ( member_set_nat @ X3 @ bot_bot_set_set_nat ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % bot_empty_eq
% 4.71/5.03 thf(fact_1193_bot__empty__eq,axiom,
% 4.71/5.03 ( bot_bo3445895781125589758_rat_o
% 4.71/5.03 = ( ^ [X3: set_nat_rat] : ( member_set_nat_rat @ X3 @ bot_bo6797373522285170759at_rat ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % bot_empty_eq
% 4.71/5.03 thf(fact_1194_bot__empty__eq,axiom,
% 4.71/5.03 ( bot_bot_real_o
% 4.71/5.03 = ( ^ [X3: real] : ( member_real @ X3 @ bot_bot_set_real ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % bot_empty_eq
% 4.71/5.03 thf(fact_1195_bot__empty__eq,axiom,
% 4.71/5.03 ( bot_bot_o_o
% 4.71/5.03 = ( ^ [X3: $o] : ( member_o @ X3 @ bot_bot_set_o ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % bot_empty_eq
% 4.71/5.03 thf(fact_1196_bot__empty__eq,axiom,
% 4.71/5.03 ( bot_bot_nat_o
% 4.71/5.03 = ( ^ [X3: nat] : ( member_nat @ X3 @ bot_bot_set_nat ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % bot_empty_eq
% 4.71/5.03 thf(fact_1197_bot__empty__eq,axiom,
% 4.71/5.03 ( bot_bot_int_o
% 4.71/5.03 = ( ^ [X3: int] : ( member_int @ X3 @ bot_bot_set_int ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % bot_empty_eq
% 4.71/5.03 thf(fact_1198_exists__least__lemma,axiom,
% 4.71/5.03 ! [P: nat > $o] :
% 4.71/5.03 ( ~ ( P @ zero_zero_nat )
% 4.71/5.03 => ( ? [X_12: nat] : ( P @ X_12 )
% 4.71/5.03 => ? [N2: nat] :
% 4.71/5.03 ( ~ ( P @ N2 )
% 4.71/5.03 & ( P @ ( suc @ N2 ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % exists_least_lemma
% 4.71/5.03 thf(fact_1199_list__decode_Ocases,axiom,
% 4.71/5.03 ! [X: nat] :
% 4.71/5.03 ( ( X != zero_zero_nat )
% 4.71/5.03 => ~ ! [N2: nat] :
% 4.71/5.03 ( X
% 4.71/5.03 != ( suc @ N2 ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % list_decode.cases
% 4.71/5.03 thf(fact_1200_Suc__diff__1,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.03 => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 4.71/5.03 = N ) ) ).
% 4.71/5.03
% 4.71/5.03 % Suc_diff_1
% 4.71/5.03 thf(fact_1201_Set_Ois__empty__def,axiom,
% 4.71/5.03 ( is_empty_real
% 4.71/5.03 = ( ^ [A6: set_real] : ( A6 = bot_bot_set_real ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % Set.is_empty_def
% 4.71/5.03 thf(fact_1202_Set_Ois__empty__def,axiom,
% 4.71/5.03 ( is_empty_o
% 4.71/5.03 = ( ^ [A6: set_o] : ( A6 = bot_bot_set_o ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % Set.is_empty_def
% 4.71/5.03 thf(fact_1203_Set_Ois__empty__def,axiom,
% 4.71/5.03 ( is_empty_nat
% 4.71/5.03 = ( ^ [A6: set_nat] : ( A6 = bot_bot_set_nat ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % Set.is_empty_def
% 4.71/5.03 thf(fact_1204_Set_Ois__empty__def,axiom,
% 4.71/5.03 ( is_empty_int
% 4.71/5.03 = ( ^ [A6: set_int] : ( A6 = bot_bot_set_int ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % Set.is_empty_def
% 4.71/5.03 thf(fact_1205_arcosh__1,axiom,
% 4.71/5.03 ( ( arcosh_real @ one_one_real )
% 4.71/5.03 = zero_zero_real ) ).
% 4.71/5.03
% 4.71/5.03 % arcosh_1
% 4.71/5.03 thf(fact_1206_of__nat__0__less__iff,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 4.71/5.03 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_0_less_iff
% 4.71/5.03 thf(fact_1207_of__nat__0__less__iff,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 4.71/5.03 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_0_less_iff
% 4.71/5.03 thf(fact_1208_of__nat__0__less__iff,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) )
% 4.71/5.03 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_0_less_iff
% 4.71/5.03 thf(fact_1209_of__nat__0__less__iff,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 4.71/5.03 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_0_less_iff
% 4.71/5.03 thf(fact_1210_VEBT_Osize_I4_J,axiom,
% 4.71/5.03 ! [X21: $o,X22: $o] :
% 4.71/5.03 ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X22 ) )
% 4.71/5.03 = zero_zero_nat ) ).
% 4.71/5.03
% 4.71/5.03 % VEBT.size(4)
% 4.71/5.03 thf(fact_1211_enumerate__mono__iff,axiom,
% 4.71/5.03 ! [S2: set_Extended_enat,M2: nat,N: nat] :
% 4.71/5.03 ( ~ ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.03 => ( ( ord_le72135733267957522d_enat @ ( infini7641415182203889163d_enat @ S2 @ M2 ) @ ( infini7641415182203889163d_enat @ S2 @ N ) )
% 4.71/5.03 = ( ord_less_nat @ M2 @ N ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % enumerate_mono_iff
% 4.71/5.03 thf(fact_1212_enumerate__mono__iff,axiom,
% 4.71/5.03 ! [S2: set_nat,M2: nat,N: nat] :
% 4.71/5.03 ( ~ ( finite_finite_nat @ S2 )
% 4.71/5.03 => ( ( ord_less_nat @ ( infini8530281810654367211te_nat @ S2 @ M2 ) @ ( infini8530281810654367211te_nat @ S2 @ N ) )
% 4.71/5.03 = ( ord_less_nat @ M2 @ N ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % enumerate_mono_iff
% 4.71/5.03 thf(fact_1213_of__nat__eq__iff,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ( semiri1314217659103216013at_int @ M2 )
% 4.71/5.03 = ( semiri1314217659103216013at_int @ N ) )
% 4.71/5.03 = ( M2 = N ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_eq_iff
% 4.71/5.03 thf(fact_1214_of__nat__eq__iff,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ( semiri5074537144036343181t_real @ M2 )
% 4.71/5.03 = ( semiri5074537144036343181t_real @ N ) )
% 4.71/5.03 = ( M2 = N ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_eq_iff
% 4.71/5.03 thf(fact_1215_of__nat__eq__iff,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ( semiri681578069525770553at_rat @ M2 )
% 4.71/5.03 = ( semiri681578069525770553at_rat @ N ) )
% 4.71/5.03 = ( M2 = N ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_eq_iff
% 4.71/5.03 thf(fact_1216_diff__self,axiom,
% 4.71/5.03 ! [A: real] :
% 4.71/5.03 ( ( minus_minus_real @ A @ A )
% 4.71/5.03 = zero_zero_real ) ).
% 4.71/5.03
% 4.71/5.03 % diff_self
% 4.71/5.03 thf(fact_1217_diff__self,axiom,
% 4.71/5.03 ! [A: rat] :
% 4.71/5.03 ( ( minus_minus_rat @ A @ A )
% 4.71/5.03 = zero_zero_rat ) ).
% 4.71/5.03
% 4.71/5.03 % diff_self
% 4.71/5.03 thf(fact_1218_diff__self,axiom,
% 4.71/5.03 ! [A: int] :
% 4.71/5.03 ( ( minus_minus_int @ A @ A )
% 4.71/5.03 = zero_zero_int ) ).
% 4.71/5.03
% 4.71/5.03 % diff_self
% 4.71/5.03 thf(fact_1219_diff__0__right,axiom,
% 4.71/5.03 ! [A: real] :
% 4.71/5.03 ( ( minus_minus_real @ A @ zero_zero_real )
% 4.71/5.03 = A ) ).
% 4.71/5.03
% 4.71/5.03 % diff_0_right
% 4.71/5.03 thf(fact_1220_diff__0__right,axiom,
% 4.71/5.03 ! [A: rat] :
% 4.71/5.03 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 4.71/5.03 = A ) ).
% 4.71/5.03
% 4.71/5.03 % diff_0_right
% 4.71/5.03 thf(fact_1221_diff__0__right,axiom,
% 4.71/5.03 ! [A: int] :
% 4.71/5.03 ( ( minus_minus_int @ A @ zero_zero_int )
% 4.71/5.03 = A ) ).
% 4.71/5.03
% 4.71/5.03 % diff_0_right
% 4.71/5.03 thf(fact_1222_zero__diff,axiom,
% 4.71/5.03 ! [A: nat] :
% 4.71/5.03 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 4.71/5.03 = zero_zero_nat ) ).
% 4.71/5.03
% 4.71/5.03 % zero_diff
% 4.71/5.03 thf(fact_1223_diff__zero,axiom,
% 4.71/5.03 ! [A: real] :
% 4.71/5.03 ( ( minus_minus_real @ A @ zero_zero_real )
% 4.71/5.03 = A ) ).
% 4.71/5.03
% 4.71/5.03 % diff_zero
% 4.71/5.03 thf(fact_1224_diff__zero,axiom,
% 4.71/5.03 ! [A: rat] :
% 4.71/5.03 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 4.71/5.03 = A ) ).
% 4.71/5.03
% 4.71/5.03 % diff_zero
% 4.71/5.03 thf(fact_1225_diff__zero,axiom,
% 4.71/5.03 ! [A: nat] :
% 4.71/5.03 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 4.71/5.03 = A ) ).
% 4.71/5.03
% 4.71/5.03 % diff_zero
% 4.71/5.03 thf(fact_1226_diff__zero,axiom,
% 4.71/5.03 ! [A: int] :
% 4.71/5.03 ( ( minus_minus_int @ A @ zero_zero_int )
% 4.71/5.03 = A ) ).
% 4.71/5.03
% 4.71/5.03 % diff_zero
% 4.71/5.03 thf(fact_1227_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 4.71/5.03 ! [A: real] :
% 4.71/5.03 ( ( minus_minus_real @ A @ A )
% 4.71/5.03 = zero_zero_real ) ).
% 4.71/5.03
% 4.71/5.03 % cancel_comm_monoid_add_class.diff_cancel
% 4.71/5.03 thf(fact_1228_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 4.71/5.03 ! [A: rat] :
% 4.71/5.03 ( ( minus_minus_rat @ A @ A )
% 4.71/5.03 = zero_zero_rat ) ).
% 4.71/5.03
% 4.71/5.03 % cancel_comm_monoid_add_class.diff_cancel
% 4.71/5.03 thf(fact_1229_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 4.71/5.03 ! [A: nat] :
% 4.71/5.03 ( ( minus_minus_nat @ A @ A )
% 4.71/5.03 = zero_zero_nat ) ).
% 4.71/5.03
% 4.71/5.03 % cancel_comm_monoid_add_class.diff_cancel
% 4.71/5.03 thf(fact_1230_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 4.71/5.03 ! [A: int] :
% 4.71/5.03 ( ( minus_minus_int @ A @ A )
% 4.71/5.03 = zero_zero_int ) ).
% 4.71/5.03
% 4.71/5.03 % cancel_comm_monoid_add_class.diff_cancel
% 4.71/5.03 thf(fact_1231_Suc__diff__diff,axiom,
% 4.71/5.03 ! [M2: nat,N: nat,K: nat] :
% 4.71/5.03 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M2 ) @ N ) @ ( suc @ K ) )
% 4.71/5.03 = ( minus_minus_nat @ ( minus_minus_nat @ M2 @ N ) @ K ) ) ).
% 4.71/5.03
% 4.71/5.03 % Suc_diff_diff
% 4.71/5.03 thf(fact_1232_diff__Suc__Suc,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( minus_minus_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 4.71/5.03 = ( minus_minus_nat @ M2 @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_Suc_Suc
% 4.71/5.03 thf(fact_1233_diff__0__eq__0,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 4.71/5.03 = zero_zero_nat ) ).
% 4.71/5.03
% 4.71/5.03 % diff_0_eq_0
% 4.71/5.03 thf(fact_1234_diff__self__eq__0,axiom,
% 4.71/5.03 ! [M2: nat] :
% 4.71/5.03 ( ( minus_minus_nat @ M2 @ M2 )
% 4.71/5.03 = zero_zero_nat ) ).
% 4.71/5.03
% 4.71/5.03 % diff_self_eq_0
% 4.71/5.03 thf(fact_1235_diff__diff__cancel,axiom,
% 4.71/5.03 ! [I: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ I @ N )
% 4.71/5.03 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 4.71/5.03 = I ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_diff_cancel
% 4.71/5.03 thf(fact_1236_diff__ge__0__iff__ge,axiom,
% 4.71/5.03 ! [A: real,B: real] :
% 4.71/5.03 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 4.71/5.03 = ( ord_less_eq_real @ B @ A ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_ge_0_iff_ge
% 4.71/5.03 thf(fact_1237_diff__ge__0__iff__ge,axiom,
% 4.71/5.03 ! [A: rat,B: rat] :
% 4.71/5.03 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 4.71/5.03 = ( ord_less_eq_rat @ B @ A ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_ge_0_iff_ge
% 4.71/5.03 thf(fact_1238_diff__ge__0__iff__ge,axiom,
% 4.71/5.03 ! [A: int,B: int] :
% 4.71/5.03 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 4.71/5.03 = ( ord_less_eq_int @ B @ A ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_ge_0_iff_ge
% 4.71/5.03 thf(fact_1239_diff__gt__0__iff__gt,axiom,
% 4.71/5.03 ! [A: real,B: real] :
% 4.71/5.03 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 4.71/5.03 = ( ord_less_real @ B @ A ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_gt_0_iff_gt
% 4.71/5.03 thf(fact_1240_diff__gt__0__iff__gt,axiom,
% 4.71/5.03 ! [A: rat,B: rat] :
% 4.71/5.03 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 4.71/5.03 = ( ord_less_rat @ B @ A ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_gt_0_iff_gt
% 4.71/5.03 thf(fact_1241_diff__gt__0__iff__gt,axiom,
% 4.71/5.03 ! [A: int,B: int] :
% 4.71/5.03 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 4.71/5.03 = ( ord_less_int @ B @ A ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_gt_0_iff_gt
% 4.71/5.03 thf(fact_1242_diff__numeral__special_I9_J,axiom,
% 4.71/5.03 ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 4.71/5.03 = zero_zero_complex ) ).
% 4.71/5.03
% 4.71/5.03 % diff_numeral_special(9)
% 4.71/5.03 thf(fact_1243_diff__numeral__special_I9_J,axiom,
% 4.71/5.03 ( ( minus_minus_real @ one_one_real @ one_one_real )
% 4.71/5.03 = zero_zero_real ) ).
% 4.71/5.03
% 4.71/5.03 % diff_numeral_special(9)
% 4.71/5.03 thf(fact_1244_diff__numeral__special_I9_J,axiom,
% 4.71/5.03 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 4.71/5.03 = zero_zero_rat ) ).
% 4.71/5.03
% 4.71/5.03 % diff_numeral_special(9)
% 4.71/5.03 thf(fact_1245_diff__numeral__special_I9_J,axiom,
% 4.71/5.03 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 4.71/5.03 = zero_zero_int ) ).
% 4.71/5.03
% 4.71/5.03 % diff_numeral_special(9)
% 4.71/5.03 thf(fact_1246_of__nat__0,axiom,
% 4.71/5.03 ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 4.71/5.03 = zero_zero_nat ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_0
% 4.71/5.03 thf(fact_1247_of__nat__0,axiom,
% 4.71/5.03 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 4.71/5.03 = zero_zero_int ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_0
% 4.71/5.03 thf(fact_1248_of__nat__0,axiom,
% 4.71/5.03 ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 4.71/5.03 = zero_zero_real ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_0
% 4.71/5.03 thf(fact_1249_of__nat__0,axiom,
% 4.71/5.03 ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 4.71/5.03 = zero_zero_rat ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_0
% 4.71/5.03 thf(fact_1250_of__nat__0__eq__iff,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( zero_zero_nat
% 4.71/5.03 = ( semiri1316708129612266289at_nat @ N ) )
% 4.71/5.03 = ( zero_zero_nat = N ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_0_eq_iff
% 4.71/5.03 thf(fact_1251_of__nat__0__eq__iff,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( zero_zero_int
% 4.71/5.03 = ( semiri1314217659103216013at_int @ N ) )
% 4.71/5.03 = ( zero_zero_nat = N ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_0_eq_iff
% 4.71/5.03 thf(fact_1252_of__nat__0__eq__iff,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( zero_zero_real
% 4.71/5.03 = ( semiri5074537144036343181t_real @ N ) )
% 4.71/5.03 = ( zero_zero_nat = N ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_0_eq_iff
% 4.71/5.03 thf(fact_1253_of__nat__0__eq__iff,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( zero_zero_rat
% 4.71/5.03 = ( semiri681578069525770553at_rat @ N ) )
% 4.71/5.03 = ( zero_zero_nat = N ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_0_eq_iff
% 4.71/5.03 thf(fact_1254_of__nat__eq__0__iff,axiom,
% 4.71/5.03 ! [M2: nat] :
% 4.71/5.03 ( ( ( semiri1316708129612266289at_nat @ M2 )
% 4.71/5.03 = zero_zero_nat )
% 4.71/5.03 = ( M2 = zero_zero_nat ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_eq_0_iff
% 4.71/5.03 thf(fact_1255_of__nat__eq__0__iff,axiom,
% 4.71/5.03 ! [M2: nat] :
% 4.71/5.03 ( ( ( semiri1314217659103216013at_int @ M2 )
% 4.71/5.03 = zero_zero_int )
% 4.71/5.03 = ( M2 = zero_zero_nat ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_eq_0_iff
% 4.71/5.03 thf(fact_1256_of__nat__eq__0__iff,axiom,
% 4.71/5.03 ! [M2: nat] :
% 4.71/5.03 ( ( ( semiri5074537144036343181t_real @ M2 )
% 4.71/5.03 = zero_zero_real )
% 4.71/5.03 = ( M2 = zero_zero_nat ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_eq_0_iff
% 4.71/5.03 thf(fact_1257_of__nat__eq__0__iff,axiom,
% 4.71/5.03 ! [M2: nat] :
% 4.71/5.03 ( ( ( semiri681578069525770553at_rat @ M2 )
% 4.71/5.03 = zero_zero_rat )
% 4.71/5.03 = ( M2 = zero_zero_nat ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_eq_0_iff
% 4.71/5.03 thf(fact_1258_of__nat__less__iff,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) )
% 4.71/5.03 = ( ord_less_nat @ M2 @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_less_iff
% 4.71/5.03 thf(fact_1259_of__nat__less__iff,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) )
% 4.71/5.03 = ( ord_less_nat @ M2 @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_less_iff
% 4.71/5.03 thf(fact_1260_of__nat__less__iff,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) )
% 4.71/5.03 = ( ord_less_nat @ M2 @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_less_iff
% 4.71/5.03 thf(fact_1261_of__nat__less__iff,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) )
% 4.71/5.03 = ( ord_less_nat @ M2 @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_less_iff
% 4.71/5.03 thf(fact_1262_of__nat__le__iff,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) )
% 4.71/5.03 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_le_iff
% 4.71/5.03 thf(fact_1263_of__nat__le__iff,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) )
% 4.71/5.03 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_le_iff
% 4.71/5.03 thf(fact_1264_of__nat__le__iff,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) )
% 4.71/5.03 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_le_iff
% 4.71/5.03 thf(fact_1265_of__nat__le__iff,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) )
% 4.71/5.03 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_le_iff
% 4.71/5.03 thf(fact_1266_zero__less__diff,axiom,
% 4.71/5.03 ! [N: nat,M2: nat] :
% 4.71/5.03 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M2 ) )
% 4.71/5.03 = ( ord_less_nat @ M2 @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % zero_less_diff
% 4.71/5.03 thf(fact_1267_diff__is__0__eq_H,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.03 => ( ( minus_minus_nat @ M2 @ N )
% 4.71/5.03 = zero_zero_nat ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_is_0_eq'
% 4.71/5.03 thf(fact_1268_diff__is__0__eq,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ( minus_minus_nat @ M2 @ N )
% 4.71/5.03 = zero_zero_nat )
% 4.71/5.03 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_is_0_eq
% 4.71/5.03 thf(fact_1269_of__nat__eq__1__iff,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( ( semiri8010041392384452111omplex @ N )
% 4.71/5.03 = one_one_complex )
% 4.71/5.03 = ( N = one_one_nat ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_eq_1_iff
% 4.71/5.03 thf(fact_1270_of__nat__eq__1__iff,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( ( semiri1316708129612266289at_nat @ N )
% 4.71/5.03 = one_one_nat )
% 4.71/5.03 = ( N = one_one_nat ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_eq_1_iff
% 4.71/5.03 thf(fact_1271_of__nat__eq__1__iff,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( ( semiri1314217659103216013at_int @ N )
% 4.71/5.03 = one_one_int )
% 4.71/5.03 = ( N = one_one_nat ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_eq_1_iff
% 4.71/5.03 thf(fact_1272_of__nat__eq__1__iff,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( ( semiri5074537144036343181t_real @ N )
% 4.71/5.03 = one_one_real )
% 4.71/5.03 = ( N = one_one_nat ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_eq_1_iff
% 4.71/5.03 thf(fact_1273_of__nat__eq__1__iff,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( ( semiri681578069525770553at_rat @ N )
% 4.71/5.03 = one_one_rat )
% 4.71/5.03 = ( N = one_one_nat ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_eq_1_iff
% 4.71/5.03 thf(fact_1274_of__nat__1__eq__iff,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( one_one_complex
% 4.71/5.03 = ( semiri8010041392384452111omplex @ N ) )
% 4.71/5.03 = ( N = one_one_nat ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_1_eq_iff
% 4.71/5.03 thf(fact_1275_of__nat__1__eq__iff,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( one_one_nat
% 4.71/5.03 = ( semiri1316708129612266289at_nat @ N ) )
% 4.71/5.03 = ( N = one_one_nat ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_1_eq_iff
% 4.71/5.03 thf(fact_1276_of__nat__1__eq__iff,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( one_one_int
% 4.71/5.03 = ( semiri1314217659103216013at_int @ N ) )
% 4.71/5.03 = ( N = one_one_nat ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_1_eq_iff
% 4.71/5.03 thf(fact_1277_of__nat__1__eq__iff,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( one_one_real
% 4.71/5.03 = ( semiri5074537144036343181t_real @ N ) )
% 4.71/5.03 = ( N = one_one_nat ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_1_eq_iff
% 4.71/5.03 thf(fact_1278_of__nat__1__eq__iff,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( one_one_rat
% 4.71/5.03 = ( semiri681578069525770553at_rat @ N ) )
% 4.71/5.03 = ( N = one_one_nat ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_1_eq_iff
% 4.71/5.03 thf(fact_1279_of__nat__1,axiom,
% 4.71/5.03 ( ( semiri8010041392384452111omplex @ one_one_nat )
% 4.71/5.03 = one_one_complex ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_1
% 4.71/5.03 thf(fact_1280_of__nat__1,axiom,
% 4.71/5.03 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 4.71/5.03 = one_one_nat ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_1
% 4.71/5.03 thf(fact_1281_of__nat__1,axiom,
% 4.71/5.03 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 4.71/5.03 = one_one_int ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_1
% 4.71/5.03 thf(fact_1282_of__nat__1,axiom,
% 4.71/5.03 ( ( semiri5074537144036343181t_real @ one_one_nat )
% 4.71/5.03 = one_one_real ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_1
% 4.71/5.03 thf(fact_1283_of__nat__1,axiom,
% 4.71/5.03 ( ( semiri681578069525770553at_rat @ one_one_nat )
% 4.71/5.03 = one_one_rat ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_1
% 4.71/5.03 thf(fact_1284_diff__Suc__1,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 4.71/5.03 = N ) ).
% 4.71/5.03
% 4.71/5.03 % diff_Suc_1
% 4.71/5.03 thf(fact_1285_of__nat__le__0__iff,axiom,
% 4.71/5.03 ! [M2: nat] :
% 4.71/5.03 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M2 ) @ zero_zero_real )
% 4.71/5.03 = ( M2 = zero_zero_nat ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_le_0_iff
% 4.71/5.03 thf(fact_1286_of__nat__le__0__iff,axiom,
% 4.71/5.03 ! [M2: nat] :
% 4.71/5.03 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M2 ) @ zero_zero_rat )
% 4.71/5.03 = ( M2 = zero_zero_nat ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_le_0_iff
% 4.71/5.03 thf(fact_1287_of__nat__le__0__iff,axiom,
% 4.71/5.03 ! [M2: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ zero_zero_nat )
% 4.71/5.03 = ( M2 = zero_zero_nat ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_le_0_iff
% 4.71/5.03 thf(fact_1288_of__nat__le__0__iff,axiom,
% 4.71/5.03 ! [M2: nat] :
% 4.71/5.03 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M2 ) @ zero_zero_int )
% 4.71/5.03 = ( M2 = zero_zero_nat ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_le_0_iff
% 4.71/5.03 thf(fact_1289_Suc__pred,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.03 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 4.71/5.03 = N ) ) ).
% 4.71/5.03
% 4.71/5.03 % Suc_pred
% 4.71/5.03 thf(fact_1290_of__nat__diff,axiom,
% 4.71/5.03 ! [N: nat,M2: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ N @ M2 )
% 4.71/5.03 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M2 @ N ) )
% 4.71/5.03 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_diff
% 4.71/5.03 thf(fact_1291_of__nat__diff,axiom,
% 4.71/5.03 ! [N: nat,M2: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ N @ M2 )
% 4.71/5.03 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M2 @ N ) )
% 4.71/5.03 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_diff
% 4.71/5.03 thf(fact_1292_of__nat__diff,axiom,
% 4.71/5.03 ! [N: nat,M2: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ N @ M2 )
% 4.71/5.03 => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M2 @ N ) )
% 4.71/5.03 = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_diff
% 4.71/5.03 thf(fact_1293_of__nat__diff,axiom,
% 4.71/5.03 ! [N: nat,M2: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ N @ M2 )
% 4.71/5.03 => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M2 @ N ) )
% 4.71/5.03 = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_diff
% 4.71/5.03 thf(fact_1294_diff__commute,axiom,
% 4.71/5.03 ! [I: nat,J: nat,K: nat] :
% 4.71/5.03 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 4.71/5.03 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_commute
% 4.71/5.03 thf(fact_1295_diff__right__commute,axiom,
% 4.71/5.03 ! [A: real,C: real,B: real] :
% 4.71/5.03 ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
% 4.71/5.03 = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_right_commute
% 4.71/5.03 thf(fact_1296_diff__right__commute,axiom,
% 4.71/5.03 ! [A: rat,C: rat,B: rat] :
% 4.71/5.03 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 4.71/5.03 = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_right_commute
% 4.71/5.03 thf(fact_1297_diff__right__commute,axiom,
% 4.71/5.03 ! [A: nat,C: nat,B: nat] :
% 4.71/5.03 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 4.71/5.03 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_right_commute
% 4.71/5.03 thf(fact_1298_diff__right__commute,axiom,
% 4.71/5.03 ! [A: int,C: int,B: int] :
% 4.71/5.03 ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 4.71/5.03 = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_right_commute
% 4.71/5.03 thf(fact_1299_diff__eq__diff__eq,axiom,
% 4.71/5.03 ! [A: real,B: real,C: real,D: real] :
% 4.71/5.03 ( ( ( minus_minus_real @ A @ B )
% 4.71/5.03 = ( minus_minus_real @ C @ D ) )
% 4.71/5.03 => ( ( A = B )
% 4.71/5.03 = ( C = D ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_eq_diff_eq
% 4.71/5.03 thf(fact_1300_diff__eq__diff__eq,axiom,
% 4.71/5.03 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.71/5.03 ( ( ( minus_minus_rat @ A @ B )
% 4.71/5.03 = ( minus_minus_rat @ C @ D ) )
% 4.71/5.03 => ( ( A = B )
% 4.71/5.03 = ( C = D ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_eq_diff_eq
% 4.71/5.03 thf(fact_1301_diff__eq__diff__eq,axiom,
% 4.71/5.03 ! [A: int,B: int,C: int,D: int] :
% 4.71/5.03 ( ( ( minus_minus_int @ A @ B )
% 4.71/5.03 = ( minus_minus_int @ C @ D ) )
% 4.71/5.03 => ( ( A = B )
% 4.71/5.03 = ( C = D ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_eq_diff_eq
% 4.71/5.03 thf(fact_1302_real__arch__simple,axiom,
% 4.71/5.03 ! [X: real] :
% 4.71/5.03 ? [N2: nat] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ).
% 4.71/5.03
% 4.71/5.03 % real_arch_simple
% 4.71/5.03 thf(fact_1303_real__arch__simple,axiom,
% 4.71/5.03 ! [X: rat] :
% 4.71/5.03 ? [N2: nat] : ( ord_less_eq_rat @ X @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 4.71/5.03
% 4.71/5.03 % real_arch_simple
% 4.71/5.03 thf(fact_1304_reals__Archimedean2,axiom,
% 4.71/5.03 ! [X: real] :
% 4.71/5.03 ? [N2: nat] : ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ).
% 4.71/5.03
% 4.71/5.03 % reals_Archimedean2
% 4.71/5.03 thf(fact_1305_reals__Archimedean2,axiom,
% 4.71/5.03 ! [X: rat] :
% 4.71/5.03 ? [N2: nat] : ( ord_less_rat @ X @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 4.71/5.03
% 4.71/5.03 % reals_Archimedean2
% 4.71/5.03 thf(fact_1306_size__neq__size__imp__neq,axiom,
% 4.71/5.03 ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 4.71/5.03 ( ( ( size_size_VEBT_VEBT @ X )
% 4.71/5.03 != ( size_size_VEBT_VEBT @ Y ) )
% 4.71/5.03 => ( X != Y ) ) ).
% 4.71/5.03
% 4.71/5.03 % size_neq_size_imp_neq
% 4.71/5.03 thf(fact_1307_size__neq__size__imp__neq,axiom,
% 4.71/5.03 ! [X: list_VEBT_VEBT,Y: list_VEBT_VEBT] :
% 4.71/5.03 ( ( ( size_s6755466524823107622T_VEBT @ X )
% 4.71/5.03 != ( size_s6755466524823107622T_VEBT @ Y ) )
% 4.71/5.03 => ( X != Y ) ) ).
% 4.71/5.03
% 4.71/5.03 % size_neq_size_imp_neq
% 4.71/5.03 thf(fact_1308_size__neq__size__imp__neq,axiom,
% 4.71/5.03 ! [X: num,Y: num] :
% 4.71/5.03 ( ( ( size_size_num @ X )
% 4.71/5.03 != ( size_size_num @ Y ) )
% 4.71/5.03 => ( X != Y ) ) ).
% 4.71/5.03
% 4.71/5.03 % size_neq_size_imp_neq
% 4.71/5.03 thf(fact_1309_size__neq__size__imp__neq,axiom,
% 4.71/5.03 ! [X: list_nat,Y: list_nat] :
% 4.71/5.03 ( ( ( size_size_list_nat @ X )
% 4.71/5.03 != ( size_size_list_nat @ Y ) )
% 4.71/5.03 => ( X != Y ) ) ).
% 4.71/5.03
% 4.71/5.03 % size_neq_size_imp_neq
% 4.71/5.03 thf(fact_1310_size__neq__size__imp__neq,axiom,
% 4.71/5.03 ! [X: char,Y: char] :
% 4.71/5.03 ( ( ( size_size_char @ X )
% 4.71/5.03 != ( size_size_char @ Y ) )
% 4.71/5.03 => ( X != Y ) ) ).
% 4.71/5.03
% 4.71/5.03 % size_neq_size_imp_neq
% 4.71/5.03 thf(fact_1311_diff__eq__diff__less__eq,axiom,
% 4.71/5.03 ! [A: real,B: real,C: real,D: real] :
% 4.71/5.03 ( ( ( minus_minus_real @ A @ B )
% 4.71/5.03 = ( minus_minus_real @ C @ D ) )
% 4.71/5.03 => ( ( ord_less_eq_real @ A @ B )
% 4.71/5.03 = ( ord_less_eq_real @ C @ D ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_eq_diff_less_eq
% 4.71/5.03 thf(fact_1312_diff__eq__diff__less__eq,axiom,
% 4.71/5.03 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.71/5.03 ( ( ( minus_minus_rat @ A @ B )
% 4.71/5.03 = ( minus_minus_rat @ C @ D ) )
% 4.71/5.03 => ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.03 = ( ord_less_eq_rat @ C @ D ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_eq_diff_less_eq
% 4.71/5.03 thf(fact_1313_diff__eq__diff__less__eq,axiom,
% 4.71/5.03 ! [A: int,B: int,C: int,D: int] :
% 4.71/5.03 ( ( ( minus_minus_int @ A @ B )
% 4.71/5.03 = ( minus_minus_int @ C @ D ) )
% 4.71/5.03 => ( ( ord_less_eq_int @ A @ B )
% 4.71/5.03 = ( ord_less_eq_int @ C @ D ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_eq_diff_less_eq
% 4.71/5.03 thf(fact_1314_diff__right__mono,axiom,
% 4.71/5.03 ! [A: real,B: real,C: real] :
% 4.71/5.03 ( ( ord_less_eq_real @ A @ B )
% 4.71/5.03 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_right_mono
% 4.71/5.03 thf(fact_1315_diff__right__mono,axiom,
% 4.71/5.03 ! [A: rat,B: rat,C: rat] :
% 4.71/5.03 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.03 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_right_mono
% 4.71/5.03 thf(fact_1316_diff__right__mono,axiom,
% 4.71/5.03 ! [A: int,B: int,C: int] :
% 4.71/5.03 ( ( ord_less_eq_int @ A @ B )
% 4.71/5.03 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_right_mono
% 4.71/5.03 thf(fact_1317_diff__left__mono,axiom,
% 4.71/5.03 ! [B: real,A: real,C: real] :
% 4.71/5.03 ( ( ord_less_eq_real @ B @ A )
% 4.71/5.03 => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_left_mono
% 4.71/5.03 thf(fact_1318_diff__left__mono,axiom,
% 4.71/5.03 ! [B: rat,A: rat,C: rat] :
% 4.71/5.03 ( ( ord_less_eq_rat @ B @ A )
% 4.71/5.03 => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_left_mono
% 4.71/5.03 thf(fact_1319_diff__left__mono,axiom,
% 4.71/5.03 ! [B: int,A: int,C: int] :
% 4.71/5.03 ( ( ord_less_eq_int @ B @ A )
% 4.71/5.03 => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_left_mono
% 4.71/5.03 thf(fact_1320_diff__mono,axiom,
% 4.71/5.03 ! [A: real,B: real,D: real,C: real] :
% 4.71/5.03 ( ( ord_less_eq_real @ A @ B )
% 4.71/5.03 => ( ( ord_less_eq_real @ D @ C )
% 4.71/5.03 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_mono
% 4.71/5.03 thf(fact_1321_diff__mono,axiom,
% 4.71/5.03 ! [A: rat,B: rat,D: rat,C: rat] :
% 4.71/5.03 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.03 => ( ( ord_less_eq_rat @ D @ C )
% 4.71/5.03 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_mono
% 4.71/5.03 thf(fact_1322_diff__mono,axiom,
% 4.71/5.03 ! [A: int,B: int,D: int,C: int] :
% 4.71/5.03 ( ( ord_less_eq_int @ A @ B )
% 4.71/5.03 => ( ( ord_less_eq_int @ D @ C )
% 4.71/5.03 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_mono
% 4.71/5.03 thf(fact_1323_eq__iff__diff__eq__0,axiom,
% 4.71/5.03 ( ( ^ [Y5: real,Z4: real] : ( Y5 = Z4 ) )
% 4.71/5.03 = ( ^ [A4: real,B4: real] :
% 4.71/5.03 ( ( minus_minus_real @ A4 @ B4 )
% 4.71/5.03 = zero_zero_real ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % eq_iff_diff_eq_0
% 4.71/5.03 thf(fact_1324_eq__iff__diff__eq__0,axiom,
% 4.71/5.03 ( ( ^ [Y5: rat,Z4: rat] : ( Y5 = Z4 ) )
% 4.71/5.03 = ( ^ [A4: rat,B4: rat] :
% 4.71/5.03 ( ( minus_minus_rat @ A4 @ B4 )
% 4.71/5.03 = zero_zero_rat ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % eq_iff_diff_eq_0
% 4.71/5.03 thf(fact_1325_eq__iff__diff__eq__0,axiom,
% 4.71/5.03 ( ( ^ [Y5: int,Z4: int] : ( Y5 = Z4 ) )
% 4.71/5.03 = ( ^ [A4: int,B4: int] :
% 4.71/5.03 ( ( minus_minus_int @ A4 @ B4 )
% 4.71/5.03 = zero_zero_int ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % eq_iff_diff_eq_0
% 4.71/5.03 thf(fact_1326_diff__strict__mono,axiom,
% 4.71/5.03 ! [A: real,B: real,D: real,C: real] :
% 4.71/5.03 ( ( ord_less_real @ A @ B )
% 4.71/5.03 => ( ( ord_less_real @ D @ C )
% 4.71/5.03 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_strict_mono
% 4.71/5.03 thf(fact_1327_diff__strict__mono,axiom,
% 4.71/5.03 ! [A: rat,B: rat,D: rat,C: rat] :
% 4.71/5.03 ( ( ord_less_rat @ A @ B )
% 4.71/5.03 => ( ( ord_less_rat @ D @ C )
% 4.71/5.03 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_strict_mono
% 4.71/5.03 thf(fact_1328_diff__strict__mono,axiom,
% 4.71/5.03 ! [A: int,B: int,D: int,C: int] :
% 4.71/5.03 ( ( ord_less_int @ A @ B )
% 4.71/5.03 => ( ( ord_less_int @ D @ C )
% 4.71/5.03 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_strict_mono
% 4.71/5.03 thf(fact_1329_diff__eq__diff__less,axiom,
% 4.71/5.03 ! [A: real,B: real,C: real,D: real] :
% 4.71/5.03 ( ( ( minus_minus_real @ A @ B )
% 4.71/5.03 = ( minus_minus_real @ C @ D ) )
% 4.71/5.03 => ( ( ord_less_real @ A @ B )
% 4.71/5.03 = ( ord_less_real @ C @ D ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_eq_diff_less
% 4.71/5.03 thf(fact_1330_diff__eq__diff__less,axiom,
% 4.71/5.03 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.71/5.03 ( ( ( minus_minus_rat @ A @ B )
% 4.71/5.03 = ( minus_minus_rat @ C @ D ) )
% 4.71/5.03 => ( ( ord_less_rat @ A @ B )
% 4.71/5.03 = ( ord_less_rat @ C @ D ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_eq_diff_less
% 4.71/5.03 thf(fact_1331_diff__eq__diff__less,axiom,
% 4.71/5.03 ! [A: int,B: int,C: int,D: int] :
% 4.71/5.03 ( ( ( minus_minus_int @ A @ B )
% 4.71/5.03 = ( minus_minus_int @ C @ D ) )
% 4.71/5.03 => ( ( ord_less_int @ A @ B )
% 4.71/5.03 = ( ord_less_int @ C @ D ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_eq_diff_less
% 4.71/5.03 thf(fact_1332_diff__strict__left__mono,axiom,
% 4.71/5.03 ! [B: real,A: real,C: real] :
% 4.71/5.03 ( ( ord_less_real @ B @ A )
% 4.71/5.03 => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_strict_left_mono
% 4.71/5.03 thf(fact_1333_diff__strict__left__mono,axiom,
% 4.71/5.03 ! [B: rat,A: rat,C: rat] :
% 4.71/5.03 ( ( ord_less_rat @ B @ A )
% 4.71/5.03 => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_strict_left_mono
% 4.71/5.03 thf(fact_1334_diff__strict__left__mono,axiom,
% 4.71/5.03 ! [B: int,A: int,C: int] :
% 4.71/5.03 ( ( ord_less_int @ B @ A )
% 4.71/5.03 => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_strict_left_mono
% 4.71/5.03 thf(fact_1335_diff__strict__right__mono,axiom,
% 4.71/5.03 ! [A: real,B: real,C: real] :
% 4.71/5.03 ( ( ord_less_real @ A @ B )
% 4.71/5.03 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_strict_right_mono
% 4.71/5.03 thf(fact_1336_diff__strict__right__mono,axiom,
% 4.71/5.03 ! [A: rat,B: rat,C: rat] :
% 4.71/5.03 ( ( ord_less_rat @ A @ B )
% 4.71/5.03 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_strict_right_mono
% 4.71/5.03 thf(fact_1337_diff__strict__right__mono,axiom,
% 4.71/5.03 ! [A: int,B: int,C: int] :
% 4.71/5.03 ( ( ord_less_int @ A @ B )
% 4.71/5.03 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_strict_right_mono
% 4.71/5.03 thf(fact_1338_int__ops_I1_J,axiom,
% 4.71/5.03 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 4.71/5.03 = zero_zero_int ) ).
% 4.71/5.03
% 4.71/5.03 % int_ops(1)
% 4.71/5.03 thf(fact_1339_nat__int__comparison_I2_J,axiom,
% 4.71/5.03 ( ord_less_nat
% 4.71/5.03 = ( ^ [A4: nat,B4: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % nat_int_comparison(2)
% 4.71/5.03 thf(fact_1340_nat__int__comparison_I3_J,axiom,
% 4.71/5.03 ( ord_less_eq_nat
% 4.71/5.03 = ( ^ [A4: nat,B4: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % nat_int_comparison(3)
% 4.71/5.03 thf(fact_1341_zero__induct__lemma,axiom,
% 4.71/5.03 ! [P: nat > $o,K: nat,I: nat] :
% 4.71/5.03 ( ( P @ K )
% 4.71/5.03 => ( ! [N2: nat] :
% 4.71/5.03 ( ( P @ ( suc @ N2 ) )
% 4.71/5.03 => ( P @ N2 ) )
% 4.71/5.03 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % zero_induct_lemma
% 4.71/5.03 thf(fact_1342_minus__nat_Odiff__0,axiom,
% 4.71/5.03 ! [M2: nat] :
% 4.71/5.03 ( ( minus_minus_nat @ M2 @ zero_zero_nat )
% 4.71/5.03 = M2 ) ).
% 4.71/5.03
% 4.71/5.03 % minus_nat.diff_0
% 4.71/5.03 thf(fact_1343_diffs0__imp__equal,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ( minus_minus_nat @ M2 @ N )
% 4.71/5.03 = zero_zero_nat )
% 4.71/5.03 => ( ( ( minus_minus_nat @ N @ M2 )
% 4.71/5.03 = zero_zero_nat )
% 4.71/5.03 => ( M2 = N ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diffs0_imp_equal
% 4.71/5.03 thf(fact_1344_diff__less__mono2,axiom,
% 4.71/5.03 ! [M2: nat,N: nat,L: nat] :
% 4.71/5.03 ( ( ord_less_nat @ M2 @ N )
% 4.71/5.03 => ( ( ord_less_nat @ M2 @ L )
% 4.71/5.03 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M2 ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_less_mono2
% 4.71/5.03 thf(fact_1345_less__imp__diff__less,axiom,
% 4.71/5.03 ! [J: nat,K: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_nat @ J @ K )
% 4.71/5.03 => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 4.71/5.03
% 4.71/5.03 % less_imp_diff_less
% 4.71/5.03 thf(fact_1346_diff__le__mono2,axiom,
% 4.71/5.03 ! [M2: nat,N: nat,L: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.03 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M2 ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_le_mono2
% 4.71/5.03 thf(fact_1347_le__diff__iff_H,axiom,
% 4.71/5.03 ! [A: nat,C: nat,B: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ A @ C )
% 4.71/5.03 => ( ( ord_less_eq_nat @ B @ C )
% 4.71/5.03 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 4.71/5.03 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % le_diff_iff'
% 4.71/5.03 thf(fact_1348_diff__le__self,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ N ) @ M2 ) ).
% 4.71/5.03
% 4.71/5.03 % diff_le_self
% 4.71/5.03 thf(fact_1349_diff__le__mono,axiom,
% 4.71/5.03 ! [M2: nat,N: nat,L: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.03 => ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_le_mono
% 4.71/5.03 thf(fact_1350_Nat_Odiff__diff__eq,axiom,
% 4.71/5.03 ! [K: nat,M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ K @ M2 )
% 4.71/5.03 => ( ( ord_less_eq_nat @ K @ N )
% 4.71/5.03 => ( ( minus_minus_nat @ ( minus_minus_nat @ M2 @ K ) @ ( minus_minus_nat @ N @ K ) )
% 4.71/5.03 = ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % Nat.diff_diff_eq
% 4.71/5.03 thf(fact_1351_le__diff__iff,axiom,
% 4.71/5.03 ! [K: nat,M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ K @ M2 )
% 4.71/5.03 => ( ( ord_less_eq_nat @ K @ N )
% 4.71/5.03 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ K ) @ ( minus_minus_nat @ N @ K ) )
% 4.71/5.03 = ( ord_less_eq_nat @ M2 @ N ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % le_diff_iff
% 4.71/5.03 thf(fact_1352_eq__diff__iff,axiom,
% 4.71/5.03 ! [K: nat,M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ K @ M2 )
% 4.71/5.03 => ( ( ord_less_eq_nat @ K @ N )
% 4.71/5.03 => ( ( ( minus_minus_nat @ M2 @ K )
% 4.71/5.03 = ( minus_minus_nat @ N @ K ) )
% 4.71/5.03 = ( M2 = N ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % eq_diff_iff
% 4.71/5.03 thf(fact_1353_int__ops_I2_J,axiom,
% 4.71/5.03 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 4.71/5.03 = one_one_int ) ).
% 4.71/5.03
% 4.71/5.03 % int_ops(2)
% 4.71/5.03 thf(fact_1354_enumerate__in__set,axiom,
% 4.71/5.03 ! [S2: set_Extended_enat,N: nat] :
% 4.71/5.03 ( ~ ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.03 => ( member_Extended_enat @ ( infini7641415182203889163d_enat @ S2 @ N ) @ S2 ) ) ).
% 4.71/5.03
% 4.71/5.03 % enumerate_in_set
% 4.71/5.03 thf(fact_1355_enumerate__in__set,axiom,
% 4.71/5.03 ! [S2: set_nat,N: nat] :
% 4.71/5.03 ( ~ ( finite_finite_nat @ S2 )
% 4.71/5.03 => ( member_nat @ ( infini8530281810654367211te_nat @ S2 @ N ) @ S2 ) ) ).
% 4.71/5.03
% 4.71/5.03 % enumerate_in_set
% 4.71/5.03 thf(fact_1356_enumerate__Ex,axiom,
% 4.71/5.03 ! [S2: set_nat,S: nat] :
% 4.71/5.03 ( ~ ( finite_finite_nat @ S2 )
% 4.71/5.03 => ( ( member_nat @ S @ S2 )
% 4.71/5.03 => ? [N2: nat] :
% 4.71/5.03 ( ( infini8530281810654367211te_nat @ S2 @ N2 )
% 4.71/5.03 = S ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % enumerate_Ex
% 4.71/5.03 thf(fact_1357_of__nat__0__le__iff,axiom,
% 4.71/5.03 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_0_le_iff
% 4.71/5.03 thf(fact_1358_of__nat__0__le__iff,axiom,
% 4.71/5.03 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_0_le_iff
% 4.71/5.03 thf(fact_1359_of__nat__0__le__iff,axiom,
% 4.71/5.03 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_0_le_iff
% 4.71/5.03 thf(fact_1360_of__nat__0__le__iff,axiom,
% 4.71/5.03 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_0_le_iff
% 4.71/5.03 thf(fact_1361_of__nat__less__0__iff,axiom,
% 4.71/5.03 ! [M2: nat] :
% 4.71/5.03 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ zero_zero_nat ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_less_0_iff
% 4.71/5.03 thf(fact_1362_of__nat__less__0__iff,axiom,
% 4.71/5.03 ! [M2: nat] :
% 4.71/5.03 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ zero_zero_int ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_less_0_iff
% 4.71/5.03 thf(fact_1363_of__nat__less__0__iff,axiom,
% 4.71/5.03 ! [M2: nat] :
% 4.71/5.03 ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ zero_zero_real ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_less_0_iff
% 4.71/5.03 thf(fact_1364_of__nat__less__0__iff,axiom,
% 4.71/5.03 ! [M2: nat] :
% 4.71/5.03 ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M2 ) @ zero_zero_rat ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_less_0_iff
% 4.71/5.03 thf(fact_1365_of__nat__neq__0,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 4.71/5.03 != zero_zero_nat ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_neq_0
% 4.71/5.03 thf(fact_1366_of__nat__neq__0,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 4.71/5.03 != zero_zero_int ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_neq_0
% 4.71/5.03 thf(fact_1367_of__nat__neq__0,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( semiri5074537144036343181t_real @ ( suc @ N ) )
% 4.71/5.03 != zero_zero_real ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_neq_0
% 4.71/5.03 thf(fact_1368_of__nat__neq__0,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 4.71/5.03 != zero_zero_rat ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_neq_0
% 4.71/5.03 thf(fact_1369_less__imp__of__nat__less,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_nat @ M2 @ N )
% 4.71/5.03 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % less_imp_of_nat_less
% 4.71/5.03 thf(fact_1370_less__imp__of__nat__less,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_nat @ M2 @ N )
% 4.71/5.03 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % less_imp_of_nat_less
% 4.71/5.03 thf(fact_1371_less__imp__of__nat__less,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_nat @ M2 @ N )
% 4.71/5.03 => ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % less_imp_of_nat_less
% 4.71/5.03 thf(fact_1372_less__imp__of__nat__less,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_nat @ M2 @ N )
% 4.71/5.03 => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % less_imp_of_nat_less
% 4.71/5.03 thf(fact_1373_of__nat__less__imp__less,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) )
% 4.71/5.03 => ( ord_less_nat @ M2 @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_less_imp_less
% 4.71/5.03 thf(fact_1374_of__nat__less__imp__less,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) )
% 4.71/5.03 => ( ord_less_nat @ M2 @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_less_imp_less
% 4.71/5.03 thf(fact_1375_of__nat__less__imp__less,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) )
% 4.71/5.03 => ( ord_less_nat @ M2 @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_less_imp_less
% 4.71/5.03 thf(fact_1376_of__nat__less__imp__less,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) )
% 4.71/5.03 => ( ord_less_nat @ M2 @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_less_imp_less
% 4.71/5.03 thf(fact_1377_of__nat__mono,axiom,
% 4.71/5.03 ! [I: nat,J: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ I @ J )
% 4.71/5.03 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_mono
% 4.71/5.03 thf(fact_1378_of__nat__mono,axiom,
% 4.71/5.03 ! [I: nat,J: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ I @ J )
% 4.71/5.03 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_mono
% 4.71/5.03 thf(fact_1379_of__nat__mono,axiom,
% 4.71/5.03 ! [I: nat,J: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ I @ J )
% 4.71/5.03 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_mono
% 4.71/5.03 thf(fact_1380_of__nat__mono,axiom,
% 4.71/5.03 ! [I: nat,J: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ I @ J )
% 4.71/5.03 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % of_nat_mono
% 4.71/5.03 thf(fact_1381_le__iff__diff__le__0,axiom,
% 4.71/5.03 ( ord_less_eq_real
% 4.71/5.03 = ( ^ [A4: real,B4: real] : ( ord_less_eq_real @ ( minus_minus_real @ A4 @ B4 ) @ zero_zero_real ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % le_iff_diff_le_0
% 4.71/5.03 thf(fact_1382_le__iff__diff__le__0,axiom,
% 4.71/5.03 ( ord_less_eq_rat
% 4.71/5.03 = ( ^ [A4: rat,B4: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A4 @ B4 ) @ zero_zero_rat ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % le_iff_diff_le_0
% 4.71/5.03 thf(fact_1383_le__iff__diff__le__0,axiom,
% 4.71/5.03 ( ord_less_eq_int
% 4.71/5.03 = ( ^ [A4: int,B4: int] : ( ord_less_eq_int @ ( minus_minus_int @ A4 @ B4 ) @ zero_zero_int ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % le_iff_diff_le_0
% 4.71/5.03 thf(fact_1384_less__iff__diff__less__0,axiom,
% 4.71/5.03 ( ord_less_real
% 4.71/5.03 = ( ^ [A4: real,B4: real] : ( ord_less_real @ ( minus_minus_real @ A4 @ B4 ) @ zero_zero_real ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % less_iff_diff_less_0
% 4.71/5.03 thf(fact_1385_less__iff__diff__less__0,axiom,
% 4.71/5.03 ( ord_less_rat
% 4.71/5.03 = ( ^ [A4: rat,B4: rat] : ( ord_less_rat @ ( minus_minus_rat @ A4 @ B4 ) @ zero_zero_rat ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % less_iff_diff_less_0
% 4.71/5.03 thf(fact_1386_less__iff__diff__less__0,axiom,
% 4.71/5.03 ( ord_less_int
% 4.71/5.03 = ( ^ [A4: int,B4: int] : ( ord_less_int @ ( minus_minus_int @ A4 @ B4 ) @ zero_zero_int ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % less_iff_diff_less_0
% 4.71/5.03 thf(fact_1387_diff__less__Suc,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M2 @ N ) @ ( suc @ M2 ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_less_Suc
% 4.71/5.03 thf(fact_1388_Suc__diff__Suc,axiom,
% 4.71/5.03 ! [N: nat,M2: nat] :
% 4.71/5.03 ( ( ord_less_nat @ N @ M2 )
% 4.71/5.03 => ( ( suc @ ( minus_minus_nat @ M2 @ ( suc @ N ) ) )
% 4.71/5.03 = ( minus_minus_nat @ M2 @ N ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % Suc_diff_Suc
% 4.71/5.03 thf(fact_1389_diff__less,axiom,
% 4.71/5.03 ! [N: nat,M2: nat] :
% 4.71/5.03 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.03 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 4.71/5.03 => ( ord_less_nat @ ( minus_minus_nat @ M2 @ N ) @ M2 ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_less
% 4.71/5.03 thf(fact_1390_Suc__diff__le,axiom,
% 4.71/5.03 ! [N: nat,M2: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ N @ M2 )
% 4.71/5.03 => ( ( minus_minus_nat @ ( suc @ M2 ) @ N )
% 4.71/5.03 = ( suc @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % Suc_diff_le
% 4.71/5.03 thf(fact_1391_diff__less__mono,axiom,
% 4.71/5.03 ! [A: nat,B: nat,C: nat] :
% 4.71/5.03 ( ( ord_less_nat @ A @ B )
% 4.71/5.03 => ( ( ord_less_eq_nat @ C @ A )
% 4.71/5.03 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_less_mono
% 4.71/5.03 thf(fact_1392_less__diff__iff,axiom,
% 4.71/5.03 ! [K: nat,M2: nat,N: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ K @ M2 )
% 4.71/5.03 => ( ( ord_less_eq_nat @ K @ N )
% 4.71/5.03 => ( ( ord_less_nat @ ( minus_minus_nat @ M2 @ K ) @ ( minus_minus_nat @ N @ K ) )
% 4.71/5.03 = ( ord_less_nat @ M2 @ N ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % less_diff_iff
% 4.71/5.03 thf(fact_1393_diff__Suc__eq__diff__pred,axiom,
% 4.71/5.03 ! [M2: nat,N: nat] :
% 4.71/5.03 ( ( minus_minus_nat @ M2 @ ( suc @ N ) )
% 4.71/5.03 = ( minus_minus_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_Suc_eq_diff_pred
% 4.71/5.03 thf(fact_1394_le__enumerate,axiom,
% 4.71/5.03 ! [S2: set_nat,N: nat] :
% 4.71/5.03 ( ~ ( finite_finite_nat @ S2 )
% 4.71/5.03 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S2 @ N ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % le_enumerate
% 4.71/5.03 thf(fact_1395_diff__Suc__less,axiom,
% 4.71/5.03 ! [N: nat,I: nat] :
% 4.71/5.03 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.03 => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I ) ) @ N ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_Suc_less
% 4.71/5.03 thf(fact_1396_enumerate__step,axiom,
% 4.71/5.03 ! [S2: set_Extended_enat,N: nat] :
% 4.71/5.03 ( ~ ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.03 => ( ord_le72135733267957522d_enat @ ( infini7641415182203889163d_enat @ S2 @ N ) @ ( infini7641415182203889163d_enat @ S2 @ ( suc @ N ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % enumerate_step
% 4.71/5.03 thf(fact_1397_enumerate__step,axiom,
% 4.71/5.03 ! [S2: set_nat,N: nat] :
% 4.71/5.03 ( ~ ( finite_finite_nat @ S2 )
% 4.71/5.03 => ( ord_less_nat @ ( infini8530281810654367211te_nat @ S2 @ N ) @ ( infini8530281810654367211te_nat @ S2 @ ( suc @ N ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % enumerate_step
% 4.71/5.03 thf(fact_1398_enumerate__mono,axiom,
% 4.71/5.03 ! [M2: nat,N: nat,S2: set_Extended_enat] :
% 4.71/5.03 ( ( ord_less_nat @ M2 @ N )
% 4.71/5.03 => ( ~ ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.03 => ( ord_le72135733267957522d_enat @ ( infini7641415182203889163d_enat @ S2 @ M2 ) @ ( infini7641415182203889163d_enat @ S2 @ N ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % enumerate_mono
% 4.71/5.03 thf(fact_1399_enumerate__mono,axiom,
% 4.71/5.03 ! [M2: nat,N: nat,S2: set_nat] :
% 4.71/5.03 ( ( ord_less_nat @ M2 @ N )
% 4.71/5.03 => ( ~ ( finite_finite_nat @ S2 )
% 4.71/5.03 => ( ord_less_nat @ ( infini8530281810654367211te_nat @ S2 @ M2 ) @ ( infini8530281810654367211te_nat @ S2 @ N ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % enumerate_mono
% 4.71/5.03 thf(fact_1400_Suc__pred_H,axiom,
% 4.71/5.03 ! [N: nat] :
% 4.71/5.03 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.03 => ( N
% 4.71/5.03 = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % Suc_pred'
% 4.71/5.03 thf(fact_1401_Suc__diff__eq__diff__pred,axiom,
% 4.71/5.03 ! [N: nat,M2: nat] :
% 4.71/5.03 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.03 => ( ( minus_minus_nat @ ( suc @ M2 ) @ N )
% 4.71/5.03 = ( minus_minus_nat @ M2 @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % Suc_diff_eq_diff_pred
% 4.71/5.03 thf(fact_1402_arsinh__0,axiom,
% 4.71/5.03 ( ( arsinh_real @ zero_zero_real )
% 4.71/5.03 = zero_zero_real ) ).
% 4.71/5.03
% 4.71/5.03 % arsinh_0
% 4.71/5.03 thf(fact_1403_artanh__0,axiom,
% 4.71/5.03 ( ( artanh_real @ zero_zero_real )
% 4.71/5.03 = zero_zero_real ) ).
% 4.71/5.03
% 4.71/5.03 % artanh_0
% 4.71/5.03 thf(fact_1404_diff__shunt__var,axiom,
% 4.71/5.03 ! [X: set_real,Y: set_real] :
% 4.71/5.03 ( ( ( minus_minus_set_real @ X @ Y )
% 4.71/5.03 = bot_bot_set_real )
% 4.71/5.03 = ( ord_less_eq_set_real @ X @ Y ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_shunt_var
% 4.71/5.03 thf(fact_1405_diff__shunt__var,axiom,
% 4.71/5.03 ! [X: set_o,Y: set_o] :
% 4.71/5.03 ( ( ( minus_minus_set_o @ X @ Y )
% 4.71/5.03 = bot_bot_set_o )
% 4.71/5.03 = ( ord_less_eq_set_o @ X @ Y ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_shunt_var
% 4.71/5.03 thf(fact_1406_diff__shunt__var,axiom,
% 4.71/5.03 ! [X: set_nat,Y: set_nat] :
% 4.71/5.03 ( ( ( minus_minus_set_nat @ X @ Y )
% 4.71/5.03 = bot_bot_set_nat )
% 4.71/5.03 = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_shunt_var
% 4.71/5.03 thf(fact_1407_diff__shunt__var,axiom,
% 4.71/5.03 ! [X: set_int,Y: set_int] :
% 4.71/5.03 ( ( ( minus_minus_set_int @ X @ Y )
% 4.71/5.03 = bot_bot_set_int )
% 4.71/5.03 = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 4.71/5.03
% 4.71/5.03 % diff_shunt_var
% 4.71/5.03 thf(fact_1408_ln__one,axiom,
% 4.71/5.03 ( ( ln_ln_real @ one_one_real )
% 4.71/5.03 = zero_zero_real ) ).
% 4.71/5.03
% 4.71/5.03 % ln_one
% 4.71/5.03 thf(fact_1409_pos__int__cases,axiom,
% 4.71/5.03 ! [K: int] :
% 4.71/5.03 ( ( ord_less_int @ zero_zero_int @ K )
% 4.71/5.03 => ~ ! [N2: nat] :
% 4.71/5.03 ( ( K
% 4.71/5.03 = ( semiri1314217659103216013at_int @ N2 ) )
% 4.71/5.03 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % pos_int_cases
% 4.71/5.03 thf(fact_1410_zero__less__imp__eq__int,axiom,
% 4.71/5.03 ! [K: int] :
% 4.71/5.03 ( ( ord_less_int @ zero_zero_int @ K )
% 4.71/5.03 => ? [N2: nat] :
% 4.71/5.03 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.71/5.03 & ( K
% 4.71/5.03 = ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % zero_less_imp_eq_int
% 4.71/5.03 thf(fact_1411_set__encode__empty,axiom,
% 4.71/5.03 ( ( nat_set_encode @ bot_bot_set_nat )
% 4.71/5.03 = zero_zero_nat ) ).
% 4.71/5.03
% 4.71/5.03 % set_encode_empty
% 4.71/5.03 thf(fact_1412_frac__eq,axiom,
% 4.71/5.03 ! [X: real] :
% 4.71/5.03 ( ( ( archim2898591450579166408c_real @ X )
% 4.71/5.03 = X )
% 4.71/5.03 = ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.03 & ( ord_less_real @ X @ one_one_real ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % frac_eq
% 4.71/5.03 thf(fact_1413_frac__eq,axiom,
% 4.71/5.03 ! [X: rat] :
% 4.71/5.03 ( ( ( archimedean_frac_rat @ X )
% 4.71/5.03 = X )
% 4.71/5.03 = ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 4.71/5.03 & ( ord_less_rat @ X @ one_one_rat ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % frac_eq
% 4.71/5.03 thf(fact_1414_finite__enum__subset,axiom,
% 4.71/5.03 ! [X5: set_Extended_enat,Y6: set_Extended_enat] :
% 4.71/5.03 ( ! [I2: nat] :
% 4.71/5.03 ( ( ord_less_nat @ I2 @ ( finite121521170596916366d_enat @ X5 ) )
% 4.71/5.03 => ( ( infini7641415182203889163d_enat @ X5 @ I2 )
% 4.71/5.03 = ( infini7641415182203889163d_enat @ Y6 @ I2 ) ) )
% 4.71/5.03 => ( ( finite4001608067531595151d_enat @ X5 )
% 4.71/5.03 => ( ( finite4001608067531595151d_enat @ Y6 )
% 4.71/5.03 => ( ( ord_less_eq_nat @ ( finite121521170596916366d_enat @ X5 ) @ ( finite121521170596916366d_enat @ Y6 ) )
% 4.71/5.03 => ( ord_le7203529160286727270d_enat @ X5 @ Y6 ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % finite_enum_subset
% 4.71/5.03 thf(fact_1415_finite__enum__subset,axiom,
% 4.71/5.03 ! [X5: set_nat,Y6: set_nat] :
% 4.71/5.03 ( ! [I2: nat] :
% 4.71/5.03 ( ( ord_less_nat @ I2 @ ( finite_card_nat @ X5 ) )
% 4.71/5.03 => ( ( infini8530281810654367211te_nat @ X5 @ I2 )
% 4.71/5.03 = ( infini8530281810654367211te_nat @ Y6 @ I2 ) ) )
% 4.71/5.03 => ( ( finite_finite_nat @ X5 )
% 4.71/5.03 => ( ( finite_finite_nat @ Y6 )
% 4.71/5.03 => ( ( ord_less_eq_nat @ ( finite_card_nat @ X5 ) @ ( finite_card_nat @ Y6 ) )
% 4.71/5.03 => ( ord_less_eq_set_nat @ X5 @ Y6 ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % finite_enum_subset
% 4.71/5.03 thf(fact_1416_inverse__of__nat__le,axiom,
% 4.71/5.03 ! [N: nat,M2: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ N @ M2 )
% 4.71/5.03 => ( ( N != zero_zero_nat )
% 4.71/5.03 => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % inverse_of_nat_le
% 4.71/5.03 thf(fact_1417_inverse__of__nat__le,axiom,
% 4.71/5.03 ! [N: nat,M2: nat] :
% 4.71/5.03 ( ( ord_less_eq_nat @ N @ M2 )
% 4.71/5.03 => ( ( N != zero_zero_nat )
% 4.71/5.03 => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M2 ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N ) ) ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % inverse_of_nat_le
% 4.71/5.03 thf(fact_1418_Diff__cancel,axiom,
% 4.71/5.03 ! [A2: set_real] :
% 4.71/5.03 ( ( minus_minus_set_real @ A2 @ A2 )
% 4.71/5.03 = bot_bot_set_real ) ).
% 4.71/5.03
% 4.71/5.03 % Diff_cancel
% 4.71/5.03 thf(fact_1419_Diff__cancel,axiom,
% 4.71/5.03 ! [A2: set_o] :
% 4.71/5.03 ( ( minus_minus_set_o @ A2 @ A2 )
% 4.71/5.03 = bot_bot_set_o ) ).
% 4.71/5.03
% 4.71/5.03 % Diff_cancel
% 4.71/5.03 thf(fact_1420_Diff__cancel,axiom,
% 4.71/5.03 ! [A2: set_int] :
% 4.71/5.03 ( ( minus_minus_set_int @ A2 @ A2 )
% 4.71/5.03 = bot_bot_set_int ) ).
% 4.71/5.03
% 4.71/5.03 % Diff_cancel
% 4.71/5.03 thf(fact_1421_Diff__cancel,axiom,
% 4.71/5.03 ! [A2: set_nat] :
% 4.71/5.03 ( ( minus_minus_set_nat @ A2 @ A2 )
% 4.71/5.03 = bot_bot_set_nat ) ).
% 4.71/5.03
% 4.71/5.03 % Diff_cancel
% 4.71/5.03 thf(fact_1422_empty__Diff,axiom,
% 4.71/5.03 ! [A2: set_real] :
% 4.71/5.03 ( ( minus_minus_set_real @ bot_bot_set_real @ A2 )
% 4.71/5.03 = bot_bot_set_real ) ).
% 4.71/5.03
% 4.71/5.03 % empty_Diff
% 4.71/5.03 thf(fact_1423_empty__Diff,axiom,
% 4.71/5.03 ! [A2: set_o] :
% 4.71/5.03 ( ( minus_minus_set_o @ bot_bot_set_o @ A2 )
% 4.71/5.03 = bot_bot_set_o ) ).
% 4.71/5.03
% 4.71/5.03 % empty_Diff
% 4.71/5.03 thf(fact_1424_empty__Diff,axiom,
% 4.71/5.03 ! [A2: set_int] :
% 4.71/5.03 ( ( minus_minus_set_int @ bot_bot_set_int @ A2 )
% 4.71/5.03 = bot_bot_set_int ) ).
% 4.71/5.03
% 4.71/5.03 % empty_Diff
% 4.71/5.03 thf(fact_1425_empty__Diff,axiom,
% 4.71/5.03 ! [A2: set_nat] :
% 4.71/5.03 ( ( minus_minus_set_nat @ bot_bot_set_nat @ A2 )
% 4.71/5.03 = bot_bot_set_nat ) ).
% 4.71/5.03
% 4.71/5.03 % empty_Diff
% 4.71/5.03 thf(fact_1426_Diff__empty,axiom,
% 4.71/5.03 ! [A2: set_real] :
% 4.71/5.03 ( ( minus_minus_set_real @ A2 @ bot_bot_set_real )
% 4.71/5.03 = A2 ) ).
% 4.71/5.03
% 4.71/5.03 % Diff_empty
% 4.71/5.03 thf(fact_1427_Diff__empty,axiom,
% 4.71/5.03 ! [A2: set_o] :
% 4.71/5.03 ( ( minus_minus_set_o @ A2 @ bot_bot_set_o )
% 4.71/5.03 = A2 ) ).
% 4.71/5.03
% 4.71/5.03 % Diff_empty
% 4.71/5.03 thf(fact_1428_Diff__empty,axiom,
% 4.71/5.03 ! [A2: set_int] :
% 4.71/5.03 ( ( minus_minus_set_int @ A2 @ bot_bot_set_int )
% 4.71/5.03 = A2 ) ).
% 4.71/5.03
% 4.71/5.03 % Diff_empty
% 4.71/5.03 thf(fact_1429_Diff__empty,axiom,
% 4.71/5.03 ! [A2: set_nat] :
% 4.71/5.03 ( ( minus_minus_set_nat @ A2 @ bot_bot_set_nat )
% 4.71/5.03 = A2 ) ).
% 4.71/5.03
% 4.71/5.03 % Diff_empty
% 4.71/5.03 thf(fact_1430_finite__Diff2,axiom,
% 4.71/5.03 ! [B2: set_int,A2: set_int] :
% 4.71/5.03 ( ( finite_finite_int @ B2 )
% 4.71/5.03 => ( ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B2 ) )
% 4.71/5.03 = ( finite_finite_int @ A2 ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % finite_Diff2
% 4.71/5.03 thf(fact_1431_finite__Diff2,axiom,
% 4.71/5.03 ! [B2: set_complex,A2: set_complex] :
% 4.71/5.03 ( ( finite3207457112153483333omplex @ B2 )
% 4.71/5.03 => ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 4.71/5.03 = ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % finite_Diff2
% 4.71/5.03 thf(fact_1432_finite__Diff2,axiom,
% 4.71/5.03 ! [B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.03 ( ( finite6177210948735845034at_nat @ B2 )
% 4.71/5.03 => ( ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) )
% 4.71/5.03 = ( finite6177210948735845034at_nat @ A2 ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % finite_Diff2
% 4.71/5.03 thf(fact_1433_finite__Diff2,axiom,
% 4.71/5.03 ! [B2: set_Extended_enat,A2: set_Extended_enat] :
% 4.71/5.03 ( ( finite4001608067531595151d_enat @ B2 )
% 4.71/5.03 => ( ( finite4001608067531595151d_enat @ ( minus_925952699566721837d_enat @ A2 @ B2 ) )
% 4.71/5.03 = ( finite4001608067531595151d_enat @ A2 ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % finite_Diff2
% 4.71/5.03 thf(fact_1434_finite__Diff2,axiom,
% 4.71/5.03 ! [B2: set_nat,A2: set_nat] :
% 4.71/5.03 ( ( finite_finite_nat @ B2 )
% 4.71/5.03 => ( ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 4.71/5.03 = ( finite_finite_nat @ A2 ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % finite_Diff2
% 4.71/5.03 thf(fact_1435_finite__Diff,axiom,
% 4.71/5.03 ! [A2: set_int,B2: set_int] :
% 4.71/5.03 ( ( finite_finite_int @ A2 )
% 4.71/5.03 => ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % finite_Diff
% 4.71/5.03 thf(fact_1436_finite__Diff,axiom,
% 4.71/5.03 ! [A2: set_complex,B2: set_complex] :
% 4.71/5.03 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.03 => ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % finite_Diff
% 4.71/5.03 thf(fact_1437_finite__Diff,axiom,
% 4.71/5.03 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 4.71/5.03 ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.03 => ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % finite_Diff
% 4.71/5.03 thf(fact_1438_finite__Diff,axiom,
% 4.71/5.03 ! [A2: set_Extended_enat,B2: set_Extended_enat] :
% 4.71/5.03 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.03 => ( finite4001608067531595151d_enat @ ( minus_925952699566721837d_enat @ A2 @ B2 ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % finite_Diff
% 4.71/5.03 thf(fact_1439_finite__Diff,axiom,
% 4.71/5.03 ! [A2: set_nat,B2: set_nat] :
% 4.71/5.03 ( ( finite_finite_nat @ A2 )
% 4.71/5.03 => ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ).
% 4.71/5.03
% 4.71/5.03 % finite_Diff
% 4.71/5.03 thf(fact_1440_div__by__0,axiom,
% 4.71/5.03 ! [A: rat] :
% 4.71/5.03 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 4.71/5.03 = zero_zero_rat ) ).
% 4.71/5.03
% 4.71/5.03 % div_by_0
% 4.71/5.03 thf(fact_1441_div__by__0,axiom,
% 4.71/5.03 ! [A: int] :
% 4.71/5.03 ( ( divide_divide_int @ A @ zero_zero_int )
% 4.71/5.03 = zero_zero_int ) ).
% 4.71/5.03
% 4.71/5.03 % div_by_0
% 4.71/5.03 thf(fact_1442_div__by__0,axiom,
% 4.71/5.03 ! [A: nat] :
% 4.71/5.03 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 4.71/5.03 = zero_zero_nat ) ).
% 4.71/5.03
% 4.71/5.03 % div_by_0
% 4.71/5.03 thf(fact_1443_div__by__0,axiom,
% 4.71/5.03 ! [A: real] :
% 4.71/5.03 ( ( divide_divide_real @ A @ zero_zero_real )
% 4.71/5.03 = zero_zero_real ) ).
% 4.71/5.03
% 4.71/5.03 % div_by_0
% 4.71/5.03 thf(fact_1444_div__0,axiom,
% 4.71/5.03 ! [A: rat] :
% 4.71/5.03 ( ( divide_divide_rat @ zero_zero_rat @ A )
% 4.71/5.03 = zero_zero_rat ) ).
% 4.71/5.03
% 4.71/5.03 % div_0
% 4.71/5.03 thf(fact_1445_div__0,axiom,
% 4.71/5.03 ! [A: int] :
% 4.71/5.03 ( ( divide_divide_int @ zero_zero_int @ A )
% 4.71/5.03 = zero_zero_int ) ).
% 4.71/5.03
% 4.71/5.03 % div_0
% 4.71/5.03 thf(fact_1446_div__0,axiom,
% 4.71/5.03 ! [A: nat] :
% 4.71/5.03 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 4.71/5.03 = zero_zero_nat ) ).
% 4.71/5.03
% 4.71/5.03 % div_0
% 4.71/5.03 thf(fact_1447_div__0,axiom,
% 4.71/5.03 ! [A: real] :
% 4.71/5.03 ( ( divide_divide_real @ zero_zero_real @ A )
% 4.71/5.03 = zero_zero_real ) ).
% 4.71/5.03
% 4.71/5.03 % div_0
% 4.71/5.03 thf(fact_1448_div__by__1,axiom,
% 4.71/5.03 ! [A: complex] :
% 4.71/5.03 ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 4.71/5.03 = A ) ).
% 4.71/5.03
% 4.71/5.03 % div_by_1
% 4.71/5.03 thf(fact_1449_div__by__1,axiom,
% 4.71/5.03 ! [A: rat] :
% 4.71/5.03 ( ( divide_divide_rat @ A @ one_one_rat )
% 4.71/5.03 = A ) ).
% 4.71/5.03
% 4.71/5.03 % div_by_1
% 4.71/5.03 thf(fact_1450_div__by__1,axiom,
% 4.71/5.03 ! [A: int] :
% 4.71/5.03 ( ( divide_divide_int @ A @ one_one_int )
% 4.71/5.03 = A ) ).
% 4.71/5.03
% 4.71/5.03 % div_by_1
% 4.71/5.03 thf(fact_1451_div__by__1,axiom,
% 4.71/5.03 ! [A: nat] :
% 4.71/5.03 ( ( divide_divide_nat @ A @ one_one_nat )
% 4.71/5.03 = A ) ).
% 4.71/5.03
% 4.71/5.03 % div_by_1
% 4.71/5.03 thf(fact_1452_div__by__1,axiom,
% 4.71/5.03 ! [A: real] :
% 4.71/5.03 ( ( divide_divide_real @ A @ one_one_real )
% 4.71/5.03 = A ) ).
% 4.71/5.03
% 4.71/5.03 % div_by_1
% 4.71/5.03 thf(fact_1453_Diff__eq__empty__iff,axiom,
% 4.71/5.03 ! [A2: set_real,B2: set_real] :
% 4.71/5.03 ( ( ( minus_minus_set_real @ A2 @ B2 )
% 4.71/5.03 = bot_bot_set_real )
% 4.71/5.03 = ( ord_less_eq_set_real @ A2 @ B2 ) ) ).
% 4.71/5.03
% 4.71/5.03 % Diff_eq_empty_iff
% 4.71/5.03 thf(fact_1454_Diff__eq__empty__iff,axiom,
% 4.71/5.03 ! [A2: set_o,B2: set_o] :
% 4.71/5.03 ( ( ( minus_minus_set_o @ A2 @ B2 )
% 4.71/5.03 = bot_bot_set_o )
% 4.71/5.03 = ( ord_less_eq_set_o @ A2 @ B2 ) ) ).
% 4.71/5.03
% 4.71/5.03 % Diff_eq_empty_iff
% 4.71/5.03 thf(fact_1455_Diff__eq__empty__iff,axiom,
% 4.71/5.03 ! [A2: set_nat,B2: set_nat] :
% 4.71/5.03 ( ( ( minus_minus_set_nat @ A2 @ B2 )
% 4.71/5.03 = bot_bot_set_nat )
% 4.71/5.03 = ( ord_less_eq_set_nat @ A2 @ B2 ) ) ).
% 4.71/5.03
% 4.71/5.03 % Diff_eq_empty_iff
% 4.71/5.03 thf(fact_1456_Diff__eq__empty__iff,axiom,
% 4.71/5.03 ! [A2: set_int,B2: set_int] :
% 4.71/5.03 ( ( ( minus_minus_set_int @ A2 @ B2 )
% 4.71/5.03 = bot_bot_set_int )
% 4.71/5.03 = ( ord_less_eq_set_int @ A2 @ B2 ) ) ).
% 4.71/5.03
% 4.71/5.03 % Diff_eq_empty_iff
% 4.71/5.03 thf(fact_1457_div__self,axiom,
% 4.71/5.03 ! [A: complex] :
% 4.71/5.03 ( ( A != zero_zero_complex )
% 4.71/5.03 => ( ( divide1717551699836669952omplex @ A @ A )
% 4.71/5.03 = one_one_complex ) ) ).
% 4.71/5.03
% 4.71/5.03 % div_self
% 4.71/5.03 thf(fact_1458_div__self,axiom,
% 4.71/5.03 ! [A: rat] :
% 4.71/5.03 ( ( A != zero_zero_rat )
% 4.71/5.03 => ( ( divide_divide_rat @ A @ A )
% 4.71/5.03 = one_one_rat ) ) ).
% 4.71/5.03
% 4.71/5.03 % div_self
% 4.71/5.03 thf(fact_1459_div__self,axiom,
% 4.71/5.03 ! [A: int] :
% 4.71/5.03 ( ( A != zero_zero_int )
% 4.71/5.03 => ( ( divide_divide_int @ A @ A )
% 4.71/5.03 = one_one_int ) ) ).
% 4.71/5.03
% 4.71/5.03 % div_self
% 4.71/5.03 thf(fact_1460_div__self,axiom,
% 4.71/5.03 ! [A: nat] :
% 4.71/5.03 ( ( A != zero_zero_nat )
% 4.71/5.03 => ( ( divide_divide_nat @ A @ A )
% 4.71/5.03 = one_one_nat ) ) ).
% 4.71/5.03
% 4.71/5.03 % div_self
% 4.71/5.03 thf(fact_1461_div__self,axiom,
% 4.71/5.03 ! [A: real] :
% 4.71/5.03 ( ( A != zero_zero_real )
% 4.71/5.03 => ( ( divide_divide_real @ A @ A )
% 4.71/5.03 = one_one_real ) ) ).
% 4.71/5.03
% 4.71/5.03 % div_self
% 4.71/5.03 thf(fact_1462_card_Oempty,axiom,
% 4.71/5.03 ( ( finite_card_complex @ bot_bot_set_complex )
% 4.71/5.03 = zero_zero_nat ) ).
% 4.71/5.03
% 4.71/5.03 % card.empty
% 4.71/5.03 thf(fact_1463_card_Oempty,axiom,
% 4.71/5.03 ( ( finite_card_list_nat @ bot_bot_set_list_nat )
% 4.71/5.03 = zero_zero_nat ) ).
% 4.71/5.03
% 4.71/5.03 % card.empty
% 4.71/5.03 thf(fact_1464_card_Oempty,axiom,
% 4.71/5.03 ( ( finite_card_set_nat @ bot_bot_set_set_nat )
% 4.71/5.03 = zero_zero_nat ) ).
% 4.71/5.03
% 4.71/5.03 % card.empty
% 4.71/5.03 thf(fact_1465_card_Oempty,axiom,
% 4.71/5.03 ( ( finite_card_real @ bot_bot_set_real )
% 4.71/5.03 = zero_zero_nat ) ).
% 4.71/5.03
% 4.71/5.03 % card.empty
% 4.71/5.03 thf(fact_1466_card_Oempty,axiom,
% 4.71/5.03 ( ( finite_card_o @ bot_bot_set_o )
% 4.71/5.03 = zero_zero_nat ) ).
% 4.71/5.03
% 4.71/5.03 % card.empty
% 4.71/5.03 thf(fact_1467_card_Oempty,axiom,
% 4.71/5.03 ( ( finite_card_nat @ bot_bot_set_nat )
% 4.71/5.03 = zero_zero_nat ) ).
% 4.71/5.03
% 4.71/5.03 % card.empty
% 4.71/5.03 thf(fact_1468_card_Oempty,axiom,
% 4.71/5.03 ( ( finite_card_int @ bot_bot_set_int )
% 4.71/5.03 = zero_zero_nat ) ).
% 4.71/5.03
% 4.71/5.03 % card.empty
% 4.71/5.03 thf(fact_1469_card_Oinfinite,axiom,
% 4.71/5.03 ! [A2: set_list_nat] :
% 4.71/5.03 ( ~ ( finite8100373058378681591st_nat @ A2 )
% 4.71/5.03 => ( ( finite_card_list_nat @ A2 )
% 4.71/5.04 = zero_zero_nat ) ) ).
% 4.71/5.04
% 4.71/5.04 % card.infinite
% 4.71/5.04 thf(fact_1470_card_Oinfinite,axiom,
% 4.71/5.04 ! [A2: set_set_nat] :
% 4.71/5.04 ( ~ ( finite1152437895449049373et_nat @ A2 )
% 4.71/5.04 => ( ( finite_card_set_nat @ A2 )
% 4.71/5.04 = zero_zero_nat ) ) ).
% 4.71/5.04
% 4.71/5.04 % card.infinite
% 4.71/5.04 thf(fact_1471_card_Oinfinite,axiom,
% 4.71/5.04 ! [A2: set_nat] :
% 4.71/5.04 ( ~ ( finite_finite_nat @ A2 )
% 4.71/5.04 => ( ( finite_card_nat @ A2 )
% 4.71/5.04 = zero_zero_nat ) ) ).
% 4.71/5.04
% 4.71/5.04 % card.infinite
% 4.71/5.04 thf(fact_1472_card_Oinfinite,axiom,
% 4.71/5.04 ! [A2: set_int] :
% 4.71/5.04 ( ~ ( finite_finite_int @ A2 )
% 4.71/5.04 => ( ( finite_card_int @ A2 )
% 4.71/5.04 = zero_zero_nat ) ) ).
% 4.71/5.04
% 4.71/5.04 % card.infinite
% 4.71/5.04 thf(fact_1473_card_Oinfinite,axiom,
% 4.71/5.04 ! [A2: set_complex] :
% 4.71/5.04 ( ~ ( finite3207457112153483333omplex @ A2 )
% 4.71/5.04 => ( ( finite_card_complex @ A2 )
% 4.71/5.04 = zero_zero_nat ) ) ).
% 4.71/5.04
% 4.71/5.04 % card.infinite
% 4.71/5.04 thf(fact_1474_card_Oinfinite,axiom,
% 4.71/5.04 ! [A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.04 ( ~ ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.04 => ( ( finite711546835091564841at_nat @ A2 )
% 4.71/5.04 = zero_zero_nat ) ) ).
% 4.71/5.04
% 4.71/5.04 % card.infinite
% 4.71/5.04 thf(fact_1475_card_Oinfinite,axiom,
% 4.71/5.04 ! [A2: set_Extended_enat] :
% 4.71/5.04 ( ~ ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.04 => ( ( finite121521170596916366d_enat @ A2 )
% 4.71/5.04 = zero_zero_nat ) ) ).
% 4.71/5.04
% 4.71/5.04 % card.infinite
% 4.71/5.04 thf(fact_1476_zle__diff1__eq,axiom,
% 4.71/5.04 ! [W2: int,Z: int] :
% 4.71/5.04 ( ( ord_less_eq_int @ W2 @ ( minus_minus_int @ Z @ one_one_int ) )
% 4.71/5.04 = ( ord_less_int @ W2 @ Z ) ) ).
% 4.71/5.04
% 4.71/5.04 % zle_diff1_eq
% 4.71/5.04 thf(fact_1477_card__0__eq,axiom,
% 4.71/5.04 ! [A2: set_list_nat] :
% 4.71/5.04 ( ( finite8100373058378681591st_nat @ A2 )
% 4.71/5.04 => ( ( ( finite_card_list_nat @ A2 )
% 4.71/5.04 = zero_zero_nat )
% 4.71/5.04 = ( A2 = bot_bot_set_list_nat ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_0_eq
% 4.71/5.04 thf(fact_1478_card__0__eq,axiom,
% 4.71/5.04 ! [A2: set_set_nat] :
% 4.71/5.04 ( ( finite1152437895449049373et_nat @ A2 )
% 4.71/5.04 => ( ( ( finite_card_set_nat @ A2 )
% 4.71/5.04 = zero_zero_nat )
% 4.71/5.04 = ( A2 = bot_bot_set_set_nat ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_0_eq
% 4.71/5.04 thf(fact_1479_card__0__eq,axiom,
% 4.71/5.04 ! [A2: set_complex] :
% 4.71/5.04 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.04 => ( ( ( finite_card_complex @ A2 )
% 4.71/5.04 = zero_zero_nat )
% 4.71/5.04 = ( A2 = bot_bot_set_complex ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_0_eq
% 4.71/5.04 thf(fact_1480_card__0__eq,axiom,
% 4.71/5.04 ! [A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.04 ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.04 => ( ( ( finite711546835091564841at_nat @ A2 )
% 4.71/5.04 = zero_zero_nat )
% 4.71/5.04 = ( A2 = bot_bo2099793752762293965at_nat ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_0_eq
% 4.71/5.04 thf(fact_1481_card__0__eq,axiom,
% 4.71/5.04 ! [A2: set_Extended_enat] :
% 4.71/5.04 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.04 => ( ( ( finite121521170596916366d_enat @ A2 )
% 4.71/5.04 = zero_zero_nat )
% 4.71/5.04 = ( A2 = bot_bo7653980558646680370d_enat ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_0_eq
% 4.71/5.04 thf(fact_1482_card__0__eq,axiom,
% 4.71/5.04 ! [A2: set_real] :
% 4.71/5.04 ( ( finite_finite_real @ A2 )
% 4.71/5.04 => ( ( ( finite_card_real @ A2 )
% 4.71/5.04 = zero_zero_nat )
% 4.71/5.04 = ( A2 = bot_bot_set_real ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_0_eq
% 4.71/5.04 thf(fact_1483_card__0__eq,axiom,
% 4.71/5.04 ! [A2: set_o] :
% 4.71/5.04 ( ( finite_finite_o @ A2 )
% 4.71/5.04 => ( ( ( finite_card_o @ A2 )
% 4.71/5.04 = zero_zero_nat )
% 4.71/5.04 = ( A2 = bot_bot_set_o ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_0_eq
% 4.71/5.04 thf(fact_1484_card__0__eq,axiom,
% 4.71/5.04 ! [A2: set_nat] :
% 4.71/5.04 ( ( finite_finite_nat @ A2 )
% 4.71/5.04 => ( ( ( finite_card_nat @ A2 )
% 4.71/5.04 = zero_zero_nat )
% 4.71/5.04 = ( A2 = bot_bot_set_nat ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_0_eq
% 4.71/5.04 thf(fact_1485_card__0__eq,axiom,
% 4.71/5.04 ! [A2: set_int] :
% 4.71/5.04 ( ( finite_finite_int @ A2 )
% 4.71/5.04 => ( ( ( finite_card_int @ A2 )
% 4.71/5.04 = zero_zero_nat )
% 4.71/5.04 = ( A2 = bot_bot_set_int ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_0_eq
% 4.71/5.04 thf(fact_1486_finite__enumerate__mono__iff,axiom,
% 4.71/5.04 ! [S2: set_Extended_enat,M2: nat,N: nat] :
% 4.71/5.04 ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.04 => ( ( ord_less_nat @ M2 @ ( finite121521170596916366d_enat @ S2 ) )
% 4.71/5.04 => ( ( ord_less_nat @ N @ ( finite121521170596916366d_enat @ S2 ) )
% 4.71/5.04 => ( ( ord_le72135733267957522d_enat @ ( infini7641415182203889163d_enat @ S2 @ M2 ) @ ( infini7641415182203889163d_enat @ S2 @ N ) )
% 4.71/5.04 = ( ord_less_nat @ M2 @ N ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % finite_enumerate_mono_iff
% 4.71/5.04 thf(fact_1487_finite__enumerate__mono__iff,axiom,
% 4.71/5.04 ! [S2: set_nat,M2: nat,N: nat] :
% 4.71/5.04 ( ( finite_finite_nat @ S2 )
% 4.71/5.04 => ( ( ord_less_nat @ M2 @ ( finite_card_nat @ S2 ) )
% 4.71/5.04 => ( ( ord_less_nat @ N @ ( finite_card_nat @ S2 ) )
% 4.71/5.04 => ( ( ord_less_nat @ ( infini8530281810654367211te_nat @ S2 @ M2 ) @ ( infini8530281810654367211te_nat @ S2 @ N ) )
% 4.71/5.04 = ( ord_less_nat @ M2 @ N ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % finite_enumerate_mono_iff
% 4.71/5.04 thf(fact_1488_nonneg__int__cases,axiom,
% 4.71/5.04 ! [K: int] :
% 4.71/5.04 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 4.71/5.04 => ~ ! [N2: nat] :
% 4.71/5.04 ( K
% 4.71/5.04 != ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % nonneg_int_cases
% 4.71/5.04 thf(fact_1489_zero__le__imp__eq__int,axiom,
% 4.71/5.04 ! [K: int] :
% 4.71/5.04 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 4.71/5.04 => ? [N2: nat] :
% 4.71/5.04 ( K
% 4.71/5.04 = ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % zero_le_imp_eq_int
% 4.71/5.04 thf(fact_1490_int__one__le__iff__zero__less,axiom,
% 4.71/5.04 ! [Z: int] :
% 4.71/5.04 ( ( ord_less_eq_int @ one_one_int @ Z )
% 4.71/5.04 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 4.71/5.04
% 4.71/5.04 % int_one_le_iff_zero_less
% 4.71/5.04 thf(fact_1491_int__le__induct,axiom,
% 4.71/5.04 ! [I: int,K: int,P: int > $o] :
% 4.71/5.04 ( ( ord_less_eq_int @ I @ K )
% 4.71/5.04 => ( ( P @ K )
% 4.71/5.04 => ( ! [I2: int] :
% 4.71/5.04 ( ( ord_less_eq_int @ I2 @ K )
% 4.71/5.04 => ( ( P @ I2 )
% 4.71/5.04 => ( P @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 4.71/5.04 => ( P @ I ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % int_le_induct
% 4.71/5.04 thf(fact_1492_verit__la__generic,axiom,
% 4.71/5.04 ! [A: int,X: int] :
% 4.71/5.04 ( ( ord_less_eq_int @ A @ X )
% 4.71/5.04 | ( A = X )
% 4.71/5.04 | ( ord_less_eq_int @ X @ A ) ) ).
% 4.71/5.04
% 4.71/5.04 % verit_la_generic
% 4.71/5.04 thf(fact_1493_conj__le__cong,axiom,
% 4.71/5.04 ! [X: int,X7: int,P: $o,P4: $o] :
% 4.71/5.04 ( ( X = X7 )
% 4.71/5.04 => ( ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 4.71/5.04 => ( P = P4 ) )
% 4.71/5.04 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 4.71/5.04 & P )
% 4.71/5.04 = ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 4.71/5.04 & P4 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % conj_le_cong
% 4.71/5.04 thf(fact_1494_imp__le__cong,axiom,
% 4.71/5.04 ! [X: int,X7: int,P: $o,P4: $o] :
% 4.71/5.04 ( ( X = X7 )
% 4.71/5.04 => ( ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 4.71/5.04 => ( P = P4 ) )
% 4.71/5.04 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 4.71/5.04 => P )
% 4.71/5.04 = ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 4.71/5.04 => P4 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % imp_le_cong
% 4.71/5.04 thf(fact_1495_less__eq__int__code_I1_J,axiom,
% 4.71/5.04 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 4.71/5.04
% 4.71/5.04 % less_eq_int_code(1)
% 4.71/5.04 thf(fact_1496_card__less__sym__Diff,axiom,
% 4.71/5.04 ! [A2: set_list_nat,B2: set_list_nat] :
% 4.71/5.04 ( ( finite8100373058378681591st_nat @ A2 )
% 4.71/5.04 => ( ( finite8100373058378681591st_nat @ B2 )
% 4.71/5.04 => ( ( ord_less_nat @ ( finite_card_list_nat @ A2 ) @ ( finite_card_list_nat @ B2 ) )
% 4.71/5.04 => ( ord_less_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ B2 ) ) @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ B2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_less_sym_Diff
% 4.71/5.04 thf(fact_1497_card__less__sym__Diff,axiom,
% 4.71/5.04 ! [A2: set_set_nat,B2: set_set_nat] :
% 4.71/5.04 ( ( finite1152437895449049373et_nat @ A2 )
% 4.71/5.04 => ( ( finite1152437895449049373et_nat @ B2 )
% 4.71/5.04 => ( ( ord_less_nat @ ( finite_card_set_nat @ A2 ) @ ( finite_card_set_nat @ B2 ) )
% 4.71/5.04 => ( ord_less_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ B2 ) ) @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ B2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_less_sym_Diff
% 4.71/5.04 thf(fact_1498_card__less__sym__Diff,axiom,
% 4.71/5.04 ! [A2: set_int,B2: set_int] :
% 4.71/5.04 ( ( finite_finite_int @ A2 )
% 4.71/5.04 => ( ( finite_finite_int @ B2 )
% 4.71/5.04 => ( ( ord_less_nat @ ( finite_card_int @ A2 ) @ ( finite_card_int @ B2 ) )
% 4.71/5.04 => ( ord_less_nat @ ( finite_card_int @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( finite_card_int @ ( minus_minus_set_int @ B2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_less_sym_Diff
% 4.71/5.04 thf(fact_1499_card__less__sym__Diff,axiom,
% 4.71/5.04 ! [A2: set_complex,B2: set_complex] :
% 4.71/5.04 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.04 => ( ( finite3207457112153483333omplex @ B2 )
% 4.71/5.04 => ( ( ord_less_nat @ ( finite_card_complex @ A2 ) @ ( finite_card_complex @ B2 ) )
% 4.71/5.04 => ( ord_less_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( finite_card_complex @ ( minus_811609699411566653omplex @ B2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_less_sym_Diff
% 4.71/5.04 thf(fact_1500_card__less__sym__Diff,axiom,
% 4.71/5.04 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 4.71/5.04 ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.04 => ( ( finite6177210948735845034at_nat @ B2 )
% 4.71/5.04 => ( ( ord_less_nat @ ( finite711546835091564841at_nat @ A2 ) @ ( finite711546835091564841at_nat @ B2 ) )
% 4.71/5.04 => ( ord_less_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ B2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_less_sym_Diff
% 4.71/5.04 thf(fact_1501_card__less__sym__Diff,axiom,
% 4.71/5.04 ! [A2: set_Extended_enat,B2: set_Extended_enat] :
% 4.71/5.04 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.04 => ( ( finite4001608067531595151d_enat @ B2 )
% 4.71/5.04 => ( ( ord_less_nat @ ( finite121521170596916366d_enat @ A2 ) @ ( finite121521170596916366d_enat @ B2 ) )
% 4.71/5.04 => ( ord_less_nat @ ( finite121521170596916366d_enat @ ( minus_925952699566721837d_enat @ A2 @ B2 ) ) @ ( finite121521170596916366d_enat @ ( minus_925952699566721837d_enat @ B2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_less_sym_Diff
% 4.71/5.04 thf(fact_1502_card__less__sym__Diff,axiom,
% 4.71/5.04 ! [A2: set_nat,B2: set_nat] :
% 4.71/5.04 ( ( finite_finite_nat @ A2 )
% 4.71/5.04 => ( ( finite_finite_nat @ B2 )
% 4.71/5.04 => ( ( ord_less_nat @ ( finite_card_nat @ A2 ) @ ( finite_card_nat @ B2 ) )
% 4.71/5.04 => ( ord_less_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( finite_card_nat @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_less_sym_Diff
% 4.71/5.04 thf(fact_1503_card__le__sym__Diff,axiom,
% 4.71/5.04 ! [A2: set_list_nat,B2: set_list_nat] :
% 4.71/5.04 ( ( finite8100373058378681591st_nat @ A2 )
% 4.71/5.04 => ( ( finite8100373058378681591st_nat @ B2 )
% 4.71/5.04 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ A2 ) @ ( finite_card_list_nat @ B2 ) )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ B2 ) ) @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ B2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_le_sym_Diff
% 4.71/5.04 thf(fact_1504_card__le__sym__Diff,axiom,
% 4.71/5.04 ! [A2: set_set_nat,B2: set_set_nat] :
% 4.71/5.04 ( ( finite1152437895449049373et_nat @ A2 )
% 4.71/5.04 => ( ( finite1152437895449049373et_nat @ B2 )
% 4.71/5.04 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ A2 ) @ ( finite_card_set_nat @ B2 ) )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ B2 ) ) @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ B2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_le_sym_Diff
% 4.71/5.04 thf(fact_1505_card__le__sym__Diff,axiom,
% 4.71/5.04 ! [A2: set_int,B2: set_int] :
% 4.71/5.04 ( ( finite_finite_int @ A2 )
% 4.71/5.04 => ( ( finite_finite_int @ B2 )
% 4.71/5.04 => ( ( ord_less_eq_nat @ ( finite_card_int @ A2 ) @ ( finite_card_int @ B2 ) )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite_card_int @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( finite_card_int @ ( minus_minus_set_int @ B2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_le_sym_Diff
% 4.71/5.04 thf(fact_1506_card__le__sym__Diff,axiom,
% 4.71/5.04 ! [A2: set_complex,B2: set_complex] :
% 4.71/5.04 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.04 => ( ( finite3207457112153483333omplex @ B2 )
% 4.71/5.04 => ( ( ord_less_eq_nat @ ( finite_card_complex @ A2 ) @ ( finite_card_complex @ B2 ) )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( finite_card_complex @ ( minus_811609699411566653omplex @ B2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_le_sym_Diff
% 4.71/5.04 thf(fact_1507_card__le__sym__Diff,axiom,
% 4.71/5.04 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 4.71/5.04 ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.04 => ( ( finite6177210948735845034at_nat @ B2 )
% 4.71/5.04 => ( ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ A2 ) @ ( finite711546835091564841at_nat @ B2 ) )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ B2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_le_sym_Diff
% 4.71/5.04 thf(fact_1508_card__le__sym__Diff,axiom,
% 4.71/5.04 ! [A2: set_Extended_enat,B2: set_Extended_enat] :
% 4.71/5.04 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.04 => ( ( finite4001608067531595151d_enat @ B2 )
% 4.71/5.04 => ( ( ord_less_eq_nat @ ( finite121521170596916366d_enat @ A2 ) @ ( finite121521170596916366d_enat @ B2 ) )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite121521170596916366d_enat @ ( minus_925952699566721837d_enat @ A2 @ B2 ) ) @ ( finite121521170596916366d_enat @ ( minus_925952699566721837d_enat @ B2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_le_sym_Diff
% 4.71/5.04 thf(fact_1509_card__le__sym__Diff,axiom,
% 4.71/5.04 ! [A2: set_nat,B2: set_nat] :
% 4.71/5.04 ( ( finite_finite_nat @ A2 )
% 4.71/5.04 => ( ( finite_finite_nat @ B2 )
% 4.71/5.04 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A2 ) @ ( finite_card_nat @ B2 ) )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( finite_card_nat @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_le_sym_Diff
% 4.71/5.04 thf(fact_1510_Diff__infinite__finite,axiom,
% 4.71/5.04 ! [T3: set_int,S2: set_int] :
% 4.71/5.04 ( ( finite_finite_int @ T3 )
% 4.71/5.04 => ( ~ ( finite_finite_int @ S2 )
% 4.71/5.04 => ~ ( finite_finite_int @ ( minus_minus_set_int @ S2 @ T3 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % Diff_infinite_finite
% 4.71/5.04 thf(fact_1511_Diff__infinite__finite,axiom,
% 4.71/5.04 ! [T3: set_complex,S2: set_complex] :
% 4.71/5.04 ( ( finite3207457112153483333omplex @ T3 )
% 4.71/5.04 => ( ~ ( finite3207457112153483333omplex @ S2 )
% 4.71/5.04 => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S2 @ T3 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % Diff_infinite_finite
% 4.71/5.04 thf(fact_1512_Diff__infinite__finite,axiom,
% 4.71/5.04 ! [T3: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 4.71/5.04 ( ( finite6177210948735845034at_nat @ T3 )
% 4.71/5.04 => ( ~ ( finite6177210948735845034at_nat @ S2 )
% 4.71/5.04 => ~ ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ S2 @ T3 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % Diff_infinite_finite
% 4.71/5.04 thf(fact_1513_Diff__infinite__finite,axiom,
% 4.71/5.04 ! [T3: set_Extended_enat,S2: set_Extended_enat] :
% 4.71/5.04 ( ( finite4001608067531595151d_enat @ T3 )
% 4.71/5.04 => ( ~ ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.04 => ~ ( finite4001608067531595151d_enat @ ( minus_925952699566721837d_enat @ S2 @ T3 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % Diff_infinite_finite
% 4.71/5.04 thf(fact_1514_Diff__infinite__finite,axiom,
% 4.71/5.04 ! [T3: set_nat,S2: set_nat] :
% 4.71/5.04 ( ( finite_finite_nat @ T3 )
% 4.71/5.04 => ( ~ ( finite_finite_nat @ S2 )
% 4.71/5.04 => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S2 @ T3 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % Diff_infinite_finite
% 4.71/5.04 thf(fact_1515_double__diff,axiom,
% 4.71/5.04 ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 4.71/5.04 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 4.71/5.04 => ( ( ord_less_eq_set_nat @ B2 @ C2 )
% 4.71/5.04 => ( ( minus_minus_set_nat @ B2 @ ( minus_minus_set_nat @ C2 @ A2 ) )
% 4.71/5.04 = A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % double_diff
% 4.71/5.04 thf(fact_1516_double__diff,axiom,
% 4.71/5.04 ! [A2: set_int,B2: set_int,C2: set_int] :
% 4.71/5.04 ( ( ord_less_eq_set_int @ A2 @ B2 )
% 4.71/5.04 => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 4.71/5.04 => ( ( minus_minus_set_int @ B2 @ ( minus_minus_set_int @ C2 @ A2 ) )
% 4.71/5.04 = A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % double_diff
% 4.71/5.04 thf(fact_1517_Diff__subset,axiom,
% 4.71/5.04 ! [A2: set_nat,B2: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ A2 ) ).
% 4.71/5.04
% 4.71/5.04 % Diff_subset
% 4.71/5.04 thf(fact_1518_Diff__subset,axiom,
% 4.71/5.04 ! [A2: set_int,B2: set_int] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B2 ) @ A2 ) ).
% 4.71/5.04
% 4.71/5.04 % Diff_subset
% 4.71/5.04 thf(fact_1519_Diff__mono,axiom,
% 4.71/5.04 ! [A2: set_nat,C2: set_nat,D4: set_nat,B2: set_nat] :
% 4.71/5.04 ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 4.71/5.04 => ( ( ord_less_eq_set_nat @ D4 @ B2 )
% 4.71/5.04 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ ( minus_minus_set_nat @ C2 @ D4 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % Diff_mono
% 4.71/5.04 thf(fact_1520_Diff__mono,axiom,
% 4.71/5.04 ! [A2: set_int,C2: set_int,D4: set_int,B2: set_int] :
% 4.71/5.04 ( ( ord_less_eq_set_int @ A2 @ C2 )
% 4.71/5.04 => ( ( ord_less_eq_set_int @ D4 @ B2 )
% 4.71/5.04 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B2 ) @ ( minus_minus_set_int @ C2 @ D4 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % Diff_mono
% 4.71/5.04 thf(fact_1521_psubset__imp__ex__mem,axiom,
% 4.71/5.04 ! [A2: set_o,B2: set_o] :
% 4.71/5.04 ( ( ord_less_set_o @ A2 @ B2 )
% 4.71/5.04 => ? [B5: $o] : ( member_o @ B5 @ ( minus_minus_set_o @ B2 @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % psubset_imp_ex_mem
% 4.71/5.04 thf(fact_1522_psubset__imp__ex__mem,axiom,
% 4.71/5.04 ! [A2: set_set_nat,B2: set_set_nat] :
% 4.71/5.04 ( ( ord_less_set_set_nat @ A2 @ B2 )
% 4.71/5.04 => ? [B5: set_nat] : ( member_set_nat @ B5 @ ( minus_2163939370556025621et_nat @ B2 @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % psubset_imp_ex_mem
% 4.71/5.04 thf(fact_1523_psubset__imp__ex__mem,axiom,
% 4.71/5.04 ! [A2: set_set_nat_rat,B2: set_set_nat_rat] :
% 4.71/5.04 ( ( ord_le1311537459589289991at_rat @ A2 @ B2 )
% 4.71/5.04 => ? [B5: set_nat_rat] : ( member_set_nat_rat @ B5 @ ( minus_1626877696091177228at_rat @ B2 @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % psubset_imp_ex_mem
% 4.71/5.04 thf(fact_1524_psubset__imp__ex__mem,axiom,
% 4.71/5.04 ! [A2: set_int,B2: set_int] :
% 4.71/5.04 ( ( ord_less_set_int @ A2 @ B2 )
% 4.71/5.04 => ? [B5: int] : ( member_int @ B5 @ ( minus_minus_set_int @ B2 @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % psubset_imp_ex_mem
% 4.71/5.04 thf(fact_1525_psubset__imp__ex__mem,axiom,
% 4.71/5.04 ! [A2: set_nat,B2: set_nat] :
% 4.71/5.04 ( ( ord_less_set_nat @ A2 @ B2 )
% 4.71/5.04 => ? [B5: nat] : ( member_nat @ B5 @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % psubset_imp_ex_mem
% 4.71/5.04 thf(fact_1526_card__Diff__subset,axiom,
% 4.71/5.04 ! [B2: set_list_nat,A2: set_list_nat] :
% 4.71/5.04 ( ( finite8100373058378681591st_nat @ B2 )
% 4.71/5.04 => ( ( ord_le6045566169113846134st_nat @ B2 @ A2 )
% 4.71/5.04 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ B2 ) )
% 4.71/5.04 = ( minus_minus_nat @ ( finite_card_list_nat @ A2 ) @ ( finite_card_list_nat @ B2 ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_Diff_subset
% 4.71/5.04 thf(fact_1527_card__Diff__subset,axiom,
% 4.71/5.04 ! [B2: set_set_nat,A2: set_set_nat] :
% 4.71/5.04 ( ( finite1152437895449049373et_nat @ B2 )
% 4.71/5.04 => ( ( ord_le6893508408891458716et_nat @ B2 @ A2 )
% 4.71/5.04 => ( ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ B2 ) )
% 4.71/5.04 = ( minus_minus_nat @ ( finite_card_set_nat @ A2 ) @ ( finite_card_set_nat @ B2 ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_Diff_subset
% 4.71/5.04 thf(fact_1528_card__Diff__subset,axiom,
% 4.71/5.04 ! [B2: set_complex,A2: set_complex] :
% 4.71/5.04 ( ( finite3207457112153483333omplex @ B2 )
% 4.71/5.04 => ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 4.71/5.04 => ( ( finite_card_complex @ ( minus_811609699411566653omplex @ A2 @ B2 ) )
% 4.71/5.04 = ( minus_minus_nat @ ( finite_card_complex @ A2 ) @ ( finite_card_complex @ B2 ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_Diff_subset
% 4.71/5.04 thf(fact_1529_card__Diff__subset,axiom,
% 4.71/5.04 ! [B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.04 ( ( finite6177210948735845034at_nat @ B2 )
% 4.71/5.04 => ( ( ord_le3146513528884898305at_nat @ B2 @ A2 )
% 4.71/5.04 => ( ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) )
% 4.71/5.04 = ( minus_minus_nat @ ( finite711546835091564841at_nat @ A2 ) @ ( finite711546835091564841at_nat @ B2 ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_Diff_subset
% 4.71/5.04 thf(fact_1530_card__Diff__subset,axiom,
% 4.71/5.04 ! [B2: set_Extended_enat,A2: set_Extended_enat] :
% 4.71/5.04 ( ( finite4001608067531595151d_enat @ B2 )
% 4.71/5.04 => ( ( ord_le7203529160286727270d_enat @ B2 @ A2 )
% 4.71/5.04 => ( ( finite121521170596916366d_enat @ ( minus_925952699566721837d_enat @ A2 @ B2 ) )
% 4.71/5.04 = ( minus_minus_nat @ ( finite121521170596916366d_enat @ A2 ) @ ( finite121521170596916366d_enat @ B2 ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_Diff_subset
% 4.71/5.04 thf(fact_1531_card__Diff__subset,axiom,
% 4.71/5.04 ! [B2: set_nat,A2: set_nat] :
% 4.71/5.04 ( ( finite_finite_nat @ B2 )
% 4.71/5.04 => ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 4.71/5.04 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 4.71/5.04 = ( minus_minus_nat @ ( finite_card_nat @ A2 ) @ ( finite_card_nat @ B2 ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_Diff_subset
% 4.71/5.04 thf(fact_1532_card__Diff__subset,axiom,
% 4.71/5.04 ! [B2: set_int,A2: set_int] :
% 4.71/5.04 ( ( finite_finite_int @ B2 )
% 4.71/5.04 => ( ( ord_less_eq_set_int @ B2 @ A2 )
% 4.71/5.04 => ( ( finite_card_int @ ( minus_minus_set_int @ A2 @ B2 ) )
% 4.71/5.04 = ( minus_minus_nat @ ( finite_card_int @ A2 ) @ ( finite_card_int @ B2 ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_Diff_subset
% 4.71/5.04 thf(fact_1533_diff__card__le__card__Diff,axiom,
% 4.71/5.04 ! [B2: set_list_nat,A2: set_list_nat] :
% 4.71/5.04 ( ( finite8100373058378681591st_nat @ B2 )
% 4.71/5.04 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_list_nat @ A2 ) @ ( finite_card_list_nat @ B2 ) ) @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % diff_card_le_card_Diff
% 4.71/5.04 thf(fact_1534_diff__card__le__card__Diff,axiom,
% 4.71/5.04 ! [B2: set_set_nat,A2: set_set_nat] :
% 4.71/5.04 ( ( finite1152437895449049373et_nat @ B2 )
% 4.71/5.04 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_set_nat @ A2 ) @ ( finite_card_set_nat @ B2 ) ) @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % diff_card_le_card_Diff
% 4.71/5.04 thf(fact_1535_diff__card__le__card__Diff,axiom,
% 4.71/5.04 ! [B2: set_int,A2: set_int] :
% 4.71/5.04 ( ( finite_finite_int @ B2 )
% 4.71/5.04 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_int @ A2 ) @ ( finite_card_int @ B2 ) ) @ ( finite_card_int @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % diff_card_le_card_Diff
% 4.71/5.04 thf(fact_1536_diff__card__le__card__Diff,axiom,
% 4.71/5.04 ! [B2: set_complex,A2: set_complex] :
% 4.71/5.04 ( ( finite3207457112153483333omplex @ B2 )
% 4.71/5.04 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_complex @ A2 ) @ ( finite_card_complex @ B2 ) ) @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % diff_card_le_card_Diff
% 4.71/5.04 thf(fact_1537_diff__card__le__card__Diff,axiom,
% 4.71/5.04 ! [B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.04 ( ( finite6177210948735845034at_nat @ B2 )
% 4.71/5.04 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite711546835091564841at_nat @ A2 ) @ ( finite711546835091564841at_nat @ B2 ) ) @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % diff_card_le_card_Diff
% 4.71/5.04 thf(fact_1538_diff__card__le__card__Diff,axiom,
% 4.71/5.04 ! [B2: set_Extended_enat,A2: set_Extended_enat] :
% 4.71/5.04 ( ( finite4001608067531595151d_enat @ B2 )
% 4.71/5.04 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite121521170596916366d_enat @ A2 ) @ ( finite121521170596916366d_enat @ B2 ) ) @ ( finite121521170596916366d_enat @ ( minus_925952699566721837d_enat @ A2 @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % diff_card_le_card_Diff
% 4.71/5.04 thf(fact_1539_diff__card__le__card__Diff,axiom,
% 4.71/5.04 ! [B2: set_nat,A2: set_nat] :
% 4.71/5.04 ( ( finite_finite_nat @ B2 )
% 4.71/5.04 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_nat @ A2 ) @ ( finite_card_nat @ B2 ) ) @ ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % diff_card_le_card_Diff
% 4.71/5.04 thf(fact_1540_card__subset__eq,axiom,
% 4.71/5.04 ! [B2: set_list_nat,A2: set_list_nat] :
% 4.71/5.04 ( ( finite8100373058378681591st_nat @ B2 )
% 4.71/5.04 => ( ( ord_le6045566169113846134st_nat @ A2 @ B2 )
% 4.71/5.04 => ( ( ( finite_card_list_nat @ A2 )
% 4.71/5.04 = ( finite_card_list_nat @ B2 ) )
% 4.71/5.04 => ( A2 = B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_subset_eq
% 4.71/5.04 thf(fact_1541_card__subset__eq,axiom,
% 4.71/5.04 ! [B2: set_set_nat,A2: set_set_nat] :
% 4.71/5.04 ( ( finite1152437895449049373et_nat @ B2 )
% 4.71/5.04 => ( ( ord_le6893508408891458716et_nat @ A2 @ B2 )
% 4.71/5.04 => ( ( ( finite_card_set_nat @ A2 )
% 4.71/5.04 = ( finite_card_set_nat @ B2 ) )
% 4.71/5.04 => ( A2 = B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_subset_eq
% 4.71/5.04 thf(fact_1542_card__subset__eq,axiom,
% 4.71/5.04 ! [B2: set_nat,A2: set_nat] :
% 4.71/5.04 ( ( finite_finite_nat @ B2 )
% 4.71/5.04 => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 4.71/5.04 => ( ( ( finite_card_nat @ A2 )
% 4.71/5.04 = ( finite_card_nat @ B2 ) )
% 4.71/5.04 => ( A2 = B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_subset_eq
% 4.71/5.04 thf(fact_1543_card__subset__eq,axiom,
% 4.71/5.04 ! [B2: set_complex,A2: set_complex] :
% 4.71/5.04 ( ( finite3207457112153483333omplex @ B2 )
% 4.71/5.04 => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 4.71/5.04 => ( ( ( finite_card_complex @ A2 )
% 4.71/5.04 = ( finite_card_complex @ B2 ) )
% 4.71/5.04 => ( A2 = B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_subset_eq
% 4.71/5.04 thf(fact_1544_card__subset__eq,axiom,
% 4.71/5.04 ! [B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.04 ( ( finite6177210948735845034at_nat @ B2 )
% 4.71/5.04 => ( ( ord_le3146513528884898305at_nat @ A2 @ B2 )
% 4.71/5.04 => ( ( ( finite711546835091564841at_nat @ A2 )
% 4.71/5.04 = ( finite711546835091564841at_nat @ B2 ) )
% 4.71/5.04 => ( A2 = B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_subset_eq
% 4.71/5.04 thf(fact_1545_card__subset__eq,axiom,
% 4.71/5.04 ! [B2: set_Extended_enat,A2: set_Extended_enat] :
% 4.71/5.04 ( ( finite4001608067531595151d_enat @ B2 )
% 4.71/5.04 => ( ( ord_le7203529160286727270d_enat @ A2 @ B2 )
% 4.71/5.04 => ( ( ( finite121521170596916366d_enat @ A2 )
% 4.71/5.04 = ( finite121521170596916366d_enat @ B2 ) )
% 4.71/5.04 => ( A2 = B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_subset_eq
% 4.71/5.04 thf(fact_1546_card__subset__eq,axiom,
% 4.71/5.04 ! [B2: set_int,A2: set_int] :
% 4.71/5.04 ( ( finite_finite_int @ B2 )
% 4.71/5.04 => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 4.71/5.04 => ( ( ( finite_card_int @ A2 )
% 4.71/5.04 = ( finite_card_int @ B2 ) )
% 4.71/5.04 => ( A2 = B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_subset_eq
% 4.71/5.04 thf(fact_1547_infinite__arbitrarily__large,axiom,
% 4.71/5.04 ! [A2: set_list_nat,N: nat] :
% 4.71/5.04 ( ~ ( finite8100373058378681591st_nat @ A2 )
% 4.71/5.04 => ? [B8: set_list_nat] :
% 4.71/5.04 ( ( finite8100373058378681591st_nat @ B8 )
% 4.71/5.04 & ( ( finite_card_list_nat @ B8 )
% 4.71/5.04 = N )
% 4.71/5.04 & ( ord_le6045566169113846134st_nat @ B8 @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % infinite_arbitrarily_large
% 4.71/5.04 thf(fact_1548_infinite__arbitrarily__large,axiom,
% 4.71/5.04 ! [A2: set_set_nat,N: nat] :
% 4.71/5.04 ( ~ ( finite1152437895449049373et_nat @ A2 )
% 4.71/5.04 => ? [B8: set_set_nat] :
% 4.71/5.04 ( ( finite1152437895449049373et_nat @ B8 )
% 4.71/5.04 & ( ( finite_card_set_nat @ B8 )
% 4.71/5.04 = N )
% 4.71/5.04 & ( ord_le6893508408891458716et_nat @ B8 @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % infinite_arbitrarily_large
% 4.71/5.04 thf(fact_1549_infinite__arbitrarily__large,axiom,
% 4.71/5.04 ! [A2: set_nat,N: nat] :
% 4.71/5.04 ( ~ ( finite_finite_nat @ A2 )
% 4.71/5.04 => ? [B8: set_nat] :
% 4.71/5.04 ( ( finite_finite_nat @ B8 )
% 4.71/5.04 & ( ( finite_card_nat @ B8 )
% 4.71/5.04 = N )
% 4.71/5.04 & ( ord_less_eq_set_nat @ B8 @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % infinite_arbitrarily_large
% 4.71/5.04 thf(fact_1550_infinite__arbitrarily__large,axiom,
% 4.71/5.04 ! [A2: set_complex,N: nat] :
% 4.71/5.04 ( ~ ( finite3207457112153483333omplex @ A2 )
% 4.71/5.04 => ? [B8: set_complex] :
% 4.71/5.04 ( ( finite3207457112153483333omplex @ B8 )
% 4.71/5.04 & ( ( finite_card_complex @ B8 )
% 4.71/5.04 = N )
% 4.71/5.04 & ( ord_le211207098394363844omplex @ B8 @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % infinite_arbitrarily_large
% 4.71/5.04 thf(fact_1551_infinite__arbitrarily__large,axiom,
% 4.71/5.04 ! [A2: set_Pr1261947904930325089at_nat,N: nat] :
% 4.71/5.04 ( ~ ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.04 => ? [B8: set_Pr1261947904930325089at_nat] :
% 4.71/5.04 ( ( finite6177210948735845034at_nat @ B8 )
% 4.71/5.04 & ( ( finite711546835091564841at_nat @ B8 )
% 4.71/5.04 = N )
% 4.71/5.04 & ( ord_le3146513528884898305at_nat @ B8 @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % infinite_arbitrarily_large
% 4.71/5.04 thf(fact_1552_infinite__arbitrarily__large,axiom,
% 4.71/5.04 ! [A2: set_Extended_enat,N: nat] :
% 4.71/5.04 ( ~ ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.04 => ? [B8: set_Extended_enat] :
% 4.71/5.04 ( ( finite4001608067531595151d_enat @ B8 )
% 4.71/5.04 & ( ( finite121521170596916366d_enat @ B8 )
% 4.71/5.04 = N )
% 4.71/5.04 & ( ord_le7203529160286727270d_enat @ B8 @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % infinite_arbitrarily_large
% 4.71/5.04 thf(fact_1553_infinite__arbitrarily__large,axiom,
% 4.71/5.04 ! [A2: set_int,N: nat] :
% 4.71/5.04 ( ~ ( finite_finite_int @ A2 )
% 4.71/5.04 => ? [B8: set_int] :
% 4.71/5.04 ( ( finite_finite_int @ B8 )
% 4.71/5.04 & ( ( finite_card_int @ B8 )
% 4.71/5.04 = N )
% 4.71/5.04 & ( ord_less_eq_set_int @ B8 @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % infinite_arbitrarily_large
% 4.71/5.04 thf(fact_1554_card__le__if__inj__on__rel,axiom,
% 4.71/5.04 ! [B2: set_o,A2: set_o,R2: $o > $o > $o] :
% 4.71/5.04 ( ( finite_finite_o @ B2 )
% 4.71/5.04 => ( ! [A5: $o] :
% 4.71/5.04 ( ( member_o @ A5 @ A2 )
% 4.71/5.04 => ? [B9: $o] :
% 4.71/5.04 ( ( member_o @ B9 @ B2 )
% 4.71/5.04 & ( R2 @ A5 @ B9 ) ) )
% 4.71/5.04 => ( ! [A1: $o,A22: $o,B5: $o] :
% 4.71/5.04 ( ( member_o @ A1 @ A2 )
% 4.71/5.04 => ( ( member_o @ A22 @ A2 )
% 4.71/5.04 => ( ( member_o @ B5 @ B2 )
% 4.71/5.04 => ( ( R2 @ A1 @ B5 )
% 4.71/5.04 => ( ( R2 @ A22 @ B5 )
% 4.71/5.04 => ( A1 = A22 ) ) ) ) ) )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite_card_o @ A2 ) @ ( finite_card_o @ B2 ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_le_if_inj_on_rel
% 4.71/5.04 thf(fact_1555_card__le__if__inj__on__rel,axiom,
% 4.71/5.04 ! [B2: set_o,A2: set_complex,R2: complex > $o > $o] :
% 4.71/5.04 ( ( finite_finite_o @ B2 )
% 4.71/5.04 => ( ! [A5: complex] :
% 4.71/5.04 ( ( member_complex @ A5 @ A2 )
% 4.71/5.04 => ? [B9: $o] :
% 4.71/5.04 ( ( member_o @ B9 @ B2 )
% 4.71/5.04 & ( R2 @ A5 @ B9 ) ) )
% 4.71/5.04 => ( ! [A1: complex,A22: complex,B5: $o] :
% 4.71/5.04 ( ( member_complex @ A1 @ A2 )
% 4.71/5.04 => ( ( member_complex @ A22 @ A2 )
% 4.71/5.04 => ( ( member_o @ B5 @ B2 )
% 4.71/5.04 => ( ( R2 @ A1 @ B5 )
% 4.71/5.04 => ( ( R2 @ A22 @ B5 )
% 4.71/5.04 => ( A1 = A22 ) ) ) ) ) )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite_card_complex @ A2 ) @ ( finite_card_o @ B2 ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_le_if_inj_on_rel
% 4.71/5.04 thf(fact_1556_card__le__if__inj__on__rel,axiom,
% 4.71/5.04 ! [B2: set_o,A2: set_nat,R2: nat > $o > $o] :
% 4.71/5.04 ( ( finite_finite_o @ B2 )
% 4.71/5.04 => ( ! [A5: nat] :
% 4.71/5.04 ( ( member_nat @ A5 @ A2 )
% 4.71/5.04 => ? [B9: $o] :
% 4.71/5.04 ( ( member_o @ B9 @ B2 )
% 4.71/5.04 & ( R2 @ A5 @ B9 ) ) )
% 4.71/5.04 => ( ! [A1: nat,A22: nat,B5: $o] :
% 4.71/5.04 ( ( member_nat @ A1 @ A2 )
% 4.71/5.04 => ( ( member_nat @ A22 @ A2 )
% 4.71/5.04 => ( ( member_o @ B5 @ B2 )
% 4.71/5.04 => ( ( R2 @ A1 @ B5 )
% 4.71/5.04 => ( ( R2 @ A22 @ B5 )
% 4.71/5.04 => ( A1 = A22 ) ) ) ) ) )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite_card_nat @ A2 ) @ ( finite_card_o @ B2 ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_le_if_inj_on_rel
% 4.71/5.04 thf(fact_1557_card__le__if__inj__on__rel,axiom,
% 4.71/5.04 ! [B2: set_o,A2: set_int,R2: int > $o > $o] :
% 4.71/5.04 ( ( finite_finite_o @ B2 )
% 4.71/5.04 => ( ! [A5: int] :
% 4.71/5.04 ( ( member_int @ A5 @ A2 )
% 4.71/5.04 => ? [B9: $o] :
% 4.71/5.04 ( ( member_o @ B9 @ B2 )
% 4.71/5.04 & ( R2 @ A5 @ B9 ) ) )
% 4.71/5.04 => ( ! [A1: int,A22: int,B5: $o] :
% 4.71/5.04 ( ( member_int @ A1 @ A2 )
% 4.71/5.04 => ( ( member_int @ A22 @ A2 )
% 4.71/5.04 => ( ( member_o @ B5 @ B2 )
% 4.71/5.04 => ( ( R2 @ A1 @ B5 )
% 4.71/5.04 => ( ( R2 @ A22 @ B5 )
% 4.71/5.04 => ( A1 = A22 ) ) ) ) ) )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite_card_int @ A2 ) @ ( finite_card_o @ B2 ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_le_if_inj_on_rel
% 4.71/5.04 thf(fact_1558_card__le__if__inj__on__rel,axiom,
% 4.71/5.04 ! [B2: set_nat,A2: set_o,R2: $o > nat > $o] :
% 4.71/5.04 ( ( finite_finite_nat @ B2 )
% 4.71/5.04 => ( ! [A5: $o] :
% 4.71/5.04 ( ( member_o @ A5 @ A2 )
% 4.71/5.04 => ? [B9: nat] :
% 4.71/5.04 ( ( member_nat @ B9 @ B2 )
% 4.71/5.04 & ( R2 @ A5 @ B9 ) ) )
% 4.71/5.04 => ( ! [A1: $o,A22: $o,B5: nat] :
% 4.71/5.04 ( ( member_o @ A1 @ A2 )
% 4.71/5.04 => ( ( member_o @ A22 @ A2 )
% 4.71/5.04 => ( ( member_nat @ B5 @ B2 )
% 4.71/5.04 => ( ( R2 @ A1 @ B5 )
% 4.71/5.04 => ( ( R2 @ A22 @ B5 )
% 4.71/5.04 => ( A1 = A22 ) ) ) ) ) )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite_card_o @ A2 ) @ ( finite_card_nat @ B2 ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_le_if_inj_on_rel
% 4.71/5.04 thf(fact_1559_card__le__if__inj__on__rel,axiom,
% 4.71/5.04 ! [B2: set_nat,A2: set_complex,R2: complex > nat > $o] :
% 4.71/5.04 ( ( finite_finite_nat @ B2 )
% 4.71/5.04 => ( ! [A5: complex] :
% 4.71/5.04 ( ( member_complex @ A5 @ A2 )
% 4.71/5.04 => ? [B9: nat] :
% 4.71/5.04 ( ( member_nat @ B9 @ B2 )
% 4.71/5.04 & ( R2 @ A5 @ B9 ) ) )
% 4.71/5.04 => ( ! [A1: complex,A22: complex,B5: nat] :
% 4.71/5.04 ( ( member_complex @ A1 @ A2 )
% 4.71/5.04 => ( ( member_complex @ A22 @ A2 )
% 4.71/5.04 => ( ( member_nat @ B5 @ B2 )
% 4.71/5.04 => ( ( R2 @ A1 @ B5 )
% 4.71/5.04 => ( ( R2 @ A22 @ B5 )
% 4.71/5.04 => ( A1 = A22 ) ) ) ) ) )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite_card_complex @ A2 ) @ ( finite_card_nat @ B2 ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_le_if_inj_on_rel
% 4.71/5.04 thf(fact_1560_card__le__if__inj__on__rel,axiom,
% 4.71/5.04 ! [B2: set_nat,A2: set_nat,R2: nat > nat > $o] :
% 4.71/5.04 ( ( finite_finite_nat @ B2 )
% 4.71/5.04 => ( ! [A5: nat] :
% 4.71/5.04 ( ( member_nat @ A5 @ A2 )
% 4.71/5.04 => ? [B9: nat] :
% 4.71/5.04 ( ( member_nat @ B9 @ B2 )
% 4.71/5.04 & ( R2 @ A5 @ B9 ) ) )
% 4.71/5.04 => ( ! [A1: nat,A22: nat,B5: nat] :
% 4.71/5.04 ( ( member_nat @ A1 @ A2 )
% 4.71/5.04 => ( ( member_nat @ A22 @ A2 )
% 4.71/5.04 => ( ( member_nat @ B5 @ B2 )
% 4.71/5.04 => ( ( R2 @ A1 @ B5 )
% 4.71/5.04 => ( ( R2 @ A22 @ B5 )
% 4.71/5.04 => ( A1 = A22 ) ) ) ) ) )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite_card_nat @ A2 ) @ ( finite_card_nat @ B2 ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_le_if_inj_on_rel
% 4.71/5.04 thf(fact_1561_card__le__if__inj__on__rel,axiom,
% 4.71/5.04 ! [B2: set_nat,A2: set_int,R2: int > nat > $o] :
% 4.71/5.04 ( ( finite_finite_nat @ B2 )
% 4.71/5.04 => ( ! [A5: int] :
% 4.71/5.04 ( ( member_int @ A5 @ A2 )
% 4.71/5.04 => ? [B9: nat] :
% 4.71/5.04 ( ( member_nat @ B9 @ B2 )
% 4.71/5.04 & ( R2 @ A5 @ B9 ) ) )
% 4.71/5.04 => ( ! [A1: int,A22: int,B5: nat] :
% 4.71/5.04 ( ( member_int @ A1 @ A2 )
% 4.71/5.04 => ( ( member_int @ A22 @ A2 )
% 4.71/5.04 => ( ( member_nat @ B5 @ B2 )
% 4.71/5.04 => ( ( R2 @ A1 @ B5 )
% 4.71/5.04 => ( ( R2 @ A22 @ B5 )
% 4.71/5.04 => ( A1 = A22 ) ) ) ) ) )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite_card_int @ A2 ) @ ( finite_card_nat @ B2 ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_le_if_inj_on_rel
% 4.71/5.04 thf(fact_1562_card__le__if__inj__on__rel,axiom,
% 4.71/5.04 ! [B2: set_int,A2: set_o,R2: $o > int > $o] :
% 4.71/5.04 ( ( finite_finite_int @ B2 )
% 4.71/5.04 => ( ! [A5: $o] :
% 4.71/5.04 ( ( member_o @ A5 @ A2 )
% 4.71/5.04 => ? [B9: int] :
% 4.71/5.04 ( ( member_int @ B9 @ B2 )
% 4.71/5.04 & ( R2 @ A5 @ B9 ) ) )
% 4.71/5.04 => ( ! [A1: $o,A22: $o,B5: int] :
% 4.71/5.04 ( ( member_o @ A1 @ A2 )
% 4.71/5.04 => ( ( member_o @ A22 @ A2 )
% 4.71/5.04 => ( ( member_int @ B5 @ B2 )
% 4.71/5.04 => ( ( R2 @ A1 @ B5 )
% 4.71/5.04 => ( ( R2 @ A22 @ B5 )
% 4.71/5.04 => ( A1 = A22 ) ) ) ) ) )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite_card_o @ A2 ) @ ( finite_card_int @ B2 ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_le_if_inj_on_rel
% 4.71/5.04 thf(fact_1563_card__le__if__inj__on__rel,axiom,
% 4.71/5.04 ! [B2: set_int,A2: set_complex,R2: complex > int > $o] :
% 4.71/5.04 ( ( finite_finite_int @ B2 )
% 4.71/5.04 => ( ! [A5: complex] :
% 4.71/5.04 ( ( member_complex @ A5 @ A2 )
% 4.71/5.04 => ? [B9: int] :
% 4.71/5.04 ( ( member_int @ B9 @ B2 )
% 4.71/5.04 & ( R2 @ A5 @ B9 ) ) )
% 4.71/5.04 => ( ! [A1: complex,A22: complex,B5: int] :
% 4.71/5.04 ( ( member_complex @ A1 @ A2 )
% 4.71/5.04 => ( ( member_complex @ A22 @ A2 )
% 4.71/5.04 => ( ( member_int @ B5 @ B2 )
% 4.71/5.04 => ( ( R2 @ A1 @ B5 )
% 4.71/5.04 => ( ( R2 @ A22 @ B5 )
% 4.71/5.04 => ( A1 = A22 ) ) ) ) ) )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite_card_complex @ A2 ) @ ( finite_card_int @ B2 ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_le_if_inj_on_rel
% 4.71/5.04 thf(fact_1564_set__encode__eq,axiom,
% 4.71/5.04 ! [A2: set_nat,B2: set_nat] :
% 4.71/5.04 ( ( finite_finite_nat @ A2 )
% 4.71/5.04 => ( ( finite_finite_nat @ B2 )
% 4.71/5.04 => ( ( ( nat_set_encode @ A2 )
% 4.71/5.04 = ( nat_set_encode @ B2 ) )
% 4.71/5.04 = ( A2 = B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % set_encode_eq
% 4.71/5.04 thf(fact_1565_frac__ge__0,axiom,
% 4.71/5.04 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X ) ) ).
% 4.71/5.04
% 4.71/5.04 % frac_ge_0
% 4.71/5.04 thf(fact_1566_frac__ge__0,axiom,
% 4.71/5.04 ! [X: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X ) ) ).
% 4.71/5.04
% 4.71/5.04 % frac_ge_0
% 4.71/5.04 thf(fact_1567_frac__lt__1,axiom,
% 4.71/5.04 ! [X: real] : ( ord_less_real @ ( archim2898591450579166408c_real @ X ) @ one_one_real ) ).
% 4.71/5.04
% 4.71/5.04 % frac_lt_1
% 4.71/5.04 thf(fact_1568_frac__lt__1,axiom,
% 4.71/5.04 ! [X: rat] : ( ord_less_rat @ ( archimedean_frac_rat @ X ) @ one_one_rat ) ).
% 4.71/5.04
% 4.71/5.04 % frac_lt_1
% 4.71/5.04 thf(fact_1569_card__eq__0__iff,axiom,
% 4.71/5.04 ! [A2: set_list_nat] :
% 4.71/5.04 ( ( ( finite_card_list_nat @ A2 )
% 4.71/5.04 = zero_zero_nat )
% 4.71/5.04 = ( ( A2 = bot_bot_set_list_nat )
% 4.71/5.04 | ~ ( finite8100373058378681591st_nat @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_eq_0_iff
% 4.71/5.04 thf(fact_1570_card__eq__0__iff,axiom,
% 4.71/5.04 ! [A2: set_set_nat] :
% 4.71/5.04 ( ( ( finite_card_set_nat @ A2 )
% 4.71/5.04 = zero_zero_nat )
% 4.71/5.04 = ( ( A2 = bot_bot_set_set_nat )
% 4.71/5.04 | ~ ( finite1152437895449049373et_nat @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_eq_0_iff
% 4.71/5.04 thf(fact_1571_card__eq__0__iff,axiom,
% 4.71/5.04 ! [A2: set_complex] :
% 4.71/5.04 ( ( ( finite_card_complex @ A2 )
% 4.71/5.04 = zero_zero_nat )
% 4.71/5.04 = ( ( A2 = bot_bot_set_complex )
% 4.71/5.04 | ~ ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_eq_0_iff
% 4.71/5.04 thf(fact_1572_card__eq__0__iff,axiom,
% 4.71/5.04 ! [A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.04 ( ( ( finite711546835091564841at_nat @ A2 )
% 4.71/5.04 = zero_zero_nat )
% 4.71/5.04 = ( ( A2 = bot_bo2099793752762293965at_nat )
% 4.71/5.04 | ~ ( finite6177210948735845034at_nat @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_eq_0_iff
% 4.71/5.04 thf(fact_1573_card__eq__0__iff,axiom,
% 4.71/5.04 ! [A2: set_Extended_enat] :
% 4.71/5.04 ( ( ( finite121521170596916366d_enat @ A2 )
% 4.71/5.04 = zero_zero_nat )
% 4.71/5.04 = ( ( A2 = bot_bo7653980558646680370d_enat )
% 4.71/5.04 | ~ ( finite4001608067531595151d_enat @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_eq_0_iff
% 4.71/5.04 thf(fact_1574_card__eq__0__iff,axiom,
% 4.71/5.04 ! [A2: set_real] :
% 4.71/5.04 ( ( ( finite_card_real @ A2 )
% 4.71/5.04 = zero_zero_nat )
% 4.71/5.04 = ( ( A2 = bot_bot_set_real )
% 4.71/5.04 | ~ ( finite_finite_real @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_eq_0_iff
% 4.71/5.04 thf(fact_1575_card__eq__0__iff,axiom,
% 4.71/5.04 ! [A2: set_o] :
% 4.71/5.04 ( ( ( finite_card_o @ A2 )
% 4.71/5.04 = zero_zero_nat )
% 4.71/5.04 = ( ( A2 = bot_bot_set_o )
% 4.71/5.04 | ~ ( finite_finite_o @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_eq_0_iff
% 4.71/5.04 thf(fact_1576_card__eq__0__iff,axiom,
% 4.71/5.04 ! [A2: set_nat] :
% 4.71/5.04 ( ( ( finite_card_nat @ A2 )
% 4.71/5.04 = zero_zero_nat )
% 4.71/5.04 = ( ( A2 = bot_bot_set_nat )
% 4.71/5.04 | ~ ( finite_finite_nat @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_eq_0_iff
% 4.71/5.04 thf(fact_1577_card__eq__0__iff,axiom,
% 4.71/5.04 ! [A2: set_int] :
% 4.71/5.04 ( ( ( finite_card_int @ A2 )
% 4.71/5.04 = zero_zero_nat )
% 4.71/5.04 = ( ( A2 = bot_bot_set_int )
% 4.71/5.04 | ~ ( finite_finite_int @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_eq_0_iff
% 4.71/5.04 thf(fact_1578_card__ge__0__finite,axiom,
% 4.71/5.04 ! [A2: set_list_nat] :
% 4.71/5.04 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_list_nat @ A2 ) )
% 4.71/5.04 => ( finite8100373058378681591st_nat @ A2 ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_ge_0_finite
% 4.71/5.04 thf(fact_1579_card__ge__0__finite,axiom,
% 4.71/5.04 ! [A2: set_set_nat] :
% 4.71/5.04 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_set_nat @ A2 ) )
% 4.71/5.04 => ( finite1152437895449049373et_nat @ A2 ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_ge_0_finite
% 4.71/5.04 thf(fact_1580_card__ge__0__finite,axiom,
% 4.71/5.04 ! [A2: set_nat] :
% 4.71/5.04 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A2 ) )
% 4.71/5.04 => ( finite_finite_nat @ A2 ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_ge_0_finite
% 4.71/5.04 thf(fact_1581_card__ge__0__finite,axiom,
% 4.71/5.04 ! [A2: set_int] :
% 4.71/5.04 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A2 ) )
% 4.71/5.04 => ( finite_finite_int @ A2 ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_ge_0_finite
% 4.71/5.04 thf(fact_1582_card__ge__0__finite,axiom,
% 4.71/5.04 ! [A2: set_complex] :
% 4.71/5.04 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A2 ) )
% 4.71/5.04 => ( finite3207457112153483333omplex @ A2 ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_ge_0_finite
% 4.71/5.04 thf(fact_1583_card__ge__0__finite,axiom,
% 4.71/5.04 ! [A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.04 ( ( ord_less_nat @ zero_zero_nat @ ( finite711546835091564841at_nat @ A2 ) )
% 4.71/5.04 => ( finite6177210948735845034at_nat @ A2 ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_ge_0_finite
% 4.71/5.04 thf(fact_1584_card__ge__0__finite,axiom,
% 4.71/5.04 ! [A2: set_Extended_enat] :
% 4.71/5.04 ( ( ord_less_nat @ zero_zero_nat @ ( finite121521170596916366d_enat @ A2 ) )
% 4.71/5.04 => ( finite4001608067531595151d_enat @ A2 ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_ge_0_finite
% 4.71/5.04 thf(fact_1585_finite__if__finite__subsets__card__bdd,axiom,
% 4.71/5.04 ! [F2: set_list_nat,C2: nat] :
% 4.71/5.04 ( ! [G: set_list_nat] :
% 4.71/5.04 ( ( ord_le6045566169113846134st_nat @ G @ F2 )
% 4.71/5.04 => ( ( finite8100373058378681591st_nat @ G )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite_card_list_nat @ G ) @ C2 ) ) )
% 4.71/5.04 => ( ( finite8100373058378681591st_nat @ F2 )
% 4.71/5.04 & ( ord_less_eq_nat @ ( finite_card_list_nat @ F2 ) @ C2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % finite_if_finite_subsets_card_bdd
% 4.71/5.04 thf(fact_1586_finite__if__finite__subsets__card__bdd,axiom,
% 4.71/5.04 ! [F2: set_set_nat,C2: nat] :
% 4.71/5.04 ( ! [G: set_set_nat] :
% 4.71/5.04 ( ( ord_le6893508408891458716et_nat @ G @ F2 )
% 4.71/5.04 => ( ( finite1152437895449049373et_nat @ G )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite_card_set_nat @ G ) @ C2 ) ) )
% 4.71/5.04 => ( ( finite1152437895449049373et_nat @ F2 )
% 4.71/5.04 & ( ord_less_eq_nat @ ( finite_card_set_nat @ F2 ) @ C2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % finite_if_finite_subsets_card_bdd
% 4.71/5.04 thf(fact_1587_finite__if__finite__subsets__card__bdd,axiom,
% 4.71/5.04 ! [F2: set_nat,C2: nat] :
% 4.71/5.04 ( ! [G: set_nat] :
% 4.71/5.04 ( ( ord_less_eq_set_nat @ G @ F2 )
% 4.71/5.04 => ( ( finite_finite_nat @ G )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite_card_nat @ G ) @ C2 ) ) )
% 4.71/5.04 => ( ( finite_finite_nat @ F2 )
% 4.71/5.04 & ( ord_less_eq_nat @ ( finite_card_nat @ F2 ) @ C2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % finite_if_finite_subsets_card_bdd
% 4.71/5.04 thf(fact_1588_finite__if__finite__subsets__card__bdd,axiom,
% 4.71/5.04 ! [F2: set_complex,C2: nat] :
% 4.71/5.04 ( ! [G: set_complex] :
% 4.71/5.04 ( ( ord_le211207098394363844omplex @ G @ F2 )
% 4.71/5.04 => ( ( finite3207457112153483333omplex @ G )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite_card_complex @ G ) @ C2 ) ) )
% 4.71/5.04 => ( ( finite3207457112153483333omplex @ F2 )
% 4.71/5.04 & ( ord_less_eq_nat @ ( finite_card_complex @ F2 ) @ C2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % finite_if_finite_subsets_card_bdd
% 4.71/5.04 thf(fact_1589_finite__if__finite__subsets__card__bdd,axiom,
% 4.71/5.04 ! [F2: set_Pr1261947904930325089at_nat,C2: nat] :
% 4.71/5.04 ( ! [G: set_Pr1261947904930325089at_nat] :
% 4.71/5.04 ( ( ord_le3146513528884898305at_nat @ G @ F2 )
% 4.71/5.04 => ( ( finite6177210948735845034at_nat @ G )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ G ) @ C2 ) ) )
% 4.71/5.04 => ( ( finite6177210948735845034at_nat @ F2 )
% 4.71/5.04 & ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ F2 ) @ C2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % finite_if_finite_subsets_card_bdd
% 4.71/5.04 thf(fact_1590_finite__if__finite__subsets__card__bdd,axiom,
% 4.71/5.04 ! [F2: set_Extended_enat,C2: nat] :
% 4.71/5.04 ( ! [G: set_Extended_enat] :
% 4.71/5.04 ( ( ord_le7203529160286727270d_enat @ G @ F2 )
% 4.71/5.04 => ( ( finite4001608067531595151d_enat @ G )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite121521170596916366d_enat @ G ) @ C2 ) ) )
% 4.71/5.04 => ( ( finite4001608067531595151d_enat @ F2 )
% 4.71/5.04 & ( ord_less_eq_nat @ ( finite121521170596916366d_enat @ F2 ) @ C2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % finite_if_finite_subsets_card_bdd
% 4.71/5.04 thf(fact_1591_finite__if__finite__subsets__card__bdd,axiom,
% 4.71/5.04 ! [F2: set_int,C2: nat] :
% 4.71/5.04 ( ! [G: set_int] :
% 4.71/5.04 ( ( ord_less_eq_set_int @ G @ F2 )
% 4.71/5.04 => ( ( finite_finite_int @ G )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite_card_int @ G ) @ C2 ) ) )
% 4.71/5.04 => ( ( finite_finite_int @ F2 )
% 4.71/5.04 & ( ord_less_eq_nat @ ( finite_card_int @ F2 ) @ C2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % finite_if_finite_subsets_card_bdd
% 4.71/5.04 thf(fact_1592_obtain__subset__with__card__n,axiom,
% 4.71/5.04 ! [N: nat,S2: set_list_nat] :
% 4.71/5.04 ( ( ord_less_eq_nat @ N @ ( finite_card_list_nat @ S2 ) )
% 4.71/5.04 => ~ ! [T4: set_list_nat] :
% 4.71/5.04 ( ( ord_le6045566169113846134st_nat @ T4 @ S2 )
% 4.71/5.04 => ( ( ( finite_card_list_nat @ T4 )
% 4.71/5.04 = N )
% 4.71/5.04 => ~ ( finite8100373058378681591st_nat @ T4 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % obtain_subset_with_card_n
% 4.71/5.04 thf(fact_1593_obtain__subset__with__card__n,axiom,
% 4.71/5.04 ! [N: nat,S2: set_set_nat] :
% 4.71/5.04 ( ( ord_less_eq_nat @ N @ ( finite_card_set_nat @ S2 ) )
% 4.71/5.04 => ~ ! [T4: set_set_nat] :
% 4.71/5.04 ( ( ord_le6893508408891458716et_nat @ T4 @ S2 )
% 4.71/5.04 => ( ( ( finite_card_set_nat @ T4 )
% 4.71/5.04 = N )
% 4.71/5.04 => ~ ( finite1152437895449049373et_nat @ T4 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % obtain_subset_with_card_n
% 4.71/5.04 thf(fact_1594_obtain__subset__with__card__n,axiom,
% 4.71/5.04 ! [N: nat,S2: set_nat] :
% 4.71/5.04 ( ( ord_less_eq_nat @ N @ ( finite_card_nat @ S2 ) )
% 4.71/5.04 => ~ ! [T4: set_nat] :
% 4.71/5.04 ( ( ord_less_eq_set_nat @ T4 @ S2 )
% 4.71/5.04 => ( ( ( finite_card_nat @ T4 )
% 4.71/5.04 = N )
% 4.71/5.04 => ~ ( finite_finite_nat @ T4 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % obtain_subset_with_card_n
% 4.71/5.04 thf(fact_1595_obtain__subset__with__card__n,axiom,
% 4.71/5.04 ! [N: nat,S2: set_complex] :
% 4.71/5.04 ( ( ord_less_eq_nat @ N @ ( finite_card_complex @ S2 ) )
% 4.71/5.04 => ~ ! [T4: set_complex] :
% 4.71/5.04 ( ( ord_le211207098394363844omplex @ T4 @ S2 )
% 4.71/5.04 => ( ( ( finite_card_complex @ T4 )
% 4.71/5.04 = N )
% 4.71/5.04 => ~ ( finite3207457112153483333omplex @ T4 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % obtain_subset_with_card_n
% 4.71/5.04 thf(fact_1596_obtain__subset__with__card__n,axiom,
% 4.71/5.04 ! [N: nat,S2: set_Pr1261947904930325089at_nat] :
% 4.71/5.04 ( ( ord_less_eq_nat @ N @ ( finite711546835091564841at_nat @ S2 ) )
% 4.71/5.04 => ~ ! [T4: set_Pr1261947904930325089at_nat] :
% 4.71/5.04 ( ( ord_le3146513528884898305at_nat @ T4 @ S2 )
% 4.71/5.04 => ( ( ( finite711546835091564841at_nat @ T4 )
% 4.71/5.04 = N )
% 4.71/5.04 => ~ ( finite6177210948735845034at_nat @ T4 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % obtain_subset_with_card_n
% 4.71/5.04 thf(fact_1597_obtain__subset__with__card__n,axiom,
% 4.71/5.04 ! [N: nat,S2: set_Extended_enat] :
% 4.71/5.04 ( ( ord_less_eq_nat @ N @ ( finite121521170596916366d_enat @ S2 ) )
% 4.71/5.04 => ~ ! [T4: set_Extended_enat] :
% 4.71/5.04 ( ( ord_le7203529160286727270d_enat @ T4 @ S2 )
% 4.71/5.04 => ( ( ( finite121521170596916366d_enat @ T4 )
% 4.71/5.04 = N )
% 4.71/5.04 => ~ ( finite4001608067531595151d_enat @ T4 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % obtain_subset_with_card_n
% 4.71/5.04 thf(fact_1598_obtain__subset__with__card__n,axiom,
% 4.71/5.04 ! [N: nat,S2: set_int] :
% 4.71/5.04 ( ( ord_less_eq_nat @ N @ ( finite_card_int @ S2 ) )
% 4.71/5.04 => ~ ! [T4: set_int] :
% 4.71/5.04 ( ( ord_less_eq_set_int @ T4 @ S2 )
% 4.71/5.04 => ( ( ( finite_card_int @ T4 )
% 4.71/5.04 = N )
% 4.71/5.04 => ~ ( finite_finite_int @ T4 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % obtain_subset_with_card_n
% 4.71/5.04 thf(fact_1599_card__seteq,axiom,
% 4.71/5.04 ! [B2: set_list_nat,A2: set_list_nat] :
% 4.71/5.04 ( ( finite8100373058378681591st_nat @ B2 )
% 4.71/5.04 => ( ( ord_le6045566169113846134st_nat @ A2 @ B2 )
% 4.71/5.04 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ B2 ) @ ( finite_card_list_nat @ A2 ) )
% 4.71/5.04 => ( A2 = B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_seteq
% 4.71/5.04 thf(fact_1600_card__seteq,axiom,
% 4.71/5.04 ! [B2: set_set_nat,A2: set_set_nat] :
% 4.71/5.04 ( ( finite1152437895449049373et_nat @ B2 )
% 4.71/5.04 => ( ( ord_le6893508408891458716et_nat @ A2 @ B2 )
% 4.71/5.04 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ B2 ) @ ( finite_card_set_nat @ A2 ) )
% 4.71/5.04 => ( A2 = B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_seteq
% 4.71/5.04 thf(fact_1601_card__seteq,axiom,
% 4.71/5.04 ! [B2: set_nat,A2: set_nat] :
% 4.71/5.04 ( ( finite_finite_nat @ B2 )
% 4.71/5.04 => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 4.71/5.04 => ( ( ord_less_eq_nat @ ( finite_card_nat @ B2 ) @ ( finite_card_nat @ A2 ) )
% 4.71/5.04 => ( A2 = B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_seteq
% 4.71/5.04 thf(fact_1602_card__seteq,axiom,
% 4.71/5.04 ! [B2: set_complex,A2: set_complex] :
% 4.71/5.04 ( ( finite3207457112153483333omplex @ B2 )
% 4.71/5.04 => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 4.71/5.04 => ( ( ord_less_eq_nat @ ( finite_card_complex @ B2 ) @ ( finite_card_complex @ A2 ) )
% 4.71/5.04 => ( A2 = B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_seteq
% 4.71/5.04 thf(fact_1603_card__seteq,axiom,
% 4.71/5.04 ! [B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.04 ( ( finite6177210948735845034at_nat @ B2 )
% 4.71/5.04 => ( ( ord_le3146513528884898305at_nat @ A2 @ B2 )
% 4.71/5.04 => ( ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ B2 ) @ ( finite711546835091564841at_nat @ A2 ) )
% 4.71/5.04 => ( A2 = B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_seteq
% 4.71/5.04 thf(fact_1604_card__seteq,axiom,
% 4.71/5.04 ! [B2: set_Extended_enat,A2: set_Extended_enat] :
% 4.71/5.04 ( ( finite4001608067531595151d_enat @ B2 )
% 4.71/5.04 => ( ( ord_le7203529160286727270d_enat @ A2 @ B2 )
% 4.71/5.04 => ( ( ord_less_eq_nat @ ( finite121521170596916366d_enat @ B2 ) @ ( finite121521170596916366d_enat @ A2 ) )
% 4.71/5.04 => ( A2 = B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_seteq
% 4.71/5.04 thf(fact_1605_card__seteq,axiom,
% 4.71/5.04 ! [B2: set_int,A2: set_int] :
% 4.71/5.04 ( ( finite_finite_int @ B2 )
% 4.71/5.04 => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 4.71/5.04 => ( ( ord_less_eq_nat @ ( finite_card_int @ B2 ) @ ( finite_card_int @ A2 ) )
% 4.71/5.04 => ( A2 = B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_seteq
% 4.71/5.04 thf(fact_1606_card__mono,axiom,
% 4.71/5.04 ! [B2: set_list_nat,A2: set_list_nat] :
% 4.71/5.04 ( ( finite8100373058378681591st_nat @ B2 )
% 4.71/5.04 => ( ( ord_le6045566169113846134st_nat @ A2 @ B2 )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite_card_list_nat @ A2 ) @ ( finite_card_list_nat @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_mono
% 4.71/5.04 thf(fact_1607_card__mono,axiom,
% 4.71/5.04 ! [B2: set_set_nat,A2: set_set_nat] :
% 4.71/5.04 ( ( finite1152437895449049373et_nat @ B2 )
% 4.71/5.04 => ( ( ord_le6893508408891458716et_nat @ A2 @ B2 )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite_card_set_nat @ A2 ) @ ( finite_card_set_nat @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_mono
% 4.71/5.04 thf(fact_1608_card__mono,axiom,
% 4.71/5.04 ! [B2: set_nat,A2: set_nat] :
% 4.71/5.04 ( ( finite_finite_nat @ B2 )
% 4.71/5.04 => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite_card_nat @ A2 ) @ ( finite_card_nat @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_mono
% 4.71/5.04 thf(fact_1609_card__mono,axiom,
% 4.71/5.04 ! [B2: set_complex,A2: set_complex] :
% 4.71/5.04 ( ( finite3207457112153483333omplex @ B2 )
% 4.71/5.04 => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite_card_complex @ A2 ) @ ( finite_card_complex @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_mono
% 4.71/5.04 thf(fact_1610_card__mono,axiom,
% 4.71/5.04 ! [B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.04 ( ( finite6177210948735845034at_nat @ B2 )
% 4.71/5.04 => ( ( ord_le3146513528884898305at_nat @ A2 @ B2 )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ A2 ) @ ( finite711546835091564841at_nat @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_mono
% 4.71/5.04 thf(fact_1611_card__mono,axiom,
% 4.71/5.04 ! [B2: set_Extended_enat,A2: set_Extended_enat] :
% 4.71/5.04 ( ( finite4001608067531595151d_enat @ B2 )
% 4.71/5.04 => ( ( ord_le7203529160286727270d_enat @ A2 @ B2 )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite121521170596916366d_enat @ A2 ) @ ( finite121521170596916366d_enat @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_mono
% 4.71/5.04 thf(fact_1612_card__mono,axiom,
% 4.71/5.04 ! [B2: set_int,A2: set_int] :
% 4.71/5.04 ( ( finite_finite_int @ B2 )
% 4.71/5.04 => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 4.71/5.04 => ( ord_less_eq_nat @ ( finite_card_int @ A2 ) @ ( finite_card_int @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_mono
% 4.71/5.04 thf(fact_1613_psubset__card__mono,axiom,
% 4.71/5.04 ! [B2: set_list_nat,A2: set_list_nat] :
% 4.71/5.04 ( ( finite8100373058378681591st_nat @ B2 )
% 4.71/5.04 => ( ( ord_le1190675801316882794st_nat @ A2 @ B2 )
% 4.71/5.04 => ( ord_less_nat @ ( finite_card_list_nat @ A2 ) @ ( finite_card_list_nat @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % psubset_card_mono
% 4.71/5.04 thf(fact_1614_psubset__card__mono,axiom,
% 4.71/5.04 ! [B2: set_set_nat,A2: set_set_nat] :
% 4.71/5.04 ( ( finite1152437895449049373et_nat @ B2 )
% 4.71/5.04 => ( ( ord_less_set_set_nat @ A2 @ B2 )
% 4.71/5.04 => ( ord_less_nat @ ( finite_card_set_nat @ A2 ) @ ( finite_card_set_nat @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % psubset_card_mono
% 4.71/5.04 thf(fact_1615_psubset__card__mono,axiom,
% 4.71/5.04 ! [B2: set_nat,A2: set_nat] :
% 4.71/5.04 ( ( finite_finite_nat @ B2 )
% 4.71/5.04 => ( ( ord_less_set_nat @ A2 @ B2 )
% 4.71/5.04 => ( ord_less_nat @ ( finite_card_nat @ A2 ) @ ( finite_card_nat @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % psubset_card_mono
% 4.71/5.04 thf(fact_1616_psubset__card__mono,axiom,
% 4.71/5.04 ! [B2: set_int,A2: set_int] :
% 4.71/5.04 ( ( finite_finite_int @ B2 )
% 4.71/5.04 => ( ( ord_less_set_int @ A2 @ B2 )
% 4.71/5.04 => ( ord_less_nat @ ( finite_card_int @ A2 ) @ ( finite_card_int @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % psubset_card_mono
% 4.71/5.04 thf(fact_1617_psubset__card__mono,axiom,
% 4.71/5.04 ! [B2: set_complex,A2: set_complex] :
% 4.71/5.04 ( ( finite3207457112153483333omplex @ B2 )
% 4.71/5.04 => ( ( ord_less_set_complex @ A2 @ B2 )
% 4.71/5.04 => ( ord_less_nat @ ( finite_card_complex @ A2 ) @ ( finite_card_complex @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % psubset_card_mono
% 4.71/5.04 thf(fact_1618_psubset__card__mono,axiom,
% 4.71/5.04 ! [B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.04 ( ( finite6177210948735845034at_nat @ B2 )
% 4.71/5.04 => ( ( ord_le7866589430770878221at_nat @ A2 @ B2 )
% 4.71/5.04 => ( ord_less_nat @ ( finite711546835091564841at_nat @ A2 ) @ ( finite711546835091564841at_nat @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % psubset_card_mono
% 4.71/5.04 thf(fact_1619_psubset__card__mono,axiom,
% 4.71/5.04 ! [B2: set_Extended_enat,A2: set_Extended_enat] :
% 4.71/5.04 ( ( finite4001608067531595151d_enat @ B2 )
% 4.71/5.04 => ( ( ord_le2529575680413868914d_enat @ A2 @ B2 )
% 4.71/5.04 => ( ord_less_nat @ ( finite121521170596916366d_enat @ A2 ) @ ( finite121521170596916366d_enat @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % psubset_card_mono
% 4.71/5.04 thf(fact_1620_finite__le__enumerate,axiom,
% 4.71/5.04 ! [S2: set_nat,N: nat] :
% 4.71/5.04 ( ( finite_finite_nat @ S2 )
% 4.71/5.04 => ( ( ord_less_nat @ N @ ( finite_card_nat @ S2 ) )
% 4.71/5.04 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S2 @ N ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % finite_le_enumerate
% 4.71/5.04 thf(fact_1621_zdiff__int__split,axiom,
% 4.71/5.04 ! [P: int > $o,X: nat,Y: nat] :
% 4.71/5.04 ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X @ Y ) ) )
% 4.71/5.04 = ( ( ( ord_less_eq_nat @ Y @ X )
% 4.71/5.04 => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 4.71/5.04 & ( ( ord_less_nat @ X @ Y )
% 4.71/5.04 => ( P @ zero_zero_int ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % zdiff_int_split
% 4.71/5.04 thf(fact_1622_finite__enumerate__in__set,axiom,
% 4.71/5.04 ! [S2: set_Extended_enat,N: nat] :
% 4.71/5.04 ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.04 => ( ( ord_less_nat @ N @ ( finite121521170596916366d_enat @ S2 ) )
% 4.71/5.04 => ( member_Extended_enat @ ( infini7641415182203889163d_enat @ S2 @ N ) @ S2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % finite_enumerate_in_set
% 4.71/5.04 thf(fact_1623_finite__enumerate__in__set,axiom,
% 4.71/5.04 ! [S2: set_nat,N: nat] :
% 4.71/5.04 ( ( finite_finite_nat @ S2 )
% 4.71/5.04 => ( ( ord_less_nat @ N @ ( finite_card_nat @ S2 ) )
% 4.71/5.04 => ( member_nat @ ( infini8530281810654367211te_nat @ S2 @ N ) @ S2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % finite_enumerate_in_set
% 4.71/5.04 thf(fact_1624_finite__enumerate__Ex,axiom,
% 4.71/5.04 ! [S2: set_Extended_enat,S: extended_enat] :
% 4.71/5.04 ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.04 => ( ( member_Extended_enat @ S @ S2 )
% 4.71/5.04 => ? [N2: nat] :
% 4.71/5.04 ( ( ord_less_nat @ N2 @ ( finite121521170596916366d_enat @ S2 ) )
% 4.71/5.04 & ( ( infini7641415182203889163d_enat @ S2 @ N2 )
% 4.71/5.04 = S ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % finite_enumerate_Ex
% 4.71/5.04 thf(fact_1625_finite__enumerate__Ex,axiom,
% 4.71/5.04 ! [S2: set_nat,S: nat] :
% 4.71/5.04 ( ( finite_finite_nat @ S2 )
% 4.71/5.04 => ( ( member_nat @ S @ S2 )
% 4.71/5.04 => ? [N2: nat] :
% 4.71/5.04 ( ( ord_less_nat @ N2 @ ( finite_card_nat @ S2 ) )
% 4.71/5.04 & ( ( infini8530281810654367211te_nat @ S2 @ N2 )
% 4.71/5.04 = S ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % finite_enumerate_Ex
% 4.71/5.04 thf(fact_1626_finite__enum__ext,axiom,
% 4.71/5.04 ! [X5: set_Extended_enat,Y6: set_Extended_enat] :
% 4.71/5.04 ( ! [I2: nat] :
% 4.71/5.04 ( ( ord_less_nat @ I2 @ ( finite121521170596916366d_enat @ X5 ) )
% 4.71/5.04 => ( ( infini7641415182203889163d_enat @ X5 @ I2 )
% 4.71/5.04 = ( infini7641415182203889163d_enat @ Y6 @ I2 ) ) )
% 4.71/5.04 => ( ( finite4001608067531595151d_enat @ X5 )
% 4.71/5.04 => ( ( finite4001608067531595151d_enat @ Y6 )
% 4.71/5.04 => ( ( ( finite121521170596916366d_enat @ X5 )
% 4.71/5.04 = ( finite121521170596916366d_enat @ Y6 ) )
% 4.71/5.04 => ( X5 = Y6 ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % finite_enum_ext
% 4.71/5.04 thf(fact_1627_finite__enum__ext,axiom,
% 4.71/5.04 ! [X5: set_nat,Y6: set_nat] :
% 4.71/5.04 ( ! [I2: nat] :
% 4.71/5.04 ( ( ord_less_nat @ I2 @ ( finite_card_nat @ X5 ) )
% 4.71/5.04 => ( ( infini8530281810654367211te_nat @ X5 @ I2 )
% 4.71/5.04 = ( infini8530281810654367211te_nat @ Y6 @ I2 ) ) )
% 4.71/5.04 => ( ( finite_finite_nat @ X5 )
% 4.71/5.04 => ( ( finite_finite_nat @ Y6 )
% 4.71/5.04 => ( ( ( finite_card_nat @ X5 )
% 4.71/5.04 = ( finite_card_nat @ Y6 ) )
% 4.71/5.04 => ( X5 = Y6 ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % finite_enum_ext
% 4.71/5.04 thf(fact_1628_zle__int,axiom,
% 4.71/5.04 ! [M2: nat,N: nat] :
% 4.71/5.04 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) )
% 4.71/5.04 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 4.71/5.04
% 4.71/5.04 % zle_int
% 4.71/5.04 thf(fact_1629_set__encode__inf,axiom,
% 4.71/5.04 ! [A2: set_nat] :
% 4.71/5.04 ( ~ ( finite_finite_nat @ A2 )
% 4.71/5.04 => ( ( nat_set_encode @ A2 )
% 4.71/5.04 = zero_zero_nat ) ) ).
% 4.71/5.04
% 4.71/5.04 % set_encode_inf
% 4.71/5.04 thf(fact_1630_card__gt__0__iff,axiom,
% 4.71/5.04 ! [A2: set_list_nat] :
% 4.71/5.04 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_list_nat @ A2 ) )
% 4.71/5.04 = ( ( A2 != bot_bot_set_list_nat )
% 4.71/5.04 & ( finite8100373058378681591st_nat @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_gt_0_iff
% 4.71/5.04 thf(fact_1631_card__gt__0__iff,axiom,
% 4.71/5.04 ! [A2: set_set_nat] :
% 4.71/5.04 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_set_nat @ A2 ) )
% 4.71/5.04 = ( ( A2 != bot_bot_set_set_nat )
% 4.71/5.04 & ( finite1152437895449049373et_nat @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_gt_0_iff
% 4.71/5.04 thf(fact_1632_card__gt__0__iff,axiom,
% 4.71/5.04 ! [A2: set_complex] :
% 4.71/5.04 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A2 ) )
% 4.71/5.04 = ( ( A2 != bot_bot_set_complex )
% 4.71/5.04 & ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_gt_0_iff
% 4.71/5.04 thf(fact_1633_card__gt__0__iff,axiom,
% 4.71/5.04 ! [A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.04 ( ( ord_less_nat @ zero_zero_nat @ ( finite711546835091564841at_nat @ A2 ) )
% 4.71/5.04 = ( ( A2 != bot_bo2099793752762293965at_nat )
% 4.71/5.04 & ( finite6177210948735845034at_nat @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_gt_0_iff
% 4.71/5.04 thf(fact_1634_card__gt__0__iff,axiom,
% 4.71/5.04 ! [A2: set_Extended_enat] :
% 4.71/5.04 ( ( ord_less_nat @ zero_zero_nat @ ( finite121521170596916366d_enat @ A2 ) )
% 4.71/5.04 = ( ( A2 != bot_bo7653980558646680370d_enat )
% 4.71/5.04 & ( finite4001608067531595151d_enat @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_gt_0_iff
% 4.71/5.04 thf(fact_1635_card__gt__0__iff,axiom,
% 4.71/5.04 ! [A2: set_real] :
% 4.71/5.04 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_real @ A2 ) )
% 4.71/5.04 = ( ( A2 != bot_bot_set_real )
% 4.71/5.04 & ( finite_finite_real @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_gt_0_iff
% 4.71/5.04 thf(fact_1636_card__gt__0__iff,axiom,
% 4.71/5.04 ! [A2: set_o] :
% 4.71/5.04 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_o @ A2 ) )
% 4.71/5.04 = ( ( A2 != bot_bot_set_o )
% 4.71/5.04 & ( finite_finite_o @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_gt_0_iff
% 4.71/5.04 thf(fact_1637_card__gt__0__iff,axiom,
% 4.71/5.04 ! [A2: set_nat] :
% 4.71/5.04 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A2 ) )
% 4.71/5.04 = ( ( A2 != bot_bot_set_nat )
% 4.71/5.04 & ( finite_finite_nat @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_gt_0_iff
% 4.71/5.04 thf(fact_1638_card__gt__0__iff,axiom,
% 4.71/5.04 ! [A2: set_int] :
% 4.71/5.04 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A2 ) )
% 4.71/5.04 = ( ( A2 != bot_bot_set_int )
% 4.71/5.04 & ( finite_finite_int @ A2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_gt_0_iff
% 4.71/5.04 thf(fact_1639_card__le__Suc0__iff__eq,axiom,
% 4.71/5.04 ! [A2: set_list_nat] :
% 4.71/5.04 ( ( finite8100373058378681591st_nat @ A2 )
% 4.71/5.04 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ A2 ) @ ( suc @ zero_zero_nat ) )
% 4.71/5.04 = ( ! [X3: list_nat] :
% 4.71/5.04 ( ( member_list_nat @ X3 @ A2 )
% 4.71/5.04 => ! [Y2: list_nat] :
% 4.71/5.04 ( ( member_list_nat @ Y2 @ A2 )
% 4.71/5.04 => ( X3 = Y2 ) ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_le_Suc0_iff_eq
% 4.71/5.04 thf(fact_1640_card__le__Suc0__iff__eq,axiom,
% 4.71/5.04 ! [A2: set_set_nat] :
% 4.71/5.04 ( ( finite1152437895449049373et_nat @ A2 )
% 4.71/5.04 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ A2 ) @ ( suc @ zero_zero_nat ) )
% 4.71/5.04 = ( ! [X3: set_nat] :
% 4.71/5.04 ( ( member_set_nat @ X3 @ A2 )
% 4.71/5.04 => ! [Y2: set_nat] :
% 4.71/5.04 ( ( member_set_nat @ Y2 @ A2 )
% 4.71/5.04 => ( X3 = Y2 ) ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_le_Suc0_iff_eq
% 4.71/5.04 thf(fact_1641_card__le__Suc0__iff__eq,axiom,
% 4.71/5.04 ! [A2: set_nat] :
% 4.71/5.04 ( ( finite_finite_nat @ A2 )
% 4.71/5.04 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A2 ) @ ( suc @ zero_zero_nat ) )
% 4.71/5.04 = ( ! [X3: nat] :
% 4.71/5.04 ( ( member_nat @ X3 @ A2 )
% 4.71/5.04 => ! [Y2: nat] :
% 4.71/5.04 ( ( member_nat @ Y2 @ A2 )
% 4.71/5.04 => ( X3 = Y2 ) ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_le_Suc0_iff_eq
% 4.71/5.04 thf(fact_1642_card__le__Suc0__iff__eq,axiom,
% 4.71/5.04 ! [A2: set_int] :
% 4.71/5.04 ( ( finite_finite_int @ A2 )
% 4.71/5.04 => ( ( ord_less_eq_nat @ ( finite_card_int @ A2 ) @ ( suc @ zero_zero_nat ) )
% 4.71/5.04 = ( ! [X3: int] :
% 4.71/5.04 ( ( member_int @ X3 @ A2 )
% 4.71/5.04 => ! [Y2: int] :
% 4.71/5.04 ( ( member_int @ Y2 @ A2 )
% 4.71/5.04 => ( X3 = Y2 ) ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_le_Suc0_iff_eq
% 4.71/5.04 thf(fact_1643_card__le__Suc0__iff__eq,axiom,
% 4.71/5.04 ! [A2: set_complex] :
% 4.71/5.04 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.04 => ( ( ord_less_eq_nat @ ( finite_card_complex @ A2 ) @ ( suc @ zero_zero_nat ) )
% 4.71/5.04 = ( ! [X3: complex] :
% 4.71/5.04 ( ( member_complex @ X3 @ A2 )
% 4.71/5.04 => ! [Y2: complex] :
% 4.71/5.04 ( ( member_complex @ Y2 @ A2 )
% 4.71/5.04 => ( X3 = Y2 ) ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_le_Suc0_iff_eq
% 4.71/5.04 thf(fact_1644_card__le__Suc0__iff__eq,axiom,
% 4.71/5.04 ! [A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.04 ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.04 => ( ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ A2 ) @ ( suc @ zero_zero_nat ) )
% 4.71/5.04 = ( ! [X3: product_prod_nat_nat] :
% 4.71/5.04 ( ( member8440522571783428010at_nat @ X3 @ A2 )
% 4.71/5.04 => ! [Y2: product_prod_nat_nat] :
% 4.71/5.04 ( ( member8440522571783428010at_nat @ Y2 @ A2 )
% 4.71/5.04 => ( X3 = Y2 ) ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_le_Suc0_iff_eq
% 4.71/5.04 thf(fact_1645_card__le__Suc0__iff__eq,axiom,
% 4.71/5.04 ! [A2: set_Extended_enat] :
% 4.71/5.04 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.04 => ( ( ord_less_eq_nat @ ( finite121521170596916366d_enat @ A2 ) @ ( suc @ zero_zero_nat ) )
% 4.71/5.04 = ( ! [X3: extended_enat] :
% 4.71/5.04 ( ( member_Extended_enat @ X3 @ A2 )
% 4.71/5.04 => ! [Y2: extended_enat] :
% 4.71/5.04 ( ( member_Extended_enat @ Y2 @ A2 )
% 4.71/5.04 => ( X3 = Y2 ) ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_le_Suc0_iff_eq
% 4.71/5.04 thf(fact_1646_card__psubset,axiom,
% 4.71/5.04 ! [B2: set_list_nat,A2: set_list_nat] :
% 4.71/5.04 ( ( finite8100373058378681591st_nat @ B2 )
% 4.71/5.04 => ( ( ord_le6045566169113846134st_nat @ A2 @ B2 )
% 4.71/5.04 => ( ( ord_less_nat @ ( finite_card_list_nat @ A2 ) @ ( finite_card_list_nat @ B2 ) )
% 4.71/5.04 => ( ord_le1190675801316882794st_nat @ A2 @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_psubset
% 4.71/5.04 thf(fact_1647_card__psubset,axiom,
% 4.71/5.04 ! [B2: set_set_nat,A2: set_set_nat] :
% 4.71/5.04 ( ( finite1152437895449049373et_nat @ B2 )
% 4.71/5.04 => ( ( ord_le6893508408891458716et_nat @ A2 @ B2 )
% 4.71/5.04 => ( ( ord_less_nat @ ( finite_card_set_nat @ A2 ) @ ( finite_card_set_nat @ B2 ) )
% 4.71/5.04 => ( ord_less_set_set_nat @ A2 @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_psubset
% 4.71/5.04 thf(fact_1648_card__psubset,axiom,
% 4.71/5.04 ! [B2: set_nat,A2: set_nat] :
% 4.71/5.04 ( ( finite_finite_nat @ B2 )
% 4.71/5.04 => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 4.71/5.04 => ( ( ord_less_nat @ ( finite_card_nat @ A2 ) @ ( finite_card_nat @ B2 ) )
% 4.71/5.04 => ( ord_less_set_nat @ A2 @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_psubset
% 4.71/5.04 thf(fact_1649_card__psubset,axiom,
% 4.71/5.04 ! [B2: set_complex,A2: set_complex] :
% 4.71/5.04 ( ( finite3207457112153483333omplex @ B2 )
% 4.71/5.04 => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 4.71/5.04 => ( ( ord_less_nat @ ( finite_card_complex @ A2 ) @ ( finite_card_complex @ B2 ) )
% 4.71/5.04 => ( ord_less_set_complex @ A2 @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_psubset
% 4.71/5.04 thf(fact_1650_card__psubset,axiom,
% 4.71/5.04 ! [B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.04 ( ( finite6177210948735845034at_nat @ B2 )
% 4.71/5.04 => ( ( ord_le3146513528884898305at_nat @ A2 @ B2 )
% 4.71/5.04 => ( ( ord_less_nat @ ( finite711546835091564841at_nat @ A2 ) @ ( finite711546835091564841at_nat @ B2 ) )
% 4.71/5.04 => ( ord_le7866589430770878221at_nat @ A2 @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_psubset
% 4.71/5.04 thf(fact_1651_card__psubset,axiom,
% 4.71/5.04 ! [B2: set_Extended_enat,A2: set_Extended_enat] :
% 4.71/5.04 ( ( finite4001608067531595151d_enat @ B2 )
% 4.71/5.04 => ( ( ord_le7203529160286727270d_enat @ A2 @ B2 )
% 4.71/5.04 => ( ( ord_less_nat @ ( finite121521170596916366d_enat @ A2 ) @ ( finite121521170596916366d_enat @ B2 ) )
% 4.71/5.04 => ( ord_le2529575680413868914d_enat @ A2 @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_psubset
% 4.71/5.04 thf(fact_1652_card__psubset,axiom,
% 4.71/5.04 ! [B2: set_int,A2: set_int] :
% 4.71/5.04 ( ( finite_finite_int @ B2 )
% 4.71/5.04 => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 4.71/5.04 => ( ( ord_less_nat @ ( finite_card_int @ A2 ) @ ( finite_card_int @ B2 ) )
% 4.71/5.04 => ( ord_less_set_int @ A2 @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % card_psubset
% 4.71/5.04 thf(fact_1653_finite__enumerate__mono,axiom,
% 4.71/5.04 ! [M2: nat,N: nat,S2: set_Extended_enat] :
% 4.71/5.04 ( ( ord_less_nat @ M2 @ N )
% 4.71/5.04 => ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.04 => ( ( ord_less_nat @ N @ ( finite121521170596916366d_enat @ S2 ) )
% 4.71/5.04 => ( ord_le72135733267957522d_enat @ ( infini7641415182203889163d_enat @ S2 @ M2 ) @ ( infini7641415182203889163d_enat @ S2 @ N ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % finite_enumerate_mono
% 4.71/5.04 thf(fact_1654_finite__enumerate__mono,axiom,
% 4.71/5.04 ! [M2: nat,N: nat,S2: set_nat] :
% 4.71/5.04 ( ( ord_less_nat @ M2 @ N )
% 4.71/5.04 => ( ( finite_finite_nat @ S2 )
% 4.71/5.04 => ( ( ord_less_nat @ N @ ( finite_card_nat @ S2 ) )
% 4.71/5.04 => ( ord_less_nat @ ( infini8530281810654367211te_nat @ S2 @ M2 ) @ ( infini8530281810654367211te_nat @ S2 @ N ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % finite_enumerate_mono
% 4.71/5.04 thf(fact_1655_nat__approx__posE,axiom,
% 4.71/5.04 ! [E2: real] :
% 4.71/5.04 ( ( ord_less_real @ zero_zero_real @ E2 )
% 4.71/5.04 => ~ ! [N2: nat] :
% 4.71/5.04 ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ E2 ) ) ).
% 4.71/5.04
% 4.71/5.04 % nat_approx_posE
% 4.71/5.04 thf(fact_1656_nat__approx__posE,axiom,
% 4.71/5.04 ! [E2: rat] :
% 4.71/5.04 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 4.71/5.04 => ~ ! [N2: nat] :
% 4.71/5.04 ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N2 ) ) ) @ E2 ) ) ).
% 4.71/5.04
% 4.71/5.04 % nat_approx_posE
% 4.71/5.04 thf(fact_1657_finite__enumerate__step,axiom,
% 4.71/5.04 ! [S2: set_Extended_enat,N: nat] :
% 4.71/5.04 ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.04 => ( ( ord_less_nat @ ( suc @ N ) @ ( finite121521170596916366d_enat @ S2 ) )
% 4.71/5.04 => ( ord_le72135733267957522d_enat @ ( infini7641415182203889163d_enat @ S2 @ N ) @ ( infini7641415182203889163d_enat @ S2 @ ( suc @ N ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % finite_enumerate_step
% 4.71/5.04 thf(fact_1658_finite__enumerate__step,axiom,
% 4.71/5.04 ! [S2: set_nat,N: nat] :
% 4.71/5.04 ( ( finite_finite_nat @ S2 )
% 4.71/5.04 => ( ( ord_less_nat @ ( suc @ N ) @ ( finite_card_nat @ S2 ) )
% 4.71/5.04 => ( ord_less_nat @ ( infini8530281810654367211te_nat @ S2 @ N ) @ ( infini8530281810654367211te_nat @ S2 @ ( suc @ N ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % finite_enumerate_step
% 4.71/5.04 thf(fact_1659_le__divide__eq__1__pos,axiom,
% 4.71/5.04 ! [A: real,B: real] :
% 4.71/5.04 ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.04 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 4.71/5.04 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % le_divide_eq_1_pos
% 4.71/5.04 thf(fact_1660_le__divide__eq__1__pos,axiom,
% 4.71/5.04 ! [A: rat,B: rat] :
% 4.71/5.04 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.04 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 4.71/5.04 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % le_divide_eq_1_pos
% 4.71/5.04 thf(fact_1661_le__divide__eq__1__neg,axiom,
% 4.71/5.04 ! [A: real,B: real] :
% 4.71/5.04 ( ( ord_less_real @ A @ zero_zero_real )
% 4.71/5.04 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 4.71/5.04 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % le_divide_eq_1_neg
% 4.71/5.04 thf(fact_1662_le__divide__eq__1__neg,axiom,
% 4.71/5.04 ! [A: rat,B: rat] :
% 4.71/5.04 ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.71/5.04 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 4.71/5.04 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % le_divide_eq_1_neg
% 4.71/5.04 thf(fact_1663_divide__le__eq__1__pos,axiom,
% 4.71/5.04 ! [A: real,B: real] :
% 4.71/5.04 ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.04 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 4.71/5.04 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_le_eq_1_pos
% 4.71/5.04 thf(fact_1664_divide__le__eq__1__pos,axiom,
% 4.71/5.04 ! [A: rat,B: rat] :
% 4.71/5.04 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.04 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 4.71/5.04 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_le_eq_1_pos
% 4.71/5.04 thf(fact_1665_divide__le__eq__1__neg,axiom,
% 4.71/5.04 ! [A: real,B: real] :
% 4.71/5.04 ( ( ord_less_real @ A @ zero_zero_real )
% 4.71/5.04 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 4.71/5.04 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_le_eq_1_neg
% 4.71/5.04 thf(fact_1666_divide__le__eq__1__neg,axiom,
% 4.71/5.04 ! [A: rat,B: rat] :
% 4.71/5.04 ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.71/5.04 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 4.71/5.04 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_le_eq_1_neg
% 4.71/5.04 thf(fact_1667_zero__less__divide__1__iff,axiom,
% 4.71/5.04 ! [A: rat] :
% 4.71/5.04 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 4.71/5.04 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 4.71/5.04
% 4.71/5.04 % zero_less_divide_1_iff
% 4.71/5.04 thf(fact_1668_zero__less__divide__1__iff,axiom,
% 4.71/5.04 ! [A: real] :
% 4.71/5.04 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 4.71/5.04 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 4.71/5.04
% 4.71/5.04 % zero_less_divide_1_iff
% 4.71/5.04 thf(fact_1669_less__divide__eq__1__pos,axiom,
% 4.71/5.04 ! [A: rat,B: rat] :
% 4.71/5.04 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.04 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 4.71/5.04 = ( ord_less_rat @ A @ B ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % less_divide_eq_1_pos
% 4.71/5.04 thf(fact_1670_less__divide__eq__1__pos,axiom,
% 4.71/5.04 ! [A: real,B: real] :
% 4.71/5.04 ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.04 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 4.71/5.04 = ( ord_less_real @ A @ B ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % less_divide_eq_1_pos
% 4.71/5.04 thf(fact_1671_less__divide__eq__1__neg,axiom,
% 4.71/5.04 ! [A: rat,B: rat] :
% 4.71/5.04 ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.71/5.04 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 4.71/5.04 = ( ord_less_rat @ B @ A ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % less_divide_eq_1_neg
% 4.71/5.04 thf(fact_1672_less__divide__eq__1__neg,axiom,
% 4.71/5.04 ! [A: real,B: real] :
% 4.71/5.04 ( ( ord_less_real @ A @ zero_zero_real )
% 4.71/5.04 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 4.71/5.04 = ( ord_less_real @ B @ A ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % less_divide_eq_1_neg
% 4.71/5.04 thf(fact_1673_divide__less__eq__1__pos,axiom,
% 4.71/5.04 ! [A: rat,B: rat] :
% 4.71/5.04 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.04 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 4.71/5.04 = ( ord_less_rat @ B @ A ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_less_eq_1_pos
% 4.71/5.04 thf(fact_1674_divide__less__eq__1__pos,axiom,
% 4.71/5.04 ! [A: real,B: real] :
% 4.71/5.04 ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.04 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 4.71/5.04 = ( ord_less_real @ B @ A ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_less_eq_1_pos
% 4.71/5.04 thf(fact_1675_divide__less__eq__1__neg,axiom,
% 4.71/5.04 ! [A: rat,B: rat] :
% 4.71/5.04 ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.71/5.04 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 4.71/5.04 = ( ord_less_rat @ A @ B ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_less_eq_1_neg
% 4.71/5.04 thf(fact_1676_divide__less__eq__1__neg,axiom,
% 4.71/5.04 ! [A: real,B: real] :
% 4.71/5.04 ( ( ord_less_real @ A @ zero_zero_real )
% 4.71/5.04 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 4.71/5.04 = ( ord_less_real @ A @ B ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_less_eq_1_neg
% 4.71/5.04 thf(fact_1677_divide__less__0__1__iff,axiom,
% 4.71/5.04 ! [A: rat] :
% 4.71/5.04 ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 4.71/5.04 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_less_0_1_iff
% 4.71/5.04 thf(fact_1678_divide__less__0__1__iff,axiom,
% 4.71/5.04 ! [A: real] :
% 4.71/5.04 ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 4.71/5.04 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_less_0_1_iff
% 4.71/5.04 thf(fact_1679_Diff__idemp,axiom,
% 4.71/5.04 ! [A2: set_nat,B2: set_nat] :
% 4.71/5.04 ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ B2 )
% 4.71/5.04 = ( minus_minus_set_nat @ A2 @ B2 ) ) ).
% 4.71/5.04
% 4.71/5.04 % Diff_idemp
% 4.71/5.04 thf(fact_1680_Diff__iff,axiom,
% 4.71/5.04 ! [C: $o,A2: set_o,B2: set_o] :
% 4.71/5.04 ( ( member_o @ C @ ( minus_minus_set_o @ A2 @ B2 ) )
% 4.71/5.04 = ( ( member_o @ C @ A2 )
% 4.71/5.04 & ~ ( member_o @ C @ B2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % Diff_iff
% 4.71/5.04 thf(fact_1681_Diff__iff,axiom,
% 4.71/5.04 ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 4.71/5.04 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B2 ) )
% 4.71/5.04 = ( ( member_set_nat @ C @ A2 )
% 4.71/5.04 & ~ ( member_set_nat @ C @ B2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % Diff_iff
% 4.71/5.04 thf(fact_1682_Diff__iff,axiom,
% 4.71/5.04 ! [C: set_nat_rat,A2: set_set_nat_rat,B2: set_set_nat_rat] :
% 4.71/5.04 ( ( member_set_nat_rat @ C @ ( minus_1626877696091177228at_rat @ A2 @ B2 ) )
% 4.71/5.04 = ( ( member_set_nat_rat @ C @ A2 )
% 4.71/5.04 & ~ ( member_set_nat_rat @ C @ B2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % Diff_iff
% 4.71/5.04 thf(fact_1683_Diff__iff,axiom,
% 4.71/5.04 ! [C: int,A2: set_int,B2: set_int] :
% 4.71/5.04 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B2 ) )
% 4.71/5.04 = ( ( member_int @ C @ A2 )
% 4.71/5.04 & ~ ( member_int @ C @ B2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % Diff_iff
% 4.71/5.04 thf(fact_1684_Diff__iff,axiom,
% 4.71/5.04 ! [C: nat,A2: set_nat,B2: set_nat] :
% 4.71/5.04 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 4.71/5.04 = ( ( member_nat @ C @ A2 )
% 4.71/5.04 & ~ ( member_nat @ C @ B2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % Diff_iff
% 4.71/5.04 thf(fact_1685_DiffI,axiom,
% 4.71/5.04 ! [C: $o,A2: set_o,B2: set_o] :
% 4.71/5.04 ( ( member_o @ C @ A2 )
% 4.71/5.04 => ( ~ ( member_o @ C @ B2 )
% 4.71/5.04 => ( member_o @ C @ ( minus_minus_set_o @ A2 @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % DiffI
% 4.71/5.04 thf(fact_1686_DiffI,axiom,
% 4.71/5.04 ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 4.71/5.04 ( ( member_set_nat @ C @ A2 )
% 4.71/5.04 => ( ~ ( member_set_nat @ C @ B2 )
% 4.71/5.04 => ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % DiffI
% 4.71/5.04 thf(fact_1687_DiffI,axiom,
% 4.71/5.04 ! [C: set_nat_rat,A2: set_set_nat_rat,B2: set_set_nat_rat] :
% 4.71/5.04 ( ( member_set_nat_rat @ C @ A2 )
% 4.71/5.04 => ( ~ ( member_set_nat_rat @ C @ B2 )
% 4.71/5.04 => ( member_set_nat_rat @ C @ ( minus_1626877696091177228at_rat @ A2 @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % DiffI
% 4.71/5.04 thf(fact_1688_DiffI,axiom,
% 4.71/5.04 ! [C: int,A2: set_int,B2: set_int] :
% 4.71/5.04 ( ( member_int @ C @ A2 )
% 4.71/5.04 => ( ~ ( member_int @ C @ B2 )
% 4.71/5.04 => ( member_int @ C @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % DiffI
% 4.71/5.04 thf(fact_1689_DiffI,axiom,
% 4.71/5.04 ! [C: nat,A2: set_nat,B2: set_nat] :
% 4.71/5.04 ( ( member_nat @ C @ A2 )
% 4.71/5.04 => ( ~ ( member_nat @ C @ B2 )
% 4.71/5.04 => ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % DiffI
% 4.71/5.04 thf(fact_1690_divide__eq__0__iff,axiom,
% 4.71/5.04 ! [A: rat,B: rat] :
% 4.71/5.04 ( ( ( divide_divide_rat @ A @ B )
% 4.71/5.04 = zero_zero_rat )
% 4.71/5.04 = ( ( A = zero_zero_rat )
% 4.71/5.04 | ( B = zero_zero_rat ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_eq_0_iff
% 4.71/5.04 thf(fact_1691_divide__eq__0__iff,axiom,
% 4.71/5.04 ! [A: real,B: real] :
% 4.71/5.04 ( ( ( divide_divide_real @ A @ B )
% 4.71/5.04 = zero_zero_real )
% 4.71/5.04 = ( ( A = zero_zero_real )
% 4.71/5.04 | ( B = zero_zero_real ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_eq_0_iff
% 4.71/5.04 thf(fact_1692_divide__cancel__left,axiom,
% 4.71/5.04 ! [C: rat,A: rat,B: rat] :
% 4.71/5.04 ( ( ( divide_divide_rat @ C @ A )
% 4.71/5.04 = ( divide_divide_rat @ C @ B ) )
% 4.71/5.04 = ( ( C = zero_zero_rat )
% 4.71/5.04 | ( A = B ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_cancel_left
% 4.71/5.04 thf(fact_1693_divide__cancel__left,axiom,
% 4.71/5.04 ! [C: real,A: real,B: real] :
% 4.71/5.04 ( ( ( divide_divide_real @ C @ A )
% 4.71/5.04 = ( divide_divide_real @ C @ B ) )
% 4.71/5.04 = ( ( C = zero_zero_real )
% 4.71/5.04 | ( A = B ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_cancel_left
% 4.71/5.04 thf(fact_1694_divide__cancel__right,axiom,
% 4.71/5.04 ! [A: rat,C: rat,B: rat] :
% 4.71/5.04 ( ( ( divide_divide_rat @ A @ C )
% 4.71/5.04 = ( divide_divide_rat @ B @ C ) )
% 4.71/5.04 = ( ( C = zero_zero_rat )
% 4.71/5.04 | ( A = B ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_cancel_right
% 4.71/5.04 thf(fact_1695_divide__cancel__right,axiom,
% 4.71/5.04 ! [A: real,C: real,B: real] :
% 4.71/5.04 ( ( ( divide_divide_real @ A @ C )
% 4.71/5.04 = ( divide_divide_real @ B @ C ) )
% 4.71/5.04 = ( ( C = zero_zero_real )
% 4.71/5.04 | ( A = B ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_cancel_right
% 4.71/5.04 thf(fact_1696_division__ring__divide__zero,axiom,
% 4.71/5.04 ! [A: rat] :
% 4.71/5.04 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 4.71/5.04 = zero_zero_rat ) ).
% 4.71/5.04
% 4.71/5.04 % division_ring_divide_zero
% 4.71/5.04 thf(fact_1697_division__ring__divide__zero,axiom,
% 4.71/5.04 ! [A: real] :
% 4.71/5.04 ( ( divide_divide_real @ A @ zero_zero_real )
% 4.71/5.04 = zero_zero_real ) ).
% 4.71/5.04
% 4.71/5.04 % division_ring_divide_zero
% 4.71/5.04 thf(fact_1698_divide__eq__1__iff,axiom,
% 4.71/5.04 ! [A: complex,B: complex] :
% 4.71/5.04 ( ( ( divide1717551699836669952omplex @ A @ B )
% 4.71/5.04 = one_one_complex )
% 4.71/5.04 = ( ( B != zero_zero_complex )
% 4.71/5.04 & ( A = B ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_eq_1_iff
% 4.71/5.04 thf(fact_1699_divide__eq__1__iff,axiom,
% 4.71/5.04 ! [A: rat,B: rat] :
% 4.71/5.04 ( ( ( divide_divide_rat @ A @ B )
% 4.71/5.04 = one_one_rat )
% 4.71/5.04 = ( ( B != zero_zero_rat )
% 4.71/5.04 & ( A = B ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_eq_1_iff
% 4.71/5.04 thf(fact_1700_divide__eq__1__iff,axiom,
% 4.71/5.04 ! [A: real,B: real] :
% 4.71/5.04 ( ( ( divide_divide_real @ A @ B )
% 4.71/5.04 = one_one_real )
% 4.71/5.04 = ( ( B != zero_zero_real )
% 4.71/5.04 & ( A = B ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_eq_1_iff
% 4.71/5.04 thf(fact_1701_one__eq__divide__iff,axiom,
% 4.71/5.04 ! [A: complex,B: complex] :
% 4.71/5.04 ( ( one_one_complex
% 4.71/5.04 = ( divide1717551699836669952omplex @ A @ B ) )
% 4.71/5.04 = ( ( B != zero_zero_complex )
% 4.71/5.04 & ( A = B ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % one_eq_divide_iff
% 4.71/5.04 thf(fact_1702_one__eq__divide__iff,axiom,
% 4.71/5.04 ! [A: rat,B: rat] :
% 4.71/5.04 ( ( one_one_rat
% 4.71/5.04 = ( divide_divide_rat @ A @ B ) )
% 4.71/5.04 = ( ( B != zero_zero_rat )
% 4.71/5.04 & ( A = B ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % one_eq_divide_iff
% 4.71/5.04 thf(fact_1703_one__eq__divide__iff,axiom,
% 4.71/5.04 ! [A: real,B: real] :
% 4.71/5.04 ( ( one_one_real
% 4.71/5.04 = ( divide_divide_real @ A @ B ) )
% 4.71/5.04 = ( ( B != zero_zero_real )
% 4.71/5.04 & ( A = B ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % one_eq_divide_iff
% 4.71/5.04 thf(fact_1704_divide__self,axiom,
% 4.71/5.04 ! [A: complex] :
% 4.71/5.04 ( ( A != zero_zero_complex )
% 4.71/5.04 => ( ( divide1717551699836669952omplex @ A @ A )
% 4.71/5.04 = one_one_complex ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_self
% 4.71/5.04 thf(fact_1705_divide__self,axiom,
% 4.71/5.04 ! [A: rat] :
% 4.71/5.04 ( ( A != zero_zero_rat )
% 4.71/5.04 => ( ( divide_divide_rat @ A @ A )
% 4.71/5.04 = one_one_rat ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_self
% 4.71/5.04 thf(fact_1706_divide__self,axiom,
% 4.71/5.04 ! [A: real] :
% 4.71/5.04 ( ( A != zero_zero_real )
% 4.71/5.04 => ( ( divide_divide_real @ A @ A )
% 4.71/5.04 = one_one_real ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_self
% 4.71/5.04 thf(fact_1707_divide__self__if,axiom,
% 4.71/5.04 ! [A: complex] :
% 4.71/5.04 ( ( ( A = zero_zero_complex )
% 4.71/5.04 => ( ( divide1717551699836669952omplex @ A @ A )
% 4.71/5.04 = zero_zero_complex ) )
% 4.71/5.04 & ( ( A != zero_zero_complex )
% 4.71/5.04 => ( ( divide1717551699836669952omplex @ A @ A )
% 4.71/5.04 = one_one_complex ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_self_if
% 4.71/5.04 thf(fact_1708_divide__self__if,axiom,
% 4.71/5.04 ! [A: rat] :
% 4.71/5.04 ( ( ( A = zero_zero_rat )
% 4.71/5.04 => ( ( divide_divide_rat @ A @ A )
% 4.71/5.04 = zero_zero_rat ) )
% 4.71/5.04 & ( ( A != zero_zero_rat )
% 4.71/5.04 => ( ( divide_divide_rat @ A @ A )
% 4.71/5.04 = one_one_rat ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_self_if
% 4.71/5.04 thf(fact_1709_divide__self__if,axiom,
% 4.71/5.04 ! [A: real] :
% 4.71/5.04 ( ( ( A = zero_zero_real )
% 4.71/5.04 => ( ( divide_divide_real @ A @ A )
% 4.71/5.04 = zero_zero_real ) )
% 4.71/5.04 & ( ( A != zero_zero_real )
% 4.71/5.04 => ( ( divide_divide_real @ A @ A )
% 4.71/5.04 = one_one_real ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_self_if
% 4.71/5.04 thf(fact_1710_divide__eq__eq__1,axiom,
% 4.71/5.04 ! [B: rat,A: rat] :
% 4.71/5.04 ( ( ( divide_divide_rat @ B @ A )
% 4.71/5.04 = one_one_rat )
% 4.71/5.04 = ( ( A != zero_zero_rat )
% 4.71/5.04 & ( A = B ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_eq_eq_1
% 4.71/5.04 thf(fact_1711_divide__eq__eq__1,axiom,
% 4.71/5.04 ! [B: real,A: real] :
% 4.71/5.04 ( ( ( divide_divide_real @ B @ A )
% 4.71/5.04 = one_one_real )
% 4.71/5.04 = ( ( A != zero_zero_real )
% 4.71/5.04 & ( A = B ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_eq_eq_1
% 4.71/5.04 thf(fact_1712_eq__divide__eq__1,axiom,
% 4.71/5.04 ! [B: rat,A: rat] :
% 4.71/5.04 ( ( one_one_rat
% 4.71/5.04 = ( divide_divide_rat @ B @ A ) )
% 4.71/5.04 = ( ( A != zero_zero_rat )
% 4.71/5.04 & ( A = B ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % eq_divide_eq_1
% 4.71/5.04 thf(fact_1713_eq__divide__eq__1,axiom,
% 4.71/5.04 ! [B: real,A: real] :
% 4.71/5.04 ( ( one_one_real
% 4.71/5.04 = ( divide_divide_real @ B @ A ) )
% 4.71/5.04 = ( ( A != zero_zero_real )
% 4.71/5.04 & ( A = B ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % eq_divide_eq_1
% 4.71/5.04 thf(fact_1714_one__divide__eq__0__iff,axiom,
% 4.71/5.04 ! [A: rat] :
% 4.71/5.04 ( ( ( divide_divide_rat @ one_one_rat @ A )
% 4.71/5.04 = zero_zero_rat )
% 4.71/5.04 = ( A = zero_zero_rat ) ) ).
% 4.71/5.04
% 4.71/5.04 % one_divide_eq_0_iff
% 4.71/5.04 thf(fact_1715_one__divide__eq__0__iff,axiom,
% 4.71/5.04 ! [A: real] :
% 4.71/5.04 ( ( ( divide_divide_real @ one_one_real @ A )
% 4.71/5.04 = zero_zero_real )
% 4.71/5.04 = ( A = zero_zero_real ) ) ).
% 4.71/5.04
% 4.71/5.04 % one_divide_eq_0_iff
% 4.71/5.04 thf(fact_1716_zero__eq__1__divide__iff,axiom,
% 4.71/5.04 ! [A: rat] :
% 4.71/5.04 ( ( zero_zero_rat
% 4.71/5.04 = ( divide_divide_rat @ one_one_rat @ A ) )
% 4.71/5.04 = ( A = zero_zero_rat ) ) ).
% 4.71/5.04
% 4.71/5.04 % zero_eq_1_divide_iff
% 4.71/5.04 thf(fact_1717_zero__eq__1__divide__iff,axiom,
% 4.71/5.04 ! [A: real] :
% 4.71/5.04 ( ( zero_zero_real
% 4.71/5.04 = ( divide_divide_real @ one_one_real @ A ) )
% 4.71/5.04 = ( A = zero_zero_real ) ) ).
% 4.71/5.04
% 4.71/5.04 % zero_eq_1_divide_iff
% 4.71/5.04 thf(fact_1718_divide__le__0__1__iff,axiom,
% 4.71/5.04 ! [A: real] :
% 4.71/5.04 ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 4.71/5.04 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_le_0_1_iff
% 4.71/5.04 thf(fact_1719_divide__le__0__1__iff,axiom,
% 4.71/5.04 ! [A: rat] :
% 4.71/5.04 ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 4.71/5.04 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_le_0_1_iff
% 4.71/5.04 thf(fact_1720_zero__le__divide__1__iff,axiom,
% 4.71/5.04 ! [A: real] :
% 4.71/5.04 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 4.71/5.04 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 4.71/5.04
% 4.71/5.04 % zero_le_divide_1_iff
% 4.71/5.04 thf(fact_1721_zero__le__divide__1__iff,axiom,
% 4.71/5.04 ! [A: rat] :
% 4.71/5.04 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 4.71/5.04 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 4.71/5.04
% 4.71/5.04 % zero_le_divide_1_iff
% 4.71/5.04 thf(fact_1722_DiffD2,axiom,
% 4.71/5.04 ! [C: $o,A2: set_o,B2: set_o] :
% 4.71/5.04 ( ( member_o @ C @ ( minus_minus_set_o @ A2 @ B2 ) )
% 4.71/5.04 => ~ ( member_o @ C @ B2 ) ) ).
% 4.71/5.04
% 4.71/5.04 % DiffD2
% 4.71/5.04 thf(fact_1723_DiffD2,axiom,
% 4.71/5.04 ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 4.71/5.04 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B2 ) )
% 4.71/5.04 => ~ ( member_set_nat @ C @ B2 ) ) ).
% 4.71/5.04
% 4.71/5.04 % DiffD2
% 4.71/5.04 thf(fact_1724_DiffD2,axiom,
% 4.71/5.04 ! [C: set_nat_rat,A2: set_set_nat_rat,B2: set_set_nat_rat] :
% 4.71/5.04 ( ( member_set_nat_rat @ C @ ( minus_1626877696091177228at_rat @ A2 @ B2 ) )
% 4.71/5.04 => ~ ( member_set_nat_rat @ C @ B2 ) ) ).
% 4.71/5.04
% 4.71/5.04 % DiffD2
% 4.71/5.04 thf(fact_1725_DiffD2,axiom,
% 4.71/5.04 ! [C: int,A2: set_int,B2: set_int] :
% 4.71/5.04 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B2 ) )
% 4.71/5.04 => ~ ( member_int @ C @ B2 ) ) ).
% 4.71/5.04
% 4.71/5.04 % DiffD2
% 4.71/5.04 thf(fact_1726_DiffD2,axiom,
% 4.71/5.04 ! [C: nat,A2: set_nat,B2: set_nat] :
% 4.71/5.04 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 4.71/5.04 => ~ ( member_nat @ C @ B2 ) ) ).
% 4.71/5.04
% 4.71/5.04 % DiffD2
% 4.71/5.04 thf(fact_1727_DiffD1,axiom,
% 4.71/5.04 ! [C: $o,A2: set_o,B2: set_o] :
% 4.71/5.04 ( ( member_o @ C @ ( minus_minus_set_o @ A2 @ B2 ) )
% 4.71/5.04 => ( member_o @ C @ A2 ) ) ).
% 4.71/5.04
% 4.71/5.04 % DiffD1
% 4.71/5.04 thf(fact_1728_DiffD1,axiom,
% 4.71/5.04 ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 4.71/5.04 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B2 ) )
% 4.71/5.04 => ( member_set_nat @ C @ A2 ) ) ).
% 4.71/5.04
% 4.71/5.04 % DiffD1
% 4.71/5.04 thf(fact_1729_DiffD1,axiom,
% 4.71/5.04 ! [C: set_nat_rat,A2: set_set_nat_rat,B2: set_set_nat_rat] :
% 4.71/5.04 ( ( member_set_nat_rat @ C @ ( minus_1626877696091177228at_rat @ A2 @ B2 ) )
% 4.71/5.04 => ( member_set_nat_rat @ C @ A2 ) ) ).
% 4.71/5.04
% 4.71/5.04 % DiffD1
% 4.71/5.04 thf(fact_1730_DiffD1,axiom,
% 4.71/5.04 ! [C: int,A2: set_int,B2: set_int] :
% 4.71/5.04 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B2 ) )
% 4.71/5.04 => ( member_int @ C @ A2 ) ) ).
% 4.71/5.04
% 4.71/5.04 % DiffD1
% 4.71/5.04 thf(fact_1731_DiffD1,axiom,
% 4.71/5.04 ! [C: nat,A2: set_nat,B2: set_nat] :
% 4.71/5.04 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 4.71/5.04 => ( member_nat @ C @ A2 ) ) ).
% 4.71/5.04
% 4.71/5.04 % DiffD1
% 4.71/5.04 thf(fact_1732_DiffE,axiom,
% 4.71/5.04 ! [C: $o,A2: set_o,B2: set_o] :
% 4.71/5.04 ( ( member_o @ C @ ( minus_minus_set_o @ A2 @ B2 ) )
% 4.71/5.04 => ~ ( ( member_o @ C @ A2 )
% 4.71/5.04 => ( member_o @ C @ B2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % DiffE
% 4.71/5.04 thf(fact_1733_DiffE,axiom,
% 4.71/5.04 ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 4.71/5.04 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B2 ) )
% 4.71/5.04 => ~ ( ( member_set_nat @ C @ A2 )
% 4.71/5.04 => ( member_set_nat @ C @ B2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % DiffE
% 4.71/5.04 thf(fact_1734_DiffE,axiom,
% 4.71/5.04 ! [C: set_nat_rat,A2: set_set_nat_rat,B2: set_set_nat_rat] :
% 4.71/5.04 ( ( member_set_nat_rat @ C @ ( minus_1626877696091177228at_rat @ A2 @ B2 ) )
% 4.71/5.04 => ~ ( ( member_set_nat_rat @ C @ A2 )
% 4.71/5.04 => ( member_set_nat_rat @ C @ B2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % DiffE
% 4.71/5.04 thf(fact_1735_DiffE,axiom,
% 4.71/5.04 ! [C: int,A2: set_int,B2: set_int] :
% 4.71/5.04 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B2 ) )
% 4.71/5.04 => ~ ( ( member_int @ C @ A2 )
% 4.71/5.04 => ( member_int @ C @ B2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % DiffE
% 4.71/5.04 thf(fact_1736_DiffE,axiom,
% 4.71/5.04 ! [C: nat,A2: set_nat,B2: set_nat] :
% 4.71/5.04 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 4.71/5.04 => ~ ( ( member_nat @ C @ A2 )
% 4.71/5.04 => ( member_nat @ C @ B2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % DiffE
% 4.71/5.04 thf(fact_1737_linordered__field__no__lb,axiom,
% 4.71/5.04 ! [X2: real] :
% 4.71/5.04 ? [Y3: real] : ( ord_less_real @ Y3 @ X2 ) ).
% 4.71/5.04
% 4.71/5.04 % linordered_field_no_lb
% 4.71/5.04 thf(fact_1738_linordered__field__no__lb,axiom,
% 4.71/5.04 ! [X2: rat] :
% 4.71/5.04 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X2 ) ).
% 4.71/5.04
% 4.71/5.04 % linordered_field_no_lb
% 4.71/5.04 thf(fact_1739_linordered__field__no__ub,axiom,
% 4.71/5.04 ! [X2: real] :
% 4.71/5.04 ? [X_1: real] : ( ord_less_real @ X2 @ X_1 ) ).
% 4.71/5.04
% 4.71/5.04 % linordered_field_no_ub
% 4.71/5.04 thf(fact_1740_linordered__field__no__ub,axiom,
% 4.71/5.04 ! [X2: rat] :
% 4.71/5.04 ? [X_1: rat] : ( ord_less_rat @ X2 @ X_1 ) ).
% 4.71/5.04
% 4.71/5.04 % linordered_field_no_ub
% 4.71/5.04 thf(fact_1741_divide__le__0__iff,axiom,
% 4.71/5.04 ! [A: real,B: real] :
% 4.71/5.04 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 4.71/5.04 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.04 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 4.71/5.04 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 4.71/5.04 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_le_0_iff
% 4.71/5.04 thf(fact_1742_divide__le__0__iff,axiom,
% 4.71/5.04 ! [A: rat,B: rat] :
% 4.71/5.04 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 4.71/5.04 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.04 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 4.71/5.04 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 4.71/5.04 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_le_0_iff
% 4.71/5.04 thf(fact_1743_divide__right__mono,axiom,
% 4.71/5.04 ! [A: real,B: real,C: real] :
% 4.71/5.04 ( ( ord_less_eq_real @ A @ B )
% 4.71/5.04 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.71/5.04 => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_right_mono
% 4.71/5.04 thf(fact_1744_divide__right__mono,axiom,
% 4.71/5.04 ! [A: rat,B: rat,C: rat] :
% 4.71/5.04 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.04 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.71/5.04 => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_right_mono
% 4.71/5.04 thf(fact_1745_zero__le__divide__iff,axiom,
% 4.71/5.04 ! [A: real,B: real] :
% 4.71/5.04 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 4.71/5.04 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.04 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 4.71/5.04 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 4.71/5.04 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % zero_le_divide_iff
% 4.71/5.04 thf(fact_1746_zero__le__divide__iff,axiom,
% 4.71/5.04 ! [A: rat,B: rat] :
% 4.71/5.04 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 4.71/5.04 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.04 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 4.71/5.04 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 4.71/5.04 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % zero_le_divide_iff
% 4.71/5.04 thf(fact_1747_divide__nonneg__nonneg,axiom,
% 4.71/5.04 ! [X: real,Y: real] :
% 4.71/5.04 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.04 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.71/5.04 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_nonneg_nonneg
% 4.71/5.04 thf(fact_1748_divide__nonneg__nonneg,axiom,
% 4.71/5.04 ! [X: rat,Y: rat] :
% 4.71/5.04 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 4.71/5.04 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 4.71/5.04 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_nonneg_nonneg
% 4.71/5.04 thf(fact_1749_divide__nonneg__nonpos,axiom,
% 4.71/5.04 ! [X: real,Y: real] :
% 4.71/5.04 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.04 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 4.71/5.04 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_nonneg_nonpos
% 4.71/5.04 thf(fact_1750_divide__nonneg__nonpos,axiom,
% 4.71/5.04 ! [X: rat,Y: rat] :
% 4.71/5.04 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 4.71/5.04 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 4.71/5.04 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_nonneg_nonpos
% 4.71/5.04 thf(fact_1751_divide__nonpos__nonneg,axiom,
% 4.71/5.04 ! [X: real,Y: real] :
% 4.71/5.04 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 4.71/5.04 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.71/5.04 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_nonpos_nonneg
% 4.71/5.04 thf(fact_1752_divide__nonpos__nonneg,axiom,
% 4.71/5.04 ! [X: rat,Y: rat] :
% 4.71/5.04 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 4.71/5.04 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 4.71/5.04 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_nonpos_nonneg
% 4.71/5.04 thf(fact_1753_divide__nonpos__nonpos,axiom,
% 4.71/5.04 ! [X: real,Y: real] :
% 4.71/5.04 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 4.71/5.04 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 4.71/5.04 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_nonpos_nonpos
% 4.71/5.04 thf(fact_1754_divide__nonpos__nonpos,axiom,
% 4.71/5.04 ! [X: rat,Y: rat] :
% 4.71/5.04 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 4.71/5.04 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 4.71/5.04 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_nonpos_nonpos
% 4.71/5.04 thf(fact_1755_divide__right__mono__neg,axiom,
% 4.71/5.04 ! [A: real,B: real,C: real] :
% 4.71/5.04 ( ( ord_less_eq_real @ A @ B )
% 4.71/5.04 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 4.71/5.04 => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_right_mono_neg
% 4.71/5.04 thf(fact_1756_divide__right__mono__neg,axiom,
% 4.71/5.04 ! [A: rat,B: rat,C: rat] :
% 4.71/5.04 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.04 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.71/5.04 => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_right_mono_neg
% 4.71/5.04 thf(fact_1757_divide__neg__neg,axiom,
% 4.71/5.04 ! [X: rat,Y: rat] :
% 4.71/5.04 ( ( ord_less_rat @ X @ zero_zero_rat )
% 4.71/5.04 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 4.71/5.04 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_neg_neg
% 4.71/5.04 thf(fact_1758_divide__neg__neg,axiom,
% 4.71/5.04 ! [X: real,Y: real] :
% 4.71/5.04 ( ( ord_less_real @ X @ zero_zero_real )
% 4.71/5.04 => ( ( ord_less_real @ Y @ zero_zero_real )
% 4.71/5.04 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_neg_neg
% 4.71/5.04 thf(fact_1759_divide__neg__pos,axiom,
% 4.71/5.04 ! [X: rat,Y: rat] :
% 4.71/5.04 ( ( ord_less_rat @ X @ zero_zero_rat )
% 4.71/5.04 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 4.71/5.04 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_neg_pos
% 4.71/5.04 thf(fact_1760_divide__neg__pos,axiom,
% 4.71/5.04 ! [X: real,Y: real] :
% 4.71/5.04 ( ( ord_less_real @ X @ zero_zero_real )
% 4.71/5.04 => ( ( ord_less_real @ zero_zero_real @ Y )
% 4.71/5.04 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_neg_pos
% 4.71/5.04 thf(fact_1761_divide__pos__neg,axiom,
% 4.71/5.04 ! [X: rat,Y: rat] :
% 4.71/5.04 ( ( ord_less_rat @ zero_zero_rat @ X )
% 4.71/5.04 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 4.71/5.04 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_pos_neg
% 4.71/5.04 thf(fact_1762_divide__pos__neg,axiom,
% 4.71/5.04 ! [X: real,Y: real] :
% 4.71/5.04 ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.04 => ( ( ord_less_real @ Y @ zero_zero_real )
% 4.71/5.04 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_pos_neg
% 4.71/5.04 thf(fact_1763_divide__pos__pos,axiom,
% 4.71/5.04 ! [X: rat,Y: rat] :
% 4.71/5.04 ( ( ord_less_rat @ zero_zero_rat @ X )
% 4.71/5.04 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 4.71/5.04 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_pos_pos
% 4.71/5.04 thf(fact_1764_divide__pos__pos,axiom,
% 4.71/5.04 ! [X: real,Y: real] :
% 4.71/5.04 ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.04 => ( ( ord_less_real @ zero_zero_real @ Y )
% 4.71/5.04 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_pos_pos
% 4.71/5.04 thf(fact_1765_divide__less__0__iff,axiom,
% 4.71/5.04 ! [A: rat,B: rat] :
% 4.71/5.04 ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 4.71/5.04 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.04 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 4.71/5.04 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.71/5.04 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_less_0_iff
% 4.71/5.04 thf(fact_1766_divide__less__0__iff,axiom,
% 4.71/5.04 ! [A: real,B: real] :
% 4.71/5.04 ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 4.71/5.04 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.04 & ( ord_less_real @ B @ zero_zero_real ) )
% 4.71/5.04 | ( ( ord_less_real @ A @ zero_zero_real )
% 4.71/5.04 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_less_0_iff
% 4.71/5.04 thf(fact_1767_divide__less__cancel,axiom,
% 4.71/5.04 ! [A: rat,C: rat,B: rat] :
% 4.71/5.04 ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 4.71/5.04 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.04 => ( ord_less_rat @ A @ B ) )
% 4.71/5.04 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.04 => ( ord_less_rat @ B @ A ) )
% 4.71/5.04 & ( C != zero_zero_rat ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_less_cancel
% 4.71/5.04 thf(fact_1768_divide__less__cancel,axiom,
% 4.71/5.04 ! [A: real,C: real,B: real] :
% 4.71/5.04 ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 4.71/5.04 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.04 => ( ord_less_real @ A @ B ) )
% 4.71/5.04 & ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.04 => ( ord_less_real @ B @ A ) )
% 4.71/5.04 & ( C != zero_zero_real ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_less_cancel
% 4.71/5.04 thf(fact_1769_zero__less__divide__iff,axiom,
% 4.71/5.04 ! [A: rat,B: rat] :
% 4.71/5.04 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 4.71/5.04 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.04 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 4.71/5.04 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.71/5.04 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % zero_less_divide_iff
% 4.71/5.04 thf(fact_1770_zero__less__divide__iff,axiom,
% 4.71/5.04 ! [A: real,B: real] :
% 4.71/5.04 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 4.71/5.04 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.04 & ( ord_less_real @ zero_zero_real @ B ) )
% 4.71/5.04 | ( ( ord_less_real @ A @ zero_zero_real )
% 4.71/5.04 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % zero_less_divide_iff
% 4.71/5.04 thf(fact_1771_divide__strict__right__mono,axiom,
% 4.71/5.04 ! [A: rat,B: rat,C: rat] :
% 4.71/5.04 ( ( ord_less_rat @ A @ B )
% 4.71/5.04 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.04 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_strict_right_mono
% 4.71/5.04 thf(fact_1772_divide__strict__right__mono,axiom,
% 4.71/5.04 ! [A: real,B: real,C: real] :
% 4.71/5.04 ( ( ord_less_real @ A @ B )
% 4.71/5.04 => ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.04 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_strict_right_mono
% 4.71/5.04 thf(fact_1773_divide__strict__right__mono__neg,axiom,
% 4.71/5.04 ! [B: rat,A: rat,C: rat] :
% 4.71/5.04 ( ( ord_less_rat @ B @ A )
% 4.71/5.04 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.04 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_strict_right_mono_neg
% 4.71/5.04 thf(fact_1774_divide__strict__right__mono__neg,axiom,
% 4.71/5.04 ! [B: real,A: real,C: real] :
% 4.71/5.04 ( ( ord_less_real @ B @ A )
% 4.71/5.04 => ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.04 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_strict_right_mono_neg
% 4.71/5.04 thf(fact_1775_right__inverse__eq,axiom,
% 4.71/5.04 ! [B: complex,A: complex] :
% 4.71/5.04 ( ( B != zero_zero_complex )
% 4.71/5.04 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 4.71/5.04 = one_one_complex )
% 4.71/5.04 = ( A = B ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % right_inverse_eq
% 4.71/5.04 thf(fact_1776_right__inverse__eq,axiom,
% 4.71/5.04 ! [B: rat,A: rat] :
% 4.71/5.04 ( ( B != zero_zero_rat )
% 4.71/5.04 => ( ( ( divide_divide_rat @ A @ B )
% 4.71/5.04 = one_one_rat )
% 4.71/5.04 = ( A = B ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % right_inverse_eq
% 4.71/5.04 thf(fact_1777_right__inverse__eq,axiom,
% 4.71/5.04 ! [B: real,A: real] :
% 4.71/5.04 ( ( B != zero_zero_real )
% 4.71/5.04 => ( ( ( divide_divide_real @ A @ B )
% 4.71/5.04 = one_one_real )
% 4.71/5.04 = ( A = B ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % right_inverse_eq
% 4.71/5.04 thf(fact_1778_frac__le,axiom,
% 4.71/5.04 ! [Y: real,X: real,W2: real,Z: real] :
% 4.71/5.04 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.71/5.04 => ( ( ord_less_eq_real @ X @ Y )
% 4.71/5.04 => ( ( ord_less_real @ zero_zero_real @ W2 )
% 4.71/5.04 => ( ( ord_less_eq_real @ W2 @ Z )
% 4.71/5.04 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W2 ) ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % frac_le
% 4.71/5.04 thf(fact_1779_frac__le,axiom,
% 4.71/5.04 ! [Y: rat,X: rat,W2: rat,Z: rat] :
% 4.71/5.04 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 4.71/5.04 => ( ( ord_less_eq_rat @ X @ Y )
% 4.71/5.04 => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 4.71/5.04 => ( ( ord_less_eq_rat @ W2 @ Z )
% 4.71/5.04 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % frac_le
% 4.71/5.04 thf(fact_1780_frac__less,axiom,
% 4.71/5.04 ! [X: real,Y: real,W2: real,Z: real] :
% 4.71/5.04 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.04 => ( ( ord_less_real @ X @ Y )
% 4.71/5.04 => ( ( ord_less_real @ zero_zero_real @ W2 )
% 4.71/5.04 => ( ( ord_less_eq_real @ W2 @ Z )
% 4.71/5.04 => ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W2 ) ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % frac_less
% 4.71/5.04 thf(fact_1781_frac__less,axiom,
% 4.71/5.04 ! [X: rat,Y: rat,W2: rat,Z: rat] :
% 4.71/5.04 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 4.71/5.04 => ( ( ord_less_rat @ X @ Y )
% 4.71/5.04 => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 4.71/5.04 => ( ( ord_less_eq_rat @ W2 @ Z )
% 4.71/5.04 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % frac_less
% 4.71/5.04 thf(fact_1782_frac__less2,axiom,
% 4.71/5.04 ! [X: real,Y: real,W2: real,Z: real] :
% 4.71/5.04 ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.04 => ( ( ord_less_eq_real @ X @ Y )
% 4.71/5.04 => ( ( ord_less_real @ zero_zero_real @ W2 )
% 4.71/5.04 => ( ( ord_less_real @ W2 @ Z )
% 4.71/5.04 => ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W2 ) ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % frac_less2
% 4.71/5.04 thf(fact_1783_frac__less2,axiom,
% 4.71/5.04 ! [X: rat,Y: rat,W2: rat,Z: rat] :
% 4.71/5.04 ( ( ord_less_rat @ zero_zero_rat @ X )
% 4.71/5.04 => ( ( ord_less_eq_rat @ X @ Y )
% 4.71/5.04 => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 4.71/5.04 => ( ( ord_less_rat @ W2 @ Z )
% 4.71/5.04 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % frac_less2
% 4.71/5.04 thf(fact_1784_divide__le__cancel,axiom,
% 4.71/5.04 ! [A: real,C: real,B: real] :
% 4.71/5.04 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 4.71/5.04 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.04 => ( ord_less_eq_real @ A @ B ) )
% 4.71/5.04 & ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.04 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_le_cancel
% 4.71/5.04 thf(fact_1785_divide__le__cancel,axiom,
% 4.71/5.04 ! [A: rat,C: rat,B: rat] :
% 4.71/5.04 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 4.71/5.04 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.04 => ( ord_less_eq_rat @ A @ B ) )
% 4.71/5.04 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.04 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_le_cancel
% 4.71/5.04 thf(fact_1786_divide__nonneg__neg,axiom,
% 4.71/5.04 ! [X: real,Y: real] :
% 4.71/5.04 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.04 => ( ( ord_less_real @ Y @ zero_zero_real )
% 4.71/5.04 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_nonneg_neg
% 4.71/5.04 thf(fact_1787_divide__nonneg__neg,axiom,
% 4.71/5.04 ! [X: rat,Y: rat] :
% 4.71/5.04 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 4.71/5.04 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 4.71/5.04 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_nonneg_neg
% 4.71/5.04 thf(fact_1788_divide__nonneg__pos,axiom,
% 4.71/5.04 ! [X: real,Y: real] :
% 4.71/5.04 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.04 => ( ( ord_less_real @ zero_zero_real @ Y )
% 4.71/5.04 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_nonneg_pos
% 4.71/5.04 thf(fact_1789_divide__nonneg__pos,axiom,
% 4.71/5.04 ! [X: rat,Y: rat] :
% 4.71/5.04 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 4.71/5.04 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 4.71/5.04 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_nonneg_pos
% 4.71/5.04 thf(fact_1790_divide__nonpos__neg,axiom,
% 4.71/5.04 ! [X: real,Y: real] :
% 4.71/5.04 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 4.71/5.04 => ( ( ord_less_real @ Y @ zero_zero_real )
% 4.71/5.04 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_nonpos_neg
% 4.71/5.04 thf(fact_1791_divide__nonpos__neg,axiom,
% 4.71/5.04 ! [X: rat,Y: rat] :
% 4.71/5.04 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 4.71/5.04 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 4.71/5.04 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_nonpos_neg
% 4.71/5.04 thf(fact_1792_divide__nonpos__pos,axiom,
% 4.71/5.04 ! [X: real,Y: real] :
% 4.71/5.04 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 4.71/5.04 => ( ( ord_less_real @ zero_zero_real @ Y )
% 4.71/5.04 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_nonpos_pos
% 4.71/5.04 thf(fact_1793_divide__nonpos__pos,axiom,
% 4.71/5.04 ! [X: rat,Y: rat] :
% 4.71/5.04 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 4.71/5.04 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 4.71/5.04 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_nonpos_pos
% 4.71/5.04 thf(fact_1794_divide__less__eq__1,axiom,
% 4.71/5.04 ! [B: rat,A: rat] :
% 4.71/5.04 ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 4.71/5.04 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.04 & ( ord_less_rat @ B @ A ) )
% 4.71/5.04 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.71/5.04 & ( ord_less_rat @ A @ B ) )
% 4.71/5.04 | ( A = zero_zero_rat ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_less_eq_1
% 4.71/5.04 thf(fact_1795_divide__less__eq__1,axiom,
% 4.71/5.04 ! [B: real,A: real] :
% 4.71/5.04 ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 4.71/5.04 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.04 & ( ord_less_real @ B @ A ) )
% 4.71/5.04 | ( ( ord_less_real @ A @ zero_zero_real )
% 4.71/5.04 & ( ord_less_real @ A @ B ) )
% 4.71/5.04 | ( A = zero_zero_real ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_less_eq_1
% 4.71/5.04 thf(fact_1796_less__divide__eq__1,axiom,
% 4.71/5.04 ! [B: rat,A: rat] :
% 4.71/5.04 ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 4.71/5.04 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.04 & ( ord_less_rat @ A @ B ) )
% 4.71/5.04 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.71/5.04 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % less_divide_eq_1
% 4.71/5.04 thf(fact_1797_less__divide__eq__1,axiom,
% 4.71/5.04 ! [B: real,A: real] :
% 4.71/5.04 ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 4.71/5.04 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.04 & ( ord_less_real @ A @ B ) )
% 4.71/5.04 | ( ( ord_less_real @ A @ zero_zero_real )
% 4.71/5.04 & ( ord_less_real @ B @ A ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % less_divide_eq_1
% 4.71/5.04 thf(fact_1798_divide__le__eq__1,axiom,
% 4.71/5.04 ! [B: real,A: real] :
% 4.71/5.04 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 4.71/5.04 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.04 & ( ord_less_eq_real @ B @ A ) )
% 4.71/5.04 | ( ( ord_less_real @ A @ zero_zero_real )
% 4.71/5.04 & ( ord_less_eq_real @ A @ B ) )
% 4.71/5.04 | ( A = zero_zero_real ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_le_eq_1
% 4.71/5.04 thf(fact_1799_divide__le__eq__1,axiom,
% 4.71/5.04 ! [B: rat,A: rat] :
% 4.71/5.04 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 4.71/5.04 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.04 & ( ord_less_eq_rat @ B @ A ) )
% 4.71/5.04 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.71/5.04 & ( ord_less_eq_rat @ A @ B ) )
% 4.71/5.04 | ( A = zero_zero_rat ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % divide_le_eq_1
% 4.71/5.04 thf(fact_1800_le__divide__eq__1,axiom,
% 4.71/5.04 ! [B: real,A: real] :
% 4.71/5.04 ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 4.71/5.04 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.04 & ( ord_less_eq_real @ A @ B ) )
% 4.71/5.04 | ( ( ord_less_real @ A @ zero_zero_real )
% 4.71/5.04 & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % le_divide_eq_1
% 4.71/5.04 thf(fact_1801_le__divide__eq__1,axiom,
% 4.71/5.04 ! [B: rat,A: rat] :
% 4.71/5.04 ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 4.71/5.04 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.04 & ( ord_less_eq_rat @ A @ B ) )
% 4.71/5.04 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.71/5.04 & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % le_divide_eq_1
% 4.71/5.04 thf(fact_1802_div__pos__pos__trivial,axiom,
% 4.71/5.04 ! [K: int,L: int] :
% 4.71/5.04 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 4.71/5.04 => ( ( ord_less_int @ K @ L )
% 4.71/5.04 => ( ( divide_divide_int @ K @ L )
% 4.71/5.04 = zero_zero_int ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % div_pos_pos_trivial
% 4.71/5.04 thf(fact_1803_div__neg__neg__trivial,axiom,
% 4.71/5.04 ! [K: int,L: int] :
% 4.71/5.04 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 4.71/5.04 => ( ( ord_less_int @ L @ K )
% 4.71/5.04 => ( ( divide_divide_int @ K @ L )
% 4.71/5.04 = zero_zero_int ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % div_neg_neg_trivial
% 4.71/5.04 thf(fact_1804_le__div__geq,axiom,
% 4.71/5.04 ! [N: nat,M2: nat] :
% 4.71/5.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.04 => ( ( ord_less_eq_nat @ N @ M2 )
% 4.71/5.04 => ( ( divide_divide_nat @ M2 @ N )
% 4.71/5.04 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M2 @ N ) @ N ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % le_div_geq
% 4.71/5.04 thf(fact_1805_div__less,axiom,
% 4.71/5.04 ! [M2: nat,N: nat] :
% 4.71/5.04 ( ( ord_less_nat @ M2 @ N )
% 4.71/5.04 => ( ( divide_divide_nat @ M2 @ N )
% 4.71/5.04 = zero_zero_nat ) ) ).
% 4.71/5.04
% 4.71/5.04 % div_less
% 4.71/5.04 thf(fact_1806_div__by__Suc__0,axiom,
% 4.71/5.04 ! [M2: nat] :
% 4.71/5.04 ( ( divide_divide_nat @ M2 @ ( suc @ zero_zero_nat ) )
% 4.71/5.04 = M2 ) ).
% 4.71/5.04
% 4.71/5.04 % div_by_Suc_0
% 4.71/5.04 thf(fact_1807_bits__div__by__1,axiom,
% 4.71/5.04 ! [A: int] :
% 4.71/5.04 ( ( divide_divide_int @ A @ one_one_int )
% 4.71/5.04 = A ) ).
% 4.71/5.04
% 4.71/5.04 % bits_div_by_1
% 4.71/5.04 thf(fact_1808_bits__div__by__1,axiom,
% 4.71/5.04 ! [A: nat] :
% 4.71/5.04 ( ( divide_divide_nat @ A @ one_one_nat )
% 4.71/5.04 = A ) ).
% 4.71/5.04
% 4.71/5.04 % bits_div_by_1
% 4.71/5.04 thf(fact_1809_bits__div__0,axiom,
% 4.71/5.04 ! [A: int] :
% 4.71/5.04 ( ( divide_divide_int @ zero_zero_int @ A )
% 4.71/5.04 = zero_zero_int ) ).
% 4.71/5.04
% 4.71/5.04 % bits_div_0
% 4.71/5.04 thf(fact_1810_bits__div__0,axiom,
% 4.71/5.04 ! [A: nat] :
% 4.71/5.04 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 4.71/5.04 = zero_zero_nat ) ).
% 4.71/5.04
% 4.71/5.04 % bits_div_0
% 4.71/5.04 thf(fact_1811_bits__div__by__0,axiom,
% 4.71/5.04 ! [A: int] :
% 4.71/5.04 ( ( divide_divide_int @ A @ zero_zero_int )
% 4.71/5.04 = zero_zero_int ) ).
% 4.71/5.04
% 4.71/5.04 % bits_div_by_0
% 4.71/5.04 thf(fact_1812_bits__div__by__0,axiom,
% 4.71/5.04 ! [A: nat] :
% 4.71/5.04 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 4.71/5.04 = zero_zero_nat ) ).
% 4.71/5.04
% 4.71/5.04 % bits_div_by_0
% 4.71/5.04 thf(fact_1813_div__geq,axiom,
% 4.71/5.04 ! [N: nat,M2: nat] :
% 4.71/5.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.04 => ( ~ ( ord_less_nat @ M2 @ N )
% 4.71/5.04 => ( ( divide_divide_nat @ M2 @ N )
% 4.71/5.04 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M2 @ N ) @ N ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % div_geq
% 4.71/5.04 thf(fact_1814_div__if,axiom,
% 4.71/5.04 ( divide_divide_nat
% 4.71/5.04 = ( ^ [M3: nat,N4: nat] :
% 4.71/5.04 ( if_nat
% 4.71/5.04 @ ( ( ord_less_nat @ M3 @ N4 )
% 4.71/5.04 | ( N4 = zero_zero_nat ) )
% 4.71/5.04 @ zero_zero_nat
% 4.71/5.04 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M3 @ N4 ) @ N4 ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % div_if
% 4.71/5.04 thf(fact_1815_real__of__nat__div2,axiom,
% 4.71/5.04 ! [N: nat,X: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % real_of_nat_div2
% 4.71/5.04 thf(fact_1816_real__of__nat__div3,axiom,
% 4.71/5.04 ! [N: nat,X: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) ) @ one_one_real ) ).
% 4.71/5.04
% 4.71/5.04 % real_of_nat_div3
% 4.71/5.04 thf(fact_1817_real__of__nat__div4,axiom,
% 4.71/5.04 ! [N: nat,X: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % real_of_nat_div4
% 4.71/5.04 thf(fact_1818_div__le__dividend,axiom,
% 4.71/5.04 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M2 @ N ) @ M2 ) ).
% 4.71/5.04
% 4.71/5.04 % div_le_dividend
% 4.71/5.04 thf(fact_1819_div__le__mono,axiom,
% 4.71/5.04 ! [M2: nat,N: nat,K: nat] :
% 4.71/5.04 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.04 => ( ord_less_eq_nat @ ( divide_divide_nat @ M2 @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % div_le_mono
% 4.71/5.04 thf(fact_1820_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 4.71/5.04 ! [M2: nat,N: nat] :
% 4.71/5.04 ( ( ( divide_divide_nat @ M2 @ N )
% 4.71/5.04 = zero_zero_nat )
% 4.71/5.04 = ( ( ord_less_nat @ M2 @ N )
% 4.71/5.04 | ( N = zero_zero_nat ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % Euclidean_Division.div_eq_0_iff
% 4.71/5.04 thf(fact_1821_Suc__div__le__mono,axiom,
% 4.71/5.04 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M2 @ N ) @ ( divide_divide_nat @ ( suc @ M2 ) @ N ) ) ).
% 4.71/5.04
% 4.71/5.04 % Suc_div_le_mono
% 4.71/5.04 thf(fact_1822_div__greater__zero__iff,axiom,
% 4.71/5.04 ! [M2: nat,N: nat] :
% 4.71/5.04 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M2 @ N ) )
% 4.71/5.04 = ( ( ord_less_eq_nat @ N @ M2 )
% 4.71/5.04 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % div_greater_zero_iff
% 4.71/5.04 thf(fact_1823_div__le__mono2,axiom,
% 4.71/5.04 ! [M2: nat,N: nat,K: nat] :
% 4.71/5.04 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 4.71/5.04 => ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.04 => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M2 ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % div_le_mono2
% 4.71/5.04 thf(fact_1824_div__eq__dividend__iff,axiom,
% 4.71/5.04 ! [M2: nat,N: nat] :
% 4.71/5.04 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 4.71/5.04 => ( ( ( divide_divide_nat @ M2 @ N )
% 4.71/5.04 = M2 )
% 4.71/5.04 = ( N = one_one_nat ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % div_eq_dividend_iff
% 4.71/5.04 thf(fact_1825_div__less__dividend,axiom,
% 4.71/5.04 ! [N: nat,M2: nat] :
% 4.71/5.04 ( ( ord_less_nat @ one_one_nat @ N )
% 4.71/5.04 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 4.71/5.04 => ( ord_less_nat @ ( divide_divide_nat @ M2 @ N ) @ M2 ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % div_less_dividend
% 4.71/5.04 thf(fact_1826_zdiv__mono1,axiom,
% 4.71/5.04 ! [A: int,A7: int,B: int] :
% 4.71/5.04 ( ( ord_less_eq_int @ A @ A7 )
% 4.71/5.04 => ( ( ord_less_int @ zero_zero_int @ B )
% 4.71/5.04 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A7 @ B ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % zdiv_mono1
% 4.71/5.04 thf(fact_1827_zdiv__mono2,axiom,
% 4.71/5.04 ! [A: int,B7: int,B: int] :
% 4.71/5.04 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.04 => ( ( ord_less_int @ zero_zero_int @ B7 )
% 4.71/5.04 => ( ( ord_less_eq_int @ B7 @ B )
% 4.71/5.04 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B7 ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % zdiv_mono2
% 4.71/5.04 thf(fact_1828_zdiv__eq__0__iff,axiom,
% 4.71/5.04 ! [I: int,K: int] :
% 4.71/5.04 ( ( ( divide_divide_int @ I @ K )
% 4.71/5.04 = zero_zero_int )
% 4.71/5.04 = ( ( K = zero_zero_int )
% 4.71/5.04 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 4.71/5.04 & ( ord_less_int @ I @ K ) )
% 4.71/5.04 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 4.71/5.04 & ( ord_less_int @ K @ I ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % zdiv_eq_0_iff
% 4.71/5.04 thf(fact_1829_zdiv__mono1__neg,axiom,
% 4.71/5.04 ! [A: int,A7: int,B: int] :
% 4.71/5.04 ( ( ord_less_eq_int @ A @ A7 )
% 4.71/5.04 => ( ( ord_less_int @ B @ zero_zero_int )
% 4.71/5.04 => ( ord_less_eq_int @ ( divide_divide_int @ A7 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % zdiv_mono1_neg
% 4.71/5.04 thf(fact_1830_zdiv__mono2__neg,axiom,
% 4.71/5.04 ! [A: int,B7: int,B: int] :
% 4.71/5.04 ( ( ord_less_int @ A @ zero_zero_int )
% 4.71/5.04 => ( ( ord_less_int @ zero_zero_int @ B7 )
% 4.71/5.04 => ( ( ord_less_eq_int @ B7 @ B )
% 4.71/5.04 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B7 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % zdiv_mono2_neg
% 4.71/5.04 thf(fact_1831_div__int__pos__iff,axiom,
% 4.71/5.04 ! [K: int,L: int] :
% 4.71/5.04 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) )
% 4.71/5.04 = ( ( K = zero_zero_int )
% 4.71/5.04 | ( L = zero_zero_int )
% 4.71/5.04 | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 4.71/5.04 & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 4.71/5.04 | ( ( ord_less_int @ K @ zero_zero_int )
% 4.71/5.04 & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % div_int_pos_iff
% 4.71/5.04 thf(fact_1832_div__positive__int,axiom,
% 4.71/5.04 ! [L: int,K: int] :
% 4.71/5.04 ( ( ord_less_eq_int @ L @ K )
% 4.71/5.04 => ( ( ord_less_int @ zero_zero_int @ L )
% 4.71/5.04 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % div_positive_int
% 4.71/5.04 thf(fact_1833_div__nonneg__neg__le0,axiom,
% 4.71/5.04 ! [A: int,B: int] :
% 4.71/5.04 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.04 => ( ( ord_less_int @ B @ zero_zero_int )
% 4.71/5.04 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % div_nonneg_neg_le0
% 4.71/5.04 thf(fact_1834_div__nonpos__pos__le0,axiom,
% 4.71/5.04 ! [A: int,B: int] :
% 4.71/5.04 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 4.71/5.04 => ( ( ord_less_int @ zero_zero_int @ B )
% 4.71/5.04 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % div_nonpos_pos_le0
% 4.71/5.04 thf(fact_1835_pos__imp__zdiv__pos__iff,axiom,
% 4.71/5.04 ! [K: int,I: int] :
% 4.71/5.04 ( ( ord_less_int @ zero_zero_int @ K )
% 4.71/5.04 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I @ K ) )
% 4.71/5.04 = ( ord_less_eq_int @ K @ I ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % pos_imp_zdiv_pos_iff
% 4.71/5.04 thf(fact_1836_neg__imp__zdiv__nonneg__iff,axiom,
% 4.71/5.04 ! [B: int,A: int] :
% 4.71/5.04 ( ( ord_less_int @ B @ zero_zero_int )
% 4.71/5.04 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 4.71/5.04 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 4.71/5.04
% 4.71/5.04 % neg_imp_zdiv_nonneg_iff
% 4.71/5.04 thf(fact_1837_pos__imp__zdiv__nonneg__iff,axiom,
% 4.71/5.04 ! [B: int,A: int] :
% 4.71/5.05 ( ( ord_less_int @ zero_zero_int @ B )
% 4.71/5.05 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 4.71/5.05 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % pos_imp_zdiv_nonneg_iff
% 4.71/5.05 thf(fact_1838_nonneg1__imp__zdiv__pos__iff,axiom,
% 4.71/5.05 ! [A: int,B: int] :
% 4.71/5.05 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.05 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 4.71/5.05 = ( ( ord_less_eq_int @ B @ A )
% 4.71/5.05 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % nonneg1_imp_zdiv_pos_iff
% 4.71/5.05 thf(fact_1839_div__positive,axiom,
% 4.71/5.05 ! [B: nat,A: nat] :
% 4.71/5.05 ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.71/5.05 => ( ( ord_less_eq_nat @ B @ A )
% 4.71/5.05 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % div_positive
% 4.71/5.05 thf(fact_1840_div__positive,axiom,
% 4.71/5.05 ! [B: int,A: int] :
% 4.71/5.05 ( ( ord_less_int @ zero_zero_int @ B )
% 4.71/5.05 => ( ( ord_less_eq_int @ B @ A )
% 4.71/5.05 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % div_positive
% 4.71/5.05 thf(fact_1841_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 4.71/5.05 ! [A: nat,B: nat] :
% 4.71/5.05 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.71/5.05 => ( ( ord_less_nat @ A @ B )
% 4.71/5.05 => ( ( divide_divide_nat @ A @ B )
% 4.71/5.05 = zero_zero_nat ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % unique_euclidean_semiring_numeral_class.div_less
% 4.71/5.05 thf(fact_1842_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 4.71/5.05 ! [A: int,B: int] :
% 4.71/5.05 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.05 => ( ( ord_less_int @ A @ B )
% 4.71/5.05 => ( ( divide_divide_int @ A @ B )
% 4.71/5.05 = zero_zero_int ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % unique_euclidean_semiring_numeral_class.div_less
% 4.71/5.05 thf(fact_1843_int__power__div__base,axiom,
% 4.71/5.05 ! [M2: nat,K: int] :
% 4.71/5.05 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 4.71/5.05 => ( ( ord_less_int @ zero_zero_int @ K )
% 4.71/5.05 => ( ( divide_divide_int @ ( power_power_int @ K @ M2 ) @ K )
% 4.71/5.05 = ( power_power_int @ K @ ( minus_minus_nat @ M2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % int_power_div_base
% 4.71/5.05 thf(fact_1844_nat__ivt__aux,axiom,
% 4.71/5.05 ! [N: nat,F: nat > int,K: int] :
% 4.71/5.05 ( ! [I2: nat] :
% 4.71/5.05 ( ( ord_less_nat @ I2 @ N )
% 4.71/5.05 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I2 ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 4.71/5.05 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 4.71/5.05 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 4.71/5.05 => ? [I2: nat] :
% 4.71/5.05 ( ( ord_less_eq_nat @ I2 @ N )
% 4.71/5.05 & ( ( F @ I2 )
% 4.71/5.05 = K ) ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % nat_ivt_aux
% 4.71/5.05 thf(fact_1845_div__pos__geq,axiom,
% 4.71/5.05 ! [L: int,K: int] :
% 4.71/5.05 ( ( ord_less_int @ zero_zero_int @ L )
% 4.71/5.05 => ( ( ord_less_eq_int @ L @ K )
% 4.71/5.05 => ( ( divide_divide_int @ K @ L )
% 4.71/5.05 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % div_pos_geq
% 4.71/5.05 thf(fact_1846_frac__unique__iff,axiom,
% 4.71/5.05 ! [X: real,A: real] :
% 4.71/5.05 ( ( ( archim2898591450579166408c_real @ X )
% 4.71/5.05 = A )
% 4.71/5.05 = ( ( member_real @ ( minus_minus_real @ X @ A ) @ ring_1_Ints_real )
% 4.71/5.05 & ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.05 & ( ord_less_real @ A @ one_one_real ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % frac_unique_iff
% 4.71/5.05 thf(fact_1847_frac__unique__iff,axiom,
% 4.71/5.05 ! [X: rat,A: rat] :
% 4.71/5.05 ( ( ( archimedean_frac_rat @ X )
% 4.71/5.05 = A )
% 4.71/5.05 = ( ( member_rat @ ( minus_minus_rat @ X @ A ) @ ring_1_Ints_rat )
% 4.71/5.05 & ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.05 & ( ord_less_rat @ A @ one_one_rat ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % frac_unique_iff
% 4.71/5.05 thf(fact_1848_card__insert__le__m1,axiom,
% 4.71/5.05 ! [N: nat,Y: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 4.71/5.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.05 => ( ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 4.71/5.05 => ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ ( insert8211810215607154385at_nat @ X @ Y ) ) @ N ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % card_insert_le_m1
% 4.71/5.05 thf(fact_1849_card__insert__le__m1,axiom,
% 4.71/5.05 ! [N: nat,Y: set_real,X: real] :
% 4.71/5.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.05 => ( ( ord_less_eq_nat @ ( finite_card_real @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 4.71/5.05 => ( ord_less_eq_nat @ ( finite_card_real @ ( insert_real @ X @ Y ) ) @ N ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % card_insert_le_m1
% 4.71/5.05 thf(fact_1850_card__insert__le__m1,axiom,
% 4.71/5.05 ! [N: nat,Y: set_o,X: $o] :
% 4.71/5.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.05 => ( ( ord_less_eq_nat @ ( finite_card_o @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 4.71/5.05 => ( ord_less_eq_nat @ ( finite_card_o @ ( insert_o @ X @ Y ) ) @ N ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % card_insert_le_m1
% 4.71/5.05 thf(fact_1851_card__insert__le__m1,axiom,
% 4.71/5.05 ! [N: nat,Y: set_complex,X: complex] :
% 4.71/5.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.05 => ( ( ord_less_eq_nat @ ( finite_card_complex @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 4.71/5.05 => ( ord_less_eq_nat @ ( finite_card_complex @ ( insert_complex @ X @ Y ) ) @ N ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % card_insert_le_m1
% 4.71/5.05 thf(fact_1852_card__insert__le__m1,axiom,
% 4.71/5.05 ! [N: nat,Y: set_list_nat,X: list_nat] :
% 4.71/5.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.05 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 4.71/5.05 => ( ord_less_eq_nat @ ( finite_card_list_nat @ ( insert_list_nat @ X @ Y ) ) @ N ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % card_insert_le_m1
% 4.71/5.05 thf(fact_1853_card__insert__le__m1,axiom,
% 4.71/5.05 ! [N: nat,Y: set_set_nat,X: set_nat] :
% 4.71/5.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.05 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 4.71/5.05 => ( ord_less_eq_nat @ ( finite_card_set_nat @ ( insert_set_nat @ X @ Y ) ) @ N ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % card_insert_le_m1
% 4.71/5.05 thf(fact_1854_card__insert__le__m1,axiom,
% 4.71/5.05 ! [N: nat,Y: set_nat,X: nat] :
% 4.71/5.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.05 => ( ( ord_less_eq_nat @ ( finite_card_nat @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 4.71/5.05 => ( ord_less_eq_nat @ ( finite_card_nat @ ( insert_nat @ X @ Y ) ) @ N ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % card_insert_le_m1
% 4.71/5.05 thf(fact_1855_card__insert__le__m1,axiom,
% 4.71/5.05 ! [N: nat,Y: set_int,X: int] :
% 4.71/5.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.05 => ( ( ord_less_eq_nat @ ( finite_card_int @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 4.71/5.05 => ( ord_less_eq_nat @ ( finite_card_int @ ( insert_int @ X @ Y ) ) @ N ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % card_insert_le_m1
% 4.71/5.05 thf(fact_1856_nat__intermed__int__val,axiom,
% 4.71/5.05 ! [M2: nat,N: nat,F: nat > int,K: int] :
% 4.71/5.05 ( ! [I2: nat] :
% 4.71/5.05 ( ( ( ord_less_eq_nat @ M2 @ I2 )
% 4.71/5.05 & ( ord_less_nat @ I2 @ N ) )
% 4.71/5.05 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I2 ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 4.71/5.05 => ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.05 => ( ( ord_less_eq_int @ ( F @ M2 ) @ K )
% 4.71/5.05 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 4.71/5.05 => ? [I2: nat] :
% 4.71/5.05 ( ( ord_less_eq_nat @ M2 @ I2 )
% 4.71/5.05 & ( ord_less_eq_nat @ I2 @ N )
% 4.71/5.05 & ( ( F @ I2 )
% 4.71/5.05 = K ) ) ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % nat_intermed_int_val
% 4.71/5.05 thf(fact_1857_one__less__nat__eq,axiom,
% 4.71/5.05 ! [Z: int] :
% 4.71/5.05 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 4.71/5.05 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 4.71/5.05
% 4.71/5.05 % one_less_nat_eq
% 4.71/5.05 thf(fact_1858_set__encode__inverse,axiom,
% 4.71/5.05 ! [A2: set_nat] :
% 4.71/5.05 ( ( finite_finite_nat @ A2 )
% 4.71/5.05 => ( ( nat_set_decode @ ( nat_set_encode @ A2 ) )
% 4.71/5.05 = A2 ) ) ).
% 4.71/5.05
% 4.71/5.05 % set_encode_inverse
% 4.71/5.05 thf(fact_1859_enumerate__Suc_H,axiom,
% 4.71/5.05 ! [S2: set_nat,N: nat] :
% 4.71/5.05 ( ( infini8530281810654367211te_nat @ S2 @ ( suc @ N ) )
% 4.71/5.05 = ( infini8530281810654367211te_nat @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ ( infini8530281810654367211te_nat @ S2 @ zero_zero_nat ) @ bot_bot_set_nat ) ) @ N ) ) ).
% 4.71/5.05
% 4.71/5.05 % enumerate_Suc'
% 4.71/5.05 thf(fact_1860_split__div_H,axiom,
% 4.71/5.05 ! [P: nat > $o,M2: nat,N: nat] :
% 4.71/5.05 ( ( P @ ( divide_divide_nat @ M2 @ N ) )
% 4.71/5.05 = ( ( ( N = zero_zero_nat )
% 4.71/5.05 & ( P @ zero_zero_nat ) )
% 4.71/5.05 | ? [Q3: nat] :
% 4.71/5.05 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q3 ) @ M2 )
% 4.71/5.05 & ( ord_less_nat @ M2 @ ( times_times_nat @ N @ ( suc @ Q3 ) ) )
% 4.71/5.05 & ( P @ Q3 ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % split_div'
% 4.71/5.05 thf(fact_1861_add__right__cancel,axiom,
% 4.71/5.05 ! [B: real,A: real,C: real] :
% 4.71/5.05 ( ( ( plus_plus_real @ B @ A )
% 4.71/5.05 = ( plus_plus_real @ C @ A ) )
% 4.71/5.05 = ( B = C ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_right_cancel
% 4.71/5.05 thf(fact_1862_add__right__cancel,axiom,
% 4.71/5.05 ! [B: rat,A: rat,C: rat] :
% 4.71/5.05 ( ( ( plus_plus_rat @ B @ A )
% 4.71/5.05 = ( plus_plus_rat @ C @ A ) )
% 4.71/5.05 = ( B = C ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_right_cancel
% 4.71/5.05 thf(fact_1863_add__right__cancel,axiom,
% 4.71/5.05 ! [B: nat,A: nat,C: nat] :
% 4.71/5.05 ( ( ( plus_plus_nat @ B @ A )
% 4.71/5.05 = ( plus_plus_nat @ C @ A ) )
% 4.71/5.05 = ( B = C ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_right_cancel
% 4.71/5.05 thf(fact_1864_add__right__cancel,axiom,
% 4.71/5.05 ! [B: int,A: int,C: int] :
% 4.71/5.05 ( ( ( plus_plus_int @ B @ A )
% 4.71/5.05 = ( plus_plus_int @ C @ A ) )
% 4.71/5.05 = ( B = C ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_right_cancel
% 4.71/5.05 thf(fact_1865_add__left__cancel,axiom,
% 4.71/5.05 ! [A: real,B: real,C: real] :
% 4.71/5.05 ( ( ( plus_plus_real @ A @ B )
% 4.71/5.05 = ( plus_plus_real @ A @ C ) )
% 4.71/5.05 = ( B = C ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_left_cancel
% 4.71/5.05 thf(fact_1866_add__left__cancel,axiom,
% 4.71/5.05 ! [A: rat,B: rat,C: rat] :
% 4.71/5.05 ( ( ( plus_plus_rat @ A @ B )
% 4.71/5.05 = ( plus_plus_rat @ A @ C ) )
% 4.71/5.05 = ( B = C ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_left_cancel
% 4.71/5.05 thf(fact_1867_add__left__cancel,axiom,
% 4.71/5.05 ! [A: nat,B: nat,C: nat] :
% 4.71/5.05 ( ( ( plus_plus_nat @ A @ B )
% 4.71/5.05 = ( plus_plus_nat @ A @ C ) )
% 4.71/5.05 = ( B = C ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_left_cancel
% 4.71/5.05 thf(fact_1868_add__left__cancel,axiom,
% 4.71/5.05 ! [A: int,B: int,C: int] :
% 4.71/5.05 ( ( ( plus_plus_int @ A @ B )
% 4.71/5.05 = ( plus_plus_int @ A @ C ) )
% 4.71/5.05 = ( B = C ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_left_cancel
% 4.71/5.05 thf(fact_1869_insert__absorb2,axiom,
% 4.71/5.05 ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.05 ( ( insert8211810215607154385at_nat @ X @ ( insert8211810215607154385at_nat @ X @ A2 ) )
% 4.71/5.05 = ( insert8211810215607154385at_nat @ X @ A2 ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_absorb2
% 4.71/5.05 thf(fact_1870_insert__absorb2,axiom,
% 4.71/5.05 ! [X: real,A2: set_real] :
% 4.71/5.05 ( ( insert_real @ X @ ( insert_real @ X @ A2 ) )
% 4.71/5.05 = ( insert_real @ X @ A2 ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_absorb2
% 4.71/5.05 thf(fact_1871_insert__absorb2,axiom,
% 4.71/5.05 ! [X: $o,A2: set_o] :
% 4.71/5.05 ( ( insert_o @ X @ ( insert_o @ X @ A2 ) )
% 4.71/5.05 = ( insert_o @ X @ A2 ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_absorb2
% 4.71/5.05 thf(fact_1872_insert__absorb2,axiom,
% 4.71/5.05 ! [X: nat,A2: set_nat] :
% 4.71/5.05 ( ( insert_nat @ X @ ( insert_nat @ X @ A2 ) )
% 4.71/5.05 = ( insert_nat @ X @ A2 ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_absorb2
% 4.71/5.05 thf(fact_1873_insert__absorb2,axiom,
% 4.71/5.05 ! [X: int,A2: set_int] :
% 4.71/5.05 ( ( insert_int @ X @ ( insert_int @ X @ A2 ) )
% 4.71/5.05 = ( insert_int @ X @ A2 ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_absorb2
% 4.71/5.05 thf(fact_1874_insert__iff,axiom,
% 4.71/5.05 ! [A: product_prod_nat_nat,B: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.05 ( ( member8440522571783428010at_nat @ A @ ( insert8211810215607154385at_nat @ B @ A2 ) )
% 4.71/5.05 = ( ( A = B )
% 4.71/5.05 | ( member8440522571783428010at_nat @ A @ A2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_iff
% 4.71/5.05 thf(fact_1875_insert__iff,axiom,
% 4.71/5.05 ! [A: real,B: real,A2: set_real] :
% 4.71/5.05 ( ( member_real @ A @ ( insert_real @ B @ A2 ) )
% 4.71/5.05 = ( ( A = B )
% 4.71/5.05 | ( member_real @ A @ A2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_iff
% 4.71/5.05 thf(fact_1876_insert__iff,axiom,
% 4.71/5.05 ! [A: $o,B: $o,A2: set_o] :
% 4.71/5.05 ( ( member_o @ A @ ( insert_o @ B @ A2 ) )
% 4.71/5.05 = ( ( A = B )
% 4.71/5.05 | ( member_o @ A @ A2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_iff
% 4.71/5.05 thf(fact_1877_insert__iff,axiom,
% 4.71/5.05 ! [A: set_nat,B: set_nat,A2: set_set_nat] :
% 4.71/5.05 ( ( member_set_nat @ A @ ( insert_set_nat @ B @ A2 ) )
% 4.71/5.05 = ( ( A = B )
% 4.71/5.05 | ( member_set_nat @ A @ A2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_iff
% 4.71/5.05 thf(fact_1878_insert__iff,axiom,
% 4.71/5.05 ! [A: set_nat_rat,B: set_nat_rat,A2: set_set_nat_rat] :
% 4.71/5.05 ( ( member_set_nat_rat @ A @ ( insert_set_nat_rat @ B @ A2 ) )
% 4.71/5.05 = ( ( A = B )
% 4.71/5.05 | ( member_set_nat_rat @ A @ A2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_iff
% 4.71/5.05 thf(fact_1879_insert__iff,axiom,
% 4.71/5.05 ! [A: nat,B: nat,A2: set_nat] :
% 4.71/5.05 ( ( member_nat @ A @ ( insert_nat @ B @ A2 ) )
% 4.71/5.05 = ( ( A = B )
% 4.71/5.05 | ( member_nat @ A @ A2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_iff
% 4.71/5.05 thf(fact_1880_insert__iff,axiom,
% 4.71/5.05 ! [A: int,B: int,A2: set_int] :
% 4.71/5.05 ( ( member_int @ A @ ( insert_int @ B @ A2 ) )
% 4.71/5.05 = ( ( A = B )
% 4.71/5.05 | ( member_int @ A @ A2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_iff
% 4.71/5.05 thf(fact_1881_insertCI,axiom,
% 4.71/5.05 ! [A: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat,B: product_prod_nat_nat] :
% 4.71/5.05 ( ( ~ ( member8440522571783428010at_nat @ A @ B2 )
% 4.71/5.05 => ( A = B ) )
% 4.71/5.05 => ( member8440522571783428010at_nat @ A @ ( insert8211810215607154385at_nat @ B @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insertCI
% 4.71/5.05 thf(fact_1882_insertCI,axiom,
% 4.71/5.05 ! [A: real,B2: set_real,B: real] :
% 4.71/5.05 ( ( ~ ( member_real @ A @ B2 )
% 4.71/5.05 => ( A = B ) )
% 4.71/5.05 => ( member_real @ A @ ( insert_real @ B @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insertCI
% 4.71/5.05 thf(fact_1883_insertCI,axiom,
% 4.71/5.05 ! [A: $o,B2: set_o,B: $o] :
% 4.71/5.05 ( ( ~ ( member_o @ A @ B2 )
% 4.71/5.05 => ( A = B ) )
% 4.71/5.05 => ( member_o @ A @ ( insert_o @ B @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insertCI
% 4.71/5.05 thf(fact_1884_insertCI,axiom,
% 4.71/5.05 ! [A: set_nat,B2: set_set_nat,B: set_nat] :
% 4.71/5.05 ( ( ~ ( member_set_nat @ A @ B2 )
% 4.71/5.05 => ( A = B ) )
% 4.71/5.05 => ( member_set_nat @ A @ ( insert_set_nat @ B @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insertCI
% 4.71/5.05 thf(fact_1885_insertCI,axiom,
% 4.71/5.05 ! [A: set_nat_rat,B2: set_set_nat_rat,B: set_nat_rat] :
% 4.71/5.05 ( ( ~ ( member_set_nat_rat @ A @ B2 )
% 4.71/5.05 => ( A = B ) )
% 4.71/5.05 => ( member_set_nat_rat @ A @ ( insert_set_nat_rat @ B @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insertCI
% 4.71/5.05 thf(fact_1886_insertCI,axiom,
% 4.71/5.05 ! [A: nat,B2: set_nat,B: nat] :
% 4.71/5.05 ( ( ~ ( member_nat @ A @ B2 )
% 4.71/5.05 => ( A = B ) )
% 4.71/5.05 => ( member_nat @ A @ ( insert_nat @ B @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insertCI
% 4.71/5.05 thf(fact_1887_insertCI,axiom,
% 4.71/5.05 ! [A: int,B2: set_int,B: int] :
% 4.71/5.05 ( ( ~ ( member_int @ A @ B2 )
% 4.71/5.05 => ( A = B ) )
% 4.71/5.05 => ( member_int @ A @ ( insert_int @ B @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insertCI
% 4.71/5.05 thf(fact_1888_abs__abs,axiom,
% 4.71/5.05 ! [A: int] :
% 4.71/5.05 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 4.71/5.05 = ( abs_abs_int @ A ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_abs
% 4.71/5.05 thf(fact_1889_abs__abs,axiom,
% 4.71/5.05 ! [A: real] :
% 4.71/5.05 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 4.71/5.05 = ( abs_abs_real @ A ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_abs
% 4.71/5.05 thf(fact_1890_abs__abs,axiom,
% 4.71/5.05 ! [A: rat] :
% 4.71/5.05 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 4.71/5.05 = ( abs_abs_rat @ A ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_abs
% 4.71/5.05 thf(fact_1891_abs__idempotent,axiom,
% 4.71/5.05 ! [A: int] :
% 4.71/5.05 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 4.71/5.05 = ( abs_abs_int @ A ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_idempotent
% 4.71/5.05 thf(fact_1892_abs__idempotent,axiom,
% 4.71/5.05 ! [A: real] :
% 4.71/5.05 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 4.71/5.05 = ( abs_abs_real @ A ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_idempotent
% 4.71/5.05 thf(fact_1893_abs__idempotent,axiom,
% 4.71/5.05 ! [A: rat] :
% 4.71/5.05 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 4.71/5.05 = ( abs_abs_rat @ A ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_idempotent
% 4.71/5.05 thf(fact_1894_mult__zero__left,axiom,
% 4.71/5.05 ! [A: real] :
% 4.71/5.05 ( ( times_times_real @ zero_zero_real @ A )
% 4.71/5.05 = zero_zero_real ) ).
% 4.71/5.05
% 4.71/5.05 % mult_zero_left
% 4.71/5.05 thf(fact_1895_mult__zero__left,axiom,
% 4.71/5.05 ! [A: rat] :
% 4.71/5.05 ( ( times_times_rat @ zero_zero_rat @ A )
% 4.71/5.05 = zero_zero_rat ) ).
% 4.71/5.05
% 4.71/5.05 % mult_zero_left
% 4.71/5.05 thf(fact_1896_mult__zero__left,axiom,
% 4.71/5.05 ! [A: nat] :
% 4.71/5.05 ( ( times_times_nat @ zero_zero_nat @ A )
% 4.71/5.05 = zero_zero_nat ) ).
% 4.71/5.05
% 4.71/5.05 % mult_zero_left
% 4.71/5.05 thf(fact_1897_mult__zero__left,axiom,
% 4.71/5.05 ! [A: int] :
% 4.71/5.05 ( ( times_times_int @ zero_zero_int @ A )
% 4.71/5.05 = zero_zero_int ) ).
% 4.71/5.05
% 4.71/5.05 % mult_zero_left
% 4.71/5.05 thf(fact_1898_mult__zero__right,axiom,
% 4.71/5.05 ! [A: real] :
% 4.71/5.05 ( ( times_times_real @ A @ zero_zero_real )
% 4.71/5.05 = zero_zero_real ) ).
% 4.71/5.05
% 4.71/5.05 % mult_zero_right
% 4.71/5.05 thf(fact_1899_mult__zero__right,axiom,
% 4.71/5.05 ! [A: rat] :
% 4.71/5.05 ( ( times_times_rat @ A @ zero_zero_rat )
% 4.71/5.05 = zero_zero_rat ) ).
% 4.71/5.05
% 4.71/5.05 % mult_zero_right
% 4.71/5.05 thf(fact_1900_mult__zero__right,axiom,
% 4.71/5.05 ! [A: nat] :
% 4.71/5.05 ( ( times_times_nat @ A @ zero_zero_nat )
% 4.71/5.05 = zero_zero_nat ) ).
% 4.71/5.05
% 4.71/5.05 % mult_zero_right
% 4.71/5.05 thf(fact_1901_mult__zero__right,axiom,
% 4.71/5.05 ! [A: int] :
% 4.71/5.05 ( ( times_times_int @ A @ zero_zero_int )
% 4.71/5.05 = zero_zero_int ) ).
% 4.71/5.05
% 4.71/5.05 % mult_zero_right
% 4.71/5.05 thf(fact_1902_mult__eq__0__iff,axiom,
% 4.71/5.05 ! [A: real,B: real] :
% 4.71/5.05 ( ( ( times_times_real @ A @ B )
% 4.71/5.05 = zero_zero_real )
% 4.71/5.05 = ( ( A = zero_zero_real )
% 4.71/5.05 | ( B = zero_zero_real ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_eq_0_iff
% 4.71/5.05 thf(fact_1903_mult__eq__0__iff,axiom,
% 4.71/5.05 ! [A: rat,B: rat] :
% 4.71/5.05 ( ( ( times_times_rat @ A @ B )
% 4.71/5.05 = zero_zero_rat )
% 4.71/5.05 = ( ( A = zero_zero_rat )
% 4.71/5.05 | ( B = zero_zero_rat ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_eq_0_iff
% 4.71/5.05 thf(fact_1904_mult__eq__0__iff,axiom,
% 4.71/5.05 ! [A: nat,B: nat] :
% 4.71/5.05 ( ( ( times_times_nat @ A @ B )
% 4.71/5.05 = zero_zero_nat )
% 4.71/5.05 = ( ( A = zero_zero_nat )
% 4.71/5.05 | ( B = zero_zero_nat ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_eq_0_iff
% 4.71/5.05 thf(fact_1905_mult__eq__0__iff,axiom,
% 4.71/5.05 ! [A: int,B: int] :
% 4.71/5.05 ( ( ( times_times_int @ A @ B )
% 4.71/5.05 = zero_zero_int )
% 4.71/5.05 = ( ( A = zero_zero_int )
% 4.71/5.05 | ( B = zero_zero_int ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_eq_0_iff
% 4.71/5.05 thf(fact_1906_mult__cancel__left,axiom,
% 4.71/5.05 ! [C: real,A: real,B: real] :
% 4.71/5.05 ( ( ( times_times_real @ C @ A )
% 4.71/5.05 = ( times_times_real @ C @ B ) )
% 4.71/5.05 = ( ( C = zero_zero_real )
% 4.71/5.05 | ( A = B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_cancel_left
% 4.71/5.05 thf(fact_1907_mult__cancel__left,axiom,
% 4.71/5.05 ! [C: rat,A: rat,B: rat] :
% 4.71/5.05 ( ( ( times_times_rat @ C @ A )
% 4.71/5.05 = ( times_times_rat @ C @ B ) )
% 4.71/5.05 = ( ( C = zero_zero_rat )
% 4.71/5.05 | ( A = B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_cancel_left
% 4.71/5.05 thf(fact_1908_mult__cancel__left,axiom,
% 4.71/5.05 ! [C: nat,A: nat,B: nat] :
% 4.71/5.05 ( ( ( times_times_nat @ C @ A )
% 4.71/5.05 = ( times_times_nat @ C @ B ) )
% 4.71/5.05 = ( ( C = zero_zero_nat )
% 4.71/5.05 | ( A = B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_cancel_left
% 4.71/5.05 thf(fact_1909_mult__cancel__left,axiom,
% 4.71/5.05 ! [C: int,A: int,B: int] :
% 4.71/5.05 ( ( ( times_times_int @ C @ A )
% 4.71/5.05 = ( times_times_int @ C @ B ) )
% 4.71/5.05 = ( ( C = zero_zero_int )
% 4.71/5.05 | ( A = B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_cancel_left
% 4.71/5.05 thf(fact_1910_mult__cancel__right,axiom,
% 4.71/5.05 ! [A: real,C: real,B: real] :
% 4.71/5.05 ( ( ( times_times_real @ A @ C )
% 4.71/5.05 = ( times_times_real @ B @ C ) )
% 4.71/5.05 = ( ( C = zero_zero_real )
% 4.71/5.05 | ( A = B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_cancel_right
% 4.71/5.05 thf(fact_1911_mult__cancel__right,axiom,
% 4.71/5.05 ! [A: rat,C: rat,B: rat] :
% 4.71/5.05 ( ( ( times_times_rat @ A @ C )
% 4.71/5.05 = ( times_times_rat @ B @ C ) )
% 4.71/5.05 = ( ( C = zero_zero_rat )
% 4.71/5.05 | ( A = B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_cancel_right
% 4.71/5.05 thf(fact_1912_mult__cancel__right,axiom,
% 4.71/5.05 ! [A: nat,C: nat,B: nat] :
% 4.71/5.05 ( ( ( times_times_nat @ A @ C )
% 4.71/5.05 = ( times_times_nat @ B @ C ) )
% 4.71/5.05 = ( ( C = zero_zero_nat )
% 4.71/5.05 | ( A = B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_cancel_right
% 4.71/5.05 thf(fact_1913_mult__cancel__right,axiom,
% 4.71/5.05 ! [A: int,C: int,B: int] :
% 4.71/5.05 ( ( ( times_times_int @ A @ C )
% 4.71/5.05 = ( times_times_int @ B @ C ) )
% 4.71/5.05 = ( ( C = zero_zero_int )
% 4.71/5.05 | ( A = B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_cancel_right
% 4.71/5.05 thf(fact_1914_add__le__cancel__right,axiom,
% 4.71/5.05 ! [A: real,C: real,B: real] :
% 4.71/5.05 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 4.71/5.05 = ( ord_less_eq_real @ A @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_le_cancel_right
% 4.71/5.05 thf(fact_1915_add__le__cancel__right,axiom,
% 4.71/5.05 ! [A: rat,C: rat,B: rat] :
% 4.71/5.05 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 4.71/5.05 = ( ord_less_eq_rat @ A @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_le_cancel_right
% 4.71/5.05 thf(fact_1916_add__le__cancel__right,axiom,
% 4.71/5.05 ! [A: nat,C: nat,B: nat] :
% 4.71/5.05 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 4.71/5.05 = ( ord_less_eq_nat @ A @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_le_cancel_right
% 4.71/5.05 thf(fact_1917_add__le__cancel__right,axiom,
% 4.71/5.05 ! [A: int,C: int,B: int] :
% 4.71/5.05 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 4.71/5.05 = ( ord_less_eq_int @ A @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_le_cancel_right
% 4.71/5.05 thf(fact_1918_add__le__cancel__left,axiom,
% 4.71/5.05 ! [C: real,A: real,B: real] :
% 4.71/5.05 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 4.71/5.05 = ( ord_less_eq_real @ A @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_le_cancel_left
% 4.71/5.05 thf(fact_1919_add__le__cancel__left,axiom,
% 4.71/5.05 ! [C: rat,A: rat,B: rat] :
% 4.71/5.05 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 4.71/5.05 = ( ord_less_eq_rat @ A @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_le_cancel_left
% 4.71/5.05 thf(fact_1920_add__le__cancel__left,axiom,
% 4.71/5.05 ! [C: nat,A: nat,B: nat] :
% 4.71/5.05 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 4.71/5.05 = ( ord_less_eq_nat @ A @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_le_cancel_left
% 4.71/5.05 thf(fact_1921_add__le__cancel__left,axiom,
% 4.71/5.05 ! [C: int,A: int,B: int] :
% 4.71/5.05 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 4.71/5.05 = ( ord_less_eq_int @ A @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_le_cancel_left
% 4.71/5.05 thf(fact_1922_add_Oright__neutral,axiom,
% 4.71/5.05 ! [A: literal] :
% 4.71/5.05 ( ( plus_plus_literal @ A @ zero_zero_literal )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % add.right_neutral
% 4.71/5.05 thf(fact_1923_add_Oright__neutral,axiom,
% 4.71/5.05 ! [A: real] :
% 4.71/5.05 ( ( plus_plus_real @ A @ zero_zero_real )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % add.right_neutral
% 4.71/5.05 thf(fact_1924_add_Oright__neutral,axiom,
% 4.71/5.05 ! [A: rat] :
% 4.71/5.05 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % add.right_neutral
% 4.71/5.05 thf(fact_1925_add_Oright__neutral,axiom,
% 4.71/5.05 ! [A: nat] :
% 4.71/5.05 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % add.right_neutral
% 4.71/5.05 thf(fact_1926_add_Oright__neutral,axiom,
% 4.71/5.05 ! [A: int] :
% 4.71/5.05 ( ( plus_plus_int @ A @ zero_zero_int )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % add.right_neutral
% 4.71/5.05 thf(fact_1927_double__zero__sym,axiom,
% 4.71/5.05 ! [A: real] :
% 4.71/5.05 ( ( zero_zero_real
% 4.71/5.05 = ( plus_plus_real @ A @ A ) )
% 4.71/5.05 = ( A = zero_zero_real ) ) ).
% 4.71/5.05
% 4.71/5.05 % double_zero_sym
% 4.71/5.05 thf(fact_1928_double__zero__sym,axiom,
% 4.71/5.05 ! [A: rat] :
% 4.71/5.05 ( ( zero_zero_rat
% 4.71/5.05 = ( plus_plus_rat @ A @ A ) )
% 4.71/5.05 = ( A = zero_zero_rat ) ) ).
% 4.71/5.05
% 4.71/5.05 % double_zero_sym
% 4.71/5.05 thf(fact_1929_double__zero__sym,axiom,
% 4.71/5.05 ! [A: int] :
% 4.71/5.05 ( ( zero_zero_int
% 4.71/5.05 = ( plus_plus_int @ A @ A ) )
% 4.71/5.05 = ( A = zero_zero_int ) ) ).
% 4.71/5.05
% 4.71/5.05 % double_zero_sym
% 4.71/5.05 thf(fact_1930_add__cancel__left__left,axiom,
% 4.71/5.05 ! [B: real,A: real] :
% 4.71/5.05 ( ( ( plus_plus_real @ B @ A )
% 4.71/5.05 = A )
% 4.71/5.05 = ( B = zero_zero_real ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_cancel_left_left
% 4.71/5.05 thf(fact_1931_add__cancel__left__left,axiom,
% 4.71/5.05 ! [B: rat,A: rat] :
% 4.71/5.05 ( ( ( plus_plus_rat @ B @ A )
% 4.71/5.05 = A )
% 4.71/5.05 = ( B = zero_zero_rat ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_cancel_left_left
% 4.71/5.05 thf(fact_1932_add__cancel__left__left,axiom,
% 4.71/5.05 ! [B: nat,A: nat] :
% 4.71/5.05 ( ( ( plus_plus_nat @ B @ A )
% 4.71/5.05 = A )
% 4.71/5.05 = ( B = zero_zero_nat ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_cancel_left_left
% 4.71/5.05 thf(fact_1933_add__cancel__left__left,axiom,
% 4.71/5.05 ! [B: int,A: int] :
% 4.71/5.05 ( ( ( plus_plus_int @ B @ A )
% 4.71/5.05 = A )
% 4.71/5.05 = ( B = zero_zero_int ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_cancel_left_left
% 4.71/5.05 thf(fact_1934_add__cancel__left__right,axiom,
% 4.71/5.05 ! [A: real,B: real] :
% 4.71/5.05 ( ( ( plus_plus_real @ A @ B )
% 4.71/5.05 = A )
% 4.71/5.05 = ( B = zero_zero_real ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_cancel_left_right
% 4.71/5.05 thf(fact_1935_add__cancel__left__right,axiom,
% 4.71/5.05 ! [A: rat,B: rat] :
% 4.71/5.05 ( ( ( plus_plus_rat @ A @ B )
% 4.71/5.05 = A )
% 4.71/5.05 = ( B = zero_zero_rat ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_cancel_left_right
% 4.71/5.05 thf(fact_1936_add__cancel__left__right,axiom,
% 4.71/5.05 ! [A: nat,B: nat] :
% 4.71/5.05 ( ( ( plus_plus_nat @ A @ B )
% 4.71/5.05 = A )
% 4.71/5.05 = ( B = zero_zero_nat ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_cancel_left_right
% 4.71/5.05 thf(fact_1937_add__cancel__left__right,axiom,
% 4.71/5.05 ! [A: int,B: int] :
% 4.71/5.05 ( ( ( plus_plus_int @ A @ B )
% 4.71/5.05 = A )
% 4.71/5.05 = ( B = zero_zero_int ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_cancel_left_right
% 4.71/5.05 thf(fact_1938_add__cancel__right__left,axiom,
% 4.71/5.05 ! [A: real,B: real] :
% 4.71/5.05 ( ( A
% 4.71/5.05 = ( plus_plus_real @ B @ A ) )
% 4.71/5.05 = ( B = zero_zero_real ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_cancel_right_left
% 4.71/5.05 thf(fact_1939_add__cancel__right__left,axiom,
% 4.71/5.05 ! [A: rat,B: rat] :
% 4.71/5.05 ( ( A
% 4.71/5.05 = ( plus_plus_rat @ B @ A ) )
% 4.71/5.05 = ( B = zero_zero_rat ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_cancel_right_left
% 4.71/5.05 thf(fact_1940_add__cancel__right__left,axiom,
% 4.71/5.05 ! [A: nat,B: nat] :
% 4.71/5.05 ( ( A
% 4.71/5.05 = ( plus_plus_nat @ B @ A ) )
% 4.71/5.05 = ( B = zero_zero_nat ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_cancel_right_left
% 4.71/5.05 thf(fact_1941_add__cancel__right__left,axiom,
% 4.71/5.05 ! [A: int,B: int] :
% 4.71/5.05 ( ( A
% 4.71/5.05 = ( plus_plus_int @ B @ A ) )
% 4.71/5.05 = ( B = zero_zero_int ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_cancel_right_left
% 4.71/5.05 thf(fact_1942_add__cancel__right__right,axiom,
% 4.71/5.05 ! [A: real,B: real] :
% 4.71/5.05 ( ( A
% 4.71/5.05 = ( plus_plus_real @ A @ B ) )
% 4.71/5.05 = ( B = zero_zero_real ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_cancel_right_right
% 4.71/5.05 thf(fact_1943_add__cancel__right__right,axiom,
% 4.71/5.05 ! [A: rat,B: rat] :
% 4.71/5.05 ( ( A
% 4.71/5.05 = ( plus_plus_rat @ A @ B ) )
% 4.71/5.05 = ( B = zero_zero_rat ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_cancel_right_right
% 4.71/5.05 thf(fact_1944_add__cancel__right__right,axiom,
% 4.71/5.05 ! [A: nat,B: nat] :
% 4.71/5.05 ( ( A
% 4.71/5.05 = ( plus_plus_nat @ A @ B ) )
% 4.71/5.05 = ( B = zero_zero_nat ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_cancel_right_right
% 4.71/5.05 thf(fact_1945_add__cancel__right__right,axiom,
% 4.71/5.05 ! [A: int,B: int] :
% 4.71/5.05 ( ( A
% 4.71/5.05 = ( plus_plus_int @ A @ B ) )
% 4.71/5.05 = ( B = zero_zero_int ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_cancel_right_right
% 4.71/5.05 thf(fact_1946_add__eq__0__iff__both__eq__0,axiom,
% 4.71/5.05 ! [X: nat,Y: nat] :
% 4.71/5.05 ( ( ( plus_plus_nat @ X @ Y )
% 4.71/5.05 = zero_zero_nat )
% 4.71/5.05 = ( ( X = zero_zero_nat )
% 4.71/5.05 & ( Y = zero_zero_nat ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_eq_0_iff_both_eq_0
% 4.71/5.05 thf(fact_1947_zero__eq__add__iff__both__eq__0,axiom,
% 4.71/5.05 ! [X: nat,Y: nat] :
% 4.71/5.05 ( ( zero_zero_nat
% 4.71/5.05 = ( plus_plus_nat @ X @ Y ) )
% 4.71/5.05 = ( ( X = zero_zero_nat )
% 4.71/5.05 & ( Y = zero_zero_nat ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % zero_eq_add_iff_both_eq_0
% 4.71/5.05 thf(fact_1948_add__0,axiom,
% 4.71/5.05 ! [A: literal] :
% 4.71/5.05 ( ( plus_plus_literal @ zero_zero_literal @ A )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % add_0
% 4.71/5.05 thf(fact_1949_add__0,axiom,
% 4.71/5.05 ! [A: real] :
% 4.71/5.05 ( ( plus_plus_real @ zero_zero_real @ A )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % add_0
% 4.71/5.05 thf(fact_1950_add__0,axiom,
% 4.71/5.05 ! [A: rat] :
% 4.71/5.05 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % add_0
% 4.71/5.05 thf(fact_1951_add__0,axiom,
% 4.71/5.05 ! [A: nat] :
% 4.71/5.05 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % add_0
% 4.71/5.05 thf(fact_1952_add__0,axiom,
% 4.71/5.05 ! [A: int] :
% 4.71/5.05 ( ( plus_plus_int @ zero_zero_int @ A )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % add_0
% 4.71/5.05 thf(fact_1953_double__eq__0__iff,axiom,
% 4.71/5.05 ! [A: real] :
% 4.71/5.05 ( ( ( plus_plus_real @ A @ A )
% 4.71/5.05 = zero_zero_real )
% 4.71/5.05 = ( A = zero_zero_real ) ) ).
% 4.71/5.05
% 4.71/5.05 % double_eq_0_iff
% 4.71/5.05 thf(fact_1954_double__eq__0__iff,axiom,
% 4.71/5.05 ! [A: rat] :
% 4.71/5.05 ( ( ( plus_plus_rat @ A @ A )
% 4.71/5.05 = zero_zero_rat )
% 4.71/5.05 = ( A = zero_zero_rat ) ) ).
% 4.71/5.05
% 4.71/5.05 % double_eq_0_iff
% 4.71/5.05 thf(fact_1955_double__eq__0__iff,axiom,
% 4.71/5.05 ! [A: int] :
% 4.71/5.05 ( ( ( plus_plus_int @ A @ A )
% 4.71/5.05 = zero_zero_int )
% 4.71/5.05 = ( A = zero_zero_int ) ) ).
% 4.71/5.05
% 4.71/5.05 % double_eq_0_iff
% 4.71/5.05 thf(fact_1956_add__less__cancel__left,axiom,
% 4.71/5.05 ! [C: real,A: real,B: real] :
% 4.71/5.05 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 4.71/5.05 = ( ord_less_real @ A @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_less_cancel_left
% 4.71/5.05 thf(fact_1957_add__less__cancel__left,axiom,
% 4.71/5.05 ! [C: rat,A: rat,B: rat] :
% 4.71/5.05 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 4.71/5.05 = ( ord_less_rat @ A @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_less_cancel_left
% 4.71/5.05 thf(fact_1958_add__less__cancel__left,axiom,
% 4.71/5.05 ! [C: nat,A: nat,B: nat] :
% 4.71/5.05 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 4.71/5.05 = ( ord_less_nat @ A @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_less_cancel_left
% 4.71/5.05 thf(fact_1959_add__less__cancel__left,axiom,
% 4.71/5.05 ! [C: int,A: int,B: int] :
% 4.71/5.05 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 4.71/5.05 = ( ord_less_int @ A @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_less_cancel_left
% 4.71/5.05 thf(fact_1960_add__less__cancel__right,axiom,
% 4.71/5.05 ! [A: real,C: real,B: real] :
% 4.71/5.05 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 4.71/5.05 = ( ord_less_real @ A @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_less_cancel_right
% 4.71/5.05 thf(fact_1961_add__less__cancel__right,axiom,
% 4.71/5.05 ! [A: rat,C: rat,B: rat] :
% 4.71/5.05 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 4.71/5.05 = ( ord_less_rat @ A @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_less_cancel_right
% 4.71/5.05 thf(fact_1962_add__less__cancel__right,axiom,
% 4.71/5.05 ! [A: nat,C: nat,B: nat] :
% 4.71/5.05 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 4.71/5.05 = ( ord_less_nat @ A @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_less_cancel_right
% 4.71/5.05 thf(fact_1963_add__less__cancel__right,axiom,
% 4.71/5.05 ! [A: int,C: int,B: int] :
% 4.71/5.05 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 4.71/5.05 = ( ord_less_int @ A @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_less_cancel_right
% 4.71/5.05 thf(fact_1964_mult__1,axiom,
% 4.71/5.05 ! [A: complex] :
% 4.71/5.05 ( ( times_times_complex @ one_one_complex @ A )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % mult_1
% 4.71/5.05 thf(fact_1965_mult__1,axiom,
% 4.71/5.05 ! [A: real] :
% 4.71/5.05 ( ( times_times_real @ one_one_real @ A )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % mult_1
% 4.71/5.05 thf(fact_1966_mult__1,axiom,
% 4.71/5.05 ! [A: rat] :
% 4.71/5.05 ( ( times_times_rat @ one_one_rat @ A )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % mult_1
% 4.71/5.05 thf(fact_1967_mult__1,axiom,
% 4.71/5.05 ! [A: nat] :
% 4.71/5.05 ( ( times_times_nat @ one_one_nat @ A )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % mult_1
% 4.71/5.05 thf(fact_1968_mult__1,axiom,
% 4.71/5.05 ! [A: int] :
% 4.71/5.05 ( ( times_times_int @ one_one_int @ A )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % mult_1
% 4.71/5.05 thf(fact_1969_mult_Oright__neutral,axiom,
% 4.71/5.05 ! [A: complex] :
% 4.71/5.05 ( ( times_times_complex @ A @ one_one_complex )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % mult.right_neutral
% 4.71/5.05 thf(fact_1970_mult_Oright__neutral,axiom,
% 4.71/5.05 ! [A: real] :
% 4.71/5.05 ( ( times_times_real @ A @ one_one_real )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % mult.right_neutral
% 4.71/5.05 thf(fact_1971_mult_Oright__neutral,axiom,
% 4.71/5.05 ! [A: rat] :
% 4.71/5.05 ( ( times_times_rat @ A @ one_one_rat )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % mult.right_neutral
% 4.71/5.05 thf(fact_1972_mult_Oright__neutral,axiom,
% 4.71/5.05 ! [A: nat] :
% 4.71/5.05 ( ( times_times_nat @ A @ one_one_nat )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % mult.right_neutral
% 4.71/5.05 thf(fact_1973_mult_Oright__neutral,axiom,
% 4.71/5.05 ! [A: int] :
% 4.71/5.05 ( ( times_times_int @ A @ one_one_int )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % mult.right_neutral
% 4.71/5.05 thf(fact_1974_add__diff__cancel__right_H,axiom,
% 4.71/5.05 ! [A: real,B: real] :
% 4.71/5.05 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % add_diff_cancel_right'
% 4.71/5.05 thf(fact_1975_add__diff__cancel__right_H,axiom,
% 4.71/5.05 ! [A: rat,B: rat] :
% 4.71/5.05 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % add_diff_cancel_right'
% 4.71/5.05 thf(fact_1976_add__diff__cancel__right_H,axiom,
% 4.71/5.05 ! [A: nat,B: nat] :
% 4.71/5.05 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % add_diff_cancel_right'
% 4.71/5.05 thf(fact_1977_add__diff__cancel__right_H,axiom,
% 4.71/5.05 ! [A: int,B: int] :
% 4.71/5.05 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % add_diff_cancel_right'
% 4.71/5.05 thf(fact_1978_add__diff__cancel__right,axiom,
% 4.71/5.05 ! [A: real,C: real,B: real] :
% 4.71/5.05 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 4.71/5.05 = ( minus_minus_real @ A @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_diff_cancel_right
% 4.71/5.05 thf(fact_1979_add__diff__cancel__right,axiom,
% 4.71/5.05 ! [A: rat,C: rat,B: rat] :
% 4.71/5.05 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 4.71/5.05 = ( minus_minus_rat @ A @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_diff_cancel_right
% 4.71/5.05 thf(fact_1980_add__diff__cancel__right,axiom,
% 4.71/5.05 ! [A: nat,C: nat,B: nat] :
% 4.71/5.05 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 4.71/5.05 = ( minus_minus_nat @ A @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_diff_cancel_right
% 4.71/5.05 thf(fact_1981_add__diff__cancel__right,axiom,
% 4.71/5.05 ! [A: int,C: int,B: int] :
% 4.71/5.05 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 4.71/5.05 = ( minus_minus_int @ A @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_diff_cancel_right
% 4.71/5.05 thf(fact_1982_add__diff__cancel__left_H,axiom,
% 4.71/5.05 ! [A: real,B: real] :
% 4.71/5.05 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 4.71/5.05 = B ) ).
% 4.71/5.05
% 4.71/5.05 % add_diff_cancel_left'
% 4.71/5.05 thf(fact_1983_add__diff__cancel__left_H,axiom,
% 4.71/5.05 ! [A: rat,B: rat] :
% 4.71/5.05 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 4.71/5.05 = B ) ).
% 4.71/5.05
% 4.71/5.05 % add_diff_cancel_left'
% 4.71/5.05 thf(fact_1984_add__diff__cancel__left_H,axiom,
% 4.71/5.05 ! [A: nat,B: nat] :
% 4.71/5.05 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 4.71/5.05 = B ) ).
% 4.71/5.05
% 4.71/5.05 % add_diff_cancel_left'
% 4.71/5.05 thf(fact_1985_add__diff__cancel__left_H,axiom,
% 4.71/5.05 ! [A: int,B: int] :
% 4.71/5.05 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 4.71/5.05 = B ) ).
% 4.71/5.05
% 4.71/5.05 % add_diff_cancel_left'
% 4.71/5.05 thf(fact_1986_add__diff__cancel__left,axiom,
% 4.71/5.05 ! [C: real,A: real,B: real] :
% 4.71/5.05 ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 4.71/5.05 = ( minus_minus_real @ A @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_diff_cancel_left
% 4.71/5.05 thf(fact_1987_add__diff__cancel__left,axiom,
% 4.71/5.05 ! [C: rat,A: rat,B: rat] :
% 4.71/5.05 ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 4.71/5.05 = ( minus_minus_rat @ A @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_diff_cancel_left
% 4.71/5.05 thf(fact_1988_add__diff__cancel__left,axiom,
% 4.71/5.05 ! [C: nat,A: nat,B: nat] :
% 4.71/5.05 ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 4.71/5.05 = ( minus_minus_nat @ A @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_diff_cancel_left
% 4.71/5.05 thf(fact_1989_add__diff__cancel__left,axiom,
% 4.71/5.05 ! [C: int,A: int,B: int] :
% 4.71/5.05 ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 4.71/5.05 = ( minus_minus_int @ A @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_diff_cancel_left
% 4.71/5.05 thf(fact_1990_diff__add__cancel,axiom,
% 4.71/5.05 ! [A: real,B: real] :
% 4.71/5.05 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % diff_add_cancel
% 4.71/5.05 thf(fact_1991_diff__add__cancel,axiom,
% 4.71/5.05 ! [A: rat,B: rat] :
% 4.71/5.05 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % diff_add_cancel
% 4.71/5.05 thf(fact_1992_diff__add__cancel,axiom,
% 4.71/5.05 ! [A: int,B: int] :
% 4.71/5.05 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % diff_add_cancel
% 4.71/5.05 thf(fact_1993_add__diff__cancel,axiom,
% 4.71/5.05 ! [A: real,B: real] :
% 4.71/5.05 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % add_diff_cancel
% 4.71/5.05 thf(fact_1994_add__diff__cancel,axiom,
% 4.71/5.05 ! [A: rat,B: rat] :
% 4.71/5.05 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % add_diff_cancel
% 4.71/5.05 thf(fact_1995_add__diff__cancel,axiom,
% 4.71/5.05 ! [A: int,B: int] :
% 4.71/5.05 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 4.71/5.05 = A ) ).
% 4.71/5.05
% 4.71/5.05 % add_diff_cancel
% 4.71/5.05 thf(fact_1996_abs__0__eq,axiom,
% 4.71/5.05 ! [A: real] :
% 4.71/5.05 ( ( zero_zero_real
% 4.71/5.05 = ( abs_abs_real @ A ) )
% 4.71/5.05 = ( A = zero_zero_real ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_0_eq
% 4.71/5.05 thf(fact_1997_abs__0__eq,axiom,
% 4.71/5.05 ! [A: rat] :
% 4.71/5.05 ( ( zero_zero_rat
% 4.71/5.05 = ( abs_abs_rat @ A ) )
% 4.71/5.05 = ( A = zero_zero_rat ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_0_eq
% 4.71/5.05 thf(fact_1998_abs__0__eq,axiom,
% 4.71/5.05 ! [A: int] :
% 4.71/5.05 ( ( zero_zero_int
% 4.71/5.05 = ( abs_abs_int @ A ) )
% 4.71/5.05 = ( A = zero_zero_int ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_0_eq
% 4.71/5.05 thf(fact_1999_abs__eq__0,axiom,
% 4.71/5.05 ! [A: real] :
% 4.71/5.05 ( ( ( abs_abs_real @ A )
% 4.71/5.05 = zero_zero_real )
% 4.71/5.05 = ( A = zero_zero_real ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_eq_0
% 4.71/5.05 thf(fact_2000_abs__eq__0,axiom,
% 4.71/5.05 ! [A: rat] :
% 4.71/5.05 ( ( ( abs_abs_rat @ A )
% 4.71/5.05 = zero_zero_rat )
% 4.71/5.05 = ( A = zero_zero_rat ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_eq_0
% 4.71/5.05 thf(fact_2001_abs__eq__0,axiom,
% 4.71/5.05 ! [A: int] :
% 4.71/5.05 ( ( ( abs_abs_int @ A )
% 4.71/5.05 = zero_zero_int )
% 4.71/5.05 = ( A = zero_zero_int ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_eq_0
% 4.71/5.05 thf(fact_2002_abs__zero,axiom,
% 4.71/5.05 ( ( abs_abs_real @ zero_zero_real )
% 4.71/5.05 = zero_zero_real ) ).
% 4.71/5.05
% 4.71/5.05 % abs_zero
% 4.71/5.05 thf(fact_2003_abs__zero,axiom,
% 4.71/5.05 ( ( abs_abs_rat @ zero_zero_rat )
% 4.71/5.05 = zero_zero_rat ) ).
% 4.71/5.05
% 4.71/5.05 % abs_zero
% 4.71/5.05 thf(fact_2004_abs__zero,axiom,
% 4.71/5.05 ( ( abs_abs_int @ zero_zero_int )
% 4.71/5.05 = zero_zero_int ) ).
% 4.71/5.05
% 4.71/5.05 % abs_zero
% 4.71/5.05 thf(fact_2005_abs__0,axiom,
% 4.71/5.05 ( ( abs_abs_real @ zero_zero_real )
% 4.71/5.05 = zero_zero_real ) ).
% 4.71/5.05
% 4.71/5.05 % abs_0
% 4.71/5.05 thf(fact_2006_abs__0,axiom,
% 4.71/5.05 ( ( abs_abs_rat @ zero_zero_rat )
% 4.71/5.05 = zero_zero_rat ) ).
% 4.71/5.05
% 4.71/5.05 % abs_0
% 4.71/5.05 thf(fact_2007_abs__0,axiom,
% 4.71/5.05 ( ( abs_abs_int @ zero_zero_int )
% 4.71/5.05 = zero_zero_int ) ).
% 4.71/5.05
% 4.71/5.05 % abs_0
% 4.71/5.05 thf(fact_2008_of__nat__add,axiom,
% 4.71/5.05 ! [M2: nat,N: nat] :
% 4.71/5.05 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M2 @ N ) )
% 4.71/5.05 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % of_nat_add
% 4.71/5.05 thf(fact_2009_of__nat__add,axiom,
% 4.71/5.05 ! [M2: nat,N: nat] :
% 4.71/5.05 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M2 @ N ) )
% 4.71/5.05 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % of_nat_add
% 4.71/5.05 thf(fact_2010_of__nat__add,axiom,
% 4.71/5.05 ! [M2: nat,N: nat] :
% 4.71/5.05 ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M2 @ N ) )
% 4.71/5.05 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % of_nat_add
% 4.71/5.05 thf(fact_2011_of__nat__add,axiom,
% 4.71/5.05 ! [M2: nat,N: nat] :
% 4.71/5.05 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M2 @ N ) )
% 4.71/5.05 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % of_nat_add
% 4.71/5.05 thf(fact_2012_abs__mult__self__eq,axiom,
% 4.71/5.05 ! [A: real] :
% 4.71/5.05 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 4.71/5.05 = ( times_times_real @ A @ A ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_mult_self_eq
% 4.71/5.05 thf(fact_2013_abs__mult__self__eq,axiom,
% 4.71/5.05 ! [A: rat] :
% 4.71/5.05 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 4.71/5.05 = ( times_times_rat @ A @ A ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_mult_self_eq
% 4.71/5.05 thf(fact_2014_abs__mult__self__eq,axiom,
% 4.71/5.05 ! [A: int] :
% 4.71/5.05 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 4.71/5.05 = ( times_times_int @ A @ A ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_mult_self_eq
% 4.71/5.05 thf(fact_2015_abs__add__abs,axiom,
% 4.71/5.05 ! [A: real,B: real] :
% 4.71/5.05 ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 4.71/5.05 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_add_abs
% 4.71/5.05 thf(fact_2016_abs__add__abs,axiom,
% 4.71/5.05 ! [A: rat,B: rat] :
% 4.71/5.05 ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 4.71/5.05 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_add_abs
% 4.71/5.05 thf(fact_2017_abs__add__abs,axiom,
% 4.71/5.05 ! [A: int,B: int] :
% 4.71/5.05 ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 4.71/5.05 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_add_abs
% 4.71/5.05 thf(fact_2018_abs__1,axiom,
% 4.71/5.05 ( ( abs_abs_complex @ one_one_complex )
% 4.71/5.05 = one_one_complex ) ).
% 4.71/5.05
% 4.71/5.05 % abs_1
% 4.71/5.05 thf(fact_2019_abs__1,axiom,
% 4.71/5.05 ( ( abs_abs_real @ one_one_real )
% 4.71/5.05 = one_one_real ) ).
% 4.71/5.05
% 4.71/5.05 % abs_1
% 4.71/5.05 thf(fact_2020_abs__1,axiom,
% 4.71/5.05 ( ( abs_abs_rat @ one_one_rat )
% 4.71/5.05 = one_one_rat ) ).
% 4.71/5.05
% 4.71/5.05 % abs_1
% 4.71/5.05 thf(fact_2021_abs__1,axiom,
% 4.71/5.05 ( ( abs_abs_int @ one_one_int )
% 4.71/5.05 = one_one_int ) ).
% 4.71/5.05
% 4.71/5.05 % abs_1
% 4.71/5.05 thf(fact_2022_singletonI,axiom,
% 4.71/5.05 ! [A: product_prod_nat_nat] : ( member8440522571783428010at_nat @ A @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ).
% 4.71/5.05
% 4.71/5.05 % singletonI
% 4.71/5.05 thf(fact_2023_singletonI,axiom,
% 4.71/5.05 ! [A: set_nat] : ( member_set_nat @ A @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 4.71/5.05
% 4.71/5.05 % singletonI
% 4.71/5.05 thf(fact_2024_singletonI,axiom,
% 4.71/5.05 ! [A: set_nat_rat] : ( member_set_nat_rat @ A @ ( insert_set_nat_rat @ A @ bot_bo6797373522285170759at_rat ) ) ).
% 4.71/5.05
% 4.71/5.05 % singletonI
% 4.71/5.05 thf(fact_2025_singletonI,axiom,
% 4.71/5.05 ! [A: real] : ( member_real @ A @ ( insert_real @ A @ bot_bot_set_real ) ) ).
% 4.71/5.05
% 4.71/5.05 % singletonI
% 4.71/5.05 thf(fact_2026_singletonI,axiom,
% 4.71/5.05 ! [A: $o] : ( member_o @ A @ ( insert_o @ A @ bot_bot_set_o ) ) ).
% 4.71/5.05
% 4.71/5.05 % singletonI
% 4.71/5.05 thf(fact_2027_singletonI,axiom,
% 4.71/5.05 ! [A: nat] : ( member_nat @ A @ ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 4.71/5.05
% 4.71/5.05 % singletonI
% 4.71/5.05 thf(fact_2028_singletonI,axiom,
% 4.71/5.05 ! [A: int] : ( member_int @ A @ ( insert_int @ A @ bot_bot_set_int ) ) ).
% 4.71/5.05
% 4.71/5.05 % singletonI
% 4.71/5.05 thf(fact_2029_finite__insert,axiom,
% 4.71/5.05 ! [A: real,A2: set_real] :
% 4.71/5.05 ( ( finite_finite_real @ ( insert_real @ A @ A2 ) )
% 4.71/5.05 = ( finite_finite_real @ A2 ) ) ).
% 4.71/5.05
% 4.71/5.05 % finite_insert
% 4.71/5.05 thf(fact_2030_finite__insert,axiom,
% 4.71/5.05 ! [A: $o,A2: set_o] :
% 4.71/5.05 ( ( finite_finite_o @ ( insert_o @ A @ A2 ) )
% 4.71/5.05 = ( finite_finite_o @ A2 ) ) ).
% 4.71/5.05
% 4.71/5.05 % finite_insert
% 4.71/5.05 thf(fact_2031_finite__insert,axiom,
% 4.71/5.05 ! [A: nat,A2: set_nat] :
% 4.71/5.05 ( ( finite_finite_nat @ ( insert_nat @ A @ A2 ) )
% 4.71/5.05 = ( finite_finite_nat @ A2 ) ) ).
% 4.71/5.05
% 4.71/5.05 % finite_insert
% 4.71/5.05 thf(fact_2032_finite__insert,axiom,
% 4.71/5.05 ! [A: int,A2: set_int] :
% 4.71/5.05 ( ( finite_finite_int @ ( insert_int @ A @ A2 ) )
% 4.71/5.05 = ( finite_finite_int @ A2 ) ) ).
% 4.71/5.05
% 4.71/5.05 % finite_insert
% 4.71/5.05 thf(fact_2033_finite__insert,axiom,
% 4.71/5.05 ! [A: complex,A2: set_complex] :
% 4.71/5.05 ( ( finite3207457112153483333omplex @ ( insert_complex @ A @ A2 ) )
% 4.71/5.05 = ( finite3207457112153483333omplex @ A2 ) ) ).
% 4.71/5.05
% 4.71/5.05 % finite_insert
% 4.71/5.05 thf(fact_2034_finite__insert,axiom,
% 4.71/5.05 ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.05 ( ( finite6177210948735845034at_nat @ ( insert8211810215607154385at_nat @ A @ A2 ) )
% 4.71/5.05 = ( finite6177210948735845034at_nat @ A2 ) ) ).
% 4.71/5.05
% 4.71/5.05 % finite_insert
% 4.71/5.05 thf(fact_2035_finite__insert,axiom,
% 4.71/5.05 ! [A: extended_enat,A2: set_Extended_enat] :
% 4.71/5.05 ( ( finite4001608067531595151d_enat @ ( insert_Extended_enat @ A @ A2 ) )
% 4.71/5.05 = ( finite4001608067531595151d_enat @ A2 ) ) ).
% 4.71/5.05
% 4.71/5.05 % finite_insert
% 4.71/5.05 thf(fact_2036_ln__le__cancel__iff,axiom,
% 4.71/5.05 ! [X: real,Y: real] :
% 4.71/5.05 ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.05 => ( ( ord_less_real @ zero_zero_real @ Y )
% 4.71/5.05 => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) )
% 4.71/5.05 = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % ln_le_cancel_iff
% 4.71/5.05 thf(fact_2037_insert__subset,axiom,
% 4.71/5.05 ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 4.71/5.05 ( ( ord_le3146513528884898305at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) @ B2 )
% 4.71/5.05 = ( ( member8440522571783428010at_nat @ X @ B2 )
% 4.71/5.05 & ( ord_le3146513528884898305at_nat @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_subset
% 4.71/5.05 thf(fact_2038_insert__subset,axiom,
% 4.71/5.05 ! [X: real,A2: set_real,B2: set_real] :
% 4.71/5.05 ( ( ord_less_eq_set_real @ ( insert_real @ X @ A2 ) @ B2 )
% 4.71/5.05 = ( ( member_real @ X @ B2 )
% 4.71/5.05 & ( ord_less_eq_set_real @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_subset
% 4.71/5.05 thf(fact_2039_insert__subset,axiom,
% 4.71/5.05 ! [X: $o,A2: set_o,B2: set_o] :
% 4.71/5.05 ( ( ord_less_eq_set_o @ ( insert_o @ X @ A2 ) @ B2 )
% 4.71/5.05 = ( ( member_o @ X @ B2 )
% 4.71/5.05 & ( ord_less_eq_set_o @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_subset
% 4.71/5.05 thf(fact_2040_insert__subset,axiom,
% 4.71/5.05 ! [X: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 4.71/5.05 ( ( ord_le6893508408891458716et_nat @ ( insert_set_nat @ X @ A2 ) @ B2 )
% 4.71/5.05 = ( ( member_set_nat @ X @ B2 )
% 4.71/5.05 & ( ord_le6893508408891458716et_nat @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_subset
% 4.71/5.05 thf(fact_2041_insert__subset,axiom,
% 4.71/5.05 ! [X: set_nat_rat,A2: set_set_nat_rat,B2: set_set_nat_rat] :
% 4.71/5.05 ( ( ord_le4375437777232675859at_rat @ ( insert_set_nat_rat @ X @ A2 ) @ B2 )
% 4.71/5.05 = ( ( member_set_nat_rat @ X @ B2 )
% 4.71/5.05 & ( ord_le4375437777232675859at_rat @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_subset
% 4.71/5.05 thf(fact_2042_insert__subset,axiom,
% 4.71/5.05 ! [X: nat,A2: set_nat,B2: set_nat] :
% 4.71/5.05 ( ( ord_less_eq_set_nat @ ( insert_nat @ X @ A2 ) @ B2 )
% 4.71/5.05 = ( ( member_nat @ X @ B2 )
% 4.71/5.05 & ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_subset
% 4.71/5.05 thf(fact_2043_insert__subset,axiom,
% 4.71/5.05 ! [X: int,A2: set_int,B2: set_int] :
% 4.71/5.05 ( ( ord_less_eq_set_int @ ( insert_int @ X @ A2 ) @ B2 )
% 4.71/5.05 = ( ( member_int @ X @ B2 )
% 4.71/5.05 & ( ord_less_eq_set_int @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_subset
% 4.71/5.05 thf(fact_2044_mult__is__0,axiom,
% 4.71/5.05 ! [M2: nat,N: nat] :
% 4.71/5.05 ( ( ( times_times_nat @ M2 @ N )
% 4.71/5.05 = zero_zero_nat )
% 4.71/5.05 = ( ( M2 = zero_zero_nat )
% 4.71/5.05 | ( N = zero_zero_nat ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_is_0
% 4.71/5.05 thf(fact_2045_mult__0__right,axiom,
% 4.71/5.05 ! [M2: nat] :
% 4.71/5.05 ( ( times_times_nat @ M2 @ zero_zero_nat )
% 4.71/5.05 = zero_zero_nat ) ).
% 4.71/5.05
% 4.71/5.05 % mult_0_right
% 4.71/5.05 thf(fact_2046_mult__cancel1,axiom,
% 4.71/5.05 ! [K: nat,M2: nat,N: nat] :
% 4.71/5.05 ( ( ( times_times_nat @ K @ M2 )
% 4.71/5.05 = ( times_times_nat @ K @ N ) )
% 4.71/5.05 = ( ( M2 = N )
% 4.71/5.05 | ( K = zero_zero_nat ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_cancel1
% 4.71/5.05 thf(fact_2047_mult__cancel2,axiom,
% 4.71/5.05 ! [M2: nat,K: nat,N: nat] :
% 4.71/5.05 ( ( ( times_times_nat @ M2 @ K )
% 4.71/5.05 = ( times_times_nat @ N @ K ) )
% 4.71/5.05 = ( ( M2 = N )
% 4.71/5.05 | ( K = zero_zero_nat ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_cancel2
% 4.71/5.05 thf(fact_2048_abs__of__nat,axiom,
% 4.71/5.05 ! [N: nat] :
% 4.71/5.05 ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N ) )
% 4.71/5.05 = ( semiri1314217659103216013at_int @ N ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_of_nat
% 4.71/5.05 thf(fact_2049_abs__of__nat,axiom,
% 4.71/5.05 ! [N: nat] :
% 4.71/5.05 ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N ) )
% 4.71/5.05 = ( semiri5074537144036343181t_real @ N ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_of_nat
% 4.71/5.05 thf(fact_2050_abs__of__nat,axiom,
% 4.71/5.05 ! [N: nat] :
% 4.71/5.05 ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N ) )
% 4.71/5.05 = ( semiri681578069525770553at_rat @ N ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_of_nat
% 4.71/5.05 thf(fact_2051_insert__Diff1,axiom,
% 4.71/5.05 ! [X: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.05 ( ( member8440522571783428010at_nat @ X @ B2 )
% 4.71/5.05 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) @ B2 )
% 4.71/5.05 = ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_Diff1
% 4.71/5.05 thf(fact_2052_insert__Diff1,axiom,
% 4.71/5.05 ! [X: real,B2: set_real,A2: set_real] :
% 4.71/5.05 ( ( member_real @ X @ B2 )
% 4.71/5.05 => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ B2 )
% 4.71/5.05 = ( minus_minus_set_real @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_Diff1
% 4.71/5.05 thf(fact_2053_insert__Diff1,axiom,
% 4.71/5.05 ! [X: $o,B2: set_o,A2: set_o] :
% 4.71/5.05 ( ( member_o @ X @ B2 )
% 4.71/5.05 => ( ( minus_minus_set_o @ ( insert_o @ X @ A2 ) @ B2 )
% 4.71/5.05 = ( minus_minus_set_o @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_Diff1
% 4.71/5.05 thf(fact_2054_insert__Diff1,axiom,
% 4.71/5.05 ! [X: set_nat,B2: set_set_nat,A2: set_set_nat] :
% 4.71/5.05 ( ( member_set_nat @ X @ B2 )
% 4.71/5.05 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A2 ) @ B2 )
% 4.71/5.05 = ( minus_2163939370556025621et_nat @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_Diff1
% 4.71/5.05 thf(fact_2055_insert__Diff1,axiom,
% 4.71/5.05 ! [X: set_nat_rat,B2: set_set_nat_rat,A2: set_set_nat_rat] :
% 4.71/5.05 ( ( member_set_nat_rat @ X @ B2 )
% 4.71/5.05 => ( ( minus_1626877696091177228at_rat @ ( insert_set_nat_rat @ X @ A2 ) @ B2 )
% 4.71/5.05 = ( minus_1626877696091177228at_rat @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_Diff1
% 4.71/5.05 thf(fact_2056_insert__Diff1,axiom,
% 4.71/5.05 ! [X: int,B2: set_int,A2: set_int] :
% 4.71/5.05 ( ( member_int @ X @ B2 )
% 4.71/5.05 => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ B2 )
% 4.71/5.05 = ( minus_minus_set_int @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_Diff1
% 4.71/5.05 thf(fact_2057_insert__Diff1,axiom,
% 4.71/5.05 ! [X: nat,B2: set_nat,A2: set_nat] :
% 4.71/5.05 ( ( member_nat @ X @ B2 )
% 4.71/5.05 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ B2 )
% 4.71/5.05 = ( minus_minus_set_nat @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_Diff1
% 4.71/5.05 thf(fact_2058_Diff__insert0,axiom,
% 4.71/5.05 ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 4.71/5.05 ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 4.71/5.05 => ( ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ B2 ) )
% 4.71/5.05 = ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % Diff_insert0
% 4.71/5.05 thf(fact_2059_Diff__insert0,axiom,
% 4.71/5.05 ! [X: real,A2: set_real,B2: set_real] :
% 4.71/5.05 ( ~ ( member_real @ X @ A2 )
% 4.71/5.05 => ( ( minus_minus_set_real @ A2 @ ( insert_real @ X @ B2 ) )
% 4.71/5.05 = ( minus_minus_set_real @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % Diff_insert0
% 4.71/5.05 thf(fact_2060_Diff__insert0,axiom,
% 4.71/5.05 ! [X: $o,A2: set_o,B2: set_o] :
% 4.71/5.05 ( ~ ( member_o @ X @ A2 )
% 4.71/5.05 => ( ( minus_minus_set_o @ A2 @ ( insert_o @ X @ B2 ) )
% 4.71/5.05 = ( minus_minus_set_o @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % Diff_insert0
% 4.71/5.05 thf(fact_2061_Diff__insert0,axiom,
% 4.71/5.05 ! [X: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 4.71/5.05 ( ~ ( member_set_nat @ X @ A2 )
% 4.71/5.05 => ( ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ B2 ) )
% 4.71/5.05 = ( minus_2163939370556025621et_nat @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % Diff_insert0
% 4.71/5.05 thf(fact_2062_Diff__insert0,axiom,
% 4.71/5.05 ! [X: set_nat_rat,A2: set_set_nat_rat,B2: set_set_nat_rat] :
% 4.71/5.05 ( ~ ( member_set_nat_rat @ X @ A2 )
% 4.71/5.05 => ( ( minus_1626877696091177228at_rat @ A2 @ ( insert_set_nat_rat @ X @ B2 ) )
% 4.71/5.05 = ( minus_1626877696091177228at_rat @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % Diff_insert0
% 4.71/5.05 thf(fact_2063_Diff__insert0,axiom,
% 4.71/5.05 ! [X: int,A2: set_int,B2: set_int] :
% 4.71/5.05 ( ~ ( member_int @ X @ A2 )
% 4.71/5.05 => ( ( minus_minus_set_int @ A2 @ ( insert_int @ X @ B2 ) )
% 4.71/5.05 = ( minus_minus_set_int @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % Diff_insert0
% 4.71/5.05 thf(fact_2064_Diff__insert0,axiom,
% 4.71/5.05 ! [X: nat,A2: set_nat,B2: set_nat] :
% 4.71/5.05 ( ~ ( member_nat @ X @ A2 )
% 4.71/5.05 => ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ B2 ) )
% 4.71/5.05 = ( minus_minus_set_nat @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % Diff_insert0
% 4.71/5.05 thf(fact_2065_nat__mult__eq__1__iff,axiom,
% 4.71/5.05 ! [M2: nat,N: nat] :
% 4.71/5.05 ( ( ( times_times_nat @ M2 @ N )
% 4.71/5.05 = one_one_nat )
% 4.71/5.05 = ( ( M2 = one_one_nat )
% 4.71/5.05 & ( N = one_one_nat ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % nat_mult_eq_1_iff
% 4.71/5.05 thf(fact_2066_nat__1__eq__mult__iff,axiom,
% 4.71/5.05 ! [M2: nat,N: nat] :
% 4.71/5.05 ( ( one_one_nat
% 4.71/5.05 = ( times_times_nat @ M2 @ N ) )
% 4.71/5.05 = ( ( M2 = one_one_nat )
% 4.71/5.05 & ( N = one_one_nat ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % nat_1_eq_mult_iff
% 4.71/5.05 thf(fact_2067_zero__le__double__add__iff__zero__le__single__add,axiom,
% 4.71/5.05 ! [A: real] :
% 4.71/5.05 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 4.71/5.05 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 4.71/5.05
% 4.71/5.05 % zero_le_double_add_iff_zero_le_single_add
% 4.71/5.05 thf(fact_2068_zero__le__double__add__iff__zero__le__single__add,axiom,
% 4.71/5.05 ! [A: rat] :
% 4.71/5.05 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 4.71/5.05 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 4.71/5.05
% 4.71/5.05 % zero_le_double_add_iff_zero_le_single_add
% 4.71/5.05 thf(fact_2069_zero__le__double__add__iff__zero__le__single__add,axiom,
% 4.71/5.05 ! [A: int] :
% 4.71/5.05 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 4.71/5.05 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 4.71/5.05
% 4.71/5.05 % zero_le_double_add_iff_zero_le_single_add
% 4.71/5.05 thf(fact_2070_double__add__le__zero__iff__single__add__le__zero,axiom,
% 4.71/5.05 ! [A: real] :
% 4.71/5.05 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 4.71/5.05 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 4.71/5.05
% 4.71/5.05 % double_add_le_zero_iff_single_add_le_zero
% 4.71/5.05 thf(fact_2071_double__add__le__zero__iff__single__add__le__zero,axiom,
% 4.71/5.05 ! [A: rat] :
% 4.71/5.05 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 4.71/5.05 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 4.71/5.05
% 4.71/5.05 % double_add_le_zero_iff_single_add_le_zero
% 4.71/5.05 thf(fact_2072_double__add__le__zero__iff__single__add__le__zero,axiom,
% 4.71/5.05 ! [A: int] :
% 4.71/5.05 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 4.71/5.05 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 4.71/5.05
% 4.71/5.05 % double_add_le_zero_iff_single_add_le_zero
% 4.71/5.05 thf(fact_2073_le__add__same__cancel2,axiom,
% 4.71/5.05 ! [A: real,B: real] :
% 4.71/5.05 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 4.71/5.05 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % le_add_same_cancel2
% 4.71/5.05 thf(fact_2074_le__add__same__cancel2,axiom,
% 4.71/5.05 ! [A: rat,B: rat] :
% 4.71/5.05 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 4.71/5.05 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % le_add_same_cancel2
% 4.71/5.05 thf(fact_2075_le__add__same__cancel2,axiom,
% 4.71/5.05 ! [A: nat,B: nat] :
% 4.71/5.05 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 4.71/5.05 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % le_add_same_cancel2
% 4.71/5.05 thf(fact_2076_le__add__same__cancel2,axiom,
% 4.71/5.05 ! [A: int,B: int] :
% 4.71/5.05 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 4.71/5.05 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % le_add_same_cancel2
% 4.71/5.05 thf(fact_2077_le__add__same__cancel1,axiom,
% 4.71/5.05 ! [A: real,B: real] :
% 4.71/5.05 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 4.71/5.05 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % le_add_same_cancel1
% 4.71/5.05 thf(fact_2078_le__add__same__cancel1,axiom,
% 4.71/5.05 ! [A: rat,B: rat] :
% 4.71/5.05 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 4.71/5.05 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % le_add_same_cancel1
% 4.71/5.05 thf(fact_2079_le__add__same__cancel1,axiom,
% 4.71/5.05 ! [A: nat,B: nat] :
% 4.71/5.05 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 4.71/5.05 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % le_add_same_cancel1
% 4.71/5.05 thf(fact_2080_le__add__same__cancel1,axiom,
% 4.71/5.05 ! [A: int,B: int] :
% 4.71/5.05 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 4.71/5.05 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % le_add_same_cancel1
% 4.71/5.05 thf(fact_2081_add__le__same__cancel2,axiom,
% 4.71/5.05 ! [A: real,B: real] :
% 4.71/5.05 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 4.71/5.05 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_le_same_cancel2
% 4.71/5.05 thf(fact_2082_add__le__same__cancel2,axiom,
% 4.71/5.05 ! [A: rat,B: rat] :
% 4.71/5.05 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 4.71/5.05 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_le_same_cancel2
% 4.71/5.05 thf(fact_2083_add__le__same__cancel2,axiom,
% 4.71/5.05 ! [A: nat,B: nat] :
% 4.71/5.05 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 4.71/5.05 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_le_same_cancel2
% 4.71/5.05 thf(fact_2084_add__le__same__cancel2,axiom,
% 4.71/5.05 ! [A: int,B: int] :
% 4.71/5.05 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 4.71/5.05 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_le_same_cancel2
% 4.71/5.05 thf(fact_2085_add__le__same__cancel1,axiom,
% 4.71/5.05 ! [B: real,A: real] :
% 4.71/5.05 ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 4.71/5.05 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_le_same_cancel1
% 4.71/5.05 thf(fact_2086_add__le__same__cancel1,axiom,
% 4.71/5.05 ! [B: rat,A: rat] :
% 4.71/5.05 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 4.71/5.05 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_le_same_cancel1
% 4.71/5.05 thf(fact_2087_add__le__same__cancel1,axiom,
% 4.71/5.05 ! [B: nat,A: nat] :
% 4.71/5.05 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 4.71/5.05 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_le_same_cancel1
% 4.71/5.05 thf(fact_2088_add__le__same__cancel1,axiom,
% 4.71/5.05 ! [B: int,A: int] :
% 4.71/5.05 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 4.71/5.05 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_le_same_cancel1
% 4.71/5.05 thf(fact_2089_add__less__same__cancel1,axiom,
% 4.71/5.05 ! [B: real,A: real] :
% 4.71/5.05 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 4.71/5.05 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_less_same_cancel1
% 4.71/5.05 thf(fact_2090_add__less__same__cancel1,axiom,
% 4.71/5.05 ! [B: rat,A: rat] :
% 4.71/5.05 ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 4.71/5.05 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_less_same_cancel1
% 4.71/5.05 thf(fact_2091_add__less__same__cancel1,axiom,
% 4.71/5.05 ! [B: nat,A: nat] :
% 4.71/5.05 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 4.71/5.05 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_less_same_cancel1
% 4.71/5.05 thf(fact_2092_add__less__same__cancel1,axiom,
% 4.71/5.05 ! [B: int,A: int] :
% 4.71/5.05 ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 4.71/5.05 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_less_same_cancel1
% 4.71/5.05 thf(fact_2093_add__less__same__cancel2,axiom,
% 4.71/5.05 ! [A: real,B: real] :
% 4.71/5.05 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 4.71/5.05 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_less_same_cancel2
% 4.71/5.05 thf(fact_2094_add__less__same__cancel2,axiom,
% 4.71/5.05 ! [A: rat,B: rat] :
% 4.71/5.05 ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 4.71/5.05 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_less_same_cancel2
% 4.71/5.05 thf(fact_2095_add__less__same__cancel2,axiom,
% 4.71/5.05 ! [A: nat,B: nat] :
% 4.71/5.05 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 4.71/5.05 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_less_same_cancel2
% 4.71/5.05 thf(fact_2096_add__less__same__cancel2,axiom,
% 4.71/5.05 ! [A: int,B: int] :
% 4.71/5.05 ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 4.71/5.05 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 4.71/5.05
% 4.71/5.05 % add_less_same_cancel2
% 4.71/5.05 thf(fact_2097_less__add__same__cancel1,axiom,
% 4.71/5.05 ! [A: real,B: real] :
% 4.71/5.05 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 4.71/5.05 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % less_add_same_cancel1
% 4.71/5.05 thf(fact_2098_less__add__same__cancel1,axiom,
% 4.71/5.05 ! [A: rat,B: rat] :
% 4.71/5.05 ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 4.71/5.05 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % less_add_same_cancel1
% 4.71/5.05 thf(fact_2099_less__add__same__cancel1,axiom,
% 4.71/5.05 ! [A: nat,B: nat] :
% 4.71/5.05 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 4.71/5.05 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % less_add_same_cancel1
% 4.71/5.05 thf(fact_2100_less__add__same__cancel1,axiom,
% 4.71/5.05 ! [A: int,B: int] :
% 4.71/5.05 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 4.71/5.05 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % less_add_same_cancel1
% 4.71/5.05 thf(fact_2101_less__add__same__cancel2,axiom,
% 4.71/5.05 ! [A: real,B: real] :
% 4.71/5.05 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 4.71/5.05 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % less_add_same_cancel2
% 4.71/5.05 thf(fact_2102_less__add__same__cancel2,axiom,
% 4.71/5.05 ! [A: rat,B: rat] :
% 4.71/5.05 ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 4.71/5.05 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % less_add_same_cancel2
% 4.71/5.05 thf(fact_2103_less__add__same__cancel2,axiom,
% 4.71/5.05 ! [A: nat,B: nat] :
% 4.71/5.05 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 4.71/5.05 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % less_add_same_cancel2
% 4.71/5.05 thf(fact_2104_less__add__same__cancel2,axiom,
% 4.71/5.05 ! [A: int,B: int] :
% 4.71/5.05 ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 4.71/5.05 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 4.71/5.05
% 4.71/5.05 % less_add_same_cancel2
% 4.71/5.05 thf(fact_2105_double__add__less__zero__iff__single__add__less__zero,axiom,
% 4.71/5.05 ! [A: real] :
% 4.71/5.05 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 4.71/5.05 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 4.71/5.05
% 4.71/5.05 % double_add_less_zero_iff_single_add_less_zero
% 4.71/5.05 thf(fact_2106_double__add__less__zero__iff__single__add__less__zero,axiom,
% 4.71/5.05 ! [A: rat] :
% 4.71/5.05 ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 4.71/5.05 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 4.71/5.05
% 4.71/5.05 % double_add_less_zero_iff_single_add_less_zero
% 4.71/5.05 thf(fact_2107_double__add__less__zero__iff__single__add__less__zero,axiom,
% 4.71/5.05 ! [A: int] :
% 4.71/5.05 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 4.71/5.05 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 4.71/5.05
% 4.71/5.05 % double_add_less_zero_iff_single_add_less_zero
% 4.71/5.05 thf(fact_2108_zero__less__double__add__iff__zero__less__single__add,axiom,
% 4.71/5.05 ! [A: real] :
% 4.71/5.05 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 4.71/5.05 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 4.71/5.05
% 4.71/5.05 % zero_less_double_add_iff_zero_less_single_add
% 4.71/5.05 thf(fact_2109_zero__less__double__add__iff__zero__less__single__add,axiom,
% 4.71/5.05 ! [A: rat] :
% 4.71/5.05 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 4.71/5.05 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 4.71/5.05
% 4.71/5.05 % zero_less_double_add_iff_zero_less_single_add
% 4.71/5.05 thf(fact_2110_zero__less__double__add__iff__zero__less__single__add,axiom,
% 4.71/5.05 ! [A: int] :
% 4.71/5.05 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 4.71/5.05 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 4.71/5.05
% 4.71/5.05 % zero_less_double_add_iff_zero_less_single_add
% 4.71/5.05 thf(fact_2111_mult__cancel__left1,axiom,
% 4.71/5.05 ! [C: complex,B: complex] :
% 4.71/5.05 ( ( C
% 4.71/5.05 = ( times_times_complex @ C @ B ) )
% 4.71/5.05 = ( ( C = zero_zero_complex )
% 4.71/5.05 | ( B = one_one_complex ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_cancel_left1
% 4.71/5.05 thf(fact_2112_mult__cancel__left1,axiom,
% 4.71/5.05 ! [C: real,B: real] :
% 4.71/5.05 ( ( C
% 4.71/5.05 = ( times_times_real @ C @ B ) )
% 4.71/5.05 = ( ( C = zero_zero_real )
% 4.71/5.05 | ( B = one_one_real ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_cancel_left1
% 4.71/5.05 thf(fact_2113_mult__cancel__left1,axiom,
% 4.71/5.05 ! [C: rat,B: rat] :
% 4.71/5.05 ( ( C
% 4.71/5.05 = ( times_times_rat @ C @ B ) )
% 4.71/5.05 = ( ( C = zero_zero_rat )
% 4.71/5.05 | ( B = one_one_rat ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_cancel_left1
% 4.71/5.05 thf(fact_2114_mult__cancel__left1,axiom,
% 4.71/5.05 ! [C: int,B: int] :
% 4.71/5.05 ( ( C
% 4.71/5.05 = ( times_times_int @ C @ B ) )
% 4.71/5.05 = ( ( C = zero_zero_int )
% 4.71/5.05 | ( B = one_one_int ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_cancel_left1
% 4.71/5.05 thf(fact_2115_mult__cancel__left2,axiom,
% 4.71/5.05 ! [C: complex,A: complex] :
% 4.71/5.05 ( ( ( times_times_complex @ C @ A )
% 4.71/5.05 = C )
% 4.71/5.05 = ( ( C = zero_zero_complex )
% 4.71/5.05 | ( A = one_one_complex ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_cancel_left2
% 4.71/5.05 thf(fact_2116_mult__cancel__left2,axiom,
% 4.71/5.05 ! [C: real,A: real] :
% 4.71/5.05 ( ( ( times_times_real @ C @ A )
% 4.71/5.05 = C )
% 4.71/5.05 = ( ( C = zero_zero_real )
% 4.71/5.05 | ( A = one_one_real ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_cancel_left2
% 4.71/5.05 thf(fact_2117_mult__cancel__left2,axiom,
% 4.71/5.05 ! [C: rat,A: rat] :
% 4.71/5.05 ( ( ( times_times_rat @ C @ A )
% 4.71/5.05 = C )
% 4.71/5.05 = ( ( C = zero_zero_rat )
% 4.71/5.05 | ( A = one_one_rat ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_cancel_left2
% 4.71/5.05 thf(fact_2118_mult__cancel__left2,axiom,
% 4.71/5.05 ! [C: int,A: int] :
% 4.71/5.05 ( ( ( times_times_int @ C @ A )
% 4.71/5.05 = C )
% 4.71/5.05 = ( ( C = zero_zero_int )
% 4.71/5.05 | ( A = one_one_int ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_cancel_left2
% 4.71/5.05 thf(fact_2119_mult__cancel__right1,axiom,
% 4.71/5.05 ! [C: complex,B: complex] :
% 4.71/5.05 ( ( C
% 4.71/5.05 = ( times_times_complex @ B @ C ) )
% 4.71/5.05 = ( ( C = zero_zero_complex )
% 4.71/5.05 | ( B = one_one_complex ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_cancel_right1
% 4.71/5.05 thf(fact_2120_mult__cancel__right1,axiom,
% 4.71/5.05 ! [C: real,B: real] :
% 4.71/5.05 ( ( C
% 4.71/5.05 = ( times_times_real @ B @ C ) )
% 4.71/5.05 = ( ( C = zero_zero_real )
% 4.71/5.05 | ( B = one_one_real ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_cancel_right1
% 4.71/5.05 thf(fact_2121_mult__cancel__right1,axiom,
% 4.71/5.05 ! [C: rat,B: rat] :
% 4.71/5.05 ( ( C
% 4.71/5.05 = ( times_times_rat @ B @ C ) )
% 4.71/5.05 = ( ( C = zero_zero_rat )
% 4.71/5.05 | ( B = one_one_rat ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_cancel_right1
% 4.71/5.05 thf(fact_2122_mult__cancel__right1,axiom,
% 4.71/5.05 ! [C: int,B: int] :
% 4.71/5.05 ( ( C
% 4.71/5.05 = ( times_times_int @ B @ C ) )
% 4.71/5.05 = ( ( C = zero_zero_int )
% 4.71/5.05 | ( B = one_one_int ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_cancel_right1
% 4.71/5.05 thf(fact_2123_mult__cancel__right2,axiom,
% 4.71/5.05 ! [A: complex,C: complex] :
% 4.71/5.05 ( ( ( times_times_complex @ A @ C )
% 4.71/5.05 = C )
% 4.71/5.05 = ( ( C = zero_zero_complex )
% 4.71/5.05 | ( A = one_one_complex ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_cancel_right2
% 4.71/5.05 thf(fact_2124_mult__cancel__right2,axiom,
% 4.71/5.05 ! [A: real,C: real] :
% 4.71/5.05 ( ( ( times_times_real @ A @ C )
% 4.71/5.05 = C )
% 4.71/5.05 = ( ( C = zero_zero_real )
% 4.71/5.05 | ( A = one_one_real ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_cancel_right2
% 4.71/5.05 thf(fact_2125_mult__cancel__right2,axiom,
% 4.71/5.05 ! [A: rat,C: rat] :
% 4.71/5.05 ( ( ( times_times_rat @ A @ C )
% 4.71/5.05 = C )
% 4.71/5.05 = ( ( C = zero_zero_rat )
% 4.71/5.05 | ( A = one_one_rat ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_cancel_right2
% 4.71/5.05 thf(fact_2126_mult__cancel__right2,axiom,
% 4.71/5.05 ! [A: int,C: int] :
% 4.71/5.05 ( ( ( times_times_int @ A @ C )
% 4.71/5.05 = C )
% 4.71/5.05 = ( ( C = zero_zero_int )
% 4.71/5.05 | ( A = one_one_int ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_cancel_right2
% 4.71/5.05 thf(fact_2127_mult__divide__mult__cancel__left__if,axiom,
% 4.71/5.05 ! [C: rat,A: rat,B: rat] :
% 4.71/5.05 ( ( ( C = zero_zero_rat )
% 4.71/5.05 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.71/5.05 = zero_zero_rat ) )
% 4.71/5.05 & ( ( C != zero_zero_rat )
% 4.71/5.05 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.71/5.05 = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_divide_mult_cancel_left_if
% 4.71/5.05 thf(fact_2128_mult__divide__mult__cancel__left__if,axiom,
% 4.71/5.05 ! [C: real,A: real,B: real] :
% 4.71/5.05 ( ( ( C = zero_zero_real )
% 4.71/5.05 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.71/5.05 = zero_zero_real ) )
% 4.71/5.05 & ( ( C != zero_zero_real )
% 4.71/5.05 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.71/5.05 = ( divide_divide_real @ A @ B ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_divide_mult_cancel_left_if
% 4.71/5.05 thf(fact_2129_nonzero__mult__divide__mult__cancel__left,axiom,
% 4.71/5.05 ! [C: rat,A: rat,B: rat] :
% 4.71/5.05 ( ( C != zero_zero_rat )
% 4.71/5.05 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.71/5.05 = ( divide_divide_rat @ A @ B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % nonzero_mult_divide_mult_cancel_left
% 4.71/5.05 thf(fact_2130_nonzero__mult__divide__mult__cancel__left,axiom,
% 4.71/5.05 ! [C: real,A: real,B: real] :
% 4.71/5.05 ( ( C != zero_zero_real )
% 4.71/5.05 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.71/5.05 = ( divide_divide_real @ A @ B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % nonzero_mult_divide_mult_cancel_left
% 4.71/5.05 thf(fact_2131_nonzero__mult__divide__mult__cancel__left2,axiom,
% 4.71/5.05 ! [C: rat,A: rat,B: rat] :
% 4.71/5.05 ( ( C != zero_zero_rat )
% 4.71/5.05 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 4.71/5.05 = ( divide_divide_rat @ A @ B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % nonzero_mult_divide_mult_cancel_left2
% 4.71/5.05 thf(fact_2132_nonzero__mult__divide__mult__cancel__left2,axiom,
% 4.71/5.05 ! [C: real,A: real,B: real] :
% 4.71/5.05 ( ( C != zero_zero_real )
% 4.71/5.05 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ C ) )
% 4.71/5.05 = ( divide_divide_real @ A @ B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % nonzero_mult_divide_mult_cancel_left2
% 4.71/5.05 thf(fact_2133_nonzero__mult__divide__mult__cancel__right,axiom,
% 4.71/5.05 ! [C: rat,A: rat,B: rat] :
% 4.71/5.05 ( ( C != zero_zero_rat )
% 4.71/5.05 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 4.71/5.05 = ( divide_divide_rat @ A @ B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % nonzero_mult_divide_mult_cancel_right
% 4.71/5.05 thf(fact_2134_nonzero__mult__divide__mult__cancel__right,axiom,
% 4.71/5.05 ! [C: real,A: real,B: real] :
% 4.71/5.05 ( ( C != zero_zero_real )
% 4.71/5.05 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 4.71/5.05 = ( divide_divide_real @ A @ B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % nonzero_mult_divide_mult_cancel_right
% 4.71/5.05 thf(fact_2135_nonzero__mult__divide__mult__cancel__right2,axiom,
% 4.71/5.05 ! [C: rat,A: rat,B: rat] :
% 4.71/5.05 ( ( C != zero_zero_rat )
% 4.71/5.05 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 4.71/5.05 = ( divide_divide_rat @ A @ B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % nonzero_mult_divide_mult_cancel_right2
% 4.71/5.05 thf(fact_2136_nonzero__mult__divide__mult__cancel__right2,axiom,
% 4.71/5.05 ! [C: real,A: real,B: real] :
% 4.71/5.05 ( ( C != zero_zero_real )
% 4.71/5.05 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B ) )
% 4.71/5.05 = ( divide_divide_real @ A @ B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % nonzero_mult_divide_mult_cancel_right2
% 4.71/5.05 thf(fact_2137_nonzero__mult__div__cancel__left,axiom,
% 4.71/5.05 ! [A: rat,B: rat] :
% 4.71/5.05 ( ( A != zero_zero_rat )
% 4.71/5.05 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 4.71/5.05 = B ) ) ).
% 4.71/5.05
% 4.71/5.05 % nonzero_mult_div_cancel_left
% 4.71/5.05 thf(fact_2138_nonzero__mult__div__cancel__left,axiom,
% 4.71/5.05 ! [A: int,B: int] :
% 4.71/5.05 ( ( A != zero_zero_int )
% 4.71/5.05 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 4.71/5.05 = B ) ) ).
% 4.71/5.05
% 4.71/5.05 % nonzero_mult_div_cancel_left
% 4.71/5.05 thf(fact_2139_nonzero__mult__div__cancel__left,axiom,
% 4.71/5.05 ! [A: nat,B: nat] :
% 4.71/5.05 ( ( A != zero_zero_nat )
% 4.71/5.05 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 4.71/5.05 = B ) ) ).
% 4.71/5.05
% 4.71/5.05 % nonzero_mult_div_cancel_left
% 4.71/5.05 thf(fact_2140_nonzero__mult__div__cancel__left,axiom,
% 4.71/5.05 ! [A: real,B: real] :
% 4.71/5.05 ( ( A != zero_zero_real )
% 4.71/5.05 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 4.71/5.05 = B ) ) ).
% 4.71/5.05
% 4.71/5.05 % nonzero_mult_div_cancel_left
% 4.71/5.05 thf(fact_2141_nonzero__mult__div__cancel__right,axiom,
% 4.71/5.05 ! [B: rat,A: rat] :
% 4.71/5.05 ( ( B != zero_zero_rat )
% 4.71/5.05 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 4.71/5.05 = A ) ) ).
% 4.71/5.05
% 4.71/5.05 % nonzero_mult_div_cancel_right
% 4.71/5.05 thf(fact_2142_nonzero__mult__div__cancel__right,axiom,
% 4.71/5.05 ! [B: int,A: int] :
% 4.71/5.05 ( ( B != zero_zero_int )
% 4.71/5.05 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 4.71/5.05 = A ) ) ).
% 4.71/5.05
% 4.71/5.05 % nonzero_mult_div_cancel_right
% 4.71/5.05 thf(fact_2143_nonzero__mult__div__cancel__right,axiom,
% 4.71/5.05 ! [B: nat,A: nat] :
% 4.71/5.05 ( ( B != zero_zero_nat )
% 4.71/5.05 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 4.71/5.05 = A ) ) ).
% 4.71/5.05
% 4.71/5.05 % nonzero_mult_div_cancel_right
% 4.71/5.05 thf(fact_2144_nonzero__mult__div__cancel__right,axiom,
% 4.71/5.05 ! [B: real,A: real] :
% 4.71/5.05 ( ( B != zero_zero_real )
% 4.71/5.05 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 4.71/5.05 = A ) ) ).
% 4.71/5.05
% 4.71/5.05 % nonzero_mult_div_cancel_right
% 4.71/5.05 thf(fact_2145_div__mult__mult1,axiom,
% 4.71/5.05 ! [C: int,A: int,B: int] :
% 4.71/5.05 ( ( C != zero_zero_int )
% 4.71/5.05 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.71/5.05 = ( divide_divide_int @ A @ B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % div_mult_mult1
% 4.71/5.05 thf(fact_2146_div__mult__mult1,axiom,
% 4.71/5.05 ! [C: nat,A: nat,B: nat] :
% 4.71/5.05 ( ( C != zero_zero_nat )
% 4.71/5.05 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 4.71/5.05 = ( divide_divide_nat @ A @ B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % div_mult_mult1
% 4.71/5.05 thf(fact_2147_div__mult__mult2,axiom,
% 4.71/5.05 ! [C: int,A: int,B: int] :
% 4.71/5.05 ( ( C != zero_zero_int )
% 4.71/5.05 => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 4.71/5.05 = ( divide_divide_int @ A @ B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % div_mult_mult2
% 4.71/5.05 thf(fact_2148_div__mult__mult2,axiom,
% 4.71/5.05 ! [C: nat,A: nat,B: nat] :
% 4.71/5.05 ( ( C != zero_zero_nat )
% 4.71/5.05 => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 4.71/5.05 = ( divide_divide_nat @ A @ B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % div_mult_mult2
% 4.71/5.05 thf(fact_2149_div__mult__mult1__if,axiom,
% 4.71/5.05 ! [C: int,A: int,B: int] :
% 4.71/5.05 ( ( ( C = zero_zero_int )
% 4.71/5.05 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.71/5.05 = zero_zero_int ) )
% 4.71/5.05 & ( ( C != zero_zero_int )
% 4.71/5.05 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.71/5.05 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % div_mult_mult1_if
% 4.71/5.05 thf(fact_2150_div__mult__mult1__if,axiom,
% 4.71/5.05 ! [C: nat,A: nat,B: nat] :
% 4.71/5.05 ( ( ( C = zero_zero_nat )
% 4.71/5.05 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 4.71/5.05 = zero_zero_nat ) )
% 4.71/5.05 & ( ( C != zero_zero_nat )
% 4.71/5.05 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 4.71/5.05 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % div_mult_mult1_if
% 4.71/5.05 thf(fact_2151_le__add__diff__inverse2,axiom,
% 4.71/5.05 ! [B: real,A: real] :
% 4.71/5.05 ( ( ord_less_eq_real @ B @ A )
% 4.71/5.05 => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 4.71/5.05 = A ) ) ).
% 4.71/5.05
% 4.71/5.05 % le_add_diff_inverse2
% 4.71/5.05 thf(fact_2152_le__add__diff__inverse2,axiom,
% 4.71/5.05 ! [B: rat,A: rat] :
% 4.71/5.05 ( ( ord_less_eq_rat @ B @ A )
% 4.71/5.05 => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 4.71/5.05 = A ) ) ).
% 4.71/5.05
% 4.71/5.05 % le_add_diff_inverse2
% 4.71/5.05 thf(fact_2153_le__add__diff__inverse2,axiom,
% 4.71/5.05 ! [B: nat,A: nat] :
% 4.71/5.05 ( ( ord_less_eq_nat @ B @ A )
% 4.71/5.05 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 4.71/5.05 = A ) ) ).
% 4.71/5.05
% 4.71/5.05 % le_add_diff_inverse2
% 4.71/5.05 thf(fact_2154_le__add__diff__inverse2,axiom,
% 4.71/5.05 ! [B: int,A: int] :
% 4.71/5.05 ( ( ord_less_eq_int @ B @ A )
% 4.71/5.05 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 4.71/5.05 = A ) ) ).
% 4.71/5.05
% 4.71/5.05 % le_add_diff_inverse2
% 4.71/5.05 thf(fact_2155_le__add__diff__inverse,axiom,
% 4.71/5.05 ! [B: real,A: real] :
% 4.71/5.05 ( ( ord_less_eq_real @ B @ A )
% 4.71/5.05 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 4.71/5.05 = A ) ) ).
% 4.71/5.05
% 4.71/5.05 % le_add_diff_inverse
% 4.71/5.05 thf(fact_2156_le__add__diff__inverse,axiom,
% 4.71/5.05 ! [B: rat,A: rat] :
% 4.71/5.05 ( ( ord_less_eq_rat @ B @ A )
% 4.71/5.05 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 4.71/5.05 = A ) ) ).
% 4.71/5.05
% 4.71/5.05 % le_add_diff_inverse
% 4.71/5.05 thf(fact_2157_le__add__diff__inverse,axiom,
% 4.71/5.05 ! [B: nat,A: nat] :
% 4.71/5.05 ( ( ord_less_eq_nat @ B @ A )
% 4.71/5.05 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 4.71/5.05 = A ) ) ).
% 4.71/5.05
% 4.71/5.05 % le_add_diff_inverse
% 4.71/5.05 thf(fact_2158_le__add__diff__inverse,axiom,
% 4.71/5.05 ! [B: int,A: int] :
% 4.71/5.05 ( ( ord_less_eq_int @ B @ A )
% 4.71/5.05 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 4.71/5.05 = A ) ) ).
% 4.71/5.05
% 4.71/5.05 % le_add_diff_inverse
% 4.71/5.05 thf(fact_2159_diff__add__zero,axiom,
% 4.71/5.05 ! [A: nat,B: nat] :
% 4.71/5.05 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 4.71/5.05 = zero_zero_nat ) ).
% 4.71/5.05
% 4.71/5.05 % diff_add_zero
% 4.71/5.05 thf(fact_2160_abs__le__zero__iff,axiom,
% 4.71/5.05 ! [A: real] :
% 4.71/5.05 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 4.71/5.05 = ( A = zero_zero_real ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_le_zero_iff
% 4.71/5.05 thf(fact_2161_abs__le__zero__iff,axiom,
% 4.71/5.05 ! [A: rat] :
% 4.71/5.05 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 4.71/5.05 = ( A = zero_zero_rat ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_le_zero_iff
% 4.71/5.05 thf(fact_2162_abs__le__zero__iff,axiom,
% 4.71/5.05 ! [A: int] :
% 4.71/5.05 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 4.71/5.05 = ( A = zero_zero_int ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_le_zero_iff
% 4.71/5.05 thf(fact_2163_abs__le__self__iff,axiom,
% 4.71/5.05 ! [A: real] :
% 4.71/5.05 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 4.71/5.05 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_le_self_iff
% 4.71/5.05 thf(fact_2164_abs__le__self__iff,axiom,
% 4.71/5.05 ! [A: rat] :
% 4.71/5.05 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 4.71/5.05 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_le_self_iff
% 4.71/5.05 thf(fact_2165_abs__le__self__iff,axiom,
% 4.71/5.05 ! [A: int] :
% 4.71/5.05 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 4.71/5.05 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_le_self_iff
% 4.71/5.05 thf(fact_2166_abs__of__nonneg,axiom,
% 4.71/5.05 ! [A: real] :
% 4.71/5.05 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.05 => ( ( abs_abs_real @ A )
% 4.71/5.05 = A ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_of_nonneg
% 4.71/5.05 thf(fact_2167_abs__of__nonneg,axiom,
% 4.71/5.05 ! [A: rat] :
% 4.71/5.05 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.05 => ( ( abs_abs_rat @ A )
% 4.71/5.05 = A ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_of_nonneg
% 4.71/5.05 thf(fact_2168_abs__of__nonneg,axiom,
% 4.71/5.05 ! [A: int] :
% 4.71/5.05 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.05 => ( ( abs_abs_int @ A )
% 4.71/5.05 = A ) ) ).
% 4.71/5.05
% 4.71/5.05 % abs_of_nonneg
% 4.71/5.05 thf(fact_2169_zero__less__abs__iff,axiom,
% 4.71/5.05 ! [A: real] :
% 4.71/5.05 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 4.71/5.05 = ( A != zero_zero_real ) ) ).
% 4.71/5.05
% 4.71/5.05 % zero_less_abs_iff
% 4.71/5.05 thf(fact_2170_zero__less__abs__iff,axiom,
% 4.71/5.05 ! [A: rat] :
% 4.71/5.05 ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 4.71/5.05 = ( A != zero_zero_rat ) ) ).
% 4.71/5.05
% 4.71/5.05 % zero_less_abs_iff
% 4.71/5.05 thf(fact_2171_zero__less__abs__iff,axiom,
% 4.71/5.05 ! [A: int] :
% 4.71/5.05 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 4.71/5.05 = ( A != zero_zero_int ) ) ).
% 4.71/5.05
% 4.71/5.05 % zero_less_abs_iff
% 4.71/5.05 thf(fact_2172_singleton__insert__inj__eq_H,axiom,
% 4.71/5.05 ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B: product_prod_nat_nat] :
% 4.71/5.05 ( ( ( insert8211810215607154385at_nat @ A @ A2 )
% 4.71/5.05 = ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) )
% 4.71/5.05 = ( ( A = B )
% 4.71/5.05 & ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % singleton_insert_inj_eq'
% 4.71/5.05 thf(fact_2173_singleton__insert__inj__eq_H,axiom,
% 4.71/5.05 ! [A: real,A2: set_real,B: real] :
% 4.71/5.05 ( ( ( insert_real @ A @ A2 )
% 4.71/5.05 = ( insert_real @ B @ bot_bot_set_real ) )
% 4.71/5.05 = ( ( A = B )
% 4.71/5.05 & ( ord_less_eq_set_real @ A2 @ ( insert_real @ B @ bot_bot_set_real ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % singleton_insert_inj_eq'
% 4.71/5.05 thf(fact_2174_singleton__insert__inj__eq_H,axiom,
% 4.71/5.05 ! [A: $o,A2: set_o,B: $o] :
% 4.71/5.05 ( ( ( insert_o @ A @ A2 )
% 4.71/5.05 = ( insert_o @ B @ bot_bot_set_o ) )
% 4.71/5.05 = ( ( A = B )
% 4.71/5.05 & ( ord_less_eq_set_o @ A2 @ ( insert_o @ B @ bot_bot_set_o ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % singleton_insert_inj_eq'
% 4.71/5.05 thf(fact_2175_singleton__insert__inj__eq_H,axiom,
% 4.71/5.05 ! [A: nat,A2: set_nat,B: nat] :
% 4.71/5.05 ( ( ( insert_nat @ A @ A2 )
% 4.71/5.05 = ( insert_nat @ B @ bot_bot_set_nat ) )
% 4.71/5.05 = ( ( A = B )
% 4.71/5.05 & ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % singleton_insert_inj_eq'
% 4.71/5.05 thf(fact_2176_singleton__insert__inj__eq_H,axiom,
% 4.71/5.05 ! [A: int,A2: set_int,B: int] :
% 4.71/5.05 ( ( ( insert_int @ A @ A2 )
% 4.71/5.05 = ( insert_int @ B @ bot_bot_set_int ) )
% 4.71/5.05 = ( ( A = B )
% 4.71/5.05 & ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % singleton_insert_inj_eq'
% 4.71/5.05 thf(fact_2177_singleton__insert__inj__eq,axiom,
% 4.71/5.05 ! [B: product_prod_nat_nat,A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.05 ( ( ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat )
% 4.71/5.05 = ( insert8211810215607154385at_nat @ A @ A2 ) )
% 4.71/5.05 = ( ( A = B )
% 4.71/5.05 & ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % singleton_insert_inj_eq
% 4.71/5.05 thf(fact_2178_singleton__insert__inj__eq,axiom,
% 4.71/5.05 ! [B: real,A: real,A2: set_real] :
% 4.71/5.05 ( ( ( insert_real @ B @ bot_bot_set_real )
% 4.71/5.05 = ( insert_real @ A @ A2 ) )
% 4.71/5.05 = ( ( A = B )
% 4.71/5.05 & ( ord_less_eq_set_real @ A2 @ ( insert_real @ B @ bot_bot_set_real ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % singleton_insert_inj_eq
% 4.71/5.05 thf(fact_2179_singleton__insert__inj__eq,axiom,
% 4.71/5.05 ! [B: $o,A: $o,A2: set_o] :
% 4.71/5.05 ( ( ( insert_o @ B @ bot_bot_set_o )
% 4.71/5.05 = ( insert_o @ A @ A2 ) )
% 4.71/5.05 = ( ( A = B )
% 4.71/5.05 & ( ord_less_eq_set_o @ A2 @ ( insert_o @ B @ bot_bot_set_o ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % singleton_insert_inj_eq
% 4.71/5.05 thf(fact_2180_singleton__insert__inj__eq,axiom,
% 4.71/5.05 ! [B: nat,A: nat,A2: set_nat] :
% 4.71/5.05 ( ( ( insert_nat @ B @ bot_bot_set_nat )
% 4.71/5.05 = ( insert_nat @ A @ A2 ) )
% 4.71/5.05 = ( ( A = B )
% 4.71/5.05 & ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % singleton_insert_inj_eq
% 4.71/5.05 thf(fact_2181_singleton__insert__inj__eq,axiom,
% 4.71/5.05 ! [B: int,A: int,A2: set_int] :
% 4.71/5.05 ( ( ( insert_int @ B @ bot_bot_set_int )
% 4.71/5.05 = ( insert_int @ A @ A2 ) )
% 4.71/5.05 = ( ( A = B )
% 4.71/5.05 & ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % singleton_insert_inj_eq
% 4.71/5.05 thf(fact_2182_one__eq__mult__iff,axiom,
% 4.71/5.05 ! [M2: nat,N: nat] :
% 4.71/5.05 ( ( ( suc @ zero_zero_nat )
% 4.71/5.05 = ( times_times_nat @ M2 @ N ) )
% 4.71/5.05 = ( ( M2
% 4.71/5.05 = ( suc @ zero_zero_nat ) )
% 4.71/5.05 & ( N
% 4.71/5.05 = ( suc @ zero_zero_nat ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % one_eq_mult_iff
% 4.71/5.05 thf(fact_2183_mult__eq__1__iff,axiom,
% 4.71/5.05 ! [M2: nat,N: nat] :
% 4.71/5.05 ( ( ( times_times_nat @ M2 @ N )
% 4.71/5.05 = ( suc @ zero_zero_nat ) )
% 4.71/5.05 = ( ( M2
% 4.71/5.05 = ( suc @ zero_zero_nat ) )
% 4.71/5.05 & ( N
% 4.71/5.05 = ( suc @ zero_zero_nat ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_eq_1_iff
% 4.71/5.05 thf(fact_2184_of__nat__mult,axiom,
% 4.71/5.05 ! [M2: nat,N: nat] :
% 4.71/5.05 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M2 @ N ) )
% 4.71/5.05 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % of_nat_mult
% 4.71/5.05 thf(fact_2185_of__nat__mult,axiom,
% 4.71/5.05 ! [M2: nat,N: nat] :
% 4.71/5.05 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M2 @ N ) )
% 4.71/5.05 = ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % of_nat_mult
% 4.71/5.05 thf(fact_2186_of__nat__mult,axiom,
% 4.71/5.05 ! [M2: nat,N: nat] :
% 4.71/5.05 ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M2 @ N ) )
% 4.71/5.05 = ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % of_nat_mult
% 4.71/5.05 thf(fact_2187_of__nat__mult,axiom,
% 4.71/5.05 ! [M2: nat,N: nat] :
% 4.71/5.05 ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M2 @ N ) )
% 4.71/5.05 = ( times_times_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % of_nat_mult
% 4.71/5.05 thf(fact_2188_mult__less__cancel2,axiom,
% 4.71/5.05 ! [M2: nat,K: nat,N: nat] :
% 4.71/5.05 ( ( ord_less_nat @ ( times_times_nat @ M2 @ K ) @ ( times_times_nat @ N @ K ) )
% 4.71/5.05 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.71/5.05 & ( ord_less_nat @ M2 @ N ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_less_cancel2
% 4.71/5.05 thf(fact_2189_nat__0__less__mult__iff,axiom,
% 4.71/5.05 ! [M2: nat,N: nat] :
% 4.71/5.05 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M2 @ N ) )
% 4.71/5.05 = ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 4.71/5.05 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % nat_0_less_mult_iff
% 4.71/5.05 thf(fact_2190_ln__ge__zero__iff,axiom,
% 4.71/5.05 ! [X: real] :
% 4.71/5.05 ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.05 => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 4.71/5.05 = ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % ln_ge_zero_iff
% 4.71/5.05 thf(fact_2191_ln__le__zero__iff,axiom,
% 4.71/5.05 ! [X: real] :
% 4.71/5.05 ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.05 => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 4.71/5.05 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % ln_le_zero_iff
% 4.71/5.05 thf(fact_2192_insert__Diff__single,axiom,
% 4.71/5.05 ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.05 ( ( insert8211810215607154385at_nat @ A @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 4.71/5.05 = ( insert8211810215607154385at_nat @ A @ A2 ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_Diff_single
% 4.71/5.05 thf(fact_2193_insert__Diff__single,axiom,
% 4.71/5.05 ! [A: real,A2: set_real] :
% 4.71/5.05 ( ( insert_real @ A @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 4.71/5.05 = ( insert_real @ A @ A2 ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_Diff_single
% 4.71/5.05 thf(fact_2194_insert__Diff__single,axiom,
% 4.71/5.05 ! [A: $o,A2: set_o] :
% 4.71/5.05 ( ( insert_o @ A @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 4.71/5.05 = ( insert_o @ A @ A2 ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_Diff_single
% 4.71/5.05 thf(fact_2195_insert__Diff__single,axiom,
% 4.71/5.05 ! [A: int,A2: set_int] :
% 4.71/5.05 ( ( insert_int @ A @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 4.71/5.05 = ( insert_int @ A @ A2 ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_Diff_single
% 4.71/5.05 thf(fact_2196_insert__Diff__single,axiom,
% 4.71/5.05 ! [A: nat,A2: set_nat] :
% 4.71/5.05 ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 4.71/5.05 = ( insert_nat @ A @ A2 ) ) ).
% 4.71/5.05
% 4.71/5.05 % insert_Diff_single
% 4.71/5.05 thf(fact_2197_finite__Diff__insert,axiom,
% 4.71/5.05 ! [A2: set_real,A: real,B2: set_real] :
% 4.71/5.05 ( ( finite_finite_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B2 ) ) )
% 4.71/5.05 = ( finite_finite_real @ ( minus_minus_set_real @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % finite_Diff_insert
% 4.71/5.05 thf(fact_2198_finite__Diff__insert,axiom,
% 4.71/5.05 ! [A2: set_o,A: $o,B2: set_o] :
% 4.71/5.05 ( ( finite_finite_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ B2 ) ) )
% 4.71/5.05 = ( finite_finite_o @ ( minus_minus_set_o @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % finite_Diff_insert
% 4.71/5.05 thf(fact_2199_finite__Diff__insert,axiom,
% 4.71/5.05 ! [A2: set_int,A: int,B2: set_int] :
% 4.71/5.05 ( ( finite_finite_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B2 ) ) )
% 4.71/5.05 = ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % finite_Diff_insert
% 4.71/5.05 thf(fact_2200_finite__Diff__insert,axiom,
% 4.71/5.05 ! [A2: set_complex,A: complex,B2: set_complex] :
% 4.71/5.05 ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ B2 ) ) )
% 4.71/5.05 = ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % finite_Diff_insert
% 4.71/5.05 thf(fact_2201_finite__Diff__insert,axiom,
% 4.71/5.05 ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 4.71/5.05 ( ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B2 ) ) )
% 4.71/5.05 = ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % finite_Diff_insert
% 4.71/5.05 thf(fact_2202_finite__Diff__insert,axiom,
% 4.71/5.05 ! [A2: set_Extended_enat,A: extended_enat,B2: set_Extended_enat] :
% 4.71/5.05 ( ( finite4001608067531595151d_enat @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ A @ B2 ) ) )
% 4.71/5.05 = ( finite4001608067531595151d_enat @ ( minus_925952699566721837d_enat @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % finite_Diff_insert
% 4.71/5.05 thf(fact_2203_finite__Diff__insert,axiom,
% 4.71/5.05 ! [A2: set_nat,A: nat,B2: set_nat] :
% 4.71/5.05 ( ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B2 ) ) )
% 4.71/5.05 = ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % finite_Diff_insert
% 4.71/5.05 thf(fact_2204_frac__eq__0__iff,axiom,
% 4.71/5.05 ! [X: real] :
% 4.71/5.05 ( ( ( archim2898591450579166408c_real @ X )
% 4.71/5.05 = zero_zero_real )
% 4.71/5.05 = ( member_real @ X @ ring_1_Ints_real ) ) ).
% 4.71/5.05
% 4.71/5.05 % frac_eq_0_iff
% 4.71/5.05 thf(fact_2205_frac__eq__0__iff,axiom,
% 4.71/5.05 ! [X: rat] :
% 4.71/5.05 ( ( ( archimedean_frac_rat @ X )
% 4.71/5.05 = zero_zero_rat )
% 4.71/5.05 = ( member_rat @ X @ ring_1_Ints_rat ) ) ).
% 4.71/5.05
% 4.71/5.05 % frac_eq_0_iff
% 4.71/5.05 thf(fact_2206_set__decode__zero,axiom,
% 4.71/5.05 ( ( nat_set_decode @ zero_zero_nat )
% 4.71/5.05 = bot_bot_set_nat ) ).
% 4.71/5.05
% 4.71/5.05 % set_decode_zero
% 4.71/5.05 thf(fact_2207_div__mult__self1,axiom,
% 4.71/5.05 ! [B: int,A: int,C: int] :
% 4.71/5.05 ( ( B != zero_zero_int )
% 4.71/5.05 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 4.71/5.05 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % div_mult_self1
% 4.71/5.05 thf(fact_2208_div__mult__self1,axiom,
% 4.71/5.05 ! [B: nat,A: nat,C: nat] :
% 4.71/5.05 ( ( B != zero_zero_nat )
% 4.71/5.05 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 4.71/5.05 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % div_mult_self1
% 4.71/5.05 thf(fact_2209_div__mult__self2,axiom,
% 4.71/5.05 ! [B: int,A: int,C: int] :
% 4.71/5.05 ( ( B != zero_zero_int )
% 4.71/5.05 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 4.71/5.05 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % div_mult_self2
% 4.71/5.05 thf(fact_2210_div__mult__self2,axiom,
% 4.71/5.05 ! [B: nat,A: nat,C: nat] :
% 4.71/5.05 ( ( B != zero_zero_nat )
% 4.71/5.05 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 4.71/5.05 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % div_mult_self2
% 4.71/5.05 thf(fact_2211_div__mult__self3,axiom,
% 4.71/5.05 ! [B: int,C: int,A: int] :
% 4.71/5.05 ( ( B != zero_zero_int )
% 4.71/5.05 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 4.71/5.05 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % div_mult_self3
% 4.71/5.05 thf(fact_2212_div__mult__self3,axiom,
% 4.71/5.05 ! [B: nat,C: nat,A: nat] :
% 4.71/5.05 ( ( B != zero_zero_nat )
% 4.71/5.05 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 4.71/5.05 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % div_mult_self3
% 4.71/5.05 thf(fact_2213_div__mult__self4,axiom,
% 4.71/5.05 ! [B: int,C: int,A: int] :
% 4.71/5.05 ( ( B != zero_zero_int )
% 4.71/5.05 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 4.71/5.05 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % div_mult_self4
% 4.71/5.05 thf(fact_2214_div__mult__self4,axiom,
% 4.71/5.05 ! [B: nat,C: nat,A: nat] :
% 4.71/5.05 ( ( B != zero_zero_nat )
% 4.71/5.05 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 4.71/5.05 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % div_mult_self4
% 4.71/5.05 thf(fact_2215_nonzero__divide__mult__cancel__left,axiom,
% 4.71/5.05 ! [A: complex,B: complex] :
% 4.71/5.05 ( ( A != zero_zero_complex )
% 4.71/5.05 => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 4.71/5.05 = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % nonzero_divide_mult_cancel_left
% 4.71/5.05 thf(fact_2216_nonzero__divide__mult__cancel__left,axiom,
% 4.71/5.05 ! [A: rat,B: rat] :
% 4.71/5.05 ( ( A != zero_zero_rat )
% 4.71/5.05 => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 4.71/5.05 = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % nonzero_divide_mult_cancel_left
% 4.71/5.05 thf(fact_2217_nonzero__divide__mult__cancel__left,axiom,
% 4.71/5.05 ! [A: real,B: real] :
% 4.71/5.05 ( ( A != zero_zero_real )
% 4.71/5.05 => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 4.71/5.05 = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % nonzero_divide_mult_cancel_left
% 4.71/5.05 thf(fact_2218_nonzero__divide__mult__cancel__right,axiom,
% 4.71/5.05 ! [B: complex,A: complex] :
% 4.71/5.05 ( ( B != zero_zero_complex )
% 4.71/5.05 => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 4.71/5.05 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % nonzero_divide_mult_cancel_right
% 4.71/5.05 thf(fact_2219_nonzero__divide__mult__cancel__right,axiom,
% 4.71/5.05 ! [B: rat,A: rat] :
% 4.71/5.05 ( ( B != zero_zero_rat )
% 4.71/5.05 => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 4.71/5.05 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % nonzero_divide_mult_cancel_right
% 4.71/5.05 thf(fact_2220_nonzero__divide__mult__cancel__right,axiom,
% 4.71/5.05 ! [B: real,A: real] :
% 4.71/5.05 ( ( B != zero_zero_real )
% 4.71/5.05 => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 4.71/5.05 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % nonzero_divide_mult_cancel_right
% 4.71/5.05 thf(fact_2221_divide__le__0__abs__iff,axiom,
% 4.71/5.05 ! [A: real,B: real] :
% 4.71/5.05 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 4.71/5.05 = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 4.71/5.05 | ( B = zero_zero_real ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % divide_le_0_abs_iff
% 4.71/5.05 thf(fact_2222_divide__le__0__abs__iff,axiom,
% 4.71/5.05 ! [A: rat,B: rat] :
% 4.71/5.05 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 4.71/5.05 = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 4.71/5.05 | ( B = zero_zero_rat ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % divide_le_0_abs_iff
% 4.71/5.05 thf(fact_2223_zero__le__divide__abs__iff,axiom,
% 4.71/5.05 ! [A: real,B: real] :
% 4.71/5.05 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 4.71/5.05 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.05 | ( B = zero_zero_real ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % zero_le_divide_abs_iff
% 4.71/5.05 thf(fact_2224_zero__le__divide__abs__iff,axiom,
% 4.71/5.05 ! [A: rat,B: rat] :
% 4.71/5.05 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 4.71/5.05 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.05 | ( B = zero_zero_rat ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % zero_le_divide_abs_iff
% 4.71/5.05 thf(fact_2225_of__nat__Suc,axiom,
% 4.71/5.05 ! [M2: nat] :
% 4.71/5.05 ( ( semiri8010041392384452111omplex @ ( suc @ M2 ) )
% 4.71/5.05 = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % of_nat_Suc
% 4.71/5.05 thf(fact_2226_of__nat__Suc,axiom,
% 4.71/5.05 ! [M2: nat] :
% 4.71/5.05 ( ( semiri1316708129612266289at_nat @ ( suc @ M2 ) )
% 4.71/5.05 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % of_nat_Suc
% 4.71/5.05 thf(fact_2227_of__nat__Suc,axiom,
% 4.71/5.05 ! [M2: nat] :
% 4.71/5.05 ( ( semiri1314217659103216013at_int @ ( suc @ M2 ) )
% 4.71/5.05 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % of_nat_Suc
% 4.71/5.05 thf(fact_2228_of__nat__Suc,axiom,
% 4.71/5.05 ! [M2: nat] :
% 4.71/5.05 ( ( semiri5074537144036343181t_real @ ( suc @ M2 ) )
% 4.71/5.05 = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % of_nat_Suc
% 4.71/5.05 thf(fact_2229_of__nat__Suc,axiom,
% 4.71/5.05 ! [M2: nat] :
% 4.71/5.05 ( ( semiri681578069525770553at_rat @ ( suc @ M2 ) )
% 4.71/5.05 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M2 ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % of_nat_Suc
% 4.71/5.05 thf(fact_2230_one__le__mult__iff,axiom,
% 4.71/5.05 ! [M2: nat,N: nat] :
% 4.71/5.05 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M2 @ N ) )
% 4.71/5.05 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 4.71/5.05 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % one_le_mult_iff
% 4.71/5.05 thf(fact_2231_card__insert__disjoint,axiom,
% 4.71/5.05 ! [A2: set_real,X: real] :
% 4.71/5.05 ( ( finite_finite_real @ A2 )
% 4.71/5.05 => ( ~ ( member_real @ X @ A2 )
% 4.71/5.05 => ( ( finite_card_real @ ( insert_real @ X @ A2 ) )
% 4.71/5.05 = ( suc @ ( finite_card_real @ A2 ) ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % card_insert_disjoint
% 4.71/5.05 thf(fact_2232_card__insert__disjoint,axiom,
% 4.71/5.05 ! [A2: set_o,X: $o] :
% 4.71/5.05 ( ( finite_finite_o @ A2 )
% 4.71/5.05 => ( ~ ( member_o @ X @ A2 )
% 4.71/5.05 => ( ( finite_card_o @ ( insert_o @ X @ A2 ) )
% 4.71/5.05 = ( suc @ ( finite_card_o @ A2 ) ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % card_insert_disjoint
% 4.71/5.05 thf(fact_2233_card__insert__disjoint,axiom,
% 4.71/5.05 ! [A2: set_set_nat_rat,X: set_nat_rat] :
% 4.71/5.05 ( ( finite6430367030675640852at_rat @ A2 )
% 4.71/5.05 => ( ~ ( member_set_nat_rat @ X @ A2 )
% 4.71/5.05 => ( ( finite8736671560171388117at_rat @ ( insert_set_nat_rat @ X @ A2 ) )
% 4.71/5.05 = ( suc @ ( finite8736671560171388117at_rat @ A2 ) ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % card_insert_disjoint
% 4.71/5.05 thf(fact_2234_card__insert__disjoint,axiom,
% 4.71/5.05 ! [A2: set_list_nat,X: list_nat] :
% 4.71/5.05 ( ( finite8100373058378681591st_nat @ A2 )
% 4.71/5.05 => ( ~ ( member_list_nat @ X @ A2 )
% 4.71/5.05 => ( ( finite_card_list_nat @ ( insert_list_nat @ X @ A2 ) )
% 4.71/5.05 = ( suc @ ( finite_card_list_nat @ A2 ) ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % card_insert_disjoint
% 4.71/5.05 thf(fact_2235_card__insert__disjoint,axiom,
% 4.71/5.05 ! [A2: set_set_nat,X: set_nat] :
% 4.71/5.05 ( ( finite1152437895449049373et_nat @ A2 )
% 4.71/5.05 => ( ~ ( member_set_nat @ X @ A2 )
% 4.71/5.05 => ( ( finite_card_set_nat @ ( insert_set_nat @ X @ A2 ) )
% 4.71/5.05 = ( suc @ ( finite_card_set_nat @ A2 ) ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % card_insert_disjoint
% 4.71/5.05 thf(fact_2236_card__insert__disjoint,axiom,
% 4.71/5.05 ! [A2: set_nat,X: nat] :
% 4.71/5.05 ( ( finite_finite_nat @ A2 )
% 4.71/5.05 => ( ~ ( member_nat @ X @ A2 )
% 4.71/5.05 => ( ( finite_card_nat @ ( insert_nat @ X @ A2 ) )
% 4.71/5.05 = ( suc @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % card_insert_disjoint
% 4.71/5.05 thf(fact_2237_card__insert__disjoint,axiom,
% 4.71/5.05 ! [A2: set_int,X: int] :
% 4.71/5.05 ( ( finite_finite_int @ A2 )
% 4.71/5.05 => ( ~ ( member_int @ X @ A2 )
% 4.71/5.05 => ( ( finite_card_int @ ( insert_int @ X @ A2 ) )
% 4.71/5.05 = ( suc @ ( finite_card_int @ A2 ) ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % card_insert_disjoint
% 4.71/5.05 thf(fact_2238_card__insert__disjoint,axiom,
% 4.71/5.05 ! [A2: set_complex,X: complex] :
% 4.71/5.05 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.05 => ( ~ ( member_complex @ X @ A2 )
% 4.71/5.05 => ( ( finite_card_complex @ ( insert_complex @ X @ A2 ) )
% 4.71/5.05 = ( suc @ ( finite_card_complex @ A2 ) ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % card_insert_disjoint
% 4.71/5.05 thf(fact_2239_card__insert__disjoint,axiom,
% 4.71/5.05 ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 4.71/5.05 ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.05 => ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 4.71/5.05 => ( ( finite711546835091564841at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) )
% 4.71/5.05 = ( suc @ ( finite711546835091564841at_nat @ A2 ) ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % card_insert_disjoint
% 4.71/5.05 thf(fact_2240_card__insert__disjoint,axiom,
% 4.71/5.05 ! [A2: set_Extended_enat,X: extended_enat] :
% 4.71/5.05 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.05 => ( ~ ( member_Extended_enat @ X @ A2 )
% 4.71/5.05 => ( ( finite121521170596916366d_enat @ ( insert_Extended_enat @ X @ A2 ) )
% 4.71/5.05 = ( suc @ ( finite121521170596916366d_enat @ A2 ) ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % card_insert_disjoint
% 4.71/5.05 thf(fact_2241_mult__le__cancel2,axiom,
% 4.71/5.05 ! [M2: nat,K: nat,N: nat] :
% 4.71/5.05 ( ( ord_less_eq_nat @ ( times_times_nat @ M2 @ K ) @ ( times_times_nat @ N @ K ) )
% 4.71/5.05 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.71/5.05 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_le_cancel2
% 4.71/5.05 thf(fact_2242_div__mult__self__is__m,axiom,
% 4.71/5.05 ! [N: nat,M2: nat] :
% 4.71/5.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.05 => ( ( divide_divide_nat @ ( times_times_nat @ M2 @ N ) @ N )
% 4.71/5.05 = M2 ) ) ).
% 4.71/5.05
% 4.71/5.05 % div_mult_self_is_m
% 4.71/5.05 thf(fact_2243_div__mult__self1__is__m,axiom,
% 4.71/5.05 ! [N: nat,M2: nat] :
% 4.71/5.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.05 => ( ( divide_divide_nat @ ( times_times_nat @ N @ M2 ) @ N )
% 4.71/5.05 = M2 ) ) ).
% 4.71/5.05
% 4.71/5.05 % div_mult_self1_is_m
% 4.71/5.05 thf(fact_2244_nat__1,axiom,
% 4.71/5.05 ( ( nat2 @ one_one_int )
% 4.71/5.05 = ( suc @ zero_zero_nat ) ) ).
% 4.71/5.05
% 4.71/5.05 % nat_1
% 4.71/5.05 thf(fact_2245_nat__0__iff,axiom,
% 4.71/5.05 ! [I: int] :
% 4.71/5.05 ( ( ( nat2 @ I )
% 4.71/5.05 = zero_zero_nat )
% 4.71/5.05 = ( ord_less_eq_int @ I @ zero_zero_int ) ) ).
% 4.71/5.05
% 4.71/5.05 % nat_0_iff
% 4.71/5.05 thf(fact_2246_nat__le__0,axiom,
% 4.71/5.05 ! [Z: int] :
% 4.71/5.05 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 4.71/5.05 => ( ( nat2 @ Z )
% 4.71/5.05 = zero_zero_nat ) ) ).
% 4.71/5.05
% 4.71/5.05 % nat_le_0
% 4.71/5.05 thf(fact_2247_zless__nat__conj,axiom,
% 4.71/5.05 ! [W2: int,Z: int] :
% 4.71/5.05 ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z ) )
% 4.71/5.05 = ( ( ord_less_int @ zero_zero_int @ Z )
% 4.71/5.05 & ( ord_less_int @ W2 @ Z ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % zless_nat_conj
% 4.71/5.05 thf(fact_2248_zle__add1__eq__le,axiom,
% 4.71/5.05 ! [W2: int,Z: int] :
% 4.71/5.05 ( ( ord_less_int @ W2 @ ( plus_plus_int @ Z @ one_one_int ) )
% 4.71/5.05 = ( ord_less_eq_int @ W2 @ Z ) ) ).
% 4.71/5.05
% 4.71/5.05 % zle_add1_eq_le
% 4.71/5.05 thf(fact_2249_int__nat__eq,axiom,
% 4.71/5.05 ! [Z: int] :
% 4.71/5.05 ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 4.71/5.05 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 4.71/5.05 = Z ) )
% 4.71/5.05 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 4.71/5.05 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 4.71/5.05 = zero_zero_int ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % int_nat_eq
% 4.71/5.05 thf(fact_2250_frac__gt__0__iff,axiom,
% 4.71/5.05 ! [X: real] :
% 4.71/5.05 ( ( ord_less_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X ) )
% 4.71/5.05 = ( ~ ( member_real @ X @ ring_1_Ints_real ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % frac_gt_0_iff
% 4.71/5.05 thf(fact_2251_frac__gt__0__iff,axiom,
% 4.71/5.05 ! [X: rat] :
% 4.71/5.05 ( ( ord_less_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X ) )
% 4.71/5.05 = ( ~ ( member_rat @ X @ ring_1_Ints_rat ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % frac_gt_0_iff
% 4.71/5.05 thf(fact_2252_zero__less__nat__eq,axiom,
% 4.71/5.05 ! [Z: int] :
% 4.71/5.05 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 4.71/5.05 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 4.71/5.05
% 4.71/5.05 % zero_less_nat_eq
% 4.71/5.05 thf(fact_2253_card__Diff__insert,axiom,
% 4.71/5.05 ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 4.71/5.05 ( ( member8440522571783428010at_nat @ A @ A2 )
% 4.71/5.05 => ( ~ ( member8440522571783428010at_nat @ A @ B2 )
% 4.71/5.05 => ( ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B2 ) ) )
% 4.71/5.05 = ( minus_minus_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % card_Diff_insert
% 4.71/5.05 thf(fact_2254_card__Diff__insert,axiom,
% 4.71/5.05 ! [A: real,A2: set_real,B2: set_real] :
% 4.71/5.05 ( ( member_real @ A @ A2 )
% 4.71/5.05 => ( ~ ( member_real @ A @ B2 )
% 4.71/5.05 => ( ( finite_card_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B2 ) ) )
% 4.71/5.05 = ( minus_minus_nat @ ( finite_card_real @ ( minus_minus_set_real @ A2 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % card_Diff_insert
% 4.71/5.05 thf(fact_2255_card__Diff__insert,axiom,
% 4.71/5.05 ! [A: $o,A2: set_o,B2: set_o] :
% 4.71/5.05 ( ( member_o @ A @ A2 )
% 4.71/5.05 => ( ~ ( member_o @ A @ B2 )
% 4.71/5.05 => ( ( finite_card_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ B2 ) ) )
% 4.71/5.05 = ( minus_minus_nat @ ( finite_card_o @ ( minus_minus_set_o @ A2 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % card_Diff_insert
% 4.71/5.05 thf(fact_2256_card__Diff__insert,axiom,
% 4.71/5.05 ! [A: set_nat_rat,A2: set_set_nat_rat,B2: set_set_nat_rat] :
% 4.71/5.05 ( ( member_set_nat_rat @ A @ A2 )
% 4.71/5.05 => ( ~ ( member_set_nat_rat @ A @ B2 )
% 4.71/5.05 => ( ( finite8736671560171388117at_rat @ ( minus_1626877696091177228at_rat @ A2 @ ( insert_set_nat_rat @ A @ B2 ) ) )
% 4.71/5.05 = ( minus_minus_nat @ ( finite8736671560171388117at_rat @ ( minus_1626877696091177228at_rat @ A2 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % card_Diff_insert
% 4.71/5.05 thf(fact_2257_card__Diff__insert,axiom,
% 4.71/5.05 ! [A: complex,A2: set_complex,B2: set_complex] :
% 4.71/5.05 ( ( member_complex @ A @ A2 )
% 4.71/5.05 => ( ~ ( member_complex @ A @ B2 )
% 4.71/5.05 => ( ( finite_card_complex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ B2 ) ) )
% 4.71/5.05 = ( minus_minus_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % card_Diff_insert
% 4.71/5.05 thf(fact_2258_card__Diff__insert,axiom,
% 4.71/5.05 ! [A: list_nat,A2: set_list_nat,B2: set_list_nat] :
% 4.71/5.05 ( ( member_list_nat @ A @ A2 )
% 4.71/5.05 => ( ~ ( member_list_nat @ A @ B2 )
% 4.71/5.05 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ ( insert_list_nat @ A @ B2 ) ) )
% 4.71/5.05 = ( minus_minus_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % card_Diff_insert
% 4.71/5.05 thf(fact_2259_card__Diff__insert,axiom,
% 4.71/5.05 ! [A: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 4.71/5.05 ( ( member_set_nat @ A @ A2 )
% 4.71/5.05 => ( ~ ( member_set_nat @ A @ B2 )
% 4.71/5.05 => ( ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ B2 ) ) )
% 4.71/5.05 = ( minus_minus_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % card_Diff_insert
% 4.71/5.05 thf(fact_2260_card__Diff__insert,axiom,
% 4.71/5.05 ! [A: int,A2: set_int,B2: set_int] :
% 4.71/5.05 ( ( member_int @ A @ A2 )
% 4.71/5.05 => ( ~ ( member_int @ A @ B2 )
% 4.71/5.05 => ( ( finite_card_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B2 ) ) )
% 4.71/5.05 = ( minus_minus_nat @ ( finite_card_int @ ( minus_minus_set_int @ A2 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % card_Diff_insert
% 4.71/5.05 thf(fact_2261_card__Diff__insert,axiom,
% 4.71/5.05 ! [A: nat,A2: set_nat,B2: set_nat] :
% 4.71/5.05 ( ( member_nat @ A @ A2 )
% 4.71/5.05 => ( ~ ( member_nat @ A @ B2 )
% 4.71/5.05 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B2 ) ) )
% 4.71/5.05 = ( minus_minus_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % card_Diff_insert
% 4.71/5.05 thf(fact_2262_ln__diff__le,axiom,
% 4.71/5.05 ! [X: real,Y: real] :
% 4.71/5.05 ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.05 => ( ( ord_less_real @ zero_zero_real @ Y )
% 4.71/5.05 => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) @ ( divide_divide_real @ ( minus_minus_real @ X @ Y ) @ Y ) ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % ln_diff_le
% 4.71/5.05 thf(fact_2263_mult__diff__mult,axiom,
% 4.71/5.05 ! [X: real,Y: real,A: real,B: real] :
% 4.71/5.05 ( ( minus_minus_real @ ( times_times_real @ X @ Y ) @ ( times_times_real @ A @ B ) )
% 4.71/5.05 = ( plus_plus_real @ ( times_times_real @ X @ ( minus_minus_real @ Y @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X @ A ) @ B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_diff_mult
% 4.71/5.05 thf(fact_2264_mult__diff__mult,axiom,
% 4.71/5.05 ! [X: rat,Y: rat,A: rat,B: rat] :
% 4.71/5.05 ( ( minus_minus_rat @ ( times_times_rat @ X @ Y ) @ ( times_times_rat @ A @ B ) )
% 4.71/5.05 = ( plus_plus_rat @ ( times_times_rat @ X @ ( minus_minus_rat @ Y @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X @ A ) @ B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_diff_mult
% 4.71/5.05 thf(fact_2265_mult__diff__mult,axiom,
% 4.71/5.05 ! [X: int,Y: int,A: int,B: int] :
% 4.71/5.05 ( ( minus_minus_int @ ( times_times_int @ X @ Y ) @ ( times_times_int @ A @ B ) )
% 4.71/5.05 = ( plus_plus_int @ ( times_times_int @ X @ ( minus_minus_int @ Y @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X @ A ) @ B ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % mult_diff_mult
% 4.71/5.05 thf(fact_2266_eq__add__iff1,axiom,
% 4.71/5.05 ! [A: real,E2: real,C: real,B: real,D: real] :
% 4.71/5.05 ( ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C )
% 4.71/5.05 = ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 4.71/5.05 = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C )
% 4.71/5.05 = D ) ) ).
% 4.71/5.05
% 4.71/5.05 % eq_add_iff1
% 4.71/5.05 thf(fact_2267_eq__add__iff1,axiom,
% 4.71/5.05 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 4.71/5.05 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C )
% 4.71/5.05 = ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 4.71/5.05 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C )
% 4.71/5.05 = D ) ) ).
% 4.71/5.05
% 4.71/5.05 % eq_add_iff1
% 4.71/5.05 thf(fact_2268_eq__add__iff1,axiom,
% 4.71/5.05 ! [A: int,E2: int,C: int,B: int,D: int] :
% 4.71/5.05 ( ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C )
% 4.71/5.05 = ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 4.71/5.05 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C )
% 4.71/5.05 = D ) ) ).
% 4.71/5.05
% 4.71/5.05 % eq_add_iff1
% 4.71/5.05 thf(fact_2269_eq__add__iff2,axiom,
% 4.71/5.05 ! [A: real,E2: real,C: real,B: real,D: real] :
% 4.71/5.05 ( ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C )
% 4.71/5.05 = ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 4.71/5.05 = ( C
% 4.71/5.05 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % eq_add_iff2
% 4.71/5.05 thf(fact_2270_eq__add__iff2,axiom,
% 4.71/5.05 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 4.71/5.05 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C )
% 4.71/5.05 = ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 4.71/5.05 = ( C
% 4.71/5.05 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % eq_add_iff2
% 4.71/5.05 thf(fact_2271_eq__add__iff2,axiom,
% 4.71/5.05 ! [A: int,E2: int,C: int,B: int,D: int] :
% 4.71/5.05 ( ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C )
% 4.71/5.05 = ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 4.71/5.05 = ( C
% 4.71/5.05 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 4.71/5.05
% 4.71/5.05 % eq_add_iff2
% 4.71/5.05 thf(fact_2272_square__diff__square__factored,axiom,
% 4.71/5.05 ! [X: real,Y: real] :
% 4.71/5.05 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 4.71/5.05 = ( times_times_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ X @ Y ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % square_diff_square_factored
% 4.71/5.06 thf(fact_2273_square__diff__square__factored,axiom,
% 4.71/5.06 ! [X: rat,Y: rat] :
% 4.71/5.06 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 4.71/5.06 = ( times_times_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_rat @ X @ Y ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % square_diff_square_factored
% 4.71/5.06 thf(fact_2274_square__diff__square__factored,axiom,
% 4.71/5.06 ! [X: int,Y: int] :
% 4.71/5.06 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 4.71/5.06 = ( times_times_int @ ( plus_plus_int @ X @ Y ) @ ( minus_minus_int @ X @ Y ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % square_diff_square_factored
% 4.71/5.06 thf(fact_2275_less__eq__real__def,axiom,
% 4.71/5.06 ( ord_less_eq_real
% 4.71/5.06 = ( ^ [X3: real,Y2: real] :
% 4.71/5.06 ( ( ord_less_real @ X3 @ Y2 )
% 4.71/5.06 | ( X3 = Y2 ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % less_eq_real_def
% 4.71/5.06 thf(fact_2276_ln__bound,axiom,
% 4.71/5.06 ! [X: real] :
% 4.71/5.06 ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.06 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 4.71/5.06
% 4.71/5.06 % ln_bound
% 4.71/5.06 thf(fact_2277_ln__ge__zero,axiom,
% 4.71/5.06 ! [X: real] :
% 4.71/5.06 ( ( ord_less_eq_real @ one_one_real @ X )
% 4.71/5.06 => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % ln_ge_zero
% 4.71/5.06 thf(fact_2278_ln__ge__zero__imp__ge__one,axiom,
% 4.71/5.06 ! [X: real] :
% 4.71/5.06 ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 4.71/5.06 => ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.06 => ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % ln_ge_zero_imp_ge_one
% 4.71/5.06 thf(fact_2279_abs__triangle__ineq,axiom,
% 4.71/5.06 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_triangle_ineq
% 4.71/5.06 thf(fact_2280_abs__triangle__ineq,axiom,
% 4.71/5.06 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_triangle_ineq
% 4.71/5.06 thf(fact_2281_abs__triangle__ineq,axiom,
% 4.71/5.06 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_triangle_ineq
% 4.71/5.06 thf(fact_2282_complete__real,axiom,
% 4.71/5.06 ! [S2: set_real] :
% 4.71/5.06 ( ? [X2: real] : ( member_real @ X2 @ S2 )
% 4.71/5.06 => ( ? [Z5: real] :
% 4.71/5.06 ! [X4: real] :
% 4.71/5.06 ( ( member_real @ X4 @ S2 )
% 4.71/5.06 => ( ord_less_eq_real @ X4 @ Z5 ) )
% 4.71/5.06 => ? [Y3: real] :
% 4.71/5.06 ( ! [X2: real] :
% 4.71/5.06 ( ( member_real @ X2 @ S2 )
% 4.71/5.06 => ( ord_less_eq_real @ X2 @ Y3 ) )
% 4.71/5.06 & ! [Z5: real] :
% 4.71/5.06 ( ! [X4: real] :
% 4.71/5.06 ( ( member_real @ X4 @ S2 )
% 4.71/5.06 => ( ord_less_eq_real @ X4 @ Z5 ) )
% 4.71/5.06 => ( ord_less_eq_real @ Y3 @ Z5 ) ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % complete_real
% 4.71/5.06 thf(fact_2283_abs__mult__less,axiom,
% 4.71/5.06 ! [A: real,C: real,B: real,D: real] :
% 4.71/5.06 ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 4.71/5.06 => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D )
% 4.71/5.06 => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C @ D ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_mult_less
% 4.71/5.06 thf(fact_2284_abs__mult__less,axiom,
% 4.71/5.06 ! [A: rat,C: rat,B: rat,D: rat] :
% 4.71/5.06 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 4.71/5.06 => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D )
% 4.71/5.06 => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_mult_less
% 4.71/5.06 thf(fact_2285_abs__mult__less,axiom,
% 4.71/5.06 ! [A: int,C: int,B: int,D: int] :
% 4.71/5.06 ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 4.71/5.06 => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D )
% 4.71/5.06 => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_mult_less
% 4.71/5.06 thf(fact_2286_mk__disjoint__insert,axiom,
% 4.71/5.06 ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.06 ( ( member8440522571783428010at_nat @ A @ A2 )
% 4.71/5.06 => ? [B8: set_Pr1261947904930325089at_nat] :
% 4.71/5.06 ( ( A2
% 4.71/5.06 = ( insert8211810215607154385at_nat @ A @ B8 ) )
% 4.71/5.06 & ~ ( member8440522571783428010at_nat @ A @ B8 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mk_disjoint_insert
% 4.71/5.06 thf(fact_2287_mk__disjoint__insert,axiom,
% 4.71/5.06 ! [A: real,A2: set_real] :
% 4.71/5.06 ( ( member_real @ A @ A2 )
% 4.71/5.06 => ? [B8: set_real] :
% 4.71/5.06 ( ( A2
% 4.71/5.06 = ( insert_real @ A @ B8 ) )
% 4.71/5.06 & ~ ( member_real @ A @ B8 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mk_disjoint_insert
% 4.71/5.06 thf(fact_2288_mk__disjoint__insert,axiom,
% 4.71/5.06 ! [A: $o,A2: set_o] :
% 4.71/5.06 ( ( member_o @ A @ A2 )
% 4.71/5.06 => ? [B8: set_o] :
% 4.71/5.06 ( ( A2
% 4.71/5.06 = ( insert_o @ A @ B8 ) )
% 4.71/5.06 & ~ ( member_o @ A @ B8 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mk_disjoint_insert
% 4.71/5.06 thf(fact_2289_mk__disjoint__insert,axiom,
% 4.71/5.06 ! [A: set_nat,A2: set_set_nat] :
% 4.71/5.06 ( ( member_set_nat @ A @ A2 )
% 4.71/5.06 => ? [B8: set_set_nat] :
% 4.71/5.06 ( ( A2
% 4.71/5.06 = ( insert_set_nat @ A @ B8 ) )
% 4.71/5.06 & ~ ( member_set_nat @ A @ B8 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mk_disjoint_insert
% 4.71/5.06 thf(fact_2290_mk__disjoint__insert,axiom,
% 4.71/5.06 ! [A: set_nat_rat,A2: set_set_nat_rat] :
% 4.71/5.06 ( ( member_set_nat_rat @ A @ A2 )
% 4.71/5.06 => ? [B8: set_set_nat_rat] :
% 4.71/5.06 ( ( A2
% 4.71/5.06 = ( insert_set_nat_rat @ A @ B8 ) )
% 4.71/5.06 & ~ ( member_set_nat_rat @ A @ B8 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mk_disjoint_insert
% 4.71/5.06 thf(fact_2291_mk__disjoint__insert,axiom,
% 4.71/5.06 ! [A: nat,A2: set_nat] :
% 4.71/5.06 ( ( member_nat @ A @ A2 )
% 4.71/5.06 => ? [B8: set_nat] :
% 4.71/5.06 ( ( A2
% 4.71/5.06 = ( insert_nat @ A @ B8 ) )
% 4.71/5.06 & ~ ( member_nat @ A @ B8 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mk_disjoint_insert
% 4.71/5.06 thf(fact_2292_mk__disjoint__insert,axiom,
% 4.71/5.06 ! [A: int,A2: set_int] :
% 4.71/5.06 ( ( member_int @ A @ A2 )
% 4.71/5.06 => ? [B8: set_int] :
% 4.71/5.06 ( ( A2
% 4.71/5.06 = ( insert_int @ A @ B8 ) )
% 4.71/5.06 & ~ ( member_int @ A @ B8 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mk_disjoint_insert
% 4.71/5.06 thf(fact_2293_insert__commute,axiom,
% 4.71/5.06 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.06 ( ( insert8211810215607154385at_nat @ X @ ( insert8211810215607154385at_nat @ Y @ A2 ) )
% 4.71/5.06 = ( insert8211810215607154385at_nat @ Y @ ( insert8211810215607154385at_nat @ X @ A2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_commute
% 4.71/5.06 thf(fact_2294_insert__commute,axiom,
% 4.71/5.06 ! [X: real,Y: real,A2: set_real] :
% 4.71/5.06 ( ( insert_real @ X @ ( insert_real @ Y @ A2 ) )
% 4.71/5.06 = ( insert_real @ Y @ ( insert_real @ X @ A2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_commute
% 4.71/5.06 thf(fact_2295_insert__commute,axiom,
% 4.71/5.06 ! [X: $o,Y: $o,A2: set_o] :
% 4.71/5.06 ( ( insert_o @ X @ ( insert_o @ Y @ A2 ) )
% 4.71/5.06 = ( insert_o @ Y @ ( insert_o @ X @ A2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_commute
% 4.71/5.06 thf(fact_2296_insert__commute,axiom,
% 4.71/5.06 ! [X: nat,Y: nat,A2: set_nat] :
% 4.71/5.06 ( ( insert_nat @ X @ ( insert_nat @ Y @ A2 ) )
% 4.71/5.06 = ( insert_nat @ Y @ ( insert_nat @ X @ A2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_commute
% 4.71/5.06 thf(fact_2297_insert__commute,axiom,
% 4.71/5.06 ! [X: int,Y: int,A2: set_int] :
% 4.71/5.06 ( ( insert_int @ X @ ( insert_int @ Y @ A2 ) )
% 4.71/5.06 = ( insert_int @ Y @ ( insert_int @ X @ A2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_commute
% 4.71/5.06 thf(fact_2298_insert__eq__iff,axiom,
% 4.71/5.06 ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 4.71/5.06 ( ~ ( member8440522571783428010at_nat @ A @ A2 )
% 4.71/5.06 => ( ~ ( member8440522571783428010at_nat @ B @ B2 )
% 4.71/5.06 => ( ( ( insert8211810215607154385at_nat @ A @ A2 )
% 4.71/5.06 = ( insert8211810215607154385at_nat @ B @ B2 ) )
% 4.71/5.06 = ( ( ( A = B )
% 4.71/5.06 => ( A2 = B2 ) )
% 4.71/5.06 & ( ( A != B )
% 4.71/5.06 => ? [C4: set_Pr1261947904930325089at_nat] :
% 4.71/5.06 ( ( A2
% 4.71/5.06 = ( insert8211810215607154385at_nat @ B @ C4 ) )
% 4.71/5.06 & ~ ( member8440522571783428010at_nat @ B @ C4 )
% 4.71/5.06 & ( B2
% 4.71/5.06 = ( insert8211810215607154385at_nat @ A @ C4 ) )
% 4.71/5.06 & ~ ( member8440522571783428010at_nat @ A @ C4 ) ) ) ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_eq_iff
% 4.71/5.06 thf(fact_2299_insert__eq__iff,axiom,
% 4.71/5.06 ! [A: real,A2: set_real,B: real,B2: set_real] :
% 4.71/5.06 ( ~ ( member_real @ A @ A2 )
% 4.71/5.06 => ( ~ ( member_real @ B @ B2 )
% 4.71/5.06 => ( ( ( insert_real @ A @ A2 )
% 4.71/5.06 = ( insert_real @ B @ B2 ) )
% 4.71/5.06 = ( ( ( A = B )
% 4.71/5.06 => ( A2 = B2 ) )
% 4.71/5.06 & ( ( A != B )
% 4.71/5.06 => ? [C4: set_real] :
% 4.71/5.06 ( ( A2
% 4.71/5.06 = ( insert_real @ B @ C4 ) )
% 4.71/5.06 & ~ ( member_real @ B @ C4 )
% 4.71/5.06 & ( B2
% 4.71/5.06 = ( insert_real @ A @ C4 ) )
% 4.71/5.06 & ~ ( member_real @ A @ C4 ) ) ) ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_eq_iff
% 4.71/5.06 thf(fact_2300_insert__eq__iff,axiom,
% 4.71/5.06 ! [A: $o,A2: set_o,B: $o,B2: set_o] :
% 4.71/5.06 ( ~ ( member_o @ A @ A2 )
% 4.71/5.06 => ( ~ ( member_o @ B @ B2 )
% 4.71/5.06 => ( ( ( insert_o @ A @ A2 )
% 4.71/5.06 = ( insert_o @ B @ B2 ) )
% 4.71/5.06 = ( ( ( A = B )
% 4.71/5.06 => ( A2 = B2 ) )
% 4.71/5.06 & ( ( A = ~ B )
% 4.71/5.06 => ? [C4: set_o] :
% 4.71/5.06 ( ( A2
% 4.71/5.06 = ( insert_o @ B @ C4 ) )
% 4.71/5.06 & ~ ( member_o @ B @ C4 )
% 4.71/5.06 & ( B2
% 4.71/5.06 = ( insert_o @ A @ C4 ) )
% 4.71/5.06 & ~ ( member_o @ A @ C4 ) ) ) ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_eq_iff
% 4.71/5.06 thf(fact_2301_insert__eq__iff,axiom,
% 4.71/5.06 ! [A: set_nat,A2: set_set_nat,B: set_nat,B2: set_set_nat] :
% 4.71/5.06 ( ~ ( member_set_nat @ A @ A2 )
% 4.71/5.06 => ( ~ ( member_set_nat @ B @ B2 )
% 4.71/5.06 => ( ( ( insert_set_nat @ A @ A2 )
% 4.71/5.06 = ( insert_set_nat @ B @ B2 ) )
% 4.71/5.06 = ( ( ( A = B )
% 4.71/5.06 => ( A2 = B2 ) )
% 4.71/5.06 & ( ( A != B )
% 4.71/5.06 => ? [C4: set_set_nat] :
% 4.71/5.06 ( ( A2
% 4.71/5.06 = ( insert_set_nat @ B @ C4 ) )
% 4.71/5.06 & ~ ( member_set_nat @ B @ C4 )
% 4.71/5.06 & ( B2
% 4.71/5.06 = ( insert_set_nat @ A @ C4 ) )
% 4.71/5.06 & ~ ( member_set_nat @ A @ C4 ) ) ) ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_eq_iff
% 4.71/5.06 thf(fact_2302_insert__eq__iff,axiom,
% 4.71/5.06 ! [A: set_nat_rat,A2: set_set_nat_rat,B: set_nat_rat,B2: set_set_nat_rat] :
% 4.71/5.06 ( ~ ( member_set_nat_rat @ A @ A2 )
% 4.71/5.06 => ( ~ ( member_set_nat_rat @ B @ B2 )
% 4.71/5.06 => ( ( ( insert_set_nat_rat @ A @ A2 )
% 4.71/5.06 = ( insert_set_nat_rat @ B @ B2 ) )
% 4.71/5.06 = ( ( ( A = B )
% 4.71/5.06 => ( A2 = B2 ) )
% 4.71/5.06 & ( ( A != B )
% 4.71/5.06 => ? [C4: set_set_nat_rat] :
% 4.71/5.06 ( ( A2
% 4.71/5.06 = ( insert_set_nat_rat @ B @ C4 ) )
% 4.71/5.06 & ~ ( member_set_nat_rat @ B @ C4 )
% 4.71/5.06 & ( B2
% 4.71/5.06 = ( insert_set_nat_rat @ A @ C4 ) )
% 4.71/5.06 & ~ ( member_set_nat_rat @ A @ C4 ) ) ) ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_eq_iff
% 4.71/5.06 thf(fact_2303_insert__eq__iff,axiom,
% 4.71/5.06 ! [A: nat,A2: set_nat,B: nat,B2: set_nat] :
% 4.71/5.06 ( ~ ( member_nat @ A @ A2 )
% 4.71/5.06 => ( ~ ( member_nat @ B @ B2 )
% 4.71/5.06 => ( ( ( insert_nat @ A @ A2 )
% 4.71/5.06 = ( insert_nat @ B @ B2 ) )
% 4.71/5.06 = ( ( ( A = B )
% 4.71/5.06 => ( A2 = B2 ) )
% 4.71/5.06 & ( ( A != B )
% 4.71/5.06 => ? [C4: set_nat] :
% 4.71/5.06 ( ( A2
% 4.71/5.06 = ( insert_nat @ B @ C4 ) )
% 4.71/5.06 & ~ ( member_nat @ B @ C4 )
% 4.71/5.06 & ( B2
% 4.71/5.06 = ( insert_nat @ A @ C4 ) )
% 4.71/5.06 & ~ ( member_nat @ A @ C4 ) ) ) ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_eq_iff
% 4.71/5.06 thf(fact_2304_insert__eq__iff,axiom,
% 4.71/5.06 ! [A: int,A2: set_int,B: int,B2: set_int] :
% 4.71/5.06 ( ~ ( member_int @ A @ A2 )
% 4.71/5.06 => ( ~ ( member_int @ B @ B2 )
% 4.71/5.06 => ( ( ( insert_int @ A @ A2 )
% 4.71/5.06 = ( insert_int @ B @ B2 ) )
% 4.71/5.06 = ( ( ( A = B )
% 4.71/5.06 => ( A2 = B2 ) )
% 4.71/5.06 & ( ( A != B )
% 4.71/5.06 => ? [C4: set_int] :
% 4.71/5.06 ( ( A2
% 4.71/5.06 = ( insert_int @ B @ C4 ) )
% 4.71/5.06 & ~ ( member_int @ B @ C4 )
% 4.71/5.06 & ( B2
% 4.71/5.06 = ( insert_int @ A @ C4 ) )
% 4.71/5.06 & ~ ( member_int @ A @ C4 ) ) ) ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_eq_iff
% 4.71/5.06 thf(fact_2305_insert__absorb,axiom,
% 4.71/5.06 ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.06 ( ( member8440522571783428010at_nat @ A @ A2 )
% 4.71/5.06 => ( ( insert8211810215607154385at_nat @ A @ A2 )
% 4.71/5.06 = A2 ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_absorb
% 4.71/5.06 thf(fact_2306_insert__absorb,axiom,
% 4.71/5.06 ! [A: real,A2: set_real] :
% 4.71/5.06 ( ( member_real @ A @ A2 )
% 4.71/5.06 => ( ( insert_real @ A @ A2 )
% 4.71/5.06 = A2 ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_absorb
% 4.71/5.06 thf(fact_2307_insert__absorb,axiom,
% 4.71/5.06 ! [A: $o,A2: set_o] :
% 4.71/5.06 ( ( member_o @ A @ A2 )
% 4.71/5.06 => ( ( insert_o @ A @ A2 )
% 4.71/5.06 = A2 ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_absorb
% 4.71/5.06 thf(fact_2308_insert__absorb,axiom,
% 4.71/5.06 ! [A: set_nat,A2: set_set_nat] :
% 4.71/5.06 ( ( member_set_nat @ A @ A2 )
% 4.71/5.06 => ( ( insert_set_nat @ A @ A2 )
% 4.71/5.06 = A2 ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_absorb
% 4.71/5.06 thf(fact_2309_insert__absorb,axiom,
% 4.71/5.06 ! [A: set_nat_rat,A2: set_set_nat_rat] :
% 4.71/5.06 ( ( member_set_nat_rat @ A @ A2 )
% 4.71/5.06 => ( ( insert_set_nat_rat @ A @ A2 )
% 4.71/5.06 = A2 ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_absorb
% 4.71/5.06 thf(fact_2310_insert__absorb,axiom,
% 4.71/5.06 ! [A: nat,A2: set_nat] :
% 4.71/5.06 ( ( member_nat @ A @ A2 )
% 4.71/5.06 => ( ( insert_nat @ A @ A2 )
% 4.71/5.06 = A2 ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_absorb
% 4.71/5.06 thf(fact_2311_insert__absorb,axiom,
% 4.71/5.06 ! [A: int,A2: set_int] :
% 4.71/5.06 ( ( member_int @ A @ A2 )
% 4.71/5.06 => ( ( insert_int @ A @ A2 )
% 4.71/5.06 = A2 ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_absorb
% 4.71/5.06 thf(fact_2312_insert__ident,axiom,
% 4.71/5.06 ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 4.71/5.06 ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 4.71/5.06 => ( ~ ( member8440522571783428010at_nat @ X @ B2 )
% 4.71/5.06 => ( ( ( insert8211810215607154385at_nat @ X @ A2 )
% 4.71/5.06 = ( insert8211810215607154385at_nat @ X @ B2 ) )
% 4.71/5.06 = ( A2 = B2 ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_ident
% 4.71/5.06 thf(fact_2313_insert__ident,axiom,
% 4.71/5.06 ! [X: real,A2: set_real,B2: set_real] :
% 4.71/5.06 ( ~ ( member_real @ X @ A2 )
% 4.71/5.06 => ( ~ ( member_real @ X @ B2 )
% 4.71/5.06 => ( ( ( insert_real @ X @ A2 )
% 4.71/5.06 = ( insert_real @ X @ B2 ) )
% 4.71/5.06 = ( A2 = B2 ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_ident
% 4.71/5.06 thf(fact_2314_insert__ident,axiom,
% 4.71/5.06 ! [X: $o,A2: set_o,B2: set_o] :
% 4.71/5.06 ( ~ ( member_o @ X @ A2 )
% 4.71/5.06 => ( ~ ( member_o @ X @ B2 )
% 4.71/5.06 => ( ( ( insert_o @ X @ A2 )
% 4.71/5.06 = ( insert_o @ X @ B2 ) )
% 4.71/5.06 = ( A2 = B2 ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_ident
% 4.71/5.06 thf(fact_2315_insert__ident,axiom,
% 4.71/5.06 ! [X: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 4.71/5.06 ( ~ ( member_set_nat @ X @ A2 )
% 4.71/5.06 => ( ~ ( member_set_nat @ X @ B2 )
% 4.71/5.06 => ( ( ( insert_set_nat @ X @ A2 )
% 4.71/5.06 = ( insert_set_nat @ X @ B2 ) )
% 4.71/5.06 = ( A2 = B2 ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_ident
% 4.71/5.06 thf(fact_2316_insert__ident,axiom,
% 4.71/5.06 ! [X: set_nat_rat,A2: set_set_nat_rat,B2: set_set_nat_rat] :
% 4.71/5.06 ( ~ ( member_set_nat_rat @ X @ A2 )
% 4.71/5.06 => ( ~ ( member_set_nat_rat @ X @ B2 )
% 4.71/5.06 => ( ( ( insert_set_nat_rat @ X @ A2 )
% 4.71/5.06 = ( insert_set_nat_rat @ X @ B2 ) )
% 4.71/5.06 = ( A2 = B2 ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_ident
% 4.71/5.06 thf(fact_2317_insert__ident,axiom,
% 4.71/5.06 ! [X: nat,A2: set_nat,B2: set_nat] :
% 4.71/5.06 ( ~ ( member_nat @ X @ A2 )
% 4.71/5.06 => ( ~ ( member_nat @ X @ B2 )
% 4.71/5.06 => ( ( ( insert_nat @ X @ A2 )
% 4.71/5.06 = ( insert_nat @ X @ B2 ) )
% 4.71/5.06 = ( A2 = B2 ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_ident
% 4.71/5.06 thf(fact_2318_insert__ident,axiom,
% 4.71/5.06 ! [X: int,A2: set_int,B2: set_int] :
% 4.71/5.06 ( ~ ( member_int @ X @ A2 )
% 4.71/5.06 => ( ~ ( member_int @ X @ B2 )
% 4.71/5.06 => ( ( ( insert_int @ X @ A2 )
% 4.71/5.06 = ( insert_int @ X @ B2 ) )
% 4.71/5.06 = ( A2 = B2 ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_ident
% 4.71/5.06 thf(fact_2319_Set_Oset__insert,axiom,
% 4.71/5.06 ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.06 ( ( member8440522571783428010at_nat @ X @ A2 )
% 4.71/5.06 => ~ ! [B8: set_Pr1261947904930325089at_nat] :
% 4.71/5.06 ( ( A2
% 4.71/5.06 = ( insert8211810215607154385at_nat @ X @ B8 ) )
% 4.71/5.06 => ( member8440522571783428010at_nat @ X @ B8 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % Set.set_insert
% 4.71/5.06 thf(fact_2320_Set_Oset__insert,axiom,
% 4.71/5.06 ! [X: real,A2: set_real] :
% 4.71/5.06 ( ( member_real @ X @ A2 )
% 4.71/5.06 => ~ ! [B8: set_real] :
% 4.71/5.06 ( ( A2
% 4.71/5.06 = ( insert_real @ X @ B8 ) )
% 4.71/5.06 => ( member_real @ X @ B8 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % Set.set_insert
% 4.71/5.06 thf(fact_2321_Set_Oset__insert,axiom,
% 4.71/5.06 ! [X: $o,A2: set_o] :
% 4.71/5.06 ( ( member_o @ X @ A2 )
% 4.71/5.06 => ~ ! [B8: set_o] :
% 4.71/5.06 ( ( A2
% 4.71/5.06 = ( insert_o @ X @ B8 ) )
% 4.71/5.06 => ( member_o @ X @ B8 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % Set.set_insert
% 4.71/5.06 thf(fact_2322_Set_Oset__insert,axiom,
% 4.71/5.06 ! [X: set_nat,A2: set_set_nat] :
% 4.71/5.06 ( ( member_set_nat @ X @ A2 )
% 4.71/5.06 => ~ ! [B8: set_set_nat] :
% 4.71/5.06 ( ( A2
% 4.71/5.06 = ( insert_set_nat @ X @ B8 ) )
% 4.71/5.06 => ( member_set_nat @ X @ B8 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % Set.set_insert
% 4.71/5.06 thf(fact_2323_Set_Oset__insert,axiom,
% 4.71/5.06 ! [X: set_nat_rat,A2: set_set_nat_rat] :
% 4.71/5.06 ( ( member_set_nat_rat @ X @ A2 )
% 4.71/5.06 => ~ ! [B8: set_set_nat_rat] :
% 4.71/5.06 ( ( A2
% 4.71/5.06 = ( insert_set_nat_rat @ X @ B8 ) )
% 4.71/5.06 => ( member_set_nat_rat @ X @ B8 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % Set.set_insert
% 4.71/5.06 thf(fact_2324_Set_Oset__insert,axiom,
% 4.71/5.06 ! [X: nat,A2: set_nat] :
% 4.71/5.06 ( ( member_nat @ X @ A2 )
% 4.71/5.06 => ~ ! [B8: set_nat] :
% 4.71/5.06 ( ( A2
% 4.71/5.06 = ( insert_nat @ X @ B8 ) )
% 4.71/5.06 => ( member_nat @ X @ B8 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % Set.set_insert
% 4.71/5.06 thf(fact_2325_Set_Oset__insert,axiom,
% 4.71/5.06 ! [X: int,A2: set_int] :
% 4.71/5.06 ( ( member_int @ X @ A2 )
% 4.71/5.06 => ~ ! [B8: set_int] :
% 4.71/5.06 ( ( A2
% 4.71/5.06 = ( insert_int @ X @ B8 ) )
% 4.71/5.06 => ( member_int @ X @ B8 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % Set.set_insert
% 4.71/5.06 thf(fact_2326_insertI2,axiom,
% 4.71/5.06 ! [A: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat,B: product_prod_nat_nat] :
% 4.71/5.06 ( ( member8440522571783428010at_nat @ A @ B2 )
% 4.71/5.06 => ( member8440522571783428010at_nat @ A @ ( insert8211810215607154385at_nat @ B @ B2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insertI2
% 4.71/5.06 thf(fact_2327_insertI2,axiom,
% 4.71/5.06 ! [A: real,B2: set_real,B: real] :
% 4.71/5.06 ( ( member_real @ A @ B2 )
% 4.71/5.06 => ( member_real @ A @ ( insert_real @ B @ B2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insertI2
% 4.71/5.06 thf(fact_2328_insertI2,axiom,
% 4.71/5.06 ! [A: $o,B2: set_o,B: $o] :
% 4.71/5.06 ( ( member_o @ A @ B2 )
% 4.71/5.06 => ( member_o @ A @ ( insert_o @ B @ B2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insertI2
% 4.71/5.06 thf(fact_2329_insertI2,axiom,
% 4.71/5.06 ! [A: set_nat,B2: set_set_nat,B: set_nat] :
% 4.71/5.06 ( ( member_set_nat @ A @ B2 )
% 4.71/5.06 => ( member_set_nat @ A @ ( insert_set_nat @ B @ B2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insertI2
% 4.71/5.06 thf(fact_2330_insertI2,axiom,
% 4.71/5.06 ! [A: set_nat_rat,B2: set_set_nat_rat,B: set_nat_rat] :
% 4.71/5.06 ( ( member_set_nat_rat @ A @ B2 )
% 4.71/5.06 => ( member_set_nat_rat @ A @ ( insert_set_nat_rat @ B @ B2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insertI2
% 4.71/5.06 thf(fact_2331_insertI2,axiom,
% 4.71/5.06 ! [A: nat,B2: set_nat,B: nat] :
% 4.71/5.06 ( ( member_nat @ A @ B2 )
% 4.71/5.06 => ( member_nat @ A @ ( insert_nat @ B @ B2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insertI2
% 4.71/5.06 thf(fact_2332_insertI2,axiom,
% 4.71/5.06 ! [A: int,B2: set_int,B: int] :
% 4.71/5.06 ( ( member_int @ A @ B2 )
% 4.71/5.06 => ( member_int @ A @ ( insert_int @ B @ B2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insertI2
% 4.71/5.06 thf(fact_2333_insertI1,axiom,
% 4.71/5.06 ! [A: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] : ( member8440522571783428010at_nat @ A @ ( insert8211810215607154385at_nat @ A @ B2 ) ) ).
% 4.71/5.06
% 4.71/5.06 % insertI1
% 4.71/5.06 thf(fact_2334_insertI1,axiom,
% 4.71/5.06 ! [A: real,B2: set_real] : ( member_real @ A @ ( insert_real @ A @ B2 ) ) ).
% 4.71/5.06
% 4.71/5.06 % insertI1
% 4.71/5.06 thf(fact_2335_insertI1,axiom,
% 4.71/5.06 ! [A: $o,B2: set_o] : ( member_o @ A @ ( insert_o @ A @ B2 ) ) ).
% 4.71/5.06
% 4.71/5.06 % insertI1
% 4.71/5.06 thf(fact_2336_insertI1,axiom,
% 4.71/5.06 ! [A: set_nat,B2: set_set_nat] : ( member_set_nat @ A @ ( insert_set_nat @ A @ B2 ) ) ).
% 4.71/5.06
% 4.71/5.06 % insertI1
% 4.71/5.06 thf(fact_2337_insertI1,axiom,
% 4.71/5.06 ! [A: set_nat_rat,B2: set_set_nat_rat] : ( member_set_nat_rat @ A @ ( insert_set_nat_rat @ A @ B2 ) ) ).
% 4.71/5.06
% 4.71/5.06 % insertI1
% 4.71/5.06 thf(fact_2338_insertI1,axiom,
% 4.71/5.06 ! [A: nat,B2: set_nat] : ( member_nat @ A @ ( insert_nat @ A @ B2 ) ) ).
% 4.71/5.06
% 4.71/5.06 % insertI1
% 4.71/5.06 thf(fact_2339_insertI1,axiom,
% 4.71/5.06 ! [A: int,B2: set_int] : ( member_int @ A @ ( insert_int @ A @ B2 ) ) ).
% 4.71/5.06
% 4.71/5.06 % insertI1
% 4.71/5.06 thf(fact_2340_insertE,axiom,
% 4.71/5.06 ! [A: product_prod_nat_nat,B: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.06 ( ( member8440522571783428010at_nat @ A @ ( insert8211810215607154385at_nat @ B @ A2 ) )
% 4.71/5.06 => ( ( A != B )
% 4.71/5.06 => ( member8440522571783428010at_nat @ A @ A2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insertE
% 4.71/5.06 thf(fact_2341_insertE,axiom,
% 4.71/5.06 ! [A: real,B: real,A2: set_real] :
% 4.71/5.06 ( ( member_real @ A @ ( insert_real @ B @ A2 ) )
% 4.71/5.06 => ( ( A != B )
% 4.71/5.06 => ( member_real @ A @ A2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insertE
% 4.71/5.06 thf(fact_2342_insertE,axiom,
% 4.71/5.06 ! [A: $o,B: $o,A2: set_o] :
% 4.71/5.06 ( ( member_o @ A @ ( insert_o @ B @ A2 ) )
% 4.71/5.06 => ( ( A = ~ B )
% 4.71/5.06 => ( member_o @ A @ A2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insertE
% 4.71/5.06 thf(fact_2343_insertE,axiom,
% 4.71/5.06 ! [A: set_nat,B: set_nat,A2: set_set_nat] :
% 4.71/5.06 ( ( member_set_nat @ A @ ( insert_set_nat @ B @ A2 ) )
% 4.71/5.06 => ( ( A != B )
% 4.71/5.06 => ( member_set_nat @ A @ A2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insertE
% 4.71/5.06 thf(fact_2344_insertE,axiom,
% 4.71/5.06 ! [A: set_nat_rat,B: set_nat_rat,A2: set_set_nat_rat] :
% 4.71/5.06 ( ( member_set_nat_rat @ A @ ( insert_set_nat_rat @ B @ A2 ) )
% 4.71/5.06 => ( ( A != B )
% 4.71/5.06 => ( member_set_nat_rat @ A @ A2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insertE
% 4.71/5.06 thf(fact_2345_insertE,axiom,
% 4.71/5.06 ! [A: nat,B: nat,A2: set_nat] :
% 4.71/5.06 ( ( member_nat @ A @ ( insert_nat @ B @ A2 ) )
% 4.71/5.06 => ( ( A != B )
% 4.71/5.06 => ( member_nat @ A @ A2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insertE
% 4.71/5.06 thf(fact_2346_insertE,axiom,
% 4.71/5.06 ! [A: int,B: int,A2: set_int] :
% 4.71/5.06 ( ( member_int @ A @ ( insert_int @ B @ A2 ) )
% 4.71/5.06 => ( ( A != B )
% 4.71/5.06 => ( member_int @ A @ A2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insertE
% 4.71/5.06 thf(fact_2347_combine__common__factor,axiom,
% 4.71/5.06 ! [A: real,E2: real,B: real,C: real] :
% 4.71/5.06 ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ C ) )
% 4.71/5.06 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E2 ) @ C ) ) ).
% 4.71/5.06
% 4.71/5.06 % combine_common_factor
% 4.71/5.06 thf(fact_2348_combine__common__factor,axiom,
% 4.71/5.06 ! [A: rat,E2: rat,B: rat,C: rat] :
% 4.71/5.06 ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ C ) )
% 4.71/5.06 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E2 ) @ C ) ) ).
% 4.71/5.06
% 4.71/5.06 % combine_common_factor
% 4.71/5.06 thf(fact_2349_combine__common__factor,axiom,
% 4.71/5.06 ! [A: nat,E2: nat,B: nat,C: nat] :
% 4.71/5.06 ( ( plus_plus_nat @ ( times_times_nat @ A @ E2 ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E2 ) @ C ) )
% 4.71/5.06 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E2 ) @ C ) ) ).
% 4.71/5.06
% 4.71/5.06 % combine_common_factor
% 4.71/5.06 thf(fact_2350_combine__common__factor,axiom,
% 4.71/5.06 ! [A: int,E2: int,B: int,C: int] :
% 4.71/5.06 ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ C ) )
% 4.71/5.06 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E2 ) @ C ) ) ).
% 4.71/5.06
% 4.71/5.06 % combine_common_factor
% 4.71/5.06 thf(fact_2351_distrib__right,axiom,
% 4.71/5.06 ! [A: real,B: real,C: real] :
% 4.71/5.06 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 4.71/5.06 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % distrib_right
% 4.71/5.06 thf(fact_2352_distrib__right,axiom,
% 4.71/5.06 ! [A: rat,B: rat,C: rat] :
% 4.71/5.06 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 4.71/5.06 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % distrib_right
% 4.71/5.06 thf(fact_2353_distrib__right,axiom,
% 4.71/5.06 ! [A: nat,B: nat,C: nat] :
% 4.71/5.06 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 4.71/5.06 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % distrib_right
% 4.71/5.06 thf(fact_2354_distrib__right,axiom,
% 4.71/5.06 ! [A: int,B: int,C: int] :
% 4.71/5.06 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 4.71/5.06 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % distrib_right
% 4.71/5.06 thf(fact_2355_distrib__left,axiom,
% 4.71/5.06 ! [A: real,B: real,C: real] :
% 4.71/5.06 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 4.71/5.06 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % distrib_left
% 4.71/5.06 thf(fact_2356_distrib__left,axiom,
% 4.71/5.06 ! [A: rat,B: rat,C: rat] :
% 4.71/5.06 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 4.71/5.06 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % distrib_left
% 4.71/5.06 thf(fact_2357_distrib__left,axiom,
% 4.71/5.06 ! [A: nat,B: nat,C: nat] :
% 4.71/5.06 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 4.71/5.06 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % distrib_left
% 4.71/5.06 thf(fact_2358_distrib__left,axiom,
% 4.71/5.06 ! [A: int,B: int,C: int] :
% 4.71/5.06 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 4.71/5.06 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % distrib_left
% 4.71/5.06 thf(fact_2359_abs__mult,axiom,
% 4.71/5.06 ! [A: real,B: real] :
% 4.71/5.06 ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 4.71/5.06 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_mult
% 4.71/5.06 thf(fact_2360_abs__mult,axiom,
% 4.71/5.06 ! [A: rat,B: rat] :
% 4.71/5.06 ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 4.71/5.06 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_mult
% 4.71/5.06 thf(fact_2361_abs__mult,axiom,
% 4.71/5.06 ! [A: int,B: int] :
% 4.71/5.06 ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 4.71/5.06 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_mult
% 4.71/5.06 thf(fact_2362_comm__semiring__class_Odistrib,axiom,
% 4.71/5.06 ! [A: real,B: real,C: real] :
% 4.71/5.06 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 4.71/5.06 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % comm_semiring_class.distrib
% 4.71/5.06 thf(fact_2363_comm__semiring__class_Odistrib,axiom,
% 4.71/5.06 ! [A: rat,B: rat,C: rat] :
% 4.71/5.06 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 4.71/5.06 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % comm_semiring_class.distrib
% 4.71/5.06 thf(fact_2364_comm__semiring__class_Odistrib,axiom,
% 4.71/5.06 ! [A: nat,B: nat,C: nat] :
% 4.71/5.06 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 4.71/5.06 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % comm_semiring_class.distrib
% 4.71/5.06 thf(fact_2365_comm__semiring__class_Odistrib,axiom,
% 4.71/5.06 ! [A: int,B: int,C: int] :
% 4.71/5.06 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 4.71/5.06 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % comm_semiring_class.distrib
% 4.71/5.06 thf(fact_2366_is__num__normalize_I1_J,axiom,
% 4.71/5.06 ! [A: real,B: real,C: real] :
% 4.71/5.06 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 4.71/5.06 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % is_num_normalize(1)
% 4.71/5.06 thf(fact_2367_is__num__normalize_I1_J,axiom,
% 4.71/5.06 ! [A: rat,B: rat,C: rat] :
% 4.71/5.06 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 4.71/5.06 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % is_num_normalize(1)
% 4.71/5.06 thf(fact_2368_is__num__normalize_I1_J,axiom,
% 4.71/5.06 ! [A: int,B: int,C: int] :
% 4.71/5.06 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 4.71/5.06 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % is_num_normalize(1)
% 4.71/5.06 thf(fact_2369_ring__class_Oring__distribs_I1_J,axiom,
% 4.71/5.06 ! [A: real,B: real,C: real] :
% 4.71/5.06 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 4.71/5.06 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % ring_class.ring_distribs(1)
% 4.71/5.06 thf(fact_2370_ring__class_Oring__distribs_I1_J,axiom,
% 4.71/5.06 ! [A: rat,B: rat,C: rat] :
% 4.71/5.06 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 4.71/5.06 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % ring_class.ring_distribs(1)
% 4.71/5.06 thf(fact_2371_ring__class_Oring__distribs_I1_J,axiom,
% 4.71/5.06 ! [A: int,B: int,C: int] :
% 4.71/5.06 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 4.71/5.06 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % ring_class.ring_distribs(1)
% 4.71/5.06 thf(fact_2372_ring__class_Oring__distribs_I2_J,axiom,
% 4.71/5.06 ! [A: real,B: real,C: real] :
% 4.71/5.06 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 4.71/5.06 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % ring_class.ring_distribs(2)
% 4.71/5.06 thf(fact_2373_ring__class_Oring__distribs_I2_J,axiom,
% 4.71/5.06 ! [A: rat,B: rat,C: rat] :
% 4.71/5.06 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 4.71/5.06 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % ring_class.ring_distribs(2)
% 4.71/5.06 thf(fact_2374_ring__class_Oring__distribs_I2_J,axiom,
% 4.71/5.06 ! [A: int,B: int,C: int] :
% 4.71/5.06 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 4.71/5.06 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % ring_class.ring_distribs(2)
% 4.71/5.06 thf(fact_2375_add__right__imp__eq,axiom,
% 4.71/5.06 ! [B: real,A: real,C: real] :
% 4.71/5.06 ( ( ( plus_plus_real @ B @ A )
% 4.71/5.06 = ( plus_plus_real @ C @ A ) )
% 4.71/5.06 => ( B = C ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_right_imp_eq
% 4.71/5.06 thf(fact_2376_add__right__imp__eq,axiom,
% 4.71/5.06 ! [B: rat,A: rat,C: rat] :
% 4.71/5.06 ( ( ( plus_plus_rat @ B @ A )
% 4.71/5.06 = ( plus_plus_rat @ C @ A ) )
% 4.71/5.06 => ( B = C ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_right_imp_eq
% 4.71/5.06 thf(fact_2377_add__right__imp__eq,axiom,
% 4.71/5.06 ! [B: nat,A: nat,C: nat] :
% 4.71/5.06 ( ( ( plus_plus_nat @ B @ A )
% 4.71/5.06 = ( plus_plus_nat @ C @ A ) )
% 4.71/5.06 => ( B = C ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_right_imp_eq
% 4.71/5.06 thf(fact_2378_add__right__imp__eq,axiom,
% 4.71/5.06 ! [B: int,A: int,C: int] :
% 4.71/5.06 ( ( ( plus_plus_int @ B @ A )
% 4.71/5.06 = ( plus_plus_int @ C @ A ) )
% 4.71/5.06 => ( B = C ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_right_imp_eq
% 4.71/5.06 thf(fact_2379_add__left__imp__eq,axiom,
% 4.71/5.06 ! [A: real,B: real,C: real] :
% 4.71/5.06 ( ( ( plus_plus_real @ A @ B )
% 4.71/5.06 = ( plus_plus_real @ A @ C ) )
% 4.71/5.06 => ( B = C ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_left_imp_eq
% 4.71/5.06 thf(fact_2380_add__left__imp__eq,axiom,
% 4.71/5.06 ! [A: rat,B: rat,C: rat] :
% 4.71/5.06 ( ( ( plus_plus_rat @ A @ B )
% 4.71/5.06 = ( plus_plus_rat @ A @ C ) )
% 4.71/5.06 => ( B = C ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_left_imp_eq
% 4.71/5.06 thf(fact_2381_add__left__imp__eq,axiom,
% 4.71/5.06 ! [A: nat,B: nat,C: nat] :
% 4.71/5.06 ( ( ( plus_plus_nat @ A @ B )
% 4.71/5.06 = ( plus_plus_nat @ A @ C ) )
% 4.71/5.06 => ( B = C ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_left_imp_eq
% 4.71/5.06 thf(fact_2382_add__left__imp__eq,axiom,
% 4.71/5.06 ! [A: int,B: int,C: int] :
% 4.71/5.06 ( ( ( plus_plus_int @ A @ B )
% 4.71/5.06 = ( plus_plus_int @ A @ C ) )
% 4.71/5.06 => ( B = C ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_left_imp_eq
% 4.71/5.06 thf(fact_2383_mult_Oleft__commute,axiom,
% 4.71/5.06 ! [B: real,A: real,C: real] :
% 4.71/5.06 ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 4.71/5.06 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mult.left_commute
% 4.71/5.06 thf(fact_2384_mult_Oleft__commute,axiom,
% 4.71/5.06 ! [B: rat,A: rat,C: rat] :
% 4.71/5.06 ( ( times_times_rat @ B @ ( times_times_rat @ A @ C ) )
% 4.71/5.06 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mult.left_commute
% 4.71/5.06 thf(fact_2385_mult_Oleft__commute,axiom,
% 4.71/5.06 ! [B: nat,A: nat,C: nat] :
% 4.71/5.06 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 4.71/5.06 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mult.left_commute
% 4.71/5.06 thf(fact_2386_mult_Oleft__commute,axiom,
% 4.71/5.06 ! [B: int,A: int,C: int] :
% 4.71/5.06 ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 4.71/5.06 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mult.left_commute
% 4.71/5.06 thf(fact_2387_add_Oleft__commute,axiom,
% 4.71/5.06 ! [B: real,A: real,C: real] :
% 4.71/5.06 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 4.71/5.06 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add.left_commute
% 4.71/5.06 thf(fact_2388_add_Oleft__commute,axiom,
% 4.71/5.06 ! [B: rat,A: rat,C: rat] :
% 4.71/5.06 ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 4.71/5.06 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add.left_commute
% 4.71/5.06 thf(fact_2389_add_Oleft__commute,axiom,
% 4.71/5.06 ! [B: nat,A: nat,C: nat] :
% 4.71/5.06 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 4.71/5.06 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add.left_commute
% 4.71/5.06 thf(fact_2390_add_Oleft__commute,axiom,
% 4.71/5.06 ! [B: int,A: int,C: int] :
% 4.71/5.06 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 4.71/5.06 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add.left_commute
% 4.71/5.06 thf(fact_2391_mult_Ocommute,axiom,
% 4.71/5.06 ( times_times_real
% 4.71/5.06 = ( ^ [A4: real,B4: real] : ( times_times_real @ B4 @ A4 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mult.commute
% 4.71/5.06 thf(fact_2392_mult_Ocommute,axiom,
% 4.71/5.06 ( times_times_rat
% 4.71/5.06 = ( ^ [A4: rat,B4: rat] : ( times_times_rat @ B4 @ A4 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mult.commute
% 4.71/5.06 thf(fact_2393_mult_Ocommute,axiom,
% 4.71/5.06 ( times_times_nat
% 4.71/5.06 = ( ^ [A4: nat,B4: nat] : ( times_times_nat @ B4 @ A4 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mult.commute
% 4.71/5.06 thf(fact_2394_mult_Ocommute,axiom,
% 4.71/5.06 ( times_times_int
% 4.71/5.06 = ( ^ [A4: int,B4: int] : ( times_times_int @ B4 @ A4 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mult.commute
% 4.71/5.06 thf(fact_2395_add_Ocommute,axiom,
% 4.71/5.06 ( plus_plus_real
% 4.71/5.06 = ( ^ [A4: real,B4: real] : ( plus_plus_real @ B4 @ A4 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add.commute
% 4.71/5.06 thf(fact_2396_add_Ocommute,axiom,
% 4.71/5.06 ( plus_plus_rat
% 4.71/5.06 = ( ^ [A4: rat,B4: rat] : ( plus_plus_rat @ B4 @ A4 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add.commute
% 4.71/5.06 thf(fact_2397_add_Ocommute,axiom,
% 4.71/5.06 ( plus_plus_nat
% 4.71/5.06 = ( ^ [A4: nat,B4: nat] : ( plus_plus_nat @ B4 @ A4 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add.commute
% 4.71/5.06 thf(fact_2398_add_Ocommute,axiom,
% 4.71/5.06 ( plus_plus_int
% 4.71/5.06 = ( ^ [A4: int,B4: int] : ( plus_plus_int @ B4 @ A4 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add.commute
% 4.71/5.06 thf(fact_2399_add_Oright__cancel,axiom,
% 4.71/5.06 ! [B: real,A: real,C: real] :
% 4.71/5.06 ( ( ( plus_plus_real @ B @ A )
% 4.71/5.06 = ( plus_plus_real @ C @ A ) )
% 4.71/5.06 = ( B = C ) ) ).
% 4.71/5.06
% 4.71/5.06 % add.right_cancel
% 4.71/5.06 thf(fact_2400_add_Oright__cancel,axiom,
% 4.71/5.06 ! [B: rat,A: rat,C: rat] :
% 4.71/5.06 ( ( ( plus_plus_rat @ B @ A )
% 4.71/5.06 = ( plus_plus_rat @ C @ A ) )
% 4.71/5.06 = ( B = C ) ) ).
% 4.71/5.06
% 4.71/5.06 % add.right_cancel
% 4.71/5.06 thf(fact_2401_add_Oright__cancel,axiom,
% 4.71/5.06 ! [B: int,A: int,C: int] :
% 4.71/5.06 ( ( ( plus_plus_int @ B @ A )
% 4.71/5.06 = ( plus_plus_int @ C @ A ) )
% 4.71/5.06 = ( B = C ) ) ).
% 4.71/5.06
% 4.71/5.06 % add.right_cancel
% 4.71/5.06 thf(fact_2402_mult_Oassoc,axiom,
% 4.71/5.06 ! [A: real,B: real,C: real] :
% 4.71/5.06 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 4.71/5.06 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mult.assoc
% 4.71/5.06 thf(fact_2403_mult_Oassoc,axiom,
% 4.71/5.06 ! [A: rat,B: rat,C: rat] :
% 4.71/5.06 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 4.71/5.06 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mult.assoc
% 4.71/5.06 thf(fact_2404_mult_Oassoc,axiom,
% 4.71/5.06 ! [A: nat,B: nat,C: nat] :
% 4.71/5.06 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 4.71/5.06 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mult.assoc
% 4.71/5.06 thf(fact_2405_mult_Oassoc,axiom,
% 4.71/5.06 ! [A: int,B: int,C: int] :
% 4.71/5.06 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 4.71/5.06 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mult.assoc
% 4.71/5.06 thf(fact_2406_add_Oleft__cancel,axiom,
% 4.71/5.06 ! [A: real,B: real,C: real] :
% 4.71/5.06 ( ( ( plus_plus_real @ A @ B )
% 4.71/5.06 = ( plus_plus_real @ A @ C ) )
% 4.71/5.06 = ( B = C ) ) ).
% 4.71/5.06
% 4.71/5.06 % add.left_cancel
% 4.71/5.06 thf(fact_2407_add_Oleft__cancel,axiom,
% 4.71/5.06 ! [A: rat,B: rat,C: rat] :
% 4.71/5.06 ( ( ( plus_plus_rat @ A @ B )
% 4.71/5.06 = ( plus_plus_rat @ A @ C ) )
% 4.71/5.06 = ( B = C ) ) ).
% 4.71/5.06
% 4.71/5.06 % add.left_cancel
% 4.71/5.06 thf(fact_2408_add_Oleft__cancel,axiom,
% 4.71/5.06 ! [A: int,B: int,C: int] :
% 4.71/5.06 ( ( ( plus_plus_int @ A @ B )
% 4.71/5.06 = ( plus_plus_int @ A @ C ) )
% 4.71/5.06 = ( B = C ) ) ).
% 4.71/5.06
% 4.71/5.06 % add.left_cancel
% 4.71/5.06 thf(fact_2409_add_Oassoc,axiom,
% 4.71/5.06 ! [A: real,B: real,C: real] :
% 4.71/5.06 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 4.71/5.06 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add.assoc
% 4.71/5.06 thf(fact_2410_add_Oassoc,axiom,
% 4.71/5.06 ! [A: rat,B: rat,C: rat] :
% 4.71/5.06 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 4.71/5.06 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add.assoc
% 4.71/5.06 thf(fact_2411_add_Oassoc,axiom,
% 4.71/5.06 ! [A: nat,B: nat,C: nat] :
% 4.71/5.06 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 4.71/5.06 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add.assoc
% 4.71/5.06 thf(fact_2412_add_Oassoc,axiom,
% 4.71/5.06 ! [A: int,B: int,C: int] :
% 4.71/5.06 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 4.71/5.06 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add.assoc
% 4.71/5.06 thf(fact_2413_group__cancel_Oadd2,axiom,
% 4.71/5.06 ! [B2: real,K: real,B: real,A: real] :
% 4.71/5.06 ( ( B2
% 4.71/5.06 = ( plus_plus_real @ K @ B ) )
% 4.71/5.06 => ( ( plus_plus_real @ A @ B2 )
% 4.71/5.06 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % group_cancel.add2
% 4.71/5.06 thf(fact_2414_group__cancel_Oadd2,axiom,
% 4.71/5.06 ! [B2: rat,K: rat,B: rat,A: rat] :
% 4.71/5.06 ( ( B2
% 4.71/5.06 = ( plus_plus_rat @ K @ B ) )
% 4.71/5.06 => ( ( plus_plus_rat @ A @ B2 )
% 4.71/5.06 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % group_cancel.add2
% 4.71/5.06 thf(fact_2415_group__cancel_Oadd2,axiom,
% 4.71/5.06 ! [B2: nat,K: nat,B: nat,A: nat] :
% 4.71/5.06 ( ( B2
% 4.71/5.06 = ( plus_plus_nat @ K @ B ) )
% 4.71/5.06 => ( ( plus_plus_nat @ A @ B2 )
% 4.71/5.06 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % group_cancel.add2
% 4.71/5.06 thf(fact_2416_group__cancel_Oadd2,axiom,
% 4.71/5.06 ! [B2: int,K: int,B: int,A: int] :
% 4.71/5.06 ( ( B2
% 4.71/5.06 = ( plus_plus_int @ K @ B ) )
% 4.71/5.06 => ( ( plus_plus_int @ A @ B2 )
% 4.71/5.06 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % group_cancel.add2
% 4.71/5.06 thf(fact_2417_group__cancel_Oadd1,axiom,
% 4.71/5.06 ! [A2: real,K: real,A: real,B: real] :
% 4.71/5.06 ( ( A2
% 4.71/5.06 = ( plus_plus_real @ K @ A ) )
% 4.71/5.06 => ( ( plus_plus_real @ A2 @ B )
% 4.71/5.06 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % group_cancel.add1
% 4.71/5.06 thf(fact_2418_group__cancel_Oadd1,axiom,
% 4.71/5.06 ! [A2: rat,K: rat,A: rat,B: rat] :
% 4.71/5.06 ( ( A2
% 4.71/5.06 = ( plus_plus_rat @ K @ A ) )
% 4.71/5.06 => ( ( plus_plus_rat @ A2 @ B )
% 4.71/5.06 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % group_cancel.add1
% 4.71/5.06 thf(fact_2419_group__cancel_Oadd1,axiom,
% 4.71/5.06 ! [A2: nat,K: nat,A: nat,B: nat] :
% 4.71/5.06 ( ( A2
% 4.71/5.06 = ( plus_plus_nat @ K @ A ) )
% 4.71/5.06 => ( ( plus_plus_nat @ A2 @ B )
% 4.71/5.06 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % group_cancel.add1
% 4.71/5.06 thf(fact_2420_group__cancel_Oadd1,axiom,
% 4.71/5.06 ! [A2: int,K: int,A: int,B: int] :
% 4.71/5.06 ( ( A2
% 4.71/5.06 = ( plus_plus_int @ K @ A ) )
% 4.71/5.06 => ( ( plus_plus_int @ A2 @ B )
% 4.71/5.06 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % group_cancel.add1
% 4.71/5.06 thf(fact_2421_add__mono__thms__linordered__semiring_I4_J,axiom,
% 4.71/5.06 ! [I: real,J: real,K: real,L: real] :
% 4.71/5.06 ( ( ( I = J )
% 4.71/5.06 & ( K = L ) )
% 4.71/5.06 => ( ( plus_plus_real @ I @ K )
% 4.71/5.06 = ( plus_plus_real @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_semiring(4)
% 4.71/5.06 thf(fact_2422_add__mono__thms__linordered__semiring_I4_J,axiom,
% 4.71/5.06 ! [I: rat,J: rat,K: rat,L: rat] :
% 4.71/5.06 ( ( ( I = J )
% 4.71/5.06 & ( K = L ) )
% 4.71/5.06 => ( ( plus_plus_rat @ I @ K )
% 4.71/5.06 = ( plus_plus_rat @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_semiring(4)
% 4.71/5.06 thf(fact_2423_add__mono__thms__linordered__semiring_I4_J,axiom,
% 4.71/5.06 ! [I: nat,J: nat,K: nat,L: nat] :
% 4.71/5.06 ( ( ( I = J )
% 4.71/5.06 & ( K = L ) )
% 4.71/5.06 => ( ( plus_plus_nat @ I @ K )
% 4.71/5.06 = ( plus_plus_nat @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_semiring(4)
% 4.71/5.06 thf(fact_2424_add__mono__thms__linordered__semiring_I4_J,axiom,
% 4.71/5.06 ! [I: int,J: int,K: int,L: int] :
% 4.71/5.06 ( ( ( I = J )
% 4.71/5.06 & ( K = L ) )
% 4.71/5.06 => ( ( plus_plus_int @ I @ K )
% 4.71/5.06 = ( plus_plus_int @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_semiring(4)
% 4.71/5.06 thf(fact_2425_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 4.71/5.06 ! [A: real,B: real,C: real] :
% 4.71/5.06 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 4.71/5.06 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % ab_semigroup_mult_class.mult_ac(1)
% 4.71/5.06 thf(fact_2426_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 4.71/5.06 ! [A: rat,B: rat,C: rat] :
% 4.71/5.06 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 4.71/5.06 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % ab_semigroup_mult_class.mult_ac(1)
% 4.71/5.06 thf(fact_2427_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 4.71/5.06 ! [A: nat,B: nat,C: nat] :
% 4.71/5.06 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 4.71/5.06 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % ab_semigroup_mult_class.mult_ac(1)
% 4.71/5.06 thf(fact_2428_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 4.71/5.06 ! [A: int,B: int,C: int] :
% 4.71/5.06 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 4.71/5.06 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % ab_semigroup_mult_class.mult_ac(1)
% 4.71/5.06 thf(fact_2429_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 4.71/5.06 ! [A: real,B: real,C: real] :
% 4.71/5.06 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 4.71/5.06 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % ab_semigroup_add_class.add_ac(1)
% 4.71/5.06 thf(fact_2430_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 4.71/5.06 ! [A: rat,B: rat,C: rat] :
% 4.71/5.06 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 4.71/5.06 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % ab_semigroup_add_class.add_ac(1)
% 4.71/5.06 thf(fact_2431_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 4.71/5.06 ! [A: nat,B: nat,C: nat] :
% 4.71/5.06 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 4.71/5.06 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % ab_semigroup_add_class.add_ac(1)
% 4.71/5.06 thf(fact_2432_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 4.71/5.06 ! [A: int,B: int,C: int] :
% 4.71/5.06 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 4.71/5.06 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % ab_semigroup_add_class.add_ac(1)
% 4.71/5.06 thf(fact_2433_Ints__double__eq__0__iff,axiom,
% 4.71/5.06 ! [A: real] :
% 4.71/5.06 ( ( member_real @ A @ ring_1_Ints_real )
% 4.71/5.06 => ( ( ( plus_plus_real @ A @ A )
% 4.71/5.06 = zero_zero_real )
% 4.71/5.06 = ( A = zero_zero_real ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % Ints_double_eq_0_iff
% 4.71/5.06 thf(fact_2434_Ints__double__eq__0__iff,axiom,
% 4.71/5.06 ! [A: rat] :
% 4.71/5.06 ( ( member_rat @ A @ ring_1_Ints_rat )
% 4.71/5.06 => ( ( ( plus_plus_rat @ A @ A )
% 4.71/5.06 = zero_zero_rat )
% 4.71/5.06 = ( A = zero_zero_rat ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % Ints_double_eq_0_iff
% 4.71/5.06 thf(fact_2435_Ints__double__eq__0__iff,axiom,
% 4.71/5.06 ! [A: int] :
% 4.71/5.06 ( ( member_int @ A @ ring_1_Ints_int )
% 4.71/5.06 => ( ( ( plus_plus_int @ A @ A )
% 4.71/5.06 = zero_zero_int )
% 4.71/5.06 = ( A = zero_zero_int ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % Ints_double_eq_0_iff
% 4.71/5.06 thf(fact_2436_ln__le__minus__one,axiom,
% 4.71/5.06 ! [X: real] :
% 4.71/5.06 ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.06 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % ln_le_minus_one
% 4.71/5.06 thf(fact_2437_abs__mult__pos,axiom,
% 4.71/5.06 ! [X: real,Y: real] :
% 4.71/5.06 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.06 => ( ( times_times_real @ ( abs_abs_real @ Y ) @ X )
% 4.71/5.06 = ( abs_abs_real @ ( times_times_real @ Y @ X ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_mult_pos
% 4.71/5.06 thf(fact_2438_abs__mult__pos,axiom,
% 4.71/5.06 ! [X: rat,Y: rat] :
% 4.71/5.06 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 4.71/5.06 => ( ( times_times_rat @ ( abs_abs_rat @ Y ) @ X )
% 4.71/5.06 = ( abs_abs_rat @ ( times_times_rat @ Y @ X ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_mult_pos
% 4.71/5.06 thf(fact_2439_abs__mult__pos,axiom,
% 4.71/5.06 ! [X: int,Y: int] :
% 4.71/5.06 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 4.71/5.06 => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X )
% 4.71/5.06 = ( abs_abs_int @ ( times_times_int @ Y @ X ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_mult_pos
% 4.71/5.06 thf(fact_2440_abs__eq__mult,axiom,
% 4.71/5.06 ! [A: real,B: real] :
% 4.71/5.06 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.06 | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 4.71/5.06 & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.71/5.06 | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 4.71/5.06 => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 4.71/5.06 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_eq_mult
% 4.71/5.06 thf(fact_2441_abs__eq__mult,axiom,
% 4.71/5.06 ! [A: rat,B: rat] :
% 4.71/5.06 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.06 | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 4.71/5.06 & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.71/5.06 | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 4.71/5.06 => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 4.71/5.06 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_eq_mult
% 4.71/5.06 thf(fact_2442_abs__eq__mult,axiom,
% 4.71/5.06 ! [A: int,B: int] :
% 4.71/5.06 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.06 | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 4.71/5.06 & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.71/5.06 | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 4.71/5.06 => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 4.71/5.06 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_eq_mult
% 4.71/5.06 thf(fact_2443_abs__diff__triangle__ineq,axiom,
% 4.71/5.06 ! [A: real,B: real,C: real,D: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_diff_triangle_ineq
% 4.71/5.06 thf(fact_2444_abs__diff__triangle__ineq,axiom,
% 4.71/5.06 ! [A: rat,B: rat,C: rat,D: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C @ D ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_diff_triangle_ineq
% 4.71/5.06 thf(fact_2445_abs__diff__triangle__ineq,axiom,
% 4.71/5.06 ! [A: int,B: int,C: int,D: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_diff_triangle_ineq
% 4.71/5.06 thf(fact_2446_abs__triangle__ineq4,axiom,
% 4.71/5.06 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_triangle_ineq4
% 4.71/5.06 thf(fact_2447_abs__triangle__ineq4,axiom,
% 4.71/5.06 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_triangle_ineq4
% 4.71/5.06 thf(fact_2448_abs__triangle__ineq4,axiom,
% 4.71/5.06 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_triangle_ineq4
% 4.71/5.06 thf(fact_2449_abs__diff__le__iff,axiom,
% 4.71/5.06 ! [X: real,A: real,R2: real] :
% 4.71/5.06 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R2 )
% 4.71/5.06 = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R2 ) @ X )
% 4.71/5.06 & ( ord_less_eq_real @ X @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_diff_le_iff
% 4.71/5.06 thf(fact_2450_abs__diff__le__iff,axiom,
% 4.71/5.06 ! [X: rat,A: rat,R2: rat] :
% 4.71/5.06 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R2 )
% 4.71/5.06 = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R2 ) @ X )
% 4.71/5.06 & ( ord_less_eq_rat @ X @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_diff_le_iff
% 4.71/5.06 thf(fact_2451_abs__diff__le__iff,axiom,
% 4.71/5.06 ! [X: int,A: int,R2: int] :
% 4.71/5.06 ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R2 )
% 4.71/5.06 = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R2 ) @ X )
% 4.71/5.06 & ( ord_less_eq_int @ X @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_diff_le_iff
% 4.71/5.06 thf(fact_2452_abs__diff__less__iff,axiom,
% 4.71/5.06 ! [X: real,A: real,R2: real] :
% 4.71/5.06 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R2 )
% 4.71/5.06 = ( ( ord_less_real @ ( minus_minus_real @ A @ R2 ) @ X )
% 4.71/5.06 & ( ord_less_real @ X @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_diff_less_iff
% 4.71/5.06 thf(fact_2453_abs__diff__less__iff,axiom,
% 4.71/5.06 ! [X: rat,A: rat,R2: rat] :
% 4.71/5.06 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R2 )
% 4.71/5.06 = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R2 ) @ X )
% 4.71/5.06 & ( ord_less_rat @ X @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_diff_less_iff
% 4.71/5.06 thf(fact_2454_abs__diff__less__iff,axiom,
% 4.71/5.06 ! [X: int,A: int,R2: int] :
% 4.71/5.06 ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R2 )
% 4.71/5.06 = ( ( ord_less_int @ ( minus_minus_int @ A @ R2 ) @ X )
% 4.71/5.06 & ( ord_less_int @ X @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_diff_less_iff
% 4.71/5.06 thf(fact_2455_sum__squares__ge__zero,axiom,
% 4.71/5.06 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % sum_squares_ge_zero
% 4.71/5.06 thf(fact_2456_sum__squares__ge__zero,axiom,
% 4.71/5.06 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % sum_squares_ge_zero
% 4.71/5.06 thf(fact_2457_sum__squares__ge__zero,axiom,
% 4.71/5.06 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % sum_squares_ge_zero
% 4.71/5.06 thf(fact_2458_not__sum__squares__lt__zero,axiom,
% 4.71/5.06 ! [X: real,Y: real] :
% 4.71/5.06 ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real ) ).
% 4.71/5.06
% 4.71/5.06 % not_sum_squares_lt_zero
% 4.71/5.06 thf(fact_2459_not__sum__squares__lt__zero,axiom,
% 4.71/5.06 ! [X: rat,Y: rat] :
% 4.71/5.06 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 4.71/5.06
% 4.71/5.06 % not_sum_squares_lt_zero
% 4.71/5.06 thf(fact_2460_not__sum__squares__lt__zero,axiom,
% 4.71/5.06 ! [X: int,Y: int] :
% 4.71/5.06 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 4.71/5.06
% 4.71/5.06 % not_sum_squares_lt_zero
% 4.71/5.06 thf(fact_2461_ordered__ring__class_Ole__add__iff1,axiom,
% 4.71/5.06 ! [A: real,E2: real,C: real,B: real,D: real] :
% 4.71/5.06 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 4.71/5.06 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 4.71/5.06
% 4.71/5.06 % ordered_ring_class.le_add_iff1
% 4.71/5.06 thf(fact_2462_ordered__ring__class_Ole__add__iff1,axiom,
% 4.71/5.06 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 4.71/5.06 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 4.71/5.06 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 4.71/5.06
% 4.71/5.06 % ordered_ring_class.le_add_iff1
% 4.71/5.06 thf(fact_2463_ordered__ring__class_Ole__add__iff1,axiom,
% 4.71/5.06 ! [A: int,E2: int,C: int,B: int,D: int] :
% 4.71/5.06 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 4.71/5.06 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 4.71/5.06
% 4.71/5.06 % ordered_ring_class.le_add_iff1
% 4.71/5.06 thf(fact_2464_ordered__ring__class_Ole__add__iff2,axiom,
% 4.71/5.06 ! [A: real,E2: real,C: real,B: real,D: real] :
% 4.71/5.06 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 4.71/5.06 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % ordered_ring_class.le_add_iff2
% 4.71/5.06 thf(fact_2465_ordered__ring__class_Ole__add__iff2,axiom,
% 4.71/5.06 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 4.71/5.06 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 4.71/5.06 = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % ordered_ring_class.le_add_iff2
% 4.71/5.06 thf(fact_2466_ordered__ring__class_Ole__add__iff2,axiom,
% 4.71/5.06 ! [A: int,E2: int,C: int,B: int,D: int] :
% 4.71/5.06 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 4.71/5.06 = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % ordered_ring_class.le_add_iff2
% 4.71/5.06 thf(fact_2467_add__divide__eq__if__simps_I2_J,axiom,
% 4.71/5.06 ! [Z: rat,A: rat,B: rat] :
% 4.71/5.06 ( ( ( Z = zero_zero_rat )
% 4.71/5.06 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 4.71/5.06 = B ) )
% 4.71/5.06 & ( ( Z != zero_zero_rat )
% 4.71/5.06 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 4.71/5.06 = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_divide_eq_if_simps(2)
% 4.71/5.06 thf(fact_2468_add__divide__eq__if__simps_I2_J,axiom,
% 4.71/5.06 ! [Z: real,A: real,B: real] :
% 4.71/5.06 ( ( ( Z = zero_zero_real )
% 4.71/5.06 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 4.71/5.06 = B ) )
% 4.71/5.06 & ( ( Z != zero_zero_real )
% 4.71/5.06 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 4.71/5.06 = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_divide_eq_if_simps(2)
% 4.71/5.06 thf(fact_2469_add__divide__eq__if__simps_I1_J,axiom,
% 4.71/5.06 ! [Z: rat,A: rat,B: rat] :
% 4.71/5.06 ( ( ( Z = zero_zero_rat )
% 4.71/5.06 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 4.71/5.06 = A ) )
% 4.71/5.06 & ( ( Z != zero_zero_rat )
% 4.71/5.06 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 4.71/5.06 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_divide_eq_if_simps(1)
% 4.71/5.06 thf(fact_2470_add__divide__eq__if__simps_I1_J,axiom,
% 4.71/5.06 ! [Z: real,A: real,B: real] :
% 4.71/5.06 ( ( ( Z = zero_zero_real )
% 4.71/5.06 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 4.71/5.06 = A ) )
% 4.71/5.06 & ( ( Z != zero_zero_real )
% 4.71/5.06 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 4.71/5.06 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_divide_eq_if_simps(1)
% 4.71/5.06 thf(fact_2471_add__frac__eq,axiom,
% 4.71/5.06 ! [Y: rat,Z: rat,X: rat,W2: rat] :
% 4.71/5.06 ( ( Y != zero_zero_rat )
% 4.71/5.06 => ( ( Z != zero_zero_rat )
% 4.71/5.06 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W2 @ Z ) )
% 4.71/5.06 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_frac_eq
% 4.71/5.06 thf(fact_2472_add__frac__eq,axiom,
% 4.71/5.06 ! [Y: real,Z: real,X: real,W2: real] :
% 4.71/5.06 ( ( Y != zero_zero_real )
% 4.71/5.06 => ( ( Z != zero_zero_real )
% 4.71/5.06 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W2 @ Z ) )
% 4.71/5.06 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_frac_eq
% 4.71/5.06 thf(fact_2473_add__frac__num,axiom,
% 4.71/5.06 ! [Y: rat,X: rat,Z: rat] :
% 4.71/5.06 ( ( Y != zero_zero_rat )
% 4.71/5.06 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ Z )
% 4.71/5.06 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_frac_num
% 4.71/5.06 thf(fact_2474_add__frac__num,axiom,
% 4.71/5.06 ! [Y: real,X: real,Z: real] :
% 4.71/5.06 ( ( Y != zero_zero_real )
% 4.71/5.06 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y ) @ Z )
% 4.71/5.06 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_frac_num
% 4.71/5.06 thf(fact_2475_add__num__frac,axiom,
% 4.71/5.06 ! [Y: rat,Z: rat,X: rat] :
% 4.71/5.06 ( ( Y != zero_zero_rat )
% 4.71/5.06 => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X @ Y ) )
% 4.71/5.06 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_num_frac
% 4.71/5.06 thf(fact_2476_add__num__frac,axiom,
% 4.71/5.06 ! [Y: real,Z: real,X: real] :
% 4.71/5.06 ( ( Y != zero_zero_real )
% 4.71/5.06 => ( ( plus_plus_real @ Z @ ( divide_divide_real @ X @ Y ) )
% 4.71/5.06 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_num_frac
% 4.71/5.06 thf(fact_2477_add__divide__eq__iff,axiom,
% 4.71/5.06 ! [Z: rat,X: rat,Y: rat] :
% 4.71/5.06 ( ( Z != zero_zero_rat )
% 4.71/5.06 => ( ( plus_plus_rat @ X @ ( divide_divide_rat @ Y @ Z ) )
% 4.71/5.06 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_divide_eq_iff
% 4.71/5.06 thf(fact_2478_add__divide__eq__iff,axiom,
% 4.71/5.06 ! [Z: real,X: real,Y: real] :
% 4.71/5.06 ( ( Z != zero_zero_real )
% 4.71/5.06 => ( ( plus_plus_real @ X @ ( divide_divide_real @ Y @ Z ) )
% 4.71/5.06 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_divide_eq_iff
% 4.71/5.06 thf(fact_2479_divide__add__eq__iff,axiom,
% 4.71/5.06 ! [Z: rat,X: rat,Y: rat] :
% 4.71/5.06 ( ( Z != zero_zero_rat )
% 4.71/5.06 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Z ) @ Y )
% 4.71/5.06 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % divide_add_eq_iff
% 4.71/5.06 thf(fact_2480_divide__add__eq__iff,axiom,
% 4.71/5.06 ! [Z: real,X: real,Y: real] :
% 4.71/5.06 ( ( Z != zero_zero_real )
% 4.71/5.06 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Z ) @ Y )
% 4.71/5.06 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % divide_add_eq_iff
% 4.71/5.06 thf(fact_2481_less__add__iff1,axiom,
% 4.71/5.06 ! [A: real,E2: real,C: real,B: real,D: real] :
% 4.71/5.06 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 4.71/5.06 = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 4.71/5.06
% 4.71/5.06 % less_add_iff1
% 4.71/5.06 thf(fact_2482_less__add__iff1,axiom,
% 4.71/5.06 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 4.71/5.06 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 4.71/5.06 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 4.71/5.06
% 4.71/5.06 % less_add_iff1
% 4.71/5.06 thf(fact_2483_less__add__iff1,axiom,
% 4.71/5.06 ! [A: int,E2: int,C: int,B: int,D: int] :
% 4.71/5.06 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 4.71/5.06 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 4.71/5.06
% 4.71/5.06 % less_add_iff1
% 4.71/5.06 thf(fact_2484_less__add__iff2,axiom,
% 4.71/5.06 ! [A: real,E2: real,C: real,B: real,D: real] :
% 4.71/5.06 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 4.71/5.06 = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % less_add_iff2
% 4.71/5.06 thf(fact_2485_less__add__iff2,axiom,
% 4.71/5.06 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 4.71/5.06 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 4.71/5.06 = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % less_add_iff2
% 4.71/5.06 thf(fact_2486_less__add__iff2,axiom,
% 4.71/5.06 ! [A: int,E2: int,C: int,B: int,D: int] :
% 4.71/5.06 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 4.71/5.06 = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % less_add_iff2
% 4.71/5.06 thf(fact_2487_square__diff__one__factored,axiom,
% 4.71/5.06 ! [X: complex] :
% 4.71/5.06 ( ( minus_minus_complex @ ( times_times_complex @ X @ X ) @ one_one_complex )
% 4.71/5.06 = ( times_times_complex @ ( plus_plus_complex @ X @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % square_diff_one_factored
% 4.71/5.06 thf(fact_2488_square__diff__one__factored,axiom,
% 4.71/5.06 ! [X: real] :
% 4.71/5.06 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ one_one_real )
% 4.71/5.06 = ( times_times_real @ ( plus_plus_real @ X @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % square_diff_one_factored
% 4.71/5.06 thf(fact_2489_square__diff__one__factored,axiom,
% 4.71/5.06 ! [X: rat] :
% 4.71/5.06 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ one_one_rat )
% 4.71/5.06 = ( times_times_rat @ ( plus_plus_rat @ X @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % square_diff_one_factored
% 4.71/5.06 thf(fact_2490_square__diff__one__factored,axiom,
% 4.71/5.06 ! [X: int] :
% 4.71/5.06 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
% 4.71/5.06 = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % square_diff_one_factored
% 4.71/5.06 thf(fact_2491_Ints__odd__nonzero,axiom,
% 4.71/5.06 ! [A: complex] :
% 4.71/5.06 ( ( member_complex @ A @ ring_1_Ints_complex )
% 4.71/5.06 => ( ( plus_plus_complex @ ( plus_plus_complex @ one_one_complex @ A ) @ A )
% 4.71/5.06 != zero_zero_complex ) ) ).
% 4.71/5.06
% 4.71/5.06 % Ints_odd_nonzero
% 4.71/5.06 thf(fact_2492_Ints__odd__nonzero,axiom,
% 4.71/5.06 ! [A: real] :
% 4.71/5.06 ( ( member_real @ A @ ring_1_Ints_real )
% 4.71/5.06 => ( ( plus_plus_real @ ( plus_plus_real @ one_one_real @ A ) @ A )
% 4.71/5.06 != zero_zero_real ) ) ).
% 4.71/5.06
% 4.71/5.06 % Ints_odd_nonzero
% 4.71/5.06 thf(fact_2493_Ints__odd__nonzero,axiom,
% 4.71/5.06 ! [A: rat] :
% 4.71/5.06 ( ( member_rat @ A @ ring_1_Ints_rat )
% 4.71/5.06 => ( ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A )
% 4.71/5.06 != zero_zero_rat ) ) ).
% 4.71/5.06
% 4.71/5.06 % Ints_odd_nonzero
% 4.71/5.06 thf(fact_2494_Ints__odd__nonzero,axiom,
% 4.71/5.06 ! [A: int] :
% 4.71/5.06 ( ( member_int @ A @ ring_1_Ints_int )
% 4.71/5.06 => ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A )
% 4.71/5.06 != zero_zero_int ) ) ).
% 4.71/5.06
% 4.71/5.06 % Ints_odd_nonzero
% 4.71/5.06 thf(fact_2495_abs__ge__self,axiom,
% 4.71/5.06 ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_ge_self
% 4.71/5.06 thf(fact_2496_abs__ge__self,axiom,
% 4.71/5.06 ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_ge_self
% 4.71/5.06 thf(fact_2497_abs__ge__self,axiom,
% 4.71/5.06 ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_ge_self
% 4.71/5.06 thf(fact_2498_abs__le__D1,axiom,
% 4.71/5.06 ! [A: real,B: real] :
% 4.71/5.06 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 4.71/5.06 => ( ord_less_eq_real @ A @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_le_D1
% 4.71/5.06 thf(fact_2499_abs__le__D1,axiom,
% 4.71/5.06 ! [A: rat,B: rat] :
% 4.71/5.06 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 4.71/5.06 => ( ord_less_eq_rat @ A @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_le_D1
% 4.71/5.06 thf(fact_2500_abs__le__D1,axiom,
% 4.71/5.06 ! [A: int,B: int] :
% 4.71/5.06 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 4.71/5.06 => ( ord_less_eq_int @ A @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_le_D1
% 4.71/5.06 thf(fact_2501_abs__eq__0__iff,axiom,
% 4.71/5.06 ! [A: real] :
% 4.71/5.06 ( ( ( abs_abs_real @ A )
% 4.71/5.06 = zero_zero_real )
% 4.71/5.06 = ( A = zero_zero_real ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_eq_0_iff
% 4.71/5.06 thf(fact_2502_abs__eq__0__iff,axiom,
% 4.71/5.06 ! [A: rat] :
% 4.71/5.06 ( ( ( abs_abs_rat @ A )
% 4.71/5.06 = zero_zero_rat )
% 4.71/5.06 = ( A = zero_zero_rat ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_eq_0_iff
% 4.71/5.06 thf(fact_2503_abs__eq__0__iff,axiom,
% 4.71/5.06 ! [A: int] :
% 4.71/5.06 ( ( ( abs_abs_int @ A )
% 4.71/5.06 = zero_zero_int )
% 4.71/5.06 = ( A = zero_zero_int ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_eq_0_iff
% 4.71/5.06 thf(fact_2504_abs__one,axiom,
% 4.71/5.06 ( ( abs_abs_real @ one_one_real )
% 4.71/5.06 = one_one_real ) ).
% 4.71/5.06
% 4.71/5.06 % abs_one
% 4.71/5.06 thf(fact_2505_abs__one,axiom,
% 4.71/5.06 ( ( abs_abs_rat @ one_one_rat )
% 4.71/5.06 = one_one_rat ) ).
% 4.71/5.06
% 4.71/5.06 % abs_one
% 4.71/5.06 thf(fact_2506_abs__one,axiom,
% 4.71/5.06 ( ( abs_abs_int @ one_one_int )
% 4.71/5.06 = one_one_int ) ).
% 4.71/5.06
% 4.71/5.06 % abs_one
% 4.71/5.06 thf(fact_2507_abs__minus__commute,axiom,
% 4.71/5.06 ! [A: real,B: real] :
% 4.71/5.06 ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 4.71/5.06 = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_minus_commute
% 4.71/5.06 thf(fact_2508_abs__minus__commute,axiom,
% 4.71/5.06 ! [A: rat,B: rat] :
% 4.71/5.06 ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 4.71/5.06 = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_minus_commute
% 4.71/5.06 thf(fact_2509_abs__minus__commute,axiom,
% 4.71/5.06 ! [A: int,B: int] :
% 4.71/5.06 ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 4.71/5.06 = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % abs_minus_commute
% 4.71/5.06 thf(fact_2510_add__le__imp__le__right,axiom,
% 4.71/5.06 ! [A: real,C: real,B: real] :
% 4.71/5.06 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 4.71/5.06 => ( ord_less_eq_real @ A @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_le_imp_le_right
% 4.71/5.06 thf(fact_2511_add__le__imp__le__right,axiom,
% 4.71/5.06 ! [A: rat,C: rat,B: rat] :
% 4.71/5.06 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 4.71/5.06 => ( ord_less_eq_rat @ A @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_le_imp_le_right
% 4.71/5.06 thf(fact_2512_add__le__imp__le__right,axiom,
% 4.71/5.06 ! [A: nat,C: nat,B: nat] :
% 4.71/5.06 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 4.71/5.06 => ( ord_less_eq_nat @ A @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_le_imp_le_right
% 4.71/5.06 thf(fact_2513_add__le__imp__le__right,axiom,
% 4.71/5.06 ! [A: int,C: int,B: int] :
% 4.71/5.06 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 4.71/5.06 => ( ord_less_eq_int @ A @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_le_imp_le_right
% 4.71/5.06 thf(fact_2514_add__le__imp__le__left,axiom,
% 4.71/5.06 ! [C: real,A: real,B: real] :
% 4.71/5.06 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 4.71/5.06 => ( ord_less_eq_real @ A @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_le_imp_le_left
% 4.71/5.06 thf(fact_2515_add__le__imp__le__left,axiom,
% 4.71/5.06 ! [C: rat,A: rat,B: rat] :
% 4.71/5.06 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 4.71/5.06 => ( ord_less_eq_rat @ A @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_le_imp_le_left
% 4.71/5.06 thf(fact_2516_add__le__imp__le__left,axiom,
% 4.71/5.06 ! [C: nat,A: nat,B: nat] :
% 4.71/5.06 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 4.71/5.06 => ( ord_less_eq_nat @ A @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_le_imp_le_left
% 4.71/5.06 thf(fact_2517_add__le__imp__le__left,axiom,
% 4.71/5.06 ! [C: int,A: int,B: int] :
% 4.71/5.06 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 4.71/5.06 => ( ord_less_eq_int @ A @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_le_imp_le_left
% 4.71/5.06 thf(fact_2518_le__iff__add,axiom,
% 4.71/5.06 ( ord_less_eq_nat
% 4.71/5.06 = ( ^ [A4: nat,B4: nat] :
% 4.71/5.06 ? [C5: nat] :
% 4.71/5.06 ( B4
% 4.71/5.06 = ( plus_plus_nat @ A4 @ C5 ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % le_iff_add
% 4.71/5.06 thf(fact_2519_add__right__mono,axiom,
% 4.71/5.06 ! [A: real,B: real,C: real] :
% 4.71/5.06 ( ( ord_less_eq_real @ A @ B )
% 4.71/5.06 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_right_mono
% 4.71/5.06 thf(fact_2520_add__right__mono,axiom,
% 4.71/5.06 ! [A: rat,B: rat,C: rat] :
% 4.71/5.06 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.06 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_right_mono
% 4.71/5.06 thf(fact_2521_add__right__mono,axiom,
% 4.71/5.06 ! [A: nat,B: nat,C: nat] :
% 4.71/5.06 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.06 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_right_mono
% 4.71/5.06 thf(fact_2522_add__right__mono,axiom,
% 4.71/5.06 ! [A: int,B: int,C: int] :
% 4.71/5.06 ( ( ord_less_eq_int @ A @ B )
% 4.71/5.06 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_right_mono
% 4.71/5.06 thf(fact_2523_less__eqE,axiom,
% 4.71/5.06 ! [A: nat,B: nat] :
% 4.71/5.06 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.06 => ~ ! [C3: nat] :
% 4.71/5.06 ( B
% 4.71/5.06 != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % less_eqE
% 4.71/5.06 thf(fact_2524_add__left__mono,axiom,
% 4.71/5.06 ! [A: real,B: real,C: real] :
% 4.71/5.06 ( ( ord_less_eq_real @ A @ B )
% 4.71/5.06 => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_left_mono
% 4.71/5.06 thf(fact_2525_add__left__mono,axiom,
% 4.71/5.06 ! [A: rat,B: rat,C: rat] :
% 4.71/5.06 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.06 => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_left_mono
% 4.71/5.06 thf(fact_2526_add__left__mono,axiom,
% 4.71/5.06 ! [A: nat,B: nat,C: nat] :
% 4.71/5.06 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.06 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_left_mono
% 4.71/5.06 thf(fact_2527_add__left__mono,axiom,
% 4.71/5.06 ! [A: int,B: int,C: int] :
% 4.71/5.06 ( ( ord_less_eq_int @ A @ B )
% 4.71/5.06 => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_left_mono
% 4.71/5.06 thf(fact_2528_add__mono,axiom,
% 4.71/5.06 ! [A: real,B: real,C: real,D: real] :
% 4.71/5.06 ( ( ord_less_eq_real @ A @ B )
% 4.71/5.06 => ( ( ord_less_eq_real @ C @ D )
% 4.71/5.06 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono
% 4.71/5.06 thf(fact_2529_add__mono,axiom,
% 4.71/5.06 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.71/5.06 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.06 => ( ( ord_less_eq_rat @ C @ D )
% 4.71/5.06 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono
% 4.71/5.06 thf(fact_2530_add__mono,axiom,
% 4.71/5.06 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.71/5.06 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.06 => ( ( ord_less_eq_nat @ C @ D )
% 4.71/5.06 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono
% 4.71/5.06 thf(fact_2531_add__mono,axiom,
% 4.71/5.06 ! [A: int,B: int,C: int,D: int] :
% 4.71/5.06 ( ( ord_less_eq_int @ A @ B )
% 4.71/5.06 => ( ( ord_less_eq_int @ C @ D )
% 4.71/5.06 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono
% 4.71/5.06 thf(fact_2532_add__mono__thms__linordered__semiring_I1_J,axiom,
% 4.71/5.06 ! [I: real,J: real,K: real,L: real] :
% 4.71/5.06 ( ( ( ord_less_eq_real @ I @ J )
% 4.71/5.06 & ( ord_less_eq_real @ K @ L ) )
% 4.71/5.06 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_semiring(1)
% 4.71/5.06 thf(fact_2533_add__mono__thms__linordered__semiring_I1_J,axiom,
% 4.71/5.06 ! [I: rat,J: rat,K: rat,L: rat] :
% 4.71/5.06 ( ( ( ord_less_eq_rat @ I @ J )
% 4.71/5.06 & ( ord_less_eq_rat @ K @ L ) )
% 4.71/5.06 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_semiring(1)
% 4.71/5.06 thf(fact_2534_add__mono__thms__linordered__semiring_I1_J,axiom,
% 4.71/5.06 ! [I: nat,J: nat,K: nat,L: nat] :
% 4.71/5.06 ( ( ( ord_less_eq_nat @ I @ J )
% 4.71/5.06 & ( ord_less_eq_nat @ K @ L ) )
% 4.71/5.06 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_semiring(1)
% 4.71/5.06 thf(fact_2535_add__mono__thms__linordered__semiring_I1_J,axiom,
% 4.71/5.06 ! [I: int,J: int,K: int,L: int] :
% 4.71/5.06 ( ( ( ord_less_eq_int @ I @ J )
% 4.71/5.06 & ( ord_less_eq_int @ K @ L ) )
% 4.71/5.06 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_semiring(1)
% 4.71/5.06 thf(fact_2536_add__mono__thms__linordered__semiring_I2_J,axiom,
% 4.71/5.06 ! [I: real,J: real,K: real,L: real] :
% 4.71/5.06 ( ( ( I = J )
% 4.71/5.06 & ( ord_less_eq_real @ K @ L ) )
% 4.71/5.06 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_semiring(2)
% 4.71/5.06 thf(fact_2537_add__mono__thms__linordered__semiring_I2_J,axiom,
% 4.71/5.06 ! [I: rat,J: rat,K: rat,L: rat] :
% 4.71/5.06 ( ( ( I = J )
% 4.71/5.06 & ( ord_less_eq_rat @ K @ L ) )
% 4.71/5.06 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_semiring(2)
% 4.71/5.06 thf(fact_2538_add__mono__thms__linordered__semiring_I2_J,axiom,
% 4.71/5.06 ! [I: nat,J: nat,K: nat,L: nat] :
% 4.71/5.06 ( ( ( I = J )
% 4.71/5.06 & ( ord_less_eq_nat @ K @ L ) )
% 4.71/5.06 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_semiring(2)
% 4.71/5.06 thf(fact_2539_add__mono__thms__linordered__semiring_I2_J,axiom,
% 4.71/5.06 ! [I: int,J: int,K: int,L: int] :
% 4.71/5.06 ( ( ( I = J )
% 4.71/5.06 & ( ord_less_eq_int @ K @ L ) )
% 4.71/5.06 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_semiring(2)
% 4.71/5.06 thf(fact_2540_add__mono__thms__linordered__semiring_I3_J,axiom,
% 4.71/5.06 ! [I: real,J: real,K: real,L: real] :
% 4.71/5.06 ( ( ( ord_less_eq_real @ I @ J )
% 4.71/5.06 & ( K = L ) )
% 4.71/5.06 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_semiring(3)
% 4.71/5.06 thf(fact_2541_add__mono__thms__linordered__semiring_I3_J,axiom,
% 4.71/5.06 ! [I: rat,J: rat,K: rat,L: rat] :
% 4.71/5.06 ( ( ( ord_less_eq_rat @ I @ J )
% 4.71/5.06 & ( K = L ) )
% 4.71/5.06 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_semiring(3)
% 4.71/5.06 thf(fact_2542_add__mono__thms__linordered__semiring_I3_J,axiom,
% 4.71/5.06 ! [I: nat,J: nat,K: nat,L: nat] :
% 4.71/5.06 ( ( ( ord_less_eq_nat @ I @ J )
% 4.71/5.06 & ( K = L ) )
% 4.71/5.06 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_semiring(3)
% 4.71/5.06 thf(fact_2543_add__mono__thms__linordered__semiring_I3_J,axiom,
% 4.71/5.06 ! [I: int,J: int,K: int,L: int] :
% 4.71/5.06 ( ( ( ord_less_eq_int @ I @ J )
% 4.71/5.06 & ( K = L ) )
% 4.71/5.06 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_semiring(3)
% 4.71/5.06 thf(fact_2544_comm__monoid__add__class_Oadd__0,axiom,
% 4.71/5.06 ! [A: real] :
% 4.71/5.06 ( ( plus_plus_real @ zero_zero_real @ A )
% 4.71/5.06 = A ) ).
% 4.71/5.06
% 4.71/5.06 % comm_monoid_add_class.add_0
% 4.71/5.06 thf(fact_2545_comm__monoid__add__class_Oadd__0,axiom,
% 4.71/5.06 ! [A: rat] :
% 4.71/5.06 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 4.71/5.06 = A ) ).
% 4.71/5.06
% 4.71/5.06 % comm_monoid_add_class.add_0
% 4.71/5.06 thf(fact_2546_comm__monoid__add__class_Oadd__0,axiom,
% 4.71/5.06 ! [A: nat] :
% 4.71/5.06 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 4.71/5.06 = A ) ).
% 4.71/5.06
% 4.71/5.06 % comm_monoid_add_class.add_0
% 4.71/5.06 thf(fact_2547_comm__monoid__add__class_Oadd__0,axiom,
% 4.71/5.06 ! [A: int] :
% 4.71/5.06 ( ( plus_plus_int @ zero_zero_int @ A )
% 4.71/5.06 = A ) ).
% 4.71/5.06
% 4.71/5.06 % comm_monoid_add_class.add_0
% 4.71/5.06 thf(fact_2548_add_Ocomm__neutral,axiom,
% 4.71/5.06 ! [A: real] :
% 4.71/5.06 ( ( plus_plus_real @ A @ zero_zero_real )
% 4.71/5.06 = A ) ).
% 4.71/5.06
% 4.71/5.06 % add.comm_neutral
% 4.71/5.06 thf(fact_2549_add_Ocomm__neutral,axiom,
% 4.71/5.06 ! [A: rat] :
% 4.71/5.06 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 4.71/5.06 = A ) ).
% 4.71/5.06
% 4.71/5.06 % add.comm_neutral
% 4.71/5.06 thf(fact_2550_add_Ocomm__neutral,axiom,
% 4.71/5.06 ! [A: nat] :
% 4.71/5.06 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 4.71/5.06 = A ) ).
% 4.71/5.06
% 4.71/5.06 % add.comm_neutral
% 4.71/5.06 thf(fact_2551_add_Ocomm__neutral,axiom,
% 4.71/5.06 ! [A: int] :
% 4.71/5.06 ( ( plus_plus_int @ A @ zero_zero_int )
% 4.71/5.06 = A ) ).
% 4.71/5.06
% 4.71/5.06 % add.comm_neutral
% 4.71/5.06 thf(fact_2552_add_Ogroup__left__neutral,axiom,
% 4.71/5.06 ! [A: real] :
% 4.71/5.06 ( ( plus_plus_real @ zero_zero_real @ A )
% 4.71/5.06 = A ) ).
% 4.71/5.06
% 4.71/5.06 % add.group_left_neutral
% 4.71/5.06 thf(fact_2553_add_Ogroup__left__neutral,axiom,
% 4.71/5.06 ! [A: rat] :
% 4.71/5.06 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 4.71/5.06 = A ) ).
% 4.71/5.06
% 4.71/5.06 % add.group_left_neutral
% 4.71/5.06 thf(fact_2554_add_Ogroup__left__neutral,axiom,
% 4.71/5.06 ! [A: int] :
% 4.71/5.06 ( ( plus_plus_int @ zero_zero_int @ A )
% 4.71/5.06 = A ) ).
% 4.71/5.06
% 4.71/5.06 % add.group_left_neutral
% 4.71/5.06 thf(fact_2555_verit__sum__simplify,axiom,
% 4.71/5.06 ! [A: real] :
% 4.71/5.06 ( ( plus_plus_real @ A @ zero_zero_real )
% 4.71/5.06 = A ) ).
% 4.71/5.06
% 4.71/5.06 % verit_sum_simplify
% 4.71/5.06 thf(fact_2556_verit__sum__simplify,axiom,
% 4.71/5.06 ! [A: rat] :
% 4.71/5.06 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 4.71/5.06 = A ) ).
% 4.71/5.06
% 4.71/5.06 % verit_sum_simplify
% 4.71/5.06 thf(fact_2557_verit__sum__simplify,axiom,
% 4.71/5.06 ! [A: nat] :
% 4.71/5.06 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 4.71/5.06 = A ) ).
% 4.71/5.06
% 4.71/5.06 % verit_sum_simplify
% 4.71/5.06 thf(fact_2558_verit__sum__simplify,axiom,
% 4.71/5.06 ! [A: int] :
% 4.71/5.06 ( ( plus_plus_int @ A @ zero_zero_int )
% 4.71/5.06 = A ) ).
% 4.71/5.06
% 4.71/5.06 % verit_sum_simplify
% 4.71/5.06 thf(fact_2559_add__mono__thms__linordered__field_I5_J,axiom,
% 4.71/5.06 ! [I: real,J: real,K: real,L: real] :
% 4.71/5.06 ( ( ( ord_less_real @ I @ J )
% 4.71/5.06 & ( ord_less_real @ K @ L ) )
% 4.71/5.06 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_field(5)
% 4.71/5.06 thf(fact_2560_add__mono__thms__linordered__field_I5_J,axiom,
% 4.71/5.06 ! [I: rat,J: rat,K: rat,L: rat] :
% 4.71/5.06 ( ( ( ord_less_rat @ I @ J )
% 4.71/5.06 & ( ord_less_rat @ K @ L ) )
% 4.71/5.06 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_field(5)
% 4.71/5.06 thf(fact_2561_add__mono__thms__linordered__field_I5_J,axiom,
% 4.71/5.06 ! [I: nat,J: nat,K: nat,L: nat] :
% 4.71/5.06 ( ( ( ord_less_nat @ I @ J )
% 4.71/5.06 & ( ord_less_nat @ K @ L ) )
% 4.71/5.06 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_field(5)
% 4.71/5.06 thf(fact_2562_add__mono__thms__linordered__field_I5_J,axiom,
% 4.71/5.06 ! [I: int,J: int,K: int,L: int] :
% 4.71/5.06 ( ( ( ord_less_int @ I @ J )
% 4.71/5.06 & ( ord_less_int @ K @ L ) )
% 4.71/5.06 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_field(5)
% 4.71/5.06 thf(fact_2563_add__mono__thms__linordered__field_I2_J,axiom,
% 4.71/5.06 ! [I: real,J: real,K: real,L: real] :
% 4.71/5.06 ( ( ( I = J )
% 4.71/5.06 & ( ord_less_real @ K @ L ) )
% 4.71/5.06 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_field(2)
% 4.71/5.06 thf(fact_2564_add__mono__thms__linordered__field_I2_J,axiom,
% 4.71/5.06 ! [I: rat,J: rat,K: rat,L: rat] :
% 4.71/5.06 ( ( ( I = J )
% 4.71/5.06 & ( ord_less_rat @ K @ L ) )
% 4.71/5.06 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_field(2)
% 4.71/5.06 thf(fact_2565_add__mono__thms__linordered__field_I2_J,axiom,
% 4.71/5.06 ! [I: nat,J: nat,K: nat,L: nat] :
% 4.71/5.06 ( ( ( I = J )
% 4.71/5.06 & ( ord_less_nat @ K @ L ) )
% 4.71/5.06 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_field(2)
% 4.71/5.06 thf(fact_2566_add__mono__thms__linordered__field_I2_J,axiom,
% 4.71/5.06 ! [I: int,J: int,K: int,L: int] :
% 4.71/5.06 ( ( ( I = J )
% 4.71/5.06 & ( ord_less_int @ K @ L ) )
% 4.71/5.06 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_field(2)
% 4.71/5.06 thf(fact_2567_add__mono__thms__linordered__field_I1_J,axiom,
% 4.71/5.06 ! [I: real,J: real,K: real,L: real] :
% 4.71/5.06 ( ( ( ord_less_real @ I @ J )
% 4.71/5.06 & ( K = L ) )
% 4.71/5.06 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_field(1)
% 4.71/5.06 thf(fact_2568_add__mono__thms__linordered__field_I1_J,axiom,
% 4.71/5.06 ! [I: rat,J: rat,K: rat,L: rat] :
% 4.71/5.06 ( ( ( ord_less_rat @ I @ J )
% 4.71/5.06 & ( K = L ) )
% 4.71/5.06 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_field(1)
% 4.71/5.06 thf(fact_2569_add__mono__thms__linordered__field_I1_J,axiom,
% 4.71/5.06 ! [I: nat,J: nat,K: nat,L: nat] :
% 4.71/5.06 ( ( ( ord_less_nat @ I @ J )
% 4.71/5.06 & ( K = L ) )
% 4.71/5.06 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_field(1)
% 4.71/5.06 thf(fact_2570_add__mono__thms__linordered__field_I1_J,axiom,
% 4.71/5.06 ! [I: int,J: int,K: int,L: int] :
% 4.71/5.06 ( ( ( ord_less_int @ I @ J )
% 4.71/5.06 & ( K = L ) )
% 4.71/5.06 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_mono_thms_linordered_field(1)
% 4.71/5.06 thf(fact_2571_add__strict__mono,axiom,
% 4.71/5.06 ! [A: real,B: real,C: real,D: real] :
% 4.71/5.06 ( ( ord_less_real @ A @ B )
% 4.71/5.06 => ( ( ord_less_real @ C @ D )
% 4.71/5.06 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_strict_mono
% 4.71/5.06 thf(fact_2572_add__strict__mono,axiom,
% 4.71/5.06 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.71/5.06 ( ( ord_less_rat @ A @ B )
% 4.71/5.06 => ( ( ord_less_rat @ C @ D )
% 4.71/5.06 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_strict_mono
% 4.71/5.06 thf(fact_2573_add__strict__mono,axiom,
% 4.71/5.06 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.71/5.06 ( ( ord_less_nat @ A @ B )
% 4.71/5.06 => ( ( ord_less_nat @ C @ D )
% 4.71/5.06 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_strict_mono
% 4.71/5.06 thf(fact_2574_add__strict__mono,axiom,
% 4.71/5.06 ! [A: int,B: int,C: int,D: int] :
% 4.71/5.06 ( ( ord_less_int @ A @ B )
% 4.71/5.06 => ( ( ord_less_int @ C @ D )
% 4.71/5.06 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_strict_mono
% 4.71/5.06 thf(fact_2575_add__strict__left__mono,axiom,
% 4.71/5.06 ! [A: real,B: real,C: real] :
% 4.71/5.06 ( ( ord_less_real @ A @ B )
% 4.71/5.06 => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_strict_left_mono
% 4.71/5.06 thf(fact_2576_add__strict__left__mono,axiom,
% 4.71/5.06 ! [A: rat,B: rat,C: rat] :
% 4.71/5.06 ( ( ord_less_rat @ A @ B )
% 4.71/5.06 => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_strict_left_mono
% 4.71/5.06 thf(fact_2577_add__strict__left__mono,axiom,
% 4.71/5.06 ! [A: nat,B: nat,C: nat] :
% 4.71/5.06 ( ( ord_less_nat @ A @ B )
% 4.71/5.06 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_strict_left_mono
% 4.71/5.06 thf(fact_2578_add__strict__left__mono,axiom,
% 4.71/5.06 ! [A: int,B: int,C: int] :
% 4.71/5.06 ( ( ord_less_int @ A @ B )
% 4.71/5.06 => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_strict_left_mono
% 4.71/5.06 thf(fact_2579_add__strict__right__mono,axiom,
% 4.71/5.06 ! [A: real,B: real,C: real] :
% 4.71/5.06 ( ( ord_less_real @ A @ B )
% 4.71/5.06 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_strict_right_mono
% 4.71/5.06 thf(fact_2580_add__strict__right__mono,axiom,
% 4.71/5.06 ! [A: rat,B: rat,C: rat] :
% 4.71/5.06 ( ( ord_less_rat @ A @ B )
% 4.71/5.06 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_strict_right_mono
% 4.71/5.06 thf(fact_2581_add__strict__right__mono,axiom,
% 4.71/5.06 ! [A: nat,B: nat,C: nat] :
% 4.71/5.06 ( ( ord_less_nat @ A @ B )
% 4.71/5.06 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_strict_right_mono
% 4.71/5.06 thf(fact_2582_add__strict__right__mono,axiom,
% 4.71/5.06 ! [A: int,B: int,C: int] :
% 4.71/5.06 ( ( ord_less_int @ A @ B )
% 4.71/5.06 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_strict_right_mono
% 4.71/5.06 thf(fact_2583_add__less__imp__less__left,axiom,
% 4.71/5.06 ! [C: real,A: real,B: real] :
% 4.71/5.06 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 4.71/5.06 => ( ord_less_real @ A @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_less_imp_less_left
% 4.71/5.06 thf(fact_2584_add__less__imp__less__left,axiom,
% 4.71/5.06 ! [C: rat,A: rat,B: rat] :
% 4.71/5.06 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 4.71/5.06 => ( ord_less_rat @ A @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_less_imp_less_left
% 4.71/5.06 thf(fact_2585_add__less__imp__less__left,axiom,
% 4.71/5.06 ! [C: nat,A: nat,B: nat] :
% 4.71/5.06 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 4.71/5.06 => ( ord_less_nat @ A @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_less_imp_less_left
% 4.71/5.06 thf(fact_2586_add__less__imp__less__left,axiom,
% 4.71/5.06 ! [C: int,A: int,B: int] :
% 4.71/5.06 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 4.71/5.06 => ( ord_less_int @ A @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_less_imp_less_left
% 4.71/5.06 thf(fact_2587_add__less__imp__less__right,axiom,
% 4.71/5.06 ! [A: real,C: real,B: real] :
% 4.71/5.06 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 4.71/5.06 => ( ord_less_real @ A @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_less_imp_less_right
% 4.71/5.06 thf(fact_2588_add__less__imp__less__right,axiom,
% 4.71/5.06 ! [A: rat,C: rat,B: rat] :
% 4.71/5.06 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 4.71/5.06 => ( ord_less_rat @ A @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_less_imp_less_right
% 4.71/5.06 thf(fact_2589_add__less__imp__less__right,axiom,
% 4.71/5.06 ! [A: nat,C: nat,B: nat] :
% 4.71/5.06 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 4.71/5.06 => ( ord_less_nat @ A @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_less_imp_less_right
% 4.71/5.06 thf(fact_2590_add__less__imp__less__right,axiom,
% 4.71/5.06 ! [A: int,C: int,B: int] :
% 4.71/5.06 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 4.71/5.06 => ( ord_less_int @ A @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_less_imp_less_right
% 4.71/5.06 thf(fact_2591_mult__not__zero,axiom,
% 4.71/5.06 ! [A: real,B: real] :
% 4.71/5.06 ( ( ( times_times_real @ A @ B )
% 4.71/5.06 != zero_zero_real )
% 4.71/5.06 => ( ( A != zero_zero_real )
% 4.71/5.06 & ( B != zero_zero_real ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mult_not_zero
% 4.71/5.06 thf(fact_2592_mult__not__zero,axiom,
% 4.71/5.06 ! [A: rat,B: rat] :
% 4.71/5.06 ( ( ( times_times_rat @ A @ B )
% 4.71/5.06 != zero_zero_rat )
% 4.71/5.06 => ( ( A != zero_zero_rat )
% 4.71/5.06 & ( B != zero_zero_rat ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mult_not_zero
% 4.71/5.06 thf(fact_2593_mult__not__zero,axiom,
% 4.71/5.06 ! [A: nat,B: nat] :
% 4.71/5.06 ( ( ( times_times_nat @ A @ B )
% 4.71/5.06 != zero_zero_nat )
% 4.71/5.06 => ( ( A != zero_zero_nat )
% 4.71/5.06 & ( B != zero_zero_nat ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mult_not_zero
% 4.71/5.06 thf(fact_2594_mult__not__zero,axiom,
% 4.71/5.06 ! [A: int,B: int] :
% 4.71/5.06 ( ( ( times_times_int @ A @ B )
% 4.71/5.06 != zero_zero_int )
% 4.71/5.06 => ( ( A != zero_zero_int )
% 4.71/5.06 & ( B != zero_zero_int ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mult_not_zero
% 4.71/5.06 thf(fact_2595_divisors__zero,axiom,
% 4.71/5.06 ! [A: real,B: real] :
% 4.71/5.06 ( ( ( times_times_real @ A @ B )
% 4.71/5.06 = zero_zero_real )
% 4.71/5.06 => ( ( A = zero_zero_real )
% 4.71/5.06 | ( B = zero_zero_real ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % divisors_zero
% 4.71/5.06 thf(fact_2596_divisors__zero,axiom,
% 4.71/5.06 ! [A: rat,B: rat] :
% 4.71/5.06 ( ( ( times_times_rat @ A @ B )
% 4.71/5.06 = zero_zero_rat )
% 4.71/5.06 => ( ( A = zero_zero_rat )
% 4.71/5.06 | ( B = zero_zero_rat ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % divisors_zero
% 4.71/5.06 thf(fact_2597_divisors__zero,axiom,
% 4.71/5.06 ! [A: nat,B: nat] :
% 4.71/5.06 ( ( ( times_times_nat @ A @ B )
% 4.71/5.06 = zero_zero_nat )
% 4.71/5.06 => ( ( A = zero_zero_nat )
% 4.71/5.06 | ( B = zero_zero_nat ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % divisors_zero
% 4.71/5.06 thf(fact_2598_divisors__zero,axiom,
% 4.71/5.06 ! [A: int,B: int] :
% 4.71/5.06 ( ( ( times_times_int @ A @ B )
% 4.71/5.06 = zero_zero_int )
% 4.71/5.06 => ( ( A = zero_zero_int )
% 4.71/5.06 | ( B = zero_zero_int ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % divisors_zero
% 4.71/5.06 thf(fact_2599_no__zero__divisors,axiom,
% 4.71/5.06 ! [A: real,B: real] :
% 4.71/5.06 ( ( A != zero_zero_real )
% 4.71/5.06 => ( ( B != zero_zero_real )
% 4.71/5.06 => ( ( times_times_real @ A @ B )
% 4.71/5.06 != zero_zero_real ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % no_zero_divisors
% 4.71/5.06 thf(fact_2600_no__zero__divisors,axiom,
% 4.71/5.06 ! [A: rat,B: rat] :
% 4.71/5.06 ( ( A != zero_zero_rat )
% 4.71/5.06 => ( ( B != zero_zero_rat )
% 4.71/5.06 => ( ( times_times_rat @ A @ B )
% 4.71/5.06 != zero_zero_rat ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % no_zero_divisors
% 4.71/5.06 thf(fact_2601_no__zero__divisors,axiom,
% 4.71/5.06 ! [A: nat,B: nat] :
% 4.71/5.06 ( ( A != zero_zero_nat )
% 4.71/5.06 => ( ( B != zero_zero_nat )
% 4.71/5.06 => ( ( times_times_nat @ A @ B )
% 4.71/5.06 != zero_zero_nat ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % no_zero_divisors
% 4.71/5.06 thf(fact_2602_no__zero__divisors,axiom,
% 4.71/5.06 ! [A: int,B: int] :
% 4.71/5.06 ( ( A != zero_zero_int )
% 4.71/5.06 => ( ( B != zero_zero_int )
% 4.71/5.06 => ( ( times_times_int @ A @ B )
% 4.71/5.06 != zero_zero_int ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % no_zero_divisors
% 4.71/5.06 thf(fact_2603_mult__left__cancel,axiom,
% 4.71/5.06 ! [C: real,A: real,B: real] :
% 4.71/5.06 ( ( C != zero_zero_real )
% 4.71/5.06 => ( ( ( times_times_real @ C @ A )
% 4.71/5.06 = ( times_times_real @ C @ B ) )
% 4.71/5.06 = ( A = B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mult_left_cancel
% 4.71/5.06 thf(fact_2604_mult__left__cancel,axiom,
% 4.71/5.06 ! [C: rat,A: rat,B: rat] :
% 4.71/5.06 ( ( C != zero_zero_rat )
% 4.71/5.06 => ( ( ( times_times_rat @ C @ A )
% 4.71/5.06 = ( times_times_rat @ C @ B ) )
% 4.71/5.06 = ( A = B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mult_left_cancel
% 4.71/5.06 thf(fact_2605_mult__left__cancel,axiom,
% 4.71/5.06 ! [C: nat,A: nat,B: nat] :
% 4.71/5.06 ( ( C != zero_zero_nat )
% 4.71/5.06 => ( ( ( times_times_nat @ C @ A )
% 4.71/5.06 = ( times_times_nat @ C @ B ) )
% 4.71/5.06 = ( A = B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mult_left_cancel
% 4.71/5.06 thf(fact_2606_mult__left__cancel,axiom,
% 4.71/5.06 ! [C: int,A: int,B: int] :
% 4.71/5.06 ( ( C != zero_zero_int )
% 4.71/5.06 => ( ( ( times_times_int @ C @ A )
% 4.71/5.06 = ( times_times_int @ C @ B ) )
% 4.71/5.06 = ( A = B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mult_left_cancel
% 4.71/5.06 thf(fact_2607_mult__right__cancel,axiom,
% 4.71/5.06 ! [C: real,A: real,B: real] :
% 4.71/5.06 ( ( C != zero_zero_real )
% 4.71/5.06 => ( ( ( times_times_real @ A @ C )
% 4.71/5.06 = ( times_times_real @ B @ C ) )
% 4.71/5.06 = ( A = B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mult_right_cancel
% 4.71/5.06 thf(fact_2608_mult__right__cancel,axiom,
% 4.71/5.06 ! [C: rat,A: rat,B: rat] :
% 4.71/5.06 ( ( C != zero_zero_rat )
% 4.71/5.06 => ( ( ( times_times_rat @ A @ C )
% 4.71/5.06 = ( times_times_rat @ B @ C ) )
% 4.71/5.06 = ( A = B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mult_right_cancel
% 4.71/5.06 thf(fact_2609_mult__right__cancel,axiom,
% 4.71/5.06 ! [C: nat,A: nat,B: nat] :
% 4.71/5.06 ( ( C != zero_zero_nat )
% 4.71/5.06 => ( ( ( times_times_nat @ A @ C )
% 4.71/5.06 = ( times_times_nat @ B @ C ) )
% 4.71/5.06 = ( A = B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mult_right_cancel
% 4.71/5.06 thf(fact_2610_mult__right__cancel,axiom,
% 4.71/5.06 ! [C: int,A: int,B: int] :
% 4.71/5.06 ( ( C != zero_zero_int )
% 4.71/5.06 => ( ( ( times_times_int @ A @ C )
% 4.71/5.06 = ( times_times_int @ B @ C ) )
% 4.71/5.06 = ( A = B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % mult_right_cancel
% 4.71/5.06 thf(fact_2611_infinite__int__iff__unbounded__le,axiom,
% 4.71/5.06 ! [S2: set_int] :
% 4.71/5.06 ( ( ~ ( finite_finite_int @ S2 ) )
% 4.71/5.06 = ( ! [M3: int] :
% 4.71/5.06 ? [N4: int] :
% 4.71/5.06 ( ( ord_less_eq_int @ M3 @ ( abs_abs_int @ N4 ) )
% 4.71/5.06 & ( member_int @ N4 @ S2 ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % infinite_int_iff_unbounded_le
% 4.71/5.06 thf(fact_2612_singletonD,axiom,
% 4.71/5.06 ! [B: product_prod_nat_nat,A: product_prod_nat_nat] :
% 4.71/5.06 ( ( member8440522571783428010at_nat @ B @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) )
% 4.71/5.06 => ( B = A ) ) ).
% 4.71/5.06
% 4.71/5.06 % singletonD
% 4.71/5.06 thf(fact_2613_singletonD,axiom,
% 4.71/5.06 ! [B: set_nat,A: set_nat] :
% 4.71/5.06 ( ( member_set_nat @ B @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) )
% 4.71/5.06 => ( B = A ) ) ).
% 4.71/5.06
% 4.71/5.06 % singletonD
% 4.71/5.06 thf(fact_2614_singletonD,axiom,
% 4.71/5.06 ! [B: set_nat_rat,A: set_nat_rat] :
% 4.71/5.06 ( ( member_set_nat_rat @ B @ ( insert_set_nat_rat @ A @ bot_bo6797373522285170759at_rat ) )
% 4.71/5.06 => ( B = A ) ) ).
% 4.71/5.06
% 4.71/5.06 % singletonD
% 4.71/5.06 thf(fact_2615_singletonD,axiom,
% 4.71/5.06 ! [B: real,A: real] :
% 4.71/5.06 ( ( member_real @ B @ ( insert_real @ A @ bot_bot_set_real ) )
% 4.71/5.06 => ( B = A ) ) ).
% 4.71/5.06
% 4.71/5.06 % singletonD
% 4.71/5.06 thf(fact_2616_singletonD,axiom,
% 4.71/5.06 ! [B: $o,A: $o] :
% 4.71/5.06 ( ( member_o @ B @ ( insert_o @ A @ bot_bot_set_o ) )
% 4.71/5.06 => ( B = A ) ) ).
% 4.71/5.06
% 4.71/5.06 % singletonD
% 4.71/5.06 thf(fact_2617_singletonD,axiom,
% 4.71/5.06 ! [B: nat,A: nat] :
% 4.71/5.06 ( ( member_nat @ B @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 4.71/5.06 => ( B = A ) ) ).
% 4.71/5.06
% 4.71/5.06 % singletonD
% 4.71/5.06 thf(fact_2618_singletonD,axiom,
% 4.71/5.06 ! [B: int,A: int] :
% 4.71/5.06 ( ( member_int @ B @ ( insert_int @ A @ bot_bot_set_int ) )
% 4.71/5.06 => ( B = A ) ) ).
% 4.71/5.06
% 4.71/5.06 % singletonD
% 4.71/5.06 thf(fact_2619_singleton__iff,axiom,
% 4.71/5.06 ! [B: product_prod_nat_nat,A: product_prod_nat_nat] :
% 4.71/5.06 ( ( member8440522571783428010at_nat @ B @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) )
% 4.71/5.06 = ( B = A ) ) ).
% 4.71/5.06
% 4.71/5.06 % singleton_iff
% 4.71/5.06 thf(fact_2620_singleton__iff,axiom,
% 4.71/5.06 ! [B: set_nat,A: set_nat] :
% 4.71/5.06 ( ( member_set_nat @ B @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) )
% 4.71/5.06 = ( B = A ) ) ).
% 4.71/5.06
% 4.71/5.06 % singleton_iff
% 4.71/5.06 thf(fact_2621_singleton__iff,axiom,
% 4.71/5.06 ! [B: set_nat_rat,A: set_nat_rat] :
% 4.71/5.06 ( ( member_set_nat_rat @ B @ ( insert_set_nat_rat @ A @ bot_bo6797373522285170759at_rat ) )
% 4.71/5.06 = ( B = A ) ) ).
% 4.71/5.06
% 4.71/5.06 % singleton_iff
% 4.71/5.06 thf(fact_2622_singleton__iff,axiom,
% 4.71/5.06 ! [B: real,A: real] :
% 4.71/5.06 ( ( member_real @ B @ ( insert_real @ A @ bot_bot_set_real ) )
% 4.71/5.06 = ( B = A ) ) ).
% 4.71/5.06
% 4.71/5.06 % singleton_iff
% 4.71/5.06 thf(fact_2623_singleton__iff,axiom,
% 4.71/5.06 ! [B: $o,A: $o] :
% 4.71/5.06 ( ( member_o @ B @ ( insert_o @ A @ bot_bot_set_o ) )
% 4.71/5.06 = ( B = A ) ) ).
% 4.71/5.06
% 4.71/5.06 % singleton_iff
% 4.71/5.06 thf(fact_2624_singleton__iff,axiom,
% 4.71/5.06 ! [B: nat,A: nat] :
% 4.71/5.06 ( ( member_nat @ B @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 4.71/5.06 = ( B = A ) ) ).
% 4.71/5.06
% 4.71/5.06 % singleton_iff
% 4.71/5.06 thf(fact_2625_singleton__iff,axiom,
% 4.71/5.06 ! [B: int,A: int] :
% 4.71/5.06 ( ( member_int @ B @ ( insert_int @ A @ bot_bot_set_int ) )
% 4.71/5.06 = ( B = A ) ) ).
% 4.71/5.06
% 4.71/5.06 % singleton_iff
% 4.71/5.06 thf(fact_2626_doubleton__eq__iff,axiom,
% 4.71/5.06 ! [A: product_prod_nat_nat,B: product_prod_nat_nat,C: product_prod_nat_nat,D: product_prod_nat_nat] :
% 4.71/5.06 ( ( ( insert8211810215607154385at_nat @ A @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) )
% 4.71/5.06 = ( insert8211810215607154385at_nat @ C @ ( insert8211810215607154385at_nat @ D @ bot_bo2099793752762293965at_nat ) ) )
% 4.71/5.06 = ( ( ( A = C )
% 4.71/5.06 & ( B = D ) )
% 4.71/5.06 | ( ( A = D )
% 4.71/5.06 & ( B = C ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % doubleton_eq_iff
% 4.71/5.06 thf(fact_2627_doubleton__eq__iff,axiom,
% 4.71/5.06 ! [A: real,B: real,C: real,D: real] :
% 4.71/5.06 ( ( ( insert_real @ A @ ( insert_real @ B @ bot_bot_set_real ) )
% 4.71/5.06 = ( insert_real @ C @ ( insert_real @ D @ bot_bot_set_real ) ) )
% 4.71/5.06 = ( ( ( A = C )
% 4.71/5.06 & ( B = D ) )
% 4.71/5.06 | ( ( A = D )
% 4.71/5.06 & ( B = C ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % doubleton_eq_iff
% 4.71/5.06 thf(fact_2628_doubleton__eq__iff,axiom,
% 4.71/5.06 ! [A: $o,B: $o,C: $o,D: $o] :
% 4.71/5.06 ( ( ( insert_o @ A @ ( insert_o @ B @ bot_bot_set_o ) )
% 4.71/5.06 = ( insert_o @ C @ ( insert_o @ D @ bot_bot_set_o ) ) )
% 4.71/5.06 = ( ( ( A = C )
% 4.71/5.06 & ( B = D ) )
% 4.71/5.06 | ( ( A = D )
% 4.71/5.06 & ( B = C ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % doubleton_eq_iff
% 4.71/5.06 thf(fact_2629_doubleton__eq__iff,axiom,
% 4.71/5.06 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.71/5.06 ( ( ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_set_nat ) )
% 4.71/5.06 = ( insert_nat @ C @ ( insert_nat @ D @ bot_bot_set_nat ) ) )
% 4.71/5.06 = ( ( ( A = C )
% 4.71/5.06 & ( B = D ) )
% 4.71/5.06 | ( ( A = D )
% 4.71/5.06 & ( B = C ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % doubleton_eq_iff
% 4.71/5.06 thf(fact_2630_doubleton__eq__iff,axiom,
% 4.71/5.06 ! [A: int,B: int,C: int,D: int] :
% 4.71/5.06 ( ( ( insert_int @ A @ ( insert_int @ B @ bot_bot_set_int ) )
% 4.71/5.06 = ( insert_int @ C @ ( insert_int @ D @ bot_bot_set_int ) ) )
% 4.71/5.06 = ( ( ( A = C )
% 4.71/5.06 & ( B = D ) )
% 4.71/5.06 | ( ( A = D )
% 4.71/5.06 & ( B = C ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % doubleton_eq_iff
% 4.71/5.06 thf(fact_2631_insert__not__empty,axiom,
% 4.71/5.06 ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.06 ( ( insert8211810215607154385at_nat @ A @ A2 )
% 4.71/5.06 != bot_bo2099793752762293965at_nat ) ).
% 4.71/5.06
% 4.71/5.06 % insert_not_empty
% 4.71/5.06 thf(fact_2632_insert__not__empty,axiom,
% 4.71/5.06 ! [A: real,A2: set_real] :
% 4.71/5.06 ( ( insert_real @ A @ A2 )
% 4.71/5.06 != bot_bot_set_real ) ).
% 4.71/5.06
% 4.71/5.06 % insert_not_empty
% 4.71/5.06 thf(fact_2633_insert__not__empty,axiom,
% 4.71/5.06 ! [A: $o,A2: set_o] :
% 4.71/5.06 ( ( insert_o @ A @ A2 )
% 4.71/5.06 != bot_bot_set_o ) ).
% 4.71/5.06
% 4.71/5.06 % insert_not_empty
% 4.71/5.06 thf(fact_2634_insert__not__empty,axiom,
% 4.71/5.06 ! [A: nat,A2: set_nat] :
% 4.71/5.06 ( ( insert_nat @ A @ A2 )
% 4.71/5.06 != bot_bot_set_nat ) ).
% 4.71/5.06
% 4.71/5.06 % insert_not_empty
% 4.71/5.06 thf(fact_2635_insert__not__empty,axiom,
% 4.71/5.06 ! [A: int,A2: set_int] :
% 4.71/5.06 ( ( insert_int @ A @ A2 )
% 4.71/5.06 != bot_bot_set_int ) ).
% 4.71/5.06
% 4.71/5.06 % insert_not_empty
% 4.71/5.06 thf(fact_2636_singleton__inject,axiom,
% 4.71/5.06 ! [A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 4.71/5.06 ( ( ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat )
% 4.71/5.06 = ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) )
% 4.71/5.06 => ( A = B ) ) ).
% 4.71/5.06
% 4.71/5.06 % singleton_inject
% 4.71/5.06 thf(fact_2637_singleton__inject,axiom,
% 4.71/5.06 ! [A: real,B: real] :
% 4.71/5.06 ( ( ( insert_real @ A @ bot_bot_set_real )
% 4.71/5.06 = ( insert_real @ B @ bot_bot_set_real ) )
% 4.71/5.06 => ( A = B ) ) ).
% 4.71/5.06
% 4.71/5.06 % singleton_inject
% 4.71/5.06 thf(fact_2638_singleton__inject,axiom,
% 4.71/5.06 ! [A: $o,B: $o] :
% 4.71/5.06 ( ( ( insert_o @ A @ bot_bot_set_o )
% 4.71/5.06 = ( insert_o @ B @ bot_bot_set_o ) )
% 4.71/5.06 => ( A = B ) ) ).
% 4.71/5.06
% 4.71/5.06 % singleton_inject
% 4.71/5.06 thf(fact_2639_singleton__inject,axiom,
% 4.71/5.06 ! [A: nat,B: nat] :
% 4.71/5.06 ( ( ( insert_nat @ A @ bot_bot_set_nat )
% 4.71/5.06 = ( insert_nat @ B @ bot_bot_set_nat ) )
% 4.71/5.06 => ( A = B ) ) ).
% 4.71/5.06
% 4.71/5.06 % singleton_inject
% 4.71/5.06 thf(fact_2640_singleton__inject,axiom,
% 4.71/5.06 ! [A: int,B: int] :
% 4.71/5.06 ( ( ( insert_int @ A @ bot_bot_set_int )
% 4.71/5.06 = ( insert_int @ B @ bot_bot_set_int ) )
% 4.71/5.06 => ( A = B ) ) ).
% 4.71/5.06
% 4.71/5.06 % singleton_inject
% 4.71/5.06 thf(fact_2641_finite_OinsertI,axiom,
% 4.71/5.06 ! [A2: set_real,A: real] :
% 4.71/5.06 ( ( finite_finite_real @ A2 )
% 4.71/5.06 => ( finite_finite_real @ ( insert_real @ A @ A2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % finite.insertI
% 4.71/5.06 thf(fact_2642_finite_OinsertI,axiom,
% 4.71/5.06 ! [A2: set_o,A: $o] :
% 4.71/5.06 ( ( finite_finite_o @ A2 )
% 4.71/5.06 => ( finite_finite_o @ ( insert_o @ A @ A2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % finite.insertI
% 4.71/5.06 thf(fact_2643_finite_OinsertI,axiom,
% 4.71/5.06 ! [A2: set_nat,A: nat] :
% 4.71/5.06 ( ( finite_finite_nat @ A2 )
% 4.71/5.06 => ( finite_finite_nat @ ( insert_nat @ A @ A2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % finite.insertI
% 4.71/5.06 thf(fact_2644_finite_OinsertI,axiom,
% 4.71/5.06 ! [A2: set_int,A: int] :
% 4.71/5.06 ( ( finite_finite_int @ A2 )
% 4.71/5.06 => ( finite_finite_int @ ( insert_int @ A @ A2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % finite.insertI
% 4.71/5.06 thf(fact_2645_finite_OinsertI,axiom,
% 4.71/5.06 ! [A2: set_complex,A: complex] :
% 4.71/5.06 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.06 => ( finite3207457112153483333omplex @ ( insert_complex @ A @ A2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % finite.insertI
% 4.71/5.06 thf(fact_2646_finite_OinsertI,axiom,
% 4.71/5.06 ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat] :
% 4.71/5.06 ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.06 => ( finite6177210948735845034at_nat @ ( insert8211810215607154385at_nat @ A @ A2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % finite.insertI
% 4.71/5.06 thf(fact_2647_finite_OinsertI,axiom,
% 4.71/5.06 ! [A2: set_Extended_enat,A: extended_enat] :
% 4.71/5.06 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.06 => ( finite4001608067531595151d_enat @ ( insert_Extended_enat @ A @ A2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % finite.insertI
% 4.71/5.06 thf(fact_2648_infinite__int__iff__unbounded,axiom,
% 4.71/5.06 ! [S2: set_int] :
% 4.71/5.06 ( ( ~ ( finite_finite_int @ S2 ) )
% 4.71/5.06 = ( ! [M3: int] :
% 4.71/5.06 ? [N4: int] :
% 4.71/5.06 ( ( ord_less_int @ M3 @ ( abs_abs_int @ N4 ) )
% 4.71/5.06 & ( member_int @ N4 @ S2 ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % infinite_int_iff_unbounded
% 4.71/5.06 thf(fact_2649_insert__mono,axiom,
% 4.71/5.06 ! [C2: set_Pr1261947904930325089at_nat,D4: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat] :
% 4.71/5.06 ( ( ord_le3146513528884898305at_nat @ C2 @ D4 )
% 4.71/5.06 => ( ord_le3146513528884898305at_nat @ ( insert8211810215607154385at_nat @ A @ C2 ) @ ( insert8211810215607154385at_nat @ A @ D4 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_mono
% 4.71/5.06 thf(fact_2650_insert__mono,axiom,
% 4.71/5.06 ! [C2: set_real,D4: set_real,A: real] :
% 4.71/5.06 ( ( ord_less_eq_set_real @ C2 @ D4 )
% 4.71/5.06 => ( ord_less_eq_set_real @ ( insert_real @ A @ C2 ) @ ( insert_real @ A @ D4 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_mono
% 4.71/5.06 thf(fact_2651_insert__mono,axiom,
% 4.71/5.06 ! [C2: set_o,D4: set_o,A: $o] :
% 4.71/5.06 ( ( ord_less_eq_set_o @ C2 @ D4 )
% 4.71/5.06 => ( ord_less_eq_set_o @ ( insert_o @ A @ C2 ) @ ( insert_o @ A @ D4 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_mono
% 4.71/5.06 thf(fact_2652_insert__mono,axiom,
% 4.71/5.06 ! [C2: set_nat,D4: set_nat,A: nat] :
% 4.71/5.06 ( ( ord_less_eq_set_nat @ C2 @ D4 )
% 4.71/5.06 => ( ord_less_eq_set_nat @ ( insert_nat @ A @ C2 ) @ ( insert_nat @ A @ D4 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_mono
% 4.71/5.06 thf(fact_2653_insert__mono,axiom,
% 4.71/5.06 ! [C2: set_int,D4: set_int,A: int] :
% 4.71/5.06 ( ( ord_less_eq_set_int @ C2 @ D4 )
% 4.71/5.06 => ( ord_less_eq_set_int @ ( insert_int @ A @ C2 ) @ ( insert_int @ A @ D4 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_mono
% 4.71/5.06 thf(fact_2654_subset__insert,axiom,
% 4.71/5.06 ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 4.71/5.06 ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 4.71/5.06 => ( ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ B2 ) )
% 4.71/5.06 = ( ord_le3146513528884898305at_nat @ A2 @ B2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % subset_insert
% 4.71/5.06 thf(fact_2655_subset__insert,axiom,
% 4.71/5.06 ! [X: real,A2: set_real,B2: set_real] :
% 4.71/5.06 ( ~ ( member_real @ X @ A2 )
% 4.71/5.06 => ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ B2 ) )
% 4.71/5.06 = ( ord_less_eq_set_real @ A2 @ B2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % subset_insert
% 4.71/5.06 thf(fact_2656_subset__insert,axiom,
% 4.71/5.06 ! [X: $o,A2: set_o,B2: set_o] :
% 4.71/5.06 ( ~ ( member_o @ X @ A2 )
% 4.71/5.06 => ( ( ord_less_eq_set_o @ A2 @ ( insert_o @ X @ B2 ) )
% 4.71/5.06 = ( ord_less_eq_set_o @ A2 @ B2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % subset_insert
% 4.71/5.06 thf(fact_2657_subset__insert,axiom,
% 4.71/5.06 ! [X: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 4.71/5.06 ( ~ ( member_set_nat @ X @ A2 )
% 4.71/5.06 => ( ( ord_le6893508408891458716et_nat @ A2 @ ( insert_set_nat @ X @ B2 ) )
% 4.71/5.06 = ( ord_le6893508408891458716et_nat @ A2 @ B2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % subset_insert
% 4.71/5.06 thf(fact_2658_subset__insert,axiom,
% 4.71/5.06 ! [X: set_nat_rat,A2: set_set_nat_rat,B2: set_set_nat_rat] :
% 4.71/5.06 ( ~ ( member_set_nat_rat @ X @ A2 )
% 4.71/5.06 => ( ( ord_le4375437777232675859at_rat @ A2 @ ( insert_set_nat_rat @ X @ B2 ) )
% 4.71/5.06 = ( ord_le4375437777232675859at_rat @ A2 @ B2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % subset_insert
% 4.71/5.06 thf(fact_2659_subset__insert,axiom,
% 4.71/5.06 ! [X: nat,A2: set_nat,B2: set_nat] :
% 4.71/5.06 ( ~ ( member_nat @ X @ A2 )
% 4.71/5.06 => ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B2 ) )
% 4.71/5.06 = ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % subset_insert
% 4.71/5.06 thf(fact_2660_subset__insert,axiom,
% 4.71/5.06 ! [X: int,A2: set_int,B2: set_int] :
% 4.71/5.06 ( ~ ( member_int @ X @ A2 )
% 4.71/5.06 => ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B2 ) )
% 4.71/5.06 = ( ord_less_eq_set_int @ A2 @ B2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % subset_insert
% 4.71/5.06 thf(fact_2661_subset__insertI,axiom,
% 4.71/5.06 ! [B2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ B2 @ ( insert8211810215607154385at_nat @ A @ B2 ) ) ).
% 4.71/5.06
% 4.71/5.06 % subset_insertI
% 4.71/5.06 thf(fact_2662_subset__insertI,axiom,
% 4.71/5.06 ! [B2: set_real,A: real] : ( ord_less_eq_set_real @ B2 @ ( insert_real @ A @ B2 ) ) ).
% 4.71/5.06
% 4.71/5.06 % subset_insertI
% 4.71/5.06 thf(fact_2663_subset__insertI,axiom,
% 4.71/5.06 ! [B2: set_o,A: $o] : ( ord_less_eq_set_o @ B2 @ ( insert_o @ A @ B2 ) ) ).
% 4.71/5.06
% 4.71/5.06 % subset_insertI
% 4.71/5.06 thf(fact_2664_subset__insertI,axiom,
% 4.71/5.06 ! [B2: set_nat,A: nat] : ( ord_less_eq_set_nat @ B2 @ ( insert_nat @ A @ B2 ) ) ).
% 4.71/5.06
% 4.71/5.06 % subset_insertI
% 4.71/5.06 thf(fact_2665_subset__insertI,axiom,
% 4.71/5.06 ! [B2: set_int,A: int] : ( ord_less_eq_set_int @ B2 @ ( insert_int @ A @ B2 ) ) ).
% 4.71/5.06
% 4.71/5.06 % subset_insertI
% 4.71/5.06 thf(fact_2666_subset__insertI2,axiom,
% 4.71/5.06 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,B: product_prod_nat_nat] :
% 4.71/5.06 ( ( ord_le3146513528884898305at_nat @ A2 @ B2 )
% 4.71/5.06 => ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ B @ B2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % subset_insertI2
% 4.71/5.06 thf(fact_2667_subset__insertI2,axiom,
% 4.71/5.06 ! [A2: set_real,B2: set_real,B: real] :
% 4.71/5.06 ( ( ord_less_eq_set_real @ A2 @ B2 )
% 4.71/5.06 => ( ord_less_eq_set_real @ A2 @ ( insert_real @ B @ B2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % subset_insertI2
% 4.71/5.06 thf(fact_2668_subset__insertI2,axiom,
% 4.71/5.06 ! [A2: set_o,B2: set_o,B: $o] :
% 4.71/5.06 ( ( ord_less_eq_set_o @ A2 @ B2 )
% 4.71/5.06 => ( ord_less_eq_set_o @ A2 @ ( insert_o @ B @ B2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % subset_insertI2
% 4.71/5.06 thf(fact_2669_subset__insertI2,axiom,
% 4.71/5.06 ! [A2: set_nat,B2: set_nat,B: nat] :
% 4.71/5.06 ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 4.71/5.06 => ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ B2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % subset_insertI2
% 4.71/5.06 thf(fact_2670_subset__insertI2,axiom,
% 4.71/5.06 ! [A2: set_int,B2: set_int,B: int] :
% 4.71/5.06 ( ( ord_less_eq_set_int @ A2 @ B2 )
% 4.71/5.06 => ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ B2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % subset_insertI2
% 4.71/5.06 thf(fact_2671_insert__subsetI,axiom,
% 4.71/5.06 ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,X5: set_Pr1261947904930325089at_nat] :
% 4.71/5.06 ( ( member8440522571783428010at_nat @ X @ A2 )
% 4.71/5.06 => ( ( ord_le3146513528884898305at_nat @ X5 @ A2 )
% 4.71/5.06 => ( ord_le3146513528884898305at_nat @ ( insert8211810215607154385at_nat @ X @ X5 ) @ A2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_subsetI
% 4.71/5.06 thf(fact_2672_insert__subsetI,axiom,
% 4.71/5.06 ! [X: real,A2: set_real,X5: set_real] :
% 4.71/5.06 ( ( member_real @ X @ A2 )
% 4.71/5.06 => ( ( ord_less_eq_set_real @ X5 @ A2 )
% 4.71/5.06 => ( ord_less_eq_set_real @ ( insert_real @ X @ X5 ) @ A2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_subsetI
% 4.71/5.06 thf(fact_2673_insert__subsetI,axiom,
% 4.71/5.06 ! [X: $o,A2: set_o,X5: set_o] :
% 4.71/5.06 ( ( member_o @ X @ A2 )
% 4.71/5.06 => ( ( ord_less_eq_set_o @ X5 @ A2 )
% 4.71/5.06 => ( ord_less_eq_set_o @ ( insert_o @ X @ X5 ) @ A2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_subsetI
% 4.71/5.06 thf(fact_2674_insert__subsetI,axiom,
% 4.71/5.06 ! [X: set_nat,A2: set_set_nat,X5: set_set_nat] :
% 4.71/5.06 ( ( member_set_nat @ X @ A2 )
% 4.71/5.06 => ( ( ord_le6893508408891458716et_nat @ X5 @ A2 )
% 4.71/5.06 => ( ord_le6893508408891458716et_nat @ ( insert_set_nat @ X @ X5 ) @ A2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_subsetI
% 4.71/5.06 thf(fact_2675_insert__subsetI,axiom,
% 4.71/5.06 ! [X: set_nat_rat,A2: set_set_nat_rat,X5: set_set_nat_rat] :
% 4.71/5.06 ( ( member_set_nat_rat @ X @ A2 )
% 4.71/5.06 => ( ( ord_le4375437777232675859at_rat @ X5 @ A2 )
% 4.71/5.06 => ( ord_le4375437777232675859at_rat @ ( insert_set_nat_rat @ X @ X5 ) @ A2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_subsetI
% 4.71/5.06 thf(fact_2676_insert__subsetI,axiom,
% 4.71/5.06 ! [X: nat,A2: set_nat,X5: set_nat] :
% 4.71/5.06 ( ( member_nat @ X @ A2 )
% 4.71/5.06 => ( ( ord_less_eq_set_nat @ X5 @ A2 )
% 4.71/5.06 => ( ord_less_eq_set_nat @ ( insert_nat @ X @ X5 ) @ A2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_subsetI
% 4.71/5.06 thf(fact_2677_insert__subsetI,axiom,
% 4.71/5.06 ! [X: int,A2: set_int,X5: set_int] :
% 4.71/5.06 ( ( member_int @ X @ A2 )
% 4.71/5.06 => ( ( ord_less_eq_set_int @ X5 @ A2 )
% 4.71/5.06 => ( ord_less_eq_set_int @ ( insert_int @ X @ X5 ) @ A2 ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % insert_subsetI
% 4.71/5.06 thf(fact_2678_diff__diff__eq,axiom,
% 4.71/5.06 ! [A: real,B: real,C: real] :
% 4.71/5.06 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 4.71/5.06 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % diff_diff_eq
% 4.71/5.06 thf(fact_2679_diff__diff__eq,axiom,
% 4.71/5.06 ! [A: rat,B: rat,C: rat] :
% 4.71/5.06 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 4.71/5.06 = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % diff_diff_eq
% 4.71/5.06 thf(fact_2680_diff__diff__eq,axiom,
% 4.71/5.06 ! [A: nat,B: nat,C: nat] :
% 4.71/5.06 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 4.71/5.06 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % diff_diff_eq
% 4.71/5.06 thf(fact_2681_diff__diff__eq,axiom,
% 4.71/5.06 ! [A: int,B: int,C: int] :
% 4.71/5.06 ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 4.71/5.06 = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % diff_diff_eq
% 4.71/5.06 thf(fact_2682_add__implies__diff,axiom,
% 4.71/5.06 ! [C: real,B: real,A: real] :
% 4.71/5.06 ( ( ( plus_plus_real @ C @ B )
% 4.71/5.06 = A )
% 4.71/5.06 => ( C
% 4.71/5.06 = ( minus_minus_real @ A @ B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_implies_diff
% 4.71/5.06 thf(fact_2683_add__implies__diff,axiom,
% 4.71/5.06 ! [C: rat,B: rat,A: rat] :
% 4.71/5.06 ( ( ( plus_plus_rat @ C @ B )
% 4.71/5.06 = A )
% 4.71/5.06 => ( C
% 4.71/5.06 = ( minus_minus_rat @ A @ B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_implies_diff
% 4.71/5.06 thf(fact_2684_add__implies__diff,axiom,
% 4.71/5.06 ! [C: nat,B: nat,A: nat] :
% 4.71/5.06 ( ( ( plus_plus_nat @ C @ B )
% 4.71/5.06 = A )
% 4.71/5.06 => ( C
% 4.71/5.06 = ( minus_minus_nat @ A @ B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_implies_diff
% 4.71/5.06 thf(fact_2685_add__implies__diff,axiom,
% 4.71/5.06 ! [C: int,B: int,A: int] :
% 4.71/5.06 ( ( ( plus_plus_int @ C @ B )
% 4.71/5.06 = A )
% 4.71/5.06 => ( C
% 4.71/5.06 = ( minus_minus_int @ A @ B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_implies_diff
% 4.71/5.06 thf(fact_2686_diff__add__eq__diff__diff__swap,axiom,
% 4.71/5.06 ! [A: real,B: real,C: real] :
% 4.71/5.06 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 4.71/5.06 = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % diff_add_eq_diff_diff_swap
% 4.71/5.06 thf(fact_2687_diff__add__eq__diff__diff__swap,axiom,
% 4.71/5.06 ! [A: rat,B: rat,C: rat] :
% 4.71/5.06 ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 4.71/5.06 = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % diff_add_eq_diff_diff_swap
% 4.71/5.06 thf(fact_2688_diff__add__eq__diff__diff__swap,axiom,
% 4.71/5.06 ! [A: int,B: int,C: int] :
% 4.71/5.06 ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 4.71/5.06 = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % diff_add_eq_diff_diff_swap
% 4.71/5.06 thf(fact_2689_diff__add__eq,axiom,
% 4.71/5.06 ! [A: real,B: real,C: real] :
% 4.71/5.06 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 4.71/5.06 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % diff_add_eq
% 4.71/5.06 thf(fact_2690_diff__add__eq,axiom,
% 4.71/5.06 ! [A: rat,B: rat,C: rat] :
% 4.71/5.06 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 4.71/5.06 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % diff_add_eq
% 4.71/5.06 thf(fact_2691_diff__add__eq,axiom,
% 4.71/5.06 ! [A: int,B: int,C: int] :
% 4.71/5.06 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 4.71/5.06 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % diff_add_eq
% 4.71/5.06 thf(fact_2692_diff__diff__eq2,axiom,
% 4.71/5.06 ! [A: real,B: real,C: real] :
% 4.71/5.06 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 4.71/5.06 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % diff_diff_eq2
% 4.71/5.06 thf(fact_2693_diff__diff__eq2,axiom,
% 4.71/5.06 ! [A: rat,B: rat,C: rat] :
% 4.71/5.06 ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 4.71/5.06 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % diff_diff_eq2
% 4.71/5.06 thf(fact_2694_diff__diff__eq2,axiom,
% 4.71/5.06 ! [A: int,B: int,C: int] :
% 4.71/5.06 ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 4.71/5.06 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 4.71/5.06
% 4.71/5.06 % diff_diff_eq2
% 4.71/5.06 thf(fact_2695_add__diff__eq,axiom,
% 4.71/5.06 ! [A: real,B: real,C: real] :
% 4.71/5.06 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 4.71/5.06 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_diff_eq
% 4.71/5.06 thf(fact_2696_add__diff__eq,axiom,
% 4.71/5.06 ! [A: rat,B: rat,C: rat] :
% 4.71/5.06 ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 4.71/5.06 = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_diff_eq
% 4.71/5.06 thf(fact_2697_add__diff__eq,axiom,
% 4.71/5.06 ! [A: int,B: int,C: int] :
% 4.71/5.06 ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 4.71/5.06 = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 4.71/5.06
% 4.71/5.06 % add_diff_eq
% 4.71/5.06 thf(fact_2698_eq__diff__eq,axiom,
% 4.71/5.06 ! [A: real,C: real,B: real] :
% 4.71/5.06 ( ( A
% 4.71/5.06 = ( minus_minus_real @ C @ B ) )
% 4.71/5.06 = ( ( plus_plus_real @ A @ B )
% 4.71/5.06 = C ) ) ).
% 4.71/5.06
% 4.71/5.06 % eq_diff_eq
% 4.71/5.06 thf(fact_2699_eq__diff__eq,axiom,
% 4.71/5.06 ! [A: rat,C: rat,B: rat] :
% 4.71/5.06 ( ( A
% 4.71/5.06 = ( minus_minus_rat @ C @ B ) )
% 4.71/5.06 = ( ( plus_plus_rat @ A @ B )
% 4.71/5.06 = C ) ) ).
% 4.71/5.06
% 4.71/5.06 % eq_diff_eq
% 4.71/5.06 thf(fact_2700_eq__diff__eq,axiom,
% 4.71/5.06 ! [A: int,C: int,B: int] :
% 4.71/5.06 ( ( A
% 4.71/5.06 = ( minus_minus_int @ C @ B ) )
% 4.71/5.06 = ( ( plus_plus_int @ A @ B )
% 4.71/5.06 = C ) ) ).
% 4.71/5.06
% 4.71/5.06 % eq_diff_eq
% 4.71/5.06 thf(fact_2701_diff__eq__eq,axiom,
% 4.71/5.06 ! [A: real,B: real,C: real] :
% 4.71/5.06 ( ( ( minus_minus_real @ A @ B )
% 4.71/5.06 = C )
% 4.71/5.06 = ( A
% 4.71/5.06 = ( plus_plus_real @ C @ B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % diff_eq_eq
% 4.71/5.06 thf(fact_2702_diff__eq__eq,axiom,
% 4.71/5.06 ! [A: rat,B: rat,C: rat] :
% 4.71/5.06 ( ( ( minus_minus_rat @ A @ B )
% 4.71/5.06 = C )
% 4.71/5.06 = ( A
% 4.71/5.06 = ( plus_plus_rat @ C @ B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % diff_eq_eq
% 4.71/5.06 thf(fact_2703_diff__eq__eq,axiom,
% 4.71/5.06 ! [A: int,B: int,C: int] :
% 4.71/5.06 ( ( ( minus_minus_int @ A @ B )
% 4.71/5.06 = C )
% 4.71/5.06 = ( A
% 4.71/5.06 = ( plus_plus_int @ C @ B ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % diff_eq_eq
% 4.71/5.06 thf(fact_2704_group__cancel_Osub1,axiom,
% 4.71/5.06 ! [A2: real,K: real,A: real,B: real] :
% 4.71/5.06 ( ( A2
% 4.71/5.06 = ( plus_plus_real @ K @ A ) )
% 4.71/5.06 => ( ( minus_minus_real @ A2 @ B )
% 4.71/5.06 = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % group_cancel.sub1
% 4.71/5.06 thf(fact_2705_group__cancel_Osub1,axiom,
% 4.71/5.06 ! [A2: rat,K: rat,A: rat,B: rat] :
% 4.71/5.06 ( ( A2
% 4.71/5.06 = ( plus_plus_rat @ K @ A ) )
% 4.71/5.06 => ( ( minus_minus_rat @ A2 @ B )
% 4.71/5.06 = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 4.71/5.06
% 4.71/5.06 % group_cancel.sub1
% 4.71/5.06 thf(fact_2706_group__cancel_Osub1,axiom,
% 4.71/5.06 ! [A2: int,K: int,A: int,B: int] :
% 4.71/5.06 ( ( A2
% 4.71/5.07 = ( plus_plus_int @ K @ A ) )
% 4.71/5.07 => ( ( minus_minus_int @ A2 @ B )
% 4.71/5.07 = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % group_cancel.sub1
% 4.71/5.07 thf(fact_2707_add__diff__add,axiom,
% 4.71/5.07 ! [A: real,C: real,B: real,D: real] :
% 4.71/5.07 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) )
% 4.71/5.07 = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_diff_add
% 4.71/5.07 thf(fact_2708_add__diff__add,axiom,
% 4.71/5.07 ! [A: rat,C: rat,B: rat,D: rat] :
% 4.71/5.07 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) )
% 4.71/5.07 = ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ ( minus_minus_rat @ C @ D ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_diff_add
% 4.71/5.07 thf(fact_2709_add__diff__add,axiom,
% 4.71/5.07 ! [A: int,C: int,B: int,D: int] :
% 4.71/5.07 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) )
% 4.71/5.07 = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_diff_add
% 4.71/5.07 thf(fact_2710_mult_Ocomm__neutral,axiom,
% 4.71/5.07 ! [A: complex] :
% 4.71/5.07 ( ( times_times_complex @ A @ one_one_complex )
% 4.71/5.07 = A ) ).
% 4.71/5.07
% 4.71/5.07 % mult.comm_neutral
% 4.71/5.07 thf(fact_2711_mult_Ocomm__neutral,axiom,
% 4.71/5.07 ! [A: real] :
% 4.71/5.07 ( ( times_times_real @ A @ one_one_real )
% 4.71/5.07 = A ) ).
% 4.71/5.07
% 4.71/5.07 % mult.comm_neutral
% 4.71/5.07 thf(fact_2712_mult_Ocomm__neutral,axiom,
% 4.71/5.07 ! [A: rat] :
% 4.71/5.07 ( ( times_times_rat @ A @ one_one_rat )
% 4.71/5.07 = A ) ).
% 4.71/5.07
% 4.71/5.07 % mult.comm_neutral
% 4.71/5.07 thf(fact_2713_mult_Ocomm__neutral,axiom,
% 4.71/5.07 ! [A: nat] :
% 4.71/5.07 ( ( times_times_nat @ A @ one_one_nat )
% 4.71/5.07 = A ) ).
% 4.71/5.07
% 4.71/5.07 % mult.comm_neutral
% 4.71/5.07 thf(fact_2714_mult_Ocomm__neutral,axiom,
% 4.71/5.07 ! [A: int] :
% 4.71/5.07 ( ( times_times_int @ A @ one_one_int )
% 4.71/5.07 = A ) ).
% 4.71/5.07
% 4.71/5.07 % mult.comm_neutral
% 4.71/5.07 thf(fact_2715_comm__monoid__mult__class_Omult__1,axiom,
% 4.71/5.07 ! [A: complex] :
% 4.71/5.07 ( ( times_times_complex @ one_one_complex @ A )
% 4.71/5.07 = A ) ).
% 4.71/5.07
% 4.71/5.07 % comm_monoid_mult_class.mult_1
% 4.71/5.07 thf(fact_2716_comm__monoid__mult__class_Omult__1,axiom,
% 4.71/5.07 ! [A: real] :
% 4.71/5.07 ( ( times_times_real @ one_one_real @ A )
% 4.71/5.07 = A ) ).
% 4.71/5.07
% 4.71/5.07 % comm_monoid_mult_class.mult_1
% 4.71/5.07 thf(fact_2717_comm__monoid__mult__class_Omult__1,axiom,
% 4.71/5.07 ! [A: rat] :
% 4.71/5.07 ( ( times_times_rat @ one_one_rat @ A )
% 4.71/5.07 = A ) ).
% 4.71/5.07
% 4.71/5.07 % comm_monoid_mult_class.mult_1
% 4.71/5.07 thf(fact_2718_comm__monoid__mult__class_Omult__1,axiom,
% 4.71/5.07 ! [A: nat] :
% 4.71/5.07 ( ( times_times_nat @ one_one_nat @ A )
% 4.71/5.07 = A ) ).
% 4.71/5.07
% 4.71/5.07 % comm_monoid_mult_class.mult_1
% 4.71/5.07 thf(fact_2719_comm__monoid__mult__class_Omult__1,axiom,
% 4.71/5.07 ! [A: int] :
% 4.71/5.07 ( ( times_times_int @ one_one_int @ A )
% 4.71/5.07 = A ) ).
% 4.71/5.07
% 4.71/5.07 % comm_monoid_mult_class.mult_1
% 4.71/5.07 thf(fact_2720_right__diff__distrib_H,axiom,
% 4.71/5.07 ! [A: real,B: real,C: real] :
% 4.71/5.07 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 4.71/5.07 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % right_diff_distrib'
% 4.71/5.07 thf(fact_2721_right__diff__distrib_H,axiom,
% 4.71/5.07 ! [A: rat,B: rat,C: rat] :
% 4.71/5.07 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 4.71/5.07 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % right_diff_distrib'
% 4.71/5.07 thf(fact_2722_right__diff__distrib_H,axiom,
% 4.71/5.07 ! [A: nat,B: nat,C: nat] :
% 4.71/5.07 ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 4.71/5.07 = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % right_diff_distrib'
% 4.71/5.07 thf(fact_2723_right__diff__distrib_H,axiom,
% 4.71/5.07 ! [A: int,B: int,C: int] :
% 4.71/5.07 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 4.71/5.07 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % right_diff_distrib'
% 4.71/5.07 thf(fact_2724_left__diff__distrib_H,axiom,
% 4.71/5.07 ! [B: real,C: real,A: real] :
% 4.71/5.07 ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 4.71/5.07 = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % left_diff_distrib'
% 4.71/5.07 thf(fact_2725_left__diff__distrib_H,axiom,
% 4.71/5.07 ! [B: rat,C: rat,A: rat] :
% 4.71/5.07 ( ( times_times_rat @ ( minus_minus_rat @ B @ C ) @ A )
% 4.71/5.07 = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C @ A ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % left_diff_distrib'
% 4.71/5.07 thf(fact_2726_left__diff__distrib_H,axiom,
% 4.71/5.07 ! [B: nat,C: nat,A: nat] :
% 4.71/5.07 ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 4.71/5.07 = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % left_diff_distrib'
% 4.71/5.07 thf(fact_2727_left__diff__distrib_H,axiom,
% 4.71/5.07 ! [B: int,C: int,A: int] :
% 4.71/5.07 ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 4.71/5.07 = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % left_diff_distrib'
% 4.71/5.07 thf(fact_2728_right__diff__distrib,axiom,
% 4.71/5.07 ! [A: real,B: real,C: real] :
% 4.71/5.07 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 4.71/5.07 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % right_diff_distrib
% 4.71/5.07 thf(fact_2729_right__diff__distrib,axiom,
% 4.71/5.07 ! [A: rat,B: rat,C: rat] :
% 4.71/5.07 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 4.71/5.07 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % right_diff_distrib
% 4.71/5.07 thf(fact_2730_right__diff__distrib,axiom,
% 4.71/5.07 ! [A: int,B: int,C: int] :
% 4.71/5.07 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 4.71/5.07 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % right_diff_distrib
% 4.71/5.07 thf(fact_2731_left__diff__distrib,axiom,
% 4.71/5.07 ! [A: real,B: real,C: real] :
% 4.71/5.07 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 4.71/5.07 = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % left_diff_distrib
% 4.71/5.07 thf(fact_2732_left__diff__distrib,axiom,
% 4.71/5.07 ! [A: rat,B: rat,C: rat] :
% 4.71/5.07 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 4.71/5.07 = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % left_diff_distrib
% 4.71/5.07 thf(fact_2733_left__diff__distrib,axiom,
% 4.71/5.07 ! [A: int,B: int,C: int] :
% 4.71/5.07 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 4.71/5.07 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % left_diff_distrib
% 4.71/5.07 thf(fact_2734_Ints__0,axiom,
% 4.71/5.07 member_real @ zero_zero_real @ ring_1_Ints_real ).
% 4.71/5.07
% 4.71/5.07 % Ints_0
% 4.71/5.07 thf(fact_2735_Ints__0,axiom,
% 4.71/5.07 member_rat @ zero_zero_rat @ ring_1_Ints_rat ).
% 4.71/5.07
% 4.71/5.07 % Ints_0
% 4.71/5.07 thf(fact_2736_Ints__0,axiom,
% 4.71/5.07 member_int @ zero_zero_int @ ring_1_Ints_int ).
% 4.71/5.07
% 4.71/5.07 % Ints_0
% 4.71/5.07 thf(fact_2737_Suc__mult__cancel1,axiom,
% 4.71/5.07 ! [K: nat,M2: nat,N: nat] :
% 4.71/5.07 ( ( ( times_times_nat @ ( suc @ K ) @ M2 )
% 4.71/5.07 = ( times_times_nat @ ( suc @ K ) @ N ) )
% 4.71/5.07 = ( M2 = N ) ) ).
% 4.71/5.07
% 4.71/5.07 % Suc_mult_cancel1
% 4.71/5.07 thf(fact_2738_insert__Diff__if,axiom,
% 4.71/5.07 ! [X: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.07 ( ( ( member8440522571783428010at_nat @ X @ B2 )
% 4.71/5.07 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) @ B2 )
% 4.71/5.07 = ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) )
% 4.71/5.07 & ( ~ ( member8440522571783428010at_nat @ X @ B2 )
% 4.71/5.07 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) @ B2 )
% 4.71/5.07 = ( insert8211810215607154385at_nat @ X @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % insert_Diff_if
% 4.71/5.07 thf(fact_2739_insert__Diff__if,axiom,
% 4.71/5.07 ! [X: real,B2: set_real,A2: set_real] :
% 4.71/5.07 ( ( ( member_real @ X @ B2 )
% 4.71/5.07 => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ B2 )
% 4.71/5.07 = ( minus_minus_set_real @ A2 @ B2 ) ) )
% 4.71/5.07 & ( ~ ( member_real @ X @ B2 )
% 4.71/5.07 => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ B2 )
% 4.71/5.07 = ( insert_real @ X @ ( minus_minus_set_real @ A2 @ B2 ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % insert_Diff_if
% 4.71/5.07 thf(fact_2740_insert__Diff__if,axiom,
% 4.71/5.07 ! [X: $o,B2: set_o,A2: set_o] :
% 4.71/5.07 ( ( ( member_o @ X @ B2 )
% 4.71/5.07 => ( ( minus_minus_set_o @ ( insert_o @ X @ A2 ) @ B2 )
% 4.71/5.07 = ( minus_minus_set_o @ A2 @ B2 ) ) )
% 4.71/5.07 & ( ~ ( member_o @ X @ B2 )
% 4.71/5.07 => ( ( minus_minus_set_o @ ( insert_o @ X @ A2 ) @ B2 )
% 4.71/5.07 = ( insert_o @ X @ ( minus_minus_set_o @ A2 @ B2 ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % insert_Diff_if
% 4.71/5.07 thf(fact_2741_insert__Diff__if,axiom,
% 4.71/5.07 ! [X: set_nat,B2: set_set_nat,A2: set_set_nat] :
% 4.71/5.07 ( ( ( member_set_nat @ X @ B2 )
% 4.71/5.07 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A2 ) @ B2 )
% 4.71/5.07 = ( minus_2163939370556025621et_nat @ A2 @ B2 ) ) )
% 4.71/5.07 & ( ~ ( member_set_nat @ X @ B2 )
% 4.71/5.07 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A2 ) @ B2 )
% 4.71/5.07 = ( insert_set_nat @ X @ ( minus_2163939370556025621et_nat @ A2 @ B2 ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % insert_Diff_if
% 4.71/5.07 thf(fact_2742_insert__Diff__if,axiom,
% 4.71/5.07 ! [X: set_nat_rat,B2: set_set_nat_rat,A2: set_set_nat_rat] :
% 4.71/5.07 ( ( ( member_set_nat_rat @ X @ B2 )
% 4.71/5.07 => ( ( minus_1626877696091177228at_rat @ ( insert_set_nat_rat @ X @ A2 ) @ B2 )
% 4.71/5.07 = ( minus_1626877696091177228at_rat @ A2 @ B2 ) ) )
% 4.71/5.07 & ( ~ ( member_set_nat_rat @ X @ B2 )
% 4.71/5.07 => ( ( minus_1626877696091177228at_rat @ ( insert_set_nat_rat @ X @ A2 ) @ B2 )
% 4.71/5.07 = ( insert_set_nat_rat @ X @ ( minus_1626877696091177228at_rat @ A2 @ B2 ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % insert_Diff_if
% 4.71/5.07 thf(fact_2743_insert__Diff__if,axiom,
% 4.71/5.07 ! [X: int,B2: set_int,A2: set_int] :
% 4.71/5.07 ( ( ( member_int @ X @ B2 )
% 4.71/5.07 => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ B2 )
% 4.71/5.07 = ( minus_minus_set_int @ A2 @ B2 ) ) )
% 4.71/5.07 & ( ~ ( member_int @ X @ B2 )
% 4.71/5.07 => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ B2 )
% 4.71/5.07 = ( insert_int @ X @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % insert_Diff_if
% 4.71/5.07 thf(fact_2744_insert__Diff__if,axiom,
% 4.71/5.07 ! [X: nat,B2: set_nat,A2: set_nat] :
% 4.71/5.07 ( ( ( member_nat @ X @ B2 )
% 4.71/5.07 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ B2 )
% 4.71/5.07 = ( minus_minus_set_nat @ A2 @ B2 ) ) )
% 4.71/5.07 & ( ~ ( member_nat @ X @ B2 )
% 4.71/5.07 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ B2 )
% 4.71/5.07 = ( insert_nat @ X @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % insert_Diff_if
% 4.71/5.07 thf(fact_2745_mult__0,axiom,
% 4.71/5.07 ! [N: nat] :
% 4.71/5.07 ( ( times_times_nat @ zero_zero_nat @ N )
% 4.71/5.07 = zero_zero_nat ) ).
% 4.71/5.07
% 4.71/5.07 % mult_0
% 4.71/5.07 thf(fact_2746_Ints__1,axiom,
% 4.71/5.07 member_complex @ one_one_complex @ ring_1_Ints_complex ).
% 4.71/5.07
% 4.71/5.07 % Ints_1
% 4.71/5.07 thf(fact_2747_Ints__1,axiom,
% 4.71/5.07 member_real @ one_one_real @ ring_1_Ints_real ).
% 4.71/5.07
% 4.71/5.07 % Ints_1
% 4.71/5.07 thf(fact_2748_Ints__1,axiom,
% 4.71/5.07 member_rat @ one_one_rat @ ring_1_Ints_rat ).
% 4.71/5.07
% 4.71/5.07 % Ints_1
% 4.71/5.07 thf(fact_2749_Ints__1,axiom,
% 4.71/5.07 member_int @ one_one_int @ ring_1_Ints_int ).
% 4.71/5.07
% 4.71/5.07 % Ints_1
% 4.71/5.07 thf(fact_2750_mult__of__nat__commute,axiom,
% 4.71/5.07 ! [X: nat,Y: nat] :
% 4.71/5.07 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y )
% 4.71/5.07 = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_of_nat_commute
% 4.71/5.07 thf(fact_2751_mult__of__nat__commute,axiom,
% 4.71/5.07 ! [X: nat,Y: int] :
% 4.71/5.07 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X ) @ Y )
% 4.71/5.07 = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_of_nat_commute
% 4.71/5.07 thf(fact_2752_mult__of__nat__commute,axiom,
% 4.71/5.07 ! [X: nat,Y: real] :
% 4.71/5.07 ( ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ Y )
% 4.71/5.07 = ( times_times_real @ Y @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_of_nat_commute
% 4.71/5.07 thf(fact_2753_mult__of__nat__commute,axiom,
% 4.71/5.07 ! [X: nat,Y: rat] :
% 4.71/5.07 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X ) @ Y )
% 4.71/5.07 = ( times_times_rat @ Y @ ( semiri681578069525770553at_rat @ X ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_of_nat_commute
% 4.71/5.07 thf(fact_2754_mult__le__mono2,axiom,
% 4.71/5.07 ! [I: nat,J: nat,K: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ I @ J )
% 4.71/5.07 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_le_mono2
% 4.71/5.07 thf(fact_2755_mult__le__mono1,axiom,
% 4.71/5.07 ! [I: nat,J: nat,K: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ I @ J )
% 4.71/5.07 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_le_mono1
% 4.71/5.07 thf(fact_2756_mult__le__mono,axiom,
% 4.71/5.07 ! [I: nat,J: nat,K: nat,L: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ I @ J )
% 4.71/5.07 => ( ( ord_less_eq_nat @ K @ L )
% 4.71/5.07 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_le_mono
% 4.71/5.07 thf(fact_2757_le__square,axiom,
% 4.71/5.07 ! [M2: nat] : ( ord_less_eq_nat @ M2 @ ( times_times_nat @ M2 @ M2 ) ) ).
% 4.71/5.07
% 4.71/5.07 % le_square
% 4.71/5.07 thf(fact_2758_le__cube,axiom,
% 4.71/5.07 ! [M2: nat] : ( ord_less_eq_nat @ M2 @ ( times_times_nat @ M2 @ ( times_times_nat @ M2 @ M2 ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % le_cube
% 4.71/5.07 thf(fact_2759_diff__mult__distrib2,axiom,
% 4.71/5.07 ! [K: nat,M2: nat,N: nat] :
% 4.71/5.07 ( ( times_times_nat @ K @ ( minus_minus_nat @ M2 @ N ) )
% 4.71/5.07 = ( minus_minus_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % diff_mult_distrib2
% 4.71/5.07 thf(fact_2760_diff__mult__distrib,axiom,
% 4.71/5.07 ! [M2: nat,N: nat,K: nat] :
% 4.71/5.07 ( ( times_times_nat @ ( minus_minus_nat @ M2 @ N ) @ K )
% 4.71/5.07 = ( minus_minus_nat @ ( times_times_nat @ M2 @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % diff_mult_distrib
% 4.71/5.07 thf(fact_2761_nat__mult__1__right,axiom,
% 4.71/5.07 ! [N: nat] :
% 4.71/5.07 ( ( times_times_nat @ N @ one_one_nat )
% 4.71/5.07 = N ) ).
% 4.71/5.07
% 4.71/5.07 % nat_mult_1_right
% 4.71/5.07 thf(fact_2762_nat__mult__1,axiom,
% 4.71/5.07 ! [N: nat] :
% 4.71/5.07 ( ( times_times_nat @ one_one_nat @ N )
% 4.71/5.07 = N ) ).
% 4.71/5.07
% 4.71/5.07 % nat_mult_1
% 4.71/5.07 thf(fact_2763_abs__add__one__gt__zero,axiom,
% 4.71/5.07 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % abs_add_one_gt_zero
% 4.71/5.07 thf(fact_2764_abs__add__one__gt__zero,axiom,
% 4.71/5.07 ! [X: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % abs_add_one_gt_zero
% 4.71/5.07 thf(fact_2765_abs__add__one__gt__zero,axiom,
% 4.71/5.07 ! [X: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % abs_add_one_gt_zero
% 4.71/5.07 thf(fact_2766_Ints__nonzero__abs__ge1,axiom,
% 4.71/5.07 ! [X: real] :
% 4.71/5.07 ( ( member_real @ X @ ring_1_Ints_real )
% 4.71/5.07 => ( ( X != zero_zero_real )
% 4.71/5.07 => ( ord_less_eq_real @ one_one_real @ ( abs_abs_real @ X ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % Ints_nonzero_abs_ge1
% 4.71/5.07 thf(fact_2767_Ints__nonzero__abs__ge1,axiom,
% 4.71/5.07 ! [X: rat] :
% 4.71/5.07 ( ( member_rat @ X @ ring_1_Ints_rat )
% 4.71/5.07 => ( ( X != zero_zero_rat )
% 4.71/5.07 => ( ord_less_eq_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % Ints_nonzero_abs_ge1
% 4.71/5.07 thf(fact_2768_Ints__nonzero__abs__ge1,axiom,
% 4.71/5.07 ! [X: int] :
% 4.71/5.07 ( ( member_int @ X @ ring_1_Ints_int )
% 4.71/5.07 => ( ( X != zero_zero_int )
% 4.71/5.07 => ( ord_less_eq_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % Ints_nonzero_abs_ge1
% 4.71/5.07 thf(fact_2769_Ints__nonzero__abs__less1,axiom,
% 4.71/5.07 ! [X: real] :
% 4.71/5.07 ( ( member_real @ X @ ring_1_Ints_real )
% 4.71/5.07 => ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 4.71/5.07 => ( X = zero_zero_real ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % Ints_nonzero_abs_less1
% 4.71/5.07 thf(fact_2770_Ints__nonzero__abs__less1,axiom,
% 4.71/5.07 ! [X: rat] :
% 4.71/5.07 ( ( member_rat @ X @ ring_1_Ints_rat )
% 4.71/5.07 => ( ( ord_less_rat @ ( abs_abs_rat @ X ) @ one_one_rat )
% 4.71/5.07 => ( X = zero_zero_rat ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % Ints_nonzero_abs_less1
% 4.71/5.07 thf(fact_2771_Ints__nonzero__abs__less1,axiom,
% 4.71/5.07 ! [X: int] :
% 4.71/5.07 ( ( member_int @ X @ ring_1_Ints_int )
% 4.71/5.07 => ( ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int )
% 4.71/5.07 => ( X = zero_zero_int ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % Ints_nonzero_abs_less1
% 4.71/5.07 thf(fact_2772_Ints__eq__abs__less1,axiom,
% 4.71/5.07 ! [X: real,Y: real] :
% 4.71/5.07 ( ( member_real @ X @ ring_1_Ints_real )
% 4.71/5.07 => ( ( member_real @ Y @ ring_1_Ints_real )
% 4.71/5.07 => ( ( X = Y )
% 4.71/5.07 = ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y ) ) @ one_one_real ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % Ints_eq_abs_less1
% 4.71/5.07 thf(fact_2773_Ints__eq__abs__less1,axiom,
% 4.71/5.07 ! [X: rat,Y: rat] :
% 4.71/5.07 ( ( member_rat @ X @ ring_1_Ints_rat )
% 4.71/5.07 => ( ( member_rat @ Y @ ring_1_Ints_rat )
% 4.71/5.07 => ( ( X = Y )
% 4.71/5.07 = ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ Y ) ) @ one_one_rat ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % Ints_eq_abs_less1
% 4.71/5.07 thf(fact_2774_Ints__eq__abs__less1,axiom,
% 4.71/5.07 ! [X: int,Y: int] :
% 4.71/5.07 ( ( member_int @ X @ ring_1_Ints_int )
% 4.71/5.07 => ( ( member_int @ Y @ ring_1_Ints_int )
% 4.71/5.07 => ( ( X = Y )
% 4.71/5.07 = ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Y ) ) @ one_one_int ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % Ints_eq_abs_less1
% 4.71/5.07 thf(fact_2775_convex__bound__le,axiom,
% 4.71/5.07 ! [X: real,A: real,Y: real,U: real,V: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ X @ A )
% 4.71/5.07 => ( ( ord_less_eq_real @ Y @ A )
% 4.71/5.07 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 4.71/5.07 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 4.71/5.07 => ( ( ( plus_plus_real @ U @ V )
% 4.71/5.07 = one_one_real )
% 4.71/5.07 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % convex_bound_le
% 4.71/5.07 thf(fact_2776_convex__bound__le,axiom,
% 4.71/5.07 ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ X @ A )
% 4.71/5.07 => ( ( ord_less_eq_rat @ Y @ A )
% 4.71/5.07 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 4.71/5.07 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 4.71/5.07 => ( ( ( plus_plus_rat @ U @ V )
% 4.71/5.07 = one_one_rat )
% 4.71/5.07 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % convex_bound_le
% 4.71/5.07 thf(fact_2777_convex__bound__le,axiom,
% 4.71/5.07 ! [X: int,A: int,Y: int,U: int,V: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ X @ A )
% 4.71/5.07 => ( ( ord_less_eq_int @ Y @ A )
% 4.71/5.07 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 4.71/5.07 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 4.71/5.07 => ( ( ( plus_plus_int @ U @ V )
% 4.71/5.07 = one_one_int )
% 4.71/5.07 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % convex_bound_le
% 4.71/5.07 thf(fact_2778_Ints__odd__less__0,axiom,
% 4.71/5.07 ! [A: real] :
% 4.71/5.07 ( ( member_real @ A @ ring_1_Ints_real )
% 4.71/5.07 => ( ( ord_less_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ A ) @ A ) @ zero_zero_real )
% 4.71/5.07 = ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % Ints_odd_less_0
% 4.71/5.07 thf(fact_2779_Ints__odd__less__0,axiom,
% 4.71/5.07 ! [A: rat] :
% 4.71/5.07 ( ( member_rat @ A @ ring_1_Ints_rat )
% 4.71/5.07 => ( ( ord_less_rat @ ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A ) @ zero_zero_rat )
% 4.71/5.07 = ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % Ints_odd_less_0
% 4.71/5.07 thf(fact_2780_Ints__odd__less__0,axiom,
% 4.71/5.07 ! [A: int] :
% 4.71/5.07 ( ( member_int @ A @ ring_1_Ints_int )
% 4.71/5.07 => ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) @ zero_zero_int )
% 4.71/5.07 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % Ints_odd_less_0
% 4.71/5.07 thf(fact_2781_subset__decode__imp__le,axiom,
% 4.71/5.07 ! [M2: nat,N: nat] :
% 4.71/5.07 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M2 ) @ ( nat_set_decode @ N ) )
% 4.71/5.07 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 4.71/5.07
% 4.71/5.07 % subset_decode_imp_le
% 4.71/5.07 thf(fact_2782_convex__bound__lt,axiom,
% 4.71/5.07 ! [X: real,A: real,Y: real,U: real,V: real] :
% 4.71/5.07 ( ( ord_less_real @ X @ A )
% 4.71/5.07 => ( ( ord_less_real @ Y @ A )
% 4.71/5.07 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 4.71/5.07 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 4.71/5.07 => ( ( ( plus_plus_real @ U @ V )
% 4.71/5.07 = one_one_real )
% 4.71/5.07 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % convex_bound_lt
% 4.71/5.07 thf(fact_2783_convex__bound__lt,axiom,
% 4.71/5.07 ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 4.71/5.07 ( ( ord_less_rat @ X @ A )
% 4.71/5.07 => ( ( ord_less_rat @ Y @ A )
% 4.71/5.07 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 4.71/5.07 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 4.71/5.07 => ( ( ( plus_plus_rat @ U @ V )
% 4.71/5.07 = one_one_rat )
% 4.71/5.07 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % convex_bound_lt
% 4.71/5.07 thf(fact_2784_convex__bound__lt,axiom,
% 4.71/5.07 ! [X: int,A: int,Y: int,U: int,V: int] :
% 4.71/5.07 ( ( ord_less_int @ X @ A )
% 4.71/5.07 => ( ( ord_less_int @ Y @ A )
% 4.71/5.07 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 4.71/5.07 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 4.71/5.07 => ( ( ( plus_plus_int @ U @ V )
% 4.71/5.07 = one_one_int )
% 4.71/5.07 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % convex_bound_lt
% 4.71/5.07 thf(fact_2785_abs__ge__zero,axiom,
% 4.71/5.07 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 4.71/5.07
% 4.71/5.07 % abs_ge_zero
% 4.71/5.07 thf(fact_2786_abs__ge__zero,axiom,
% 4.71/5.07 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 4.71/5.07
% 4.71/5.07 % abs_ge_zero
% 4.71/5.07 thf(fact_2787_abs__ge__zero,axiom,
% 4.71/5.07 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 4.71/5.07
% 4.71/5.07 % abs_ge_zero
% 4.71/5.07 thf(fact_2788_abs__of__pos,axiom,
% 4.71/5.07 ! [A: real] :
% 4.71/5.07 ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.07 => ( ( abs_abs_real @ A )
% 4.71/5.07 = A ) ) ).
% 4.71/5.07
% 4.71/5.07 % abs_of_pos
% 4.71/5.07 thf(fact_2789_abs__of__pos,axiom,
% 4.71/5.07 ! [A: rat] :
% 4.71/5.07 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.07 => ( ( abs_abs_rat @ A )
% 4.71/5.07 = A ) ) ).
% 4.71/5.07
% 4.71/5.07 % abs_of_pos
% 4.71/5.07 thf(fact_2790_abs__of__pos,axiom,
% 4.71/5.07 ! [A: int] :
% 4.71/5.07 ( ( ord_less_int @ zero_zero_int @ A )
% 4.71/5.07 => ( ( abs_abs_int @ A )
% 4.71/5.07 = A ) ) ).
% 4.71/5.07
% 4.71/5.07 % abs_of_pos
% 4.71/5.07 thf(fact_2791_abs__not__less__zero,axiom,
% 4.71/5.07 ! [A: real] :
% 4.71/5.07 ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 4.71/5.07
% 4.71/5.07 % abs_not_less_zero
% 4.71/5.07 thf(fact_2792_abs__not__less__zero,axiom,
% 4.71/5.07 ! [A: rat] :
% 4.71/5.07 ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 4.71/5.07
% 4.71/5.07 % abs_not_less_zero
% 4.71/5.07 thf(fact_2793_abs__not__less__zero,axiom,
% 4.71/5.07 ! [A: int] :
% 4.71/5.07 ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 4.71/5.07
% 4.71/5.07 % abs_not_less_zero
% 4.71/5.07 thf(fact_2794_scaling__mono,axiom,
% 4.71/5.07 ! [U: real,V: real,R2: real,S: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ U @ V )
% 4.71/5.07 => ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 4.71/5.07 => ( ( ord_less_eq_real @ R2 @ S )
% 4.71/5.07 => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R2 @ ( minus_minus_real @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % scaling_mono
% 4.71/5.07 thf(fact_2795_scaling__mono,axiom,
% 4.71/5.07 ! [U: rat,V: rat,R2: rat,S: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ U @ V )
% 4.71/5.07 => ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 4.71/5.07 => ( ( ord_less_eq_rat @ R2 @ S )
% 4.71/5.07 => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R2 @ ( minus_minus_rat @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % scaling_mono
% 4.71/5.07 thf(fact_2796_nat__abs__int__diff,axiom,
% 4.71/5.07 ! [A: nat,B: nat] :
% 4.71/5.07 ( ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.07 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 4.71/5.07 = ( minus_minus_nat @ B @ A ) ) )
% 4.71/5.07 & ( ~ ( ord_less_eq_nat @ A @ B )
% 4.71/5.07 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 4.71/5.07 = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % nat_abs_int_diff
% 4.71/5.07 thf(fact_2797_abs__triangle__ineq2__sym,axiom,
% 4.71/5.07 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % abs_triangle_ineq2_sym
% 4.71/5.07 thf(fact_2798_abs__triangle__ineq2__sym,axiom,
% 4.71/5.07 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % abs_triangle_ineq2_sym
% 4.71/5.07 thf(fact_2799_abs__triangle__ineq2__sym,axiom,
% 4.71/5.07 ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % abs_triangle_ineq2_sym
% 4.71/5.07 thf(fact_2800_abs__triangle__ineq3,axiom,
% 4.71/5.07 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % abs_triangle_ineq3
% 4.71/5.07 thf(fact_2801_abs__triangle__ineq3,axiom,
% 4.71/5.07 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % abs_triangle_ineq3
% 4.71/5.07 thf(fact_2802_abs__triangle__ineq3,axiom,
% 4.71/5.07 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % abs_triangle_ineq3
% 4.71/5.07 thf(fact_2803_abs__triangle__ineq2,axiom,
% 4.71/5.07 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % abs_triangle_ineq2
% 4.71/5.07 thf(fact_2804_abs__triangle__ineq2,axiom,
% 4.71/5.07 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % abs_triangle_ineq2
% 4.71/5.07 thf(fact_2805_abs__triangle__ineq2,axiom,
% 4.71/5.07 ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % abs_triangle_ineq2
% 4.71/5.07 thf(fact_2806_nonzero__abs__divide,axiom,
% 4.71/5.07 ! [B: rat,A: rat] :
% 4.71/5.07 ( ( B != zero_zero_rat )
% 4.71/5.07 => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 4.71/5.07 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % nonzero_abs_divide
% 4.71/5.07 thf(fact_2807_nonzero__abs__divide,axiom,
% 4.71/5.07 ! [B: real,A: real] :
% 4.71/5.07 ( ( B != zero_zero_real )
% 4.71/5.07 => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 4.71/5.07 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % nonzero_abs_divide
% 4.71/5.07 thf(fact_2808_Suc__nat__eq__nat__zadd1,axiom,
% 4.71/5.07 ! [Z: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 4.71/5.07 => ( ( suc @ ( nat2 @ Z ) )
% 4.71/5.07 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % Suc_nat_eq_nat_zadd1
% 4.71/5.07 thf(fact_2809_nat__zero__as__int,axiom,
% 4.71/5.07 ( zero_zero_nat
% 4.71/5.07 = ( nat2 @ zero_zero_int ) ) ).
% 4.71/5.07
% 4.71/5.07 % nat_zero_as_int
% 4.71/5.07 thf(fact_2810_nat__mono,axiom,
% 4.71/5.07 ! [X: int,Y: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ X @ Y )
% 4.71/5.07 => ( ord_less_eq_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % nat_mono
% 4.71/5.07 thf(fact_2811_finite__set__decode,axiom,
% 4.71/5.07 ! [N: nat] : ( finite_finite_nat @ ( nat_set_decode @ N ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite_set_decode
% 4.71/5.07 thf(fact_2812_ex__nat,axiom,
% 4.71/5.07 ( ( ^ [P2: nat > $o] :
% 4.71/5.07 ? [X6: nat] : ( P2 @ X6 ) )
% 4.71/5.07 = ( ^ [P3: nat > $o] :
% 4.71/5.07 ? [X3: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 4.71/5.07 & ( P3 @ ( nat2 @ X3 ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % ex_nat
% 4.71/5.07 thf(fact_2813_all__nat,axiom,
% 4.71/5.07 ( ( ^ [P2: nat > $o] :
% 4.71/5.07 ! [X6: nat] : ( P2 @ X6 ) )
% 4.71/5.07 = ( ^ [P3: nat > $o] :
% 4.71/5.07 ! [X3: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 4.71/5.07 => ( P3 @ ( nat2 @ X3 ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % all_nat
% 4.71/5.07 thf(fact_2814_eq__nat__nat__iff,axiom,
% 4.71/5.07 ! [Z: int,Z6: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 4.71/5.07 => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 4.71/5.07 => ( ( ( nat2 @ Z )
% 4.71/5.07 = ( nat2 @ Z6 ) )
% 4.71/5.07 = ( Z = Z6 ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % eq_nat_nat_iff
% 4.71/5.07 thf(fact_2815_add__nonpos__eq__0__iff,axiom,
% 4.71/5.07 ! [X: real,Y: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 4.71/5.07 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 4.71/5.07 => ( ( ( plus_plus_real @ X @ Y )
% 4.71/5.07 = zero_zero_real )
% 4.71/5.07 = ( ( X = zero_zero_real )
% 4.71/5.07 & ( Y = zero_zero_real ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_nonpos_eq_0_iff
% 4.71/5.07 thf(fact_2816_add__nonpos__eq__0__iff,axiom,
% 4.71/5.07 ! [X: rat,Y: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 4.71/5.07 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 4.71/5.07 => ( ( ( plus_plus_rat @ X @ Y )
% 4.71/5.07 = zero_zero_rat )
% 4.71/5.07 = ( ( X = zero_zero_rat )
% 4.71/5.07 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_nonpos_eq_0_iff
% 4.71/5.07 thf(fact_2817_add__nonpos__eq__0__iff,axiom,
% 4.71/5.07 ! [X: nat,Y: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 4.71/5.07 => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 4.71/5.07 => ( ( ( plus_plus_nat @ X @ Y )
% 4.71/5.07 = zero_zero_nat )
% 4.71/5.07 = ( ( X = zero_zero_nat )
% 4.71/5.07 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_nonpos_eq_0_iff
% 4.71/5.07 thf(fact_2818_add__nonpos__eq__0__iff,axiom,
% 4.71/5.07 ! [X: int,Y: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ X @ zero_zero_int )
% 4.71/5.07 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 4.71/5.07 => ( ( ( plus_plus_int @ X @ Y )
% 4.71/5.07 = zero_zero_int )
% 4.71/5.07 = ( ( X = zero_zero_int )
% 4.71/5.07 & ( Y = zero_zero_int ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_nonpos_eq_0_iff
% 4.71/5.07 thf(fact_2819_add__nonneg__eq__0__iff,axiom,
% 4.71/5.07 ! [X: real,Y: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.07 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.71/5.07 => ( ( ( plus_plus_real @ X @ Y )
% 4.71/5.07 = zero_zero_real )
% 4.71/5.07 = ( ( X = zero_zero_real )
% 4.71/5.07 & ( Y = zero_zero_real ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_nonneg_eq_0_iff
% 4.71/5.07 thf(fact_2820_add__nonneg__eq__0__iff,axiom,
% 4.71/5.07 ! [X: rat,Y: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 4.71/5.07 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 4.71/5.07 => ( ( ( plus_plus_rat @ X @ Y )
% 4.71/5.07 = zero_zero_rat )
% 4.71/5.07 = ( ( X = zero_zero_rat )
% 4.71/5.07 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_nonneg_eq_0_iff
% 4.71/5.07 thf(fact_2821_add__nonneg__eq__0__iff,axiom,
% 4.71/5.07 ! [X: nat,Y: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 4.71/5.07 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 4.71/5.07 => ( ( ( plus_plus_nat @ X @ Y )
% 4.71/5.07 = zero_zero_nat )
% 4.71/5.07 = ( ( X = zero_zero_nat )
% 4.71/5.07 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_nonneg_eq_0_iff
% 4.71/5.07 thf(fact_2822_add__nonneg__eq__0__iff,axiom,
% 4.71/5.07 ! [X: int,Y: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 4.71/5.07 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.71/5.07 => ( ( ( plus_plus_int @ X @ Y )
% 4.71/5.07 = zero_zero_int )
% 4.71/5.07 = ( ( X = zero_zero_int )
% 4.71/5.07 & ( Y = zero_zero_int ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_nonneg_eq_0_iff
% 4.71/5.07 thf(fact_2823_add__nonpos__nonpos,axiom,
% 4.71/5.07 ! [A: real,B: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 4.71/5.07 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 4.71/5.07 => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_nonpos_nonpos
% 4.71/5.07 thf(fact_2824_add__nonpos__nonpos,axiom,
% 4.71/5.07 ! [A: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 4.71/5.07 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 4.71/5.07 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_nonpos_nonpos
% 4.71/5.07 thf(fact_2825_add__nonpos__nonpos,axiom,
% 4.71/5.07 ! [A: nat,B: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 4.71/5.07 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 4.71/5.07 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_nonpos_nonpos
% 4.71/5.07 thf(fact_2826_add__nonpos__nonpos,axiom,
% 4.71/5.07 ! [A: int,B: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 4.71/5.07 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 4.71/5.07 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_nonpos_nonpos
% 4.71/5.07 thf(fact_2827_add__nonneg__nonneg,axiom,
% 4.71/5.07 ! [A: real,B: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.07 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.71/5.07 => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_nonneg_nonneg
% 4.71/5.07 thf(fact_2828_add__nonneg__nonneg,axiom,
% 4.71/5.07 ! [A: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.07 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.71/5.07 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_nonneg_nonneg
% 4.71/5.07 thf(fact_2829_add__nonneg__nonneg,axiom,
% 4.71/5.07 ! [A: nat,B: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.71/5.07 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.71/5.07 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_nonneg_nonneg
% 4.71/5.07 thf(fact_2830_add__nonneg__nonneg,axiom,
% 4.71/5.07 ! [A: int,B: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.07 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.71/5.07 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_nonneg_nonneg
% 4.71/5.07 thf(fact_2831_add__increasing2,axiom,
% 4.71/5.07 ! [C: real,B: real,A: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.71/5.07 => ( ( ord_less_eq_real @ B @ A )
% 4.71/5.07 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_increasing2
% 4.71/5.07 thf(fact_2832_add__increasing2,axiom,
% 4.71/5.07 ! [C: rat,B: rat,A: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.71/5.07 => ( ( ord_less_eq_rat @ B @ A )
% 4.71/5.07 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_increasing2
% 4.71/5.07 thf(fact_2833_add__increasing2,axiom,
% 4.71/5.07 ! [C: nat,B: nat,A: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.71/5.07 => ( ( ord_less_eq_nat @ B @ A )
% 4.71/5.07 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_increasing2
% 4.71/5.07 thf(fact_2834_add__increasing2,axiom,
% 4.71/5.07 ! [C: int,B: int,A: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.71/5.07 => ( ( ord_less_eq_int @ B @ A )
% 4.71/5.07 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_increasing2
% 4.71/5.07 thf(fact_2835_add__decreasing2,axiom,
% 4.71/5.07 ! [C: real,A: real,B: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ C @ zero_zero_real )
% 4.71/5.07 => ( ( ord_less_eq_real @ A @ B )
% 4.71/5.07 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_decreasing2
% 4.71/5.07 thf(fact_2836_add__decreasing2,axiom,
% 4.71/5.07 ! [C: rat,A: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.71/5.07 => ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.07 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_decreasing2
% 4.71/5.07 thf(fact_2837_add__decreasing2,axiom,
% 4.71/5.07 ! [C: nat,A: nat,B: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 4.71/5.07 => ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.07 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_decreasing2
% 4.71/5.07 thf(fact_2838_add__decreasing2,axiom,
% 4.71/5.07 ! [C: int,A: int,B: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ C @ zero_zero_int )
% 4.71/5.07 => ( ( ord_less_eq_int @ A @ B )
% 4.71/5.07 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_decreasing2
% 4.71/5.07 thf(fact_2839_add__increasing,axiom,
% 4.71/5.07 ! [A: real,B: real,C: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.07 => ( ( ord_less_eq_real @ B @ C )
% 4.71/5.07 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_increasing
% 4.71/5.07 thf(fact_2840_add__increasing,axiom,
% 4.71/5.07 ! [A: rat,B: rat,C: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.07 => ( ( ord_less_eq_rat @ B @ C )
% 4.71/5.07 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_increasing
% 4.71/5.07 thf(fact_2841_add__increasing,axiom,
% 4.71/5.07 ! [A: nat,B: nat,C: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.71/5.07 => ( ( ord_less_eq_nat @ B @ C )
% 4.71/5.07 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_increasing
% 4.71/5.07 thf(fact_2842_add__increasing,axiom,
% 4.71/5.07 ! [A: int,B: int,C: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.07 => ( ( ord_less_eq_int @ B @ C )
% 4.71/5.07 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_increasing
% 4.71/5.07 thf(fact_2843_add__decreasing,axiom,
% 4.71/5.07 ! [A: real,C: real,B: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 4.71/5.07 => ( ( ord_less_eq_real @ C @ B )
% 4.71/5.07 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_decreasing
% 4.71/5.07 thf(fact_2844_add__decreasing,axiom,
% 4.71/5.07 ! [A: rat,C: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 4.71/5.07 => ( ( ord_less_eq_rat @ C @ B )
% 4.71/5.07 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_decreasing
% 4.71/5.07 thf(fact_2845_add__decreasing,axiom,
% 4.71/5.07 ! [A: nat,C: nat,B: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 4.71/5.07 => ( ( ord_less_eq_nat @ C @ B )
% 4.71/5.07 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_decreasing
% 4.71/5.07 thf(fact_2846_add__decreasing,axiom,
% 4.71/5.07 ! [A: int,C: int,B: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 4.71/5.07 => ( ( ord_less_eq_int @ C @ B )
% 4.71/5.07 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_decreasing
% 4.71/5.07 thf(fact_2847_add__less__le__mono,axiom,
% 4.71/5.07 ! [A: real,B: real,C: real,D: real] :
% 4.71/5.07 ( ( ord_less_real @ A @ B )
% 4.71/5.07 => ( ( ord_less_eq_real @ C @ D )
% 4.71/5.07 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_less_le_mono
% 4.71/5.07 thf(fact_2848_add__less__le__mono,axiom,
% 4.71/5.07 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.71/5.07 ( ( ord_less_rat @ A @ B )
% 4.71/5.07 => ( ( ord_less_eq_rat @ C @ D )
% 4.71/5.07 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_less_le_mono
% 4.71/5.07 thf(fact_2849_add__less__le__mono,axiom,
% 4.71/5.07 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.71/5.07 ( ( ord_less_nat @ A @ B )
% 4.71/5.07 => ( ( ord_less_eq_nat @ C @ D )
% 4.71/5.07 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_less_le_mono
% 4.71/5.07 thf(fact_2850_add__less__le__mono,axiom,
% 4.71/5.07 ! [A: int,B: int,C: int,D: int] :
% 4.71/5.07 ( ( ord_less_int @ A @ B )
% 4.71/5.07 => ( ( ord_less_eq_int @ C @ D )
% 4.71/5.07 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_less_le_mono
% 4.71/5.07 thf(fact_2851_add__le__less__mono,axiom,
% 4.71/5.07 ! [A: real,B: real,C: real,D: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ A @ B )
% 4.71/5.07 => ( ( ord_less_real @ C @ D )
% 4.71/5.07 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_le_less_mono
% 4.71/5.07 thf(fact_2852_add__le__less__mono,axiom,
% 4.71/5.07 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.07 => ( ( ord_less_rat @ C @ D )
% 4.71/5.07 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_le_less_mono
% 4.71/5.07 thf(fact_2853_add__le__less__mono,axiom,
% 4.71/5.07 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.07 => ( ( ord_less_nat @ C @ D )
% 4.71/5.07 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_le_less_mono
% 4.71/5.07 thf(fact_2854_add__le__less__mono,axiom,
% 4.71/5.07 ! [A: int,B: int,C: int,D: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ A @ B )
% 4.71/5.07 => ( ( ord_less_int @ C @ D )
% 4.71/5.07 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_le_less_mono
% 4.71/5.07 thf(fact_2855_add__mono__thms__linordered__field_I3_J,axiom,
% 4.71/5.07 ! [I: real,J: real,K: real,L: real] :
% 4.71/5.07 ( ( ( ord_less_real @ I @ J )
% 4.71/5.07 & ( ord_less_eq_real @ K @ L ) )
% 4.71/5.07 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_mono_thms_linordered_field(3)
% 4.71/5.07 thf(fact_2856_add__mono__thms__linordered__field_I3_J,axiom,
% 4.71/5.07 ! [I: rat,J: rat,K: rat,L: rat] :
% 4.71/5.07 ( ( ( ord_less_rat @ I @ J )
% 4.71/5.07 & ( ord_less_eq_rat @ K @ L ) )
% 4.71/5.07 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_mono_thms_linordered_field(3)
% 4.71/5.07 thf(fact_2857_add__mono__thms__linordered__field_I3_J,axiom,
% 4.71/5.07 ! [I: nat,J: nat,K: nat,L: nat] :
% 4.71/5.07 ( ( ( ord_less_nat @ I @ J )
% 4.71/5.07 & ( ord_less_eq_nat @ K @ L ) )
% 4.71/5.07 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_mono_thms_linordered_field(3)
% 4.71/5.07 thf(fact_2858_add__mono__thms__linordered__field_I3_J,axiom,
% 4.71/5.07 ! [I: int,J: int,K: int,L: int] :
% 4.71/5.07 ( ( ( ord_less_int @ I @ J )
% 4.71/5.07 & ( ord_less_eq_int @ K @ L ) )
% 4.71/5.07 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_mono_thms_linordered_field(3)
% 4.71/5.07 thf(fact_2859_add__mono__thms__linordered__field_I4_J,axiom,
% 4.71/5.07 ! [I: real,J: real,K: real,L: real] :
% 4.71/5.07 ( ( ( ord_less_eq_real @ I @ J )
% 4.71/5.07 & ( ord_less_real @ K @ L ) )
% 4.71/5.07 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_mono_thms_linordered_field(4)
% 4.71/5.07 thf(fact_2860_add__mono__thms__linordered__field_I4_J,axiom,
% 4.71/5.07 ! [I: rat,J: rat,K: rat,L: rat] :
% 4.71/5.07 ( ( ( ord_less_eq_rat @ I @ J )
% 4.71/5.07 & ( ord_less_rat @ K @ L ) )
% 4.71/5.07 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_mono_thms_linordered_field(4)
% 4.71/5.07 thf(fact_2861_add__mono__thms__linordered__field_I4_J,axiom,
% 4.71/5.07 ! [I: nat,J: nat,K: nat,L: nat] :
% 4.71/5.07 ( ( ( ord_less_eq_nat @ I @ J )
% 4.71/5.07 & ( ord_less_nat @ K @ L ) )
% 4.71/5.07 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_mono_thms_linordered_field(4)
% 4.71/5.07 thf(fact_2862_add__mono__thms__linordered__field_I4_J,axiom,
% 4.71/5.07 ! [I: int,J: int,K: int,L: int] :
% 4.71/5.07 ( ( ( ord_less_eq_int @ I @ J )
% 4.71/5.07 & ( ord_less_int @ K @ L ) )
% 4.71/5.07 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_mono_thms_linordered_field(4)
% 4.71/5.07 thf(fact_2863_add__neg__neg,axiom,
% 4.71/5.07 ! [A: real,B: real] :
% 4.71/5.07 ( ( ord_less_real @ A @ zero_zero_real )
% 4.71/5.07 => ( ( ord_less_real @ B @ zero_zero_real )
% 4.71/5.07 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_neg_neg
% 4.71/5.07 thf(fact_2864_add__neg__neg,axiom,
% 4.71/5.07 ! [A: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.71/5.07 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 4.71/5.07 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_neg_neg
% 4.71/5.07 thf(fact_2865_add__neg__neg,axiom,
% 4.71/5.07 ! [A: nat,B: nat] :
% 4.71/5.07 ( ( ord_less_nat @ A @ zero_zero_nat )
% 4.71/5.07 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 4.71/5.07 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_neg_neg
% 4.71/5.07 thf(fact_2866_add__neg__neg,axiom,
% 4.71/5.07 ! [A: int,B: int] :
% 4.71/5.07 ( ( ord_less_int @ A @ zero_zero_int )
% 4.71/5.07 => ( ( ord_less_int @ B @ zero_zero_int )
% 4.71/5.07 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_neg_neg
% 4.71/5.07 thf(fact_2867_add__pos__pos,axiom,
% 4.71/5.07 ! [A: real,B: real] :
% 4.71/5.07 ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.07 => ( ( ord_less_real @ zero_zero_real @ B )
% 4.71/5.07 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_pos_pos
% 4.71/5.07 thf(fact_2868_add__pos__pos,axiom,
% 4.71/5.07 ! [A: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.07 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 4.71/5.07 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_pos_pos
% 4.71/5.07 thf(fact_2869_add__pos__pos,axiom,
% 4.71/5.07 ! [A: nat,B: nat] :
% 4.71/5.07 ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.71/5.07 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.71/5.07 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_pos_pos
% 4.71/5.07 thf(fact_2870_add__pos__pos,axiom,
% 4.71/5.07 ! [A: int,B: int] :
% 4.71/5.07 ( ( ord_less_int @ zero_zero_int @ A )
% 4.71/5.07 => ( ( ord_less_int @ zero_zero_int @ B )
% 4.71/5.07 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_pos_pos
% 4.71/5.07 thf(fact_2871_canonically__ordered__monoid__add__class_OlessE,axiom,
% 4.71/5.07 ! [A: nat,B: nat] :
% 4.71/5.07 ( ( ord_less_nat @ A @ B )
% 4.71/5.07 => ~ ! [C3: nat] :
% 4.71/5.07 ( ( B
% 4.71/5.07 = ( plus_plus_nat @ A @ C3 ) )
% 4.71/5.07 => ( C3 = zero_zero_nat ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % canonically_ordered_monoid_add_class.lessE
% 4.71/5.07 thf(fact_2872_pos__add__strict,axiom,
% 4.71/5.07 ! [A: real,B: real,C: real] :
% 4.71/5.07 ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.07 => ( ( ord_less_real @ B @ C )
% 4.71/5.07 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % pos_add_strict
% 4.71/5.07 thf(fact_2873_pos__add__strict,axiom,
% 4.71/5.07 ! [A: rat,B: rat,C: rat] :
% 4.71/5.07 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.07 => ( ( ord_less_rat @ B @ C )
% 4.71/5.07 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % pos_add_strict
% 4.71/5.07 thf(fact_2874_pos__add__strict,axiom,
% 4.71/5.07 ! [A: nat,B: nat,C: nat] :
% 4.71/5.07 ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.71/5.07 => ( ( ord_less_nat @ B @ C )
% 4.71/5.07 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % pos_add_strict
% 4.71/5.07 thf(fact_2875_pos__add__strict,axiom,
% 4.71/5.07 ! [A: int,B: int,C: int] :
% 4.71/5.07 ( ( ord_less_int @ zero_zero_int @ A )
% 4.71/5.07 => ( ( ord_less_int @ B @ C )
% 4.71/5.07 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % pos_add_strict
% 4.71/5.07 thf(fact_2876_add__less__zeroD,axiom,
% 4.71/5.07 ! [X: real,Y: real] :
% 4.71/5.07 ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 4.71/5.07 => ( ( ord_less_real @ X @ zero_zero_real )
% 4.71/5.07 | ( ord_less_real @ Y @ zero_zero_real ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_less_zeroD
% 4.71/5.07 thf(fact_2877_add__less__zeroD,axiom,
% 4.71/5.07 ! [X: rat,Y: rat] :
% 4.71/5.07 ( ( ord_less_rat @ ( plus_plus_rat @ X @ Y ) @ zero_zero_rat )
% 4.71/5.07 => ( ( ord_less_rat @ X @ zero_zero_rat )
% 4.71/5.07 | ( ord_less_rat @ Y @ zero_zero_rat ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_less_zeroD
% 4.71/5.07 thf(fact_2878_add__less__zeroD,axiom,
% 4.71/5.07 ! [X: int,Y: int] :
% 4.71/5.07 ( ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ zero_zero_int )
% 4.71/5.07 => ( ( ord_less_int @ X @ zero_zero_int )
% 4.71/5.07 | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_less_zeroD
% 4.71/5.07 thf(fact_2879_nat__one__as__int,axiom,
% 4.71/5.07 ( one_one_nat
% 4.71/5.07 = ( nat2 @ one_one_int ) ) ).
% 4.71/5.07
% 4.71/5.07 % nat_one_as_int
% 4.71/5.07 thf(fact_2880_mult__mono,axiom,
% 4.71/5.07 ! [A: real,B: real,C: real,D: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ A @ B )
% 4.71/5.07 => ( ( ord_less_eq_real @ C @ D )
% 4.71/5.07 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.71/5.07 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.71/5.07 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_mono
% 4.71/5.07 thf(fact_2881_mult__mono,axiom,
% 4.71/5.07 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.07 => ( ( ord_less_eq_rat @ C @ D )
% 4.71/5.07 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.71/5.07 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.71/5.07 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_mono
% 4.71/5.07 thf(fact_2882_mult__mono,axiom,
% 4.71/5.07 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.07 => ( ( ord_less_eq_nat @ C @ D )
% 4.71/5.07 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.71/5.07 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.71/5.07 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_mono
% 4.71/5.07 thf(fact_2883_mult__mono,axiom,
% 4.71/5.07 ! [A: int,B: int,C: int,D: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ A @ B )
% 4.71/5.07 => ( ( ord_less_eq_int @ C @ D )
% 4.71/5.07 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.71/5.07 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.71/5.07 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_mono
% 4.71/5.07 thf(fact_2884_mult__mono_H,axiom,
% 4.71/5.07 ! [A: real,B: real,C: real,D: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ A @ B )
% 4.71/5.07 => ( ( ord_less_eq_real @ C @ D )
% 4.71/5.07 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.07 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.71/5.07 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_mono'
% 4.71/5.07 thf(fact_2885_mult__mono_H,axiom,
% 4.71/5.07 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.07 => ( ( ord_less_eq_rat @ C @ D )
% 4.71/5.07 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.07 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.71/5.07 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_mono'
% 4.71/5.07 thf(fact_2886_mult__mono_H,axiom,
% 4.71/5.07 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.07 => ( ( ord_less_eq_nat @ C @ D )
% 4.71/5.07 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.71/5.07 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.71/5.07 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_mono'
% 4.71/5.07 thf(fact_2887_mult__mono_H,axiom,
% 4.71/5.07 ! [A: int,B: int,C: int,D: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ A @ B )
% 4.71/5.07 => ( ( ord_less_eq_int @ C @ D )
% 4.71/5.07 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.07 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.71/5.07 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_mono'
% 4.71/5.07 thf(fact_2888_zero__le__square,axiom,
% 4.71/5.07 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 4.71/5.07
% 4.71/5.07 % zero_le_square
% 4.71/5.07 thf(fact_2889_zero__le__square,axiom,
% 4.71/5.07 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 4.71/5.07
% 4.71/5.07 % zero_le_square
% 4.71/5.07 thf(fact_2890_zero__le__square,axiom,
% 4.71/5.07 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 4.71/5.07
% 4.71/5.07 % zero_le_square
% 4.71/5.07 thf(fact_2891_split__mult__pos__le,axiom,
% 4.71/5.07 ! [A: real,B: real] :
% 4.71/5.07 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.07 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 4.71/5.07 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 4.71/5.07 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 4.71/5.07 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % split_mult_pos_le
% 4.71/5.07 thf(fact_2892_split__mult__pos__le,axiom,
% 4.71/5.07 ! [A: rat,B: rat] :
% 4.71/5.07 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.07 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 4.71/5.07 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 4.71/5.07 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 4.71/5.07 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % split_mult_pos_le
% 4.71/5.07 thf(fact_2893_split__mult__pos__le,axiom,
% 4.71/5.07 ! [A: int,B: int] :
% 4.71/5.07 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.07 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 4.71/5.07 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 4.71/5.07 & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 4.71/5.07 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % split_mult_pos_le
% 4.71/5.07 thf(fact_2894_mult__left__mono__neg,axiom,
% 4.71/5.07 ! [B: real,A: real,C: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ B @ A )
% 4.71/5.07 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 4.71/5.07 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_left_mono_neg
% 4.71/5.07 thf(fact_2895_mult__left__mono__neg,axiom,
% 4.71/5.07 ! [B: rat,A: rat,C: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ B @ A )
% 4.71/5.07 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.71/5.07 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_left_mono_neg
% 4.71/5.07 thf(fact_2896_mult__left__mono__neg,axiom,
% 4.71/5.07 ! [B: int,A: int,C: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ B @ A )
% 4.71/5.07 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 4.71/5.07 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_left_mono_neg
% 4.71/5.07 thf(fact_2897_mult__nonpos__nonpos,axiom,
% 4.71/5.07 ! [A: real,B: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 4.71/5.07 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 4.71/5.07 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_nonpos_nonpos
% 4.71/5.07 thf(fact_2898_mult__nonpos__nonpos,axiom,
% 4.71/5.07 ! [A: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 4.71/5.07 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 4.71/5.07 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_nonpos_nonpos
% 4.71/5.07 thf(fact_2899_mult__nonpos__nonpos,axiom,
% 4.71/5.07 ! [A: int,B: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 4.71/5.07 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 4.71/5.07 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_nonpos_nonpos
% 4.71/5.07 thf(fact_2900_mult__left__mono,axiom,
% 4.71/5.07 ! [A: real,B: real,C: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ A @ B )
% 4.71/5.07 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.71/5.07 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_left_mono
% 4.71/5.07 thf(fact_2901_mult__left__mono,axiom,
% 4.71/5.07 ! [A: rat,B: rat,C: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.07 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.71/5.07 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_left_mono
% 4.71/5.07 thf(fact_2902_mult__left__mono,axiom,
% 4.71/5.07 ! [A: nat,B: nat,C: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.07 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.71/5.07 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_left_mono
% 4.71/5.07 thf(fact_2903_mult__left__mono,axiom,
% 4.71/5.07 ! [A: int,B: int,C: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ A @ B )
% 4.71/5.07 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.71/5.07 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_left_mono
% 4.71/5.07 thf(fact_2904_mult__right__mono__neg,axiom,
% 4.71/5.07 ! [B: real,A: real,C: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ B @ A )
% 4.71/5.07 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 4.71/5.07 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_right_mono_neg
% 4.71/5.07 thf(fact_2905_mult__right__mono__neg,axiom,
% 4.71/5.07 ! [B: rat,A: rat,C: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ B @ A )
% 4.71/5.07 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.71/5.07 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_right_mono_neg
% 4.71/5.07 thf(fact_2906_mult__right__mono__neg,axiom,
% 4.71/5.07 ! [B: int,A: int,C: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ B @ A )
% 4.71/5.07 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 4.71/5.07 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_right_mono_neg
% 4.71/5.07 thf(fact_2907_mult__right__mono,axiom,
% 4.71/5.07 ! [A: real,B: real,C: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ A @ B )
% 4.71/5.07 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.71/5.07 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_right_mono
% 4.71/5.07 thf(fact_2908_mult__right__mono,axiom,
% 4.71/5.07 ! [A: rat,B: rat,C: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.07 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.71/5.07 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_right_mono
% 4.71/5.07 thf(fact_2909_mult__right__mono,axiom,
% 4.71/5.07 ! [A: nat,B: nat,C: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.07 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.71/5.07 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_right_mono
% 4.71/5.07 thf(fact_2910_mult__right__mono,axiom,
% 4.71/5.07 ! [A: int,B: int,C: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ A @ B )
% 4.71/5.07 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.71/5.07 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_right_mono
% 4.71/5.07 thf(fact_2911_mult__le__0__iff,axiom,
% 4.71/5.07 ! [A: real,B: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 4.71/5.07 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.07 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 4.71/5.07 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 4.71/5.07 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_le_0_iff
% 4.71/5.07 thf(fact_2912_mult__le__0__iff,axiom,
% 4.71/5.07 ! [A: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 4.71/5.07 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.07 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 4.71/5.07 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 4.71/5.07 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_le_0_iff
% 4.71/5.07 thf(fact_2913_mult__le__0__iff,axiom,
% 4.71/5.07 ! [A: int,B: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 4.71/5.07 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.07 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 4.71/5.07 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 4.71/5.07 & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_le_0_iff
% 4.71/5.07 thf(fact_2914_split__mult__neg__le,axiom,
% 4.71/5.07 ! [A: real,B: real] :
% 4.71/5.07 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.07 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 4.71/5.07 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 4.71/5.07 & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 4.71/5.07 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 4.71/5.07
% 4.71/5.07 % split_mult_neg_le
% 4.71/5.07 thf(fact_2915_split__mult__neg__le,axiom,
% 4.71/5.07 ! [A: rat,B: rat] :
% 4.71/5.07 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.07 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 4.71/5.07 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 4.71/5.07 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 4.71/5.07 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 4.71/5.07
% 4.71/5.07 % split_mult_neg_le
% 4.71/5.07 thf(fact_2916_split__mult__neg__le,axiom,
% 4.71/5.07 ! [A: nat,B: nat] :
% 4.71/5.07 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.71/5.07 & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 4.71/5.07 | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 4.71/5.07 & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 4.71/5.07 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 4.71/5.07
% 4.71/5.07 % split_mult_neg_le
% 4.71/5.07 thf(fact_2917_split__mult__neg__le,axiom,
% 4.71/5.07 ! [A: int,B: int] :
% 4.71/5.07 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.07 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 4.71/5.07 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 4.71/5.07 & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 4.71/5.07 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 4.71/5.07
% 4.71/5.07 % split_mult_neg_le
% 4.71/5.07 thf(fact_2918_mult__nonneg__nonneg,axiom,
% 4.71/5.07 ! [A: real,B: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.07 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.71/5.07 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_nonneg_nonneg
% 4.71/5.07 thf(fact_2919_mult__nonneg__nonneg,axiom,
% 4.71/5.07 ! [A: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.07 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.71/5.07 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_nonneg_nonneg
% 4.71/5.07 thf(fact_2920_mult__nonneg__nonneg,axiom,
% 4.71/5.07 ! [A: nat,B: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.71/5.07 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.71/5.07 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_nonneg_nonneg
% 4.71/5.07 thf(fact_2921_mult__nonneg__nonneg,axiom,
% 4.71/5.07 ! [A: int,B: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.07 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.71/5.07 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_nonneg_nonneg
% 4.71/5.07 thf(fact_2922_mult__nonneg__nonpos,axiom,
% 4.71/5.07 ! [A: real,B: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.07 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 4.71/5.07 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_nonneg_nonpos
% 4.71/5.07 thf(fact_2923_mult__nonneg__nonpos,axiom,
% 4.71/5.07 ! [A: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.07 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 4.71/5.07 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_nonneg_nonpos
% 4.71/5.07 thf(fact_2924_mult__nonneg__nonpos,axiom,
% 4.71/5.07 ! [A: nat,B: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.71/5.07 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 4.71/5.07 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_nonneg_nonpos
% 4.71/5.07 thf(fact_2925_mult__nonneg__nonpos,axiom,
% 4.71/5.07 ! [A: int,B: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.07 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 4.71/5.07 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_nonneg_nonpos
% 4.71/5.07 thf(fact_2926_mult__nonpos__nonneg,axiom,
% 4.71/5.07 ! [A: real,B: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 4.71/5.07 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.71/5.07 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_nonpos_nonneg
% 4.71/5.07 thf(fact_2927_mult__nonpos__nonneg,axiom,
% 4.71/5.07 ! [A: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 4.71/5.07 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.71/5.07 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_nonpos_nonneg
% 4.71/5.07 thf(fact_2928_mult__nonpos__nonneg,axiom,
% 4.71/5.07 ! [A: nat,B: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 4.71/5.07 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.71/5.07 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_nonpos_nonneg
% 4.71/5.07 thf(fact_2929_mult__nonpos__nonneg,axiom,
% 4.71/5.07 ! [A: int,B: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 4.71/5.07 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.71/5.07 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_nonpos_nonneg
% 4.71/5.07 thf(fact_2930_mult__nonneg__nonpos2,axiom,
% 4.71/5.07 ! [A: real,B: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.07 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 4.71/5.07 => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_nonneg_nonpos2
% 4.71/5.07 thf(fact_2931_mult__nonneg__nonpos2,axiom,
% 4.71/5.07 ! [A: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.07 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 4.71/5.07 => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_nonneg_nonpos2
% 4.71/5.07 thf(fact_2932_mult__nonneg__nonpos2,axiom,
% 4.71/5.07 ! [A: nat,B: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.71/5.07 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 4.71/5.07 => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_nonneg_nonpos2
% 4.71/5.07 thf(fact_2933_mult__nonneg__nonpos2,axiom,
% 4.71/5.07 ! [A: int,B: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.07 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 4.71/5.07 => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_nonneg_nonpos2
% 4.71/5.07 thf(fact_2934_zero__le__mult__iff,axiom,
% 4.71/5.07 ! [A: real,B: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 4.71/5.07 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.07 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 4.71/5.07 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 4.71/5.07 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % zero_le_mult_iff
% 4.71/5.07 thf(fact_2935_zero__le__mult__iff,axiom,
% 4.71/5.07 ! [A: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 4.71/5.07 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.07 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 4.71/5.07 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 4.71/5.07 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % zero_le_mult_iff
% 4.71/5.07 thf(fact_2936_zero__le__mult__iff,axiom,
% 4.71/5.07 ! [A: int,B: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 4.71/5.07 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.07 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 4.71/5.07 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 4.71/5.07 & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % zero_le_mult_iff
% 4.71/5.07 thf(fact_2937_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 4.71/5.07 ! [A: real,B: real,C: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ A @ B )
% 4.71/5.07 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.71/5.07 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % ordered_comm_semiring_class.comm_mult_left_mono
% 4.71/5.07 thf(fact_2938_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 4.71/5.07 ! [A: rat,B: rat,C: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.07 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.71/5.07 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % ordered_comm_semiring_class.comm_mult_left_mono
% 4.71/5.07 thf(fact_2939_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 4.71/5.07 ! [A: nat,B: nat,C: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.07 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.71/5.07 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % ordered_comm_semiring_class.comm_mult_left_mono
% 4.71/5.07 thf(fact_2940_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 4.71/5.07 ! [A: int,B: int,C: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ A @ B )
% 4.71/5.07 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.71/5.07 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % ordered_comm_semiring_class.comm_mult_left_mono
% 4.71/5.07 thf(fact_2941_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 4.71/5.07 ! [A: nat,B: nat,C: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.07 => ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.07 => ( ( ( minus_minus_nat @ B @ A )
% 4.71/5.07 = C )
% 4.71/5.07 = ( B
% 4.71/5.07 = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 4.71/5.07 thf(fact_2942_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 4.71/5.07 ! [A: nat,B: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.07 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 4.71/5.07 = B ) ) ).
% 4.71/5.07
% 4.71/5.07 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 4.71/5.07 thf(fact_2943_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 4.71/5.07 ! [A: nat,B: nat,C: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.07 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 4.71/5.07 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 4.71/5.07 thf(fact_2944_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 4.71/5.07 ! [A: nat,B: nat,C: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.07 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 4.71/5.07 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 4.71/5.07 thf(fact_2945_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 4.71/5.07 ! [A: nat,B: nat,C: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.07 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 4.71/5.07 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 4.71/5.07 thf(fact_2946_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 4.71/5.07 ! [A: nat,B: nat,C: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.07 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 4.71/5.07 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 4.71/5.07 thf(fact_2947_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 4.71/5.07 ! [A: nat,B: nat,C: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.07 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 4.71/5.07 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 4.71/5.07 thf(fact_2948_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 4.71/5.07 ! [A: nat,B: nat,C: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.07 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 4.71/5.07 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 4.71/5.07 thf(fact_2949_le__add__diff,axiom,
% 4.71/5.07 ! [A: nat,B: nat,C: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.07 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % le_add_diff
% 4.71/5.07 thf(fact_2950_diff__add,axiom,
% 4.71/5.07 ! [A: nat,B: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.07 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 4.71/5.07 = B ) ) ).
% 4.71/5.07
% 4.71/5.07 % diff_add
% 4.71/5.07 thf(fact_2951_le__diff__eq,axiom,
% 4.71/5.07 ! [A: real,C: real,B: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 4.71/5.07 = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 4.71/5.07
% 4.71/5.07 % le_diff_eq
% 4.71/5.07 thf(fact_2952_le__diff__eq,axiom,
% 4.71/5.07 ! [A: rat,C: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 4.71/5.07 = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 4.71/5.07
% 4.71/5.07 % le_diff_eq
% 4.71/5.07 thf(fact_2953_le__diff__eq,axiom,
% 4.71/5.07 ! [A: int,C: int,B: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 4.71/5.07 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 4.71/5.07
% 4.71/5.07 % le_diff_eq
% 4.71/5.07 thf(fact_2954_diff__le__eq,axiom,
% 4.71/5.07 ! [A: real,B: real,C: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 4.71/5.07 = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % diff_le_eq
% 4.71/5.07 thf(fact_2955_diff__le__eq,axiom,
% 4.71/5.07 ! [A: rat,B: rat,C: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 4.71/5.07 = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % diff_le_eq
% 4.71/5.07 thf(fact_2956_diff__le__eq,axiom,
% 4.71/5.07 ! [A: int,B: int,C: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 4.71/5.07 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % diff_le_eq
% 4.71/5.07 thf(fact_2957_add__le__add__imp__diff__le,axiom,
% 4.71/5.07 ! [I: real,K: real,N: real,J: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 4.71/5.07 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 4.71/5.07 => ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 4.71/5.07 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 4.71/5.07 => ( ord_less_eq_real @ ( minus_minus_real @ N @ K ) @ J ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_le_add_imp_diff_le
% 4.71/5.07 thf(fact_2958_add__le__add__imp__diff__le,axiom,
% 4.71/5.07 ! [I: rat,K: rat,N: rat,J: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 4.71/5.07 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 4.71/5.07 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 4.71/5.07 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 4.71/5.07 => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K ) @ J ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_le_add_imp_diff_le
% 4.71/5.07 thf(fact_2959_add__le__add__imp__diff__le,axiom,
% 4.71/5.07 ! [I: nat,K: nat,N: nat,J: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 4.71/5.07 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 4.71/5.07 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 4.71/5.07 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 4.71/5.07 => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_le_add_imp_diff_le
% 4.71/5.07 thf(fact_2960_add__le__add__imp__diff__le,axiom,
% 4.71/5.07 ! [I: int,K: int,N: int,J: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 4.71/5.07 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 4.71/5.07 => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 4.71/5.07 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 4.71/5.07 => ( ord_less_eq_int @ ( minus_minus_int @ N @ K ) @ J ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_le_add_imp_diff_le
% 4.71/5.07 thf(fact_2961_add__le__imp__le__diff,axiom,
% 4.71/5.07 ! [I: real,K: real,N: real] :
% 4.71/5.07 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 4.71/5.07 => ( ord_less_eq_real @ I @ ( minus_minus_real @ N @ K ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_le_imp_le_diff
% 4.71/5.07 thf(fact_2962_add__le__imp__le__diff,axiom,
% 4.71/5.07 ! [I: rat,K: rat,N: rat] :
% 4.71/5.07 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 4.71/5.07 => ( ord_less_eq_rat @ I @ ( minus_minus_rat @ N @ K ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_le_imp_le_diff
% 4.71/5.07 thf(fact_2963_add__le__imp__le__diff,axiom,
% 4.71/5.07 ! [I: nat,K: nat,N: nat] :
% 4.71/5.07 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 4.71/5.07 => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N @ K ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_le_imp_le_diff
% 4.71/5.07 thf(fact_2964_add__le__imp__le__diff,axiom,
% 4.71/5.07 ! [I: int,K: int,N: int] :
% 4.71/5.07 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 4.71/5.07 => ( ord_less_eq_int @ I @ ( minus_minus_int @ N @ K ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_le_imp_le_diff
% 4.71/5.07 thf(fact_2965_less__add__one,axiom,
% 4.71/5.07 ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 4.71/5.07
% 4.71/5.07 % less_add_one
% 4.71/5.07 thf(fact_2966_less__add__one,axiom,
% 4.71/5.07 ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 4.71/5.07
% 4.71/5.07 % less_add_one
% 4.71/5.07 thf(fact_2967_less__add__one,axiom,
% 4.71/5.07 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 4.71/5.07
% 4.71/5.07 % less_add_one
% 4.71/5.07 thf(fact_2968_less__add__one,axiom,
% 4.71/5.07 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 4.71/5.07
% 4.71/5.07 % less_add_one
% 4.71/5.07 thf(fact_2969_add__mono1,axiom,
% 4.71/5.07 ! [A: real,B: real] :
% 4.71/5.07 ( ( ord_less_real @ A @ B )
% 4.71/5.07 => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_mono1
% 4.71/5.07 thf(fact_2970_add__mono1,axiom,
% 4.71/5.07 ! [A: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_rat @ A @ B )
% 4.71/5.07 => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_mono1
% 4.71/5.07 thf(fact_2971_add__mono1,axiom,
% 4.71/5.07 ! [A: nat,B: nat] :
% 4.71/5.07 ( ( ord_less_nat @ A @ B )
% 4.71/5.07 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_mono1
% 4.71/5.07 thf(fact_2972_add__mono1,axiom,
% 4.71/5.07 ! [A: int,B: int] :
% 4.71/5.07 ( ( ord_less_int @ A @ B )
% 4.71/5.07 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % add_mono1
% 4.71/5.07 thf(fact_2973_mult__neg__neg,axiom,
% 4.71/5.07 ! [A: real,B: real] :
% 4.71/5.07 ( ( ord_less_real @ A @ zero_zero_real )
% 4.71/5.07 => ( ( ord_less_real @ B @ zero_zero_real )
% 4.71/5.07 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_neg_neg
% 4.71/5.07 thf(fact_2974_mult__neg__neg,axiom,
% 4.71/5.07 ! [A: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.71/5.07 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 4.71/5.07 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_neg_neg
% 4.71/5.07 thf(fact_2975_mult__neg__neg,axiom,
% 4.71/5.07 ! [A: int,B: int] :
% 4.71/5.07 ( ( ord_less_int @ A @ zero_zero_int )
% 4.71/5.07 => ( ( ord_less_int @ B @ zero_zero_int )
% 4.71/5.07 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_neg_neg
% 4.71/5.07 thf(fact_2976_not__square__less__zero,axiom,
% 4.71/5.07 ! [A: real] :
% 4.71/5.07 ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 4.71/5.07
% 4.71/5.07 % not_square_less_zero
% 4.71/5.07 thf(fact_2977_not__square__less__zero,axiom,
% 4.71/5.07 ! [A: rat] :
% 4.71/5.07 ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 4.71/5.07
% 4.71/5.07 % not_square_less_zero
% 4.71/5.07 thf(fact_2978_not__square__less__zero,axiom,
% 4.71/5.07 ! [A: int] :
% 4.71/5.07 ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 4.71/5.07
% 4.71/5.07 % not_square_less_zero
% 4.71/5.07 thf(fact_2979_mult__less__0__iff,axiom,
% 4.71/5.07 ! [A: real,B: real] :
% 4.71/5.07 ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 4.71/5.07 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.07 & ( ord_less_real @ B @ zero_zero_real ) )
% 4.71/5.07 | ( ( ord_less_real @ A @ zero_zero_real )
% 4.71/5.07 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_less_0_iff
% 4.71/5.07 thf(fact_2980_mult__less__0__iff,axiom,
% 4.71/5.07 ! [A: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 4.71/5.07 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.07 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 4.71/5.07 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.71/5.07 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_less_0_iff
% 4.71/5.07 thf(fact_2981_mult__less__0__iff,axiom,
% 4.71/5.07 ! [A: int,B: int] :
% 4.71/5.07 ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 4.71/5.07 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 4.71/5.07 & ( ord_less_int @ B @ zero_zero_int ) )
% 4.71/5.07 | ( ( ord_less_int @ A @ zero_zero_int )
% 4.71/5.07 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_less_0_iff
% 4.71/5.07 thf(fact_2982_mult__neg__pos,axiom,
% 4.71/5.07 ! [A: real,B: real] :
% 4.71/5.07 ( ( ord_less_real @ A @ zero_zero_real )
% 4.71/5.07 => ( ( ord_less_real @ zero_zero_real @ B )
% 4.71/5.07 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_neg_pos
% 4.71/5.07 thf(fact_2983_mult__neg__pos,axiom,
% 4.71/5.07 ! [A: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.71/5.07 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 4.71/5.07 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_neg_pos
% 4.71/5.07 thf(fact_2984_mult__neg__pos,axiom,
% 4.71/5.07 ! [A: nat,B: nat] :
% 4.71/5.07 ( ( ord_less_nat @ A @ zero_zero_nat )
% 4.71/5.07 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.71/5.07 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_neg_pos
% 4.71/5.07 thf(fact_2985_mult__neg__pos,axiom,
% 4.71/5.07 ! [A: int,B: int] :
% 4.71/5.07 ( ( ord_less_int @ A @ zero_zero_int )
% 4.71/5.07 => ( ( ord_less_int @ zero_zero_int @ B )
% 4.71/5.07 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_neg_pos
% 4.71/5.07 thf(fact_2986_mult__pos__neg,axiom,
% 4.71/5.07 ! [A: real,B: real] :
% 4.71/5.07 ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.07 => ( ( ord_less_real @ B @ zero_zero_real )
% 4.71/5.07 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_pos_neg
% 4.71/5.07 thf(fact_2987_mult__pos__neg,axiom,
% 4.71/5.07 ! [A: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.07 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 4.71/5.07 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_pos_neg
% 4.71/5.07 thf(fact_2988_mult__pos__neg,axiom,
% 4.71/5.07 ! [A: nat,B: nat] :
% 4.71/5.07 ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.71/5.07 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 4.71/5.07 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_pos_neg
% 4.71/5.07 thf(fact_2989_mult__pos__neg,axiom,
% 4.71/5.07 ! [A: int,B: int] :
% 4.71/5.07 ( ( ord_less_int @ zero_zero_int @ A )
% 4.71/5.07 => ( ( ord_less_int @ B @ zero_zero_int )
% 4.71/5.07 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_pos_neg
% 4.71/5.07 thf(fact_2990_mult__pos__pos,axiom,
% 4.71/5.07 ! [A: real,B: real] :
% 4.71/5.07 ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.07 => ( ( ord_less_real @ zero_zero_real @ B )
% 4.71/5.07 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_pos_pos
% 4.71/5.07 thf(fact_2991_mult__pos__pos,axiom,
% 4.71/5.07 ! [A: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.07 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 4.71/5.07 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_pos_pos
% 4.71/5.07 thf(fact_2992_mult__pos__pos,axiom,
% 4.71/5.07 ! [A: nat,B: nat] :
% 4.71/5.07 ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.71/5.07 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.71/5.07 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_pos_pos
% 4.71/5.07 thf(fact_2993_mult__pos__pos,axiom,
% 4.71/5.07 ! [A: int,B: int] :
% 4.71/5.07 ( ( ord_less_int @ zero_zero_int @ A )
% 4.71/5.07 => ( ( ord_less_int @ zero_zero_int @ B )
% 4.71/5.07 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_pos_pos
% 4.71/5.07 thf(fact_2994_mult__pos__neg2,axiom,
% 4.71/5.07 ! [A: real,B: real] :
% 4.71/5.07 ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.07 => ( ( ord_less_real @ B @ zero_zero_real )
% 4.71/5.07 => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_pos_neg2
% 4.71/5.07 thf(fact_2995_mult__pos__neg2,axiom,
% 4.71/5.07 ! [A: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.07 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 4.71/5.07 => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_pos_neg2
% 4.71/5.07 thf(fact_2996_mult__pos__neg2,axiom,
% 4.71/5.07 ! [A: nat,B: nat] :
% 4.71/5.07 ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.71/5.07 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 4.71/5.07 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_pos_neg2
% 4.71/5.07 thf(fact_2997_mult__pos__neg2,axiom,
% 4.71/5.07 ! [A: int,B: int] :
% 4.71/5.07 ( ( ord_less_int @ zero_zero_int @ A )
% 4.71/5.07 => ( ( ord_less_int @ B @ zero_zero_int )
% 4.71/5.07 => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_pos_neg2
% 4.71/5.07 thf(fact_2998_zero__less__mult__iff,axiom,
% 4.71/5.07 ! [A: real,B: real] :
% 4.71/5.07 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 4.71/5.07 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.07 & ( ord_less_real @ zero_zero_real @ B ) )
% 4.71/5.07 | ( ( ord_less_real @ A @ zero_zero_real )
% 4.71/5.07 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % zero_less_mult_iff
% 4.71/5.07 thf(fact_2999_zero__less__mult__iff,axiom,
% 4.71/5.07 ! [A: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 4.71/5.07 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.07 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 4.71/5.07 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.71/5.07 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % zero_less_mult_iff
% 4.71/5.07 thf(fact_3000_zero__less__mult__iff,axiom,
% 4.71/5.07 ! [A: int,B: int] :
% 4.71/5.07 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 4.71/5.07 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 4.71/5.07 & ( ord_less_int @ zero_zero_int @ B ) )
% 4.71/5.07 | ( ( ord_less_int @ A @ zero_zero_int )
% 4.71/5.07 & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % zero_less_mult_iff
% 4.71/5.07 thf(fact_3001_zero__less__mult__pos,axiom,
% 4.71/5.07 ! [A: real,B: real] :
% 4.71/5.07 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 4.71/5.07 => ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.07 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % zero_less_mult_pos
% 4.71/5.07 thf(fact_3002_zero__less__mult__pos,axiom,
% 4.71/5.07 ! [A: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 4.71/5.07 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.07 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % zero_less_mult_pos
% 4.71/5.07 thf(fact_3003_zero__less__mult__pos,axiom,
% 4.71/5.07 ! [A: nat,B: nat] :
% 4.71/5.07 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 4.71/5.07 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.71/5.07 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % zero_less_mult_pos
% 4.71/5.07 thf(fact_3004_zero__less__mult__pos,axiom,
% 4.71/5.07 ! [A: int,B: int] :
% 4.71/5.07 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 4.71/5.07 => ( ( ord_less_int @ zero_zero_int @ A )
% 4.71/5.07 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % zero_less_mult_pos
% 4.71/5.07 thf(fact_3005_zero__less__mult__pos2,axiom,
% 4.71/5.07 ! [B: real,A: real] :
% 4.71/5.07 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 4.71/5.07 => ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.07 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % zero_less_mult_pos2
% 4.71/5.07 thf(fact_3006_zero__less__mult__pos2,axiom,
% 4.71/5.07 ! [B: rat,A: rat] :
% 4.71/5.07 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 4.71/5.07 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.07 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % zero_less_mult_pos2
% 4.71/5.07 thf(fact_3007_zero__less__mult__pos2,axiom,
% 4.71/5.07 ! [B: nat,A: nat] :
% 4.71/5.07 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 4.71/5.07 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.71/5.07 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % zero_less_mult_pos2
% 4.71/5.07 thf(fact_3008_zero__less__mult__pos2,axiom,
% 4.71/5.07 ! [B: int,A: int] :
% 4.71/5.07 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 4.71/5.07 => ( ( ord_less_int @ zero_zero_int @ A )
% 4.71/5.07 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % zero_less_mult_pos2
% 4.71/5.07 thf(fact_3009_mult__less__cancel__left__neg,axiom,
% 4.71/5.07 ! [C: real,A: real,B: real] :
% 4.71/5.07 ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.07 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.71/5.07 = ( ord_less_real @ B @ A ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_less_cancel_left_neg
% 4.71/5.07 thf(fact_3010_mult__less__cancel__left__neg,axiom,
% 4.71/5.07 ! [C: rat,A: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.07 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.71/5.07 = ( ord_less_rat @ B @ A ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_less_cancel_left_neg
% 4.71/5.07 thf(fact_3011_mult__less__cancel__left__neg,axiom,
% 4.71/5.07 ! [C: int,A: int,B: int] :
% 4.71/5.07 ( ( ord_less_int @ C @ zero_zero_int )
% 4.71/5.07 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.71/5.07 = ( ord_less_int @ B @ A ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_less_cancel_left_neg
% 4.71/5.07 thf(fact_3012_mult__less__cancel__left__pos,axiom,
% 4.71/5.07 ! [C: real,A: real,B: real] :
% 4.71/5.07 ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.07 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.71/5.07 = ( ord_less_real @ A @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_less_cancel_left_pos
% 4.71/5.07 thf(fact_3013_mult__less__cancel__left__pos,axiom,
% 4.71/5.07 ! [C: rat,A: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.07 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.71/5.07 = ( ord_less_rat @ A @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_less_cancel_left_pos
% 4.71/5.07 thf(fact_3014_mult__less__cancel__left__pos,axiom,
% 4.71/5.07 ! [C: int,A: int,B: int] :
% 4.71/5.07 ( ( ord_less_int @ zero_zero_int @ C )
% 4.71/5.07 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.71/5.07 = ( ord_less_int @ A @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_less_cancel_left_pos
% 4.71/5.07 thf(fact_3015_mult__strict__left__mono__neg,axiom,
% 4.71/5.07 ! [B: real,A: real,C: real] :
% 4.71/5.07 ( ( ord_less_real @ B @ A )
% 4.71/5.07 => ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.07 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_strict_left_mono_neg
% 4.71/5.07 thf(fact_3016_mult__strict__left__mono__neg,axiom,
% 4.71/5.07 ! [B: rat,A: rat,C: rat] :
% 4.71/5.07 ( ( ord_less_rat @ B @ A )
% 4.71/5.07 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.07 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_strict_left_mono_neg
% 4.71/5.07 thf(fact_3017_mult__strict__left__mono__neg,axiom,
% 4.71/5.07 ! [B: int,A: int,C: int] :
% 4.71/5.07 ( ( ord_less_int @ B @ A )
% 4.71/5.07 => ( ( ord_less_int @ C @ zero_zero_int )
% 4.71/5.07 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_strict_left_mono_neg
% 4.71/5.07 thf(fact_3018_mult__strict__left__mono,axiom,
% 4.71/5.07 ! [A: real,B: real,C: real] :
% 4.71/5.07 ( ( ord_less_real @ A @ B )
% 4.71/5.07 => ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.07 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_strict_left_mono
% 4.71/5.07 thf(fact_3019_mult__strict__left__mono,axiom,
% 4.71/5.07 ! [A: rat,B: rat,C: rat] :
% 4.71/5.07 ( ( ord_less_rat @ A @ B )
% 4.71/5.07 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.07 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_strict_left_mono
% 4.71/5.07 thf(fact_3020_mult__strict__left__mono,axiom,
% 4.71/5.07 ! [A: nat,B: nat,C: nat] :
% 4.71/5.07 ( ( ord_less_nat @ A @ B )
% 4.71/5.07 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 4.71/5.07 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_strict_left_mono
% 4.71/5.07 thf(fact_3021_mult__strict__left__mono,axiom,
% 4.71/5.07 ! [A: int,B: int,C: int] :
% 4.71/5.07 ( ( ord_less_int @ A @ B )
% 4.71/5.07 => ( ( ord_less_int @ zero_zero_int @ C )
% 4.71/5.07 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_strict_left_mono
% 4.71/5.07 thf(fact_3022_mult__less__cancel__left__disj,axiom,
% 4.71/5.07 ! [C: real,A: real,B: real] :
% 4.71/5.07 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.71/5.07 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.07 & ( ord_less_real @ A @ B ) )
% 4.71/5.07 | ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.07 & ( ord_less_real @ B @ A ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_less_cancel_left_disj
% 4.71/5.07 thf(fact_3023_mult__less__cancel__left__disj,axiom,
% 4.71/5.07 ! [C: rat,A: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.71/5.07 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.07 & ( ord_less_rat @ A @ B ) )
% 4.71/5.07 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.07 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_less_cancel_left_disj
% 4.71/5.07 thf(fact_3024_mult__less__cancel__left__disj,axiom,
% 4.71/5.07 ! [C: int,A: int,B: int] :
% 4.71/5.07 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.71/5.07 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 4.71/5.07 & ( ord_less_int @ A @ B ) )
% 4.71/5.07 | ( ( ord_less_int @ C @ zero_zero_int )
% 4.71/5.07 & ( ord_less_int @ B @ A ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_less_cancel_left_disj
% 4.71/5.07 thf(fact_3025_mult__strict__right__mono__neg,axiom,
% 4.71/5.07 ! [B: real,A: real,C: real] :
% 4.71/5.07 ( ( ord_less_real @ B @ A )
% 4.71/5.07 => ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.07 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_strict_right_mono_neg
% 4.71/5.07 thf(fact_3026_mult__strict__right__mono__neg,axiom,
% 4.71/5.07 ! [B: rat,A: rat,C: rat] :
% 4.71/5.07 ( ( ord_less_rat @ B @ A )
% 4.71/5.07 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.07 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_strict_right_mono_neg
% 4.71/5.07 thf(fact_3027_mult__strict__right__mono__neg,axiom,
% 4.71/5.07 ! [B: int,A: int,C: int] :
% 4.71/5.07 ( ( ord_less_int @ B @ A )
% 4.71/5.07 => ( ( ord_less_int @ C @ zero_zero_int )
% 4.71/5.07 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_strict_right_mono_neg
% 4.71/5.07 thf(fact_3028_mult__strict__right__mono,axiom,
% 4.71/5.07 ! [A: real,B: real,C: real] :
% 4.71/5.07 ( ( ord_less_real @ A @ B )
% 4.71/5.07 => ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.07 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_strict_right_mono
% 4.71/5.07 thf(fact_3029_mult__strict__right__mono,axiom,
% 4.71/5.07 ! [A: rat,B: rat,C: rat] :
% 4.71/5.07 ( ( ord_less_rat @ A @ B )
% 4.71/5.07 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.07 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_strict_right_mono
% 4.71/5.07 thf(fact_3030_mult__strict__right__mono,axiom,
% 4.71/5.07 ! [A: nat,B: nat,C: nat] :
% 4.71/5.07 ( ( ord_less_nat @ A @ B )
% 4.71/5.07 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 4.71/5.07 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_strict_right_mono
% 4.71/5.07 thf(fact_3031_mult__strict__right__mono,axiom,
% 4.71/5.07 ! [A: int,B: int,C: int] :
% 4.71/5.07 ( ( ord_less_int @ A @ B )
% 4.71/5.07 => ( ( ord_less_int @ zero_zero_int @ C )
% 4.71/5.07 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_strict_right_mono
% 4.71/5.07 thf(fact_3032_mult__less__cancel__right__disj,axiom,
% 4.71/5.07 ! [A: real,C: real,B: real] :
% 4.71/5.07 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 4.71/5.07 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.07 & ( ord_less_real @ A @ B ) )
% 4.71/5.07 | ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.07 & ( ord_less_real @ B @ A ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_less_cancel_right_disj
% 4.71/5.07 thf(fact_3033_mult__less__cancel__right__disj,axiom,
% 4.71/5.07 ! [A: rat,C: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 4.71/5.07 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.07 & ( ord_less_rat @ A @ B ) )
% 4.71/5.07 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.07 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_less_cancel_right_disj
% 4.71/5.07 thf(fact_3034_mult__less__cancel__right__disj,axiom,
% 4.71/5.07 ! [A: int,C: int,B: int] :
% 4.71/5.07 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 4.71/5.07 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 4.71/5.07 & ( ord_less_int @ A @ B ) )
% 4.71/5.07 | ( ( ord_less_int @ C @ zero_zero_int )
% 4.71/5.07 & ( ord_less_int @ B @ A ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % mult_less_cancel_right_disj
% 4.71/5.07 thf(fact_3035_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 4.71/5.07 ! [A: real,B: real,C: real] :
% 4.71/5.07 ( ( ord_less_real @ A @ B )
% 4.71/5.07 => ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.07 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 4.71/5.07 thf(fact_3036_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 4.71/5.07 ! [A: rat,B: rat,C: rat] :
% 4.71/5.07 ( ( ord_less_rat @ A @ B )
% 4.71/5.07 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.07 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 4.71/5.07 thf(fact_3037_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 4.71/5.07 ! [A: nat,B: nat,C: nat] :
% 4.71/5.07 ( ( ord_less_nat @ A @ B )
% 4.71/5.07 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 4.71/5.07 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 4.71/5.07 thf(fact_3038_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 4.71/5.07 ! [A: int,B: int,C: int] :
% 4.71/5.07 ( ( ord_less_int @ A @ B )
% 4.71/5.07 => ( ( ord_less_int @ zero_zero_int @ C )
% 4.71/5.07 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 4.71/5.07 thf(fact_3039_less__diff__eq,axiom,
% 4.71/5.07 ! [A: real,C: real,B: real] :
% 4.71/5.07 ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 4.71/5.07 = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 4.71/5.07
% 4.71/5.07 % less_diff_eq
% 4.71/5.07 thf(fact_3040_less__diff__eq,axiom,
% 4.71/5.07 ! [A: rat,C: rat,B: rat] :
% 4.71/5.07 ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 4.71/5.07 = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 4.71/5.07
% 4.71/5.07 % less_diff_eq
% 4.71/5.07 thf(fact_3041_less__diff__eq,axiom,
% 4.71/5.07 ! [A: int,C: int,B: int] :
% 4.71/5.07 ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 4.71/5.07 = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 4.71/5.07
% 4.71/5.07 % less_diff_eq
% 4.71/5.07 thf(fact_3042_diff__less__eq,axiom,
% 4.71/5.07 ! [A: real,B: real,C: real] :
% 4.71/5.07 ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 4.71/5.07 = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % diff_less_eq
% 4.71/5.07 thf(fact_3043_diff__less__eq,axiom,
% 4.71/5.07 ! [A: rat,B: rat,C: rat] :
% 4.71/5.07 ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 4.71/5.07 = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % diff_less_eq
% 4.71/5.07 thf(fact_3044_diff__less__eq,axiom,
% 4.71/5.07 ! [A: int,B: int,C: int] :
% 4.71/5.07 ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 4.71/5.07 = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % diff_less_eq
% 4.71/5.07 thf(fact_3045_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 4.71/5.07 ! [A: real,B: real] :
% 4.71/5.07 ( ~ ( ord_less_real @ A @ B )
% 4.71/5.07 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 4.71/5.07 = A ) ) ).
% 4.71/5.07
% 4.71/5.07 % linordered_semidom_class.add_diff_inverse
% 4.71/5.07 thf(fact_3046_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 4.71/5.07 ! [A: rat,B: rat] :
% 4.71/5.07 ( ~ ( ord_less_rat @ A @ B )
% 4.71/5.07 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 4.71/5.07 = A ) ) ).
% 4.71/5.07
% 4.71/5.07 % linordered_semidom_class.add_diff_inverse
% 4.71/5.07 thf(fact_3047_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 4.71/5.07 ! [A: nat,B: nat] :
% 4.71/5.07 ( ~ ( ord_less_nat @ A @ B )
% 4.71/5.07 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 4.71/5.07 = A ) ) ).
% 4.71/5.07
% 4.71/5.07 % linordered_semidom_class.add_diff_inverse
% 4.71/5.07 thf(fact_3048_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 4.71/5.07 ! [A: int,B: int] :
% 4.71/5.07 ( ~ ( ord_less_int @ A @ B )
% 4.71/5.07 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 4.71/5.07 = A ) ) ).
% 4.71/5.07
% 4.71/5.07 % linordered_semidom_class.add_diff_inverse
% 4.71/5.07 thf(fact_3049_infinite__finite__induct,axiom,
% 4.71/5.07 ! [P: set_set_nat > $o,A2: set_set_nat] :
% 4.71/5.07 ( ! [A3: set_set_nat] :
% 4.71/5.07 ( ~ ( finite1152437895449049373et_nat @ A3 )
% 4.71/5.07 => ( P @ A3 ) )
% 4.71/5.07 => ( ( P @ bot_bot_set_set_nat )
% 4.71/5.07 => ( ! [X4: set_nat,F3: set_set_nat] :
% 4.71/5.07 ( ( finite1152437895449049373et_nat @ F3 )
% 4.71/5.07 => ( ~ ( member_set_nat @ X4 @ F3 )
% 4.71/5.07 => ( ( P @ F3 )
% 4.71/5.07 => ( P @ ( insert_set_nat @ X4 @ F3 ) ) ) ) )
% 4.71/5.07 => ( P @ A2 ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % infinite_finite_induct
% 4.71/5.07 thf(fact_3050_infinite__finite__induct,axiom,
% 4.71/5.07 ! [P: set_set_nat_rat > $o,A2: set_set_nat_rat] :
% 4.71/5.07 ( ! [A3: set_set_nat_rat] :
% 4.71/5.07 ( ~ ( finite6430367030675640852at_rat @ A3 )
% 4.71/5.07 => ( P @ A3 ) )
% 4.71/5.07 => ( ( P @ bot_bo6797373522285170759at_rat )
% 4.71/5.07 => ( ! [X4: set_nat_rat,F3: set_set_nat_rat] :
% 4.71/5.07 ( ( finite6430367030675640852at_rat @ F3 )
% 4.71/5.07 => ( ~ ( member_set_nat_rat @ X4 @ F3 )
% 4.71/5.07 => ( ( P @ F3 )
% 4.71/5.07 => ( P @ ( insert_set_nat_rat @ X4 @ F3 ) ) ) ) )
% 4.71/5.07 => ( P @ A2 ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % infinite_finite_induct
% 4.71/5.07 thf(fact_3051_infinite__finite__induct,axiom,
% 4.71/5.07 ! [P: set_complex > $o,A2: set_complex] :
% 4.71/5.07 ( ! [A3: set_complex] :
% 4.71/5.07 ( ~ ( finite3207457112153483333omplex @ A3 )
% 4.71/5.07 => ( P @ A3 ) )
% 4.71/5.07 => ( ( P @ bot_bot_set_complex )
% 4.71/5.07 => ( ! [X4: complex,F3: set_complex] :
% 4.71/5.07 ( ( finite3207457112153483333omplex @ F3 )
% 4.71/5.07 => ( ~ ( member_complex @ X4 @ F3 )
% 4.71/5.07 => ( ( P @ F3 )
% 4.71/5.07 => ( P @ ( insert_complex @ X4 @ F3 ) ) ) ) )
% 4.71/5.07 => ( P @ A2 ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % infinite_finite_induct
% 4.71/5.07 thf(fact_3052_infinite__finite__induct,axiom,
% 4.71/5.07 ! [P: set_Pr1261947904930325089at_nat > $o,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.07 ( ! [A3: set_Pr1261947904930325089at_nat] :
% 4.71/5.07 ( ~ ( finite6177210948735845034at_nat @ A3 )
% 4.71/5.07 => ( P @ A3 ) )
% 4.71/5.07 => ( ( P @ bot_bo2099793752762293965at_nat )
% 4.71/5.07 => ( ! [X4: product_prod_nat_nat,F3: set_Pr1261947904930325089at_nat] :
% 4.71/5.07 ( ( finite6177210948735845034at_nat @ F3 )
% 4.71/5.07 => ( ~ ( member8440522571783428010at_nat @ X4 @ F3 )
% 4.71/5.07 => ( ( P @ F3 )
% 4.71/5.07 => ( P @ ( insert8211810215607154385at_nat @ X4 @ F3 ) ) ) ) )
% 4.71/5.07 => ( P @ A2 ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % infinite_finite_induct
% 4.71/5.07 thf(fact_3053_infinite__finite__induct,axiom,
% 4.71/5.07 ! [P: set_Extended_enat > $o,A2: set_Extended_enat] :
% 4.71/5.07 ( ! [A3: set_Extended_enat] :
% 4.71/5.07 ( ~ ( finite4001608067531595151d_enat @ A3 )
% 4.71/5.07 => ( P @ A3 ) )
% 4.71/5.07 => ( ( P @ bot_bo7653980558646680370d_enat )
% 4.71/5.07 => ( ! [X4: extended_enat,F3: set_Extended_enat] :
% 4.71/5.07 ( ( finite4001608067531595151d_enat @ F3 )
% 4.71/5.07 => ( ~ ( member_Extended_enat @ X4 @ F3 )
% 4.71/5.07 => ( ( P @ F3 )
% 4.71/5.07 => ( P @ ( insert_Extended_enat @ X4 @ F3 ) ) ) ) )
% 4.71/5.07 => ( P @ A2 ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % infinite_finite_induct
% 4.71/5.07 thf(fact_3054_infinite__finite__induct,axiom,
% 4.71/5.07 ! [P: set_real > $o,A2: set_real] :
% 4.71/5.07 ( ! [A3: set_real] :
% 4.71/5.07 ( ~ ( finite_finite_real @ A3 )
% 4.71/5.07 => ( P @ A3 ) )
% 4.71/5.07 => ( ( P @ bot_bot_set_real )
% 4.71/5.07 => ( ! [X4: real,F3: set_real] :
% 4.71/5.07 ( ( finite_finite_real @ F3 )
% 4.71/5.07 => ( ~ ( member_real @ X4 @ F3 )
% 4.71/5.07 => ( ( P @ F3 )
% 4.71/5.07 => ( P @ ( insert_real @ X4 @ F3 ) ) ) ) )
% 4.71/5.07 => ( P @ A2 ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % infinite_finite_induct
% 4.71/5.07 thf(fact_3055_infinite__finite__induct,axiom,
% 4.71/5.07 ! [P: set_o > $o,A2: set_o] :
% 4.71/5.07 ( ! [A3: set_o] :
% 4.71/5.07 ( ~ ( finite_finite_o @ A3 )
% 4.71/5.07 => ( P @ A3 ) )
% 4.71/5.07 => ( ( P @ bot_bot_set_o )
% 4.71/5.07 => ( ! [X4: $o,F3: set_o] :
% 4.71/5.07 ( ( finite_finite_o @ F3 )
% 4.71/5.07 => ( ~ ( member_o @ X4 @ F3 )
% 4.71/5.07 => ( ( P @ F3 )
% 4.71/5.07 => ( P @ ( insert_o @ X4 @ F3 ) ) ) ) )
% 4.71/5.07 => ( P @ A2 ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % infinite_finite_induct
% 4.71/5.07 thf(fact_3056_infinite__finite__induct,axiom,
% 4.71/5.07 ! [P: set_nat > $o,A2: set_nat] :
% 4.71/5.07 ( ! [A3: set_nat] :
% 4.71/5.07 ( ~ ( finite_finite_nat @ A3 )
% 4.71/5.07 => ( P @ A3 ) )
% 4.71/5.07 => ( ( P @ bot_bot_set_nat )
% 4.71/5.07 => ( ! [X4: nat,F3: set_nat] :
% 4.71/5.07 ( ( finite_finite_nat @ F3 )
% 4.71/5.07 => ( ~ ( member_nat @ X4 @ F3 )
% 4.71/5.07 => ( ( P @ F3 )
% 4.71/5.07 => ( P @ ( insert_nat @ X4 @ F3 ) ) ) ) )
% 4.71/5.07 => ( P @ A2 ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % infinite_finite_induct
% 4.71/5.07 thf(fact_3057_infinite__finite__induct,axiom,
% 4.71/5.07 ! [P: set_int > $o,A2: set_int] :
% 4.71/5.07 ( ! [A3: set_int] :
% 4.71/5.07 ( ~ ( finite_finite_int @ A3 )
% 4.71/5.07 => ( P @ A3 ) )
% 4.71/5.07 => ( ( P @ bot_bot_set_int )
% 4.71/5.07 => ( ! [X4: int,F3: set_int] :
% 4.71/5.07 ( ( finite_finite_int @ F3 )
% 4.71/5.07 => ( ~ ( member_int @ X4 @ F3 )
% 4.71/5.07 => ( ( P @ F3 )
% 4.71/5.07 => ( P @ ( insert_int @ X4 @ F3 ) ) ) ) )
% 4.71/5.07 => ( P @ A2 ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % infinite_finite_induct
% 4.71/5.07 thf(fact_3058_finite__ne__induct,axiom,
% 4.71/5.07 ! [F2: set_set_nat,P: set_set_nat > $o] :
% 4.71/5.07 ( ( finite1152437895449049373et_nat @ F2 )
% 4.71/5.07 => ( ( F2 != bot_bot_set_set_nat )
% 4.71/5.07 => ( ! [X4: set_nat] : ( P @ ( insert_set_nat @ X4 @ bot_bot_set_set_nat ) )
% 4.71/5.07 => ( ! [X4: set_nat,F3: set_set_nat] :
% 4.71/5.07 ( ( finite1152437895449049373et_nat @ F3 )
% 4.71/5.07 => ( ( F3 != bot_bot_set_set_nat )
% 4.71/5.07 => ( ~ ( member_set_nat @ X4 @ F3 )
% 4.71/5.07 => ( ( P @ F3 )
% 4.71/5.07 => ( P @ ( insert_set_nat @ X4 @ F3 ) ) ) ) ) )
% 4.71/5.07 => ( P @ F2 ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite_ne_induct
% 4.71/5.07 thf(fact_3059_finite__ne__induct,axiom,
% 4.71/5.07 ! [F2: set_set_nat_rat,P: set_set_nat_rat > $o] :
% 4.71/5.07 ( ( finite6430367030675640852at_rat @ F2 )
% 4.71/5.07 => ( ( F2 != bot_bo6797373522285170759at_rat )
% 4.71/5.07 => ( ! [X4: set_nat_rat] : ( P @ ( insert_set_nat_rat @ X4 @ bot_bo6797373522285170759at_rat ) )
% 4.71/5.07 => ( ! [X4: set_nat_rat,F3: set_set_nat_rat] :
% 4.71/5.07 ( ( finite6430367030675640852at_rat @ F3 )
% 4.71/5.07 => ( ( F3 != bot_bo6797373522285170759at_rat )
% 4.71/5.07 => ( ~ ( member_set_nat_rat @ X4 @ F3 )
% 4.71/5.07 => ( ( P @ F3 )
% 4.71/5.07 => ( P @ ( insert_set_nat_rat @ X4 @ F3 ) ) ) ) ) )
% 4.71/5.07 => ( P @ F2 ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite_ne_induct
% 4.71/5.07 thf(fact_3060_finite__ne__induct,axiom,
% 4.71/5.07 ! [F2: set_complex,P: set_complex > $o] :
% 4.71/5.07 ( ( finite3207457112153483333omplex @ F2 )
% 4.71/5.07 => ( ( F2 != bot_bot_set_complex )
% 4.71/5.07 => ( ! [X4: complex] : ( P @ ( insert_complex @ X4 @ bot_bot_set_complex ) )
% 4.71/5.07 => ( ! [X4: complex,F3: set_complex] :
% 4.71/5.07 ( ( finite3207457112153483333omplex @ F3 )
% 4.71/5.07 => ( ( F3 != bot_bot_set_complex )
% 4.71/5.07 => ( ~ ( member_complex @ X4 @ F3 )
% 4.71/5.07 => ( ( P @ F3 )
% 4.71/5.07 => ( P @ ( insert_complex @ X4 @ F3 ) ) ) ) ) )
% 4.71/5.07 => ( P @ F2 ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite_ne_induct
% 4.71/5.07 thf(fact_3061_finite__ne__induct,axiom,
% 4.71/5.07 ! [F2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 4.71/5.07 ( ( finite6177210948735845034at_nat @ F2 )
% 4.71/5.07 => ( ( F2 != bot_bo2099793752762293965at_nat )
% 4.71/5.07 => ( ! [X4: product_prod_nat_nat] : ( P @ ( insert8211810215607154385at_nat @ X4 @ bot_bo2099793752762293965at_nat ) )
% 4.71/5.07 => ( ! [X4: product_prod_nat_nat,F3: set_Pr1261947904930325089at_nat] :
% 4.71/5.07 ( ( finite6177210948735845034at_nat @ F3 )
% 4.71/5.07 => ( ( F3 != bot_bo2099793752762293965at_nat )
% 4.71/5.07 => ( ~ ( member8440522571783428010at_nat @ X4 @ F3 )
% 4.71/5.07 => ( ( P @ F3 )
% 4.71/5.07 => ( P @ ( insert8211810215607154385at_nat @ X4 @ F3 ) ) ) ) ) )
% 4.71/5.07 => ( P @ F2 ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite_ne_induct
% 4.71/5.07 thf(fact_3062_finite__ne__induct,axiom,
% 4.71/5.07 ! [F2: set_Extended_enat,P: set_Extended_enat > $o] :
% 4.71/5.07 ( ( finite4001608067531595151d_enat @ F2 )
% 4.71/5.07 => ( ( F2 != bot_bo7653980558646680370d_enat )
% 4.71/5.07 => ( ! [X4: extended_enat] : ( P @ ( insert_Extended_enat @ X4 @ bot_bo7653980558646680370d_enat ) )
% 4.71/5.07 => ( ! [X4: extended_enat,F3: set_Extended_enat] :
% 4.71/5.07 ( ( finite4001608067531595151d_enat @ F3 )
% 4.71/5.07 => ( ( F3 != bot_bo7653980558646680370d_enat )
% 4.71/5.07 => ( ~ ( member_Extended_enat @ X4 @ F3 )
% 4.71/5.07 => ( ( P @ F3 )
% 4.71/5.07 => ( P @ ( insert_Extended_enat @ X4 @ F3 ) ) ) ) ) )
% 4.71/5.07 => ( P @ F2 ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite_ne_induct
% 4.71/5.07 thf(fact_3063_finite__ne__induct,axiom,
% 4.71/5.07 ! [F2: set_real,P: set_real > $o] :
% 4.71/5.07 ( ( finite_finite_real @ F2 )
% 4.71/5.07 => ( ( F2 != bot_bot_set_real )
% 4.71/5.07 => ( ! [X4: real] : ( P @ ( insert_real @ X4 @ bot_bot_set_real ) )
% 4.71/5.07 => ( ! [X4: real,F3: set_real] :
% 4.71/5.07 ( ( finite_finite_real @ F3 )
% 4.71/5.07 => ( ( F3 != bot_bot_set_real )
% 4.71/5.07 => ( ~ ( member_real @ X4 @ F3 )
% 4.71/5.07 => ( ( P @ F3 )
% 4.71/5.07 => ( P @ ( insert_real @ X4 @ F3 ) ) ) ) ) )
% 4.71/5.07 => ( P @ F2 ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite_ne_induct
% 4.71/5.07 thf(fact_3064_finite__ne__induct,axiom,
% 4.71/5.07 ! [F2: set_o,P: set_o > $o] :
% 4.71/5.07 ( ( finite_finite_o @ F2 )
% 4.71/5.07 => ( ( F2 != bot_bot_set_o )
% 4.71/5.07 => ( ! [X4: $o] : ( P @ ( insert_o @ X4 @ bot_bot_set_o ) )
% 4.71/5.07 => ( ! [X4: $o,F3: set_o] :
% 4.71/5.07 ( ( finite_finite_o @ F3 )
% 4.71/5.07 => ( ( F3 != bot_bot_set_o )
% 4.71/5.07 => ( ~ ( member_o @ X4 @ F3 )
% 4.71/5.07 => ( ( P @ F3 )
% 4.71/5.07 => ( P @ ( insert_o @ X4 @ F3 ) ) ) ) ) )
% 4.71/5.07 => ( P @ F2 ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite_ne_induct
% 4.71/5.07 thf(fact_3065_finite__ne__induct,axiom,
% 4.71/5.07 ! [F2: set_nat,P: set_nat > $o] :
% 4.71/5.07 ( ( finite_finite_nat @ F2 )
% 4.71/5.07 => ( ( F2 != bot_bot_set_nat )
% 4.71/5.07 => ( ! [X4: nat] : ( P @ ( insert_nat @ X4 @ bot_bot_set_nat ) )
% 4.71/5.07 => ( ! [X4: nat,F3: set_nat] :
% 4.71/5.07 ( ( finite_finite_nat @ F3 )
% 4.71/5.07 => ( ( F3 != bot_bot_set_nat )
% 4.71/5.07 => ( ~ ( member_nat @ X4 @ F3 )
% 4.71/5.07 => ( ( P @ F3 )
% 4.71/5.07 => ( P @ ( insert_nat @ X4 @ F3 ) ) ) ) ) )
% 4.71/5.07 => ( P @ F2 ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite_ne_induct
% 4.71/5.07 thf(fact_3066_finite__ne__induct,axiom,
% 4.71/5.07 ! [F2: set_int,P: set_int > $o] :
% 4.71/5.07 ( ( finite_finite_int @ F2 )
% 4.71/5.07 => ( ( F2 != bot_bot_set_int )
% 4.71/5.07 => ( ! [X4: int] : ( P @ ( insert_int @ X4 @ bot_bot_set_int ) )
% 4.71/5.07 => ( ! [X4: int,F3: set_int] :
% 4.71/5.07 ( ( finite_finite_int @ F3 )
% 4.71/5.07 => ( ( F3 != bot_bot_set_int )
% 4.71/5.07 => ( ~ ( member_int @ X4 @ F3 )
% 4.71/5.07 => ( ( P @ F3 )
% 4.71/5.07 => ( P @ ( insert_int @ X4 @ F3 ) ) ) ) ) )
% 4.71/5.07 => ( P @ F2 ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite_ne_induct
% 4.71/5.07 thf(fact_3067_finite__induct,axiom,
% 4.71/5.07 ! [F2: set_set_nat,P: set_set_nat > $o] :
% 4.71/5.07 ( ( finite1152437895449049373et_nat @ F2 )
% 4.71/5.07 => ( ( P @ bot_bot_set_set_nat )
% 4.71/5.07 => ( ! [X4: set_nat,F3: set_set_nat] :
% 4.71/5.07 ( ( finite1152437895449049373et_nat @ F3 )
% 4.71/5.07 => ( ~ ( member_set_nat @ X4 @ F3 )
% 4.71/5.07 => ( ( P @ F3 )
% 4.71/5.07 => ( P @ ( insert_set_nat @ X4 @ F3 ) ) ) ) )
% 4.71/5.07 => ( P @ F2 ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite_induct
% 4.71/5.07 thf(fact_3068_finite__induct,axiom,
% 4.71/5.07 ! [F2: set_set_nat_rat,P: set_set_nat_rat > $o] :
% 4.71/5.07 ( ( finite6430367030675640852at_rat @ F2 )
% 4.71/5.07 => ( ( P @ bot_bo6797373522285170759at_rat )
% 4.71/5.07 => ( ! [X4: set_nat_rat,F3: set_set_nat_rat] :
% 4.71/5.07 ( ( finite6430367030675640852at_rat @ F3 )
% 4.71/5.07 => ( ~ ( member_set_nat_rat @ X4 @ F3 )
% 4.71/5.07 => ( ( P @ F3 )
% 4.71/5.07 => ( P @ ( insert_set_nat_rat @ X4 @ F3 ) ) ) ) )
% 4.71/5.07 => ( P @ F2 ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite_induct
% 4.71/5.07 thf(fact_3069_finite__induct,axiom,
% 4.71/5.07 ! [F2: set_complex,P: set_complex > $o] :
% 4.71/5.07 ( ( finite3207457112153483333omplex @ F2 )
% 4.71/5.07 => ( ( P @ bot_bot_set_complex )
% 4.71/5.07 => ( ! [X4: complex,F3: set_complex] :
% 4.71/5.07 ( ( finite3207457112153483333omplex @ F3 )
% 4.71/5.07 => ( ~ ( member_complex @ X4 @ F3 )
% 4.71/5.07 => ( ( P @ F3 )
% 4.71/5.07 => ( P @ ( insert_complex @ X4 @ F3 ) ) ) ) )
% 4.71/5.07 => ( P @ F2 ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite_induct
% 4.71/5.07 thf(fact_3070_finite__induct,axiom,
% 4.71/5.07 ! [F2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 4.71/5.07 ( ( finite6177210948735845034at_nat @ F2 )
% 4.71/5.07 => ( ( P @ bot_bo2099793752762293965at_nat )
% 4.71/5.07 => ( ! [X4: product_prod_nat_nat,F3: set_Pr1261947904930325089at_nat] :
% 4.71/5.07 ( ( finite6177210948735845034at_nat @ F3 )
% 4.71/5.07 => ( ~ ( member8440522571783428010at_nat @ X4 @ F3 )
% 4.71/5.07 => ( ( P @ F3 )
% 4.71/5.07 => ( P @ ( insert8211810215607154385at_nat @ X4 @ F3 ) ) ) ) )
% 4.71/5.07 => ( P @ F2 ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite_induct
% 4.71/5.07 thf(fact_3071_finite__induct,axiom,
% 4.71/5.07 ! [F2: set_Extended_enat,P: set_Extended_enat > $o] :
% 4.71/5.07 ( ( finite4001608067531595151d_enat @ F2 )
% 4.71/5.07 => ( ( P @ bot_bo7653980558646680370d_enat )
% 4.71/5.07 => ( ! [X4: extended_enat,F3: set_Extended_enat] :
% 4.71/5.07 ( ( finite4001608067531595151d_enat @ F3 )
% 4.71/5.07 => ( ~ ( member_Extended_enat @ X4 @ F3 )
% 4.71/5.07 => ( ( P @ F3 )
% 4.71/5.07 => ( P @ ( insert_Extended_enat @ X4 @ F3 ) ) ) ) )
% 4.71/5.07 => ( P @ F2 ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite_induct
% 4.71/5.07 thf(fact_3072_finite__induct,axiom,
% 4.71/5.07 ! [F2: set_real,P: set_real > $o] :
% 4.71/5.07 ( ( finite_finite_real @ F2 )
% 4.71/5.07 => ( ( P @ bot_bot_set_real )
% 4.71/5.07 => ( ! [X4: real,F3: set_real] :
% 4.71/5.07 ( ( finite_finite_real @ F3 )
% 4.71/5.07 => ( ~ ( member_real @ X4 @ F3 )
% 4.71/5.07 => ( ( P @ F3 )
% 4.71/5.07 => ( P @ ( insert_real @ X4 @ F3 ) ) ) ) )
% 4.71/5.07 => ( P @ F2 ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite_induct
% 4.71/5.07 thf(fact_3073_finite__induct,axiom,
% 4.71/5.07 ! [F2: set_o,P: set_o > $o] :
% 4.71/5.07 ( ( finite_finite_o @ F2 )
% 4.71/5.07 => ( ( P @ bot_bot_set_o )
% 4.71/5.07 => ( ! [X4: $o,F3: set_o] :
% 4.71/5.07 ( ( finite_finite_o @ F3 )
% 4.71/5.07 => ( ~ ( member_o @ X4 @ F3 )
% 4.71/5.07 => ( ( P @ F3 )
% 4.71/5.07 => ( P @ ( insert_o @ X4 @ F3 ) ) ) ) )
% 4.71/5.07 => ( P @ F2 ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite_induct
% 4.71/5.07 thf(fact_3074_finite__induct,axiom,
% 4.71/5.07 ! [F2: set_nat,P: set_nat > $o] :
% 4.71/5.07 ( ( finite_finite_nat @ F2 )
% 4.71/5.07 => ( ( P @ bot_bot_set_nat )
% 4.71/5.07 => ( ! [X4: nat,F3: set_nat] :
% 4.71/5.07 ( ( finite_finite_nat @ F3 )
% 4.71/5.07 => ( ~ ( member_nat @ X4 @ F3 )
% 4.71/5.07 => ( ( P @ F3 )
% 4.71/5.07 => ( P @ ( insert_nat @ X4 @ F3 ) ) ) ) )
% 4.71/5.07 => ( P @ F2 ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite_induct
% 4.71/5.07 thf(fact_3075_finite__induct,axiom,
% 4.71/5.07 ! [F2: set_int,P: set_int > $o] :
% 4.71/5.07 ( ( finite_finite_int @ F2 )
% 4.71/5.07 => ( ( P @ bot_bot_set_int )
% 4.71/5.07 => ( ! [X4: int,F3: set_int] :
% 4.71/5.07 ( ( finite_finite_int @ F3 )
% 4.71/5.07 => ( ~ ( member_int @ X4 @ F3 )
% 4.71/5.07 => ( ( P @ F3 )
% 4.71/5.07 => ( P @ ( insert_int @ X4 @ F3 ) ) ) ) )
% 4.71/5.07 => ( P @ F2 ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite_induct
% 4.71/5.07 thf(fact_3076_finite_Osimps,axiom,
% 4.71/5.07 ( finite3207457112153483333omplex
% 4.71/5.07 = ( ^ [A4: set_complex] :
% 4.71/5.07 ( ( A4 = bot_bot_set_complex )
% 4.71/5.07 | ? [A6: set_complex,B4: complex] :
% 4.71/5.07 ( ( A4
% 4.71/5.07 = ( insert_complex @ B4 @ A6 ) )
% 4.71/5.07 & ( finite3207457112153483333omplex @ A6 ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite.simps
% 4.71/5.07 thf(fact_3077_finite_Osimps,axiom,
% 4.71/5.07 ( finite6177210948735845034at_nat
% 4.71/5.07 = ( ^ [A4: set_Pr1261947904930325089at_nat] :
% 4.71/5.07 ( ( A4 = bot_bo2099793752762293965at_nat )
% 4.71/5.07 | ? [A6: set_Pr1261947904930325089at_nat,B4: product_prod_nat_nat] :
% 4.71/5.07 ( ( A4
% 4.71/5.07 = ( insert8211810215607154385at_nat @ B4 @ A6 ) )
% 4.71/5.07 & ( finite6177210948735845034at_nat @ A6 ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite.simps
% 4.71/5.07 thf(fact_3078_finite_Osimps,axiom,
% 4.71/5.07 ( finite4001608067531595151d_enat
% 4.71/5.07 = ( ^ [A4: set_Extended_enat] :
% 4.71/5.07 ( ( A4 = bot_bo7653980558646680370d_enat )
% 4.71/5.07 | ? [A6: set_Extended_enat,B4: extended_enat] :
% 4.71/5.07 ( ( A4
% 4.71/5.07 = ( insert_Extended_enat @ B4 @ A6 ) )
% 4.71/5.07 & ( finite4001608067531595151d_enat @ A6 ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite.simps
% 4.71/5.07 thf(fact_3079_finite_Osimps,axiom,
% 4.71/5.07 ( finite_finite_real
% 4.71/5.07 = ( ^ [A4: set_real] :
% 4.71/5.07 ( ( A4 = bot_bot_set_real )
% 4.71/5.07 | ? [A6: set_real,B4: real] :
% 4.71/5.07 ( ( A4
% 4.71/5.07 = ( insert_real @ B4 @ A6 ) )
% 4.71/5.07 & ( finite_finite_real @ A6 ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite.simps
% 4.71/5.07 thf(fact_3080_finite_Osimps,axiom,
% 4.71/5.07 ( finite_finite_o
% 4.71/5.07 = ( ^ [A4: set_o] :
% 4.71/5.07 ( ( A4 = bot_bot_set_o )
% 4.71/5.07 | ? [A6: set_o,B4: $o] :
% 4.71/5.07 ( ( A4
% 4.71/5.07 = ( insert_o @ B4 @ A6 ) )
% 4.71/5.07 & ( finite_finite_o @ A6 ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite.simps
% 4.71/5.07 thf(fact_3081_finite_Osimps,axiom,
% 4.71/5.07 ( finite_finite_nat
% 4.71/5.07 = ( ^ [A4: set_nat] :
% 4.71/5.07 ( ( A4 = bot_bot_set_nat )
% 4.71/5.07 | ? [A6: set_nat,B4: nat] :
% 4.71/5.07 ( ( A4
% 4.71/5.07 = ( insert_nat @ B4 @ A6 ) )
% 4.71/5.07 & ( finite_finite_nat @ A6 ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite.simps
% 4.71/5.07 thf(fact_3082_finite_Osimps,axiom,
% 4.71/5.07 ( finite_finite_int
% 4.71/5.07 = ( ^ [A4: set_int] :
% 4.71/5.07 ( ( A4 = bot_bot_set_int )
% 4.71/5.07 | ? [A6: set_int,B4: int] :
% 4.71/5.07 ( ( A4
% 4.71/5.07 = ( insert_int @ B4 @ A6 ) )
% 4.71/5.07 & ( finite_finite_int @ A6 ) ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite.simps
% 4.71/5.07 thf(fact_3083_finite_Ocases,axiom,
% 4.71/5.07 ! [A: set_complex] :
% 4.71/5.07 ( ( finite3207457112153483333omplex @ A )
% 4.71/5.07 => ( ( A != bot_bot_set_complex )
% 4.71/5.07 => ~ ! [A3: set_complex] :
% 4.71/5.07 ( ? [A5: complex] :
% 4.71/5.07 ( A
% 4.71/5.07 = ( insert_complex @ A5 @ A3 ) )
% 4.71/5.07 => ~ ( finite3207457112153483333omplex @ A3 ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite.cases
% 4.71/5.07 thf(fact_3084_finite_Ocases,axiom,
% 4.71/5.07 ! [A: set_Pr1261947904930325089at_nat] :
% 4.71/5.07 ( ( finite6177210948735845034at_nat @ A )
% 4.71/5.07 => ( ( A != bot_bo2099793752762293965at_nat )
% 4.71/5.07 => ~ ! [A3: set_Pr1261947904930325089at_nat] :
% 4.71/5.07 ( ? [A5: product_prod_nat_nat] :
% 4.71/5.07 ( A
% 4.71/5.07 = ( insert8211810215607154385at_nat @ A5 @ A3 ) )
% 4.71/5.07 => ~ ( finite6177210948735845034at_nat @ A3 ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite.cases
% 4.71/5.07 thf(fact_3085_finite_Ocases,axiom,
% 4.71/5.07 ! [A: set_Extended_enat] :
% 4.71/5.07 ( ( finite4001608067531595151d_enat @ A )
% 4.71/5.07 => ( ( A != bot_bo7653980558646680370d_enat )
% 4.71/5.07 => ~ ! [A3: set_Extended_enat] :
% 4.71/5.07 ( ? [A5: extended_enat] :
% 4.71/5.07 ( A
% 4.71/5.07 = ( insert_Extended_enat @ A5 @ A3 ) )
% 4.71/5.07 => ~ ( finite4001608067531595151d_enat @ A3 ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite.cases
% 4.71/5.07 thf(fact_3086_finite_Ocases,axiom,
% 4.71/5.07 ! [A: set_real] :
% 4.71/5.07 ( ( finite_finite_real @ A )
% 4.71/5.07 => ( ( A != bot_bot_set_real )
% 4.71/5.07 => ~ ! [A3: set_real] :
% 4.71/5.07 ( ? [A5: real] :
% 4.71/5.07 ( A
% 4.71/5.07 = ( insert_real @ A5 @ A3 ) )
% 4.71/5.07 => ~ ( finite_finite_real @ A3 ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite.cases
% 4.71/5.07 thf(fact_3087_finite_Ocases,axiom,
% 4.71/5.07 ! [A: set_o] :
% 4.71/5.07 ( ( finite_finite_o @ A )
% 4.71/5.07 => ( ( A != bot_bot_set_o )
% 4.71/5.07 => ~ ! [A3: set_o] :
% 4.71/5.07 ( ? [A5: $o] :
% 4.71/5.07 ( A
% 4.71/5.07 = ( insert_o @ A5 @ A3 ) )
% 4.71/5.07 => ~ ( finite_finite_o @ A3 ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite.cases
% 4.71/5.07 thf(fact_3088_finite_Ocases,axiom,
% 4.71/5.07 ! [A: set_nat] :
% 4.71/5.07 ( ( finite_finite_nat @ A )
% 4.71/5.07 => ( ( A != bot_bot_set_nat )
% 4.71/5.07 => ~ ! [A3: set_nat] :
% 4.71/5.07 ( ? [A5: nat] :
% 4.71/5.07 ( A
% 4.71/5.07 = ( insert_nat @ A5 @ A3 ) )
% 4.71/5.07 => ~ ( finite_finite_nat @ A3 ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite.cases
% 4.71/5.07 thf(fact_3089_finite_Ocases,axiom,
% 4.71/5.07 ! [A: set_int] :
% 4.71/5.07 ( ( finite_finite_int @ A )
% 4.71/5.07 => ( ( A != bot_bot_set_int )
% 4.71/5.07 => ~ ! [A3: set_int] :
% 4.71/5.07 ( ? [A5: int] :
% 4.71/5.07 ( A
% 4.71/5.07 = ( insert_int @ A5 @ A3 ) )
% 4.71/5.07 => ~ ( finite_finite_int @ A3 ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % finite.cases
% 4.71/5.07 thf(fact_3090_subset__singleton__iff,axiom,
% 4.71/5.07 ! [X5: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat] :
% 4.71/5.07 ( ( ord_le3146513528884898305at_nat @ X5 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) )
% 4.71/5.07 = ( ( X5 = bot_bo2099793752762293965at_nat )
% 4.71/5.07 | ( X5
% 4.71/5.07 = ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 4.71/5.07
% 4.71/5.07 % subset_singleton_iff
% 4.71/5.07 thf(fact_3091_subset__singleton__iff,axiom,
% 4.71/5.08 ! [X5: set_real,A: real] :
% 4.71/5.08 ( ( ord_less_eq_set_real @ X5 @ ( insert_real @ A @ bot_bot_set_real ) )
% 4.71/5.08 = ( ( X5 = bot_bot_set_real )
% 4.71/5.08 | ( X5
% 4.71/5.08 = ( insert_real @ A @ bot_bot_set_real ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % subset_singleton_iff
% 4.71/5.08 thf(fact_3092_subset__singleton__iff,axiom,
% 4.71/5.08 ! [X5: set_o,A: $o] :
% 4.71/5.08 ( ( ord_less_eq_set_o @ X5 @ ( insert_o @ A @ bot_bot_set_o ) )
% 4.71/5.08 = ( ( X5 = bot_bot_set_o )
% 4.71/5.08 | ( X5
% 4.71/5.08 = ( insert_o @ A @ bot_bot_set_o ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % subset_singleton_iff
% 4.71/5.08 thf(fact_3093_subset__singleton__iff,axiom,
% 4.71/5.08 ! [X5: set_nat,A: nat] :
% 4.71/5.08 ( ( ord_less_eq_set_nat @ X5 @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 4.71/5.08 = ( ( X5 = bot_bot_set_nat )
% 4.71/5.08 | ( X5
% 4.71/5.08 = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % subset_singleton_iff
% 4.71/5.08 thf(fact_3094_subset__singleton__iff,axiom,
% 4.71/5.08 ! [X5: set_int,A: int] :
% 4.71/5.08 ( ( ord_less_eq_set_int @ X5 @ ( insert_int @ A @ bot_bot_set_int ) )
% 4.71/5.08 = ( ( X5 = bot_bot_set_int )
% 4.71/5.08 | ( X5
% 4.71/5.08 = ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % subset_singleton_iff
% 4.71/5.08 thf(fact_3095_subset__singletonD,axiom,
% 4.71/5.08 ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 4.71/5.08 ( ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 4.71/5.08 => ( ( A2 = bot_bo2099793752762293965at_nat )
% 4.71/5.08 | ( A2
% 4.71/5.08 = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % subset_singletonD
% 4.71/5.08 thf(fact_3096_subset__singletonD,axiom,
% 4.71/5.08 ! [A2: set_real,X: real] :
% 4.71/5.08 ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) )
% 4.71/5.08 => ( ( A2 = bot_bot_set_real )
% 4.71/5.08 | ( A2
% 4.71/5.08 = ( insert_real @ X @ bot_bot_set_real ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % subset_singletonD
% 4.71/5.08 thf(fact_3097_subset__singletonD,axiom,
% 4.71/5.08 ! [A2: set_o,X: $o] :
% 4.71/5.08 ( ( ord_less_eq_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.71/5.08 => ( ( A2 = bot_bot_set_o )
% 4.71/5.08 | ( A2
% 4.71/5.08 = ( insert_o @ X @ bot_bot_set_o ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % subset_singletonD
% 4.71/5.08 thf(fact_3098_subset__singletonD,axiom,
% 4.71/5.08 ! [A2: set_nat,X: nat] :
% 4.71/5.08 ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.71/5.08 => ( ( A2 = bot_bot_set_nat )
% 4.71/5.08 | ( A2
% 4.71/5.08 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % subset_singletonD
% 4.71/5.08 thf(fact_3099_subset__singletonD,axiom,
% 4.71/5.08 ! [A2: set_int,X: int] :
% 4.71/5.08 ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) )
% 4.71/5.08 => ( ( A2 = bot_bot_set_int )
% 4.71/5.08 | ( A2
% 4.71/5.08 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % subset_singletonD
% 4.71/5.08 thf(fact_3100_less__1__mult,axiom,
% 4.71/5.08 ! [M2: real,N: real] :
% 4.71/5.08 ( ( ord_less_real @ one_one_real @ M2 )
% 4.71/5.08 => ( ( ord_less_real @ one_one_real @ N )
% 4.71/5.08 => ( ord_less_real @ one_one_real @ ( times_times_real @ M2 @ N ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % less_1_mult
% 4.71/5.08 thf(fact_3101_less__1__mult,axiom,
% 4.71/5.08 ! [M2: rat,N: rat] :
% 4.71/5.08 ( ( ord_less_rat @ one_one_rat @ M2 )
% 4.71/5.08 => ( ( ord_less_rat @ one_one_rat @ N )
% 4.71/5.08 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M2 @ N ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % less_1_mult
% 4.71/5.08 thf(fact_3102_less__1__mult,axiom,
% 4.71/5.08 ! [M2: nat,N: nat] :
% 4.71/5.08 ( ( ord_less_nat @ one_one_nat @ M2 )
% 4.71/5.08 => ( ( ord_less_nat @ one_one_nat @ N )
% 4.71/5.08 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M2 @ N ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % less_1_mult
% 4.71/5.08 thf(fact_3103_less__1__mult,axiom,
% 4.71/5.08 ! [M2: int,N: int] :
% 4.71/5.08 ( ( ord_less_int @ one_one_int @ M2 )
% 4.71/5.08 => ( ( ord_less_int @ one_one_int @ N )
% 4.71/5.08 => ( ord_less_int @ one_one_int @ ( times_times_int @ M2 @ N ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % less_1_mult
% 4.71/5.08 thf(fact_3104_frac__eq__eq,axiom,
% 4.71/5.08 ! [Y: rat,Z: rat,X: rat,W2: rat] :
% 4.71/5.08 ( ( Y != zero_zero_rat )
% 4.71/5.08 => ( ( Z != zero_zero_rat )
% 4.71/5.08 => ( ( ( divide_divide_rat @ X @ Y )
% 4.71/5.08 = ( divide_divide_rat @ W2 @ Z ) )
% 4.71/5.08 = ( ( times_times_rat @ X @ Z )
% 4.71/5.08 = ( times_times_rat @ W2 @ Y ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % frac_eq_eq
% 4.71/5.08 thf(fact_3105_frac__eq__eq,axiom,
% 4.71/5.08 ! [Y: real,Z: real,X: real,W2: real] :
% 4.71/5.08 ( ( Y != zero_zero_real )
% 4.71/5.08 => ( ( Z != zero_zero_real )
% 4.71/5.08 => ( ( ( divide_divide_real @ X @ Y )
% 4.71/5.08 = ( divide_divide_real @ W2 @ Z ) )
% 4.71/5.08 = ( ( times_times_real @ X @ Z )
% 4.71/5.08 = ( times_times_real @ W2 @ Y ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % frac_eq_eq
% 4.71/5.08 thf(fact_3106_divide__eq__eq,axiom,
% 4.71/5.08 ! [B: rat,C: rat,A: rat] :
% 4.71/5.08 ( ( ( divide_divide_rat @ B @ C )
% 4.71/5.08 = A )
% 4.71/5.08 = ( ( ( C != zero_zero_rat )
% 4.71/5.08 => ( B
% 4.71/5.08 = ( times_times_rat @ A @ C ) ) )
% 4.71/5.08 & ( ( C = zero_zero_rat )
% 4.71/5.08 => ( A = zero_zero_rat ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % divide_eq_eq
% 4.71/5.08 thf(fact_3107_divide__eq__eq,axiom,
% 4.71/5.08 ! [B: real,C: real,A: real] :
% 4.71/5.08 ( ( ( divide_divide_real @ B @ C )
% 4.71/5.08 = A )
% 4.71/5.08 = ( ( ( C != zero_zero_real )
% 4.71/5.08 => ( B
% 4.71/5.08 = ( times_times_real @ A @ C ) ) )
% 4.71/5.08 & ( ( C = zero_zero_real )
% 4.71/5.08 => ( A = zero_zero_real ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % divide_eq_eq
% 4.71/5.08 thf(fact_3108_eq__divide__eq,axiom,
% 4.71/5.08 ! [A: rat,B: rat,C: rat] :
% 4.71/5.08 ( ( A
% 4.71/5.08 = ( divide_divide_rat @ B @ C ) )
% 4.71/5.08 = ( ( ( C != zero_zero_rat )
% 4.71/5.08 => ( ( times_times_rat @ A @ C )
% 4.71/5.08 = B ) )
% 4.71/5.08 & ( ( C = zero_zero_rat )
% 4.71/5.08 => ( A = zero_zero_rat ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % eq_divide_eq
% 4.71/5.08 thf(fact_3109_eq__divide__eq,axiom,
% 4.71/5.08 ! [A: real,B: real,C: real] :
% 4.71/5.08 ( ( A
% 4.71/5.08 = ( divide_divide_real @ B @ C ) )
% 4.71/5.08 = ( ( ( C != zero_zero_real )
% 4.71/5.08 => ( ( times_times_real @ A @ C )
% 4.71/5.08 = B ) )
% 4.71/5.08 & ( ( C = zero_zero_real )
% 4.71/5.08 => ( A = zero_zero_real ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % eq_divide_eq
% 4.71/5.08 thf(fact_3110_divide__eq__imp,axiom,
% 4.71/5.08 ! [C: rat,B: rat,A: rat] :
% 4.71/5.08 ( ( C != zero_zero_rat )
% 4.71/5.08 => ( ( B
% 4.71/5.08 = ( times_times_rat @ A @ C ) )
% 4.71/5.08 => ( ( divide_divide_rat @ B @ C )
% 4.71/5.08 = A ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % divide_eq_imp
% 4.71/5.08 thf(fact_3111_divide__eq__imp,axiom,
% 4.71/5.08 ! [C: real,B: real,A: real] :
% 4.71/5.08 ( ( C != zero_zero_real )
% 4.71/5.08 => ( ( B
% 4.71/5.08 = ( times_times_real @ A @ C ) )
% 4.71/5.08 => ( ( divide_divide_real @ B @ C )
% 4.71/5.08 = A ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % divide_eq_imp
% 4.71/5.08 thf(fact_3112_eq__divide__imp,axiom,
% 4.71/5.08 ! [C: rat,A: rat,B: rat] :
% 4.71/5.08 ( ( C != zero_zero_rat )
% 4.71/5.08 => ( ( ( times_times_rat @ A @ C )
% 4.71/5.08 = B )
% 4.71/5.08 => ( A
% 4.71/5.08 = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % eq_divide_imp
% 4.71/5.08 thf(fact_3113_eq__divide__imp,axiom,
% 4.71/5.08 ! [C: real,A: real,B: real] :
% 4.71/5.08 ( ( C != zero_zero_real )
% 4.71/5.08 => ( ( ( times_times_real @ A @ C )
% 4.71/5.08 = B )
% 4.71/5.08 => ( A
% 4.71/5.08 = ( divide_divide_real @ B @ C ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % eq_divide_imp
% 4.71/5.08 thf(fact_3114_nonzero__divide__eq__eq,axiom,
% 4.71/5.08 ! [C: rat,B: rat,A: rat] :
% 4.71/5.08 ( ( C != zero_zero_rat )
% 4.71/5.08 => ( ( ( divide_divide_rat @ B @ C )
% 4.71/5.08 = A )
% 4.71/5.08 = ( B
% 4.71/5.08 = ( times_times_rat @ A @ C ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % nonzero_divide_eq_eq
% 4.71/5.08 thf(fact_3115_nonzero__divide__eq__eq,axiom,
% 4.71/5.08 ! [C: real,B: real,A: real] :
% 4.71/5.08 ( ( C != zero_zero_real )
% 4.71/5.08 => ( ( ( divide_divide_real @ B @ C )
% 4.71/5.08 = A )
% 4.71/5.08 = ( B
% 4.71/5.08 = ( times_times_real @ A @ C ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % nonzero_divide_eq_eq
% 4.71/5.08 thf(fact_3116_nonzero__eq__divide__eq,axiom,
% 4.71/5.08 ! [C: rat,A: rat,B: rat] :
% 4.71/5.08 ( ( C != zero_zero_rat )
% 4.71/5.08 => ( ( A
% 4.71/5.08 = ( divide_divide_rat @ B @ C ) )
% 4.71/5.08 = ( ( times_times_rat @ A @ C )
% 4.71/5.08 = B ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % nonzero_eq_divide_eq
% 4.71/5.08 thf(fact_3117_nonzero__eq__divide__eq,axiom,
% 4.71/5.08 ! [C: real,A: real,B: real] :
% 4.71/5.08 ( ( C != zero_zero_real )
% 4.71/5.08 => ( ( A
% 4.71/5.08 = ( divide_divide_real @ B @ C ) )
% 4.71/5.08 = ( ( times_times_real @ A @ C )
% 4.71/5.08 = B ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % nonzero_eq_divide_eq
% 4.71/5.08 thf(fact_3118_Diff__insert__absorb,axiom,
% 4.71/5.08 ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.08 ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 4.71/5.08 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 4.71/5.08 = A2 ) ) ).
% 4.71/5.08
% 4.71/5.08 % Diff_insert_absorb
% 4.71/5.08 thf(fact_3119_Diff__insert__absorb,axiom,
% 4.71/5.08 ! [X: set_nat,A2: set_set_nat] :
% 4.71/5.08 ( ~ ( member_set_nat @ X @ A2 )
% 4.71/5.08 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A2 ) @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 4.71/5.08 = A2 ) ) ).
% 4.71/5.08
% 4.71/5.08 % Diff_insert_absorb
% 4.71/5.08 thf(fact_3120_Diff__insert__absorb,axiom,
% 4.71/5.08 ! [X: set_nat_rat,A2: set_set_nat_rat] :
% 4.71/5.08 ( ~ ( member_set_nat_rat @ X @ A2 )
% 4.71/5.08 => ( ( minus_1626877696091177228at_rat @ ( insert_set_nat_rat @ X @ A2 ) @ ( insert_set_nat_rat @ X @ bot_bo6797373522285170759at_rat ) )
% 4.71/5.08 = A2 ) ) ).
% 4.71/5.08
% 4.71/5.08 % Diff_insert_absorb
% 4.71/5.08 thf(fact_3121_Diff__insert__absorb,axiom,
% 4.71/5.08 ! [X: real,A2: set_real] :
% 4.71/5.08 ( ~ ( member_real @ X @ A2 )
% 4.71/5.08 => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ ( insert_real @ X @ bot_bot_set_real ) )
% 4.71/5.08 = A2 ) ) ).
% 4.71/5.08
% 4.71/5.08 % Diff_insert_absorb
% 4.71/5.08 thf(fact_3122_Diff__insert__absorb,axiom,
% 4.71/5.08 ! [X: $o,A2: set_o] :
% 4.71/5.08 ( ~ ( member_o @ X @ A2 )
% 4.71/5.08 => ( ( minus_minus_set_o @ ( insert_o @ X @ A2 ) @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.71/5.08 = A2 ) ) ).
% 4.71/5.08
% 4.71/5.08 % Diff_insert_absorb
% 4.71/5.08 thf(fact_3123_Diff__insert__absorb,axiom,
% 4.71/5.08 ! [X: int,A2: set_int] :
% 4.71/5.08 ( ~ ( member_int @ X @ A2 )
% 4.71/5.08 => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ ( insert_int @ X @ bot_bot_set_int ) )
% 4.71/5.08 = A2 ) ) ).
% 4.71/5.08
% 4.71/5.08 % Diff_insert_absorb
% 4.71/5.08 thf(fact_3124_Diff__insert__absorb,axiom,
% 4.71/5.08 ! [X: nat,A2: set_nat] :
% 4.71/5.08 ( ~ ( member_nat @ X @ A2 )
% 4.71/5.08 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.71/5.08 = A2 ) ) ).
% 4.71/5.08
% 4.71/5.08 % Diff_insert_absorb
% 4.71/5.08 thf(fact_3125_Diff__insert2,axiom,
% 4.71/5.08 ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 4.71/5.08 ( ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B2 ) )
% 4.71/5.08 = ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) @ B2 ) ) ).
% 4.71/5.08
% 4.71/5.08 % Diff_insert2
% 4.71/5.08 thf(fact_3126_Diff__insert2,axiom,
% 4.71/5.08 ! [A2: set_real,A: real,B2: set_real] :
% 4.71/5.08 ( ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B2 ) )
% 4.71/5.08 = ( minus_minus_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) @ B2 ) ) ).
% 4.71/5.08
% 4.71/5.08 % Diff_insert2
% 4.71/5.08 thf(fact_3127_Diff__insert2,axiom,
% 4.71/5.08 ! [A2: set_o,A: $o,B2: set_o] :
% 4.71/5.08 ( ( minus_minus_set_o @ A2 @ ( insert_o @ A @ B2 ) )
% 4.71/5.08 = ( minus_minus_set_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) @ B2 ) ) ).
% 4.71/5.08
% 4.71/5.08 % Diff_insert2
% 4.71/5.08 thf(fact_3128_Diff__insert2,axiom,
% 4.71/5.08 ! [A2: set_int,A: int,B2: set_int] :
% 4.71/5.08 ( ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B2 ) )
% 4.71/5.08 = ( minus_minus_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) @ B2 ) ) ).
% 4.71/5.08
% 4.71/5.08 % Diff_insert2
% 4.71/5.08 thf(fact_3129_Diff__insert2,axiom,
% 4.71/5.08 ! [A2: set_nat,A: nat,B2: set_nat] :
% 4.71/5.08 ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B2 ) )
% 4.71/5.08 = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) @ B2 ) ) ).
% 4.71/5.08
% 4.71/5.08 % Diff_insert2
% 4.71/5.08 thf(fact_3130_insert__Diff,axiom,
% 4.71/5.08 ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.08 ( ( member8440522571783428010at_nat @ A @ A2 )
% 4.71/5.08 => ( ( insert8211810215607154385at_nat @ A @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 4.71/5.08 = A2 ) ) ).
% 4.71/5.08
% 4.71/5.08 % insert_Diff
% 4.71/5.08 thf(fact_3131_insert__Diff,axiom,
% 4.71/5.08 ! [A: set_nat,A2: set_set_nat] :
% 4.71/5.08 ( ( member_set_nat @ A @ A2 )
% 4.71/5.08 => ( ( insert_set_nat @ A @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 4.71/5.08 = A2 ) ) ).
% 4.71/5.08
% 4.71/5.08 % insert_Diff
% 4.71/5.08 thf(fact_3132_insert__Diff,axiom,
% 4.71/5.08 ! [A: set_nat_rat,A2: set_set_nat_rat] :
% 4.71/5.08 ( ( member_set_nat_rat @ A @ A2 )
% 4.71/5.08 => ( ( insert_set_nat_rat @ A @ ( minus_1626877696091177228at_rat @ A2 @ ( insert_set_nat_rat @ A @ bot_bo6797373522285170759at_rat ) ) )
% 4.71/5.08 = A2 ) ) ).
% 4.71/5.08
% 4.71/5.08 % insert_Diff
% 4.71/5.08 thf(fact_3133_insert__Diff,axiom,
% 4.71/5.08 ! [A: real,A2: set_real] :
% 4.71/5.08 ( ( member_real @ A @ A2 )
% 4.71/5.08 => ( ( insert_real @ A @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 4.71/5.08 = A2 ) ) ).
% 4.71/5.08
% 4.71/5.08 % insert_Diff
% 4.71/5.08 thf(fact_3134_insert__Diff,axiom,
% 4.71/5.08 ! [A: $o,A2: set_o] :
% 4.71/5.08 ( ( member_o @ A @ A2 )
% 4.71/5.08 => ( ( insert_o @ A @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 4.71/5.08 = A2 ) ) ).
% 4.71/5.08
% 4.71/5.08 % insert_Diff
% 4.71/5.08 thf(fact_3135_insert__Diff,axiom,
% 4.71/5.08 ! [A: int,A2: set_int] :
% 4.71/5.08 ( ( member_int @ A @ A2 )
% 4.71/5.08 => ( ( insert_int @ A @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 4.71/5.08 = A2 ) ) ).
% 4.71/5.08
% 4.71/5.08 % insert_Diff
% 4.71/5.08 thf(fact_3136_insert__Diff,axiom,
% 4.71/5.08 ! [A: nat,A2: set_nat] :
% 4.71/5.08 ( ( member_nat @ A @ A2 )
% 4.71/5.08 => ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 4.71/5.08 = A2 ) ) ).
% 4.71/5.08
% 4.71/5.08 % insert_Diff
% 4.71/5.08 thf(fact_3137_Diff__insert,axiom,
% 4.71/5.08 ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 4.71/5.08 ( ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B2 ) )
% 4.71/5.08 = ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % Diff_insert
% 4.71/5.08 thf(fact_3138_Diff__insert,axiom,
% 4.71/5.08 ! [A2: set_real,A: real,B2: set_real] :
% 4.71/5.08 ( ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B2 ) )
% 4.71/5.08 = ( minus_minus_set_real @ ( minus_minus_set_real @ A2 @ B2 ) @ ( insert_real @ A @ bot_bot_set_real ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % Diff_insert
% 4.71/5.08 thf(fact_3139_Diff__insert,axiom,
% 4.71/5.08 ! [A2: set_o,A: $o,B2: set_o] :
% 4.71/5.08 ( ( minus_minus_set_o @ A2 @ ( insert_o @ A @ B2 ) )
% 4.71/5.08 = ( minus_minus_set_o @ ( minus_minus_set_o @ A2 @ B2 ) @ ( insert_o @ A @ bot_bot_set_o ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % Diff_insert
% 4.71/5.08 thf(fact_3140_Diff__insert,axiom,
% 4.71/5.08 ! [A2: set_int,A: int,B2: set_int] :
% 4.71/5.08 ( ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B2 ) )
% 4.71/5.08 = ( minus_minus_set_int @ ( minus_minus_set_int @ A2 @ B2 ) @ ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % Diff_insert
% 4.71/5.08 thf(fact_3141_Diff__insert,axiom,
% 4.71/5.08 ! [A2: set_nat,A: nat,B2: set_nat] :
% 4.71/5.08 ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B2 ) )
% 4.71/5.08 = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % Diff_insert
% 4.71/5.08 thf(fact_3142_subset__Diff__insert,axiom,
% 4.71/5.08 ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,C2: set_Pr1261947904930325089at_nat] :
% 4.71/5.08 ( ( ord_le3146513528884898305at_nat @ A2 @ ( minus_1356011639430497352at_nat @ B2 @ ( insert8211810215607154385at_nat @ X @ C2 ) ) )
% 4.71/5.08 = ( ( ord_le3146513528884898305at_nat @ A2 @ ( minus_1356011639430497352at_nat @ B2 @ C2 ) )
% 4.71/5.08 & ~ ( member8440522571783428010at_nat @ X @ A2 ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % subset_Diff_insert
% 4.71/5.08 thf(fact_3143_subset__Diff__insert,axiom,
% 4.71/5.08 ! [A2: set_real,B2: set_real,X: real,C2: set_real] :
% 4.71/5.08 ( ( ord_less_eq_set_real @ A2 @ ( minus_minus_set_real @ B2 @ ( insert_real @ X @ C2 ) ) )
% 4.71/5.08 = ( ( ord_less_eq_set_real @ A2 @ ( minus_minus_set_real @ B2 @ C2 ) )
% 4.71/5.08 & ~ ( member_real @ X @ A2 ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % subset_Diff_insert
% 4.71/5.08 thf(fact_3144_subset__Diff__insert,axiom,
% 4.71/5.08 ! [A2: set_o,B2: set_o,X: $o,C2: set_o] :
% 4.71/5.08 ( ( ord_less_eq_set_o @ A2 @ ( minus_minus_set_o @ B2 @ ( insert_o @ X @ C2 ) ) )
% 4.71/5.08 = ( ( ord_less_eq_set_o @ A2 @ ( minus_minus_set_o @ B2 @ C2 ) )
% 4.71/5.08 & ~ ( member_o @ X @ A2 ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % subset_Diff_insert
% 4.71/5.08 thf(fact_3145_subset__Diff__insert,axiom,
% 4.71/5.08 ! [A2: set_set_nat,B2: set_set_nat,X: set_nat,C2: set_set_nat] :
% 4.71/5.08 ( ( ord_le6893508408891458716et_nat @ A2 @ ( minus_2163939370556025621et_nat @ B2 @ ( insert_set_nat @ X @ C2 ) ) )
% 4.71/5.08 = ( ( ord_le6893508408891458716et_nat @ A2 @ ( minus_2163939370556025621et_nat @ B2 @ C2 ) )
% 4.71/5.08 & ~ ( member_set_nat @ X @ A2 ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % subset_Diff_insert
% 4.71/5.08 thf(fact_3146_subset__Diff__insert,axiom,
% 4.71/5.08 ! [A2: set_set_nat_rat,B2: set_set_nat_rat,X: set_nat_rat,C2: set_set_nat_rat] :
% 4.71/5.08 ( ( ord_le4375437777232675859at_rat @ A2 @ ( minus_1626877696091177228at_rat @ B2 @ ( insert_set_nat_rat @ X @ C2 ) ) )
% 4.71/5.08 = ( ( ord_le4375437777232675859at_rat @ A2 @ ( minus_1626877696091177228at_rat @ B2 @ C2 ) )
% 4.71/5.08 & ~ ( member_set_nat_rat @ X @ A2 ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % subset_Diff_insert
% 4.71/5.08 thf(fact_3147_subset__Diff__insert,axiom,
% 4.71/5.08 ! [A2: set_nat,B2: set_nat,X: nat,C2: set_nat] :
% 4.71/5.08 ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B2 @ ( insert_nat @ X @ C2 ) ) )
% 4.71/5.08 = ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B2 @ C2 ) )
% 4.71/5.08 & ~ ( member_nat @ X @ A2 ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % subset_Diff_insert
% 4.71/5.08 thf(fact_3148_subset__Diff__insert,axiom,
% 4.71/5.08 ! [A2: set_int,B2: set_int,X: int,C2: set_int] :
% 4.71/5.08 ( ( ord_less_eq_set_int @ A2 @ ( minus_minus_set_int @ B2 @ ( insert_int @ X @ C2 ) ) )
% 4.71/5.08 = ( ( ord_less_eq_set_int @ A2 @ ( minus_minus_set_int @ B2 @ C2 ) )
% 4.71/5.08 & ~ ( member_int @ X @ A2 ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % subset_Diff_insert
% 4.71/5.08 thf(fact_3149_card__insert__le,axiom,
% 4.71/5.08 ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] : ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ A2 ) @ ( finite711546835091564841at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_insert_le
% 4.71/5.08 thf(fact_3150_card__insert__le,axiom,
% 4.71/5.08 ! [A2: set_real,X: real] : ( ord_less_eq_nat @ ( finite_card_real @ A2 ) @ ( finite_card_real @ ( insert_real @ X @ A2 ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_insert_le
% 4.71/5.08 thf(fact_3151_card__insert__le,axiom,
% 4.71/5.08 ! [A2: set_o,X: $o] : ( ord_less_eq_nat @ ( finite_card_o @ A2 ) @ ( finite_card_o @ ( insert_o @ X @ A2 ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_insert_le
% 4.71/5.08 thf(fact_3152_card__insert__le,axiom,
% 4.71/5.08 ! [A2: set_complex,X: complex] : ( ord_less_eq_nat @ ( finite_card_complex @ A2 ) @ ( finite_card_complex @ ( insert_complex @ X @ A2 ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_insert_le
% 4.71/5.08 thf(fact_3153_card__insert__le,axiom,
% 4.71/5.08 ! [A2: set_list_nat,X: list_nat] : ( ord_less_eq_nat @ ( finite_card_list_nat @ A2 ) @ ( finite_card_list_nat @ ( insert_list_nat @ X @ A2 ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_insert_le
% 4.71/5.08 thf(fact_3154_card__insert__le,axiom,
% 4.71/5.08 ! [A2: set_set_nat,X: set_nat] : ( ord_less_eq_nat @ ( finite_card_set_nat @ A2 ) @ ( finite_card_set_nat @ ( insert_set_nat @ X @ A2 ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_insert_le
% 4.71/5.08 thf(fact_3155_card__insert__le,axiom,
% 4.71/5.08 ! [A2: set_nat,X: nat] : ( ord_less_eq_nat @ ( finite_card_nat @ A2 ) @ ( finite_card_nat @ ( insert_nat @ X @ A2 ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_insert_le
% 4.71/5.08 thf(fact_3156_card__insert__le,axiom,
% 4.71/5.08 ! [A2: set_int,X: int] : ( ord_less_eq_nat @ ( finite_card_int @ A2 ) @ ( finite_card_int @ ( insert_int @ X @ A2 ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_insert_le
% 4.71/5.08 thf(fact_3157_Suc__mult__less__cancel1,axiom,
% 4.71/5.08 ! [K: nat,M2: nat,N: nat] :
% 4.71/5.08 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M2 ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 4.71/5.08 = ( ord_less_nat @ M2 @ N ) ) ).
% 4.71/5.08
% 4.71/5.08 % Suc_mult_less_cancel1
% 4.71/5.08 thf(fact_3158_mult__less__mono1,axiom,
% 4.71/5.08 ! [I: nat,J: nat,K: nat] :
% 4.71/5.08 ( ( ord_less_nat @ I @ J )
% 4.71/5.08 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.71/5.08 => ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_less_mono1
% 4.71/5.08 thf(fact_3159_mult__less__mono2,axiom,
% 4.71/5.08 ! [I: nat,J: nat,K: nat] :
% 4.71/5.08 ( ( ord_less_nat @ I @ J )
% 4.71/5.08 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.71/5.08 => ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_less_mono2
% 4.71/5.08 thf(fact_3160_Suc__mult__le__cancel1,axiom,
% 4.71/5.08 ! [K: nat,M2: nat,N: nat] :
% 4.71/5.08 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M2 ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 4.71/5.08 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 4.71/5.08
% 4.71/5.08 % Suc_mult_le_cancel1
% 4.71/5.08 thf(fact_3161_less__mult__imp__div__less,axiom,
% 4.71/5.08 ! [M2: nat,I: nat,N: nat] :
% 4.71/5.08 ( ( ord_less_nat @ M2 @ ( times_times_nat @ I @ N ) )
% 4.71/5.08 => ( ord_less_nat @ ( divide_divide_nat @ M2 @ N ) @ I ) ) ).
% 4.71/5.08
% 4.71/5.08 % less_mult_imp_div_less
% 4.71/5.08 thf(fact_3162_mult__eq__self__implies__10,axiom,
% 4.71/5.08 ! [M2: nat,N: nat] :
% 4.71/5.08 ( ( M2
% 4.71/5.08 = ( times_times_nat @ M2 @ N ) )
% 4.71/5.08 => ( ( N = one_one_nat )
% 4.71/5.08 | ( M2 = zero_zero_nat ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_eq_self_implies_10
% 4.71/5.08 thf(fact_3163_div__times__less__eq__dividend,axiom,
% 4.71/5.08 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M2 @ N ) @ N ) @ M2 ) ).
% 4.71/5.08
% 4.71/5.08 % div_times_less_eq_dividend
% 4.71/5.08 thf(fact_3164_times__div__less__eq__dividend,axiom,
% 4.71/5.08 ! [N: nat,M2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M2 @ N ) ) @ M2 ) ).
% 4.71/5.08
% 4.71/5.08 % times_div_less_eq_dividend
% 4.71/5.08 thf(fact_3165_int__ge__induct,axiom,
% 4.71/5.08 ! [K: int,I: int,P: int > $o] :
% 4.71/5.08 ( ( ord_less_eq_int @ K @ I )
% 4.71/5.08 => ( ( P @ K )
% 4.71/5.08 => ( ! [I2: int] :
% 4.71/5.08 ( ( ord_less_eq_int @ K @ I2 )
% 4.71/5.08 => ( ( P @ I2 )
% 4.71/5.08 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 4.71/5.08 => ( P @ I ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % int_ge_induct
% 4.71/5.08 thf(fact_3166_zle__iff__zadd,axiom,
% 4.71/5.08 ( ord_less_eq_int
% 4.71/5.08 = ( ^ [W3: int,Z2: int] :
% 4.71/5.08 ? [N4: nat] :
% 4.71/5.08 ( Z2
% 4.71/5.08 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ N4 ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % zle_iff_zadd
% 4.71/5.08 thf(fact_3167_frac__1__eq,axiom,
% 4.71/5.08 ! [X: real] :
% 4.71/5.08 ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X @ one_one_real ) )
% 4.71/5.08 = ( archim2898591450579166408c_real @ X ) ) ).
% 4.71/5.08
% 4.71/5.08 % frac_1_eq
% 4.71/5.08 thf(fact_3168_frac__1__eq,axiom,
% 4.71/5.08 ! [X: rat] :
% 4.71/5.08 ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ one_one_rat ) )
% 4.71/5.08 = ( archimedean_frac_rat @ X ) ) ).
% 4.71/5.08
% 4.71/5.08 % frac_1_eq
% 4.71/5.08 thf(fact_3169_dbl__inc__def,axiom,
% 4.71/5.08 ( neg_nu8557863876264182079omplex
% 4.71/5.08 = ( ^ [X3: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X3 @ X3 ) @ one_one_complex ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % dbl_inc_def
% 4.71/5.08 thf(fact_3170_dbl__inc__def,axiom,
% 4.71/5.08 ( neg_nu8295874005876285629c_real
% 4.71/5.08 = ( ^ [X3: real] : ( plus_plus_real @ ( plus_plus_real @ X3 @ X3 ) @ one_one_real ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % dbl_inc_def
% 4.71/5.08 thf(fact_3171_dbl__inc__def,axiom,
% 4.71/5.08 ( neg_nu5219082963157363817nc_rat
% 4.71/5.08 = ( ^ [X3: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X3 @ X3 ) @ one_one_rat ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % dbl_inc_def
% 4.71/5.08 thf(fact_3172_dbl__inc__def,axiom,
% 4.71/5.08 ( neg_nu5851722552734809277nc_int
% 4.71/5.08 = ( ^ [X3: int] : ( plus_plus_int @ ( plus_plus_int @ X3 @ X3 ) @ one_one_int ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % dbl_inc_def
% 4.71/5.08 thf(fact_3173_dense__eq0__I,axiom,
% 4.71/5.08 ! [X: real] :
% 4.71/5.08 ( ! [E: real] :
% 4.71/5.08 ( ( ord_less_real @ zero_zero_real @ E )
% 4.71/5.08 => ( ord_less_eq_real @ ( abs_abs_real @ X ) @ E ) )
% 4.71/5.08 => ( X = zero_zero_real ) ) ).
% 4.71/5.08
% 4.71/5.08 % dense_eq0_I
% 4.71/5.08 thf(fact_3174_dense__eq0__I,axiom,
% 4.71/5.08 ! [X: rat] :
% 4.71/5.08 ( ! [E: rat] :
% 4.71/5.08 ( ( ord_less_rat @ zero_zero_rat @ E )
% 4.71/5.08 => ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ E ) )
% 4.71/5.08 => ( X = zero_zero_rat ) ) ).
% 4.71/5.08
% 4.71/5.08 % dense_eq0_I
% 4.71/5.08 thf(fact_3175_abs__div__pos,axiom,
% 4.71/5.08 ! [Y: rat,X: rat] :
% 4.71/5.08 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 4.71/5.08 => ( ( divide_divide_rat @ ( abs_abs_rat @ X ) @ Y )
% 4.71/5.08 = ( abs_abs_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % abs_div_pos
% 4.71/5.08 thf(fact_3176_abs__div__pos,axiom,
% 4.71/5.08 ! [Y: real,X: real] :
% 4.71/5.08 ( ( ord_less_real @ zero_zero_real @ Y )
% 4.71/5.08 => ( ( divide_divide_real @ ( abs_abs_real @ X ) @ Y )
% 4.71/5.08 = ( abs_abs_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % abs_div_pos
% 4.71/5.08 thf(fact_3177_nat__mono__iff,axiom,
% 4.71/5.08 ! [Z: int,W2: int] :
% 4.71/5.08 ( ( ord_less_int @ zero_zero_int @ Z )
% 4.71/5.08 => ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z ) )
% 4.71/5.08 = ( ord_less_int @ W2 @ Z ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % nat_mono_iff
% 4.71/5.08 thf(fact_3178_zless__nat__eq__int__zless,axiom,
% 4.71/5.08 ! [M2: nat,Z: int] :
% 4.71/5.08 ( ( ord_less_nat @ M2 @ ( nat2 @ Z ) )
% 4.71/5.08 = ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ Z ) ) ).
% 4.71/5.08
% 4.71/5.08 % zless_nat_eq_int_zless
% 4.71/5.08 thf(fact_3179_field__le__epsilon,axiom,
% 4.71/5.08 ! [X: real,Y: real] :
% 4.71/5.08 ( ! [E: real] :
% 4.71/5.08 ( ( ord_less_real @ zero_zero_real @ E )
% 4.71/5.08 => ( ord_less_eq_real @ X @ ( plus_plus_real @ Y @ E ) ) )
% 4.71/5.08 => ( ord_less_eq_real @ X @ Y ) ) ).
% 4.71/5.08
% 4.71/5.08 % field_le_epsilon
% 4.71/5.08 thf(fact_3180_field__le__epsilon,axiom,
% 4.71/5.08 ! [X: rat,Y: rat] :
% 4.71/5.08 ( ! [E: rat] :
% 4.71/5.08 ( ( ord_less_rat @ zero_zero_rat @ E )
% 4.71/5.08 => ( ord_less_eq_rat @ X @ ( plus_plus_rat @ Y @ E ) ) )
% 4.71/5.08 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 4.71/5.08
% 4.71/5.08 % field_le_epsilon
% 4.71/5.08 thf(fact_3181_add__neg__nonpos,axiom,
% 4.71/5.08 ! [A: real,B: real] :
% 4.71/5.08 ( ( ord_less_real @ A @ zero_zero_real )
% 4.71/5.08 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 4.71/5.08 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % add_neg_nonpos
% 4.71/5.08 thf(fact_3182_add__neg__nonpos,axiom,
% 4.71/5.08 ! [A: rat,B: rat] :
% 4.71/5.08 ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.71/5.08 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 4.71/5.08 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % add_neg_nonpos
% 4.71/5.08 thf(fact_3183_add__neg__nonpos,axiom,
% 4.71/5.08 ! [A: nat,B: nat] :
% 4.71/5.08 ( ( ord_less_nat @ A @ zero_zero_nat )
% 4.71/5.08 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 4.71/5.08 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % add_neg_nonpos
% 4.71/5.08 thf(fact_3184_add__neg__nonpos,axiom,
% 4.71/5.08 ! [A: int,B: int] :
% 4.71/5.08 ( ( ord_less_int @ A @ zero_zero_int )
% 4.71/5.08 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 4.71/5.08 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % add_neg_nonpos
% 4.71/5.08 thf(fact_3185_add__nonneg__pos,axiom,
% 4.71/5.08 ! [A: real,B: real] :
% 4.71/5.08 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.08 => ( ( ord_less_real @ zero_zero_real @ B )
% 4.71/5.08 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % add_nonneg_pos
% 4.71/5.08 thf(fact_3186_add__nonneg__pos,axiom,
% 4.71/5.08 ! [A: rat,B: rat] :
% 4.71/5.08 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.08 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 4.71/5.08 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % add_nonneg_pos
% 4.71/5.08 thf(fact_3187_add__nonneg__pos,axiom,
% 4.71/5.08 ! [A: nat,B: nat] :
% 4.71/5.08 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.71/5.08 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.71/5.08 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % add_nonneg_pos
% 4.71/5.08 thf(fact_3188_add__nonneg__pos,axiom,
% 4.71/5.08 ! [A: int,B: int] :
% 4.71/5.08 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.08 => ( ( ord_less_int @ zero_zero_int @ B )
% 4.71/5.08 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % add_nonneg_pos
% 4.71/5.08 thf(fact_3189_add__nonpos__neg,axiom,
% 4.71/5.08 ! [A: real,B: real] :
% 4.71/5.08 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 4.71/5.08 => ( ( ord_less_real @ B @ zero_zero_real )
% 4.71/5.08 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % add_nonpos_neg
% 4.71/5.08 thf(fact_3190_add__nonpos__neg,axiom,
% 4.71/5.08 ! [A: rat,B: rat] :
% 4.71/5.08 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 4.71/5.08 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 4.71/5.08 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % add_nonpos_neg
% 4.71/5.08 thf(fact_3191_add__nonpos__neg,axiom,
% 4.71/5.08 ! [A: nat,B: nat] :
% 4.71/5.08 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 4.71/5.08 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 4.71/5.08 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % add_nonpos_neg
% 4.71/5.08 thf(fact_3192_add__nonpos__neg,axiom,
% 4.71/5.08 ! [A: int,B: int] :
% 4.71/5.08 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 4.71/5.08 => ( ( ord_less_int @ B @ zero_zero_int )
% 4.71/5.08 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % add_nonpos_neg
% 4.71/5.08 thf(fact_3193_add__pos__nonneg,axiom,
% 4.71/5.08 ! [A: real,B: real] :
% 4.71/5.08 ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.08 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.71/5.08 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % add_pos_nonneg
% 4.71/5.08 thf(fact_3194_add__pos__nonneg,axiom,
% 4.71/5.08 ! [A: rat,B: rat] :
% 4.71/5.08 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.08 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.71/5.08 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % add_pos_nonneg
% 4.71/5.08 thf(fact_3195_add__pos__nonneg,axiom,
% 4.71/5.08 ! [A: nat,B: nat] :
% 4.71/5.08 ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.71/5.08 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.71/5.08 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % add_pos_nonneg
% 4.71/5.08 thf(fact_3196_add__pos__nonneg,axiom,
% 4.71/5.08 ! [A: int,B: int] :
% 4.71/5.08 ( ( ord_less_int @ zero_zero_int @ A )
% 4.71/5.08 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.71/5.08 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % add_pos_nonneg
% 4.71/5.08 thf(fact_3197_add__strict__increasing,axiom,
% 4.71/5.08 ! [A: real,B: real,C: real] :
% 4.71/5.08 ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.08 => ( ( ord_less_eq_real @ B @ C )
% 4.71/5.08 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % add_strict_increasing
% 4.71/5.08 thf(fact_3198_add__strict__increasing,axiom,
% 4.71/5.08 ! [A: rat,B: rat,C: rat] :
% 4.71/5.08 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.08 => ( ( ord_less_eq_rat @ B @ C )
% 4.71/5.08 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % add_strict_increasing
% 4.71/5.08 thf(fact_3199_add__strict__increasing,axiom,
% 4.71/5.08 ! [A: nat,B: nat,C: nat] :
% 4.71/5.08 ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.71/5.08 => ( ( ord_less_eq_nat @ B @ C )
% 4.71/5.08 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % add_strict_increasing
% 4.71/5.08 thf(fact_3200_add__strict__increasing,axiom,
% 4.71/5.08 ! [A: int,B: int,C: int] :
% 4.71/5.08 ( ( ord_less_int @ zero_zero_int @ A )
% 4.71/5.08 => ( ( ord_less_eq_int @ B @ C )
% 4.71/5.08 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % add_strict_increasing
% 4.71/5.08 thf(fact_3201_add__strict__increasing2,axiom,
% 4.71/5.08 ! [A: real,B: real,C: real] :
% 4.71/5.08 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.08 => ( ( ord_less_real @ B @ C )
% 4.71/5.08 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % add_strict_increasing2
% 4.71/5.08 thf(fact_3202_add__strict__increasing2,axiom,
% 4.71/5.08 ! [A: rat,B: rat,C: rat] :
% 4.71/5.08 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.08 => ( ( ord_less_rat @ B @ C )
% 4.71/5.08 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % add_strict_increasing2
% 4.71/5.08 thf(fact_3203_add__strict__increasing2,axiom,
% 4.71/5.08 ! [A: nat,B: nat,C: nat] :
% 4.71/5.08 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.71/5.08 => ( ( ord_less_nat @ B @ C )
% 4.71/5.08 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % add_strict_increasing2
% 4.71/5.08 thf(fact_3204_add__strict__increasing2,axiom,
% 4.71/5.08 ! [A: int,B: int,C: int] :
% 4.71/5.08 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.08 => ( ( ord_less_int @ B @ C )
% 4.71/5.08 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % add_strict_increasing2
% 4.71/5.08 thf(fact_3205_nat__le__iff,axiom,
% 4.71/5.08 ! [X: int,N: nat] :
% 4.71/5.08 ( ( ord_less_eq_nat @ ( nat2 @ X ) @ N )
% 4.71/5.08 = ( ord_less_eq_int @ X @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % nat_le_iff
% 4.71/5.08 thf(fact_3206_int__eq__iff,axiom,
% 4.71/5.08 ! [M2: nat,Z: int] :
% 4.71/5.08 ( ( ( semiri1314217659103216013at_int @ M2 )
% 4.71/5.08 = Z )
% 4.71/5.08 = ( ( M2
% 4.71/5.08 = ( nat2 @ Z ) )
% 4.71/5.08 & ( ord_less_eq_int @ zero_zero_int @ Z ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % int_eq_iff
% 4.71/5.08 thf(fact_3207_nat__0__le,axiom,
% 4.71/5.08 ! [Z: int] :
% 4.71/5.08 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 4.71/5.08 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 4.71/5.08 = Z ) ) ).
% 4.71/5.08
% 4.71/5.08 % nat_0_le
% 4.71/5.08 thf(fact_3208_finite__ranking__induct,axiom,
% 4.71/5.08 ! [S2: set_complex,P: set_complex > $o,F: complex > rat] :
% 4.71/5.08 ( ( finite3207457112153483333omplex @ S2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_complex )
% 4.71/5.08 => ( ! [X4: complex,S4: set_complex] :
% 4.71/5.08 ( ( finite3207457112153483333omplex @ S4 )
% 4.71/5.08 => ( ! [Y4: complex] :
% 4.71/5.08 ( ( member_complex @ Y4 @ S4 )
% 4.71/5.08 => ( ord_less_eq_rat @ ( F @ Y4 ) @ ( F @ X4 ) ) )
% 4.71/5.08 => ( ( P @ S4 )
% 4.71/5.08 => ( P @ ( insert_complex @ X4 @ S4 ) ) ) ) )
% 4.71/5.08 => ( P @ S2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_ranking_induct
% 4.71/5.08 thf(fact_3209_finite__ranking__induct,axiom,
% 4.71/5.08 ! [S2: set_Extended_enat,P: set_Extended_enat > $o,F: extended_enat > rat] :
% 4.71/5.08 ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.08 => ( ( P @ bot_bo7653980558646680370d_enat )
% 4.71/5.08 => ( ! [X4: extended_enat,S4: set_Extended_enat] :
% 4.71/5.08 ( ( finite4001608067531595151d_enat @ S4 )
% 4.71/5.08 => ( ! [Y4: extended_enat] :
% 4.71/5.08 ( ( member_Extended_enat @ Y4 @ S4 )
% 4.71/5.08 => ( ord_less_eq_rat @ ( F @ Y4 ) @ ( F @ X4 ) ) )
% 4.71/5.08 => ( ( P @ S4 )
% 4.71/5.08 => ( P @ ( insert_Extended_enat @ X4 @ S4 ) ) ) ) )
% 4.71/5.08 => ( P @ S2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_ranking_induct
% 4.71/5.08 thf(fact_3210_finite__ranking__induct,axiom,
% 4.71/5.08 ! [S2: set_real,P: set_real > $o,F: real > rat] :
% 4.71/5.08 ( ( finite_finite_real @ S2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_real )
% 4.71/5.08 => ( ! [X4: real,S4: set_real] :
% 4.71/5.08 ( ( finite_finite_real @ S4 )
% 4.71/5.08 => ( ! [Y4: real] :
% 4.71/5.08 ( ( member_real @ Y4 @ S4 )
% 4.71/5.08 => ( ord_less_eq_rat @ ( F @ Y4 ) @ ( F @ X4 ) ) )
% 4.71/5.08 => ( ( P @ S4 )
% 4.71/5.08 => ( P @ ( insert_real @ X4 @ S4 ) ) ) ) )
% 4.71/5.08 => ( P @ S2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_ranking_induct
% 4.71/5.08 thf(fact_3211_finite__ranking__induct,axiom,
% 4.71/5.08 ! [S2: set_o,P: set_o > $o,F: $o > rat] :
% 4.71/5.08 ( ( finite_finite_o @ S2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_o )
% 4.71/5.08 => ( ! [X4: $o,S4: set_o] :
% 4.71/5.08 ( ( finite_finite_o @ S4 )
% 4.71/5.08 => ( ! [Y4: $o] :
% 4.71/5.08 ( ( member_o @ Y4 @ S4 )
% 4.71/5.08 => ( ord_less_eq_rat @ ( F @ Y4 ) @ ( F @ X4 ) ) )
% 4.71/5.08 => ( ( P @ S4 )
% 4.71/5.08 => ( P @ ( insert_o @ X4 @ S4 ) ) ) ) )
% 4.71/5.08 => ( P @ S2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_ranking_induct
% 4.71/5.08 thf(fact_3212_finite__ranking__induct,axiom,
% 4.71/5.08 ! [S2: set_nat,P: set_nat > $o,F: nat > rat] :
% 4.71/5.08 ( ( finite_finite_nat @ S2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_nat )
% 4.71/5.08 => ( ! [X4: nat,S4: set_nat] :
% 4.71/5.08 ( ( finite_finite_nat @ S4 )
% 4.71/5.08 => ( ! [Y4: nat] :
% 4.71/5.08 ( ( member_nat @ Y4 @ S4 )
% 4.71/5.08 => ( ord_less_eq_rat @ ( F @ Y4 ) @ ( F @ X4 ) ) )
% 4.71/5.08 => ( ( P @ S4 )
% 4.71/5.08 => ( P @ ( insert_nat @ X4 @ S4 ) ) ) ) )
% 4.71/5.08 => ( P @ S2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_ranking_induct
% 4.71/5.08 thf(fact_3213_finite__ranking__induct,axiom,
% 4.71/5.08 ! [S2: set_int,P: set_int > $o,F: int > rat] :
% 4.71/5.08 ( ( finite_finite_int @ S2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_int )
% 4.71/5.08 => ( ! [X4: int,S4: set_int] :
% 4.71/5.08 ( ( finite_finite_int @ S4 )
% 4.71/5.08 => ( ! [Y4: int] :
% 4.71/5.08 ( ( member_int @ Y4 @ S4 )
% 4.71/5.08 => ( ord_less_eq_rat @ ( F @ Y4 ) @ ( F @ X4 ) ) )
% 4.71/5.08 => ( ( P @ S4 )
% 4.71/5.08 => ( P @ ( insert_int @ X4 @ S4 ) ) ) ) )
% 4.71/5.08 => ( P @ S2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_ranking_induct
% 4.71/5.08 thf(fact_3214_finite__ranking__induct,axiom,
% 4.71/5.08 ! [S2: set_complex,P: set_complex > $o,F: complex > num] :
% 4.71/5.08 ( ( finite3207457112153483333omplex @ S2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_complex )
% 4.71/5.08 => ( ! [X4: complex,S4: set_complex] :
% 4.71/5.08 ( ( finite3207457112153483333omplex @ S4 )
% 4.71/5.08 => ( ! [Y4: complex] :
% 4.71/5.08 ( ( member_complex @ Y4 @ S4 )
% 4.71/5.08 => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X4 ) ) )
% 4.71/5.08 => ( ( P @ S4 )
% 4.71/5.08 => ( P @ ( insert_complex @ X4 @ S4 ) ) ) ) )
% 4.71/5.08 => ( P @ S2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_ranking_induct
% 4.71/5.08 thf(fact_3215_finite__ranking__induct,axiom,
% 4.71/5.08 ! [S2: set_Extended_enat,P: set_Extended_enat > $o,F: extended_enat > num] :
% 4.71/5.08 ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.08 => ( ( P @ bot_bo7653980558646680370d_enat )
% 4.71/5.08 => ( ! [X4: extended_enat,S4: set_Extended_enat] :
% 4.71/5.08 ( ( finite4001608067531595151d_enat @ S4 )
% 4.71/5.08 => ( ! [Y4: extended_enat] :
% 4.71/5.08 ( ( member_Extended_enat @ Y4 @ S4 )
% 4.71/5.08 => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X4 ) ) )
% 4.71/5.08 => ( ( P @ S4 )
% 4.71/5.08 => ( P @ ( insert_Extended_enat @ X4 @ S4 ) ) ) ) )
% 4.71/5.08 => ( P @ S2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_ranking_induct
% 4.71/5.08 thf(fact_3216_finite__ranking__induct,axiom,
% 4.71/5.08 ! [S2: set_real,P: set_real > $o,F: real > num] :
% 4.71/5.08 ( ( finite_finite_real @ S2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_real )
% 4.71/5.08 => ( ! [X4: real,S4: set_real] :
% 4.71/5.08 ( ( finite_finite_real @ S4 )
% 4.71/5.08 => ( ! [Y4: real] :
% 4.71/5.08 ( ( member_real @ Y4 @ S4 )
% 4.71/5.08 => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X4 ) ) )
% 4.71/5.08 => ( ( P @ S4 )
% 4.71/5.08 => ( P @ ( insert_real @ X4 @ S4 ) ) ) ) )
% 4.71/5.08 => ( P @ S2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_ranking_induct
% 4.71/5.08 thf(fact_3217_finite__ranking__induct,axiom,
% 4.71/5.08 ! [S2: set_o,P: set_o > $o,F: $o > num] :
% 4.71/5.08 ( ( finite_finite_o @ S2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_o )
% 4.71/5.08 => ( ! [X4: $o,S4: set_o] :
% 4.71/5.08 ( ( finite_finite_o @ S4 )
% 4.71/5.08 => ( ! [Y4: $o] :
% 4.71/5.08 ( ( member_o @ Y4 @ S4 )
% 4.71/5.08 => ( ord_less_eq_num @ ( F @ Y4 ) @ ( F @ X4 ) ) )
% 4.71/5.08 => ( ( P @ S4 )
% 4.71/5.08 => ( P @ ( insert_o @ X4 @ S4 ) ) ) ) )
% 4.71/5.08 => ( P @ S2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_ranking_induct
% 4.71/5.08 thf(fact_3218_discrete,axiom,
% 4.71/5.08 ( ord_less_nat
% 4.71/5.08 = ( ^ [A4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A4 @ one_one_nat ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % discrete
% 4.71/5.08 thf(fact_3219_discrete,axiom,
% 4.71/5.08 ( ord_less_int
% 4.71/5.08 = ( ^ [A4: int] : ( ord_less_eq_int @ ( plus_plus_int @ A4 @ one_one_int ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % discrete
% 4.71/5.08 thf(fact_3220_zero__less__two,axiom,
% 4.71/5.08 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 4.71/5.08
% 4.71/5.08 % zero_less_two
% 4.71/5.08 thf(fact_3221_zero__less__two,axiom,
% 4.71/5.08 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 4.71/5.08
% 4.71/5.08 % zero_less_two
% 4.71/5.08 thf(fact_3222_zero__less__two,axiom,
% 4.71/5.08 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 4.71/5.08
% 4.71/5.08 % zero_less_two
% 4.71/5.08 thf(fact_3223_zero__less__two,axiom,
% 4.71/5.08 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 4.71/5.08
% 4.71/5.08 % zero_less_two
% 4.71/5.08 thf(fact_3224_finite__linorder__max__induct,axiom,
% 4.71/5.08 ! [A2: set_Extended_enat,P: set_Extended_enat > $o] :
% 4.71/5.08 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.08 => ( ( P @ bot_bo7653980558646680370d_enat )
% 4.71/5.08 => ( ! [B5: extended_enat,A3: set_Extended_enat] :
% 4.71/5.08 ( ( finite4001608067531595151d_enat @ A3 )
% 4.71/5.08 => ( ! [X2: extended_enat] :
% 4.71/5.08 ( ( member_Extended_enat @ X2 @ A3 )
% 4.71/5.08 => ( ord_le72135733267957522d_enat @ X2 @ B5 ) )
% 4.71/5.08 => ( ( P @ A3 )
% 4.71/5.08 => ( P @ ( insert_Extended_enat @ B5 @ A3 ) ) ) ) )
% 4.71/5.08 => ( P @ A2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_linorder_max_induct
% 4.71/5.08 thf(fact_3225_finite__linorder__max__induct,axiom,
% 4.71/5.08 ! [A2: set_o,P: set_o > $o] :
% 4.71/5.08 ( ( finite_finite_o @ A2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_o )
% 4.71/5.08 => ( ! [B5: $o,A3: set_o] :
% 4.71/5.08 ( ( finite_finite_o @ A3 )
% 4.71/5.08 => ( ! [X2: $o] :
% 4.71/5.08 ( ( member_o @ X2 @ A3 )
% 4.71/5.08 => ( ord_less_o @ X2 @ B5 ) )
% 4.71/5.08 => ( ( P @ A3 )
% 4.71/5.08 => ( P @ ( insert_o @ B5 @ A3 ) ) ) ) )
% 4.71/5.08 => ( P @ A2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_linorder_max_induct
% 4.71/5.08 thf(fact_3226_finite__linorder__max__induct,axiom,
% 4.71/5.08 ! [A2: set_real,P: set_real > $o] :
% 4.71/5.08 ( ( finite_finite_real @ A2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_real )
% 4.71/5.08 => ( ! [B5: real,A3: set_real] :
% 4.71/5.08 ( ( finite_finite_real @ A3 )
% 4.71/5.08 => ( ! [X2: real] :
% 4.71/5.08 ( ( member_real @ X2 @ A3 )
% 4.71/5.08 => ( ord_less_real @ X2 @ B5 ) )
% 4.71/5.08 => ( ( P @ A3 )
% 4.71/5.08 => ( P @ ( insert_real @ B5 @ A3 ) ) ) ) )
% 4.71/5.08 => ( P @ A2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_linorder_max_induct
% 4.71/5.08 thf(fact_3227_finite__linorder__max__induct,axiom,
% 4.71/5.08 ! [A2: set_rat,P: set_rat > $o] :
% 4.71/5.08 ( ( finite_finite_rat @ A2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_rat )
% 4.71/5.08 => ( ! [B5: rat,A3: set_rat] :
% 4.71/5.08 ( ( finite_finite_rat @ A3 )
% 4.71/5.08 => ( ! [X2: rat] :
% 4.71/5.08 ( ( member_rat @ X2 @ A3 )
% 4.71/5.08 => ( ord_less_rat @ X2 @ B5 ) )
% 4.71/5.08 => ( ( P @ A3 )
% 4.71/5.08 => ( P @ ( insert_rat @ B5 @ A3 ) ) ) ) )
% 4.71/5.08 => ( P @ A2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_linorder_max_induct
% 4.71/5.08 thf(fact_3228_finite__linorder__max__induct,axiom,
% 4.71/5.08 ! [A2: set_num,P: set_num > $o] :
% 4.71/5.08 ( ( finite_finite_num @ A2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_num )
% 4.71/5.08 => ( ! [B5: num,A3: set_num] :
% 4.71/5.08 ( ( finite_finite_num @ A3 )
% 4.71/5.08 => ( ! [X2: num] :
% 4.71/5.08 ( ( member_num @ X2 @ A3 )
% 4.71/5.08 => ( ord_less_num @ X2 @ B5 ) )
% 4.71/5.08 => ( ( P @ A3 )
% 4.71/5.08 => ( P @ ( insert_num @ B5 @ A3 ) ) ) ) )
% 4.71/5.08 => ( P @ A2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_linorder_max_induct
% 4.71/5.08 thf(fact_3229_finite__linorder__max__induct,axiom,
% 4.71/5.08 ! [A2: set_nat,P: set_nat > $o] :
% 4.71/5.08 ( ( finite_finite_nat @ A2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_nat )
% 4.71/5.08 => ( ! [B5: nat,A3: set_nat] :
% 4.71/5.08 ( ( finite_finite_nat @ A3 )
% 4.71/5.08 => ( ! [X2: nat] :
% 4.71/5.08 ( ( member_nat @ X2 @ A3 )
% 4.71/5.08 => ( ord_less_nat @ X2 @ B5 ) )
% 4.71/5.08 => ( ( P @ A3 )
% 4.71/5.08 => ( P @ ( insert_nat @ B5 @ A3 ) ) ) ) )
% 4.71/5.08 => ( P @ A2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_linorder_max_induct
% 4.71/5.08 thf(fact_3230_finite__linorder__max__induct,axiom,
% 4.71/5.08 ! [A2: set_int,P: set_int > $o] :
% 4.71/5.08 ( ( finite_finite_int @ A2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_int )
% 4.71/5.08 => ( ! [B5: int,A3: set_int] :
% 4.71/5.08 ( ( finite_finite_int @ A3 )
% 4.71/5.08 => ( ! [X2: int] :
% 4.71/5.08 ( ( member_int @ X2 @ A3 )
% 4.71/5.08 => ( ord_less_int @ X2 @ B5 ) )
% 4.71/5.08 => ( ( P @ A3 )
% 4.71/5.08 => ( P @ ( insert_int @ B5 @ A3 ) ) ) ) )
% 4.71/5.08 => ( P @ A2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_linorder_max_induct
% 4.71/5.08 thf(fact_3231_finite__linorder__min__induct,axiom,
% 4.71/5.08 ! [A2: set_Extended_enat,P: set_Extended_enat > $o] :
% 4.71/5.08 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.08 => ( ( P @ bot_bo7653980558646680370d_enat )
% 4.71/5.08 => ( ! [B5: extended_enat,A3: set_Extended_enat] :
% 4.71/5.08 ( ( finite4001608067531595151d_enat @ A3 )
% 4.71/5.08 => ( ! [X2: extended_enat] :
% 4.71/5.08 ( ( member_Extended_enat @ X2 @ A3 )
% 4.71/5.08 => ( ord_le72135733267957522d_enat @ B5 @ X2 ) )
% 4.71/5.08 => ( ( P @ A3 )
% 4.71/5.08 => ( P @ ( insert_Extended_enat @ B5 @ A3 ) ) ) ) )
% 4.71/5.08 => ( P @ A2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_linorder_min_induct
% 4.71/5.08 thf(fact_3232_finite__linorder__min__induct,axiom,
% 4.71/5.08 ! [A2: set_o,P: set_o > $o] :
% 4.71/5.08 ( ( finite_finite_o @ A2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_o )
% 4.71/5.08 => ( ! [B5: $o,A3: set_o] :
% 4.71/5.08 ( ( finite_finite_o @ A3 )
% 4.71/5.08 => ( ! [X2: $o] :
% 4.71/5.08 ( ( member_o @ X2 @ A3 )
% 4.71/5.08 => ( ord_less_o @ B5 @ X2 ) )
% 4.71/5.08 => ( ( P @ A3 )
% 4.71/5.08 => ( P @ ( insert_o @ B5 @ A3 ) ) ) ) )
% 4.71/5.08 => ( P @ A2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_linorder_min_induct
% 4.71/5.08 thf(fact_3233_finite__linorder__min__induct,axiom,
% 4.71/5.08 ! [A2: set_real,P: set_real > $o] :
% 4.71/5.08 ( ( finite_finite_real @ A2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_real )
% 4.71/5.08 => ( ! [B5: real,A3: set_real] :
% 4.71/5.08 ( ( finite_finite_real @ A3 )
% 4.71/5.08 => ( ! [X2: real] :
% 4.71/5.08 ( ( member_real @ X2 @ A3 )
% 4.71/5.08 => ( ord_less_real @ B5 @ X2 ) )
% 4.71/5.08 => ( ( P @ A3 )
% 4.71/5.08 => ( P @ ( insert_real @ B5 @ A3 ) ) ) ) )
% 4.71/5.08 => ( P @ A2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_linorder_min_induct
% 4.71/5.08 thf(fact_3234_finite__linorder__min__induct,axiom,
% 4.71/5.08 ! [A2: set_rat,P: set_rat > $o] :
% 4.71/5.08 ( ( finite_finite_rat @ A2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_rat )
% 4.71/5.08 => ( ! [B5: rat,A3: set_rat] :
% 4.71/5.08 ( ( finite_finite_rat @ A3 )
% 4.71/5.08 => ( ! [X2: rat] :
% 4.71/5.08 ( ( member_rat @ X2 @ A3 )
% 4.71/5.08 => ( ord_less_rat @ B5 @ X2 ) )
% 4.71/5.08 => ( ( P @ A3 )
% 4.71/5.08 => ( P @ ( insert_rat @ B5 @ A3 ) ) ) ) )
% 4.71/5.08 => ( P @ A2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_linorder_min_induct
% 4.71/5.08 thf(fact_3235_finite__linorder__min__induct,axiom,
% 4.71/5.08 ! [A2: set_num,P: set_num > $o] :
% 4.71/5.08 ( ( finite_finite_num @ A2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_num )
% 4.71/5.08 => ( ! [B5: num,A3: set_num] :
% 4.71/5.08 ( ( finite_finite_num @ A3 )
% 4.71/5.08 => ( ! [X2: num] :
% 4.71/5.08 ( ( member_num @ X2 @ A3 )
% 4.71/5.08 => ( ord_less_num @ B5 @ X2 ) )
% 4.71/5.08 => ( ( P @ A3 )
% 4.71/5.08 => ( P @ ( insert_num @ B5 @ A3 ) ) ) ) )
% 4.71/5.08 => ( P @ A2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_linorder_min_induct
% 4.71/5.08 thf(fact_3236_finite__linorder__min__induct,axiom,
% 4.71/5.08 ! [A2: set_nat,P: set_nat > $o] :
% 4.71/5.08 ( ( finite_finite_nat @ A2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_nat )
% 4.71/5.08 => ( ! [B5: nat,A3: set_nat] :
% 4.71/5.08 ( ( finite_finite_nat @ A3 )
% 4.71/5.08 => ( ! [X2: nat] :
% 4.71/5.08 ( ( member_nat @ X2 @ A3 )
% 4.71/5.08 => ( ord_less_nat @ B5 @ X2 ) )
% 4.71/5.08 => ( ( P @ A3 )
% 4.71/5.08 => ( P @ ( insert_nat @ B5 @ A3 ) ) ) ) )
% 4.71/5.08 => ( P @ A2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_linorder_min_induct
% 4.71/5.08 thf(fact_3237_finite__linorder__min__induct,axiom,
% 4.71/5.08 ! [A2: set_int,P: set_int > $o] :
% 4.71/5.08 ( ( finite_finite_int @ A2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_int )
% 4.71/5.08 => ( ! [B5: int,A3: set_int] :
% 4.71/5.08 ( ( finite_finite_int @ A3 )
% 4.71/5.08 => ( ! [X2: int] :
% 4.71/5.08 ( ( member_int @ X2 @ A3 )
% 4.71/5.08 => ( ord_less_int @ B5 @ X2 ) )
% 4.71/5.08 => ( ( P @ A3 )
% 4.71/5.08 => ( P @ ( insert_int @ B5 @ A3 ) ) ) ) )
% 4.71/5.08 => ( P @ A2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_linorder_min_induct
% 4.71/5.08 thf(fact_3238_mult__le__cancel__left,axiom,
% 4.71/5.08 ! [C: real,A: real,B: real] :
% 4.71/5.08 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.71/5.08 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.08 => ( ord_less_eq_real @ A @ B ) )
% 4.71/5.08 & ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.08 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_le_cancel_left
% 4.71/5.08 thf(fact_3239_mult__le__cancel__left,axiom,
% 4.71/5.08 ! [C: rat,A: rat,B: rat] :
% 4.71/5.08 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.71/5.08 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.08 => ( ord_less_eq_rat @ A @ B ) )
% 4.71/5.08 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.08 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_le_cancel_left
% 4.71/5.08 thf(fact_3240_mult__le__cancel__left,axiom,
% 4.71/5.08 ! [C: int,A: int,B: int] :
% 4.71/5.08 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.71/5.08 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 4.71/5.08 => ( ord_less_eq_int @ A @ B ) )
% 4.71/5.08 & ( ( ord_less_int @ C @ zero_zero_int )
% 4.71/5.08 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_le_cancel_left
% 4.71/5.08 thf(fact_3241_mult__le__cancel__right,axiom,
% 4.71/5.08 ! [A: real,C: real,B: real] :
% 4.71/5.08 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 4.71/5.08 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.08 => ( ord_less_eq_real @ A @ B ) )
% 4.71/5.08 & ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.08 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_le_cancel_right
% 4.71/5.08 thf(fact_3242_mult__le__cancel__right,axiom,
% 4.71/5.08 ! [A: rat,C: rat,B: rat] :
% 4.71/5.08 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 4.71/5.08 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.08 => ( ord_less_eq_rat @ A @ B ) )
% 4.71/5.08 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.08 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_le_cancel_right
% 4.71/5.08 thf(fact_3243_mult__le__cancel__right,axiom,
% 4.71/5.08 ! [A: int,C: int,B: int] :
% 4.71/5.08 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 4.71/5.08 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 4.71/5.08 => ( ord_less_eq_int @ A @ B ) )
% 4.71/5.08 & ( ( ord_less_int @ C @ zero_zero_int )
% 4.71/5.08 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_le_cancel_right
% 4.71/5.08 thf(fact_3244_mult__left__less__imp__less,axiom,
% 4.71/5.08 ! [C: real,A: real,B: real] :
% 4.71/5.08 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.71/5.08 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.71/5.08 => ( ord_less_real @ A @ B ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_left_less_imp_less
% 4.71/5.08 thf(fact_3245_mult__left__less__imp__less,axiom,
% 4.71/5.08 ! [C: rat,A: rat,B: rat] :
% 4.71/5.08 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.71/5.08 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.71/5.08 => ( ord_less_rat @ A @ B ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_left_less_imp_less
% 4.71/5.08 thf(fact_3246_mult__left__less__imp__less,axiom,
% 4.71/5.08 ! [C: nat,A: nat,B: nat] :
% 4.71/5.08 ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 4.71/5.08 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.71/5.08 => ( ord_less_nat @ A @ B ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_left_less_imp_less
% 4.71/5.08 thf(fact_3247_mult__left__less__imp__less,axiom,
% 4.71/5.08 ! [C: int,A: int,B: int] :
% 4.71/5.08 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.71/5.08 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.71/5.08 => ( ord_less_int @ A @ B ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_left_less_imp_less
% 4.71/5.08 thf(fact_3248_mult__strict__mono,axiom,
% 4.71/5.08 ! [A: real,B: real,C: real,D: real] :
% 4.71/5.08 ( ( ord_less_real @ A @ B )
% 4.71/5.08 => ( ( ord_less_real @ C @ D )
% 4.71/5.08 => ( ( ord_less_real @ zero_zero_real @ B )
% 4.71/5.08 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.71/5.08 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_strict_mono
% 4.71/5.08 thf(fact_3249_mult__strict__mono,axiom,
% 4.71/5.08 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.71/5.08 ( ( ord_less_rat @ A @ B )
% 4.71/5.08 => ( ( ord_less_rat @ C @ D )
% 4.71/5.08 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 4.71/5.08 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.71/5.08 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_strict_mono
% 4.71/5.08 thf(fact_3250_mult__strict__mono,axiom,
% 4.71/5.08 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.71/5.08 ( ( ord_less_nat @ A @ B )
% 4.71/5.08 => ( ( ord_less_nat @ C @ D )
% 4.71/5.08 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.71/5.08 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.71/5.08 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_strict_mono
% 4.71/5.08 thf(fact_3251_mult__strict__mono,axiom,
% 4.71/5.08 ! [A: int,B: int,C: int,D: int] :
% 4.71/5.08 ( ( ord_less_int @ A @ B )
% 4.71/5.08 => ( ( ord_less_int @ C @ D )
% 4.71/5.08 => ( ( ord_less_int @ zero_zero_int @ B )
% 4.71/5.08 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.71/5.08 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_strict_mono
% 4.71/5.08 thf(fact_3252_mult__less__cancel__left,axiom,
% 4.71/5.08 ! [C: real,A: real,B: real] :
% 4.71/5.08 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.71/5.08 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.71/5.08 => ( ord_less_real @ A @ B ) )
% 4.71/5.08 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 4.71/5.08 => ( ord_less_real @ B @ A ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_less_cancel_left
% 4.71/5.08 thf(fact_3253_mult__less__cancel__left,axiom,
% 4.71/5.08 ! [C: rat,A: rat,B: rat] :
% 4.71/5.08 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.71/5.08 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.71/5.08 => ( ord_less_rat @ A @ B ) )
% 4.71/5.08 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.71/5.08 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_less_cancel_left
% 4.71/5.08 thf(fact_3254_mult__less__cancel__left,axiom,
% 4.71/5.08 ! [C: int,A: int,B: int] :
% 4.71/5.08 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.71/5.08 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.71/5.08 => ( ord_less_int @ A @ B ) )
% 4.71/5.08 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 4.71/5.08 => ( ord_less_int @ B @ A ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_less_cancel_left
% 4.71/5.08 thf(fact_3255_mult__right__less__imp__less,axiom,
% 4.71/5.08 ! [A: real,C: real,B: real] :
% 4.71/5.08 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 4.71/5.08 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.71/5.08 => ( ord_less_real @ A @ B ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_right_less_imp_less
% 4.71/5.08 thf(fact_3256_mult__right__less__imp__less,axiom,
% 4.71/5.08 ! [A: rat,C: rat,B: rat] :
% 4.71/5.08 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 4.71/5.08 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.71/5.08 => ( ord_less_rat @ A @ B ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_right_less_imp_less
% 4.71/5.08 thf(fact_3257_mult__right__less__imp__less,axiom,
% 4.71/5.08 ! [A: nat,C: nat,B: nat] :
% 4.71/5.08 ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 4.71/5.08 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.71/5.08 => ( ord_less_nat @ A @ B ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_right_less_imp_less
% 4.71/5.08 thf(fact_3258_mult__right__less__imp__less,axiom,
% 4.71/5.08 ! [A: int,C: int,B: int] :
% 4.71/5.08 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 4.71/5.08 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.71/5.08 => ( ord_less_int @ A @ B ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_right_less_imp_less
% 4.71/5.08 thf(fact_3259_mult__strict__mono_H,axiom,
% 4.71/5.08 ! [A: real,B: real,C: real,D: real] :
% 4.71/5.08 ( ( ord_less_real @ A @ B )
% 4.71/5.08 => ( ( ord_less_real @ C @ D )
% 4.71/5.08 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.08 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.71/5.08 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_strict_mono'
% 4.71/5.08 thf(fact_3260_mult__strict__mono_H,axiom,
% 4.71/5.08 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.71/5.08 ( ( ord_less_rat @ A @ B )
% 4.71/5.08 => ( ( ord_less_rat @ C @ D )
% 4.71/5.08 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.08 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.71/5.08 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_strict_mono'
% 4.71/5.08 thf(fact_3261_mult__strict__mono_H,axiom,
% 4.71/5.08 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.71/5.08 ( ( ord_less_nat @ A @ B )
% 4.71/5.08 => ( ( ord_less_nat @ C @ D )
% 4.71/5.08 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.71/5.08 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.71/5.08 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_strict_mono'
% 4.71/5.08 thf(fact_3262_mult__strict__mono_H,axiom,
% 4.71/5.08 ! [A: int,B: int,C: int,D: int] :
% 4.71/5.08 ( ( ord_less_int @ A @ B )
% 4.71/5.08 => ( ( ord_less_int @ C @ D )
% 4.71/5.08 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.08 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.71/5.08 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_strict_mono'
% 4.71/5.08 thf(fact_3263_mult__less__cancel__right,axiom,
% 4.71/5.08 ! [A: real,C: real,B: real] :
% 4.71/5.08 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 4.71/5.08 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.71/5.08 => ( ord_less_real @ A @ B ) )
% 4.71/5.08 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 4.71/5.08 => ( ord_less_real @ B @ A ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_less_cancel_right
% 4.71/5.08 thf(fact_3264_mult__less__cancel__right,axiom,
% 4.71/5.08 ! [A: rat,C: rat,B: rat] :
% 4.71/5.08 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 4.71/5.08 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.71/5.08 => ( ord_less_rat @ A @ B ) )
% 4.71/5.08 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.71/5.08 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_less_cancel_right
% 4.71/5.08 thf(fact_3265_mult__less__cancel__right,axiom,
% 4.71/5.08 ! [A: int,C: int,B: int] :
% 4.71/5.08 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 4.71/5.08 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.71/5.08 => ( ord_less_int @ A @ B ) )
% 4.71/5.08 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 4.71/5.08 => ( ord_less_int @ B @ A ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_less_cancel_right
% 4.71/5.08 thf(fact_3266_mult__le__cancel__left__neg,axiom,
% 4.71/5.08 ! [C: real,A: real,B: real] :
% 4.71/5.08 ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.08 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.71/5.08 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_le_cancel_left_neg
% 4.71/5.08 thf(fact_3267_mult__le__cancel__left__neg,axiom,
% 4.71/5.08 ! [C: rat,A: rat,B: rat] :
% 4.71/5.08 ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.08 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.71/5.08 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_le_cancel_left_neg
% 4.71/5.08 thf(fact_3268_mult__le__cancel__left__neg,axiom,
% 4.71/5.08 ! [C: int,A: int,B: int] :
% 4.71/5.08 ( ( ord_less_int @ C @ zero_zero_int )
% 4.71/5.08 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.71/5.08 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_le_cancel_left_neg
% 4.71/5.08 thf(fact_3269_mult__le__cancel__left__pos,axiom,
% 4.71/5.08 ! [C: real,A: real,B: real] :
% 4.71/5.08 ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.08 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.71/5.08 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_le_cancel_left_pos
% 4.71/5.08 thf(fact_3270_mult__le__cancel__left__pos,axiom,
% 4.71/5.08 ! [C: rat,A: rat,B: rat] :
% 4.71/5.08 ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.08 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.71/5.08 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_le_cancel_left_pos
% 4.71/5.08 thf(fact_3271_mult__le__cancel__left__pos,axiom,
% 4.71/5.08 ! [C: int,A: int,B: int] :
% 4.71/5.08 ( ( ord_less_int @ zero_zero_int @ C )
% 4.71/5.08 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.71/5.08 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_le_cancel_left_pos
% 4.71/5.08 thf(fact_3272_mult__left__le__imp__le,axiom,
% 4.71/5.08 ! [C: real,A: real,B: real] :
% 4.71/5.08 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.71/5.08 => ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.08 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_left_le_imp_le
% 4.71/5.08 thf(fact_3273_mult__left__le__imp__le,axiom,
% 4.71/5.08 ! [C: rat,A: rat,B: rat] :
% 4.71/5.08 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.71/5.08 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.08 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_left_le_imp_le
% 4.71/5.08 thf(fact_3274_mult__left__le__imp__le,axiom,
% 4.71/5.08 ! [C: nat,A: nat,B: nat] :
% 4.71/5.08 ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 4.71/5.08 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 4.71/5.08 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_left_le_imp_le
% 4.71/5.08 thf(fact_3275_mult__left__le__imp__le,axiom,
% 4.71/5.08 ! [C: int,A: int,B: int] :
% 4.71/5.08 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.71/5.08 => ( ( ord_less_int @ zero_zero_int @ C )
% 4.71/5.08 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_left_le_imp_le
% 4.71/5.08 thf(fact_3276_mult__right__le__imp__le,axiom,
% 4.71/5.08 ! [A: real,C: real,B: real] :
% 4.71/5.08 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 4.71/5.08 => ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.08 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_right_le_imp_le
% 4.71/5.08 thf(fact_3277_mult__right__le__imp__le,axiom,
% 4.71/5.08 ! [A: rat,C: rat,B: rat] :
% 4.71/5.08 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 4.71/5.08 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.08 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_right_le_imp_le
% 4.71/5.08 thf(fact_3278_mult__right__le__imp__le,axiom,
% 4.71/5.08 ! [A: nat,C: nat,B: nat] :
% 4.71/5.08 ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 4.71/5.08 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 4.71/5.08 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_right_le_imp_le
% 4.71/5.08 thf(fact_3279_mult__right__le__imp__le,axiom,
% 4.71/5.08 ! [A: int,C: int,B: int] :
% 4.71/5.08 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 4.71/5.08 => ( ( ord_less_int @ zero_zero_int @ C )
% 4.71/5.08 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_right_le_imp_le
% 4.71/5.08 thf(fact_3280_mult__le__less__imp__less,axiom,
% 4.71/5.08 ! [A: real,B: real,C: real,D: real] :
% 4.71/5.08 ( ( ord_less_eq_real @ A @ B )
% 4.71/5.08 => ( ( ord_less_real @ C @ D )
% 4.71/5.08 => ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.08 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.71/5.08 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_le_less_imp_less
% 4.71/5.08 thf(fact_3281_mult__le__less__imp__less,axiom,
% 4.71/5.08 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.71/5.08 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.08 => ( ( ord_less_rat @ C @ D )
% 4.71/5.08 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.08 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.71/5.08 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_le_less_imp_less
% 4.71/5.08 thf(fact_3282_mult__le__less__imp__less,axiom,
% 4.71/5.08 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.71/5.08 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.08 => ( ( ord_less_nat @ C @ D )
% 4.71/5.08 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.71/5.08 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.71/5.08 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_le_less_imp_less
% 4.71/5.08 thf(fact_3283_mult__le__less__imp__less,axiom,
% 4.71/5.08 ! [A: int,B: int,C: int,D: int] :
% 4.71/5.08 ( ( ord_less_eq_int @ A @ B )
% 4.71/5.08 => ( ( ord_less_int @ C @ D )
% 4.71/5.08 => ( ( ord_less_int @ zero_zero_int @ A )
% 4.71/5.08 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.71/5.08 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_le_less_imp_less
% 4.71/5.08 thf(fact_3284_mult__less__le__imp__less,axiom,
% 4.71/5.08 ! [A: real,B: real,C: real,D: real] :
% 4.71/5.08 ( ( ord_less_real @ A @ B )
% 4.71/5.08 => ( ( ord_less_eq_real @ C @ D )
% 4.71/5.08 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.08 => ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.08 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_less_le_imp_less
% 4.71/5.08 thf(fact_3285_mult__less__le__imp__less,axiom,
% 4.71/5.08 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.71/5.08 ( ( ord_less_rat @ A @ B )
% 4.71/5.08 => ( ( ord_less_eq_rat @ C @ D )
% 4.71/5.08 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.08 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.08 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_less_le_imp_less
% 4.71/5.08 thf(fact_3286_mult__less__le__imp__less,axiom,
% 4.71/5.08 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.71/5.08 ( ( ord_less_nat @ A @ B )
% 4.71/5.08 => ( ( ord_less_eq_nat @ C @ D )
% 4.71/5.08 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.71/5.08 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 4.71/5.08 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_less_le_imp_less
% 4.71/5.08 thf(fact_3287_mult__less__le__imp__less,axiom,
% 4.71/5.08 ! [A: int,B: int,C: int,D: int] :
% 4.71/5.08 ( ( ord_less_int @ A @ B )
% 4.71/5.08 => ( ( ord_less_eq_int @ C @ D )
% 4.71/5.08 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.08 => ( ( ord_less_int @ zero_zero_int @ C )
% 4.71/5.08 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_less_le_imp_less
% 4.71/5.08 thf(fact_3288_div__add__self1,axiom,
% 4.71/5.08 ! [B: int,A: int] :
% 4.71/5.08 ( ( B != zero_zero_int )
% 4.71/5.08 => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 4.71/5.08 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % div_add_self1
% 4.71/5.08 thf(fact_3289_div__add__self1,axiom,
% 4.71/5.08 ! [B: nat,A: nat] :
% 4.71/5.08 ( ( B != zero_zero_nat )
% 4.71/5.08 => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 4.71/5.08 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % div_add_self1
% 4.71/5.08 thf(fact_3290_div__add__self2,axiom,
% 4.71/5.08 ! [B: int,A: int] :
% 4.71/5.08 ( ( B != zero_zero_int )
% 4.71/5.08 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 4.71/5.08 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % div_add_self2
% 4.71/5.08 thf(fact_3291_div__add__self2,axiom,
% 4.71/5.08 ! [B: nat,A: nat] :
% 4.71/5.08 ( ( B != zero_zero_nat )
% 4.71/5.08 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 4.71/5.08 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % div_add_self2
% 4.71/5.08 thf(fact_3292_gt__half__sum,axiom,
% 4.71/5.08 ! [A: rat,B: rat] :
% 4.71/5.08 ( ( ord_less_rat @ A @ B )
% 4.71/5.08 => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 4.71/5.08
% 4.71/5.08 % gt_half_sum
% 4.71/5.08 thf(fact_3293_gt__half__sum,axiom,
% 4.71/5.08 ! [A: real,B: real] :
% 4.71/5.08 ( ( ord_less_real @ A @ B )
% 4.71/5.08 => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B ) ) ).
% 4.71/5.08
% 4.71/5.08 % gt_half_sum
% 4.71/5.08 thf(fact_3294_less__half__sum,axiom,
% 4.71/5.08 ! [A: rat,B: rat] :
% 4.71/5.08 ( ( ord_less_rat @ A @ B )
% 4.71/5.08 => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % less_half_sum
% 4.71/5.08 thf(fact_3295_less__half__sum,axiom,
% 4.71/5.08 ! [A: real,B: real] :
% 4.71/5.08 ( ( ord_less_real @ A @ B )
% 4.71/5.08 => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % less_half_sum
% 4.71/5.08 thf(fact_3296_mult__left__le__one__le,axiom,
% 4.71/5.08 ! [X: real,Y: real] :
% 4.71/5.08 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.08 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.71/5.08 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 4.71/5.08 => ( ord_less_eq_real @ ( times_times_real @ Y @ X ) @ X ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_left_le_one_le
% 4.71/5.08 thf(fact_3297_mult__left__le__one__le,axiom,
% 4.71/5.08 ! [X: rat,Y: rat] :
% 4.71/5.08 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 4.71/5.08 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 4.71/5.08 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 4.71/5.08 => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X ) @ X ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_left_le_one_le
% 4.71/5.08 thf(fact_3298_mult__left__le__one__le,axiom,
% 4.71/5.08 ! [X: int,Y: int] :
% 4.71/5.08 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 4.71/5.08 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.71/5.08 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 4.71/5.08 => ( ord_less_eq_int @ ( times_times_int @ Y @ X ) @ X ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_left_le_one_le
% 4.71/5.08 thf(fact_3299_mult__right__le__one__le,axiom,
% 4.71/5.08 ! [X: real,Y: real] :
% 4.71/5.08 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.08 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.71/5.08 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 4.71/5.08 => ( ord_less_eq_real @ ( times_times_real @ X @ Y ) @ X ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_right_le_one_le
% 4.71/5.08 thf(fact_3300_mult__right__le__one__le,axiom,
% 4.71/5.08 ! [X: rat,Y: rat] :
% 4.71/5.08 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 4.71/5.08 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 4.71/5.08 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 4.71/5.08 => ( ord_less_eq_rat @ ( times_times_rat @ X @ Y ) @ X ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_right_le_one_le
% 4.71/5.08 thf(fact_3301_mult__right__le__one__le,axiom,
% 4.71/5.08 ! [X: int,Y: int] :
% 4.71/5.08 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 4.71/5.08 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.71/5.08 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 4.71/5.08 => ( ord_less_eq_int @ ( times_times_int @ X @ Y ) @ X ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_right_le_one_le
% 4.71/5.08 thf(fact_3302_mult__le__one,axiom,
% 4.71/5.08 ! [A: real,B: real] :
% 4.71/5.08 ( ( ord_less_eq_real @ A @ one_one_real )
% 4.71/5.08 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.71/5.08 => ( ( ord_less_eq_real @ B @ one_one_real )
% 4.71/5.08 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_le_one
% 4.71/5.08 thf(fact_3303_mult__le__one,axiom,
% 4.71/5.08 ! [A: rat,B: rat] :
% 4.71/5.08 ( ( ord_less_eq_rat @ A @ one_one_rat )
% 4.71/5.08 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.71/5.08 => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 4.71/5.08 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_le_one
% 4.71/5.08 thf(fact_3304_mult__le__one,axiom,
% 4.71/5.08 ! [A: nat,B: nat] :
% 4.71/5.08 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 4.71/5.08 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.71/5.08 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 4.71/5.08 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_le_one
% 4.71/5.08 thf(fact_3305_mult__le__one,axiom,
% 4.71/5.08 ! [A: int,B: int] :
% 4.71/5.08 ( ( ord_less_eq_int @ A @ one_one_int )
% 4.71/5.08 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.71/5.08 => ( ( ord_less_eq_int @ B @ one_one_int )
% 4.71/5.08 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_le_one
% 4.71/5.08 thf(fact_3306_mult__left__le,axiom,
% 4.71/5.08 ! [C: real,A: real] :
% 4.71/5.08 ( ( ord_less_eq_real @ C @ one_one_real )
% 4.71/5.08 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.08 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_left_le
% 4.71/5.08 thf(fact_3307_mult__left__le,axiom,
% 4.71/5.08 ! [C: rat,A: rat] :
% 4.71/5.08 ( ( ord_less_eq_rat @ C @ one_one_rat )
% 4.71/5.08 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.08 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_left_le
% 4.71/5.08 thf(fact_3308_mult__left__le,axiom,
% 4.71/5.08 ! [C: nat,A: nat] :
% 4.71/5.08 ( ( ord_less_eq_nat @ C @ one_one_nat )
% 4.71/5.08 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.71/5.08 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_left_le
% 4.71/5.08 thf(fact_3309_mult__left__le,axiom,
% 4.71/5.08 ! [C: int,A: int] :
% 4.71/5.08 ( ( ord_less_eq_int @ C @ one_one_int )
% 4.71/5.08 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.08 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_left_le
% 4.71/5.08 thf(fact_3310_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 4.71/5.08 ! [C: nat,A: nat,B: nat] :
% 4.71/5.08 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.71/5.08 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 4.71/5.08 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 4.71/5.08 thf(fact_3311_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 4.71/5.08 ! [C: int,A: int,B: int] :
% 4.71/5.08 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.71/5.08 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 4.71/5.08 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 4.71/5.08 thf(fact_3312_finite__subset__induct,axiom,
% 4.71/5.08 ! [F2: set_set_nat,A2: set_set_nat,P: set_set_nat > $o] :
% 4.71/5.08 ( ( finite1152437895449049373et_nat @ F2 )
% 4.71/5.08 => ( ( ord_le6893508408891458716et_nat @ F2 @ A2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_set_nat )
% 4.71/5.08 => ( ! [A5: set_nat,F3: set_set_nat] :
% 4.71/5.08 ( ( finite1152437895449049373et_nat @ F3 )
% 4.71/5.08 => ( ( member_set_nat @ A5 @ A2 )
% 4.71/5.08 => ( ~ ( member_set_nat @ A5 @ F3 )
% 4.71/5.08 => ( ( P @ F3 )
% 4.71/5.08 => ( P @ ( insert_set_nat @ A5 @ F3 ) ) ) ) ) )
% 4.71/5.08 => ( P @ F2 ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_subset_induct
% 4.71/5.08 thf(fact_3313_finite__subset__induct,axiom,
% 4.71/5.08 ! [F2: set_set_nat_rat,A2: set_set_nat_rat,P: set_set_nat_rat > $o] :
% 4.71/5.08 ( ( finite6430367030675640852at_rat @ F2 )
% 4.71/5.08 => ( ( ord_le4375437777232675859at_rat @ F2 @ A2 )
% 4.71/5.08 => ( ( P @ bot_bo6797373522285170759at_rat )
% 4.71/5.08 => ( ! [A5: set_nat_rat,F3: set_set_nat_rat] :
% 4.71/5.08 ( ( finite6430367030675640852at_rat @ F3 )
% 4.71/5.08 => ( ( member_set_nat_rat @ A5 @ A2 )
% 4.71/5.08 => ( ~ ( member_set_nat_rat @ A5 @ F3 )
% 4.71/5.08 => ( ( P @ F3 )
% 4.71/5.08 => ( P @ ( insert_set_nat_rat @ A5 @ F3 ) ) ) ) ) )
% 4.71/5.08 => ( P @ F2 ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_subset_induct
% 4.71/5.08 thf(fact_3314_finite__subset__induct,axiom,
% 4.71/5.08 ! [F2: set_complex,A2: set_complex,P: set_complex > $o] :
% 4.71/5.08 ( ( finite3207457112153483333omplex @ F2 )
% 4.71/5.08 => ( ( ord_le211207098394363844omplex @ F2 @ A2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_complex )
% 4.71/5.08 => ( ! [A5: complex,F3: set_complex] :
% 4.71/5.08 ( ( finite3207457112153483333omplex @ F3 )
% 4.71/5.08 => ( ( member_complex @ A5 @ A2 )
% 4.71/5.08 => ( ~ ( member_complex @ A5 @ F3 )
% 4.71/5.08 => ( ( P @ F3 )
% 4.71/5.08 => ( P @ ( insert_complex @ A5 @ F3 ) ) ) ) ) )
% 4.71/5.08 => ( P @ F2 ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_subset_induct
% 4.71/5.08 thf(fact_3315_finite__subset__induct,axiom,
% 4.71/5.08 ! [F2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 4.71/5.08 ( ( finite6177210948735845034at_nat @ F2 )
% 4.71/5.08 => ( ( ord_le3146513528884898305at_nat @ F2 @ A2 )
% 4.71/5.08 => ( ( P @ bot_bo2099793752762293965at_nat )
% 4.71/5.08 => ( ! [A5: product_prod_nat_nat,F3: set_Pr1261947904930325089at_nat] :
% 4.71/5.08 ( ( finite6177210948735845034at_nat @ F3 )
% 4.71/5.08 => ( ( member8440522571783428010at_nat @ A5 @ A2 )
% 4.71/5.08 => ( ~ ( member8440522571783428010at_nat @ A5 @ F3 )
% 4.71/5.08 => ( ( P @ F3 )
% 4.71/5.08 => ( P @ ( insert8211810215607154385at_nat @ A5 @ F3 ) ) ) ) ) )
% 4.71/5.08 => ( P @ F2 ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_subset_induct
% 4.71/5.08 thf(fact_3316_finite__subset__induct,axiom,
% 4.71/5.08 ! [F2: set_Extended_enat,A2: set_Extended_enat,P: set_Extended_enat > $o] :
% 4.71/5.08 ( ( finite4001608067531595151d_enat @ F2 )
% 4.71/5.08 => ( ( ord_le7203529160286727270d_enat @ F2 @ A2 )
% 4.71/5.08 => ( ( P @ bot_bo7653980558646680370d_enat )
% 4.71/5.08 => ( ! [A5: extended_enat,F3: set_Extended_enat] :
% 4.71/5.08 ( ( finite4001608067531595151d_enat @ F3 )
% 4.71/5.08 => ( ( member_Extended_enat @ A5 @ A2 )
% 4.71/5.08 => ( ~ ( member_Extended_enat @ A5 @ F3 )
% 4.71/5.08 => ( ( P @ F3 )
% 4.71/5.08 => ( P @ ( insert_Extended_enat @ A5 @ F3 ) ) ) ) ) )
% 4.71/5.08 => ( P @ F2 ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_subset_induct
% 4.71/5.08 thf(fact_3317_finite__subset__induct,axiom,
% 4.71/5.08 ! [F2: set_real,A2: set_real,P: set_real > $o] :
% 4.71/5.08 ( ( finite_finite_real @ F2 )
% 4.71/5.08 => ( ( ord_less_eq_set_real @ F2 @ A2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_real )
% 4.71/5.08 => ( ! [A5: real,F3: set_real] :
% 4.71/5.08 ( ( finite_finite_real @ F3 )
% 4.71/5.08 => ( ( member_real @ A5 @ A2 )
% 4.71/5.08 => ( ~ ( member_real @ A5 @ F3 )
% 4.71/5.08 => ( ( P @ F3 )
% 4.71/5.08 => ( P @ ( insert_real @ A5 @ F3 ) ) ) ) ) )
% 4.71/5.08 => ( P @ F2 ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_subset_induct
% 4.71/5.08 thf(fact_3318_finite__subset__induct,axiom,
% 4.71/5.08 ! [F2: set_o,A2: set_o,P: set_o > $o] :
% 4.71/5.08 ( ( finite_finite_o @ F2 )
% 4.71/5.08 => ( ( ord_less_eq_set_o @ F2 @ A2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_o )
% 4.71/5.08 => ( ! [A5: $o,F3: set_o] :
% 4.71/5.08 ( ( finite_finite_o @ F3 )
% 4.71/5.08 => ( ( member_o @ A5 @ A2 )
% 4.71/5.08 => ( ~ ( member_o @ A5 @ F3 )
% 4.71/5.08 => ( ( P @ F3 )
% 4.71/5.08 => ( P @ ( insert_o @ A5 @ F3 ) ) ) ) ) )
% 4.71/5.08 => ( P @ F2 ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_subset_induct
% 4.71/5.08 thf(fact_3319_finite__subset__induct,axiom,
% 4.71/5.08 ! [F2: set_nat,A2: set_nat,P: set_nat > $o] :
% 4.71/5.08 ( ( finite_finite_nat @ F2 )
% 4.71/5.08 => ( ( ord_less_eq_set_nat @ F2 @ A2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_nat )
% 4.71/5.08 => ( ! [A5: nat,F3: set_nat] :
% 4.71/5.08 ( ( finite_finite_nat @ F3 )
% 4.71/5.08 => ( ( member_nat @ A5 @ A2 )
% 4.71/5.08 => ( ~ ( member_nat @ A5 @ F3 )
% 4.71/5.08 => ( ( P @ F3 )
% 4.71/5.08 => ( P @ ( insert_nat @ A5 @ F3 ) ) ) ) ) )
% 4.71/5.08 => ( P @ F2 ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_subset_induct
% 4.71/5.08 thf(fact_3320_finite__subset__induct,axiom,
% 4.71/5.08 ! [F2: set_int,A2: set_int,P: set_int > $o] :
% 4.71/5.08 ( ( finite_finite_int @ F2 )
% 4.71/5.08 => ( ( ord_less_eq_set_int @ F2 @ A2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_int )
% 4.71/5.08 => ( ! [A5: int,F3: set_int] :
% 4.71/5.08 ( ( finite_finite_int @ F3 )
% 4.71/5.08 => ( ( member_int @ A5 @ A2 )
% 4.71/5.08 => ( ~ ( member_int @ A5 @ F3 )
% 4.71/5.08 => ( ( P @ F3 )
% 4.71/5.08 => ( P @ ( insert_int @ A5 @ F3 ) ) ) ) ) )
% 4.71/5.08 => ( P @ F2 ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_subset_induct
% 4.71/5.08 thf(fact_3321_finite__subset__induct_H,axiom,
% 4.71/5.08 ! [F2: set_set_nat,A2: set_set_nat,P: set_set_nat > $o] :
% 4.71/5.08 ( ( finite1152437895449049373et_nat @ F2 )
% 4.71/5.08 => ( ( ord_le6893508408891458716et_nat @ F2 @ A2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_set_nat )
% 4.71/5.08 => ( ! [A5: set_nat,F3: set_set_nat] :
% 4.71/5.08 ( ( finite1152437895449049373et_nat @ F3 )
% 4.71/5.08 => ( ( member_set_nat @ A5 @ A2 )
% 4.71/5.08 => ( ( ord_le6893508408891458716et_nat @ F3 @ A2 )
% 4.71/5.08 => ( ~ ( member_set_nat @ A5 @ F3 )
% 4.71/5.08 => ( ( P @ F3 )
% 4.71/5.08 => ( P @ ( insert_set_nat @ A5 @ F3 ) ) ) ) ) ) )
% 4.71/5.08 => ( P @ F2 ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_subset_induct'
% 4.71/5.08 thf(fact_3322_finite__subset__induct_H,axiom,
% 4.71/5.08 ! [F2: set_set_nat_rat,A2: set_set_nat_rat,P: set_set_nat_rat > $o] :
% 4.71/5.08 ( ( finite6430367030675640852at_rat @ F2 )
% 4.71/5.08 => ( ( ord_le4375437777232675859at_rat @ F2 @ A2 )
% 4.71/5.08 => ( ( P @ bot_bo6797373522285170759at_rat )
% 4.71/5.08 => ( ! [A5: set_nat_rat,F3: set_set_nat_rat] :
% 4.71/5.08 ( ( finite6430367030675640852at_rat @ F3 )
% 4.71/5.08 => ( ( member_set_nat_rat @ A5 @ A2 )
% 4.71/5.08 => ( ( ord_le4375437777232675859at_rat @ F3 @ A2 )
% 4.71/5.08 => ( ~ ( member_set_nat_rat @ A5 @ F3 )
% 4.71/5.08 => ( ( P @ F3 )
% 4.71/5.08 => ( P @ ( insert_set_nat_rat @ A5 @ F3 ) ) ) ) ) ) )
% 4.71/5.08 => ( P @ F2 ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_subset_induct'
% 4.71/5.08 thf(fact_3323_finite__subset__induct_H,axiom,
% 4.71/5.08 ! [F2: set_complex,A2: set_complex,P: set_complex > $o] :
% 4.71/5.08 ( ( finite3207457112153483333omplex @ F2 )
% 4.71/5.08 => ( ( ord_le211207098394363844omplex @ F2 @ A2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_complex )
% 4.71/5.08 => ( ! [A5: complex,F3: set_complex] :
% 4.71/5.08 ( ( finite3207457112153483333omplex @ F3 )
% 4.71/5.08 => ( ( member_complex @ A5 @ A2 )
% 4.71/5.08 => ( ( ord_le211207098394363844omplex @ F3 @ A2 )
% 4.71/5.08 => ( ~ ( member_complex @ A5 @ F3 )
% 4.71/5.08 => ( ( P @ F3 )
% 4.71/5.08 => ( P @ ( insert_complex @ A5 @ F3 ) ) ) ) ) ) )
% 4.71/5.08 => ( P @ F2 ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_subset_induct'
% 4.71/5.08 thf(fact_3324_finite__subset__induct_H,axiom,
% 4.71/5.08 ! [F2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 4.71/5.08 ( ( finite6177210948735845034at_nat @ F2 )
% 4.71/5.08 => ( ( ord_le3146513528884898305at_nat @ F2 @ A2 )
% 4.71/5.08 => ( ( P @ bot_bo2099793752762293965at_nat )
% 4.71/5.08 => ( ! [A5: product_prod_nat_nat,F3: set_Pr1261947904930325089at_nat] :
% 4.71/5.08 ( ( finite6177210948735845034at_nat @ F3 )
% 4.71/5.08 => ( ( member8440522571783428010at_nat @ A5 @ A2 )
% 4.71/5.08 => ( ( ord_le3146513528884898305at_nat @ F3 @ A2 )
% 4.71/5.08 => ( ~ ( member8440522571783428010at_nat @ A5 @ F3 )
% 4.71/5.08 => ( ( P @ F3 )
% 4.71/5.08 => ( P @ ( insert8211810215607154385at_nat @ A5 @ F3 ) ) ) ) ) ) )
% 4.71/5.08 => ( P @ F2 ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_subset_induct'
% 4.71/5.08 thf(fact_3325_finite__subset__induct_H,axiom,
% 4.71/5.08 ! [F2: set_Extended_enat,A2: set_Extended_enat,P: set_Extended_enat > $o] :
% 4.71/5.08 ( ( finite4001608067531595151d_enat @ F2 )
% 4.71/5.08 => ( ( ord_le7203529160286727270d_enat @ F2 @ A2 )
% 4.71/5.08 => ( ( P @ bot_bo7653980558646680370d_enat )
% 4.71/5.08 => ( ! [A5: extended_enat,F3: set_Extended_enat] :
% 4.71/5.08 ( ( finite4001608067531595151d_enat @ F3 )
% 4.71/5.08 => ( ( member_Extended_enat @ A5 @ A2 )
% 4.71/5.08 => ( ( ord_le7203529160286727270d_enat @ F3 @ A2 )
% 4.71/5.08 => ( ~ ( member_Extended_enat @ A5 @ F3 )
% 4.71/5.08 => ( ( P @ F3 )
% 4.71/5.08 => ( P @ ( insert_Extended_enat @ A5 @ F3 ) ) ) ) ) ) )
% 4.71/5.08 => ( P @ F2 ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_subset_induct'
% 4.71/5.08 thf(fact_3326_finite__subset__induct_H,axiom,
% 4.71/5.08 ! [F2: set_real,A2: set_real,P: set_real > $o] :
% 4.71/5.08 ( ( finite_finite_real @ F2 )
% 4.71/5.08 => ( ( ord_less_eq_set_real @ F2 @ A2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_real )
% 4.71/5.08 => ( ! [A5: real,F3: set_real] :
% 4.71/5.08 ( ( finite_finite_real @ F3 )
% 4.71/5.08 => ( ( member_real @ A5 @ A2 )
% 4.71/5.08 => ( ( ord_less_eq_set_real @ F3 @ A2 )
% 4.71/5.08 => ( ~ ( member_real @ A5 @ F3 )
% 4.71/5.08 => ( ( P @ F3 )
% 4.71/5.08 => ( P @ ( insert_real @ A5 @ F3 ) ) ) ) ) ) )
% 4.71/5.08 => ( P @ F2 ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_subset_induct'
% 4.71/5.08 thf(fact_3327_finite__subset__induct_H,axiom,
% 4.71/5.08 ! [F2: set_o,A2: set_o,P: set_o > $o] :
% 4.71/5.08 ( ( finite_finite_o @ F2 )
% 4.71/5.08 => ( ( ord_less_eq_set_o @ F2 @ A2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_o )
% 4.71/5.08 => ( ! [A5: $o,F3: set_o] :
% 4.71/5.08 ( ( finite_finite_o @ F3 )
% 4.71/5.08 => ( ( member_o @ A5 @ A2 )
% 4.71/5.08 => ( ( ord_less_eq_set_o @ F3 @ A2 )
% 4.71/5.08 => ( ~ ( member_o @ A5 @ F3 )
% 4.71/5.08 => ( ( P @ F3 )
% 4.71/5.08 => ( P @ ( insert_o @ A5 @ F3 ) ) ) ) ) ) )
% 4.71/5.08 => ( P @ F2 ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_subset_induct'
% 4.71/5.08 thf(fact_3328_finite__subset__induct_H,axiom,
% 4.71/5.08 ! [F2: set_nat,A2: set_nat,P: set_nat > $o] :
% 4.71/5.08 ( ( finite_finite_nat @ F2 )
% 4.71/5.08 => ( ( ord_less_eq_set_nat @ F2 @ A2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_nat )
% 4.71/5.08 => ( ! [A5: nat,F3: set_nat] :
% 4.71/5.08 ( ( finite_finite_nat @ F3 )
% 4.71/5.08 => ( ( member_nat @ A5 @ A2 )
% 4.71/5.08 => ( ( ord_less_eq_set_nat @ F3 @ A2 )
% 4.71/5.08 => ( ~ ( member_nat @ A5 @ F3 )
% 4.71/5.08 => ( ( P @ F3 )
% 4.71/5.08 => ( P @ ( insert_nat @ A5 @ F3 ) ) ) ) ) ) )
% 4.71/5.08 => ( P @ F2 ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_subset_induct'
% 4.71/5.08 thf(fact_3329_finite__subset__induct_H,axiom,
% 4.71/5.08 ! [F2: set_int,A2: set_int,P: set_int > $o] :
% 4.71/5.08 ( ( finite_finite_int @ F2 )
% 4.71/5.08 => ( ( ord_less_eq_set_int @ F2 @ A2 )
% 4.71/5.08 => ( ( P @ bot_bot_set_int )
% 4.71/5.08 => ( ! [A5: int,F3: set_int] :
% 4.71/5.08 ( ( finite_finite_int @ F3 )
% 4.71/5.08 => ( ( member_int @ A5 @ A2 )
% 4.71/5.08 => ( ( ord_less_eq_set_int @ F3 @ A2 )
% 4.71/5.08 => ( ~ ( member_int @ A5 @ F3 )
% 4.71/5.08 => ( ( P @ F3 )
% 4.71/5.08 => ( P @ ( insert_int @ A5 @ F3 ) ) ) ) ) ) )
% 4.71/5.08 => ( P @ F2 ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_subset_induct'
% 4.71/5.08 thf(fact_3330_divide__less__eq,axiom,
% 4.71/5.08 ! [B: rat,C: rat,A: rat] :
% 4.71/5.08 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 4.71/5.08 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.08 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 4.71/5.08 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.08 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.08 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 4.71/5.08 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.08 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % divide_less_eq
% 4.71/5.08 thf(fact_3331_divide__less__eq,axiom,
% 4.71/5.08 ! [B: real,C: real,A: real] :
% 4.71/5.08 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 4.71/5.08 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.08 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 4.71/5.08 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.08 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.08 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 4.71/5.08 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.08 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % divide_less_eq
% 4.71/5.08 thf(fact_3332_less__divide__eq,axiom,
% 4.71/5.08 ! [A: rat,B: rat,C: rat] :
% 4.71/5.08 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 4.71/5.08 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.08 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 4.71/5.08 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.08 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.08 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 4.71/5.08 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.08 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % less_divide_eq
% 4.71/5.08 thf(fact_3333_less__divide__eq,axiom,
% 4.71/5.08 ! [A: real,B: real,C: real] :
% 4.71/5.08 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 4.71/5.08 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.08 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 4.71/5.08 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.08 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.08 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 4.71/5.08 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.08 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % less_divide_eq
% 4.71/5.08 thf(fact_3334_neg__divide__less__eq,axiom,
% 4.71/5.08 ! [C: rat,B: rat,A: rat] :
% 4.71/5.08 ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.08 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 4.71/5.08 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % neg_divide_less_eq
% 4.71/5.08 thf(fact_3335_neg__divide__less__eq,axiom,
% 4.71/5.08 ! [C: real,B: real,A: real] :
% 4.71/5.08 ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.08 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 4.71/5.08 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % neg_divide_less_eq
% 4.71/5.08 thf(fact_3336_neg__less__divide__eq,axiom,
% 4.71/5.08 ! [C: rat,A: rat,B: rat] :
% 4.71/5.08 ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.08 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 4.71/5.08 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % neg_less_divide_eq
% 4.71/5.08 thf(fact_3337_neg__less__divide__eq,axiom,
% 4.71/5.08 ! [C: real,A: real,B: real] :
% 4.71/5.08 ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.08 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 4.71/5.08 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % neg_less_divide_eq
% 4.71/5.08 thf(fact_3338_pos__divide__less__eq,axiom,
% 4.71/5.08 ! [C: rat,B: rat,A: rat] :
% 4.71/5.08 ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.08 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 4.71/5.08 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % pos_divide_less_eq
% 4.71/5.08 thf(fact_3339_pos__divide__less__eq,axiom,
% 4.71/5.08 ! [C: real,B: real,A: real] :
% 4.71/5.08 ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.08 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 4.71/5.08 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % pos_divide_less_eq
% 4.71/5.08 thf(fact_3340_pos__less__divide__eq,axiom,
% 4.71/5.08 ! [C: rat,A: rat,B: rat] :
% 4.71/5.08 ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.08 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 4.71/5.08 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % pos_less_divide_eq
% 4.71/5.08 thf(fact_3341_pos__less__divide__eq,axiom,
% 4.71/5.08 ! [C: real,A: real,B: real] :
% 4.71/5.08 ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.08 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 4.71/5.08 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % pos_less_divide_eq
% 4.71/5.08 thf(fact_3342_mult__imp__div__pos__less,axiom,
% 4.71/5.08 ! [Y: rat,X: rat,Z: rat] :
% 4.71/5.08 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 4.71/5.08 => ( ( ord_less_rat @ X @ ( times_times_rat @ Z @ Y ) )
% 4.71/5.08 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ Z ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_imp_div_pos_less
% 4.71/5.08 thf(fact_3343_mult__imp__div__pos__less,axiom,
% 4.71/5.08 ! [Y: real,X: real,Z: real] :
% 4.71/5.08 ( ( ord_less_real @ zero_zero_real @ Y )
% 4.71/5.08 => ( ( ord_less_real @ X @ ( times_times_real @ Z @ Y ) )
% 4.71/5.08 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ Z ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_imp_div_pos_less
% 4.71/5.08 thf(fact_3344_mult__imp__less__div__pos,axiom,
% 4.71/5.08 ! [Y: rat,Z: rat,X: rat] :
% 4.71/5.08 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 4.71/5.08 => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y ) @ X )
% 4.71/5.08 => ( ord_less_rat @ Z @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_imp_less_div_pos
% 4.71/5.08 thf(fact_3345_mult__imp__less__div__pos,axiom,
% 4.71/5.08 ! [Y: real,Z: real,X: real] :
% 4.71/5.08 ( ( ord_less_real @ zero_zero_real @ Y )
% 4.71/5.08 => ( ( ord_less_real @ ( times_times_real @ Z @ Y ) @ X )
% 4.71/5.08 => ( ord_less_real @ Z @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % mult_imp_less_div_pos
% 4.71/5.08 thf(fact_3346_divide__strict__left__mono,axiom,
% 4.71/5.08 ! [B: rat,A: rat,C: rat] :
% 4.71/5.08 ( ( ord_less_rat @ B @ A )
% 4.71/5.08 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.08 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 4.71/5.08 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % divide_strict_left_mono
% 4.71/5.08 thf(fact_3347_divide__strict__left__mono,axiom,
% 4.71/5.08 ! [B: real,A: real,C: real] :
% 4.71/5.08 ( ( ord_less_real @ B @ A )
% 4.71/5.08 => ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.08 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 4.71/5.08 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % divide_strict_left_mono
% 4.71/5.08 thf(fact_3348_divide__strict__left__mono__neg,axiom,
% 4.71/5.08 ! [A: rat,B: rat,C: rat] :
% 4.71/5.08 ( ( ord_less_rat @ A @ B )
% 4.71/5.08 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.08 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 4.71/5.08 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % divide_strict_left_mono_neg
% 4.71/5.08 thf(fact_3349_divide__strict__left__mono__neg,axiom,
% 4.71/5.08 ! [A: real,B: real,C: real] :
% 4.71/5.08 ( ( ord_less_real @ A @ B )
% 4.71/5.08 => ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.08 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 4.71/5.08 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % divide_strict_left_mono_neg
% 4.71/5.08 thf(fact_3350_add__divide__eq__if__simps_I4_J,axiom,
% 4.71/5.08 ! [Z: rat,A: rat,B: rat] :
% 4.71/5.08 ( ( ( Z = zero_zero_rat )
% 4.71/5.08 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 4.71/5.08 = A ) )
% 4.71/5.08 & ( ( Z != zero_zero_rat )
% 4.71/5.08 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 4.71/5.08 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % add_divide_eq_if_simps(4)
% 4.71/5.08 thf(fact_3351_add__divide__eq__if__simps_I4_J,axiom,
% 4.71/5.08 ! [Z: real,A: real,B: real] :
% 4.71/5.08 ( ( ( Z = zero_zero_real )
% 4.71/5.08 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 4.71/5.08 = A ) )
% 4.71/5.08 & ( ( Z != zero_zero_real )
% 4.71/5.08 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 4.71/5.08 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % add_divide_eq_if_simps(4)
% 4.71/5.08 thf(fact_3352_diff__frac__eq,axiom,
% 4.71/5.08 ! [Y: rat,Z: rat,X: rat,W2: rat] :
% 4.71/5.08 ( ( Y != zero_zero_rat )
% 4.71/5.08 => ( ( Z != zero_zero_rat )
% 4.71/5.08 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W2 @ Z ) )
% 4.71/5.08 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % diff_frac_eq
% 4.71/5.08 thf(fact_3353_diff__frac__eq,axiom,
% 4.71/5.08 ! [Y: real,Z: real,X: real,W2: real] :
% 4.71/5.08 ( ( Y != zero_zero_real )
% 4.71/5.08 => ( ( Z != zero_zero_real )
% 4.71/5.08 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W2 @ Z ) )
% 4.71/5.08 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % diff_frac_eq
% 4.71/5.08 thf(fact_3354_diff__divide__eq__iff,axiom,
% 4.71/5.08 ! [Z: rat,X: rat,Y: rat] :
% 4.71/5.08 ( ( Z != zero_zero_rat )
% 4.71/5.08 => ( ( minus_minus_rat @ X @ ( divide_divide_rat @ Y @ Z ) )
% 4.71/5.08 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % diff_divide_eq_iff
% 4.71/5.08 thf(fact_3355_diff__divide__eq__iff,axiom,
% 4.71/5.08 ! [Z: real,X: real,Y: real] :
% 4.71/5.08 ( ( Z != zero_zero_real )
% 4.71/5.08 => ( ( minus_minus_real @ X @ ( divide_divide_real @ Y @ Z ) )
% 4.71/5.08 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % diff_divide_eq_iff
% 4.71/5.08 thf(fact_3356_divide__diff__eq__iff,axiom,
% 4.71/5.08 ! [Z: rat,X: rat,Y: rat] :
% 4.71/5.08 ( ( Z != zero_zero_rat )
% 4.71/5.08 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Z ) @ Y )
% 4.71/5.08 = ( divide_divide_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % divide_diff_eq_iff
% 4.71/5.08 thf(fact_3357_divide__diff__eq__iff,axiom,
% 4.71/5.08 ! [Z: real,X: real,Y: real] :
% 4.71/5.08 ( ( Z != zero_zero_real )
% 4.71/5.08 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Z ) @ Y )
% 4.71/5.08 = ( divide_divide_real @ ( minus_minus_real @ X @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % divide_diff_eq_iff
% 4.71/5.08 thf(fact_3358_ex__less__of__nat__mult,axiom,
% 4.71/5.08 ! [X: real,Y: real] :
% 4.71/5.08 ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.08 => ? [N2: nat] : ( ord_less_real @ Y @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % ex_less_of_nat_mult
% 4.71/5.08 thf(fact_3359_ex__less__of__nat__mult,axiom,
% 4.71/5.08 ! [X: rat,Y: rat] :
% 4.71/5.08 ( ( ord_less_rat @ zero_zero_rat @ X )
% 4.71/5.08 => ? [N2: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ X ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % ex_less_of_nat_mult
% 4.71/5.08 thf(fact_3360_card__insert__if,axiom,
% 4.71/5.08 ! [A2: set_real,X: real] :
% 4.71/5.08 ( ( finite_finite_real @ A2 )
% 4.71/5.08 => ( ( ( member_real @ X @ A2 )
% 4.71/5.08 => ( ( finite_card_real @ ( insert_real @ X @ A2 ) )
% 4.71/5.08 = ( finite_card_real @ A2 ) ) )
% 4.71/5.08 & ( ~ ( member_real @ X @ A2 )
% 4.71/5.08 => ( ( finite_card_real @ ( insert_real @ X @ A2 ) )
% 4.71/5.08 = ( suc @ ( finite_card_real @ A2 ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_insert_if
% 4.71/5.08 thf(fact_3361_card__insert__if,axiom,
% 4.71/5.08 ! [A2: set_o,X: $o] :
% 4.71/5.08 ( ( finite_finite_o @ A2 )
% 4.71/5.08 => ( ( ( member_o @ X @ A2 )
% 4.71/5.08 => ( ( finite_card_o @ ( insert_o @ X @ A2 ) )
% 4.71/5.08 = ( finite_card_o @ A2 ) ) )
% 4.71/5.08 & ( ~ ( member_o @ X @ A2 )
% 4.71/5.08 => ( ( finite_card_o @ ( insert_o @ X @ A2 ) )
% 4.71/5.08 = ( suc @ ( finite_card_o @ A2 ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_insert_if
% 4.71/5.08 thf(fact_3362_card__insert__if,axiom,
% 4.71/5.08 ! [A2: set_set_nat_rat,X: set_nat_rat] :
% 4.71/5.08 ( ( finite6430367030675640852at_rat @ A2 )
% 4.71/5.08 => ( ( ( member_set_nat_rat @ X @ A2 )
% 4.71/5.08 => ( ( finite8736671560171388117at_rat @ ( insert_set_nat_rat @ X @ A2 ) )
% 4.71/5.08 = ( finite8736671560171388117at_rat @ A2 ) ) )
% 4.71/5.08 & ( ~ ( member_set_nat_rat @ X @ A2 )
% 4.71/5.08 => ( ( finite8736671560171388117at_rat @ ( insert_set_nat_rat @ X @ A2 ) )
% 4.71/5.08 = ( suc @ ( finite8736671560171388117at_rat @ A2 ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_insert_if
% 4.71/5.08 thf(fact_3363_card__insert__if,axiom,
% 4.71/5.08 ! [A2: set_list_nat,X: list_nat] :
% 4.71/5.08 ( ( finite8100373058378681591st_nat @ A2 )
% 4.71/5.08 => ( ( ( member_list_nat @ X @ A2 )
% 4.71/5.08 => ( ( finite_card_list_nat @ ( insert_list_nat @ X @ A2 ) )
% 4.71/5.08 = ( finite_card_list_nat @ A2 ) ) )
% 4.71/5.08 & ( ~ ( member_list_nat @ X @ A2 )
% 4.71/5.08 => ( ( finite_card_list_nat @ ( insert_list_nat @ X @ A2 ) )
% 4.71/5.08 = ( suc @ ( finite_card_list_nat @ A2 ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_insert_if
% 4.71/5.08 thf(fact_3364_card__insert__if,axiom,
% 4.71/5.08 ! [A2: set_set_nat,X: set_nat] :
% 4.71/5.08 ( ( finite1152437895449049373et_nat @ A2 )
% 4.71/5.08 => ( ( ( member_set_nat @ X @ A2 )
% 4.71/5.08 => ( ( finite_card_set_nat @ ( insert_set_nat @ X @ A2 ) )
% 4.71/5.08 = ( finite_card_set_nat @ A2 ) ) )
% 4.71/5.08 & ( ~ ( member_set_nat @ X @ A2 )
% 4.71/5.08 => ( ( finite_card_set_nat @ ( insert_set_nat @ X @ A2 ) )
% 4.71/5.08 = ( suc @ ( finite_card_set_nat @ A2 ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_insert_if
% 4.71/5.08 thf(fact_3365_card__insert__if,axiom,
% 4.71/5.08 ! [A2: set_nat,X: nat] :
% 4.71/5.08 ( ( finite_finite_nat @ A2 )
% 4.71/5.08 => ( ( ( member_nat @ X @ A2 )
% 4.71/5.08 => ( ( finite_card_nat @ ( insert_nat @ X @ A2 ) )
% 4.71/5.08 = ( finite_card_nat @ A2 ) ) )
% 4.71/5.08 & ( ~ ( member_nat @ X @ A2 )
% 4.71/5.08 => ( ( finite_card_nat @ ( insert_nat @ X @ A2 ) )
% 4.71/5.08 = ( suc @ ( finite_card_nat @ A2 ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_insert_if
% 4.71/5.08 thf(fact_3366_card__insert__if,axiom,
% 4.71/5.08 ! [A2: set_int,X: int] :
% 4.71/5.08 ( ( finite_finite_int @ A2 )
% 4.71/5.08 => ( ( ( member_int @ X @ A2 )
% 4.71/5.08 => ( ( finite_card_int @ ( insert_int @ X @ A2 ) )
% 4.71/5.08 = ( finite_card_int @ A2 ) ) )
% 4.71/5.08 & ( ~ ( member_int @ X @ A2 )
% 4.71/5.08 => ( ( finite_card_int @ ( insert_int @ X @ A2 ) )
% 4.71/5.08 = ( suc @ ( finite_card_int @ A2 ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_insert_if
% 4.71/5.08 thf(fact_3367_card__insert__if,axiom,
% 4.71/5.08 ! [A2: set_complex,X: complex] :
% 4.71/5.08 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.08 => ( ( ( member_complex @ X @ A2 )
% 4.71/5.08 => ( ( finite_card_complex @ ( insert_complex @ X @ A2 ) )
% 4.71/5.08 = ( finite_card_complex @ A2 ) ) )
% 4.71/5.08 & ( ~ ( member_complex @ X @ A2 )
% 4.71/5.08 => ( ( finite_card_complex @ ( insert_complex @ X @ A2 ) )
% 4.71/5.08 = ( suc @ ( finite_card_complex @ A2 ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_insert_if
% 4.71/5.08 thf(fact_3368_card__insert__if,axiom,
% 4.71/5.08 ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 4.71/5.08 ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.08 => ( ( ( member8440522571783428010at_nat @ X @ A2 )
% 4.71/5.08 => ( ( finite711546835091564841at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) )
% 4.71/5.08 = ( finite711546835091564841at_nat @ A2 ) ) )
% 4.71/5.08 & ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 4.71/5.08 => ( ( finite711546835091564841at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) )
% 4.71/5.08 = ( suc @ ( finite711546835091564841at_nat @ A2 ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_insert_if
% 4.71/5.08 thf(fact_3369_card__insert__if,axiom,
% 4.71/5.08 ! [A2: set_Extended_enat,X: extended_enat] :
% 4.71/5.08 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.08 => ( ( ( member_Extended_enat @ X @ A2 )
% 4.71/5.08 => ( ( finite121521170596916366d_enat @ ( insert_Extended_enat @ X @ A2 ) )
% 4.71/5.08 = ( finite121521170596916366d_enat @ A2 ) ) )
% 4.71/5.08 & ( ~ ( member_Extended_enat @ X @ A2 )
% 4.71/5.08 => ( ( finite121521170596916366d_enat @ ( insert_Extended_enat @ X @ A2 ) )
% 4.71/5.08 = ( suc @ ( finite121521170596916366d_enat @ A2 ) ) ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_insert_if
% 4.71/5.08 thf(fact_3370_card__Suc__eq__finite,axiom,
% 4.71/5.08 ! [A2: set_real,K: nat] :
% 4.71/5.08 ( ( ( finite_card_real @ A2 )
% 4.71/5.08 = ( suc @ K ) )
% 4.71/5.08 = ( ? [B4: real,B6: set_real] :
% 4.71/5.08 ( ( A2
% 4.71/5.08 = ( insert_real @ B4 @ B6 ) )
% 4.71/5.08 & ~ ( member_real @ B4 @ B6 )
% 4.71/5.08 & ( ( finite_card_real @ B6 )
% 4.71/5.08 = K )
% 4.71/5.08 & ( finite_finite_real @ B6 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_Suc_eq_finite
% 4.71/5.08 thf(fact_3371_card__Suc__eq__finite,axiom,
% 4.71/5.08 ! [A2: set_o,K: nat] :
% 4.71/5.08 ( ( ( finite_card_o @ A2 )
% 4.71/5.08 = ( suc @ K ) )
% 4.71/5.08 = ( ? [B4: $o,B6: set_o] :
% 4.71/5.08 ( ( A2
% 4.71/5.08 = ( insert_o @ B4 @ B6 ) )
% 4.71/5.08 & ~ ( member_o @ B4 @ B6 )
% 4.71/5.08 & ( ( finite_card_o @ B6 )
% 4.71/5.08 = K )
% 4.71/5.08 & ( finite_finite_o @ B6 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_Suc_eq_finite
% 4.71/5.08 thf(fact_3372_card__Suc__eq__finite,axiom,
% 4.71/5.08 ! [A2: set_set_nat_rat,K: nat] :
% 4.71/5.08 ( ( ( finite8736671560171388117at_rat @ A2 )
% 4.71/5.08 = ( suc @ K ) )
% 4.71/5.08 = ( ? [B4: set_nat_rat,B6: set_set_nat_rat] :
% 4.71/5.08 ( ( A2
% 4.71/5.08 = ( insert_set_nat_rat @ B4 @ B6 ) )
% 4.71/5.08 & ~ ( member_set_nat_rat @ B4 @ B6 )
% 4.71/5.08 & ( ( finite8736671560171388117at_rat @ B6 )
% 4.71/5.08 = K )
% 4.71/5.08 & ( finite6430367030675640852at_rat @ B6 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_Suc_eq_finite
% 4.71/5.08 thf(fact_3373_card__Suc__eq__finite,axiom,
% 4.71/5.08 ! [A2: set_list_nat,K: nat] :
% 4.71/5.08 ( ( ( finite_card_list_nat @ A2 )
% 4.71/5.08 = ( suc @ K ) )
% 4.71/5.08 = ( ? [B4: list_nat,B6: set_list_nat] :
% 4.71/5.08 ( ( A2
% 4.71/5.08 = ( insert_list_nat @ B4 @ B6 ) )
% 4.71/5.08 & ~ ( member_list_nat @ B4 @ B6 )
% 4.71/5.08 & ( ( finite_card_list_nat @ B6 )
% 4.71/5.08 = K )
% 4.71/5.08 & ( finite8100373058378681591st_nat @ B6 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_Suc_eq_finite
% 4.71/5.08 thf(fact_3374_card__Suc__eq__finite,axiom,
% 4.71/5.08 ! [A2: set_set_nat,K: nat] :
% 4.71/5.08 ( ( ( finite_card_set_nat @ A2 )
% 4.71/5.08 = ( suc @ K ) )
% 4.71/5.08 = ( ? [B4: set_nat,B6: set_set_nat] :
% 4.71/5.08 ( ( A2
% 4.71/5.08 = ( insert_set_nat @ B4 @ B6 ) )
% 4.71/5.08 & ~ ( member_set_nat @ B4 @ B6 )
% 4.71/5.08 & ( ( finite_card_set_nat @ B6 )
% 4.71/5.08 = K )
% 4.71/5.08 & ( finite1152437895449049373et_nat @ B6 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_Suc_eq_finite
% 4.71/5.08 thf(fact_3375_card__Suc__eq__finite,axiom,
% 4.71/5.08 ! [A2: set_nat,K: nat] :
% 4.71/5.08 ( ( ( finite_card_nat @ A2 )
% 4.71/5.08 = ( suc @ K ) )
% 4.71/5.08 = ( ? [B4: nat,B6: set_nat] :
% 4.71/5.08 ( ( A2
% 4.71/5.08 = ( insert_nat @ B4 @ B6 ) )
% 4.71/5.08 & ~ ( member_nat @ B4 @ B6 )
% 4.71/5.08 & ( ( finite_card_nat @ B6 )
% 4.71/5.08 = K )
% 4.71/5.08 & ( finite_finite_nat @ B6 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_Suc_eq_finite
% 4.71/5.08 thf(fact_3376_card__Suc__eq__finite,axiom,
% 4.71/5.08 ! [A2: set_int,K: nat] :
% 4.71/5.08 ( ( ( finite_card_int @ A2 )
% 4.71/5.08 = ( suc @ K ) )
% 4.71/5.08 = ( ? [B4: int,B6: set_int] :
% 4.71/5.08 ( ( A2
% 4.71/5.08 = ( insert_int @ B4 @ B6 ) )
% 4.71/5.08 & ~ ( member_int @ B4 @ B6 )
% 4.71/5.08 & ( ( finite_card_int @ B6 )
% 4.71/5.08 = K )
% 4.71/5.08 & ( finite_finite_int @ B6 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_Suc_eq_finite
% 4.71/5.08 thf(fact_3377_card__Suc__eq__finite,axiom,
% 4.71/5.08 ! [A2: set_complex,K: nat] :
% 4.71/5.08 ( ( ( finite_card_complex @ A2 )
% 4.71/5.08 = ( suc @ K ) )
% 4.71/5.08 = ( ? [B4: complex,B6: set_complex] :
% 4.71/5.08 ( ( A2
% 4.71/5.08 = ( insert_complex @ B4 @ B6 ) )
% 4.71/5.08 & ~ ( member_complex @ B4 @ B6 )
% 4.71/5.08 & ( ( finite_card_complex @ B6 )
% 4.71/5.08 = K )
% 4.71/5.08 & ( finite3207457112153483333omplex @ B6 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_Suc_eq_finite
% 4.71/5.08 thf(fact_3378_card__Suc__eq__finite,axiom,
% 4.71/5.08 ! [A2: set_Pr1261947904930325089at_nat,K: nat] :
% 4.71/5.08 ( ( ( finite711546835091564841at_nat @ A2 )
% 4.71/5.08 = ( suc @ K ) )
% 4.71/5.08 = ( ? [B4: product_prod_nat_nat,B6: set_Pr1261947904930325089at_nat] :
% 4.71/5.08 ( ( A2
% 4.71/5.08 = ( insert8211810215607154385at_nat @ B4 @ B6 ) )
% 4.71/5.08 & ~ ( member8440522571783428010at_nat @ B4 @ B6 )
% 4.71/5.08 & ( ( finite711546835091564841at_nat @ B6 )
% 4.71/5.08 = K )
% 4.71/5.08 & ( finite6177210948735845034at_nat @ B6 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_Suc_eq_finite
% 4.71/5.08 thf(fact_3379_card__Suc__eq__finite,axiom,
% 4.71/5.08 ! [A2: set_Extended_enat,K: nat] :
% 4.71/5.08 ( ( ( finite121521170596916366d_enat @ A2 )
% 4.71/5.08 = ( suc @ K ) )
% 4.71/5.08 = ( ? [B4: extended_enat,B6: set_Extended_enat] :
% 4.71/5.08 ( ( A2
% 4.71/5.08 = ( insert_Extended_enat @ B4 @ B6 ) )
% 4.71/5.08 & ~ ( member_Extended_enat @ B4 @ B6 )
% 4.71/5.08 & ( ( finite121521170596916366d_enat @ B6 )
% 4.71/5.08 = K )
% 4.71/5.08 & ( finite4001608067531595151d_enat @ B6 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_Suc_eq_finite
% 4.71/5.08 thf(fact_3380_infinite__remove,axiom,
% 4.71/5.08 ! [S2: set_complex,A: complex] :
% 4.71/5.08 ( ~ ( finite3207457112153483333omplex @ S2 )
% 4.71/5.08 => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % infinite_remove
% 4.71/5.08 thf(fact_3381_infinite__remove,axiom,
% 4.71/5.08 ! [S2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat] :
% 4.71/5.08 ( ~ ( finite6177210948735845034at_nat @ S2 )
% 4.71/5.08 => ~ ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ S2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % infinite_remove
% 4.71/5.08 thf(fact_3382_infinite__remove,axiom,
% 4.71/5.08 ! [S2: set_Extended_enat,A: extended_enat] :
% 4.71/5.08 ( ~ ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.08 => ~ ( finite4001608067531595151d_enat @ ( minus_925952699566721837d_enat @ S2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % infinite_remove
% 4.71/5.08 thf(fact_3383_infinite__remove,axiom,
% 4.71/5.08 ! [S2: set_real,A: real] :
% 4.71/5.08 ( ~ ( finite_finite_real @ S2 )
% 4.71/5.08 => ~ ( finite_finite_real @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % infinite_remove
% 4.71/5.08 thf(fact_3384_infinite__remove,axiom,
% 4.71/5.08 ! [S2: set_o,A: $o] :
% 4.71/5.08 ( ~ ( finite_finite_o @ S2 )
% 4.71/5.08 => ~ ( finite_finite_o @ ( minus_minus_set_o @ S2 @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % infinite_remove
% 4.71/5.08 thf(fact_3385_infinite__remove,axiom,
% 4.71/5.08 ! [S2: set_int,A: int] :
% 4.71/5.08 ( ~ ( finite_finite_int @ S2 )
% 4.71/5.08 => ~ ( finite_finite_int @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % infinite_remove
% 4.71/5.08 thf(fact_3386_infinite__remove,axiom,
% 4.71/5.08 ! [S2: set_nat,A: nat] :
% 4.71/5.08 ( ~ ( finite_finite_nat @ S2 )
% 4.71/5.08 => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % infinite_remove
% 4.71/5.08 thf(fact_3387_infinite__coinduct,axiom,
% 4.71/5.08 ! [X5: set_complex > $o,A2: set_complex] :
% 4.71/5.08 ( ( X5 @ A2 )
% 4.71/5.08 => ( ! [A3: set_complex] :
% 4.71/5.08 ( ( X5 @ A3 )
% 4.71/5.08 => ? [X2: complex] :
% 4.71/5.08 ( ( member_complex @ X2 @ A3 )
% 4.71/5.08 & ( ( X5 @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) )
% 4.71/5.08 | ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) )
% 4.71/5.08 => ~ ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % infinite_coinduct
% 4.71/5.08 thf(fact_3388_infinite__coinduct,axiom,
% 4.71/5.08 ! [X5: set_Pr1261947904930325089at_nat > $o,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.08 ( ( X5 @ A2 )
% 4.71/5.08 => ( ! [A3: set_Pr1261947904930325089at_nat] :
% 4.71/5.08 ( ( X5 @ A3 )
% 4.71/5.08 => ? [X2: product_prod_nat_nat] :
% 4.71/5.08 ( ( member8440522571783428010at_nat @ X2 @ A3 )
% 4.71/5.08 & ( ( X5 @ ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) )
% 4.71/5.08 | ~ ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) ) ) ) )
% 4.71/5.08 => ~ ( finite6177210948735845034at_nat @ A2 ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % infinite_coinduct
% 4.71/5.08 thf(fact_3389_infinite__coinduct,axiom,
% 4.71/5.08 ! [X5: set_Extended_enat > $o,A2: set_Extended_enat] :
% 4.71/5.08 ( ( X5 @ A2 )
% 4.71/5.08 => ( ! [A3: set_Extended_enat] :
% 4.71/5.08 ( ( X5 @ A3 )
% 4.71/5.08 => ? [X2: extended_enat] :
% 4.71/5.08 ( ( member_Extended_enat @ X2 @ A3 )
% 4.71/5.08 & ( ( X5 @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ X2 @ bot_bo7653980558646680370d_enat ) ) )
% 4.71/5.08 | ~ ( finite4001608067531595151d_enat @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ X2 @ bot_bo7653980558646680370d_enat ) ) ) ) ) )
% 4.71/5.08 => ~ ( finite4001608067531595151d_enat @ A2 ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % infinite_coinduct
% 4.71/5.08 thf(fact_3390_infinite__coinduct,axiom,
% 4.71/5.08 ! [X5: set_real > $o,A2: set_real] :
% 4.71/5.08 ( ( X5 @ A2 )
% 4.71/5.08 => ( ! [A3: set_real] :
% 4.71/5.08 ( ( X5 @ A3 )
% 4.71/5.08 => ? [X2: real] :
% 4.71/5.08 ( ( member_real @ X2 @ A3 )
% 4.71/5.08 & ( ( X5 @ ( minus_minus_set_real @ A3 @ ( insert_real @ X2 @ bot_bot_set_real ) ) )
% 4.71/5.08 | ~ ( finite_finite_real @ ( minus_minus_set_real @ A3 @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) ) ) )
% 4.71/5.08 => ~ ( finite_finite_real @ A2 ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % infinite_coinduct
% 4.71/5.08 thf(fact_3391_infinite__coinduct,axiom,
% 4.71/5.08 ! [X5: set_o > $o,A2: set_o] :
% 4.71/5.08 ( ( X5 @ A2 )
% 4.71/5.08 => ( ! [A3: set_o] :
% 4.71/5.08 ( ( X5 @ A3 )
% 4.71/5.08 => ? [X2: $o] :
% 4.71/5.08 ( ( member_o @ X2 @ A3 )
% 4.71/5.08 & ( ( X5 @ ( minus_minus_set_o @ A3 @ ( insert_o @ X2 @ bot_bot_set_o ) ) )
% 4.71/5.08 | ~ ( finite_finite_o @ ( minus_minus_set_o @ A3 @ ( insert_o @ X2 @ bot_bot_set_o ) ) ) ) ) )
% 4.71/5.08 => ~ ( finite_finite_o @ A2 ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % infinite_coinduct
% 4.71/5.08 thf(fact_3392_infinite__coinduct,axiom,
% 4.71/5.08 ! [X5: set_int > $o,A2: set_int] :
% 4.71/5.08 ( ( X5 @ A2 )
% 4.71/5.08 => ( ! [A3: set_int] :
% 4.71/5.08 ( ( X5 @ A3 )
% 4.71/5.08 => ? [X2: int] :
% 4.71/5.08 ( ( member_int @ X2 @ A3 )
% 4.71/5.08 & ( ( X5 @ ( minus_minus_set_int @ A3 @ ( insert_int @ X2 @ bot_bot_set_int ) ) )
% 4.71/5.08 | ~ ( finite_finite_int @ ( minus_minus_set_int @ A3 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) )
% 4.71/5.08 => ~ ( finite_finite_int @ A2 ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % infinite_coinduct
% 4.71/5.08 thf(fact_3393_infinite__coinduct,axiom,
% 4.71/5.08 ! [X5: set_nat > $o,A2: set_nat] :
% 4.71/5.08 ( ( X5 @ A2 )
% 4.71/5.08 => ( ! [A3: set_nat] :
% 4.71/5.08 ( ( X5 @ A3 )
% 4.71/5.08 => ? [X2: nat] :
% 4.71/5.08 ( ( member_nat @ X2 @ A3 )
% 4.71/5.08 & ( ( X5 @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) )
% 4.71/5.08 | ~ ( finite_finite_nat @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ) )
% 4.71/5.08 => ~ ( finite_finite_nat @ A2 ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % infinite_coinduct
% 4.71/5.08 thf(fact_3394_finite__empty__induct,axiom,
% 4.71/5.08 ! [A2: set_set_nat,P: set_set_nat > $o] :
% 4.71/5.08 ( ( finite1152437895449049373et_nat @ A2 )
% 4.71/5.08 => ( ( P @ A2 )
% 4.71/5.08 => ( ! [A5: set_nat,A3: set_set_nat] :
% 4.71/5.08 ( ( finite1152437895449049373et_nat @ A3 )
% 4.71/5.08 => ( ( member_set_nat @ A5 @ A3 )
% 4.71/5.08 => ( ( P @ A3 )
% 4.71/5.08 => ( P @ ( minus_2163939370556025621et_nat @ A3 @ ( insert_set_nat @ A5 @ bot_bot_set_set_nat ) ) ) ) ) )
% 4.71/5.08 => ( P @ bot_bot_set_set_nat ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_empty_induct
% 4.71/5.08 thf(fact_3395_finite__empty__induct,axiom,
% 4.71/5.08 ! [A2: set_set_nat_rat,P: set_set_nat_rat > $o] :
% 4.71/5.08 ( ( finite6430367030675640852at_rat @ A2 )
% 4.71/5.08 => ( ( P @ A2 )
% 4.71/5.08 => ( ! [A5: set_nat_rat,A3: set_set_nat_rat] :
% 4.71/5.08 ( ( finite6430367030675640852at_rat @ A3 )
% 4.71/5.08 => ( ( member_set_nat_rat @ A5 @ A3 )
% 4.71/5.08 => ( ( P @ A3 )
% 4.71/5.08 => ( P @ ( minus_1626877696091177228at_rat @ A3 @ ( insert_set_nat_rat @ A5 @ bot_bo6797373522285170759at_rat ) ) ) ) ) )
% 4.71/5.08 => ( P @ bot_bo6797373522285170759at_rat ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_empty_induct
% 4.71/5.08 thf(fact_3396_finite__empty__induct,axiom,
% 4.71/5.08 ! [A2: set_complex,P: set_complex > $o] :
% 4.71/5.08 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.08 => ( ( P @ A2 )
% 4.71/5.08 => ( ! [A5: complex,A3: set_complex] :
% 4.71/5.08 ( ( finite3207457112153483333omplex @ A3 )
% 4.71/5.08 => ( ( member_complex @ A5 @ A3 )
% 4.71/5.08 => ( ( P @ A3 )
% 4.71/5.08 => ( P @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ A5 @ bot_bot_set_complex ) ) ) ) ) )
% 4.71/5.08 => ( P @ bot_bot_set_complex ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_empty_induct
% 4.71/5.08 thf(fact_3397_finite__empty__induct,axiom,
% 4.71/5.08 ! [A2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 4.71/5.08 ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.08 => ( ( P @ A2 )
% 4.71/5.08 => ( ! [A5: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat] :
% 4.71/5.08 ( ( finite6177210948735845034at_nat @ A3 )
% 4.71/5.08 => ( ( member8440522571783428010at_nat @ A5 @ A3 )
% 4.71/5.08 => ( ( P @ A3 )
% 4.71/5.08 => ( P @ ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ A5 @ bot_bo2099793752762293965at_nat ) ) ) ) ) )
% 4.71/5.08 => ( P @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_empty_induct
% 4.71/5.08 thf(fact_3398_finite__empty__induct,axiom,
% 4.71/5.08 ! [A2: set_Extended_enat,P: set_Extended_enat > $o] :
% 4.71/5.08 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.08 => ( ( P @ A2 )
% 4.71/5.08 => ( ! [A5: extended_enat,A3: set_Extended_enat] :
% 4.71/5.08 ( ( finite4001608067531595151d_enat @ A3 )
% 4.71/5.08 => ( ( member_Extended_enat @ A5 @ A3 )
% 4.71/5.08 => ( ( P @ A3 )
% 4.71/5.08 => ( P @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ A5 @ bot_bo7653980558646680370d_enat ) ) ) ) ) )
% 4.71/5.08 => ( P @ bot_bo7653980558646680370d_enat ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_empty_induct
% 4.71/5.08 thf(fact_3399_finite__empty__induct,axiom,
% 4.71/5.08 ! [A2: set_real,P: set_real > $o] :
% 4.71/5.08 ( ( finite_finite_real @ A2 )
% 4.71/5.08 => ( ( P @ A2 )
% 4.71/5.08 => ( ! [A5: real,A3: set_real] :
% 4.71/5.08 ( ( finite_finite_real @ A3 )
% 4.71/5.08 => ( ( member_real @ A5 @ A3 )
% 4.71/5.08 => ( ( P @ A3 )
% 4.71/5.08 => ( P @ ( minus_minus_set_real @ A3 @ ( insert_real @ A5 @ bot_bot_set_real ) ) ) ) ) )
% 4.71/5.08 => ( P @ bot_bot_set_real ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_empty_induct
% 4.71/5.08 thf(fact_3400_finite__empty__induct,axiom,
% 4.71/5.08 ! [A2: set_o,P: set_o > $o] :
% 4.71/5.08 ( ( finite_finite_o @ A2 )
% 4.71/5.08 => ( ( P @ A2 )
% 4.71/5.08 => ( ! [A5: $o,A3: set_o] :
% 4.71/5.08 ( ( finite_finite_o @ A3 )
% 4.71/5.08 => ( ( member_o @ A5 @ A3 )
% 4.71/5.08 => ( ( P @ A3 )
% 4.71/5.08 => ( P @ ( minus_minus_set_o @ A3 @ ( insert_o @ A5 @ bot_bot_set_o ) ) ) ) ) )
% 4.71/5.08 => ( P @ bot_bot_set_o ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_empty_induct
% 4.71/5.08 thf(fact_3401_finite__empty__induct,axiom,
% 4.71/5.08 ! [A2: set_int,P: set_int > $o] :
% 4.71/5.08 ( ( finite_finite_int @ A2 )
% 4.71/5.08 => ( ( P @ A2 )
% 4.71/5.08 => ( ! [A5: int,A3: set_int] :
% 4.71/5.08 ( ( finite_finite_int @ A3 )
% 4.71/5.08 => ( ( member_int @ A5 @ A3 )
% 4.71/5.08 => ( ( P @ A3 )
% 4.71/5.08 => ( P @ ( minus_minus_set_int @ A3 @ ( insert_int @ A5 @ bot_bot_set_int ) ) ) ) ) )
% 4.71/5.08 => ( P @ bot_bot_set_int ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_empty_induct
% 4.71/5.08 thf(fact_3402_finite__empty__induct,axiom,
% 4.71/5.08 ! [A2: set_nat,P: set_nat > $o] :
% 4.71/5.08 ( ( finite_finite_nat @ A2 )
% 4.71/5.08 => ( ( P @ A2 )
% 4.71/5.08 => ( ! [A5: nat,A3: set_nat] :
% 4.71/5.08 ( ( finite_finite_nat @ A3 )
% 4.71/5.08 => ( ( member_nat @ A5 @ A3 )
% 4.71/5.08 => ( ( P @ A3 )
% 4.71/5.08 => ( P @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ A5 @ bot_bot_set_nat ) ) ) ) ) )
% 4.71/5.08 => ( P @ bot_bot_set_nat ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % finite_empty_induct
% 4.71/5.08 thf(fact_3403_Diff__single__insert,axiom,
% 4.71/5.08 ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 4.71/5.08 ( ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ B2 )
% 4.71/5.08 => ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ B2 ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % Diff_single_insert
% 4.71/5.08 thf(fact_3404_Diff__single__insert,axiom,
% 4.71/5.08 ! [A2: set_real,X: real,B2: set_real] :
% 4.71/5.08 ( ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B2 )
% 4.71/5.08 => ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ B2 ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % Diff_single_insert
% 4.71/5.08 thf(fact_3405_Diff__single__insert,axiom,
% 4.71/5.08 ! [A2: set_o,X: $o,B2: set_o] :
% 4.71/5.08 ( ( ord_less_eq_set_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) @ B2 )
% 4.71/5.08 => ( ord_less_eq_set_o @ A2 @ ( insert_o @ X @ B2 ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % Diff_single_insert
% 4.71/5.08 thf(fact_3406_Diff__single__insert,axiom,
% 4.71/5.08 ! [A2: set_nat,X: nat,B2: set_nat] :
% 4.71/5.08 ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B2 )
% 4.71/5.08 => ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B2 ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % Diff_single_insert
% 4.71/5.08 thf(fact_3407_Diff__single__insert,axiom,
% 4.71/5.08 ! [A2: set_int,X: int,B2: set_int] :
% 4.71/5.08 ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B2 )
% 4.71/5.08 => ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B2 ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % Diff_single_insert
% 4.71/5.08 thf(fact_3408_subset__insert__iff,axiom,
% 4.71/5.08 ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 4.71/5.08 ( ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ B2 ) )
% 4.71/5.08 = ( ( ( member8440522571783428010at_nat @ X @ A2 )
% 4.71/5.08 => ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ B2 ) )
% 4.71/5.08 & ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 4.71/5.08 => ( ord_le3146513528884898305at_nat @ A2 @ B2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % subset_insert_iff
% 4.71/5.08 thf(fact_3409_subset__insert__iff,axiom,
% 4.71/5.08 ! [A2: set_set_nat,X: set_nat,B2: set_set_nat] :
% 4.71/5.08 ( ( ord_le6893508408891458716et_nat @ A2 @ ( insert_set_nat @ X @ B2 ) )
% 4.71/5.08 = ( ( ( member_set_nat @ X @ A2 )
% 4.71/5.08 => ( ord_le6893508408891458716et_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ B2 ) )
% 4.71/5.08 & ( ~ ( member_set_nat @ X @ A2 )
% 4.71/5.08 => ( ord_le6893508408891458716et_nat @ A2 @ B2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % subset_insert_iff
% 4.71/5.08 thf(fact_3410_subset__insert__iff,axiom,
% 4.71/5.08 ! [A2: set_set_nat_rat,X: set_nat_rat,B2: set_set_nat_rat] :
% 4.71/5.08 ( ( ord_le4375437777232675859at_rat @ A2 @ ( insert_set_nat_rat @ X @ B2 ) )
% 4.71/5.08 = ( ( ( member_set_nat_rat @ X @ A2 )
% 4.71/5.08 => ( ord_le4375437777232675859at_rat @ ( minus_1626877696091177228at_rat @ A2 @ ( insert_set_nat_rat @ X @ bot_bo6797373522285170759at_rat ) ) @ B2 ) )
% 4.71/5.08 & ( ~ ( member_set_nat_rat @ X @ A2 )
% 4.71/5.08 => ( ord_le4375437777232675859at_rat @ A2 @ B2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % subset_insert_iff
% 4.71/5.08 thf(fact_3411_subset__insert__iff,axiom,
% 4.71/5.08 ! [A2: set_real,X: real,B2: set_real] :
% 4.71/5.08 ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ B2 ) )
% 4.71/5.08 = ( ( ( member_real @ X @ A2 )
% 4.71/5.08 => ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B2 ) )
% 4.71/5.08 & ( ~ ( member_real @ X @ A2 )
% 4.71/5.08 => ( ord_less_eq_set_real @ A2 @ B2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % subset_insert_iff
% 4.71/5.08 thf(fact_3412_subset__insert__iff,axiom,
% 4.71/5.08 ! [A2: set_o,X: $o,B2: set_o] :
% 4.71/5.08 ( ( ord_less_eq_set_o @ A2 @ ( insert_o @ X @ B2 ) )
% 4.71/5.08 = ( ( ( member_o @ X @ A2 )
% 4.71/5.08 => ( ord_less_eq_set_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) @ B2 ) )
% 4.71/5.08 & ( ~ ( member_o @ X @ A2 )
% 4.71/5.08 => ( ord_less_eq_set_o @ A2 @ B2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % subset_insert_iff
% 4.71/5.08 thf(fact_3413_subset__insert__iff,axiom,
% 4.71/5.08 ! [A2: set_nat,X: nat,B2: set_nat] :
% 4.71/5.08 ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B2 ) )
% 4.71/5.08 = ( ( ( member_nat @ X @ A2 )
% 4.71/5.08 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B2 ) )
% 4.71/5.08 & ( ~ ( member_nat @ X @ A2 )
% 4.71/5.08 => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % subset_insert_iff
% 4.71/5.08 thf(fact_3414_subset__insert__iff,axiom,
% 4.71/5.08 ! [A2: set_int,X: int,B2: set_int] :
% 4.71/5.08 ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B2 ) )
% 4.71/5.08 = ( ( ( member_int @ X @ A2 )
% 4.71/5.08 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B2 ) )
% 4.71/5.08 & ( ~ ( member_int @ X @ A2 )
% 4.71/5.08 => ( ord_less_eq_set_int @ A2 @ B2 ) ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % subset_insert_iff
% 4.71/5.08 thf(fact_3415_card__1__singletonE,axiom,
% 4.71/5.08 ! [A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.08 ( ( ( finite711546835091564841at_nat @ A2 )
% 4.71/5.08 = one_one_nat )
% 4.71/5.08 => ~ ! [X4: product_prod_nat_nat] :
% 4.71/5.08 ( A2
% 4.71/5.08 != ( insert8211810215607154385at_nat @ X4 @ bot_bo2099793752762293965at_nat ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_1_singletonE
% 4.71/5.08 thf(fact_3416_card__1__singletonE,axiom,
% 4.71/5.08 ! [A2: set_complex] :
% 4.71/5.08 ( ( ( finite_card_complex @ A2 )
% 4.71/5.08 = one_one_nat )
% 4.71/5.08 => ~ ! [X4: complex] :
% 4.71/5.08 ( A2
% 4.71/5.08 != ( insert_complex @ X4 @ bot_bot_set_complex ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_1_singletonE
% 4.71/5.08 thf(fact_3417_card__1__singletonE,axiom,
% 4.71/5.08 ! [A2: set_list_nat] :
% 4.71/5.08 ( ( ( finite_card_list_nat @ A2 )
% 4.71/5.08 = one_one_nat )
% 4.71/5.08 => ~ ! [X4: list_nat] :
% 4.71/5.08 ( A2
% 4.71/5.08 != ( insert_list_nat @ X4 @ bot_bot_set_list_nat ) ) ) ).
% 4.71/5.08
% 4.71/5.08 % card_1_singletonE
% 4.71/5.08 thf(fact_3418_card__1__singletonE,axiom,
% 4.71/5.08 ! [A2: set_set_nat] :
% 4.71/5.08 ( ( ( finite_card_set_nat @ A2 )
% 4.71/5.09 = one_one_nat )
% 4.71/5.09 => ~ ! [X4: set_nat] :
% 4.71/5.09 ( A2
% 4.71/5.09 != ( insert_set_nat @ X4 @ bot_bot_set_set_nat ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_1_singletonE
% 4.71/5.09 thf(fact_3419_card__1__singletonE,axiom,
% 4.71/5.09 ! [A2: set_real] :
% 4.71/5.09 ( ( ( finite_card_real @ A2 )
% 4.71/5.09 = one_one_nat )
% 4.71/5.09 => ~ ! [X4: real] :
% 4.71/5.09 ( A2
% 4.71/5.09 != ( insert_real @ X4 @ bot_bot_set_real ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_1_singletonE
% 4.71/5.09 thf(fact_3420_card__1__singletonE,axiom,
% 4.71/5.09 ! [A2: set_o] :
% 4.71/5.09 ( ( ( finite_card_o @ A2 )
% 4.71/5.09 = one_one_nat )
% 4.71/5.09 => ~ ! [X4: $o] :
% 4.71/5.09 ( A2
% 4.71/5.09 != ( insert_o @ X4 @ bot_bot_set_o ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_1_singletonE
% 4.71/5.09 thf(fact_3421_card__1__singletonE,axiom,
% 4.71/5.09 ! [A2: set_nat] :
% 4.71/5.09 ( ( ( finite_card_nat @ A2 )
% 4.71/5.09 = one_one_nat )
% 4.71/5.09 => ~ ! [X4: nat] :
% 4.71/5.09 ( A2
% 4.71/5.09 != ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_1_singletonE
% 4.71/5.09 thf(fact_3422_card__1__singletonE,axiom,
% 4.71/5.09 ! [A2: set_int] :
% 4.71/5.09 ( ( ( finite_card_int @ A2 )
% 4.71/5.09 = one_one_nat )
% 4.71/5.09 => ~ ! [X4: int] :
% 4.71/5.09 ( A2
% 4.71/5.09 != ( insert_int @ X4 @ bot_bot_set_int ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_1_singletonE
% 4.71/5.09 thf(fact_3423_one__less__mult,axiom,
% 4.71/5.09 ! [N: nat,M2: nat] :
% 4.71/5.09 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 4.71/5.09 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 4.71/5.09 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M2 @ N ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % one_less_mult
% 4.71/5.09 thf(fact_3424_n__less__m__mult__n,axiom,
% 4.71/5.09 ! [N: nat,M2: nat] :
% 4.71/5.09 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.09 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 4.71/5.09 => ( ord_less_nat @ N @ ( times_times_nat @ M2 @ N ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % n_less_m_mult_n
% 4.71/5.09 thf(fact_3425_n__less__n__mult__m,axiom,
% 4.71/5.09 ! [N: nat,M2: nat] :
% 4.71/5.09 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.09 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 4.71/5.09 => ( ord_less_nat @ N @ ( times_times_nat @ N @ M2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % n_less_n_mult_m
% 4.71/5.09 thf(fact_3426_div__less__iff__less__mult,axiom,
% 4.71/5.09 ! [Q4: nat,M2: nat,N: nat] :
% 4.71/5.09 ( ( ord_less_nat @ zero_zero_nat @ Q4 )
% 4.71/5.09 => ( ( ord_less_nat @ ( divide_divide_nat @ M2 @ Q4 ) @ N )
% 4.71/5.09 = ( ord_less_nat @ M2 @ ( times_times_nat @ N @ Q4 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % div_less_iff_less_mult
% 4.71/5.09 thf(fact_3427_zless__imp__add1__zle,axiom,
% 4.71/5.09 ! [W2: int,Z: int] :
% 4.71/5.09 ( ( ord_less_int @ W2 @ Z )
% 4.71/5.09 => ( ord_less_eq_int @ ( plus_plus_int @ W2 @ one_one_int ) @ Z ) ) ).
% 4.71/5.09
% 4.71/5.09 % zless_imp_add1_zle
% 4.71/5.09 thf(fact_3428_add1__zle__eq,axiom,
% 4.71/5.09 ! [W2: int,Z: int] :
% 4.71/5.09 ( ( ord_less_eq_int @ ( plus_plus_int @ W2 @ one_one_int ) @ Z )
% 4.71/5.09 = ( ord_less_int @ W2 @ Z ) ) ).
% 4.71/5.09
% 4.71/5.09 % add1_zle_eq
% 4.71/5.09 thf(fact_3429_int__induct,axiom,
% 4.71/5.09 ! [P: int > $o,K: int,I: int] :
% 4.71/5.09 ( ( P @ K )
% 4.71/5.09 => ( ! [I2: int] :
% 4.71/5.09 ( ( ord_less_eq_int @ K @ I2 )
% 4.71/5.09 => ( ( P @ I2 )
% 4.71/5.09 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 4.71/5.09 => ( ! [I2: int] :
% 4.71/5.09 ( ( ord_less_eq_int @ I2 @ K )
% 4.71/5.09 => ( ( P @ I2 )
% 4.71/5.09 => ( P @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 4.71/5.09 => ( P @ I ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % int_induct
% 4.71/5.09 thf(fact_3430_nat__less__eq__zless,axiom,
% 4.71/5.09 ! [W2: int,Z: int] :
% 4.71/5.09 ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 4.71/5.09 => ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z ) )
% 4.71/5.09 = ( ord_less_int @ W2 @ Z ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % nat_less_eq_zless
% 4.71/5.09 thf(fact_3431_nat__le__eq__zle,axiom,
% 4.71/5.09 ! [W2: int,Z: int] :
% 4.71/5.09 ( ( ( ord_less_int @ zero_zero_int @ W2 )
% 4.71/5.09 | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 4.71/5.09 => ( ( ord_less_eq_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z ) )
% 4.71/5.09 = ( ord_less_eq_int @ W2 @ Z ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % nat_le_eq_zle
% 4.71/5.09 thf(fact_3432_nat__eq__iff,axiom,
% 4.71/5.09 ! [W2: int,M2: nat] :
% 4.71/5.09 ( ( ( nat2 @ W2 )
% 4.71/5.09 = M2 )
% 4.71/5.09 = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 4.71/5.09 => ( W2
% 4.71/5.09 = ( semiri1314217659103216013at_int @ M2 ) ) )
% 4.71/5.09 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 4.71/5.09 => ( M2 = zero_zero_nat ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % nat_eq_iff
% 4.71/5.09 thf(fact_3433_nat__eq__iff2,axiom,
% 4.71/5.09 ! [M2: nat,W2: int] :
% 4.71/5.09 ( ( M2
% 4.71/5.09 = ( nat2 @ W2 ) )
% 4.71/5.09 = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 4.71/5.09 => ( W2
% 4.71/5.09 = ( semiri1314217659103216013at_int @ M2 ) ) )
% 4.71/5.09 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 4.71/5.09 => ( M2 = zero_zero_nat ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % nat_eq_iff2
% 4.71/5.09 thf(fact_3434_split__nat,axiom,
% 4.71/5.09 ! [P: nat > $o,I: int] :
% 4.71/5.09 ( ( P @ ( nat2 @ I ) )
% 4.71/5.09 = ( ! [N4: nat] :
% 4.71/5.09 ( ( I
% 4.71/5.09 = ( semiri1314217659103216013at_int @ N4 ) )
% 4.71/5.09 => ( P @ N4 ) )
% 4.71/5.09 & ( ( ord_less_int @ I @ zero_zero_int )
% 4.71/5.09 => ( P @ zero_zero_nat ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % split_nat
% 4.71/5.09 thf(fact_3435_le__nat__iff,axiom,
% 4.71/5.09 ! [K: int,N: nat] :
% 4.71/5.09 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 4.71/5.09 => ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
% 4.71/5.09 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % le_nat_iff
% 4.71/5.09 thf(fact_3436_nat__diff__distrib_H,axiom,
% 4.71/5.09 ! [X: int,Y: int] :
% 4.71/5.09 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 4.71/5.09 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.71/5.09 => ( ( nat2 @ ( minus_minus_int @ X @ Y ) )
% 4.71/5.09 = ( minus_minus_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % nat_diff_distrib'
% 4.71/5.09 thf(fact_3437_nat__diff__distrib,axiom,
% 4.71/5.09 ! [Z6: int,Z: int] :
% 4.71/5.09 ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 4.71/5.09 => ( ( ord_less_eq_int @ Z6 @ Z )
% 4.71/5.09 => ( ( nat2 @ ( minus_minus_int @ Z @ Z6 ) )
% 4.71/5.09 = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % nat_diff_distrib
% 4.71/5.09 thf(fact_3438_nat__div__distrib,axiom,
% 4.71/5.09 ! [X: int,Y: int] :
% 4.71/5.09 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 4.71/5.09 => ( ( nat2 @ ( divide_divide_int @ X @ Y ) )
% 4.71/5.09 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % nat_div_distrib
% 4.71/5.09 thf(fact_3439_nat__div__distrib_H,axiom,
% 4.71/5.09 ! [Y: int,X: int] :
% 4.71/5.09 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.71/5.09 => ( ( nat2 @ ( divide_divide_int @ X @ Y ) )
% 4.71/5.09 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % nat_div_distrib'
% 4.71/5.09 thf(fact_3440_field__le__mult__one__interval,axiom,
% 4.71/5.09 ! [X: real,Y: real] :
% 4.71/5.09 ( ! [Z3: real] :
% 4.71/5.09 ( ( ord_less_real @ zero_zero_real @ Z3 )
% 4.71/5.09 => ( ( ord_less_real @ Z3 @ one_one_real )
% 4.71/5.09 => ( ord_less_eq_real @ ( times_times_real @ Z3 @ X ) @ Y ) ) )
% 4.71/5.09 => ( ord_less_eq_real @ X @ Y ) ) ).
% 4.71/5.09
% 4.71/5.09 % field_le_mult_one_interval
% 4.71/5.09 thf(fact_3441_field__le__mult__one__interval,axiom,
% 4.71/5.09 ! [X: rat,Y: rat] :
% 4.71/5.09 ( ! [Z3: rat] :
% 4.71/5.09 ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 4.71/5.09 => ( ( ord_less_rat @ Z3 @ one_one_rat )
% 4.71/5.09 => ( ord_less_eq_rat @ ( times_times_rat @ Z3 @ X ) @ Y ) ) )
% 4.71/5.09 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 4.71/5.09
% 4.71/5.09 % field_le_mult_one_interval
% 4.71/5.09 thf(fact_3442_mult__le__cancel__left1,axiom,
% 4.71/5.09 ! [C: real,B: real] :
% 4.71/5.09 ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B ) )
% 4.71/5.09 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.09 => ( ord_less_eq_real @ one_one_real @ B ) )
% 4.71/5.09 & ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.09 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_le_cancel_left1
% 4.71/5.09 thf(fact_3443_mult__le__cancel__left1,axiom,
% 4.71/5.09 ! [C: rat,B: rat] :
% 4.71/5.09 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 4.71/5.09 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.09 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 4.71/5.09 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.09 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_le_cancel_left1
% 4.71/5.09 thf(fact_3444_mult__le__cancel__left1,axiom,
% 4.71/5.09 ! [C: int,B: int] :
% 4.71/5.09 ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 4.71/5.09 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 4.71/5.09 => ( ord_less_eq_int @ one_one_int @ B ) )
% 4.71/5.09 & ( ( ord_less_int @ C @ zero_zero_int )
% 4.71/5.09 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_le_cancel_left1
% 4.71/5.09 thf(fact_3445_mult__le__cancel__left2,axiom,
% 4.71/5.09 ! [C: real,A: real] :
% 4.71/5.09 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 4.71/5.09 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.09 => ( ord_less_eq_real @ A @ one_one_real ) )
% 4.71/5.09 & ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.09 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_le_cancel_left2
% 4.71/5.09 thf(fact_3446_mult__le__cancel__left2,axiom,
% 4.71/5.09 ! [C: rat,A: rat] :
% 4.71/5.09 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 4.71/5.09 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.09 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 4.71/5.09 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.09 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_le_cancel_left2
% 4.71/5.09 thf(fact_3447_mult__le__cancel__left2,axiom,
% 4.71/5.09 ! [C: int,A: int] :
% 4.71/5.09 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 4.71/5.09 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 4.71/5.09 => ( ord_less_eq_int @ A @ one_one_int ) )
% 4.71/5.09 & ( ( ord_less_int @ C @ zero_zero_int )
% 4.71/5.09 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_le_cancel_left2
% 4.71/5.09 thf(fact_3448_mult__le__cancel__right1,axiom,
% 4.71/5.09 ! [C: real,B: real] :
% 4.71/5.09 ( ( ord_less_eq_real @ C @ ( times_times_real @ B @ C ) )
% 4.71/5.09 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.09 => ( ord_less_eq_real @ one_one_real @ B ) )
% 4.71/5.09 & ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.09 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_le_cancel_right1
% 4.71/5.09 thf(fact_3449_mult__le__cancel__right1,axiom,
% 4.71/5.09 ! [C: rat,B: rat] :
% 4.71/5.09 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 4.71/5.09 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.09 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 4.71/5.09 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.09 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_le_cancel_right1
% 4.71/5.09 thf(fact_3450_mult__le__cancel__right1,axiom,
% 4.71/5.09 ! [C: int,B: int] :
% 4.71/5.09 ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 4.71/5.09 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 4.71/5.09 => ( ord_less_eq_int @ one_one_int @ B ) )
% 4.71/5.09 & ( ( ord_less_int @ C @ zero_zero_int )
% 4.71/5.09 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_le_cancel_right1
% 4.71/5.09 thf(fact_3451_mult__le__cancel__right2,axiom,
% 4.71/5.09 ! [A: real,C: real] :
% 4.71/5.09 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 4.71/5.09 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.09 => ( ord_less_eq_real @ A @ one_one_real ) )
% 4.71/5.09 & ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.09 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_le_cancel_right2
% 4.71/5.09 thf(fact_3452_mult__le__cancel__right2,axiom,
% 4.71/5.09 ! [A: rat,C: rat] :
% 4.71/5.09 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 4.71/5.09 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.09 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 4.71/5.09 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.09 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_le_cancel_right2
% 4.71/5.09 thf(fact_3453_mult__le__cancel__right2,axiom,
% 4.71/5.09 ! [A: int,C: int] :
% 4.71/5.09 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 4.71/5.09 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 4.71/5.09 => ( ord_less_eq_int @ A @ one_one_int ) )
% 4.71/5.09 & ( ( ord_less_int @ C @ zero_zero_int )
% 4.71/5.09 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_le_cancel_right2
% 4.71/5.09 thf(fact_3454_mult__less__cancel__left1,axiom,
% 4.71/5.09 ! [C: real,B: real] :
% 4.71/5.09 ( ( ord_less_real @ C @ ( times_times_real @ C @ B ) )
% 4.71/5.09 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.71/5.09 => ( ord_less_real @ one_one_real @ B ) )
% 4.71/5.09 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 4.71/5.09 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_less_cancel_left1
% 4.71/5.09 thf(fact_3455_mult__less__cancel__left1,axiom,
% 4.71/5.09 ! [C: rat,B: rat] :
% 4.71/5.09 ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 4.71/5.09 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.71/5.09 => ( ord_less_rat @ one_one_rat @ B ) )
% 4.71/5.09 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.71/5.09 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_less_cancel_left1
% 4.71/5.09 thf(fact_3456_mult__less__cancel__left1,axiom,
% 4.71/5.09 ! [C: int,B: int] :
% 4.71/5.09 ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 4.71/5.09 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.71/5.09 => ( ord_less_int @ one_one_int @ B ) )
% 4.71/5.09 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 4.71/5.09 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_less_cancel_left1
% 4.71/5.09 thf(fact_3457_mult__less__cancel__left2,axiom,
% 4.71/5.09 ! [C: real,A: real] :
% 4.71/5.09 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 4.71/5.09 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.71/5.09 => ( ord_less_real @ A @ one_one_real ) )
% 4.71/5.09 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 4.71/5.09 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_less_cancel_left2
% 4.71/5.09 thf(fact_3458_mult__less__cancel__left2,axiom,
% 4.71/5.09 ! [C: rat,A: rat] :
% 4.71/5.09 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 4.71/5.09 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.71/5.09 => ( ord_less_rat @ A @ one_one_rat ) )
% 4.71/5.09 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.71/5.09 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_less_cancel_left2
% 4.71/5.09 thf(fact_3459_mult__less__cancel__left2,axiom,
% 4.71/5.09 ! [C: int,A: int] :
% 4.71/5.09 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 4.71/5.09 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.71/5.09 => ( ord_less_int @ A @ one_one_int ) )
% 4.71/5.09 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 4.71/5.09 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_less_cancel_left2
% 4.71/5.09 thf(fact_3460_mult__less__cancel__right1,axiom,
% 4.71/5.09 ! [C: real,B: real] :
% 4.71/5.09 ( ( ord_less_real @ C @ ( times_times_real @ B @ C ) )
% 4.71/5.09 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.71/5.09 => ( ord_less_real @ one_one_real @ B ) )
% 4.71/5.09 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 4.71/5.09 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_less_cancel_right1
% 4.71/5.09 thf(fact_3461_mult__less__cancel__right1,axiom,
% 4.71/5.09 ! [C: rat,B: rat] :
% 4.71/5.09 ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 4.71/5.09 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.71/5.09 => ( ord_less_rat @ one_one_rat @ B ) )
% 4.71/5.09 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.71/5.09 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_less_cancel_right1
% 4.71/5.09 thf(fact_3462_mult__less__cancel__right1,axiom,
% 4.71/5.09 ! [C: int,B: int] :
% 4.71/5.09 ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 4.71/5.09 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.71/5.09 => ( ord_less_int @ one_one_int @ B ) )
% 4.71/5.09 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 4.71/5.09 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_less_cancel_right1
% 4.71/5.09 thf(fact_3463_mult__less__cancel__right2,axiom,
% 4.71/5.09 ! [A: real,C: real] :
% 4.71/5.09 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 4.71/5.09 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.71/5.09 => ( ord_less_real @ A @ one_one_real ) )
% 4.71/5.09 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 4.71/5.09 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_less_cancel_right2
% 4.71/5.09 thf(fact_3464_mult__less__cancel__right2,axiom,
% 4.71/5.09 ! [A: rat,C: rat] :
% 4.71/5.09 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 4.71/5.09 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.71/5.09 => ( ord_less_rat @ A @ one_one_rat ) )
% 4.71/5.09 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.71/5.09 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_less_cancel_right2
% 4.71/5.09 thf(fact_3465_mult__less__cancel__right2,axiom,
% 4.71/5.09 ! [A: int,C: int] :
% 4.71/5.09 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 4.71/5.09 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.71/5.09 => ( ord_less_int @ A @ one_one_int ) )
% 4.71/5.09 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 4.71/5.09 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_less_cancel_right2
% 4.71/5.09 thf(fact_3466_divide__le__eq,axiom,
% 4.71/5.09 ! [B: real,C: real,A: real] :
% 4.71/5.09 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 4.71/5.09 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.09 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 4.71/5.09 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.09 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.09 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 4.71/5.09 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.09 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % divide_le_eq
% 4.71/5.09 thf(fact_3467_divide__le__eq,axiom,
% 4.71/5.09 ! [B: rat,C: rat,A: rat] :
% 4.71/5.09 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 4.71/5.09 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.09 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 4.71/5.09 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.09 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.09 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 4.71/5.09 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.09 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % divide_le_eq
% 4.71/5.09 thf(fact_3468_le__divide__eq,axiom,
% 4.71/5.09 ! [A: real,B: real,C: real] :
% 4.71/5.09 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 4.71/5.09 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.09 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 4.71/5.09 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.09 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.09 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 4.71/5.09 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.09 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % le_divide_eq
% 4.71/5.09 thf(fact_3469_le__divide__eq,axiom,
% 4.71/5.09 ! [A: rat,B: rat,C: rat] :
% 4.71/5.09 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 4.71/5.09 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.09 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 4.71/5.09 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.09 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.09 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 4.71/5.09 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.09 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % le_divide_eq
% 4.71/5.09 thf(fact_3470_divide__left__mono,axiom,
% 4.71/5.09 ! [B: real,A: real,C: real] :
% 4.71/5.09 ( ( ord_less_eq_real @ B @ A )
% 4.71/5.09 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.71/5.09 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 4.71/5.09 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % divide_left_mono
% 4.71/5.09 thf(fact_3471_divide__left__mono,axiom,
% 4.71/5.09 ! [B: rat,A: rat,C: rat] :
% 4.71/5.09 ( ( ord_less_eq_rat @ B @ A )
% 4.71/5.09 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.71/5.09 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 4.71/5.09 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % divide_left_mono
% 4.71/5.09 thf(fact_3472_neg__divide__le__eq,axiom,
% 4.71/5.09 ! [C: real,B: real,A: real] :
% 4.71/5.09 ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.09 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 4.71/5.09 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % neg_divide_le_eq
% 4.71/5.09 thf(fact_3473_neg__divide__le__eq,axiom,
% 4.71/5.09 ! [C: rat,B: rat,A: rat] :
% 4.71/5.09 ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.09 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 4.71/5.09 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % neg_divide_le_eq
% 4.71/5.09 thf(fact_3474_neg__le__divide__eq,axiom,
% 4.71/5.09 ! [C: real,A: real,B: real] :
% 4.71/5.09 ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.09 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 4.71/5.09 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % neg_le_divide_eq
% 4.71/5.09 thf(fact_3475_neg__le__divide__eq,axiom,
% 4.71/5.09 ! [C: rat,A: rat,B: rat] :
% 4.71/5.09 ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.09 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 4.71/5.09 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % neg_le_divide_eq
% 4.71/5.09 thf(fact_3476_pos__divide__le__eq,axiom,
% 4.71/5.09 ! [C: real,B: real,A: real] :
% 4.71/5.09 ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.09 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 4.71/5.09 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % pos_divide_le_eq
% 4.71/5.09 thf(fact_3477_pos__divide__le__eq,axiom,
% 4.71/5.09 ! [C: rat,B: rat,A: rat] :
% 4.71/5.09 ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.09 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 4.71/5.09 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % pos_divide_le_eq
% 4.71/5.09 thf(fact_3478_pos__le__divide__eq,axiom,
% 4.71/5.09 ! [C: real,A: real,B: real] :
% 4.71/5.09 ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.09 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 4.71/5.09 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % pos_le_divide_eq
% 4.71/5.09 thf(fact_3479_pos__le__divide__eq,axiom,
% 4.71/5.09 ! [C: rat,A: rat,B: rat] :
% 4.71/5.09 ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.09 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 4.71/5.09 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % pos_le_divide_eq
% 4.71/5.09 thf(fact_3480_mult__imp__div__pos__le,axiom,
% 4.71/5.09 ! [Y: real,X: real,Z: real] :
% 4.71/5.09 ( ( ord_less_real @ zero_zero_real @ Y )
% 4.71/5.09 => ( ( ord_less_eq_real @ X @ ( times_times_real @ Z @ Y ) )
% 4.71/5.09 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ Z ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_imp_div_pos_le
% 4.71/5.09 thf(fact_3481_mult__imp__div__pos__le,axiom,
% 4.71/5.09 ! [Y: rat,X: rat,Z: rat] :
% 4.71/5.09 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 4.71/5.09 => ( ( ord_less_eq_rat @ X @ ( times_times_rat @ Z @ Y ) )
% 4.71/5.09 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ Z ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_imp_div_pos_le
% 4.71/5.09 thf(fact_3482_mult__imp__le__div__pos,axiom,
% 4.71/5.09 ! [Y: real,Z: real,X: real] :
% 4.71/5.09 ( ( ord_less_real @ zero_zero_real @ Y )
% 4.71/5.09 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ Y ) @ X )
% 4.71/5.09 => ( ord_less_eq_real @ Z @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_imp_le_div_pos
% 4.71/5.09 thf(fact_3483_mult__imp__le__div__pos,axiom,
% 4.71/5.09 ! [Y: rat,Z: rat,X: rat] :
% 4.71/5.09 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 4.71/5.09 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y ) @ X )
% 4.71/5.09 => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_imp_le_div_pos
% 4.71/5.09 thf(fact_3484_divide__left__mono__neg,axiom,
% 4.71/5.09 ! [A: real,B: real,C: real] :
% 4.71/5.09 ( ( ord_less_eq_real @ A @ B )
% 4.71/5.09 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 4.71/5.09 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 4.71/5.09 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % divide_left_mono_neg
% 4.71/5.09 thf(fact_3485_divide__left__mono__neg,axiom,
% 4.71/5.09 ! [A: rat,B: rat,C: rat] :
% 4.71/5.09 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.09 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.71/5.09 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 4.71/5.09 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % divide_left_mono_neg
% 4.71/5.09 thf(fact_3486_frac__le__eq,axiom,
% 4.71/5.09 ! [Y: real,Z: real,X: real,W2: real] :
% 4.71/5.09 ( ( Y != zero_zero_real )
% 4.71/5.09 => ( ( Z != zero_zero_real )
% 4.71/5.09 => ( ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W2 @ Z ) )
% 4.71/5.09 = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % frac_le_eq
% 4.71/5.09 thf(fact_3487_frac__le__eq,axiom,
% 4.71/5.09 ! [Y: rat,Z: rat,X: rat,W2: rat] :
% 4.71/5.09 ( ( Y != zero_zero_rat )
% 4.71/5.09 => ( ( Z != zero_zero_rat )
% 4.71/5.09 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W2 @ Z ) )
% 4.71/5.09 = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % frac_le_eq
% 4.71/5.09 thf(fact_3488_frac__less__eq,axiom,
% 4.71/5.09 ! [Y: rat,Z: rat,X: rat,W2: rat] :
% 4.71/5.09 ( ( Y != zero_zero_rat )
% 4.71/5.09 => ( ( Z != zero_zero_rat )
% 4.71/5.09 => ( ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W2 @ Z ) )
% 4.71/5.09 = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % frac_less_eq
% 4.71/5.09 thf(fact_3489_frac__less__eq,axiom,
% 4.71/5.09 ! [Y: real,Z: real,X: real,W2: real] :
% 4.71/5.09 ( ( Y != zero_zero_real )
% 4.71/5.09 => ( ( Z != zero_zero_real )
% 4.71/5.09 => ( ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W2 @ Z ) )
% 4.71/5.09 = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % frac_less_eq
% 4.71/5.09 thf(fact_3490_card__Suc__eq,axiom,
% 4.71/5.09 ! [A2: set_Pr1261947904930325089at_nat,K: nat] :
% 4.71/5.09 ( ( ( finite711546835091564841at_nat @ A2 )
% 4.71/5.09 = ( suc @ K ) )
% 4.71/5.09 = ( ? [B4: product_prod_nat_nat,B6: set_Pr1261947904930325089at_nat] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert8211810215607154385at_nat @ B4 @ B6 ) )
% 4.71/5.09 & ~ ( member8440522571783428010at_nat @ B4 @ B6 )
% 4.71/5.09 & ( ( finite711546835091564841at_nat @ B6 )
% 4.71/5.09 = K )
% 4.71/5.09 & ( ( K = zero_zero_nat )
% 4.71/5.09 => ( B6 = bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Suc_eq
% 4.71/5.09 thf(fact_3491_card__Suc__eq,axiom,
% 4.71/5.09 ! [A2: set_set_nat_rat,K: nat] :
% 4.71/5.09 ( ( ( finite8736671560171388117at_rat @ A2 )
% 4.71/5.09 = ( suc @ K ) )
% 4.71/5.09 = ( ? [B4: set_nat_rat,B6: set_set_nat_rat] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert_set_nat_rat @ B4 @ B6 ) )
% 4.71/5.09 & ~ ( member_set_nat_rat @ B4 @ B6 )
% 4.71/5.09 & ( ( finite8736671560171388117at_rat @ B6 )
% 4.71/5.09 = K )
% 4.71/5.09 & ( ( K = zero_zero_nat )
% 4.71/5.09 => ( B6 = bot_bo6797373522285170759at_rat ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Suc_eq
% 4.71/5.09 thf(fact_3492_card__Suc__eq,axiom,
% 4.71/5.09 ! [A2: set_complex,K: nat] :
% 4.71/5.09 ( ( ( finite_card_complex @ A2 )
% 4.71/5.09 = ( suc @ K ) )
% 4.71/5.09 = ( ? [B4: complex,B6: set_complex] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert_complex @ B4 @ B6 ) )
% 4.71/5.09 & ~ ( member_complex @ B4 @ B6 )
% 4.71/5.09 & ( ( finite_card_complex @ B6 )
% 4.71/5.09 = K )
% 4.71/5.09 & ( ( K = zero_zero_nat )
% 4.71/5.09 => ( B6 = bot_bot_set_complex ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Suc_eq
% 4.71/5.09 thf(fact_3493_card__Suc__eq,axiom,
% 4.71/5.09 ! [A2: set_list_nat,K: nat] :
% 4.71/5.09 ( ( ( finite_card_list_nat @ A2 )
% 4.71/5.09 = ( suc @ K ) )
% 4.71/5.09 = ( ? [B4: list_nat,B6: set_list_nat] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert_list_nat @ B4 @ B6 ) )
% 4.71/5.09 & ~ ( member_list_nat @ B4 @ B6 )
% 4.71/5.09 & ( ( finite_card_list_nat @ B6 )
% 4.71/5.09 = K )
% 4.71/5.09 & ( ( K = zero_zero_nat )
% 4.71/5.09 => ( B6 = bot_bot_set_list_nat ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Suc_eq
% 4.71/5.09 thf(fact_3494_card__Suc__eq,axiom,
% 4.71/5.09 ! [A2: set_set_nat,K: nat] :
% 4.71/5.09 ( ( ( finite_card_set_nat @ A2 )
% 4.71/5.09 = ( suc @ K ) )
% 4.71/5.09 = ( ? [B4: set_nat,B6: set_set_nat] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert_set_nat @ B4 @ B6 ) )
% 4.71/5.09 & ~ ( member_set_nat @ B4 @ B6 )
% 4.71/5.09 & ( ( finite_card_set_nat @ B6 )
% 4.71/5.09 = K )
% 4.71/5.09 & ( ( K = zero_zero_nat )
% 4.71/5.09 => ( B6 = bot_bot_set_set_nat ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Suc_eq
% 4.71/5.09 thf(fact_3495_card__Suc__eq,axiom,
% 4.71/5.09 ! [A2: set_real,K: nat] :
% 4.71/5.09 ( ( ( finite_card_real @ A2 )
% 4.71/5.09 = ( suc @ K ) )
% 4.71/5.09 = ( ? [B4: real,B6: set_real] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert_real @ B4 @ B6 ) )
% 4.71/5.09 & ~ ( member_real @ B4 @ B6 )
% 4.71/5.09 & ( ( finite_card_real @ B6 )
% 4.71/5.09 = K )
% 4.71/5.09 & ( ( K = zero_zero_nat )
% 4.71/5.09 => ( B6 = bot_bot_set_real ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Suc_eq
% 4.71/5.09 thf(fact_3496_card__Suc__eq,axiom,
% 4.71/5.09 ! [A2: set_o,K: nat] :
% 4.71/5.09 ( ( ( finite_card_o @ A2 )
% 4.71/5.09 = ( suc @ K ) )
% 4.71/5.09 = ( ? [B4: $o,B6: set_o] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert_o @ B4 @ B6 ) )
% 4.71/5.09 & ~ ( member_o @ B4 @ B6 )
% 4.71/5.09 & ( ( finite_card_o @ B6 )
% 4.71/5.09 = K )
% 4.71/5.09 & ( ( K = zero_zero_nat )
% 4.71/5.09 => ( B6 = bot_bot_set_o ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Suc_eq
% 4.71/5.09 thf(fact_3497_card__Suc__eq,axiom,
% 4.71/5.09 ! [A2: set_nat,K: nat] :
% 4.71/5.09 ( ( ( finite_card_nat @ A2 )
% 4.71/5.09 = ( suc @ K ) )
% 4.71/5.09 = ( ? [B4: nat,B6: set_nat] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert_nat @ B4 @ B6 ) )
% 4.71/5.09 & ~ ( member_nat @ B4 @ B6 )
% 4.71/5.09 & ( ( finite_card_nat @ B6 )
% 4.71/5.09 = K )
% 4.71/5.09 & ( ( K = zero_zero_nat )
% 4.71/5.09 => ( B6 = bot_bot_set_nat ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Suc_eq
% 4.71/5.09 thf(fact_3498_card__Suc__eq,axiom,
% 4.71/5.09 ! [A2: set_int,K: nat] :
% 4.71/5.09 ( ( ( finite_card_int @ A2 )
% 4.71/5.09 = ( suc @ K ) )
% 4.71/5.09 = ( ? [B4: int,B6: set_int] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert_int @ B4 @ B6 ) )
% 4.71/5.09 & ~ ( member_int @ B4 @ B6 )
% 4.71/5.09 & ( ( finite_card_int @ B6 )
% 4.71/5.09 = K )
% 4.71/5.09 & ( ( K = zero_zero_nat )
% 4.71/5.09 => ( B6 = bot_bot_set_int ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Suc_eq
% 4.71/5.09 thf(fact_3499_card__eq__SucD,axiom,
% 4.71/5.09 ! [A2: set_Pr1261947904930325089at_nat,K: nat] :
% 4.71/5.09 ( ( ( finite711546835091564841at_nat @ A2 )
% 4.71/5.09 = ( suc @ K ) )
% 4.71/5.09 => ? [B5: product_prod_nat_nat,B8: set_Pr1261947904930325089at_nat] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert8211810215607154385at_nat @ B5 @ B8 ) )
% 4.71/5.09 & ~ ( member8440522571783428010at_nat @ B5 @ B8 )
% 4.71/5.09 & ( ( finite711546835091564841at_nat @ B8 )
% 4.71/5.09 = K )
% 4.71/5.09 & ( ( K = zero_zero_nat )
% 4.71/5.09 => ( B8 = bot_bo2099793752762293965at_nat ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_eq_SucD
% 4.71/5.09 thf(fact_3500_card__eq__SucD,axiom,
% 4.71/5.09 ! [A2: set_set_nat_rat,K: nat] :
% 4.71/5.09 ( ( ( finite8736671560171388117at_rat @ A2 )
% 4.71/5.09 = ( suc @ K ) )
% 4.71/5.09 => ? [B5: set_nat_rat,B8: set_set_nat_rat] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert_set_nat_rat @ B5 @ B8 ) )
% 4.71/5.09 & ~ ( member_set_nat_rat @ B5 @ B8 )
% 4.71/5.09 & ( ( finite8736671560171388117at_rat @ B8 )
% 4.71/5.09 = K )
% 4.71/5.09 & ( ( K = zero_zero_nat )
% 4.71/5.09 => ( B8 = bot_bo6797373522285170759at_rat ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_eq_SucD
% 4.71/5.09 thf(fact_3501_card__eq__SucD,axiom,
% 4.71/5.09 ! [A2: set_complex,K: nat] :
% 4.71/5.09 ( ( ( finite_card_complex @ A2 )
% 4.71/5.09 = ( suc @ K ) )
% 4.71/5.09 => ? [B5: complex,B8: set_complex] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert_complex @ B5 @ B8 ) )
% 4.71/5.09 & ~ ( member_complex @ B5 @ B8 )
% 4.71/5.09 & ( ( finite_card_complex @ B8 )
% 4.71/5.09 = K )
% 4.71/5.09 & ( ( K = zero_zero_nat )
% 4.71/5.09 => ( B8 = bot_bot_set_complex ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_eq_SucD
% 4.71/5.09 thf(fact_3502_card__eq__SucD,axiom,
% 4.71/5.09 ! [A2: set_list_nat,K: nat] :
% 4.71/5.09 ( ( ( finite_card_list_nat @ A2 )
% 4.71/5.09 = ( suc @ K ) )
% 4.71/5.09 => ? [B5: list_nat,B8: set_list_nat] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert_list_nat @ B5 @ B8 ) )
% 4.71/5.09 & ~ ( member_list_nat @ B5 @ B8 )
% 4.71/5.09 & ( ( finite_card_list_nat @ B8 )
% 4.71/5.09 = K )
% 4.71/5.09 & ( ( K = zero_zero_nat )
% 4.71/5.09 => ( B8 = bot_bot_set_list_nat ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_eq_SucD
% 4.71/5.09 thf(fact_3503_card__eq__SucD,axiom,
% 4.71/5.09 ! [A2: set_set_nat,K: nat] :
% 4.71/5.09 ( ( ( finite_card_set_nat @ A2 )
% 4.71/5.09 = ( suc @ K ) )
% 4.71/5.09 => ? [B5: set_nat,B8: set_set_nat] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert_set_nat @ B5 @ B8 ) )
% 4.71/5.09 & ~ ( member_set_nat @ B5 @ B8 )
% 4.71/5.09 & ( ( finite_card_set_nat @ B8 )
% 4.71/5.09 = K )
% 4.71/5.09 & ( ( K = zero_zero_nat )
% 4.71/5.09 => ( B8 = bot_bot_set_set_nat ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_eq_SucD
% 4.71/5.09 thf(fact_3504_card__eq__SucD,axiom,
% 4.71/5.09 ! [A2: set_real,K: nat] :
% 4.71/5.09 ( ( ( finite_card_real @ A2 )
% 4.71/5.09 = ( suc @ K ) )
% 4.71/5.09 => ? [B5: real,B8: set_real] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert_real @ B5 @ B8 ) )
% 4.71/5.09 & ~ ( member_real @ B5 @ B8 )
% 4.71/5.09 & ( ( finite_card_real @ B8 )
% 4.71/5.09 = K )
% 4.71/5.09 & ( ( K = zero_zero_nat )
% 4.71/5.09 => ( B8 = bot_bot_set_real ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_eq_SucD
% 4.71/5.09 thf(fact_3505_card__eq__SucD,axiom,
% 4.71/5.09 ! [A2: set_o,K: nat] :
% 4.71/5.09 ( ( ( finite_card_o @ A2 )
% 4.71/5.09 = ( suc @ K ) )
% 4.71/5.09 => ? [B5: $o,B8: set_o] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert_o @ B5 @ B8 ) )
% 4.71/5.09 & ~ ( member_o @ B5 @ B8 )
% 4.71/5.09 & ( ( finite_card_o @ B8 )
% 4.71/5.09 = K )
% 4.71/5.09 & ( ( K = zero_zero_nat )
% 4.71/5.09 => ( B8 = bot_bot_set_o ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_eq_SucD
% 4.71/5.09 thf(fact_3506_card__eq__SucD,axiom,
% 4.71/5.09 ! [A2: set_nat,K: nat] :
% 4.71/5.09 ( ( ( finite_card_nat @ A2 )
% 4.71/5.09 = ( suc @ K ) )
% 4.71/5.09 => ? [B5: nat,B8: set_nat] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert_nat @ B5 @ B8 ) )
% 4.71/5.09 & ~ ( member_nat @ B5 @ B8 )
% 4.71/5.09 & ( ( finite_card_nat @ B8 )
% 4.71/5.09 = K )
% 4.71/5.09 & ( ( K = zero_zero_nat )
% 4.71/5.09 => ( B8 = bot_bot_set_nat ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_eq_SucD
% 4.71/5.09 thf(fact_3507_card__eq__SucD,axiom,
% 4.71/5.09 ! [A2: set_int,K: nat] :
% 4.71/5.09 ( ( ( finite_card_int @ A2 )
% 4.71/5.09 = ( suc @ K ) )
% 4.71/5.09 => ? [B5: int,B8: set_int] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert_int @ B5 @ B8 ) )
% 4.71/5.09 & ~ ( member_int @ B5 @ B8 )
% 4.71/5.09 & ( ( finite_card_int @ B8 )
% 4.71/5.09 = K )
% 4.71/5.09 & ( ( K = zero_zero_nat )
% 4.71/5.09 => ( B8 = bot_bot_set_int ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_eq_SucD
% 4.71/5.09 thf(fact_3508_card__1__singleton__iff,axiom,
% 4.71/5.09 ! [A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.09 ( ( ( finite711546835091564841at_nat @ A2 )
% 4.71/5.09 = ( suc @ zero_zero_nat ) )
% 4.71/5.09 = ( ? [X3: product_prod_nat_nat] :
% 4.71/5.09 ( A2
% 4.71/5.09 = ( insert8211810215607154385at_nat @ X3 @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_1_singleton_iff
% 4.71/5.09 thf(fact_3509_card__1__singleton__iff,axiom,
% 4.71/5.09 ! [A2: set_complex] :
% 4.71/5.09 ( ( ( finite_card_complex @ A2 )
% 4.71/5.09 = ( suc @ zero_zero_nat ) )
% 4.71/5.09 = ( ? [X3: complex] :
% 4.71/5.09 ( A2
% 4.71/5.09 = ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_1_singleton_iff
% 4.71/5.09 thf(fact_3510_card__1__singleton__iff,axiom,
% 4.71/5.09 ! [A2: set_list_nat] :
% 4.71/5.09 ( ( ( finite_card_list_nat @ A2 )
% 4.71/5.09 = ( suc @ zero_zero_nat ) )
% 4.71/5.09 = ( ? [X3: list_nat] :
% 4.71/5.09 ( A2
% 4.71/5.09 = ( insert_list_nat @ X3 @ bot_bot_set_list_nat ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_1_singleton_iff
% 4.71/5.09 thf(fact_3511_card__1__singleton__iff,axiom,
% 4.71/5.09 ! [A2: set_set_nat] :
% 4.71/5.09 ( ( ( finite_card_set_nat @ A2 )
% 4.71/5.09 = ( suc @ zero_zero_nat ) )
% 4.71/5.09 = ( ? [X3: set_nat] :
% 4.71/5.09 ( A2
% 4.71/5.09 = ( insert_set_nat @ X3 @ bot_bot_set_set_nat ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_1_singleton_iff
% 4.71/5.09 thf(fact_3512_card__1__singleton__iff,axiom,
% 4.71/5.09 ! [A2: set_real] :
% 4.71/5.09 ( ( ( finite_card_real @ A2 )
% 4.71/5.09 = ( suc @ zero_zero_nat ) )
% 4.71/5.09 = ( ? [X3: real] :
% 4.71/5.09 ( A2
% 4.71/5.09 = ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_1_singleton_iff
% 4.71/5.09 thf(fact_3513_card__1__singleton__iff,axiom,
% 4.71/5.09 ! [A2: set_o] :
% 4.71/5.09 ( ( ( finite_card_o @ A2 )
% 4.71/5.09 = ( suc @ zero_zero_nat ) )
% 4.71/5.09 = ( ? [X3: $o] :
% 4.71/5.09 ( A2
% 4.71/5.09 = ( insert_o @ X3 @ bot_bot_set_o ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_1_singleton_iff
% 4.71/5.09 thf(fact_3514_card__1__singleton__iff,axiom,
% 4.71/5.09 ! [A2: set_nat] :
% 4.71/5.09 ( ( ( finite_card_nat @ A2 )
% 4.71/5.09 = ( suc @ zero_zero_nat ) )
% 4.71/5.09 = ( ? [X3: nat] :
% 4.71/5.09 ( A2
% 4.71/5.09 = ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_1_singleton_iff
% 4.71/5.09 thf(fact_3515_card__1__singleton__iff,axiom,
% 4.71/5.09 ! [A2: set_int] :
% 4.71/5.09 ( ( ( finite_card_int @ A2 )
% 4.71/5.09 = ( suc @ zero_zero_nat ) )
% 4.71/5.09 = ( ? [X3: int] :
% 4.71/5.09 ( A2
% 4.71/5.09 = ( insert_int @ X3 @ bot_bot_set_int ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_1_singleton_iff
% 4.71/5.09 thf(fact_3516_remove__induct,axiom,
% 4.71/5.09 ! [P: set_set_nat > $o,B2: set_set_nat] :
% 4.71/5.09 ( ( P @ bot_bot_set_set_nat )
% 4.71/5.09 => ( ( ~ ( finite1152437895449049373et_nat @ B2 )
% 4.71/5.09 => ( P @ B2 ) )
% 4.71/5.09 => ( ! [A3: set_set_nat] :
% 4.71/5.09 ( ( finite1152437895449049373et_nat @ A3 )
% 4.71/5.09 => ( ( A3 != bot_bot_set_set_nat )
% 4.71/5.09 => ( ( ord_le6893508408891458716et_nat @ A3 @ B2 )
% 4.71/5.09 => ( ! [X2: set_nat] :
% 4.71/5.09 ( ( member_set_nat @ X2 @ A3 )
% 4.71/5.09 => ( P @ ( minus_2163939370556025621et_nat @ A3 @ ( insert_set_nat @ X2 @ bot_bot_set_set_nat ) ) ) )
% 4.71/5.09 => ( P @ A3 ) ) ) ) )
% 4.71/5.09 => ( P @ B2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % remove_induct
% 4.71/5.09 thf(fact_3517_remove__induct,axiom,
% 4.71/5.09 ! [P: set_set_nat_rat > $o,B2: set_set_nat_rat] :
% 4.71/5.09 ( ( P @ bot_bo6797373522285170759at_rat )
% 4.71/5.09 => ( ( ~ ( finite6430367030675640852at_rat @ B2 )
% 4.71/5.09 => ( P @ B2 ) )
% 4.71/5.09 => ( ! [A3: set_set_nat_rat] :
% 4.71/5.09 ( ( finite6430367030675640852at_rat @ A3 )
% 4.71/5.09 => ( ( A3 != bot_bo6797373522285170759at_rat )
% 4.71/5.09 => ( ( ord_le4375437777232675859at_rat @ A3 @ B2 )
% 4.71/5.09 => ( ! [X2: set_nat_rat] :
% 4.71/5.09 ( ( member_set_nat_rat @ X2 @ A3 )
% 4.71/5.09 => ( P @ ( minus_1626877696091177228at_rat @ A3 @ ( insert_set_nat_rat @ X2 @ bot_bo6797373522285170759at_rat ) ) ) )
% 4.71/5.09 => ( P @ A3 ) ) ) ) )
% 4.71/5.09 => ( P @ B2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % remove_induct
% 4.71/5.09 thf(fact_3518_remove__induct,axiom,
% 4.71/5.09 ! [P: set_complex > $o,B2: set_complex] :
% 4.71/5.09 ( ( P @ bot_bot_set_complex )
% 4.71/5.09 => ( ( ~ ( finite3207457112153483333omplex @ B2 )
% 4.71/5.09 => ( P @ B2 ) )
% 4.71/5.09 => ( ! [A3: set_complex] :
% 4.71/5.09 ( ( finite3207457112153483333omplex @ A3 )
% 4.71/5.09 => ( ( A3 != bot_bot_set_complex )
% 4.71/5.09 => ( ( ord_le211207098394363844omplex @ A3 @ B2 )
% 4.71/5.09 => ( ! [X2: complex] :
% 4.71/5.09 ( ( member_complex @ X2 @ A3 )
% 4.71/5.09 => ( P @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) )
% 4.71/5.09 => ( P @ A3 ) ) ) ) )
% 4.71/5.09 => ( P @ B2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % remove_induct
% 4.71/5.09 thf(fact_3519_remove__induct,axiom,
% 4.71/5.09 ! [P: set_Pr1261947904930325089at_nat > $o,B2: set_Pr1261947904930325089at_nat] :
% 4.71/5.09 ( ( P @ bot_bo2099793752762293965at_nat )
% 4.71/5.09 => ( ( ~ ( finite6177210948735845034at_nat @ B2 )
% 4.71/5.09 => ( P @ B2 ) )
% 4.71/5.09 => ( ! [A3: set_Pr1261947904930325089at_nat] :
% 4.71/5.09 ( ( finite6177210948735845034at_nat @ A3 )
% 4.71/5.09 => ( ( A3 != bot_bo2099793752762293965at_nat )
% 4.71/5.09 => ( ( ord_le3146513528884898305at_nat @ A3 @ B2 )
% 4.71/5.09 => ( ! [X2: product_prod_nat_nat] :
% 4.71/5.09 ( ( member8440522571783428010at_nat @ X2 @ A3 )
% 4.71/5.09 => ( P @ ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) ) )
% 4.71/5.09 => ( P @ A3 ) ) ) ) )
% 4.71/5.09 => ( P @ B2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % remove_induct
% 4.71/5.09 thf(fact_3520_remove__induct,axiom,
% 4.71/5.09 ! [P: set_Extended_enat > $o,B2: set_Extended_enat] :
% 4.71/5.09 ( ( P @ bot_bo7653980558646680370d_enat )
% 4.71/5.09 => ( ( ~ ( finite4001608067531595151d_enat @ B2 )
% 4.71/5.09 => ( P @ B2 ) )
% 4.71/5.09 => ( ! [A3: set_Extended_enat] :
% 4.71/5.09 ( ( finite4001608067531595151d_enat @ A3 )
% 4.71/5.09 => ( ( A3 != bot_bo7653980558646680370d_enat )
% 4.71/5.09 => ( ( ord_le7203529160286727270d_enat @ A3 @ B2 )
% 4.71/5.09 => ( ! [X2: extended_enat] :
% 4.71/5.09 ( ( member_Extended_enat @ X2 @ A3 )
% 4.71/5.09 => ( P @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ X2 @ bot_bo7653980558646680370d_enat ) ) ) )
% 4.71/5.09 => ( P @ A3 ) ) ) ) )
% 4.71/5.09 => ( P @ B2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % remove_induct
% 4.71/5.09 thf(fact_3521_remove__induct,axiom,
% 4.71/5.09 ! [P: set_real > $o,B2: set_real] :
% 4.71/5.09 ( ( P @ bot_bot_set_real )
% 4.71/5.09 => ( ( ~ ( finite_finite_real @ B2 )
% 4.71/5.09 => ( P @ B2 ) )
% 4.71/5.09 => ( ! [A3: set_real] :
% 4.71/5.09 ( ( finite_finite_real @ A3 )
% 4.71/5.09 => ( ( A3 != bot_bot_set_real )
% 4.71/5.09 => ( ( ord_less_eq_set_real @ A3 @ B2 )
% 4.71/5.09 => ( ! [X2: real] :
% 4.71/5.09 ( ( member_real @ X2 @ A3 )
% 4.71/5.09 => ( P @ ( minus_minus_set_real @ A3 @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) )
% 4.71/5.09 => ( P @ A3 ) ) ) ) )
% 4.71/5.09 => ( P @ B2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % remove_induct
% 4.71/5.09 thf(fact_3522_remove__induct,axiom,
% 4.71/5.09 ! [P: set_o > $o,B2: set_o] :
% 4.71/5.09 ( ( P @ bot_bot_set_o )
% 4.71/5.09 => ( ( ~ ( finite_finite_o @ B2 )
% 4.71/5.09 => ( P @ B2 ) )
% 4.71/5.09 => ( ! [A3: set_o] :
% 4.71/5.09 ( ( finite_finite_o @ A3 )
% 4.71/5.09 => ( ( A3 != bot_bot_set_o )
% 4.71/5.09 => ( ( ord_less_eq_set_o @ A3 @ B2 )
% 4.71/5.09 => ( ! [X2: $o] :
% 4.71/5.09 ( ( member_o @ X2 @ A3 )
% 4.71/5.09 => ( P @ ( minus_minus_set_o @ A3 @ ( insert_o @ X2 @ bot_bot_set_o ) ) ) )
% 4.71/5.09 => ( P @ A3 ) ) ) ) )
% 4.71/5.09 => ( P @ B2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % remove_induct
% 4.71/5.09 thf(fact_3523_remove__induct,axiom,
% 4.71/5.09 ! [P: set_nat > $o,B2: set_nat] :
% 4.71/5.09 ( ( P @ bot_bot_set_nat )
% 4.71/5.09 => ( ( ~ ( finite_finite_nat @ B2 )
% 4.71/5.09 => ( P @ B2 ) )
% 4.71/5.09 => ( ! [A3: set_nat] :
% 4.71/5.09 ( ( finite_finite_nat @ A3 )
% 4.71/5.09 => ( ( A3 != bot_bot_set_nat )
% 4.71/5.09 => ( ( ord_less_eq_set_nat @ A3 @ B2 )
% 4.71/5.09 => ( ! [X2: nat] :
% 4.71/5.09 ( ( member_nat @ X2 @ A3 )
% 4.71/5.09 => ( P @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) )
% 4.71/5.09 => ( P @ A3 ) ) ) ) )
% 4.71/5.09 => ( P @ B2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % remove_induct
% 4.71/5.09 thf(fact_3524_remove__induct,axiom,
% 4.71/5.09 ! [P: set_int > $o,B2: set_int] :
% 4.71/5.09 ( ( P @ bot_bot_set_int )
% 4.71/5.09 => ( ( ~ ( finite_finite_int @ B2 )
% 4.71/5.09 => ( P @ B2 ) )
% 4.71/5.09 => ( ! [A3: set_int] :
% 4.71/5.09 ( ( finite_finite_int @ A3 )
% 4.71/5.09 => ( ( A3 != bot_bot_set_int )
% 4.71/5.09 => ( ( ord_less_eq_set_int @ A3 @ B2 )
% 4.71/5.09 => ( ! [X2: int] :
% 4.71/5.09 ( ( member_int @ X2 @ A3 )
% 4.71/5.09 => ( P @ ( minus_minus_set_int @ A3 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) )
% 4.71/5.09 => ( P @ A3 ) ) ) ) )
% 4.71/5.09 => ( P @ B2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % remove_induct
% 4.71/5.09 thf(fact_3525_finite__remove__induct,axiom,
% 4.71/5.09 ! [B2: set_set_nat,P: set_set_nat > $o] :
% 4.71/5.09 ( ( finite1152437895449049373et_nat @ B2 )
% 4.71/5.09 => ( ( P @ bot_bot_set_set_nat )
% 4.71/5.09 => ( ! [A3: set_set_nat] :
% 4.71/5.09 ( ( finite1152437895449049373et_nat @ A3 )
% 4.71/5.09 => ( ( A3 != bot_bot_set_set_nat )
% 4.71/5.09 => ( ( ord_le6893508408891458716et_nat @ A3 @ B2 )
% 4.71/5.09 => ( ! [X2: set_nat] :
% 4.71/5.09 ( ( member_set_nat @ X2 @ A3 )
% 4.71/5.09 => ( P @ ( minus_2163939370556025621et_nat @ A3 @ ( insert_set_nat @ X2 @ bot_bot_set_set_nat ) ) ) )
% 4.71/5.09 => ( P @ A3 ) ) ) ) )
% 4.71/5.09 => ( P @ B2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % finite_remove_induct
% 4.71/5.09 thf(fact_3526_finite__remove__induct,axiom,
% 4.71/5.09 ! [B2: set_set_nat_rat,P: set_set_nat_rat > $o] :
% 4.71/5.09 ( ( finite6430367030675640852at_rat @ B2 )
% 4.71/5.09 => ( ( P @ bot_bo6797373522285170759at_rat )
% 4.71/5.09 => ( ! [A3: set_set_nat_rat] :
% 4.71/5.09 ( ( finite6430367030675640852at_rat @ A3 )
% 4.71/5.09 => ( ( A3 != bot_bo6797373522285170759at_rat )
% 4.71/5.09 => ( ( ord_le4375437777232675859at_rat @ A3 @ B2 )
% 4.71/5.09 => ( ! [X2: set_nat_rat] :
% 4.71/5.09 ( ( member_set_nat_rat @ X2 @ A3 )
% 4.71/5.09 => ( P @ ( minus_1626877696091177228at_rat @ A3 @ ( insert_set_nat_rat @ X2 @ bot_bo6797373522285170759at_rat ) ) ) )
% 4.71/5.09 => ( P @ A3 ) ) ) ) )
% 4.71/5.09 => ( P @ B2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % finite_remove_induct
% 4.71/5.09 thf(fact_3527_finite__remove__induct,axiom,
% 4.71/5.09 ! [B2: set_complex,P: set_complex > $o] :
% 4.71/5.09 ( ( finite3207457112153483333omplex @ B2 )
% 4.71/5.09 => ( ( P @ bot_bot_set_complex )
% 4.71/5.09 => ( ! [A3: set_complex] :
% 4.71/5.09 ( ( finite3207457112153483333omplex @ A3 )
% 4.71/5.09 => ( ( A3 != bot_bot_set_complex )
% 4.71/5.09 => ( ( ord_le211207098394363844omplex @ A3 @ B2 )
% 4.71/5.09 => ( ! [X2: complex] :
% 4.71/5.09 ( ( member_complex @ X2 @ A3 )
% 4.71/5.09 => ( P @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) )
% 4.71/5.09 => ( P @ A3 ) ) ) ) )
% 4.71/5.09 => ( P @ B2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % finite_remove_induct
% 4.71/5.09 thf(fact_3528_finite__remove__induct,axiom,
% 4.71/5.09 ! [B2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 4.71/5.09 ( ( finite6177210948735845034at_nat @ B2 )
% 4.71/5.09 => ( ( P @ bot_bo2099793752762293965at_nat )
% 4.71/5.09 => ( ! [A3: set_Pr1261947904930325089at_nat] :
% 4.71/5.09 ( ( finite6177210948735845034at_nat @ A3 )
% 4.71/5.09 => ( ( A3 != bot_bo2099793752762293965at_nat )
% 4.71/5.09 => ( ( ord_le3146513528884898305at_nat @ A3 @ B2 )
% 4.71/5.09 => ( ! [X2: product_prod_nat_nat] :
% 4.71/5.09 ( ( member8440522571783428010at_nat @ X2 @ A3 )
% 4.71/5.09 => ( P @ ( minus_1356011639430497352at_nat @ A3 @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) ) )
% 4.71/5.09 => ( P @ A3 ) ) ) ) )
% 4.71/5.09 => ( P @ B2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % finite_remove_induct
% 4.71/5.09 thf(fact_3529_finite__remove__induct,axiom,
% 4.71/5.09 ! [B2: set_Extended_enat,P: set_Extended_enat > $o] :
% 4.71/5.09 ( ( finite4001608067531595151d_enat @ B2 )
% 4.71/5.09 => ( ( P @ bot_bo7653980558646680370d_enat )
% 4.71/5.09 => ( ! [A3: set_Extended_enat] :
% 4.71/5.09 ( ( finite4001608067531595151d_enat @ A3 )
% 4.71/5.09 => ( ( A3 != bot_bo7653980558646680370d_enat )
% 4.71/5.09 => ( ( ord_le7203529160286727270d_enat @ A3 @ B2 )
% 4.71/5.09 => ( ! [X2: extended_enat] :
% 4.71/5.09 ( ( member_Extended_enat @ X2 @ A3 )
% 4.71/5.09 => ( P @ ( minus_925952699566721837d_enat @ A3 @ ( insert_Extended_enat @ X2 @ bot_bo7653980558646680370d_enat ) ) ) )
% 4.71/5.09 => ( P @ A3 ) ) ) ) )
% 4.71/5.09 => ( P @ B2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % finite_remove_induct
% 4.71/5.09 thf(fact_3530_finite__remove__induct,axiom,
% 4.71/5.09 ! [B2: set_real,P: set_real > $o] :
% 4.71/5.09 ( ( finite_finite_real @ B2 )
% 4.71/5.09 => ( ( P @ bot_bot_set_real )
% 4.71/5.09 => ( ! [A3: set_real] :
% 4.71/5.09 ( ( finite_finite_real @ A3 )
% 4.71/5.09 => ( ( A3 != bot_bot_set_real )
% 4.71/5.09 => ( ( ord_less_eq_set_real @ A3 @ B2 )
% 4.71/5.09 => ( ! [X2: real] :
% 4.71/5.09 ( ( member_real @ X2 @ A3 )
% 4.71/5.09 => ( P @ ( minus_minus_set_real @ A3 @ ( insert_real @ X2 @ bot_bot_set_real ) ) ) )
% 4.71/5.09 => ( P @ A3 ) ) ) ) )
% 4.71/5.09 => ( P @ B2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % finite_remove_induct
% 4.71/5.09 thf(fact_3531_finite__remove__induct,axiom,
% 4.71/5.09 ! [B2: set_o,P: set_o > $o] :
% 4.71/5.09 ( ( finite_finite_o @ B2 )
% 4.71/5.09 => ( ( P @ bot_bot_set_o )
% 4.71/5.09 => ( ! [A3: set_o] :
% 4.71/5.09 ( ( finite_finite_o @ A3 )
% 4.71/5.09 => ( ( A3 != bot_bot_set_o )
% 4.71/5.09 => ( ( ord_less_eq_set_o @ A3 @ B2 )
% 4.71/5.09 => ( ! [X2: $o] :
% 4.71/5.09 ( ( member_o @ X2 @ A3 )
% 4.71/5.09 => ( P @ ( minus_minus_set_o @ A3 @ ( insert_o @ X2 @ bot_bot_set_o ) ) ) )
% 4.71/5.09 => ( P @ A3 ) ) ) ) )
% 4.71/5.09 => ( P @ B2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % finite_remove_induct
% 4.71/5.09 thf(fact_3532_finite__remove__induct,axiom,
% 4.71/5.09 ! [B2: set_nat,P: set_nat > $o] :
% 4.71/5.09 ( ( finite_finite_nat @ B2 )
% 4.71/5.09 => ( ( P @ bot_bot_set_nat )
% 4.71/5.09 => ( ! [A3: set_nat] :
% 4.71/5.09 ( ( finite_finite_nat @ A3 )
% 4.71/5.09 => ( ( A3 != bot_bot_set_nat )
% 4.71/5.09 => ( ( ord_less_eq_set_nat @ A3 @ B2 )
% 4.71/5.09 => ( ! [X2: nat] :
% 4.71/5.09 ( ( member_nat @ X2 @ A3 )
% 4.71/5.09 => ( P @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) )
% 4.71/5.09 => ( P @ A3 ) ) ) ) )
% 4.71/5.09 => ( P @ B2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % finite_remove_induct
% 4.71/5.09 thf(fact_3533_finite__remove__induct,axiom,
% 4.71/5.09 ! [B2: set_int,P: set_int > $o] :
% 4.71/5.09 ( ( finite_finite_int @ B2 )
% 4.71/5.09 => ( ( P @ bot_bot_set_int )
% 4.71/5.09 => ( ! [A3: set_int] :
% 4.71/5.09 ( ( finite_finite_int @ A3 )
% 4.71/5.09 => ( ( A3 != bot_bot_set_int )
% 4.71/5.09 => ( ( ord_less_eq_set_int @ A3 @ B2 )
% 4.71/5.09 => ( ! [X2: int] :
% 4.71/5.09 ( ( member_int @ X2 @ A3 )
% 4.71/5.09 => ( P @ ( minus_minus_set_int @ A3 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) )
% 4.71/5.09 => ( P @ A3 ) ) ) ) )
% 4.71/5.09 => ( P @ B2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % finite_remove_induct
% 4.71/5.09 thf(fact_3534_card__le__Suc__iff,axiom,
% 4.71/5.09 ! [N: nat,A2: set_real] :
% 4.71/5.09 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_real @ A2 ) )
% 4.71/5.09 = ( ? [A4: real,B6: set_real] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert_real @ A4 @ B6 ) )
% 4.71/5.09 & ~ ( member_real @ A4 @ B6 )
% 4.71/5.09 & ( ord_less_eq_nat @ N @ ( finite_card_real @ B6 ) )
% 4.71/5.09 & ( finite_finite_real @ B6 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_le_Suc_iff
% 4.71/5.09 thf(fact_3535_card__le__Suc__iff,axiom,
% 4.71/5.09 ! [N: nat,A2: set_o] :
% 4.71/5.09 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_o @ A2 ) )
% 4.71/5.09 = ( ? [A4: $o,B6: set_o] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert_o @ A4 @ B6 ) )
% 4.71/5.09 & ~ ( member_o @ A4 @ B6 )
% 4.71/5.09 & ( ord_less_eq_nat @ N @ ( finite_card_o @ B6 ) )
% 4.71/5.09 & ( finite_finite_o @ B6 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_le_Suc_iff
% 4.71/5.09 thf(fact_3536_card__le__Suc__iff,axiom,
% 4.71/5.09 ! [N: nat,A2: set_set_nat_rat] :
% 4.71/5.09 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite8736671560171388117at_rat @ A2 ) )
% 4.71/5.09 = ( ? [A4: set_nat_rat,B6: set_set_nat_rat] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert_set_nat_rat @ A4 @ B6 ) )
% 4.71/5.09 & ~ ( member_set_nat_rat @ A4 @ B6 )
% 4.71/5.09 & ( ord_less_eq_nat @ N @ ( finite8736671560171388117at_rat @ B6 ) )
% 4.71/5.09 & ( finite6430367030675640852at_rat @ B6 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_le_Suc_iff
% 4.71/5.09 thf(fact_3537_card__le__Suc__iff,axiom,
% 4.71/5.09 ! [N: nat,A2: set_list_nat] :
% 4.71/5.09 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_list_nat @ A2 ) )
% 4.71/5.09 = ( ? [A4: list_nat,B6: set_list_nat] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert_list_nat @ A4 @ B6 ) )
% 4.71/5.09 & ~ ( member_list_nat @ A4 @ B6 )
% 4.71/5.09 & ( ord_less_eq_nat @ N @ ( finite_card_list_nat @ B6 ) )
% 4.71/5.09 & ( finite8100373058378681591st_nat @ B6 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_le_Suc_iff
% 4.71/5.09 thf(fact_3538_card__le__Suc__iff,axiom,
% 4.71/5.09 ! [N: nat,A2: set_set_nat] :
% 4.71/5.09 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_set_nat @ A2 ) )
% 4.71/5.09 = ( ? [A4: set_nat,B6: set_set_nat] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert_set_nat @ A4 @ B6 ) )
% 4.71/5.09 & ~ ( member_set_nat @ A4 @ B6 )
% 4.71/5.09 & ( ord_less_eq_nat @ N @ ( finite_card_set_nat @ B6 ) )
% 4.71/5.09 & ( finite1152437895449049373et_nat @ B6 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_le_Suc_iff
% 4.71/5.09 thf(fact_3539_card__le__Suc__iff,axiom,
% 4.71/5.09 ! [N: nat,A2: set_nat] :
% 4.71/5.09 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_nat @ A2 ) )
% 4.71/5.09 = ( ? [A4: nat,B6: set_nat] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert_nat @ A4 @ B6 ) )
% 4.71/5.09 & ~ ( member_nat @ A4 @ B6 )
% 4.71/5.09 & ( ord_less_eq_nat @ N @ ( finite_card_nat @ B6 ) )
% 4.71/5.09 & ( finite_finite_nat @ B6 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_le_Suc_iff
% 4.71/5.09 thf(fact_3540_card__le__Suc__iff,axiom,
% 4.71/5.09 ! [N: nat,A2: set_int] :
% 4.71/5.09 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_int @ A2 ) )
% 4.71/5.09 = ( ? [A4: int,B6: set_int] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert_int @ A4 @ B6 ) )
% 4.71/5.09 & ~ ( member_int @ A4 @ B6 )
% 4.71/5.09 & ( ord_less_eq_nat @ N @ ( finite_card_int @ B6 ) )
% 4.71/5.09 & ( finite_finite_int @ B6 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_le_Suc_iff
% 4.71/5.09 thf(fact_3541_card__le__Suc__iff,axiom,
% 4.71/5.09 ! [N: nat,A2: set_complex] :
% 4.71/5.09 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_complex @ A2 ) )
% 4.71/5.09 = ( ? [A4: complex,B6: set_complex] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert_complex @ A4 @ B6 ) )
% 4.71/5.09 & ~ ( member_complex @ A4 @ B6 )
% 4.71/5.09 & ( ord_less_eq_nat @ N @ ( finite_card_complex @ B6 ) )
% 4.71/5.09 & ( finite3207457112153483333omplex @ B6 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_le_Suc_iff
% 4.71/5.09 thf(fact_3542_card__le__Suc__iff,axiom,
% 4.71/5.09 ! [N: nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.09 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite711546835091564841at_nat @ A2 ) )
% 4.71/5.09 = ( ? [A4: product_prod_nat_nat,B6: set_Pr1261947904930325089at_nat] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert8211810215607154385at_nat @ A4 @ B6 ) )
% 4.71/5.09 & ~ ( member8440522571783428010at_nat @ A4 @ B6 )
% 4.71/5.09 & ( ord_less_eq_nat @ N @ ( finite711546835091564841at_nat @ B6 ) )
% 4.71/5.09 & ( finite6177210948735845034at_nat @ B6 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_le_Suc_iff
% 4.71/5.09 thf(fact_3543_card__le__Suc__iff,axiom,
% 4.71/5.09 ! [N: nat,A2: set_Extended_enat] :
% 4.71/5.09 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite121521170596916366d_enat @ A2 ) )
% 4.71/5.09 = ( ? [A4: extended_enat,B6: set_Extended_enat] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( insert_Extended_enat @ A4 @ B6 ) )
% 4.71/5.09 & ~ ( member_Extended_enat @ A4 @ B6 )
% 4.71/5.09 & ( ord_less_eq_nat @ N @ ( finite121521170596916366d_enat @ B6 ) )
% 4.71/5.09 & ( finite4001608067531595151d_enat @ B6 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_le_Suc_iff
% 4.71/5.09 thf(fact_3544_card__Diff1__le,axiom,
% 4.71/5.09 ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] : ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) @ ( finite711546835091564841at_nat @ A2 ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_le
% 4.71/5.09 thf(fact_3545_card__Diff1__le,axiom,
% 4.71/5.09 ! [A2: set_complex,X: complex] : ( ord_less_eq_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) @ ( finite_card_complex @ A2 ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_le
% 4.71/5.09 thf(fact_3546_card__Diff1__le,axiom,
% 4.71/5.09 ! [A2: set_list_nat,X: list_nat] : ( ord_less_eq_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) @ ( finite_card_list_nat @ A2 ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_le
% 4.71/5.09 thf(fact_3547_card__Diff1__le,axiom,
% 4.71/5.09 ! [A2: set_set_nat,X: set_nat] : ( ord_less_eq_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) @ ( finite_card_set_nat @ A2 ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_le
% 4.71/5.09 thf(fact_3548_card__Diff1__le,axiom,
% 4.71/5.09 ! [A2: set_real,X: real] : ( ord_less_eq_nat @ ( finite_card_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) @ ( finite_card_real @ A2 ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_le
% 4.71/5.09 thf(fact_3549_card__Diff1__le,axiom,
% 4.71/5.09 ! [A2: set_o,X: $o] : ( ord_less_eq_nat @ ( finite_card_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) @ ( finite_card_o @ A2 ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_le
% 4.71/5.09 thf(fact_3550_card__Diff1__le,axiom,
% 4.71/5.09 ! [A2: set_int,X: int] : ( ord_less_eq_nat @ ( finite_card_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) @ ( finite_card_int @ A2 ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_le
% 4.71/5.09 thf(fact_3551_card__Diff1__le,axiom,
% 4.71/5.09 ! [A2: set_nat,X: nat] : ( ord_less_eq_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) @ ( finite_card_nat @ A2 ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_le
% 4.71/5.09 thf(fact_3552_finite__induct__select,axiom,
% 4.71/5.09 ! [S2: set_complex,P: set_complex > $o] :
% 4.71/5.09 ( ( finite3207457112153483333omplex @ S2 )
% 4.71/5.09 => ( ( P @ bot_bot_set_complex )
% 4.71/5.09 => ( ! [T4: set_complex] :
% 4.71/5.09 ( ( ord_less_set_complex @ T4 @ S2 )
% 4.71/5.09 => ( ( P @ T4 )
% 4.71/5.09 => ? [X2: complex] :
% 4.71/5.09 ( ( member_complex @ X2 @ ( minus_811609699411566653omplex @ S2 @ T4 ) )
% 4.71/5.09 & ( P @ ( insert_complex @ X2 @ T4 ) ) ) ) )
% 4.71/5.09 => ( P @ S2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % finite_induct_select
% 4.71/5.09 thf(fact_3553_finite__induct__select,axiom,
% 4.71/5.09 ! [S2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 4.71/5.09 ( ( finite6177210948735845034at_nat @ S2 )
% 4.71/5.09 => ( ( P @ bot_bo2099793752762293965at_nat )
% 4.71/5.09 => ( ! [T4: set_Pr1261947904930325089at_nat] :
% 4.71/5.09 ( ( ord_le7866589430770878221at_nat @ T4 @ S2 )
% 4.71/5.09 => ( ( P @ T4 )
% 4.71/5.09 => ? [X2: product_prod_nat_nat] :
% 4.71/5.09 ( ( member8440522571783428010at_nat @ X2 @ ( minus_1356011639430497352at_nat @ S2 @ T4 ) )
% 4.71/5.09 & ( P @ ( insert8211810215607154385at_nat @ X2 @ T4 ) ) ) ) )
% 4.71/5.09 => ( P @ S2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % finite_induct_select
% 4.71/5.09 thf(fact_3554_finite__induct__select,axiom,
% 4.71/5.09 ! [S2: set_Extended_enat,P: set_Extended_enat > $o] :
% 4.71/5.09 ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.09 => ( ( P @ bot_bo7653980558646680370d_enat )
% 4.71/5.09 => ( ! [T4: set_Extended_enat] :
% 4.71/5.09 ( ( ord_le2529575680413868914d_enat @ T4 @ S2 )
% 4.71/5.09 => ( ( P @ T4 )
% 4.71/5.09 => ? [X2: extended_enat] :
% 4.71/5.09 ( ( member_Extended_enat @ X2 @ ( minus_925952699566721837d_enat @ S2 @ T4 ) )
% 4.71/5.09 & ( P @ ( insert_Extended_enat @ X2 @ T4 ) ) ) ) )
% 4.71/5.09 => ( P @ S2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % finite_induct_select
% 4.71/5.09 thf(fact_3555_finite__induct__select,axiom,
% 4.71/5.09 ! [S2: set_real,P: set_real > $o] :
% 4.71/5.09 ( ( finite_finite_real @ S2 )
% 4.71/5.09 => ( ( P @ bot_bot_set_real )
% 4.71/5.09 => ( ! [T4: set_real] :
% 4.71/5.09 ( ( ord_less_set_real @ T4 @ S2 )
% 4.71/5.09 => ( ( P @ T4 )
% 4.71/5.09 => ? [X2: real] :
% 4.71/5.09 ( ( member_real @ X2 @ ( minus_minus_set_real @ S2 @ T4 ) )
% 4.71/5.09 & ( P @ ( insert_real @ X2 @ T4 ) ) ) ) )
% 4.71/5.09 => ( P @ S2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % finite_induct_select
% 4.71/5.09 thf(fact_3556_finite__induct__select,axiom,
% 4.71/5.09 ! [S2: set_o,P: set_o > $o] :
% 4.71/5.09 ( ( finite_finite_o @ S2 )
% 4.71/5.09 => ( ( P @ bot_bot_set_o )
% 4.71/5.09 => ( ! [T4: set_o] :
% 4.71/5.09 ( ( ord_less_set_o @ T4 @ S2 )
% 4.71/5.09 => ( ( P @ T4 )
% 4.71/5.09 => ? [X2: $o] :
% 4.71/5.09 ( ( member_o @ X2 @ ( minus_minus_set_o @ S2 @ T4 ) )
% 4.71/5.09 & ( P @ ( insert_o @ X2 @ T4 ) ) ) ) )
% 4.71/5.09 => ( P @ S2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % finite_induct_select
% 4.71/5.09 thf(fact_3557_finite__induct__select,axiom,
% 4.71/5.09 ! [S2: set_int,P: set_int > $o] :
% 4.71/5.09 ( ( finite_finite_int @ S2 )
% 4.71/5.09 => ( ( P @ bot_bot_set_int )
% 4.71/5.09 => ( ! [T4: set_int] :
% 4.71/5.09 ( ( ord_less_set_int @ T4 @ S2 )
% 4.71/5.09 => ( ( P @ T4 )
% 4.71/5.09 => ? [X2: int] :
% 4.71/5.09 ( ( member_int @ X2 @ ( minus_minus_set_int @ S2 @ T4 ) )
% 4.71/5.09 & ( P @ ( insert_int @ X2 @ T4 ) ) ) ) )
% 4.71/5.09 => ( P @ S2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % finite_induct_select
% 4.71/5.09 thf(fact_3558_finite__induct__select,axiom,
% 4.71/5.09 ! [S2: set_nat,P: set_nat > $o] :
% 4.71/5.09 ( ( finite_finite_nat @ S2 )
% 4.71/5.09 => ( ( P @ bot_bot_set_nat )
% 4.71/5.09 => ( ! [T4: set_nat] :
% 4.71/5.09 ( ( ord_less_set_nat @ T4 @ S2 )
% 4.71/5.09 => ( ( P @ T4 )
% 4.71/5.09 => ? [X2: nat] :
% 4.71/5.09 ( ( member_nat @ X2 @ ( minus_minus_set_nat @ S2 @ T4 ) )
% 4.71/5.09 & ( P @ ( insert_nat @ X2 @ T4 ) ) ) ) )
% 4.71/5.09 => ( P @ S2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % finite_induct_select
% 4.71/5.09 thf(fact_3559_psubset__insert__iff,axiom,
% 4.71/5.09 ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 4.71/5.09 ( ( ord_le7866589430770878221at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ B2 ) )
% 4.71/5.09 = ( ( ( member8440522571783428010at_nat @ X @ B2 )
% 4.71/5.09 => ( ord_le7866589430770878221at_nat @ A2 @ B2 ) )
% 4.71/5.09 & ( ~ ( member8440522571783428010at_nat @ X @ B2 )
% 4.71/5.09 => ( ( ( member8440522571783428010at_nat @ X @ A2 )
% 4.71/5.09 => ( ord_le7866589430770878221at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ B2 ) )
% 4.71/5.09 & ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 4.71/5.09 => ( ord_le3146513528884898305at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % psubset_insert_iff
% 4.71/5.09 thf(fact_3560_psubset__insert__iff,axiom,
% 4.71/5.09 ! [A2: set_set_nat,X: set_nat,B2: set_set_nat] :
% 4.71/5.09 ( ( ord_less_set_set_nat @ A2 @ ( insert_set_nat @ X @ B2 ) )
% 4.71/5.09 = ( ( ( member_set_nat @ X @ B2 )
% 4.71/5.09 => ( ord_less_set_set_nat @ A2 @ B2 ) )
% 4.71/5.09 & ( ~ ( member_set_nat @ X @ B2 )
% 4.71/5.09 => ( ( ( member_set_nat @ X @ A2 )
% 4.71/5.09 => ( ord_less_set_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ B2 ) )
% 4.71/5.09 & ( ~ ( member_set_nat @ X @ A2 )
% 4.71/5.09 => ( ord_le6893508408891458716et_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % psubset_insert_iff
% 4.71/5.09 thf(fact_3561_psubset__insert__iff,axiom,
% 4.71/5.09 ! [A2: set_set_nat_rat,X: set_nat_rat,B2: set_set_nat_rat] :
% 4.71/5.09 ( ( ord_le1311537459589289991at_rat @ A2 @ ( insert_set_nat_rat @ X @ B2 ) )
% 4.71/5.09 = ( ( ( member_set_nat_rat @ X @ B2 )
% 4.71/5.09 => ( ord_le1311537459589289991at_rat @ A2 @ B2 ) )
% 4.71/5.09 & ( ~ ( member_set_nat_rat @ X @ B2 )
% 4.71/5.09 => ( ( ( member_set_nat_rat @ X @ A2 )
% 4.71/5.09 => ( ord_le1311537459589289991at_rat @ ( minus_1626877696091177228at_rat @ A2 @ ( insert_set_nat_rat @ X @ bot_bo6797373522285170759at_rat ) ) @ B2 ) )
% 4.71/5.09 & ( ~ ( member_set_nat_rat @ X @ A2 )
% 4.71/5.09 => ( ord_le4375437777232675859at_rat @ A2 @ B2 ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % psubset_insert_iff
% 4.71/5.09 thf(fact_3562_psubset__insert__iff,axiom,
% 4.71/5.09 ! [A2: set_real,X: real,B2: set_real] :
% 4.71/5.09 ( ( ord_less_set_real @ A2 @ ( insert_real @ X @ B2 ) )
% 4.71/5.09 = ( ( ( member_real @ X @ B2 )
% 4.71/5.09 => ( ord_less_set_real @ A2 @ B2 ) )
% 4.71/5.09 & ( ~ ( member_real @ X @ B2 )
% 4.71/5.09 => ( ( ( member_real @ X @ A2 )
% 4.71/5.09 => ( ord_less_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B2 ) )
% 4.71/5.09 & ( ~ ( member_real @ X @ A2 )
% 4.71/5.09 => ( ord_less_eq_set_real @ A2 @ B2 ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % psubset_insert_iff
% 4.71/5.09 thf(fact_3563_psubset__insert__iff,axiom,
% 4.71/5.09 ! [A2: set_o,X: $o,B2: set_o] :
% 4.71/5.09 ( ( ord_less_set_o @ A2 @ ( insert_o @ X @ B2 ) )
% 4.71/5.09 = ( ( ( member_o @ X @ B2 )
% 4.71/5.09 => ( ord_less_set_o @ A2 @ B2 ) )
% 4.71/5.09 & ( ~ ( member_o @ X @ B2 )
% 4.71/5.09 => ( ( ( member_o @ X @ A2 )
% 4.71/5.09 => ( ord_less_set_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) @ B2 ) )
% 4.71/5.09 & ( ~ ( member_o @ X @ A2 )
% 4.71/5.09 => ( ord_less_eq_set_o @ A2 @ B2 ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % psubset_insert_iff
% 4.71/5.09 thf(fact_3564_psubset__insert__iff,axiom,
% 4.71/5.09 ! [A2: set_nat,X: nat,B2: set_nat] :
% 4.71/5.09 ( ( ord_less_set_nat @ A2 @ ( insert_nat @ X @ B2 ) )
% 4.71/5.09 = ( ( ( member_nat @ X @ B2 )
% 4.71/5.09 => ( ord_less_set_nat @ A2 @ B2 ) )
% 4.71/5.09 & ( ~ ( member_nat @ X @ B2 )
% 4.71/5.09 => ( ( ( member_nat @ X @ A2 )
% 4.71/5.09 => ( ord_less_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B2 ) )
% 4.71/5.09 & ( ~ ( member_nat @ X @ A2 )
% 4.71/5.09 => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % psubset_insert_iff
% 4.71/5.09 thf(fact_3565_psubset__insert__iff,axiom,
% 4.71/5.09 ! [A2: set_int,X: int,B2: set_int] :
% 4.71/5.09 ( ( ord_less_set_int @ A2 @ ( insert_int @ X @ B2 ) )
% 4.71/5.09 = ( ( ( member_int @ X @ B2 )
% 4.71/5.09 => ( ord_less_set_int @ A2 @ B2 ) )
% 4.71/5.09 & ( ~ ( member_int @ X @ B2 )
% 4.71/5.09 => ( ( ( member_int @ X @ A2 )
% 4.71/5.09 => ( ord_less_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B2 ) )
% 4.71/5.09 & ( ~ ( member_int @ X @ A2 )
% 4.71/5.09 => ( ord_less_eq_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % psubset_insert_iff
% 4.71/5.09 thf(fact_3566_div__nat__eqI,axiom,
% 4.71/5.09 ! [N: nat,Q4: nat,M2: nat] :
% 4.71/5.09 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q4 ) @ M2 )
% 4.71/5.09 => ( ( ord_less_nat @ M2 @ ( times_times_nat @ N @ ( suc @ Q4 ) ) )
% 4.71/5.09 => ( ( divide_divide_nat @ M2 @ N )
% 4.71/5.09 = Q4 ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % div_nat_eqI
% 4.71/5.09 thf(fact_3567_less__eq__div__iff__mult__less__eq,axiom,
% 4.71/5.09 ! [Q4: nat,M2: nat,N: nat] :
% 4.71/5.09 ( ( ord_less_nat @ zero_zero_nat @ Q4 )
% 4.71/5.09 => ( ( ord_less_eq_nat @ M2 @ ( divide_divide_nat @ N @ Q4 ) )
% 4.71/5.09 = ( ord_less_eq_nat @ ( times_times_nat @ M2 @ Q4 ) @ N ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % less_eq_div_iff_mult_less_eq
% 4.71/5.09 thf(fact_3568_le__imp__0__less,axiom,
% 4.71/5.09 ! [Z: int] :
% 4.71/5.09 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 4.71/5.09 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % le_imp_0_less
% 4.71/5.09 thf(fact_3569_frac__add,axiom,
% 4.71/5.09 ! [X: real,Y: real] :
% 4.71/5.09 ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 4.71/5.09 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X @ Y ) )
% 4.71/5.09 = ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) ) )
% 4.71/5.09 & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 4.71/5.09 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X @ Y ) )
% 4.71/5.09 = ( minus_minus_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % frac_add
% 4.71/5.09 thf(fact_3570_frac__add,axiom,
% 4.71/5.09 ! [X: rat,Y: rat] :
% 4.71/5.09 ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 4.71/5.09 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y ) )
% 4.71/5.09 = ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) ) )
% 4.71/5.09 & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 4.71/5.09 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y ) )
% 4.71/5.09 = ( minus_minus_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % frac_add
% 4.71/5.09 thf(fact_3571_nat__less__iff,axiom,
% 4.71/5.09 ! [W2: int,M2: nat] :
% 4.71/5.09 ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 4.71/5.09 => ( ( ord_less_nat @ ( nat2 @ W2 ) @ M2 )
% 4.71/5.09 = ( ord_less_int @ W2 @ ( semiri1314217659103216013at_int @ M2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % nat_less_iff
% 4.71/5.09 thf(fact_3572_power__diff__power__eq,axiom,
% 4.71/5.09 ! [A: int,N: nat,M2: nat] :
% 4.71/5.09 ( ( A != zero_zero_int )
% 4.71/5.09 => ( ( ( ord_less_eq_nat @ N @ M2 )
% 4.71/5.09 => ( ( divide_divide_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) )
% 4.71/5.09 = ( power_power_int @ A @ ( minus_minus_nat @ M2 @ N ) ) ) )
% 4.71/5.09 & ( ~ ( ord_less_eq_nat @ N @ M2 )
% 4.71/5.09 => ( ( divide_divide_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) )
% 4.71/5.09 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_diff_power_eq
% 4.71/5.09 thf(fact_3573_power__diff__power__eq,axiom,
% 4.71/5.09 ! [A: nat,N: nat,M2: nat] :
% 4.71/5.09 ( ( A != zero_zero_nat )
% 4.71/5.09 => ( ( ( ord_less_eq_nat @ N @ M2 )
% 4.71/5.09 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) )
% 4.71/5.09 = ( power_power_nat @ A @ ( minus_minus_nat @ M2 @ N ) ) ) )
% 4.71/5.09 & ( ~ ( ord_less_eq_nat @ N @ M2 )
% 4.71/5.09 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) )
% 4.71/5.09 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_diff_power_eq
% 4.71/5.09 thf(fact_3574_card_Oremove,axiom,
% 4.71/5.09 ! [A2: set_set_nat_rat,X: set_nat_rat] :
% 4.71/5.09 ( ( finite6430367030675640852at_rat @ A2 )
% 4.71/5.09 => ( ( member_set_nat_rat @ X @ A2 )
% 4.71/5.09 => ( ( finite8736671560171388117at_rat @ A2 )
% 4.71/5.09 = ( suc @ ( finite8736671560171388117at_rat @ ( minus_1626877696091177228at_rat @ A2 @ ( insert_set_nat_rat @ X @ bot_bo6797373522285170759at_rat ) ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card.remove
% 4.71/5.09 thf(fact_3575_card_Oremove,axiom,
% 4.71/5.09 ! [A2: set_list_nat,X: list_nat] :
% 4.71/5.09 ( ( finite8100373058378681591st_nat @ A2 )
% 4.71/5.09 => ( ( member_list_nat @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_list_nat @ A2 )
% 4.71/5.09 = ( suc @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card.remove
% 4.71/5.09 thf(fact_3576_card_Oremove,axiom,
% 4.71/5.09 ! [A2: set_set_nat,X: set_nat] :
% 4.71/5.09 ( ( finite1152437895449049373et_nat @ A2 )
% 4.71/5.09 => ( ( member_set_nat @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_set_nat @ A2 )
% 4.71/5.09 = ( suc @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card.remove
% 4.71/5.09 thf(fact_3577_card_Oremove,axiom,
% 4.71/5.09 ! [A2: set_complex,X: complex] :
% 4.71/5.09 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.09 => ( ( member_complex @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_complex @ A2 )
% 4.71/5.09 = ( suc @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card.remove
% 4.71/5.09 thf(fact_3578_card_Oremove,axiom,
% 4.71/5.09 ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 4.71/5.09 ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.09 => ( ( member8440522571783428010at_nat @ X @ A2 )
% 4.71/5.09 => ( ( finite711546835091564841at_nat @ A2 )
% 4.71/5.09 = ( suc @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card.remove
% 4.71/5.09 thf(fact_3579_card_Oremove,axiom,
% 4.71/5.09 ! [A2: set_Extended_enat,X: extended_enat] :
% 4.71/5.09 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.09 => ( ( member_Extended_enat @ X @ A2 )
% 4.71/5.09 => ( ( finite121521170596916366d_enat @ A2 )
% 4.71/5.09 = ( suc @ ( finite121521170596916366d_enat @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card.remove
% 4.71/5.09 thf(fact_3580_card_Oremove,axiom,
% 4.71/5.09 ! [A2: set_real,X: real] :
% 4.71/5.09 ( ( finite_finite_real @ A2 )
% 4.71/5.09 => ( ( member_real @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_real @ A2 )
% 4.71/5.09 = ( suc @ ( finite_card_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card.remove
% 4.71/5.09 thf(fact_3581_card_Oremove,axiom,
% 4.71/5.09 ! [A2: set_o,X: $o] :
% 4.71/5.09 ( ( finite_finite_o @ A2 )
% 4.71/5.09 => ( ( member_o @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_o @ A2 )
% 4.71/5.09 = ( suc @ ( finite_card_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card.remove
% 4.71/5.09 thf(fact_3582_card_Oremove,axiom,
% 4.71/5.09 ! [A2: set_int,X: int] :
% 4.71/5.09 ( ( finite_finite_int @ A2 )
% 4.71/5.09 => ( ( member_int @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_int @ A2 )
% 4.71/5.09 = ( suc @ ( finite_card_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card.remove
% 4.71/5.09 thf(fact_3583_card_Oremove,axiom,
% 4.71/5.09 ! [A2: set_nat,X: nat] :
% 4.71/5.09 ( ( finite_finite_nat @ A2 )
% 4.71/5.09 => ( ( member_nat @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_nat @ A2 )
% 4.71/5.09 = ( suc @ ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card.remove
% 4.71/5.09 thf(fact_3584_card_Oinsert__remove,axiom,
% 4.71/5.09 ! [A2: set_list_nat,X: list_nat] :
% 4.71/5.09 ( ( finite8100373058378681591st_nat @ A2 )
% 4.71/5.09 => ( ( finite_card_list_nat @ ( insert_list_nat @ X @ A2 ) )
% 4.71/5.09 = ( suc @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card.insert_remove
% 4.71/5.09 thf(fact_3585_card_Oinsert__remove,axiom,
% 4.71/5.09 ! [A2: set_set_nat,X: set_nat] :
% 4.71/5.09 ( ( finite1152437895449049373et_nat @ A2 )
% 4.71/5.09 => ( ( finite_card_set_nat @ ( insert_set_nat @ X @ A2 ) )
% 4.71/5.09 = ( suc @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card.insert_remove
% 4.71/5.09 thf(fact_3586_card_Oinsert__remove,axiom,
% 4.71/5.09 ! [A2: set_complex,X: complex] :
% 4.71/5.09 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.09 => ( ( finite_card_complex @ ( insert_complex @ X @ A2 ) )
% 4.71/5.09 = ( suc @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card.insert_remove
% 4.71/5.09 thf(fact_3587_card_Oinsert__remove,axiom,
% 4.71/5.09 ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 4.71/5.09 ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.09 => ( ( finite711546835091564841at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) )
% 4.71/5.09 = ( suc @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card.insert_remove
% 4.71/5.09 thf(fact_3588_card_Oinsert__remove,axiom,
% 4.71/5.09 ! [A2: set_Extended_enat,X: extended_enat] :
% 4.71/5.09 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.09 => ( ( finite121521170596916366d_enat @ ( insert_Extended_enat @ X @ A2 ) )
% 4.71/5.09 = ( suc @ ( finite121521170596916366d_enat @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card.insert_remove
% 4.71/5.09 thf(fact_3589_card_Oinsert__remove,axiom,
% 4.71/5.09 ! [A2: set_real,X: real] :
% 4.71/5.09 ( ( finite_finite_real @ A2 )
% 4.71/5.09 => ( ( finite_card_real @ ( insert_real @ X @ A2 ) )
% 4.71/5.09 = ( suc @ ( finite_card_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card.insert_remove
% 4.71/5.09 thf(fact_3590_card_Oinsert__remove,axiom,
% 4.71/5.09 ! [A2: set_o,X: $o] :
% 4.71/5.09 ( ( finite_finite_o @ A2 )
% 4.71/5.09 => ( ( finite_card_o @ ( insert_o @ X @ A2 ) )
% 4.71/5.09 = ( suc @ ( finite_card_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card.insert_remove
% 4.71/5.09 thf(fact_3591_card_Oinsert__remove,axiom,
% 4.71/5.09 ! [A2: set_int,X: int] :
% 4.71/5.09 ( ( finite_finite_int @ A2 )
% 4.71/5.09 => ( ( finite_card_int @ ( insert_int @ X @ A2 ) )
% 4.71/5.09 = ( suc @ ( finite_card_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card.insert_remove
% 4.71/5.09 thf(fact_3592_card_Oinsert__remove,axiom,
% 4.71/5.09 ! [A2: set_nat,X: nat] :
% 4.71/5.09 ( ( finite_finite_nat @ A2 )
% 4.71/5.09 => ( ( finite_card_nat @ ( insert_nat @ X @ A2 ) )
% 4.71/5.09 = ( suc @ ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card.insert_remove
% 4.71/5.09 thf(fact_3593_card__Suc__Diff1,axiom,
% 4.71/5.09 ! [A2: set_set_nat_rat,X: set_nat_rat] :
% 4.71/5.09 ( ( finite6430367030675640852at_rat @ A2 )
% 4.71/5.09 => ( ( member_set_nat_rat @ X @ A2 )
% 4.71/5.09 => ( ( suc @ ( finite8736671560171388117at_rat @ ( minus_1626877696091177228at_rat @ A2 @ ( insert_set_nat_rat @ X @ bot_bo6797373522285170759at_rat ) ) ) )
% 4.71/5.09 = ( finite8736671560171388117at_rat @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Suc_Diff1
% 4.71/5.09 thf(fact_3594_card__Suc__Diff1,axiom,
% 4.71/5.09 ! [A2: set_list_nat,X: list_nat] :
% 4.71/5.09 ( ( finite8100373058378681591st_nat @ A2 )
% 4.71/5.09 => ( ( member_list_nat @ X @ A2 )
% 4.71/5.09 => ( ( suc @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) )
% 4.71/5.09 = ( finite_card_list_nat @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Suc_Diff1
% 4.71/5.09 thf(fact_3595_card__Suc__Diff1,axiom,
% 4.71/5.09 ! [A2: set_set_nat,X: set_nat] :
% 4.71/5.09 ( ( finite1152437895449049373et_nat @ A2 )
% 4.71/5.09 => ( ( member_set_nat @ X @ A2 )
% 4.71/5.09 => ( ( suc @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) )
% 4.71/5.09 = ( finite_card_set_nat @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Suc_Diff1
% 4.71/5.09 thf(fact_3596_card__Suc__Diff1,axiom,
% 4.71/5.09 ! [A2: set_complex,X: complex] :
% 4.71/5.09 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.09 => ( ( member_complex @ X @ A2 )
% 4.71/5.09 => ( ( suc @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) )
% 4.71/5.09 = ( finite_card_complex @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Suc_Diff1
% 4.71/5.09 thf(fact_3597_card__Suc__Diff1,axiom,
% 4.71/5.09 ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 4.71/5.09 ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.09 => ( ( member8440522571783428010at_nat @ X @ A2 )
% 4.71/5.09 => ( ( suc @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) )
% 4.71/5.09 = ( finite711546835091564841at_nat @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Suc_Diff1
% 4.71/5.09 thf(fact_3598_card__Suc__Diff1,axiom,
% 4.71/5.09 ! [A2: set_Extended_enat,X: extended_enat] :
% 4.71/5.09 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.09 => ( ( member_Extended_enat @ X @ A2 )
% 4.71/5.09 => ( ( suc @ ( finite121521170596916366d_enat @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ) )
% 4.71/5.09 = ( finite121521170596916366d_enat @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Suc_Diff1
% 4.71/5.09 thf(fact_3599_card__Suc__Diff1,axiom,
% 4.71/5.09 ! [A2: set_real,X: real] :
% 4.71/5.09 ( ( finite_finite_real @ A2 )
% 4.71/5.09 => ( ( member_real @ X @ A2 )
% 4.71/5.09 => ( ( suc @ ( finite_card_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) )
% 4.71/5.09 = ( finite_card_real @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Suc_Diff1
% 4.71/5.09 thf(fact_3600_card__Suc__Diff1,axiom,
% 4.71/5.09 ! [A2: set_o,X: $o] :
% 4.71/5.09 ( ( finite_finite_o @ A2 )
% 4.71/5.09 => ( ( member_o @ X @ A2 )
% 4.71/5.09 => ( ( suc @ ( finite_card_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) )
% 4.71/5.09 = ( finite_card_o @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Suc_Diff1
% 4.71/5.09 thf(fact_3601_card__Suc__Diff1,axiom,
% 4.71/5.09 ! [A2: set_int,X: int] :
% 4.71/5.09 ( ( finite_finite_int @ A2 )
% 4.71/5.09 => ( ( member_int @ X @ A2 )
% 4.71/5.09 => ( ( suc @ ( finite_card_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) )
% 4.71/5.09 = ( finite_card_int @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Suc_Diff1
% 4.71/5.09 thf(fact_3602_card__Suc__Diff1,axiom,
% 4.71/5.09 ! [A2: set_nat,X: nat] :
% 4.71/5.09 ( ( finite_finite_nat @ A2 )
% 4.71/5.09 => ( ( member_nat @ X @ A2 )
% 4.71/5.09 => ( ( suc @ ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) )
% 4.71/5.09 = ( finite_card_nat @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Suc_Diff1
% 4.71/5.09 thf(fact_3603_card__Diff1__less__iff,axiom,
% 4.71/5.09 ! [A2: set_set_nat_rat,X: set_nat_rat] :
% 4.71/5.09 ( ( ord_less_nat @ ( finite8736671560171388117at_rat @ ( minus_1626877696091177228at_rat @ A2 @ ( insert_set_nat_rat @ X @ bot_bo6797373522285170759at_rat ) ) ) @ ( finite8736671560171388117at_rat @ A2 ) )
% 4.71/5.09 = ( ( finite6430367030675640852at_rat @ A2 )
% 4.71/5.09 & ( member_set_nat_rat @ X @ A2 ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_less_iff
% 4.71/5.09 thf(fact_3604_card__Diff1__less__iff,axiom,
% 4.71/5.09 ! [A2: set_list_nat,X: list_nat] :
% 4.71/5.09 ( ( ord_less_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) @ ( finite_card_list_nat @ A2 ) )
% 4.71/5.09 = ( ( finite8100373058378681591st_nat @ A2 )
% 4.71/5.09 & ( member_list_nat @ X @ A2 ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_less_iff
% 4.71/5.09 thf(fact_3605_card__Diff1__less__iff,axiom,
% 4.71/5.09 ! [A2: set_set_nat,X: set_nat] :
% 4.71/5.09 ( ( ord_less_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) @ ( finite_card_set_nat @ A2 ) )
% 4.71/5.09 = ( ( finite1152437895449049373et_nat @ A2 )
% 4.71/5.09 & ( member_set_nat @ X @ A2 ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_less_iff
% 4.71/5.09 thf(fact_3606_card__Diff1__less__iff,axiom,
% 4.71/5.09 ! [A2: set_complex,X: complex] :
% 4.71/5.09 ( ( ord_less_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) @ ( finite_card_complex @ A2 ) )
% 4.71/5.09 = ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.09 & ( member_complex @ X @ A2 ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_less_iff
% 4.71/5.09 thf(fact_3607_card__Diff1__less__iff,axiom,
% 4.71/5.09 ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 4.71/5.09 ( ( ord_less_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) @ ( finite711546835091564841at_nat @ A2 ) )
% 4.71/5.09 = ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.09 & ( member8440522571783428010at_nat @ X @ A2 ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_less_iff
% 4.71/5.09 thf(fact_3608_card__Diff1__less__iff,axiom,
% 4.71/5.09 ! [A2: set_Extended_enat,X: extended_enat] :
% 4.71/5.09 ( ( ord_less_nat @ ( finite121521170596916366d_enat @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ) @ ( finite121521170596916366d_enat @ A2 ) )
% 4.71/5.09 = ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.09 & ( member_Extended_enat @ X @ A2 ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_less_iff
% 4.71/5.09 thf(fact_3609_card__Diff1__less__iff,axiom,
% 4.71/5.09 ! [A2: set_real,X: real] :
% 4.71/5.09 ( ( ord_less_nat @ ( finite_card_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) @ ( finite_card_real @ A2 ) )
% 4.71/5.09 = ( ( finite_finite_real @ A2 )
% 4.71/5.09 & ( member_real @ X @ A2 ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_less_iff
% 4.71/5.09 thf(fact_3610_card__Diff1__less__iff,axiom,
% 4.71/5.09 ! [A2: set_o,X: $o] :
% 4.71/5.09 ( ( ord_less_nat @ ( finite_card_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) @ ( finite_card_o @ A2 ) )
% 4.71/5.09 = ( ( finite_finite_o @ A2 )
% 4.71/5.09 & ( member_o @ X @ A2 ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_less_iff
% 4.71/5.09 thf(fact_3611_card__Diff1__less__iff,axiom,
% 4.71/5.09 ! [A2: set_int,X: int] :
% 4.71/5.09 ( ( ord_less_nat @ ( finite_card_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) @ ( finite_card_int @ A2 ) )
% 4.71/5.09 = ( ( finite_finite_int @ A2 )
% 4.71/5.09 & ( member_int @ X @ A2 ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_less_iff
% 4.71/5.09 thf(fact_3612_card__Diff1__less__iff,axiom,
% 4.71/5.09 ! [A2: set_nat,X: nat] :
% 4.71/5.09 ( ( ord_less_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) @ ( finite_card_nat @ A2 ) )
% 4.71/5.09 = ( ( finite_finite_nat @ A2 )
% 4.71/5.09 & ( member_nat @ X @ A2 ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_less_iff
% 4.71/5.09 thf(fact_3613_card__Diff2__less,axiom,
% 4.71/5.09 ! [A2: set_set_nat_rat,X: set_nat_rat,Y: set_nat_rat] :
% 4.71/5.09 ( ( finite6430367030675640852at_rat @ A2 )
% 4.71/5.09 => ( ( member_set_nat_rat @ X @ A2 )
% 4.71/5.09 => ( ( member_set_nat_rat @ Y @ A2 )
% 4.71/5.09 => ( ord_less_nat @ ( finite8736671560171388117at_rat @ ( minus_1626877696091177228at_rat @ ( minus_1626877696091177228at_rat @ A2 @ ( insert_set_nat_rat @ X @ bot_bo6797373522285170759at_rat ) ) @ ( insert_set_nat_rat @ Y @ bot_bo6797373522285170759at_rat ) ) ) @ ( finite8736671560171388117at_rat @ A2 ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff2_less
% 4.71/5.09 thf(fact_3614_card__Diff2__less,axiom,
% 4.71/5.09 ! [A2: set_list_nat,X: list_nat,Y: list_nat] :
% 4.71/5.09 ( ( finite8100373058378681591st_nat @ A2 )
% 4.71/5.09 => ( ( member_list_nat @ X @ A2 )
% 4.71/5.09 => ( ( member_list_nat @ Y @ A2 )
% 4.71/5.09 => ( ord_less_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ ( minus_7954133019191499631st_nat @ A2 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) @ ( insert_list_nat @ Y @ bot_bot_set_list_nat ) ) ) @ ( finite_card_list_nat @ A2 ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff2_less
% 4.71/5.09 thf(fact_3615_card__Diff2__less,axiom,
% 4.71/5.09 ! [A2: set_set_nat,X: set_nat,Y: set_nat] :
% 4.71/5.09 ( ( finite1152437895449049373et_nat @ A2 )
% 4.71/5.09 => ( ( member_set_nat @ X @ A2 )
% 4.71/5.09 => ( ( member_set_nat @ Y @ A2 )
% 4.71/5.09 => ( ord_less_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ ( insert_set_nat @ Y @ bot_bot_set_set_nat ) ) ) @ ( finite_card_set_nat @ A2 ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff2_less
% 4.71/5.09 thf(fact_3616_card__Diff2__less,axiom,
% 4.71/5.09 ! [A2: set_complex,X: complex,Y: complex] :
% 4.71/5.09 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.09 => ( ( member_complex @ X @ A2 )
% 4.71/5.09 => ( ( member_complex @ Y @ A2 )
% 4.71/5.09 => ( ord_less_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) @ ( insert_complex @ Y @ bot_bot_set_complex ) ) ) @ ( finite_card_complex @ A2 ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff2_less
% 4.71/5.09 thf(fact_3617_card__Diff2__less,axiom,
% 4.71/5.09 ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 4.71/5.09 ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.09 => ( ( member8440522571783428010at_nat @ X @ A2 )
% 4.71/5.09 => ( ( member8440522571783428010at_nat @ Y @ A2 )
% 4.71/5.09 => ( ord_less_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ ( insert8211810215607154385at_nat @ Y @ bot_bo2099793752762293965at_nat ) ) ) @ ( finite711546835091564841at_nat @ A2 ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff2_less
% 4.71/5.09 thf(fact_3618_card__Diff2__less,axiom,
% 4.71/5.09 ! [A2: set_Extended_enat,X: extended_enat,Y: extended_enat] :
% 4.71/5.09 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.09 => ( ( member_Extended_enat @ X @ A2 )
% 4.71/5.09 => ( ( member_Extended_enat @ Y @ A2 )
% 4.71/5.09 => ( ord_less_nat @ ( finite121521170596916366d_enat @ ( minus_925952699566721837d_enat @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) @ ( insert_Extended_enat @ Y @ bot_bo7653980558646680370d_enat ) ) ) @ ( finite121521170596916366d_enat @ A2 ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff2_less
% 4.71/5.09 thf(fact_3619_card__Diff2__less,axiom,
% 4.71/5.09 ! [A2: set_real,X: real,Y: real] :
% 4.71/5.09 ( ( finite_finite_real @ A2 )
% 4.71/5.09 => ( ( member_real @ X @ A2 )
% 4.71/5.09 => ( ( member_real @ Y @ A2 )
% 4.71/5.09 => ( ord_less_nat @ ( finite_card_real @ ( minus_minus_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ ( insert_real @ Y @ bot_bot_set_real ) ) ) @ ( finite_card_real @ A2 ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff2_less
% 4.71/5.09 thf(fact_3620_card__Diff2__less,axiom,
% 4.71/5.09 ! [A2: set_o,X: $o,Y: $o] :
% 4.71/5.09 ( ( finite_finite_o @ A2 )
% 4.71/5.09 => ( ( member_o @ X @ A2 )
% 4.71/5.09 => ( ( member_o @ Y @ A2 )
% 4.71/5.09 => ( ord_less_nat @ ( finite_card_o @ ( minus_minus_set_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) @ ( insert_o @ Y @ bot_bot_set_o ) ) ) @ ( finite_card_o @ A2 ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff2_less
% 4.71/5.09 thf(fact_3621_card__Diff2__less,axiom,
% 4.71/5.09 ! [A2: set_int,X: int,Y: int] :
% 4.71/5.09 ( ( finite_finite_int @ A2 )
% 4.71/5.09 => ( ( member_int @ X @ A2 )
% 4.71/5.09 => ( ( member_int @ Y @ A2 )
% 4.71/5.09 => ( ord_less_nat @ ( finite_card_int @ ( minus_minus_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ ( insert_int @ Y @ bot_bot_set_int ) ) ) @ ( finite_card_int @ A2 ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff2_less
% 4.71/5.09 thf(fact_3622_card__Diff2__less,axiom,
% 4.71/5.09 ! [A2: set_nat,X: nat,Y: nat] :
% 4.71/5.09 ( ( finite_finite_nat @ A2 )
% 4.71/5.09 => ( ( member_nat @ X @ A2 )
% 4.71/5.09 => ( ( member_nat @ Y @ A2 )
% 4.71/5.09 => ( ord_less_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ ( insert_nat @ Y @ bot_bot_set_nat ) ) ) @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff2_less
% 4.71/5.09 thf(fact_3623_card__Diff1__less,axiom,
% 4.71/5.09 ! [A2: set_set_nat_rat,X: set_nat_rat] :
% 4.71/5.09 ( ( finite6430367030675640852at_rat @ A2 )
% 4.71/5.09 => ( ( member_set_nat_rat @ X @ A2 )
% 4.71/5.09 => ( ord_less_nat @ ( finite8736671560171388117at_rat @ ( minus_1626877696091177228at_rat @ A2 @ ( insert_set_nat_rat @ X @ bot_bo6797373522285170759at_rat ) ) ) @ ( finite8736671560171388117at_rat @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_less
% 4.71/5.09 thf(fact_3624_card__Diff1__less,axiom,
% 4.71/5.09 ! [A2: set_list_nat,X: list_nat] :
% 4.71/5.09 ( ( finite8100373058378681591st_nat @ A2 )
% 4.71/5.09 => ( ( member_list_nat @ X @ A2 )
% 4.71/5.09 => ( ord_less_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) @ ( finite_card_list_nat @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_less
% 4.71/5.09 thf(fact_3625_card__Diff1__less,axiom,
% 4.71/5.09 ! [A2: set_set_nat,X: set_nat] :
% 4.71/5.09 ( ( finite1152437895449049373et_nat @ A2 )
% 4.71/5.09 => ( ( member_set_nat @ X @ A2 )
% 4.71/5.09 => ( ord_less_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) @ ( finite_card_set_nat @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_less
% 4.71/5.09 thf(fact_3626_card__Diff1__less,axiom,
% 4.71/5.09 ! [A2: set_complex,X: complex] :
% 4.71/5.09 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.09 => ( ( member_complex @ X @ A2 )
% 4.71/5.09 => ( ord_less_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) @ ( finite_card_complex @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_less
% 4.71/5.09 thf(fact_3627_card__Diff1__less,axiom,
% 4.71/5.09 ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 4.71/5.09 ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.09 => ( ( member8440522571783428010at_nat @ X @ A2 )
% 4.71/5.09 => ( ord_less_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) @ ( finite711546835091564841at_nat @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_less
% 4.71/5.09 thf(fact_3628_card__Diff1__less,axiom,
% 4.71/5.09 ! [A2: set_Extended_enat,X: extended_enat] :
% 4.71/5.09 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.09 => ( ( member_Extended_enat @ X @ A2 )
% 4.71/5.09 => ( ord_less_nat @ ( finite121521170596916366d_enat @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ) @ ( finite121521170596916366d_enat @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_less
% 4.71/5.09 thf(fact_3629_card__Diff1__less,axiom,
% 4.71/5.09 ! [A2: set_real,X: real] :
% 4.71/5.09 ( ( finite_finite_real @ A2 )
% 4.71/5.09 => ( ( member_real @ X @ A2 )
% 4.71/5.09 => ( ord_less_nat @ ( finite_card_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) @ ( finite_card_real @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_less
% 4.71/5.09 thf(fact_3630_card__Diff1__less,axiom,
% 4.71/5.09 ! [A2: set_o,X: $o] :
% 4.71/5.09 ( ( finite_finite_o @ A2 )
% 4.71/5.09 => ( ( member_o @ X @ A2 )
% 4.71/5.09 => ( ord_less_nat @ ( finite_card_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) @ ( finite_card_o @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_less
% 4.71/5.09 thf(fact_3631_card__Diff1__less,axiom,
% 4.71/5.09 ! [A2: set_int,X: int] :
% 4.71/5.09 ( ( finite_finite_int @ A2 )
% 4.71/5.09 => ( ( member_int @ X @ A2 )
% 4.71/5.09 => ( ord_less_nat @ ( finite_card_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) @ ( finite_card_int @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_less
% 4.71/5.09 thf(fact_3632_card__Diff1__less,axiom,
% 4.71/5.09 ! [A2: set_nat,X: nat] :
% 4.71/5.09 ( ( finite_finite_nat @ A2 )
% 4.71/5.09 => ( ( member_nat @ X @ A2 )
% 4.71/5.09 => ( ord_less_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) @ ( finite_card_nat @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff1_less
% 4.71/5.09 thf(fact_3633_card__Diff__singleton__if,axiom,
% 4.71/5.09 ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.09 ( ( ( member8440522571783428010at_nat @ X @ A2 )
% 4.71/5.09 => ( ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) )
% 4.71/5.09 = ( minus_minus_nat @ ( finite711546835091564841at_nat @ A2 ) @ one_one_nat ) ) )
% 4.71/5.09 & ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 4.71/5.09 => ( ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) )
% 4.71/5.09 = ( finite711546835091564841at_nat @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff_singleton_if
% 4.71/5.09 thf(fact_3634_card__Diff__singleton__if,axiom,
% 4.71/5.09 ! [X: set_nat_rat,A2: set_set_nat_rat] :
% 4.71/5.09 ( ( ( member_set_nat_rat @ X @ A2 )
% 4.71/5.09 => ( ( finite8736671560171388117at_rat @ ( minus_1626877696091177228at_rat @ A2 @ ( insert_set_nat_rat @ X @ bot_bo6797373522285170759at_rat ) ) )
% 4.71/5.09 = ( minus_minus_nat @ ( finite8736671560171388117at_rat @ A2 ) @ one_one_nat ) ) )
% 4.71/5.09 & ( ~ ( member_set_nat_rat @ X @ A2 )
% 4.71/5.09 => ( ( finite8736671560171388117at_rat @ ( minus_1626877696091177228at_rat @ A2 @ ( insert_set_nat_rat @ X @ bot_bo6797373522285170759at_rat ) ) )
% 4.71/5.09 = ( finite8736671560171388117at_rat @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff_singleton_if
% 4.71/5.09 thf(fact_3635_card__Diff__singleton__if,axiom,
% 4.71/5.09 ! [X: complex,A2: set_complex] :
% 4.71/5.09 ( ( ( member_complex @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_complex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) )
% 4.71/5.09 = ( minus_minus_nat @ ( finite_card_complex @ A2 ) @ one_one_nat ) ) )
% 4.71/5.09 & ( ~ ( member_complex @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_complex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) )
% 4.71/5.09 = ( finite_card_complex @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff_singleton_if
% 4.71/5.09 thf(fact_3636_card__Diff__singleton__if,axiom,
% 4.71/5.09 ! [X: list_nat,A2: set_list_nat] :
% 4.71/5.09 ( ( ( member_list_nat @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) )
% 4.71/5.09 = ( minus_minus_nat @ ( finite_card_list_nat @ A2 ) @ one_one_nat ) ) )
% 4.71/5.09 & ( ~ ( member_list_nat @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) )
% 4.71/5.09 = ( finite_card_list_nat @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff_singleton_if
% 4.71/5.09 thf(fact_3637_card__Diff__singleton__if,axiom,
% 4.71/5.09 ! [X: set_nat,A2: set_set_nat] :
% 4.71/5.09 ( ( ( member_set_nat @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) )
% 4.71/5.09 = ( minus_minus_nat @ ( finite_card_set_nat @ A2 ) @ one_one_nat ) ) )
% 4.71/5.09 & ( ~ ( member_set_nat @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) )
% 4.71/5.09 = ( finite_card_set_nat @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff_singleton_if
% 4.71/5.09 thf(fact_3638_card__Diff__singleton__if,axiom,
% 4.71/5.09 ! [X: real,A2: set_real] :
% 4.71/5.09 ( ( ( member_real @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) )
% 4.71/5.09 = ( minus_minus_nat @ ( finite_card_real @ A2 ) @ one_one_nat ) ) )
% 4.71/5.09 & ( ~ ( member_real @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) )
% 4.71/5.09 = ( finite_card_real @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff_singleton_if
% 4.71/5.09 thf(fact_3639_card__Diff__singleton__if,axiom,
% 4.71/5.09 ! [X: $o,A2: set_o] :
% 4.71/5.09 ( ( ( member_o @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) )
% 4.71/5.09 = ( minus_minus_nat @ ( finite_card_o @ A2 ) @ one_one_nat ) ) )
% 4.71/5.09 & ( ~ ( member_o @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) )
% 4.71/5.09 = ( finite_card_o @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff_singleton_if
% 4.71/5.09 thf(fact_3640_card__Diff__singleton__if,axiom,
% 4.71/5.09 ! [X: int,A2: set_int] :
% 4.71/5.09 ( ( ( member_int @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) )
% 4.71/5.09 = ( minus_minus_nat @ ( finite_card_int @ A2 ) @ one_one_nat ) ) )
% 4.71/5.09 & ( ~ ( member_int @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) )
% 4.71/5.09 = ( finite_card_int @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff_singleton_if
% 4.71/5.09 thf(fact_3641_card__Diff__singleton__if,axiom,
% 4.71/5.09 ! [X: nat,A2: set_nat] :
% 4.71/5.09 ( ( ( member_nat @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 4.71/5.09 = ( minus_minus_nat @ ( finite_card_nat @ A2 ) @ one_one_nat ) ) )
% 4.71/5.09 & ( ~ ( member_nat @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 4.71/5.09 = ( finite_card_nat @ A2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff_singleton_if
% 4.71/5.09 thf(fact_3642_card__Diff__singleton,axiom,
% 4.71/5.09 ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.09 ( ( member8440522571783428010at_nat @ X @ A2 )
% 4.71/5.09 => ( ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) )
% 4.71/5.09 = ( minus_minus_nat @ ( finite711546835091564841at_nat @ A2 ) @ one_one_nat ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff_singleton
% 4.71/5.09 thf(fact_3643_card__Diff__singleton,axiom,
% 4.71/5.09 ! [X: set_nat_rat,A2: set_set_nat_rat] :
% 4.71/5.09 ( ( member_set_nat_rat @ X @ A2 )
% 4.71/5.09 => ( ( finite8736671560171388117at_rat @ ( minus_1626877696091177228at_rat @ A2 @ ( insert_set_nat_rat @ X @ bot_bo6797373522285170759at_rat ) ) )
% 4.71/5.09 = ( minus_minus_nat @ ( finite8736671560171388117at_rat @ A2 ) @ one_one_nat ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff_singleton
% 4.71/5.09 thf(fact_3644_card__Diff__singleton,axiom,
% 4.71/5.09 ! [X: complex,A2: set_complex] :
% 4.71/5.09 ( ( member_complex @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_complex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) )
% 4.71/5.09 = ( minus_minus_nat @ ( finite_card_complex @ A2 ) @ one_one_nat ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff_singleton
% 4.71/5.09 thf(fact_3645_card__Diff__singleton,axiom,
% 4.71/5.09 ! [X: list_nat,A2: set_list_nat] :
% 4.71/5.09 ( ( member_list_nat @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) )
% 4.71/5.09 = ( minus_minus_nat @ ( finite_card_list_nat @ A2 ) @ one_one_nat ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff_singleton
% 4.71/5.09 thf(fact_3646_card__Diff__singleton,axiom,
% 4.71/5.09 ! [X: set_nat,A2: set_set_nat] :
% 4.71/5.09 ( ( member_set_nat @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) )
% 4.71/5.09 = ( minus_minus_nat @ ( finite_card_set_nat @ A2 ) @ one_one_nat ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff_singleton
% 4.71/5.09 thf(fact_3647_card__Diff__singleton,axiom,
% 4.71/5.09 ! [X: real,A2: set_real] :
% 4.71/5.09 ( ( member_real @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) )
% 4.71/5.09 = ( minus_minus_nat @ ( finite_card_real @ A2 ) @ one_one_nat ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff_singleton
% 4.71/5.09 thf(fact_3648_card__Diff__singleton,axiom,
% 4.71/5.09 ! [X: $o,A2: set_o] :
% 4.71/5.09 ( ( member_o @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) )
% 4.71/5.09 = ( minus_minus_nat @ ( finite_card_o @ A2 ) @ one_one_nat ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff_singleton
% 4.71/5.09 thf(fact_3649_card__Diff__singleton,axiom,
% 4.71/5.09 ! [X: int,A2: set_int] :
% 4.71/5.09 ( ( member_int @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) )
% 4.71/5.09 = ( minus_minus_nat @ ( finite_card_int @ A2 ) @ one_one_nat ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff_singleton
% 4.71/5.09 thf(fact_3650_card__Diff__singleton,axiom,
% 4.71/5.09 ! [X: nat,A2: set_nat] :
% 4.71/5.09 ( ( member_nat @ X @ A2 )
% 4.71/5.09 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 4.71/5.09 = ( minus_minus_nat @ ( finite_card_nat @ A2 ) @ one_one_nat ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % card_Diff_singleton
% 4.71/5.09 thf(fact_3651_of__nat__zero__less__power__iff,axiom,
% 4.71/5.09 ! [X: nat,N: nat] :
% 4.71/5.09 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X ) @ N ) )
% 4.71/5.09 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 4.71/5.09 | ( N = zero_zero_nat ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % of_nat_zero_less_power_iff
% 4.71/5.09 thf(fact_3652_of__nat__zero__less__power__iff,axiom,
% 4.71/5.09 ! [X: nat,N: nat] :
% 4.71/5.09 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X ) @ N ) )
% 4.71/5.09 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 4.71/5.09 | ( N = zero_zero_nat ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % of_nat_zero_less_power_iff
% 4.71/5.09 thf(fact_3653_of__nat__zero__less__power__iff,axiom,
% 4.71/5.09 ! [X: nat,N: nat] :
% 4.71/5.09 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X ) @ N ) )
% 4.71/5.09 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 4.71/5.09 | ( N = zero_zero_nat ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % of_nat_zero_less_power_iff
% 4.71/5.09 thf(fact_3654_of__nat__zero__less__power__iff,axiom,
% 4.71/5.09 ! [X: nat,N: nat] :
% 4.71/5.09 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X ) @ N ) )
% 4.71/5.09 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 4.71/5.09 | ( N = zero_zero_nat ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % of_nat_zero_less_power_iff
% 4.71/5.09 thf(fact_3655_power__decreasing__iff,axiom,
% 4.71/5.09 ! [B: real,M2: nat,N: nat] :
% 4.71/5.09 ( ( ord_less_real @ zero_zero_real @ B )
% 4.71/5.09 => ( ( ord_less_real @ B @ one_one_real )
% 4.71/5.09 => ( ( ord_less_eq_real @ ( power_power_real @ B @ M2 ) @ ( power_power_real @ B @ N ) )
% 4.71/5.09 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_decreasing_iff
% 4.71/5.09 thf(fact_3656_power__decreasing__iff,axiom,
% 4.71/5.09 ! [B: rat,M2: nat,N: nat] :
% 4.71/5.09 ( ( ord_less_rat @ zero_zero_rat @ B )
% 4.71/5.09 => ( ( ord_less_rat @ B @ one_one_rat )
% 4.71/5.09 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M2 ) @ ( power_power_rat @ B @ N ) )
% 4.71/5.09 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_decreasing_iff
% 4.71/5.09 thf(fact_3657_power__decreasing__iff,axiom,
% 4.71/5.09 ! [B: nat,M2: nat,N: nat] :
% 4.71/5.09 ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.71/5.09 => ( ( ord_less_nat @ B @ one_one_nat )
% 4.71/5.09 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M2 ) @ ( power_power_nat @ B @ N ) )
% 4.71/5.09 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_decreasing_iff
% 4.71/5.09 thf(fact_3658_power__decreasing__iff,axiom,
% 4.71/5.09 ! [B: int,M2: nat,N: nat] :
% 4.71/5.09 ( ( ord_less_int @ zero_zero_int @ B )
% 4.71/5.09 => ( ( ord_less_int @ B @ one_one_int )
% 4.71/5.09 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M2 ) @ ( power_power_int @ B @ N ) )
% 4.71/5.09 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_decreasing_iff
% 4.71/5.09 thf(fact_3659_zero__less__power__abs__iff,axiom,
% 4.71/5.09 ! [A: real,N: nat] :
% 4.71/5.09 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 4.71/5.09 = ( ( A != zero_zero_real )
% 4.71/5.09 | ( N = zero_zero_nat ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % zero_less_power_abs_iff
% 4.71/5.09 thf(fact_3660_zero__less__power__abs__iff,axiom,
% 4.71/5.09 ! [A: rat,N: nat] :
% 4.71/5.09 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) )
% 4.71/5.09 = ( ( A != zero_zero_rat )
% 4.71/5.09 | ( N = zero_zero_nat ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % zero_less_power_abs_iff
% 4.71/5.09 thf(fact_3661_zero__less__power__abs__iff,axiom,
% 4.71/5.09 ! [A: int,N: nat] :
% 4.71/5.09 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) )
% 4.71/5.09 = ( ( A != zero_zero_int )
% 4.71/5.09 | ( N = zero_zero_nat ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % zero_less_power_abs_iff
% 4.71/5.09 thf(fact_3662_power__mono__iff,axiom,
% 4.71/5.09 ! [A: real,B: real,N: nat] :
% 4.71/5.09 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.09 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.71/5.09 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.09 => ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 4.71/5.09 = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_mono_iff
% 4.71/5.09 thf(fact_3663_power__mono__iff,axiom,
% 4.71/5.09 ! [A: rat,B: rat,N: nat] :
% 4.71/5.09 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.09 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.71/5.09 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.09 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 4.71/5.09 = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_mono_iff
% 4.71/5.09 thf(fact_3664_power__mono__iff,axiom,
% 4.71/5.09 ! [A: nat,B: nat,N: nat] :
% 4.71/5.09 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.71/5.09 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.71/5.09 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.09 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 4.71/5.09 = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_mono_iff
% 4.71/5.09 thf(fact_3665_power__mono__iff,axiom,
% 4.71/5.09 ! [A: int,B: int,N: nat] :
% 4.71/5.09 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.09 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.71/5.09 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.09 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 4.71/5.09 = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_mono_iff
% 4.71/5.09 thf(fact_3666_power__increasing__iff,axiom,
% 4.71/5.09 ! [B: real,X: nat,Y: nat] :
% 4.71/5.09 ( ( ord_less_real @ one_one_real @ B )
% 4.71/5.09 => ( ( ord_less_eq_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y ) )
% 4.71/5.09 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_increasing_iff
% 4.71/5.09 thf(fact_3667_power__increasing__iff,axiom,
% 4.71/5.09 ! [B: rat,X: nat,Y: nat] :
% 4.71/5.09 ( ( ord_less_rat @ one_one_rat @ B )
% 4.71/5.09 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 4.71/5.09 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_increasing_iff
% 4.71/5.09 thf(fact_3668_power__increasing__iff,axiom,
% 4.71/5.09 ! [B: nat,X: nat,Y: nat] :
% 4.71/5.09 ( ( ord_less_nat @ one_one_nat @ B )
% 4.71/5.09 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 4.71/5.09 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_increasing_iff
% 4.71/5.09 thf(fact_3669_power__increasing__iff,axiom,
% 4.71/5.09 ! [B: int,X: nat,Y: nat] :
% 4.71/5.09 ( ( ord_less_int @ one_one_int @ B )
% 4.71/5.09 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 4.71/5.09 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_increasing_iff
% 4.71/5.09 thf(fact_3670_power__strict__decreasing__iff,axiom,
% 4.71/5.09 ! [B: real,M2: nat,N: nat] :
% 4.71/5.09 ( ( ord_less_real @ zero_zero_real @ B )
% 4.71/5.09 => ( ( ord_less_real @ B @ one_one_real )
% 4.71/5.09 => ( ( ord_less_real @ ( power_power_real @ B @ M2 ) @ ( power_power_real @ B @ N ) )
% 4.71/5.09 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_strict_decreasing_iff
% 4.71/5.09 thf(fact_3671_power__strict__decreasing__iff,axiom,
% 4.71/5.09 ! [B: rat,M2: nat,N: nat] :
% 4.71/5.09 ( ( ord_less_rat @ zero_zero_rat @ B )
% 4.71/5.09 => ( ( ord_less_rat @ B @ one_one_rat )
% 4.71/5.09 => ( ( ord_less_rat @ ( power_power_rat @ B @ M2 ) @ ( power_power_rat @ B @ N ) )
% 4.71/5.09 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_strict_decreasing_iff
% 4.71/5.09 thf(fact_3672_power__strict__decreasing__iff,axiom,
% 4.71/5.09 ! [B: nat,M2: nat,N: nat] :
% 4.71/5.09 ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.71/5.09 => ( ( ord_less_nat @ B @ one_one_nat )
% 4.71/5.09 => ( ( ord_less_nat @ ( power_power_nat @ B @ M2 ) @ ( power_power_nat @ B @ N ) )
% 4.71/5.09 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_strict_decreasing_iff
% 4.71/5.09 thf(fact_3673_power__strict__decreasing__iff,axiom,
% 4.71/5.09 ! [B: int,M2: nat,N: nat] :
% 4.71/5.09 ( ( ord_less_int @ zero_zero_int @ B )
% 4.71/5.09 => ( ( ord_less_int @ B @ one_one_int )
% 4.71/5.09 => ( ( ord_less_int @ ( power_power_int @ B @ M2 ) @ ( power_power_int @ B @ N ) )
% 4.71/5.09 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_strict_decreasing_iff
% 4.71/5.09 thf(fact_3674_nat__mult__le__cancel__disj,axiom,
% 4.71/5.09 ! [K: nat,M2: nat,N: nat] :
% 4.71/5.09 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N ) )
% 4.71/5.09 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.71/5.09 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % nat_mult_le_cancel_disj
% 4.71/5.09 thf(fact_3675_of__nat__power__le__of__nat__cancel__iff,axiom,
% 4.71/5.09 ! [X: nat,B: nat,W2: nat] :
% 4.71/5.09 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) )
% 4.71/5.09 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % of_nat_power_le_of_nat_cancel_iff
% 4.71/5.09 thf(fact_3676_of__nat__power__le__of__nat__cancel__iff,axiom,
% 4.71/5.09 ! [X: nat,B: nat,W2: nat] :
% 4.71/5.09 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) )
% 4.71/5.09 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % of_nat_power_le_of_nat_cancel_iff
% 4.71/5.09 thf(fact_3677_of__nat__power__le__of__nat__cancel__iff,axiom,
% 4.71/5.09 ! [X: nat,B: nat,W2: nat] :
% 4.71/5.09 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) )
% 4.71/5.09 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % of_nat_power_le_of_nat_cancel_iff
% 4.71/5.09 thf(fact_3678_of__nat__power__le__of__nat__cancel__iff,axiom,
% 4.71/5.09 ! [X: nat,B: nat,W2: nat] :
% 4.71/5.09 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) )
% 4.71/5.09 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % of_nat_power_le_of_nat_cancel_iff
% 4.71/5.09 thf(fact_3679_of__nat__le__of__nat__power__cancel__iff,axiom,
% 4.71/5.09 ! [B: nat,W2: nat,X: nat] :
% 4.71/5.09 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) @ ( semiri5074537144036343181t_real @ X ) )
% 4.71/5.09 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 4.71/5.09
% 4.71/5.09 % of_nat_le_of_nat_power_cancel_iff
% 4.71/5.09 thf(fact_3680_of__nat__le__of__nat__power__cancel__iff,axiom,
% 4.71/5.09 ! [B: nat,W2: nat,X: nat] :
% 4.71/5.09 ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) @ ( semiri681578069525770553at_rat @ X ) )
% 4.71/5.09 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 4.71/5.09
% 4.71/5.09 % of_nat_le_of_nat_power_cancel_iff
% 4.71/5.09 thf(fact_3681_of__nat__le__of__nat__power__cancel__iff,axiom,
% 4.71/5.09 ! [B: nat,W2: nat,X: nat] :
% 4.71/5.09 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 4.71/5.09 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 4.71/5.09
% 4.71/5.09 % of_nat_le_of_nat_power_cancel_iff
% 4.71/5.09 thf(fact_3682_of__nat__le__of__nat__power__cancel__iff,axiom,
% 4.71/5.09 ! [B: nat,W2: nat,X: nat] :
% 4.71/5.09 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 4.71/5.09 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 4.71/5.09
% 4.71/5.09 % of_nat_le_of_nat_power_cancel_iff
% 4.71/5.09 thf(fact_3683_of__nat__power__less__of__nat__cancel__iff,axiom,
% 4.71/5.09 ! [X: nat,B: nat,W2: nat] :
% 4.71/5.09 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) )
% 4.71/5.09 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % of_nat_power_less_of_nat_cancel_iff
% 4.71/5.09 thf(fact_3684_of__nat__power__less__of__nat__cancel__iff,axiom,
% 4.71/5.09 ! [X: nat,B: nat,W2: nat] :
% 4.71/5.09 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) )
% 4.71/5.09 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % of_nat_power_less_of_nat_cancel_iff
% 4.71/5.09 thf(fact_3685_of__nat__power__less__of__nat__cancel__iff,axiom,
% 4.71/5.09 ! [X: nat,B: nat,W2: nat] :
% 4.71/5.09 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) )
% 4.71/5.09 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % of_nat_power_less_of_nat_cancel_iff
% 4.71/5.09 thf(fact_3686_of__nat__power__less__of__nat__cancel__iff,axiom,
% 4.71/5.09 ! [X: nat,B: nat,W2: nat] :
% 4.71/5.09 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) )
% 4.71/5.09 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % of_nat_power_less_of_nat_cancel_iff
% 4.71/5.09 thf(fact_3687_even__odd__cases,axiom,
% 4.71/5.09 ! [X: nat] :
% 4.71/5.09 ( ! [N2: nat] :
% 4.71/5.09 ( X
% 4.71/5.09 != ( plus_plus_nat @ N2 @ N2 ) )
% 4.71/5.09 => ~ ! [N2: nat] :
% 4.71/5.09 ( X
% 4.71/5.09 != ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % even_odd_cases
% 4.71/5.09 thf(fact_3688_power__one,axiom,
% 4.71/5.09 ! [N: nat] :
% 4.71/5.09 ( ( power_power_rat @ one_one_rat @ N )
% 4.71/5.09 = one_one_rat ) ).
% 4.71/5.09
% 4.71/5.09 % power_one
% 4.71/5.09 thf(fact_3689_power__one,axiom,
% 4.71/5.09 ! [N: nat] :
% 4.71/5.09 ( ( power_power_int @ one_one_int @ N )
% 4.71/5.09 = one_one_int ) ).
% 4.71/5.09
% 4.71/5.09 % power_one
% 4.71/5.09 thf(fact_3690_power__one,axiom,
% 4.71/5.09 ! [N: nat] :
% 4.71/5.09 ( ( power_power_nat @ one_one_nat @ N )
% 4.71/5.09 = one_one_nat ) ).
% 4.71/5.09
% 4.71/5.09 % power_one
% 4.71/5.09 thf(fact_3691_power__one,axiom,
% 4.71/5.09 ! [N: nat] :
% 4.71/5.09 ( ( power_power_real @ one_one_real @ N )
% 4.71/5.09 = one_one_real ) ).
% 4.71/5.09
% 4.71/5.09 % power_one
% 4.71/5.09 thf(fact_3692_power__one,axiom,
% 4.71/5.09 ! [N: nat] :
% 4.71/5.09 ( ( power_power_complex @ one_one_complex @ N )
% 4.71/5.09 = one_one_complex ) ).
% 4.71/5.09
% 4.71/5.09 % power_one
% 4.71/5.09 thf(fact_3693_add__Suc__right,axiom,
% 4.71/5.09 ! [M2: nat,N: nat] :
% 4.71/5.09 ( ( plus_plus_nat @ M2 @ ( suc @ N ) )
% 4.71/5.09 = ( suc @ ( plus_plus_nat @ M2 @ N ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % add_Suc_right
% 4.71/5.09 thf(fact_3694_Nat_Oadd__0__right,axiom,
% 4.71/5.09 ! [M2: nat] :
% 4.71/5.09 ( ( plus_plus_nat @ M2 @ zero_zero_nat )
% 4.71/5.09 = M2 ) ).
% 4.71/5.09
% 4.71/5.09 % Nat.add_0_right
% 4.71/5.09 thf(fact_3695_add__is__0,axiom,
% 4.71/5.09 ! [M2: nat,N: nat] :
% 4.71/5.09 ( ( ( plus_plus_nat @ M2 @ N )
% 4.71/5.09 = zero_zero_nat )
% 4.71/5.09 = ( ( M2 = zero_zero_nat )
% 4.71/5.09 & ( N = zero_zero_nat ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % add_is_0
% 4.71/5.09 thf(fact_3696_nat__add__left__cancel__less,axiom,
% 4.71/5.09 ! [K: nat,M2: nat,N: nat] :
% 4.71/5.09 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M2 ) @ ( plus_plus_nat @ K @ N ) )
% 4.71/5.09 = ( ord_less_nat @ M2 @ N ) ) ).
% 4.71/5.09
% 4.71/5.09 % nat_add_left_cancel_less
% 4.71/5.09 thf(fact_3697_nat__add__left__cancel__le,axiom,
% 4.71/5.09 ! [K: nat,M2: nat,N: nat] :
% 4.71/5.09 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M2 ) @ ( plus_plus_nat @ K @ N ) )
% 4.71/5.09 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 4.71/5.09
% 4.71/5.09 % nat_add_left_cancel_le
% 4.71/5.09 thf(fact_3698_power__one__right,axiom,
% 4.71/5.09 ! [A: int] :
% 4.71/5.09 ( ( power_power_int @ A @ one_one_nat )
% 4.71/5.09 = A ) ).
% 4.71/5.09
% 4.71/5.09 % power_one_right
% 4.71/5.09 thf(fact_3699_power__one__right,axiom,
% 4.71/5.09 ! [A: nat] :
% 4.71/5.09 ( ( power_power_nat @ A @ one_one_nat )
% 4.71/5.09 = A ) ).
% 4.71/5.09
% 4.71/5.09 % power_one_right
% 4.71/5.09 thf(fact_3700_power__one__right,axiom,
% 4.71/5.09 ! [A: real] :
% 4.71/5.09 ( ( power_power_real @ A @ one_one_nat )
% 4.71/5.09 = A ) ).
% 4.71/5.09
% 4.71/5.09 % power_one_right
% 4.71/5.09 thf(fact_3701_power__one__right,axiom,
% 4.71/5.09 ! [A: complex] :
% 4.71/5.09 ( ( power_power_complex @ A @ one_one_nat )
% 4.71/5.09 = A ) ).
% 4.71/5.09
% 4.71/5.09 % power_one_right
% 4.71/5.09 thf(fact_3702_diff__diff__left,axiom,
% 4.71/5.09 ! [I: nat,J: nat,K: nat] :
% 4.71/5.09 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 4.71/5.09 = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % diff_diff_left
% 4.71/5.09 thf(fact_3703_sum__squares__eq__zero__iff,axiom,
% 4.71/5.09 ! [X: real,Y: real] :
% 4.71/5.09 ( ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 4.71/5.09 = zero_zero_real )
% 4.71/5.09 = ( ( X = zero_zero_real )
% 4.71/5.09 & ( Y = zero_zero_real ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % sum_squares_eq_zero_iff
% 4.71/5.09 thf(fact_3704_sum__squares__eq__zero__iff,axiom,
% 4.71/5.09 ! [X: rat,Y: rat] :
% 4.71/5.09 ( ( ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 4.71/5.09 = zero_zero_rat )
% 4.71/5.09 = ( ( X = zero_zero_rat )
% 4.71/5.09 & ( Y = zero_zero_rat ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % sum_squares_eq_zero_iff
% 4.71/5.09 thf(fact_3705_sum__squares__eq__zero__iff,axiom,
% 4.71/5.09 ! [X: int,Y: int] :
% 4.71/5.09 ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 4.71/5.09 = zero_zero_int )
% 4.71/5.09 = ( ( X = zero_zero_int )
% 4.71/5.09 & ( Y = zero_zero_int ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % sum_squares_eq_zero_iff
% 4.71/5.09 thf(fact_3706_power__inject__exp,axiom,
% 4.71/5.09 ! [A: real,M2: nat,N: nat] :
% 4.71/5.09 ( ( ord_less_real @ one_one_real @ A )
% 4.71/5.09 => ( ( ( power_power_real @ A @ M2 )
% 4.71/5.09 = ( power_power_real @ A @ N ) )
% 4.71/5.09 = ( M2 = N ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_inject_exp
% 4.71/5.09 thf(fact_3707_power__inject__exp,axiom,
% 4.71/5.09 ! [A: rat,M2: nat,N: nat] :
% 4.71/5.09 ( ( ord_less_rat @ one_one_rat @ A )
% 4.71/5.09 => ( ( ( power_power_rat @ A @ M2 )
% 4.71/5.09 = ( power_power_rat @ A @ N ) )
% 4.71/5.09 = ( M2 = N ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_inject_exp
% 4.71/5.09 thf(fact_3708_power__inject__exp,axiom,
% 4.71/5.09 ! [A: nat,M2: nat,N: nat] :
% 4.71/5.09 ( ( ord_less_nat @ one_one_nat @ A )
% 4.71/5.09 => ( ( ( power_power_nat @ A @ M2 )
% 4.71/5.09 = ( power_power_nat @ A @ N ) )
% 4.71/5.09 = ( M2 = N ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_inject_exp
% 4.71/5.09 thf(fact_3709_power__inject__exp,axiom,
% 4.71/5.09 ! [A: int,M2: nat,N: nat] :
% 4.71/5.09 ( ( ord_less_int @ one_one_int @ A )
% 4.71/5.09 => ( ( ( power_power_int @ A @ M2 )
% 4.71/5.09 = ( power_power_int @ A @ N ) )
% 4.71/5.09 = ( M2 = N ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_inject_exp
% 4.71/5.09 thf(fact_3710_power__0__Suc,axiom,
% 4.71/5.09 ! [N: nat] :
% 4.71/5.09 ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 4.71/5.09 = zero_zero_rat ) ).
% 4.71/5.09
% 4.71/5.09 % power_0_Suc
% 4.71/5.09 thf(fact_3711_power__0__Suc,axiom,
% 4.71/5.09 ! [N: nat] :
% 4.71/5.09 ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 4.71/5.09 = zero_zero_int ) ).
% 4.71/5.09
% 4.71/5.09 % power_0_Suc
% 4.71/5.09 thf(fact_3712_power__0__Suc,axiom,
% 4.71/5.09 ! [N: nat] :
% 4.71/5.09 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 4.71/5.09 = zero_zero_nat ) ).
% 4.71/5.09
% 4.71/5.09 % power_0_Suc
% 4.71/5.09 thf(fact_3713_power__0__Suc,axiom,
% 4.71/5.09 ! [N: nat] :
% 4.71/5.09 ( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
% 4.71/5.09 = zero_zero_real ) ).
% 4.71/5.09
% 4.71/5.09 % power_0_Suc
% 4.71/5.09 thf(fact_3714_power__0__Suc,axiom,
% 4.71/5.09 ! [N: nat] :
% 4.71/5.09 ( ( power_power_complex @ zero_zero_complex @ ( suc @ N ) )
% 4.71/5.09 = zero_zero_complex ) ).
% 4.71/5.09
% 4.71/5.09 % power_0_Suc
% 4.71/5.09 thf(fact_3715_power__Suc0__right,axiom,
% 4.71/5.09 ! [A: int] :
% 4.71/5.09 ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 4.71/5.09 = A ) ).
% 4.71/5.09
% 4.71/5.09 % power_Suc0_right
% 4.71/5.09 thf(fact_3716_power__Suc0__right,axiom,
% 4.71/5.09 ! [A: nat] :
% 4.71/5.09 ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 4.71/5.09 = A ) ).
% 4.71/5.09
% 4.71/5.09 % power_Suc0_right
% 4.71/5.09 thf(fact_3717_power__Suc0__right,axiom,
% 4.71/5.09 ! [A: real] :
% 4.71/5.09 ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 4.71/5.09 = A ) ).
% 4.71/5.09
% 4.71/5.09 % power_Suc0_right
% 4.71/5.09 thf(fact_3718_power__Suc0__right,axiom,
% 4.71/5.09 ! [A: complex] :
% 4.71/5.09 ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 4.71/5.09 = A ) ).
% 4.71/5.09
% 4.71/5.09 % power_Suc0_right
% 4.71/5.09 thf(fact_3719_add__gr__0,axiom,
% 4.71/5.09 ! [M2: nat,N: nat] :
% 4.71/5.09 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M2 @ N ) )
% 4.71/5.09 = ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 4.71/5.09 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % add_gr_0
% 4.71/5.09 thf(fact_3720_nat__mult__less__cancel__disj,axiom,
% 4.71/5.09 ! [K: nat,M2: nat,N: nat] :
% 4.71/5.09 ( ( ord_less_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N ) )
% 4.71/5.09 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.71/5.09 & ( ord_less_nat @ M2 @ N ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % nat_mult_less_cancel_disj
% 4.71/5.09 thf(fact_3721_nat__power__eq__Suc__0__iff,axiom,
% 4.71/5.09 ! [X: nat,M2: nat] :
% 4.71/5.09 ( ( ( power_power_nat @ X @ M2 )
% 4.71/5.09 = ( suc @ zero_zero_nat ) )
% 4.71/5.09 = ( ( M2 = zero_zero_nat )
% 4.71/5.09 | ( X
% 4.71/5.09 = ( suc @ zero_zero_nat ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % nat_power_eq_Suc_0_iff
% 4.71/5.09 thf(fact_3722_power__Suc__0,axiom,
% 4.71/5.09 ! [N: nat] :
% 4.71/5.09 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 4.71/5.09 = ( suc @ zero_zero_nat ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_Suc_0
% 4.71/5.09 thf(fact_3723_mult__Suc__right,axiom,
% 4.71/5.09 ! [M2: nat,N: nat] :
% 4.71/5.09 ( ( times_times_nat @ M2 @ ( suc @ N ) )
% 4.71/5.09 = ( plus_plus_nat @ M2 @ ( times_times_nat @ M2 @ N ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % mult_Suc_right
% 4.71/5.09 thf(fact_3724_nat__zero__less__power__iff,axiom,
% 4.71/5.09 ! [X: nat,N: nat] :
% 4.71/5.09 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
% 4.71/5.09 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 4.71/5.09 | ( N = zero_zero_nat ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % nat_zero_less_power_iff
% 4.71/5.09 thf(fact_3725_Nat_Oadd__diff__assoc,axiom,
% 4.71/5.09 ! [K: nat,J: nat,I: nat] :
% 4.71/5.09 ( ( ord_less_eq_nat @ K @ J )
% 4.71/5.09 => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 4.71/5.09 = ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % Nat.add_diff_assoc
% 4.71/5.09 thf(fact_3726_Nat_Oadd__diff__assoc2,axiom,
% 4.71/5.09 ! [K: nat,J: nat,I: nat] :
% 4.71/5.09 ( ( ord_less_eq_nat @ K @ J )
% 4.71/5.09 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 4.71/5.09 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % Nat.add_diff_assoc2
% 4.71/5.09 thf(fact_3727_Nat_Odiff__diff__right,axiom,
% 4.71/5.09 ! [K: nat,J: nat,I: nat] :
% 4.71/5.09 ( ( ord_less_eq_nat @ K @ J )
% 4.71/5.09 => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 4.71/5.09 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % Nat.diff_diff_right
% 4.71/5.09 thf(fact_3728_nat__mult__div__cancel__disj,axiom,
% 4.71/5.09 ! [K: nat,M2: nat,N: nat] :
% 4.71/5.09 ( ( ( K = zero_zero_nat )
% 4.71/5.09 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N ) )
% 4.71/5.09 = zero_zero_nat ) )
% 4.71/5.09 & ( ( K != zero_zero_nat )
% 4.71/5.09 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N ) )
% 4.71/5.09 = ( divide_divide_nat @ M2 @ N ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % nat_mult_div_cancel_disj
% 4.71/5.09 thf(fact_3729_power__strict__increasing__iff,axiom,
% 4.71/5.09 ! [B: real,X: nat,Y: nat] :
% 4.71/5.09 ( ( ord_less_real @ one_one_real @ B )
% 4.71/5.09 => ( ( ord_less_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y ) )
% 4.71/5.09 = ( ord_less_nat @ X @ Y ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_strict_increasing_iff
% 4.71/5.09 thf(fact_3730_power__strict__increasing__iff,axiom,
% 4.71/5.09 ! [B: rat,X: nat,Y: nat] :
% 4.71/5.09 ( ( ord_less_rat @ one_one_rat @ B )
% 4.71/5.09 => ( ( ord_less_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 4.71/5.09 = ( ord_less_nat @ X @ Y ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_strict_increasing_iff
% 4.71/5.09 thf(fact_3731_power__strict__increasing__iff,axiom,
% 4.71/5.09 ! [B: nat,X: nat,Y: nat] :
% 4.71/5.09 ( ( ord_less_nat @ one_one_nat @ B )
% 4.71/5.09 => ( ( ord_less_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 4.71/5.09 = ( ord_less_nat @ X @ Y ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_strict_increasing_iff
% 4.71/5.09 thf(fact_3732_power__strict__increasing__iff,axiom,
% 4.71/5.09 ! [B: int,X: nat,Y: nat] :
% 4.71/5.09 ( ( ord_less_int @ one_one_int @ B )
% 4.71/5.09 => ( ( ord_less_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 4.71/5.09 = ( ord_less_nat @ X @ Y ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_strict_increasing_iff
% 4.71/5.09 thf(fact_3733_power__eq__0__iff,axiom,
% 4.71/5.09 ! [A: rat,N: nat] :
% 4.71/5.09 ( ( ( power_power_rat @ A @ N )
% 4.71/5.09 = zero_zero_rat )
% 4.71/5.09 = ( ( A = zero_zero_rat )
% 4.71/5.09 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_eq_0_iff
% 4.71/5.09 thf(fact_3734_power__eq__0__iff,axiom,
% 4.71/5.09 ! [A: int,N: nat] :
% 4.71/5.09 ( ( ( power_power_int @ A @ N )
% 4.71/5.09 = zero_zero_int )
% 4.71/5.09 = ( ( A = zero_zero_int )
% 4.71/5.09 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_eq_0_iff
% 4.71/5.09 thf(fact_3735_power__eq__0__iff,axiom,
% 4.71/5.09 ! [A: nat,N: nat] :
% 4.71/5.09 ( ( ( power_power_nat @ A @ N )
% 4.71/5.09 = zero_zero_nat )
% 4.71/5.09 = ( ( A = zero_zero_nat )
% 4.71/5.09 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_eq_0_iff
% 4.71/5.09 thf(fact_3736_power__eq__0__iff,axiom,
% 4.71/5.09 ! [A: real,N: nat] :
% 4.71/5.09 ( ( ( power_power_real @ A @ N )
% 4.71/5.09 = zero_zero_real )
% 4.71/5.09 = ( ( A = zero_zero_real )
% 4.71/5.09 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_eq_0_iff
% 4.71/5.09 thf(fact_3737_power__eq__0__iff,axiom,
% 4.71/5.09 ! [A: complex,N: nat] :
% 4.71/5.09 ( ( ( power_power_complex @ A @ N )
% 4.71/5.09 = zero_zero_complex )
% 4.71/5.09 = ( ( A = zero_zero_complex )
% 4.71/5.09 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % power_eq_0_iff
% 4.71/5.09 thf(fact_3738_diff__Suc__diff__eq2,axiom,
% 4.71/5.09 ! [K: nat,J: nat,I: nat] :
% 4.71/5.09 ( ( ord_less_eq_nat @ K @ J )
% 4.71/5.09 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I )
% 4.71/5.09 = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % diff_Suc_diff_eq2
% 4.71/5.09 thf(fact_3739_diff__Suc__diff__eq1,axiom,
% 4.71/5.09 ! [K: nat,J: nat,I: nat] :
% 4.71/5.09 ( ( ord_less_eq_nat @ K @ J )
% 4.71/5.09 => ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 4.71/5.09 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % diff_Suc_diff_eq1
% 4.71/5.09 thf(fact_3740_of__nat__less__of__nat__power__cancel__iff,axiom,
% 4.71/5.09 ! [B: nat,W2: nat,X: nat] :
% 4.71/5.09 ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 4.71/5.09 = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 4.71/5.09
% 4.71/5.09 % of_nat_less_of_nat_power_cancel_iff
% 4.71/5.09 thf(fact_3741_of__nat__less__of__nat__power__cancel__iff,axiom,
% 4.71/5.09 ! [B: nat,W2: nat,X: nat] :
% 4.71/5.09 ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 4.71/5.09 = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 4.71/5.09
% 4.71/5.09 % of_nat_less_of_nat_power_cancel_iff
% 4.71/5.09 thf(fact_3742_of__nat__less__of__nat__power__cancel__iff,axiom,
% 4.71/5.09 ! [B: nat,W2: nat,X: nat] :
% 4.71/5.09 ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) @ ( semiri5074537144036343181t_real @ X ) )
% 4.71/5.09 = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 4.71/5.09
% 4.71/5.09 % of_nat_less_of_nat_power_cancel_iff
% 4.71/5.09 thf(fact_3743_of__nat__less__of__nat__power__cancel__iff,axiom,
% 4.71/5.09 ! [B: nat,W2: nat,X: nat] :
% 4.71/5.09 ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) @ ( semiri681578069525770553at_rat @ X ) )
% 4.71/5.09 = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 4.71/5.09
% 4.71/5.09 % of_nat_less_of_nat_power_cancel_iff
% 4.71/5.09 thf(fact_3744_nat__arith_Osuc1,axiom,
% 4.71/5.09 ! [A2: nat,K: nat,A: nat] :
% 4.71/5.09 ( ( A2
% 4.71/5.09 = ( plus_plus_nat @ K @ A ) )
% 4.71/5.09 => ( ( suc @ A2 )
% 4.71/5.09 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % nat_arith.suc1
% 4.71/5.09 thf(fact_3745_add__Suc,axiom,
% 4.71/5.09 ! [M2: nat,N: nat] :
% 4.71/5.09 ( ( plus_plus_nat @ ( suc @ M2 ) @ N )
% 4.71/5.09 = ( suc @ ( plus_plus_nat @ M2 @ N ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % add_Suc
% 4.71/5.09 thf(fact_3746_add__Suc__shift,axiom,
% 4.71/5.09 ! [M2: nat,N: nat] :
% 4.71/5.09 ( ( plus_plus_nat @ ( suc @ M2 ) @ N )
% 4.71/5.09 = ( plus_plus_nat @ M2 @ ( suc @ N ) ) ) ).
% 4.71/5.09
% 4.71/5.09 % add_Suc_shift
% 4.71/5.09 thf(fact_3747_add__eq__self__zero,axiom,
% 4.71/5.10 ! [M2: nat,N: nat] :
% 4.71/5.10 ( ( ( plus_plus_nat @ M2 @ N )
% 4.71/5.10 = M2 )
% 4.71/5.10 => ( N = zero_zero_nat ) ) ).
% 4.71/5.10
% 4.71/5.10 % add_eq_self_zero
% 4.71/5.10 thf(fact_3748_plus__nat_Oadd__0,axiom,
% 4.71/5.10 ! [N: nat] :
% 4.71/5.10 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 4.71/5.10 = N ) ).
% 4.71/5.10
% 4.71/5.10 % plus_nat.add_0
% 4.71/5.10 thf(fact_3749_less__add__eq__less,axiom,
% 4.71/5.10 ! [K: nat,L: nat,M2: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_nat @ K @ L )
% 4.71/5.10 => ( ( ( plus_plus_nat @ M2 @ L )
% 4.71/5.10 = ( plus_plus_nat @ K @ N ) )
% 4.71/5.10 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % less_add_eq_less
% 4.71/5.10 thf(fact_3750_trans__less__add2,axiom,
% 4.71/5.10 ! [I: nat,J: nat,M2: nat] :
% 4.71/5.10 ( ( ord_less_nat @ I @ J )
% 4.71/5.10 => ( ord_less_nat @ I @ ( plus_plus_nat @ M2 @ J ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % trans_less_add2
% 4.71/5.10 thf(fact_3751_trans__less__add1,axiom,
% 4.71/5.10 ! [I: nat,J: nat,M2: nat] :
% 4.71/5.10 ( ( ord_less_nat @ I @ J )
% 4.71/5.10 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M2 ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % trans_less_add1
% 4.71/5.10 thf(fact_3752_add__less__mono1,axiom,
% 4.71/5.10 ! [I: nat,J: nat,K: nat] :
% 4.71/5.10 ( ( ord_less_nat @ I @ J )
% 4.71/5.10 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % add_less_mono1
% 4.71/5.10 thf(fact_3753_not__add__less2,axiom,
% 4.71/5.10 ! [J: nat,I: nat] :
% 4.71/5.10 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 4.71/5.10
% 4.71/5.10 % not_add_less2
% 4.71/5.10 thf(fact_3754_not__add__less1,axiom,
% 4.71/5.10 ! [I: nat,J: nat] :
% 4.71/5.10 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 4.71/5.10
% 4.71/5.10 % not_add_less1
% 4.71/5.10 thf(fact_3755_add__less__mono,axiom,
% 4.71/5.10 ! [I: nat,J: nat,K: nat,L: nat] :
% 4.71/5.10 ( ( ord_less_nat @ I @ J )
% 4.71/5.10 => ( ( ord_less_nat @ K @ L )
% 4.71/5.10 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % add_less_mono
% 4.71/5.10 thf(fact_3756_add__lessD1,axiom,
% 4.71/5.10 ! [I: nat,J: nat,K: nat] :
% 4.71/5.10 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 4.71/5.10 => ( ord_less_nat @ I @ K ) ) ).
% 4.71/5.10
% 4.71/5.10 % add_lessD1
% 4.71/5.10 thf(fact_3757_real__arch__pow,axiom,
% 4.71/5.10 ! [X: real,Y: real] :
% 4.71/5.10 ( ( ord_less_real @ one_one_real @ X )
% 4.71/5.10 => ? [N2: nat] : ( ord_less_real @ Y @ ( power_power_real @ X @ N2 ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_arch_pow
% 4.71/5.10 thf(fact_3758_add__leE,axiom,
% 4.71/5.10 ! [M2: nat,K: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M2 @ K ) @ N )
% 4.71/5.10 => ~ ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.10 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % add_leE
% 4.71/5.10 thf(fact_3759_le__add1,axiom,
% 4.71/5.10 ! [N: nat,M2: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M2 ) ) ).
% 4.71/5.10
% 4.71/5.10 % le_add1
% 4.71/5.10 thf(fact_3760_le__add2,axiom,
% 4.71/5.10 ! [N: nat,M2: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M2 @ N ) ) ).
% 4.71/5.10
% 4.71/5.10 % le_add2
% 4.71/5.10 thf(fact_3761_add__leD1,axiom,
% 4.71/5.10 ! [M2: nat,K: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M2 @ K ) @ N )
% 4.71/5.10 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 4.71/5.10
% 4.71/5.10 % add_leD1
% 4.71/5.10 thf(fact_3762_add__leD2,axiom,
% 4.71/5.10 ! [M2: nat,K: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M2 @ K ) @ N )
% 4.71/5.10 => ( ord_less_eq_nat @ K @ N ) ) ).
% 4.71/5.10
% 4.71/5.10 % add_leD2
% 4.71/5.10 thf(fact_3763_le__Suc__ex,axiom,
% 4.71/5.10 ! [K: nat,L: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ K @ L )
% 4.71/5.10 => ? [N2: nat] :
% 4.71/5.10 ( L
% 4.71/5.10 = ( plus_plus_nat @ K @ N2 ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % le_Suc_ex
% 4.71/5.10 thf(fact_3764_add__le__mono,axiom,
% 4.71/5.10 ! [I: nat,J: nat,K: nat,L: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ I @ J )
% 4.71/5.10 => ( ( ord_less_eq_nat @ K @ L )
% 4.71/5.10 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % add_le_mono
% 4.71/5.10 thf(fact_3765_add__le__mono1,axiom,
% 4.71/5.10 ! [I: nat,J: nat,K: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ I @ J )
% 4.71/5.10 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % add_le_mono1
% 4.71/5.10 thf(fact_3766_trans__le__add1,axiom,
% 4.71/5.10 ! [I: nat,J: nat,M2: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ I @ J )
% 4.71/5.10 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M2 ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % trans_le_add1
% 4.71/5.10 thf(fact_3767_trans__le__add2,axiom,
% 4.71/5.10 ! [I: nat,J: nat,M2: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ I @ J )
% 4.71/5.10 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M2 @ J ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % trans_le_add2
% 4.71/5.10 thf(fact_3768_nat__le__iff__add,axiom,
% 4.71/5.10 ( ord_less_eq_nat
% 4.71/5.10 = ( ^ [M3: nat,N4: nat] :
% 4.71/5.10 ? [K3: nat] :
% 4.71/5.10 ( N4
% 4.71/5.10 = ( plus_plus_nat @ M3 @ K3 ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % nat_le_iff_add
% 4.71/5.10 thf(fact_3769_Nat_Odiff__cancel,axiom,
% 4.71/5.10 ! [K: nat,M2: nat,N: nat] :
% 4.71/5.10 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M2 ) @ ( plus_plus_nat @ K @ N ) )
% 4.71/5.10 = ( minus_minus_nat @ M2 @ N ) ) ).
% 4.71/5.10
% 4.71/5.10 % Nat.diff_cancel
% 4.71/5.10 thf(fact_3770_diff__cancel2,axiom,
% 4.71/5.10 ! [M2: nat,K: nat,N: nat] :
% 4.71/5.10 ( ( minus_minus_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N @ K ) )
% 4.71/5.10 = ( minus_minus_nat @ M2 @ N ) ) ).
% 4.71/5.10
% 4.71/5.10 % diff_cancel2
% 4.71/5.10 thf(fact_3771_diff__add__inverse,axiom,
% 4.71/5.10 ! [N: nat,M2: nat] :
% 4.71/5.10 ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M2 ) @ N )
% 4.71/5.10 = M2 ) ).
% 4.71/5.10
% 4.71/5.10 % diff_add_inverse
% 4.71/5.10 thf(fact_3772_diff__add__inverse2,axiom,
% 4.71/5.10 ! [M2: nat,N: nat] :
% 4.71/5.10 ( ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N ) @ N )
% 4.71/5.10 = M2 ) ).
% 4.71/5.10
% 4.71/5.10 % diff_add_inverse2
% 4.71/5.10 thf(fact_3773_add__mult__distrib,axiom,
% 4.71/5.10 ! [M2: nat,N: nat,K: nat] :
% 4.71/5.10 ( ( times_times_nat @ ( plus_plus_nat @ M2 @ N ) @ K )
% 4.71/5.10 = ( plus_plus_nat @ ( times_times_nat @ M2 @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % add_mult_distrib
% 4.71/5.10 thf(fact_3774_add__mult__distrib2,axiom,
% 4.71/5.10 ! [K: nat,M2: nat,N: nat] :
% 4.71/5.10 ( ( times_times_nat @ K @ ( plus_plus_nat @ M2 @ N ) )
% 4.71/5.10 = ( plus_plus_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % add_mult_distrib2
% 4.71/5.10 thf(fact_3775_nat__power__less__imp__less,axiom,
% 4.71/5.10 ! [I: nat,M2: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ I )
% 4.71/5.10 => ( ( ord_less_nat @ ( power_power_nat @ I @ M2 ) @ ( power_power_nat @ I @ N ) )
% 4.71/5.10 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % nat_power_less_imp_less
% 4.71/5.10 thf(fact_3776_power__gt__expt,axiom,
% 4.71/5.10 ! [N: nat,K: nat] :
% 4.71/5.10 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 4.71/5.10 => ( ord_less_nat @ K @ ( power_power_nat @ N @ K ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_gt_expt
% 4.71/5.10 thf(fact_3777_nat__one__le__power,axiom,
% 4.71/5.10 ! [I: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
% 4.71/5.10 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % nat_one_le_power
% 4.71/5.10 thf(fact_3778_add__is__1,axiom,
% 4.71/5.10 ! [M2: nat,N: nat] :
% 4.71/5.10 ( ( ( plus_plus_nat @ M2 @ N )
% 4.71/5.10 = ( suc @ zero_zero_nat ) )
% 4.71/5.10 = ( ( ( M2
% 4.71/5.10 = ( suc @ zero_zero_nat ) )
% 4.71/5.10 & ( N = zero_zero_nat ) )
% 4.71/5.10 | ( ( M2 = zero_zero_nat )
% 4.71/5.10 & ( N
% 4.71/5.10 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % add_is_1
% 4.71/5.10 thf(fact_3779_one__is__add,axiom,
% 4.71/5.10 ! [M2: nat,N: nat] :
% 4.71/5.10 ( ( ( suc @ zero_zero_nat )
% 4.71/5.10 = ( plus_plus_nat @ M2 @ N ) )
% 4.71/5.10 = ( ( ( M2
% 4.71/5.10 = ( suc @ zero_zero_nat ) )
% 4.71/5.10 & ( N = zero_zero_nat ) )
% 4.71/5.10 | ( ( M2 = zero_zero_nat )
% 4.71/5.10 & ( N
% 4.71/5.10 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % one_is_add
% 4.71/5.10 thf(fact_3780_less__natE,axiom,
% 4.71/5.10 ! [M2: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_nat @ M2 @ N )
% 4.71/5.10 => ~ ! [Q5: nat] :
% 4.71/5.10 ( N
% 4.71/5.10 != ( suc @ ( plus_plus_nat @ M2 @ Q5 ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % less_natE
% 4.71/5.10 thf(fact_3781_less__add__Suc1,axiom,
% 4.71/5.10 ! [I: nat,M2: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M2 ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % less_add_Suc1
% 4.71/5.10 thf(fact_3782_less__add__Suc2,axiom,
% 4.71/5.10 ! [I: nat,M2: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M2 @ I ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % less_add_Suc2
% 4.71/5.10 thf(fact_3783_less__iff__Suc__add,axiom,
% 4.71/5.10 ( ord_less_nat
% 4.71/5.10 = ( ^ [M3: nat,N4: nat] :
% 4.71/5.10 ? [K3: nat] :
% 4.71/5.10 ( N4
% 4.71/5.10 = ( suc @ ( plus_plus_nat @ M3 @ K3 ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % less_iff_Suc_add
% 4.71/5.10 thf(fact_3784_less__imp__Suc__add,axiom,
% 4.71/5.10 ! [M2: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_nat @ M2 @ N )
% 4.71/5.10 => ? [K2: nat] :
% 4.71/5.10 ( N
% 4.71/5.10 = ( suc @ ( plus_plus_nat @ M2 @ K2 ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % less_imp_Suc_add
% 4.71/5.10 thf(fact_3785_real__arch__pow__inv,axiom,
% 4.71/5.10 ! [Y: real,X: real] :
% 4.71/5.10 ( ( ord_less_real @ zero_zero_real @ Y )
% 4.71/5.10 => ( ( ord_less_real @ X @ one_one_real )
% 4.71/5.10 => ? [N2: nat] : ( ord_less_real @ ( power_power_real @ X @ N2 ) @ Y ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_arch_pow_inv
% 4.71/5.10 thf(fact_3786_less__imp__add__positive,axiom,
% 4.71/5.10 ! [I: nat,J: nat] :
% 4.71/5.10 ( ( ord_less_nat @ I @ J )
% 4.71/5.10 => ? [K2: nat] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 4.71/5.10 & ( ( plus_plus_nat @ I @ K2 )
% 4.71/5.10 = J ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % less_imp_add_positive
% 4.71/5.10 thf(fact_3787_nat__diff__add__eq2,axiom,
% 4.71/5.10 ! [I: nat,J: nat,U: nat,M2: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ I @ J )
% 4.71/5.10 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 4.71/5.10 = ( minus_minus_nat @ M2 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % nat_diff_add_eq2
% 4.71/5.10 thf(fact_3788_nat__diff__add__eq1,axiom,
% 4.71/5.10 ! [J: nat,I: nat,U: nat,M2: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ J @ I )
% 4.71/5.10 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 4.71/5.10 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M2 ) @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % nat_diff_add_eq1
% 4.71/5.10 thf(fact_3789_nat__le__add__iff2,axiom,
% 4.71/5.10 ! [I: nat,J: nat,U: nat,M2: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ I @ J )
% 4.71/5.10 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 4.71/5.10 = ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % nat_le_add_iff2
% 4.71/5.10 thf(fact_3790_nat__le__add__iff1,axiom,
% 4.71/5.10 ! [J: nat,I: nat,U: nat,M2: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ J @ I )
% 4.71/5.10 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 4.71/5.10 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M2 ) @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % nat_le_add_iff1
% 4.71/5.10 thf(fact_3791_nat__eq__add__iff2,axiom,
% 4.71/5.10 ! [I: nat,J: nat,U: nat,M2: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ I @ J )
% 4.71/5.10 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 )
% 4.71/5.10 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 4.71/5.10 = ( M2
% 4.71/5.10 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % nat_eq_add_iff2
% 4.71/5.10 thf(fact_3792_nat__eq__add__iff1,axiom,
% 4.71/5.10 ! [J: nat,I: nat,U: nat,M2: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ J @ I )
% 4.71/5.10 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 )
% 4.71/5.10 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 4.71/5.10 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M2 )
% 4.71/5.10 = N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % nat_eq_add_iff1
% 4.71/5.10 thf(fact_3793_mono__nat__linear__lb,axiom,
% 4.71/5.10 ! [F: nat > nat,M2: nat,K: nat] :
% 4.71/5.10 ( ! [M4: nat,N2: nat] :
% 4.71/5.10 ( ( ord_less_nat @ M4 @ N2 )
% 4.71/5.10 => ( ord_less_nat @ ( F @ M4 ) @ ( F @ N2 ) ) )
% 4.71/5.10 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M2 ) @ K ) @ ( F @ ( plus_plus_nat @ M2 @ K ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % mono_nat_linear_lb
% 4.71/5.10 thf(fact_3794_mult__Suc,axiom,
% 4.71/5.10 ! [M2: nat,N: nat] :
% 4.71/5.10 ( ( times_times_nat @ ( suc @ M2 ) @ N )
% 4.71/5.10 = ( plus_plus_nat @ N @ ( times_times_nat @ M2 @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % mult_Suc
% 4.71/5.10 thf(fact_3795_diff__add__0,axiom,
% 4.71/5.10 ! [N: nat,M2: nat] :
% 4.71/5.10 ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M2 ) )
% 4.71/5.10 = zero_zero_nat ) ).
% 4.71/5.10
% 4.71/5.10 % diff_add_0
% 4.71/5.10 thf(fact_3796_less__diff__conv,axiom,
% 4.71/5.10 ! [I: nat,J: nat,K: nat] :
% 4.71/5.10 ( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 4.71/5.10 = ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ).
% 4.71/5.10
% 4.71/5.10 % less_diff_conv
% 4.71/5.10 thf(fact_3797_add__diff__inverse__nat,axiom,
% 4.71/5.10 ! [M2: nat,N: nat] :
% 4.71/5.10 ( ~ ( ord_less_nat @ M2 @ N )
% 4.71/5.10 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M2 @ N ) )
% 4.71/5.10 = M2 ) ) ).
% 4.71/5.10
% 4.71/5.10 % add_diff_inverse_nat
% 4.71/5.10 thf(fact_3798_Suc__eq__plus1,axiom,
% 4.71/5.10 ( suc
% 4.71/5.10 = ( ^ [N4: nat] : ( plus_plus_nat @ N4 @ one_one_nat ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % Suc_eq_plus1
% 4.71/5.10 thf(fact_3799_plus__1__eq__Suc,axiom,
% 4.71/5.10 ( ( plus_plus_nat @ one_one_nat )
% 4.71/5.10 = suc ) ).
% 4.71/5.10
% 4.71/5.10 % plus_1_eq_Suc
% 4.71/5.10 thf(fact_3800_Suc__eq__plus1__left,axiom,
% 4.71/5.10 ( suc
% 4.71/5.10 = ( plus_plus_nat @ one_one_nat ) ) ).
% 4.71/5.10
% 4.71/5.10 % Suc_eq_plus1_left
% 4.71/5.10 thf(fact_3801_le__diff__conv,axiom,
% 4.71/5.10 ! [J: nat,K: nat,I: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 4.71/5.10 = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % le_diff_conv
% 4.71/5.10 thf(fact_3802_Nat_Ole__diff__conv2,axiom,
% 4.71/5.10 ! [K: nat,J: nat,I: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ K @ J )
% 4.71/5.10 => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 4.71/5.10 = ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % Nat.le_diff_conv2
% 4.71/5.10 thf(fact_3803_Nat_Odiff__add__assoc,axiom,
% 4.71/5.10 ! [K: nat,J: nat,I: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ K @ J )
% 4.71/5.10 => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 4.71/5.10 = ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % Nat.diff_add_assoc
% 4.71/5.10 thf(fact_3804_Nat_Odiff__add__assoc2,axiom,
% 4.71/5.10 ! [K: nat,J: nat,I: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ K @ J )
% 4.71/5.10 => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K )
% 4.71/5.10 = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % Nat.diff_add_assoc2
% 4.71/5.10 thf(fact_3805_Nat_Ole__imp__diff__is__add,axiom,
% 4.71/5.10 ! [I: nat,J: nat,K: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ I @ J )
% 4.71/5.10 => ( ( ( minus_minus_nat @ J @ I )
% 4.71/5.10 = K )
% 4.71/5.10 = ( J
% 4.71/5.10 = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % Nat.le_imp_diff_is_add
% 4.71/5.10 thf(fact_3806_reals__Archimedean3,axiom,
% 4.71/5.10 ! [X: real] :
% 4.71/5.10 ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.10 => ! [Y4: real] :
% 4.71/5.10 ? [N2: nat] : ( ord_less_real @ Y4 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % reals_Archimedean3
% 4.71/5.10 thf(fact_3807_nat__less__add__iff1,axiom,
% 4.71/5.10 ! [J: nat,I: nat,U: nat,M2: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ J @ I )
% 4.71/5.10 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 4.71/5.10 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M2 ) @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % nat_less_add_iff1
% 4.71/5.10 thf(fact_3808_nat__less__add__iff2,axiom,
% 4.71/5.10 ! [I: nat,J: nat,U: nat,M2: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ I @ J )
% 4.71/5.10 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 4.71/5.10 = ( ord_less_nat @ M2 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % nat_less_add_iff2
% 4.71/5.10 thf(fact_3809_ln__add__one__self__le__self,axiom,
% 4.71/5.10 ! [X: real] :
% 4.71/5.10 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.10 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 4.71/5.10
% 4.71/5.10 % ln_add_one_self_le_self
% 4.71/5.10 thf(fact_3810_nat__diff__split__asm,axiom,
% 4.71/5.10 ! [P: nat > $o,A: nat,B: nat] :
% 4.71/5.10 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 4.71/5.10 = ( ~ ( ( ( ord_less_nat @ A @ B )
% 4.71/5.10 & ~ ( P @ zero_zero_nat ) )
% 4.71/5.10 | ? [D5: nat] :
% 4.71/5.10 ( ( A
% 4.71/5.10 = ( plus_plus_nat @ B @ D5 ) )
% 4.71/5.10 & ~ ( P @ D5 ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % nat_diff_split_asm
% 4.71/5.10 thf(fact_3811_nat__diff__split,axiom,
% 4.71/5.10 ! [P: nat > $o,A: nat,B: nat] :
% 4.71/5.10 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 4.71/5.10 = ( ( ( ord_less_nat @ A @ B )
% 4.71/5.10 => ( P @ zero_zero_nat ) )
% 4.71/5.10 & ! [D5: nat] :
% 4.71/5.10 ( ( A
% 4.71/5.10 = ( plus_plus_nat @ B @ D5 ) )
% 4.71/5.10 => ( P @ D5 ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % nat_diff_split
% 4.71/5.10 thf(fact_3812_less__diff__conv2,axiom,
% 4.71/5.10 ! [K: nat,J: nat,I: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ K @ J )
% 4.71/5.10 => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 4.71/5.10 = ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % less_diff_conv2
% 4.71/5.10 thf(fact_3813_nat__le__real__less,axiom,
% 4.71/5.10 ( ord_less_eq_nat
% 4.71/5.10 = ( ^ [N4: nat,M3: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M3 ) @ one_one_real ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % nat_le_real_less
% 4.71/5.10 thf(fact_3814_zdiv__zmult2__eq,axiom,
% 4.71/5.10 ! [C: int,A: int,B: int] :
% 4.71/5.10 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.71/5.10 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 4.71/5.10 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % zdiv_zmult2_eq
% 4.71/5.10 thf(fact_3815_add__eq__if,axiom,
% 4.71/5.10 ( plus_plus_nat
% 4.71/5.10 = ( ^ [M3: nat,N4: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N4 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N4 ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % add_eq_if
% 4.71/5.10 thf(fact_3816_dividend__less__times__div,axiom,
% 4.71/5.10 ! [N: nat,M2: nat] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ord_less_nat @ M2 @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M2 @ N ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % dividend_less_times_div
% 4.71/5.10 thf(fact_3817_dividend__less__div__times,axiom,
% 4.71/5.10 ! [N: nat,M2: nat] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ord_less_nat @ M2 @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M2 @ N ) @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % dividend_less_div_times
% 4.71/5.10 thf(fact_3818_split__div,axiom,
% 4.71/5.10 ! [P: nat > $o,M2: nat,N: nat] :
% 4.71/5.10 ( ( P @ ( divide_divide_nat @ M2 @ N ) )
% 4.71/5.10 = ( ( ( N = zero_zero_nat )
% 4.71/5.10 => ( P @ zero_zero_nat ) )
% 4.71/5.10 & ( ( N != zero_zero_nat )
% 4.71/5.10 => ! [I4: nat,J3: nat] :
% 4.71/5.10 ( ( ord_less_nat @ J3 @ N )
% 4.71/5.10 => ( ( M2
% 4.71/5.10 = ( plus_plus_nat @ ( times_times_nat @ N @ I4 ) @ J3 ) )
% 4.71/5.10 => ( P @ I4 ) ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % split_div
% 4.71/5.10 thf(fact_3819_nat__less__real__le,axiom,
% 4.71/5.10 ( ord_less_nat
% 4.71/5.10 = ( ^ [N4: nat,M3: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N4 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M3 ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % nat_less_real_le
% 4.71/5.10 thf(fact_3820_zmult__zless__mono2__lemma,axiom,
% 4.71/5.10 ! [I: int,J: int,K: nat] :
% 4.71/5.10 ( ( ord_less_int @ I @ J )
% 4.71/5.10 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.71/5.10 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % zmult_zless_mono2_lemma
% 4.71/5.10 thf(fact_3821_mult__eq__if,axiom,
% 4.71/5.10 ( times_times_nat
% 4.71/5.10 = ( ^ [M3: nat,N4: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N4 @ ( times_times_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N4 ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % mult_eq_if
% 4.71/5.10 thf(fact_3822_q__pos__lemma,axiom,
% 4.71/5.10 ! [B7: int,Q6: int,R3: int] :
% 4.71/5.10 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B7 @ Q6 ) @ R3 ) )
% 4.71/5.10 => ( ( ord_less_int @ R3 @ B7 )
% 4.71/5.10 => ( ( ord_less_int @ zero_zero_int @ B7 )
% 4.71/5.10 => ( ord_less_eq_int @ zero_zero_int @ Q6 ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % q_pos_lemma
% 4.71/5.10 thf(fact_3823_zdiv__mono2__lemma,axiom,
% 4.71/5.10 ! [B: int,Q4: int,R2: int,B7: int,Q6: int,R3: int] :
% 4.71/5.10 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R2 )
% 4.71/5.10 = ( plus_plus_int @ ( times_times_int @ B7 @ Q6 ) @ R3 ) )
% 4.71/5.10 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B7 @ Q6 ) @ R3 ) )
% 4.71/5.10 => ( ( ord_less_int @ R3 @ B7 )
% 4.71/5.10 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 4.71/5.10 => ( ( ord_less_int @ zero_zero_int @ B7 )
% 4.71/5.10 => ( ( ord_less_eq_int @ B7 @ B )
% 4.71/5.10 => ( ord_less_eq_int @ Q4 @ Q6 ) ) ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % zdiv_mono2_lemma
% 4.71/5.10 thf(fact_3824_zdiv__mono2__neg__lemma,axiom,
% 4.71/5.10 ! [B: int,Q4: int,R2: int,B7: int,Q6: int,R3: int] :
% 4.71/5.10 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R2 )
% 4.71/5.10 = ( plus_plus_int @ ( times_times_int @ B7 @ Q6 ) @ R3 ) )
% 4.71/5.10 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B7 @ Q6 ) @ R3 ) @ zero_zero_int )
% 4.71/5.10 => ( ( ord_less_int @ R2 @ B )
% 4.71/5.10 => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 4.71/5.10 => ( ( ord_less_int @ zero_zero_int @ B7 )
% 4.71/5.10 => ( ( ord_less_eq_int @ B7 @ B )
% 4.71/5.10 => ( ord_less_eq_int @ Q6 @ Q4 ) ) ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % zdiv_mono2_neg_lemma
% 4.71/5.10 thf(fact_3825_unique__quotient__lemma,axiom,
% 4.71/5.10 ! [B: int,Q6: int,R3: int,Q4: int,R2: int] :
% 4.71/5.10 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R3 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R2 ) )
% 4.71/5.10 => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 4.71/5.10 => ( ( ord_less_int @ R3 @ B )
% 4.71/5.10 => ( ( ord_less_int @ R2 @ B )
% 4.71/5.10 => ( ord_less_eq_int @ Q6 @ Q4 ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % unique_quotient_lemma
% 4.71/5.10 thf(fact_3826_unique__quotient__lemma__neg,axiom,
% 4.71/5.10 ! [B: int,Q6: int,R3: int,Q4: int,R2: int] :
% 4.71/5.10 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R3 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R2 ) )
% 4.71/5.10 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 4.71/5.10 => ( ( ord_less_int @ B @ R2 )
% 4.71/5.10 => ( ( ord_less_int @ B @ R3 )
% 4.71/5.10 => ( ord_less_eq_int @ Q4 @ Q6 ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % unique_quotient_lemma_neg
% 4.71/5.10 thf(fact_3827_incr__mult__lemma,axiom,
% 4.71/5.10 ! [D: int,P: int > $o,K: int] :
% 4.71/5.10 ( ( ord_less_int @ zero_zero_int @ D )
% 4.71/5.10 => ( ! [X4: int] :
% 4.71/5.10 ( ( P @ X4 )
% 4.71/5.10 => ( P @ ( plus_plus_int @ X4 @ D ) ) )
% 4.71/5.10 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 4.71/5.10 => ! [X2: int] :
% 4.71/5.10 ( ( P @ X2 )
% 4.71/5.10 => ( P @ ( plus_plus_int @ X2 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % incr_mult_lemma
% 4.71/5.10 thf(fact_3828_nat__mult__distrib,axiom,
% 4.71/5.10 ! [Z: int,Z6: int] :
% 4.71/5.10 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 4.71/5.10 => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
% 4.71/5.10 = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % nat_mult_distrib
% 4.71/5.10 thf(fact_3829_nat__power__eq,axiom,
% 4.71/5.10 ! [Z: int,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 4.71/5.10 => ( ( nat2 @ ( power_power_int @ Z @ N ) )
% 4.71/5.10 = ( power_power_nat @ ( nat2 @ Z ) @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % nat_power_eq
% 4.71/5.10 thf(fact_3830_decr__mult__lemma,axiom,
% 4.71/5.10 ! [D: int,P: int > $o,K: int] :
% 4.71/5.10 ( ( ord_less_int @ zero_zero_int @ D )
% 4.71/5.10 => ( ! [X4: int] :
% 4.71/5.10 ( ( P @ X4 )
% 4.71/5.10 => ( P @ ( minus_minus_int @ X4 @ D ) ) )
% 4.71/5.10 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 4.71/5.10 => ! [X2: int] :
% 4.71/5.10 ( ( P @ X2 )
% 4.71/5.10 => ( P @ ( minus_minus_int @ X2 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % decr_mult_lemma
% 4.71/5.10 thf(fact_3831_nat__add__distrib,axiom,
% 4.71/5.10 ! [Z: int,Z6: int] :
% 4.71/5.10 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 4.71/5.10 => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 4.71/5.10 => ( ( nat2 @ ( plus_plus_int @ Z @ Z6 ) )
% 4.71/5.10 = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % nat_add_distrib
% 4.71/5.10 thf(fact_3832_nat__abs__triangle__ineq,axiom,
% 4.71/5.10 ! [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 ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % nat_abs_triangle_ineq
% 4.71/5.10 thf(fact_3833_real__archimedian__rdiv__eq__0,axiom,
% 4.71/5.10 ! [X: real,C: real] :
% 4.71/5.10 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.10 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.71/5.10 => ( ! [M4: nat] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ M4 )
% 4.71/5.10 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M4 ) @ X ) @ C ) )
% 4.71/5.10 => ( X = zero_zero_real ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_archimedian_rdiv_eq_0
% 4.71/5.10 thf(fact_3834_split__zdiv,axiom,
% 4.71/5.10 ! [P: int > $o,N: int,K: int] :
% 4.71/5.10 ( ( P @ ( divide_divide_int @ N @ K ) )
% 4.71/5.10 = ( ( ( K = zero_zero_int )
% 4.71/5.10 => ( P @ zero_zero_int ) )
% 4.71/5.10 & ( ( ord_less_int @ zero_zero_int @ K )
% 4.71/5.10 => ! [I4: int,J3: int] :
% 4.71/5.10 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 4.71/5.10 & ( ord_less_int @ J3 @ K )
% 4.71/5.10 & ( N
% 4.71/5.10 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 4.71/5.10 => ( P @ I4 ) ) )
% 4.71/5.10 & ( ( ord_less_int @ K @ zero_zero_int )
% 4.71/5.10 => ! [I4: int,J3: int] :
% 4.71/5.10 ( ( ( ord_less_int @ K @ J3 )
% 4.71/5.10 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 4.71/5.10 & ( N
% 4.71/5.10 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 4.71/5.10 => ( P @ I4 ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % split_zdiv
% 4.71/5.10 thf(fact_3835_int__div__neg__eq,axiom,
% 4.71/5.10 ! [A: int,B: int,Q4: int,R2: int] :
% 4.71/5.10 ( ( A
% 4.71/5.10 = ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R2 ) )
% 4.71/5.10 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 4.71/5.10 => ( ( ord_less_int @ B @ R2 )
% 4.71/5.10 => ( ( divide_divide_int @ A @ B )
% 4.71/5.10 = Q4 ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % int_div_neg_eq
% 4.71/5.10 thf(fact_3836_int__div__pos__eq,axiom,
% 4.71/5.10 ! [A: int,B: int,Q4: int,R2: int] :
% 4.71/5.10 ( ( A
% 4.71/5.10 = ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R2 ) )
% 4.71/5.10 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 4.71/5.10 => ( ( ord_less_int @ R2 @ B )
% 4.71/5.10 => ( ( divide_divide_int @ A @ B )
% 4.71/5.10 = Q4 ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % int_div_pos_eq
% 4.71/5.10 thf(fact_3837_power__not__zero,axiom,
% 4.71/5.10 ! [A: rat,N: nat] :
% 4.71/5.10 ( ( A != zero_zero_rat )
% 4.71/5.10 => ( ( power_power_rat @ A @ N )
% 4.71/5.10 != zero_zero_rat ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_not_zero
% 4.71/5.10 thf(fact_3838_power__not__zero,axiom,
% 4.71/5.10 ! [A: int,N: nat] :
% 4.71/5.10 ( ( A != zero_zero_int )
% 4.71/5.10 => ( ( power_power_int @ A @ N )
% 4.71/5.10 != zero_zero_int ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_not_zero
% 4.71/5.10 thf(fact_3839_power__not__zero,axiom,
% 4.71/5.10 ! [A: nat,N: nat] :
% 4.71/5.10 ( ( A != zero_zero_nat )
% 4.71/5.10 => ( ( power_power_nat @ A @ N )
% 4.71/5.10 != zero_zero_nat ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_not_zero
% 4.71/5.10 thf(fact_3840_power__not__zero,axiom,
% 4.71/5.10 ! [A: real,N: nat] :
% 4.71/5.10 ( ( A != zero_zero_real )
% 4.71/5.10 => ( ( power_power_real @ A @ N )
% 4.71/5.10 != zero_zero_real ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_not_zero
% 4.71/5.10 thf(fact_3841_power__not__zero,axiom,
% 4.71/5.10 ! [A: complex,N: nat] :
% 4.71/5.10 ( ( A != zero_zero_complex )
% 4.71/5.10 => ( ( power_power_complex @ A @ N )
% 4.71/5.10 != zero_zero_complex ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_not_zero
% 4.71/5.10 thf(fact_3842_nat__mult__eq__cancel__disj,axiom,
% 4.71/5.10 ! [K: nat,M2: nat,N: nat] :
% 4.71/5.10 ( ( ( times_times_nat @ K @ M2 )
% 4.71/5.10 = ( times_times_nat @ K @ N ) )
% 4.71/5.10 = ( ( K = zero_zero_nat )
% 4.71/5.10 | ( M2 = N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % nat_mult_eq_cancel_disj
% 4.71/5.10 thf(fact_3843_nat0__intermed__int__val,axiom,
% 4.71/5.10 ! [N: nat,F: nat > int,K: int] :
% 4.71/5.10 ( ! [I2: nat] :
% 4.71/5.10 ( ( ord_less_nat @ I2 @ N )
% 4.71/5.10 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I2 @ one_one_nat ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 4.71/5.10 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 4.71/5.10 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 4.71/5.10 => ? [I2: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ I2 @ N )
% 4.71/5.10 & ( ( F @ I2 )
% 4.71/5.10 = K ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % nat0_intermed_int_val
% 4.71/5.10 thf(fact_3844_zero__le__power,axiom,
% 4.71/5.10 ! [A: real,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.10 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % zero_le_power
% 4.71/5.10 thf(fact_3845_zero__le__power,axiom,
% 4.71/5.10 ! [A: rat,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.10 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % zero_le_power
% 4.71/5.10 thf(fact_3846_zero__le__power,axiom,
% 4.71/5.10 ! [A: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.71/5.10 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % zero_le_power
% 4.71/5.10 thf(fact_3847_zero__le__power,axiom,
% 4.71/5.10 ! [A: int,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.10 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % zero_le_power
% 4.71/5.10 thf(fact_3848_power__mono,axiom,
% 4.71/5.10 ! [A: real,B: real,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_real @ A @ B )
% 4.71/5.10 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.10 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_mono
% 4.71/5.10 thf(fact_3849_power__mono,axiom,
% 4.71/5.10 ! [A: rat,B: rat,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.10 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.10 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_mono
% 4.71/5.10 thf(fact_3850_power__mono,axiom,
% 4.71/5.10 ! [A: nat,B: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.10 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.71/5.10 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_mono
% 4.71/5.10 thf(fact_3851_power__mono,axiom,
% 4.71/5.10 ! [A: int,B: int,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_int @ A @ B )
% 4.71/5.10 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.10 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_mono
% 4.71/5.10 thf(fact_3852_zero__less__power,axiom,
% 4.71/5.10 ! [A: real,N: nat] :
% 4.71/5.10 ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.10 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % zero_less_power
% 4.71/5.10 thf(fact_3853_zero__less__power,axiom,
% 4.71/5.10 ! [A: rat,N: nat] :
% 4.71/5.10 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.10 => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % zero_less_power
% 4.71/5.10 thf(fact_3854_zero__less__power,axiom,
% 4.71/5.10 ! [A: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.71/5.10 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % zero_less_power
% 4.71/5.10 thf(fact_3855_zero__less__power,axiom,
% 4.71/5.10 ! [A: int,N: nat] :
% 4.71/5.10 ( ( ord_less_int @ zero_zero_int @ A )
% 4.71/5.10 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % zero_less_power
% 4.71/5.10 thf(fact_3856_one__le__power,axiom,
% 4.71/5.10 ! [A: real,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_real @ one_one_real @ A )
% 4.71/5.10 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % one_le_power
% 4.71/5.10 thf(fact_3857_one__le__power,axiom,
% 4.71/5.10 ! [A: rat,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 4.71/5.10 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % one_le_power
% 4.71/5.10 thf(fact_3858_one__le__power,axiom,
% 4.71/5.10 ! [A: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 4.71/5.10 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % one_le_power
% 4.71/5.10 thf(fact_3859_one__le__power,axiom,
% 4.71/5.10 ! [A: int,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_int @ one_one_int @ A )
% 4.71/5.10 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % one_le_power
% 4.71/5.10 thf(fact_3860_left__right__inverse__power,axiom,
% 4.71/5.10 ! [X: complex,Y: complex,N: nat] :
% 4.71/5.10 ( ( ( times_times_complex @ X @ Y )
% 4.71/5.10 = one_one_complex )
% 4.71/5.10 => ( ( times_times_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ N ) )
% 4.71/5.10 = one_one_complex ) ) ).
% 4.71/5.10
% 4.71/5.10 % left_right_inverse_power
% 4.71/5.10 thf(fact_3861_left__right__inverse__power,axiom,
% 4.71/5.10 ! [X: real,Y: real,N: nat] :
% 4.71/5.10 ( ( ( times_times_real @ X @ Y )
% 4.71/5.10 = one_one_real )
% 4.71/5.10 => ( ( times_times_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ N ) )
% 4.71/5.10 = one_one_real ) ) ).
% 4.71/5.10
% 4.71/5.10 % left_right_inverse_power
% 4.71/5.10 thf(fact_3862_left__right__inverse__power,axiom,
% 4.71/5.10 ! [X: rat,Y: rat,N: nat] :
% 4.71/5.10 ( ( ( times_times_rat @ X @ Y )
% 4.71/5.10 = one_one_rat )
% 4.71/5.10 => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y @ N ) )
% 4.71/5.10 = one_one_rat ) ) ).
% 4.71/5.10
% 4.71/5.10 % left_right_inverse_power
% 4.71/5.10 thf(fact_3863_left__right__inverse__power,axiom,
% 4.71/5.10 ! [X: nat,Y: nat,N: nat] :
% 4.71/5.10 ( ( ( times_times_nat @ X @ Y )
% 4.71/5.10 = one_one_nat )
% 4.71/5.10 => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ N ) )
% 4.71/5.10 = one_one_nat ) ) ).
% 4.71/5.10
% 4.71/5.10 % left_right_inverse_power
% 4.71/5.10 thf(fact_3864_left__right__inverse__power,axiom,
% 4.71/5.10 ! [X: int,Y: int,N: nat] :
% 4.71/5.10 ( ( ( times_times_int @ X @ Y )
% 4.71/5.10 = one_one_int )
% 4.71/5.10 => ( ( times_times_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) )
% 4.71/5.10 = one_one_int ) ) ).
% 4.71/5.10
% 4.71/5.10 % left_right_inverse_power
% 4.71/5.10 thf(fact_3865_power__one__over,axiom,
% 4.71/5.10 ! [A: rat,N: nat] :
% 4.71/5.10 ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N )
% 4.71/5.10 = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_one_over
% 4.71/5.10 thf(fact_3866_power__one__over,axiom,
% 4.71/5.10 ! [A: complex,N: nat] :
% 4.71/5.10 ( ( power_power_complex @ ( divide1717551699836669952omplex @ one_one_complex @ A ) @ N )
% 4.71/5.10 = ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ A @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_one_over
% 4.71/5.10 thf(fact_3867_power__one__over,axiom,
% 4.71/5.10 ! [A: real,N: nat] :
% 4.71/5.10 ( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ N )
% 4.71/5.10 = ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_one_over
% 4.71/5.10 thf(fact_3868_power__0,axiom,
% 4.71/5.10 ! [A: rat] :
% 4.71/5.10 ( ( power_power_rat @ A @ zero_zero_nat )
% 4.71/5.10 = one_one_rat ) ).
% 4.71/5.10
% 4.71/5.10 % power_0
% 4.71/5.10 thf(fact_3869_power__0,axiom,
% 4.71/5.10 ! [A: int] :
% 4.71/5.10 ( ( power_power_int @ A @ zero_zero_nat )
% 4.71/5.10 = one_one_int ) ).
% 4.71/5.10
% 4.71/5.10 % power_0
% 4.71/5.10 thf(fact_3870_power__0,axiom,
% 4.71/5.10 ! [A: nat] :
% 4.71/5.10 ( ( power_power_nat @ A @ zero_zero_nat )
% 4.71/5.10 = one_one_nat ) ).
% 4.71/5.10
% 4.71/5.10 % power_0
% 4.71/5.10 thf(fact_3871_power__0,axiom,
% 4.71/5.10 ! [A: real] :
% 4.71/5.10 ( ( power_power_real @ A @ zero_zero_nat )
% 4.71/5.10 = one_one_real ) ).
% 4.71/5.10
% 4.71/5.10 % power_0
% 4.71/5.10 thf(fact_3872_power__0,axiom,
% 4.71/5.10 ! [A: complex] :
% 4.71/5.10 ( ( power_power_complex @ A @ zero_zero_nat )
% 4.71/5.10 = one_one_complex ) ).
% 4.71/5.10
% 4.71/5.10 % power_0
% 4.71/5.10 thf(fact_3873_nat__mult__less__cancel1,axiom,
% 4.71/5.10 ! [K: nat,M2: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.71/5.10 => ( ( ord_less_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N ) )
% 4.71/5.10 = ( ord_less_nat @ M2 @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % nat_mult_less_cancel1
% 4.71/5.10 thf(fact_3874_nat__mult__eq__cancel1,axiom,
% 4.71/5.10 ! [K: nat,M2: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.71/5.10 => ( ( ( times_times_nat @ K @ M2 )
% 4.71/5.10 = ( times_times_nat @ K @ N ) )
% 4.71/5.10 = ( M2 = N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % nat_mult_eq_cancel1
% 4.71/5.10 thf(fact_3875_sum__squares__le__zero__iff,axiom,
% 4.71/5.10 ! [X: real,Y: real] :
% 4.71/5.10 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real )
% 4.71/5.10 = ( ( X = zero_zero_real )
% 4.71/5.10 & ( Y = zero_zero_real ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % sum_squares_le_zero_iff
% 4.71/5.10 thf(fact_3876_sum__squares__le__zero__iff,axiom,
% 4.71/5.10 ! [X: rat,Y: rat] :
% 4.71/5.10 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 4.71/5.10 = ( ( X = zero_zero_rat )
% 4.71/5.10 & ( Y = zero_zero_rat ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % sum_squares_le_zero_iff
% 4.71/5.10 thf(fact_3877_sum__squares__le__zero__iff,axiom,
% 4.71/5.10 ! [X: int,Y: int] :
% 4.71/5.10 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 4.71/5.10 = ( ( X = zero_zero_int )
% 4.71/5.10 & ( Y = zero_zero_int ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % sum_squares_le_zero_iff
% 4.71/5.10 thf(fact_3878_power__less__imp__less__base,axiom,
% 4.71/5.10 ! [A: real,N: nat,B: real] :
% 4.71/5.10 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 4.71/5.10 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.71/5.10 => ( ord_less_real @ A @ B ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_less_imp_less_base
% 4.71/5.10 thf(fact_3879_power__less__imp__less__base,axiom,
% 4.71/5.10 ! [A: rat,N: nat,B: rat] :
% 4.71/5.10 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 4.71/5.10 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.71/5.10 => ( ord_less_rat @ A @ B ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_less_imp_less_base
% 4.71/5.10 thf(fact_3880_power__less__imp__less__base,axiom,
% 4.71/5.10 ! [A: nat,N: nat,B: nat] :
% 4.71/5.10 ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 4.71/5.10 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.71/5.10 => ( ord_less_nat @ A @ B ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_less_imp_less_base
% 4.71/5.10 thf(fact_3881_power__less__imp__less__base,axiom,
% 4.71/5.10 ! [A: int,N: nat,B: int] :
% 4.71/5.10 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 4.71/5.10 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.71/5.10 => ( ord_less_int @ A @ B ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_less_imp_less_base
% 4.71/5.10 thf(fact_3882_sum__squares__gt__zero__iff,axiom,
% 4.71/5.10 ! [X: real,Y: real] :
% 4.71/5.10 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) )
% 4.71/5.10 = ( ( X != zero_zero_real )
% 4.71/5.10 | ( Y != zero_zero_real ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % sum_squares_gt_zero_iff
% 4.71/5.10 thf(fact_3883_sum__squares__gt__zero__iff,axiom,
% 4.71/5.10 ! [X: rat,Y: rat] :
% 4.71/5.10 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) )
% 4.71/5.10 = ( ( X != zero_zero_rat )
% 4.71/5.10 | ( Y != zero_zero_rat ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % sum_squares_gt_zero_iff
% 4.71/5.10 thf(fact_3884_sum__squares__gt__zero__iff,axiom,
% 4.71/5.10 ! [X: int,Y: int] :
% 4.71/5.10 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) )
% 4.71/5.10 = ( ( X != zero_zero_int )
% 4.71/5.10 | ( Y != zero_zero_int ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % sum_squares_gt_zero_iff
% 4.71/5.10 thf(fact_3885_power__le__one,axiom,
% 4.71/5.10 ! [A: real,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.10 => ( ( ord_less_eq_real @ A @ one_one_real )
% 4.71/5.10 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ one_one_real ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_le_one
% 4.71/5.10 thf(fact_3886_power__le__one,axiom,
% 4.71/5.10 ! [A: rat,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.10 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 4.71/5.10 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_le_one
% 4.71/5.10 thf(fact_3887_power__le__one,axiom,
% 4.71/5.10 ! [A: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.71/5.10 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 4.71/5.10 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_le_one
% 4.71/5.10 thf(fact_3888_power__le__one,axiom,
% 4.71/5.10 ! [A: int,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.10 => ( ( ord_less_eq_int @ A @ one_one_int )
% 4.71/5.10 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_le_one
% 4.71/5.10 thf(fact_3889_power__le__imp__le__base,axiom,
% 4.71/5.10 ! [A: real,N: nat,B: real] :
% 4.71/5.10 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ ( power_power_real @ B @ ( suc @ N ) ) )
% 4.71/5.10 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.71/5.10 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_le_imp_le_base
% 4.71/5.10 thf(fact_3890_power__le__imp__le__base,axiom,
% 4.71/5.10 ! [A: rat,N: nat,B: rat] :
% 4.71/5.10 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ ( power_power_rat @ B @ ( suc @ N ) ) )
% 4.71/5.10 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.71/5.10 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_le_imp_le_base
% 4.71/5.10 thf(fact_3891_power__le__imp__le__base,axiom,
% 4.71/5.10 ! [A: nat,N: nat,B: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
% 4.71/5.10 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.71/5.10 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_le_imp_le_base
% 4.71/5.10 thf(fact_3892_power__le__imp__le__base,axiom,
% 4.71/5.10 ! [A: int,N: nat,B: int] :
% 4.71/5.10 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
% 4.71/5.10 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.71/5.10 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_le_imp_le_base
% 4.71/5.10 thf(fact_3893_power__inject__base,axiom,
% 4.71/5.10 ! [A: real,N: nat,B: real] :
% 4.71/5.10 ( ( ( power_power_real @ A @ ( suc @ N ) )
% 4.71/5.10 = ( power_power_real @ B @ ( suc @ N ) ) )
% 4.71/5.10 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.10 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.71/5.10 => ( A = B ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_inject_base
% 4.71/5.10 thf(fact_3894_power__inject__base,axiom,
% 4.71/5.10 ! [A: rat,N: nat,B: rat] :
% 4.71/5.10 ( ( ( power_power_rat @ A @ ( suc @ N ) )
% 4.71/5.10 = ( power_power_rat @ B @ ( suc @ N ) ) )
% 4.71/5.10 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.10 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.71/5.10 => ( A = B ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_inject_base
% 4.71/5.10 thf(fact_3895_power__inject__base,axiom,
% 4.71/5.10 ! [A: nat,N: nat,B: nat] :
% 4.71/5.10 ( ( ( power_power_nat @ A @ ( suc @ N ) )
% 4.71/5.10 = ( power_power_nat @ B @ ( suc @ N ) ) )
% 4.71/5.10 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.71/5.10 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.71/5.10 => ( A = B ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_inject_base
% 4.71/5.10 thf(fact_3896_power__inject__base,axiom,
% 4.71/5.10 ! [A: int,N: nat,B: int] :
% 4.71/5.10 ( ( ( power_power_int @ A @ ( suc @ N ) )
% 4.71/5.10 = ( power_power_int @ B @ ( suc @ N ) ) )
% 4.71/5.10 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.10 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.71/5.10 => ( A = B ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_inject_base
% 4.71/5.10 thf(fact_3897_power__less__power__Suc,axiom,
% 4.71/5.10 ! [A: real,N: nat] :
% 4.71/5.10 ( ( ord_less_real @ one_one_real @ A )
% 4.71/5.10 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_less_power_Suc
% 4.71/5.10 thf(fact_3898_power__less__power__Suc,axiom,
% 4.71/5.10 ! [A: rat,N: nat] :
% 4.71/5.10 ( ( ord_less_rat @ one_one_rat @ A )
% 4.71/5.10 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_less_power_Suc
% 4.71/5.10 thf(fact_3899_power__less__power__Suc,axiom,
% 4.71/5.10 ! [A: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_nat @ one_one_nat @ A )
% 4.71/5.10 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_less_power_Suc
% 4.71/5.10 thf(fact_3900_power__less__power__Suc,axiom,
% 4.71/5.10 ! [A: int,N: nat] :
% 4.71/5.10 ( ( ord_less_int @ one_one_int @ A )
% 4.71/5.10 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_less_power_Suc
% 4.71/5.10 thf(fact_3901_power__gt1__lemma,axiom,
% 4.71/5.10 ! [A: real,N: nat] :
% 4.71/5.10 ( ( ord_less_real @ one_one_real @ A )
% 4.71/5.10 => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_gt1_lemma
% 4.71/5.10 thf(fact_3902_power__gt1__lemma,axiom,
% 4.71/5.10 ! [A: rat,N: nat] :
% 4.71/5.10 ( ( ord_less_rat @ one_one_rat @ A )
% 4.71/5.10 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_gt1_lemma
% 4.71/5.10 thf(fact_3903_power__gt1__lemma,axiom,
% 4.71/5.10 ! [A: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_nat @ one_one_nat @ A )
% 4.71/5.10 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_gt1_lemma
% 4.71/5.10 thf(fact_3904_power__gt1__lemma,axiom,
% 4.71/5.10 ! [A: int,N: nat] :
% 4.71/5.10 ( ( ord_less_int @ one_one_int @ A )
% 4.71/5.10 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_gt1_lemma
% 4.71/5.10 thf(fact_3905_power__gt1,axiom,
% 4.71/5.10 ! [A: real,N: nat] :
% 4.71/5.10 ( ( ord_less_real @ one_one_real @ A )
% 4.71/5.10 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_gt1
% 4.71/5.10 thf(fact_3906_power__gt1,axiom,
% 4.71/5.10 ! [A: rat,N: nat] :
% 4.71/5.10 ( ( ord_less_rat @ one_one_rat @ A )
% 4.71/5.10 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_gt1
% 4.71/5.10 thf(fact_3907_power__gt1,axiom,
% 4.71/5.10 ! [A: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_nat @ one_one_nat @ A )
% 4.71/5.10 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_gt1
% 4.71/5.10 thf(fact_3908_power__gt1,axiom,
% 4.71/5.10 ! [A: int,N: nat] :
% 4.71/5.10 ( ( ord_less_int @ one_one_int @ A )
% 4.71/5.10 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_gt1
% 4.71/5.10 thf(fact_3909_power__0__left,axiom,
% 4.71/5.10 ! [N: nat] :
% 4.71/5.10 ( ( ( N = zero_zero_nat )
% 4.71/5.10 => ( ( power_power_rat @ zero_zero_rat @ N )
% 4.71/5.10 = one_one_rat ) )
% 4.71/5.10 & ( ( N != zero_zero_nat )
% 4.71/5.10 => ( ( power_power_rat @ zero_zero_rat @ N )
% 4.71/5.10 = zero_zero_rat ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_0_left
% 4.71/5.10 thf(fact_3910_power__0__left,axiom,
% 4.71/5.10 ! [N: nat] :
% 4.71/5.10 ( ( ( N = zero_zero_nat )
% 4.71/5.10 => ( ( power_power_int @ zero_zero_int @ N )
% 4.71/5.10 = one_one_int ) )
% 4.71/5.10 & ( ( N != zero_zero_nat )
% 4.71/5.10 => ( ( power_power_int @ zero_zero_int @ N )
% 4.71/5.10 = zero_zero_int ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_0_left
% 4.71/5.10 thf(fact_3911_power__0__left,axiom,
% 4.71/5.10 ! [N: nat] :
% 4.71/5.10 ( ( ( N = zero_zero_nat )
% 4.71/5.10 => ( ( power_power_nat @ zero_zero_nat @ N )
% 4.71/5.10 = one_one_nat ) )
% 4.71/5.10 & ( ( N != zero_zero_nat )
% 4.71/5.10 => ( ( power_power_nat @ zero_zero_nat @ N )
% 4.71/5.10 = zero_zero_nat ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_0_left
% 4.71/5.10 thf(fact_3912_power__0__left,axiom,
% 4.71/5.10 ! [N: nat] :
% 4.71/5.10 ( ( ( N = zero_zero_nat )
% 4.71/5.10 => ( ( power_power_real @ zero_zero_real @ N )
% 4.71/5.10 = one_one_real ) )
% 4.71/5.10 & ( ( N != zero_zero_nat )
% 4.71/5.10 => ( ( power_power_real @ zero_zero_real @ N )
% 4.71/5.10 = zero_zero_real ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_0_left
% 4.71/5.10 thf(fact_3913_power__0__left,axiom,
% 4.71/5.10 ! [N: nat] :
% 4.71/5.10 ( ( ( N = zero_zero_nat )
% 4.71/5.10 => ( ( power_power_complex @ zero_zero_complex @ N )
% 4.71/5.10 = one_one_complex ) )
% 4.71/5.10 & ( ( N != zero_zero_nat )
% 4.71/5.10 => ( ( power_power_complex @ zero_zero_complex @ N )
% 4.71/5.10 = zero_zero_complex ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_0_left
% 4.71/5.10 thf(fact_3914_power__strict__increasing,axiom,
% 4.71/5.10 ! [N: nat,N5: nat,A: real] :
% 4.71/5.10 ( ( ord_less_nat @ N @ N5 )
% 4.71/5.10 => ( ( ord_less_real @ one_one_real @ A )
% 4.71/5.10 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N5 ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_strict_increasing
% 4.71/5.10 thf(fact_3915_power__strict__increasing,axiom,
% 4.71/5.10 ! [N: nat,N5: nat,A: rat] :
% 4.71/5.10 ( ( ord_less_nat @ N @ N5 )
% 4.71/5.10 => ( ( ord_less_rat @ one_one_rat @ A )
% 4.71/5.10 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N5 ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_strict_increasing
% 4.71/5.10 thf(fact_3916_power__strict__increasing,axiom,
% 4.71/5.10 ! [N: nat,N5: nat,A: nat] :
% 4.71/5.10 ( ( ord_less_nat @ N @ N5 )
% 4.71/5.10 => ( ( ord_less_nat @ one_one_nat @ A )
% 4.71/5.10 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N5 ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_strict_increasing
% 4.71/5.10 thf(fact_3917_power__strict__increasing,axiom,
% 4.71/5.10 ! [N: nat,N5: nat,A: int] :
% 4.71/5.10 ( ( ord_less_nat @ N @ N5 )
% 4.71/5.10 => ( ( ord_less_int @ one_one_int @ A )
% 4.71/5.10 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N5 ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_strict_increasing
% 4.71/5.10 thf(fact_3918_power__less__imp__less__exp,axiom,
% 4.71/5.10 ! [A: real,M2: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_real @ one_one_real @ A )
% 4.71/5.10 => ( ( ord_less_real @ ( power_power_real @ A @ M2 ) @ ( power_power_real @ A @ N ) )
% 4.71/5.10 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_less_imp_less_exp
% 4.71/5.10 thf(fact_3919_power__less__imp__less__exp,axiom,
% 4.71/5.10 ! [A: rat,M2: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_rat @ one_one_rat @ A )
% 4.71/5.10 => ( ( ord_less_rat @ ( power_power_rat @ A @ M2 ) @ ( power_power_rat @ A @ N ) )
% 4.71/5.10 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_less_imp_less_exp
% 4.71/5.10 thf(fact_3920_power__less__imp__less__exp,axiom,
% 4.71/5.10 ! [A: nat,M2: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_nat @ one_one_nat @ A )
% 4.71/5.10 => ( ( ord_less_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) )
% 4.71/5.10 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_less_imp_less_exp
% 4.71/5.10 thf(fact_3921_power__less__imp__less__exp,axiom,
% 4.71/5.10 ! [A: int,M2: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_int @ one_one_int @ A )
% 4.71/5.10 => ( ( ord_less_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) )
% 4.71/5.10 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_less_imp_less_exp
% 4.71/5.10 thf(fact_3922_zero__le__power__abs,axiom,
% 4.71/5.10 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 4.71/5.10
% 4.71/5.10 % zero_le_power_abs
% 4.71/5.10 thf(fact_3923_zero__le__power__abs,axiom,
% 4.71/5.10 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 4.71/5.10
% 4.71/5.10 % zero_le_power_abs
% 4.71/5.10 thf(fact_3924_zero__le__power__abs,axiom,
% 4.71/5.10 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 4.71/5.10
% 4.71/5.10 % zero_le_power_abs
% 4.71/5.10 thf(fact_3925_power__increasing,axiom,
% 4.71/5.10 ! [N: nat,N5: nat,A: real] :
% 4.71/5.10 ( ( ord_less_eq_nat @ N @ N5 )
% 4.71/5.10 => ( ( ord_less_eq_real @ one_one_real @ A )
% 4.71/5.10 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N5 ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_increasing
% 4.71/5.10 thf(fact_3926_power__increasing,axiom,
% 4.71/5.10 ! [N: nat,N5: nat,A: rat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ N @ N5 )
% 4.71/5.10 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 4.71/5.10 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N5 ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_increasing
% 4.71/5.10 thf(fact_3927_power__increasing,axiom,
% 4.71/5.10 ! [N: nat,N5: nat,A: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ N @ N5 )
% 4.71/5.10 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 4.71/5.10 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N5 ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_increasing
% 4.71/5.10 thf(fact_3928_power__increasing,axiom,
% 4.71/5.10 ! [N: nat,N5: nat,A: int] :
% 4.71/5.10 ( ( ord_less_eq_nat @ N @ N5 )
% 4.71/5.10 => ( ( ord_less_eq_int @ one_one_int @ A )
% 4.71/5.10 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N5 ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_increasing
% 4.71/5.10 thf(fact_3929_zero__power,axiom,
% 4.71/5.10 ! [N: nat] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( power_power_rat @ zero_zero_rat @ N )
% 4.71/5.10 = zero_zero_rat ) ) ).
% 4.71/5.10
% 4.71/5.10 % zero_power
% 4.71/5.10 thf(fact_3930_zero__power,axiom,
% 4.71/5.10 ! [N: nat] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( power_power_int @ zero_zero_int @ N )
% 4.71/5.10 = zero_zero_int ) ) ).
% 4.71/5.10
% 4.71/5.10 % zero_power
% 4.71/5.10 thf(fact_3931_zero__power,axiom,
% 4.71/5.10 ! [N: nat] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( power_power_nat @ zero_zero_nat @ N )
% 4.71/5.10 = zero_zero_nat ) ) ).
% 4.71/5.10
% 4.71/5.10 % zero_power
% 4.71/5.10 thf(fact_3932_zero__power,axiom,
% 4.71/5.10 ! [N: nat] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( power_power_real @ zero_zero_real @ N )
% 4.71/5.10 = zero_zero_real ) ) ).
% 4.71/5.10
% 4.71/5.10 % zero_power
% 4.71/5.10 thf(fact_3933_zero__power,axiom,
% 4.71/5.10 ! [N: nat] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( power_power_complex @ zero_zero_complex @ N )
% 4.71/5.10 = zero_zero_complex ) ) ).
% 4.71/5.10
% 4.71/5.10 % zero_power
% 4.71/5.10 thf(fact_3934_nat__mult__le__cancel1,axiom,
% 4.71/5.10 ! [K: nat,M2: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.71/5.10 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N ) )
% 4.71/5.10 = ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % nat_mult_le_cancel1
% 4.71/5.10 thf(fact_3935_nat__mult__div__cancel1,axiom,
% 4.71/5.10 ! [K: nat,M2: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.71/5.10 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N ) )
% 4.71/5.10 = ( divide_divide_nat @ M2 @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % nat_mult_div_cancel1
% 4.71/5.10 thf(fact_3936_power__Suc__less,axiom,
% 4.71/5.10 ! [A: real,N: nat] :
% 4.71/5.10 ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.10 => ( ( ord_less_real @ A @ one_one_real )
% 4.71/5.10 => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) @ ( power_power_real @ A @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_Suc_less
% 4.71/5.10 thf(fact_3937_power__Suc__less,axiom,
% 4.71/5.10 ! [A: rat,N: nat] :
% 4.71/5.10 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.10 => ( ( ord_less_rat @ A @ one_one_rat )
% 4.71/5.10 => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_Suc_less
% 4.71/5.10 thf(fact_3938_power__Suc__less,axiom,
% 4.71/5.10 ! [A: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.71/5.10 => ( ( ord_less_nat @ A @ one_one_nat )
% 4.71/5.10 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_Suc_less
% 4.71/5.10 thf(fact_3939_power__Suc__less,axiom,
% 4.71/5.10 ! [A: int,N: nat] :
% 4.71/5.10 ( ( ord_less_int @ zero_zero_int @ A )
% 4.71/5.10 => ( ( ord_less_int @ A @ one_one_int )
% 4.71/5.10 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_Suc_less
% 4.71/5.10 thf(fact_3940_power__Suc__le__self,axiom,
% 4.71/5.10 ! [A: real,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.10 => ( ( ord_less_eq_real @ A @ one_one_real )
% 4.71/5.10 => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_Suc_le_self
% 4.71/5.10 thf(fact_3941_power__Suc__le__self,axiom,
% 4.71/5.10 ! [A: rat,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.10 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 4.71/5.10 => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_Suc_le_self
% 4.71/5.10 thf(fact_3942_power__Suc__le__self,axiom,
% 4.71/5.10 ! [A: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.71/5.10 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 4.71/5.10 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_Suc_le_self
% 4.71/5.10 thf(fact_3943_power__Suc__le__self,axiom,
% 4.71/5.10 ! [A: int,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.10 => ( ( ord_less_eq_int @ A @ one_one_int )
% 4.71/5.10 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_Suc_le_self
% 4.71/5.10 thf(fact_3944_power__Suc__less__one,axiom,
% 4.71/5.10 ! [A: real,N: nat] :
% 4.71/5.10 ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.10 => ( ( ord_less_real @ A @ one_one_real )
% 4.71/5.10 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N ) ) @ one_one_real ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_Suc_less_one
% 4.71/5.10 thf(fact_3945_power__Suc__less__one,axiom,
% 4.71/5.10 ! [A: rat,N: nat] :
% 4.71/5.10 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.10 => ( ( ord_less_rat @ A @ one_one_rat )
% 4.71/5.10 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_Suc_less_one
% 4.71/5.10 thf(fact_3946_power__Suc__less__one,axiom,
% 4.71/5.10 ! [A: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.71/5.10 => ( ( ord_less_nat @ A @ one_one_nat )
% 4.71/5.10 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_Suc_less_one
% 4.71/5.10 thf(fact_3947_power__Suc__less__one,axiom,
% 4.71/5.10 ! [A: int,N: nat] :
% 4.71/5.10 ( ( ord_less_int @ zero_zero_int @ A )
% 4.71/5.10 => ( ( ord_less_int @ A @ one_one_int )
% 4.71/5.10 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_Suc_less_one
% 4.71/5.10 thf(fact_3948_power__strict__decreasing,axiom,
% 4.71/5.10 ! [N: nat,N5: nat,A: real] :
% 4.71/5.10 ( ( ord_less_nat @ N @ N5 )
% 4.71/5.10 => ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.10 => ( ( ord_less_real @ A @ one_one_real )
% 4.71/5.10 => ( ord_less_real @ ( power_power_real @ A @ N5 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_strict_decreasing
% 4.71/5.10 thf(fact_3949_power__strict__decreasing,axiom,
% 4.71/5.10 ! [N: nat,N5: nat,A: rat] :
% 4.71/5.10 ( ( ord_less_nat @ N @ N5 )
% 4.71/5.10 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.10 => ( ( ord_less_rat @ A @ one_one_rat )
% 4.71/5.10 => ( ord_less_rat @ ( power_power_rat @ A @ N5 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_strict_decreasing
% 4.71/5.10 thf(fact_3950_power__strict__decreasing,axiom,
% 4.71/5.10 ! [N: nat,N5: nat,A: nat] :
% 4.71/5.10 ( ( ord_less_nat @ N @ N5 )
% 4.71/5.10 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.71/5.10 => ( ( ord_less_nat @ A @ one_one_nat )
% 4.71/5.10 => ( ord_less_nat @ ( power_power_nat @ A @ N5 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_strict_decreasing
% 4.71/5.10 thf(fact_3951_power__strict__decreasing,axiom,
% 4.71/5.10 ! [N: nat,N5: nat,A: int] :
% 4.71/5.10 ( ( ord_less_nat @ N @ N5 )
% 4.71/5.10 => ( ( ord_less_int @ zero_zero_int @ A )
% 4.71/5.10 => ( ( ord_less_int @ A @ one_one_int )
% 4.71/5.10 => ( ord_less_int @ ( power_power_int @ A @ N5 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_strict_decreasing
% 4.71/5.10 thf(fact_3952_power__decreasing,axiom,
% 4.71/5.10 ! [N: nat,N5: nat,A: real] :
% 4.71/5.10 ( ( ord_less_eq_nat @ N @ N5 )
% 4.71/5.10 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.10 => ( ( ord_less_eq_real @ A @ one_one_real )
% 4.71/5.10 => ( ord_less_eq_real @ ( power_power_real @ A @ N5 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_decreasing
% 4.71/5.10 thf(fact_3953_power__decreasing,axiom,
% 4.71/5.10 ! [N: nat,N5: nat,A: rat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ N @ N5 )
% 4.71/5.10 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.10 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 4.71/5.10 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N5 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_decreasing
% 4.71/5.10 thf(fact_3954_power__decreasing,axiom,
% 4.71/5.10 ! [N: nat,N5: nat,A: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ N @ N5 )
% 4.71/5.10 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.71/5.10 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 4.71/5.10 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N5 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_decreasing
% 4.71/5.10 thf(fact_3955_power__decreasing,axiom,
% 4.71/5.10 ! [N: nat,N5: nat,A: int] :
% 4.71/5.10 ( ( ord_less_eq_nat @ N @ N5 )
% 4.71/5.10 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.10 => ( ( ord_less_eq_int @ A @ one_one_int )
% 4.71/5.10 => ( ord_less_eq_int @ ( power_power_int @ A @ N5 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_decreasing
% 4.71/5.10 thf(fact_3956_power__le__imp__le__exp,axiom,
% 4.71/5.10 ! [A: real,M2: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_real @ one_one_real @ A )
% 4.71/5.10 => ( ( ord_less_eq_real @ ( power_power_real @ A @ M2 ) @ ( power_power_real @ A @ N ) )
% 4.71/5.10 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_le_imp_le_exp
% 4.71/5.10 thf(fact_3957_power__le__imp__le__exp,axiom,
% 4.71/5.10 ! [A: rat,M2: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_rat @ one_one_rat @ A )
% 4.71/5.10 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M2 ) @ ( power_power_rat @ A @ N ) )
% 4.71/5.10 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_le_imp_le_exp
% 4.71/5.10 thf(fact_3958_power__le__imp__le__exp,axiom,
% 4.71/5.10 ! [A: nat,M2: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_nat @ one_one_nat @ A )
% 4.71/5.10 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) )
% 4.71/5.10 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_le_imp_le_exp
% 4.71/5.10 thf(fact_3959_power__le__imp__le__exp,axiom,
% 4.71/5.10 ! [A: int,M2: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_int @ one_one_int @ A )
% 4.71/5.10 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) )
% 4.71/5.10 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_le_imp_le_exp
% 4.71/5.10 thf(fact_3960_power__eq__imp__eq__base,axiom,
% 4.71/5.10 ! [A: real,N: nat,B: real] :
% 4.71/5.10 ( ( ( power_power_real @ A @ N )
% 4.71/5.10 = ( power_power_real @ B @ N ) )
% 4.71/5.10 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.10 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.71/5.10 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( A = B ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_eq_imp_eq_base
% 4.71/5.10 thf(fact_3961_power__eq__imp__eq__base,axiom,
% 4.71/5.10 ! [A: rat,N: nat,B: rat] :
% 4.71/5.10 ( ( ( power_power_rat @ A @ N )
% 4.71/5.10 = ( power_power_rat @ B @ N ) )
% 4.71/5.10 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.10 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.71/5.10 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( A = B ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_eq_imp_eq_base
% 4.71/5.10 thf(fact_3962_power__eq__imp__eq__base,axiom,
% 4.71/5.10 ! [A: nat,N: nat,B: nat] :
% 4.71/5.10 ( ( ( power_power_nat @ A @ N )
% 4.71/5.10 = ( power_power_nat @ B @ N ) )
% 4.71/5.10 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.71/5.10 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.71/5.10 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( A = B ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_eq_imp_eq_base
% 4.71/5.10 thf(fact_3963_power__eq__imp__eq__base,axiom,
% 4.71/5.10 ! [A: int,N: nat,B: int] :
% 4.71/5.10 ( ( ( power_power_int @ A @ N )
% 4.71/5.10 = ( power_power_int @ B @ N ) )
% 4.71/5.10 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.10 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.71/5.10 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( A = B ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_eq_imp_eq_base
% 4.71/5.10 thf(fact_3964_power__eq__iff__eq__base,axiom,
% 4.71/5.10 ! [N: nat,A: real,B: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.10 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.71/5.10 => ( ( ( power_power_real @ A @ N )
% 4.71/5.10 = ( power_power_real @ B @ N ) )
% 4.71/5.10 = ( A = B ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_eq_iff_eq_base
% 4.71/5.10 thf(fact_3965_power__eq__iff__eq__base,axiom,
% 4.71/5.10 ! [N: nat,A: rat,B: rat] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.10 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.71/5.10 => ( ( ( power_power_rat @ A @ N )
% 4.71/5.10 = ( power_power_rat @ B @ N ) )
% 4.71/5.10 = ( A = B ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_eq_iff_eq_base
% 4.71/5.10 thf(fact_3966_power__eq__iff__eq__base,axiom,
% 4.71/5.10 ! [N: nat,A: nat,B: nat] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.71/5.10 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.71/5.10 => ( ( ( power_power_nat @ A @ N )
% 4.71/5.10 = ( power_power_nat @ B @ N ) )
% 4.71/5.10 = ( A = B ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_eq_iff_eq_base
% 4.71/5.10 thf(fact_3967_power__eq__iff__eq__base,axiom,
% 4.71/5.10 ! [N: nat,A: int,B: int] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.10 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.71/5.10 => ( ( ( power_power_int @ A @ N )
% 4.71/5.10 = ( power_power_int @ B @ N ) )
% 4.71/5.10 = ( A = B ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_eq_iff_eq_base
% 4.71/5.10 thf(fact_3968_self__le__power,axiom,
% 4.71/5.10 ! [A: real,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_real @ one_one_real @ A )
% 4.71/5.10 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % self_le_power
% 4.71/5.10 thf(fact_3969_self__le__power,axiom,
% 4.71/5.10 ! [A: rat,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 4.71/5.10 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % self_le_power
% 4.71/5.10 thf(fact_3970_self__le__power,axiom,
% 4.71/5.10 ! [A: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 4.71/5.10 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % self_le_power
% 4.71/5.10 thf(fact_3971_self__le__power,axiom,
% 4.71/5.10 ! [A: int,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_int @ one_one_int @ A )
% 4.71/5.10 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % self_le_power
% 4.71/5.10 thf(fact_3972_one__less__power,axiom,
% 4.71/5.10 ! [A: real,N: nat] :
% 4.71/5.10 ( ( ord_less_real @ one_one_real @ A )
% 4.71/5.10 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % one_less_power
% 4.71/5.10 thf(fact_3973_one__less__power,axiom,
% 4.71/5.10 ! [A: rat,N: nat] :
% 4.71/5.10 ( ( ord_less_rat @ one_one_rat @ A )
% 4.71/5.10 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % one_less_power
% 4.71/5.10 thf(fact_3974_one__less__power,axiom,
% 4.71/5.10 ! [A: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_nat @ one_one_nat @ A )
% 4.71/5.10 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % one_less_power
% 4.71/5.10 thf(fact_3975_one__less__power,axiom,
% 4.71/5.10 ! [A: int,N: nat] :
% 4.71/5.10 ( ( ord_less_int @ one_one_int @ A )
% 4.71/5.10 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % one_less_power
% 4.71/5.10 thf(fact_3976_power__diff,axiom,
% 4.71/5.10 ! [A: rat,N: nat,M2: nat] :
% 4.71/5.10 ( ( A != zero_zero_rat )
% 4.71/5.10 => ( ( ord_less_eq_nat @ N @ M2 )
% 4.71/5.10 => ( ( power_power_rat @ A @ ( minus_minus_nat @ M2 @ N ) )
% 4.71/5.10 = ( divide_divide_rat @ ( power_power_rat @ A @ M2 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_diff
% 4.71/5.10 thf(fact_3977_power__diff,axiom,
% 4.71/5.10 ! [A: complex,N: nat,M2: nat] :
% 4.71/5.10 ( ( A != zero_zero_complex )
% 4.71/5.10 => ( ( ord_less_eq_nat @ N @ M2 )
% 4.71/5.10 => ( ( power_power_complex @ A @ ( minus_minus_nat @ M2 @ N ) )
% 4.71/5.10 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M2 ) @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_diff
% 4.71/5.10 thf(fact_3978_power__diff,axiom,
% 4.71/5.10 ! [A: int,N: nat,M2: nat] :
% 4.71/5.10 ( ( A != zero_zero_int )
% 4.71/5.10 => ( ( ord_less_eq_nat @ N @ M2 )
% 4.71/5.10 => ( ( power_power_int @ A @ ( minus_minus_nat @ M2 @ N ) )
% 4.71/5.10 = ( divide_divide_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_diff
% 4.71/5.10 thf(fact_3979_power__diff,axiom,
% 4.71/5.10 ! [A: nat,N: nat,M2: nat] :
% 4.71/5.10 ( ( A != zero_zero_nat )
% 4.71/5.10 => ( ( ord_less_eq_nat @ N @ M2 )
% 4.71/5.10 => ( ( power_power_nat @ A @ ( minus_minus_nat @ M2 @ N ) )
% 4.71/5.10 = ( divide_divide_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_diff
% 4.71/5.10 thf(fact_3980_power__diff,axiom,
% 4.71/5.10 ! [A: real,N: nat,M2: nat] :
% 4.71/5.10 ( ( A != zero_zero_real )
% 4.71/5.10 => ( ( ord_less_eq_nat @ N @ M2 )
% 4.71/5.10 => ( ( power_power_real @ A @ ( minus_minus_nat @ M2 @ N ) )
% 4.71/5.10 = ( divide_divide_real @ ( power_power_real @ A @ M2 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_diff
% 4.71/5.10 thf(fact_3981_power__strict__mono,axiom,
% 4.71/5.10 ! [A: real,B: real,N: nat] :
% 4.71/5.10 ( ( ord_less_real @ A @ B )
% 4.71/5.10 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.10 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_strict_mono
% 4.71/5.10 thf(fact_3982_power__strict__mono,axiom,
% 4.71/5.10 ! [A: rat,B: rat,N: nat] :
% 4.71/5.10 ( ( ord_less_rat @ A @ B )
% 4.71/5.10 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.10 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_strict_mono
% 4.71/5.10 thf(fact_3983_power__strict__mono,axiom,
% 4.71/5.10 ! [A: nat,B: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_nat @ A @ B )
% 4.71/5.10 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.71/5.10 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_strict_mono
% 4.71/5.10 thf(fact_3984_power__strict__mono,axiom,
% 4.71/5.10 ! [A: int,B: int,N: nat] :
% 4.71/5.10 ( ( ord_less_int @ A @ B )
% 4.71/5.10 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.10 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_strict_mono
% 4.71/5.10 thf(fact_3985_power__eq__if,axiom,
% 4.71/5.10 ( power_power_complex
% 4.71/5.10 = ( ^ [P5: complex,M3: nat] : ( if_complex @ ( M3 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P5 @ ( power_power_complex @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_eq_if
% 4.71/5.10 thf(fact_3986_power__eq__if,axiom,
% 4.71/5.10 ( power_power_real
% 4.71/5.10 = ( ^ [P5: real,M3: nat] : ( if_real @ ( M3 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P5 @ ( power_power_real @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_eq_if
% 4.71/5.10 thf(fact_3987_power__eq__if,axiom,
% 4.71/5.10 ( power_power_rat
% 4.71/5.10 = ( ^ [P5: rat,M3: nat] : ( if_rat @ ( M3 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P5 @ ( power_power_rat @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_eq_if
% 4.71/5.10 thf(fact_3988_power__eq__if,axiom,
% 4.71/5.10 ( power_power_nat
% 4.71/5.10 = ( ^ [P5: nat,M3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P5 @ ( power_power_nat @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_eq_if
% 4.71/5.10 thf(fact_3989_power__eq__if,axiom,
% 4.71/5.10 ( power_power_int
% 4.71/5.10 = ( ^ [P5: int,M3: nat] : ( if_int @ ( M3 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P5 @ ( power_power_int @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_eq_if
% 4.71/5.10 thf(fact_3990_power__minus__mult,axiom,
% 4.71/5.10 ! [N: nat,A: complex] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 4.71/5.10 = ( power_power_complex @ A @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_minus_mult
% 4.71/5.10 thf(fact_3991_power__minus__mult,axiom,
% 4.71/5.10 ! [N: nat,A: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 4.71/5.10 = ( power_power_real @ A @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_minus_mult
% 4.71/5.10 thf(fact_3992_power__minus__mult,axiom,
% 4.71/5.10 ! [N: nat,A: rat] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 4.71/5.10 = ( power_power_rat @ A @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_minus_mult
% 4.71/5.10 thf(fact_3993_power__minus__mult,axiom,
% 4.71/5.10 ! [N: nat,A: nat] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 4.71/5.10 = ( power_power_nat @ A @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_minus_mult
% 4.71/5.10 thf(fact_3994_power__minus__mult,axiom,
% 4.71/5.10 ! [N: nat,A: int] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 4.71/5.10 = ( power_power_int @ A @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % power_minus_mult
% 4.71/5.10 thf(fact_3995_linear__plus__1__le__power,axiom,
% 4.71/5.10 ! [X: real,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.10 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X @ one_one_real ) @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % linear_plus_1_le_power
% 4.71/5.10 thf(fact_3996_lemma__interval,axiom,
% 4.71/5.10 ! [A: real,X: real,B: real] :
% 4.71/5.10 ( ( ord_less_real @ A @ X )
% 4.71/5.10 => ( ( ord_less_real @ X @ B )
% 4.71/5.10 => ? [D6: real] :
% 4.71/5.10 ( ( ord_less_real @ zero_zero_real @ D6 )
% 4.71/5.10 & ! [Y4: real] :
% 4.71/5.10 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y4 ) ) @ D6 )
% 4.71/5.10 => ( ( ord_less_eq_real @ A @ Y4 )
% 4.71/5.10 & ( ord_less_eq_real @ Y4 @ B ) ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % lemma_interval
% 4.71/5.10 thf(fact_3997_Bolzano,axiom,
% 4.71/5.10 ! [A: real,B: real,P: real > real > $o] :
% 4.71/5.10 ( ( ord_less_eq_real @ A @ B )
% 4.71/5.10 => ( ! [A5: real,B5: real,C3: real] :
% 4.71/5.10 ( ( P @ A5 @ B5 )
% 4.71/5.10 => ( ( P @ B5 @ C3 )
% 4.71/5.10 => ( ( ord_less_eq_real @ A5 @ B5 )
% 4.71/5.10 => ( ( ord_less_eq_real @ B5 @ C3 )
% 4.71/5.10 => ( P @ A5 @ C3 ) ) ) ) )
% 4.71/5.10 => ( ! [X4: real] :
% 4.71/5.10 ( ( ord_less_eq_real @ A @ X4 )
% 4.71/5.10 => ( ( ord_less_eq_real @ X4 @ B )
% 4.71/5.10 => ? [D3: real] :
% 4.71/5.10 ( ( ord_less_real @ zero_zero_real @ D3 )
% 4.71/5.10 & ! [A5: real,B5: real] :
% 4.71/5.10 ( ( ( ord_less_eq_real @ A5 @ X4 )
% 4.71/5.10 & ( ord_less_eq_real @ X4 @ B5 )
% 4.71/5.10 & ( ord_less_real @ ( minus_minus_real @ B5 @ A5 ) @ D3 ) )
% 4.71/5.10 => ( P @ A5 @ B5 ) ) ) ) )
% 4.71/5.10 => ( P @ A @ B ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % Bolzano
% 4.71/5.10 thf(fact_3998_realpow__pos__nth__unique,axiom,
% 4.71/5.10 ! [N: nat,A: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.10 => ? [X4: real] :
% 4.71/5.10 ( ( ord_less_real @ zero_zero_real @ X4 )
% 4.71/5.10 & ( ( power_power_real @ X4 @ N )
% 4.71/5.10 = A )
% 4.71/5.10 & ! [Y4: real] :
% 4.71/5.10 ( ( ( ord_less_real @ zero_zero_real @ Y4 )
% 4.71/5.10 & ( ( power_power_real @ Y4 @ N )
% 4.71/5.10 = A ) )
% 4.71/5.10 => ( Y4 = X4 ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % realpow_pos_nth_unique
% 4.71/5.10 thf(fact_3999_realpow__pos__nth,axiom,
% 4.71/5.10 ! [N: nat,A: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.10 => ? [R4: real] :
% 4.71/5.10 ( ( ord_less_real @ zero_zero_real @ R4 )
% 4.71/5.10 & ( ( power_power_real @ R4 @ N )
% 4.71/5.10 = A ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % realpow_pos_nth
% 4.71/5.10 thf(fact_4000_mult__le__cancel__iff2,axiom,
% 4.71/5.10 ! [Z: real,X: real,Y: real] :
% 4.71/5.10 ( ( ord_less_real @ zero_zero_real @ Z )
% 4.71/5.10 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X ) @ ( times_times_real @ Z @ Y ) )
% 4.71/5.10 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % mult_le_cancel_iff2
% 4.71/5.10 thf(fact_4001_mult__le__cancel__iff2,axiom,
% 4.71/5.10 ! [Z: rat,X: rat,Y: rat] :
% 4.71/5.10 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 4.71/5.10 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X ) @ ( times_times_rat @ Z @ Y ) )
% 4.71/5.10 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % mult_le_cancel_iff2
% 4.71/5.10 thf(fact_4002_mult__le__cancel__iff2,axiom,
% 4.71/5.10 ! [Z: int,X: int,Y: int] :
% 4.71/5.10 ( ( ord_less_int @ zero_zero_int @ Z )
% 4.71/5.10 => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X ) @ ( times_times_int @ Z @ Y ) )
% 4.71/5.10 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % mult_le_cancel_iff2
% 4.71/5.10 thf(fact_4003_mult__le__cancel__iff1,axiom,
% 4.71/5.10 ! [Z: real,X: real,Y: real] :
% 4.71/5.10 ( ( ord_less_real @ zero_zero_real @ Z )
% 4.71/5.10 => ( ( ord_less_eq_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
% 4.71/5.10 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % mult_le_cancel_iff1
% 4.71/5.10 thf(fact_4004_mult__le__cancel__iff1,axiom,
% 4.71/5.10 ! [Z: rat,X: rat,Y: rat] :
% 4.71/5.10 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 4.71/5.10 => ( ( ord_less_eq_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 4.71/5.10 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % mult_le_cancel_iff1
% 4.71/5.10 thf(fact_4005_mult__le__cancel__iff1,axiom,
% 4.71/5.10 ! [Z: int,X: int,Y: int] :
% 4.71/5.10 ( ( ord_less_int @ zero_zero_int @ Z )
% 4.71/5.10 => ( ( ord_less_eq_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 4.71/5.10 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % mult_le_cancel_iff1
% 4.71/5.10 thf(fact_4006_add__scale__eq__noteq,axiom,
% 4.71/5.10 ! [R2: real,A: real,B: real,C: real,D: real] :
% 4.71/5.10 ( ( R2 != zero_zero_real )
% 4.71/5.10 => ( ( ( A = B )
% 4.71/5.10 & ( C != D ) )
% 4.71/5.10 => ( ( plus_plus_real @ A @ ( times_times_real @ R2 @ C ) )
% 4.71/5.10 != ( plus_plus_real @ B @ ( times_times_real @ R2 @ D ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % add_scale_eq_noteq
% 4.71/5.10 thf(fact_4007_add__scale__eq__noteq,axiom,
% 4.71/5.10 ! [R2: rat,A: rat,B: rat,C: rat,D: rat] :
% 4.71/5.10 ( ( R2 != zero_zero_rat )
% 4.71/5.10 => ( ( ( A = B )
% 4.71/5.10 & ( C != D ) )
% 4.71/5.10 => ( ( plus_plus_rat @ A @ ( times_times_rat @ R2 @ C ) )
% 4.71/5.10 != ( plus_plus_rat @ B @ ( times_times_rat @ R2 @ D ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % add_scale_eq_noteq
% 4.71/5.10 thf(fact_4008_add__scale__eq__noteq,axiom,
% 4.71/5.10 ! [R2: nat,A: nat,B: nat,C: nat,D: nat] :
% 4.71/5.10 ( ( R2 != zero_zero_nat )
% 4.71/5.10 => ( ( ( A = B )
% 4.71/5.10 & ( C != D ) )
% 4.71/5.10 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R2 @ C ) )
% 4.71/5.10 != ( plus_plus_nat @ B @ ( times_times_nat @ R2 @ D ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % add_scale_eq_noteq
% 4.71/5.10 thf(fact_4009_add__scale__eq__noteq,axiom,
% 4.71/5.10 ! [R2: int,A: int,B: int,C: int,D: int] :
% 4.71/5.10 ( ( R2 != zero_zero_int )
% 4.71/5.10 => ( ( ( A = B )
% 4.71/5.10 & ( C != D ) )
% 4.71/5.10 => ( ( plus_plus_int @ A @ ( times_times_int @ R2 @ C ) )
% 4.71/5.10 != ( plus_plus_int @ B @ ( times_times_int @ R2 @ D ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % add_scale_eq_noteq
% 4.71/5.10 thf(fact_4010_length__induct,axiom,
% 4.71/5.10 ! [P: list_VEBT_VEBT > $o,Xs: list_VEBT_VEBT] :
% 4.71/5.10 ( ! [Xs3: list_VEBT_VEBT] :
% 4.71/5.10 ( ! [Ys: list_VEBT_VEBT] :
% 4.71/5.10 ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys ) @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 4.71/5.10 => ( P @ Ys ) )
% 4.71/5.10 => ( P @ Xs3 ) )
% 4.71/5.10 => ( P @ Xs ) ) ).
% 4.71/5.10
% 4.71/5.10 % length_induct
% 4.71/5.10 thf(fact_4011_length__induct,axiom,
% 4.71/5.10 ! [P: list_nat > $o,Xs: list_nat] :
% 4.71/5.10 ( ! [Xs3: list_nat] :
% 4.71/5.10 ( ! [Ys: list_nat] :
% 4.71/5.10 ( ( ord_less_nat @ ( size_size_list_nat @ Ys ) @ ( size_size_list_nat @ Xs3 ) )
% 4.71/5.10 => ( P @ Ys ) )
% 4.71/5.10 => ( P @ Xs3 ) )
% 4.71/5.10 => ( P @ Xs ) ) ).
% 4.71/5.10
% 4.71/5.10 % length_induct
% 4.71/5.10 thf(fact_4012_finite__maxlen,axiom,
% 4.71/5.10 ! [M5: set_list_VEBT_VEBT] :
% 4.71/5.10 ( ( finite3004134309566078307T_VEBT @ M5 )
% 4.71/5.10 => ? [N2: nat] :
% 4.71/5.10 ! [X2: list_VEBT_VEBT] :
% 4.71/5.10 ( ( member2936631157270082147T_VEBT @ X2 @ M5 )
% 4.71/5.10 => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ X2 ) @ N2 ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % finite_maxlen
% 4.71/5.10 thf(fact_4013_finite__maxlen,axiom,
% 4.71/5.10 ! [M5: set_list_nat] :
% 4.71/5.10 ( ( finite8100373058378681591st_nat @ M5 )
% 4.71/5.10 => ? [N2: nat] :
% 4.71/5.10 ! [X2: list_nat] :
% 4.71/5.10 ( ( member_list_nat @ X2 @ M5 )
% 4.71/5.10 => ( ord_less_nat @ ( size_size_list_nat @ X2 ) @ N2 ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % finite_maxlen
% 4.71/5.10 thf(fact_4014_add__0__iff,axiom,
% 4.71/5.10 ! [B: real,A: real] :
% 4.71/5.10 ( ( B
% 4.71/5.10 = ( plus_plus_real @ B @ A ) )
% 4.71/5.10 = ( A = zero_zero_real ) ) ).
% 4.71/5.10
% 4.71/5.10 % add_0_iff
% 4.71/5.10 thf(fact_4015_add__0__iff,axiom,
% 4.71/5.10 ! [B: rat,A: rat] :
% 4.71/5.10 ( ( B
% 4.71/5.10 = ( plus_plus_rat @ B @ A ) )
% 4.71/5.10 = ( A = zero_zero_rat ) ) ).
% 4.71/5.10
% 4.71/5.10 % add_0_iff
% 4.71/5.10 thf(fact_4016_add__0__iff,axiom,
% 4.71/5.10 ! [B: nat,A: nat] :
% 4.71/5.10 ( ( B
% 4.71/5.10 = ( plus_plus_nat @ B @ A ) )
% 4.71/5.10 = ( A = zero_zero_nat ) ) ).
% 4.71/5.10
% 4.71/5.10 % add_0_iff
% 4.71/5.10 thf(fact_4017_add__0__iff,axiom,
% 4.71/5.10 ! [B: int,A: int] :
% 4.71/5.10 ( ( B
% 4.71/5.10 = ( plus_plus_int @ B @ A ) )
% 4.71/5.10 = ( A = zero_zero_int ) ) ).
% 4.71/5.10
% 4.71/5.10 % add_0_iff
% 4.71/5.10 thf(fact_4018_mult__less__iff1,axiom,
% 4.71/5.10 ! [Z: real,X: real,Y: real] :
% 4.71/5.10 ( ( ord_less_real @ zero_zero_real @ Z )
% 4.71/5.10 => ( ( ord_less_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
% 4.71/5.10 = ( ord_less_real @ X @ Y ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % mult_less_iff1
% 4.71/5.10 thf(fact_4019_mult__less__iff1,axiom,
% 4.71/5.10 ! [Z: rat,X: rat,Y: rat] :
% 4.71/5.10 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 4.71/5.10 => ( ( ord_less_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 4.71/5.10 = ( ord_less_rat @ X @ Y ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % mult_less_iff1
% 4.71/5.10 thf(fact_4020_mult__less__iff1,axiom,
% 4.71/5.10 ! [Z: int,X: int,Y: int] :
% 4.71/5.10 ( ( ord_less_int @ zero_zero_int @ Z )
% 4.71/5.10 => ( ( ord_less_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 4.71/5.10 = ( ord_less_int @ X @ Y ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % mult_less_iff1
% 4.71/5.10 thf(fact_4021_sin__bound__lemma,axiom,
% 4.71/5.10 ! [X: real,Y: real,U: real,V: real] :
% 4.71/5.10 ( ( X = Y )
% 4.71/5.10 => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
% 4.71/5.10 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X @ U ) @ Y ) ) @ V ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % sin_bound_lemma
% 4.71/5.10 thf(fact_4022_the__elem__eq,axiom,
% 4.71/5.10 ! [X: product_prod_nat_nat] :
% 4.71/5.10 ( ( the_el2281957884133575798at_nat @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 4.71/5.10 = X ) ).
% 4.71/5.10
% 4.71/5.10 % the_elem_eq
% 4.71/5.10 thf(fact_4023_the__elem__eq,axiom,
% 4.71/5.10 ! [X: real] :
% 4.71/5.10 ( ( the_elem_real @ ( insert_real @ X @ bot_bot_set_real ) )
% 4.71/5.10 = X ) ).
% 4.71/5.10
% 4.71/5.10 % the_elem_eq
% 4.71/5.10 thf(fact_4024_the__elem__eq,axiom,
% 4.71/5.10 ! [X: $o] :
% 4.71/5.10 ( ( the_elem_o @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.71/5.10 = X ) ).
% 4.71/5.10
% 4.71/5.10 % the_elem_eq
% 4.71/5.10 thf(fact_4025_the__elem__eq,axiom,
% 4.71/5.10 ! [X: nat] :
% 4.71/5.10 ( ( the_elem_nat @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.71/5.10 = X ) ).
% 4.71/5.10
% 4.71/5.10 % the_elem_eq
% 4.71/5.10 thf(fact_4026_the__elem__eq,axiom,
% 4.71/5.10 ! [X: int] :
% 4.71/5.10 ( ( the_elem_int @ ( insert_int @ X @ bot_bot_set_int ) )
% 4.71/5.10 = X ) ).
% 4.71/5.10
% 4.71/5.10 % the_elem_eq
% 4.71/5.10 thf(fact_4027_arctan__add,axiom,
% 4.71/5.10 ! [X: real,Y: real] :
% 4.71/5.10 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 4.71/5.10 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 4.71/5.10 => ( ( plus_plus_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 4.71/5.10 = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X @ Y ) ) ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % arctan_add
% 4.71/5.10 thf(fact_4028_is__singletonI,axiom,
% 4.71/5.10 ! [X: product_prod_nat_nat] : ( is_sin2850979758926227957at_nat @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singletonI
% 4.71/5.10 thf(fact_4029_is__singletonI,axiom,
% 4.71/5.10 ! [X: real] : ( is_singleton_real @ ( insert_real @ X @ bot_bot_set_real ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singletonI
% 4.71/5.10 thf(fact_4030_is__singletonI,axiom,
% 4.71/5.10 ! [X: $o] : ( is_singleton_o @ ( insert_o @ X @ bot_bot_set_o ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singletonI
% 4.71/5.10 thf(fact_4031_is__singletonI,axiom,
% 4.71/5.10 ! [X: nat] : ( is_singleton_nat @ ( insert_nat @ X @ bot_bot_set_nat ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singletonI
% 4.71/5.10 thf(fact_4032_is__singletonI,axiom,
% 4.71/5.10 ! [X: int] : ( is_singleton_int @ ( insert_int @ X @ bot_bot_set_int ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singletonI
% 4.71/5.10 thf(fact_4033_Euclid__induct,axiom,
% 4.71/5.10 ! [P: nat > nat > $o,A: nat,B: nat] :
% 4.71/5.10 ( ! [A5: nat,B5: nat] :
% 4.71/5.10 ( ( P @ A5 @ B5 )
% 4.71/5.10 = ( P @ B5 @ A5 ) )
% 4.71/5.10 => ( ! [A5: nat] : ( P @ A5 @ zero_zero_nat )
% 4.71/5.10 => ( ! [A5: nat,B5: nat] :
% 4.71/5.10 ( ( P @ A5 @ B5 )
% 4.71/5.10 => ( P @ A5 @ ( plus_plus_nat @ A5 @ B5 ) ) )
% 4.71/5.10 => ( P @ A @ B ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % Euclid_induct
% 4.71/5.10 thf(fact_4034_ln__root,axiom,
% 4.71/5.10 ! [N: nat,B: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_real @ zero_zero_real @ B )
% 4.71/5.10 => ( ( ln_ln_real @ ( root @ N @ B ) )
% 4.71/5.10 = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % ln_root
% 4.71/5.10 thf(fact_4035_log__of__power__le,axiom,
% 4.71/5.10 ! [M2: nat,B: real,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( power_power_real @ B @ N ) )
% 4.71/5.10 => ( ( ord_less_real @ one_one_real @ B )
% 4.71/5.10 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 4.71/5.10 => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % log_of_power_le
% 4.71/5.10 thf(fact_4036_gbinomial__absorption_H,axiom,
% 4.71/5.10 ! [K: nat,A: complex] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.71/5.10 => ( ( gbinomial_complex @ A @ K )
% 4.71/5.10 = ( times_times_complex @ ( divide1717551699836669952omplex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_absorption'
% 4.71/5.10 thf(fact_4037_gbinomial__absorption_H,axiom,
% 4.71/5.10 ! [K: nat,A: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.71/5.10 => ( ( gbinomial_real @ A @ K )
% 4.71/5.10 = ( times_times_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_absorption'
% 4.71/5.10 thf(fact_4038_gbinomial__absorption_H,axiom,
% 4.71/5.10 ! [K: nat,A: rat] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.71/5.10 => ( ( gbinomial_rat @ A @ K )
% 4.71/5.10 = ( times_times_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_absorption'
% 4.71/5.10 thf(fact_4039_gbinomial__0_I2_J,axiom,
% 4.71/5.10 ! [K: nat] :
% 4.71/5.10 ( ( gbinomial_real @ zero_zero_real @ ( suc @ K ) )
% 4.71/5.10 = zero_zero_real ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_0(2)
% 4.71/5.10 thf(fact_4040_gbinomial__0_I2_J,axiom,
% 4.71/5.10 ! [K: nat] :
% 4.71/5.10 ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K ) )
% 4.71/5.10 = zero_zero_rat ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_0(2)
% 4.71/5.10 thf(fact_4041_gbinomial__0_I2_J,axiom,
% 4.71/5.10 ! [K: nat] :
% 4.71/5.10 ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 4.71/5.10 = zero_zero_nat ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_0(2)
% 4.71/5.10 thf(fact_4042_gbinomial__0_I2_J,axiom,
% 4.71/5.10 ! [K: nat] :
% 4.71/5.10 ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 4.71/5.10 = zero_zero_int ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_0(2)
% 4.71/5.10 thf(fact_4043_real__root__Suc__0,axiom,
% 4.71/5.10 ! [X: real] :
% 4.71/5.10 ( ( root @ ( suc @ zero_zero_nat ) @ X )
% 4.71/5.10 = X ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_Suc_0
% 4.71/5.10 thf(fact_4044_gbinomial__0_I1_J,axiom,
% 4.71/5.10 ! [A: complex] :
% 4.71/5.10 ( ( gbinomial_complex @ A @ zero_zero_nat )
% 4.71/5.10 = one_one_complex ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_0(1)
% 4.71/5.10 thf(fact_4045_gbinomial__0_I1_J,axiom,
% 4.71/5.10 ! [A: real] :
% 4.71/5.10 ( ( gbinomial_real @ A @ zero_zero_nat )
% 4.71/5.10 = one_one_real ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_0(1)
% 4.71/5.10 thf(fact_4046_gbinomial__0_I1_J,axiom,
% 4.71/5.10 ! [A: rat] :
% 4.71/5.10 ( ( gbinomial_rat @ A @ zero_zero_nat )
% 4.71/5.10 = one_one_rat ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_0(1)
% 4.71/5.10 thf(fact_4047_gbinomial__0_I1_J,axiom,
% 4.71/5.10 ! [A: nat] :
% 4.71/5.10 ( ( gbinomial_nat @ A @ zero_zero_nat )
% 4.71/5.10 = one_one_nat ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_0(1)
% 4.71/5.10 thf(fact_4048_gbinomial__0_I1_J,axiom,
% 4.71/5.10 ! [A: int] :
% 4.71/5.10 ( ( gbinomial_int @ A @ zero_zero_nat )
% 4.71/5.10 = one_one_int ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_0(1)
% 4.71/5.10 thf(fact_4049_real__root__eq__iff,axiom,
% 4.71/5.10 ! [N: nat,X: real,Y: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ( root @ N @ X )
% 4.71/5.10 = ( root @ N @ Y ) )
% 4.71/5.10 = ( X = Y ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_eq_iff
% 4.71/5.10 thf(fact_4050_root__0,axiom,
% 4.71/5.10 ! [X: real] :
% 4.71/5.10 ( ( root @ zero_zero_nat @ X )
% 4.71/5.10 = zero_zero_real ) ).
% 4.71/5.10
% 4.71/5.10 % root_0
% 4.71/5.10 thf(fact_4051_zero__le__arctan__iff,axiom,
% 4.71/5.10 ! [X: real] :
% 4.71/5.10 ( ( ord_less_eq_real @ zero_zero_real @ ( arctan @ X ) )
% 4.71/5.10 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 4.71/5.10
% 4.71/5.10 % zero_le_arctan_iff
% 4.71/5.10 thf(fact_4052_arctan__le__zero__iff,axiom,
% 4.71/5.10 ! [X: real] :
% 4.71/5.10 ( ( ord_less_eq_real @ ( arctan @ X ) @ zero_zero_real )
% 4.71/5.10 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 4.71/5.10
% 4.71/5.10 % arctan_le_zero_iff
% 4.71/5.10 thf(fact_4053_real__root__eq__0__iff,axiom,
% 4.71/5.10 ! [N: nat,X: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ( root @ N @ X )
% 4.71/5.10 = zero_zero_real )
% 4.71/5.10 = ( X = zero_zero_real ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_eq_0_iff
% 4.71/5.10 thf(fact_4054_real__root__less__iff,axiom,
% 4.71/5.10 ! [N: nat,X: real,Y: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y ) )
% 4.71/5.10 = ( ord_less_real @ X @ Y ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_less_iff
% 4.71/5.10 thf(fact_4055_real__root__le__iff,axiom,
% 4.71/5.10 ! [N: nat,X: real,Y: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y ) )
% 4.71/5.10 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_le_iff
% 4.71/5.10 thf(fact_4056_real__root__eq__1__iff,axiom,
% 4.71/5.10 ! [N: nat,X: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ( root @ N @ X )
% 4.71/5.10 = one_one_real )
% 4.71/5.10 = ( X = one_one_real ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_eq_1_iff
% 4.71/5.10 thf(fact_4057_real__root__one,axiom,
% 4.71/5.10 ! [N: nat] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( root @ N @ one_one_real )
% 4.71/5.10 = one_one_real ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_one
% 4.71/5.10 thf(fact_4058_real__root__lt__0__iff,axiom,
% 4.71/5.10 ! [N: nat,X: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_real @ ( root @ N @ X ) @ zero_zero_real )
% 4.71/5.10 = ( ord_less_real @ X @ zero_zero_real ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_lt_0_iff
% 4.71/5.10 thf(fact_4059_real__root__gt__0__iff,axiom,
% 4.71/5.10 ! [N: nat,Y: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_real @ zero_zero_real @ ( root @ N @ Y ) )
% 4.71/5.10 = ( ord_less_real @ zero_zero_real @ Y ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_gt_0_iff
% 4.71/5.10 thf(fact_4060_real__root__le__0__iff,axiom,
% 4.71/5.10 ! [N: nat,X: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ zero_zero_real )
% 4.71/5.10 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_le_0_iff
% 4.71/5.10 thf(fact_4061_real__root__ge__0__iff,axiom,
% 4.71/5.10 ! [N: nat,Y: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ Y ) )
% 4.71/5.10 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_ge_0_iff
% 4.71/5.10 thf(fact_4062_real__root__lt__1__iff,axiom,
% 4.71/5.10 ! [N: nat,X: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_real @ ( root @ N @ X ) @ one_one_real )
% 4.71/5.10 = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_lt_1_iff
% 4.71/5.10 thf(fact_4063_real__root__gt__1__iff,axiom,
% 4.71/5.10 ! [N: nat,Y: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_real @ one_one_real @ ( root @ N @ Y ) )
% 4.71/5.10 = ( ord_less_real @ one_one_real @ Y ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_gt_1_iff
% 4.71/5.10 thf(fact_4064_real__root__le__1__iff,axiom,
% 4.71/5.10 ! [N: nat,X: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ one_one_real )
% 4.71/5.10 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_le_1_iff
% 4.71/5.10 thf(fact_4065_real__root__ge__1__iff,axiom,
% 4.71/5.10 ! [N: nat,Y: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_eq_real @ one_one_real @ ( root @ N @ Y ) )
% 4.71/5.10 = ( ord_less_eq_real @ one_one_real @ Y ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_ge_1_iff
% 4.71/5.10 thf(fact_4066_zero__le__log__cancel__iff,axiom,
% 4.71/5.10 ! [A: real,X: real] :
% 4.71/5.10 ( ( ord_less_real @ one_one_real @ A )
% 4.71/5.10 => ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.10 => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X ) )
% 4.71/5.10 = ( ord_less_eq_real @ one_one_real @ X ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % zero_le_log_cancel_iff
% 4.71/5.10 thf(fact_4067_log__le__zero__cancel__iff,axiom,
% 4.71/5.10 ! [A: real,X: real] :
% 4.71/5.10 ( ( ord_less_real @ one_one_real @ A )
% 4.71/5.10 => ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.10 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ zero_zero_real )
% 4.71/5.10 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % log_le_zero_cancel_iff
% 4.71/5.10 thf(fact_4068_one__le__log__cancel__iff,axiom,
% 4.71/5.10 ! [A: real,X: real] :
% 4.71/5.10 ( ( ord_less_real @ one_one_real @ A )
% 4.71/5.10 => ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.10 => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X ) )
% 4.71/5.10 = ( ord_less_eq_real @ A @ X ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % one_le_log_cancel_iff
% 4.71/5.10 thf(fact_4069_log__le__one__cancel__iff,axiom,
% 4.71/5.10 ! [A: real,X: real] :
% 4.71/5.10 ( ( ord_less_real @ one_one_real @ A )
% 4.71/5.10 => ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.10 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ one_one_real )
% 4.71/5.10 = ( ord_less_eq_real @ X @ A ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % log_le_one_cancel_iff
% 4.71/5.10 thf(fact_4070_log__le__cancel__iff,axiom,
% 4.71/5.10 ! [A: real,X: real,Y: real] :
% 4.71/5.10 ( ( ord_less_real @ one_one_real @ A )
% 4.71/5.10 => ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.10 => ( ( ord_less_real @ zero_zero_real @ Y )
% 4.71/5.10 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ ( log @ A @ Y ) )
% 4.71/5.10 = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % log_le_cancel_iff
% 4.71/5.10 thf(fact_4071_real__root__pow__pos2,axiom,
% 4.71/5.10 ! [N: nat,X: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.10 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 4.71/5.10 = X ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_pow_pos2
% 4.71/5.10 thf(fact_4072_arctan__monotone_H,axiom,
% 4.71/5.10 ! [X: real,Y: real] :
% 4.71/5.10 ( ( ord_less_eq_real @ X @ Y )
% 4.71/5.10 => ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % arctan_monotone'
% 4.71/5.10 thf(fact_4073_arctan__le__iff,axiom,
% 4.71/5.10 ! [X: real,Y: real] :
% 4.71/5.10 ( ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 4.71/5.10 = ( ord_less_eq_real @ X @ Y ) ) ).
% 4.71/5.10
% 4.71/5.10 % arctan_le_iff
% 4.71/5.10 thf(fact_4074_real__root__pos__pos__le,axiom,
% 4.71/5.10 ! [X: real,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.10 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_pos_pos_le
% 4.71/5.10 thf(fact_4075_gbinomial__Suc__Suc,axiom,
% 4.71/5.10 ! [A: complex,K: nat] :
% 4.71/5.10 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 4.71/5.10 = ( plus_plus_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_Suc_Suc
% 4.71/5.10 thf(fact_4076_gbinomial__Suc__Suc,axiom,
% 4.71/5.10 ! [A: real,K: nat] :
% 4.71/5.10 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 4.71/5.10 = ( plus_plus_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_Suc_Suc
% 4.71/5.10 thf(fact_4077_gbinomial__Suc__Suc,axiom,
% 4.71/5.10 ! [A: rat,K: nat] :
% 4.71/5.10 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 4.71/5.10 = ( plus_plus_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_Suc_Suc
% 4.71/5.10 thf(fact_4078_gbinomial__of__nat__symmetric,axiom,
% 4.71/5.10 ! [K: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ K @ N )
% 4.71/5.10 => ( ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K )
% 4.71/5.10 = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_of_nat_symmetric
% 4.71/5.10 thf(fact_4079_gbinomial__of__nat__symmetric,axiom,
% 4.71/5.10 ! [K: nat,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ K @ N )
% 4.71/5.10 => ( ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ K )
% 4.71/5.10 = ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_of_nat_symmetric
% 4.71/5.10 thf(fact_4080_is__singleton__the__elem,axiom,
% 4.71/5.10 ( is_sin2850979758926227957at_nat
% 4.71/5.10 = ( ^ [A6: set_Pr1261947904930325089at_nat] :
% 4.71/5.10 ( A6
% 4.71/5.10 = ( insert8211810215607154385at_nat @ ( the_el2281957884133575798at_nat @ A6 ) @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singleton_the_elem
% 4.71/5.10 thf(fact_4081_is__singleton__the__elem,axiom,
% 4.71/5.10 ( is_singleton_real
% 4.71/5.10 = ( ^ [A6: set_real] :
% 4.71/5.10 ( A6
% 4.71/5.10 = ( insert_real @ ( the_elem_real @ A6 ) @ bot_bot_set_real ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singleton_the_elem
% 4.71/5.10 thf(fact_4082_is__singleton__the__elem,axiom,
% 4.71/5.10 ( is_singleton_o
% 4.71/5.10 = ( ^ [A6: set_o] :
% 4.71/5.10 ( A6
% 4.71/5.10 = ( insert_o @ ( the_elem_o @ A6 ) @ bot_bot_set_o ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singleton_the_elem
% 4.71/5.10 thf(fact_4083_is__singleton__the__elem,axiom,
% 4.71/5.10 ( is_singleton_nat
% 4.71/5.10 = ( ^ [A6: set_nat] :
% 4.71/5.10 ( A6
% 4.71/5.10 = ( insert_nat @ ( the_elem_nat @ A6 ) @ bot_bot_set_nat ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singleton_the_elem
% 4.71/5.10 thf(fact_4084_is__singleton__the__elem,axiom,
% 4.71/5.10 ( is_singleton_int
% 4.71/5.10 = ( ^ [A6: set_int] :
% 4.71/5.10 ( A6
% 4.71/5.10 = ( insert_int @ ( the_elem_int @ A6 ) @ bot_bot_set_int ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singleton_the_elem
% 4.71/5.10 thf(fact_4085_is__singletonI_H,axiom,
% 4.71/5.10 ! [A2: set_set_nat] :
% 4.71/5.10 ( ( A2 != bot_bot_set_set_nat )
% 4.71/5.10 => ( ! [X4: set_nat,Y3: set_nat] :
% 4.71/5.10 ( ( member_set_nat @ X4 @ A2 )
% 4.71/5.10 => ( ( member_set_nat @ Y3 @ A2 )
% 4.71/5.10 => ( X4 = Y3 ) ) )
% 4.71/5.10 => ( is_singleton_set_nat @ A2 ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singletonI'
% 4.71/5.10 thf(fact_4086_is__singletonI_H,axiom,
% 4.71/5.10 ! [A2: set_set_nat_rat] :
% 4.71/5.10 ( ( A2 != bot_bo6797373522285170759at_rat )
% 4.71/5.10 => ( ! [X4: set_nat_rat,Y3: set_nat_rat] :
% 4.71/5.10 ( ( member_set_nat_rat @ X4 @ A2 )
% 4.71/5.10 => ( ( member_set_nat_rat @ Y3 @ A2 )
% 4.71/5.10 => ( X4 = Y3 ) ) )
% 4.71/5.10 => ( is_sin2571591796506819849at_rat @ A2 ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singletonI'
% 4.71/5.10 thf(fact_4087_is__singletonI_H,axiom,
% 4.71/5.10 ! [A2: set_real] :
% 4.71/5.10 ( ( A2 != bot_bot_set_real )
% 4.71/5.10 => ( ! [X4: real,Y3: real] :
% 4.71/5.10 ( ( member_real @ X4 @ A2 )
% 4.71/5.10 => ( ( member_real @ Y3 @ A2 )
% 4.71/5.10 => ( X4 = Y3 ) ) )
% 4.71/5.10 => ( is_singleton_real @ A2 ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singletonI'
% 4.71/5.10 thf(fact_4088_is__singletonI_H,axiom,
% 4.71/5.10 ! [A2: set_o] :
% 4.71/5.10 ( ( A2 != bot_bot_set_o )
% 4.71/5.10 => ( ! [X4: $o,Y3: $o] :
% 4.71/5.10 ( ( member_o @ X4 @ A2 )
% 4.71/5.10 => ( ( member_o @ Y3 @ A2 )
% 4.71/5.10 => ( X4 = Y3 ) ) )
% 4.71/5.10 => ( is_singleton_o @ A2 ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singletonI'
% 4.71/5.10 thf(fact_4089_is__singletonI_H,axiom,
% 4.71/5.10 ! [A2: set_nat] :
% 4.71/5.10 ( ( A2 != bot_bot_set_nat )
% 4.71/5.10 => ( ! [X4: nat,Y3: nat] :
% 4.71/5.10 ( ( member_nat @ X4 @ A2 )
% 4.71/5.10 => ( ( member_nat @ Y3 @ A2 )
% 4.71/5.10 => ( X4 = Y3 ) ) )
% 4.71/5.10 => ( is_singleton_nat @ A2 ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singletonI'
% 4.71/5.10 thf(fact_4090_is__singletonI_H,axiom,
% 4.71/5.10 ! [A2: set_int] :
% 4.71/5.10 ( ( A2 != bot_bot_set_int )
% 4.71/5.10 => ( ! [X4: int,Y3: int] :
% 4.71/5.10 ( ( member_int @ X4 @ A2 )
% 4.71/5.10 => ( ( member_int @ Y3 @ A2 )
% 4.71/5.10 => ( X4 = Y3 ) ) )
% 4.71/5.10 => ( is_singleton_int @ A2 ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singletonI'
% 4.71/5.10 thf(fact_4091_log__root,axiom,
% 4.71/5.10 ! [N: nat,A: real,B: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.10 => ( ( log @ B @ ( root @ N @ A ) )
% 4.71/5.10 = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % log_root
% 4.71/5.10 thf(fact_4092_log__base__root,axiom,
% 4.71/5.10 ! [N: nat,B: real,X: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_real @ zero_zero_real @ B )
% 4.71/5.10 => ( ( log @ ( root @ N @ B ) @ X )
% 4.71/5.10 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % log_base_root
% 4.71/5.10 thf(fact_4093_gbinomial__addition__formula,axiom,
% 4.71/5.10 ! [A: complex,K: nat] :
% 4.71/5.10 ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 4.71/5.10 = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_addition_formula
% 4.71/5.10 thf(fact_4094_gbinomial__addition__formula,axiom,
% 4.71/5.10 ! [A: real,K: nat] :
% 4.71/5.10 ( ( gbinomial_real @ A @ ( suc @ K ) )
% 4.71/5.10 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( suc @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_addition_formula
% 4.71/5.10 thf(fact_4095_gbinomial__addition__formula,axiom,
% 4.71/5.10 ! [A: rat,K: nat] :
% 4.71/5.10 ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 4.71/5.10 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_addition_formula
% 4.71/5.10 thf(fact_4096_gbinomial__absorb__comp,axiom,
% 4.71/5.10 ! [A: complex,K: nat] :
% 4.71/5.10 ( ( times_times_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ A @ K ) )
% 4.71/5.10 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_absorb_comp
% 4.71/5.10 thf(fact_4097_gbinomial__absorb__comp,axiom,
% 4.71/5.10 ! [A: real,K: nat] :
% 4.71/5.10 ( ( times_times_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ A @ K ) )
% 4.71/5.10 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_absorb_comp
% 4.71/5.10 thf(fact_4098_gbinomial__absorb__comp,axiom,
% 4.71/5.10 ! [A: rat,K: nat] :
% 4.71/5.10 ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ A @ K ) )
% 4.71/5.10 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_absorb_comp
% 4.71/5.10 thf(fact_4099_gbinomial__ge__n__over__k__pow__k,axiom,
% 4.71/5.10 ! [K: nat,A: real] :
% 4.71/5.10 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ K ) @ A )
% 4.71/5.10 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_ge_n_over_k_pow_k
% 4.71/5.10 thf(fact_4100_gbinomial__ge__n__over__k__pow__k,axiom,
% 4.71/5.10 ! [K: nat,A: rat] :
% 4.71/5.10 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K ) @ A )
% 4.71/5.10 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_ge_n_over_k_pow_k
% 4.71/5.10 thf(fact_4101_real__root__less__mono,axiom,
% 4.71/5.10 ! [N: nat,X: real,Y: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_real @ X @ Y )
% 4.71/5.10 => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_less_mono
% 4.71/5.10 thf(fact_4102_real__root__le__mono,axiom,
% 4.71/5.10 ! [N: nat,X: real,Y: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_eq_real @ X @ Y )
% 4.71/5.10 => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_le_mono
% 4.71/5.10 thf(fact_4103_real__root__power,axiom,
% 4.71/5.10 ! [N: nat,X: real,K: nat] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( root @ N @ ( power_power_real @ X @ K ) )
% 4.71/5.10 = ( power_power_real @ ( root @ N @ X ) @ K ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_power
% 4.71/5.10 thf(fact_4104_real__root__abs,axiom,
% 4.71/5.10 ! [N: nat,X: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( root @ N @ ( abs_abs_real @ X ) )
% 4.71/5.10 = ( abs_abs_real @ ( root @ N @ X ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_abs
% 4.71/5.10 thf(fact_4105_Suc__times__gbinomial,axiom,
% 4.71/5.10 ! [K: nat,A: complex] :
% 4.71/5.10 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) )
% 4.71/5.10 = ( times_times_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % Suc_times_gbinomial
% 4.71/5.10 thf(fact_4106_Suc__times__gbinomial,axiom,
% 4.71/5.10 ! [K: nat,A: real] :
% 4.71/5.10 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) ) )
% 4.71/5.10 = ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % Suc_times_gbinomial
% 4.71/5.10 thf(fact_4107_Suc__times__gbinomial,axiom,
% 4.71/5.10 ! [K: nat,A: rat] :
% 4.71/5.10 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) )
% 4.71/5.10 = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % Suc_times_gbinomial
% 4.71/5.10 thf(fact_4108_gbinomial__absorption,axiom,
% 4.71/5.10 ! [K: nat,A: complex] :
% 4.71/5.10 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) )
% 4.71/5.10 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_absorption
% 4.71/5.10 thf(fact_4109_gbinomial__absorption,axiom,
% 4.71/5.10 ! [K: nat,A: real] :
% 4.71/5.10 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) )
% 4.71/5.10 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_absorption
% 4.71/5.10 thf(fact_4110_gbinomial__absorption,axiom,
% 4.71/5.10 ! [K: nat,A: rat] :
% 4.71/5.10 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) )
% 4.71/5.10 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_absorption
% 4.71/5.10 thf(fact_4111_gbinomial__trinomial__revision,axiom,
% 4.71/5.10 ! [K: nat,M2: nat,A: real] :
% 4.71/5.10 ( ( ord_less_eq_nat @ K @ M2 )
% 4.71/5.10 => ( ( times_times_real @ ( gbinomial_real @ A @ M2 ) @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ M2 ) @ K ) )
% 4.71/5.10 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( minus_minus_nat @ M2 @ K ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_trinomial_revision
% 4.71/5.10 thf(fact_4112_gbinomial__trinomial__revision,axiom,
% 4.71/5.10 ! [K: nat,M2: nat,A: rat] :
% 4.71/5.10 ( ( ord_less_eq_nat @ K @ M2 )
% 4.71/5.10 => ( ( times_times_rat @ ( gbinomial_rat @ A @ M2 ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M2 ) @ K ) )
% 4.71/5.10 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( minus_minus_nat @ M2 @ K ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_trinomial_revision
% 4.71/5.10 thf(fact_4113_real__root__gt__zero,axiom,
% 4.71/5.10 ! [N: nat,X: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.10 => ( ord_less_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_gt_zero
% 4.71/5.10 thf(fact_4114_real__root__strict__decreasing,axiom,
% 4.71/5.10 ! [N: nat,N5: nat,X: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_nat @ N @ N5 )
% 4.71/5.10 => ( ( ord_less_real @ one_one_real @ X )
% 4.71/5.10 => ( ord_less_real @ ( root @ N5 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_strict_decreasing
% 4.71/5.10 thf(fact_4115_root__abs__power,axiom,
% 4.71/5.10 ! [N: nat,Y: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( abs_abs_real @ ( root @ N @ ( power_power_real @ Y @ N ) ) )
% 4.71/5.10 = ( abs_abs_real @ Y ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % root_abs_power
% 4.71/5.10 thf(fact_4116_gbinomial__rec,axiom,
% 4.71/5.10 ! [A: complex,K: nat] :
% 4.71/5.10 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 4.71/5.10 = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_rec
% 4.71/5.10 thf(fact_4117_gbinomial__rec,axiom,
% 4.71/5.10 ! [A: real,K: nat] :
% 4.71/5.10 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 4.71/5.10 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_rec
% 4.71/5.10 thf(fact_4118_gbinomial__rec,axiom,
% 4.71/5.10 ! [A: rat,K: nat] :
% 4.71/5.10 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 4.71/5.10 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_rec
% 4.71/5.10 thf(fact_4119_gbinomial__factors,axiom,
% 4.71/5.10 ! [A: complex,K: nat] :
% 4.71/5.10 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 4.71/5.10 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_factors
% 4.71/5.10 thf(fact_4120_gbinomial__factors,axiom,
% 4.71/5.10 ! [A: real,K: nat] :
% 4.71/5.10 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 4.71/5.10 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_factors
% 4.71/5.10 thf(fact_4121_gbinomial__factors,axiom,
% 4.71/5.10 ! [A: rat,K: nat] :
% 4.71/5.10 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 4.71/5.10 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_factors
% 4.71/5.10 thf(fact_4122_real__root__pos__pos,axiom,
% 4.71/5.10 ! [N: nat,X: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.10 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_pos_pos
% 4.71/5.10 thf(fact_4123_real__root__strict__increasing,axiom,
% 4.71/5.10 ! [N: nat,N5: nat,X: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_nat @ N @ N5 )
% 4.71/5.10 => ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.10 => ( ( ord_less_real @ X @ one_one_real )
% 4.71/5.10 => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N5 @ X ) ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_strict_increasing
% 4.71/5.10 thf(fact_4124_real__root__decreasing,axiom,
% 4.71/5.10 ! [N: nat,N5: nat,X: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_eq_nat @ N @ N5 )
% 4.71/5.10 => ( ( ord_less_eq_real @ one_one_real @ X )
% 4.71/5.10 => ( ord_less_eq_real @ ( root @ N5 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_decreasing
% 4.71/5.10 thf(fact_4125_real__root__pow__pos,axiom,
% 4.71/5.10 ! [N: nat,X: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.10 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 4.71/5.10 = X ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_pow_pos
% 4.71/5.10 thf(fact_4126_real__root__pos__unique,axiom,
% 4.71/5.10 ! [N: nat,Y: real,X: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.71/5.10 => ( ( ( power_power_real @ Y @ N )
% 4.71/5.10 = X )
% 4.71/5.10 => ( ( root @ N @ X )
% 4.71/5.10 = Y ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_pos_unique
% 4.71/5.10 thf(fact_4127_real__root__power__cancel,axiom,
% 4.71/5.10 ! [N: nat,X: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.10 => ( ( root @ N @ ( power_power_real @ X @ N ) )
% 4.71/5.10 = X ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_power_cancel
% 4.71/5.10 thf(fact_4128_le__log__of__power,axiom,
% 4.71/5.10 ! [B: real,N: nat,M2: real] :
% 4.71/5.10 ( ( ord_less_eq_real @ ( power_power_real @ B @ N ) @ M2 )
% 4.71/5.10 => ( ( ord_less_real @ one_one_real @ B )
% 4.71/5.10 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M2 ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % le_log_of_power
% 4.71/5.10 thf(fact_4129_is__singletonE,axiom,
% 4.71/5.10 ! [A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.10 ( ( is_sin2850979758926227957at_nat @ A2 )
% 4.71/5.10 => ~ ! [X4: product_prod_nat_nat] :
% 4.71/5.10 ( A2
% 4.71/5.10 != ( insert8211810215607154385at_nat @ X4 @ bot_bo2099793752762293965at_nat ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singletonE
% 4.71/5.10 thf(fact_4130_is__singletonE,axiom,
% 4.71/5.10 ! [A2: set_real] :
% 4.71/5.10 ( ( is_singleton_real @ A2 )
% 4.71/5.10 => ~ ! [X4: real] :
% 4.71/5.10 ( A2
% 4.71/5.10 != ( insert_real @ X4 @ bot_bot_set_real ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singletonE
% 4.71/5.10 thf(fact_4131_is__singletonE,axiom,
% 4.71/5.10 ! [A2: set_o] :
% 4.71/5.10 ( ( is_singleton_o @ A2 )
% 4.71/5.10 => ~ ! [X4: $o] :
% 4.71/5.10 ( A2
% 4.71/5.10 != ( insert_o @ X4 @ bot_bot_set_o ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singletonE
% 4.71/5.10 thf(fact_4132_is__singletonE,axiom,
% 4.71/5.10 ! [A2: set_nat] :
% 4.71/5.10 ( ( is_singleton_nat @ A2 )
% 4.71/5.10 => ~ ! [X4: nat] :
% 4.71/5.10 ( A2
% 4.71/5.10 != ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singletonE
% 4.71/5.10 thf(fact_4133_is__singletonE,axiom,
% 4.71/5.10 ! [A2: set_int] :
% 4.71/5.10 ( ( is_singleton_int @ A2 )
% 4.71/5.10 => ~ ! [X4: int] :
% 4.71/5.10 ( A2
% 4.71/5.10 != ( insert_int @ X4 @ bot_bot_set_int ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singletonE
% 4.71/5.10 thf(fact_4134_is__singleton__def,axiom,
% 4.71/5.10 ( is_sin2850979758926227957at_nat
% 4.71/5.10 = ( ^ [A6: set_Pr1261947904930325089at_nat] :
% 4.71/5.10 ? [X3: product_prod_nat_nat] :
% 4.71/5.10 ( A6
% 4.71/5.10 = ( insert8211810215607154385at_nat @ X3 @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singleton_def
% 4.71/5.10 thf(fact_4135_is__singleton__def,axiom,
% 4.71/5.10 ( is_singleton_real
% 4.71/5.10 = ( ^ [A6: set_real] :
% 4.71/5.10 ? [X3: real] :
% 4.71/5.10 ( A6
% 4.71/5.10 = ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singleton_def
% 4.71/5.10 thf(fact_4136_is__singleton__def,axiom,
% 4.71/5.10 ( is_singleton_o
% 4.71/5.10 = ( ^ [A6: set_o] :
% 4.71/5.10 ? [X3: $o] :
% 4.71/5.10 ( A6
% 4.71/5.10 = ( insert_o @ X3 @ bot_bot_set_o ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singleton_def
% 4.71/5.10 thf(fact_4137_is__singleton__def,axiom,
% 4.71/5.10 ( is_singleton_nat
% 4.71/5.10 = ( ^ [A6: set_nat] :
% 4.71/5.10 ? [X3: nat] :
% 4.71/5.10 ( A6
% 4.71/5.10 = ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singleton_def
% 4.71/5.10 thf(fact_4138_is__singleton__def,axiom,
% 4.71/5.10 ( is_singleton_int
% 4.71/5.10 = ( ^ [A6: set_int] :
% 4.71/5.10 ? [X3: int] :
% 4.71/5.10 ( A6
% 4.71/5.10 = ( insert_int @ X3 @ bot_bot_set_int ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singleton_def
% 4.71/5.10 thf(fact_4139_is__singleton__altdef,axiom,
% 4.71/5.10 ( is_singleton_complex
% 4.71/5.10 = ( ^ [A6: set_complex] :
% 4.71/5.10 ( ( finite_card_complex @ A6 )
% 4.71/5.10 = one_one_nat ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singleton_altdef
% 4.71/5.10 thf(fact_4140_is__singleton__altdef,axiom,
% 4.71/5.10 ( is_sin2641923865335537900st_nat
% 4.71/5.10 = ( ^ [A6: set_list_nat] :
% 4.71/5.10 ( ( finite_card_list_nat @ A6 )
% 4.71/5.10 = one_one_nat ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singleton_altdef
% 4.71/5.10 thf(fact_4141_is__singleton__altdef,axiom,
% 4.71/5.10 ( is_singleton_set_nat
% 4.71/5.10 = ( ^ [A6: set_set_nat] :
% 4.71/5.10 ( ( finite_card_set_nat @ A6 )
% 4.71/5.10 = one_one_nat ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singleton_altdef
% 4.71/5.10 thf(fact_4142_is__singleton__altdef,axiom,
% 4.71/5.10 ( is_singleton_nat
% 4.71/5.10 = ( ^ [A6: set_nat] :
% 4.71/5.10 ( ( finite_card_nat @ A6 )
% 4.71/5.10 = one_one_nat ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singleton_altdef
% 4.71/5.10 thf(fact_4143_is__singleton__altdef,axiom,
% 4.71/5.10 ( is_singleton_int
% 4.71/5.10 = ( ^ [A6: set_int] :
% 4.71/5.10 ( ( finite_card_int @ A6 )
% 4.71/5.10 = one_one_nat ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % is_singleton_altdef
% 4.71/5.10 thf(fact_4144_gbinomial__reduce__nat,axiom,
% 4.71/5.10 ! [K: nat,A: complex] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.71/5.10 => ( ( gbinomial_complex @ A @ K )
% 4.71/5.10 = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_reduce_nat
% 4.71/5.10 thf(fact_4145_gbinomial__reduce__nat,axiom,
% 4.71/5.10 ! [K: nat,A: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.71/5.10 => ( ( gbinomial_real @ A @ K )
% 4.71/5.10 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_reduce_nat
% 4.71/5.10 thf(fact_4146_gbinomial__reduce__nat,axiom,
% 4.71/5.10 ! [K: nat,A: rat] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.71/5.10 => ( ( gbinomial_rat @ A @ K )
% 4.71/5.10 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_reduce_nat
% 4.71/5.10 thf(fact_4147_real__root__increasing,axiom,
% 4.71/5.10 ! [N: nat,N5: nat,X: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_eq_nat @ N @ N5 )
% 4.71/5.10 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.10 => ( ( ord_less_eq_real @ X @ one_one_real )
% 4.71/5.10 => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N5 @ X ) ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % real_root_increasing
% 4.71/5.10 thf(fact_4148_log__of__power__less,axiom,
% 4.71/5.10 ! [M2: nat,B: real,N: nat] :
% 4.71/5.10 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( power_power_real @ B @ N ) )
% 4.71/5.10 => ( ( ord_less_real @ one_one_real @ B )
% 4.71/5.10 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 4.71/5.10 => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % log_of_power_less
% 4.71/5.10 thf(fact_4149_root__powr__inverse,axiom,
% 4.71/5.10 ! [N: nat,X: real] :
% 4.71/5.10 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.10 => ( ( root @ N @ X )
% 4.71/5.10 = ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % root_powr_inverse
% 4.71/5.10 thf(fact_4150_gbinomial__minus,axiom,
% 4.71/5.10 ! [A: complex,K: nat] :
% 4.71/5.10 ( ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K )
% 4.71/5.10 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_minus
% 4.71/5.10 thf(fact_4151_gbinomial__minus,axiom,
% 4.71/5.10 ! [A: real,K: nat] :
% 4.71/5.10 ( ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K )
% 4.71/5.10 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( gbinomial_real @ ( minus_minus_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_minus
% 4.71/5.10 thf(fact_4152_gbinomial__minus,axiom,
% 4.71/5.10 ! [A: rat,K: nat] :
% 4.71/5.10 ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K )
% 4.71/5.10 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % gbinomial_minus
% 4.71/5.10 thf(fact_4153_split__root,axiom,
% 4.71/5.10 ! [P: real > $o,N: nat,X: real] :
% 4.71/5.10 ( ( P @ ( root @ N @ X ) )
% 4.71/5.10 = ( ( ( N = zero_zero_nat )
% 4.71/5.10 => ( P @ zero_zero_real ) )
% 4.71/5.10 & ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.10 => ! [Y2: real] :
% 4.71/5.10 ( ( ( times_times_real @ ( sgn_sgn_real @ Y2 ) @ ( power_power_real @ ( abs_abs_real @ Y2 ) @ N ) )
% 4.71/5.10 = X )
% 4.71/5.10 => ( P @ Y2 ) ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % split_root
% 4.71/5.10 thf(fact_4154_local_Opower__def,axiom,
% 4.71/5.10 ( vEBT_VEBT_power
% 4.71/5.10 = ( vEBT_V4262088993061758097ft_nat @ power_power_nat ) ) ).
% 4.71/5.10
% 4.71/5.10 % local.power_def
% 4.71/5.10 thf(fact_4155_div__pos__neg__trivial,axiom,
% 4.71/5.10 ! [K: int,L: int] :
% 4.71/5.10 ( ( ord_less_int @ zero_zero_int @ K )
% 4.71/5.10 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 4.71/5.10 => ( ( divide_divide_int @ K @ L )
% 4.71/5.10 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % div_pos_neg_trivial
% 4.71/5.10 thf(fact_4156_Bernoulli__inequality,axiom,
% 4.71/5.10 ! [X: real,N: nat] :
% 4.71/5.10 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 4.71/5.10 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % Bernoulli_inequality
% 4.71/5.10 thf(fact_4157_ln__one__minus__pos__upper__bound,axiom,
% 4.71/5.10 ! [X: real] :
% 4.71/5.10 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.10 => ( ( ord_less_real @ X @ one_one_real )
% 4.71/5.10 => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) @ ( uminus_uminus_real @ X ) ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % ln_one_minus_pos_upper_bound
% 4.71/5.10 thf(fact_4158_Gcd__0__iff,axiom,
% 4.71/5.10 ! [A2: set_nat] :
% 4.71/5.10 ( ( ( gcd_Gcd_nat @ A2 )
% 4.71/5.10 = zero_zero_nat )
% 4.71/5.10 = ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % Gcd_0_iff
% 4.71/5.10 thf(fact_4159_Gcd__0__iff,axiom,
% 4.71/5.10 ! [A2: set_int] :
% 4.71/5.10 ( ( ( gcd_Gcd_int @ A2 )
% 4.71/5.10 = zero_zero_int )
% 4.71/5.10 = ( ord_less_eq_set_int @ A2 @ ( insert_int @ zero_zero_int @ bot_bot_set_int ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % Gcd_0_iff
% 4.71/5.10 thf(fact_4160_neg__equal__iff__equal,axiom,
% 4.71/5.10 ! [A: int,B: int] :
% 4.71/5.10 ( ( ( uminus_uminus_int @ A )
% 4.71/5.10 = ( uminus_uminus_int @ B ) )
% 4.71/5.10 = ( A = B ) ) ).
% 4.71/5.10
% 4.71/5.10 % neg_equal_iff_equal
% 4.71/5.10 thf(fact_4161_neg__equal__iff__equal,axiom,
% 4.71/5.10 ! [A: real,B: real] :
% 4.71/5.10 ( ( ( uminus_uminus_real @ A )
% 4.71/5.10 = ( uminus_uminus_real @ B ) )
% 4.71/5.10 = ( A = B ) ) ).
% 4.71/5.10
% 4.71/5.10 % neg_equal_iff_equal
% 4.71/5.10 thf(fact_4162_neg__equal__iff__equal,axiom,
% 4.71/5.10 ! [A: rat,B: rat] :
% 4.71/5.10 ( ( ( uminus_uminus_rat @ A )
% 4.71/5.10 = ( uminus_uminus_rat @ B ) )
% 4.71/5.10 = ( A = B ) ) ).
% 4.71/5.10
% 4.71/5.10 % neg_equal_iff_equal
% 4.71/5.10 thf(fact_4163_neg__equal__iff__equal,axiom,
% 4.71/5.10 ! [A: complex,B: complex] :
% 4.71/5.10 ( ( ( uminus1482373934393186551omplex @ A )
% 4.71/5.10 = ( uminus1482373934393186551omplex @ B ) )
% 4.71/5.10 = ( A = B ) ) ).
% 4.71/5.10
% 4.71/5.10 % neg_equal_iff_equal
% 4.71/5.10 thf(fact_4164_add_Oinverse__inverse,axiom,
% 4.71/5.10 ! [A: int] :
% 4.71/5.10 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 4.71/5.10 = A ) ).
% 4.71/5.10
% 4.71/5.10 % add.inverse_inverse
% 4.71/5.10 thf(fact_4165_add_Oinverse__inverse,axiom,
% 4.71/5.10 ! [A: real] :
% 4.71/5.10 ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 4.71/5.10 = A ) ).
% 4.71/5.10
% 4.71/5.10 % add.inverse_inverse
% 4.71/5.10 thf(fact_4166_add_Oinverse__inverse,axiom,
% 4.71/5.10 ! [A: rat] :
% 4.71/5.10 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 4.71/5.10 = A ) ).
% 4.71/5.10
% 4.71/5.10 % add.inverse_inverse
% 4.71/5.10 thf(fact_4167_add_Oinverse__inverse,axiom,
% 4.71/5.10 ! [A: complex] :
% 4.71/5.10 ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ A ) )
% 4.71/5.10 = A ) ).
% 4.71/5.10
% 4.71/5.10 % add.inverse_inverse
% 4.71/5.10 thf(fact_4168_Compl__anti__mono,axiom,
% 4.71/5.10 ! [A2: set_int,B2: set_int] :
% 4.71/5.10 ( ( ord_less_eq_set_int @ A2 @ B2 )
% 4.71/5.10 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ B2 ) @ ( uminus1532241313380277803et_int @ A2 ) ) ) ).
% 4.71/5.10
% 4.71/5.10 % Compl_anti_mono
% 4.71/5.10 thf(fact_4169_Compl__subset__Compl__iff,axiom,
% 4.71/5.10 ! [A2: set_int,B2: set_int] :
% 4.71/5.10 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( uminus1532241313380277803et_int @ B2 ) )
% 4.71/5.10 = ( ord_less_eq_set_int @ B2 @ A2 ) ) ).
% 4.71/5.10
% 4.71/5.10 % Compl_subset_Compl_iff
% 4.71/5.10 thf(fact_4170_sgn__sgn,axiom,
% 4.71/5.10 ! [A: real] :
% 4.71/5.10 ( ( sgn_sgn_real @ ( sgn_sgn_real @ A ) )
% 4.71/5.10 = ( sgn_sgn_real @ A ) ) ).
% 4.71/5.10
% 4.71/5.10 % sgn_sgn
% 4.71/5.10 thf(fact_4171_sgn__sgn,axiom,
% 4.71/5.10 ! [A: int] :
% 4.71/5.10 ( ( sgn_sgn_int @ ( sgn_sgn_int @ A ) )
% 4.71/5.10 = ( sgn_sgn_int @ A ) ) ).
% 4.71/5.10
% 4.71/5.10 % sgn_sgn
% 4.71/5.10 thf(fact_4172_sgn__sgn,axiom,
% 4.71/5.10 ! [A: complex] :
% 4.71/5.10 ( ( sgn_sgn_complex @ ( sgn_sgn_complex @ A ) )
% 4.71/5.10 = ( sgn_sgn_complex @ A ) ) ).
% 4.71/5.10
% 4.71/5.10 % sgn_sgn
% 4.71/5.10 thf(fact_4173_neg__le__iff__le,axiom,
% 4.71/5.10 ! [B: real,A: real] :
% 4.71/5.10 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 4.71/5.10 = ( ord_less_eq_real @ A @ B ) ) ).
% 4.71/5.10
% 4.71/5.10 % neg_le_iff_le
% 4.71/5.10 thf(fact_4174_neg__le__iff__le,axiom,
% 4.71/5.10 ! [B: rat,A: rat] :
% 4.71/5.10 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 4.71/5.10 = ( ord_less_eq_rat @ A @ B ) ) ).
% 4.71/5.10
% 4.71/5.10 % neg_le_iff_le
% 4.71/5.10 thf(fact_4175_neg__le__iff__le,axiom,
% 4.71/5.10 ! [B: int,A: int] :
% 4.71/5.10 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 4.71/5.10 = ( ord_less_eq_int @ A @ B ) ) ).
% 4.71/5.10
% 4.71/5.10 % neg_le_iff_le
% 4.71/5.10 thf(fact_4176_compl__le__compl__iff,axiom,
% 4.71/5.10 ! [X: set_int,Y: set_int] :
% 4.71/5.10 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X ) @ ( uminus1532241313380277803et_int @ Y ) )
% 4.71/5.10 = ( ord_less_eq_set_int @ Y @ X ) ) ).
% 4.71/5.10
% 4.71/5.10 % compl_le_compl_iff
% 4.71/5.10 thf(fact_4177_add_Oinverse__neutral,axiom,
% 4.71/5.10 ( ( uminus_uminus_int @ zero_zero_int )
% 4.71/5.11 = zero_zero_int ) ).
% 4.71/5.11
% 4.71/5.11 % add.inverse_neutral
% 4.71/5.11 thf(fact_4178_add_Oinverse__neutral,axiom,
% 4.71/5.11 ( ( uminus_uminus_real @ zero_zero_real )
% 4.71/5.11 = zero_zero_real ) ).
% 4.71/5.11
% 4.71/5.11 % add.inverse_neutral
% 4.71/5.11 thf(fact_4179_add_Oinverse__neutral,axiom,
% 4.71/5.11 ( ( uminus_uminus_rat @ zero_zero_rat )
% 4.71/5.11 = zero_zero_rat ) ).
% 4.71/5.11
% 4.71/5.11 % add.inverse_neutral
% 4.71/5.11 thf(fact_4180_add_Oinverse__neutral,axiom,
% 4.71/5.11 ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 4.71/5.11 = zero_zero_complex ) ).
% 4.71/5.11
% 4.71/5.11 % add.inverse_neutral
% 4.71/5.11 thf(fact_4181_neg__0__equal__iff__equal,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( zero_zero_int
% 4.71/5.11 = ( uminus_uminus_int @ A ) )
% 4.71/5.11 = ( zero_zero_int = A ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_0_equal_iff_equal
% 4.71/5.11 thf(fact_4182_neg__0__equal__iff__equal,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( zero_zero_real
% 4.71/5.11 = ( uminus_uminus_real @ A ) )
% 4.71/5.11 = ( zero_zero_real = A ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_0_equal_iff_equal
% 4.71/5.11 thf(fact_4183_neg__0__equal__iff__equal,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( zero_zero_rat
% 4.71/5.11 = ( uminus_uminus_rat @ A ) )
% 4.71/5.11 = ( zero_zero_rat = A ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_0_equal_iff_equal
% 4.71/5.11 thf(fact_4184_neg__0__equal__iff__equal,axiom,
% 4.71/5.11 ! [A: complex] :
% 4.71/5.11 ( ( zero_zero_complex
% 4.71/5.11 = ( uminus1482373934393186551omplex @ A ) )
% 4.71/5.11 = ( zero_zero_complex = A ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_0_equal_iff_equal
% 4.71/5.11 thf(fact_4185_neg__equal__0__iff__equal,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( ( uminus_uminus_int @ A )
% 4.71/5.11 = zero_zero_int )
% 4.71/5.11 = ( A = zero_zero_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_equal_0_iff_equal
% 4.71/5.11 thf(fact_4186_neg__equal__0__iff__equal,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( ( uminus_uminus_real @ A )
% 4.71/5.11 = zero_zero_real )
% 4.71/5.11 = ( A = zero_zero_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_equal_0_iff_equal
% 4.71/5.11 thf(fact_4187_neg__equal__0__iff__equal,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( ( uminus_uminus_rat @ A )
% 4.71/5.11 = zero_zero_rat )
% 4.71/5.11 = ( A = zero_zero_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_equal_0_iff_equal
% 4.71/5.11 thf(fact_4188_neg__equal__0__iff__equal,axiom,
% 4.71/5.11 ! [A: complex] :
% 4.71/5.11 ( ( ( uminus1482373934393186551omplex @ A )
% 4.71/5.11 = zero_zero_complex )
% 4.71/5.11 = ( A = zero_zero_complex ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_equal_0_iff_equal
% 4.71/5.11 thf(fact_4189_equal__neg__zero,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( A
% 4.71/5.11 = ( uminus_uminus_int @ A ) )
% 4.71/5.11 = ( A = zero_zero_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % equal_neg_zero
% 4.71/5.11 thf(fact_4190_equal__neg__zero,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( A
% 4.71/5.11 = ( uminus_uminus_real @ A ) )
% 4.71/5.11 = ( A = zero_zero_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % equal_neg_zero
% 4.71/5.11 thf(fact_4191_equal__neg__zero,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( A
% 4.71/5.11 = ( uminus_uminus_rat @ A ) )
% 4.71/5.11 = ( A = zero_zero_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % equal_neg_zero
% 4.71/5.11 thf(fact_4192_neg__equal__zero,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( ( uminus_uminus_int @ A )
% 4.71/5.11 = A )
% 4.71/5.11 = ( A = zero_zero_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_equal_zero
% 4.71/5.11 thf(fact_4193_neg__equal__zero,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( ( uminus_uminus_real @ A )
% 4.71/5.11 = A )
% 4.71/5.11 = ( A = zero_zero_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_equal_zero
% 4.71/5.11 thf(fact_4194_neg__equal__zero,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( ( uminus_uminus_rat @ A )
% 4.71/5.11 = A )
% 4.71/5.11 = ( A = zero_zero_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_equal_zero
% 4.71/5.11 thf(fact_4195_neg__less__iff__less,axiom,
% 4.71/5.11 ! [B: int,A: int] :
% 4.71/5.11 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 4.71/5.11 = ( ord_less_int @ A @ B ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_less_iff_less
% 4.71/5.11 thf(fact_4196_neg__less__iff__less,axiom,
% 4.71/5.11 ! [B: real,A: real] :
% 4.71/5.11 ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 4.71/5.11 = ( ord_less_real @ A @ B ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_less_iff_less
% 4.71/5.11 thf(fact_4197_neg__less__iff__less,axiom,
% 4.71/5.11 ! [B: rat,A: rat] :
% 4.71/5.11 ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 4.71/5.11 = ( ord_less_rat @ A @ B ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_less_iff_less
% 4.71/5.11 thf(fact_4198_mult__minus__right,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 4.71/5.11 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % mult_minus_right
% 4.71/5.11 thf(fact_4199_mult__minus__right,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 4.71/5.11 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % mult_minus_right
% 4.71/5.11 thf(fact_4200_mult__minus__right,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 4.71/5.11 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % mult_minus_right
% 4.71/5.11 thf(fact_4201_mult__minus__right,axiom,
% 4.71/5.11 ! [A: complex,B: complex] :
% 4.71/5.11 ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 4.71/5.11 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % mult_minus_right
% 4.71/5.11 thf(fact_4202_minus__mult__minus,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 4.71/5.11 = ( times_times_int @ A @ B ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_mult_minus
% 4.71/5.11 thf(fact_4203_minus__mult__minus,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 4.71/5.11 = ( times_times_real @ A @ B ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_mult_minus
% 4.71/5.11 thf(fact_4204_minus__mult__minus,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 4.71/5.11 = ( times_times_rat @ A @ B ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_mult_minus
% 4.71/5.11 thf(fact_4205_minus__mult__minus,axiom,
% 4.71/5.11 ! [A: complex,B: complex] :
% 4.71/5.11 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 4.71/5.11 = ( times_times_complex @ A @ B ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_mult_minus
% 4.71/5.11 thf(fact_4206_mult__minus__left,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 4.71/5.11 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % mult_minus_left
% 4.71/5.11 thf(fact_4207_mult__minus__left,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 4.71/5.11 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % mult_minus_left
% 4.71/5.11 thf(fact_4208_mult__minus__left,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 4.71/5.11 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % mult_minus_left
% 4.71/5.11 thf(fact_4209_mult__minus__left,axiom,
% 4.71/5.11 ! [A: complex,B: complex] :
% 4.71/5.11 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 4.71/5.11 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % mult_minus_left
% 4.71/5.11 thf(fact_4210_minus__add__distrib,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 4.71/5.11 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_add_distrib
% 4.71/5.11 thf(fact_4211_minus__add__distrib,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 4.71/5.11 = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_add_distrib
% 4.71/5.11 thf(fact_4212_minus__add__distrib,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 4.71/5.11 = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_add_distrib
% 4.71/5.11 thf(fact_4213_minus__add__distrib,axiom,
% 4.71/5.11 ! [A: complex,B: complex] :
% 4.71/5.11 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 4.71/5.11 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_add_distrib
% 4.71/5.11 thf(fact_4214_minus__add__cancel,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 4.71/5.11 = B ) ).
% 4.71/5.11
% 4.71/5.11 % minus_add_cancel
% 4.71/5.11 thf(fact_4215_minus__add__cancel,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 4.71/5.11 = B ) ).
% 4.71/5.11
% 4.71/5.11 % minus_add_cancel
% 4.71/5.11 thf(fact_4216_minus__add__cancel,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 4.71/5.11 = B ) ).
% 4.71/5.11
% 4.71/5.11 % minus_add_cancel
% 4.71/5.11 thf(fact_4217_minus__add__cancel,axiom,
% 4.71/5.11 ! [A: complex,B: complex] :
% 4.71/5.11 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 4.71/5.11 = B ) ).
% 4.71/5.11
% 4.71/5.11 % minus_add_cancel
% 4.71/5.11 thf(fact_4218_add__minus__cancel,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 4.71/5.11 = B ) ).
% 4.71/5.11
% 4.71/5.11 % add_minus_cancel
% 4.71/5.11 thf(fact_4219_add__minus__cancel,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 4.71/5.11 = B ) ).
% 4.71/5.11
% 4.71/5.11 % add_minus_cancel
% 4.71/5.11 thf(fact_4220_add__minus__cancel,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 4.71/5.11 = B ) ).
% 4.71/5.11
% 4.71/5.11 % add_minus_cancel
% 4.71/5.11 thf(fact_4221_add__minus__cancel,axiom,
% 4.71/5.11 ! [A: complex,B: complex] :
% 4.71/5.11 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 4.71/5.11 = B ) ).
% 4.71/5.11
% 4.71/5.11 % add_minus_cancel
% 4.71/5.11 thf(fact_4222_minus__diff__eq,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 4.71/5.11 = ( minus_minus_int @ B @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_diff_eq
% 4.71/5.11 thf(fact_4223_minus__diff__eq,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 4.71/5.11 = ( minus_minus_real @ B @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_diff_eq
% 4.71/5.11 thf(fact_4224_minus__diff__eq,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 4.71/5.11 = ( minus_minus_rat @ B @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_diff_eq
% 4.71/5.11 thf(fact_4225_minus__diff__eq,axiom,
% 4.71/5.11 ! [A: complex,B: complex] :
% 4.71/5.11 ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) )
% 4.71/5.11 = ( minus_minus_complex @ B @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_diff_eq
% 4.71/5.11 thf(fact_4226_abs__minus,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 4.71/5.11 = ( abs_abs_int @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_minus
% 4.71/5.11 thf(fact_4227_abs__minus,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 4.71/5.11 = ( abs_abs_real @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_minus
% 4.71/5.11 thf(fact_4228_abs__minus,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 4.71/5.11 = ( abs_abs_rat @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_minus
% 4.71/5.11 thf(fact_4229_abs__minus,axiom,
% 4.71/5.11 ! [A: complex] :
% 4.71/5.11 ( ( abs_abs_complex @ ( uminus1482373934393186551omplex @ A ) )
% 4.71/5.11 = ( abs_abs_complex @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_minus
% 4.71/5.11 thf(fact_4230_abs__minus__cancel,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 4.71/5.11 = ( abs_abs_int @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_minus_cancel
% 4.71/5.11 thf(fact_4231_abs__minus__cancel,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 4.71/5.11 = ( abs_abs_real @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_minus_cancel
% 4.71/5.11 thf(fact_4232_abs__minus__cancel,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 4.71/5.11 = ( abs_abs_rat @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_minus_cancel
% 4.71/5.11 thf(fact_4233_sgn__0,axiom,
% 4.71/5.11 ( ( sgn_sgn_complex @ zero_zero_complex )
% 4.71/5.11 = zero_zero_complex ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_0
% 4.71/5.11 thf(fact_4234_sgn__0,axiom,
% 4.71/5.11 ( ( sgn_sgn_real @ zero_zero_real )
% 4.71/5.11 = zero_zero_real ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_0
% 4.71/5.11 thf(fact_4235_sgn__0,axiom,
% 4.71/5.11 ( ( sgn_sgn_rat @ zero_zero_rat )
% 4.71/5.11 = zero_zero_rat ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_0
% 4.71/5.11 thf(fact_4236_sgn__0,axiom,
% 4.71/5.11 ( ( sgn_sgn_int @ zero_zero_int )
% 4.71/5.11 = zero_zero_int ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_0
% 4.71/5.11 thf(fact_4237_powr__0,axiom,
% 4.71/5.11 ! [Z: real] :
% 4.71/5.11 ( ( powr_real @ zero_zero_real @ Z )
% 4.71/5.11 = zero_zero_real ) ).
% 4.71/5.11
% 4.71/5.11 % powr_0
% 4.71/5.11 thf(fact_4238_powr__eq__0__iff,axiom,
% 4.71/5.11 ! [W2: real,Z: real] :
% 4.71/5.11 ( ( ( powr_real @ W2 @ Z )
% 4.71/5.11 = zero_zero_real )
% 4.71/5.11 = ( W2 = zero_zero_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % powr_eq_0_iff
% 4.71/5.11 thf(fact_4239_sgn__1,axiom,
% 4.71/5.11 ( ( sgn_sgn_rat @ one_one_rat )
% 4.71/5.11 = one_one_rat ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_1
% 4.71/5.11 thf(fact_4240_sgn__1,axiom,
% 4.71/5.11 ( ( sgn_sgn_real @ one_one_real )
% 4.71/5.11 = one_one_real ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_1
% 4.71/5.11 thf(fact_4241_sgn__1,axiom,
% 4.71/5.11 ( ( sgn_sgn_int @ one_one_int )
% 4.71/5.11 = one_one_int ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_1
% 4.71/5.11 thf(fact_4242_sgn__1,axiom,
% 4.71/5.11 ( ( sgn_sgn_complex @ one_one_complex )
% 4.71/5.11 = one_one_complex ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_1
% 4.71/5.11 thf(fact_4243_idom__abs__sgn__class_Osgn__minus,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( sgn_sgn_int @ ( uminus_uminus_int @ A ) )
% 4.71/5.11 = ( uminus_uminus_int @ ( sgn_sgn_int @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % idom_abs_sgn_class.sgn_minus
% 4.71/5.11 thf(fact_4244_idom__abs__sgn__class_Osgn__minus,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( sgn_sgn_real @ ( uminus_uminus_real @ A ) )
% 4.71/5.11 = ( uminus_uminus_real @ ( sgn_sgn_real @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % idom_abs_sgn_class.sgn_minus
% 4.71/5.11 thf(fact_4245_idom__abs__sgn__class_Osgn__minus,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ A ) )
% 4.71/5.11 = ( uminus_uminus_rat @ ( sgn_sgn_rat @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % idom_abs_sgn_class.sgn_minus
% 4.71/5.11 thf(fact_4246_idom__abs__sgn__class_Osgn__minus,axiom,
% 4.71/5.11 ! [A: complex] :
% 4.71/5.11 ( ( sgn_sgn_complex @ ( uminus1482373934393186551omplex @ A ) )
% 4.71/5.11 = ( uminus1482373934393186551omplex @ ( sgn_sgn_complex @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % idom_abs_sgn_class.sgn_minus
% 4.71/5.11 thf(fact_4247_powr__one__eq__one,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( powr_real @ one_one_real @ A )
% 4.71/5.11 = one_one_real ) ).
% 4.71/5.11
% 4.71/5.11 % powr_one_eq_one
% 4.71/5.11 thf(fact_4248_neg__less__eq__nonneg,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 4.71/5.11 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_less_eq_nonneg
% 4.71/5.11 thf(fact_4249_neg__less__eq__nonneg,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 4.71/5.11 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_less_eq_nonneg
% 4.71/5.11 thf(fact_4250_neg__less__eq__nonneg,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 4.71/5.11 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_less_eq_nonneg
% 4.71/5.11 thf(fact_4251_less__eq__neg__nonpos,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 4.71/5.11 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % less_eq_neg_nonpos
% 4.71/5.11 thf(fact_4252_less__eq__neg__nonpos,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 4.71/5.11 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % less_eq_neg_nonpos
% 4.71/5.11 thf(fact_4253_less__eq__neg__nonpos,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 4.71/5.11 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % less_eq_neg_nonpos
% 4.71/5.11 thf(fact_4254_neg__le__0__iff__le,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 4.71/5.11 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_le_0_iff_le
% 4.71/5.11 thf(fact_4255_neg__le__0__iff__le,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 4.71/5.11 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_le_0_iff_le
% 4.71/5.11 thf(fact_4256_neg__le__0__iff__le,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 4.71/5.11 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_le_0_iff_le
% 4.71/5.11 thf(fact_4257_neg__0__le__iff__le,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 4.71/5.11 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_0_le_iff_le
% 4.71/5.11 thf(fact_4258_neg__0__le__iff__le,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 4.71/5.11 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_0_le_iff_le
% 4.71/5.11 thf(fact_4259_neg__0__le__iff__le,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 4.71/5.11 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_0_le_iff_le
% 4.71/5.11 thf(fact_4260_less__neg__neg,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 4.71/5.11 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % less_neg_neg
% 4.71/5.11 thf(fact_4261_less__neg__neg,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 4.71/5.11 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % less_neg_neg
% 4.71/5.11 thf(fact_4262_less__neg__neg,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 4.71/5.11 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % less_neg_neg
% 4.71/5.11 thf(fact_4263_neg__less__pos,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 4.71/5.11 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_less_pos
% 4.71/5.11 thf(fact_4264_neg__less__pos,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 4.71/5.11 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_less_pos
% 4.71/5.11 thf(fact_4265_neg__less__pos,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 4.71/5.11 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_less_pos
% 4.71/5.11 thf(fact_4266_neg__0__less__iff__less,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 4.71/5.11 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_0_less_iff_less
% 4.71/5.11 thf(fact_4267_neg__0__less__iff__less,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 4.71/5.11 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_0_less_iff_less
% 4.71/5.11 thf(fact_4268_neg__0__less__iff__less,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 4.71/5.11 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_0_less_iff_less
% 4.71/5.11 thf(fact_4269_neg__less__0__iff__less,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 4.71/5.11 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_less_0_iff_less
% 4.71/5.11 thf(fact_4270_neg__less__0__iff__less,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 4.71/5.11 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_less_0_iff_less
% 4.71/5.11 thf(fact_4271_neg__less__0__iff__less,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 4.71/5.11 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_less_0_iff_less
% 4.71/5.11 thf(fact_4272_ab__left__minus,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 4.71/5.11 = zero_zero_int ) ).
% 4.71/5.11
% 4.71/5.11 % ab_left_minus
% 4.71/5.11 thf(fact_4273_ab__left__minus,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 4.71/5.11 = zero_zero_real ) ).
% 4.71/5.11
% 4.71/5.11 % ab_left_minus
% 4.71/5.11 thf(fact_4274_ab__left__minus,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 4.71/5.11 = zero_zero_rat ) ).
% 4.71/5.11
% 4.71/5.11 % ab_left_minus
% 4.71/5.11 thf(fact_4275_ab__left__minus,axiom,
% 4.71/5.11 ! [A: complex] :
% 4.71/5.11 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 4.71/5.11 = zero_zero_complex ) ).
% 4.71/5.11
% 4.71/5.11 % ab_left_minus
% 4.71/5.11 thf(fact_4276_add_Oright__inverse,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 4.71/5.11 = zero_zero_int ) ).
% 4.71/5.11
% 4.71/5.11 % add.right_inverse
% 4.71/5.11 thf(fact_4277_add_Oright__inverse,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 4.71/5.11 = zero_zero_real ) ).
% 4.71/5.11
% 4.71/5.11 % add.right_inverse
% 4.71/5.11 thf(fact_4278_add_Oright__inverse,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 4.71/5.11 = zero_zero_rat ) ).
% 4.71/5.11
% 4.71/5.11 % add.right_inverse
% 4.71/5.11 thf(fact_4279_add_Oright__inverse,axiom,
% 4.71/5.11 ! [A: complex] :
% 4.71/5.11 ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 4.71/5.11 = zero_zero_complex ) ).
% 4.71/5.11
% 4.71/5.11 % add.right_inverse
% 4.71/5.11 thf(fact_4280_diff__0,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( minus_minus_int @ zero_zero_int @ A )
% 4.71/5.11 = ( uminus_uminus_int @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % diff_0
% 4.71/5.11 thf(fact_4281_diff__0,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( minus_minus_real @ zero_zero_real @ A )
% 4.71/5.11 = ( uminus_uminus_real @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % diff_0
% 4.71/5.11 thf(fact_4282_diff__0,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( minus_minus_rat @ zero_zero_rat @ A )
% 4.71/5.11 = ( uminus_uminus_rat @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % diff_0
% 4.71/5.11 thf(fact_4283_diff__0,axiom,
% 4.71/5.11 ! [A: complex] :
% 4.71/5.11 ( ( minus_minus_complex @ zero_zero_complex @ A )
% 4.71/5.11 = ( uminus1482373934393186551omplex @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % diff_0
% 4.71/5.11 thf(fact_4284_verit__minus__simplify_I3_J,axiom,
% 4.71/5.11 ! [B: int] :
% 4.71/5.11 ( ( minus_minus_int @ zero_zero_int @ B )
% 4.71/5.11 = ( uminus_uminus_int @ B ) ) ).
% 4.71/5.11
% 4.71/5.11 % verit_minus_simplify(3)
% 4.71/5.11 thf(fact_4285_verit__minus__simplify_I3_J,axiom,
% 4.71/5.11 ! [B: real] :
% 4.71/5.11 ( ( minus_minus_real @ zero_zero_real @ B )
% 4.71/5.11 = ( uminus_uminus_real @ B ) ) ).
% 4.71/5.11
% 4.71/5.11 % verit_minus_simplify(3)
% 4.71/5.11 thf(fact_4286_verit__minus__simplify_I3_J,axiom,
% 4.71/5.11 ! [B: rat] :
% 4.71/5.11 ( ( minus_minus_rat @ zero_zero_rat @ B )
% 4.71/5.11 = ( uminus_uminus_rat @ B ) ) ).
% 4.71/5.11
% 4.71/5.11 % verit_minus_simplify(3)
% 4.71/5.11 thf(fact_4287_verit__minus__simplify_I3_J,axiom,
% 4.71/5.11 ! [B: complex] :
% 4.71/5.11 ( ( minus_minus_complex @ zero_zero_complex @ B )
% 4.71/5.11 = ( uminus1482373934393186551omplex @ B ) ) ).
% 4.71/5.11
% 4.71/5.11 % verit_minus_simplify(3)
% 4.71/5.11 thf(fact_4288_mult__minus1__right,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 4.71/5.11 = ( uminus_uminus_int @ Z ) ) ).
% 4.71/5.11
% 4.71/5.11 % mult_minus1_right
% 4.71/5.11 thf(fact_4289_mult__minus1__right,axiom,
% 4.71/5.11 ! [Z: real] :
% 4.71/5.11 ( ( times_times_real @ Z @ ( uminus_uminus_real @ one_one_real ) )
% 4.71/5.11 = ( uminus_uminus_real @ Z ) ) ).
% 4.71/5.11
% 4.71/5.11 % mult_minus1_right
% 4.71/5.11 thf(fact_4290_mult__minus1__right,axiom,
% 4.71/5.11 ! [Z: rat] :
% 4.71/5.11 ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 4.71/5.11 = ( uminus_uminus_rat @ Z ) ) ).
% 4.71/5.11
% 4.71/5.11 % mult_minus1_right
% 4.71/5.11 thf(fact_4291_mult__minus1__right,axiom,
% 4.71/5.11 ! [Z: complex] :
% 4.71/5.11 ( ( times_times_complex @ Z @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 4.71/5.11 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 4.71/5.11
% 4.71/5.11 % mult_minus1_right
% 4.71/5.11 thf(fact_4292_mult__minus1,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 4.71/5.11 = ( uminus_uminus_int @ Z ) ) ).
% 4.71/5.11
% 4.71/5.11 % mult_minus1
% 4.71/5.11 thf(fact_4293_mult__minus1,axiom,
% 4.71/5.11 ! [Z: real] :
% 4.71/5.11 ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z )
% 4.71/5.11 = ( uminus_uminus_real @ Z ) ) ).
% 4.71/5.11
% 4.71/5.11 % mult_minus1
% 4.71/5.11 thf(fact_4294_mult__minus1,axiom,
% 4.71/5.11 ! [Z: rat] :
% 4.71/5.11 ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 4.71/5.11 = ( uminus_uminus_rat @ Z ) ) ).
% 4.71/5.11
% 4.71/5.11 % mult_minus1
% 4.71/5.11 thf(fact_4295_mult__minus1,axiom,
% 4.71/5.11 ! [Z: complex] :
% 4.71/5.11 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z )
% 4.71/5.11 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 4.71/5.11
% 4.71/5.11 % mult_minus1
% 4.71/5.11 thf(fact_4296_uminus__add__conv__diff,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 4.71/5.11 = ( minus_minus_int @ B @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % uminus_add_conv_diff
% 4.71/5.11 thf(fact_4297_uminus__add__conv__diff,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 4.71/5.11 = ( minus_minus_real @ B @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % uminus_add_conv_diff
% 4.71/5.11 thf(fact_4298_uminus__add__conv__diff,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 4.71/5.11 = ( minus_minus_rat @ B @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % uminus_add_conv_diff
% 4.71/5.11 thf(fact_4299_uminus__add__conv__diff,axiom,
% 4.71/5.11 ! [A: complex,B: complex] :
% 4.71/5.11 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 4.71/5.11 = ( minus_minus_complex @ B @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % uminus_add_conv_diff
% 4.71/5.11 thf(fact_4300_diff__minus__eq__add,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 4.71/5.11 = ( plus_plus_int @ A @ B ) ) ).
% 4.71/5.11
% 4.71/5.11 % diff_minus_eq_add
% 4.71/5.11 thf(fact_4301_diff__minus__eq__add,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 4.71/5.11 = ( plus_plus_real @ A @ B ) ) ).
% 4.71/5.11
% 4.71/5.11 % diff_minus_eq_add
% 4.71/5.11 thf(fact_4302_diff__minus__eq__add,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 4.71/5.11 = ( plus_plus_rat @ A @ B ) ) ).
% 4.71/5.11
% 4.71/5.11 % diff_minus_eq_add
% 4.71/5.11 thf(fact_4303_diff__minus__eq__add,axiom,
% 4.71/5.11 ! [A: complex,B: complex] :
% 4.71/5.11 ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 4.71/5.11 = ( plus_plus_complex @ A @ B ) ) ).
% 4.71/5.11
% 4.71/5.11 % diff_minus_eq_add
% 4.71/5.11 thf(fact_4304_divide__minus1,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ( ( divide_divide_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 4.71/5.11 = ( uminus_uminus_real @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % divide_minus1
% 4.71/5.11 thf(fact_4305_divide__minus1,axiom,
% 4.71/5.11 ! [X: rat] :
% 4.71/5.11 ( ( divide_divide_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) )
% 4.71/5.11 = ( uminus_uminus_rat @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % divide_minus1
% 4.71/5.11 thf(fact_4306_divide__minus1,axiom,
% 4.71/5.11 ! [X: complex] :
% 4.71/5.11 ( ( divide1717551699836669952omplex @ X @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 4.71/5.11 = ( uminus1482373934393186551omplex @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % divide_minus1
% 4.71/5.11 thf(fact_4307_div__minus1__right,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 4.71/5.11 = ( uminus_uminus_int @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % div_minus1_right
% 4.71/5.11 thf(fact_4308_abs__neg__one,axiom,
% 4.71/5.11 ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 4.71/5.11 = one_one_int ) ).
% 4.71/5.11
% 4.71/5.11 % abs_neg_one
% 4.71/5.11 thf(fact_4309_abs__neg__one,axiom,
% 4.71/5.11 ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 4.71/5.11 = one_one_real ) ).
% 4.71/5.11
% 4.71/5.11 % abs_neg_one
% 4.71/5.11 thf(fact_4310_abs__neg__one,axiom,
% 4.71/5.11 ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 4.71/5.11 = one_one_rat ) ).
% 4.71/5.11
% 4.71/5.11 % abs_neg_one
% 4.71/5.11 thf(fact_4311_sgn__less,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( ord_less_real @ ( sgn_sgn_real @ A ) @ zero_zero_real )
% 4.71/5.11 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_less
% 4.71/5.11 thf(fact_4312_sgn__less,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( ord_less_rat @ ( sgn_sgn_rat @ A ) @ zero_zero_rat )
% 4.71/5.11 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_less
% 4.71/5.11 thf(fact_4313_sgn__less,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( ord_less_int @ ( sgn_sgn_int @ A ) @ zero_zero_int )
% 4.71/5.11 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_less
% 4.71/5.11 thf(fact_4314_sgn__greater,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( ord_less_real @ zero_zero_real @ ( sgn_sgn_real @ A ) )
% 4.71/5.11 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_greater
% 4.71/5.11 thf(fact_4315_sgn__greater,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( ord_less_rat @ zero_zero_rat @ ( sgn_sgn_rat @ A ) )
% 4.71/5.11 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_greater
% 4.71/5.11 thf(fact_4316_sgn__greater,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( ord_less_int @ zero_zero_int @ ( sgn_sgn_int @ A ) )
% 4.71/5.11 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_greater
% 4.71/5.11 thf(fact_4317_subset__Compl__singleton,axiom,
% 4.71/5.11 ! [A2: set_Pr1261947904930325089at_nat,B: product_prod_nat_nat] :
% 4.71/5.11 ( ( ord_le3146513528884898305at_nat @ A2 @ ( uminus6524753893492686040at_nat @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) ) )
% 4.71/5.11 = ( ~ ( member8440522571783428010at_nat @ B @ A2 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % subset_Compl_singleton
% 4.71/5.11 thf(fact_4318_subset__Compl__singleton,axiom,
% 4.71/5.11 ! [A2: set_set_nat,B: set_nat] :
% 4.71/5.11 ( ( ord_le6893508408891458716et_nat @ A2 @ ( uminus613421341184616069et_nat @ ( insert_set_nat @ B @ bot_bot_set_set_nat ) ) )
% 4.71/5.11 = ( ~ ( member_set_nat @ B @ A2 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % subset_Compl_singleton
% 4.71/5.11 thf(fact_4319_subset__Compl__singleton,axiom,
% 4.71/5.11 ! [A2: set_set_nat_rat,B: set_nat_rat] :
% 4.71/5.11 ( ( ord_le4375437777232675859at_rat @ A2 @ ( uminus3098529973357106300at_rat @ ( insert_set_nat_rat @ B @ bot_bo6797373522285170759at_rat ) ) )
% 4.71/5.11 = ( ~ ( member_set_nat_rat @ B @ A2 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % subset_Compl_singleton
% 4.71/5.11 thf(fact_4320_subset__Compl__singleton,axiom,
% 4.71/5.11 ! [A2: set_real,B: real] :
% 4.71/5.11 ( ( ord_less_eq_set_real @ A2 @ ( uminus612125837232591019t_real @ ( insert_real @ B @ bot_bot_set_real ) ) )
% 4.71/5.11 = ( ~ ( member_real @ B @ A2 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % subset_Compl_singleton
% 4.71/5.11 thf(fact_4321_subset__Compl__singleton,axiom,
% 4.71/5.11 ! [A2: set_o,B: $o] :
% 4.71/5.11 ( ( ord_less_eq_set_o @ A2 @ ( uminus_uminus_set_o @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 4.71/5.11 = ( ~ ( member_o @ B @ A2 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % subset_Compl_singleton
% 4.71/5.11 thf(fact_4322_subset__Compl__singleton,axiom,
% 4.71/5.11 ! [A2: set_nat,B: nat] :
% 4.71/5.11 ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 4.71/5.11 = ( ~ ( member_nat @ B @ A2 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % subset_Compl_singleton
% 4.71/5.11 thf(fact_4323_subset__Compl__singleton,axiom,
% 4.71/5.11 ! [A2: set_int,B: int] :
% 4.71/5.11 ( ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 4.71/5.11 = ( ~ ( member_int @ B @ A2 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % subset_Compl_singleton
% 4.71/5.11 thf(fact_4324_powr__zero__eq__one,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ( ( ( X = zero_zero_real )
% 4.71/5.11 => ( ( powr_real @ X @ zero_zero_real )
% 4.71/5.11 = zero_zero_real ) )
% 4.71/5.11 & ( ( X != zero_zero_real )
% 4.71/5.11 => ( ( powr_real @ X @ zero_zero_real )
% 4.71/5.11 = one_one_real ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % powr_zero_eq_one
% 4.71/5.11 thf(fact_4325_negative__eq__positive,axiom,
% 4.71/5.11 ! [N: nat,M2: nat] :
% 4.71/5.11 ( ( ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) )
% 4.71/5.11 = ( semiri1314217659103216013at_int @ M2 ) )
% 4.71/5.11 = ( ( N = zero_zero_nat )
% 4.71/5.11 & ( M2 = zero_zero_nat ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % negative_eq_positive
% 4.71/5.11 thf(fact_4326_real__add__minus__iff,axiom,
% 4.71/5.11 ! [X: real,A: real] :
% 4.71/5.11 ( ( ( plus_plus_real @ X @ ( uminus_uminus_real @ A ) )
% 4.71/5.11 = zero_zero_real )
% 4.71/5.11 = ( X = A ) ) ).
% 4.71/5.11
% 4.71/5.11 % real_add_minus_iff
% 4.71/5.11 thf(fact_4327_powr__nonneg__iff,axiom,
% 4.71/5.11 ! [A: real,X: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ ( powr_real @ A @ X ) @ zero_zero_real )
% 4.71/5.11 = ( A = zero_zero_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % powr_nonneg_iff
% 4.71/5.11 thf(fact_4328_Gcd__empty,axiom,
% 4.71/5.11 ( ( gcd_Gcd_nat @ bot_bot_set_nat )
% 4.71/5.11 = zero_zero_nat ) ).
% 4.71/5.11
% 4.71/5.11 % Gcd_empty
% 4.71/5.11 thf(fact_4329_Gcd__empty,axiom,
% 4.71/5.11 ( ( gcd_Gcd_int @ bot_bot_set_int )
% 4.71/5.11 = zero_zero_int ) ).
% 4.71/5.11
% 4.71/5.11 % Gcd_empty
% 4.71/5.11 thf(fact_4330_negative__zle,axiom,
% 4.71/5.11 ! [N: nat,M2: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ ( semiri1314217659103216013at_int @ M2 ) ) ).
% 4.71/5.11
% 4.71/5.11 % negative_zle
% 4.71/5.11 thf(fact_4331_dbl__inc__simps_I4_J,axiom,
% 4.71/5.11 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 4.71/5.11 = ( uminus_uminus_int @ one_one_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % dbl_inc_simps(4)
% 4.71/5.11 thf(fact_4332_dbl__inc__simps_I4_J,axiom,
% 4.71/5.11 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 4.71/5.11 = ( uminus_uminus_real @ one_one_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % dbl_inc_simps(4)
% 4.71/5.11 thf(fact_4333_dbl__inc__simps_I4_J,axiom,
% 4.71/5.11 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 4.71/5.11 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % dbl_inc_simps(4)
% 4.71/5.11 thf(fact_4334_dbl__inc__simps_I4_J,axiom,
% 4.71/5.11 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 4.71/5.11 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 4.71/5.11
% 4.71/5.11 % dbl_inc_simps(4)
% 4.71/5.11 thf(fact_4335_add__neg__numeral__special_I8_J,axiom,
% 4.71/5.11 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 4.71/5.11 = zero_zero_int ) ).
% 4.71/5.11
% 4.71/5.11 % add_neg_numeral_special(8)
% 4.71/5.11 thf(fact_4336_add__neg__numeral__special_I8_J,axiom,
% 4.71/5.11 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 4.71/5.11 = zero_zero_real ) ).
% 4.71/5.11
% 4.71/5.11 % add_neg_numeral_special(8)
% 4.71/5.11 thf(fact_4337_add__neg__numeral__special_I8_J,axiom,
% 4.71/5.11 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 4.71/5.11 = zero_zero_rat ) ).
% 4.71/5.11
% 4.71/5.11 % add_neg_numeral_special(8)
% 4.71/5.11 thf(fact_4338_add__neg__numeral__special_I8_J,axiom,
% 4.71/5.11 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 4.71/5.11 = zero_zero_complex ) ).
% 4.71/5.11
% 4.71/5.11 % add_neg_numeral_special(8)
% 4.71/5.11 thf(fact_4339_add__neg__numeral__special_I7_J,axiom,
% 4.71/5.11 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 4.71/5.11 = zero_zero_int ) ).
% 4.71/5.11
% 4.71/5.11 % add_neg_numeral_special(7)
% 4.71/5.11 thf(fact_4340_add__neg__numeral__special_I7_J,axiom,
% 4.71/5.11 ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 4.71/5.11 = zero_zero_real ) ).
% 4.71/5.11
% 4.71/5.11 % add_neg_numeral_special(7)
% 4.71/5.11 thf(fact_4341_add__neg__numeral__special_I7_J,axiom,
% 4.71/5.11 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 4.71/5.11 = zero_zero_rat ) ).
% 4.71/5.11
% 4.71/5.11 % add_neg_numeral_special(7)
% 4.71/5.11 thf(fact_4342_add__neg__numeral__special_I7_J,axiom,
% 4.71/5.11 ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 4.71/5.11 = zero_zero_complex ) ).
% 4.71/5.11
% 4.71/5.11 % add_neg_numeral_special(7)
% 4.71/5.11 thf(fact_4343_diff__numeral__special_I12_J,axiom,
% 4.71/5.11 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 4.71/5.11 = zero_zero_int ) ).
% 4.71/5.11
% 4.71/5.11 % diff_numeral_special(12)
% 4.71/5.11 thf(fact_4344_diff__numeral__special_I12_J,axiom,
% 4.71/5.11 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 4.71/5.11 = zero_zero_real ) ).
% 4.71/5.11
% 4.71/5.11 % diff_numeral_special(12)
% 4.71/5.11 thf(fact_4345_diff__numeral__special_I12_J,axiom,
% 4.71/5.11 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 4.71/5.11 = zero_zero_rat ) ).
% 4.71/5.11
% 4.71/5.11 % diff_numeral_special(12)
% 4.71/5.11 thf(fact_4346_diff__numeral__special_I12_J,axiom,
% 4.71/5.11 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 4.71/5.11 = zero_zero_complex ) ).
% 4.71/5.11
% 4.71/5.11 % diff_numeral_special(12)
% 4.71/5.11 thf(fact_4347_left__minus__one__mult__self,axiom,
% 4.71/5.11 ! [N: nat,A: int] :
% 4.71/5.11 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ A ) )
% 4.71/5.11 = A ) ).
% 4.71/5.11
% 4.71/5.11 % left_minus_one_mult_self
% 4.71/5.11 thf(fact_4348_left__minus__one__mult__self,axiom,
% 4.71/5.11 ! [N: nat,A: real] :
% 4.71/5.11 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ A ) )
% 4.71/5.11 = A ) ).
% 4.71/5.11
% 4.71/5.11 % left_minus_one_mult_self
% 4.71/5.11 thf(fact_4349_left__minus__one__mult__self,axiom,
% 4.71/5.11 ! [N: nat,A: rat] :
% 4.71/5.11 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ A ) )
% 4.71/5.11 = A ) ).
% 4.71/5.11
% 4.71/5.11 % left_minus_one_mult_self
% 4.71/5.11 thf(fact_4350_left__minus__one__mult__self,axiom,
% 4.71/5.11 ! [N: nat,A: complex] :
% 4.71/5.11 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ A ) )
% 4.71/5.11 = A ) ).
% 4.71/5.11
% 4.71/5.11 % left_minus_one_mult_self
% 4.71/5.11 thf(fact_4351_minus__one__mult__self,axiom,
% 4.71/5.11 ! [N: nat] :
% 4.71/5.11 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) )
% 4.71/5.11 = one_one_int ) ).
% 4.71/5.11
% 4.71/5.11 % minus_one_mult_self
% 4.71/5.11 thf(fact_4352_minus__one__mult__self,axiom,
% 4.71/5.11 ! [N: nat] :
% 4.71/5.11 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) )
% 4.71/5.11 = one_one_real ) ).
% 4.71/5.11
% 4.71/5.11 % minus_one_mult_self
% 4.71/5.11 thf(fact_4353_minus__one__mult__self,axiom,
% 4.71/5.11 ! [N: nat] :
% 4.71/5.11 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) )
% 4.71/5.11 = one_one_rat ) ).
% 4.71/5.11
% 4.71/5.11 % minus_one_mult_self
% 4.71/5.11 thf(fact_4354_minus__one__mult__self,axiom,
% 4.71/5.11 ! [N: nat] :
% 4.71/5.11 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) )
% 4.71/5.11 = one_one_complex ) ).
% 4.71/5.11
% 4.71/5.11 % minus_one_mult_self
% 4.71/5.11 thf(fact_4355_abs__of__nonpos,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 4.71/5.11 => ( ( abs_abs_real @ A )
% 4.71/5.11 = ( uminus_uminus_real @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_of_nonpos
% 4.71/5.11 thf(fact_4356_abs__of__nonpos,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 4.71/5.11 => ( ( abs_abs_rat @ A )
% 4.71/5.11 = ( uminus_uminus_rat @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_of_nonpos
% 4.71/5.11 thf(fact_4357_abs__of__nonpos,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 4.71/5.11 => ( ( abs_abs_int @ A )
% 4.71/5.11 = ( uminus_uminus_int @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_of_nonpos
% 4.71/5.11 thf(fact_4358_sgn__pos,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.11 => ( ( sgn_sgn_real @ A )
% 4.71/5.11 = one_one_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_pos
% 4.71/5.11 thf(fact_4359_sgn__pos,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.11 => ( ( sgn_sgn_rat @ A )
% 4.71/5.11 = one_one_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_pos
% 4.71/5.11 thf(fact_4360_sgn__pos,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( ord_less_int @ zero_zero_int @ A )
% 4.71/5.11 => ( ( sgn_sgn_int @ A )
% 4.71/5.11 = one_one_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_pos
% 4.71/5.11 thf(fact_4361_abs__sgn__eq__1,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( A != zero_zero_real )
% 4.71/5.11 => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 4.71/5.11 = one_one_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_sgn_eq_1
% 4.71/5.11 thf(fact_4362_abs__sgn__eq__1,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( A != zero_zero_rat )
% 4.71/5.11 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 4.71/5.11 = one_one_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_sgn_eq_1
% 4.71/5.11 thf(fact_4363_abs__sgn__eq__1,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( A != zero_zero_int )
% 4.71/5.11 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 4.71/5.11 = one_one_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_sgn_eq_1
% 4.71/5.11 thf(fact_4364_powr__one,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.11 => ( ( powr_real @ X @ one_one_real )
% 4.71/5.11 = X ) ) ).
% 4.71/5.11
% 4.71/5.11 % powr_one
% 4.71/5.11 thf(fact_4365_powr__one__gt__zero__iff,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ( ( ( powr_real @ X @ one_one_real )
% 4.71/5.11 = X )
% 4.71/5.11 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % powr_one_gt_zero_iff
% 4.71/5.11 thf(fact_4366_powr__le__cancel__iff,axiom,
% 4.71/5.11 ! [X: real,A: real,B: real] :
% 4.71/5.11 ( ( ord_less_real @ one_one_real @ X )
% 4.71/5.11 => ( ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 4.71/5.11 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % powr_le_cancel_iff
% 4.71/5.11 thf(fact_4367_nat__zminus__int,axiom,
% 4.71/5.11 ! [N: nat] :
% 4.71/5.11 ( ( nat2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
% 4.71/5.11 = zero_zero_nat ) ).
% 4.71/5.11
% 4.71/5.11 % nat_zminus_int
% 4.71/5.11 thf(fact_4368_sgn__neg,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( ord_less_int @ A @ zero_zero_int )
% 4.71/5.11 => ( ( sgn_sgn_int @ A )
% 4.71/5.11 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_neg
% 4.71/5.11 thf(fact_4369_sgn__neg,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( ord_less_real @ A @ zero_zero_real )
% 4.71/5.11 => ( ( sgn_sgn_real @ A )
% 4.71/5.11 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_neg
% 4.71/5.11 thf(fact_4370_sgn__neg,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.71/5.11 => ( ( sgn_sgn_rat @ A )
% 4.71/5.11 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_neg
% 4.71/5.11 thf(fact_4371_minus__equation__iff,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( ( uminus_uminus_int @ A )
% 4.71/5.11 = B )
% 4.71/5.11 = ( ( uminus_uminus_int @ B )
% 4.71/5.11 = A ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_equation_iff
% 4.71/5.11 thf(fact_4372_minus__equation__iff,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( ( uminus_uminus_real @ A )
% 4.71/5.11 = B )
% 4.71/5.11 = ( ( uminus_uminus_real @ B )
% 4.71/5.11 = A ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_equation_iff
% 4.71/5.11 thf(fact_4373_minus__equation__iff,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( ( uminus_uminus_rat @ A )
% 4.71/5.11 = B )
% 4.71/5.11 = ( ( uminus_uminus_rat @ B )
% 4.71/5.11 = A ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_equation_iff
% 4.71/5.11 thf(fact_4374_minus__equation__iff,axiom,
% 4.71/5.11 ! [A: complex,B: complex] :
% 4.71/5.11 ( ( ( uminus1482373934393186551omplex @ A )
% 4.71/5.11 = B )
% 4.71/5.11 = ( ( uminus1482373934393186551omplex @ B )
% 4.71/5.11 = A ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_equation_iff
% 4.71/5.11 thf(fact_4375_equation__minus__iff,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( A
% 4.71/5.11 = ( uminus_uminus_int @ B ) )
% 4.71/5.11 = ( B
% 4.71/5.11 = ( uminus_uminus_int @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % equation_minus_iff
% 4.71/5.11 thf(fact_4376_equation__minus__iff,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( A
% 4.71/5.11 = ( uminus_uminus_real @ B ) )
% 4.71/5.11 = ( B
% 4.71/5.11 = ( uminus_uminus_real @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % equation_minus_iff
% 4.71/5.11 thf(fact_4377_equation__minus__iff,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( A
% 4.71/5.11 = ( uminus_uminus_rat @ B ) )
% 4.71/5.11 = ( B
% 4.71/5.11 = ( uminus_uminus_rat @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % equation_minus_iff
% 4.71/5.11 thf(fact_4378_equation__minus__iff,axiom,
% 4.71/5.11 ! [A: complex,B: complex] :
% 4.71/5.11 ( ( A
% 4.71/5.11 = ( uminus1482373934393186551omplex @ B ) )
% 4.71/5.11 = ( B
% 4.71/5.11 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % equation_minus_iff
% 4.71/5.11 thf(fact_4379_sgn__minus__1,axiom,
% 4.71/5.11 ( ( sgn_sgn_int @ ( uminus_uminus_int @ one_one_int ) )
% 4.71/5.11 = ( uminus_uminus_int @ one_one_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_minus_1
% 4.71/5.11 thf(fact_4380_sgn__minus__1,axiom,
% 4.71/5.11 ( ( sgn_sgn_real @ ( uminus_uminus_real @ one_one_real ) )
% 4.71/5.11 = ( uminus_uminus_real @ one_one_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_minus_1
% 4.71/5.11 thf(fact_4381_sgn__minus__1,axiom,
% 4.71/5.11 ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 4.71/5.11 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_minus_1
% 4.71/5.11 thf(fact_4382_sgn__minus__1,axiom,
% 4.71/5.11 ( ( sgn_sgn_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 4.71/5.11 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_minus_1
% 4.71/5.11 thf(fact_4383_sgn__not__eq__imp,axiom,
% 4.71/5.11 ! [B: int,A: int] :
% 4.71/5.11 ( ( ( sgn_sgn_int @ B )
% 4.71/5.11 != ( sgn_sgn_int @ A ) )
% 4.71/5.11 => ( ( ( sgn_sgn_int @ A )
% 4.71/5.11 != zero_zero_int )
% 4.71/5.11 => ( ( ( sgn_sgn_int @ B )
% 4.71/5.11 != zero_zero_int )
% 4.71/5.11 => ( ( sgn_sgn_int @ A )
% 4.71/5.11 = ( uminus_uminus_int @ ( sgn_sgn_int @ B ) ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_not_eq_imp
% 4.71/5.11 thf(fact_4384_sgn__not__eq__imp,axiom,
% 4.71/5.11 ! [B: real,A: real] :
% 4.71/5.11 ( ( ( sgn_sgn_real @ B )
% 4.71/5.11 != ( sgn_sgn_real @ A ) )
% 4.71/5.11 => ( ( ( sgn_sgn_real @ A )
% 4.71/5.11 != zero_zero_real )
% 4.71/5.11 => ( ( ( sgn_sgn_real @ B )
% 4.71/5.11 != zero_zero_real )
% 4.71/5.11 => ( ( sgn_sgn_real @ A )
% 4.71/5.11 = ( uminus_uminus_real @ ( sgn_sgn_real @ B ) ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_not_eq_imp
% 4.71/5.11 thf(fact_4385_sgn__not__eq__imp,axiom,
% 4.71/5.11 ! [B: rat,A: rat] :
% 4.71/5.11 ( ( ( sgn_sgn_rat @ B )
% 4.71/5.11 != ( sgn_sgn_rat @ A ) )
% 4.71/5.11 => ( ( ( sgn_sgn_rat @ A )
% 4.71/5.11 != zero_zero_rat )
% 4.71/5.11 => ( ( ( sgn_sgn_rat @ B )
% 4.71/5.11 != zero_zero_rat )
% 4.71/5.11 => ( ( sgn_sgn_rat @ A )
% 4.71/5.11 = ( uminus_uminus_rat @ ( sgn_sgn_rat @ B ) ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_not_eq_imp
% 4.71/5.11 thf(fact_4386_sgn__0__0,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( ( sgn_sgn_real @ A )
% 4.71/5.11 = zero_zero_real )
% 4.71/5.11 = ( A = zero_zero_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_0_0
% 4.71/5.11 thf(fact_4387_sgn__0__0,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( ( sgn_sgn_rat @ A )
% 4.71/5.11 = zero_zero_rat )
% 4.71/5.11 = ( A = zero_zero_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_0_0
% 4.71/5.11 thf(fact_4388_sgn__0__0,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( ( sgn_sgn_int @ A )
% 4.71/5.11 = zero_zero_int )
% 4.71/5.11 = ( A = zero_zero_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_0_0
% 4.71/5.11 thf(fact_4389_sgn__eq__0__iff,axiom,
% 4.71/5.11 ! [A: complex] :
% 4.71/5.11 ( ( ( sgn_sgn_complex @ A )
% 4.71/5.11 = zero_zero_complex )
% 4.71/5.11 = ( A = zero_zero_complex ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_eq_0_iff
% 4.71/5.11 thf(fact_4390_sgn__eq__0__iff,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( ( sgn_sgn_real @ A )
% 4.71/5.11 = zero_zero_real )
% 4.71/5.11 = ( A = zero_zero_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_eq_0_iff
% 4.71/5.11 thf(fact_4391_sgn__eq__0__iff,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( ( sgn_sgn_rat @ A )
% 4.71/5.11 = zero_zero_rat )
% 4.71/5.11 = ( A = zero_zero_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_eq_0_iff
% 4.71/5.11 thf(fact_4392_sgn__eq__0__iff,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( ( sgn_sgn_int @ A )
% 4.71/5.11 = zero_zero_int )
% 4.71/5.11 = ( A = zero_zero_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_eq_0_iff
% 4.71/5.11 thf(fact_4393_sgn__mult,axiom,
% 4.71/5.11 ! [A: complex,B: complex] :
% 4.71/5.11 ( ( sgn_sgn_complex @ ( times_times_complex @ A @ B ) )
% 4.71/5.11 = ( times_times_complex @ ( sgn_sgn_complex @ A ) @ ( sgn_sgn_complex @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_mult
% 4.71/5.11 thf(fact_4394_sgn__mult,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( sgn_sgn_real @ ( times_times_real @ A @ B ) )
% 4.71/5.11 = ( times_times_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_mult
% 4.71/5.11 thf(fact_4395_sgn__mult,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( sgn_sgn_rat @ ( times_times_rat @ A @ B ) )
% 4.71/5.11 = ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_mult
% 4.71/5.11 thf(fact_4396_sgn__mult,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( sgn_sgn_int @ ( times_times_int @ A @ B ) )
% 4.71/5.11 = ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_mult
% 4.71/5.11 thf(fact_4397_same__sgn__sgn__add,axiom,
% 4.71/5.11 ! [B: real,A: real] :
% 4.71/5.11 ( ( ( sgn_sgn_real @ B )
% 4.71/5.11 = ( sgn_sgn_real @ A ) )
% 4.71/5.11 => ( ( sgn_sgn_real @ ( plus_plus_real @ A @ B ) )
% 4.71/5.11 = ( sgn_sgn_real @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % same_sgn_sgn_add
% 4.71/5.11 thf(fact_4398_same__sgn__sgn__add,axiom,
% 4.71/5.11 ! [B: rat,A: rat] :
% 4.71/5.11 ( ( ( sgn_sgn_rat @ B )
% 4.71/5.11 = ( sgn_sgn_rat @ A ) )
% 4.71/5.11 => ( ( sgn_sgn_rat @ ( plus_plus_rat @ A @ B ) )
% 4.71/5.11 = ( sgn_sgn_rat @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % same_sgn_sgn_add
% 4.71/5.11 thf(fact_4399_same__sgn__sgn__add,axiom,
% 4.71/5.11 ! [B: int,A: int] :
% 4.71/5.11 ( ( ( sgn_sgn_int @ B )
% 4.71/5.11 = ( sgn_sgn_int @ A ) )
% 4.71/5.11 => ( ( sgn_sgn_int @ ( plus_plus_int @ A @ B ) )
% 4.71/5.11 = ( sgn_sgn_int @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % same_sgn_sgn_add
% 4.71/5.11 thf(fact_4400_le__imp__neg__le,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ A @ B )
% 4.71/5.11 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % le_imp_neg_le
% 4.71/5.11 thf(fact_4401_le__imp__neg__le,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.11 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % le_imp_neg_le
% 4.71/5.11 thf(fact_4402_le__imp__neg__le,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ A @ B )
% 4.71/5.11 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % le_imp_neg_le
% 4.71/5.11 thf(fact_4403_minus__le__iff,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 4.71/5.11 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_le_iff
% 4.71/5.11 thf(fact_4404_minus__le__iff,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 4.71/5.11 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_le_iff
% 4.71/5.11 thf(fact_4405_minus__le__iff,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 4.71/5.11 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_le_iff
% 4.71/5.11 thf(fact_4406_le__minus__iff,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 4.71/5.11 = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % le_minus_iff
% 4.71/5.11 thf(fact_4407_le__minus__iff,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 4.71/5.11 = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % le_minus_iff
% 4.71/5.11 thf(fact_4408_le__minus__iff,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 4.71/5.11 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % le_minus_iff
% 4.71/5.11 thf(fact_4409_compl__mono,axiom,
% 4.71/5.11 ! [X: set_int,Y: set_int] :
% 4.71/5.11 ( ( ord_less_eq_set_int @ X @ Y )
% 4.71/5.11 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ ( uminus1532241313380277803et_int @ X ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % compl_mono
% 4.71/5.11 thf(fact_4410_compl__le__swap1,axiom,
% 4.71/5.11 ! [Y: set_int,X: set_int] :
% 4.71/5.11 ( ( ord_less_eq_set_int @ Y @ ( uminus1532241313380277803et_int @ X ) )
% 4.71/5.11 => ( ord_less_eq_set_int @ X @ ( uminus1532241313380277803et_int @ Y ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % compl_le_swap1
% 4.71/5.11 thf(fact_4411_compl__le__swap2,axiom,
% 4.71/5.11 ! [Y: set_int,X: set_int] :
% 4.71/5.11 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ X )
% 4.71/5.11 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X ) @ Y ) ) ).
% 4.71/5.11
% 4.71/5.11 % compl_le_swap2
% 4.71/5.11 thf(fact_4412_less__minus__iff,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 4.71/5.11 = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % less_minus_iff
% 4.71/5.11 thf(fact_4413_less__minus__iff,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 4.71/5.11 = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % less_minus_iff
% 4.71/5.11 thf(fact_4414_less__minus__iff,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 4.71/5.11 = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % less_minus_iff
% 4.71/5.11 thf(fact_4415_minus__less__iff,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 4.71/5.11 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_less_iff
% 4.71/5.11 thf(fact_4416_minus__less__iff,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 4.71/5.11 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_less_iff
% 4.71/5.11 thf(fact_4417_minus__less__iff,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 4.71/5.11 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_less_iff
% 4.71/5.11 thf(fact_4418_verit__negate__coefficient_I2_J,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( ord_less_int @ A @ B )
% 4.71/5.11 => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % verit_negate_coefficient(2)
% 4.71/5.11 thf(fact_4419_verit__negate__coefficient_I2_J,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( ord_less_real @ A @ B )
% 4.71/5.11 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % verit_negate_coefficient(2)
% 4.71/5.11 thf(fact_4420_verit__negate__coefficient_I2_J,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( ord_less_rat @ A @ B )
% 4.71/5.11 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % verit_negate_coefficient(2)
% 4.71/5.11 thf(fact_4421_minus__mult__commute,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 4.71/5.11 = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_mult_commute
% 4.71/5.11 thf(fact_4422_minus__mult__commute,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 4.71/5.11 = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_mult_commute
% 4.71/5.11 thf(fact_4423_minus__mult__commute,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 4.71/5.11 = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_mult_commute
% 4.71/5.11 thf(fact_4424_minus__mult__commute,axiom,
% 4.71/5.11 ! [A: complex,B: complex] :
% 4.71/5.11 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 4.71/5.11 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_mult_commute
% 4.71/5.11 thf(fact_4425_square__eq__iff,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( ( times_times_int @ A @ A )
% 4.71/5.11 = ( times_times_int @ B @ B ) )
% 4.71/5.11 = ( ( A = B )
% 4.71/5.11 | ( A
% 4.71/5.11 = ( uminus_uminus_int @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % square_eq_iff
% 4.71/5.11 thf(fact_4426_square__eq__iff,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( ( times_times_real @ A @ A )
% 4.71/5.11 = ( times_times_real @ B @ B ) )
% 4.71/5.11 = ( ( A = B )
% 4.71/5.11 | ( A
% 4.71/5.11 = ( uminus_uminus_real @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % square_eq_iff
% 4.71/5.11 thf(fact_4427_square__eq__iff,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( ( times_times_rat @ A @ A )
% 4.71/5.11 = ( times_times_rat @ B @ B ) )
% 4.71/5.11 = ( ( A = B )
% 4.71/5.11 | ( A
% 4.71/5.11 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % square_eq_iff
% 4.71/5.11 thf(fact_4428_square__eq__iff,axiom,
% 4.71/5.11 ! [A: complex,B: complex] :
% 4.71/5.11 ( ( ( times_times_complex @ A @ A )
% 4.71/5.11 = ( times_times_complex @ B @ B ) )
% 4.71/5.11 = ( ( A = B )
% 4.71/5.11 | ( A
% 4.71/5.11 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % square_eq_iff
% 4.71/5.11 thf(fact_4429_is__num__normalize_I8_J,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 4.71/5.11 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % is_num_normalize(8)
% 4.71/5.11 thf(fact_4430_is__num__normalize_I8_J,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 4.71/5.11 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % is_num_normalize(8)
% 4.71/5.11 thf(fact_4431_is__num__normalize_I8_J,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 4.71/5.11 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % is_num_normalize(8)
% 4.71/5.11 thf(fact_4432_is__num__normalize_I8_J,axiom,
% 4.71/5.11 ! [A: complex,B: complex] :
% 4.71/5.11 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 4.71/5.11 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % is_num_normalize(8)
% 4.71/5.11 thf(fact_4433_add_Oinverse__distrib__swap,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 4.71/5.11 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % add.inverse_distrib_swap
% 4.71/5.11 thf(fact_4434_add_Oinverse__distrib__swap,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 4.71/5.11 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % add.inverse_distrib_swap
% 4.71/5.11 thf(fact_4435_add_Oinverse__distrib__swap,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 4.71/5.11 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % add.inverse_distrib_swap
% 4.71/5.11 thf(fact_4436_add_Oinverse__distrib__swap,axiom,
% 4.71/5.11 ! [A: complex,B: complex] :
% 4.71/5.11 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 4.71/5.11 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % add.inverse_distrib_swap
% 4.71/5.11 thf(fact_4437_group__cancel_Oneg1,axiom,
% 4.71/5.11 ! [A2: int,K: int,A: int] :
% 4.71/5.11 ( ( A2
% 4.71/5.11 = ( plus_plus_int @ K @ A ) )
% 4.71/5.11 => ( ( uminus_uminus_int @ A2 )
% 4.71/5.11 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % group_cancel.neg1
% 4.71/5.11 thf(fact_4438_group__cancel_Oneg1,axiom,
% 4.71/5.11 ! [A2: real,K: real,A: real] :
% 4.71/5.11 ( ( A2
% 4.71/5.11 = ( plus_plus_real @ K @ A ) )
% 4.71/5.11 => ( ( uminus_uminus_real @ A2 )
% 4.71/5.11 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % group_cancel.neg1
% 4.71/5.11 thf(fact_4439_group__cancel_Oneg1,axiom,
% 4.71/5.11 ! [A2: rat,K: rat,A: rat] :
% 4.71/5.11 ( ( A2
% 4.71/5.11 = ( plus_plus_rat @ K @ A ) )
% 4.71/5.11 => ( ( uminus_uminus_rat @ A2 )
% 4.71/5.11 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % group_cancel.neg1
% 4.71/5.11 thf(fact_4440_group__cancel_Oneg1,axiom,
% 4.71/5.11 ! [A2: complex,K: complex,A: complex] :
% 4.71/5.11 ( ( A2
% 4.71/5.11 = ( plus_plus_complex @ K @ A ) )
% 4.71/5.11 => ( ( uminus1482373934393186551omplex @ A2 )
% 4.71/5.11 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % group_cancel.neg1
% 4.71/5.11 thf(fact_4441_one__neq__neg__one,axiom,
% 4.71/5.11 ( one_one_int
% 4.71/5.11 != ( uminus_uminus_int @ one_one_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % one_neq_neg_one
% 4.71/5.11 thf(fact_4442_one__neq__neg__one,axiom,
% 4.71/5.11 ( one_one_real
% 4.71/5.11 != ( uminus_uminus_real @ one_one_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % one_neq_neg_one
% 4.71/5.11 thf(fact_4443_one__neq__neg__one,axiom,
% 4.71/5.11 ( one_one_rat
% 4.71/5.11 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % one_neq_neg_one
% 4.71/5.11 thf(fact_4444_one__neq__neg__one,axiom,
% 4.71/5.11 ( one_one_complex
% 4.71/5.11 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 4.71/5.11
% 4.71/5.11 % one_neq_neg_one
% 4.71/5.11 thf(fact_4445_minus__diff__commute,axiom,
% 4.71/5.11 ! [B: int,A: int] :
% 4.71/5.11 ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 4.71/5.11 = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_diff_commute
% 4.71/5.11 thf(fact_4446_minus__diff__commute,axiom,
% 4.71/5.11 ! [B: real,A: real] :
% 4.71/5.11 ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 4.71/5.11 = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_diff_commute
% 4.71/5.11 thf(fact_4447_minus__diff__commute,axiom,
% 4.71/5.11 ! [B: rat,A: rat] :
% 4.71/5.11 ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 4.71/5.11 = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_diff_commute
% 4.71/5.11 thf(fact_4448_minus__diff__commute,axiom,
% 4.71/5.11 ! [B: complex,A: complex] :
% 4.71/5.11 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B ) @ A )
% 4.71/5.11 = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_diff_commute
% 4.71/5.11 thf(fact_4449_minus__diff__minus,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( minus_minus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 4.71/5.11 = ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_diff_minus
% 4.71/5.11 thf(fact_4450_minus__diff__minus,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 4.71/5.11 = ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_diff_minus
% 4.71/5.11 thf(fact_4451_minus__diff__minus,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 4.71/5.11 = ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_diff_minus
% 4.71/5.11 thf(fact_4452_minus__diff__minus,axiom,
% 4.71/5.11 ! [A: complex,B: complex] :
% 4.71/5.11 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 4.71/5.11 = ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_diff_minus
% 4.71/5.11 thf(fact_4453_powr__minus__divide,axiom,
% 4.71/5.11 ! [X: real,A: real] :
% 4.71/5.11 ( ( powr_real @ X @ ( uminus_uminus_real @ A ) )
% 4.71/5.11 = ( divide_divide_real @ one_one_real @ ( powr_real @ X @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % powr_minus_divide
% 4.71/5.11 thf(fact_4454_abs__eq__iff,axiom,
% 4.71/5.11 ! [X: int,Y: int] :
% 4.71/5.11 ( ( ( abs_abs_int @ X )
% 4.71/5.11 = ( abs_abs_int @ Y ) )
% 4.71/5.11 = ( ( X = Y )
% 4.71/5.11 | ( X
% 4.71/5.11 = ( uminus_uminus_int @ Y ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_eq_iff
% 4.71/5.11 thf(fact_4455_abs__eq__iff,axiom,
% 4.71/5.11 ! [X: real,Y: real] :
% 4.71/5.11 ( ( ( abs_abs_real @ X )
% 4.71/5.11 = ( abs_abs_real @ Y ) )
% 4.71/5.11 = ( ( X = Y )
% 4.71/5.11 | ( X
% 4.71/5.11 = ( uminus_uminus_real @ Y ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_eq_iff
% 4.71/5.11 thf(fact_4456_abs__eq__iff,axiom,
% 4.71/5.11 ! [X: rat,Y: rat] :
% 4.71/5.11 ( ( ( abs_abs_rat @ X )
% 4.71/5.11 = ( abs_abs_rat @ Y ) )
% 4.71/5.11 = ( ( X = Y )
% 4.71/5.11 | ( X
% 4.71/5.11 = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_eq_iff
% 4.71/5.11 thf(fact_4457_Gcd__nat__eq__one,axiom,
% 4.71/5.11 ! [N5: set_nat] :
% 4.71/5.11 ( ( member_nat @ one_one_nat @ N5 )
% 4.71/5.11 => ( ( gcd_Gcd_nat @ N5 )
% 4.71/5.11 = one_one_nat ) ) ).
% 4.71/5.11
% 4.71/5.11 % Gcd_nat_eq_one
% 4.71/5.11 thf(fact_4458_sgn__if,axiom,
% 4.71/5.11 ( sgn_sgn_int
% 4.71/5.11 = ( ^ [X3: int] : ( if_int @ ( X3 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ X3 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_if
% 4.71/5.11 thf(fact_4459_sgn__if,axiom,
% 4.71/5.11 ( sgn_sgn_real
% 4.71/5.11 = ( ^ [X3: real] : ( if_real @ ( X3 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ X3 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_if
% 4.71/5.11 thf(fact_4460_sgn__if,axiom,
% 4.71/5.11 ( sgn_sgn_rat
% 4.71/5.11 = ( ^ [X3: rat] : ( if_rat @ ( X3 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ X3 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_if
% 4.71/5.11 thf(fact_4461_sgn__1__neg,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( ( sgn_sgn_int @ A )
% 4.71/5.11 = ( uminus_uminus_int @ one_one_int ) )
% 4.71/5.11 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_1_neg
% 4.71/5.11 thf(fact_4462_sgn__1__neg,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( ( sgn_sgn_real @ A )
% 4.71/5.11 = ( uminus_uminus_real @ one_one_real ) )
% 4.71/5.11 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_1_neg
% 4.71/5.11 thf(fact_4463_sgn__1__neg,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( ( sgn_sgn_rat @ A )
% 4.71/5.11 = ( uminus_uminus_rat @ one_one_rat ) )
% 4.71/5.11 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_1_neg
% 4.71/5.11 thf(fact_4464_sgn__real__def,axiom,
% 4.71/5.11 ( sgn_sgn_real
% 4.71/5.11 = ( ^ [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 ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_real_def
% 4.71/5.11 thf(fact_4465_Gcd__1,axiom,
% 4.71/5.11 ! [A2: set_nat] :
% 4.71/5.11 ( ( member_nat @ one_one_nat @ A2 )
% 4.71/5.11 => ( ( gcd_Gcd_nat @ A2 )
% 4.71/5.11 = one_one_nat ) ) ).
% 4.71/5.11
% 4.71/5.11 % Gcd_1
% 4.71/5.11 thf(fact_4466_Gcd__1,axiom,
% 4.71/5.11 ! [A2: set_int] :
% 4.71/5.11 ( ( member_int @ one_one_int @ A2 )
% 4.71/5.11 => ( ( gcd_Gcd_int @ A2 )
% 4.71/5.11 = one_one_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % Gcd_1
% 4.71/5.11 thf(fact_4467_powr__mono2,axiom,
% 4.71/5.11 ! [A: real,X: real,Y: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.11 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.11 => ( ( ord_less_eq_real @ X @ Y )
% 4.71/5.11 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % powr_mono2
% 4.71/5.11 thf(fact_4468_powr__ge__pzero,axiom,
% 4.71/5.11 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X @ Y ) ) ).
% 4.71/5.11
% 4.71/5.11 % powr_ge_pzero
% 4.71/5.11 thf(fact_4469_powr__mono,axiom,
% 4.71/5.11 ! [A: real,B: real,X: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ A @ B )
% 4.71/5.11 => ( ( ord_less_eq_real @ one_one_real @ X )
% 4.71/5.11 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % powr_mono
% 4.71/5.11 thf(fact_4470_mult__sgn__abs,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ( ( times_times_real @ ( sgn_sgn_real @ X ) @ ( abs_abs_real @ X ) )
% 4.71/5.11 = X ) ).
% 4.71/5.11
% 4.71/5.11 % mult_sgn_abs
% 4.71/5.11 thf(fact_4471_mult__sgn__abs,axiom,
% 4.71/5.11 ! [X: rat] :
% 4.71/5.11 ( ( times_times_rat @ ( sgn_sgn_rat @ X ) @ ( abs_abs_rat @ X ) )
% 4.71/5.11 = X ) ).
% 4.71/5.11
% 4.71/5.11 % mult_sgn_abs
% 4.71/5.11 thf(fact_4472_mult__sgn__abs,axiom,
% 4.71/5.11 ! [X: int] :
% 4.71/5.11 ( ( times_times_int @ ( sgn_sgn_int @ X ) @ ( abs_abs_int @ X ) )
% 4.71/5.11 = X ) ).
% 4.71/5.11
% 4.71/5.11 % mult_sgn_abs
% 4.71/5.11 thf(fact_4473_sgn__mult__abs,axiom,
% 4.71/5.11 ! [A: complex] :
% 4.71/5.11 ( ( times_times_complex @ ( sgn_sgn_complex @ A ) @ ( abs_abs_complex @ A ) )
% 4.71/5.11 = A ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_mult_abs
% 4.71/5.11 thf(fact_4474_sgn__mult__abs,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( abs_abs_real @ A ) )
% 4.71/5.11 = A ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_mult_abs
% 4.71/5.11 thf(fact_4475_sgn__mult__abs,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( abs_abs_rat @ A ) )
% 4.71/5.11 = A ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_mult_abs
% 4.71/5.11 thf(fact_4476_sgn__mult__abs,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( abs_abs_int @ A ) )
% 4.71/5.11 = A ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_mult_abs
% 4.71/5.11 thf(fact_4477_abs__mult__sgn,axiom,
% 4.71/5.11 ! [A: complex] :
% 4.71/5.11 ( ( times_times_complex @ ( abs_abs_complex @ A ) @ ( sgn_sgn_complex @ A ) )
% 4.71/5.11 = A ) ).
% 4.71/5.11
% 4.71/5.11 % abs_mult_sgn
% 4.71/5.11 thf(fact_4478_abs__mult__sgn,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( sgn_sgn_real @ A ) )
% 4.71/5.11 = A ) ).
% 4.71/5.11
% 4.71/5.11 % abs_mult_sgn
% 4.71/5.11 thf(fact_4479_abs__mult__sgn,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 4.71/5.11 = A ) ).
% 4.71/5.11
% 4.71/5.11 % abs_mult_sgn
% 4.71/5.11 thf(fact_4480_abs__mult__sgn,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( sgn_sgn_int @ A ) )
% 4.71/5.11 = A ) ).
% 4.71/5.11
% 4.71/5.11 % abs_mult_sgn
% 4.71/5.11 thf(fact_4481_linordered__idom__class_Oabs__sgn,axiom,
% 4.71/5.11 ( abs_abs_real
% 4.71/5.11 = ( ^ [K3: real] : ( times_times_real @ K3 @ ( sgn_sgn_real @ K3 ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % linordered_idom_class.abs_sgn
% 4.71/5.11 thf(fact_4482_linordered__idom__class_Oabs__sgn,axiom,
% 4.71/5.11 ( abs_abs_rat
% 4.71/5.11 = ( ^ [K3: rat] : ( times_times_rat @ K3 @ ( sgn_sgn_rat @ K3 ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % linordered_idom_class.abs_sgn
% 4.71/5.11 thf(fact_4483_linordered__idom__class_Oabs__sgn,axiom,
% 4.71/5.11 ( abs_abs_int
% 4.71/5.11 = ( ^ [K3: int] : ( times_times_int @ K3 @ ( sgn_sgn_int @ K3 ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % linordered_idom_class.abs_sgn
% 4.71/5.11 thf(fact_4484_same__sgn__abs__add,axiom,
% 4.71/5.11 ! [B: real,A: real] :
% 4.71/5.11 ( ( ( sgn_sgn_real @ B )
% 4.71/5.11 = ( sgn_sgn_real @ A ) )
% 4.71/5.11 => ( ( abs_abs_real @ ( plus_plus_real @ A @ B ) )
% 4.71/5.11 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % same_sgn_abs_add
% 4.71/5.11 thf(fact_4485_same__sgn__abs__add,axiom,
% 4.71/5.11 ! [B: rat,A: rat] :
% 4.71/5.11 ( ( ( sgn_sgn_rat @ B )
% 4.71/5.11 = ( sgn_sgn_rat @ A ) )
% 4.71/5.11 => ( ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) )
% 4.71/5.11 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % same_sgn_abs_add
% 4.71/5.11 thf(fact_4486_same__sgn__abs__add,axiom,
% 4.71/5.11 ! [B: int,A: int] :
% 4.71/5.11 ( ( ( sgn_sgn_int @ B )
% 4.71/5.11 = ( sgn_sgn_int @ A ) )
% 4.71/5.11 => ( ( abs_abs_int @ ( plus_plus_int @ A @ B ) )
% 4.71/5.11 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % same_sgn_abs_add
% 4.71/5.11 thf(fact_4487_le__minus__one__simps_I4_J,axiom,
% 4.71/5.11 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % le_minus_one_simps(4)
% 4.71/5.11 thf(fact_4488_le__minus__one__simps_I4_J,axiom,
% 4.71/5.11 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % le_minus_one_simps(4)
% 4.71/5.11 thf(fact_4489_le__minus__one__simps_I4_J,axiom,
% 4.71/5.11 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % le_minus_one_simps(4)
% 4.71/5.11 thf(fact_4490_le__minus__one__simps_I2_J,axiom,
% 4.71/5.11 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 4.71/5.11
% 4.71/5.11 % le_minus_one_simps(2)
% 4.71/5.11 thf(fact_4491_le__minus__one__simps_I2_J,axiom,
% 4.71/5.11 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 4.71/5.11
% 4.71/5.11 % le_minus_one_simps(2)
% 4.71/5.11 thf(fact_4492_le__minus__one__simps_I2_J,axiom,
% 4.71/5.11 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 4.71/5.11
% 4.71/5.11 % le_minus_one_simps(2)
% 4.71/5.11 thf(fact_4493_add__eq__0__iff,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( ( plus_plus_int @ A @ B )
% 4.71/5.11 = zero_zero_int )
% 4.71/5.11 = ( B
% 4.71/5.11 = ( uminus_uminus_int @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % add_eq_0_iff
% 4.71/5.11 thf(fact_4494_add__eq__0__iff,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( ( plus_plus_real @ A @ B )
% 4.71/5.11 = zero_zero_real )
% 4.71/5.11 = ( B
% 4.71/5.11 = ( uminus_uminus_real @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % add_eq_0_iff
% 4.71/5.11 thf(fact_4495_add__eq__0__iff,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( ( plus_plus_rat @ A @ B )
% 4.71/5.11 = zero_zero_rat )
% 4.71/5.11 = ( B
% 4.71/5.11 = ( uminus_uminus_rat @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % add_eq_0_iff
% 4.71/5.11 thf(fact_4496_add__eq__0__iff,axiom,
% 4.71/5.11 ! [A: complex,B: complex] :
% 4.71/5.11 ( ( ( plus_plus_complex @ A @ B )
% 4.71/5.11 = zero_zero_complex )
% 4.71/5.11 = ( B
% 4.71/5.11 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % add_eq_0_iff
% 4.71/5.11 thf(fact_4497_ab__group__add__class_Oab__left__minus,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 4.71/5.11 = zero_zero_int ) ).
% 4.71/5.11
% 4.71/5.11 % ab_group_add_class.ab_left_minus
% 4.71/5.11 thf(fact_4498_ab__group__add__class_Oab__left__minus,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 4.71/5.11 = zero_zero_real ) ).
% 4.71/5.11
% 4.71/5.11 % ab_group_add_class.ab_left_minus
% 4.71/5.11 thf(fact_4499_ab__group__add__class_Oab__left__minus,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 4.71/5.11 = zero_zero_rat ) ).
% 4.71/5.11
% 4.71/5.11 % ab_group_add_class.ab_left_minus
% 4.71/5.11 thf(fact_4500_ab__group__add__class_Oab__left__minus,axiom,
% 4.71/5.11 ! [A: complex] :
% 4.71/5.11 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 4.71/5.11 = zero_zero_complex ) ).
% 4.71/5.11
% 4.71/5.11 % ab_group_add_class.ab_left_minus
% 4.71/5.11 thf(fact_4501_add_Oinverse__unique,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( ( plus_plus_int @ A @ B )
% 4.71/5.11 = zero_zero_int )
% 4.71/5.11 => ( ( uminus_uminus_int @ A )
% 4.71/5.11 = B ) ) ).
% 4.71/5.11
% 4.71/5.11 % add.inverse_unique
% 4.71/5.11 thf(fact_4502_add_Oinverse__unique,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( ( plus_plus_real @ A @ B )
% 4.71/5.11 = zero_zero_real )
% 4.71/5.11 => ( ( uminus_uminus_real @ A )
% 4.71/5.11 = B ) ) ).
% 4.71/5.11
% 4.71/5.11 % add.inverse_unique
% 4.71/5.11 thf(fact_4503_add_Oinverse__unique,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( ( plus_plus_rat @ A @ B )
% 4.71/5.11 = zero_zero_rat )
% 4.71/5.11 => ( ( uminus_uminus_rat @ A )
% 4.71/5.11 = B ) ) ).
% 4.71/5.11
% 4.71/5.11 % add.inverse_unique
% 4.71/5.11 thf(fact_4504_add_Oinverse__unique,axiom,
% 4.71/5.11 ! [A: complex,B: complex] :
% 4.71/5.11 ( ( ( plus_plus_complex @ A @ B )
% 4.71/5.11 = zero_zero_complex )
% 4.71/5.11 => ( ( uminus1482373934393186551omplex @ A )
% 4.71/5.11 = B ) ) ).
% 4.71/5.11
% 4.71/5.11 % add.inverse_unique
% 4.71/5.11 thf(fact_4505_eq__neg__iff__add__eq__0,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( A
% 4.71/5.11 = ( uminus_uminus_int @ B ) )
% 4.71/5.11 = ( ( plus_plus_int @ A @ B )
% 4.71/5.11 = zero_zero_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % eq_neg_iff_add_eq_0
% 4.71/5.11 thf(fact_4506_eq__neg__iff__add__eq__0,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( A
% 4.71/5.11 = ( uminus_uminus_real @ B ) )
% 4.71/5.11 = ( ( plus_plus_real @ A @ B )
% 4.71/5.11 = zero_zero_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % eq_neg_iff_add_eq_0
% 4.71/5.11 thf(fact_4507_eq__neg__iff__add__eq__0,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( A
% 4.71/5.11 = ( uminus_uminus_rat @ B ) )
% 4.71/5.11 = ( ( plus_plus_rat @ A @ B )
% 4.71/5.11 = zero_zero_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % eq_neg_iff_add_eq_0
% 4.71/5.11 thf(fact_4508_eq__neg__iff__add__eq__0,axiom,
% 4.71/5.11 ! [A: complex,B: complex] :
% 4.71/5.11 ( ( A
% 4.71/5.11 = ( uminus1482373934393186551omplex @ B ) )
% 4.71/5.11 = ( ( plus_plus_complex @ A @ B )
% 4.71/5.11 = zero_zero_complex ) ) ).
% 4.71/5.11
% 4.71/5.11 % eq_neg_iff_add_eq_0
% 4.71/5.11 thf(fact_4509_neg__eq__iff__add__eq__0,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( ( uminus_uminus_int @ A )
% 4.71/5.11 = B )
% 4.71/5.11 = ( ( plus_plus_int @ A @ B )
% 4.71/5.11 = zero_zero_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_eq_iff_add_eq_0
% 4.71/5.11 thf(fact_4510_neg__eq__iff__add__eq__0,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( ( uminus_uminus_real @ A )
% 4.71/5.11 = B )
% 4.71/5.11 = ( ( plus_plus_real @ A @ B )
% 4.71/5.11 = zero_zero_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_eq_iff_add_eq_0
% 4.71/5.11 thf(fact_4511_neg__eq__iff__add__eq__0,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( ( uminus_uminus_rat @ A )
% 4.71/5.11 = B )
% 4.71/5.11 = ( ( plus_plus_rat @ A @ B )
% 4.71/5.11 = zero_zero_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_eq_iff_add_eq_0
% 4.71/5.11 thf(fact_4512_neg__eq__iff__add__eq__0,axiom,
% 4.71/5.11 ! [A: complex,B: complex] :
% 4.71/5.11 ( ( ( uminus1482373934393186551omplex @ A )
% 4.71/5.11 = B )
% 4.71/5.11 = ( ( plus_plus_complex @ A @ B )
% 4.71/5.11 = zero_zero_complex ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_eq_iff_add_eq_0
% 4.71/5.11 thf(fact_4513_zero__neq__neg__one,axiom,
% 4.71/5.11 ( zero_zero_int
% 4.71/5.11 != ( uminus_uminus_int @ one_one_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % zero_neq_neg_one
% 4.71/5.11 thf(fact_4514_zero__neq__neg__one,axiom,
% 4.71/5.11 ( zero_zero_real
% 4.71/5.11 != ( uminus_uminus_real @ one_one_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % zero_neq_neg_one
% 4.71/5.11 thf(fact_4515_zero__neq__neg__one,axiom,
% 4.71/5.11 ( zero_zero_rat
% 4.71/5.11 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % zero_neq_neg_one
% 4.71/5.11 thf(fact_4516_zero__neq__neg__one,axiom,
% 4.71/5.11 ( zero_zero_complex
% 4.71/5.11 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 4.71/5.11
% 4.71/5.11 % zero_neq_neg_one
% 4.71/5.11 thf(fact_4517_less__minus__one__simps_I4_J,axiom,
% 4.71/5.11 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % less_minus_one_simps(4)
% 4.71/5.11 thf(fact_4518_less__minus__one__simps_I4_J,axiom,
% 4.71/5.11 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % less_minus_one_simps(4)
% 4.71/5.11 thf(fact_4519_less__minus__one__simps_I4_J,axiom,
% 4.71/5.11 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % less_minus_one_simps(4)
% 4.71/5.11 thf(fact_4520_less__minus__one__simps_I2_J,axiom,
% 4.71/5.11 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 4.71/5.11
% 4.71/5.11 % less_minus_one_simps(2)
% 4.71/5.11 thf(fact_4521_less__minus__one__simps_I2_J,axiom,
% 4.71/5.11 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 4.71/5.11
% 4.71/5.11 % less_minus_one_simps(2)
% 4.71/5.11 thf(fact_4522_less__minus__one__simps_I2_J,axiom,
% 4.71/5.11 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 4.71/5.11
% 4.71/5.11 % less_minus_one_simps(2)
% 4.71/5.11 thf(fact_4523_nonzero__minus__divide__right,axiom,
% 4.71/5.11 ! [B: real,A: real] :
% 4.71/5.11 ( ( B != zero_zero_real )
% 4.71/5.11 => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 4.71/5.11 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % nonzero_minus_divide_right
% 4.71/5.11 thf(fact_4524_nonzero__minus__divide__right,axiom,
% 4.71/5.11 ! [B: rat,A: rat] :
% 4.71/5.11 ( ( B != zero_zero_rat )
% 4.71/5.11 => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 4.71/5.11 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % nonzero_minus_divide_right
% 4.71/5.11 thf(fact_4525_nonzero__minus__divide__right,axiom,
% 4.71/5.11 ! [B: complex,A: complex] :
% 4.71/5.11 ( ( B != zero_zero_complex )
% 4.71/5.11 => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 4.71/5.11 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % nonzero_minus_divide_right
% 4.71/5.11 thf(fact_4526_nonzero__minus__divide__divide,axiom,
% 4.71/5.11 ! [B: real,A: real] :
% 4.71/5.11 ( ( B != zero_zero_real )
% 4.71/5.11 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 4.71/5.11 = ( divide_divide_real @ A @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % nonzero_minus_divide_divide
% 4.71/5.11 thf(fact_4527_nonzero__minus__divide__divide,axiom,
% 4.71/5.11 ! [B: rat,A: rat] :
% 4.71/5.11 ( ( B != zero_zero_rat )
% 4.71/5.11 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 4.71/5.11 = ( divide_divide_rat @ A @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % nonzero_minus_divide_divide
% 4.71/5.11 thf(fact_4528_nonzero__minus__divide__divide,axiom,
% 4.71/5.11 ! [B: complex,A: complex] :
% 4.71/5.11 ( ( B != zero_zero_complex )
% 4.71/5.11 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 4.71/5.11 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % nonzero_minus_divide_divide
% 4.71/5.11 thf(fact_4529_square__eq__1__iff,axiom,
% 4.71/5.11 ! [X: int] :
% 4.71/5.11 ( ( ( times_times_int @ X @ X )
% 4.71/5.11 = one_one_int )
% 4.71/5.11 = ( ( X = one_one_int )
% 4.71/5.11 | ( X
% 4.71/5.11 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % square_eq_1_iff
% 4.71/5.11 thf(fact_4530_square__eq__1__iff,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ( ( ( times_times_real @ X @ X )
% 4.71/5.11 = one_one_real )
% 4.71/5.11 = ( ( X = one_one_real )
% 4.71/5.11 | ( X
% 4.71/5.11 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % square_eq_1_iff
% 4.71/5.11 thf(fact_4531_square__eq__1__iff,axiom,
% 4.71/5.11 ! [X: rat] :
% 4.71/5.11 ( ( ( times_times_rat @ X @ X )
% 4.71/5.11 = one_one_rat )
% 4.71/5.11 = ( ( X = one_one_rat )
% 4.71/5.11 | ( X
% 4.71/5.11 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % square_eq_1_iff
% 4.71/5.11 thf(fact_4532_square__eq__1__iff,axiom,
% 4.71/5.11 ! [X: complex] :
% 4.71/5.11 ( ( ( times_times_complex @ X @ X )
% 4.71/5.11 = one_one_complex )
% 4.71/5.11 = ( ( X = one_one_complex )
% 4.71/5.11 | ( X
% 4.71/5.11 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % square_eq_1_iff
% 4.71/5.11 thf(fact_4533_group__cancel_Osub2,axiom,
% 4.71/5.11 ! [B2: int,K: int,B: int,A: int] :
% 4.71/5.11 ( ( B2
% 4.71/5.11 = ( plus_plus_int @ K @ B ) )
% 4.71/5.11 => ( ( minus_minus_int @ A @ B2 )
% 4.71/5.11 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % group_cancel.sub2
% 4.71/5.11 thf(fact_4534_group__cancel_Osub2,axiom,
% 4.71/5.11 ! [B2: real,K: real,B: real,A: real] :
% 4.71/5.11 ( ( B2
% 4.71/5.11 = ( plus_plus_real @ K @ B ) )
% 4.71/5.11 => ( ( minus_minus_real @ A @ B2 )
% 4.71/5.11 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % group_cancel.sub2
% 4.71/5.11 thf(fact_4535_group__cancel_Osub2,axiom,
% 4.71/5.11 ! [B2: rat,K: rat,B: rat,A: rat] :
% 4.71/5.11 ( ( B2
% 4.71/5.11 = ( plus_plus_rat @ K @ B ) )
% 4.71/5.11 => ( ( minus_minus_rat @ A @ B2 )
% 4.71/5.11 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % group_cancel.sub2
% 4.71/5.11 thf(fact_4536_group__cancel_Osub2,axiom,
% 4.71/5.11 ! [B2: complex,K: complex,B: complex,A: complex] :
% 4.71/5.11 ( ( B2
% 4.71/5.11 = ( plus_plus_complex @ K @ B ) )
% 4.71/5.11 => ( ( minus_minus_complex @ A @ B2 )
% 4.71/5.11 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % group_cancel.sub2
% 4.71/5.11 thf(fact_4537_diff__conv__add__uminus,axiom,
% 4.71/5.11 ( minus_minus_int
% 4.71/5.11 = ( ^ [A4: int,B4: int] : ( plus_plus_int @ A4 @ ( uminus_uminus_int @ B4 ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % diff_conv_add_uminus
% 4.71/5.11 thf(fact_4538_diff__conv__add__uminus,axiom,
% 4.71/5.11 ( minus_minus_real
% 4.71/5.11 = ( ^ [A4: real,B4: real] : ( plus_plus_real @ A4 @ ( uminus_uminus_real @ B4 ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % diff_conv_add_uminus
% 4.71/5.11 thf(fact_4539_diff__conv__add__uminus,axiom,
% 4.71/5.11 ( minus_minus_rat
% 4.71/5.11 = ( ^ [A4: rat,B4: rat] : ( plus_plus_rat @ A4 @ ( uminus_uminus_rat @ B4 ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % diff_conv_add_uminus
% 4.71/5.11 thf(fact_4540_diff__conv__add__uminus,axiom,
% 4.71/5.11 ( minus_minus_complex
% 4.71/5.11 = ( ^ [A4: complex,B4: complex] : ( plus_plus_complex @ A4 @ ( uminus1482373934393186551omplex @ B4 ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % diff_conv_add_uminus
% 4.71/5.11 thf(fact_4541_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 4.71/5.11 ( minus_minus_int
% 4.71/5.11 = ( ^ [A4: int,B4: int] : ( plus_plus_int @ A4 @ ( uminus_uminus_int @ B4 ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % ab_group_add_class.ab_diff_conv_add_uminus
% 4.71/5.11 thf(fact_4542_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 4.71/5.11 ( minus_minus_real
% 4.71/5.11 = ( ^ [A4: real,B4: real] : ( plus_plus_real @ A4 @ ( uminus_uminus_real @ B4 ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % ab_group_add_class.ab_diff_conv_add_uminus
% 4.71/5.11 thf(fact_4543_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 4.71/5.11 ( minus_minus_rat
% 4.71/5.11 = ( ^ [A4: rat,B4: rat] : ( plus_plus_rat @ A4 @ ( uminus_uminus_rat @ B4 ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % ab_group_add_class.ab_diff_conv_add_uminus
% 4.71/5.11 thf(fact_4544_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 4.71/5.11 ( minus_minus_complex
% 4.71/5.11 = ( ^ [A4: complex,B4: complex] : ( plus_plus_complex @ A4 @ ( uminus1482373934393186551omplex @ B4 ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % ab_group_add_class.ab_diff_conv_add_uminus
% 4.71/5.11 thf(fact_4545_abs__ge__minus__self,axiom,
% 4.71/5.11 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_ge_minus_self
% 4.71/5.11 thf(fact_4546_abs__ge__minus__self,axiom,
% 4.71/5.11 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_ge_minus_self
% 4.71/5.11 thf(fact_4547_abs__ge__minus__self,axiom,
% 4.71/5.11 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_ge_minus_self
% 4.71/5.11 thf(fact_4548_abs__le__iff,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 4.71/5.11 = ( ( ord_less_eq_real @ A @ B )
% 4.71/5.11 & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_le_iff
% 4.71/5.11 thf(fact_4549_abs__le__iff,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 4.71/5.11 = ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.11 & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_le_iff
% 4.71/5.11 thf(fact_4550_abs__le__iff,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 4.71/5.11 = ( ( ord_less_eq_int @ A @ B )
% 4.71/5.11 & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_le_iff
% 4.71/5.11 thf(fact_4551_abs__le__D2,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 4.71/5.11 => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_le_D2
% 4.71/5.11 thf(fact_4552_abs__le__D2,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 4.71/5.11 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_le_D2
% 4.71/5.11 thf(fact_4553_abs__le__D2,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 4.71/5.11 => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_le_D2
% 4.71/5.11 thf(fact_4554_abs__leI,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ A @ B )
% 4.71/5.11 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 4.71/5.11 => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_leI
% 4.71/5.11 thf(fact_4555_abs__leI,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.11 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 4.71/5.11 => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_leI
% 4.71/5.11 thf(fact_4556_abs__leI,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ A @ B )
% 4.71/5.11 => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 4.71/5.11 => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_leI
% 4.71/5.11 thf(fact_4557_abs__less__iff,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 4.71/5.11 = ( ( ord_less_int @ A @ B )
% 4.71/5.11 & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_less_iff
% 4.71/5.11 thf(fact_4558_abs__less__iff,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 4.71/5.11 = ( ( ord_less_real @ A @ B )
% 4.71/5.11 & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_less_iff
% 4.71/5.11 thf(fact_4559_abs__less__iff,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 4.71/5.11 = ( ( ord_less_rat @ A @ B )
% 4.71/5.11 & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_less_iff
% 4.71/5.11 thf(fact_4560_subset__Compl__self__eq,axiom,
% 4.71/5.11 ! [A2: set_real] :
% 4.71/5.11 ( ( ord_less_eq_set_real @ A2 @ ( uminus612125837232591019t_real @ A2 ) )
% 4.71/5.11 = ( A2 = bot_bot_set_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % subset_Compl_self_eq
% 4.71/5.11 thf(fact_4561_subset__Compl__self__eq,axiom,
% 4.71/5.11 ! [A2: set_o] :
% 4.71/5.11 ( ( ord_less_eq_set_o @ A2 @ ( uminus_uminus_set_o @ A2 ) )
% 4.71/5.11 = ( A2 = bot_bot_set_o ) ) ).
% 4.71/5.11
% 4.71/5.11 % subset_Compl_self_eq
% 4.71/5.11 thf(fact_4562_subset__Compl__self__eq,axiom,
% 4.71/5.11 ! [A2: set_nat] :
% 4.71/5.11 ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ A2 ) )
% 4.71/5.11 = ( A2 = bot_bot_set_nat ) ) ).
% 4.71/5.11
% 4.71/5.11 % subset_Compl_self_eq
% 4.71/5.11 thf(fact_4563_subset__Compl__self__eq,axiom,
% 4.71/5.11 ! [A2: set_int] :
% 4.71/5.11 ( ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ A2 ) )
% 4.71/5.11 = ( A2 = bot_bot_set_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % subset_Compl_self_eq
% 4.71/5.11 thf(fact_4564_real__minus__mult__self__le,axiom,
% 4.71/5.11 ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % real_minus_mult_self_le
% 4.71/5.11 thf(fact_4565_minus__real__def,axiom,
% 4.71/5.11 ( minus_minus_real
% 4.71/5.11 = ( ^ [X3: real,Y2: real] : ( plus_plus_real @ X3 @ ( uminus_uminus_real @ Y2 ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_real_def
% 4.71/5.11 thf(fact_4566_Gcd__int__greater__eq__0,axiom,
% 4.71/5.11 ! [K4: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Gcd_int @ K4 ) ) ).
% 4.71/5.11
% 4.71/5.11 % Gcd_int_greater_eq_0
% 4.71/5.11 thf(fact_4567_powr__mono2_H,axiom,
% 4.71/5.11 ! [A: real,X: real,Y: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 4.71/5.11 => ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.11 => ( ( ord_less_eq_real @ X @ Y )
% 4.71/5.11 => ( ord_less_eq_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % powr_mono2'
% 4.71/5.11 thf(fact_4568_powr__less__mono2,axiom,
% 4.71/5.11 ! [A: real,X: real,Y: real] :
% 4.71/5.11 ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.11 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.11 => ( ( ord_less_real @ X @ Y )
% 4.71/5.11 => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % powr_less_mono2
% 4.71/5.11 thf(fact_4569_powr__le1,axiom,
% 4.71/5.11 ! [A: real,X: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.11 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.11 => ( ( ord_less_eq_real @ X @ one_one_real )
% 4.71/5.11 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ one_one_real ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % powr_le1
% 4.71/5.11 thf(fact_4570_powr__mono__both,axiom,
% 4.71/5.11 ! [A: real,B: real,X: real,Y: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.11 => ( ( ord_less_eq_real @ A @ B )
% 4.71/5.11 => ( ( ord_less_eq_real @ one_one_real @ X )
% 4.71/5.11 => ( ( ord_less_eq_real @ X @ Y )
% 4.71/5.11 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ B ) ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % powr_mono_both
% 4.71/5.11 thf(fact_4571_ge__one__powr__ge__zero,axiom,
% 4.71/5.11 ! [X: real,A: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ one_one_real @ X )
% 4.71/5.11 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.11 => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X @ A ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % ge_one_powr_ge_zero
% 4.71/5.11 thf(fact_4572_powr__divide,axiom,
% 4.71/5.11 ! [X: real,Y: real,A: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.11 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.71/5.11 => ( ( powr_real @ ( divide_divide_real @ X @ Y ) @ A )
% 4.71/5.11 = ( divide_divide_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % powr_divide
% 4.71/5.11 thf(fact_4573_powr__mult,axiom,
% 4.71/5.11 ! [X: real,Y: real,A: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.11 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.71/5.11 => ( ( powr_real @ ( times_times_real @ X @ Y ) @ A )
% 4.71/5.11 = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % powr_mult
% 4.71/5.11 thf(fact_4574_sgn__1__pos,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( ( sgn_sgn_real @ A )
% 4.71/5.11 = one_one_real )
% 4.71/5.11 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_1_pos
% 4.71/5.11 thf(fact_4575_sgn__1__pos,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( ( sgn_sgn_rat @ A )
% 4.71/5.11 = one_one_rat )
% 4.71/5.11 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_1_pos
% 4.71/5.11 thf(fact_4576_sgn__1__pos,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( ( sgn_sgn_int @ A )
% 4.71/5.11 = one_one_int )
% 4.71/5.11 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_1_pos
% 4.71/5.11 thf(fact_4577_sgn__root,axiom,
% 4.71/5.11 ! [N: nat,X: real] :
% 4.71/5.11 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.11 => ( ( sgn_sgn_real @ ( root @ N @ X ) )
% 4.71/5.11 = ( sgn_sgn_real @ X ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_root
% 4.71/5.11 thf(fact_4578_abs__sgn__eq,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( ( A = zero_zero_real )
% 4.71/5.11 => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 4.71/5.11 = zero_zero_real ) )
% 4.71/5.11 & ( ( A != zero_zero_real )
% 4.71/5.11 => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 4.71/5.11 = one_one_real ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_sgn_eq
% 4.71/5.11 thf(fact_4579_abs__sgn__eq,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( ( A = zero_zero_rat )
% 4.71/5.11 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 4.71/5.11 = zero_zero_rat ) )
% 4.71/5.11 & ( ( A != zero_zero_rat )
% 4.71/5.11 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 4.71/5.11 = one_one_rat ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_sgn_eq
% 4.71/5.11 thf(fact_4580_abs__sgn__eq,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( ( A = zero_zero_int )
% 4.71/5.11 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 4.71/5.11 = zero_zero_int ) )
% 4.71/5.11 & ( ( A != zero_zero_int )
% 4.71/5.11 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 4.71/5.11 = one_one_int ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_sgn_eq
% 4.71/5.11 thf(fact_4581_le__minus__one__simps_I3_J,axiom,
% 4.71/5.11 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % le_minus_one_simps(3)
% 4.71/5.11 thf(fact_4582_le__minus__one__simps_I3_J,axiom,
% 4.71/5.11 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % le_minus_one_simps(3)
% 4.71/5.11 thf(fact_4583_le__minus__one__simps_I3_J,axiom,
% 4.71/5.11 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % le_minus_one_simps(3)
% 4.71/5.11 thf(fact_4584_le__minus__one__simps_I1_J,axiom,
% 4.71/5.11 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 4.71/5.11
% 4.71/5.11 % le_minus_one_simps(1)
% 4.71/5.11 thf(fact_4585_le__minus__one__simps_I1_J,axiom,
% 4.71/5.11 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 4.71/5.11
% 4.71/5.11 % le_minus_one_simps(1)
% 4.71/5.11 thf(fact_4586_le__minus__one__simps_I1_J,axiom,
% 4.71/5.11 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 4.71/5.11
% 4.71/5.11 % le_minus_one_simps(1)
% 4.71/5.11 thf(fact_4587_less__minus__one__simps_I3_J,axiom,
% 4.71/5.11 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % less_minus_one_simps(3)
% 4.71/5.11 thf(fact_4588_less__minus__one__simps_I3_J,axiom,
% 4.71/5.11 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % less_minus_one_simps(3)
% 4.71/5.11 thf(fact_4589_less__minus__one__simps_I3_J,axiom,
% 4.71/5.11 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % less_minus_one_simps(3)
% 4.71/5.11 thf(fact_4590_less__minus__one__simps_I1_J,axiom,
% 4.71/5.11 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 4.71/5.11
% 4.71/5.11 % less_minus_one_simps(1)
% 4.71/5.11 thf(fact_4591_less__minus__one__simps_I1_J,axiom,
% 4.71/5.11 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 4.71/5.11
% 4.71/5.11 % less_minus_one_simps(1)
% 4.71/5.11 thf(fact_4592_less__minus__one__simps_I1_J,axiom,
% 4.71/5.11 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 4.71/5.11
% 4.71/5.11 % less_minus_one_simps(1)
% 4.71/5.11 thf(fact_4593_eq__minus__divide__eq,axiom,
% 4.71/5.11 ! [A: real,B: real,C: real] :
% 4.71/5.11 ( ( A
% 4.71/5.11 = ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 4.71/5.11 = ( ( ( C != zero_zero_real )
% 4.71/5.11 => ( ( times_times_real @ A @ C )
% 4.71/5.11 = ( uminus_uminus_real @ B ) ) )
% 4.71/5.11 & ( ( C = zero_zero_real )
% 4.71/5.11 => ( A = zero_zero_real ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % eq_minus_divide_eq
% 4.71/5.11 thf(fact_4594_eq__minus__divide__eq,axiom,
% 4.71/5.11 ! [A: rat,B: rat,C: rat] :
% 4.71/5.11 ( ( A
% 4.71/5.11 = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 4.71/5.11 = ( ( ( C != zero_zero_rat )
% 4.71/5.11 => ( ( times_times_rat @ A @ C )
% 4.71/5.11 = ( uminus_uminus_rat @ B ) ) )
% 4.71/5.11 & ( ( C = zero_zero_rat )
% 4.71/5.11 => ( A = zero_zero_rat ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % eq_minus_divide_eq
% 4.71/5.11 thf(fact_4595_eq__minus__divide__eq,axiom,
% 4.71/5.11 ! [A: complex,B: complex,C: complex] :
% 4.71/5.11 ( ( A
% 4.71/5.11 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) ) )
% 4.71/5.11 = ( ( ( C != zero_zero_complex )
% 4.71/5.11 => ( ( times_times_complex @ A @ C )
% 4.71/5.11 = ( uminus1482373934393186551omplex @ B ) ) )
% 4.71/5.11 & ( ( C = zero_zero_complex )
% 4.71/5.11 => ( A = zero_zero_complex ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % eq_minus_divide_eq
% 4.71/5.11 thf(fact_4596_minus__divide__eq__eq,axiom,
% 4.71/5.11 ! [B: real,C: real,A: real] :
% 4.71/5.11 ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) )
% 4.71/5.11 = A )
% 4.71/5.11 = ( ( ( C != zero_zero_real )
% 4.71/5.11 => ( ( uminus_uminus_real @ B )
% 4.71/5.11 = ( times_times_real @ A @ C ) ) )
% 4.71/5.11 & ( ( C = zero_zero_real )
% 4.71/5.11 => ( A = zero_zero_real ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_divide_eq_eq
% 4.71/5.11 thf(fact_4597_minus__divide__eq__eq,axiom,
% 4.71/5.11 ! [B: rat,C: rat,A: rat] :
% 4.71/5.11 ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 4.71/5.11 = A )
% 4.71/5.11 = ( ( ( C != zero_zero_rat )
% 4.71/5.11 => ( ( uminus_uminus_rat @ B )
% 4.71/5.11 = ( times_times_rat @ A @ C ) ) )
% 4.71/5.11 & ( ( C = zero_zero_rat )
% 4.71/5.11 => ( A = zero_zero_rat ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_divide_eq_eq
% 4.71/5.11 thf(fact_4598_minus__divide__eq__eq,axiom,
% 4.71/5.11 ! [B: complex,C: complex,A: complex] :
% 4.71/5.11 ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) )
% 4.71/5.11 = A )
% 4.71/5.11 = ( ( ( C != zero_zero_complex )
% 4.71/5.11 => ( ( uminus1482373934393186551omplex @ B )
% 4.71/5.11 = ( times_times_complex @ A @ C ) ) )
% 4.71/5.11 & ( ( C = zero_zero_complex )
% 4.71/5.11 => ( A = zero_zero_complex ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_divide_eq_eq
% 4.71/5.11 thf(fact_4599_nonzero__neg__divide__eq__eq,axiom,
% 4.71/5.11 ! [B: real,A: real,C: real] :
% 4.71/5.11 ( ( B != zero_zero_real )
% 4.71/5.11 => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 4.71/5.11 = C )
% 4.71/5.11 = ( ( uminus_uminus_real @ A )
% 4.71/5.11 = ( times_times_real @ C @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % nonzero_neg_divide_eq_eq
% 4.71/5.11 thf(fact_4600_nonzero__neg__divide__eq__eq,axiom,
% 4.71/5.11 ! [B: rat,A: rat,C: rat] :
% 4.71/5.11 ( ( B != zero_zero_rat )
% 4.71/5.11 => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 4.71/5.11 = C )
% 4.71/5.11 = ( ( uminus_uminus_rat @ A )
% 4.71/5.11 = ( times_times_rat @ C @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % nonzero_neg_divide_eq_eq
% 4.71/5.11 thf(fact_4601_nonzero__neg__divide__eq__eq,axiom,
% 4.71/5.11 ! [B: complex,A: complex,C: complex] :
% 4.71/5.11 ( ( B != zero_zero_complex )
% 4.71/5.11 => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 4.71/5.11 = C )
% 4.71/5.11 = ( ( uminus1482373934393186551omplex @ A )
% 4.71/5.11 = ( times_times_complex @ C @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % nonzero_neg_divide_eq_eq
% 4.71/5.11 thf(fact_4602_nonzero__neg__divide__eq__eq2,axiom,
% 4.71/5.11 ! [B: real,C: real,A: real] :
% 4.71/5.11 ( ( B != zero_zero_real )
% 4.71/5.11 => ( ( C
% 4.71/5.11 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 4.71/5.11 = ( ( times_times_real @ C @ B )
% 4.71/5.11 = ( uminus_uminus_real @ A ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % nonzero_neg_divide_eq_eq2
% 4.71/5.11 thf(fact_4603_nonzero__neg__divide__eq__eq2,axiom,
% 4.71/5.11 ! [B: rat,C: rat,A: rat] :
% 4.71/5.11 ( ( B != zero_zero_rat )
% 4.71/5.11 => ( ( C
% 4.71/5.11 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 4.71/5.11 = ( ( times_times_rat @ C @ B )
% 4.71/5.11 = ( uminus_uminus_rat @ A ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % nonzero_neg_divide_eq_eq2
% 4.71/5.11 thf(fact_4604_nonzero__neg__divide__eq__eq2,axiom,
% 4.71/5.11 ! [B: complex,C: complex,A: complex] :
% 4.71/5.11 ( ( B != zero_zero_complex )
% 4.71/5.11 => ( ( C
% 4.71/5.11 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 4.71/5.11 = ( ( times_times_complex @ C @ B )
% 4.71/5.11 = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % nonzero_neg_divide_eq_eq2
% 4.71/5.11 thf(fact_4605_divide__eq__minus__1__iff,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( ( divide_divide_real @ A @ B )
% 4.71/5.11 = ( uminus_uminus_real @ one_one_real ) )
% 4.71/5.11 = ( ( B != zero_zero_real )
% 4.71/5.11 & ( A
% 4.71/5.11 = ( uminus_uminus_real @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % divide_eq_minus_1_iff
% 4.71/5.11 thf(fact_4606_divide__eq__minus__1__iff,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( ( divide_divide_rat @ A @ B )
% 4.71/5.11 = ( uminus_uminus_rat @ one_one_rat ) )
% 4.71/5.11 = ( ( B != zero_zero_rat )
% 4.71/5.11 & ( A
% 4.71/5.11 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % divide_eq_minus_1_iff
% 4.71/5.11 thf(fact_4607_divide__eq__minus__1__iff,axiom,
% 4.71/5.11 ! [A: complex,B: complex] :
% 4.71/5.11 ( ( ( divide1717551699836669952omplex @ A @ B )
% 4.71/5.11 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 4.71/5.11 = ( ( B != zero_zero_complex )
% 4.71/5.11 & ( A
% 4.71/5.11 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % divide_eq_minus_1_iff
% 4.71/5.11 thf(fact_4608_power__minus,axiom,
% 4.71/5.11 ! [A: int,N: nat] :
% 4.71/5.11 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 4.71/5.11 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ A @ N ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % power_minus
% 4.71/5.11 thf(fact_4609_power__minus,axiom,
% 4.71/5.11 ! [A: real,N: nat] :
% 4.71/5.11 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 4.71/5.11 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ A @ N ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % power_minus
% 4.71/5.11 thf(fact_4610_power__minus,axiom,
% 4.71/5.11 ! [A: rat,N: nat] :
% 4.71/5.11 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 4.71/5.11 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ A @ N ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % power_minus
% 4.71/5.11 thf(fact_4611_power__minus,axiom,
% 4.71/5.11 ! [A: complex,N: nat] :
% 4.71/5.11 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 4.71/5.11 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ A @ N ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % power_minus
% 4.71/5.11 thf(fact_4612_abs__minus__le__zero,axiom,
% 4.71/5.11 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 4.71/5.11
% 4.71/5.11 % abs_minus_le_zero
% 4.71/5.11 thf(fact_4613_abs__minus__le__zero,axiom,
% 4.71/5.11 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 4.71/5.11
% 4.71/5.11 % abs_minus_le_zero
% 4.71/5.11 thf(fact_4614_abs__minus__le__zero,axiom,
% 4.71/5.11 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 4.71/5.11
% 4.71/5.11 % abs_minus_le_zero
% 4.71/5.11 thf(fact_4615_abs__eq__iff_H,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( ( abs_abs_real @ A )
% 4.71/5.11 = B )
% 4.71/5.11 = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.71/5.11 & ( ( A = B )
% 4.71/5.11 | ( A
% 4.71/5.11 = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_eq_iff'
% 4.71/5.11 thf(fact_4616_abs__eq__iff_H,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( ( abs_abs_rat @ A )
% 4.71/5.11 = B )
% 4.71/5.11 = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.71/5.11 & ( ( A = B )
% 4.71/5.11 | ( A
% 4.71/5.11 = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_eq_iff'
% 4.71/5.11 thf(fact_4617_abs__eq__iff_H,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( ( abs_abs_int @ A )
% 4.71/5.11 = B )
% 4.71/5.11 = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.71/5.11 & ( ( A = B )
% 4.71/5.11 | ( A
% 4.71/5.11 = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_eq_iff'
% 4.71/5.11 thf(fact_4618_eq__abs__iff_H,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( A
% 4.71/5.11 = ( abs_abs_real @ B ) )
% 4.71/5.11 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.11 & ( ( B = A )
% 4.71/5.11 | ( B
% 4.71/5.11 = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % eq_abs_iff'
% 4.71/5.11 thf(fact_4619_eq__abs__iff_H,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( A
% 4.71/5.11 = ( abs_abs_rat @ B ) )
% 4.71/5.11 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.11 & ( ( B = A )
% 4.71/5.11 | ( B
% 4.71/5.11 = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % eq_abs_iff'
% 4.71/5.11 thf(fact_4620_eq__abs__iff_H,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( A
% 4.71/5.11 = ( abs_abs_int @ B ) )
% 4.71/5.11 = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.11 & ( ( B = A )
% 4.71/5.11 | ( B
% 4.71/5.11 = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % eq_abs_iff'
% 4.71/5.11 thf(fact_4621_abs__of__neg,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( ord_less_int @ A @ zero_zero_int )
% 4.71/5.11 => ( ( abs_abs_int @ A )
% 4.71/5.11 = ( uminus_uminus_int @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_of_neg
% 4.71/5.11 thf(fact_4622_abs__of__neg,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( ord_less_real @ A @ zero_zero_real )
% 4.71/5.11 => ( ( abs_abs_real @ A )
% 4.71/5.11 = ( uminus_uminus_real @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_of_neg
% 4.71/5.11 thf(fact_4623_abs__of__neg,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.71/5.11 => ( ( abs_abs_rat @ A )
% 4.71/5.11 = ( uminus_uminus_rat @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_of_neg
% 4.71/5.11 thf(fact_4624_abs__if,axiom,
% 4.71/5.11 ( abs_abs_int
% 4.71/5.11 = ( ^ [A4: int] : ( if_int @ ( ord_less_int @ A4 @ zero_zero_int ) @ ( uminus_uminus_int @ A4 ) @ A4 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_if
% 4.71/5.11 thf(fact_4625_abs__if,axiom,
% 4.71/5.11 ( abs_abs_real
% 4.71/5.11 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_if
% 4.71/5.11 thf(fact_4626_abs__if,axiom,
% 4.71/5.11 ( abs_abs_rat
% 4.71/5.11 = ( ^ [A4: rat] : ( if_rat @ ( ord_less_rat @ A4 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A4 ) @ A4 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_if
% 4.71/5.11 thf(fact_4627_abs__if__raw,axiom,
% 4.71/5.11 ( abs_abs_int
% 4.71/5.11 = ( ^ [A4: int] : ( if_int @ ( ord_less_int @ A4 @ zero_zero_int ) @ ( uminus_uminus_int @ A4 ) @ A4 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_if_raw
% 4.71/5.11 thf(fact_4628_abs__if__raw,axiom,
% 4.71/5.11 ( abs_abs_real
% 4.71/5.11 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_if_raw
% 4.71/5.11 thf(fact_4629_abs__if__raw,axiom,
% 4.71/5.11 ( abs_abs_rat
% 4.71/5.11 = ( ^ [A4: rat] : ( if_rat @ ( ord_less_rat @ A4 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A4 ) @ A4 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_if_raw
% 4.71/5.11 thf(fact_4630_Compl__insert,axiom,
% 4.71/5.11 ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.11 ( ( uminus6524753893492686040at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) )
% 4.71/5.11 = ( minus_1356011639430497352at_nat @ ( uminus6524753893492686040at_nat @ A2 ) @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % Compl_insert
% 4.71/5.11 thf(fact_4631_Compl__insert,axiom,
% 4.71/5.11 ! [X: real,A2: set_real] :
% 4.71/5.11 ( ( uminus612125837232591019t_real @ ( insert_real @ X @ A2 ) )
% 4.71/5.11 = ( minus_minus_set_real @ ( uminus612125837232591019t_real @ A2 ) @ ( insert_real @ X @ bot_bot_set_real ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % Compl_insert
% 4.71/5.11 thf(fact_4632_Compl__insert,axiom,
% 4.71/5.11 ! [X: $o,A2: set_o] :
% 4.71/5.11 ( ( uminus_uminus_set_o @ ( insert_o @ X @ A2 ) )
% 4.71/5.11 = ( minus_minus_set_o @ ( uminus_uminus_set_o @ A2 ) @ ( insert_o @ X @ bot_bot_set_o ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % Compl_insert
% 4.71/5.11 thf(fact_4633_Compl__insert,axiom,
% 4.71/5.11 ! [X: int,A2: set_int] :
% 4.71/5.11 ( ( uminus1532241313380277803et_int @ ( insert_int @ X @ A2 ) )
% 4.71/5.11 = ( minus_minus_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % Compl_insert
% 4.71/5.11 thf(fact_4634_Compl__insert,axiom,
% 4.71/5.11 ! [X: nat,A2: set_nat] :
% 4.71/5.11 ( ( uminus5710092332889474511et_nat @ ( insert_nat @ X @ A2 ) )
% 4.71/5.11 = ( minus_minus_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % Compl_insert
% 4.71/5.11 thf(fact_4635_int__cases4,axiom,
% 4.71/5.11 ! [M2: int] :
% 4.71/5.11 ( ! [N2: nat] :
% 4.71/5.11 ( M2
% 4.71/5.11 != ( semiri1314217659103216013at_int @ N2 ) )
% 4.71/5.11 => ~ ! [N2: nat] :
% 4.71/5.11 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.71/5.11 => ( M2
% 4.71/5.11 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % int_cases4
% 4.71/5.11 thf(fact_4636_real__add__less__0__iff,axiom,
% 4.71/5.11 ! [X: real,Y: real] :
% 4.71/5.11 ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 4.71/5.11 = ( ord_less_real @ Y @ ( uminus_uminus_real @ X ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % real_add_less_0_iff
% 4.71/5.11 thf(fact_4637_real__0__less__add__iff,axiom,
% 4.71/5.11 ! [X: real,Y: real] :
% 4.71/5.11 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ Y ) )
% 4.71/5.11 = ( ord_less_real @ ( uminus_uminus_real @ X ) @ Y ) ) ).
% 4.71/5.11
% 4.71/5.11 % real_0_less_add_iff
% 4.71/5.11 thf(fact_4638_real__add__le__0__iff,axiom,
% 4.71/5.11 ! [X: real,Y: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 4.71/5.11 = ( ord_less_eq_real @ Y @ ( uminus_uminus_real @ X ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % real_add_le_0_iff
% 4.71/5.11 thf(fact_4639_real__0__le__add__iff,axiom,
% 4.71/5.11 ! [X: real,Y: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X @ Y ) )
% 4.71/5.11 = ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ Y ) ) ).
% 4.71/5.11
% 4.71/5.11 % real_0_le_add_iff
% 4.71/5.11 thf(fact_4640_abs__real__def,axiom,
% 4.71/5.11 ( abs_abs_real
% 4.71/5.11 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % abs_real_def
% 4.71/5.11 thf(fact_4641_int__zle__neg,axiom,
% 4.71/5.11 ! [N: nat,M2: nat] :
% 4.71/5.11 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M2 ) ) )
% 4.71/5.11 = ( ( N = zero_zero_nat )
% 4.71/5.11 & ( M2 = zero_zero_nat ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % int_zle_neg
% 4.71/5.11 thf(fact_4642_nonpos__int__cases,axiom,
% 4.71/5.11 ! [K: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 4.71/5.11 => ~ ! [N2: nat] :
% 4.71/5.11 ( K
% 4.71/5.11 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % nonpos_int_cases
% 4.71/5.11 thf(fact_4643_negative__zle__0,axiom,
% 4.71/5.11 ! [N: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ zero_zero_int ) ).
% 4.71/5.11
% 4.71/5.11 % negative_zle_0
% 4.71/5.11 thf(fact_4644_Gcd__remove0__nat,axiom,
% 4.71/5.11 ! [M5: set_nat] :
% 4.71/5.11 ( ( finite_finite_nat @ M5 )
% 4.71/5.11 => ( ( gcd_Gcd_nat @ M5 )
% 4.71/5.11 = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M5 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % Gcd_remove0_nat
% 4.71/5.11 thf(fact_4645_less__minus__divide__eq,axiom,
% 4.71/5.11 ! [A: real,B: real,C: real] :
% 4.71/5.11 ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 4.71/5.11 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.11 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 4.71/5.11 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.11 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.11 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 4.71/5.11 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.11 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % less_minus_divide_eq
% 4.71/5.11 thf(fact_4646_less__minus__divide__eq,axiom,
% 4.71/5.11 ! [A: rat,B: rat,C: rat] :
% 4.71/5.11 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 4.71/5.11 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.11 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 4.71/5.11 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.11 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.11 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 4.71/5.11 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.11 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % less_minus_divide_eq
% 4.71/5.11 thf(fact_4647_minus__divide__less__eq,axiom,
% 4.71/5.11 ! [B: real,C: real,A: real] :
% 4.71/5.11 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 4.71/5.11 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.11 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 4.71/5.11 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.11 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.11 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 4.71/5.11 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.11 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_divide_less_eq
% 4.71/5.11 thf(fact_4648_minus__divide__less__eq,axiom,
% 4.71/5.11 ! [B: rat,C: rat,A: rat] :
% 4.71/5.11 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 4.71/5.11 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.11 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 4.71/5.11 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.11 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.11 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 4.71/5.11 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.11 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_divide_less_eq
% 4.71/5.11 thf(fact_4649_neg__less__minus__divide__eq,axiom,
% 4.71/5.11 ! [C: real,A: real,B: real] :
% 4.71/5.11 ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.11 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 4.71/5.11 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_less_minus_divide_eq
% 4.71/5.11 thf(fact_4650_neg__less__minus__divide__eq,axiom,
% 4.71/5.11 ! [C: rat,A: rat,B: rat] :
% 4.71/5.11 ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.11 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 4.71/5.11 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_less_minus_divide_eq
% 4.71/5.11 thf(fact_4651_neg__minus__divide__less__eq,axiom,
% 4.71/5.11 ! [C: real,B: real,A: real] :
% 4.71/5.11 ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.11 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 4.71/5.11 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_minus_divide_less_eq
% 4.71/5.11 thf(fact_4652_neg__minus__divide__less__eq,axiom,
% 4.71/5.11 ! [C: rat,B: rat,A: rat] :
% 4.71/5.11 ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.11 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 4.71/5.11 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_minus_divide_less_eq
% 4.71/5.11 thf(fact_4653_pos__less__minus__divide__eq,axiom,
% 4.71/5.11 ! [C: real,A: real,B: real] :
% 4.71/5.11 ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.11 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 4.71/5.11 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pos_less_minus_divide_eq
% 4.71/5.11 thf(fact_4654_pos__less__minus__divide__eq,axiom,
% 4.71/5.11 ! [C: rat,A: rat,B: rat] :
% 4.71/5.11 ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.11 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 4.71/5.11 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pos_less_minus_divide_eq
% 4.71/5.11 thf(fact_4655_pos__minus__divide__less__eq,axiom,
% 4.71/5.11 ! [C: real,B: real,A: real] :
% 4.71/5.11 ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.11 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 4.71/5.11 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pos_minus_divide_less_eq
% 4.71/5.11 thf(fact_4656_pos__minus__divide__less__eq,axiom,
% 4.71/5.11 ! [C: rat,B: rat,A: rat] :
% 4.71/5.11 ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.11 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 4.71/5.11 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pos_minus_divide_less_eq
% 4.71/5.11 thf(fact_4657_minus__divide__add__eq__iff,axiom,
% 4.71/5.11 ! [Z: real,X: real,Y: real] :
% 4.71/5.11 ( ( Z != zero_zero_real )
% 4.71/5.11 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z ) ) @ Y )
% 4.71/5.11 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_divide_add_eq_iff
% 4.71/5.11 thf(fact_4658_minus__divide__add__eq__iff,axiom,
% 4.71/5.11 ! [Z: rat,X: rat,Y: rat] :
% 4.71/5.11 ( ( Z != zero_zero_rat )
% 4.71/5.11 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y )
% 4.71/5.11 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_divide_add_eq_iff
% 4.71/5.11 thf(fact_4659_minus__divide__add__eq__iff,axiom,
% 4.71/5.11 ! [Z: complex,X: complex,Y: complex] :
% 4.71/5.11 ( ( Z != zero_zero_complex )
% 4.71/5.11 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z ) ) @ Y )
% 4.71/5.11 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_divide_add_eq_iff
% 4.71/5.11 thf(fact_4660_add__divide__eq__if__simps_I3_J,axiom,
% 4.71/5.11 ! [Z: real,A: real,B: real] :
% 4.71/5.11 ( ( ( Z = zero_zero_real )
% 4.71/5.11 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 4.71/5.11 = B ) )
% 4.71/5.11 & ( ( Z != zero_zero_real )
% 4.71/5.11 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 4.71/5.11 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % add_divide_eq_if_simps(3)
% 4.71/5.11 thf(fact_4661_add__divide__eq__if__simps_I3_J,axiom,
% 4.71/5.11 ! [Z: rat,A: rat,B: rat] :
% 4.71/5.11 ( ( ( Z = zero_zero_rat )
% 4.71/5.11 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 4.71/5.11 = B ) )
% 4.71/5.11 & ( ( Z != zero_zero_rat )
% 4.71/5.11 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 4.71/5.11 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % add_divide_eq_if_simps(3)
% 4.71/5.11 thf(fact_4662_add__divide__eq__if__simps_I3_J,axiom,
% 4.71/5.11 ! [Z: complex,A: complex,B: complex] :
% 4.71/5.11 ( ( ( Z = zero_zero_complex )
% 4.71/5.11 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 4.71/5.11 = B ) )
% 4.71/5.11 & ( ( Z != zero_zero_complex )
% 4.71/5.11 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 4.71/5.11 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % add_divide_eq_if_simps(3)
% 4.71/5.11 thf(fact_4663_minus__divide__diff__eq__iff,axiom,
% 4.71/5.11 ! [Z: real,X: real,Y: real] :
% 4.71/5.11 ( ( Z != zero_zero_real )
% 4.71/5.11 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z ) ) @ Y )
% 4.71/5.11 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_divide_diff_eq_iff
% 4.71/5.11 thf(fact_4664_minus__divide__diff__eq__iff,axiom,
% 4.71/5.11 ! [Z: rat,X: rat,Y: rat] :
% 4.71/5.11 ( ( Z != zero_zero_rat )
% 4.71/5.11 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y )
% 4.71/5.11 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_divide_diff_eq_iff
% 4.71/5.11 thf(fact_4665_minus__divide__diff__eq__iff,axiom,
% 4.71/5.11 ! [Z: complex,X: complex,Y: complex] :
% 4.71/5.11 ( ( Z != zero_zero_complex )
% 4.71/5.11 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z ) ) @ Y )
% 4.71/5.11 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_divide_diff_eq_iff
% 4.71/5.11 thf(fact_4666_add__divide__eq__if__simps_I5_J,axiom,
% 4.71/5.11 ! [Z: real,A: real,B: real] :
% 4.71/5.11 ( ( ( Z = zero_zero_real )
% 4.71/5.11 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 4.71/5.11 = ( uminus_uminus_real @ B ) ) )
% 4.71/5.11 & ( ( Z != zero_zero_real )
% 4.71/5.11 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 4.71/5.11 = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % add_divide_eq_if_simps(5)
% 4.71/5.11 thf(fact_4667_add__divide__eq__if__simps_I5_J,axiom,
% 4.71/5.11 ! [Z: rat,A: rat,B: rat] :
% 4.71/5.11 ( ( ( Z = zero_zero_rat )
% 4.71/5.11 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 4.71/5.11 = ( uminus_uminus_rat @ B ) ) )
% 4.71/5.11 & ( ( Z != zero_zero_rat )
% 4.71/5.11 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 4.71/5.11 = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % add_divide_eq_if_simps(5)
% 4.71/5.11 thf(fact_4668_add__divide__eq__if__simps_I5_J,axiom,
% 4.71/5.11 ! [Z: complex,A: complex,B: complex] :
% 4.71/5.11 ( ( ( Z = zero_zero_complex )
% 4.71/5.11 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 4.71/5.11 = ( uminus1482373934393186551omplex @ B ) ) )
% 4.71/5.11 & ( ( Z != zero_zero_complex )
% 4.71/5.11 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 4.71/5.11 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % add_divide_eq_if_simps(5)
% 4.71/5.11 thf(fact_4669_add__divide__eq__if__simps_I6_J,axiom,
% 4.71/5.11 ! [Z: real,A: real,B: real] :
% 4.71/5.11 ( ( ( Z = zero_zero_real )
% 4.71/5.11 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 4.71/5.11 = ( uminus_uminus_real @ B ) ) )
% 4.71/5.11 & ( ( Z != zero_zero_real )
% 4.71/5.11 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 4.71/5.11 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % add_divide_eq_if_simps(6)
% 4.71/5.11 thf(fact_4670_add__divide__eq__if__simps_I6_J,axiom,
% 4.71/5.11 ! [Z: rat,A: rat,B: rat] :
% 4.71/5.11 ( ( ( Z = zero_zero_rat )
% 4.71/5.11 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 4.71/5.11 = ( uminus_uminus_rat @ B ) ) )
% 4.71/5.11 & ( ( Z != zero_zero_rat )
% 4.71/5.11 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 4.71/5.11 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % add_divide_eq_if_simps(6)
% 4.71/5.11 thf(fact_4671_add__divide__eq__if__simps_I6_J,axiom,
% 4.71/5.11 ! [Z: complex,A: complex,B: complex] :
% 4.71/5.11 ( ( ( Z = zero_zero_complex )
% 4.71/5.11 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 4.71/5.11 = ( uminus1482373934393186551omplex @ B ) ) )
% 4.71/5.11 & ( ( Z != zero_zero_complex )
% 4.71/5.11 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 4.71/5.11 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % add_divide_eq_if_simps(6)
% 4.71/5.11 thf(fact_4672_int__cases3,axiom,
% 4.71/5.11 ! [K: int] :
% 4.71/5.11 ( ( K != zero_zero_int )
% 4.71/5.11 => ( ! [N2: nat] :
% 4.71/5.11 ( ( K
% 4.71/5.11 = ( semiri1314217659103216013at_int @ N2 ) )
% 4.71/5.11 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 4.71/5.11 => ~ ! [N2: nat] :
% 4.71/5.11 ( ( K
% 4.71/5.11 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 4.71/5.11 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % int_cases3
% 4.71/5.11 thf(fact_4673_not__zle__0__negative,axiom,
% 4.71/5.11 ! [N: nat] :
% 4.71/5.11 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % not_zle_0_negative
% 4.71/5.11 thf(fact_4674_verit__less__mono__div__int2,axiom,
% 4.71/5.11 ! [A2: int,B2: int,N: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ A2 @ B2 )
% 4.71/5.11 => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 4.71/5.11 => ( ord_less_eq_int @ ( divide_divide_int @ B2 @ N ) @ ( divide_divide_int @ A2 @ N ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % verit_less_mono_div_int2
% 4.71/5.11 thf(fact_4675_powr__mult__base,axiom,
% 4.71/5.11 ! [X: real,Y: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.11 => ( ( times_times_real @ X @ ( powr_real @ X @ Y ) )
% 4.71/5.11 = ( powr_real @ X @ ( plus_plus_real @ one_one_real @ Y ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % powr_mult_base
% 4.71/5.11 thf(fact_4676_sgn__power__injE,axiom,
% 4.71/5.11 ! [A: real,N: nat,X: real,B: real] :
% 4.71/5.11 ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 4.71/5.11 = X )
% 4.71/5.11 => ( ( X
% 4.71/5.11 = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N ) ) )
% 4.71/5.11 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.11 => ( A = B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_power_injE
% 4.71/5.11 thf(fact_4677_le__log__iff,axiom,
% 4.71/5.11 ! [B: real,X: real,Y: real] :
% 4.71/5.11 ( ( ord_less_real @ one_one_real @ B )
% 4.71/5.11 => ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.11 => ( ( ord_less_eq_real @ Y @ ( log @ B @ X ) )
% 4.71/5.11 = ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % le_log_iff
% 4.71/5.11 thf(fact_4678_log__le__iff,axiom,
% 4.71/5.11 ! [B: real,X: real,Y: real] :
% 4.71/5.11 ( ( ord_less_real @ one_one_real @ B )
% 4.71/5.11 => ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.11 => ( ( ord_less_eq_real @ ( log @ B @ X ) @ Y )
% 4.71/5.11 = ( ord_less_eq_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % log_le_iff
% 4.71/5.11 thf(fact_4679_le__powr__iff,axiom,
% 4.71/5.11 ! [B: real,X: real,Y: real] :
% 4.71/5.11 ( ( ord_less_real @ one_one_real @ B )
% 4.71/5.11 => ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.11 => ( ( ord_less_eq_real @ X @ ( powr_real @ B @ Y ) )
% 4.71/5.11 = ( ord_less_eq_real @ ( log @ B @ X ) @ Y ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % le_powr_iff
% 4.71/5.11 thf(fact_4680_powr__le__iff,axiom,
% 4.71/5.11 ! [B: real,X: real,Y: real] :
% 4.71/5.11 ( ( ord_less_real @ one_one_real @ B )
% 4.71/5.11 => ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.11 => ( ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X )
% 4.71/5.11 = ( ord_less_eq_real @ Y @ ( log @ B @ X ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % powr_le_iff
% 4.71/5.11 thf(fact_4681_le__minus__divide__eq,axiom,
% 4.71/5.11 ! [A: real,B: real,C: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 4.71/5.11 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.11 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 4.71/5.11 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.11 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.11 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 4.71/5.11 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.11 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % le_minus_divide_eq
% 4.71/5.11 thf(fact_4682_le__minus__divide__eq,axiom,
% 4.71/5.11 ! [A: rat,B: rat,C: rat] :
% 4.71/5.11 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 4.71/5.11 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.11 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 4.71/5.11 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.11 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.11 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 4.71/5.11 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.11 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % le_minus_divide_eq
% 4.71/5.11 thf(fact_4683_minus__divide__le__eq,axiom,
% 4.71/5.11 ! [B: real,C: real,A: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 4.71/5.11 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.11 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 4.71/5.11 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.11 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.11 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 4.71/5.11 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.11 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_divide_le_eq
% 4.71/5.11 thf(fact_4684_minus__divide__le__eq,axiom,
% 4.71/5.11 ! [B: rat,C: rat,A: rat] :
% 4.71/5.11 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 4.71/5.11 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.11 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 4.71/5.11 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.11 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.11 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 4.71/5.11 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.11 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % minus_divide_le_eq
% 4.71/5.11 thf(fact_4685_neg__le__minus__divide__eq,axiom,
% 4.71/5.11 ! [C: real,A: real,B: real] :
% 4.71/5.11 ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.11 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 4.71/5.11 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_le_minus_divide_eq
% 4.71/5.11 thf(fact_4686_neg__le__minus__divide__eq,axiom,
% 4.71/5.11 ! [C: rat,A: rat,B: rat] :
% 4.71/5.11 ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.11 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 4.71/5.11 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_le_minus_divide_eq
% 4.71/5.11 thf(fact_4687_neg__minus__divide__le__eq,axiom,
% 4.71/5.11 ! [C: real,B: real,A: real] :
% 4.71/5.11 ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.11 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 4.71/5.11 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_minus_divide_le_eq
% 4.71/5.11 thf(fact_4688_neg__minus__divide__le__eq,axiom,
% 4.71/5.11 ! [C: rat,B: rat,A: rat] :
% 4.71/5.11 ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.11 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 4.71/5.11 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_minus_divide_le_eq
% 4.71/5.11 thf(fact_4689_pos__le__minus__divide__eq,axiom,
% 4.71/5.11 ! [C: real,A: real,B: real] :
% 4.71/5.11 ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.11 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 4.71/5.11 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pos_le_minus_divide_eq
% 4.71/5.11 thf(fact_4690_pos__le__minus__divide__eq,axiom,
% 4.71/5.11 ! [C: rat,A: rat,B: rat] :
% 4.71/5.11 ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.11 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 4.71/5.11 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pos_le_minus_divide_eq
% 4.71/5.11 thf(fact_4691_pos__minus__divide__le__eq,axiom,
% 4.71/5.11 ! [C: real,B: real,A: real] :
% 4.71/5.11 ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.11 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 4.71/5.11 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pos_minus_divide_le_eq
% 4.71/5.11 thf(fact_4692_pos__minus__divide__le__eq,axiom,
% 4.71/5.11 ! [C: rat,B: rat,A: rat] :
% 4.71/5.11 ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.11 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 4.71/5.11 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pos_minus_divide_le_eq
% 4.71/5.11 thf(fact_4693_neg__int__cases,axiom,
% 4.71/5.11 ! [K: int] :
% 4.71/5.11 ( ( ord_less_int @ K @ zero_zero_int )
% 4.71/5.11 => ~ ! [N2: nat] :
% 4.71/5.11 ( ( K
% 4.71/5.11 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 4.71/5.11 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_int_cases
% 4.71/5.11 thf(fact_4694_nat__mult__distrib__neg,axiom,
% 4.71/5.11 ! [Z: int,Z6: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 4.71/5.11 => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
% 4.71/5.11 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z6 ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % nat_mult_distrib_neg
% 4.71/5.11 thf(fact_4695_ln__add__one__self__le__self2,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 4.71/5.11 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % ln_add_one_self_le_self2
% 4.71/5.11 thf(fact_4696_frac__neg,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ( ( ( member_real @ X @ ring_1_Ints_real )
% 4.71/5.11 => ( ( archim2898591450579166408c_real @ ( uminus_uminus_real @ X ) )
% 4.71/5.11 = zero_zero_real ) )
% 4.71/5.11 & ( ~ ( member_real @ X @ ring_1_Ints_real )
% 4.71/5.11 => ( ( archim2898591450579166408c_real @ ( uminus_uminus_real @ X ) )
% 4.71/5.11 = ( minus_minus_real @ one_one_real @ ( archim2898591450579166408c_real @ X ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % frac_neg
% 4.71/5.11 thf(fact_4697_frac__neg,axiom,
% 4.71/5.11 ! [X: rat] :
% 4.71/5.11 ( ( ( member_rat @ X @ ring_1_Ints_rat )
% 4.71/5.11 => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X ) )
% 4.71/5.11 = zero_zero_rat ) )
% 4.71/5.11 & ( ~ ( member_rat @ X @ ring_1_Ints_rat )
% 4.71/5.11 => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X ) )
% 4.71/5.11 = ( minus_minus_rat @ one_one_rat @ ( archimedean_frac_rat @ X ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % frac_neg
% 4.71/5.11 thf(fact_4698_ln__powr__bound,axiom,
% 4.71/5.11 ! [X: real,A: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ one_one_real @ X )
% 4.71/5.11 => ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.11 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( divide_divide_real @ ( powr_real @ X @ A ) @ A ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % ln_powr_bound
% 4.71/5.11 thf(fact_4699_ln__powr__bound2,axiom,
% 4.71/5.11 ! [X: real,A: real] :
% 4.71/5.11 ( ( ord_less_real @ one_one_real @ X )
% 4.71/5.11 => ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.11 => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % ln_powr_bound2
% 4.71/5.11 thf(fact_4700_sgn__power__root,axiom,
% 4.71/5.11 ! [N: nat,X: real] :
% 4.71/5.11 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.11 => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N @ X ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N @ X ) ) @ N ) )
% 4.71/5.11 = X ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_power_root
% 4.71/5.11 thf(fact_4701_root__sgn__power,axiom,
% 4.71/5.11 ! [N: nat,Y: real] :
% 4.71/5.11 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.11 => ( ( root @ N @ ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) ) )
% 4.71/5.11 = Y ) ) ).
% 4.71/5.11
% 4.71/5.11 % root_sgn_power
% 4.71/5.11 thf(fact_4702_gbinomial__negated__upper,axiom,
% 4.71/5.11 ( gbinomial_complex
% 4.71/5.11 = ( ^ [A4: complex,K3: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ K3 ) @ A4 ) @ one_one_complex ) @ K3 ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % gbinomial_negated_upper
% 4.71/5.11 thf(fact_4703_gbinomial__negated__upper,axiom,
% 4.71/5.11 ( gbinomial_real
% 4.71/5.11 = ( ^ [A4: real,K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( gbinomial_real @ ( minus_minus_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ K3 ) @ A4 ) @ one_one_real ) @ K3 ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % gbinomial_negated_upper
% 4.71/5.11 thf(fact_4704_gbinomial__negated__upper,axiom,
% 4.71/5.11 ( gbinomial_rat
% 4.71/5.11 = ( ^ [A4: rat,K3: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ K3 ) @ A4 ) @ one_one_rat ) @ K3 ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % gbinomial_negated_upper
% 4.71/5.11 thf(fact_4705_gbinomial__index__swap,axiom,
% 4.71/5.11 ! [K: nat,N: nat] :
% 4.71/5.11 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ one_one_complex ) @ K ) )
% 4.71/5.11 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ N ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % gbinomial_index_swap
% 4.71/5.11 thf(fact_4706_gbinomial__index__swap,axiom,
% 4.71/5.11 ! [K: nat,N: nat] :
% 4.71/5.11 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ one_one_real ) @ K ) )
% 4.71/5.11 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ N ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % gbinomial_index_swap
% 4.71/5.11 thf(fact_4707_gbinomial__index__swap,axiom,
% 4.71/5.11 ! [K: nat,N: nat] :
% 4.71/5.11 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ one_one_rat ) @ K ) )
% 4.71/5.11 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ N ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % gbinomial_index_swap
% 4.71/5.11 thf(fact_4708_zero__le__sgn__iff,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ X ) )
% 4.71/5.11 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % zero_le_sgn_iff
% 4.71/5.11 thf(fact_4709_sgn__le__0__iff,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ ( sgn_sgn_real @ X ) @ zero_zero_real )
% 4.71/5.11 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_le_0_iff
% 4.71/5.11 thf(fact_4710_mul__def,axiom,
% 4.71/5.11 ( vEBT_VEBT_mul
% 4.71/5.11 = ( vEBT_V4262088993061758097ft_nat @ times_times_nat ) ) ).
% 4.71/5.11
% 4.71/5.11 % mul_def
% 4.71/5.11 thf(fact_4711_add__def,axiom,
% 4.71/5.11 ( vEBT_VEBT_add
% 4.71/5.11 = ( vEBT_V4262088993061758097ft_nat @ plus_plus_nat ) ) ).
% 4.71/5.11
% 4.71/5.11 % add_def
% 4.71/5.11 thf(fact_4712_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 4.71/5.11 ! [K: nat,N: nat] :
% 4.71/5.11 ( ( ord_less_eq_nat @ K @ N )
% 4.71/5.11 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K ) )
% 4.71/5.11 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_one_power_add_eq_neg_one_power_diff
% 4.71/5.11 thf(fact_4713_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 4.71/5.11 ! [K: nat,N: nat] :
% 4.71/5.11 ( ( ord_less_eq_nat @ K @ N )
% 4.71/5.11 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N @ K ) )
% 4.71/5.11 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_one_power_add_eq_neg_one_power_diff
% 4.71/5.11 thf(fact_4714_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 4.71/5.11 ! [K: nat,N: nat] :
% 4.71/5.11 ( ( ord_less_eq_nat @ K @ N )
% 4.71/5.11 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K ) )
% 4.71/5.11 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_one_power_add_eq_neg_one_power_diff
% 4.71/5.11 thf(fact_4715_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 4.71/5.11 ! [K: nat,N: nat] :
% 4.71/5.11 ( ( ord_less_eq_nat @ K @ N )
% 4.71/5.11 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N @ K ) )
% 4.71/5.11 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % neg_one_power_add_eq_neg_one_power_diff
% 4.71/5.11 thf(fact_4716_sgn__one,axiom,
% 4.71/5.11 ( ( sgn_sgn_real @ one_one_real )
% 4.71/5.11 = one_one_real ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_one
% 4.71/5.11 thf(fact_4717_sgn__one,axiom,
% 4.71/5.11 ( ( sgn_sgn_complex @ one_one_complex )
% 4.71/5.11 = one_one_complex ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_one
% 4.71/5.11 thf(fact_4718_sgn__zero,axiom,
% 4.71/5.11 ( ( sgn_sgn_complex @ zero_zero_complex )
% 4.71/5.11 = zero_zero_complex ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_zero
% 4.71/5.11 thf(fact_4719_sgn__zero,axiom,
% 4.71/5.11 ( ( sgn_sgn_real @ zero_zero_real )
% 4.71/5.11 = zero_zero_real ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_zero
% 4.71/5.11 thf(fact_4720_ceiling__log__eq__powr__iff,axiom,
% 4.71/5.11 ! [X: real,B: real,K: nat] :
% 4.71/5.11 ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.11 => ( ( ord_less_real @ one_one_real @ B )
% 4.71/5.11 => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X ) )
% 4.71/5.11 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 4.71/5.11 = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X )
% 4.71/5.11 & ( ord_less_eq_real @ X @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_log_eq_powr_iff
% 4.71/5.11 thf(fact_4721_Compl__iff,axiom,
% 4.71/5.11 ! [C: $o,A2: set_o] :
% 4.71/5.11 ( ( member_o @ C @ ( uminus_uminus_set_o @ A2 ) )
% 4.71/5.11 = ( ~ ( member_o @ C @ A2 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % Compl_iff
% 4.71/5.11 thf(fact_4722_Compl__iff,axiom,
% 4.71/5.11 ! [C: set_nat,A2: set_set_nat] :
% 4.71/5.11 ( ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A2 ) )
% 4.71/5.11 = ( ~ ( member_set_nat @ C @ A2 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % Compl_iff
% 4.71/5.11 thf(fact_4723_Compl__iff,axiom,
% 4.71/5.11 ! [C: set_nat_rat,A2: set_set_nat_rat] :
% 4.71/5.11 ( ( member_set_nat_rat @ C @ ( uminus3098529973357106300at_rat @ A2 ) )
% 4.71/5.11 = ( ~ ( member_set_nat_rat @ C @ A2 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % Compl_iff
% 4.71/5.11 thf(fact_4724_Compl__iff,axiom,
% 4.71/5.11 ! [C: nat,A2: set_nat] :
% 4.71/5.11 ( ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A2 ) )
% 4.71/5.11 = ( ~ ( member_nat @ C @ A2 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % Compl_iff
% 4.71/5.11 thf(fact_4725_Compl__iff,axiom,
% 4.71/5.11 ! [C: int,A2: set_int] :
% 4.71/5.11 ( ( member_int @ C @ ( uminus1532241313380277803et_int @ A2 ) )
% 4.71/5.11 = ( ~ ( member_int @ C @ A2 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % Compl_iff
% 4.71/5.11 thf(fact_4726_ComplI,axiom,
% 4.71/5.11 ! [C: $o,A2: set_o] :
% 4.71/5.11 ( ~ ( member_o @ C @ A2 )
% 4.71/5.11 => ( member_o @ C @ ( uminus_uminus_set_o @ A2 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % ComplI
% 4.71/5.11 thf(fact_4727_ComplI,axiom,
% 4.71/5.11 ! [C: set_nat,A2: set_set_nat] :
% 4.71/5.11 ( ~ ( member_set_nat @ C @ A2 )
% 4.71/5.11 => ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A2 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % ComplI
% 4.71/5.11 thf(fact_4728_ComplI,axiom,
% 4.71/5.11 ! [C: set_nat_rat,A2: set_set_nat_rat] :
% 4.71/5.11 ( ~ ( member_set_nat_rat @ C @ A2 )
% 4.71/5.11 => ( member_set_nat_rat @ C @ ( uminus3098529973357106300at_rat @ A2 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % ComplI
% 4.71/5.11 thf(fact_4729_ComplI,axiom,
% 4.71/5.11 ! [C: nat,A2: set_nat] :
% 4.71/5.11 ( ~ ( member_nat @ C @ A2 )
% 4.71/5.11 => ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A2 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % ComplI
% 4.71/5.11 thf(fact_4730_ComplI,axiom,
% 4.71/5.11 ! [C: int,A2: set_int] :
% 4.71/5.11 ( ~ ( member_int @ C @ A2 )
% 4.71/5.11 => ( member_int @ C @ ( uminus1532241313380277803et_int @ A2 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % ComplI
% 4.71/5.11 thf(fact_4731_ceiling__zero,axiom,
% 4.71/5.11 ( ( archim2889992004027027881ng_rat @ zero_zero_rat )
% 4.71/5.11 = zero_zero_int ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_zero
% 4.71/5.11 thf(fact_4732_ceiling__zero,axiom,
% 4.71/5.11 ( ( archim7802044766580827645g_real @ zero_zero_real )
% 4.71/5.11 = zero_zero_int ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_zero
% 4.71/5.11 thf(fact_4733_ceiling__one,axiom,
% 4.71/5.11 ( ( archim2889992004027027881ng_rat @ one_one_rat )
% 4.71/5.11 = one_one_int ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_one
% 4.71/5.11 thf(fact_4734_ceiling__one,axiom,
% 4.71/5.11 ( ( archim7802044766580827645g_real @ one_one_real )
% 4.71/5.11 = one_one_int ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_one
% 4.71/5.11 thf(fact_4735_ceiling__le__zero,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ zero_zero_int )
% 4.71/5.11 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_le_zero
% 4.71/5.11 thf(fact_4736_ceiling__le__zero,axiom,
% 4.71/5.11 ! [X: rat] :
% 4.71/5.11 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ zero_zero_int )
% 4.71/5.11 = ( ord_less_eq_rat @ X @ zero_zero_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_le_zero
% 4.71/5.11 thf(fact_4737_zero__less__ceiling,axiom,
% 4.71/5.11 ! [X: rat] :
% 4.71/5.11 ( ( ord_less_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X ) )
% 4.71/5.11 = ( ord_less_rat @ zero_zero_rat @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % zero_less_ceiling
% 4.71/5.11 thf(fact_4738_zero__less__ceiling,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ( ( ord_less_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X ) )
% 4.71/5.11 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % zero_less_ceiling
% 4.71/5.11 thf(fact_4739_ceiling__less__one,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int )
% 4.71/5.11 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_less_one
% 4.71/5.11 thf(fact_4740_ceiling__less__one,axiom,
% 4.71/5.11 ! [X: rat] :
% 4.71/5.11 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int )
% 4.71/5.11 = ( ord_less_eq_rat @ X @ zero_zero_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_less_one
% 4.71/5.11 thf(fact_4741_one__le__ceiling,axiom,
% 4.71/5.11 ! [X: rat] :
% 4.71/5.11 ( ( ord_less_eq_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X ) )
% 4.71/5.11 = ( ord_less_rat @ zero_zero_rat @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % one_le_ceiling
% 4.71/5.11 thf(fact_4742_one__le__ceiling,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ( ( ord_less_eq_int @ one_one_int @ ( archim7802044766580827645g_real @ X ) )
% 4.71/5.11 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % one_le_ceiling
% 4.71/5.11 thf(fact_4743_ceiling__le__one,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int )
% 4.71/5.11 = ( ord_less_eq_real @ X @ one_one_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_le_one
% 4.71/5.11 thf(fact_4744_ceiling__le__one,axiom,
% 4.71/5.11 ! [X: rat] :
% 4.71/5.11 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int )
% 4.71/5.11 = ( ord_less_eq_rat @ X @ one_one_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_le_one
% 4.71/5.11 thf(fact_4745_one__less__ceiling,axiom,
% 4.71/5.11 ! [X: rat] :
% 4.71/5.11 ( ( ord_less_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X ) )
% 4.71/5.11 = ( ord_less_rat @ one_one_rat @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % one_less_ceiling
% 4.71/5.11 thf(fact_4746_one__less__ceiling,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ( ( ord_less_int @ one_one_int @ ( archim7802044766580827645g_real @ X ) )
% 4.71/5.11 = ( ord_less_real @ one_one_real @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % one_less_ceiling
% 4.71/5.11 thf(fact_4747_ceiling__add__one,axiom,
% 4.71/5.11 ! [X: rat] :
% 4.71/5.11 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ one_one_rat ) )
% 4.71/5.11 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_add_one
% 4.71/5.11 thf(fact_4748_ceiling__add__one,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ one_one_real ) )
% 4.71/5.11 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_add_one
% 4.71/5.11 thf(fact_4749_ceiling__diff__one,axiom,
% 4.71/5.11 ! [X: rat] :
% 4.71/5.11 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X @ one_one_rat ) )
% 4.71/5.11 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_diff_one
% 4.71/5.11 thf(fact_4750_ceiling__diff__one,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X @ one_one_real ) )
% 4.71/5.11 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_diff_one
% 4.71/5.11 thf(fact_4751_nat__ceiling__le__eq,axiom,
% 4.71/5.11 ! [X: real,A: nat] :
% 4.71/5.11 ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) @ A )
% 4.71/5.11 = ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % nat_ceiling_le_eq
% 4.71/5.11 thf(fact_4752_ceiling__less__zero,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ zero_zero_int )
% 4.71/5.11 = ( ord_less_eq_real @ X @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_less_zero
% 4.71/5.11 thf(fact_4753_ceiling__less__zero,axiom,
% 4.71/5.11 ! [X: rat] :
% 4.71/5.11 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ zero_zero_int )
% 4.71/5.11 = ( ord_less_eq_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_less_zero
% 4.71/5.11 thf(fact_4754_zero__le__ceiling,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ( ( ord_less_eq_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X ) )
% 4.71/5.11 = ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % zero_le_ceiling
% 4.71/5.11 thf(fact_4755_zero__le__ceiling,axiom,
% 4.71/5.11 ! [X: rat] :
% 4.71/5.11 ( ( ord_less_eq_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X ) )
% 4.71/5.11 = ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % zero_le_ceiling
% 4.71/5.11 thf(fact_4756_ComplD,axiom,
% 4.71/5.11 ! [C: $o,A2: set_o] :
% 4.71/5.11 ( ( member_o @ C @ ( uminus_uminus_set_o @ A2 ) )
% 4.71/5.11 => ~ ( member_o @ C @ A2 ) ) ).
% 4.71/5.11
% 4.71/5.11 % ComplD
% 4.71/5.11 thf(fact_4757_ComplD,axiom,
% 4.71/5.11 ! [C: set_nat,A2: set_set_nat] :
% 4.71/5.11 ( ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A2 ) )
% 4.71/5.11 => ~ ( member_set_nat @ C @ A2 ) ) ).
% 4.71/5.11
% 4.71/5.11 % ComplD
% 4.71/5.11 thf(fact_4758_ComplD,axiom,
% 4.71/5.11 ! [C: set_nat_rat,A2: set_set_nat_rat] :
% 4.71/5.11 ( ( member_set_nat_rat @ C @ ( uminus3098529973357106300at_rat @ A2 ) )
% 4.71/5.11 => ~ ( member_set_nat_rat @ C @ A2 ) ) ).
% 4.71/5.11
% 4.71/5.11 % ComplD
% 4.71/5.11 thf(fact_4759_ComplD,axiom,
% 4.71/5.11 ! [C: nat,A2: set_nat] :
% 4.71/5.11 ( ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A2 ) )
% 4.71/5.11 => ~ ( member_nat @ C @ A2 ) ) ).
% 4.71/5.11
% 4.71/5.11 % ComplD
% 4.71/5.11 thf(fact_4760_ComplD,axiom,
% 4.71/5.11 ! [C: int,A2: set_int] :
% 4.71/5.11 ( ( member_int @ C @ ( uminus1532241313380277803et_int @ A2 ) )
% 4.71/5.11 => ~ ( member_int @ C @ A2 ) ) ).
% 4.71/5.11
% 4.71/5.11 % ComplD
% 4.71/5.11 thf(fact_4761_ceiling__mono,axiom,
% 4.71/5.11 ! [Y: real,X: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ Y @ X )
% 4.71/5.11 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ Y ) @ ( archim7802044766580827645g_real @ X ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_mono
% 4.71/5.11 thf(fact_4762_ceiling__mono,axiom,
% 4.71/5.11 ! [Y: rat,X: rat] :
% 4.71/5.11 ( ( ord_less_eq_rat @ Y @ X )
% 4.71/5.11 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ Y ) @ ( archim2889992004027027881ng_rat @ X ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_mono
% 4.71/5.11 thf(fact_4763_ceiling__less__cancel,axiom,
% 4.71/5.11 ! [X: rat,Y: rat] :
% 4.71/5.11 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim2889992004027027881ng_rat @ Y ) )
% 4.71/5.11 => ( ord_less_rat @ X @ Y ) ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_less_cancel
% 4.71/5.11 thf(fact_4764_ceiling__less__cancel,axiom,
% 4.71/5.11 ! [X: real,Y: real] :
% 4.71/5.11 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( archim7802044766580827645g_real @ Y ) )
% 4.71/5.11 => ( ord_less_real @ X @ Y ) ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_less_cancel
% 4.71/5.11 thf(fact_4765_of__nat__ceiling,axiom,
% 4.71/5.11 ! [R2: real] : ( ord_less_eq_real @ R2 @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ R2 ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_nat_ceiling
% 4.71/5.11 thf(fact_4766_of__nat__ceiling,axiom,
% 4.71/5.11 ! [R2: rat] : ( ord_less_eq_rat @ R2 @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim2889992004027027881ng_rat @ R2 ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_nat_ceiling
% 4.71/5.11 thf(fact_4767_ceiling__add__le,axiom,
% 4.71/5.11 ! [X: rat,Y: rat] : ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ Y ) ) @ ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim2889992004027027881ng_rat @ Y ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_add_le
% 4.71/5.11 thf(fact_4768_ceiling__add__le,axiom,
% 4.71/5.11 ! [X: real,Y: real] : ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ ( archim7802044766580827645g_real @ Y ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_add_le
% 4.71/5.11 thf(fact_4769_real__nat__ceiling__ge,axiom,
% 4.71/5.11 ! [X: real] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % real_nat_ceiling_ge
% 4.71/5.11 thf(fact_4770_mult__ceiling__le,axiom,
% 4.71/5.11 ! [A: real,B: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.11 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.71/5.11 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % mult_ceiling_le
% 4.71/5.11 thf(fact_4771_mult__ceiling__le,axiom,
% 4.71/5.11 ! [A: rat,B: rat] :
% 4.71/5.11 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.11 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.71/5.11 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % mult_ceiling_le
% 4.71/5.11 thf(fact_4772_sgn__zero__iff,axiom,
% 4.71/5.11 ! [X: complex] :
% 4.71/5.11 ( ( ( sgn_sgn_complex @ X )
% 4.71/5.11 = zero_zero_complex )
% 4.71/5.11 = ( X = zero_zero_complex ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_zero_iff
% 4.71/5.11 thf(fact_4773_sgn__zero__iff,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ( ( ( sgn_sgn_real @ X )
% 4.71/5.11 = zero_zero_real )
% 4.71/5.11 = ( X = zero_zero_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % sgn_zero_iff
% 4.71/5.11 thf(fact_4774_powr__int,axiom,
% 4.71/5.11 ! [X: real,I: int] :
% 4.71/5.11 ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.11 => ( ( ( ord_less_eq_int @ zero_zero_int @ I )
% 4.71/5.11 => ( ( powr_real @ X @ ( ring_1_of_int_real @ I ) )
% 4.71/5.11 = ( power_power_real @ X @ ( nat2 @ I ) ) ) )
% 4.71/5.11 & ( ~ ( ord_less_eq_int @ zero_zero_int @ I )
% 4.71/5.11 => ( ( powr_real @ X @ ( ring_1_of_int_real @ I ) )
% 4.71/5.11 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ I ) ) ) ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % powr_int
% 4.71/5.11 thf(fact_4775_dbl__dec__simps_I2_J,axiom,
% 4.71/5.11 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 4.71/5.11 = ( uminus_uminus_int @ one_one_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % dbl_dec_simps(2)
% 4.71/5.11 thf(fact_4776_dbl__dec__simps_I2_J,axiom,
% 4.71/5.11 ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 4.71/5.11 = ( uminus_uminus_real @ one_one_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % dbl_dec_simps(2)
% 4.71/5.11 thf(fact_4777_dbl__dec__simps_I2_J,axiom,
% 4.71/5.11 ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 4.71/5.11 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % dbl_dec_simps(2)
% 4.71/5.11 thf(fact_4778_dbl__dec__simps_I2_J,axiom,
% 4.71/5.11 ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 4.71/5.11 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 4.71/5.11
% 4.71/5.11 % dbl_dec_simps(2)
% 4.71/5.11 thf(fact_4779_exp__ge__one__minus__x__over__n__power__n,axiom,
% 4.71/5.11 ! [X: real,N: nat] :
% 4.71/5.11 ( ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 4.71/5.11 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.11 => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % exp_ge_one_minus_x_over_n_power_n
% 4.71/5.11 thf(fact_4780_exp__ge__one__plus__x__over__n__power__n,axiom,
% 4.71/5.11 ! [N: nat,X: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ X )
% 4.71/5.11 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.11 => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ X ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % exp_ge_one_plus_x_over_n_power_n
% 4.71/5.11 thf(fact_4781_power__shift,axiom,
% 4.71/5.11 ! [X: nat,Y: nat,Z: nat] :
% 4.71/5.11 ( ( ( power_power_nat @ X @ Y )
% 4.71/5.11 = Z )
% 4.71/5.11 = ( ( vEBT_VEBT_power @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 4.71/5.11 = ( some_nat @ Z ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % power_shift
% 4.71/5.11 thf(fact_4782_pochhammer__minus,axiom,
% 4.71/5.11 ! [B: complex,K: nat] :
% 4.71/5.11 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K )
% 4.71/5.11 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_minus
% 4.71/5.11 thf(fact_4783_pochhammer__minus,axiom,
% 4.71/5.11 ! [B: int,K: nat] :
% 4.71/5.11 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 4.71/5.11 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_minus
% 4.71/5.11 thf(fact_4784_pochhammer__minus,axiom,
% 4.71/5.11 ! [B: real,K: nat] :
% 4.71/5.11 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K )
% 4.71/5.11 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_minus
% 4.71/5.11 thf(fact_4785_pochhammer__minus,axiom,
% 4.71/5.11 ! [B: rat,K: nat] :
% 4.71/5.11 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 4.71/5.11 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_minus
% 4.71/5.11 thf(fact_4786_pochhammer__minus_H,axiom,
% 4.71/5.11 ! [B: complex,K: nat] :
% 4.71/5.11 ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K )
% 4.71/5.11 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_minus'
% 4.71/5.11 thf(fact_4787_pochhammer__minus_H,axiom,
% 4.71/5.11 ! [B: int,K: nat] :
% 4.71/5.11 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 4.71/5.11 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_minus'
% 4.71/5.11 thf(fact_4788_pochhammer__minus_H,axiom,
% 4.71/5.11 ! [B: real,K: nat] :
% 4.71/5.11 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K )
% 4.71/5.11 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_minus'
% 4.71/5.11 thf(fact_4789_pochhammer__minus_H,axiom,
% 4.71/5.11 ! [B: rat,K: nat] :
% 4.71/5.11 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 4.71/5.11 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_minus'
% 4.71/5.11 thf(fact_4790_ceiling__eq,axiom,
% 4.71/5.11 ! [N: int,X: real] :
% 4.71/5.11 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X )
% 4.71/5.11 => ( ( ord_less_eq_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 4.71/5.11 => ( ( archim7802044766580827645g_real @ X )
% 4.71/5.11 = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_eq
% 4.71/5.11 thf(fact_4791_ceiling__eq,axiom,
% 4.71/5.11 ! [N: int,X: rat] :
% 4.71/5.11 ( ( ord_less_rat @ ( ring_1_of_int_rat @ N ) @ X )
% 4.71/5.11 => ( ( ord_less_eq_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ N ) @ one_one_rat ) )
% 4.71/5.11 => ( ( archim2889992004027027881ng_rat @ X )
% 4.71/5.11 = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_eq
% 4.71/5.11 thf(fact_4792_add__shift,axiom,
% 4.71/5.11 ! [X: nat,Y: nat,Z: nat] :
% 4.71/5.11 ( ( ( plus_plus_nat @ X @ Y )
% 4.71/5.11 = Z )
% 4.71/5.11 = ( ( vEBT_VEBT_add @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 4.71/5.11 = ( some_nat @ Z ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % add_shift
% 4.71/5.11 thf(fact_4793_mul__shift,axiom,
% 4.71/5.11 ! [X: nat,Y: nat,Z: nat] :
% 4.71/5.11 ( ( ( times_times_nat @ X @ Y )
% 4.71/5.11 = Z )
% 4.71/5.11 = ( ( vEBT_VEBT_mul @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 4.71/5.11 = ( some_nat @ Z ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % mul_shift
% 4.71/5.11 thf(fact_4794_exp__le__cancel__iff,axiom,
% 4.71/5.11 ! [X: real,Y: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 4.71/5.11 = ( ord_less_eq_real @ X @ Y ) ) ).
% 4.71/5.11
% 4.71/5.11 % exp_le_cancel_iff
% 4.71/5.11 thf(fact_4795_of__int__ceiling__cancel,axiom,
% 4.71/5.11 ! [X: rat] :
% 4.71/5.11 ( ( ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) )
% 4.71/5.11 = X )
% 4.71/5.11 = ( ? [N4: int] :
% 4.71/5.11 ( X
% 4.71/5.11 = ( ring_1_of_int_rat @ N4 ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_ceiling_cancel
% 4.71/5.11 thf(fact_4796_of__int__ceiling__cancel,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ( ( ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) )
% 4.71/5.11 = X )
% 4.71/5.11 = ( ? [N4: int] :
% 4.71/5.11 ( X
% 4.71/5.11 = ( ring_1_of_int_real @ N4 ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_ceiling_cancel
% 4.71/5.11 thf(fact_4797_dbl__dec__simps_I3_J,axiom,
% 4.71/5.11 ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 4.71/5.11 = one_one_complex ) ).
% 4.71/5.11
% 4.71/5.11 % dbl_dec_simps(3)
% 4.71/5.11 thf(fact_4798_dbl__dec__simps_I3_J,axiom,
% 4.71/5.11 ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 4.71/5.11 = one_one_real ) ).
% 4.71/5.11
% 4.71/5.11 % dbl_dec_simps(3)
% 4.71/5.11 thf(fact_4799_dbl__dec__simps_I3_J,axiom,
% 4.71/5.11 ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 4.71/5.11 = one_one_rat ) ).
% 4.71/5.11
% 4.71/5.11 % dbl_dec_simps(3)
% 4.71/5.11 thf(fact_4800_dbl__dec__simps_I3_J,axiom,
% 4.71/5.11 ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 4.71/5.11 = one_one_int ) ).
% 4.71/5.11
% 4.71/5.11 % dbl_dec_simps(3)
% 4.71/5.11 thf(fact_4801_of__int__0,axiom,
% 4.71/5.11 ( ( ring_1_of_int_int @ zero_zero_int )
% 4.71/5.11 = zero_zero_int ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_0
% 4.71/5.11 thf(fact_4802_of__int__0,axiom,
% 4.71/5.11 ( ( ring_1_of_int_real @ zero_zero_int )
% 4.71/5.11 = zero_zero_real ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_0
% 4.71/5.11 thf(fact_4803_of__int__0,axiom,
% 4.71/5.11 ( ( ring_1_of_int_rat @ zero_zero_int )
% 4.71/5.11 = zero_zero_rat ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_0
% 4.71/5.11 thf(fact_4804_of__int__0__eq__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( zero_zero_int
% 4.71/5.11 = ( ring_1_of_int_int @ Z ) )
% 4.71/5.11 = ( Z = zero_zero_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_0_eq_iff
% 4.71/5.11 thf(fact_4805_of__int__0__eq__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( zero_zero_real
% 4.71/5.11 = ( ring_1_of_int_real @ Z ) )
% 4.71/5.11 = ( Z = zero_zero_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_0_eq_iff
% 4.71/5.11 thf(fact_4806_of__int__0__eq__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( zero_zero_rat
% 4.71/5.11 = ( ring_1_of_int_rat @ Z ) )
% 4.71/5.11 = ( Z = zero_zero_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_0_eq_iff
% 4.71/5.11 thf(fact_4807_of__int__eq__0__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ( ring_1_of_int_int @ Z )
% 4.71/5.11 = zero_zero_int )
% 4.71/5.11 = ( Z = zero_zero_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_eq_0_iff
% 4.71/5.11 thf(fact_4808_of__int__eq__0__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ( ring_1_of_int_real @ Z )
% 4.71/5.11 = zero_zero_real )
% 4.71/5.11 = ( Z = zero_zero_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_eq_0_iff
% 4.71/5.11 thf(fact_4809_of__int__eq__0__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ( ring_1_of_int_rat @ Z )
% 4.71/5.11 = zero_zero_rat )
% 4.71/5.11 = ( Z = zero_zero_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_eq_0_iff
% 4.71/5.11 thf(fact_4810_exp__zero,axiom,
% 4.71/5.11 ( ( exp_complex @ zero_zero_complex )
% 4.71/5.11 = one_one_complex ) ).
% 4.71/5.11
% 4.71/5.11 % exp_zero
% 4.71/5.11 thf(fact_4811_exp__zero,axiom,
% 4.71/5.11 ( ( exp_real @ zero_zero_real )
% 4.71/5.11 = one_one_real ) ).
% 4.71/5.11
% 4.71/5.11 % exp_zero
% 4.71/5.11 thf(fact_4812_of__int__le__iff,axiom,
% 4.71/5.11 ! [W2: int,Z: int] :
% 4.71/5.11 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W2 ) @ ( ring_1_of_int_real @ Z ) )
% 4.71/5.11 = ( ord_less_eq_int @ W2 @ Z ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_le_iff
% 4.71/5.11 thf(fact_4813_of__int__le__iff,axiom,
% 4.71/5.11 ! [W2: int,Z: int] :
% 4.71/5.11 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z ) )
% 4.71/5.11 = ( ord_less_eq_int @ W2 @ Z ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_le_iff
% 4.71/5.11 thf(fact_4814_of__int__le__iff,axiom,
% 4.71/5.11 ! [W2: int,Z: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z ) )
% 4.71/5.11 = ( ord_less_eq_int @ W2 @ Z ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_le_iff
% 4.71/5.11 thf(fact_4815_of__int__less__iff,axiom,
% 4.71/5.11 ! [W2: int,Z: int] :
% 4.71/5.11 ( ( ord_less_real @ ( ring_1_of_int_real @ W2 ) @ ( ring_1_of_int_real @ Z ) )
% 4.71/5.11 = ( ord_less_int @ W2 @ Z ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_less_iff
% 4.71/5.11 thf(fact_4816_of__int__less__iff,axiom,
% 4.71/5.11 ! [W2: int,Z: int] :
% 4.71/5.11 ( ( ord_less_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z ) )
% 4.71/5.11 = ( ord_less_int @ W2 @ Z ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_less_iff
% 4.71/5.11 thf(fact_4817_of__int__less__iff,axiom,
% 4.71/5.11 ! [W2: int,Z: int] :
% 4.71/5.11 ( ( ord_less_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z ) )
% 4.71/5.11 = ( ord_less_int @ W2 @ Z ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_less_iff
% 4.71/5.11 thf(fact_4818_of__int__1,axiom,
% 4.71/5.11 ( ( ring_17405671764205052669omplex @ one_one_int )
% 4.71/5.11 = one_one_complex ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_1
% 4.71/5.11 thf(fact_4819_of__int__1,axiom,
% 4.71/5.11 ( ( ring_1_of_int_int @ one_one_int )
% 4.71/5.11 = one_one_int ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_1
% 4.71/5.11 thf(fact_4820_of__int__1,axiom,
% 4.71/5.11 ( ( ring_1_of_int_real @ one_one_int )
% 4.71/5.11 = one_one_real ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_1
% 4.71/5.11 thf(fact_4821_of__int__1,axiom,
% 4.71/5.11 ( ( ring_1_of_int_rat @ one_one_int )
% 4.71/5.11 = one_one_rat ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_1
% 4.71/5.11 thf(fact_4822_of__int__eq__1__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ( ring_17405671764205052669omplex @ Z )
% 4.71/5.11 = one_one_complex )
% 4.71/5.11 = ( Z = one_one_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_eq_1_iff
% 4.71/5.11 thf(fact_4823_of__int__eq__1__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ( ring_1_of_int_int @ Z )
% 4.71/5.11 = one_one_int )
% 4.71/5.11 = ( Z = one_one_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_eq_1_iff
% 4.71/5.11 thf(fact_4824_of__int__eq__1__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ( ring_1_of_int_real @ Z )
% 4.71/5.11 = one_one_real )
% 4.71/5.11 = ( Z = one_one_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_eq_1_iff
% 4.71/5.11 thf(fact_4825_of__int__eq__1__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ( ring_1_of_int_rat @ Z )
% 4.71/5.11 = one_one_rat )
% 4.71/5.11 = ( Z = one_one_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_eq_1_iff
% 4.71/5.11 thf(fact_4826_pochhammer__0,axiom,
% 4.71/5.11 ! [A: complex] :
% 4.71/5.11 ( ( comm_s2602460028002588243omplex @ A @ zero_zero_nat )
% 4.71/5.11 = one_one_complex ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_0
% 4.71/5.11 thf(fact_4827_pochhammer__0,axiom,
% 4.71/5.11 ! [A: real] :
% 4.71/5.11 ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 4.71/5.11 = one_one_real ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_0
% 4.71/5.11 thf(fact_4828_pochhammer__0,axiom,
% 4.71/5.11 ! [A: rat] :
% 4.71/5.11 ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 4.71/5.11 = one_one_rat ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_0
% 4.71/5.11 thf(fact_4829_pochhammer__0,axiom,
% 4.71/5.11 ! [A: nat] :
% 4.71/5.11 ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 4.71/5.11 = one_one_nat ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_0
% 4.71/5.11 thf(fact_4830_pochhammer__0,axiom,
% 4.71/5.11 ! [A: int] :
% 4.71/5.11 ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 4.71/5.11 = one_one_int ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_0
% 4.71/5.11 thf(fact_4831_frac__of__int,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( archim2898591450579166408c_real @ ( ring_1_of_int_real @ Z ) )
% 4.71/5.11 = zero_zero_real ) ).
% 4.71/5.11
% 4.71/5.11 % frac_of_int
% 4.71/5.11 thf(fact_4832_frac__of__int,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( archimedean_frac_rat @ ( ring_1_of_int_rat @ Z ) )
% 4.71/5.11 = zero_zero_rat ) ).
% 4.71/5.11
% 4.71/5.11 % frac_of_int
% 4.71/5.11 thf(fact_4833_exp__le__one__iff,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ ( exp_real @ X ) @ one_one_real )
% 4.71/5.11 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % exp_le_one_iff
% 4.71/5.11 thf(fact_4834_one__le__exp__iff,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X ) )
% 4.71/5.11 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % one_le_exp_iff
% 4.71/5.11 thf(fact_4835_lesseq__shift,axiom,
% 4.71/5.11 ( ord_less_eq_nat
% 4.71/5.11 = ( ^ [X3: nat,Y2: nat] : ( vEBT_VEBT_lesseq @ ( some_nat @ X3 ) @ ( some_nat @ Y2 ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % lesseq_shift
% 4.71/5.11 thf(fact_4836_of__int__0__le__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 4.71/5.11 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_0_le_iff
% 4.71/5.11 thf(fact_4837_of__int__0__le__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 4.71/5.11 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_0_le_iff
% 4.71/5.11 thf(fact_4838_of__int__0__le__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 4.71/5.11 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_0_le_iff
% 4.71/5.11 thf(fact_4839_of__int__le__0__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 4.71/5.11 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_le_0_iff
% 4.71/5.11 thf(fact_4840_of__int__le__0__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 4.71/5.11 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_le_0_iff
% 4.71/5.11 thf(fact_4841_of__int__le__0__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 4.71/5.11 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_le_0_iff
% 4.71/5.11 thf(fact_4842_of__int__0__less__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 4.71/5.11 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_0_less_iff
% 4.71/5.11 thf(fact_4843_of__int__0__less__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 4.71/5.11 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_0_less_iff
% 4.71/5.11 thf(fact_4844_of__int__0__less__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 4.71/5.11 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_0_less_iff
% 4.71/5.11 thf(fact_4845_of__int__less__0__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 4.71/5.11 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_less_0_iff
% 4.71/5.11 thf(fact_4846_of__int__less__0__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 4.71/5.11 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_less_0_iff
% 4.71/5.11 thf(fact_4847_of__int__less__0__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 4.71/5.11 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_less_0_iff
% 4.71/5.11 thf(fact_4848_of__int__1__le__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 4.71/5.11 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_1_le_iff
% 4.71/5.11 thf(fact_4849_of__int__1__le__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 4.71/5.11 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_1_le_iff
% 4.71/5.11 thf(fact_4850_of__int__1__le__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 4.71/5.11 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_1_le_iff
% 4.71/5.11 thf(fact_4851_of__int__le__1__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 4.71/5.11 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_le_1_iff
% 4.71/5.11 thf(fact_4852_of__int__le__1__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 4.71/5.11 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_le_1_iff
% 4.71/5.11 thf(fact_4853_of__int__le__1__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 4.71/5.11 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_le_1_iff
% 4.71/5.11 thf(fact_4854_of__int__1__less__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 4.71/5.11 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_1_less_iff
% 4.71/5.11 thf(fact_4855_of__int__1__less__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 4.71/5.11 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_1_less_iff
% 4.71/5.11 thf(fact_4856_of__int__1__less__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 4.71/5.11 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_1_less_iff
% 4.71/5.11 thf(fact_4857_of__int__less__1__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 4.71/5.11 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_less_1_iff
% 4.71/5.11 thf(fact_4858_of__int__less__1__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 4.71/5.11 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_less_1_iff
% 4.71/5.11 thf(fact_4859_of__int__less__1__iff,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 4.71/5.11 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_less_1_iff
% 4.71/5.11 thf(fact_4860_of__int__le__of__int__power__cancel__iff,axiom,
% 4.71/5.11 ! [B: int,W2: nat,X: int] :
% 4.71/5.11 ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W2 ) @ ( ring_1_of_int_real @ X ) )
% 4.71/5.11 = ( ord_less_eq_int @ ( power_power_int @ B @ W2 ) @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_le_of_int_power_cancel_iff
% 4.71/5.11 thf(fact_4861_of__int__le__of__int__power__cancel__iff,axiom,
% 4.71/5.11 ! [B: int,W2: nat,X: int] :
% 4.71/5.11 ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) @ ( ring_1_of_int_rat @ X ) )
% 4.71/5.11 = ( ord_less_eq_int @ ( power_power_int @ B @ W2 ) @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_le_of_int_power_cancel_iff
% 4.71/5.11 thf(fact_4862_of__int__le__of__int__power__cancel__iff,axiom,
% 4.71/5.11 ! [B: int,W2: nat,X: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) @ ( ring_1_of_int_int @ X ) )
% 4.71/5.11 = ( ord_less_eq_int @ ( power_power_int @ B @ W2 ) @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_le_of_int_power_cancel_iff
% 4.71/5.11 thf(fact_4863_of__int__power__le__of__int__cancel__iff,axiom,
% 4.71/5.11 ! [X: int,B: int,W2: nat] :
% 4.71/5.11 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W2 ) )
% 4.71/5.11 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W2 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_power_le_of_int_cancel_iff
% 4.71/5.11 thf(fact_4864_of__int__power__le__of__int__cancel__iff,axiom,
% 4.71/5.11 ! [X: int,B: int,W2: nat] :
% 4.71/5.11 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) )
% 4.71/5.11 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W2 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_power_le_of_int_cancel_iff
% 4.71/5.11 thf(fact_4865_of__int__power__le__of__int__cancel__iff,axiom,
% 4.71/5.11 ! [X: int,B: int,W2: nat] :
% 4.71/5.11 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) )
% 4.71/5.11 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W2 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_power_le_of_int_cancel_iff
% 4.71/5.11 thf(fact_4866_of__int__less__of__int__power__cancel__iff,axiom,
% 4.71/5.11 ! [B: int,W2: nat,X: int] :
% 4.71/5.11 ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W2 ) @ ( ring_1_of_int_real @ X ) )
% 4.71/5.11 = ( ord_less_int @ ( power_power_int @ B @ W2 ) @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_less_of_int_power_cancel_iff
% 4.71/5.11 thf(fact_4867_of__int__less__of__int__power__cancel__iff,axiom,
% 4.71/5.11 ! [B: int,W2: nat,X: int] :
% 4.71/5.11 ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) @ ( ring_1_of_int_rat @ X ) )
% 4.71/5.11 = ( ord_less_int @ ( power_power_int @ B @ W2 ) @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_less_of_int_power_cancel_iff
% 4.71/5.11 thf(fact_4868_of__int__less__of__int__power__cancel__iff,axiom,
% 4.71/5.11 ! [B: int,W2: nat,X: int] :
% 4.71/5.11 ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) @ ( ring_1_of_int_int @ X ) )
% 4.71/5.11 = ( ord_less_int @ ( power_power_int @ B @ W2 ) @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_less_of_int_power_cancel_iff
% 4.71/5.11 thf(fact_4869_of__int__power__less__of__int__cancel__iff,axiom,
% 4.71/5.11 ! [X: int,B: int,W2: nat] :
% 4.71/5.11 ( ( ord_less_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W2 ) )
% 4.71/5.11 = ( ord_less_int @ X @ ( power_power_int @ B @ W2 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_power_less_of_int_cancel_iff
% 4.71/5.11 thf(fact_4870_of__int__power__less__of__int__cancel__iff,axiom,
% 4.71/5.11 ! [X: int,B: int,W2: nat] :
% 4.71/5.11 ( ( ord_less_rat @ ( ring_1_of_int_rat @ X ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) )
% 4.71/5.11 = ( ord_less_int @ X @ ( power_power_int @ B @ W2 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_power_less_of_int_cancel_iff
% 4.71/5.11 thf(fact_4871_of__int__power__less__of__int__cancel__iff,axiom,
% 4.71/5.11 ! [X: int,B: int,W2: nat] :
% 4.71/5.11 ( ( ord_less_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) )
% 4.71/5.11 = ( ord_less_int @ X @ ( power_power_int @ B @ W2 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_power_less_of_int_cancel_iff
% 4.71/5.11 thf(fact_4872_of__nat__nat,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 4.71/5.11 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 4.71/5.11 = ( ring_1_of_int_int @ Z ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_nat_nat
% 4.71/5.11 thf(fact_4873_of__nat__nat,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 4.71/5.11 => ( ( semiri5074537144036343181t_real @ ( nat2 @ Z ) )
% 4.71/5.11 = ( ring_1_of_int_real @ Z ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_nat_nat
% 4.71/5.11 thf(fact_4874_of__nat__nat,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 4.71/5.11 => ( ( semiri681578069525770553at_rat @ ( nat2 @ Z ) )
% 4.71/5.11 = ( ring_1_of_int_rat @ Z ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_nat_nat
% 4.71/5.11 thf(fact_4875_ex__le__of__int,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ? [Z3: int] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z3 ) ) ).
% 4.71/5.11
% 4.71/5.11 % ex_le_of_int
% 4.71/5.11 thf(fact_4876_ex__le__of__int,axiom,
% 4.71/5.11 ! [X: rat] :
% 4.71/5.11 ? [Z3: int] : ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z3 ) ) ).
% 4.71/5.11
% 4.71/5.11 % ex_le_of_int
% 4.71/5.11 thf(fact_4877_ex__less__of__int,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ? [Z3: int] : ( ord_less_real @ X @ ( ring_1_of_int_real @ Z3 ) ) ).
% 4.71/5.11
% 4.71/5.11 % ex_less_of_int
% 4.71/5.11 thf(fact_4878_ex__less__of__int,axiom,
% 4.71/5.11 ! [X: rat] :
% 4.71/5.11 ? [Z3: int] : ( ord_less_rat @ X @ ( ring_1_of_int_rat @ Z3 ) ) ).
% 4.71/5.11
% 4.71/5.11 % ex_less_of_int
% 4.71/5.11 thf(fact_4879_ex__of__int__less,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ? [Z3: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z3 ) @ X ) ).
% 4.71/5.11
% 4.71/5.11 % ex_of_int_less
% 4.71/5.11 thf(fact_4880_ex__of__int__less,axiom,
% 4.71/5.11 ! [X: rat] :
% 4.71/5.11 ? [Z3: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z3 ) @ X ) ).
% 4.71/5.11
% 4.71/5.11 % ex_of_int_less
% 4.71/5.11 thf(fact_4881_exp__not__eq__zero,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ( ( exp_real @ X )
% 4.71/5.11 != zero_zero_real ) ).
% 4.71/5.11
% 4.71/5.11 % exp_not_eq_zero
% 4.71/5.11 thf(fact_4882_exp__ge__zero,axiom,
% 4.71/5.11 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % exp_ge_zero
% 4.71/5.11 thf(fact_4883_not__exp__le__zero,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ~ ( ord_less_eq_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 4.71/5.11
% 4.71/5.11 % not_exp_le_zero
% 4.71/5.11 thf(fact_4884_le__of__int__ceiling,axiom,
% 4.71/5.11 ! [X: real] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % le_of_int_ceiling
% 4.71/5.11 thf(fact_4885_le__of__int__ceiling,axiom,
% 4.71/5.11 ! [X: rat] : ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % le_of_int_ceiling
% 4.71/5.11 thf(fact_4886_pochhammer__pos,axiom,
% 4.71/5.11 ! [X: real,N: nat] :
% 4.71/5.11 ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.11 => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_pos
% 4.71/5.11 thf(fact_4887_pochhammer__pos,axiom,
% 4.71/5.11 ! [X: rat,N: nat] :
% 4.71/5.11 ( ( ord_less_rat @ zero_zero_rat @ X )
% 4.71/5.11 => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_pos
% 4.71/5.11 thf(fact_4888_pochhammer__pos,axiom,
% 4.71/5.11 ! [X: nat,N: nat] :
% 4.71/5.11 ( ( ord_less_nat @ zero_zero_nat @ X )
% 4.71/5.11 => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_pos
% 4.71/5.11 thf(fact_4889_pochhammer__pos,axiom,
% 4.71/5.11 ! [X: int,N: nat] :
% 4.71/5.11 ( ( ord_less_int @ zero_zero_int @ X )
% 4.71/5.11 => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_pos
% 4.71/5.11 thf(fact_4890_pochhammer__eq__0__mono,axiom,
% 4.71/5.11 ! [A: real,N: nat,M2: nat] :
% 4.71/5.11 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 4.71/5.11 = zero_zero_real )
% 4.71/5.11 => ( ( ord_less_eq_nat @ N @ M2 )
% 4.71/5.11 => ( ( comm_s7457072308508201937r_real @ A @ M2 )
% 4.71/5.11 = zero_zero_real ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_eq_0_mono
% 4.71/5.11 thf(fact_4891_pochhammer__eq__0__mono,axiom,
% 4.71/5.11 ! [A: rat,N: nat,M2: nat] :
% 4.71/5.11 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 4.71/5.11 = zero_zero_rat )
% 4.71/5.11 => ( ( ord_less_eq_nat @ N @ M2 )
% 4.71/5.11 => ( ( comm_s4028243227959126397er_rat @ A @ M2 )
% 4.71/5.11 = zero_zero_rat ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_eq_0_mono
% 4.71/5.11 thf(fact_4892_pochhammer__neq__0__mono,axiom,
% 4.71/5.11 ! [A: real,M2: nat,N: nat] :
% 4.71/5.11 ( ( ( comm_s7457072308508201937r_real @ A @ M2 )
% 4.71/5.11 != zero_zero_real )
% 4.71/5.11 => ( ( ord_less_eq_nat @ N @ M2 )
% 4.71/5.11 => ( ( comm_s7457072308508201937r_real @ A @ N )
% 4.71/5.11 != zero_zero_real ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_neq_0_mono
% 4.71/5.11 thf(fact_4893_pochhammer__neq__0__mono,axiom,
% 4.71/5.11 ! [A: rat,M2: nat,N: nat] :
% 4.71/5.11 ( ( ( comm_s4028243227959126397er_rat @ A @ M2 )
% 4.71/5.11 != zero_zero_rat )
% 4.71/5.11 => ( ( ord_less_eq_nat @ N @ M2 )
% 4.71/5.11 => ( ( comm_s4028243227959126397er_rat @ A @ N )
% 4.71/5.11 != zero_zero_rat ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_neq_0_mono
% 4.71/5.11 thf(fact_4894_exp__ge__add__one__self,axiom,
% 4.71/5.11 ! [X: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % exp_ge_add_one_self
% 4.71/5.11 thf(fact_4895_exp__minus__inverse,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ( ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) )
% 4.71/5.11 = one_one_real ) ).
% 4.71/5.11
% 4.71/5.11 % exp_minus_inverse
% 4.71/5.11 thf(fact_4896_exp__minus__inverse,axiom,
% 4.71/5.11 ! [X: complex] :
% 4.71/5.11 ( ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) )
% 4.71/5.11 = one_one_complex ) ).
% 4.71/5.11
% 4.71/5.11 % exp_minus_inverse
% 4.71/5.11 thf(fact_4897_ceiling__le,axiom,
% 4.71/5.11 ! [X: real,A: int] :
% 4.71/5.11 ( ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ A ) )
% 4.71/5.11 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_le
% 4.71/5.11 thf(fact_4898_ceiling__le,axiom,
% 4.71/5.11 ! [X: rat,A: int] :
% 4.71/5.11 ( ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ A ) )
% 4.71/5.11 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ A ) ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_le
% 4.71/5.11 thf(fact_4899_ceiling__le__iff,axiom,
% 4.71/5.11 ! [X: real,Z: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ Z )
% 4.71/5.11 = ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_le_iff
% 4.71/5.11 thf(fact_4900_ceiling__le__iff,axiom,
% 4.71/5.11 ! [X: rat,Z: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ Z )
% 4.71/5.11 = ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_le_iff
% 4.71/5.11 thf(fact_4901_less__ceiling__iff,axiom,
% 4.71/5.11 ! [Z: int,X: rat] :
% 4.71/5.11 ( ( ord_less_int @ Z @ ( archim2889992004027027881ng_rat @ X ) )
% 4.71/5.11 = ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % less_ceiling_iff
% 4.71/5.11 thf(fact_4902_less__ceiling__iff,axiom,
% 4.71/5.11 ! [Z: int,X: real] :
% 4.71/5.11 ( ( ord_less_int @ Z @ ( archim7802044766580827645g_real @ X ) )
% 4.71/5.11 = ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % less_ceiling_iff
% 4.71/5.11 thf(fact_4903_pochhammer__nonneg,axiom,
% 4.71/5.11 ! [X: real,N: nat] :
% 4.71/5.11 ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.11 => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_nonneg
% 4.71/5.11 thf(fact_4904_pochhammer__nonneg,axiom,
% 4.71/5.11 ! [X: rat,N: nat] :
% 4.71/5.11 ( ( ord_less_rat @ zero_zero_rat @ X )
% 4.71/5.11 => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_nonneg
% 4.71/5.11 thf(fact_4905_pochhammer__nonneg,axiom,
% 4.71/5.11 ! [X: nat,N: nat] :
% 4.71/5.11 ( ( ord_less_nat @ zero_zero_nat @ X )
% 4.71/5.11 => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_nonneg
% 4.71/5.11 thf(fact_4906_pochhammer__nonneg,axiom,
% 4.71/5.11 ! [X: int,N: nat] :
% 4.71/5.11 ( ( ord_less_int @ zero_zero_int @ X )
% 4.71/5.11 => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_nonneg
% 4.71/5.11 thf(fact_4907_real__of__int__div4,axiom,
% 4.71/5.11 ! [N: int,X: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % real_of_int_div4
% 4.71/5.11 thf(fact_4908_pochhammer__0__left,axiom,
% 4.71/5.11 ! [N: nat] :
% 4.71/5.11 ( ( ( N = zero_zero_nat )
% 4.71/5.11 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 4.71/5.11 = one_one_complex ) )
% 4.71/5.11 & ( ( N != zero_zero_nat )
% 4.71/5.11 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 4.71/5.11 = zero_zero_complex ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_0_left
% 4.71/5.11 thf(fact_4909_pochhammer__0__left,axiom,
% 4.71/5.11 ! [N: nat] :
% 4.71/5.11 ( ( ( N = zero_zero_nat )
% 4.71/5.11 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 4.71/5.11 = one_one_real ) )
% 4.71/5.11 & ( ( N != zero_zero_nat )
% 4.71/5.11 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 4.71/5.11 = zero_zero_real ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_0_left
% 4.71/5.11 thf(fact_4910_pochhammer__0__left,axiom,
% 4.71/5.11 ! [N: nat] :
% 4.71/5.11 ( ( ( N = zero_zero_nat )
% 4.71/5.11 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 4.71/5.11 = one_one_rat ) )
% 4.71/5.11 & ( ( N != zero_zero_nat )
% 4.71/5.11 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 4.71/5.11 = zero_zero_rat ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_0_left
% 4.71/5.11 thf(fact_4911_pochhammer__0__left,axiom,
% 4.71/5.11 ! [N: nat] :
% 4.71/5.11 ( ( ( N = zero_zero_nat )
% 4.71/5.11 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 4.71/5.11 = one_one_nat ) )
% 4.71/5.11 & ( ( N != zero_zero_nat )
% 4.71/5.11 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 4.71/5.11 = zero_zero_nat ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_0_left
% 4.71/5.11 thf(fact_4912_pochhammer__0__left,axiom,
% 4.71/5.11 ! [N: nat] :
% 4.71/5.11 ( ( ( N = zero_zero_nat )
% 4.71/5.11 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 4.71/5.11 = one_one_int ) )
% 4.71/5.11 & ( ( N != zero_zero_nat )
% 4.71/5.11 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 4.71/5.11 = zero_zero_int ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_0_left
% 4.71/5.11 thf(fact_4913_exp__ge__add__one__self__aux,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.11 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % exp_ge_add_one_self_aux
% 4.71/5.11 thf(fact_4914_of__int__nonneg,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 4.71/5.11 => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_nonneg
% 4.71/5.11 thf(fact_4915_of__int__nonneg,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 4.71/5.11 => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_nonneg
% 4.71/5.11 thf(fact_4916_of__int__nonneg,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 4.71/5.11 => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_nonneg
% 4.71/5.11 thf(fact_4917_of__int__leD,axiom,
% 4.71/5.11 ! [N: int,X: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X )
% 4.71/5.11 => ( ( N = zero_zero_int )
% 4.71/5.11 | ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_leD
% 4.71/5.11 thf(fact_4918_of__int__leD,axiom,
% 4.71/5.11 ! [N: int,X: rat] :
% 4.71/5.11 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X )
% 4.71/5.11 => ( ( N = zero_zero_int )
% 4.71/5.11 | ( ord_less_eq_rat @ one_one_rat @ X ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_leD
% 4.71/5.11 thf(fact_4919_of__int__leD,axiom,
% 4.71/5.11 ! [N: int,X: int] :
% 4.71/5.11 ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X )
% 4.71/5.11 => ( ( N = zero_zero_int )
% 4.71/5.11 | ( ord_less_eq_int @ one_one_int @ X ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_leD
% 4.71/5.11 thf(fact_4920_of__int__pos,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_int @ zero_zero_int @ Z )
% 4.71/5.11 => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_pos
% 4.71/5.11 thf(fact_4921_of__int__pos,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_int @ zero_zero_int @ Z )
% 4.71/5.11 => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_pos
% 4.71/5.11 thf(fact_4922_of__int__pos,axiom,
% 4.71/5.11 ! [Z: int] :
% 4.71/5.11 ( ( ord_less_int @ zero_zero_int @ Z )
% 4.71/5.11 => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_pos
% 4.71/5.11 thf(fact_4923_of__int__lessD,axiom,
% 4.71/5.11 ! [N: int,X: real] :
% 4.71/5.11 ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X )
% 4.71/5.11 => ( ( N = zero_zero_int )
% 4.71/5.11 | ( ord_less_real @ one_one_real @ X ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_lessD
% 4.71/5.11 thf(fact_4924_of__int__lessD,axiom,
% 4.71/5.11 ! [N: int,X: rat] :
% 4.71/5.11 ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X )
% 4.71/5.11 => ( ( N = zero_zero_int )
% 4.71/5.11 | ( ord_less_rat @ one_one_rat @ X ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_lessD
% 4.71/5.11 thf(fact_4925_of__int__lessD,axiom,
% 4.71/5.11 ! [N: int,X: int] :
% 4.71/5.11 ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X )
% 4.71/5.11 => ( ( N = zero_zero_int )
% 4.71/5.11 | ( ord_less_int @ one_one_int @ X ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_lessD
% 4.71/5.11 thf(fact_4926_lemma__exp__total,axiom,
% 4.71/5.11 ! [Y: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ one_one_real @ Y )
% 4.71/5.11 => ? [X4: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 4.71/5.11 & ( ord_less_eq_real @ X4 @ ( minus_minus_real @ Y @ one_one_real ) )
% 4.71/5.11 & ( ( exp_real @ X4 )
% 4.71/5.11 = Y ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % lemma_exp_total
% 4.71/5.11 thf(fact_4927_ln__ge__iff,axiom,
% 4.71/5.11 ! [X: real,Y: real] :
% 4.71/5.11 ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.11 => ( ( ord_less_eq_real @ Y @ ( ln_ln_real @ X ) )
% 4.71/5.11 = ( ord_less_eq_real @ ( exp_real @ Y ) @ X ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % ln_ge_iff
% 4.71/5.11 thf(fact_4928_floor__exists,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ? [Z3: int] :
% 4.71/5.11 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z3 ) @ X )
% 4.71/5.11 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % floor_exists
% 4.71/5.11 thf(fact_4929_floor__exists,axiom,
% 4.71/5.11 ! [X: rat] :
% 4.71/5.11 ? [Z3: int] :
% 4.71/5.11 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ X )
% 4.71/5.11 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % floor_exists
% 4.71/5.11 thf(fact_4930_floor__exists1,axiom,
% 4.71/5.11 ! [X: real] :
% 4.71/5.11 ? [X4: int] :
% 4.71/5.11 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X4 ) @ X )
% 4.71/5.11 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ X4 @ one_one_int ) ) )
% 4.71/5.11 & ! [Y4: int] :
% 4.71/5.11 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y4 ) @ X )
% 4.71/5.11 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Y4 @ one_one_int ) ) ) )
% 4.71/5.11 => ( Y4 = X4 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % floor_exists1
% 4.71/5.11 thf(fact_4931_floor__exists1,axiom,
% 4.71/5.11 ! [X: rat] :
% 4.71/5.11 ? [X4: int] :
% 4.71/5.11 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X4 ) @ X )
% 4.71/5.11 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ X4 @ one_one_int ) ) )
% 4.71/5.11 & ! [Y4: int] :
% 4.71/5.11 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y4 ) @ X )
% 4.71/5.11 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y4 @ one_one_int ) ) ) )
% 4.71/5.11 => ( Y4 = X4 ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % floor_exists1
% 4.71/5.11 thf(fact_4932_of__int__ceiling__le__add__one,axiom,
% 4.71/5.11 ! [R2: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R2 ) ) @ ( plus_plus_real @ R2 @ one_one_real ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_ceiling_le_add_one
% 4.71/5.11 thf(fact_4933_of__int__ceiling__le__add__one,axiom,
% 4.71/5.11 ! [R2: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R2 ) ) @ ( plus_plus_rat @ R2 @ one_one_rat ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_ceiling_le_add_one
% 4.71/5.11 thf(fact_4934_of__int__ceiling__diff__one__le,axiom,
% 4.71/5.11 ! [R2: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R2 ) ) @ one_one_real ) @ R2 ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_ceiling_diff_one_le
% 4.71/5.11 thf(fact_4935_of__int__ceiling__diff__one__le,axiom,
% 4.71/5.11 ! [R2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R2 ) ) @ one_one_rat ) @ R2 ) ).
% 4.71/5.11
% 4.71/5.11 % of_int_ceiling_diff_one_le
% 4.71/5.11 thf(fact_4936_ln__x__over__x__mono,axiom,
% 4.71/5.11 ! [X: real,Y: real] :
% 4.71/5.11 ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X )
% 4.71/5.11 => ( ( ord_less_eq_real @ X @ Y )
% 4.71/5.11 => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y ) @ Y ) @ ( divide_divide_real @ ( ln_ln_real @ X ) @ X ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % ln_x_over_x_mono
% 4.71/5.11 thf(fact_4937_of__nat__less__of__int__iff,axiom,
% 4.71/5.11 ! [N: nat,X: int] :
% 4.71/5.11 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( ring_1_of_int_int @ X ) )
% 4.71/5.11 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_nat_less_of_int_iff
% 4.71/5.11 thf(fact_4938_of__nat__less__of__int__iff,axiom,
% 4.71/5.11 ! [N: nat,X: int] :
% 4.71/5.11 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( ring_1_of_int_real @ X ) )
% 4.71/5.11 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_nat_less_of_int_iff
% 4.71/5.11 thf(fact_4939_of__nat__less__of__int__iff,axiom,
% 4.71/5.11 ! [N: nat,X: int] :
% 4.71/5.11 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( ring_1_of_int_rat @ X ) )
% 4.71/5.11 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 4.71/5.11
% 4.71/5.11 % of_nat_less_of_int_iff
% 4.71/5.11 thf(fact_4940_int__le__real__less,axiom,
% 4.71/5.11 ( ord_less_eq_int
% 4.71/5.11 = ( ^ [N4: int,M3: int] : ( ord_less_real @ ( ring_1_of_int_real @ N4 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M3 ) @ one_one_real ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % int_le_real_less
% 4.71/5.11 thf(fact_4941_int__less__real__le,axiom,
% 4.71/5.11 ( ord_less_int
% 4.71/5.11 = ( ^ [N4: int,M3: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N4 ) @ one_one_real ) @ ( ring_1_of_int_real @ M3 ) ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % int_less_real_le
% 4.71/5.11 thf(fact_4942_ceiling__divide__eq__div,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ A ) @ ( ring_1_of_int_rat @ B ) ) )
% 4.71/5.11 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_divide_eq_div
% 4.71/5.11 thf(fact_4943_ceiling__divide__eq__div,axiom,
% 4.71/5.11 ! [A: int,B: int] :
% 4.71/5.11 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) ) )
% 4.71/5.11 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % ceiling_divide_eq_div
% 4.71/5.11 thf(fact_4944_pochhammer__rec,axiom,
% 4.71/5.11 ! [A: complex,N: nat] :
% 4.71/5.11 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 4.71/5.11 = ( times_times_complex @ A @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ N ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_rec
% 4.71/5.11 thf(fact_4945_pochhammer__rec,axiom,
% 4.71/5.11 ! [A: real,N: nat] :
% 4.71/5.11 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 4.71/5.11 = ( times_times_real @ A @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ one_one_real ) @ N ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_rec
% 4.71/5.11 thf(fact_4946_pochhammer__rec,axiom,
% 4.71/5.11 ! [A: rat,N: nat] :
% 4.71/5.11 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 4.71/5.11 = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N ) ) ) ).
% 4.71/5.11
% 4.71/5.11 % pochhammer_rec
% 4.71/5.11 thf(fact_4947_pochhammer__rec,axiom,
% 4.71/5.11 ! [A: nat,N: nat] :
% 4.71/5.11 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 4.71/5.11 = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_rec
% 4.71/5.12 thf(fact_4948_pochhammer__rec,axiom,
% 4.71/5.12 ! [A: int,N: nat] :
% 4.71/5.12 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 4.71/5.12 = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_rec
% 4.71/5.12 thf(fact_4949_pochhammer__of__nat__eq__0__lemma,axiom,
% 4.71/5.12 ! [N: nat,K: nat] :
% 4.71/5.12 ( ( ord_less_nat @ N @ K )
% 4.71/5.12 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 4.71/5.12 = zero_zero_complex ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_of_nat_eq_0_lemma
% 4.71/5.12 thf(fact_4950_pochhammer__of__nat__eq__0__lemma,axiom,
% 4.71/5.12 ! [N: nat,K: nat] :
% 4.71/5.12 ( ( ord_less_nat @ N @ K )
% 4.71/5.12 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 4.71/5.12 = zero_zero_int ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_of_nat_eq_0_lemma
% 4.71/5.12 thf(fact_4951_pochhammer__of__nat__eq__0__lemma,axiom,
% 4.71/5.12 ! [N: nat,K: nat] :
% 4.71/5.12 ( ( ord_less_nat @ N @ K )
% 4.71/5.12 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 4.71/5.12 = zero_zero_real ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_of_nat_eq_0_lemma
% 4.71/5.12 thf(fact_4952_pochhammer__of__nat__eq__0__lemma,axiom,
% 4.71/5.12 ! [N: nat,K: nat] :
% 4.71/5.12 ( ( ord_less_nat @ N @ K )
% 4.71/5.12 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 4.71/5.12 = zero_zero_rat ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_of_nat_eq_0_lemma
% 4.71/5.12 thf(fact_4953_pochhammer__of__nat__eq__0__iff,axiom,
% 4.71/5.12 ! [N: nat,K: nat] :
% 4.71/5.12 ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 4.71/5.12 = zero_zero_complex )
% 4.71/5.12 = ( ord_less_nat @ N @ K ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_of_nat_eq_0_iff
% 4.71/5.12 thf(fact_4954_pochhammer__of__nat__eq__0__iff,axiom,
% 4.71/5.12 ! [N: nat,K: nat] :
% 4.71/5.12 ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 4.71/5.12 = zero_zero_int )
% 4.71/5.12 = ( ord_less_nat @ N @ K ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_of_nat_eq_0_iff
% 4.71/5.12 thf(fact_4955_pochhammer__of__nat__eq__0__iff,axiom,
% 4.71/5.12 ! [N: nat,K: nat] :
% 4.71/5.12 ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 4.71/5.12 = zero_zero_real )
% 4.71/5.12 = ( ord_less_nat @ N @ K ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_of_nat_eq_0_iff
% 4.71/5.12 thf(fact_4956_pochhammer__of__nat__eq__0__iff,axiom,
% 4.71/5.12 ! [N: nat,K: nat] :
% 4.71/5.12 ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 4.71/5.12 = zero_zero_rat )
% 4.71/5.12 = ( ord_less_nat @ N @ K ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_of_nat_eq_0_iff
% 4.71/5.12 thf(fact_4957_pochhammer__eq__0__iff,axiom,
% 4.71/5.12 ! [A: complex,N: nat] :
% 4.71/5.12 ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 4.71/5.12 = zero_zero_complex )
% 4.71/5.12 = ( ? [K3: nat] :
% 4.71/5.12 ( ( ord_less_nat @ K3 @ N )
% 4.71/5.12 & ( A
% 4.71/5.12 = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K3 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_eq_0_iff
% 4.71/5.12 thf(fact_4958_pochhammer__eq__0__iff,axiom,
% 4.71/5.12 ! [A: real,N: nat] :
% 4.71/5.12 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 4.71/5.12 = zero_zero_real )
% 4.71/5.12 = ( ? [K3: nat] :
% 4.71/5.12 ( ( ord_less_nat @ K3 @ N )
% 4.71/5.12 & ( A
% 4.71/5.12 = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K3 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_eq_0_iff
% 4.71/5.12 thf(fact_4959_pochhammer__eq__0__iff,axiom,
% 4.71/5.12 ! [A: rat,N: nat] :
% 4.71/5.12 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 4.71/5.12 = zero_zero_rat )
% 4.71/5.12 = ( ? [K3: nat] :
% 4.71/5.12 ( ( ord_less_nat @ K3 @ N )
% 4.71/5.12 & ( A
% 4.71/5.12 = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K3 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_eq_0_iff
% 4.71/5.12 thf(fact_4960_powr__def,axiom,
% 4.71/5.12 ( powr_real
% 4.71/5.12 = ( ^ [X3: real,A4: real] : ( if_real @ ( X3 = zero_zero_real ) @ zero_zero_real @ ( exp_real @ ( times_times_real @ A4 @ ( ln_ln_real @ X3 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % powr_def
% 4.71/5.12 thf(fact_4961_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 4.71/5.12 ! [K: nat,N: nat] :
% 4.71/5.12 ( ( ord_less_eq_nat @ K @ N )
% 4.71/5.12 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 4.71/5.12 != zero_zero_complex ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_of_nat_eq_0_lemma'
% 4.71/5.12 thf(fact_4962_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 4.71/5.12 ! [K: nat,N: nat] :
% 4.71/5.12 ( ( ord_less_eq_nat @ K @ N )
% 4.71/5.12 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 4.71/5.12 != zero_zero_int ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_of_nat_eq_0_lemma'
% 4.71/5.12 thf(fact_4963_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 4.71/5.12 ! [K: nat,N: nat] :
% 4.71/5.12 ( ( ord_less_eq_nat @ K @ N )
% 4.71/5.12 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 4.71/5.12 != zero_zero_real ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_of_nat_eq_0_lemma'
% 4.71/5.12 thf(fact_4964_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 4.71/5.12 ! [K: nat,N: nat] :
% 4.71/5.12 ( ( ord_less_eq_nat @ K @ N )
% 4.71/5.12 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 4.71/5.12 != zero_zero_rat ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_of_nat_eq_0_lemma'
% 4.71/5.12 thf(fact_4965_ceiling__split,axiom,
% 4.71/5.12 ! [P: int > $o,T: real] :
% 4.71/5.12 ( ( P @ ( archim7802044766580827645g_real @ T ) )
% 4.71/5.12 = ( ! [I4: int] :
% 4.71/5.12 ( ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ I4 ) @ one_one_real ) @ T )
% 4.71/5.12 & ( ord_less_eq_real @ T @ ( ring_1_of_int_real @ I4 ) ) )
% 4.71/5.12 => ( P @ I4 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % ceiling_split
% 4.71/5.12 thf(fact_4966_ceiling__split,axiom,
% 4.71/5.12 ! [P: int > $o,T: rat] :
% 4.71/5.12 ( ( P @ ( archim2889992004027027881ng_rat @ T ) )
% 4.71/5.12 = ( ! [I4: int] :
% 4.71/5.12 ( ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ I4 ) @ one_one_rat ) @ T )
% 4.71/5.12 & ( ord_less_eq_rat @ T @ ( ring_1_of_int_rat @ I4 ) ) )
% 4.71/5.12 => ( P @ I4 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % ceiling_split
% 4.71/5.12 thf(fact_4967_ceiling__eq__iff,axiom,
% 4.71/5.12 ! [X: real,A: int] :
% 4.71/5.12 ( ( ( archim7802044766580827645g_real @ X )
% 4.71/5.12 = A )
% 4.71/5.12 = ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) @ X )
% 4.71/5.12 & ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % ceiling_eq_iff
% 4.71/5.12 thf(fact_4968_ceiling__eq__iff,axiom,
% 4.71/5.12 ! [X: rat,A: int] :
% 4.71/5.12 ( ( ( archim2889992004027027881ng_rat @ X )
% 4.71/5.12 = A )
% 4.71/5.12 = ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) @ X )
% 4.71/5.12 & ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % ceiling_eq_iff
% 4.71/5.12 thf(fact_4969_ceiling__unique,axiom,
% 4.71/5.12 ! [Z: int,X: real] :
% 4.71/5.12 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X )
% 4.71/5.12 => ( ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z ) )
% 4.71/5.12 => ( ( archim7802044766580827645g_real @ X )
% 4.71/5.12 = Z ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % ceiling_unique
% 4.71/5.12 thf(fact_4970_ceiling__unique,axiom,
% 4.71/5.12 ! [Z: int,X: rat] :
% 4.71/5.12 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X )
% 4.71/5.12 => ( ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z ) )
% 4.71/5.12 => ( ( archim2889992004027027881ng_rat @ X )
% 4.71/5.12 = Z ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % ceiling_unique
% 4.71/5.12 thf(fact_4971_ceiling__correct,axiom,
% 4.71/5.12 ! [X: real] :
% 4.71/5.12 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) @ one_one_real ) @ X )
% 4.71/5.12 & ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % ceiling_correct
% 4.71/5.12 thf(fact_4972_ceiling__correct,axiom,
% 4.71/5.12 ! [X: rat] :
% 4.71/5.12 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) @ one_one_rat ) @ X )
% 4.71/5.12 & ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % ceiling_correct
% 4.71/5.12 thf(fact_4973_ceiling__less__iff,axiom,
% 4.71/5.12 ! [X: real,Z: int] :
% 4.71/5.12 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ Z )
% 4.71/5.12 = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % ceiling_less_iff
% 4.71/5.12 thf(fact_4974_ceiling__less__iff,axiom,
% 4.71/5.12 ! [X: rat,Z: int] :
% 4.71/5.12 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ Z )
% 4.71/5.12 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % ceiling_less_iff
% 4.71/5.12 thf(fact_4975_le__ceiling__iff,axiom,
% 4.71/5.12 ! [Z: int,X: rat] :
% 4.71/5.12 ( ( ord_less_eq_int @ Z @ ( archim2889992004027027881ng_rat @ X ) )
% 4.71/5.12 = ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X ) ) ).
% 4.71/5.12
% 4.71/5.12 % le_ceiling_iff
% 4.71/5.12 thf(fact_4976_le__ceiling__iff,axiom,
% 4.71/5.12 ! [Z: int,X: real] :
% 4.71/5.12 ( ( ord_less_eq_int @ Z @ ( archim7802044766580827645g_real @ X ) )
% 4.71/5.12 = ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X ) ) ).
% 4.71/5.12
% 4.71/5.12 % le_ceiling_iff
% 4.71/5.12 thf(fact_4977_exp__divide__power__eq,axiom,
% 4.71/5.12 ! [N: nat,X: complex] :
% 4.71/5.12 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.12 => ( ( power_power_complex @ ( exp_complex @ ( divide1717551699836669952omplex @ X @ ( semiri8010041392384452111omplex @ N ) ) ) @ N )
% 4.71/5.12 = ( exp_complex @ X ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % exp_divide_power_eq
% 4.71/5.12 thf(fact_4978_exp__divide__power__eq,axiom,
% 4.71/5.12 ! [N: nat,X: real] :
% 4.71/5.12 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.12 => ( ( power_power_real @ ( exp_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N )
% 4.71/5.12 = ( exp_real @ X ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % exp_divide_power_eq
% 4.71/5.12 thf(fact_4979_real__of__int__div2,axiom,
% 4.71/5.12 ! [N: int,X: int] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % real_of_int_div2
% 4.71/5.12 thf(fact_4980_real__of__int__div3,axiom,
% 4.71/5.12 ! [N: int,X: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) ) @ one_one_real ) ).
% 4.71/5.12
% 4.71/5.12 % real_of_int_div3
% 4.71/5.12 thf(fact_4981_pochhammer__product,axiom,
% 4.71/5.12 ! [M2: nat,N: nat,Z: nat] :
% 4.71/5.12 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.12 => ( ( comm_s4663373288045622133er_nat @ Z @ N )
% 4.71/5.12 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ M2 ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ M2 ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_product
% 4.71/5.12 thf(fact_4982_pochhammer__product,axiom,
% 4.71/5.12 ! [M2: nat,N: nat,Z: int] :
% 4.71/5.12 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.12 => ( ( comm_s4660882817536571857er_int @ Z @ N )
% 4.71/5.12 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ M2 ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_product
% 4.71/5.12 thf(fact_4983_pochhammer__product,axiom,
% 4.71/5.12 ! [M2: nat,N: nat,Z: real] :
% 4.71/5.12 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.12 => ( ( comm_s7457072308508201937r_real @ Z @ N )
% 4.71/5.12 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ M2 ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_product
% 4.71/5.12 thf(fact_4984_pochhammer__product,axiom,
% 4.71/5.12 ! [M2: nat,N: nat,Z: rat] :
% 4.71/5.12 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.12 => ( ( comm_s4028243227959126397er_rat @ Z @ N )
% 4.71/5.12 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ M2 ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ M2 ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_product
% 4.71/5.12 thf(fact_4985_ceiling__divide__upper,axiom,
% 4.71/5.12 ! [Q4: real,P6: real] :
% 4.71/5.12 ( ( ord_less_real @ zero_zero_real @ Q4 )
% 4.71/5.12 => ( ord_less_eq_real @ P6 @ ( times_times_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P6 @ Q4 ) ) ) @ Q4 ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % ceiling_divide_upper
% 4.71/5.12 thf(fact_4986_ceiling__divide__upper,axiom,
% 4.71/5.12 ! [Q4: rat,P6: rat] :
% 4.71/5.12 ( ( ord_less_rat @ zero_zero_rat @ Q4 )
% 4.71/5.12 => ( ord_less_eq_rat @ P6 @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P6 @ Q4 ) ) ) @ Q4 ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % ceiling_divide_upper
% 4.71/5.12 thf(fact_4987_mult__ceiling__le__Ints,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.12 => ( ( member_real @ A @ ring_1_Ints_real )
% 4.71/5.12 => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) ) @ ( ring_1_of_int_real @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % mult_ceiling_le_Ints
% 4.71/5.12 thf(fact_4988_mult__ceiling__le__Ints,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.12 => ( ( member_real @ A @ ring_1_Ints_real )
% 4.71/5.12 => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) ) @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % mult_ceiling_le_Ints
% 4.71/5.12 thf(fact_4989_mult__ceiling__le__Ints,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.12 => ( ( member_real @ A @ ring_1_Ints_real )
% 4.71/5.12 => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) ) @ ( ring_1_of_int_int @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % mult_ceiling_le_Ints
% 4.71/5.12 thf(fact_4990_mult__ceiling__le__Ints,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.12 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 4.71/5.12 => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) ) @ ( ring_1_of_int_real @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % mult_ceiling_le_Ints
% 4.71/5.12 thf(fact_4991_mult__ceiling__le__Ints,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.12 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 4.71/5.12 => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) ) @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % mult_ceiling_le_Ints
% 4.71/5.12 thf(fact_4992_mult__ceiling__le__Ints,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.12 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 4.71/5.12 => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) ) @ ( ring_1_of_int_int @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % mult_ceiling_le_Ints
% 4.71/5.12 thf(fact_4993_dbl__dec__def,axiom,
% 4.71/5.12 ( neg_nu6511756317524482435omplex
% 4.71/5.12 = ( ^ [X3: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X3 @ X3 ) @ one_one_complex ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % dbl_dec_def
% 4.71/5.12 thf(fact_4994_dbl__dec__def,axiom,
% 4.71/5.12 ( neg_nu6075765906172075777c_real
% 4.71/5.12 = ( ^ [X3: real] : ( minus_minus_real @ ( plus_plus_real @ X3 @ X3 ) @ one_one_real ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % dbl_dec_def
% 4.71/5.12 thf(fact_4995_dbl__dec__def,axiom,
% 4.71/5.12 ( neg_nu3179335615603231917ec_rat
% 4.71/5.12 = ( ^ [X3: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X3 @ X3 ) @ one_one_rat ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % dbl_dec_def
% 4.71/5.12 thf(fact_4996_dbl__dec__def,axiom,
% 4.71/5.12 ( neg_nu3811975205180677377ec_int
% 4.71/5.12 = ( ^ [X3: int] : ( minus_minus_int @ ( plus_plus_int @ X3 @ X3 ) @ one_one_int ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % dbl_dec_def
% 4.71/5.12 thf(fact_4997_pochhammer__absorb__comp,axiom,
% 4.71/5.12 ! [R2: complex,K: nat] :
% 4.71/5.12 ( ( times_times_complex @ ( minus_minus_complex @ R2 @ ( semiri8010041392384452111omplex @ K ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R2 ) @ K ) )
% 4.71/5.12 = ( times_times_complex @ R2 @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R2 ) @ one_one_complex ) @ K ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_absorb_comp
% 4.71/5.12 thf(fact_4998_pochhammer__absorb__comp,axiom,
% 4.71/5.12 ! [R2: int,K: nat] :
% 4.71/5.12 ( ( times_times_int @ ( minus_minus_int @ R2 @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R2 ) @ K ) )
% 4.71/5.12 = ( times_times_int @ R2 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R2 ) @ one_one_int ) @ K ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_absorb_comp
% 4.71/5.12 thf(fact_4999_pochhammer__absorb__comp,axiom,
% 4.71/5.12 ! [R2: real,K: nat] :
% 4.71/5.12 ( ( times_times_real @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ K ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R2 ) @ K ) )
% 4.71/5.12 = ( times_times_real @ R2 @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R2 ) @ one_one_real ) @ K ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_absorb_comp
% 4.71/5.12 thf(fact_5000_pochhammer__absorb__comp,axiom,
% 4.71/5.12 ! [R2: rat,K: nat] :
% 4.71/5.12 ( ( times_times_rat @ ( minus_minus_rat @ R2 @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R2 ) @ K ) )
% 4.71/5.12 = ( times_times_rat @ R2 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R2 ) @ one_one_rat ) @ K ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_absorb_comp
% 4.71/5.12 thf(fact_5001_ceiling__divide__lower,axiom,
% 4.71/5.12 ! [Q4: rat,P6: rat] :
% 4.71/5.12 ( ( ord_less_rat @ zero_zero_rat @ Q4 )
% 4.71/5.12 => ( ord_less_rat @ ( times_times_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P6 @ Q4 ) ) ) @ one_one_rat ) @ Q4 ) @ P6 ) ) ).
% 4.71/5.12
% 4.71/5.12 % ceiling_divide_lower
% 4.71/5.12 thf(fact_5002_ceiling__divide__lower,axiom,
% 4.71/5.12 ! [Q4: real,P6: real] :
% 4.71/5.12 ( ( ord_less_real @ zero_zero_real @ Q4 )
% 4.71/5.12 => ( ord_less_real @ ( times_times_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P6 @ Q4 ) ) ) @ one_one_real ) @ Q4 ) @ P6 ) ) ).
% 4.71/5.12
% 4.71/5.12 % ceiling_divide_lower
% 4.71/5.12 thf(fact_5003_greater__shift,axiom,
% 4.71/5.12 ( ord_less_nat
% 4.71/5.12 = ( ^ [Y2: nat,X3: nat] : ( vEBT_VEBT_greater @ ( some_nat @ X3 ) @ ( some_nat @ Y2 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % greater_shift
% 4.71/5.12 thf(fact_5004_less__shift,axiom,
% 4.71/5.12 ( ord_less_nat
% 4.71/5.12 = ( ^ [X3: nat,Y2: nat] : ( vEBT_VEBT_less @ ( some_nat @ X3 ) @ ( some_nat @ Y2 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % less_shift
% 4.71/5.12 thf(fact_5005_succ__correct,axiom,
% 4.71/5.12 ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 4.71/5.12 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.12 => ( ( ( vEBT_vebt_succ @ T @ X )
% 4.71/5.12 = ( some_nat @ Sx ) )
% 4.71/5.12 = ( vEBT_is_succ_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % succ_correct
% 4.71/5.12 thf(fact_5006_pred__correct,axiom,
% 4.71/5.12 ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 4.71/5.12 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.12 => ( ( ( vEBT_vebt_pred @ T @ X )
% 4.71/5.12 = ( some_nat @ Sx ) )
% 4.71/5.12 = ( vEBT_is_pred_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % pred_correct
% 4.71/5.12 thf(fact_5007_succ__corr,axiom,
% 4.71/5.12 ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 4.71/5.12 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.12 => ( ( ( vEBT_vebt_succ @ T @ X )
% 4.71/5.12 = ( some_nat @ Sx ) )
% 4.71/5.12 = ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % succ_corr
% 4.71/5.12 thf(fact_5008_pred__corr,axiom,
% 4.71/5.12 ! [T: vEBT_VEBT,N: nat,X: nat,Px: nat] :
% 4.71/5.12 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.12 => ( ( ( vEBT_vebt_pred @ T @ X )
% 4.71/5.12 = ( some_nat @ Px ) )
% 4.71/5.12 = ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Px ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % pred_corr
% 4.71/5.12 thf(fact_5009_maxt__sound,axiom,
% 4.71/5.12 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 4.71/5.12 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.12 => ( ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 4.71/5.12 => ( ( vEBT_vebt_maxt @ T )
% 4.71/5.12 = ( some_nat @ X ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % maxt_sound
% 4.71/5.12 thf(fact_5010_maxbmo,axiom,
% 4.71/5.12 ! [T: vEBT_VEBT,X: nat] :
% 4.71/5.12 ( ( ( vEBT_vebt_maxt @ T )
% 4.71/5.12 = ( some_nat @ X ) )
% 4.71/5.12 => ( vEBT_V8194947554948674370ptions @ T @ X ) ) ).
% 4.71/5.12
% 4.71/5.12 % maxbmo
% 4.71/5.12 thf(fact_5011_maxt__member,axiom,
% 4.71/5.12 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 4.71/5.12 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.12 => ( ( ( vEBT_vebt_maxt @ T )
% 4.71/5.12 = ( some_nat @ Maxi ) )
% 4.71/5.12 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % maxt_member
% 4.71/5.12 thf(fact_5012_maxt__corr__help,axiom,
% 4.71/5.12 ! [T: vEBT_VEBT,N: nat,Maxi: nat,X: nat] :
% 4.71/5.12 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.12 => ( ( ( vEBT_vebt_maxt @ T )
% 4.71/5.12 = ( some_nat @ Maxi ) )
% 4.71/5.12 => ( ( vEBT_vebt_member @ T @ X )
% 4.71/5.12 => ( ord_less_eq_nat @ X @ Maxi ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % maxt_corr_help
% 4.71/5.12 thf(fact_5013_maxt__corr,axiom,
% 4.71/5.12 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 4.71/5.12 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.12 => ( ( ( vEBT_vebt_maxt @ T )
% 4.71/5.12 = ( some_nat @ X ) )
% 4.71/5.12 => ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % maxt_corr
% 4.71/5.12 thf(fact_5014_mint__corr,axiom,
% 4.71/5.12 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 4.71/5.12 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.12 => ( ( ( vEBT_vebt_mint @ T )
% 4.71/5.12 = ( some_nat @ X ) )
% 4.71/5.12 => ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % mint_corr
% 4.71/5.12 thf(fact_5015_mint__sound,axiom,
% 4.71/5.12 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 4.71/5.12 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.12 => ( ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 4.71/5.12 => ( ( vEBT_vebt_mint @ T )
% 4.71/5.12 = ( some_nat @ X ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % mint_sound
% 4.71/5.12 thf(fact_5016_maxt__corr__help__empty,axiom,
% 4.71/5.12 ! [T: vEBT_VEBT,N: nat] :
% 4.71/5.12 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.12 => ( ( ( vEBT_vebt_maxt @ T )
% 4.71/5.12 = none_nat )
% 4.71/5.12 => ( ( vEBT_VEBT_set_vebt @ T )
% 4.71/5.12 = bot_bot_set_nat ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % maxt_corr_help_empty
% 4.71/5.12 thf(fact_5017_mint__corr__help,axiom,
% 4.71/5.12 ! [T: vEBT_VEBT,N: nat,Mini: nat,X: nat] :
% 4.71/5.12 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.12 => ( ( ( vEBT_vebt_mint @ T )
% 4.71/5.12 = ( some_nat @ Mini ) )
% 4.71/5.12 => ( ( vEBT_vebt_member @ T @ X )
% 4.71/5.12 => ( ord_less_eq_nat @ Mini @ X ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % mint_corr_help
% 4.71/5.12 thf(fact_5018_option_Osize_I4_J,axiom,
% 4.71/5.12 ! [X23: nat] :
% 4.71/5.12 ( ( size_size_option_nat @ ( some_nat @ X23 ) )
% 4.71/5.12 = ( suc @ zero_zero_nat ) ) ).
% 4.71/5.12
% 4.71/5.12 % option.size(4)
% 4.71/5.12 thf(fact_5019_option_Osize_I4_J,axiom,
% 4.71/5.12 ! [X23: product_prod_nat_nat] :
% 4.71/5.12 ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X23 ) )
% 4.71/5.12 = ( suc @ zero_zero_nat ) ) ).
% 4.71/5.12
% 4.71/5.12 % option.size(4)
% 4.71/5.12 thf(fact_5020_option_Osize_I4_J,axiom,
% 4.71/5.12 ! [X23: num] :
% 4.71/5.12 ( ( size_size_option_num @ ( some_num @ X23 ) )
% 4.71/5.12 = ( suc @ zero_zero_nat ) ) ).
% 4.71/5.12
% 4.71/5.12 % option.size(4)
% 4.71/5.12 thf(fact_5021_mint__member,axiom,
% 4.71/5.12 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 4.71/5.12 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.12 => ( ( ( vEBT_vebt_mint @ T )
% 4.71/5.12 = ( some_nat @ Maxi ) )
% 4.71/5.12 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % mint_member
% 4.71/5.12 thf(fact_5022_powr__real__of__int,axiom,
% 4.71/5.12 ! [X: real,N: int] :
% 4.71/5.12 ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.12 => ( ( ( ord_less_eq_int @ zero_zero_int @ N )
% 4.71/5.12 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 4.71/5.12 = ( power_power_real @ X @ ( nat2 @ N ) ) ) )
% 4.71/5.12 & ( ~ ( ord_less_eq_int @ zero_zero_int @ N )
% 4.71/5.12 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 4.71/5.12 = ( inverse_inverse_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ N ) ) ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % powr_real_of_int
% 4.71/5.12 thf(fact_5023_minNullmin,axiom,
% 4.71/5.12 ! [T: vEBT_VEBT] :
% 4.71/5.12 ( ( vEBT_VEBT_minNull @ T )
% 4.71/5.12 => ( ( vEBT_vebt_mint @ T )
% 4.71/5.12 = none_nat ) ) ).
% 4.71/5.12
% 4.71/5.12 % minNullmin
% 4.71/5.12 thf(fact_5024_minminNull,axiom,
% 4.71/5.12 ! [T: vEBT_VEBT] :
% 4.71/5.12 ( ( ( vEBT_vebt_mint @ T )
% 4.71/5.12 = none_nat )
% 4.71/5.12 => ( vEBT_VEBT_minNull @ T ) ) ).
% 4.71/5.12
% 4.71/5.12 % minminNull
% 4.71/5.12 thf(fact_5025_mint__corr__help__empty,axiom,
% 4.71/5.12 ! [T: vEBT_VEBT,N: nat] :
% 4.71/5.12 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.12 => ( ( ( vEBT_vebt_mint @ T )
% 4.71/5.12 = none_nat )
% 4.71/5.12 => ( ( vEBT_VEBT_set_vebt @ T )
% 4.71/5.12 = bot_bot_set_nat ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % mint_corr_help_empty
% 4.71/5.12 thf(fact_5026_inverse__zero,axiom,
% 4.71/5.12 ( ( inverse_inverse_real @ zero_zero_real )
% 4.71/5.12 = zero_zero_real ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_zero
% 4.71/5.12 thf(fact_5027_inverse__zero,axiom,
% 4.71/5.12 ( ( inverse_inverse_rat @ zero_zero_rat )
% 4.71/5.12 = zero_zero_rat ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_zero
% 4.71/5.12 thf(fact_5028_inverse__nonzero__iff__nonzero,axiom,
% 4.71/5.12 ! [A: real] :
% 4.71/5.12 ( ( ( inverse_inverse_real @ A )
% 4.71/5.12 = zero_zero_real )
% 4.71/5.12 = ( A = zero_zero_real ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_nonzero_iff_nonzero
% 4.71/5.12 thf(fact_5029_inverse__nonzero__iff__nonzero,axiom,
% 4.71/5.12 ! [A: rat] :
% 4.71/5.12 ( ( ( inverse_inverse_rat @ A )
% 4.71/5.12 = zero_zero_rat )
% 4.71/5.12 = ( A = zero_zero_rat ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_nonzero_iff_nonzero
% 4.71/5.12 thf(fact_5030_inverse__eq__1__iff,axiom,
% 4.71/5.12 ! [X: complex] :
% 4.71/5.12 ( ( ( invers8013647133539491842omplex @ X )
% 4.71/5.12 = one_one_complex )
% 4.71/5.12 = ( X = one_one_complex ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_eq_1_iff
% 4.71/5.12 thf(fact_5031_inverse__eq__1__iff,axiom,
% 4.71/5.12 ! [X: real] :
% 4.71/5.12 ( ( ( inverse_inverse_real @ X )
% 4.71/5.12 = one_one_real )
% 4.71/5.12 = ( X = one_one_real ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_eq_1_iff
% 4.71/5.12 thf(fact_5032_inverse__eq__1__iff,axiom,
% 4.71/5.12 ! [X: rat] :
% 4.71/5.12 ( ( ( inverse_inverse_rat @ X )
% 4.71/5.12 = one_one_rat )
% 4.71/5.12 = ( X = one_one_rat ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_eq_1_iff
% 4.71/5.12 thf(fact_5033_inverse__1,axiom,
% 4.71/5.12 ( ( invers8013647133539491842omplex @ one_one_complex )
% 4.71/5.12 = one_one_complex ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_1
% 4.71/5.12 thf(fact_5034_inverse__1,axiom,
% 4.71/5.12 ( ( inverse_inverse_real @ one_one_real )
% 4.71/5.12 = one_one_real ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_1
% 4.71/5.12 thf(fact_5035_inverse__1,axiom,
% 4.71/5.12 ( ( inverse_inverse_rat @ one_one_rat )
% 4.71/5.12 = one_one_rat ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_1
% 4.71/5.12 thf(fact_5036_inverse__nonnegative__iff__nonnegative,axiom,
% 4.71/5.12 ! [A: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 4.71/5.12 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_nonnegative_iff_nonnegative
% 4.71/5.12 thf(fact_5037_inverse__nonnegative__iff__nonnegative,axiom,
% 4.71/5.12 ! [A: rat] :
% 4.71/5.12 ( ( ord_less_eq_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 4.71/5.12 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_nonnegative_iff_nonnegative
% 4.71/5.12 thf(fact_5038_inverse__nonpositive__iff__nonpositive,axiom,
% 4.71/5.12 ! [A: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 4.71/5.12 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_nonpositive_iff_nonpositive
% 4.71/5.12 thf(fact_5039_inverse__nonpositive__iff__nonpositive,axiom,
% 4.71/5.12 ! [A: rat] :
% 4.71/5.12 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 4.71/5.12 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_nonpositive_iff_nonpositive
% 4.71/5.12 thf(fact_5040_inverse__less__iff__less,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.12 => ( ( ord_less_real @ zero_zero_real @ B )
% 4.71/5.12 => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 4.71/5.12 = ( ord_less_real @ B @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_less_iff_less
% 4.71/5.12 thf(fact_5041_inverse__less__iff__less,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.12 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 4.71/5.12 => ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 4.71/5.12 = ( ord_less_rat @ B @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_less_iff_less
% 4.71/5.12 thf(fact_5042_inverse__less__iff__less__neg,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( ord_less_real @ A @ zero_zero_real )
% 4.71/5.12 => ( ( ord_less_real @ B @ zero_zero_real )
% 4.71/5.12 => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 4.71/5.12 = ( ord_less_real @ B @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_less_iff_less_neg
% 4.71/5.12 thf(fact_5043_inverse__less__iff__less__neg,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.71/5.12 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 4.71/5.12 => ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 4.71/5.12 = ( ord_less_rat @ B @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_less_iff_less_neg
% 4.71/5.12 thf(fact_5044_inverse__negative__iff__negative,axiom,
% 4.71/5.12 ! [A: real] :
% 4.71/5.12 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 4.71/5.12 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_negative_iff_negative
% 4.71/5.12 thf(fact_5045_inverse__negative__iff__negative,axiom,
% 4.71/5.12 ! [A: rat] :
% 4.71/5.12 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 4.71/5.12 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_negative_iff_negative
% 4.71/5.12 thf(fact_5046_inverse__positive__iff__positive,axiom,
% 4.71/5.12 ! [A: real] :
% 4.71/5.12 ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 4.71/5.12 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_positive_iff_positive
% 4.71/5.12 thf(fact_5047_inverse__positive__iff__positive,axiom,
% 4.71/5.12 ! [A: rat] :
% 4.71/5.12 ( ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 4.71/5.12 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_positive_iff_positive
% 4.71/5.12 thf(fact_5048_inverse__le__iff__le,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.12 => ( ( ord_less_real @ zero_zero_real @ B )
% 4.71/5.12 => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 4.71/5.12 = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_le_iff_le
% 4.71/5.12 thf(fact_5049_inverse__le__iff__le,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.12 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 4.71/5.12 => ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 4.71/5.12 = ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_le_iff_le
% 4.71/5.12 thf(fact_5050_inverse__le__iff__le__neg,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( ord_less_real @ A @ zero_zero_real )
% 4.71/5.12 => ( ( ord_less_real @ B @ zero_zero_real )
% 4.71/5.12 => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 4.71/5.12 = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_le_iff_le_neg
% 4.71/5.12 thf(fact_5051_inverse__le__iff__le__neg,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.71/5.12 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 4.71/5.12 => ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 4.71/5.12 = ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_le_iff_le_neg
% 4.71/5.12 thf(fact_5052_left__inverse,axiom,
% 4.71/5.12 ! [A: complex] :
% 4.71/5.12 ( ( A != zero_zero_complex )
% 4.71/5.12 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ A )
% 4.71/5.12 = one_one_complex ) ) ).
% 4.71/5.12
% 4.71/5.12 % left_inverse
% 4.71/5.12 thf(fact_5053_left__inverse,axiom,
% 4.71/5.12 ! [A: real] :
% 4.71/5.12 ( ( A != zero_zero_real )
% 4.71/5.12 => ( ( times_times_real @ ( inverse_inverse_real @ A ) @ A )
% 4.71/5.12 = one_one_real ) ) ).
% 4.71/5.12
% 4.71/5.12 % left_inverse
% 4.71/5.12 thf(fact_5054_left__inverse,axiom,
% 4.71/5.12 ! [A: rat] :
% 4.71/5.12 ( ( A != zero_zero_rat )
% 4.71/5.12 => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 4.71/5.12 = one_one_rat ) ) ).
% 4.71/5.12
% 4.71/5.12 % left_inverse
% 4.71/5.12 thf(fact_5055_right__inverse,axiom,
% 4.71/5.12 ! [A: complex] :
% 4.71/5.12 ( ( A != zero_zero_complex )
% 4.71/5.12 => ( ( times_times_complex @ A @ ( invers8013647133539491842omplex @ A ) )
% 4.71/5.12 = one_one_complex ) ) ).
% 4.71/5.12
% 4.71/5.12 % right_inverse
% 4.71/5.12 thf(fact_5056_right__inverse,axiom,
% 4.71/5.12 ! [A: real] :
% 4.71/5.12 ( ( A != zero_zero_real )
% 4.71/5.12 => ( ( times_times_real @ A @ ( inverse_inverse_real @ A ) )
% 4.71/5.12 = one_one_real ) ) ).
% 4.71/5.12
% 4.71/5.12 % right_inverse
% 4.71/5.12 thf(fact_5057_right__inverse,axiom,
% 4.71/5.12 ! [A: rat] :
% 4.71/5.12 ( ( A != zero_zero_rat )
% 4.71/5.12 => ( ( times_times_rat @ A @ ( inverse_inverse_rat @ A ) )
% 4.71/5.12 = one_one_rat ) ) ).
% 4.71/5.12
% 4.71/5.12 % right_inverse
% 4.71/5.12 thf(fact_5058_field__class_Ofield__inverse__zero,axiom,
% 4.71/5.12 ( ( inverse_inverse_real @ zero_zero_real )
% 4.71/5.12 = zero_zero_real ) ).
% 4.71/5.12
% 4.71/5.12 % field_class.field_inverse_zero
% 4.71/5.12 thf(fact_5059_field__class_Ofield__inverse__zero,axiom,
% 4.71/5.12 ( ( inverse_inverse_rat @ zero_zero_rat )
% 4.71/5.12 = zero_zero_rat ) ).
% 4.71/5.12
% 4.71/5.12 % field_class.field_inverse_zero
% 4.71/5.12 thf(fact_5060_inverse__zero__imp__zero,axiom,
% 4.71/5.12 ! [A: real] :
% 4.71/5.12 ( ( ( inverse_inverse_real @ A )
% 4.71/5.12 = zero_zero_real )
% 4.71/5.12 => ( A = zero_zero_real ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_zero_imp_zero
% 4.71/5.12 thf(fact_5061_inverse__zero__imp__zero,axiom,
% 4.71/5.12 ! [A: rat] :
% 4.71/5.12 ( ( ( inverse_inverse_rat @ A )
% 4.71/5.12 = zero_zero_rat )
% 4.71/5.12 => ( A = zero_zero_rat ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_zero_imp_zero
% 4.71/5.12 thf(fact_5062_nonzero__inverse__eq__imp__eq,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( ( inverse_inverse_real @ A )
% 4.71/5.12 = ( inverse_inverse_real @ B ) )
% 4.71/5.12 => ( ( A != zero_zero_real )
% 4.71/5.12 => ( ( B != zero_zero_real )
% 4.71/5.12 => ( A = B ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nonzero_inverse_eq_imp_eq
% 4.71/5.12 thf(fact_5063_nonzero__inverse__eq__imp__eq,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( ( inverse_inverse_rat @ A )
% 4.71/5.12 = ( inverse_inverse_rat @ B ) )
% 4.71/5.12 => ( ( A != zero_zero_rat )
% 4.71/5.12 => ( ( B != zero_zero_rat )
% 4.71/5.12 => ( A = B ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nonzero_inverse_eq_imp_eq
% 4.71/5.12 thf(fact_5064_nonzero__inverse__inverse__eq,axiom,
% 4.71/5.12 ! [A: real] :
% 4.71/5.12 ( ( A != zero_zero_real )
% 4.71/5.12 => ( ( inverse_inverse_real @ ( inverse_inverse_real @ A ) )
% 4.71/5.12 = A ) ) ).
% 4.71/5.12
% 4.71/5.12 % nonzero_inverse_inverse_eq
% 4.71/5.12 thf(fact_5065_nonzero__inverse__inverse__eq,axiom,
% 4.71/5.12 ! [A: rat] :
% 4.71/5.12 ( ( A != zero_zero_rat )
% 4.71/5.12 => ( ( inverse_inverse_rat @ ( inverse_inverse_rat @ A ) )
% 4.71/5.12 = A ) ) ).
% 4.71/5.12
% 4.71/5.12 % nonzero_inverse_inverse_eq
% 4.71/5.12 thf(fact_5066_nonzero__imp__inverse__nonzero,axiom,
% 4.71/5.12 ! [A: real] :
% 4.71/5.12 ( ( A != zero_zero_real )
% 4.71/5.12 => ( ( inverse_inverse_real @ A )
% 4.71/5.12 != zero_zero_real ) ) ).
% 4.71/5.12
% 4.71/5.12 % nonzero_imp_inverse_nonzero
% 4.71/5.12 thf(fact_5067_nonzero__imp__inverse__nonzero,axiom,
% 4.71/5.12 ! [A: rat] :
% 4.71/5.12 ( ( A != zero_zero_rat )
% 4.71/5.12 => ( ( inverse_inverse_rat @ A )
% 4.71/5.12 != zero_zero_rat ) ) ).
% 4.71/5.12
% 4.71/5.12 % nonzero_imp_inverse_nonzero
% 4.71/5.12 thf(fact_5068_option_Osize_I3_J,axiom,
% 4.71/5.12 ( ( size_size_option_nat @ none_nat )
% 4.71/5.12 = ( suc @ zero_zero_nat ) ) ).
% 4.71/5.12
% 4.71/5.12 % option.size(3)
% 4.71/5.12 thf(fact_5069_option_Osize_I3_J,axiom,
% 4.71/5.12 ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 4.71/5.12 = ( suc @ zero_zero_nat ) ) ).
% 4.71/5.12
% 4.71/5.12 % option.size(3)
% 4.71/5.12 thf(fact_5070_option_Osize_I3_J,axiom,
% 4.71/5.12 ( ( size_size_option_num @ none_num )
% 4.71/5.12 = ( suc @ zero_zero_nat ) ) ).
% 4.71/5.12
% 4.71/5.12 % option.size(3)
% 4.71/5.12 thf(fact_5071_vebt__pred_Osimps_I5_J,axiom,
% 4.71/5.12 ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 4.71/5.12 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Vf )
% 4.71/5.12 = none_nat ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_pred.simps(5)
% 4.71/5.12 thf(fact_5072_vebt__succ_Osimps_I4_J,axiom,
% 4.71/5.12 ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve: nat] :
% 4.71/5.12 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd ) @ Ve )
% 4.71/5.12 = none_nat ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_succ.simps(4)
% 4.71/5.12 thf(fact_5073_inverse__less__imp__less,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 4.71/5.12 => ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.12 => ( ord_less_real @ B @ A ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_less_imp_less
% 4.71/5.12 thf(fact_5074_inverse__less__imp__less,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 4.71/5.12 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.12 => ( ord_less_rat @ B @ A ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_less_imp_less
% 4.71/5.12 thf(fact_5075_less__imp__inverse__less,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( ord_less_real @ A @ B )
% 4.71/5.12 => ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.12 => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % less_imp_inverse_less
% 4.71/5.12 thf(fact_5076_less__imp__inverse__less,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( ord_less_rat @ A @ B )
% 4.71/5.12 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.12 => ( ord_less_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % less_imp_inverse_less
% 4.71/5.12 thf(fact_5077_inverse__less__imp__less__neg,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 4.71/5.12 => ( ( ord_less_real @ B @ zero_zero_real )
% 4.71/5.12 => ( ord_less_real @ B @ A ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_less_imp_less_neg
% 4.71/5.12 thf(fact_5078_inverse__less__imp__less__neg,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 4.71/5.12 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 4.71/5.12 => ( ord_less_rat @ B @ A ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_less_imp_less_neg
% 4.71/5.12 thf(fact_5079_less__imp__inverse__less__neg,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( ord_less_real @ A @ B )
% 4.71/5.12 => ( ( ord_less_real @ B @ zero_zero_real )
% 4.71/5.12 => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % less_imp_inverse_less_neg
% 4.71/5.12 thf(fact_5080_less__imp__inverse__less__neg,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( ord_less_rat @ A @ B )
% 4.71/5.12 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 4.71/5.12 => ( ord_less_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % less_imp_inverse_less_neg
% 4.71/5.12 thf(fact_5081_inverse__negative__imp__negative,axiom,
% 4.71/5.12 ! [A: real] :
% 4.71/5.12 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 4.71/5.12 => ( ( A != zero_zero_real )
% 4.71/5.12 => ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_negative_imp_negative
% 4.71/5.12 thf(fact_5082_inverse__negative__imp__negative,axiom,
% 4.71/5.12 ! [A: rat] :
% 4.71/5.12 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 4.71/5.12 => ( ( A != zero_zero_rat )
% 4.71/5.12 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_negative_imp_negative
% 4.71/5.12 thf(fact_5083_inverse__positive__imp__positive,axiom,
% 4.71/5.12 ! [A: real] :
% 4.71/5.12 ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 4.71/5.12 => ( ( A != zero_zero_real )
% 4.71/5.12 => ( ord_less_real @ zero_zero_real @ A ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_positive_imp_positive
% 4.71/5.12 thf(fact_5084_inverse__positive__imp__positive,axiom,
% 4.71/5.12 ! [A: rat] :
% 4.71/5.12 ( ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 4.71/5.12 => ( ( A != zero_zero_rat )
% 4.71/5.12 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_positive_imp_positive
% 4.71/5.12 thf(fact_5085_negative__imp__inverse__negative,axiom,
% 4.71/5.12 ! [A: real] :
% 4.71/5.12 ( ( ord_less_real @ A @ zero_zero_real )
% 4.71/5.12 => ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real ) ) ).
% 4.71/5.12
% 4.71/5.12 % negative_imp_inverse_negative
% 4.71/5.12 thf(fact_5086_negative__imp__inverse__negative,axiom,
% 4.71/5.12 ! [A: rat] :
% 4.71/5.12 ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.71/5.12 => ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat ) ) ).
% 4.71/5.12
% 4.71/5.12 % negative_imp_inverse_negative
% 4.71/5.12 thf(fact_5087_positive__imp__inverse__positive,axiom,
% 4.71/5.12 ! [A: real] :
% 4.71/5.12 ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.12 => ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % positive_imp_inverse_positive
% 4.71/5.12 thf(fact_5088_positive__imp__inverse__positive,axiom,
% 4.71/5.12 ! [A: rat] :
% 4.71/5.12 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.12 => ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % positive_imp_inverse_positive
% 4.71/5.12 thf(fact_5089_nonzero__inverse__mult__distrib,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( A != zero_zero_real )
% 4.71/5.12 => ( ( B != zero_zero_real )
% 4.71/5.12 => ( ( inverse_inverse_real @ ( times_times_real @ A @ B ) )
% 4.71/5.12 = ( times_times_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nonzero_inverse_mult_distrib
% 4.71/5.12 thf(fact_5090_nonzero__inverse__mult__distrib,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( A != zero_zero_rat )
% 4.71/5.12 => ( ( B != zero_zero_rat )
% 4.71/5.12 => ( ( inverse_inverse_rat @ ( times_times_rat @ A @ B ) )
% 4.71/5.12 = ( times_times_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nonzero_inverse_mult_distrib
% 4.71/5.12 thf(fact_5091_nonzero__inverse__minus__eq,axiom,
% 4.71/5.12 ! [A: complex] :
% 4.71/5.12 ( ( A != zero_zero_complex )
% 4.71/5.12 => ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ A ) )
% 4.71/5.12 = ( uminus1482373934393186551omplex @ ( invers8013647133539491842omplex @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nonzero_inverse_minus_eq
% 4.71/5.12 thf(fact_5092_nonzero__inverse__minus__eq,axiom,
% 4.71/5.12 ! [A: real] :
% 4.71/5.12 ( ( A != zero_zero_real )
% 4.71/5.12 => ( ( inverse_inverse_real @ ( uminus_uminus_real @ A ) )
% 4.71/5.12 = ( uminus_uminus_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nonzero_inverse_minus_eq
% 4.71/5.12 thf(fact_5093_nonzero__inverse__minus__eq,axiom,
% 4.71/5.12 ! [A: rat] :
% 4.71/5.12 ( ( A != zero_zero_rat )
% 4.71/5.12 => ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ A ) )
% 4.71/5.12 = ( uminus_uminus_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nonzero_inverse_minus_eq
% 4.71/5.12 thf(fact_5094_inverse__unique,axiom,
% 4.71/5.12 ! [A: complex,B: complex] :
% 4.71/5.12 ( ( ( times_times_complex @ A @ B )
% 4.71/5.12 = one_one_complex )
% 4.71/5.12 => ( ( invers8013647133539491842omplex @ A )
% 4.71/5.12 = B ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_unique
% 4.71/5.12 thf(fact_5095_inverse__unique,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( ( times_times_real @ A @ B )
% 4.71/5.12 = one_one_real )
% 4.71/5.12 => ( ( inverse_inverse_real @ A )
% 4.71/5.12 = B ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_unique
% 4.71/5.12 thf(fact_5096_inverse__unique,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( ( times_times_rat @ A @ B )
% 4.71/5.12 = one_one_rat )
% 4.71/5.12 => ( ( inverse_inverse_rat @ A )
% 4.71/5.12 = B ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_unique
% 4.71/5.12 thf(fact_5097_inverse__eq__divide,axiom,
% 4.71/5.12 ( invers8013647133539491842omplex
% 4.71/5.12 = ( divide1717551699836669952omplex @ one_one_complex ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_eq_divide
% 4.71/5.12 thf(fact_5098_inverse__eq__divide,axiom,
% 4.71/5.12 ( inverse_inverse_real
% 4.71/5.12 = ( divide_divide_real @ one_one_real ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_eq_divide
% 4.71/5.12 thf(fact_5099_inverse__eq__divide,axiom,
% 4.71/5.12 ( inverse_inverse_rat
% 4.71/5.12 = ( divide_divide_rat @ one_one_rat ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_eq_divide
% 4.71/5.12 thf(fact_5100_nonzero__abs__inverse,axiom,
% 4.71/5.12 ! [A: real] :
% 4.71/5.12 ( ( A != zero_zero_real )
% 4.71/5.12 => ( ( abs_abs_real @ ( inverse_inverse_real @ A ) )
% 4.71/5.12 = ( inverse_inverse_real @ ( abs_abs_real @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nonzero_abs_inverse
% 4.71/5.12 thf(fact_5101_nonzero__abs__inverse,axiom,
% 4.71/5.12 ! [A: rat] :
% 4.71/5.12 ( ( A != zero_zero_rat )
% 4.71/5.12 => ( ( abs_abs_rat @ ( inverse_inverse_rat @ A ) )
% 4.71/5.12 = ( inverse_inverse_rat @ ( abs_abs_rat @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nonzero_abs_inverse
% 4.71/5.12 thf(fact_5102_vebt__pred_Osimps_I6_J,axiom,
% 4.71/5.12 ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 4.71/5.12 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj )
% 4.71/5.12 = none_nat ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_pred.simps(6)
% 4.71/5.12 thf(fact_5103_vebt__succ_Osimps_I5_J,axiom,
% 4.71/5.12 ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 4.71/5.12 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Vi )
% 4.71/5.12 = none_nat ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_succ.simps(5)
% 4.71/5.12 thf(fact_5104_divide__real__def,axiom,
% 4.71/5.12 ( divide_divide_real
% 4.71/5.12 = ( ^ [X3: real,Y2: real] : ( times_times_real @ X3 @ ( inverse_inverse_real @ Y2 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % divide_real_def
% 4.71/5.12 thf(fact_5105_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 4.71/5.12 ! [Uz: product_prod_nat_nat,Va2: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 4.71/5.12 ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va2 @ Vb @ Vc ) ) ).
% 4.71/5.12
% 4.71/5.12 % VEBT_internal.minNull.simps(5)
% 4.71/5.12 thf(fact_5106_inverse__le__imp__le,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 4.71/5.12 => ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.12 => ( ord_less_eq_real @ B @ A ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_le_imp_le
% 4.71/5.12 thf(fact_5107_inverse__le__imp__le,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 4.71/5.12 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.12 => ( ord_less_eq_rat @ B @ A ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_le_imp_le
% 4.71/5.12 thf(fact_5108_le__imp__inverse__le,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ A @ B )
% 4.71/5.12 => ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.12 => ( ord_less_eq_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % le_imp_inverse_le
% 4.71/5.12 thf(fact_5109_le__imp__inverse__le,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.12 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.12 => ( ord_less_eq_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % le_imp_inverse_le
% 4.71/5.12 thf(fact_5110_inverse__le__imp__le__neg,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 4.71/5.12 => ( ( ord_less_real @ B @ zero_zero_real )
% 4.71/5.12 => ( ord_less_eq_real @ B @ A ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_le_imp_le_neg
% 4.71/5.12 thf(fact_5111_inverse__le__imp__le__neg,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 4.71/5.12 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 4.71/5.12 => ( ord_less_eq_rat @ B @ A ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_le_imp_le_neg
% 4.71/5.12 thf(fact_5112_le__imp__inverse__le__neg,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ A @ B )
% 4.71/5.12 => ( ( ord_less_real @ B @ zero_zero_real )
% 4.71/5.12 => ( ord_less_eq_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % le_imp_inverse_le_neg
% 4.71/5.12 thf(fact_5113_le__imp__inverse__le__neg,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.12 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 4.71/5.12 => ( ord_less_eq_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % le_imp_inverse_le_neg
% 4.71/5.12 thf(fact_5114_inverse__le__1__iff,axiom,
% 4.71/5.12 ! [X: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ ( inverse_inverse_real @ X ) @ one_one_real )
% 4.71/5.12 = ( ( ord_less_eq_real @ X @ zero_zero_real )
% 4.71/5.12 | ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_le_1_iff
% 4.71/5.12 thf(fact_5115_inverse__le__1__iff,axiom,
% 4.71/5.12 ! [X: rat] :
% 4.71/5.12 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ X ) @ one_one_rat )
% 4.71/5.12 = ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 4.71/5.12 | ( ord_less_eq_rat @ one_one_rat @ X ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_le_1_iff
% 4.71/5.12 thf(fact_5116_one__less__inverse,axiom,
% 4.71/5.12 ! [A: real] :
% 4.71/5.12 ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.12 => ( ( ord_less_real @ A @ one_one_real )
% 4.71/5.12 => ( ord_less_real @ one_one_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % one_less_inverse
% 4.71/5.12 thf(fact_5117_one__less__inverse,axiom,
% 4.71/5.12 ! [A: rat] :
% 4.71/5.12 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.12 => ( ( ord_less_rat @ A @ one_one_rat )
% 4.71/5.12 => ( ord_less_rat @ one_one_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % one_less_inverse
% 4.71/5.12 thf(fact_5118_one__less__inverse__iff,axiom,
% 4.71/5.12 ! [X: real] :
% 4.71/5.12 ( ( ord_less_real @ one_one_real @ ( inverse_inverse_real @ X ) )
% 4.71/5.12 = ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.12 & ( ord_less_real @ X @ one_one_real ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % one_less_inverse_iff
% 4.71/5.12 thf(fact_5119_one__less__inverse__iff,axiom,
% 4.71/5.12 ! [X: rat] :
% 4.71/5.12 ( ( ord_less_rat @ one_one_rat @ ( inverse_inverse_rat @ X ) )
% 4.71/5.12 = ( ( ord_less_rat @ zero_zero_rat @ X )
% 4.71/5.12 & ( ord_less_rat @ X @ one_one_rat ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % one_less_inverse_iff
% 4.71/5.12 thf(fact_5120_inverse__add,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( A != zero_zero_real )
% 4.71/5.12 => ( ( B != zero_zero_real )
% 4.71/5.12 => ( ( plus_plus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 4.71/5.12 = ( times_times_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( inverse_inverse_real @ A ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_add
% 4.71/5.12 thf(fact_5121_inverse__add,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( A != zero_zero_rat )
% 4.71/5.12 => ( ( B != zero_zero_rat )
% 4.71/5.12 => ( ( plus_plus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 4.71/5.12 = ( times_times_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( inverse_inverse_rat @ A ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_add
% 4.71/5.12 thf(fact_5122_division__ring__inverse__add,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( A != zero_zero_real )
% 4.71/5.12 => ( ( B != zero_zero_real )
% 4.71/5.12 => ( ( plus_plus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 4.71/5.12 = ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( plus_plus_real @ A @ B ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % division_ring_inverse_add
% 4.71/5.12 thf(fact_5123_division__ring__inverse__add,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( A != zero_zero_rat )
% 4.71/5.12 => ( ( B != zero_zero_rat )
% 4.71/5.12 => ( ( plus_plus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 4.71/5.12 = ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( plus_plus_rat @ A @ B ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % division_ring_inverse_add
% 4.71/5.12 thf(fact_5124_field__class_Ofield__inverse,axiom,
% 4.71/5.12 ! [A: complex] :
% 4.71/5.12 ( ( A != zero_zero_complex )
% 4.71/5.12 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ A )
% 4.71/5.12 = one_one_complex ) ) ).
% 4.71/5.12
% 4.71/5.12 % field_class.field_inverse
% 4.71/5.12 thf(fact_5125_field__class_Ofield__inverse,axiom,
% 4.71/5.12 ! [A: real] :
% 4.71/5.12 ( ( A != zero_zero_real )
% 4.71/5.12 => ( ( times_times_real @ ( inverse_inverse_real @ A ) @ A )
% 4.71/5.12 = one_one_real ) ) ).
% 4.71/5.12
% 4.71/5.12 % field_class.field_inverse
% 4.71/5.12 thf(fact_5126_field__class_Ofield__inverse,axiom,
% 4.71/5.12 ! [A: rat] :
% 4.71/5.12 ( ( A != zero_zero_rat )
% 4.71/5.12 => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 4.71/5.12 = one_one_rat ) ) ).
% 4.71/5.12
% 4.71/5.12 % field_class.field_inverse
% 4.71/5.12 thf(fact_5127_division__ring__inverse__diff,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( A != zero_zero_real )
% 4.71/5.12 => ( ( B != zero_zero_real )
% 4.71/5.12 => ( ( minus_minus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 4.71/5.12 = ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( minus_minus_real @ B @ A ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % division_ring_inverse_diff
% 4.71/5.12 thf(fact_5128_division__ring__inverse__diff,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( A != zero_zero_rat )
% 4.71/5.12 => ( ( B != zero_zero_rat )
% 4.71/5.12 => ( ( minus_minus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 4.71/5.12 = ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( minus_minus_rat @ B @ A ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % division_ring_inverse_diff
% 4.71/5.12 thf(fact_5129_nonzero__inverse__eq__divide,axiom,
% 4.71/5.12 ! [A: complex] :
% 4.71/5.12 ( ( A != zero_zero_complex )
% 4.71/5.12 => ( ( invers8013647133539491842omplex @ A )
% 4.71/5.12 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nonzero_inverse_eq_divide
% 4.71/5.12 thf(fact_5130_nonzero__inverse__eq__divide,axiom,
% 4.71/5.12 ! [A: real] :
% 4.71/5.12 ( ( A != zero_zero_real )
% 4.71/5.12 => ( ( inverse_inverse_real @ A )
% 4.71/5.12 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nonzero_inverse_eq_divide
% 4.71/5.12 thf(fact_5131_nonzero__inverse__eq__divide,axiom,
% 4.71/5.12 ! [A: rat] :
% 4.71/5.12 ( ( A != zero_zero_rat )
% 4.71/5.12 => ( ( inverse_inverse_rat @ A )
% 4.71/5.12 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nonzero_inverse_eq_divide
% 4.71/5.12 thf(fact_5132_inverse__powr,axiom,
% 4.71/5.12 ! [Y: real,A: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.71/5.12 => ( ( powr_real @ ( inverse_inverse_real @ Y ) @ A )
% 4.71/5.12 = ( inverse_inverse_real @ ( powr_real @ Y @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_powr
% 4.71/5.12 thf(fact_5133_vebt__member_Osimps_I3_J,axiom,
% 4.71/5.12 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 4.71/5.12 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_member.simps(3)
% 4.71/5.12 thf(fact_5134_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 4.71/5.12 ! [X: vEBT_VEBT] :
% 4.71/5.12 ( ~ ( vEBT_VEBT_minNull @ X )
% 4.71/5.12 => ( ! [Uv2: $o] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 4.71/5.12 => ( ! [Uu2: $o] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 4.71/5.12 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % VEBT_internal.minNull.elims(3)
% 4.71/5.12 thf(fact_5135_vebt__succ_Osimps_I2_J,axiom,
% 4.71/5.12 ! [Uv: $o,Uw: $o,N: nat] :
% 4.71/5.12 ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N ) )
% 4.71/5.12 = none_nat ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_succ.simps(2)
% 4.71/5.12 thf(fact_5136_vebt__pred_Osimps_I1_J,axiom,
% 4.71/5.12 ! [Uu: $o,Uv: $o] :
% 4.71/5.12 ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat )
% 4.71/5.12 = none_nat ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_pred.simps(1)
% 4.71/5.12 thf(fact_5137_inverse__le__iff,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 4.71/5.12 = ( ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 4.71/5.12 => ( ord_less_eq_real @ B @ A ) )
% 4.71/5.12 & ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 4.71/5.12 => ( ord_less_eq_real @ A @ B ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_le_iff
% 4.71/5.12 thf(fact_5138_inverse__le__iff,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 4.71/5.12 = ( ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 4.71/5.12 => ( ord_less_eq_rat @ B @ A ) )
% 4.71/5.12 & ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 4.71/5.12 => ( ord_less_eq_rat @ A @ B ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_le_iff
% 4.71/5.12 thf(fact_5139_inverse__less__iff,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 4.71/5.12 = ( ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 4.71/5.12 => ( ord_less_real @ B @ A ) )
% 4.71/5.12 & ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 4.71/5.12 => ( ord_less_real @ A @ B ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_less_iff
% 4.71/5.12 thf(fact_5140_inverse__less__iff,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 4.71/5.12 = ( ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 4.71/5.12 => ( ord_less_rat @ B @ A ) )
% 4.71/5.12 & ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 4.71/5.12 => ( ord_less_rat @ A @ B ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_less_iff
% 4.71/5.12 thf(fact_5141_one__le__inverse,axiom,
% 4.71/5.12 ! [A: real] :
% 4.71/5.12 ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.12 => ( ( ord_less_eq_real @ A @ one_one_real )
% 4.71/5.12 => ( ord_less_eq_real @ one_one_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % one_le_inverse
% 4.71/5.12 thf(fact_5142_one__le__inverse,axiom,
% 4.71/5.12 ! [A: rat] :
% 4.71/5.12 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.12 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 4.71/5.12 => ( ord_less_eq_rat @ one_one_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % one_le_inverse
% 4.71/5.12 thf(fact_5143_inverse__less__1__iff,axiom,
% 4.71/5.12 ! [X: real] :
% 4.71/5.12 ( ( ord_less_real @ ( inverse_inverse_real @ X ) @ one_one_real )
% 4.71/5.12 = ( ( ord_less_eq_real @ X @ zero_zero_real )
% 4.71/5.12 | ( ord_less_real @ one_one_real @ X ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_less_1_iff
% 4.71/5.12 thf(fact_5144_inverse__less__1__iff,axiom,
% 4.71/5.12 ! [X: rat] :
% 4.71/5.12 ( ( ord_less_rat @ ( inverse_inverse_rat @ X ) @ one_one_rat )
% 4.71/5.12 = ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 4.71/5.12 | ( ord_less_rat @ one_one_rat @ X ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_less_1_iff
% 4.71/5.12 thf(fact_5145_one__le__inverse__iff,axiom,
% 4.71/5.12 ! [X: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ one_one_real @ ( inverse_inverse_real @ X ) )
% 4.71/5.12 = ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.12 & ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % one_le_inverse_iff
% 4.71/5.12 thf(fact_5146_one__le__inverse__iff,axiom,
% 4.71/5.12 ! [X: rat] :
% 4.71/5.12 ( ( ord_less_eq_rat @ one_one_rat @ ( inverse_inverse_rat @ X ) )
% 4.71/5.12 = ( ( ord_less_rat @ zero_zero_rat @ X )
% 4.71/5.12 & ( ord_less_eq_rat @ X @ one_one_rat ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % one_le_inverse_iff
% 4.71/5.12 thf(fact_5147_inverse__diff__inverse,axiom,
% 4.71/5.12 ! [A: complex,B: complex] :
% 4.71/5.12 ( ( A != zero_zero_complex )
% 4.71/5.12 => ( ( B != zero_zero_complex )
% 4.71/5.12 => ( ( minus_minus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 4.71/5.12 = ( uminus1482373934393186551omplex @ ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( minus_minus_complex @ A @ B ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_diff_inverse
% 4.71/5.12 thf(fact_5148_inverse__diff__inverse,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( A != zero_zero_real )
% 4.71/5.12 => ( ( B != zero_zero_real )
% 4.71/5.12 => ( ( minus_minus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 4.71/5.12 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( minus_minus_real @ A @ B ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_diff_inverse
% 4.71/5.12 thf(fact_5149_inverse__diff__inverse,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( A != zero_zero_rat )
% 4.71/5.12 => ( ( B != zero_zero_rat )
% 4.71/5.12 => ( ( minus_minus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 4.71/5.12 = ( uminus_uminus_rat @ ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( minus_minus_rat @ A @ B ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inverse_diff_inverse
% 4.71/5.12 thf(fact_5150_reals__Archimedean,axiom,
% 4.71/5.12 ! [X: real] :
% 4.71/5.12 ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.12 => ? [N2: nat] : ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ X ) ) ).
% 4.71/5.12
% 4.71/5.12 % reals_Archimedean
% 4.71/5.12 thf(fact_5151_reals__Archimedean,axiom,
% 4.71/5.12 ! [X: rat] :
% 4.71/5.12 ( ( ord_less_rat @ zero_zero_rat @ X )
% 4.71/5.12 => ? [N2: nat] : ( ord_less_rat @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ ( suc @ N2 ) ) ) @ X ) ) ).
% 4.71/5.12
% 4.71/5.12 % reals_Archimedean
% 4.71/5.12 thf(fact_5152_forall__pos__mono__1,axiom,
% 4.71/5.12 ! [P: real > $o,E2: real] :
% 4.71/5.12 ( ! [D6: real,E: real] :
% 4.71/5.12 ( ( ord_less_real @ D6 @ E )
% 4.71/5.12 => ( ( P @ D6 )
% 4.71/5.12 => ( P @ E ) ) )
% 4.71/5.12 => ( ! [N2: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) )
% 4.71/5.12 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 4.71/5.12 => ( P @ E2 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % forall_pos_mono_1
% 4.71/5.12 thf(fact_5153_real__arch__inverse,axiom,
% 4.71/5.12 ! [E2: real] :
% 4.71/5.12 ( ( ord_less_real @ zero_zero_real @ E2 )
% 4.71/5.12 = ( ? [N4: nat] :
% 4.71/5.12 ( ( N4 != zero_zero_nat )
% 4.71/5.12 & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N4 ) ) )
% 4.71/5.12 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N4 ) ) @ E2 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % real_arch_inverse
% 4.71/5.12 thf(fact_5154_forall__pos__mono,axiom,
% 4.71/5.12 ! [P: real > $o,E2: real] :
% 4.71/5.12 ( ! [D6: real,E: real] :
% 4.71/5.12 ( ( ord_less_real @ D6 @ E )
% 4.71/5.12 => ( ( P @ D6 )
% 4.71/5.12 => ( P @ E ) ) )
% 4.71/5.12 => ( ! [N2: nat] :
% 4.71/5.12 ( ( N2 != zero_zero_nat )
% 4.71/5.12 => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) )
% 4.71/5.12 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 4.71/5.12 => ( P @ E2 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % forall_pos_mono
% 4.71/5.12 thf(fact_5155_vebt__member_Osimps_I4_J,axiom,
% 4.71/5.12 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 4.71/5.12 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_member.simps(4)
% 4.71/5.12 thf(fact_5156_ex__inverse__of__nat__less,axiom,
% 4.71/5.12 ! [X: real] :
% 4.71/5.12 ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.12 => ? [N2: nat] :
% 4.71/5.12 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.71/5.12 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ X ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % ex_inverse_of_nat_less
% 4.71/5.12 thf(fact_5157_ex__inverse__of__nat__less,axiom,
% 4.71/5.12 ! [X: rat] :
% 4.71/5.12 ( ( ord_less_rat @ zero_zero_rat @ X )
% 4.71/5.12 => ? [N2: nat] :
% 4.71/5.12 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.71/5.12 & ( ord_less_rat @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ X ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % ex_inverse_of_nat_less
% 4.71/5.12 thf(fact_5158_power__diff__conv__inverse,axiom,
% 4.71/5.12 ! [X: complex,M2: nat,N: nat] :
% 4.71/5.12 ( ( X != zero_zero_complex )
% 4.71/5.12 => ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.12 => ( ( power_power_complex @ X @ ( minus_minus_nat @ N @ M2 ) )
% 4.71/5.12 = ( times_times_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ ( invers8013647133539491842omplex @ X ) @ M2 ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % power_diff_conv_inverse
% 4.71/5.12 thf(fact_5159_power__diff__conv__inverse,axiom,
% 4.71/5.12 ! [X: real,M2: nat,N: nat] :
% 4.71/5.12 ( ( X != zero_zero_real )
% 4.71/5.12 => ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.12 => ( ( power_power_real @ X @ ( minus_minus_nat @ N @ M2 ) )
% 4.71/5.12 = ( times_times_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ ( inverse_inverse_real @ X ) @ M2 ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % power_diff_conv_inverse
% 4.71/5.12 thf(fact_5160_power__diff__conv__inverse,axiom,
% 4.71/5.12 ! [X: rat,M2: nat,N: nat] :
% 4.71/5.12 ( ( X != zero_zero_rat )
% 4.71/5.12 => ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.12 => ( ( power_power_rat @ X @ ( minus_minus_nat @ N @ M2 ) )
% 4.71/5.12 = ( times_times_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ ( inverse_inverse_rat @ X ) @ M2 ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % power_diff_conv_inverse
% 4.71/5.12 thf(fact_5161_vebt__pred_Osimps_I2_J,axiom,
% 4.71/5.12 ! [A: $o,Uw: $o] :
% 4.71/5.12 ( ( A
% 4.71/5.12 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 4.71/5.12 = ( some_nat @ zero_zero_nat ) ) )
% 4.71/5.12 & ( ~ A
% 4.71/5.12 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 4.71/5.12 = none_nat ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_pred.simps(2)
% 4.71/5.12 thf(fact_5162_vebt__succ_Osimps_I1_J,axiom,
% 4.71/5.12 ! [B: $o,Uu: $o] :
% 4.71/5.12 ( ( B
% 4.71/5.12 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 4.71/5.12 = ( some_nat @ one_one_nat ) ) )
% 4.71/5.12 & ( ~ B
% 4.71/5.12 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 4.71/5.12 = none_nat ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_succ.simps(1)
% 4.71/5.12 thf(fact_5163_vebt__pred_Osimps_I3_J,axiom,
% 4.71/5.12 ! [B: $o,A: $o,Va2: nat] :
% 4.71/5.12 ( ( B
% 4.71/5.12 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va2 ) ) )
% 4.71/5.12 = ( some_nat @ one_one_nat ) ) )
% 4.71/5.12 & ( ~ B
% 4.71/5.12 => ( ( A
% 4.71/5.12 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va2 ) ) )
% 4.71/5.12 = ( some_nat @ zero_zero_nat ) ) )
% 4.71/5.12 & ( ~ A
% 4.71/5.12 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va2 ) ) )
% 4.71/5.12 = none_nat ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_pred.simps(3)
% 4.71/5.12 thf(fact_5164_vebt__maxt_Osimps_I1_J,axiom,
% 4.71/5.12 ! [B: $o,A: $o] :
% 4.71/5.12 ( ( B
% 4.71/5.12 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 4.71/5.12 = ( some_nat @ one_one_nat ) ) )
% 4.71/5.12 & ( ~ B
% 4.71/5.12 => ( ( A
% 4.71/5.12 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 4.71/5.12 = ( some_nat @ zero_zero_nat ) ) )
% 4.71/5.12 & ( ~ A
% 4.71/5.12 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 4.71/5.12 = none_nat ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_maxt.simps(1)
% 4.71/5.12 thf(fact_5165_vebt__mint_Osimps_I1_J,axiom,
% 4.71/5.12 ! [A: $o,B: $o] :
% 4.71/5.12 ( ( A
% 4.71/5.12 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 4.71/5.12 = ( some_nat @ zero_zero_nat ) ) )
% 4.71/5.12 & ( ~ A
% 4.71/5.12 => ( ( B
% 4.71/5.12 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 4.71/5.12 = ( some_nat @ one_one_nat ) ) )
% 4.71/5.12 & ( ~ B
% 4.71/5.12 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 4.71/5.12 = none_nat ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_mint.simps(1)
% 4.71/5.12 thf(fact_5166_geqmaxNone,axiom,
% 4.71/5.12 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 4.71/5.12 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 4.71/5.12 => ( ( ord_less_eq_nat @ Ma @ X )
% 4.71/5.12 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.12 = none_nat ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % geqmaxNone
% 4.71/5.12 thf(fact_5167_option_Osize__gen_I2_J,axiom,
% 4.71/5.12 ! [X: nat > nat,X23: nat] :
% 4.71/5.12 ( ( size_option_nat @ X @ ( some_nat @ X23 ) )
% 4.71/5.12 = ( plus_plus_nat @ ( X @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % option.size_gen(2)
% 4.71/5.12 thf(fact_5168_option_Osize__gen_I2_J,axiom,
% 4.71/5.12 ! [X: product_prod_nat_nat > nat,X23: product_prod_nat_nat] :
% 4.71/5.12 ( ( size_o8335143837870341156at_nat @ X @ ( some_P7363390416028606310at_nat @ X23 ) )
% 4.71/5.12 = ( plus_plus_nat @ ( X @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % option.size_gen(2)
% 4.71/5.12 thf(fact_5169_option_Osize__gen_I2_J,axiom,
% 4.71/5.12 ! [X: num > nat,X23: num] :
% 4.71/5.12 ( ( size_option_num @ X @ ( some_num @ X23 ) )
% 4.71/5.12 = ( plus_plus_nat @ ( X @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % option.size_gen(2)
% 4.71/5.12 thf(fact_5170_floor__log__eq__powr__iff,axiom,
% 4.71/5.12 ! [X: real,B: real,K: int] :
% 4.71/5.12 ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.12 => ( ( ord_less_real @ one_one_real @ B )
% 4.71/5.12 => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X ) )
% 4.71/5.12 = K )
% 4.71/5.12 = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X )
% 4.71/5.12 & ( ord_less_real @ X @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_log_eq_powr_iff
% 4.71/5.12 thf(fact_5171_Cauchy__iff2,axiom,
% 4.71/5.12 ( topolo4055970368930404560y_real
% 4.71/5.12 = ( ^ [X8: nat > real] :
% 4.71/5.12 ! [J3: nat] :
% 4.71/5.12 ? [M8: nat] :
% 4.71/5.12 ! [M3: nat] :
% 4.71/5.12 ( ( ord_less_eq_nat @ M8 @ M3 )
% 4.71/5.12 => ! [N4: nat] :
% 4.71/5.12 ( ( ord_less_eq_nat @ M8 @ N4 )
% 4.71/5.12 => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X8 @ M3 ) @ ( X8 @ N4 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % Cauchy_iff2
% 4.71/5.12 thf(fact_5172_option_Osize__gen_I1_J,axiom,
% 4.71/5.12 ! [X: nat > nat] :
% 4.71/5.12 ( ( size_option_nat @ X @ none_nat )
% 4.71/5.12 = ( suc @ zero_zero_nat ) ) ).
% 4.71/5.12
% 4.71/5.12 % option.size_gen(1)
% 4.71/5.12 thf(fact_5173_option_Osize__gen_I1_J,axiom,
% 4.71/5.12 ! [X: product_prod_nat_nat > nat] :
% 4.71/5.12 ( ( size_o8335143837870341156at_nat @ X @ none_P5556105721700978146at_nat )
% 4.71/5.12 = ( suc @ zero_zero_nat ) ) ).
% 4.71/5.12
% 4.71/5.12 % option.size_gen(1)
% 4.71/5.12 thf(fact_5174_option_Osize__gen_I1_J,axiom,
% 4.71/5.12 ! [X: num > nat] :
% 4.71/5.12 ( ( size_option_num @ X @ none_num )
% 4.71/5.12 = ( suc @ zero_zero_nat ) ) ).
% 4.71/5.12
% 4.71/5.12 % option.size_gen(1)
% 4.71/5.12 thf(fact_5175_of__int__floor__cancel,axiom,
% 4.71/5.12 ! [X: real] :
% 4.71/5.12 ( ( ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) )
% 4.71/5.12 = X )
% 4.71/5.12 = ( ? [N4: int] :
% 4.71/5.12 ( X
% 4.71/5.12 = ( ring_1_of_int_real @ N4 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % of_int_floor_cancel
% 4.71/5.12 thf(fact_5176_of__int__floor__cancel,axiom,
% 4.71/5.12 ! [X: rat] :
% 4.71/5.12 ( ( ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) )
% 4.71/5.12 = X )
% 4.71/5.12 = ( ? [N4: int] :
% 4.71/5.12 ( X
% 4.71/5.12 = ( ring_1_of_int_rat @ N4 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % of_int_floor_cancel
% 4.71/5.12 thf(fact_5177_floor__zero,axiom,
% 4.71/5.12 ( ( archim6058952711729229775r_real @ zero_zero_real )
% 4.71/5.12 = zero_zero_int ) ).
% 4.71/5.12
% 4.71/5.12 % floor_zero
% 4.71/5.12 thf(fact_5178_floor__zero,axiom,
% 4.71/5.12 ( ( archim3151403230148437115or_rat @ zero_zero_rat )
% 4.71/5.12 = zero_zero_int ) ).
% 4.71/5.12
% 4.71/5.12 % floor_zero
% 4.71/5.12 thf(fact_5179_floor__one,axiom,
% 4.71/5.12 ( ( archim6058952711729229775r_real @ one_one_real )
% 4.71/5.12 = one_one_int ) ).
% 4.71/5.12
% 4.71/5.12 % floor_one
% 4.71/5.12 thf(fact_5180_floor__one,axiom,
% 4.71/5.12 ( ( archim3151403230148437115or_rat @ one_one_rat )
% 4.71/5.12 = one_one_int ) ).
% 4.71/5.12
% 4.71/5.12 % floor_one
% 4.71/5.12 thf(fact_5181_zero__le__floor,axiom,
% 4.71/5.12 ! [X: real] :
% 4.71/5.12 ( ( ord_less_eq_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X ) )
% 4.71/5.12 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 4.71/5.12
% 4.71/5.12 % zero_le_floor
% 4.71/5.12 thf(fact_5182_zero__le__floor,axiom,
% 4.71/5.12 ! [X: rat] :
% 4.71/5.12 ( ( ord_less_eq_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X ) )
% 4.71/5.12 = ( ord_less_eq_rat @ zero_zero_rat @ X ) ) ).
% 4.71/5.12
% 4.71/5.12 % zero_le_floor
% 4.71/5.12 thf(fact_5183_floor__less__zero,axiom,
% 4.71/5.12 ! [X: real] :
% 4.71/5.12 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ zero_zero_int )
% 4.71/5.12 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_less_zero
% 4.71/5.12 thf(fact_5184_floor__less__zero,axiom,
% 4.71/5.12 ! [X: rat] :
% 4.71/5.12 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ zero_zero_int )
% 4.71/5.12 = ( ord_less_rat @ X @ zero_zero_rat ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_less_zero
% 4.71/5.12 thf(fact_5185_zero__less__floor,axiom,
% 4.71/5.12 ! [X: real] :
% 4.71/5.12 ( ( ord_less_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X ) )
% 4.71/5.12 = ( ord_less_eq_real @ one_one_real @ X ) ) ).
% 4.71/5.12
% 4.71/5.12 % zero_less_floor
% 4.71/5.12 thf(fact_5186_zero__less__floor,axiom,
% 4.71/5.12 ! [X: rat] :
% 4.71/5.12 ( ( ord_less_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X ) )
% 4.71/5.12 = ( ord_less_eq_rat @ one_one_rat @ X ) ) ).
% 4.71/5.12
% 4.71/5.12 % zero_less_floor
% 4.71/5.12 thf(fact_5187_floor__le__zero,axiom,
% 4.71/5.12 ! [X: real] :
% 4.71/5.12 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ zero_zero_int )
% 4.71/5.12 = ( ord_less_real @ X @ one_one_real ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_le_zero
% 4.71/5.12 thf(fact_5188_floor__le__zero,axiom,
% 4.71/5.12 ! [X: rat] :
% 4.71/5.12 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ zero_zero_int )
% 4.71/5.12 = ( ord_less_rat @ X @ one_one_rat ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_le_zero
% 4.71/5.12 thf(fact_5189_one__le__floor,axiom,
% 4.71/5.12 ! [X: real] :
% 4.71/5.12 ( ( ord_less_eq_int @ one_one_int @ ( archim6058952711729229775r_real @ X ) )
% 4.71/5.12 = ( ord_less_eq_real @ one_one_real @ X ) ) ).
% 4.71/5.12
% 4.71/5.12 % one_le_floor
% 4.71/5.12 thf(fact_5190_one__le__floor,axiom,
% 4.71/5.12 ! [X: rat] :
% 4.71/5.12 ( ( ord_less_eq_int @ one_one_int @ ( archim3151403230148437115or_rat @ X ) )
% 4.71/5.12 = ( ord_less_eq_rat @ one_one_rat @ X ) ) ).
% 4.71/5.12
% 4.71/5.12 % one_le_floor
% 4.71/5.12 thf(fact_5191_floor__less__one,axiom,
% 4.71/5.12 ! [X: real] :
% 4.71/5.12 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int )
% 4.71/5.12 = ( ord_less_real @ X @ one_one_real ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_less_one
% 4.71/5.12 thf(fact_5192_floor__less__one,axiom,
% 4.71/5.12 ! [X: rat] :
% 4.71/5.12 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 4.71/5.12 = ( ord_less_rat @ X @ one_one_rat ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_less_one
% 4.71/5.12 thf(fact_5193_floor__diff__one,axiom,
% 4.71/5.12 ! [X: real] :
% 4.71/5.12 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X @ one_one_real ) )
% 4.71/5.12 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_diff_one
% 4.71/5.12 thf(fact_5194_floor__diff__one,axiom,
% 4.71/5.12 ! [X: rat] :
% 4.71/5.12 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X @ one_one_rat ) )
% 4.71/5.12 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_diff_one
% 4.71/5.12 thf(fact_5195_vebt__mint_Ocases,axiom,
% 4.71/5.12 ! [X: vEBT_VEBT] :
% 4.71/5.12 ( ! [A5: $o,B5: $o] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.12 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 4.71/5.12 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_mint.cases
% 4.71/5.12 thf(fact_5196_subrelI,axiom,
% 4.71/5.12 ! [R2: set_Pr8693737435421807431at_nat,S: set_Pr8693737435421807431at_nat] :
% 4.71/5.12 ( ! [X4: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 4.71/5.12 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X4 @ Y3 ) @ R2 )
% 4.71/5.12 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X4 @ Y3 ) @ S ) )
% 4.71/5.12 => ( ord_le3000389064537975527at_nat @ R2 @ S ) ) ).
% 4.71/5.12
% 4.71/5.12 % subrelI
% 4.71/5.12 thf(fact_5197_subrelI,axiom,
% 4.71/5.12 ! [R2: set_Pr7459493094073627847at_nat,S: set_Pr7459493094073627847at_nat] :
% 4.71/5.12 ( ! [X4: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] :
% 4.71/5.12 ( ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y3 ) @ R2 )
% 4.71/5.12 => ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X4 @ Y3 ) @ S ) )
% 4.71/5.12 => ( ord_le5997549366648089703at_nat @ R2 @ S ) ) ).
% 4.71/5.12
% 4.71/5.12 % subrelI
% 4.71/5.12 thf(fact_5198_subrelI,axiom,
% 4.71/5.12 ! [R2: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
% 4.71/5.12 ( ! [X4: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 4.71/5.12 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y3 ) @ R2 )
% 4.71/5.12 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y3 ) @ S ) )
% 4.71/5.12 => ( ord_le1268244103169919719at_nat @ R2 @ S ) ) ).
% 4.71/5.12
% 4.71/5.12 % subrelI
% 4.71/5.12 thf(fact_5199_subrelI,axiom,
% 4.71/5.12 ! [R2: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 4.71/5.12 ( ! [X4: nat,Y3: nat] :
% 4.71/5.12 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y3 ) @ R2 )
% 4.71/5.12 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y3 ) @ S ) )
% 4.71/5.12 => ( ord_le3146513528884898305at_nat @ R2 @ S ) ) ).
% 4.71/5.12
% 4.71/5.12 % subrelI
% 4.71/5.12 thf(fact_5200_subrelI,axiom,
% 4.71/5.12 ! [R2: set_Pr958786334691620121nt_int,S: set_Pr958786334691620121nt_int] :
% 4.71/5.12 ( ! [X4: int,Y3: int] :
% 4.71/5.12 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y3 ) @ R2 )
% 4.71/5.12 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y3 ) @ S ) )
% 4.71/5.12 => ( ord_le2843351958646193337nt_int @ R2 @ S ) ) ).
% 4.71/5.12
% 4.71/5.12 % subrelI
% 4.71/5.12 thf(fact_5201_floor__mono,axiom,
% 4.71/5.12 ! [X: real,Y: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ X @ Y )
% 4.71/5.12 => ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_mono
% 4.71/5.12 thf(fact_5202_floor__mono,axiom,
% 4.71/5.12 ! [X: rat,Y: rat] :
% 4.71/5.12 ( ( ord_less_eq_rat @ X @ Y )
% 4.71/5.12 => ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_mono
% 4.71/5.12 thf(fact_5203_of__int__floor__le,axiom,
% 4.71/5.12 ! [X: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) @ X ) ).
% 4.71/5.12
% 4.71/5.12 % of_int_floor_le
% 4.71/5.12 thf(fact_5204_of__int__floor__le,axiom,
% 4.71/5.12 ! [X: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) @ X ) ).
% 4.71/5.12
% 4.71/5.12 % of_int_floor_le
% 4.71/5.12 thf(fact_5205_floor__less__cancel,axiom,
% 4.71/5.12 ! [X: real,Y: real] :
% 4.71/5.12 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) )
% 4.71/5.12 => ( ord_less_real @ X @ Y ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_less_cancel
% 4.71/5.12 thf(fact_5206_floor__less__cancel,axiom,
% 4.71/5.12 ! [X: rat,Y: rat] :
% 4.71/5.12 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) )
% 4.71/5.12 => ( ord_less_rat @ X @ Y ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_less_cancel
% 4.71/5.12 thf(fact_5207_floor__le__ceiling,axiom,
% 4.71/5.12 ! [X: real] : ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( archim7802044766580827645g_real @ X ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_le_ceiling
% 4.71/5.12 thf(fact_5208_floor__le__ceiling,axiom,
% 4.71/5.12 ! [X: rat] : ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim2889992004027027881ng_rat @ X ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_le_ceiling
% 4.71/5.12 thf(fact_5209_VEBT__internal_OminNull_Ocases,axiom,
% 4.71/5.12 ! [X: vEBT_VEBT] :
% 4.71/5.12 ( ( X
% 4.71/5.12 != ( vEBT_Leaf @ $false @ $false ) )
% 4.71/5.12 => ( ! [Uv2: $o] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 4.71/5.12 => ( ! [Uu2: $o] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 4.71/5.12 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 4.71/5.12 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % VEBT_internal.minNull.cases
% 4.71/5.12 thf(fact_5210_vebt__mint_Osimps_I3_J,axiom,
% 4.71/5.12 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 4.71/5.12 ( ( vEBT_vebt_mint @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 4.71/5.12 = ( some_nat @ Mi ) ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_mint.simps(3)
% 4.71/5.12 thf(fact_5211_vebt__maxt_Osimps_I3_J,axiom,
% 4.71/5.12 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 4.71/5.12 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 4.71/5.12 = ( some_nat @ Ma ) ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_maxt.simps(3)
% 4.71/5.12 thf(fact_5212_vebt__mint_Osimps_I2_J,axiom,
% 4.71/5.12 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 4.71/5.12 ( ( vEBT_vebt_mint @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 4.71/5.12 = none_nat ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_mint.simps(2)
% 4.71/5.12 thf(fact_5213_vebt__maxt_Osimps_I2_J,axiom,
% 4.71/5.12 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 4.71/5.12 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 4.71/5.12 = none_nat ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_maxt.simps(2)
% 4.71/5.12 thf(fact_5214_vebt__delete_Osimps_I4_J,axiom,
% 4.71/5.12 ! [Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Uu: nat] :
% 4.71/5.12 ( ( vEBT_vebt_delete @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Uu )
% 4.71/5.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_delete.simps(4)
% 4.71/5.12 thf(fact_5215_vebt__member_Osimps_I2_J,axiom,
% 4.71/5.12 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X: nat] :
% 4.71/5.12 ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_member.simps(2)
% 4.71/5.12 thf(fact_5216_VEBT__internal_OminNull_Osimps_I4_J,axiom,
% 4.71/5.12 ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] : ( vEBT_VEBT_minNull @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ).
% 4.71/5.12
% 4.71/5.12 % VEBT_internal.minNull.simps(4)
% 4.71/5.12 thf(fact_5217_le__floor__iff,axiom,
% 4.71/5.12 ! [Z: int,X: real] :
% 4.71/5.12 ( ( ord_less_eq_int @ Z @ ( archim6058952711729229775r_real @ X ) )
% 4.71/5.12 = ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X ) ) ).
% 4.71/5.12
% 4.71/5.12 % le_floor_iff
% 4.71/5.12 thf(fact_5218_le__floor__iff,axiom,
% 4.71/5.12 ! [Z: int,X: rat] :
% 4.71/5.12 ( ( ord_less_eq_int @ Z @ ( archim3151403230148437115or_rat @ X ) )
% 4.71/5.12 = ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X ) ) ).
% 4.71/5.12
% 4.71/5.12 % le_floor_iff
% 4.71/5.12 thf(fact_5219_floor__less__iff,axiom,
% 4.71/5.12 ! [X: real,Z: int] :
% 4.71/5.12 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ Z )
% 4.71/5.12 = ( ord_less_real @ X @ ( ring_1_of_int_real @ Z ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_less_iff
% 4.71/5.12 thf(fact_5220_floor__less__iff,axiom,
% 4.71/5.12 ! [X: rat,Z: int] :
% 4.71/5.12 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ Z )
% 4.71/5.12 = ( ord_less_rat @ X @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_less_iff
% 4.71/5.12 thf(fact_5221_le__floor__add,axiom,
% 4.71/5.12 ! [X: real,Y: real] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) ) @ ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ Y ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % le_floor_add
% 4.71/5.12 thf(fact_5222_le__floor__add,axiom,
% 4.71/5.12 ! [X: rat,Y: rat] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) @ ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % le_floor_add
% 4.71/5.12 thf(fact_5223_floor__power,axiom,
% 4.71/5.12 ! [X: real,N: nat] :
% 4.71/5.12 ( ( X
% 4.71/5.12 = ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) )
% 4.71/5.12 => ( ( archim6058952711729229775r_real @ ( power_power_real @ X @ N ) )
% 4.71/5.12 = ( power_power_int @ ( archim6058952711729229775r_real @ X ) @ N ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_power
% 4.71/5.12 thf(fact_5224_floor__power,axiom,
% 4.71/5.12 ! [X: rat,N: nat] :
% 4.71/5.12 ( ( X
% 4.71/5.12 = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) )
% 4.71/5.12 => ( ( archim3151403230148437115or_rat @ ( power_power_rat @ X @ N ) )
% 4.71/5.12 = ( power_power_int @ ( archim3151403230148437115or_rat @ X ) @ N ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_power
% 4.71/5.12 thf(fact_5225_vebt__mint_Oelims,axiom,
% 4.71/5.12 ! [X: vEBT_VEBT,Y: option_nat] :
% 4.71/5.12 ( ( ( vEBT_vebt_mint @ X )
% 4.71/5.12 = Y )
% 4.71/5.12 => ( ! [A5: $o,B5: $o] :
% 4.71/5.12 ( ( X
% 4.71/5.12 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.12 => ~ ( ( A5
% 4.71/5.12 => ( Y
% 4.71/5.12 = ( some_nat @ zero_zero_nat ) ) )
% 4.71/5.12 & ( ~ A5
% 4.71/5.12 => ( ( B5
% 4.71/5.12 => ( Y
% 4.71/5.12 = ( some_nat @ one_one_nat ) ) )
% 4.71/5.12 & ( ~ B5
% 4.71/5.12 => ( Y = none_nat ) ) ) ) ) )
% 4.71/5.12 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 4.71/5.12 ( X
% 4.71/5.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 4.71/5.12 => ( Y != none_nat ) )
% 4.71/5.12 => ~ ! [Mi2: nat] :
% 4.71/5.12 ( ? [Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 4.71/5.12 ( X
% 4.71/5.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 4.71/5.12 => ( Y
% 4.71/5.12 != ( some_nat @ Mi2 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_mint.elims
% 4.71/5.12 thf(fact_5226_vebt__maxt_Oelims,axiom,
% 4.71/5.12 ! [X: vEBT_VEBT,Y: option_nat] :
% 4.71/5.12 ( ( ( vEBT_vebt_maxt @ X )
% 4.71/5.12 = Y )
% 4.71/5.12 => ( ! [A5: $o,B5: $o] :
% 4.71/5.12 ( ( X
% 4.71/5.12 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.12 => ~ ( ( B5
% 4.71/5.12 => ( Y
% 4.71/5.12 = ( some_nat @ one_one_nat ) ) )
% 4.71/5.12 & ( ~ B5
% 4.71/5.12 => ( ( A5
% 4.71/5.12 => ( Y
% 4.71/5.12 = ( some_nat @ zero_zero_nat ) ) )
% 4.71/5.12 & ( ~ A5
% 4.71/5.12 => ( Y = none_nat ) ) ) ) ) )
% 4.71/5.12 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 4.71/5.12 ( X
% 4.71/5.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 4.71/5.12 => ( Y != none_nat ) )
% 4.71/5.12 => ~ ! [Mi2: nat,Ma2: nat] :
% 4.71/5.12 ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 4.71/5.12 ( X
% 4.71/5.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 4.71/5.12 => ( Y
% 4.71/5.12 != ( some_nat @ Ma2 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_maxt.elims
% 4.71/5.12 thf(fact_5227_vebt__delete_Osimps_I5_J,axiom,
% 4.71/5.12 ! [Mi: nat,Ma: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT,X: nat] :
% 4.71/5.12 ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst @ Smry ) @ X )
% 4.71/5.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst @ Smry ) ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_delete.simps(5)
% 4.71/5.12 thf(fact_5228_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 4.71/5.12 ! [Mi: nat,Ma: nat,Va2: list_VEBT_VEBT,Vb: vEBT_VEBT,X: nat] :
% 4.71/5.12 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va2 @ Vb ) @ X )
% 4.71/5.12 = ( ( X = Mi )
% 4.71/5.12 | ( X = Ma ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % VEBT_internal.membermima.simps(3)
% 4.71/5.12 thf(fact_5229_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 4.71/5.12 ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 4.71/5.12 ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) ).
% 4.71/5.12
% 4.71/5.12 % VEBT_internal.membermima.simps(2)
% 4.71/5.12 thf(fact_5230_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 4.71/5.12 ! [X: vEBT_VEBT] :
% 4.71/5.12 ( ( vEBT_VEBT_minNull @ X )
% 4.71/5.12 => ( ( X
% 4.71/5.12 != ( vEBT_Leaf @ $false @ $false ) )
% 4.71/5.12 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % VEBT_internal.minNull.elims(2)
% 4.71/5.12 thf(fact_5231_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 4.71/5.12 ! [X: vEBT_VEBT,Y: $o] :
% 4.71/5.12 ( ( ( vEBT_VEBT_minNull @ X )
% 4.71/5.12 = Y )
% 4.71/5.12 => ( ( ( X
% 4.71/5.12 = ( vEBT_Leaf @ $false @ $false ) )
% 4.71/5.12 => ~ Y )
% 4.71/5.12 => ( ( ? [Uv2: $o] :
% 4.71/5.12 ( X
% 4.71/5.12 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 4.71/5.12 => Y )
% 4.71/5.12 => ( ( ? [Uu2: $o] :
% 4.71/5.12 ( X
% 4.71/5.12 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 4.71/5.12 => Y )
% 4.71/5.12 => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 4.71/5.12 ( X
% 4.71/5.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 4.71/5.12 => ~ Y )
% 4.71/5.12 => ~ ( ? [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 4.71/5.12 ( X
% 4.71/5.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 4.71/5.12 => Y ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % VEBT_internal.minNull.elims(1)
% 4.71/5.12 thf(fact_5232_vebt__succ_Osimps_I3_J,axiom,
% 4.71/5.12 ! [Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,Va2: nat] :
% 4.71/5.12 ( ( vEBT_vebt_succ @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz ) @ Va2 )
% 4.71/5.12 = none_nat ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_succ.simps(3)
% 4.71/5.12 thf(fact_5233_vebt__pred_Osimps_I4_J,axiom,
% 4.71/5.12 ! [Uy: nat,Uz: list_VEBT_VEBT,Va2: vEBT_VEBT,Vb: nat] :
% 4.71/5.12 ( ( vEBT_vebt_pred @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz @ Va2 ) @ Vb )
% 4.71/5.12 = none_nat ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_pred.simps(4)
% 4.71/5.12 thf(fact_5234_of__nat__floor,axiom,
% 4.71/5.12 ! [R2: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 4.71/5.12 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim6058952711729229775r_real @ R2 ) ) ) @ R2 ) ) ).
% 4.71/5.12
% 4.71/5.12 % of_nat_floor
% 4.71/5.12 thf(fact_5235_of__nat__floor,axiom,
% 4.71/5.12 ! [R2: rat] :
% 4.71/5.12 ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 4.71/5.12 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim3151403230148437115or_rat @ R2 ) ) ) @ R2 ) ) ).
% 4.71/5.12
% 4.71/5.12 % of_nat_floor
% 4.71/5.12 thf(fact_5236_one__add__floor,axiom,
% 4.71/5.12 ! [X: real] :
% 4.71/5.12 ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int )
% 4.71/5.12 = ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ one_one_real ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % one_add_floor
% 4.71/5.12 thf(fact_5237_one__add__floor,axiom,
% 4.71/5.12 ! [X: rat] :
% 4.71/5.12 ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 4.71/5.12 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ one_one_rat ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % one_add_floor
% 4.71/5.12 thf(fact_5238_le__mult__nat__floor,axiom,
% 4.71/5.12 ! [A: real,B: real] : ( ord_less_eq_nat @ ( times_times_nat @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) @ ( nat2 @ ( archim6058952711729229775r_real @ B ) ) ) @ ( nat2 @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % le_mult_nat_floor
% 4.71/5.12 thf(fact_5239_le__mult__nat__floor,axiom,
% 4.71/5.12 ! [A: rat,B: rat] : ( ord_less_eq_nat @ ( times_times_nat @ ( nat2 @ ( archim3151403230148437115or_rat @ A ) ) @ ( nat2 @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( nat2 @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % le_mult_nat_floor
% 4.71/5.12 thf(fact_5240_nat__floor__neg,axiom,
% 4.71/5.12 ! [X: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 4.71/5.12 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 4.71/5.12 = zero_zero_nat ) ) ).
% 4.71/5.12
% 4.71/5.12 % nat_floor_neg
% 4.71/5.12 thf(fact_5241_floor__eq3,axiom,
% 4.71/5.12 ! [N: nat,X: real] :
% 4.71/5.12 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 4.71/5.12 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 4.71/5.12 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 4.71/5.12 = N ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_eq3
% 4.71/5.12 thf(fact_5242_le__nat__floor,axiom,
% 4.71/5.12 ! [X: nat,A: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ A )
% 4.71/5.12 => ( ord_less_eq_nat @ X @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % le_nat_floor
% 4.71/5.12 thf(fact_5243_ceiling__diff__floor__le__1,axiom,
% 4.71/5.12 ! [X: real] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ ( archim6058952711729229775r_real @ X ) ) @ one_one_int ) ).
% 4.71/5.12
% 4.71/5.12 % ceiling_diff_floor_le_1
% 4.71/5.12 thf(fact_5244_ceiling__diff__floor__le__1,axiom,
% 4.71/5.12 ! [X: rat] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim3151403230148437115or_rat @ X ) ) @ one_one_int ) ).
% 4.71/5.12
% 4.71/5.12 % ceiling_diff_floor_le_1
% 4.71/5.12 thf(fact_5245_real__of__int__floor__add__one__gt,axiom,
% 4.71/5.12 ! [R2: real] : ( ord_less_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 4.71/5.12
% 4.71/5.12 % real_of_int_floor_add_one_gt
% 4.71/5.12 thf(fact_5246_floor__eq,axiom,
% 4.71/5.12 ! [N: int,X: real] :
% 4.71/5.12 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X )
% 4.71/5.12 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 4.71/5.12 => ( ( archim6058952711729229775r_real @ X )
% 4.71/5.12 = N ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_eq
% 4.71/5.12 thf(fact_5247_real__of__int__floor__add__one__ge,axiom,
% 4.71/5.12 ! [R2: real] : ( ord_less_eq_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 4.71/5.12
% 4.71/5.12 % real_of_int_floor_add_one_ge
% 4.71/5.12 thf(fact_5248_real__of__int__floor__gt__diff__one,axiom,
% 4.71/5.12 ! [R2: real] : ( ord_less_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % real_of_int_floor_gt_diff_one
% 4.71/5.12 thf(fact_5249_real__of__int__floor__ge__diff__one,axiom,
% 4.71/5.12 ! [R2: real] : ( ord_less_eq_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % real_of_int_floor_ge_diff_one
% 4.71/5.12 thf(fact_5250_vebt__delete_Osimps_I6_J,axiom,
% 4.71/5.12 ! [Mi: nat,Ma: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT,X: nat] :
% 4.71/5.12 ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) @ X )
% 4.71/5.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_delete.simps(6)
% 4.71/5.12 thf(fact_5251_floor__unique,axiom,
% 4.71/5.12 ! [Z: int,X: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X )
% 4.71/5.12 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) )
% 4.71/5.12 => ( ( archim6058952711729229775r_real @ X )
% 4.71/5.12 = Z ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_unique
% 4.71/5.12 thf(fact_5252_floor__unique,axiom,
% 4.71/5.12 ! [Z: int,X: rat] :
% 4.71/5.12 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X )
% 4.71/5.12 => ( ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) )
% 4.71/5.12 => ( ( archim3151403230148437115or_rat @ X )
% 4.71/5.12 = Z ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_unique
% 4.71/5.12 thf(fact_5253_floor__eq__iff,axiom,
% 4.71/5.12 ! [X: real,A: int] :
% 4.71/5.12 ( ( ( archim6058952711729229775r_real @ X )
% 4.71/5.12 = A )
% 4.71/5.12 = ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ X )
% 4.71/5.12 & ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_eq_iff
% 4.71/5.12 thf(fact_5254_floor__eq__iff,axiom,
% 4.71/5.12 ! [X: rat,A: int] :
% 4.71/5.12 ( ( ( archim3151403230148437115or_rat @ X )
% 4.71/5.12 = A )
% 4.71/5.12 = ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ X )
% 4.71/5.12 & ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_eq_iff
% 4.71/5.12 thf(fact_5255_floor__split,axiom,
% 4.71/5.12 ! [P: int > $o,T: real] :
% 4.71/5.12 ( ( P @ ( archim6058952711729229775r_real @ T ) )
% 4.71/5.12 = ( ! [I4: int] :
% 4.71/5.12 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ I4 ) @ T )
% 4.71/5.12 & ( ord_less_real @ T @ ( plus_plus_real @ ( ring_1_of_int_real @ I4 ) @ one_one_real ) ) )
% 4.71/5.12 => ( P @ I4 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_split
% 4.71/5.12 thf(fact_5256_floor__split,axiom,
% 4.71/5.12 ! [P: int > $o,T: rat] :
% 4.71/5.12 ( ( P @ ( archim3151403230148437115or_rat @ T ) )
% 4.71/5.12 = ( ! [I4: int] :
% 4.71/5.12 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ I4 ) @ T )
% 4.71/5.12 & ( ord_less_rat @ T @ ( plus_plus_rat @ ( ring_1_of_int_rat @ I4 ) @ one_one_rat ) ) )
% 4.71/5.12 => ( P @ I4 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_split
% 4.71/5.12 thf(fact_5257_le__mult__floor,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.12 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.71/5.12 => ( ord_less_eq_int @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % le_mult_floor
% 4.71/5.12 thf(fact_5258_le__mult__floor,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.12 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.71/5.12 => ( ord_less_eq_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % le_mult_floor
% 4.71/5.12 thf(fact_5259_less__floor__iff,axiom,
% 4.71/5.12 ! [Z: int,X: real] :
% 4.71/5.12 ( ( ord_less_int @ Z @ ( archim6058952711729229775r_real @ X ) )
% 4.71/5.12 = ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X ) ) ).
% 4.71/5.12
% 4.71/5.12 % less_floor_iff
% 4.71/5.12 thf(fact_5260_less__floor__iff,axiom,
% 4.71/5.12 ! [Z: int,X: rat] :
% 4.71/5.12 ( ( ord_less_int @ Z @ ( archim3151403230148437115or_rat @ X ) )
% 4.71/5.12 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X ) ) ).
% 4.71/5.12
% 4.71/5.12 % less_floor_iff
% 4.71/5.12 thf(fact_5261_floor__le__iff,axiom,
% 4.71/5.12 ! [X: real,Z: int] :
% 4.71/5.12 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ Z )
% 4.71/5.12 = ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_le_iff
% 4.71/5.12 thf(fact_5262_floor__le__iff,axiom,
% 4.71/5.12 ! [X: rat,Z: int] :
% 4.71/5.12 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ Z )
% 4.71/5.12 = ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_le_iff
% 4.71/5.12 thf(fact_5263_floor__correct,axiom,
% 4.71/5.12 ! [X: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) @ X )
% 4.71/5.12 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_correct
% 4.71/5.12 thf(fact_5264_floor__correct,axiom,
% 4.71/5.12 ! [X: rat] :
% 4.71/5.12 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) @ X )
% 4.71/5.12 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_correct
% 4.71/5.12 thf(fact_5265_floor__eq4,axiom,
% 4.71/5.12 ! [N: nat,X: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 4.71/5.12 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 4.71/5.12 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 4.71/5.12 = N ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_eq4
% 4.71/5.12 thf(fact_5266_floor__eq2,axiom,
% 4.71/5.12 ! [N: int,X: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N ) @ X )
% 4.71/5.12 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 4.71/5.12 => ( ( archim6058952711729229775r_real @ X )
% 4.71/5.12 = N ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_eq2
% 4.71/5.12 thf(fact_5267_floor__divide__real__eq__div,axiom,
% 4.71/5.12 ! [B: int,A: real] :
% 4.71/5.12 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.71/5.12 => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B ) ) )
% 4.71/5.12 = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_divide_real_eq_div
% 4.71/5.12 thf(fact_5268_floor__divide__lower,axiom,
% 4.71/5.12 ! [Q4: real,P6: real] :
% 4.71/5.12 ( ( ord_less_real @ zero_zero_real @ Q4 )
% 4.71/5.12 => ( ord_less_eq_real @ ( times_times_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P6 @ Q4 ) ) ) @ Q4 ) @ P6 ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_divide_lower
% 4.71/5.12 thf(fact_5269_floor__divide__lower,axiom,
% 4.71/5.12 ! [Q4: rat,P6: rat] :
% 4.71/5.12 ( ( ord_less_rat @ zero_zero_rat @ Q4 )
% 4.71/5.12 => ( ord_less_eq_rat @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P6 @ Q4 ) ) ) @ Q4 ) @ P6 ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_divide_lower
% 4.71/5.12 thf(fact_5270_le__mult__floor__Ints,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.12 => ( ( member_real @ A @ ring_1_Ints_real )
% 4.71/5.12 => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % le_mult_floor_Ints
% 4.71/5.12 thf(fact_5271_le__mult__floor__Ints,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.12 => ( ( member_real @ A @ ring_1_Ints_real )
% 4.71/5.12 => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) ) @ ( ring_1_of_int_rat @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % le_mult_floor_Ints
% 4.71/5.12 thf(fact_5272_le__mult__floor__Ints,axiom,
% 4.71/5.12 ! [A: real,B: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.71/5.12 => ( ( member_real @ A @ ring_1_Ints_real )
% 4.71/5.12 => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) ) @ ( ring_1_of_int_int @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % le_mult_floor_Ints
% 4.71/5.12 thf(fact_5273_le__mult__floor__Ints,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.12 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 4.71/5.12 => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( ring_1_of_int_real @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % le_mult_floor_Ints
% 4.71/5.12 thf(fact_5274_le__mult__floor__Ints,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.12 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 4.71/5.12 => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % le_mult_floor_Ints
% 4.71/5.12 thf(fact_5275_le__mult__floor__Ints,axiom,
% 4.71/5.12 ! [A: rat,B: rat] :
% 4.71/5.12 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.71/5.12 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 4.71/5.12 => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( ring_1_of_int_int @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % le_mult_floor_Ints
% 4.71/5.12 thf(fact_5276_floor__add,axiom,
% 4.71/5.12 ! [X: real,Y: real] :
% 4.71/5.12 ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 4.71/5.12 => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ Y ) )
% 4.71/5.12 = ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) ) ) )
% 4.71/5.12 & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 4.71/5.12 => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ Y ) )
% 4.71/5.12 = ( plus_plus_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) ) @ one_one_int ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_add
% 4.71/5.12 thf(fact_5277_floor__add,axiom,
% 4.71/5.12 ! [X: rat,Y: rat] :
% 4.71/5.12 ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 4.71/5.12 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) )
% 4.71/5.12 = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) ) )
% 4.71/5.12 & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 4.71/5.12 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) )
% 4.71/5.12 = ( plus_plus_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) @ one_one_int ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_add
% 4.71/5.12 thf(fact_5278_floor__divide__upper,axiom,
% 4.71/5.12 ! [Q4: real,P6: real] :
% 4.71/5.12 ( ( ord_less_real @ zero_zero_real @ Q4 )
% 4.71/5.12 => ( ord_less_real @ P6 @ ( times_times_real @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P6 @ Q4 ) ) ) @ one_one_real ) @ Q4 ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_divide_upper
% 4.71/5.12 thf(fact_5279_floor__divide__upper,axiom,
% 4.71/5.12 ! [Q4: rat,P6: rat] :
% 4.71/5.12 ( ( ord_less_rat @ zero_zero_rat @ Q4 )
% 4.71/5.12 => ( ord_less_rat @ P6 @ ( times_times_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P6 @ Q4 ) ) ) @ one_one_rat ) @ Q4 ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % floor_divide_upper
% 4.71/5.12 thf(fact_5280_mi__eq__ma__no__ch,axiom,
% 4.71/5.12 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 4.71/5.12 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg )
% 4.71/5.12 => ( ( Mi = Ma )
% 4.71/5.12 => ( ! [X2: vEBT_VEBT] :
% 4.71/5.12 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.71/5.12 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X_12 ) )
% 4.71/5.12 & ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % mi_eq_ma_no_ch
% 4.71/5.12 thf(fact_5281_divides__aux__eq,axiom,
% 4.71/5.12 ! [Q4: nat,R2: nat] :
% 4.71/5.12 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q4 @ R2 ) )
% 4.71/5.12 = ( R2 = zero_zero_nat ) ) ).
% 4.71/5.12
% 4.71/5.12 % divides_aux_eq
% 4.71/5.12 thf(fact_5282_divides__aux__eq,axiom,
% 4.71/5.12 ! [Q4: int,R2: int] :
% 4.71/5.12 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q4 @ R2 ) )
% 4.71/5.12 = ( R2 = zero_zero_int ) ) ).
% 4.71/5.12
% 4.71/5.12 % divides_aux_eq
% 4.71/5.12 thf(fact_5283_prod__decode__aux_Oelims,axiom,
% 4.71/5.12 ! [X: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 4.71/5.12 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 4.71/5.12 = Y )
% 4.71/5.12 => ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 4.71/5.12 => ( Y
% 4.71/5.12 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 4.71/5.12 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 4.71/5.12 => ( Y
% 4.71/5.12 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % prod_decode_aux.elims
% 4.71/5.12 thf(fact_5284_prod__decode__aux_Osimps,axiom,
% 4.71/5.12 ( nat_prod_decode_aux
% 4.71/5.12 = ( ^ [K3: nat,M3: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M3 @ K3 ) @ ( product_Pair_nat_nat @ M3 @ ( minus_minus_nat @ K3 @ M3 ) ) @ ( nat_prod_decode_aux @ ( suc @ K3 ) @ ( minus_minus_nat @ M3 @ ( suc @ K3 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % prod_decode_aux.simps
% 4.71/5.12 thf(fact_5285_gbinomial__pochhammer_H,axiom,
% 4.71/5.12 ( gbinomial_complex
% 4.71/5.12 = ( ^ [A4: complex,K3: nat] : ( divide1717551699836669952omplex @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ A4 @ ( semiri8010041392384452111omplex @ K3 ) ) @ one_one_complex ) @ K3 ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % gbinomial_pochhammer'
% 4.71/5.12 thf(fact_5286_gbinomial__pochhammer_H,axiom,
% 4.71/5.12 ( gbinomial_rat
% 4.71/5.12 = ( ^ [A4: rat,K3: nat] : ( divide_divide_rat @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ A4 @ ( semiri681578069525770553at_rat @ K3 ) ) @ one_one_rat ) @ K3 ) @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % gbinomial_pochhammer'
% 4.71/5.12 thf(fact_5287_gbinomial__pochhammer_H,axiom,
% 4.71/5.12 ( gbinomial_real
% 4.71/5.12 = ( ^ [A4: real,K3: nat] : ( divide_divide_real @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ A4 @ ( semiri5074537144036343181t_real @ K3 ) ) @ one_one_real ) @ K3 ) @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % gbinomial_pochhammer'
% 4.71/5.12 thf(fact_5288_gbinomial__pochhammer,axiom,
% 4.71/5.12 ( gbinomial_rat
% 4.71/5.12 = ( ^ [A4: rat,K3: nat] : ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ A4 ) @ K3 ) ) @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % gbinomial_pochhammer
% 4.71/5.12 thf(fact_5289_gbinomial__pochhammer,axiom,
% 4.71/5.12 ( gbinomial_complex
% 4.71/5.12 = ( ^ [A4: complex,K3: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ A4 ) @ K3 ) ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % gbinomial_pochhammer
% 4.71/5.12 thf(fact_5290_gbinomial__pochhammer,axiom,
% 4.71/5.12 ( gbinomial_real
% 4.71/5.12 = ( ^ [A4: real,K3: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ A4 ) @ K3 ) ) @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % gbinomial_pochhammer
% 4.71/5.12 thf(fact_5291_sinh__zero__iff,axiom,
% 4.71/5.12 ! [X: real] :
% 4.71/5.12 ( ( ( sinh_real @ X )
% 4.71/5.12 = zero_zero_real )
% 4.71/5.12 = ( member_real @ ( exp_real @ X ) @ ( insert_real @ one_one_real @ ( insert_real @ ( uminus_uminus_real @ one_one_real ) @ bot_bot_set_real ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % sinh_zero_iff
% 4.71/5.12 thf(fact_5292_sinh__zero__iff,axiom,
% 4.71/5.12 ! [X: complex] :
% 4.71/5.12 ( ( ( sinh_complex @ X )
% 4.71/5.12 = zero_zero_complex )
% 4.71/5.12 = ( member_complex @ ( exp_complex @ X ) @ ( insert_complex @ one_one_complex @ ( insert_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ bot_bot_set_complex ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % sinh_zero_iff
% 4.71/5.12 thf(fact_5293_sinh__real__le__iff,axiom,
% 4.71/5.12 ! [X: real,Y: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ ( sinh_real @ X ) @ ( sinh_real @ Y ) )
% 4.71/5.12 = ( ord_less_eq_real @ X @ Y ) ) ).
% 4.71/5.12
% 4.71/5.12 % sinh_real_le_iff
% 4.71/5.12 thf(fact_5294_sinh__real__nonneg__iff,axiom,
% 4.71/5.12 ! [X: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ zero_zero_real @ ( sinh_real @ X ) )
% 4.71/5.12 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 4.71/5.12
% 4.71/5.12 % sinh_real_nonneg_iff
% 4.71/5.12 thf(fact_5295_sinh__real__nonpos__iff,axiom,
% 4.71/5.12 ! [X: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ ( sinh_real @ X ) @ zero_zero_real )
% 4.71/5.12 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 4.71/5.12
% 4.71/5.12 % sinh_real_nonpos_iff
% 4.71/5.12 thf(fact_5296_List_Ofinite__set,axiom,
% 4.71/5.12 ! [Xs: list_VEBT_VEBT] : ( finite5795047828879050333T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) ) ).
% 4.71/5.12
% 4.71/5.12 % List.finite_set
% 4.71/5.12 thf(fact_5297_List_Ofinite__set,axiom,
% 4.71/5.12 ! [Xs: list_nat] : ( finite_finite_nat @ ( set_nat2 @ Xs ) ) ).
% 4.71/5.12
% 4.71/5.12 % List.finite_set
% 4.71/5.12 thf(fact_5298_List_Ofinite__set,axiom,
% 4.71/5.12 ! [Xs: list_int] : ( finite_finite_int @ ( set_int2 @ Xs ) ) ).
% 4.71/5.12
% 4.71/5.12 % List.finite_set
% 4.71/5.12 thf(fact_5299_List_Ofinite__set,axiom,
% 4.71/5.12 ! [Xs: list_complex] : ( finite3207457112153483333omplex @ ( set_complex2 @ Xs ) ) ).
% 4.71/5.12
% 4.71/5.12 % List.finite_set
% 4.71/5.12 thf(fact_5300_List_Ofinite__set,axiom,
% 4.71/5.12 ! [Xs: list_P6011104703257516679at_nat] : ( finite6177210948735845034at_nat @ ( set_Pr5648618587558075414at_nat @ Xs ) ) ).
% 4.71/5.12
% 4.71/5.12 % List.finite_set
% 4.71/5.12 thf(fact_5301_List_Ofinite__set,axiom,
% 4.71/5.12 ! [Xs: list_Extended_enat] : ( finite4001608067531595151d_enat @ ( set_Extended_enat2 @ Xs ) ) ).
% 4.71/5.12
% 4.71/5.12 % List.finite_set
% 4.71/5.12 thf(fact_5302_sinh__0,axiom,
% 4.71/5.12 ( ( sinh_real @ zero_zero_real )
% 4.71/5.12 = zero_zero_real ) ).
% 4.71/5.12
% 4.71/5.12 % sinh_0
% 4.71/5.12 thf(fact_5303_fact__0,axiom,
% 4.71/5.12 ( ( semiri5044797733671781792omplex @ zero_zero_nat )
% 4.71/5.12 = one_one_complex ) ).
% 4.71/5.12
% 4.71/5.12 % fact_0
% 4.71/5.12 thf(fact_5304_fact__0,axiom,
% 4.71/5.12 ( ( semiri773545260158071498ct_rat @ zero_zero_nat )
% 4.71/5.12 = one_one_rat ) ).
% 4.71/5.12
% 4.71/5.12 % fact_0
% 4.71/5.12 thf(fact_5305_fact__0,axiom,
% 4.71/5.12 ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 4.71/5.12 = one_one_int ) ).
% 4.71/5.12
% 4.71/5.12 % fact_0
% 4.71/5.12 thf(fact_5306_fact__0,axiom,
% 4.71/5.12 ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 4.71/5.12 = one_one_nat ) ).
% 4.71/5.12
% 4.71/5.12 % fact_0
% 4.71/5.12 thf(fact_5307_fact__0,axiom,
% 4.71/5.12 ( ( semiri2265585572941072030t_real @ zero_zero_nat )
% 4.71/5.12 = one_one_real ) ).
% 4.71/5.12
% 4.71/5.12 % fact_0
% 4.71/5.12 thf(fact_5308_fact__1,axiom,
% 4.71/5.12 ( ( semiri5044797733671781792omplex @ one_one_nat )
% 4.71/5.12 = one_one_complex ) ).
% 4.71/5.12
% 4.71/5.12 % fact_1
% 4.71/5.12 thf(fact_5309_fact__1,axiom,
% 4.71/5.12 ( ( semiri773545260158071498ct_rat @ one_one_nat )
% 4.71/5.12 = one_one_rat ) ).
% 4.71/5.12
% 4.71/5.12 % fact_1
% 4.71/5.12 thf(fact_5310_fact__1,axiom,
% 4.71/5.12 ( ( semiri1406184849735516958ct_int @ one_one_nat )
% 4.71/5.12 = one_one_int ) ).
% 4.71/5.12
% 4.71/5.12 % fact_1
% 4.71/5.12 thf(fact_5311_fact__1,axiom,
% 4.71/5.12 ( ( semiri1408675320244567234ct_nat @ one_one_nat )
% 4.71/5.12 = one_one_nat ) ).
% 4.71/5.12
% 4.71/5.12 % fact_1
% 4.71/5.12 thf(fact_5312_fact__1,axiom,
% 4.71/5.12 ( ( semiri2265585572941072030t_real @ one_one_nat )
% 4.71/5.12 = one_one_real ) ).
% 4.71/5.12
% 4.71/5.12 % fact_1
% 4.71/5.12 thf(fact_5313_fact__Suc__0,axiom,
% 4.71/5.12 ( ( semiri5044797733671781792omplex @ ( suc @ zero_zero_nat ) )
% 4.71/5.12 = one_one_complex ) ).
% 4.71/5.12
% 4.71/5.12 % fact_Suc_0
% 4.71/5.12 thf(fact_5314_fact__Suc__0,axiom,
% 4.71/5.12 ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 4.71/5.12 = one_one_rat ) ).
% 4.71/5.12
% 4.71/5.12 % fact_Suc_0
% 4.71/5.12 thf(fact_5315_fact__Suc__0,axiom,
% 4.71/5.12 ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 4.71/5.12 = one_one_int ) ).
% 4.71/5.12
% 4.71/5.12 % fact_Suc_0
% 4.71/5.12 thf(fact_5316_fact__Suc__0,axiom,
% 4.71/5.12 ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 4.71/5.12 = one_one_nat ) ).
% 4.71/5.12
% 4.71/5.12 % fact_Suc_0
% 4.71/5.12 thf(fact_5317_fact__Suc__0,axiom,
% 4.71/5.12 ( ( semiri2265585572941072030t_real @ ( suc @ zero_zero_nat ) )
% 4.71/5.12 = one_one_real ) ).
% 4.71/5.12
% 4.71/5.12 % fact_Suc_0
% 4.71/5.12 thf(fact_5318_fact__mono__nat,axiom,
% 4.71/5.12 ! [M2: nat,N: nat] :
% 4.71/5.12 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.12 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_mono_nat
% 4.71/5.12 thf(fact_5319_fact__ge__self,axiom,
% 4.71/5.12 ! [N: nat] : ( ord_less_eq_nat @ N @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_ge_self
% 4.71/5.12 thf(fact_5320_fact__nonzero,axiom,
% 4.71/5.12 ! [N: nat] :
% 4.71/5.12 ( ( semiri773545260158071498ct_rat @ N )
% 4.71/5.12 != zero_zero_rat ) ).
% 4.71/5.12
% 4.71/5.12 % fact_nonzero
% 4.71/5.12 thf(fact_5321_fact__nonzero,axiom,
% 4.71/5.12 ! [N: nat] :
% 4.71/5.12 ( ( semiri1406184849735516958ct_int @ N )
% 4.71/5.12 != zero_zero_int ) ).
% 4.71/5.12
% 4.71/5.12 % fact_nonzero
% 4.71/5.12 thf(fact_5322_fact__nonzero,axiom,
% 4.71/5.12 ! [N: nat] :
% 4.71/5.12 ( ( semiri1408675320244567234ct_nat @ N )
% 4.71/5.12 != zero_zero_nat ) ).
% 4.71/5.12
% 4.71/5.12 % fact_nonzero
% 4.71/5.12 thf(fact_5323_fact__nonzero,axiom,
% 4.71/5.12 ! [N: nat] :
% 4.71/5.12 ( ( semiri2265585572941072030t_real @ N )
% 4.71/5.12 != zero_zero_real ) ).
% 4.71/5.12
% 4.71/5.12 % fact_nonzero
% 4.71/5.12 thf(fact_5324_finite__list,axiom,
% 4.71/5.12 ! [A2: set_VEBT_VEBT] :
% 4.71/5.12 ( ( finite5795047828879050333T_VEBT @ A2 )
% 4.71/5.12 => ? [Xs3: list_VEBT_VEBT] :
% 4.71/5.12 ( ( set_VEBT_VEBT2 @ Xs3 )
% 4.71/5.12 = A2 ) ) ).
% 4.71/5.12
% 4.71/5.12 % finite_list
% 4.71/5.12 thf(fact_5325_finite__list,axiom,
% 4.71/5.12 ! [A2: set_nat] :
% 4.71/5.12 ( ( finite_finite_nat @ A2 )
% 4.71/5.12 => ? [Xs3: list_nat] :
% 4.71/5.12 ( ( set_nat2 @ Xs3 )
% 4.71/5.12 = A2 ) ) ).
% 4.71/5.12
% 4.71/5.12 % finite_list
% 4.71/5.12 thf(fact_5326_finite__list,axiom,
% 4.71/5.12 ! [A2: set_int] :
% 4.71/5.12 ( ( finite_finite_int @ A2 )
% 4.71/5.12 => ? [Xs3: list_int] :
% 4.71/5.12 ( ( set_int2 @ Xs3 )
% 4.71/5.12 = A2 ) ) ).
% 4.71/5.12
% 4.71/5.12 % finite_list
% 4.71/5.12 thf(fact_5327_finite__list,axiom,
% 4.71/5.12 ! [A2: set_complex] :
% 4.71/5.12 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.12 => ? [Xs3: list_complex] :
% 4.71/5.12 ( ( set_complex2 @ Xs3 )
% 4.71/5.12 = A2 ) ) ).
% 4.71/5.12
% 4.71/5.12 % finite_list
% 4.71/5.12 thf(fact_5328_finite__list,axiom,
% 4.71/5.12 ! [A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.12 ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.12 => ? [Xs3: list_P6011104703257516679at_nat] :
% 4.71/5.12 ( ( set_Pr5648618587558075414at_nat @ Xs3 )
% 4.71/5.12 = A2 ) ) ).
% 4.71/5.12
% 4.71/5.12 % finite_list
% 4.71/5.12 thf(fact_5329_finite__list,axiom,
% 4.71/5.12 ! [A2: set_Extended_enat] :
% 4.71/5.12 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.12 => ? [Xs3: list_Extended_enat] :
% 4.71/5.12 ( ( set_Extended_enat2 @ Xs3 )
% 4.71/5.12 = A2 ) ) ).
% 4.71/5.12
% 4.71/5.12 % finite_list
% 4.71/5.12 thf(fact_5330_subset__code_I1_J,axiom,
% 4.71/5.12 ! [Xs: list_o,B2: set_o] :
% 4.71/5.12 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ B2 )
% 4.71/5.12 = ( ! [X3: $o] :
% 4.71/5.12 ( ( member_o @ X3 @ ( set_o2 @ Xs ) )
% 4.71/5.12 => ( member_o @ X3 @ B2 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % subset_code(1)
% 4.71/5.12 thf(fact_5331_subset__code_I1_J,axiom,
% 4.71/5.12 ! [Xs: list_set_nat,B2: set_set_nat] :
% 4.71/5.12 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ B2 )
% 4.71/5.12 = ( ! [X3: set_nat] :
% 4.71/5.12 ( ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs ) )
% 4.71/5.12 => ( member_set_nat @ X3 @ B2 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % subset_code(1)
% 4.71/5.12 thf(fact_5332_subset__code_I1_J,axiom,
% 4.71/5.12 ! [Xs: list_set_nat_rat,B2: set_set_nat_rat] :
% 4.71/5.12 ( ( ord_le4375437777232675859at_rat @ ( set_set_nat_rat2 @ Xs ) @ B2 )
% 4.71/5.12 = ( ! [X3: set_nat_rat] :
% 4.71/5.12 ( ( member_set_nat_rat @ X3 @ ( set_set_nat_rat2 @ Xs ) )
% 4.71/5.12 => ( member_set_nat_rat @ X3 @ B2 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % subset_code(1)
% 4.71/5.12 thf(fact_5333_subset__code_I1_J,axiom,
% 4.71/5.12 ! [Xs: list_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 4.71/5.12 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ B2 )
% 4.71/5.12 = ( ! [X3: vEBT_VEBT] :
% 4.71/5.12 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 4.71/5.12 => ( member_VEBT_VEBT @ X3 @ B2 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % subset_code(1)
% 4.71/5.12 thf(fact_5334_subset__code_I1_J,axiom,
% 4.71/5.12 ! [Xs: list_nat,B2: set_nat] :
% 4.71/5.12 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ B2 )
% 4.71/5.12 = ( ! [X3: nat] :
% 4.71/5.12 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 4.71/5.12 => ( member_nat @ X3 @ B2 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % subset_code(1)
% 4.71/5.12 thf(fact_5335_subset__code_I1_J,axiom,
% 4.71/5.12 ! [Xs: list_int,B2: set_int] :
% 4.71/5.12 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ B2 )
% 4.71/5.12 = ( ! [X3: int] :
% 4.71/5.12 ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 4.71/5.12 => ( member_int @ X3 @ B2 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % subset_code(1)
% 4.71/5.12 thf(fact_5336_fold__atLeastAtMost__nat_Ocases,axiom,
% 4.71/5.12 ! [X: produc4471711990508489141at_nat] :
% 4.71/5.12 ~ ! [F4: nat > nat > nat,A5: nat,B5: nat,Acc: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc3209952032786966637at_nat @ F4 @ ( produc487386426758144856at_nat @ A5 @ ( product_Pair_nat_nat @ B5 @ Acc ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % fold_atLeastAtMost_nat.cases
% 4.71/5.12 thf(fact_5337_fact__less__mono__nat,axiom,
% 4.71/5.12 ! [M2: nat,N: nat] :
% 4.71/5.12 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 4.71/5.12 => ( ( ord_less_nat @ M2 @ N )
% 4.71/5.12 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_less_mono_nat
% 4.71/5.12 thf(fact_5338_fact__ge__zero,axiom,
% 4.71/5.12 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_ge_zero
% 4.71/5.12 thf(fact_5339_fact__ge__zero,axiom,
% 4.71/5.12 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_ge_zero
% 4.71/5.12 thf(fact_5340_fact__ge__zero,axiom,
% 4.71/5.12 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_ge_zero
% 4.71/5.12 thf(fact_5341_fact__ge__zero,axiom,
% 4.71/5.12 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_ge_zero
% 4.71/5.12 thf(fact_5342_fact__gt__zero,axiom,
% 4.71/5.12 ! [N: nat] : ( ord_less_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_gt_zero
% 4.71/5.12 thf(fact_5343_fact__gt__zero,axiom,
% 4.71/5.12 ! [N: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_gt_zero
% 4.71/5.12 thf(fact_5344_fact__gt__zero,axiom,
% 4.71/5.12 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_gt_zero
% 4.71/5.12 thf(fact_5345_fact__gt__zero,axiom,
% 4.71/5.12 ! [N: nat] : ( ord_less_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_gt_zero
% 4.71/5.12 thf(fact_5346_fact__not__neg,axiom,
% 4.71/5.12 ! [N: nat] :
% 4.71/5.12 ~ ( ord_less_rat @ ( semiri773545260158071498ct_rat @ N ) @ zero_zero_rat ) ).
% 4.71/5.12
% 4.71/5.12 % fact_not_neg
% 4.71/5.12 thf(fact_5347_fact__not__neg,axiom,
% 4.71/5.12 ! [N: nat] :
% 4.71/5.12 ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N ) @ zero_zero_int ) ).
% 4.71/5.12
% 4.71/5.12 % fact_not_neg
% 4.71/5.12 thf(fact_5348_fact__not__neg,axiom,
% 4.71/5.12 ! [N: nat] :
% 4.71/5.12 ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N ) @ zero_zero_nat ) ).
% 4.71/5.12
% 4.71/5.12 % fact_not_neg
% 4.71/5.12 thf(fact_5349_fact__not__neg,axiom,
% 4.71/5.12 ! [N: nat] :
% 4.71/5.12 ~ ( ord_less_real @ ( semiri2265585572941072030t_real @ N ) @ zero_zero_real ) ).
% 4.71/5.12
% 4.71/5.12 % fact_not_neg
% 4.71/5.12 thf(fact_5350_fact__ge__1,axiom,
% 4.71/5.12 ! [N: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_ge_1
% 4.71/5.12 thf(fact_5351_fact__ge__1,axiom,
% 4.71/5.12 ! [N: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_ge_1
% 4.71/5.12 thf(fact_5352_fact__ge__1,axiom,
% 4.71/5.12 ! [N: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_ge_1
% 4.71/5.12 thf(fact_5353_fact__ge__1,axiom,
% 4.71/5.12 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_ge_1
% 4.71/5.12 thf(fact_5354_fact__mono,axiom,
% 4.71/5.12 ! [M2: nat,N: nat] :
% 4.71/5.12 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.12 => ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ M2 ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_mono
% 4.71/5.12 thf(fact_5355_fact__mono,axiom,
% 4.71/5.12 ! [M2: nat,N: nat] :
% 4.71/5.12 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.12 => ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ M2 ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_mono
% 4.71/5.12 thf(fact_5356_fact__mono,axiom,
% 4.71/5.12 ! [M2: nat,N: nat] :
% 4.71/5.12 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.12 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_mono
% 4.71/5.12 thf(fact_5357_fact__mono,axiom,
% 4.71/5.12 ! [M2: nat,N: nat] :
% 4.71/5.12 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.12 => ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ M2 ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_mono
% 4.71/5.12 thf(fact_5358_pochhammer__fact,axiom,
% 4.71/5.12 ( semiri5044797733671781792omplex
% 4.71/5.12 = ( comm_s2602460028002588243omplex @ one_one_complex ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_fact
% 4.71/5.12 thf(fact_5359_pochhammer__fact,axiom,
% 4.71/5.12 ( semiri773545260158071498ct_rat
% 4.71/5.12 = ( comm_s4028243227959126397er_rat @ one_one_rat ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_fact
% 4.71/5.12 thf(fact_5360_pochhammer__fact,axiom,
% 4.71/5.12 ( semiri1406184849735516958ct_int
% 4.71/5.12 = ( comm_s4660882817536571857er_int @ one_one_int ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_fact
% 4.71/5.12 thf(fact_5361_pochhammer__fact,axiom,
% 4.71/5.12 ( semiri1408675320244567234ct_nat
% 4.71/5.12 = ( comm_s4663373288045622133er_nat @ one_one_nat ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_fact
% 4.71/5.12 thf(fact_5362_pochhammer__fact,axiom,
% 4.71/5.12 ( semiri2265585572941072030t_real
% 4.71/5.12 = ( comm_s7457072308508201937r_real @ one_one_real ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_fact
% 4.71/5.12 thf(fact_5363_VEBT__internal_Ovalid_H_Ocases,axiom,
% 4.71/5.12 ! [X: produc9072475918466114483BT_nat] :
% 4.71/5.12 ( ! [Uu2: $o,Uv2: $o,D6: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ D6 ) )
% 4.71/5.12 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,Deg3: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Deg3 ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % VEBT_internal.valid'.cases
% 4.71/5.12 thf(fact_5364_fact__ge__Suc__0__nat,axiom,
% 4.71/5.12 ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_ge_Suc_0_nat
% 4.71/5.12 thf(fact_5365_fact__less__mono,axiom,
% 4.71/5.12 ! [M2: nat,N: nat] :
% 4.71/5.12 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 4.71/5.12 => ( ( ord_less_nat @ M2 @ N )
% 4.71/5.12 => ( ord_less_rat @ ( semiri773545260158071498ct_rat @ M2 ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_less_mono
% 4.71/5.12 thf(fact_5366_fact__less__mono,axiom,
% 4.71/5.12 ! [M2: nat,N: nat] :
% 4.71/5.12 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 4.71/5.12 => ( ( ord_less_nat @ M2 @ N )
% 4.71/5.12 => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M2 ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_less_mono
% 4.71/5.12 thf(fact_5367_fact__less__mono,axiom,
% 4.71/5.12 ! [M2: nat,N: nat] :
% 4.71/5.12 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 4.71/5.12 => ( ( ord_less_nat @ M2 @ N )
% 4.71/5.12 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_less_mono
% 4.71/5.12 thf(fact_5368_fact__less__mono,axiom,
% 4.71/5.12 ! [M2: nat,N: nat] :
% 4.71/5.12 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 4.71/5.12 => ( ( ord_less_nat @ M2 @ N )
% 4.71/5.12 => ( ord_less_real @ ( semiri2265585572941072030t_real @ M2 ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_less_mono
% 4.71/5.12 thf(fact_5369_length__pos__if__in__set,axiom,
% 4.71/5.12 ! [X: $o,Xs: list_o] :
% 4.71/5.12 ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 4.71/5.12 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % length_pos_if_in_set
% 4.71/5.12 thf(fact_5370_length__pos__if__in__set,axiom,
% 4.71/5.12 ! [X: set_nat,Xs: list_set_nat] :
% 4.71/5.12 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 4.71/5.12 => ( ord_less_nat @ zero_zero_nat @ ( size_s3254054031482475050et_nat @ Xs ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % length_pos_if_in_set
% 4.71/5.12 thf(fact_5371_length__pos__if__in__set,axiom,
% 4.71/5.12 ! [X: set_nat_rat,Xs: list_set_nat_rat] :
% 4.71/5.12 ( ( member_set_nat_rat @ X @ ( set_set_nat_rat2 @ Xs ) )
% 4.71/5.12 => ( ord_less_nat @ zero_zero_nat @ ( size_s3959913991096427681at_rat @ Xs ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % length_pos_if_in_set
% 4.71/5.12 thf(fact_5372_length__pos__if__in__set,axiom,
% 4.71/5.12 ! [X: int,Xs: list_int] :
% 4.71/5.12 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 4.71/5.12 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % length_pos_if_in_set
% 4.71/5.12 thf(fact_5373_length__pos__if__in__set,axiom,
% 4.71/5.12 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 4.71/5.12 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 4.71/5.12 => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % length_pos_if_in_set
% 4.71/5.12 thf(fact_5374_length__pos__if__in__set,axiom,
% 4.71/5.12 ! [X: nat,Xs: list_nat] :
% 4.71/5.12 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 4.71/5.12 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % length_pos_if_in_set
% 4.71/5.12 thf(fact_5375_card__length,axiom,
% 4.71/5.12 ! [Xs: list_complex] : ( ord_less_eq_nat @ ( finite_card_complex @ ( set_complex2 @ Xs ) ) @ ( size_s3451745648224563538omplex @ Xs ) ) ).
% 4.71/5.12
% 4.71/5.12 % card_length
% 4.71/5.12 thf(fact_5376_card__length,axiom,
% 4.71/5.12 ! [Xs: list_list_nat] : ( ord_less_eq_nat @ ( finite_card_list_nat @ ( set_list_nat2 @ Xs ) ) @ ( size_s3023201423986296836st_nat @ Xs ) ) ).
% 4.71/5.12
% 4.71/5.12 % card_length
% 4.71/5.12 thf(fact_5377_card__length,axiom,
% 4.71/5.12 ! [Xs: list_set_nat] : ( ord_less_eq_nat @ ( finite_card_set_nat @ ( set_set_nat2 @ Xs ) ) @ ( size_s3254054031482475050et_nat @ Xs ) ) ).
% 4.71/5.12
% 4.71/5.12 % card_length
% 4.71/5.12 thf(fact_5378_card__length,axiom,
% 4.71/5.12 ! [Xs: list_int] : ( ord_less_eq_nat @ ( finite_card_int @ ( set_int2 @ Xs ) ) @ ( size_size_list_int @ Xs ) ) ).
% 4.71/5.12
% 4.71/5.12 % card_length
% 4.71/5.12 thf(fact_5379_card__length,axiom,
% 4.71/5.12 ! [Xs: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( finite7802652506058667612T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) ) @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 4.71/5.12
% 4.71/5.12 % card_length
% 4.71/5.12 thf(fact_5380_card__length,axiom,
% 4.71/5.12 ! [Xs: list_nat] : ( ord_less_eq_nat @ ( finite_card_nat @ ( set_nat2 @ Xs ) ) @ ( size_size_list_nat @ Xs ) ) ).
% 4.71/5.12
% 4.71/5.12 % card_length
% 4.71/5.12 thf(fact_5381_fact__le__power,axiom,
% 4.71/5.12 ! [N: nat] : ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri681578069525770553at_rat @ ( power_power_nat @ N @ N ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_le_power
% 4.71/5.12 thf(fact_5382_fact__le__power,axiom,
% 4.71/5.12 ! [N: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N @ N ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_le_power
% 4.71/5.12 thf(fact_5383_fact__le__power,axiom,
% 4.71/5.12 ! [N: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N @ N ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_le_power
% 4.71/5.12 thf(fact_5384_fact__le__power,axiom,
% 4.71/5.12 ! [N: nat] : ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri5074537144036343181t_real @ ( power_power_nat @ N @ N ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_le_power
% 4.71/5.12 thf(fact_5385_fact__diff__Suc,axiom,
% 4.71/5.12 ! [N: nat,M2: nat] :
% 4.71/5.12 ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 4.71/5.12 => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M2 ) @ N ) )
% 4.71/5.12 = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M2 ) @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M2 @ N ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_diff_Suc
% 4.71/5.12 thf(fact_5386_fact__div__fact__le__pow,axiom,
% 4.71/5.12 ! [R2: nat,N: nat] :
% 4.71/5.12 ( ( ord_less_eq_nat @ R2 @ N )
% 4.71/5.12 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R2 ) ) ) @ ( power_power_nat @ N @ R2 ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_div_fact_le_pow
% 4.71/5.12 thf(fact_5387_VEBT__internal_Onaive__member_Ocases,axiom,
% 4.71/5.12 ! [X: produc9072475918466114483BT_nat] :
% 4.71/5.12 ( ! [A5: $o,B5: $o,X4: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X4 ) )
% 4.71/5.12 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) )
% 4.71/5.12 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S3: vEBT_VEBT,X4: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) @ X4 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % VEBT_internal.naive_member.cases
% 4.71/5.12 thf(fact_5388_fact__num__eq__if,axiom,
% 4.71/5.12 ( semiri5044797733671781792omplex
% 4.71/5.12 = ( ^ [M3: nat] : ( if_complex @ ( M3 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ M3 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_num_eq_if
% 4.71/5.12 thf(fact_5389_fact__num__eq__if,axiom,
% 4.71/5.12 ( semiri1406184849735516958ct_int
% 4.71/5.12 = ( ^ [M3: nat] : ( if_int @ ( M3 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_num_eq_if
% 4.71/5.12 thf(fact_5390_fact__num__eq__if,axiom,
% 4.71/5.12 ( semiri773545260158071498ct_rat
% 4.71/5.12 = ( ^ [M3: nat] : ( if_rat @ ( M3 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ M3 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_num_eq_if
% 4.71/5.12 thf(fact_5391_fact__num__eq__if,axiom,
% 4.71/5.12 ( semiri1408675320244567234ct_nat
% 4.71/5.12 = ( ^ [M3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M3 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_num_eq_if
% 4.71/5.12 thf(fact_5392_fact__num__eq__if,axiom,
% 4.71/5.12 ( semiri2265585572941072030t_real
% 4.71/5.12 = ( ^ [M3: nat] : ( if_real @ ( M3 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M3 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_num_eq_if
% 4.71/5.12 thf(fact_5393_fact__reduce,axiom,
% 4.71/5.12 ! [N: nat] :
% 4.71/5.12 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.12 => ( ( semiri1406184849735516958ct_int @ N )
% 4.71/5.12 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_reduce
% 4.71/5.12 thf(fact_5394_fact__reduce,axiom,
% 4.71/5.12 ! [N: nat] :
% 4.71/5.12 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.12 => ( ( semiri773545260158071498ct_rat @ N )
% 4.71/5.12 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_reduce
% 4.71/5.12 thf(fact_5395_fact__reduce,axiom,
% 4.71/5.12 ! [N: nat] :
% 4.71/5.12 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.12 => ( ( semiri1408675320244567234ct_nat @ N )
% 4.71/5.12 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_reduce
% 4.71/5.12 thf(fact_5396_fact__reduce,axiom,
% 4.71/5.12 ! [N: nat] :
% 4.71/5.12 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.12 => ( ( semiri2265585572941072030t_real @ N )
% 4.71/5.12 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_reduce
% 4.71/5.12 thf(fact_5397_pochhammer__same,axiom,
% 4.71/5.12 ! [N: nat] :
% 4.71/5.12 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ N )
% 4.71/5.12 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_same
% 4.71/5.12 thf(fact_5398_pochhammer__same,axiom,
% 4.71/5.12 ! [N: nat] :
% 4.71/5.12 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ N )
% 4.71/5.12 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_same
% 4.71/5.12 thf(fact_5399_pochhammer__same,axiom,
% 4.71/5.12 ! [N: nat] :
% 4.71/5.12 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ N )
% 4.71/5.12 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_same
% 4.71/5.12 thf(fact_5400_pochhammer__same,axiom,
% 4.71/5.12 ! [N: nat] :
% 4.71/5.12 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ N )
% 4.71/5.12 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % pochhammer_same
% 4.71/5.12 thf(fact_5401_vebt__delete_Ocases,axiom,
% 4.71/5.12 ! [X: produc9072475918466114483BT_nat] :
% 4.71/5.12 ( ! [A5: $o,B5: $o] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ zero_zero_nat ) )
% 4.71/5.12 => ( ! [A5: $o,B5: $o] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ zero_zero_nat ) ) )
% 4.71/5.12 => ( ! [A5: $o,B5: $o,N2: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ ( suc @ N2 ) ) ) )
% 4.71/5.12 => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,Uu2: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) @ Uu2 ) )
% 4.71/5.12 => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT,X4: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) @ X4 ) )
% 4.71/5.12 => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT,X4: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) @ X4 ) )
% 4.71/5.12 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ X4 ) ) ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_delete.cases
% 4.71/5.12 thf(fact_5402_VEBT__internal_Omembermima_Ocases,axiom,
% 4.71/5.12 ! [X: produc9072475918466114483BT_nat] :
% 4.71/5.12 ( ! [Uu2: $o,Uv2: $o,Uw2: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw2 ) )
% 4.71/5.12 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) )
% 4.71/5.12 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT,X4: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ X4 ) )
% 4.71/5.12 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X4: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ X4 ) )
% 4.71/5.12 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT,X4: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ X4 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % VEBT_internal.membermima.cases
% 4.71/5.12 thf(fact_5403_vebt__pred_Ocases,axiom,
% 4.71/5.12 ! [X: produc9072475918466114483BT_nat] :
% 4.71/5.12 ( ! [Uu2: $o,Uv2: $o] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) )
% 4.71/5.12 => ( ! [A5: $o,Uw2: $o] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) )
% 4.71/5.12 => ( ! [A5: $o,B5: $o,Va: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ ( suc @ Va ) ) ) )
% 4.71/5.12 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT,Vb2: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Vb2 ) )
% 4.71/5.12 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf2: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Vf2 ) )
% 4.71/5.12 => ( ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 ) )
% 4.71/5.12 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ X4 ) ) ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_pred.cases
% 4.71/5.12 thf(fact_5404_vebt__succ_Ocases,axiom,
% 4.71/5.12 ! [X: produc9072475918466114483BT_nat] :
% 4.71/5.12 ( ! [Uu2: $o,B5: $o] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B5 ) @ zero_zero_nat ) )
% 4.71/5.12 => ( ! [Uv2: $o,Uw2: $o,N2: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N2 ) ) )
% 4.71/5.12 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,Va3: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Va3 ) )
% 4.71/5.12 => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT,Ve2: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Ve2 ) )
% 4.71/5.12 => ( ! [V2: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 ) )
% 4.71/5.12 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ X4 ) ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_succ.cases
% 4.71/5.12 thf(fact_5405_vebt__member_Ocases,axiom,
% 4.71/5.12 ! [X: produc9072475918466114483BT_nat] :
% 4.71/5.12 ( ! [A5: $o,B5: $o,X4: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X4 ) )
% 4.71/5.12 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X4: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X4 ) )
% 4.71/5.12 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,X4: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ X4 ) )
% 4.71/5.12 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X4: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X4 ) )
% 4.71/5.12 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ X4 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_member.cases
% 4.71/5.12 thf(fact_5406_vebt__insert_Ocases,axiom,
% 4.71/5.12 ! [X: produc9072475918466114483BT_nat] :
% 4.71/5.12 ( ! [A5: $o,B5: $o,X4: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X4 ) )
% 4.71/5.12 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT,X4: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) @ X4 ) )
% 4.71/5.12 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT,X4: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) @ X4 ) )
% 4.71/5.12 => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) @ X4 ) )
% 4.71/5.12 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 4.71/5.12 ( X
% 4.71/5.12 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ X4 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_insert.cases
% 4.71/5.12 thf(fact_5407_vebt__maxt_Opelims,axiom,
% 4.71/5.12 ! [X: vEBT_VEBT,Y: option_nat] :
% 4.71/5.12 ( ( ( vEBT_vebt_maxt @ X )
% 4.71/5.12 = Y )
% 4.71/5.12 => ( ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ X )
% 4.71/5.12 => ( ! [A5: $o,B5: $o] :
% 4.71/5.12 ( ( X
% 4.71/5.12 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.12 => ( ( ( B5
% 4.71/5.12 => ( Y
% 4.71/5.12 = ( some_nat @ one_one_nat ) ) )
% 4.71/5.12 & ( ~ B5
% 4.71/5.12 => ( ( A5
% 4.71/5.12 => ( Y
% 4.71/5.12 = ( some_nat @ zero_zero_nat ) ) )
% 4.71/5.12 & ( ~ A5
% 4.71/5.12 => ( Y = none_nat ) ) ) ) )
% 4.71/5.12 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Leaf @ A5 @ B5 ) ) ) )
% 4.71/5.12 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 4.71/5.12 ( ( X
% 4.71/5.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 4.71/5.12 => ( ( Y = none_nat )
% 4.71/5.12 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 4.71/5.12 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 4.71/5.12 ( ( X
% 4.71/5.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 4.71/5.12 => ( ( Y
% 4.71/5.12 = ( some_nat @ Ma2 ) )
% 4.71/5.12 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_maxt.pelims
% 4.71/5.12 thf(fact_5408_vebt__mint_Opelims,axiom,
% 4.71/5.12 ! [X: vEBT_VEBT,Y: option_nat] :
% 4.71/5.12 ( ( ( vEBT_vebt_mint @ X )
% 4.71/5.12 = Y )
% 4.71/5.12 => ( ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ X )
% 4.71/5.12 => ( ! [A5: $o,B5: $o] :
% 4.71/5.12 ( ( X
% 4.71/5.12 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.12 => ( ( ( A5
% 4.71/5.12 => ( Y
% 4.71/5.12 = ( some_nat @ zero_zero_nat ) ) )
% 4.71/5.12 & ( ~ A5
% 4.71/5.12 => ( ( B5
% 4.71/5.12 => ( Y
% 4.71/5.12 = ( some_nat @ one_one_nat ) ) )
% 4.71/5.12 & ( ~ B5
% 4.71/5.12 => ( Y = none_nat ) ) ) ) )
% 4.71/5.12 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Leaf @ A5 @ B5 ) ) ) )
% 4.71/5.12 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 4.71/5.12 ( ( X
% 4.71/5.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 4.71/5.12 => ( ( Y = none_nat )
% 4.71/5.12 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 4.71/5.12 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 4.71/5.12 ( ( X
% 4.71/5.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 4.71/5.12 => ( ( Y
% 4.71/5.12 = ( some_nat @ Mi2 ) )
% 4.71/5.12 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_mint.pelims
% 4.71/5.12 thf(fact_5409_eucl__rel__int__iff,axiom,
% 4.71/5.12 ! [K: int,L: int,Q4: int,R2: int] :
% 4.71/5.12 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q4 @ R2 ) )
% 4.71/5.12 = ( ( K
% 4.71/5.12 = ( plus_plus_int @ ( times_times_int @ L @ Q4 ) @ R2 ) )
% 4.71/5.12 & ( ( ord_less_int @ zero_zero_int @ L )
% 4.71/5.12 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 4.71/5.12 & ( ord_less_int @ R2 @ L ) ) )
% 4.71/5.12 & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 4.71/5.12 => ( ( ( ord_less_int @ L @ zero_zero_int )
% 4.71/5.12 => ( ( ord_less_int @ L @ R2 )
% 4.71/5.12 & ( ord_less_eq_int @ R2 @ zero_zero_int ) ) )
% 4.71/5.12 & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 4.71/5.12 => ( Q4 = zero_zero_int ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % eucl_rel_int_iff
% 4.71/5.12 thf(fact_5410_set__removeAll,axiom,
% 4.71/5.12 ! [X: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 4.71/5.12 ( ( set_Pr5648618587558075414at_nat @ ( remove3673390508374433037at_nat @ X @ Xs ) )
% 4.71/5.12 = ( minus_1356011639430497352at_nat @ ( set_Pr5648618587558075414at_nat @ Xs ) @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % set_removeAll
% 4.71/5.12 thf(fact_5411_set__removeAll,axiom,
% 4.71/5.12 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 4.71/5.12 ( ( set_VEBT_VEBT2 @ ( removeAll_VEBT_VEBT @ X @ Xs ) )
% 4.71/5.12 = ( minus_5127226145743854075T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % set_removeAll
% 4.71/5.12 thf(fact_5412_set__removeAll,axiom,
% 4.71/5.12 ! [X: real,Xs: list_real] :
% 4.71/5.12 ( ( set_real2 @ ( removeAll_real @ X @ Xs ) )
% 4.71/5.12 = ( minus_minus_set_real @ ( set_real2 @ Xs ) @ ( insert_real @ X @ bot_bot_set_real ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % set_removeAll
% 4.71/5.12 thf(fact_5413_set__removeAll,axiom,
% 4.71/5.12 ! [X: $o,Xs: list_o] :
% 4.71/5.12 ( ( set_o2 @ ( removeAll_o @ X @ Xs ) )
% 4.71/5.12 = ( minus_minus_set_o @ ( set_o2 @ Xs ) @ ( insert_o @ X @ bot_bot_set_o ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % set_removeAll
% 4.71/5.12 thf(fact_5414_set__removeAll,axiom,
% 4.71/5.12 ! [X: int,Xs: list_int] :
% 4.71/5.12 ( ( set_int2 @ ( removeAll_int @ X @ Xs ) )
% 4.71/5.12 = ( minus_minus_set_int @ ( set_int2 @ Xs ) @ ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % set_removeAll
% 4.71/5.12 thf(fact_5415_set__removeAll,axiom,
% 4.71/5.12 ! [X: nat,Xs: list_nat] :
% 4.71/5.12 ( ( set_nat2 @ ( removeAll_nat @ X @ Xs ) )
% 4.71/5.12 = ( minus_minus_set_nat @ ( set_nat2 @ Xs ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % set_removeAll
% 4.71/5.12 thf(fact_5416_inthall,axiom,
% 4.71/5.12 ! [Xs: list_o,P: $o > $o,N: nat] :
% 4.71/5.12 ( ! [X4: $o] :
% 4.71/5.12 ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 4.71/5.12 => ( P @ X4 ) )
% 4.71/5.12 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 4.71/5.12 => ( P @ ( nth_o @ Xs @ N ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inthall
% 4.71/5.12 thf(fact_5417_inthall,axiom,
% 4.71/5.12 ! [Xs: list_set_nat,P: set_nat > $o,N: nat] :
% 4.71/5.12 ( ! [X4: set_nat] :
% 4.71/5.12 ( ( member_set_nat @ X4 @ ( set_set_nat2 @ Xs ) )
% 4.71/5.12 => ( P @ X4 ) )
% 4.71/5.12 => ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 4.71/5.12 => ( P @ ( nth_set_nat @ Xs @ N ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inthall
% 4.71/5.12 thf(fact_5418_inthall,axiom,
% 4.71/5.12 ! [Xs: list_set_nat_rat,P: set_nat_rat > $o,N: nat] :
% 4.71/5.12 ( ! [X4: set_nat_rat] :
% 4.71/5.12 ( ( member_set_nat_rat @ X4 @ ( set_set_nat_rat2 @ Xs ) )
% 4.71/5.12 => ( P @ X4 ) )
% 4.71/5.12 => ( ( ord_less_nat @ N @ ( size_s3959913991096427681at_rat @ Xs ) )
% 4.71/5.12 => ( P @ ( nth_set_nat_rat @ Xs @ N ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inthall
% 4.71/5.12 thf(fact_5419_inthall,axiom,
% 4.71/5.12 ! [Xs: list_int,P: int > $o,N: nat] :
% 4.71/5.12 ( ! [X4: int] :
% 4.71/5.12 ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 4.71/5.12 => ( P @ X4 ) )
% 4.71/5.12 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 4.71/5.12 => ( P @ ( nth_int @ Xs @ N ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inthall
% 4.71/5.12 thf(fact_5420_inthall,axiom,
% 4.71/5.12 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,N: nat] :
% 4.71/5.12 ( ! [X4: vEBT_VEBT] :
% 4.71/5.12 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 4.71/5.12 => ( P @ X4 ) )
% 4.71/5.12 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.71/5.12 => ( P @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inthall
% 4.71/5.12 thf(fact_5421_inthall,axiom,
% 4.71/5.12 ! [Xs: list_nat,P: nat > $o,N: nat] :
% 4.71/5.12 ( ! [X4: nat] :
% 4.71/5.12 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 4.71/5.12 => ( P @ X4 ) )
% 4.71/5.12 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 4.71/5.12 => ( P @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % inthall
% 4.71/5.12 thf(fact_5422_nth__equalityI,axiom,
% 4.71/5.12 ! [Xs: list_int,Ys2: list_int] :
% 4.71/5.12 ( ( ( size_size_list_int @ Xs )
% 4.71/5.12 = ( size_size_list_int @ Ys2 ) )
% 4.71/5.12 => ( ! [I2: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 4.71/5.12 => ( ( nth_int @ Xs @ I2 )
% 4.71/5.12 = ( nth_int @ Ys2 @ I2 ) ) )
% 4.71/5.12 => ( Xs = Ys2 ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_equalityI
% 4.71/5.12 thf(fact_5423_nth__equalityI,axiom,
% 4.71/5.12 ! [Xs: list_VEBT_VEBT,Ys2: list_VEBT_VEBT] :
% 4.71/5.12 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 4.71/5.12 = ( size_s6755466524823107622T_VEBT @ Ys2 ) )
% 4.71/5.12 => ( ! [I2: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.71/5.12 => ( ( nth_VEBT_VEBT @ Xs @ I2 )
% 4.71/5.12 = ( nth_VEBT_VEBT @ Ys2 @ I2 ) ) )
% 4.71/5.12 => ( Xs = Ys2 ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_equalityI
% 4.71/5.12 thf(fact_5424_nth__equalityI,axiom,
% 4.71/5.12 ! [Xs: list_nat,Ys2: list_nat] :
% 4.71/5.12 ( ( ( size_size_list_nat @ Xs )
% 4.71/5.12 = ( size_size_list_nat @ Ys2 ) )
% 4.71/5.12 => ( ! [I2: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 4.71/5.12 => ( ( nth_nat @ Xs @ I2 )
% 4.71/5.12 = ( nth_nat @ Ys2 @ I2 ) ) )
% 4.71/5.12 => ( Xs = Ys2 ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_equalityI
% 4.71/5.12 thf(fact_5425_Skolem__list__nth,axiom,
% 4.71/5.12 ! [K: nat,P: nat > int > $o] :
% 4.71/5.12 ( ( ! [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ K )
% 4.71/5.12 => ? [X8: int] : ( P @ I4 @ X8 ) ) )
% 4.71/5.12 = ( ? [Xs2: list_int] :
% 4.71/5.12 ( ( ( size_size_list_int @ Xs2 )
% 4.71/5.12 = K )
% 4.71/5.12 & ! [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ K )
% 4.71/5.12 => ( P @ I4 @ ( nth_int @ Xs2 @ I4 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % Skolem_list_nth
% 4.71/5.12 thf(fact_5426_Skolem__list__nth,axiom,
% 4.71/5.12 ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 4.71/5.12 ( ( ! [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ K )
% 4.71/5.12 => ? [X8: vEBT_VEBT] : ( P @ I4 @ X8 ) ) )
% 4.71/5.12 = ( ? [Xs2: list_VEBT_VEBT] :
% 4.71/5.12 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 4.71/5.12 = K )
% 4.71/5.12 & ! [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ K )
% 4.71/5.12 => ( P @ I4 @ ( nth_VEBT_VEBT @ Xs2 @ I4 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % Skolem_list_nth
% 4.71/5.12 thf(fact_5427_Skolem__list__nth,axiom,
% 4.71/5.12 ! [K: nat,P: nat > nat > $o] :
% 4.71/5.12 ( ( ! [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ K )
% 4.71/5.12 => ? [X8: nat] : ( P @ I4 @ X8 ) ) )
% 4.71/5.12 = ( ? [Xs2: list_nat] :
% 4.71/5.12 ( ( ( size_size_list_nat @ Xs2 )
% 4.71/5.12 = K )
% 4.71/5.12 & ! [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ K )
% 4.71/5.12 => ( P @ I4 @ ( nth_nat @ Xs2 @ I4 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % Skolem_list_nth
% 4.71/5.12 thf(fact_5428_list__eq__iff__nth__eq,axiom,
% 4.71/5.12 ( ( ^ [Y5: list_int,Z4: list_int] : ( Y5 = Z4 ) )
% 4.71/5.12 = ( ^ [Xs2: list_int,Ys3: list_int] :
% 4.71/5.12 ( ( ( size_size_list_int @ Xs2 )
% 4.71/5.12 = ( size_size_list_int @ Ys3 ) )
% 4.71/5.12 & ! [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs2 ) )
% 4.71/5.12 => ( ( nth_int @ Xs2 @ I4 )
% 4.71/5.12 = ( nth_int @ Ys3 @ I4 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % list_eq_iff_nth_eq
% 4.71/5.12 thf(fact_5429_list__eq__iff__nth__eq,axiom,
% 4.71/5.12 ( ( ^ [Y5: list_VEBT_VEBT,Z4: list_VEBT_VEBT] : ( Y5 = Z4 ) )
% 4.71/5.12 = ( ^ [Xs2: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 4.71/5.12 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 4.71/5.12 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 4.71/5.12 & ! [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 4.71/5.12 => ( ( nth_VEBT_VEBT @ Xs2 @ I4 )
% 4.71/5.12 = ( nth_VEBT_VEBT @ Ys3 @ I4 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % list_eq_iff_nth_eq
% 4.71/5.12 thf(fact_5430_list__eq__iff__nth__eq,axiom,
% 4.71/5.12 ( ( ^ [Y5: list_nat,Z4: list_nat] : ( Y5 = Z4 ) )
% 4.71/5.12 = ( ^ [Xs2: list_nat,Ys3: list_nat] :
% 4.71/5.12 ( ( ( size_size_list_nat @ Xs2 )
% 4.71/5.12 = ( size_size_list_nat @ Ys3 ) )
% 4.71/5.12 & ! [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs2 ) )
% 4.71/5.12 => ( ( nth_nat @ Xs2 @ I4 )
% 4.71/5.12 = ( nth_nat @ Ys3 @ I4 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % list_eq_iff_nth_eq
% 4.71/5.12 thf(fact_5431_length__removeAll__less__eq,axiom,
% 4.71/5.12 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ ( removeAll_VEBT_VEBT @ X @ Xs ) ) @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 4.71/5.12
% 4.71/5.12 % length_removeAll_less_eq
% 4.71/5.12 thf(fact_5432_length__removeAll__less__eq,axiom,
% 4.71/5.12 ! [X: nat,Xs: list_nat] : ( ord_less_eq_nat @ ( size_size_list_nat @ ( removeAll_nat @ X @ Xs ) ) @ ( size_size_list_nat @ Xs ) ) ).
% 4.71/5.12
% 4.71/5.12 % length_removeAll_less_eq
% 4.71/5.12 thf(fact_5433_nth__mem,axiom,
% 4.71/5.12 ! [N: nat,Xs: list_o] :
% 4.71/5.12 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 4.71/5.12 => ( member_o @ ( nth_o @ Xs @ N ) @ ( set_o2 @ Xs ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_mem
% 4.71/5.12 thf(fact_5434_nth__mem,axiom,
% 4.71/5.12 ! [N: nat,Xs: list_set_nat] :
% 4.71/5.12 ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 4.71/5.12 => ( member_set_nat @ ( nth_set_nat @ Xs @ N ) @ ( set_set_nat2 @ Xs ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_mem
% 4.71/5.12 thf(fact_5435_nth__mem,axiom,
% 4.71/5.12 ! [N: nat,Xs: list_set_nat_rat] :
% 4.71/5.12 ( ( ord_less_nat @ N @ ( size_s3959913991096427681at_rat @ Xs ) )
% 4.71/5.12 => ( member_set_nat_rat @ ( nth_set_nat_rat @ Xs @ N ) @ ( set_set_nat_rat2 @ Xs ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_mem
% 4.71/5.12 thf(fact_5436_nth__mem,axiom,
% 4.71/5.12 ! [N: nat,Xs: list_int] :
% 4.71/5.12 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 4.71/5.12 => ( member_int @ ( nth_int @ Xs @ N ) @ ( set_int2 @ Xs ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_mem
% 4.71/5.12 thf(fact_5437_nth__mem,axiom,
% 4.71/5.12 ! [N: nat,Xs: list_VEBT_VEBT] :
% 4.71/5.12 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.71/5.12 => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs @ N ) @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_mem
% 4.71/5.12 thf(fact_5438_nth__mem,axiom,
% 4.71/5.12 ! [N: nat,Xs: list_nat] :
% 4.71/5.12 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 4.71/5.12 => ( member_nat @ ( nth_nat @ Xs @ N ) @ ( set_nat2 @ Xs ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_mem
% 4.71/5.12 thf(fact_5439_list__ball__nth,axiom,
% 4.71/5.12 ! [N: nat,Xs: list_int,P: int > $o] :
% 4.71/5.12 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 4.71/5.12 => ( ! [X4: int] :
% 4.71/5.12 ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 4.71/5.12 => ( P @ X4 ) )
% 4.71/5.12 => ( P @ ( nth_int @ Xs @ N ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % list_ball_nth
% 4.71/5.12 thf(fact_5440_list__ball__nth,axiom,
% 4.71/5.12 ! [N: nat,Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 4.71/5.12 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.71/5.12 => ( ! [X4: vEBT_VEBT] :
% 4.71/5.12 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 4.71/5.12 => ( P @ X4 ) )
% 4.71/5.12 => ( P @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % list_ball_nth
% 4.71/5.12 thf(fact_5441_list__ball__nth,axiom,
% 4.71/5.12 ! [N: nat,Xs: list_nat,P: nat > $o] :
% 4.71/5.12 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 4.71/5.12 => ( ! [X4: nat] :
% 4.71/5.12 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 4.71/5.12 => ( P @ X4 ) )
% 4.71/5.12 => ( P @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % list_ball_nth
% 4.71/5.12 thf(fact_5442_in__set__conv__nth,axiom,
% 4.71/5.12 ! [X: $o,Xs: list_o] :
% 4.71/5.12 ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 4.71/5.12 = ( ? [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 4.71/5.12 & ( ( nth_o @ Xs @ I4 )
% 4.71/5.12 = X ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % in_set_conv_nth
% 4.71/5.12 thf(fact_5443_in__set__conv__nth,axiom,
% 4.71/5.12 ! [X: set_nat,Xs: list_set_nat] :
% 4.71/5.12 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 4.71/5.12 = ( ? [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 4.71/5.12 & ( ( nth_set_nat @ Xs @ I4 )
% 4.71/5.12 = X ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % in_set_conv_nth
% 4.71/5.12 thf(fact_5444_in__set__conv__nth,axiom,
% 4.71/5.12 ! [X: set_nat_rat,Xs: list_set_nat_rat] :
% 4.71/5.12 ( ( member_set_nat_rat @ X @ ( set_set_nat_rat2 @ Xs ) )
% 4.71/5.12 = ( ? [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ ( size_s3959913991096427681at_rat @ Xs ) )
% 4.71/5.12 & ( ( nth_set_nat_rat @ Xs @ I4 )
% 4.71/5.12 = X ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % in_set_conv_nth
% 4.71/5.12 thf(fact_5445_in__set__conv__nth,axiom,
% 4.71/5.12 ! [X: int,Xs: list_int] :
% 4.71/5.12 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 4.71/5.12 = ( ? [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 4.71/5.12 & ( ( nth_int @ Xs @ I4 )
% 4.71/5.12 = X ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % in_set_conv_nth
% 4.71/5.12 thf(fact_5446_in__set__conv__nth,axiom,
% 4.71/5.12 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 4.71/5.12 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 4.71/5.12 = ( ? [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.71/5.12 & ( ( nth_VEBT_VEBT @ Xs @ I4 )
% 4.71/5.12 = X ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % in_set_conv_nth
% 4.71/5.12 thf(fact_5447_in__set__conv__nth,axiom,
% 4.71/5.12 ! [X: nat,Xs: list_nat] :
% 4.71/5.12 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 4.71/5.12 = ( ? [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 4.71/5.12 & ( ( nth_nat @ Xs @ I4 )
% 4.71/5.12 = X ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % in_set_conv_nth
% 4.71/5.12 thf(fact_5448_all__nth__imp__all__set,axiom,
% 4.71/5.12 ! [Xs: list_o,P: $o > $o,X: $o] :
% 4.71/5.12 ( ! [I2: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) )
% 4.71/5.12 => ( P @ ( nth_o @ Xs @ I2 ) ) )
% 4.71/5.12 => ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 4.71/5.12 => ( P @ X ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % all_nth_imp_all_set
% 4.71/5.12 thf(fact_5449_all__nth__imp__all__set,axiom,
% 4.71/5.12 ! [Xs: list_set_nat,P: set_nat > $o,X: set_nat] :
% 4.71/5.12 ( ! [I2: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I2 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 4.71/5.12 => ( P @ ( nth_set_nat @ Xs @ I2 ) ) )
% 4.71/5.12 => ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 4.71/5.12 => ( P @ X ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % all_nth_imp_all_set
% 4.71/5.12 thf(fact_5450_all__nth__imp__all__set,axiom,
% 4.71/5.12 ! [Xs: list_set_nat_rat,P: set_nat_rat > $o,X: set_nat_rat] :
% 4.71/5.12 ( ! [I2: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I2 @ ( size_s3959913991096427681at_rat @ Xs ) )
% 4.71/5.12 => ( P @ ( nth_set_nat_rat @ Xs @ I2 ) ) )
% 4.71/5.12 => ( ( member_set_nat_rat @ X @ ( set_set_nat_rat2 @ Xs ) )
% 4.71/5.12 => ( P @ X ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % all_nth_imp_all_set
% 4.71/5.12 thf(fact_5451_all__nth__imp__all__set,axiom,
% 4.71/5.12 ! [Xs: list_int,P: int > $o,X: int] :
% 4.71/5.12 ( ! [I2: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 4.71/5.12 => ( P @ ( nth_int @ Xs @ I2 ) ) )
% 4.71/5.12 => ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 4.71/5.12 => ( P @ X ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % all_nth_imp_all_set
% 4.71/5.12 thf(fact_5452_all__nth__imp__all__set,axiom,
% 4.71/5.12 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 4.71/5.12 ( ! [I2: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.71/5.12 => ( P @ ( nth_VEBT_VEBT @ Xs @ I2 ) ) )
% 4.71/5.12 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 4.71/5.12 => ( P @ X ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % all_nth_imp_all_set
% 4.71/5.12 thf(fact_5453_all__nth__imp__all__set,axiom,
% 4.71/5.12 ! [Xs: list_nat,P: nat > $o,X: nat] :
% 4.71/5.12 ( ! [I2: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 4.71/5.12 => ( P @ ( nth_nat @ Xs @ I2 ) ) )
% 4.71/5.12 => ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 4.71/5.12 => ( P @ X ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % all_nth_imp_all_set
% 4.71/5.12 thf(fact_5454_all__set__conv__all__nth,axiom,
% 4.71/5.12 ! [Xs: list_int,P: int > $o] :
% 4.71/5.12 ( ( ! [X3: int] :
% 4.71/5.12 ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 4.71/5.12 => ( P @ X3 ) ) )
% 4.71/5.12 = ( ! [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 4.71/5.12 => ( P @ ( nth_int @ Xs @ I4 ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % all_set_conv_all_nth
% 4.71/5.12 thf(fact_5455_all__set__conv__all__nth,axiom,
% 4.71/5.12 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 4.71/5.12 ( ( ! [X3: vEBT_VEBT] :
% 4.71/5.12 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 4.71/5.12 => ( P @ X3 ) ) )
% 4.71/5.12 = ( ! [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.71/5.12 => ( P @ ( nth_VEBT_VEBT @ Xs @ I4 ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % all_set_conv_all_nth
% 4.71/5.12 thf(fact_5456_all__set__conv__all__nth,axiom,
% 4.71/5.12 ! [Xs: list_nat,P: nat > $o] :
% 4.71/5.12 ( ( ! [X3: nat] :
% 4.71/5.12 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 4.71/5.12 => ( P @ X3 ) ) )
% 4.71/5.12 = ( ! [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 4.71/5.12 => ( P @ ( nth_nat @ Xs @ I4 ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % all_set_conv_all_nth
% 4.71/5.12 thf(fact_5457_length__removeAll__less,axiom,
% 4.71/5.12 ! [X: $o,Xs: list_o] :
% 4.71/5.12 ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 4.71/5.12 => ( ord_less_nat @ ( size_size_list_o @ ( removeAll_o @ X @ Xs ) ) @ ( size_size_list_o @ Xs ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % length_removeAll_less
% 4.71/5.12 thf(fact_5458_length__removeAll__less,axiom,
% 4.71/5.12 ! [X: set_nat,Xs: list_set_nat] :
% 4.71/5.12 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 4.71/5.12 => ( ord_less_nat @ ( size_s3254054031482475050et_nat @ ( removeAll_set_nat @ X @ Xs ) ) @ ( size_s3254054031482475050et_nat @ Xs ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % length_removeAll_less
% 4.71/5.12 thf(fact_5459_length__removeAll__less,axiom,
% 4.71/5.12 ! [X: set_nat_rat,Xs: list_set_nat_rat] :
% 4.71/5.12 ( ( member_set_nat_rat @ X @ ( set_set_nat_rat2 @ Xs ) )
% 4.71/5.12 => ( ord_less_nat @ ( size_s3959913991096427681at_rat @ ( remove939820145577552881at_rat @ X @ Xs ) ) @ ( size_s3959913991096427681at_rat @ Xs ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % length_removeAll_less
% 4.71/5.12 thf(fact_5460_length__removeAll__less,axiom,
% 4.71/5.12 ! [X: int,Xs: list_int] :
% 4.71/5.12 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 4.71/5.12 => ( ord_less_nat @ ( size_size_list_int @ ( removeAll_int @ X @ Xs ) ) @ ( size_size_list_int @ Xs ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % length_removeAll_less
% 4.71/5.12 thf(fact_5461_length__removeAll__less,axiom,
% 4.71/5.12 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 4.71/5.12 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 4.71/5.12 => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ ( removeAll_VEBT_VEBT @ X @ Xs ) ) @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % length_removeAll_less
% 4.71/5.12 thf(fact_5462_length__removeAll__less,axiom,
% 4.71/5.12 ! [X: nat,Xs: list_nat] :
% 4.71/5.12 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 4.71/5.12 => ( ord_less_nat @ ( size_size_list_nat @ ( removeAll_nat @ X @ Xs ) ) @ ( size_size_list_nat @ Xs ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % length_removeAll_less
% 4.71/5.12 thf(fact_5463_VEBT__internal_OminNull_Opelims_I1_J,axiom,
% 4.71/5.12 ! [X: vEBT_VEBT,Y: $o] :
% 4.71/5.12 ( ( ( vEBT_VEBT_minNull @ X )
% 4.71/5.12 = Y )
% 4.71/5.12 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 4.71/5.12 => ( ( ( X
% 4.71/5.12 = ( vEBT_Leaf @ $false @ $false ) )
% 4.71/5.12 => ( Y
% 4.71/5.12 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 4.71/5.12 => ( ! [Uv2: $o] :
% 4.71/5.12 ( ( X
% 4.71/5.12 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 4.71/5.12 => ( ~ Y
% 4.71/5.12 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) ) )
% 4.71/5.12 => ( ! [Uu2: $o] :
% 4.71/5.12 ( ( X
% 4.71/5.12 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 4.71/5.12 => ( ~ Y
% 4.71/5.12 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) ) )
% 4.71/5.12 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 4.71/5.12 ( ( X
% 4.71/5.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 4.71/5.12 => ( Y
% 4.71/5.12 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) )
% 4.71/5.12 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 4.71/5.12 ( ( X
% 4.71/5.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 4.71/5.12 => ( ~ Y
% 4.71/5.12 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % VEBT_internal.minNull.pelims(1)
% 4.71/5.12 thf(fact_5464_VEBT__internal_OminNull_Opelims_I2_J,axiom,
% 4.71/5.12 ! [X: vEBT_VEBT] :
% 4.71/5.12 ( ( vEBT_VEBT_minNull @ X )
% 4.71/5.12 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 4.71/5.12 => ( ( ( X
% 4.71/5.12 = ( vEBT_Leaf @ $false @ $false ) )
% 4.71/5.12 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) )
% 4.71/5.12 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 4.71/5.12 ( ( X
% 4.71/5.12 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 4.71/5.12 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % VEBT_internal.minNull.pelims(2)
% 4.71/5.12 thf(fact_5465_VEBT__internal_OminNull_Opelims_I3_J,axiom,
% 4.71/5.12 ! [X: vEBT_VEBT] :
% 4.71/5.12 ( ~ ( vEBT_VEBT_minNull @ X )
% 4.71/5.12 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 4.71/5.12 => ( ! [Uv2: $o] :
% 4.71/5.12 ( ( X
% 4.71/5.12 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 4.71/5.12 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) )
% 4.71/5.12 => ( ! [Uu2: $o] :
% 4.71/5.12 ( ( X
% 4.71/5.12 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 4.71/5.12 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) )
% 4.71/5.12 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 4.71/5.12 ( ( X
% 4.71/5.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 4.71/5.12 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % VEBT_internal.minNull.pelims(3)
% 4.71/5.12 thf(fact_5466_bezw__0,axiom,
% 4.71/5.12 ! [X: nat] :
% 4.71/5.12 ( ( bezw @ X @ zero_zero_nat )
% 4.71/5.12 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 4.71/5.12
% 4.71/5.12 % bezw_0
% 4.71/5.12 thf(fact_5467_nth__enumerate__eq,axiom,
% 4.71/5.12 ! [M2: nat,Xs: list_int,N: nat] :
% 4.71/5.12 ( ( ord_less_nat @ M2 @ ( size_size_list_int @ Xs ) )
% 4.71/5.12 => ( ( nth_Pr3440142176431000676at_int @ ( enumerate_int @ N @ Xs ) @ M2 )
% 4.71/5.12 = ( product_Pair_nat_int @ ( plus_plus_nat @ N @ M2 ) @ ( nth_int @ Xs @ M2 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_enumerate_eq
% 4.71/5.12 thf(fact_5468_nth__enumerate__eq,axiom,
% 4.71/5.12 ! [M2: nat,Xs: list_VEBT_VEBT,N: nat] :
% 4.71/5.12 ( ( ord_less_nat @ M2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.71/5.12 => ( ( nth_Pr744662078594809490T_VEBT @ ( enumerate_VEBT_VEBT @ N @ Xs ) @ M2 )
% 4.71/5.12 = ( produc599794634098209291T_VEBT @ ( plus_plus_nat @ N @ M2 ) @ ( nth_VEBT_VEBT @ Xs @ M2 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_enumerate_eq
% 4.71/5.12 thf(fact_5469_nth__enumerate__eq,axiom,
% 4.71/5.12 ! [M2: nat,Xs: list_nat,N: nat] :
% 4.71/5.12 ( ( ord_less_nat @ M2 @ ( size_size_list_nat @ Xs ) )
% 4.71/5.12 => ( ( nth_Pr7617993195940197384at_nat @ ( enumerate_nat @ N @ Xs ) @ M2 )
% 4.71/5.12 = ( product_Pair_nat_nat @ ( plus_plus_nat @ N @ M2 ) @ ( nth_nat @ Xs @ M2 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_enumerate_eq
% 4.71/5.12 thf(fact_5470_vebt__insert_Osimps_I4_J,axiom,
% 4.71/5.12 ! [V: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 4.71/5.12 ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) @ X )
% 4.71/5.12 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ X ) ) @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_insert.simps(4)
% 4.71/5.12 thf(fact_5471_length__mul__elem,axiom,
% 4.71/5.12 ! [Xs: list_list_VEBT_VEBT,N: nat] :
% 4.71/5.12 ( ! [X4: list_VEBT_VEBT] :
% 4.71/5.12 ( ( member2936631157270082147T_VEBT @ X4 @ ( set_list_VEBT_VEBT2 @ Xs ) )
% 4.71/5.12 => ( ( size_s6755466524823107622T_VEBT @ X4 )
% 4.71/5.12 = N ) )
% 4.71/5.12 => ( ( size_s6755466524823107622T_VEBT @ ( concat_VEBT_VEBT @ Xs ) )
% 4.71/5.12 = ( times_times_nat @ ( size_s8217280938318005548T_VEBT @ Xs ) @ N ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % length_mul_elem
% 4.71/5.12 thf(fact_5472_length__mul__elem,axiom,
% 4.71/5.12 ! [Xs: list_list_nat,N: nat] :
% 4.71/5.12 ( ! [X4: list_nat] :
% 4.71/5.12 ( ( member_list_nat @ X4 @ ( set_list_nat2 @ Xs ) )
% 4.71/5.12 => ( ( size_size_list_nat @ X4 )
% 4.71/5.12 = N ) )
% 4.71/5.12 => ( ( size_size_list_nat @ ( concat_nat @ Xs ) )
% 4.71/5.12 = ( times_times_nat @ ( size_s3023201423986296836st_nat @ Xs ) @ N ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % length_mul_elem
% 4.71/5.12 thf(fact_5473_vebt__insert_Osimps_I2_J,axiom,
% 4.71/5.12 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 4.71/5.12 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S ) @ X )
% 4.71/5.12 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S ) ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_insert.simps(2)
% 4.71/5.12 thf(fact_5474_vebt__insert_Osimps_I3_J,axiom,
% 4.71/5.12 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 4.71/5.12 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ X )
% 4.71/5.12 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_insert.simps(3)
% 4.71/5.12 thf(fact_5475_vebt__insert_Osimps_I1_J,axiom,
% 4.71/5.12 ! [X: nat,A: $o,B: $o] :
% 4.71/5.12 ( ( ( X = zero_zero_nat )
% 4.71/5.12 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 4.71/5.12 = ( vEBT_Leaf @ $true @ B ) ) )
% 4.71/5.12 & ( ( X != zero_zero_nat )
% 4.71/5.12 => ( ( ( X = one_one_nat )
% 4.71/5.12 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 4.71/5.12 = ( vEBT_Leaf @ A @ $true ) ) )
% 4.71/5.12 & ( ( X != one_one_nat )
% 4.71/5.12 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 4.71/5.12 = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % vebt_insert.simps(1)
% 4.71/5.12 thf(fact_5476_nth__zip,axiom,
% 4.71/5.12 ! [I: nat,Xs: list_int,Ys2: list_int] :
% 4.71/5.12 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 4.71/5.12 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Ys2 ) )
% 4.71/5.12 => ( ( nth_Pr4439495888332055232nt_int @ ( zip_int_int @ Xs @ Ys2 ) @ I )
% 4.71/5.12 = ( product_Pair_int_int @ ( nth_int @ Xs @ I ) @ ( nth_int @ Ys2 @ I ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_zip
% 4.71/5.12 thf(fact_5477_nth__zip,axiom,
% 4.71/5.12 ! [I: nat,Xs: list_int,Ys2: list_VEBT_VEBT] :
% 4.71/5.12 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 4.71/5.12 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Ys2 ) )
% 4.71/5.12 => ( ( nth_Pr3474266648193625910T_VEBT @ ( zip_int_VEBT_VEBT @ Xs @ Ys2 ) @ I )
% 4.71/5.12 = ( produc3329399203697025711T_VEBT @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBT @ Ys2 @ I ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_zip
% 4.71/5.12 thf(fact_5478_nth__zip,axiom,
% 4.71/5.12 ! [I: nat,Xs: list_int,Ys2: list_nat] :
% 4.71/5.12 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 4.71/5.12 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Ys2 ) )
% 4.71/5.12 => ( ( nth_Pr8617346907841251940nt_nat @ ( zip_int_nat @ Xs @ Ys2 ) @ I )
% 4.71/5.12 = ( product_Pair_int_nat @ ( nth_int @ Xs @ I ) @ ( nth_nat @ Ys2 @ I ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_zip
% 4.71/5.12 thf(fact_5479_nth__zip,axiom,
% 4.71/5.12 ! [I: nat,Xs: list_VEBT_VEBT,Ys2: list_int] :
% 4.71/5.12 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.71/5.12 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Ys2 ) )
% 4.71/5.12 => ( ( nth_Pr6837108013167703752BT_int @ ( zip_VEBT_VEBT_int @ Xs @ Ys2 ) @ I )
% 4.71/5.12 = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_int @ Ys2 @ I ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_zip
% 4.71/5.12 thf(fact_5480_nth__zip,axiom,
% 4.71/5.12 ! [I: nat,Xs: list_VEBT_VEBT,Ys2: list_VEBT_VEBT] :
% 4.71/5.12 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.71/5.12 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Ys2 ) )
% 4.71/5.12 => ( ( nth_Pr4953567300277697838T_VEBT @ ( zip_VE537291747668921783T_VEBT @ Xs @ Ys2 ) @ I )
% 4.71/5.12 = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_VEBT_VEBT @ Ys2 @ I ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_zip
% 4.71/5.12 thf(fact_5481_nth__zip,axiom,
% 4.71/5.12 ! [I: nat,Xs: list_VEBT_VEBT,Ys2: list_nat] :
% 4.71/5.12 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.71/5.12 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Ys2 ) )
% 4.71/5.12 => ( ( nth_Pr1791586995822124652BT_nat @ ( zip_VEBT_VEBT_nat @ Xs @ Ys2 ) @ I )
% 4.71/5.12 = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_nat @ Ys2 @ I ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_zip
% 4.71/5.12 thf(fact_5482_nth__zip,axiom,
% 4.71/5.12 ! [I: nat,Xs: list_nat,Ys2: list_int] :
% 4.71/5.12 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 4.71/5.12 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Ys2 ) )
% 4.71/5.12 => ( ( nth_Pr3440142176431000676at_int @ ( zip_nat_int @ Xs @ Ys2 ) @ I )
% 4.71/5.12 = ( product_Pair_nat_int @ ( nth_nat @ Xs @ I ) @ ( nth_int @ Ys2 @ I ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_zip
% 4.71/5.12 thf(fact_5483_nth__zip,axiom,
% 4.71/5.12 ! [I: nat,Xs: list_nat,Ys2: list_VEBT_VEBT] :
% 4.71/5.12 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 4.71/5.12 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Ys2 ) )
% 4.71/5.12 => ( ( nth_Pr744662078594809490T_VEBT @ ( zip_nat_VEBT_VEBT @ Xs @ Ys2 ) @ I )
% 4.71/5.12 = ( produc599794634098209291T_VEBT @ ( nth_nat @ Xs @ I ) @ ( nth_VEBT_VEBT @ Ys2 @ I ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_zip
% 4.71/5.12 thf(fact_5484_nth__zip,axiom,
% 4.71/5.12 ! [I: nat,Xs: list_nat,Ys2: list_nat] :
% 4.71/5.12 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 4.71/5.12 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Ys2 ) )
% 4.71/5.12 => ( ( nth_Pr7617993195940197384at_nat @ ( zip_nat_nat @ Xs @ Ys2 ) @ I )
% 4.71/5.12 = ( product_Pair_nat_nat @ ( nth_nat @ Xs @ I ) @ ( nth_nat @ Ys2 @ I ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_zip
% 4.71/5.12 thf(fact_5485_nth__zip,axiom,
% 4.71/5.12 ! [I: nat,Xs: list_P6011104703257516679at_nat,Ys2: list_P6011104703257516679at_nat] :
% 4.71/5.12 ( ( ord_less_nat @ I @ ( size_s5460976970255530739at_nat @ Xs ) )
% 4.71/5.12 => ( ( ord_less_nat @ I @ ( size_s5460976970255530739at_nat @ Ys2 ) )
% 4.71/5.12 => ( ( nth_Pr6744343527793145070at_nat @ ( zip_Pr4664179122662387191at_nat @ Xs @ Ys2 ) @ I )
% 4.71/5.12 = ( produc6161850002892822231at_nat @ ( nth_Pr7617993195940197384at_nat @ Xs @ I ) @ ( nth_Pr7617993195940197384at_nat @ Ys2 @ I ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_zip
% 4.71/5.12 thf(fact_5486_find__Some__iff,axiom,
% 4.71/5.12 ! [P: int > $o,Xs: list_int,X: int] :
% 4.71/5.12 ( ( ( find_int @ P @ Xs )
% 4.71/5.12 = ( some_int @ X ) )
% 4.71/5.12 = ( ? [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 4.71/5.12 & ( P @ ( nth_int @ Xs @ I4 ) )
% 4.71/5.12 & ( X
% 4.71/5.12 = ( nth_int @ Xs @ I4 ) )
% 4.71/5.12 & ! [J3: nat] :
% 4.71/5.12 ( ( ord_less_nat @ J3 @ I4 )
% 4.71/5.12 => ~ ( P @ ( nth_int @ Xs @ J3 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % find_Some_iff
% 4.71/5.12 thf(fact_5487_find__Some__iff,axiom,
% 4.71/5.12 ! [P: product_prod_nat_nat > $o,Xs: list_P6011104703257516679at_nat,X: product_prod_nat_nat] :
% 4.71/5.12 ( ( ( find_P8199882355184865565at_nat @ P @ Xs )
% 4.71/5.12 = ( some_P7363390416028606310at_nat @ X ) )
% 4.71/5.12 = ( ? [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ ( size_s5460976970255530739at_nat @ Xs ) )
% 4.71/5.12 & ( P @ ( nth_Pr7617993195940197384at_nat @ Xs @ I4 ) )
% 4.71/5.12 & ( X
% 4.71/5.12 = ( nth_Pr7617993195940197384at_nat @ Xs @ I4 ) )
% 4.71/5.12 & ! [J3: nat] :
% 4.71/5.12 ( ( ord_less_nat @ J3 @ I4 )
% 4.71/5.12 => ~ ( P @ ( nth_Pr7617993195940197384at_nat @ Xs @ J3 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % find_Some_iff
% 4.71/5.12 thf(fact_5488_find__Some__iff,axiom,
% 4.71/5.12 ! [P: num > $o,Xs: list_num,X: num] :
% 4.71/5.12 ( ( ( find_num @ P @ Xs )
% 4.71/5.12 = ( some_num @ X ) )
% 4.71/5.12 = ( ? [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ ( size_size_list_num @ Xs ) )
% 4.71/5.12 & ( P @ ( nth_num @ Xs @ I4 ) )
% 4.71/5.12 & ( X
% 4.71/5.12 = ( nth_num @ Xs @ I4 ) )
% 4.71/5.12 & ! [J3: nat] :
% 4.71/5.12 ( ( ord_less_nat @ J3 @ I4 )
% 4.71/5.12 => ~ ( P @ ( nth_num @ Xs @ J3 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % find_Some_iff
% 4.71/5.12 thf(fact_5489_find__Some__iff,axiom,
% 4.71/5.12 ! [P: vEBT_VEBT > $o,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 4.71/5.12 ( ( ( find_VEBT_VEBT @ P @ Xs )
% 4.71/5.12 = ( some_VEBT_VEBT @ X ) )
% 4.71/5.12 = ( ? [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.71/5.12 & ( P @ ( nth_VEBT_VEBT @ Xs @ I4 ) )
% 4.71/5.12 & ( X
% 4.71/5.12 = ( nth_VEBT_VEBT @ Xs @ I4 ) )
% 4.71/5.12 & ! [J3: nat] :
% 4.71/5.12 ( ( ord_less_nat @ J3 @ I4 )
% 4.71/5.12 => ~ ( P @ ( nth_VEBT_VEBT @ Xs @ J3 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % find_Some_iff
% 4.71/5.12 thf(fact_5490_find__Some__iff,axiom,
% 4.71/5.12 ! [P: nat > $o,Xs: list_nat,X: nat] :
% 4.71/5.12 ( ( ( find_nat @ P @ Xs )
% 4.71/5.12 = ( some_nat @ X ) )
% 4.71/5.12 = ( ? [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 4.71/5.12 & ( P @ ( nth_nat @ Xs @ I4 ) )
% 4.71/5.12 & ( X
% 4.71/5.12 = ( nth_nat @ Xs @ I4 ) )
% 4.71/5.12 & ! [J3: nat] :
% 4.71/5.12 ( ( ord_less_nat @ J3 @ I4 )
% 4.71/5.12 => ~ ( P @ ( nth_nat @ Xs @ J3 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % find_Some_iff
% 4.71/5.12 thf(fact_5491_find__Some__iff2,axiom,
% 4.71/5.12 ! [X: int,P: int > $o,Xs: list_int] :
% 4.71/5.12 ( ( ( some_int @ X )
% 4.71/5.12 = ( find_int @ P @ Xs ) )
% 4.71/5.12 = ( ? [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 4.71/5.12 & ( P @ ( nth_int @ Xs @ I4 ) )
% 4.71/5.12 & ( X
% 4.71/5.12 = ( nth_int @ Xs @ I4 ) )
% 4.71/5.12 & ! [J3: nat] :
% 4.71/5.12 ( ( ord_less_nat @ J3 @ I4 )
% 4.71/5.12 => ~ ( P @ ( nth_int @ Xs @ J3 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % find_Some_iff2
% 4.71/5.12 thf(fact_5492_find__Some__iff2,axiom,
% 4.71/5.12 ! [X: product_prod_nat_nat,P: product_prod_nat_nat > $o,Xs: list_P6011104703257516679at_nat] :
% 4.71/5.12 ( ( ( some_P7363390416028606310at_nat @ X )
% 4.71/5.12 = ( find_P8199882355184865565at_nat @ P @ Xs ) )
% 4.71/5.12 = ( ? [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ ( size_s5460976970255530739at_nat @ Xs ) )
% 4.71/5.12 & ( P @ ( nth_Pr7617993195940197384at_nat @ Xs @ I4 ) )
% 4.71/5.12 & ( X
% 4.71/5.12 = ( nth_Pr7617993195940197384at_nat @ Xs @ I4 ) )
% 4.71/5.12 & ! [J3: nat] :
% 4.71/5.12 ( ( ord_less_nat @ J3 @ I4 )
% 4.71/5.12 => ~ ( P @ ( nth_Pr7617993195940197384at_nat @ Xs @ J3 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % find_Some_iff2
% 4.71/5.12 thf(fact_5493_find__Some__iff2,axiom,
% 4.71/5.12 ! [X: num,P: num > $o,Xs: list_num] :
% 4.71/5.12 ( ( ( some_num @ X )
% 4.71/5.12 = ( find_num @ P @ Xs ) )
% 4.71/5.12 = ( ? [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ ( size_size_list_num @ Xs ) )
% 4.71/5.12 & ( P @ ( nth_num @ Xs @ I4 ) )
% 4.71/5.12 & ( X
% 4.71/5.12 = ( nth_num @ Xs @ I4 ) )
% 4.71/5.12 & ! [J3: nat] :
% 4.71/5.12 ( ( ord_less_nat @ J3 @ I4 )
% 4.71/5.12 => ~ ( P @ ( nth_num @ Xs @ J3 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % find_Some_iff2
% 4.71/5.12 thf(fact_5494_find__Some__iff2,axiom,
% 4.71/5.12 ! [X: vEBT_VEBT,P: vEBT_VEBT > $o,Xs: list_VEBT_VEBT] :
% 4.71/5.12 ( ( ( some_VEBT_VEBT @ X )
% 4.71/5.12 = ( find_VEBT_VEBT @ P @ Xs ) )
% 4.71/5.12 = ( ? [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.71/5.12 & ( P @ ( nth_VEBT_VEBT @ Xs @ I4 ) )
% 4.71/5.12 & ( X
% 4.71/5.12 = ( nth_VEBT_VEBT @ Xs @ I4 ) )
% 4.71/5.12 & ! [J3: nat] :
% 4.71/5.12 ( ( ord_less_nat @ J3 @ I4 )
% 4.71/5.12 => ~ ( P @ ( nth_VEBT_VEBT @ Xs @ J3 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % find_Some_iff2
% 4.71/5.12 thf(fact_5495_find__Some__iff2,axiom,
% 4.71/5.12 ! [X: nat,P: nat > $o,Xs: list_nat] :
% 4.71/5.12 ( ( ( some_nat @ X )
% 4.71/5.12 = ( find_nat @ P @ Xs ) )
% 4.71/5.12 = ( ? [I4: nat] :
% 4.71/5.12 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 4.71/5.12 & ( P @ ( nth_nat @ Xs @ I4 ) )
% 4.71/5.12 & ( X
% 4.71/5.12 = ( nth_nat @ Xs @ I4 ) )
% 4.71/5.12 & ! [J3: nat] :
% 4.71/5.12 ( ( ord_less_nat @ J3 @ I4 )
% 4.71/5.12 => ~ ( P @ ( nth_nat @ Xs @ J3 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % find_Some_iff2
% 4.71/5.12 thf(fact_5496_nth__Cons__pos,axiom,
% 4.71/5.12 ! [N: nat,X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 4.71/5.12 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.12 => ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ N )
% 4.71/5.12 = ( nth_VEBT_VEBT @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_Cons_pos
% 4.71/5.12 thf(fact_5497_nth__Cons__pos,axiom,
% 4.71/5.12 ! [N: nat,X: int,Xs: list_int] :
% 4.71/5.12 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.12 => ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
% 4.71/5.12 = ( nth_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_Cons_pos
% 4.71/5.12 thf(fact_5498_nth__Cons__pos,axiom,
% 4.71/5.12 ! [N: nat,X: nat,Xs: list_nat] :
% 4.71/5.12 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.12 => ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ N )
% 4.71/5.12 = ( nth_nat @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_Cons_pos
% 4.71/5.12 thf(fact_5499_rotate1__length01,axiom,
% 4.71/5.12 ! [Xs: list_VEBT_VEBT] :
% 4.71/5.12 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ one_one_nat )
% 4.71/5.12 => ( ( rotate1_VEBT_VEBT @ Xs )
% 4.71/5.12 = Xs ) ) ).
% 4.71/5.12
% 4.71/5.12 % rotate1_length01
% 4.71/5.12 thf(fact_5500_rotate1__length01,axiom,
% 4.71/5.12 ! [Xs: list_nat] :
% 4.71/5.12 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat )
% 4.71/5.12 => ( ( rotate1_nat @ Xs )
% 4.71/5.12 = Xs ) ) ).
% 4.71/5.12
% 4.71/5.12 % rotate1_length01
% 4.71/5.12 thf(fact_5501_remove__def,axiom,
% 4.71/5.12 ( remove6466555014256735590at_nat
% 4.71/5.12 = ( ^ [X3: product_prod_nat_nat,A6: set_Pr1261947904930325089at_nat] : ( minus_1356011639430497352at_nat @ A6 @ ( insert8211810215607154385at_nat @ X3 @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % remove_def
% 4.71/5.12 thf(fact_5502_remove__def,axiom,
% 4.71/5.12 ( remove_real
% 4.71/5.12 = ( ^ [X3: real,A6: set_real] : ( minus_minus_set_real @ A6 @ ( insert_real @ X3 @ bot_bot_set_real ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % remove_def
% 4.71/5.12 thf(fact_5503_remove__def,axiom,
% 4.71/5.12 ( remove_o
% 4.71/5.12 = ( ^ [X3: $o,A6: set_o] : ( minus_minus_set_o @ A6 @ ( insert_o @ X3 @ bot_bot_set_o ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % remove_def
% 4.71/5.12 thf(fact_5504_remove__def,axiom,
% 4.71/5.12 ( remove_int
% 4.71/5.12 = ( ^ [X3: int,A6: set_int] : ( minus_minus_set_int @ A6 @ ( insert_int @ X3 @ bot_bot_set_int ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % remove_def
% 4.71/5.12 thf(fact_5505_remove__def,axiom,
% 4.71/5.12 ( remove_nat
% 4.71/5.12 = ( ^ [X3: nat,A6: set_nat] : ( minus_minus_set_nat @ A6 @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % remove_def
% 4.71/5.12 thf(fact_5506_split__pos__lemma,axiom,
% 4.71/5.12 ! [K: int,P: int > int > $o,N: int] :
% 4.71/5.12 ( ( ord_less_int @ zero_zero_int @ K )
% 4.71/5.12 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 4.71/5.12 = ( ! [I4: int,J3: int] :
% 4.71/5.12 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 4.71/5.12 & ( ord_less_int @ J3 @ K )
% 4.71/5.12 & ( N
% 4.71/5.12 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 4.71/5.12 => ( P @ I4 @ J3 ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % split_pos_lemma
% 4.71/5.12 thf(fact_5507_member__remove,axiom,
% 4.71/5.12 ! [X: $o,Y: $o,A2: set_o] :
% 4.71/5.12 ( ( member_o @ X @ ( remove_o @ Y @ A2 ) )
% 4.71/5.12 = ( ( member_o @ X @ A2 )
% 4.71/5.12 & ( X != Y ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % member_remove
% 4.71/5.12 thf(fact_5508_member__remove,axiom,
% 4.71/5.12 ! [X: set_nat,Y: set_nat,A2: set_set_nat] :
% 4.71/5.12 ( ( member_set_nat @ X @ ( remove_set_nat @ Y @ A2 ) )
% 4.71/5.12 = ( ( member_set_nat @ X @ A2 )
% 4.71/5.12 & ( X != Y ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % member_remove
% 4.71/5.12 thf(fact_5509_member__remove,axiom,
% 4.71/5.12 ! [X: set_nat_rat,Y: set_nat_rat,A2: set_set_nat_rat] :
% 4.71/5.12 ( ( member_set_nat_rat @ X @ ( remove_set_nat_rat @ Y @ A2 ) )
% 4.71/5.12 = ( ( member_set_nat_rat @ X @ A2 )
% 4.71/5.12 & ( X != Y ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % member_remove
% 4.71/5.12 thf(fact_5510_member__remove,axiom,
% 4.71/5.12 ! [X: nat,Y: nat,A2: set_nat] :
% 4.71/5.12 ( ( member_nat @ X @ ( remove_nat @ Y @ A2 ) )
% 4.71/5.12 = ( ( member_nat @ X @ A2 )
% 4.71/5.12 & ( X != Y ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % member_remove
% 4.71/5.12 thf(fact_5511_member__remove,axiom,
% 4.71/5.12 ! [X: int,Y: int,A2: set_int] :
% 4.71/5.12 ( ( member_int @ X @ ( remove_int @ Y @ A2 ) )
% 4.71/5.12 = ( ( member_int @ X @ A2 )
% 4.71/5.12 & ( X != Y ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % member_remove
% 4.71/5.12 thf(fact_5512_bits__mod__0,axiom,
% 4.71/5.12 ! [A: int] :
% 4.71/5.12 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 4.71/5.12 = zero_zero_int ) ).
% 4.71/5.12
% 4.71/5.12 % bits_mod_0
% 4.71/5.12 thf(fact_5513_bits__mod__0,axiom,
% 4.71/5.12 ! [A: nat] :
% 4.71/5.12 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 4.71/5.12 = zero_zero_nat ) ).
% 4.71/5.12
% 4.71/5.12 % bits_mod_0
% 4.71/5.12 thf(fact_5514_mod__self,axiom,
% 4.71/5.12 ! [A: int] :
% 4.71/5.12 ( ( modulo_modulo_int @ A @ A )
% 4.71/5.12 = zero_zero_int ) ).
% 4.71/5.12
% 4.71/5.12 % mod_self
% 4.71/5.12 thf(fact_5515_mod__self,axiom,
% 4.71/5.12 ! [A: nat] :
% 4.71/5.12 ( ( modulo_modulo_nat @ A @ A )
% 4.71/5.12 = zero_zero_nat ) ).
% 4.71/5.12
% 4.71/5.12 % mod_self
% 4.71/5.12 thf(fact_5516_mod__by__0,axiom,
% 4.71/5.12 ! [A: int] :
% 4.71/5.12 ( ( modulo_modulo_int @ A @ zero_zero_int )
% 4.71/5.12 = A ) ).
% 4.71/5.12
% 4.71/5.12 % mod_by_0
% 4.71/5.12 thf(fact_5517_mod__by__0,axiom,
% 4.71/5.12 ! [A: nat] :
% 4.71/5.12 ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 4.71/5.12 = A ) ).
% 4.71/5.12
% 4.71/5.12 % mod_by_0
% 4.71/5.12 thf(fact_5518_mod__0,axiom,
% 4.71/5.12 ! [A: int] :
% 4.71/5.12 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 4.71/5.12 = zero_zero_int ) ).
% 4.71/5.12
% 4.71/5.12 % mod_0
% 4.71/5.12 thf(fact_5519_mod__0,axiom,
% 4.71/5.12 ! [A: nat] :
% 4.71/5.12 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 4.71/5.12 = zero_zero_nat ) ).
% 4.71/5.12
% 4.71/5.12 % mod_0
% 4.71/5.12 thf(fact_5520_mod__mult__self1__is__0,axiom,
% 4.71/5.12 ! [B: int,A: int] :
% 4.71/5.12 ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 4.71/5.12 = zero_zero_int ) ).
% 4.71/5.12
% 4.71/5.12 % mod_mult_self1_is_0
% 4.71/5.12 thf(fact_5521_mod__mult__self1__is__0,axiom,
% 4.71/5.12 ! [B: nat,A: nat] :
% 4.71/5.12 ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 4.71/5.12 = zero_zero_nat ) ).
% 4.71/5.12
% 4.71/5.12 % mod_mult_self1_is_0
% 4.71/5.12 thf(fact_5522_mod__mult__self2__is__0,axiom,
% 4.71/5.12 ! [A: int,B: int] :
% 4.71/5.12 ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 4.71/5.12 = zero_zero_int ) ).
% 4.71/5.12
% 4.71/5.12 % mod_mult_self2_is_0
% 4.71/5.12 thf(fact_5523_mod__mult__self2__is__0,axiom,
% 4.71/5.12 ! [A: nat,B: nat] :
% 4.71/5.12 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 4.71/5.12 = zero_zero_nat ) ).
% 4.71/5.12
% 4.71/5.12 % mod_mult_self2_is_0
% 4.71/5.12 thf(fact_5524_bits__mod__by__1,axiom,
% 4.71/5.12 ! [A: int] :
% 4.71/5.12 ( ( modulo_modulo_int @ A @ one_one_int )
% 4.71/5.12 = zero_zero_int ) ).
% 4.71/5.12
% 4.71/5.12 % bits_mod_by_1
% 4.71/5.12 thf(fact_5525_bits__mod__by__1,axiom,
% 4.71/5.12 ! [A: nat] :
% 4.71/5.12 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 4.71/5.12 = zero_zero_nat ) ).
% 4.71/5.12
% 4.71/5.12 % bits_mod_by_1
% 4.71/5.12 thf(fact_5526_mod__by__1,axiom,
% 4.71/5.12 ! [A: int] :
% 4.71/5.12 ( ( modulo_modulo_int @ A @ one_one_int )
% 4.71/5.12 = zero_zero_int ) ).
% 4.71/5.12
% 4.71/5.12 % mod_by_1
% 4.71/5.12 thf(fact_5527_mod__by__1,axiom,
% 4.71/5.12 ! [A: nat] :
% 4.71/5.12 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 4.71/5.12 = zero_zero_nat ) ).
% 4.71/5.12
% 4.71/5.12 % mod_by_1
% 4.71/5.12 thf(fact_5528_mod__div__trivial,axiom,
% 4.71/5.12 ! [A: int,B: int] :
% 4.71/5.12 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 4.71/5.12 = zero_zero_int ) ).
% 4.71/5.12
% 4.71/5.12 % mod_div_trivial
% 4.71/5.12 thf(fact_5529_mod__div__trivial,axiom,
% 4.71/5.12 ! [A: nat,B: nat] :
% 4.71/5.12 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 4.71/5.12 = zero_zero_nat ) ).
% 4.71/5.12
% 4.71/5.12 % mod_div_trivial
% 4.71/5.12 thf(fact_5530_bits__mod__div__trivial,axiom,
% 4.71/5.12 ! [A: int,B: int] :
% 4.71/5.12 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 4.71/5.12 = zero_zero_int ) ).
% 4.71/5.12
% 4.71/5.12 % bits_mod_div_trivial
% 4.71/5.12 thf(fact_5531_bits__mod__div__trivial,axiom,
% 4.71/5.12 ! [A: nat,B: nat] :
% 4.71/5.12 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 4.71/5.12 = zero_zero_nat ) ).
% 4.71/5.12
% 4.71/5.12 % bits_mod_div_trivial
% 4.71/5.12 thf(fact_5532_nth__Cons__0,axiom,
% 4.71/5.12 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 4.71/5.12 ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ zero_zero_nat )
% 4.71/5.12 = X ) ).
% 4.71/5.12
% 4.71/5.12 % nth_Cons_0
% 4.71/5.12 thf(fact_5533_nth__Cons__0,axiom,
% 4.71/5.12 ! [X: int,Xs: list_int] :
% 4.71/5.12 ( ( nth_int @ ( cons_int @ X @ Xs ) @ zero_zero_nat )
% 4.71/5.12 = X ) ).
% 4.71/5.12
% 4.71/5.12 % nth_Cons_0
% 4.71/5.12 thf(fact_5534_nth__Cons__0,axiom,
% 4.71/5.12 ! [X: nat,Xs: list_nat] :
% 4.71/5.12 ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ zero_zero_nat )
% 4.71/5.12 = X ) ).
% 4.71/5.12
% 4.71/5.12 % nth_Cons_0
% 4.71/5.12 thf(fact_5535_mod__minus1__right,axiom,
% 4.71/5.12 ! [A: int] :
% 4.71/5.12 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 4.71/5.12 = zero_zero_int ) ).
% 4.71/5.12
% 4.71/5.12 % mod_minus1_right
% 4.71/5.12 thf(fact_5536_mod__neg__neg__trivial,axiom,
% 4.71/5.12 ! [K: int,L: int] :
% 4.71/5.12 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 4.71/5.12 => ( ( ord_less_int @ L @ K )
% 4.71/5.12 => ( ( modulo_modulo_int @ K @ L )
% 4.71/5.12 = K ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % mod_neg_neg_trivial
% 4.71/5.12 thf(fact_5537_mod__pos__pos__trivial,axiom,
% 4.71/5.12 ! [K: int,L: int] :
% 4.71/5.12 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 4.71/5.12 => ( ( ord_less_int @ K @ L )
% 4.71/5.12 => ( ( modulo_modulo_int @ K @ L )
% 4.71/5.12 = K ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % mod_pos_pos_trivial
% 4.71/5.12 thf(fact_5538_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 4.71/5.12 ! [A: nat,B: nat] :
% 4.71/5.12 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.71/5.12 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 4.71/5.12
% 4.71/5.12 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 4.71/5.12 thf(fact_5539_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 4.71/5.12 ! [A: int,B: int] :
% 4.71/5.12 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.12 => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 4.71/5.12
% 4.71/5.12 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 4.71/5.12 thf(fact_5540_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 4.71/5.12 ! [B: int,A: int] :
% 4.71/5.12 ( ( ord_less_int @ zero_zero_int @ B )
% 4.71/5.12 => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 4.71/5.12
% 4.71/5.12 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 4.71/5.12 thf(fact_5541_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 4.71/5.12 ! [B: nat,A: nat] :
% 4.71/5.12 ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.71/5.12 => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 4.71/5.12
% 4.71/5.12 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 4.71/5.12 thf(fact_5542_mod__eq__self__iff__div__eq__0,axiom,
% 4.71/5.12 ! [A: int,B: int] :
% 4.71/5.12 ( ( ( modulo_modulo_int @ A @ B )
% 4.71/5.12 = A )
% 4.71/5.12 = ( ( divide_divide_int @ A @ B )
% 4.71/5.12 = zero_zero_int ) ) ).
% 4.71/5.12
% 4.71/5.12 % mod_eq_self_iff_div_eq_0
% 4.71/5.12 thf(fact_5543_mod__eq__self__iff__div__eq__0,axiom,
% 4.71/5.12 ! [A: nat,B: nat] :
% 4.71/5.12 ( ( ( modulo_modulo_nat @ A @ B )
% 4.71/5.12 = A )
% 4.71/5.12 = ( ( divide_divide_nat @ A @ B )
% 4.71/5.12 = zero_zero_nat ) ) ).
% 4.71/5.12
% 4.71/5.12 % mod_eq_self_iff_div_eq_0
% 4.71/5.12 thf(fact_5544_zmod__le__nonneg__dividend,axiom,
% 4.71/5.12 ! [M2: int,K: int] :
% 4.71/5.12 ( ( ord_less_eq_int @ zero_zero_int @ M2 )
% 4.71/5.12 => ( ord_less_eq_int @ ( modulo_modulo_int @ M2 @ K ) @ M2 ) ) ).
% 4.71/5.12
% 4.71/5.12 % zmod_le_nonneg_dividend
% 4.71/5.12 thf(fact_5545_set__subset__Cons,axiom,
% 4.71/5.12 ! [Xs: list_VEBT_VEBT,X: vEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ ( set_VEBT_VEBT2 @ ( cons_VEBT_VEBT @ X @ Xs ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % set_subset_Cons
% 4.71/5.12 thf(fact_5546_set__subset__Cons,axiom,
% 4.71/5.12 ! [Xs: list_nat,X: nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ ( set_nat2 @ ( cons_nat @ X @ Xs ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % set_subset_Cons
% 4.71/5.12 thf(fact_5547_set__subset__Cons,axiom,
% 4.71/5.12 ! [Xs: list_int,X: int] : ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ ( set_int2 @ ( cons_int @ X @ Xs ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % set_subset_Cons
% 4.71/5.12 thf(fact_5548_impossible__Cons,axiom,
% 4.71/5.12 ! [Xs: list_int,Ys2: list_int,X: int] :
% 4.71/5.12 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_int @ Ys2 ) )
% 4.71/5.12 => ( Xs
% 4.71/5.12 != ( cons_int @ X @ Ys2 ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % impossible_Cons
% 4.71/5.12 thf(fact_5549_impossible__Cons,axiom,
% 4.71/5.12 ! [Xs: list_VEBT_VEBT,Ys2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 4.71/5.12 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys2 ) )
% 4.71/5.12 => ( Xs
% 4.71/5.12 != ( cons_VEBT_VEBT @ X @ Ys2 ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % impossible_Cons
% 4.71/5.12 thf(fact_5550_impossible__Cons,axiom,
% 4.71/5.12 ! [Xs: list_nat,Ys2: list_nat,X: nat] :
% 4.71/5.12 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_nat @ Ys2 ) )
% 4.71/5.12 => ( Xs
% 4.71/5.12 != ( cons_nat @ X @ Ys2 ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % impossible_Cons
% 4.71/5.12 thf(fact_5551_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 4.71/5.12 ! [B: nat,A: nat] :
% 4.71/5.12 ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.71/5.12 => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 4.71/5.12 thf(fact_5552_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 4.71/5.12 ! [B: int,A: int] :
% 4.71/5.12 ( ( ord_less_int @ zero_zero_int @ B )
% 4.71/5.12 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 4.71/5.12 thf(fact_5553_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 4.71/5.12 ! [A: nat,B: nat] :
% 4.71/5.12 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.71/5.12 => ( ( ord_less_nat @ A @ B )
% 4.71/5.12 => ( ( modulo_modulo_nat @ A @ B )
% 4.71/5.12 = A ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % unique_euclidean_semiring_numeral_class.mod_less
% 4.71/5.12 thf(fact_5554_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 4.71/5.12 ! [A: int,B: int] :
% 4.71/5.12 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.12 => ( ( ord_less_int @ A @ B )
% 4.71/5.12 => ( ( modulo_modulo_int @ A @ B )
% 4.71/5.12 = A ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % unique_euclidean_semiring_numeral_class.mod_less
% 4.71/5.12 thf(fact_5555_cancel__div__mod__rules_I2_J,axiom,
% 4.71/5.12 ! [B: int,A: int,C: int] :
% 4.71/5.12 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 4.71/5.12 = ( plus_plus_int @ A @ C ) ) ).
% 4.71/5.12
% 4.71/5.12 % cancel_div_mod_rules(2)
% 4.71/5.12 thf(fact_5556_cancel__div__mod__rules_I2_J,axiom,
% 4.71/5.12 ! [B: nat,A: nat,C: nat] :
% 4.71/5.12 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 4.71/5.12 = ( plus_plus_nat @ A @ C ) ) ).
% 4.71/5.12
% 4.71/5.12 % cancel_div_mod_rules(2)
% 4.71/5.12 thf(fact_5557_cancel__div__mod__rules_I1_J,axiom,
% 4.71/5.12 ! [A: int,B: int,C: int] :
% 4.71/5.12 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 4.71/5.12 = ( plus_plus_int @ A @ C ) ) ).
% 4.71/5.12
% 4.71/5.12 % cancel_div_mod_rules(1)
% 4.71/5.12 thf(fact_5558_cancel__div__mod__rules_I1_J,axiom,
% 4.71/5.12 ! [A: nat,B: nat,C: nat] :
% 4.71/5.12 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 4.71/5.12 = ( plus_plus_nat @ A @ C ) ) ).
% 4.71/5.12
% 4.71/5.12 % cancel_div_mod_rules(1)
% 4.71/5.12 thf(fact_5559_mod__div__decomp,axiom,
% 4.71/5.12 ! [A: int,B: int] :
% 4.71/5.12 ( A
% 4.71/5.12 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % mod_div_decomp
% 4.71/5.12 thf(fact_5560_mod__div__decomp,axiom,
% 4.71/5.12 ! [A: nat,B: nat] :
% 4.71/5.12 ( A
% 4.71/5.12 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % mod_div_decomp
% 4.71/5.12 thf(fact_5561_div__mult__mod__eq,axiom,
% 4.71/5.12 ! [A: int,B: int] :
% 4.71/5.12 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 4.71/5.12 = A ) ).
% 4.71/5.12
% 4.71/5.12 % div_mult_mod_eq
% 4.71/5.12 thf(fact_5562_div__mult__mod__eq,axiom,
% 4.71/5.12 ! [A: nat,B: nat] :
% 4.71/5.12 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 4.71/5.12 = A ) ).
% 4.71/5.12
% 4.71/5.12 % div_mult_mod_eq
% 4.71/5.12 thf(fact_5563_mod__div__mult__eq,axiom,
% 4.71/5.12 ! [A: int,B: int] :
% 4.71/5.12 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 4.71/5.12 = A ) ).
% 4.71/5.12
% 4.71/5.12 % mod_div_mult_eq
% 4.71/5.12 thf(fact_5564_mod__div__mult__eq,axiom,
% 4.71/5.12 ! [A: nat,B: nat] :
% 4.71/5.12 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 4.71/5.12 = A ) ).
% 4.71/5.12
% 4.71/5.12 % mod_div_mult_eq
% 4.71/5.12 thf(fact_5565_mod__mult__div__eq,axiom,
% 4.71/5.12 ! [A: int,B: int] :
% 4.71/5.12 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 4.71/5.12 = A ) ).
% 4.71/5.12
% 4.71/5.12 % mod_mult_div_eq
% 4.71/5.12 thf(fact_5566_mod__mult__div__eq,axiom,
% 4.71/5.12 ! [A: nat,B: nat] :
% 4.71/5.12 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 4.71/5.12 = A ) ).
% 4.71/5.12
% 4.71/5.12 % mod_mult_div_eq
% 4.71/5.12 thf(fact_5567_mult__div__mod__eq,axiom,
% 4.71/5.12 ! [B: int,A: int] :
% 4.71/5.12 ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 4.71/5.12 = A ) ).
% 4.71/5.12
% 4.71/5.12 % mult_div_mod_eq
% 4.71/5.12 thf(fact_5568_mult__div__mod__eq,axiom,
% 4.71/5.12 ! [B: nat,A: nat] :
% 4.71/5.12 ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 4.71/5.12 = A ) ).
% 4.71/5.12
% 4.71/5.12 % mult_div_mod_eq
% 4.71/5.12 thf(fact_5569_minus__mult__div__eq__mod,axiom,
% 4.71/5.12 ! [A: int,B: int] :
% 4.71/5.12 ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 4.71/5.12 = ( modulo_modulo_int @ A @ B ) ) ).
% 4.71/5.12
% 4.71/5.12 % minus_mult_div_eq_mod
% 4.71/5.12 thf(fact_5570_minus__mult__div__eq__mod,axiom,
% 4.71/5.12 ! [A: nat,B: nat] :
% 4.71/5.12 ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 4.71/5.12 = ( modulo_modulo_nat @ A @ B ) ) ).
% 4.71/5.12
% 4.71/5.12 % minus_mult_div_eq_mod
% 4.71/5.12 thf(fact_5571_minus__mod__eq__mult__div,axiom,
% 4.71/5.12 ! [A: int,B: int] :
% 4.71/5.12 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 4.71/5.12 = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % minus_mod_eq_mult_div
% 4.71/5.12 thf(fact_5572_minus__mod__eq__mult__div,axiom,
% 4.71/5.12 ! [A: nat,B: nat] :
% 4.71/5.12 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 4.71/5.12 = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % minus_mod_eq_mult_div
% 4.71/5.12 thf(fact_5573_minus__mod__eq__div__mult,axiom,
% 4.71/5.12 ! [A: int,B: int] :
% 4.71/5.12 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 4.71/5.12 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 4.71/5.12
% 4.71/5.12 % minus_mod_eq_div_mult
% 4.71/5.12 thf(fact_5574_minus__mod__eq__div__mult,axiom,
% 4.71/5.12 ! [A: nat,B: nat] :
% 4.71/5.12 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 4.71/5.12 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 4.71/5.12
% 4.71/5.12 % minus_mod_eq_div_mult
% 4.71/5.12 thf(fact_5575_minus__div__mult__eq__mod,axiom,
% 4.71/5.12 ! [A: int,B: int] :
% 4.71/5.12 ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 4.71/5.12 = ( modulo_modulo_int @ A @ B ) ) ).
% 4.71/5.12
% 4.71/5.12 % minus_div_mult_eq_mod
% 4.71/5.12 thf(fact_5576_minus__div__mult__eq__mod,axiom,
% 4.71/5.12 ! [A: nat,B: nat] :
% 4.71/5.12 ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 4.71/5.12 = ( modulo_modulo_nat @ A @ B ) ) ).
% 4.71/5.12
% 4.71/5.12 % minus_div_mult_eq_mod
% 4.71/5.12 thf(fact_5577_fact__mod,axiom,
% 4.71/5.12 ! [M2: nat,N: nat] :
% 4.71/5.12 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.12 => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M2 ) )
% 4.71/5.12 = zero_zero_int ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_mod
% 4.71/5.12 thf(fact_5578_fact__mod,axiom,
% 4.71/5.12 ! [M2: nat,N: nat] :
% 4.71/5.12 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.12 => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M2 ) )
% 4.71/5.12 = zero_zero_nat ) ) ).
% 4.71/5.12
% 4.71/5.12 % fact_mod
% 4.71/5.12 thf(fact_5579_neg__mod__conj,axiom,
% 4.71/5.12 ! [B: int,A: int] :
% 4.71/5.12 ( ( ord_less_int @ B @ zero_zero_int )
% 4.71/5.12 => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 4.71/5.12 & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % neg_mod_conj
% 4.71/5.12 thf(fact_5580_pos__mod__conj,axiom,
% 4.71/5.12 ! [B: int,A: int] :
% 4.71/5.12 ( ( ord_less_int @ zero_zero_int @ B )
% 4.71/5.12 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 4.71/5.12 & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % pos_mod_conj
% 4.71/5.12 thf(fact_5581_zmod__trivial__iff,axiom,
% 4.71/5.12 ! [I: int,K: int] :
% 4.71/5.12 ( ( ( modulo_modulo_int @ I @ K )
% 4.71/5.12 = I )
% 4.71/5.12 = ( ( K = zero_zero_int )
% 4.71/5.12 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 4.71/5.12 & ( ord_less_int @ I @ K ) )
% 4.71/5.12 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 4.71/5.12 & ( ord_less_int @ K @ I ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % zmod_trivial_iff
% 4.71/5.12 thf(fact_5582_neg__mod__sign,axiom,
% 4.71/5.12 ! [L: int,K: int] :
% 4.71/5.12 ( ( ord_less_int @ L @ zero_zero_int )
% 4.71/5.12 => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L ) @ zero_zero_int ) ) ).
% 4.71/5.12
% 4.71/5.12 % neg_mod_sign
% 4.71/5.12 thf(fact_5583_Euclidean__Division_Opos__mod__sign,axiom,
% 4.71/5.12 ! [L: int,K: int] :
% 4.71/5.12 ( ( ord_less_int @ zero_zero_int @ L )
% 4.71/5.12 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % Euclidean_Division.pos_mod_sign
% 4.71/5.12 thf(fact_5584_Suc__le__length__iff,axiom,
% 4.71/5.12 ! [N: nat,Xs: list_int] :
% 4.71/5.12 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_int @ Xs ) )
% 4.71/5.12 = ( ? [X3: int,Ys3: list_int] :
% 4.71/5.12 ( ( Xs
% 4.71/5.12 = ( cons_int @ X3 @ Ys3 ) )
% 4.71/5.12 & ( ord_less_eq_nat @ N @ ( size_size_list_int @ Ys3 ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % Suc_le_length_iff
% 4.71/5.12 thf(fact_5585_Suc__le__length__iff,axiom,
% 4.71/5.12 ! [N: nat,Xs: list_VEBT_VEBT] :
% 4.71/5.12 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.71/5.12 = ( ? [X3: vEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 4.71/5.12 ( ( Xs
% 4.71/5.12 = ( cons_VEBT_VEBT @ X3 @ Ys3 ) )
% 4.71/5.12 & ( ord_less_eq_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys3 ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % Suc_le_length_iff
% 4.71/5.12 thf(fact_5586_Suc__le__length__iff,axiom,
% 4.71/5.12 ! [N: nat,Xs: list_nat] :
% 4.71/5.12 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_nat @ Xs ) )
% 4.71/5.12 = ( ? [X3: nat,Ys3: list_nat] :
% 4.71/5.12 ( ( Xs
% 4.71/5.12 = ( cons_nat @ X3 @ Ys3 ) )
% 4.71/5.12 & ( ord_less_eq_nat @ N @ ( size_size_list_nat @ Ys3 ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % Suc_le_length_iff
% 4.71/5.12 thf(fact_5587_mod__pos__neg__trivial,axiom,
% 4.71/5.12 ! [K: int,L: int] :
% 4.71/5.12 ( ( ord_less_int @ zero_zero_int @ K )
% 4.71/5.12 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 4.71/5.12 => ( ( modulo_modulo_int @ K @ L )
% 4.71/5.12 = ( plus_plus_int @ K @ L ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % mod_pos_neg_trivial
% 4.71/5.12 thf(fact_5588_list_Osize_I4_J,axiom,
% 4.71/5.12 ! [X21: int,X22: list_int] :
% 4.71/5.12 ( ( size_size_list_int @ ( cons_int @ X21 @ X22 ) )
% 4.71/5.12 = ( plus_plus_nat @ ( size_size_list_int @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % list.size(4)
% 4.71/5.12 thf(fact_5589_list_Osize_I4_J,axiom,
% 4.71/5.12 ! [X21: vEBT_VEBT,X22: list_VEBT_VEBT] :
% 4.71/5.12 ( ( size_s6755466524823107622T_VEBT @ ( cons_VEBT_VEBT @ X21 @ X22 ) )
% 4.71/5.12 = ( plus_plus_nat @ ( size_s6755466524823107622T_VEBT @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % list.size(4)
% 4.71/5.12 thf(fact_5590_list_Osize_I4_J,axiom,
% 4.71/5.12 ! [X21: nat,X22: list_nat] :
% 4.71/5.12 ( ( size_size_list_nat @ ( cons_nat @ X21 @ X22 ) )
% 4.71/5.12 = ( plus_plus_nat @ ( size_size_list_nat @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % list.size(4)
% 4.71/5.12 thf(fact_5591_mod__pos__geq,axiom,
% 4.71/5.12 ! [L: int,K: int] :
% 4.71/5.12 ( ( ord_less_int @ zero_zero_int @ L )
% 4.71/5.12 => ( ( ord_less_eq_int @ L @ K )
% 4.71/5.12 => ( ( modulo_modulo_int @ K @ L )
% 4.71/5.12 = ( modulo_modulo_int @ ( minus_minus_int @ K @ L ) @ L ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % mod_pos_geq
% 4.71/5.12 thf(fact_5592_nth__Cons_H,axiom,
% 4.71/5.12 ! [N: nat,X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 4.71/5.12 ( ( ( N = zero_zero_nat )
% 4.71/5.12 => ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ N )
% 4.71/5.12 = X ) )
% 4.71/5.12 & ( ( N != zero_zero_nat )
% 4.71/5.12 => ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ N )
% 4.71/5.12 = ( nth_VEBT_VEBT @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_Cons'
% 4.71/5.12 thf(fact_5593_nth__Cons_H,axiom,
% 4.71/5.12 ! [N: nat,X: int,Xs: list_int] :
% 4.71/5.12 ( ( ( N = zero_zero_nat )
% 4.71/5.12 => ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
% 4.71/5.12 = X ) )
% 4.71/5.12 & ( ( N != zero_zero_nat )
% 4.71/5.12 => ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
% 4.71/5.12 = ( nth_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_Cons'
% 4.71/5.12 thf(fact_5594_nth__Cons_H,axiom,
% 4.71/5.12 ! [N: nat,X: nat,Xs: list_nat] :
% 4.71/5.12 ( ( ( N = zero_zero_nat )
% 4.71/5.12 => ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ N )
% 4.71/5.12 = X ) )
% 4.71/5.12 & ( ( N != zero_zero_nat )
% 4.71/5.12 => ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ N )
% 4.71/5.12 = ( nth_nat @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_Cons'
% 4.71/5.12 thf(fact_5595_real__of__int__div__aux,axiom,
% 4.71/5.12 ! [X: int,D: int] :
% 4.71/5.12 ( ( divide_divide_real @ ( ring_1_of_int_real @ X ) @ ( ring_1_of_int_real @ D ) )
% 4.71/5.12 = ( plus_plus_real @ ( ring_1_of_int_real @ ( divide_divide_int @ X @ D ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ ( modulo_modulo_int @ X @ D ) ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % real_of_int_div_aux
% 4.71/5.12 thf(fact_5596_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 4.71/5.12 ! [C: nat,A: nat,B: nat] :
% 4.71/5.12 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.71/5.12 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 4.71/5.12 = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 4.71/5.12 thf(fact_5597_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 4.71/5.12 ! [C: int,A: int,B: int] :
% 4.71/5.12 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.71/5.12 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 4.71/5.12 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 4.71/5.12 thf(fact_5598_split__zmod,axiom,
% 4.71/5.12 ! [P: int > $o,N: int,K: int] :
% 4.71/5.12 ( ( P @ ( modulo_modulo_int @ N @ K ) )
% 4.71/5.12 = ( ( ( K = zero_zero_int )
% 4.71/5.12 => ( P @ N ) )
% 4.71/5.12 & ( ( ord_less_int @ zero_zero_int @ K )
% 4.71/5.12 => ! [I4: int,J3: int] :
% 4.71/5.12 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 4.71/5.12 & ( ord_less_int @ J3 @ K )
% 4.71/5.12 & ( N
% 4.71/5.12 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 4.71/5.12 => ( P @ J3 ) ) )
% 4.71/5.12 & ( ( ord_less_int @ K @ zero_zero_int )
% 4.71/5.12 => ! [I4: int,J3: int] :
% 4.71/5.12 ( ( ( ord_less_int @ K @ J3 )
% 4.71/5.12 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 4.71/5.12 & ( N
% 4.71/5.12 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 4.71/5.12 => ( P @ J3 ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % split_zmod
% 4.71/5.12 thf(fact_5599_int__mod__neg__eq,axiom,
% 4.71/5.12 ! [A: int,B: int,Q4: int,R2: int] :
% 4.71/5.12 ( ( A
% 4.71/5.12 = ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R2 ) )
% 4.71/5.12 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 4.71/5.12 => ( ( ord_less_int @ B @ R2 )
% 4.71/5.12 => ( ( modulo_modulo_int @ A @ B )
% 4.71/5.12 = R2 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % int_mod_neg_eq
% 4.71/5.12 thf(fact_5600_int__mod__pos__eq,axiom,
% 4.71/5.12 ! [A: int,B: int,Q4: int,R2: int] :
% 4.71/5.12 ( ( A
% 4.71/5.12 = ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R2 ) )
% 4.71/5.12 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 4.71/5.12 => ( ( ord_less_int @ R2 @ B )
% 4.71/5.12 => ( ( modulo_modulo_int @ A @ B )
% 4.71/5.12 = R2 ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % int_mod_pos_eq
% 4.71/5.12 thf(fact_5601_minus__mod__int__eq,axiom,
% 4.71/5.12 ! [L: int,K: int] :
% 4.71/5.12 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 4.71/5.12 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 4.71/5.12 = ( minus_minus_int @ ( minus_minus_int @ L @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % minus_mod_int_eq
% 4.71/5.12 thf(fact_5602_zmod__zmult2__eq,axiom,
% 4.71/5.12 ! [C: int,A: int,B: int] :
% 4.71/5.12 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.71/5.12 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 4.71/5.12 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % zmod_zmult2_eq
% 4.71/5.12 thf(fact_5603_nth__equal__first__eq,axiom,
% 4.71/5.12 ! [X: $o,Xs: list_o,N: nat] :
% 4.71/5.12 ( ~ ( member_o @ X @ ( set_o2 @ Xs ) )
% 4.71/5.12 => ( ( ord_less_eq_nat @ N @ ( size_size_list_o @ Xs ) )
% 4.71/5.12 => ( ( ( nth_o @ ( cons_o @ X @ Xs ) @ N )
% 4.71/5.12 = X )
% 4.71/5.12 = ( N = zero_zero_nat ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_equal_first_eq
% 4.71/5.12 thf(fact_5604_nth__equal__first__eq,axiom,
% 4.71/5.12 ! [X: set_nat,Xs: list_set_nat,N: nat] :
% 4.71/5.12 ( ~ ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 4.71/5.12 => ( ( ord_less_eq_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 4.71/5.12 => ( ( ( nth_set_nat @ ( cons_set_nat @ X @ Xs ) @ N )
% 4.71/5.12 = X )
% 4.71/5.12 = ( N = zero_zero_nat ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_equal_first_eq
% 4.71/5.12 thf(fact_5605_nth__equal__first__eq,axiom,
% 4.71/5.12 ! [X: set_nat_rat,Xs: list_set_nat_rat,N: nat] :
% 4.71/5.12 ( ~ ( member_set_nat_rat @ X @ ( set_set_nat_rat2 @ Xs ) )
% 4.71/5.12 => ( ( ord_less_eq_nat @ N @ ( size_s3959913991096427681at_rat @ Xs ) )
% 4.71/5.12 => ( ( ( nth_set_nat_rat @ ( cons_set_nat_rat @ X @ Xs ) @ N )
% 4.71/5.12 = X )
% 4.71/5.12 = ( N = zero_zero_nat ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_equal_first_eq
% 4.71/5.12 thf(fact_5606_nth__equal__first__eq,axiom,
% 4.71/5.12 ! [X: int,Xs: list_int,N: nat] :
% 4.71/5.12 ( ~ ( member_int @ X @ ( set_int2 @ Xs ) )
% 4.71/5.12 => ( ( ord_less_eq_nat @ N @ ( size_size_list_int @ Xs ) )
% 4.71/5.12 => ( ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
% 4.71/5.12 = X )
% 4.71/5.12 = ( N = zero_zero_nat ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_equal_first_eq
% 4.71/5.12 thf(fact_5607_nth__equal__first__eq,axiom,
% 4.71/5.12 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT,N: nat] :
% 4.71/5.12 ( ~ ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 4.71/5.12 => ( ( ord_less_eq_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.71/5.12 => ( ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ N )
% 4.71/5.12 = X )
% 4.71/5.12 = ( N = zero_zero_nat ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_equal_first_eq
% 4.71/5.12 thf(fact_5608_nth__equal__first__eq,axiom,
% 4.71/5.12 ! [X: nat,Xs: list_nat,N: nat] :
% 4.71/5.12 ( ~ ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 4.71/5.12 => ( ( ord_less_eq_nat @ N @ ( size_size_list_nat @ Xs ) )
% 4.71/5.12 => ( ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ N )
% 4.71/5.12 = X )
% 4.71/5.12 = ( N = zero_zero_nat ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_equal_first_eq
% 4.71/5.12 thf(fact_5609_nth__non__equal__first__eq,axiom,
% 4.71/5.12 ! [X: vEBT_VEBT,Y: vEBT_VEBT,Xs: list_VEBT_VEBT,N: nat] :
% 4.71/5.12 ( ( X != Y )
% 4.71/5.12 => ( ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ N )
% 4.71/5.12 = Y )
% 4.71/5.12 = ( ( ( nth_VEBT_VEBT @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) )
% 4.71/5.12 = Y )
% 4.71/5.12 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_non_equal_first_eq
% 4.71/5.12 thf(fact_5610_nth__non__equal__first__eq,axiom,
% 4.71/5.12 ! [X: int,Y: int,Xs: list_int,N: nat] :
% 4.71/5.12 ( ( X != Y )
% 4.71/5.12 => ( ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
% 4.71/5.12 = Y )
% 4.71/5.12 = ( ( ( nth_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) )
% 4.71/5.12 = Y )
% 4.71/5.12 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_non_equal_first_eq
% 4.71/5.12 thf(fact_5611_nth__non__equal__first__eq,axiom,
% 4.71/5.12 ! [X: nat,Y: nat,Xs: list_nat,N: nat] :
% 4.71/5.12 ( ( X != Y )
% 4.71/5.12 => ( ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ N )
% 4.71/5.12 = Y )
% 4.71/5.12 = ( ( ( nth_nat @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) )
% 4.71/5.12 = Y )
% 4.71/5.12 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % nth_non_equal_first_eq
% 4.71/5.12 thf(fact_5612_verit__le__mono__div__int,axiom,
% 4.71/5.12 ! [A2: int,B2: int,N: int] :
% 4.71/5.12 ( ( ord_less_int @ A2 @ B2 )
% 4.71/5.12 => ( ( ord_less_int @ zero_zero_int @ N )
% 4.71/5.12 => ( ord_less_eq_int
% 4.71/5.12 @ ( plus_plus_int @ ( divide_divide_int @ A2 @ N )
% 4.71/5.12 @ ( if_int
% 4.71/5.12 @ ( ( modulo_modulo_int @ B2 @ N )
% 4.71/5.12 = zero_zero_int )
% 4.71/5.12 @ one_one_int
% 4.71/5.12 @ zero_zero_int ) )
% 4.71/5.12 @ ( divide_divide_int @ B2 @ N ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % verit_le_mono_div_int
% 4.71/5.12 thf(fact_5613_split__neg__lemma,axiom,
% 4.71/5.12 ! [K: int,P: int > int > $o,N: int] :
% 4.71/5.12 ( ( ord_less_int @ K @ zero_zero_int )
% 4.71/5.12 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 4.71/5.12 = ( ! [I4: int,J3: int] :
% 4.71/5.12 ( ( ( ord_less_int @ K @ J3 )
% 4.71/5.12 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 4.71/5.12 & ( N
% 4.71/5.12 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 4.71/5.12 => ( P @ I4 @ J3 ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % split_neg_lemma
% 4.71/5.12 thf(fact_5614_verit__le__mono__div,axiom,
% 4.71/5.12 ! [A2: nat,B2: nat,N: nat] :
% 4.71/5.12 ( ( ord_less_nat @ A2 @ B2 )
% 4.71/5.12 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.12 => ( ord_less_eq_nat
% 4.71/5.12 @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N )
% 4.71/5.12 @ ( if_nat
% 4.71/5.12 @ ( ( modulo_modulo_nat @ B2 @ N )
% 4.71/5.12 = zero_zero_nat )
% 4.71/5.12 @ one_one_nat
% 4.71/5.12 @ zero_zero_nat ) )
% 4.71/5.12 @ ( divide_divide_nat @ B2 @ N ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % verit_le_mono_div
% 4.71/5.12 thf(fact_5615_norm__power__diff,axiom,
% 4.71/5.12 ! [Z: real,W2: real,M2: nat] :
% 4.71/5.12 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 4.71/5.12 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W2 ) @ one_one_real )
% 4.71/5.12 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( power_power_real @ Z @ M2 ) @ ( power_power_real @ W2 @ M2 ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Z @ W2 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % norm_power_diff
% 4.71/5.12 thf(fact_5616_norm__power__diff,axiom,
% 4.71/5.12 ! [Z: complex,W2: complex,M2: nat] :
% 4.71/5.12 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 4.71/5.12 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W2 ) @ one_one_real )
% 4.71/5.12 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( power_power_complex @ Z @ M2 ) @ ( power_power_complex @ W2 @ M2 ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Z @ W2 ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % norm_power_diff
% 4.71/5.12 thf(fact_5617_le__divide__eq__numeral_I2_J,axiom,
% 4.71/5.12 ! [W2: num,B: real,C: real] :
% 4.71/5.12 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ ( divide_divide_real @ B @ C ) )
% 4.71/5.12 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.12 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) @ B ) )
% 4.71/5.12 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.12 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.12 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 4.71/5.12 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.12 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % le_divide_eq_numeral(2)
% 4.71/5.12 thf(fact_5618_le__divide__eq__numeral_I2_J,axiom,
% 4.71/5.12 ! [W2: num,B: rat,C: rat] :
% 4.71/5.12 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ ( divide_divide_rat @ B @ C ) )
% 4.71/5.12 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.12 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 4.71/5.12 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.12 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.12 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 4.71/5.12 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.12 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % le_divide_eq_numeral(2)
% 4.71/5.12 thf(fact_5619_divide__le__eq__numeral_I2_J,axiom,
% 4.71/5.12 ! [B: real,C: real,W2: num] :
% 4.71/5.12 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 4.71/5.12 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.12 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 4.71/5.12 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.12 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.12 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) @ B ) )
% 4.71/5.12 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.12 => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % divide_le_eq_numeral(2)
% 4.71/5.12 thf(fact_5620_divide__le__eq__numeral_I2_J,axiom,
% 4.71/5.12 ! [B: rat,C: rat,W2: num] :
% 4.71/5.12 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 4.71/5.12 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.12 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 4.71/5.12 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.12 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.12 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 4.71/5.12 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.12 => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % divide_le_eq_numeral(2)
% 4.71/5.12 thf(fact_5621_Gcd__fin__0__iff,axiom,
% 4.71/5.12 ! [A2: set_nat] :
% 4.71/5.12 ( ( ( semiri4258706085729940814in_nat @ A2 )
% 4.71/5.12 = zero_zero_nat )
% 4.71/5.12 = ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
% 4.71/5.12 & ( finite_finite_nat @ A2 ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % Gcd_fin_0_iff
% 4.71/5.12 thf(fact_5622_Gcd__fin__0__iff,axiom,
% 4.71/5.12 ! [A2: set_int] :
% 4.71/5.12 ( ( ( semiri4256215615220890538in_int @ A2 )
% 4.71/5.12 = zero_zero_int )
% 4.71/5.12 = ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ zero_zero_int @ bot_bot_set_int ) )
% 4.71/5.12 & ( finite_finite_int @ A2 ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % Gcd_fin_0_iff
% 4.71/5.12 thf(fact_5623_count__list_Osimps_I2_J,axiom,
% 4.71/5.12 ! [X: int,Y: int,Xs: list_int] :
% 4.71/5.12 ( ( ( X = Y )
% 4.71/5.12 => ( ( count_list_int @ ( cons_int @ X @ Xs ) @ Y )
% 4.71/5.12 = ( plus_plus_nat @ ( count_list_int @ Xs @ Y ) @ one_one_nat ) ) )
% 4.71/5.12 & ( ( X != Y )
% 4.71/5.12 => ( ( count_list_int @ ( cons_int @ X @ Xs ) @ Y )
% 4.71/5.12 = ( count_list_int @ Xs @ Y ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % count_list.simps(2)
% 4.71/5.12 thf(fact_5624_count__list_Osimps_I2_J,axiom,
% 4.71/5.12 ! [X: nat,Y: nat,Xs: list_nat] :
% 4.71/5.12 ( ( ( X = Y )
% 4.71/5.12 => ( ( count_list_nat @ ( cons_nat @ X @ Xs ) @ Y )
% 4.71/5.12 = ( plus_plus_nat @ ( count_list_nat @ Xs @ Y ) @ one_one_nat ) ) )
% 4.71/5.12 & ( ( X != Y )
% 4.71/5.12 => ( ( count_list_nat @ ( cons_nat @ X @ Xs ) @ Y )
% 4.71/5.12 = ( count_list_nat @ Xs @ Y ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % count_list.simps(2)
% 4.71/5.12 thf(fact_5625_aset_I8_J,axiom,
% 4.71/5.12 ! [D4: int,A2: set_int,T: int] :
% 4.71/5.12 ( ( ord_less_int @ zero_zero_int @ D4 )
% 4.71/5.12 => ! [X2: int] :
% 4.71/5.12 ( ! [Xa3: int] :
% 4.71/5.12 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 4.71/5.12 => ! [Xb: int] :
% 4.71/5.12 ( ( member_int @ Xb @ A2 )
% 4.71/5.12 => ( X2
% 4.71/5.12 != ( minus_minus_int @ Xb @ Xa3 ) ) ) )
% 4.71/5.12 => ( ( ord_less_eq_int @ T @ X2 )
% 4.71/5.12 => ( ord_less_eq_int @ T @ ( plus_plus_int @ X2 @ D4 ) ) ) ) ) ).
% 4.71/5.12
% 4.71/5.12 % aset(8)
% 4.71/5.12 thf(fact_5626_numeral__eq__iff,axiom,
% 4.71/5.12 ! [M2: num,N: num] :
% 4.71/5.12 ( ( ( numeral_numeral_real @ M2 )
% 4.71/5.12 = ( numeral_numeral_real @ N ) )
% 4.71/5.12 = ( M2 = N ) ) ).
% 4.71/5.12
% 4.71/5.12 % numeral_eq_iff
% 4.71/5.12 thf(fact_5627_numeral__eq__iff,axiom,
% 4.71/5.12 ! [M2: num,N: num] :
% 4.71/5.12 ( ( ( numeral_numeral_nat @ M2 )
% 4.71/5.12 = ( numeral_numeral_nat @ N ) )
% 4.71/5.12 = ( M2 = N ) ) ).
% 4.71/5.12
% 4.71/5.12 % numeral_eq_iff
% 4.71/5.12 thf(fact_5628_numeral__eq__iff,axiom,
% 4.71/5.12 ! [M2: num,N: num] :
% 4.71/5.12 ( ( ( numeral_numeral_int @ M2 )
% 4.71/5.12 = ( numeral_numeral_int @ N ) )
% 4.71/5.12 = ( M2 = N ) ) ).
% 4.71/5.12
% 4.71/5.12 % numeral_eq_iff
% 4.71/5.12 thf(fact_5629_numeral__eq__iff,axiom,
% 4.71/5.12 ! [M2: num,N: num] :
% 4.71/5.12 ( ( ( numera1916890842035813515d_enat @ M2 )
% 4.71/5.12 = ( numera1916890842035813515d_enat @ N ) )
% 4.71/5.12 = ( M2 = N ) ) ).
% 4.71/5.12
% 4.71/5.12 % numeral_eq_iff
% 4.71/5.12 thf(fact_5630_numeral__eq__iff,axiom,
% 4.71/5.12 ! [M2: num,N: num] :
% 4.71/5.12 ( ( ( numera6620942414471956472nteger @ M2 )
% 4.71/5.12 = ( numera6620942414471956472nteger @ N ) )
% 4.71/5.12 = ( M2 = N ) ) ).
% 4.71/5.12
% 4.71/5.12 % numeral_eq_iff
% 4.71/5.12 thf(fact_5631_numeral__le__iff,axiom,
% 4.71/5.12 ! [M2: num,N: num] :
% 4.71/5.12 ( ( ord_less_eq_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N ) )
% 4.71/5.12 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 4.71/5.12
% 4.71/5.12 % numeral_le_iff
% 4.71/5.12 thf(fact_5632_numeral__le__iff,axiom,
% 4.71/5.12 ! [M2: num,N: num] :
% 4.71/5.12 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( numera1916890842035813515d_enat @ N ) )
% 4.71/5.12 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 4.71/5.12
% 4.71/5.12 % numeral_le_iff
% 4.71/5.12 thf(fact_5633_numeral__le__iff,axiom,
% 4.71/5.12 ! [M2: num,N: num] :
% 4.71/5.12 ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N ) )
% 4.71/5.12 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 4.71/5.12
% 4.71/5.12 % numeral_le_iff
% 4.71/5.12 thf(fact_5634_numeral__le__iff,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N ) )
% 4.71/5.13 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_le_iff
% 4.71/5.13 thf(fact_5635_numeral__le__iff,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 4.71/5.13 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_le_iff
% 4.71/5.13 thf(fact_5636_numeral__le__iff,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 4.71/5.13 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_le_iff
% 4.71/5.13 thf(fact_5637_numeral__less__iff,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( ord_less_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N ) )
% 4.71/5.13 = ( ord_less_num @ M2 @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_less_iff
% 4.71/5.13 thf(fact_5638_numeral__less__iff,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( ord_less_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N ) )
% 4.71/5.13 = ( ord_less_num @ M2 @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_less_iff
% 4.71/5.13 thf(fact_5639_numeral__less__iff,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 4.71/5.13 = ( ord_less_num @ M2 @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_less_iff
% 4.71/5.13 thf(fact_5640_numeral__less__iff,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( ord_less_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 4.71/5.13 = ( ord_less_num @ M2 @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_less_iff
% 4.71/5.13 thf(fact_5641_numeral__less__iff,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( numera1916890842035813515d_enat @ N ) )
% 4.71/5.13 = ( ord_less_num @ M2 @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_less_iff
% 4.71/5.13 thf(fact_5642_numeral__less__iff,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N ) )
% 4.71/5.13 = ( ord_less_num @ M2 @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_less_iff
% 4.71/5.13 thf(fact_5643_mult__numeral__left__semiring__numeral,axiom,
% 4.71/5.13 ! [V: num,W2: num,Z: rat] :
% 4.71/5.13 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ Z ) )
% 4.71/5.13 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W2 ) ) @ Z ) ) ).
% 4.71/5.13
% 4.71/5.13 % mult_numeral_left_semiring_numeral
% 4.71/5.13 thf(fact_5644_mult__numeral__left__semiring__numeral,axiom,
% 4.71/5.13 ! [V: num,W2: num,Z: real] :
% 4.71/5.13 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ Z ) )
% 4.71/5.13 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W2 ) ) @ Z ) ) ).
% 4.71/5.13
% 4.71/5.13 % mult_numeral_left_semiring_numeral
% 4.71/5.13 thf(fact_5645_mult__numeral__left__semiring__numeral,axiom,
% 4.71/5.13 ! [V: num,W2: num,Z: nat] :
% 4.71/5.13 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W2 ) @ Z ) )
% 4.71/5.13 = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W2 ) ) @ Z ) ) ).
% 4.71/5.13
% 4.71/5.13 % mult_numeral_left_semiring_numeral
% 4.71/5.13 thf(fact_5646_mult__numeral__left__semiring__numeral,axiom,
% 4.71/5.13 ! [V: num,W2: num,Z: int] :
% 4.71/5.13 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W2 ) @ Z ) )
% 4.71/5.13 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W2 ) ) @ Z ) ) ).
% 4.71/5.13
% 4.71/5.13 % mult_numeral_left_semiring_numeral
% 4.71/5.13 thf(fact_5647_mult__numeral__left__semiring__numeral,axiom,
% 4.71/5.13 ! [V: num,W2: num,Z: extended_enat] :
% 4.71/5.13 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ W2 ) @ Z ) )
% 4.71/5.13 = ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( times_times_num @ V @ W2 ) ) @ Z ) ) ).
% 4.71/5.13
% 4.71/5.13 % mult_numeral_left_semiring_numeral
% 4.71/5.13 thf(fact_5648_mult__numeral__left__semiring__numeral,axiom,
% 4.71/5.13 ! [V: num,W2: num,Z: code_integer] :
% 4.71/5.13 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W2 ) @ Z ) )
% 4.71/5.13 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W2 ) ) @ Z ) ) ).
% 4.71/5.13
% 4.71/5.13 % mult_numeral_left_semiring_numeral
% 4.71/5.13 thf(fact_5649_numeral__times__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( times_times_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N ) )
% 4.71/5.13 = ( numeral_numeral_rat @ ( times_times_num @ M2 @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_times_numeral
% 4.71/5.13 thf(fact_5650_numeral__times__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( times_times_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N ) )
% 4.71/5.13 = ( numeral_numeral_real @ ( times_times_num @ M2 @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_times_numeral
% 4.71/5.13 thf(fact_5651_numeral__times__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( times_times_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 4.71/5.13 = ( numeral_numeral_nat @ ( times_times_num @ M2 @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_times_numeral
% 4.71/5.13 thf(fact_5652_numeral__times__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( times_times_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 4.71/5.13 = ( numeral_numeral_int @ ( times_times_num @ M2 @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_times_numeral
% 4.71/5.13 thf(fact_5653_numeral__times__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( numera1916890842035813515d_enat @ N ) )
% 4.71/5.13 = ( numera1916890842035813515d_enat @ ( times_times_num @ M2 @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_times_numeral
% 4.71/5.13 thf(fact_5654_numeral__times__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N ) )
% 4.71/5.13 = ( numera6620942414471956472nteger @ ( times_times_num @ M2 @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_times_numeral
% 4.71/5.13 thf(fact_5655_add__numeral__left,axiom,
% 4.71/5.13 ! [V: num,W2: num,Z: rat] :
% 4.71/5.13 ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W2 ) @ Z ) )
% 4.71/5.13 = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W2 ) ) @ Z ) ) ).
% 4.71/5.13
% 4.71/5.13 % add_numeral_left
% 4.71/5.13 thf(fact_5656_add__numeral__left,axiom,
% 4.71/5.13 ! [V: num,W2: num,Z: real] :
% 4.71/5.13 ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W2 ) @ Z ) )
% 4.71/5.13 = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W2 ) ) @ Z ) ) ).
% 4.71/5.13
% 4.71/5.13 % add_numeral_left
% 4.71/5.13 thf(fact_5657_add__numeral__left,axiom,
% 4.71/5.13 ! [V: num,W2: num,Z: nat] :
% 4.71/5.13 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W2 ) @ Z ) )
% 4.71/5.13 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W2 ) ) @ Z ) ) ).
% 4.71/5.13
% 4.71/5.13 % add_numeral_left
% 4.71/5.13 thf(fact_5658_add__numeral__left,axiom,
% 4.71/5.13 ! [V: num,W2: num,Z: int] :
% 4.71/5.13 ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W2 ) @ Z ) )
% 4.71/5.13 = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W2 ) ) @ Z ) ) ).
% 4.71/5.13
% 4.71/5.13 % add_numeral_left
% 4.71/5.13 thf(fact_5659_add__numeral__left,axiom,
% 4.71/5.13 ! [V: num,W2: num,Z: extended_enat] :
% 4.71/5.13 ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ V ) @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ W2 ) @ Z ) )
% 4.71/5.13 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ ( plus_plus_num @ V @ W2 ) ) @ Z ) ) ).
% 4.71/5.13
% 4.71/5.13 % add_numeral_left
% 4.71/5.13 thf(fact_5660_add__numeral__left,axiom,
% 4.71/5.13 ! [V: num,W2: num,Z: code_integer] :
% 4.71/5.13 ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ V ) @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ W2 ) @ Z ) )
% 4.71/5.13 = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W2 ) ) @ Z ) ) ).
% 4.71/5.13
% 4.71/5.13 % add_numeral_left
% 4.71/5.13 thf(fact_5661_numeral__plus__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N ) )
% 4.71/5.13 = ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_plus_numeral
% 4.71/5.13 thf(fact_5662_numeral__plus__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( plus_plus_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N ) )
% 4.71/5.13 = ( numeral_numeral_real @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_plus_numeral
% 4.71/5.13 thf(fact_5663_numeral__plus__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 4.71/5.13 = ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_plus_numeral
% 4.71/5.13 thf(fact_5664_numeral__plus__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 4.71/5.13 = ( numeral_numeral_int @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_plus_numeral
% 4.71/5.13 thf(fact_5665_numeral__plus__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( numera1916890842035813515d_enat @ N ) )
% 4.71/5.13 = ( numera1916890842035813515d_enat @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_plus_numeral
% 4.71/5.13 thf(fact_5666_numeral__plus__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N ) )
% 4.71/5.13 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_plus_numeral
% 4.71/5.13 thf(fact_5667_power__zero__numeral,axiom,
% 4.71/5.13 ! [K: num] :
% 4.71/5.13 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 4.71/5.13 = zero_zero_rat ) ).
% 4.71/5.13
% 4.71/5.13 % power_zero_numeral
% 4.71/5.13 thf(fact_5668_power__zero__numeral,axiom,
% 4.71/5.13 ! [K: num] :
% 4.71/5.13 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 4.71/5.13 = zero_zero_int ) ).
% 4.71/5.13
% 4.71/5.13 % power_zero_numeral
% 4.71/5.13 thf(fact_5669_power__zero__numeral,axiom,
% 4.71/5.13 ! [K: num] :
% 4.71/5.13 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 4.71/5.13 = zero_zero_nat ) ).
% 4.71/5.13
% 4.71/5.13 % power_zero_numeral
% 4.71/5.13 thf(fact_5670_power__zero__numeral,axiom,
% 4.71/5.13 ! [K: num] :
% 4.71/5.13 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 4.71/5.13 = zero_zero_real ) ).
% 4.71/5.13
% 4.71/5.13 % power_zero_numeral
% 4.71/5.13 thf(fact_5671_power__zero__numeral,axiom,
% 4.71/5.13 ! [K: num] :
% 4.71/5.13 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 4.71/5.13 = zero_zero_complex ) ).
% 4.71/5.13
% 4.71/5.13 % power_zero_numeral
% 4.71/5.13 thf(fact_5672_neg__numeral__eq__iff,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) )
% 4.71/5.13 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 4.71/5.13 = ( M2 = N ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_eq_iff
% 4.71/5.13 thf(fact_5673_neg__numeral__eq__iff,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) )
% 4.71/5.13 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 4.71/5.13 = ( M2 = N ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_eq_iff
% 4.71/5.13 thf(fact_5674_neg__numeral__eq__iff,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) )
% 4.71/5.13 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 4.71/5.13 = ( M2 = N ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_eq_iff
% 4.71/5.13 thf(fact_5675_neg__numeral__eq__iff,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) )
% 4.71/5.13 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 4.71/5.13 = ( M2 = N ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_eq_iff
% 4.71/5.13 thf(fact_5676_neg__numeral__eq__iff,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) )
% 4.71/5.13 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 4.71/5.13 = ( M2 = N ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_eq_iff
% 4.71/5.13 thf(fact_5677_of__nat__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N ) )
% 4.71/5.13 = ( numeral_numeral_nat @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_nat_numeral
% 4.71/5.13 thf(fact_5678_of__nat__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( semiri4216267220026989637d_enat @ ( numeral_numeral_nat @ N ) )
% 4.71/5.13 = ( numera1916890842035813515d_enat @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_nat_numeral
% 4.71/5.13 thf(fact_5679_of__nat__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( semiri4939895301339042750nteger @ ( numeral_numeral_nat @ N ) )
% 4.71/5.13 = ( numera6620942414471956472nteger @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_nat_numeral
% 4.71/5.13 thf(fact_5680_of__nat__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 4.71/5.13 = ( numeral_numeral_int @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_nat_numeral
% 4.71/5.13 thf(fact_5681_of__nat__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N ) )
% 4.71/5.13 = ( numeral_numeral_real @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_nat_numeral
% 4.71/5.13 thf(fact_5682_of__nat__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( semiri681578069525770553at_rat @ ( numeral_numeral_nat @ N ) )
% 4.71/5.13 = ( numeral_numeral_rat @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_nat_numeral
% 4.71/5.13 thf(fact_5683_Icc__eq__Icc,axiom,
% 4.71/5.13 ! [L: set_int,H: set_int,L2: set_int,H2: set_int] :
% 4.71/5.13 ( ( ( set_or370866239135849197et_int @ L @ H )
% 4.71/5.13 = ( set_or370866239135849197et_int @ L2 @ H2 ) )
% 4.71/5.13 = ( ( ( L = L2 )
% 4.71/5.13 & ( H = H2 ) )
% 4.71/5.13 | ( ~ ( ord_less_eq_set_int @ L @ H )
% 4.71/5.13 & ~ ( ord_less_eq_set_int @ L2 @ H2 ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % Icc_eq_Icc
% 4.71/5.13 thf(fact_5684_Icc__eq__Icc,axiom,
% 4.71/5.13 ! [L: rat,H: rat,L2: rat,H2: rat] :
% 4.71/5.13 ( ( ( set_or633870826150836451st_rat @ L @ H )
% 4.71/5.13 = ( set_or633870826150836451st_rat @ L2 @ H2 ) )
% 4.71/5.13 = ( ( ( L = L2 )
% 4.71/5.13 & ( H = H2 ) )
% 4.71/5.13 | ( ~ ( ord_less_eq_rat @ L @ H )
% 4.71/5.13 & ~ ( ord_less_eq_rat @ L2 @ H2 ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % Icc_eq_Icc
% 4.71/5.13 thf(fact_5685_Icc__eq__Icc,axiom,
% 4.71/5.13 ! [L: num,H: num,L2: num,H2: num] :
% 4.71/5.13 ( ( ( set_or7049704709247886629st_num @ L @ H )
% 4.71/5.13 = ( set_or7049704709247886629st_num @ L2 @ H2 ) )
% 4.71/5.13 = ( ( ( L = L2 )
% 4.71/5.13 & ( H = H2 ) )
% 4.71/5.13 | ( ~ ( ord_less_eq_num @ L @ H )
% 4.71/5.13 & ~ ( ord_less_eq_num @ L2 @ H2 ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % Icc_eq_Icc
% 4.71/5.13 thf(fact_5686_Icc__eq__Icc,axiom,
% 4.71/5.13 ! [L: int,H: int,L2: int,H2: int] :
% 4.71/5.13 ( ( ( set_or1266510415728281911st_int @ L @ H )
% 4.71/5.13 = ( set_or1266510415728281911st_int @ L2 @ H2 ) )
% 4.71/5.13 = ( ( ( L = L2 )
% 4.71/5.13 & ( H = H2 ) )
% 4.71/5.13 | ( ~ ( ord_less_eq_int @ L @ H )
% 4.71/5.13 & ~ ( ord_less_eq_int @ L2 @ H2 ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % Icc_eq_Icc
% 4.71/5.13 thf(fact_5687_Icc__eq__Icc,axiom,
% 4.71/5.13 ! [L: nat,H: nat,L2: nat,H2: nat] :
% 4.71/5.13 ( ( ( set_or1269000886237332187st_nat @ L @ H )
% 4.71/5.13 = ( set_or1269000886237332187st_nat @ L2 @ H2 ) )
% 4.71/5.13 = ( ( ( L = L2 )
% 4.71/5.13 & ( H = H2 ) )
% 4.71/5.13 | ( ~ ( ord_less_eq_nat @ L @ H )
% 4.71/5.13 & ~ ( ord_less_eq_nat @ L2 @ H2 ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % Icc_eq_Icc
% 4.71/5.13 thf(fact_5688_Icc__eq__Icc,axiom,
% 4.71/5.13 ! [L: real,H: real,L2: real,H2: real] :
% 4.71/5.13 ( ( ( set_or1222579329274155063t_real @ L @ H )
% 4.71/5.13 = ( set_or1222579329274155063t_real @ L2 @ H2 ) )
% 4.71/5.13 = ( ( ( L = L2 )
% 4.71/5.13 & ( H = H2 ) )
% 4.71/5.13 | ( ~ ( ord_less_eq_real @ L @ H )
% 4.71/5.13 & ~ ( ord_less_eq_real @ L2 @ H2 ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % Icc_eq_Icc
% 4.71/5.13 thf(fact_5689_atLeastAtMost__iff,axiom,
% 4.71/5.13 ! [I: $o,L: $o,U: $o] :
% 4.71/5.13 ( ( member_o @ I @ ( set_or8904488021354931149Most_o @ L @ U ) )
% 4.71/5.13 = ( ( ord_less_eq_o @ L @ I )
% 4.71/5.13 & ( ord_less_eq_o @ I @ U ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastAtMost_iff
% 4.71/5.13 thf(fact_5690_atLeastAtMost__iff,axiom,
% 4.71/5.13 ! [I: set_nat,L: set_nat,U: set_nat] :
% 4.71/5.13 ( ( member_set_nat @ I @ ( set_or4548717258645045905et_nat @ L @ U ) )
% 4.71/5.13 = ( ( ord_less_eq_set_nat @ L @ I )
% 4.71/5.13 & ( ord_less_eq_set_nat @ I @ U ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastAtMost_iff
% 4.71/5.13 thf(fact_5691_atLeastAtMost__iff,axiom,
% 4.71/5.13 ! [I: set_nat_rat,L: set_nat_rat,U: set_nat_rat] :
% 4.71/5.13 ( ( member_set_nat_rat @ I @ ( set_or5795412311047298440at_rat @ L @ U ) )
% 4.71/5.13 = ( ( ord_le2679597024174929757at_rat @ L @ I )
% 4.71/5.13 & ( ord_le2679597024174929757at_rat @ I @ U ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastAtMost_iff
% 4.71/5.13 thf(fact_5692_atLeastAtMost__iff,axiom,
% 4.71/5.13 ! [I: set_int,L: set_int,U: set_int] :
% 4.71/5.13 ( ( member_set_int @ I @ ( set_or370866239135849197et_int @ L @ U ) )
% 4.71/5.13 = ( ( ord_less_eq_set_int @ L @ I )
% 4.71/5.13 & ( ord_less_eq_set_int @ I @ U ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastAtMost_iff
% 4.71/5.13 thf(fact_5693_atLeastAtMost__iff,axiom,
% 4.71/5.13 ! [I: rat,L: rat,U: rat] :
% 4.71/5.13 ( ( member_rat @ I @ ( set_or633870826150836451st_rat @ L @ U ) )
% 4.71/5.13 = ( ( ord_less_eq_rat @ L @ I )
% 4.71/5.13 & ( ord_less_eq_rat @ I @ U ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastAtMost_iff
% 4.71/5.13 thf(fact_5694_atLeastAtMost__iff,axiom,
% 4.71/5.13 ! [I: num,L: num,U: num] :
% 4.71/5.13 ( ( member_num @ I @ ( set_or7049704709247886629st_num @ L @ U ) )
% 4.71/5.13 = ( ( ord_less_eq_num @ L @ I )
% 4.71/5.13 & ( ord_less_eq_num @ I @ U ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastAtMost_iff
% 4.71/5.13 thf(fact_5695_atLeastAtMost__iff,axiom,
% 4.71/5.13 ! [I: int,L: int,U: int] :
% 4.71/5.13 ( ( member_int @ I @ ( set_or1266510415728281911st_int @ L @ U ) )
% 4.71/5.13 = ( ( ord_less_eq_int @ L @ I )
% 4.71/5.13 & ( ord_less_eq_int @ I @ U ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastAtMost_iff
% 4.71/5.13 thf(fact_5696_atLeastAtMost__iff,axiom,
% 4.71/5.13 ! [I: nat,L: nat,U: nat] :
% 4.71/5.13 ( ( member_nat @ I @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 4.71/5.13 = ( ( ord_less_eq_nat @ L @ I )
% 4.71/5.13 & ( ord_less_eq_nat @ I @ U ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastAtMost_iff
% 4.71/5.13 thf(fact_5697_atLeastAtMost__iff,axiom,
% 4.71/5.13 ! [I: real,L: real,U: real] :
% 4.71/5.13 ( ( member_real @ I @ ( set_or1222579329274155063t_real @ L @ U ) )
% 4.71/5.13 = ( ( ord_less_eq_real @ L @ I )
% 4.71/5.13 & ( ord_less_eq_real @ I @ U ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastAtMost_iff
% 4.71/5.13 thf(fact_5698_abs__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( abs_abs_rat @ ( numeral_numeral_rat @ N ) )
% 4.71/5.13 = ( numeral_numeral_rat @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % abs_numeral
% 4.71/5.13 thf(fact_5699_abs__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( abs_abs_real @ ( numeral_numeral_real @ N ) )
% 4.71/5.13 = ( numeral_numeral_real @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % abs_numeral
% 4.71/5.13 thf(fact_5700_abs__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( abs_abs_int @ ( numeral_numeral_int @ N ) )
% 4.71/5.13 = ( numeral_numeral_int @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % abs_numeral
% 4.71/5.13 thf(fact_5701_abs__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 4.71/5.13 = ( numera6620942414471956472nteger @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % abs_numeral
% 4.71/5.13 thf(fact_5702_mod__less,axiom,
% 4.71/5.13 ! [M2: nat,N: nat] :
% 4.71/5.13 ( ( ord_less_nat @ M2 @ N )
% 4.71/5.13 => ( ( modulo_modulo_nat @ M2 @ N )
% 4.71/5.13 = M2 ) ) ).
% 4.71/5.13
% 4.71/5.13 % mod_less
% 4.71/5.13 thf(fact_5703_finite__atLeastAtMost__int,axiom,
% 4.71/5.13 ! [L: int,U: int] : ( finite_finite_int @ ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 4.71/5.13
% 4.71/5.13 % finite_atLeastAtMost_int
% 4.71/5.13 thf(fact_5704_neg__numeral__le__iff,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 4.71/5.13 = ( ord_less_eq_num @ N @ M2 ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_le_iff
% 4.71/5.13 thf(fact_5705_neg__numeral__le__iff,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 4.71/5.13 = ( ord_less_eq_num @ N @ M2 ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_le_iff
% 4.71/5.13 thf(fact_5706_neg__numeral__le__iff,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 4.71/5.13 = ( ord_less_eq_num @ N @ M2 ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_le_iff
% 4.71/5.13 thf(fact_5707_neg__numeral__le__iff,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 4.71/5.13 = ( ord_less_eq_num @ N @ M2 ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_le_iff
% 4.71/5.13 thf(fact_5708_distrib__right__numeral,axiom,
% 4.71/5.13 ! [A: rat,B: rat,V: num] :
% 4.71/5.13 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 4.71/5.13 = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % distrib_right_numeral
% 4.71/5.13 thf(fact_5709_distrib__right__numeral,axiom,
% 4.71/5.13 ! [A: real,B: real,V: num] :
% 4.71/5.13 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 4.71/5.13 = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % distrib_right_numeral
% 4.71/5.13 thf(fact_5710_distrib__right__numeral,axiom,
% 4.71/5.13 ! [A: nat,B: nat,V: num] :
% 4.71/5.13 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 4.71/5.13 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % distrib_right_numeral
% 4.71/5.13 thf(fact_5711_distrib__right__numeral,axiom,
% 4.71/5.13 ! [A: int,B: int,V: num] :
% 4.71/5.13 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 4.71/5.13 = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % distrib_right_numeral
% 4.71/5.13 thf(fact_5712_distrib__right__numeral,axiom,
% 4.71/5.13 ! [A: extended_enat,B: extended_enat,V: num] :
% 4.71/5.13 ( ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ A @ B ) @ ( numera1916890842035813515d_enat @ V ) )
% 4.71/5.13 = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ A @ ( numera1916890842035813515d_enat @ V ) ) @ ( times_7803423173614009249d_enat @ B @ ( numera1916890842035813515d_enat @ V ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % distrib_right_numeral
% 4.71/5.13 thf(fact_5713_distrib__right__numeral,axiom,
% 4.71/5.13 ! [A: code_integer,B: code_integer,V: num] :
% 4.71/5.13 ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( numera6620942414471956472nteger @ V ) )
% 4.71/5.13 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ B @ ( numera6620942414471956472nteger @ V ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % distrib_right_numeral
% 4.71/5.13 thf(fact_5714_distrib__left__numeral,axiom,
% 4.71/5.13 ! [V: num,B: rat,C: rat] :
% 4.71/5.13 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 4.71/5.13 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % distrib_left_numeral
% 4.71/5.13 thf(fact_5715_distrib__left__numeral,axiom,
% 4.71/5.13 ! [V: num,B: real,C: real] :
% 4.71/5.13 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 4.71/5.13 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % distrib_left_numeral
% 4.71/5.13 thf(fact_5716_distrib__left__numeral,axiom,
% 4.71/5.13 ! [V: num,B: nat,C: nat] :
% 4.71/5.13 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 4.71/5.13 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % distrib_left_numeral
% 4.71/5.13 thf(fact_5717_distrib__left__numeral,axiom,
% 4.71/5.13 ! [V: num,B: int,C: int] :
% 4.71/5.13 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 4.71/5.13 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % distrib_left_numeral
% 4.71/5.13 thf(fact_5718_distrib__left__numeral,axiom,
% 4.71/5.13 ! [V: num,B: extended_enat,C: extended_enat] :
% 4.71/5.13 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ ( plus_p3455044024723400733d_enat @ B @ C ) )
% 4.71/5.13 = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ B ) @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ C ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % distrib_left_numeral
% 4.71/5.13 thf(fact_5719_distrib__left__numeral,axiom,
% 4.71/5.13 ! [V: num,B: code_integer,C: code_integer] :
% 4.71/5.13 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 4.71/5.13 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ B ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ C ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % distrib_left_numeral
% 4.71/5.13 thf(fact_5720_neg__numeral__less__iff,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 4.71/5.13 = ( ord_less_num @ N @ M2 ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_less_iff
% 4.71/5.13 thf(fact_5721_neg__numeral__less__iff,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 4.71/5.13 = ( ord_less_num @ N @ M2 ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_less_iff
% 4.71/5.13 thf(fact_5722_neg__numeral__less__iff,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 4.71/5.13 = ( ord_less_num @ N @ M2 ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_less_iff
% 4.71/5.13 thf(fact_5723_neg__numeral__less__iff,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 4.71/5.13 = ( ord_less_num @ N @ M2 ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_less_iff
% 4.71/5.13 thf(fact_5724_right__diff__distrib__numeral,axiom,
% 4.71/5.13 ! [V: num,B: rat,C: rat] :
% 4.71/5.13 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 4.71/5.13 = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % right_diff_distrib_numeral
% 4.71/5.13 thf(fact_5725_right__diff__distrib__numeral,axiom,
% 4.71/5.13 ! [V: num,B: real,C: real] :
% 4.71/5.13 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 4.71/5.13 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % right_diff_distrib_numeral
% 4.71/5.13 thf(fact_5726_right__diff__distrib__numeral,axiom,
% 4.71/5.13 ! [V: num,B: int,C: int] :
% 4.71/5.13 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 4.71/5.13 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % right_diff_distrib_numeral
% 4.71/5.13 thf(fact_5727_right__diff__distrib__numeral,axiom,
% 4.71/5.13 ! [V: num,B: code_integer,C: code_integer] :
% 4.71/5.13 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( minus_8373710615458151222nteger @ B @ C ) )
% 4.71/5.13 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ B ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ C ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % right_diff_distrib_numeral
% 4.71/5.13 thf(fact_5728_left__diff__distrib__numeral,axiom,
% 4.71/5.13 ! [A: rat,B: rat,V: num] :
% 4.71/5.13 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 4.71/5.13 = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % left_diff_distrib_numeral
% 4.71/5.13 thf(fact_5729_left__diff__distrib__numeral,axiom,
% 4.71/5.13 ! [A: real,B: real,V: num] :
% 4.71/5.13 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 4.71/5.13 = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % left_diff_distrib_numeral
% 4.71/5.13 thf(fact_5730_left__diff__distrib__numeral,axiom,
% 4.71/5.13 ! [A: int,B: int,V: num] :
% 4.71/5.13 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 4.71/5.13 = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % left_diff_distrib_numeral
% 4.71/5.13 thf(fact_5731_left__diff__distrib__numeral,axiom,
% 4.71/5.13 ! [A: code_integer,B: code_integer,V: num] :
% 4.71/5.13 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ ( numera6620942414471956472nteger @ V ) )
% 4.71/5.13 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ B @ ( numera6620942414471956472nteger @ V ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % left_diff_distrib_numeral
% 4.71/5.13 thf(fact_5732_mult__neg__numeral__simps_I1_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 4.71/5.13 = ( numera6620942414471956472nteger @ ( times_times_num @ M2 @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % mult_neg_numeral_simps(1)
% 4.71/5.13 thf(fact_5733_mult__neg__numeral__simps_I1_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 4.71/5.13 = ( numeral_numeral_int @ ( times_times_num @ M2 @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % mult_neg_numeral_simps(1)
% 4.71/5.13 thf(fact_5734_mult__neg__numeral__simps_I1_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 4.71/5.13 = ( numeral_numeral_real @ ( times_times_num @ M2 @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % mult_neg_numeral_simps(1)
% 4.71/5.13 thf(fact_5735_mult__neg__numeral__simps_I1_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 4.71/5.13 = ( numeral_numeral_rat @ ( times_times_num @ M2 @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % mult_neg_numeral_simps(1)
% 4.71/5.13 thf(fact_5736_mult__neg__numeral__simps_I1_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 4.71/5.13 = ( numera6690914467698888265omplex @ ( times_times_num @ M2 @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % mult_neg_numeral_simps(1)
% 4.71/5.13 thf(fact_5737_mult__neg__numeral__simps_I2_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( numera6620942414471956472nteger @ N ) )
% 4.71/5.13 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % mult_neg_numeral_simps(2)
% 4.71/5.13 thf(fact_5738_mult__neg__numeral__simps_I2_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 4.71/5.13 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % mult_neg_numeral_simps(2)
% 4.71/5.13 thf(fact_5739_mult__neg__numeral__simps_I2_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( numeral_numeral_real @ N ) )
% 4.71/5.13 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % mult_neg_numeral_simps(2)
% 4.71/5.13 thf(fact_5740_mult__neg__numeral__simps_I2_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( numeral_numeral_rat @ N ) )
% 4.71/5.13 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % mult_neg_numeral_simps(2)
% 4.71/5.13 thf(fact_5741_mult__neg__numeral__simps_I2_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) ) @ ( numera6690914467698888265omplex @ N ) )
% 4.71/5.13 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % mult_neg_numeral_simps(2)
% 4.71/5.13 thf(fact_5742_mult__neg__numeral__simps_I3_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 4.71/5.13 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % mult_neg_numeral_simps(3)
% 4.71/5.13 thf(fact_5743_mult__neg__numeral__simps_I3_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( times_times_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 4.71/5.13 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % mult_neg_numeral_simps(3)
% 4.71/5.13 thf(fact_5744_mult__neg__numeral__simps_I3_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( times_times_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 4.71/5.13 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % mult_neg_numeral_simps(3)
% 4.71/5.13 thf(fact_5745_mult__neg__numeral__simps_I3_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( times_times_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 4.71/5.13 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % mult_neg_numeral_simps(3)
% 4.71/5.13 thf(fact_5746_mult__neg__numeral__simps_I3_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M2 ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 4.71/5.13 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % mult_neg_numeral_simps(3)
% 4.71/5.13 thf(fact_5747_add__neg__numeral__simps_I3_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 4.71/5.13 = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % add_neg_numeral_simps(3)
% 4.71/5.13 thf(fact_5748_add__neg__numeral__simps_I3_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 4.71/5.13 = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % add_neg_numeral_simps(3)
% 4.71/5.13 thf(fact_5749_add__neg__numeral__simps_I3_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 4.71/5.13 = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % add_neg_numeral_simps(3)
% 4.71/5.13 thf(fact_5750_add__neg__numeral__simps_I3_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 4.71/5.13 = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % add_neg_numeral_simps(3)
% 4.71/5.13 thf(fact_5751_add__neg__numeral__simps_I3_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 4.71/5.13 = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M2 ) @ ( numera6690914467698888265omplex @ N ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % add_neg_numeral_simps(3)
% 4.71/5.13 thf(fact_5752_diff__numeral__simps_I2_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 4.71/5.13 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % diff_numeral_simps(2)
% 4.71/5.13 thf(fact_5753_diff__numeral__simps_I2_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 4.71/5.13 = ( numeral_numeral_int @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % diff_numeral_simps(2)
% 4.71/5.13 thf(fact_5754_diff__numeral__simps_I2_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( minus_minus_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 4.71/5.13 = ( numeral_numeral_real @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % diff_numeral_simps(2)
% 4.71/5.13 thf(fact_5755_diff__numeral__simps_I2_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 4.71/5.13 = ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % diff_numeral_simps(2)
% 4.71/5.13 thf(fact_5756_diff__numeral__simps_I2_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M2 ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 4.71/5.13 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % diff_numeral_simps(2)
% 4.71/5.13 thf(fact_5757_diff__numeral__simps_I3_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( numera6620942414471956472nteger @ N ) )
% 4.71/5.13 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % diff_numeral_simps(3)
% 4.71/5.13 thf(fact_5758_diff__numeral__simps_I3_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 4.71/5.13 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % diff_numeral_simps(3)
% 4.71/5.13 thf(fact_5759_diff__numeral__simps_I3_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( numeral_numeral_real @ N ) )
% 4.71/5.13 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % diff_numeral_simps(3)
% 4.71/5.13 thf(fact_5760_diff__numeral__simps_I3_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( numeral_numeral_rat @ N ) )
% 4.71/5.13 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % diff_numeral_simps(3)
% 4.71/5.13 thf(fact_5761_diff__numeral__simps_I3_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) ) @ ( numera6690914467698888265omplex @ N ) )
% 4.71/5.13 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % diff_numeral_simps(3)
% 4.71/5.13 thf(fact_5762_abs__neg__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 4.71/5.13 = ( numera6620942414471956472nteger @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % abs_neg_numeral
% 4.71/5.13 thf(fact_5763_abs__neg__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 4.71/5.13 = ( numeral_numeral_int @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % abs_neg_numeral
% 4.71/5.13 thf(fact_5764_abs__neg__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 4.71/5.13 = ( numeral_numeral_real @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % abs_neg_numeral
% 4.71/5.13 thf(fact_5765_abs__neg__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 4.71/5.13 = ( numeral_numeral_rat @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % abs_neg_numeral
% 4.71/5.13 thf(fact_5766_atLeastatMost__empty__iff,axiom,
% 4.71/5.13 ! [A: $o,B: $o] :
% 4.71/5.13 ( ( ( set_or8904488021354931149Most_o @ A @ B )
% 4.71/5.13 = bot_bot_set_o )
% 4.71/5.13 = ( ~ ( ord_less_eq_o @ A @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_empty_iff
% 4.71/5.13 thf(fact_5767_atLeastatMost__empty__iff,axiom,
% 4.71/5.13 ! [A: set_int,B: set_int] :
% 4.71/5.13 ( ( ( set_or370866239135849197et_int @ A @ B )
% 4.71/5.13 = bot_bot_set_set_int )
% 4.71/5.13 = ( ~ ( ord_less_eq_set_int @ A @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_empty_iff
% 4.71/5.13 thf(fact_5768_atLeastatMost__empty__iff,axiom,
% 4.71/5.13 ! [A: rat,B: rat] :
% 4.71/5.13 ( ( ( set_or633870826150836451st_rat @ A @ B )
% 4.71/5.13 = bot_bot_set_rat )
% 4.71/5.13 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_empty_iff
% 4.71/5.13 thf(fact_5769_atLeastatMost__empty__iff,axiom,
% 4.71/5.13 ! [A: num,B: num] :
% 4.71/5.13 ( ( ( set_or7049704709247886629st_num @ A @ B )
% 4.71/5.13 = bot_bot_set_num )
% 4.71/5.13 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_empty_iff
% 4.71/5.13 thf(fact_5770_atLeastatMost__empty__iff,axiom,
% 4.71/5.13 ! [A: int,B: int] :
% 4.71/5.13 ( ( ( set_or1266510415728281911st_int @ A @ B )
% 4.71/5.13 = bot_bot_set_int )
% 4.71/5.13 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_empty_iff
% 4.71/5.13 thf(fact_5771_atLeastatMost__empty__iff,axiom,
% 4.71/5.13 ! [A: nat,B: nat] :
% 4.71/5.13 ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 4.71/5.13 = bot_bot_set_nat )
% 4.71/5.13 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_empty_iff
% 4.71/5.13 thf(fact_5772_atLeastatMost__empty__iff,axiom,
% 4.71/5.13 ! [A: real,B: real] :
% 4.71/5.13 ( ( ( set_or1222579329274155063t_real @ A @ B )
% 4.71/5.13 = bot_bot_set_real )
% 4.71/5.13 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_empty_iff
% 4.71/5.13 thf(fact_5773_atLeastatMost__empty__iff2,axiom,
% 4.71/5.13 ! [A: $o,B: $o] :
% 4.71/5.13 ( ( bot_bot_set_o
% 4.71/5.13 = ( set_or8904488021354931149Most_o @ A @ B ) )
% 4.71/5.13 = ( ~ ( ord_less_eq_o @ A @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_empty_iff2
% 4.71/5.13 thf(fact_5774_atLeastatMost__empty__iff2,axiom,
% 4.71/5.13 ! [A: set_int,B: set_int] :
% 4.71/5.13 ( ( bot_bot_set_set_int
% 4.71/5.13 = ( set_or370866239135849197et_int @ A @ B ) )
% 4.71/5.13 = ( ~ ( ord_less_eq_set_int @ A @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_empty_iff2
% 4.71/5.13 thf(fact_5775_atLeastatMost__empty__iff2,axiom,
% 4.71/5.13 ! [A: rat,B: rat] :
% 4.71/5.13 ( ( bot_bot_set_rat
% 4.71/5.13 = ( set_or633870826150836451st_rat @ A @ B ) )
% 4.71/5.13 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_empty_iff2
% 4.71/5.13 thf(fact_5776_atLeastatMost__empty__iff2,axiom,
% 4.71/5.13 ! [A: num,B: num] :
% 4.71/5.13 ( ( bot_bot_set_num
% 4.71/5.13 = ( set_or7049704709247886629st_num @ A @ B ) )
% 4.71/5.13 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_empty_iff2
% 4.71/5.13 thf(fact_5777_atLeastatMost__empty__iff2,axiom,
% 4.71/5.13 ! [A: int,B: int] :
% 4.71/5.13 ( ( bot_bot_set_int
% 4.71/5.13 = ( set_or1266510415728281911st_int @ A @ B ) )
% 4.71/5.13 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_empty_iff2
% 4.71/5.13 thf(fact_5778_atLeastatMost__empty__iff2,axiom,
% 4.71/5.13 ! [A: nat,B: nat] :
% 4.71/5.13 ( ( bot_bot_set_nat
% 4.71/5.13 = ( set_or1269000886237332187st_nat @ A @ B ) )
% 4.71/5.13 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_empty_iff2
% 4.71/5.13 thf(fact_5779_atLeastatMost__empty__iff2,axiom,
% 4.71/5.13 ! [A: real,B: real] :
% 4.71/5.13 ( ( bot_bot_set_real
% 4.71/5.13 = ( set_or1222579329274155063t_real @ A @ B ) )
% 4.71/5.13 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_empty_iff2
% 4.71/5.13 thf(fact_5780_atLeastatMost__subset__iff,axiom,
% 4.71/5.13 ! [A: set_int,B: set_int,C: set_int,D: set_int] :
% 4.71/5.13 ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 4.71/5.13 = ( ~ ( ord_less_eq_set_int @ A @ B )
% 4.71/5.13 | ( ( ord_less_eq_set_int @ C @ A )
% 4.71/5.13 & ( ord_less_eq_set_int @ B @ D ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_subset_iff
% 4.71/5.13 thf(fact_5781_atLeastatMost__subset__iff,axiom,
% 4.71/5.13 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.71/5.13 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 4.71/5.13 = ( ~ ( ord_less_eq_rat @ A @ B )
% 4.71/5.13 | ( ( ord_less_eq_rat @ C @ A )
% 4.71/5.13 & ( ord_less_eq_rat @ B @ D ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_subset_iff
% 4.71/5.13 thf(fact_5782_atLeastatMost__subset__iff,axiom,
% 4.71/5.13 ! [A: num,B: num,C: num,D: num] :
% 4.71/5.13 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 4.71/5.13 = ( ~ ( ord_less_eq_num @ A @ B )
% 4.71/5.13 | ( ( ord_less_eq_num @ C @ A )
% 4.71/5.13 & ( ord_less_eq_num @ B @ D ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_subset_iff
% 4.71/5.13 thf(fact_5783_atLeastatMost__subset__iff,axiom,
% 4.71/5.13 ! [A: int,B: int,C: int,D: int] :
% 4.71/5.13 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 4.71/5.13 = ( ~ ( ord_less_eq_int @ A @ B )
% 4.71/5.13 | ( ( ord_less_eq_int @ C @ A )
% 4.71/5.13 & ( ord_less_eq_int @ B @ D ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_subset_iff
% 4.71/5.13 thf(fact_5784_atLeastatMost__subset__iff,axiom,
% 4.71/5.13 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.71/5.13 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 4.71/5.13 = ( ~ ( ord_less_eq_nat @ A @ B )
% 4.71/5.13 | ( ( ord_less_eq_nat @ C @ A )
% 4.71/5.13 & ( ord_less_eq_nat @ B @ D ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_subset_iff
% 4.71/5.13 thf(fact_5785_atLeastatMost__subset__iff,axiom,
% 4.71/5.13 ! [A: real,B: real,C: real,D: real] :
% 4.71/5.13 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 4.71/5.13 = ( ~ ( ord_less_eq_real @ A @ B )
% 4.71/5.13 | ( ( ord_less_eq_real @ C @ A )
% 4.71/5.13 & ( ord_less_eq_real @ B @ D ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_subset_iff
% 4.71/5.13 thf(fact_5786_atLeastatMost__empty,axiom,
% 4.71/5.13 ! [B: $o,A: $o] :
% 4.71/5.13 ( ( ord_less_o @ B @ A )
% 4.71/5.13 => ( ( set_or8904488021354931149Most_o @ A @ B )
% 4.71/5.13 = bot_bot_set_o ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_empty
% 4.71/5.13 thf(fact_5787_atLeastatMost__empty,axiom,
% 4.71/5.13 ! [B: rat,A: rat] :
% 4.71/5.13 ( ( ord_less_rat @ B @ A )
% 4.71/5.13 => ( ( set_or633870826150836451st_rat @ A @ B )
% 4.71/5.13 = bot_bot_set_rat ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_empty
% 4.71/5.13 thf(fact_5788_atLeastatMost__empty,axiom,
% 4.71/5.13 ! [B: num,A: num] :
% 4.71/5.13 ( ( ord_less_num @ B @ A )
% 4.71/5.13 => ( ( set_or7049704709247886629st_num @ A @ B )
% 4.71/5.13 = bot_bot_set_num ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_empty
% 4.71/5.13 thf(fact_5789_atLeastatMost__empty,axiom,
% 4.71/5.13 ! [B: int,A: int] :
% 4.71/5.13 ( ( ord_less_int @ B @ A )
% 4.71/5.13 => ( ( set_or1266510415728281911st_int @ A @ B )
% 4.71/5.13 = bot_bot_set_int ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_empty
% 4.71/5.13 thf(fact_5790_atLeastatMost__empty,axiom,
% 4.71/5.13 ! [B: nat,A: nat] :
% 4.71/5.13 ( ( ord_less_nat @ B @ A )
% 4.71/5.13 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 4.71/5.13 = bot_bot_set_nat ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_empty
% 4.71/5.13 thf(fact_5791_atLeastatMost__empty,axiom,
% 4.71/5.13 ! [B: real,A: real] :
% 4.71/5.13 ( ( ord_less_real @ B @ A )
% 4.71/5.13 => ( ( set_or1222579329274155063t_real @ A @ B )
% 4.71/5.13 = bot_bot_set_real ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_empty
% 4.71/5.13 thf(fact_5792_infinite__Icc__iff,axiom,
% 4.71/5.13 ! [A: rat,B: rat] :
% 4.71/5.13 ( ( ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) )
% 4.71/5.13 = ( ord_less_rat @ A @ B ) ) ).
% 4.71/5.13
% 4.71/5.13 % infinite_Icc_iff
% 4.71/5.13 thf(fact_5793_infinite__Icc__iff,axiom,
% 4.71/5.13 ! [A: real,B: real] :
% 4.71/5.13 ( ( ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) )
% 4.71/5.13 = ( ord_less_real @ A @ B ) ) ).
% 4.71/5.13
% 4.71/5.13 % infinite_Icc_iff
% 4.71/5.13 thf(fact_5794_norm__zero,axiom,
% 4.71/5.13 ( ( real_V7735802525324610683m_real @ zero_zero_real )
% 4.71/5.13 = zero_zero_real ) ).
% 4.71/5.13
% 4.71/5.13 % norm_zero
% 4.71/5.13 thf(fact_5795_norm__zero,axiom,
% 4.71/5.13 ( ( real_V1022390504157884413omplex @ zero_zero_complex )
% 4.71/5.13 = zero_zero_real ) ).
% 4.71/5.13
% 4.71/5.13 % norm_zero
% 4.71/5.13 thf(fact_5796_norm__eq__zero,axiom,
% 4.71/5.13 ! [X: real] :
% 4.71/5.13 ( ( ( real_V7735802525324610683m_real @ X )
% 4.71/5.13 = zero_zero_real )
% 4.71/5.13 = ( X = zero_zero_real ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_eq_zero
% 4.71/5.13 thf(fact_5797_norm__eq__zero,axiom,
% 4.71/5.13 ! [X: complex] :
% 4.71/5.13 ( ( ( real_V1022390504157884413omplex @ X )
% 4.71/5.13 = zero_zero_real )
% 4.71/5.13 = ( X = zero_zero_complex ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_eq_zero
% 4.71/5.13 thf(fact_5798_norm__one,axiom,
% 4.71/5.13 ( ( real_V7735802525324610683m_real @ one_one_real )
% 4.71/5.13 = one_one_real ) ).
% 4.71/5.13
% 4.71/5.13 % norm_one
% 4.71/5.13 thf(fact_5799_norm__one,axiom,
% 4.71/5.13 ( ( real_V1022390504157884413omplex @ one_one_complex )
% 4.71/5.13 = one_one_real ) ).
% 4.71/5.13
% 4.71/5.13 % norm_one
% 4.71/5.13 thf(fact_5800_atLeastAtMost__singleton,axiom,
% 4.71/5.13 ! [A: $o] :
% 4.71/5.13 ( ( set_or8904488021354931149Most_o @ A @ A )
% 4.71/5.13 = ( insert_o @ A @ bot_bot_set_o ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastAtMost_singleton
% 4.71/5.13 thf(fact_5801_atLeastAtMost__singleton,axiom,
% 4.71/5.13 ! [A: int] :
% 4.71/5.13 ( ( set_or1266510415728281911st_int @ A @ A )
% 4.71/5.13 = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastAtMost_singleton
% 4.71/5.13 thf(fact_5802_atLeastAtMost__singleton,axiom,
% 4.71/5.13 ! [A: nat] :
% 4.71/5.13 ( ( set_or1269000886237332187st_nat @ A @ A )
% 4.71/5.13 = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastAtMost_singleton
% 4.71/5.13 thf(fact_5803_atLeastAtMost__singleton,axiom,
% 4.71/5.13 ! [A: real] :
% 4.71/5.13 ( ( set_or1222579329274155063t_real @ A @ A )
% 4.71/5.13 = ( insert_real @ A @ bot_bot_set_real ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastAtMost_singleton
% 4.71/5.13 thf(fact_5804_atLeastAtMost__singleton__iff,axiom,
% 4.71/5.13 ! [A: $o,B: $o,C: $o] :
% 4.71/5.13 ( ( ( set_or8904488021354931149Most_o @ A @ B )
% 4.71/5.13 = ( insert_o @ C @ bot_bot_set_o ) )
% 4.71/5.13 = ( ( A = B )
% 4.71/5.13 & ( B = C ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastAtMost_singleton_iff
% 4.71/5.13 thf(fact_5805_atLeastAtMost__singleton__iff,axiom,
% 4.71/5.13 ! [A: int,B: int,C: int] :
% 4.71/5.13 ( ( ( set_or1266510415728281911st_int @ A @ B )
% 4.71/5.13 = ( insert_int @ C @ bot_bot_set_int ) )
% 4.71/5.13 = ( ( A = B )
% 4.71/5.13 & ( B = C ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastAtMost_singleton_iff
% 4.71/5.13 thf(fact_5806_atLeastAtMost__singleton__iff,axiom,
% 4.71/5.13 ! [A: nat,B: nat,C: nat] :
% 4.71/5.13 ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 4.71/5.13 = ( insert_nat @ C @ bot_bot_set_nat ) )
% 4.71/5.13 = ( ( A = B )
% 4.71/5.13 & ( B = C ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastAtMost_singleton_iff
% 4.71/5.13 thf(fact_5807_atLeastAtMost__singleton__iff,axiom,
% 4.71/5.13 ! [A: real,B: real,C: real] :
% 4.71/5.13 ( ( ( set_or1222579329274155063t_real @ A @ B )
% 4.71/5.13 = ( insert_real @ C @ bot_bot_set_real ) )
% 4.71/5.13 = ( ( A = B )
% 4.71/5.13 & ( B = C ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastAtMost_singleton_iff
% 4.71/5.13 thf(fact_5808_mod__by__Suc__0,axiom,
% 4.71/5.13 ! [M2: nat] :
% 4.71/5.13 ( ( modulo_modulo_nat @ M2 @ ( suc @ zero_zero_nat ) )
% 4.71/5.13 = zero_zero_nat ) ).
% 4.71/5.13
% 4.71/5.13 % mod_by_Suc_0
% 4.71/5.13 thf(fact_5809_numeral__less__real__of__nat__iff,axiom,
% 4.71/5.13 ! [W2: num,N: nat] :
% 4.71/5.13 ( ( ord_less_real @ ( numeral_numeral_real @ W2 ) @ ( semiri5074537144036343181t_real @ N ) )
% 4.71/5.13 = ( ord_less_nat @ ( numeral_numeral_nat @ W2 ) @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_less_real_of_nat_iff
% 4.71/5.13 thf(fact_5810_real__of__nat__less__numeral__iff,axiom,
% 4.71/5.13 ! [N: nat,W2: num] :
% 4.71/5.13 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( numeral_numeral_real @ W2 ) )
% 4.71/5.13 = ( ord_less_nat @ N @ ( numeral_numeral_nat @ W2 ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % real_of_nat_less_numeral_iff
% 4.71/5.13 thf(fact_5811_numeral__le__real__of__nat__iff,axiom,
% 4.71/5.13 ! [N: num,M2: nat] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( semiri5074537144036343181t_real @ M2 ) )
% 4.71/5.13 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ M2 ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_le_real_of_nat_iff
% 4.71/5.13 thf(fact_5812_nat__neg__numeral,axiom,
% 4.71/5.13 ! [K: num] :
% 4.71/5.13 ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 4.71/5.13 = zero_zero_nat ) ).
% 4.71/5.13
% 4.71/5.13 % nat_neg_numeral
% 4.71/5.13 thf(fact_5813_Gcd__fin_Oempty,axiom,
% 4.71/5.13 ( ( semiri4258706085729940814in_nat @ bot_bot_set_nat )
% 4.71/5.13 = zero_zero_nat ) ).
% 4.71/5.13
% 4.71/5.13 % Gcd_fin.empty
% 4.71/5.13 thf(fact_5814_Gcd__fin_Oempty,axiom,
% 4.71/5.13 ( ( semiri4256215615220890538in_int @ bot_bot_set_int )
% 4.71/5.13 = zero_zero_int ) ).
% 4.71/5.13
% 4.71/5.13 % Gcd_fin.empty
% 4.71/5.13 thf(fact_5815_Gcd__fin_Oinfinite,axiom,
% 4.71/5.13 ! [A2: set_nat] :
% 4.71/5.13 ( ~ ( finite_finite_nat @ A2 )
% 4.71/5.13 => ( ( semiri4258706085729940814in_nat @ A2 )
% 4.71/5.13 = one_one_nat ) ) ).
% 4.71/5.13
% 4.71/5.13 % Gcd_fin.infinite
% 4.71/5.13 thf(fact_5816_Gcd__fin_Oinfinite,axiom,
% 4.71/5.13 ! [A2: set_int] :
% 4.71/5.13 ( ~ ( finite_finite_int @ A2 )
% 4.71/5.13 => ( ( semiri4256215615220890538in_int @ A2 )
% 4.71/5.13 = one_one_int ) ) ).
% 4.71/5.13
% 4.71/5.13 % Gcd_fin.infinite
% 4.71/5.13 thf(fact_5817_floor__divide__eq__div__numeral,axiom,
% 4.71/5.13 ! [A: num,B: num] :
% 4.71/5.13 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 4.71/5.13 = ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % floor_divide_eq_div_numeral
% 4.71/5.13 thf(fact_5818_Gcd__fin__eq__Gcd,axiom,
% 4.71/5.13 ! [A2: set_nat] :
% 4.71/5.13 ( ( finite_finite_nat @ A2 )
% 4.71/5.13 => ( ( semiri4258706085729940814in_nat @ A2 )
% 4.71/5.13 = ( gcd_Gcd_nat @ A2 ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % Gcd_fin_eq_Gcd
% 4.71/5.13 thf(fact_5819_Gcd__fin__eq__Gcd,axiom,
% 4.71/5.13 ! [A2: set_int] :
% 4.71/5.13 ( ( finite_finite_int @ A2 )
% 4.71/5.13 => ( ( semiri4256215615220890538in_int @ A2 )
% 4.71/5.13 = ( gcd_Gcd_int @ A2 ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % Gcd_fin_eq_Gcd
% 4.71/5.13 thf(fact_5820_count__notin,axiom,
% 4.71/5.13 ! [X: $o,Xs: list_o] :
% 4.71/5.13 ( ~ ( member_o @ X @ ( set_o2 @ Xs ) )
% 4.71/5.13 => ( ( count_list_o @ Xs @ X )
% 4.71/5.13 = zero_zero_nat ) ) ).
% 4.71/5.13
% 4.71/5.13 % count_notin
% 4.71/5.13 thf(fact_5821_count__notin,axiom,
% 4.71/5.13 ! [X: set_nat,Xs: list_set_nat] :
% 4.71/5.13 ( ~ ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 4.71/5.13 => ( ( count_list_set_nat @ Xs @ X )
% 4.71/5.13 = zero_zero_nat ) ) ).
% 4.71/5.13
% 4.71/5.13 % count_notin
% 4.71/5.13 thf(fact_5822_count__notin,axiom,
% 4.71/5.13 ! [X: set_nat_rat,Xs: list_set_nat_rat] :
% 4.71/5.13 ( ~ ( member_set_nat_rat @ X @ ( set_set_nat_rat2 @ Xs ) )
% 4.71/5.13 => ( ( count_6735058137522573441at_rat @ Xs @ X )
% 4.71/5.13 = zero_zero_nat ) ) ).
% 4.71/5.13
% 4.71/5.13 % count_notin
% 4.71/5.13 thf(fact_5823_count__notin,axiom,
% 4.71/5.13 ! [X: int,Xs: list_int] :
% 4.71/5.13 ( ~ ( member_int @ X @ ( set_int2 @ Xs ) )
% 4.71/5.13 => ( ( count_list_int @ Xs @ X )
% 4.71/5.13 = zero_zero_nat ) ) ).
% 4.71/5.13
% 4.71/5.13 % count_notin
% 4.71/5.13 thf(fact_5824_count__notin,axiom,
% 4.71/5.13 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 4.71/5.13 ( ~ ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 4.71/5.13 => ( ( count_list_VEBT_VEBT @ Xs @ X )
% 4.71/5.13 = zero_zero_nat ) ) ).
% 4.71/5.13
% 4.71/5.13 % count_notin
% 4.71/5.13 thf(fact_5825_count__notin,axiom,
% 4.71/5.13 ! [X: nat,Xs: list_nat] :
% 4.71/5.13 ( ~ ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 4.71/5.13 => ( ( count_list_nat @ Xs @ X )
% 4.71/5.13 = zero_zero_nat ) ) ).
% 4.71/5.13
% 4.71/5.13 % count_notin
% 4.71/5.13 thf(fact_5826_divide__le__eq__numeral1_I1_J,axiom,
% 4.71/5.13 ! [B: real,W2: num,A: real] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) @ A )
% 4.71/5.13 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % divide_le_eq_numeral1(1)
% 4.71/5.13 thf(fact_5827_divide__le__eq__numeral1_I1_J,axiom,
% 4.71/5.13 ! [B: rat,W2: num,A: rat] :
% 4.71/5.13 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) @ A )
% 4.71/5.13 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % divide_le_eq_numeral1(1)
% 4.71/5.13 thf(fact_5828_le__divide__eq__numeral1_I1_J,axiom,
% 4.71/5.13 ! [A: real,B: real,W2: num] :
% 4.71/5.13 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) )
% 4.71/5.13 = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) @ B ) ) ).
% 4.71/5.13
% 4.71/5.13 % le_divide_eq_numeral1(1)
% 4.71/5.13 thf(fact_5829_le__divide__eq__numeral1_I1_J,axiom,
% 4.71/5.13 ! [A: rat,B: rat,W2: num] :
% 4.71/5.13 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 4.71/5.13 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) @ B ) ) ).
% 4.71/5.13
% 4.71/5.13 % le_divide_eq_numeral1(1)
% 4.71/5.13 thf(fact_5830_eq__divide__eq__numeral1_I1_J,axiom,
% 4.71/5.13 ! [A: rat,B: rat,W2: num] :
% 4.71/5.13 ( ( A
% 4.71/5.13 = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 4.71/5.13 = ( ( ( ( numeral_numeral_rat @ W2 )
% 4.71/5.13 != zero_zero_rat )
% 4.71/5.13 => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) )
% 4.71/5.13 = B ) )
% 4.71/5.13 & ( ( ( numeral_numeral_rat @ W2 )
% 4.71/5.13 = zero_zero_rat )
% 4.71/5.13 => ( A = zero_zero_rat ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % eq_divide_eq_numeral1(1)
% 4.71/5.13 thf(fact_5831_eq__divide__eq__numeral1_I1_J,axiom,
% 4.71/5.13 ! [A: real,B: real,W2: num] :
% 4.71/5.13 ( ( A
% 4.71/5.13 = ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) )
% 4.71/5.13 = ( ( ( ( numeral_numeral_real @ W2 )
% 4.71/5.13 != zero_zero_real )
% 4.71/5.13 => ( ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) )
% 4.71/5.13 = B ) )
% 4.71/5.13 & ( ( ( numeral_numeral_real @ W2 )
% 4.71/5.13 = zero_zero_real )
% 4.71/5.13 => ( A = zero_zero_real ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % eq_divide_eq_numeral1(1)
% 4.71/5.13 thf(fact_5832_divide__eq__eq__numeral1_I1_J,axiom,
% 4.71/5.13 ! [B: rat,W2: num,A: rat] :
% 4.71/5.13 ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) )
% 4.71/5.13 = A )
% 4.71/5.13 = ( ( ( ( numeral_numeral_rat @ W2 )
% 4.71/5.13 != zero_zero_rat )
% 4.71/5.13 => ( B
% 4.71/5.13 = ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) )
% 4.71/5.13 & ( ( ( numeral_numeral_rat @ W2 )
% 4.71/5.13 = zero_zero_rat )
% 4.71/5.13 => ( A = zero_zero_rat ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % divide_eq_eq_numeral1(1)
% 4.71/5.13 thf(fact_5833_divide__eq__eq__numeral1_I1_J,axiom,
% 4.71/5.13 ! [B: real,W2: num,A: real] :
% 4.71/5.13 ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) )
% 4.71/5.13 = A )
% 4.71/5.13 = ( ( ( ( numeral_numeral_real @ W2 )
% 4.71/5.13 != zero_zero_real )
% 4.71/5.13 => ( B
% 4.71/5.13 = ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) ) )
% 4.71/5.13 & ( ( ( numeral_numeral_real @ W2 )
% 4.71/5.13 = zero_zero_real )
% 4.71/5.13 => ( A = zero_zero_real ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % divide_eq_eq_numeral1(1)
% 4.71/5.13 thf(fact_5834_less__divide__eq__numeral1_I1_J,axiom,
% 4.71/5.13 ! [A: rat,B: rat,W2: num] :
% 4.71/5.13 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 4.71/5.13 = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) @ B ) ) ).
% 4.71/5.13
% 4.71/5.13 % less_divide_eq_numeral1(1)
% 4.71/5.13 thf(fact_5835_less__divide__eq__numeral1_I1_J,axiom,
% 4.71/5.13 ! [A: real,B: real,W2: num] :
% 4.71/5.13 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) )
% 4.71/5.13 = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) @ B ) ) ).
% 4.71/5.13
% 4.71/5.13 % less_divide_eq_numeral1(1)
% 4.71/5.13 thf(fact_5836_divide__less__eq__numeral1_I1_J,axiom,
% 4.71/5.13 ! [B: rat,W2: num,A: rat] :
% 4.71/5.13 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) @ A )
% 4.71/5.13 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % divide_less_eq_numeral1(1)
% 4.71/5.13 thf(fact_5837_divide__less__eq__numeral1_I1_J,axiom,
% 4.71/5.13 ! [B: real,W2: num,A: real] :
% 4.71/5.13 ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) @ A )
% 4.71/5.13 = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % divide_less_eq_numeral1(1)
% 4.71/5.13 thf(fact_5838_inverse__eq__divide__numeral,axiom,
% 4.71/5.13 ! [W2: num] :
% 4.71/5.13 ( ( invers8013647133539491842omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 4.71/5.13 = ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ W2 ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % inverse_eq_divide_numeral
% 4.71/5.13 thf(fact_5839_inverse__eq__divide__numeral,axiom,
% 4.71/5.13 ! [W2: num] :
% 4.71/5.13 ( ( inverse_inverse_real @ ( numeral_numeral_real @ W2 ) )
% 4.71/5.13 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ W2 ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % inverse_eq_divide_numeral
% 4.71/5.13 thf(fact_5840_inverse__eq__divide__numeral,axiom,
% 4.71/5.13 ! [W2: num] :
% 4.71/5.13 ( ( inverse_inverse_rat @ ( numeral_numeral_rat @ W2 ) )
% 4.71/5.13 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ W2 ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % inverse_eq_divide_numeral
% 4.71/5.13 thf(fact_5841_zero__less__norm__iff,axiom,
% 4.71/5.13 ! [X: real] :
% 4.71/5.13 ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X ) )
% 4.71/5.13 = ( X != zero_zero_real ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_less_norm_iff
% 4.71/5.13 thf(fact_5842_zero__less__norm__iff,axiom,
% 4.71/5.13 ! [X: complex] :
% 4.71/5.13 ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X ) )
% 4.71/5.13 = ( X != zero_zero_complex ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_less_norm_iff
% 4.71/5.13 thf(fact_5843_norm__le__zero__iff,axiom,
% 4.71/5.13 ! [X: real] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X ) @ zero_zero_real )
% 4.71/5.13 = ( X = zero_zero_real ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_le_zero_iff
% 4.71/5.13 thf(fact_5844_norm__le__zero__iff,axiom,
% 4.71/5.13 ! [X: complex] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ zero_zero_real )
% 4.71/5.13 = ( X = zero_zero_complex ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_le_zero_iff
% 4.71/5.13 thf(fact_5845_of__int__numeral__le__iff,axiom,
% 4.71/5.13 ! [N: num,Z: int] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 4.71/5.13 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_numeral_le_iff
% 4.71/5.13 thf(fact_5846_of__int__numeral__le__iff,axiom,
% 4.71/5.13 ! [N: num,Z: int] :
% 4.71/5.13 ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N ) @ ( ring_18347121197199848620nteger @ Z ) )
% 4.71/5.13 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_numeral_le_iff
% 4.71/5.13 thf(fact_5847_of__int__numeral__le__iff,axiom,
% 4.71/5.13 ! [N: num,Z: int] :
% 4.71/5.13 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 4.71/5.13 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_numeral_le_iff
% 4.71/5.13 thf(fact_5848_of__int__numeral__le__iff,axiom,
% 4.71/5.13 ! [N: num,Z: int] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 4.71/5.13 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_numeral_le_iff
% 4.71/5.13 thf(fact_5849_of__int__le__numeral__iff,axiom,
% 4.71/5.13 ! [Z: int,N: num] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 4.71/5.13 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_le_numeral_iff
% 4.71/5.13 thf(fact_5850_of__int__le__numeral__iff,axiom,
% 4.71/5.13 ! [Z: int,N: num] :
% 4.71/5.13 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ Z ) @ ( numera6620942414471956472nteger @ N ) )
% 4.71/5.13 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_le_numeral_iff
% 4.71/5.13 thf(fact_5851_of__int__le__numeral__iff,axiom,
% 4.71/5.13 ! [Z: int,N: num] :
% 4.71/5.13 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 4.71/5.13 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_le_numeral_iff
% 4.71/5.13 thf(fact_5852_of__int__le__numeral__iff,axiom,
% 4.71/5.13 ! [Z: int,N: num] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 4.71/5.13 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_le_numeral_iff
% 4.71/5.13 thf(fact_5853_of__int__numeral__less__iff,axiom,
% 4.71/5.13 ! [N: num,Z: int] :
% 4.71/5.13 ( ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 4.71/5.13 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_numeral_less_iff
% 4.71/5.13 thf(fact_5854_of__int__numeral__less__iff,axiom,
% 4.71/5.13 ! [N: num,Z: int] :
% 4.71/5.13 ( ( ord_less_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 4.71/5.13 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_numeral_less_iff
% 4.71/5.13 thf(fact_5855_of__int__numeral__less__iff,axiom,
% 4.71/5.13 ! [N: num,Z: int] :
% 4.71/5.13 ( ( ord_less_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 4.71/5.13 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_numeral_less_iff
% 4.71/5.13 thf(fact_5856_of__int__numeral__less__iff,axiom,
% 4.71/5.13 ! [N: num,Z: int] :
% 4.71/5.13 ( ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N ) @ ( ring_18347121197199848620nteger @ Z ) )
% 4.71/5.13 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_numeral_less_iff
% 4.71/5.13 thf(fact_5857_of__int__less__numeral__iff,axiom,
% 4.71/5.13 ! [Z: int,N: num] :
% 4.71/5.13 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 4.71/5.13 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_less_numeral_iff
% 4.71/5.13 thf(fact_5858_of__int__less__numeral__iff,axiom,
% 4.71/5.13 ! [Z: int,N: num] :
% 4.71/5.13 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 4.71/5.13 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_less_numeral_iff
% 4.71/5.13 thf(fact_5859_of__int__less__numeral__iff,axiom,
% 4.71/5.13 ! [Z: int,N: num] :
% 4.71/5.13 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 4.71/5.13 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_less_numeral_iff
% 4.71/5.13 thf(fact_5860_of__int__less__numeral__iff,axiom,
% 4.71/5.13 ! [Z: int,N: num] :
% 4.71/5.13 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ Z ) @ ( numera6620942414471956472nteger @ N ) )
% 4.71/5.13 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_less_numeral_iff
% 4.71/5.13 thf(fact_5861_numeral__le__floor,axiom,
% 4.71/5.13 ! [V: num,X: real] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X ) )
% 4.71/5.13 = ( ord_less_eq_real @ ( numeral_numeral_real @ V ) @ X ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_le_floor
% 4.71/5.13 thf(fact_5862_numeral__le__floor,axiom,
% 4.71/5.13 ! [V: num,X: rat] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X ) )
% 4.71/5.13 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ V ) @ X ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_le_floor
% 4.71/5.13 thf(fact_5863_floor__less__numeral,axiom,
% 4.71/5.13 ! [X: real,V: num] :
% 4.71/5.13 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ ( numeral_numeral_int @ V ) )
% 4.71/5.13 = ( ord_less_real @ X @ ( numeral_numeral_real @ V ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % floor_less_numeral
% 4.71/5.13 thf(fact_5864_floor__less__numeral,axiom,
% 4.71/5.13 ! [X: rat,V: num] :
% 4.71/5.13 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 4.71/5.13 = ( ord_less_rat @ X @ ( numeral_numeral_rat @ V ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % floor_less_numeral
% 4.71/5.13 thf(fact_5865_ceiling__le__numeral,axiom,
% 4.71/5.13 ! [X: real,V: num] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) )
% 4.71/5.13 = ( ord_less_eq_real @ X @ ( numeral_numeral_real @ V ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % ceiling_le_numeral
% 4.71/5.13 thf(fact_5866_ceiling__le__numeral,axiom,
% 4.71/5.13 ! [X: rat,V: num] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 4.71/5.13 = ( ord_less_eq_rat @ X @ ( numeral_numeral_rat @ V ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % ceiling_le_numeral
% 4.71/5.13 thf(fact_5867_numeral__less__ceiling,axiom,
% 4.71/5.13 ! [V: num,X: rat] :
% 4.71/5.13 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X ) )
% 4.71/5.13 = ( ord_less_rat @ ( numeral_numeral_rat @ V ) @ X ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_less_ceiling
% 4.71/5.13 thf(fact_5868_numeral__less__ceiling,axiom,
% 4.71/5.13 ! [V: num,X: real] :
% 4.71/5.13 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X ) )
% 4.71/5.13 = ( ord_less_real @ ( numeral_numeral_real @ V ) @ X ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_less_ceiling
% 4.71/5.13 thf(fact_5869_nth__Cons__numeral,axiom,
% 4.71/5.13 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT,V: num] :
% 4.71/5.13 ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ ( numeral_numeral_nat @ V ) )
% 4.71/5.13 = ( nth_VEBT_VEBT @ Xs @ ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % nth_Cons_numeral
% 4.71/5.13 thf(fact_5870_nth__Cons__numeral,axiom,
% 4.71/5.13 ! [X: int,Xs: list_int,V: num] :
% 4.71/5.13 ( ( nth_int @ ( cons_int @ X @ Xs ) @ ( numeral_numeral_nat @ V ) )
% 4.71/5.13 = ( nth_int @ Xs @ ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % nth_Cons_numeral
% 4.71/5.13 thf(fact_5871_nth__Cons__numeral,axiom,
% 4.71/5.13 ! [X: nat,Xs: list_nat,V: num] :
% 4.71/5.13 ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ ( numeral_numeral_nat @ V ) )
% 4.71/5.13 = ( nth_nat @ Xs @ ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % nth_Cons_numeral
% 4.71/5.13 thf(fact_5872_Suc__times__numeral__mod__eq,axiom,
% 4.71/5.13 ! [K: num,N: nat] :
% 4.71/5.13 ( ( ( numeral_numeral_nat @ K )
% 4.71/5.13 != one_one_nat )
% 4.71/5.13 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 4.71/5.13 = one_one_nat ) ) ).
% 4.71/5.13
% 4.71/5.13 % Suc_times_numeral_mod_eq
% 4.71/5.13 thf(fact_5873_powr__numeral,axiom,
% 4.71/5.13 ! [X: real,N: num] :
% 4.71/5.13 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.13 => ( ( powr_real @ X @ ( numeral_numeral_real @ N ) )
% 4.71/5.13 = ( power_power_real @ X @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % powr_numeral
% 4.71/5.13 thf(fact_5874_floor__numeral__power,axiom,
% 4.71/5.13 ! [X: num,N: nat] :
% 4.71/5.13 ( ( archim6058952711729229775r_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 4.71/5.13 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % floor_numeral_power
% 4.71/5.13 thf(fact_5875_floor__numeral__power,axiom,
% 4.71/5.13 ! [X: num,N: nat] :
% 4.71/5.13 ( ( archim3151403230148437115or_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 4.71/5.13 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % floor_numeral_power
% 4.71/5.13 thf(fact_5876_ceiling__numeral__power,axiom,
% 4.71/5.13 ! [X: num,N: nat] :
% 4.71/5.13 ( ( archim7802044766580827645g_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 4.71/5.13 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % ceiling_numeral_power
% 4.71/5.13 thf(fact_5877_ceiling__divide__eq__div__numeral,axiom,
% 4.71/5.13 ! [A: num,B: num] :
% 4.71/5.13 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 4.71/5.13 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % ceiling_divide_eq_div_numeral
% 4.71/5.13 thf(fact_5878_divide__le__eq__numeral1_I2_J,axiom,
% 4.71/5.13 ! [B: real,W2: num,A: real] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ A )
% 4.71/5.13 = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ B ) ) ).
% 4.71/5.13
% 4.71/5.13 % divide_le_eq_numeral1(2)
% 4.71/5.13 thf(fact_5879_divide__le__eq__numeral1_I2_J,axiom,
% 4.71/5.13 ! [B: rat,W2: num,A: rat] :
% 4.71/5.13 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ A )
% 4.71/5.13 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ B ) ) ).
% 4.71/5.13
% 4.71/5.13 % divide_le_eq_numeral1(2)
% 4.71/5.13 thf(fact_5880_le__divide__eq__numeral1_I2_J,axiom,
% 4.71/5.13 ! [A: real,B: real,W2: num] :
% 4.71/5.13 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) )
% 4.71/5.13 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % le_divide_eq_numeral1(2)
% 4.71/5.13 thf(fact_5881_le__divide__eq__numeral1_I2_J,axiom,
% 4.71/5.13 ! [A: rat,B: rat,W2: num] :
% 4.71/5.13 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 4.71/5.13 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % le_divide_eq_numeral1(2)
% 4.71/5.13 thf(fact_5882_eq__divide__eq__numeral1_I2_J,axiom,
% 4.71/5.13 ! [A: real,B: real,W2: num] :
% 4.71/5.13 ( ( A
% 4.71/5.13 = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) )
% 4.71/5.13 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 4.71/5.13 != zero_zero_real )
% 4.71/5.13 => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 4.71/5.13 = B ) )
% 4.71/5.13 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 4.71/5.13 = zero_zero_real )
% 4.71/5.13 => ( A = zero_zero_real ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % eq_divide_eq_numeral1(2)
% 4.71/5.13 thf(fact_5883_eq__divide__eq__numeral1_I2_J,axiom,
% 4.71/5.13 ! [A: rat,B: rat,W2: num] :
% 4.71/5.13 ( ( A
% 4.71/5.13 = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 4.71/5.13 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 4.71/5.13 != zero_zero_rat )
% 4.71/5.13 => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 4.71/5.13 = B ) )
% 4.71/5.13 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 4.71/5.13 = zero_zero_rat )
% 4.71/5.13 => ( A = zero_zero_rat ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % eq_divide_eq_numeral1(2)
% 4.71/5.13 thf(fact_5884_eq__divide__eq__numeral1_I2_J,axiom,
% 4.71/5.13 ! [A: complex,B: complex,W2: num] :
% 4.71/5.13 ( ( A
% 4.71/5.13 = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) ) )
% 4.71/5.13 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 4.71/5.13 != zero_zero_complex )
% 4.71/5.13 => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 4.71/5.13 = B ) )
% 4.71/5.13 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 4.71/5.13 = zero_zero_complex )
% 4.71/5.13 => ( A = zero_zero_complex ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % eq_divide_eq_numeral1(2)
% 4.71/5.13 thf(fact_5885_divide__eq__eq__numeral1_I2_J,axiom,
% 4.71/5.13 ! [B: real,W2: num,A: real] :
% 4.71/5.13 ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 4.71/5.13 = A )
% 4.71/5.13 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 4.71/5.13 != zero_zero_real )
% 4.71/5.13 => ( B
% 4.71/5.13 = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) )
% 4.71/5.13 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 4.71/5.13 = zero_zero_real )
% 4.71/5.13 => ( A = zero_zero_real ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % divide_eq_eq_numeral1(2)
% 4.71/5.13 thf(fact_5886_divide__eq__eq__numeral1_I2_J,axiom,
% 4.71/5.13 ! [B: rat,W2: num,A: rat] :
% 4.71/5.13 ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 4.71/5.13 = A )
% 4.71/5.13 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 4.71/5.13 != zero_zero_rat )
% 4.71/5.13 => ( B
% 4.71/5.13 = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) )
% 4.71/5.13 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 4.71/5.13 = zero_zero_rat )
% 4.71/5.13 => ( A = zero_zero_rat ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % divide_eq_eq_numeral1(2)
% 4.71/5.13 thf(fact_5887_divide__eq__eq__numeral1_I2_J,axiom,
% 4.71/5.13 ! [B: complex,W2: num,A: complex] :
% 4.71/5.13 ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 4.71/5.13 = A )
% 4.71/5.13 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 4.71/5.13 != zero_zero_complex )
% 4.71/5.13 => ( B
% 4.71/5.13 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) ) ) )
% 4.71/5.13 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 4.71/5.13 = zero_zero_complex )
% 4.71/5.13 => ( A = zero_zero_complex ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % divide_eq_eq_numeral1(2)
% 4.71/5.13 thf(fact_5888_less__divide__eq__numeral1_I2_J,axiom,
% 4.71/5.13 ! [A: real,B: real,W2: num] :
% 4.71/5.13 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) )
% 4.71/5.13 = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % less_divide_eq_numeral1(2)
% 4.71/5.13 thf(fact_5889_less__divide__eq__numeral1_I2_J,axiom,
% 4.71/5.13 ! [A: rat,B: rat,W2: num] :
% 4.71/5.13 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 4.71/5.13 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % less_divide_eq_numeral1(2)
% 4.71/5.13 thf(fact_5890_divide__less__eq__numeral1_I2_J,axiom,
% 4.71/5.13 ! [B: real,W2: num,A: real] :
% 4.71/5.13 ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ A )
% 4.71/5.13 = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ B ) ) ).
% 4.71/5.13
% 4.71/5.13 % divide_less_eq_numeral1(2)
% 4.71/5.13 thf(fact_5891_divide__less__eq__numeral1_I2_J,axiom,
% 4.71/5.13 ! [B: rat,W2: num,A: rat] :
% 4.71/5.13 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ A )
% 4.71/5.13 = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ B ) ) ).
% 4.71/5.13
% 4.71/5.13 % divide_less_eq_numeral1(2)
% 4.71/5.13 thf(fact_5892_dbl__dec__simps_I1_J,axiom,
% 4.71/5.13 ! [K: num] :
% 4.71/5.13 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 4.71/5.13 = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % dbl_dec_simps(1)
% 4.71/5.13 thf(fact_5893_dbl__dec__simps_I1_J,axiom,
% 4.71/5.13 ! [K: num] :
% 4.71/5.13 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 4.71/5.13 = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % dbl_dec_simps(1)
% 4.71/5.13 thf(fact_5894_dbl__dec__simps_I1_J,axiom,
% 4.71/5.13 ! [K: num] :
% 4.71/5.13 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 4.71/5.13 = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % dbl_dec_simps(1)
% 4.71/5.13 thf(fact_5895_dbl__dec__simps_I1_J,axiom,
% 4.71/5.13 ! [K: num] :
% 4.71/5.13 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 4.71/5.13 = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % dbl_dec_simps(1)
% 4.71/5.13 thf(fact_5896_dbl__dec__simps_I1_J,axiom,
% 4.71/5.13 ! [K: num] :
% 4.71/5.13 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 4.71/5.13 = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % dbl_dec_simps(1)
% 4.71/5.13 thf(fact_5897_dbl__inc__simps_I1_J,axiom,
% 4.71/5.13 ! [K: num] :
% 4.71/5.13 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 4.71/5.13 = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % dbl_inc_simps(1)
% 4.71/5.13 thf(fact_5898_dbl__inc__simps_I1_J,axiom,
% 4.71/5.13 ! [K: num] :
% 4.71/5.13 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 4.71/5.13 = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % dbl_inc_simps(1)
% 4.71/5.13 thf(fact_5899_dbl__inc__simps_I1_J,axiom,
% 4.71/5.13 ! [K: num] :
% 4.71/5.13 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 4.71/5.13 = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % dbl_inc_simps(1)
% 4.71/5.13 thf(fact_5900_dbl__inc__simps_I1_J,axiom,
% 4.71/5.13 ! [K: num] :
% 4.71/5.13 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 4.71/5.13 = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % dbl_inc_simps(1)
% 4.71/5.13 thf(fact_5901_dbl__inc__simps_I1_J,axiom,
% 4.71/5.13 ! [K: num] :
% 4.71/5.13 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 4.71/5.13 = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % dbl_inc_simps(1)
% 4.71/5.13 thf(fact_5902_inverse__eq__divide__neg__numeral,axiom,
% 4.71/5.13 ! [W2: num] :
% 4.71/5.13 ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 4.71/5.13 = ( divide1717551699836669952omplex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % inverse_eq_divide_neg_numeral
% 4.71/5.13 thf(fact_5903_inverse__eq__divide__neg__numeral,axiom,
% 4.71/5.13 ! [W2: num] :
% 4.71/5.13 ( ( inverse_inverse_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 4.71/5.13 = ( divide_divide_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % inverse_eq_divide_neg_numeral
% 4.71/5.13 thf(fact_5904_inverse__eq__divide__neg__numeral,axiom,
% 4.71/5.13 ! [W2: num] :
% 4.71/5.13 ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 4.71/5.13 = ( divide_divide_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % inverse_eq_divide_neg_numeral
% 4.71/5.13 thf(fact_5905_nat__numeral__diff__1,axiom,
% 4.71/5.13 ! [V: num] :
% 4.71/5.13 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 4.71/5.13 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % nat_numeral_diff_1
% 4.71/5.13 thf(fact_5906_numeral__power__less__nat__cancel__iff,axiom,
% 4.71/5.13 ! [X: num,N: nat,A: int] :
% 4.71/5.13 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 4.71/5.13 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_power_less_nat_cancel_iff
% 4.71/5.13 thf(fact_5907_nat__less__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [A: int,X: num,N: nat] :
% 4.71/5.13 ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 4.71/5.13 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % nat_less_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5908_numeral__power__le__nat__cancel__iff,axiom,
% 4.71/5.13 ! [X: num,N: nat,A: int] :
% 4.71/5.13 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 4.71/5.13 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_power_le_nat_cancel_iff
% 4.71/5.13 thf(fact_5909_nat__le__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [A: int,X: num,N: nat] :
% 4.71/5.13 ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 4.71/5.13 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % nat_le_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5910_card__atLeastAtMost__int,axiom,
% 4.71/5.13 ! [L: int,U: int] :
% 4.71/5.13 ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L @ U ) )
% 4.71/5.13 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L ) @ one_one_int ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % card_atLeastAtMost_int
% 4.71/5.13 thf(fact_5911_floor__one__divide__eq__div__numeral,axiom,
% 4.71/5.13 ! [B: num] :
% 4.71/5.13 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) )
% 4.71/5.13 = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % floor_one_divide_eq_div_numeral
% 4.71/5.13 thf(fact_5912_floor__minus__divide__eq__div__numeral,axiom,
% 4.71/5.13 ! [A: num,B: num] :
% 4.71/5.13 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 4.71/5.13 = ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % floor_minus_divide_eq_div_numeral
% 4.71/5.13 thf(fact_5913_ceiling__minus__divide__eq__div__numeral,axiom,
% 4.71/5.13 ! [A: num,B: num] :
% 4.71/5.13 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 4.71/5.13 = ( uminus_uminus_int @ ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % ceiling_minus_divide_eq_div_numeral
% 4.71/5.13 thf(fact_5914_of__nat__less__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [X: nat,I: num,N: nat] :
% 4.71/5.13 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 4.71/5.13 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_nat_less_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5915_of__nat__less__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [X: nat,I: num,N: nat] :
% 4.71/5.13 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ X ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) )
% 4.71/5.13 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_nat_less_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5916_of__nat__less__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [X: nat,I: num,N: nat] :
% 4.71/5.13 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 4.71/5.13 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_nat_less_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5917_of__nat__less__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [X: nat,I: num,N: nat] :
% 4.71/5.13 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 4.71/5.13 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_nat_less_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5918_of__nat__less__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [X: nat,I: num,N: nat] :
% 4.71/5.13 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 4.71/5.13 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_nat_less_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5919_numeral__power__less__of__nat__cancel__iff,axiom,
% 4.71/5.13 ! [I: num,N: nat,X: nat] :
% 4.71/5.13 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X ) )
% 4.71/5.13 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_power_less_of_nat_cancel_iff
% 4.71/5.13 thf(fact_5920_numeral__power__less__of__nat__cancel__iff,axiom,
% 4.71/5.13 ! [I: num,N: nat,X: nat] :
% 4.71/5.13 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) @ ( semiri4939895301339042750nteger @ X ) )
% 4.71/5.13 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_power_less_of_nat_cancel_iff
% 4.71/5.13 thf(fact_5921_numeral__power__less__of__nat__cancel__iff,axiom,
% 4.71/5.13 ! [I: num,N: nat,X: nat] :
% 4.71/5.13 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X ) )
% 4.71/5.13 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_power_less_of_nat_cancel_iff
% 4.71/5.13 thf(fact_5922_numeral__power__less__of__nat__cancel__iff,axiom,
% 4.71/5.13 ! [I: num,N: nat,X: nat] :
% 4.71/5.13 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X ) )
% 4.71/5.13 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_power_less_of_nat_cancel_iff
% 4.71/5.13 thf(fact_5923_numeral__power__less__of__nat__cancel__iff,axiom,
% 4.71/5.13 ! [I: num,N: nat,X: nat] :
% 4.71/5.13 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X ) )
% 4.71/5.13 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_power_less_of_nat_cancel_iff
% 4.71/5.13 thf(fact_5924_numeral__power__le__of__nat__cancel__iff,axiom,
% 4.71/5.13 ! [I: num,N: nat,X: nat] :
% 4.71/5.13 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) @ ( semiri4939895301339042750nteger @ X ) )
% 4.71/5.13 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_power_le_of_nat_cancel_iff
% 4.71/5.13 thf(fact_5925_numeral__power__le__of__nat__cancel__iff,axiom,
% 4.71/5.13 ! [I: num,N: nat,X: nat] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X ) )
% 4.71/5.13 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_power_le_of_nat_cancel_iff
% 4.71/5.13 thf(fact_5926_numeral__power__le__of__nat__cancel__iff,axiom,
% 4.71/5.13 ! [I: num,N: nat,X: nat] :
% 4.71/5.13 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X ) )
% 4.71/5.13 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_power_le_of_nat_cancel_iff
% 4.71/5.13 thf(fact_5927_numeral__power__le__of__nat__cancel__iff,axiom,
% 4.71/5.13 ! [I: num,N: nat,X: nat] :
% 4.71/5.13 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X ) )
% 4.71/5.13 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_power_le_of_nat_cancel_iff
% 4.71/5.13 thf(fact_5928_numeral__power__le__of__nat__cancel__iff,axiom,
% 4.71/5.13 ! [I: num,N: nat,X: nat] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X ) )
% 4.71/5.13 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_power_le_of_nat_cancel_iff
% 4.71/5.13 thf(fact_5929_of__nat__le__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [X: nat,I: num,N: nat] :
% 4.71/5.13 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ X ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) )
% 4.71/5.13 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_nat_le_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5930_of__nat__le__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [X: nat,I: num,N: nat] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 4.71/5.13 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_nat_le_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5931_of__nat__le__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [X: nat,I: num,N: nat] :
% 4.71/5.13 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 4.71/5.13 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_nat_le_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5932_of__nat__le__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [X: nat,I: num,N: nat] :
% 4.71/5.13 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 4.71/5.13 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_nat_le_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5933_of__nat__le__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [X: nat,I: num,N: nat] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 4.71/5.13 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_nat_le_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5934_numeral__less__floor,axiom,
% 4.71/5.13 ! [V: num,X: real] :
% 4.71/5.13 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X ) )
% 4.71/5.13 = ( ord_less_eq_real @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_less_floor
% 4.71/5.13 thf(fact_5935_numeral__less__floor,axiom,
% 4.71/5.13 ! [V: num,X: rat] :
% 4.71/5.13 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X ) )
% 4.71/5.13 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_less_floor
% 4.71/5.13 thf(fact_5936_floor__le__numeral,axiom,
% 4.71/5.13 ! [X: real,V: num] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( numeral_numeral_int @ V ) )
% 4.71/5.13 = ( ord_less_real @ X @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % floor_le_numeral
% 4.71/5.13 thf(fact_5937_floor__le__numeral,axiom,
% 4.71/5.13 ! [X: rat,V: num] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 4.71/5.13 = ( ord_less_rat @ X @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % floor_le_numeral
% 4.71/5.13 thf(fact_5938_ceiling__less__numeral,axiom,
% 4.71/5.13 ! [X: real,V: num] :
% 4.71/5.13 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) )
% 4.71/5.13 = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % ceiling_less_numeral
% 4.71/5.13 thf(fact_5939_ceiling__less__numeral,axiom,
% 4.71/5.13 ! [X: rat,V: num] :
% 4.71/5.13 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 4.71/5.13 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % ceiling_less_numeral
% 4.71/5.13 thf(fact_5940_numeral__le__ceiling,axiom,
% 4.71/5.13 ! [V: num,X: rat] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X ) )
% 4.71/5.13 = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_le_ceiling
% 4.71/5.13 thf(fact_5941_numeral__le__ceiling,axiom,
% 4.71/5.13 ! [V: num,X: real] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X ) )
% 4.71/5.13 = ( ord_less_real @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_le_ceiling
% 4.71/5.13 thf(fact_5942_neg__numeral__le__floor,axiom,
% 4.71/5.13 ! [V: num,X: real] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X ) )
% 4.71/5.13 = ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_le_floor
% 4.71/5.13 thf(fact_5943_neg__numeral__le__floor,axiom,
% 4.71/5.13 ! [V: num,X: rat] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X ) )
% 4.71/5.13 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_le_floor
% 4.71/5.13 thf(fact_5944_floor__less__neg__numeral,axiom,
% 4.71/5.13 ! [X: real,V: num] :
% 4.71/5.13 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 4.71/5.13 = ( ord_less_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % floor_less_neg_numeral
% 4.71/5.13 thf(fact_5945_floor__less__neg__numeral,axiom,
% 4.71/5.13 ! [X: rat,V: num] :
% 4.71/5.13 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 4.71/5.13 = ( ord_less_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % floor_less_neg_numeral
% 4.71/5.13 thf(fact_5946_ceiling__le__neg__numeral,axiom,
% 4.71/5.13 ! [X: real,V: num] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 4.71/5.13 = ( ord_less_eq_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % ceiling_le_neg_numeral
% 4.71/5.13 thf(fact_5947_ceiling__le__neg__numeral,axiom,
% 4.71/5.13 ! [X: rat,V: num] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 4.71/5.13 = ( ord_less_eq_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % ceiling_le_neg_numeral
% 4.71/5.13 thf(fact_5948_of__int__le__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [A: int,X: num,N: nat] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 4.71/5.13 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_le_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5949_of__int__le__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [A: int,X: num,N: nat] :
% 4.71/5.13 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X ) @ N ) )
% 4.71/5.13 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_le_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5950_of__int__le__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [A: int,X: num,N: nat] :
% 4.71/5.13 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 4.71/5.13 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_le_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5951_of__int__le__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [A: int,X: num,N: nat] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 4.71/5.13 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_le_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5952_numeral__power__le__of__int__cancel__iff,axiom,
% 4.71/5.13 ! [X: num,N: nat,A: int] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 4.71/5.13 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_power_le_of_int_cancel_iff
% 4.71/5.13 thf(fact_5953_numeral__power__le__of__int__cancel__iff,axiom,
% 4.71/5.13 ! [X: num,N: nat,A: int] :
% 4.71/5.13 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 4.71/5.13 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_power_le_of_int_cancel_iff
% 4.71/5.13 thf(fact_5954_numeral__power__le__of__int__cancel__iff,axiom,
% 4.71/5.13 ! [X: num,N: nat,A: int] :
% 4.71/5.13 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 4.71/5.13 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_power_le_of_int_cancel_iff
% 4.71/5.13 thf(fact_5955_numeral__power__le__of__int__cancel__iff,axiom,
% 4.71/5.13 ! [X: num,N: nat,A: int] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 4.71/5.13 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_power_le_of_int_cancel_iff
% 4.71/5.13 thf(fact_5956_neg__numeral__less__ceiling,axiom,
% 4.71/5.13 ! [V: num,X: real] :
% 4.71/5.13 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X ) )
% 4.71/5.13 = ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_less_ceiling
% 4.71/5.13 thf(fact_5957_neg__numeral__less__ceiling,axiom,
% 4.71/5.13 ! [V: num,X: rat] :
% 4.71/5.13 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X ) )
% 4.71/5.13 = ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_less_ceiling
% 4.71/5.13 thf(fact_5958_of__int__less__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [A: int,X: num,N: nat] :
% 4.71/5.13 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 4.71/5.13 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_less_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5959_of__int__less__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [A: int,X: num,N: nat] :
% 4.71/5.13 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 4.71/5.13 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_less_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5960_of__int__less__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [A: int,X: num,N: nat] :
% 4.71/5.13 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 4.71/5.13 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_less_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5961_of__int__less__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [A: int,X: num,N: nat] :
% 4.71/5.13 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X ) @ N ) )
% 4.71/5.13 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_less_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5962_numeral__power__less__of__int__cancel__iff,axiom,
% 4.71/5.13 ! [X: num,N: nat,A: int] :
% 4.71/5.13 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 4.71/5.13 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_power_less_of_int_cancel_iff
% 4.71/5.13 thf(fact_5963_numeral__power__less__of__int__cancel__iff,axiom,
% 4.71/5.13 ! [X: num,N: nat,A: int] :
% 4.71/5.13 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 4.71/5.13 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_power_less_of_int_cancel_iff
% 4.71/5.13 thf(fact_5964_numeral__power__less__of__int__cancel__iff,axiom,
% 4.71/5.13 ! [X: num,N: nat,A: int] :
% 4.71/5.13 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 4.71/5.13 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_power_less_of_int_cancel_iff
% 4.71/5.13 thf(fact_5965_numeral__power__less__of__int__cancel__iff,axiom,
% 4.71/5.13 ! [X: num,N: nat,A: int] :
% 4.71/5.13 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 4.71/5.13 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_power_less_of_int_cancel_iff
% 4.71/5.13 thf(fact_5966_floor__minus__one__divide__eq__div__numeral,axiom,
% 4.71/5.13 ! [B: num] :
% 4.71/5.13 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) ) )
% 4.71/5.13 = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % floor_minus_one_divide_eq_div_numeral
% 4.71/5.13 thf(fact_5967_neg__numeral__less__floor,axiom,
% 4.71/5.13 ! [V: num,X: real] :
% 4.71/5.13 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X ) )
% 4.71/5.13 = ( ord_less_eq_real @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_less_floor
% 4.71/5.13 thf(fact_5968_neg__numeral__less__floor,axiom,
% 4.71/5.13 ! [V: num,X: rat] :
% 4.71/5.13 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X ) )
% 4.71/5.13 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_less_floor
% 4.71/5.13 thf(fact_5969_floor__le__neg__numeral,axiom,
% 4.71/5.13 ! [X: real,V: num] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 4.71/5.13 = ( ord_less_real @ X @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % floor_le_neg_numeral
% 4.71/5.13 thf(fact_5970_floor__le__neg__numeral,axiom,
% 4.71/5.13 ! [X: rat,V: num] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 4.71/5.13 = ( ord_less_rat @ X @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % floor_le_neg_numeral
% 4.71/5.13 thf(fact_5971_ceiling__less__neg__numeral,axiom,
% 4.71/5.13 ! [X: real,V: num] :
% 4.71/5.13 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 4.71/5.13 = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % ceiling_less_neg_numeral
% 4.71/5.13 thf(fact_5972_ceiling__less__neg__numeral,axiom,
% 4.71/5.13 ! [X: rat,V: num] :
% 4.71/5.13 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 4.71/5.13 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % ceiling_less_neg_numeral
% 4.71/5.13 thf(fact_5973_neg__numeral__le__ceiling,axiom,
% 4.71/5.13 ! [V: num,X: real] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X ) )
% 4.71/5.13 = ( ord_less_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_le_ceiling
% 4.71/5.13 thf(fact_5974_neg__numeral__le__ceiling,axiom,
% 4.71/5.13 ! [V: num,X: rat] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X ) )
% 4.71/5.13 = ( ord_less_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_le_ceiling
% 4.71/5.13 thf(fact_5975_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [A: int,X: num,N: nat] :
% 4.71/5.13 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 4.71/5.13 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_le_neg_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5976_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [A: int,X: num,N: nat] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 4.71/5.13 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_le_neg_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5977_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [A: int,X: num,N: nat] :
% 4.71/5.13 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 4.71/5.13 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_le_neg_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5978_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [A: int,X: num,N: nat] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 4.71/5.13 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_le_neg_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5979_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 4.71/5.13 ! [X: num,N: nat,A: int] :
% 4.71/5.13 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 4.71/5.13 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_power_le_of_int_cancel_iff
% 4.71/5.13 thf(fact_5980_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 4.71/5.13 ! [X: num,N: nat,A: int] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 4.71/5.13 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_power_le_of_int_cancel_iff
% 4.71/5.13 thf(fact_5981_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 4.71/5.13 ! [X: num,N: nat,A: int] :
% 4.71/5.13 ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 4.71/5.13 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_power_le_of_int_cancel_iff
% 4.71/5.13 thf(fact_5982_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 4.71/5.13 ! [X: num,N: nat,A: int] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 4.71/5.13 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_power_le_of_int_cancel_iff
% 4.71/5.13 thf(fact_5983_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [A: int,X: num,N: nat] :
% 4.71/5.13 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 4.71/5.13 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_less_neg_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5984_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [A: int,X: num,N: nat] :
% 4.71/5.13 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 4.71/5.13 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_less_neg_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5985_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [A: int,X: num,N: nat] :
% 4.71/5.13 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 4.71/5.13 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_less_neg_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5986_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 4.71/5.13 ! [A: int,X: num,N: nat] :
% 4.71/5.13 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 4.71/5.13 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % of_int_less_neg_numeral_power_cancel_iff
% 4.71/5.13 thf(fact_5987_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 4.71/5.13 ! [X: num,N: nat,A: int] :
% 4.71/5.13 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 4.71/5.13 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_power_less_of_int_cancel_iff
% 4.71/5.13 thf(fact_5988_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 4.71/5.13 ! [X: num,N: nat,A: int] :
% 4.71/5.13 ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 4.71/5.13 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_power_less_of_int_cancel_iff
% 4.71/5.13 thf(fact_5989_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 4.71/5.13 ! [X: num,N: nat,A: int] :
% 4.71/5.13 ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 4.71/5.13 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_power_less_of_int_cancel_iff
% 4.71/5.13 thf(fact_5990_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 4.71/5.13 ! [X: num,N: nat,A: int] :
% 4.71/5.13 ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 4.71/5.13 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_power_less_of_int_cancel_iff
% 4.71/5.13 thf(fact_5991_mod__less__eq__dividend,axiom,
% 4.71/5.13 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M2 @ N ) @ M2 ) ).
% 4.71/5.13
% 4.71/5.13 % mod_less_eq_dividend
% 4.71/5.13 thf(fact_5992_zero__neq__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( zero_zero_rat
% 4.71/5.13 != ( numeral_numeral_rat @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_neq_numeral
% 4.71/5.13 thf(fact_5993_zero__neq__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( zero_zero_real
% 4.71/5.13 != ( numeral_numeral_real @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_neq_numeral
% 4.71/5.13 thf(fact_5994_zero__neq__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( zero_zero_nat
% 4.71/5.13 != ( numeral_numeral_nat @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_neq_numeral
% 4.71/5.13 thf(fact_5995_zero__neq__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( zero_zero_int
% 4.71/5.13 != ( numeral_numeral_int @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_neq_numeral
% 4.71/5.13 thf(fact_5996_zero__neq__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( zero_z5237406670263579293d_enat
% 4.71/5.13 != ( numera1916890842035813515d_enat @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_neq_numeral
% 4.71/5.13 thf(fact_5997_zero__neq__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( zero_z3403309356797280102nteger
% 4.71/5.13 != ( numera6620942414471956472nteger @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_neq_numeral
% 4.71/5.13 thf(fact_5998_numeral__neq__neg__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( numera6620942414471956472nteger @ M2 )
% 4.71/5.13 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_neq_neg_numeral
% 4.71/5.13 thf(fact_5999_numeral__neq__neg__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( numeral_numeral_int @ M2 )
% 4.71/5.13 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_neq_neg_numeral
% 4.71/5.13 thf(fact_6000_numeral__neq__neg__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( numeral_numeral_real @ M2 )
% 4.71/5.13 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_neq_neg_numeral
% 4.71/5.13 thf(fact_6001_numeral__neq__neg__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( numeral_numeral_rat @ M2 )
% 4.71/5.13 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_neq_neg_numeral
% 4.71/5.13 thf(fact_6002_numeral__neq__neg__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( numera6690914467698888265omplex @ M2 )
% 4.71/5.13 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_neq_neg_numeral
% 4.71/5.13 thf(fact_6003_neg__numeral__neq__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) )
% 4.71/5.13 != ( numera6620942414471956472nteger @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_neq_numeral
% 4.71/5.13 thf(fact_6004_neg__numeral__neq__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) )
% 4.71/5.13 != ( numeral_numeral_int @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_neq_numeral
% 4.71/5.13 thf(fact_6005_neg__numeral__neq__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) )
% 4.71/5.13 != ( numeral_numeral_real @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_neq_numeral
% 4.71/5.13 thf(fact_6006_neg__numeral__neq__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) )
% 4.71/5.13 != ( numeral_numeral_rat @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_neq_numeral
% 4.71/5.13 thf(fact_6007_neg__numeral__neq__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) )
% 4.71/5.13 != ( numera6690914467698888265omplex @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_neq_numeral
% 4.71/5.13 thf(fact_6008_infinite__Icc,axiom,
% 4.71/5.13 ! [A: rat,B: rat] :
% 4.71/5.13 ( ( ord_less_rat @ A @ B )
% 4.71/5.13 => ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % infinite_Icc
% 4.71/5.13 thf(fact_6009_infinite__Icc,axiom,
% 4.71/5.13 ! [A: real,B: real] :
% 4.71/5.13 ( ( ord_less_real @ A @ B )
% 4.71/5.13 => ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % infinite_Icc
% 4.71/5.13 thf(fact_6010_atLeastAtMost__singleton_H,axiom,
% 4.71/5.13 ! [A: $o,B: $o] :
% 4.71/5.13 ( ( A = B )
% 4.71/5.13 => ( ( set_or8904488021354931149Most_o @ A @ B )
% 4.71/5.13 = ( insert_o @ A @ bot_bot_set_o ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastAtMost_singleton'
% 4.71/5.13 thf(fact_6011_atLeastAtMost__singleton_H,axiom,
% 4.71/5.13 ! [A: int,B: int] :
% 4.71/5.13 ( ( A = B )
% 4.71/5.13 => ( ( set_or1266510415728281911st_int @ A @ B )
% 4.71/5.13 = ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastAtMost_singleton'
% 4.71/5.13 thf(fact_6012_atLeastAtMost__singleton_H,axiom,
% 4.71/5.13 ! [A: nat,B: nat] :
% 4.71/5.13 ( ( A = B )
% 4.71/5.13 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 4.71/5.13 = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastAtMost_singleton'
% 4.71/5.13 thf(fact_6013_atLeastAtMost__singleton_H,axiom,
% 4.71/5.13 ! [A: real,B: real] :
% 4.71/5.13 ( ( A = B )
% 4.71/5.13 => ( ( set_or1222579329274155063t_real @ A @ B )
% 4.71/5.13 = ( insert_real @ A @ bot_bot_set_real ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastAtMost_singleton'
% 4.71/5.13 thf(fact_6014_mod__Suc,axiom,
% 4.71/5.13 ! [M2: nat,N: nat] :
% 4.71/5.13 ( ( ( ( suc @ ( modulo_modulo_nat @ M2 @ N ) )
% 4.71/5.13 = N )
% 4.71/5.13 => ( ( modulo_modulo_nat @ ( suc @ M2 ) @ N )
% 4.71/5.13 = zero_zero_nat ) )
% 4.71/5.13 & ( ( ( suc @ ( modulo_modulo_nat @ M2 @ N ) )
% 4.71/5.13 != N )
% 4.71/5.13 => ( ( modulo_modulo_nat @ ( suc @ M2 ) @ N )
% 4.71/5.13 = ( suc @ ( modulo_modulo_nat @ M2 @ N ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % mod_Suc
% 4.71/5.13 thf(fact_6015_mod__induct,axiom,
% 4.71/5.13 ! [P: nat > $o,N: nat,P6: nat,M2: nat] :
% 4.71/5.13 ( ( P @ N )
% 4.71/5.13 => ( ( ord_less_nat @ N @ P6 )
% 4.71/5.13 => ( ( ord_less_nat @ M2 @ P6 )
% 4.71/5.13 => ( ! [N2: nat] :
% 4.71/5.13 ( ( ord_less_nat @ N2 @ P6 )
% 4.71/5.13 => ( ( P @ N2 )
% 4.71/5.13 => ( P @ ( modulo_modulo_nat @ ( suc @ N2 ) @ P6 ) ) ) )
% 4.71/5.13 => ( P @ M2 ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % mod_induct
% 4.71/5.13 thf(fact_6016_norm__ge__zero,axiom,
% 4.71/5.13 ! [X: complex] : ( ord_less_eq_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_ge_zero
% 4.71/5.13 thf(fact_6017_mod__less__divisor,axiom,
% 4.71/5.13 ! [N: nat,M2: nat] :
% 4.71/5.13 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.13 => ( ord_less_nat @ ( modulo_modulo_nat @ M2 @ N ) @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % mod_less_divisor
% 4.71/5.13 thf(fact_6018_gcd__nat__induct,axiom,
% 4.71/5.13 ! [P: nat > nat > $o,M2: nat,N: nat] :
% 4.71/5.13 ( ! [M4: nat] : ( P @ M4 @ zero_zero_nat )
% 4.71/5.13 => ( ! [M4: nat,N2: nat] :
% 4.71/5.13 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.71/5.13 => ( ( P @ N2 @ ( modulo_modulo_nat @ M4 @ N2 ) )
% 4.71/5.13 => ( P @ M4 @ N2 ) ) )
% 4.71/5.13 => ( P @ M2 @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % gcd_nat_induct
% 4.71/5.13 thf(fact_6019_mod__Suc__le__divisor,axiom,
% 4.71/5.13 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M2 @ ( suc @ N ) ) @ N ) ).
% 4.71/5.13
% 4.71/5.13 % mod_Suc_le_divisor
% 4.71/5.13 thf(fact_6020_zero__le__numeral,axiom,
% 4.71/5.13 ! [N: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_le_numeral
% 4.71/5.13 thf(fact_6021_zero__le__numeral,axiom,
% 4.71/5.13 ! [N: num] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_le_numeral
% 4.71/5.13 thf(fact_6022_zero__le__numeral,axiom,
% 4.71/5.13 ! [N: num] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_le_numeral
% 4.71/5.13 thf(fact_6023_zero__le__numeral,axiom,
% 4.71/5.13 ! [N: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_le_numeral
% 4.71/5.13 thf(fact_6024_zero__le__numeral,axiom,
% 4.71/5.13 ! [N: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_le_numeral
% 4.71/5.13 thf(fact_6025_zero__le__numeral,axiom,
% 4.71/5.13 ! [N: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_le_numeral
% 4.71/5.13 thf(fact_6026_not__numeral__le__zero,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_le_zero
% 4.71/5.13 thf(fact_6027_not__numeral__le__zero,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ N ) @ zero_z5237406670263579293d_enat ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_le_zero
% 4.71/5.13 thf(fact_6028_not__numeral__le__zero,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N ) @ zero_z3403309356797280102nteger ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_le_zero
% 4.71/5.13 thf(fact_6029_not__numeral__le__zero,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_le_zero
% 4.71/5.13 thf(fact_6030_not__numeral__le__zero,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_le_zero
% 4.71/5.13 thf(fact_6031_not__numeral__le__zero,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_le_zero
% 4.71/5.13 thf(fact_6032_zero__less__numeral,axiom,
% 4.71/5.13 ! [N: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_less_numeral
% 4.71/5.13 thf(fact_6033_zero__less__numeral,axiom,
% 4.71/5.13 ! [N: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_less_numeral
% 4.71/5.13 thf(fact_6034_zero__less__numeral,axiom,
% 4.71/5.13 ! [N: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_less_numeral
% 4.71/5.13 thf(fact_6035_zero__less__numeral,axiom,
% 4.71/5.13 ! [N: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_less_numeral
% 4.71/5.13 thf(fact_6036_zero__less__numeral,axiom,
% 4.71/5.13 ! [N: num] : ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_less_numeral
% 4.71/5.13 thf(fact_6037_zero__less__numeral,axiom,
% 4.71/5.13 ! [N: num] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_less_numeral
% 4.71/5.13 thf(fact_6038_not__numeral__less__zero,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_less_zero
% 4.71/5.13 thf(fact_6039_not__numeral__less__zero,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_less_zero
% 4.71/5.13 thf(fact_6040_not__numeral__less__zero,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_less_zero
% 4.71/5.13 thf(fact_6041_not__numeral__less__zero,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_less_zero
% 4.71/5.13 thf(fact_6042_not__numeral__less__zero,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ~ ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ N ) @ zero_z5237406670263579293d_enat ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_less_zero
% 4.71/5.13 thf(fact_6043_not__numeral__less__zero,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N ) @ zero_z3403309356797280102nteger ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_less_zero
% 4.71/5.13 thf(fact_6044_mod__eq__0D,axiom,
% 4.71/5.13 ! [M2: nat,D: nat] :
% 4.71/5.13 ( ( ( modulo_modulo_nat @ M2 @ D )
% 4.71/5.13 = zero_zero_nat )
% 4.71/5.13 => ? [Q5: nat] :
% 4.71/5.13 ( M2
% 4.71/5.13 = ( times_times_nat @ D @ Q5 ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % mod_eq_0D
% 4.71/5.13 thf(fact_6045_one__le__numeral,axiom,
% 4.71/5.13 ! [N: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_le_numeral
% 4.71/5.13 thf(fact_6046_one__le__numeral,axiom,
% 4.71/5.13 ! [N: num] : ( ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_le_numeral
% 4.71/5.13 thf(fact_6047_one__le__numeral,axiom,
% 4.71/5.13 ! [N: num] : ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_le_numeral
% 4.71/5.13 thf(fact_6048_one__le__numeral,axiom,
% 4.71/5.13 ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_le_numeral
% 4.71/5.13 thf(fact_6049_one__le__numeral,axiom,
% 4.71/5.13 ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_le_numeral
% 4.71/5.13 thf(fact_6050_one__le__numeral,axiom,
% 4.71/5.13 ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_le_numeral
% 4.71/5.13 thf(fact_6051_mod__if,axiom,
% 4.71/5.13 ( modulo_modulo_nat
% 4.71/5.13 = ( ^ [M3: nat,N4: nat] : ( if_nat @ ( ord_less_nat @ M3 @ N4 ) @ M3 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M3 @ N4 ) @ N4 ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % mod_if
% 4.71/5.13 thf(fact_6052_mod__geq,axiom,
% 4.71/5.13 ! [M2: nat,N: nat] :
% 4.71/5.13 ( ~ ( ord_less_nat @ M2 @ N )
% 4.71/5.13 => ( ( modulo_modulo_nat @ M2 @ N )
% 4.71/5.13 = ( modulo_modulo_nat @ ( minus_minus_nat @ M2 @ N ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % mod_geq
% 4.71/5.13 thf(fact_6053_not__numeral__less__one,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_less_one
% 4.71/5.13 thf(fact_6054_not__numeral__less__one,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ one_one_real ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_less_one
% 4.71/5.13 thf(fact_6055_not__numeral__less__one,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_less_one
% 4.71/5.13 thf(fact_6056_not__numeral__less__one,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_less_one
% 4.71/5.13 thf(fact_6057_not__numeral__less__one,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ~ ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ N ) @ one_on7984719198319812577d_enat ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_less_one
% 4.71/5.13 thf(fact_6058_not__numeral__less__one,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N ) @ one_one_Code_integer ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_less_one
% 4.71/5.13 thf(fact_6059_neg__numeral__le__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_le_numeral
% 4.71/5.13 thf(fact_6060_neg__numeral__le__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( numeral_numeral_real @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_le_numeral
% 4.71/5.13 thf(fact_6061_neg__numeral__le__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_le_numeral
% 4.71/5.13 thf(fact_6062_neg__numeral__le__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_le_numeral
% 4.71/5.13 thf(fact_6063_not__numeral__le__neg__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_le_neg_numeral
% 4.71/5.13 thf(fact_6064_not__numeral__le__neg__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_le_neg_numeral
% 4.71/5.13 thf(fact_6065_not__numeral__le__neg__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_le_neg_numeral
% 4.71/5.13 thf(fact_6066_not__numeral__le__neg__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_le_neg_numeral
% 4.71/5.13 thf(fact_6067_zero__neq__neg__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( zero_z3403309356797280102nteger
% 4.71/5.13 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_neq_neg_numeral
% 4.71/5.13 thf(fact_6068_zero__neq__neg__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( zero_zero_int
% 4.71/5.13 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_neq_neg_numeral
% 4.71/5.13 thf(fact_6069_zero__neq__neg__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( zero_zero_real
% 4.71/5.13 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_neq_neg_numeral
% 4.71/5.13 thf(fact_6070_zero__neq__neg__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( zero_zero_rat
% 4.71/5.13 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_neq_neg_numeral
% 4.71/5.13 thf(fact_6071_zero__neq__neg__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( zero_zero_complex
% 4.71/5.13 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_neq_neg_numeral
% 4.71/5.13 thf(fact_6072_le__mod__geq,axiom,
% 4.71/5.13 ! [N: nat,M2: nat] :
% 4.71/5.13 ( ( ord_less_eq_nat @ N @ M2 )
% 4.71/5.13 => ( ( modulo_modulo_nat @ M2 @ N )
% 4.71/5.13 = ( modulo_modulo_nat @ ( minus_minus_nat @ M2 @ N ) @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % le_mod_geq
% 4.71/5.13 thf(fact_6073_not__numeral__less__neg__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_less_neg_numeral
% 4.71/5.13 thf(fact_6074_not__numeral__less__neg__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ~ ( ord_less_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_less_neg_numeral
% 4.71/5.13 thf(fact_6075_not__numeral__less__neg__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ~ ( ord_less_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_less_neg_numeral
% 4.71/5.13 thf(fact_6076_not__numeral__less__neg__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_less_neg_numeral
% 4.71/5.13 thf(fact_6077_neg__numeral__less__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_less_numeral
% 4.71/5.13 thf(fact_6078_neg__numeral__less__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_less_numeral
% 4.71/5.13 thf(fact_6079_neg__numeral__less__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( numeral_numeral_real @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_less_numeral
% 4.71/5.13 thf(fact_6080_neg__numeral__less__numeral,axiom,
% 4.71/5.13 ! [M2: num,N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_less_numeral
% 4.71/5.13 thf(fact_6081_one__plus__numeral__commute,axiom,
% 4.71/5.13 ! [X: num] :
% 4.71/5.13 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X ) )
% 4.71/5.13 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_plus_numeral_commute
% 4.71/5.13 thf(fact_6082_one__plus__numeral__commute,axiom,
% 4.71/5.13 ! [X: num] :
% 4.71/5.13 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 4.71/5.13 = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_plus_numeral_commute
% 4.71/5.13 thf(fact_6083_one__plus__numeral__commute,axiom,
% 4.71/5.13 ! [X: num] :
% 4.71/5.13 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 4.71/5.13 = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_plus_numeral_commute
% 4.71/5.13 thf(fact_6084_one__plus__numeral__commute,axiom,
% 4.71/5.13 ! [X: num] :
% 4.71/5.13 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 4.71/5.13 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_plus_numeral_commute
% 4.71/5.13 thf(fact_6085_one__plus__numeral__commute,axiom,
% 4.71/5.13 ! [X: num] :
% 4.71/5.13 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 4.71/5.13 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_plus_numeral_commute
% 4.71/5.13 thf(fact_6086_one__plus__numeral__commute,axiom,
% 4.71/5.13 ! [X: num] :
% 4.71/5.13 ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 4.71/5.13 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ X ) @ one_on7984719198319812577d_enat ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_plus_numeral_commute
% 4.71/5.13 thf(fact_6087_one__plus__numeral__commute,axiom,
% 4.71/5.13 ! [X: num] :
% 4.71/5.13 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X ) )
% 4.71/5.13 = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_plus_numeral_commute
% 4.71/5.13 thf(fact_6088_one__neq__neg__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( one_one_Code_integer
% 4.71/5.13 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_neq_neg_numeral
% 4.71/5.13 thf(fact_6089_one__neq__neg__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( one_one_int
% 4.71/5.13 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_neq_neg_numeral
% 4.71/5.13 thf(fact_6090_one__neq__neg__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( one_one_real
% 4.71/5.13 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_neq_neg_numeral
% 4.71/5.13 thf(fact_6091_one__neq__neg__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( one_one_rat
% 4.71/5.13 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_neq_neg_numeral
% 4.71/5.13 thf(fact_6092_one__neq__neg__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( one_one_complex
% 4.71/5.13 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_neq_neg_numeral
% 4.71/5.13 thf(fact_6093_numeral__neq__neg__one,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( numera6620942414471956472nteger @ N )
% 4.71/5.13 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_neq_neg_one
% 4.71/5.13 thf(fact_6094_numeral__neq__neg__one,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( numeral_numeral_int @ N )
% 4.71/5.13 != ( uminus_uminus_int @ one_one_int ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_neq_neg_one
% 4.71/5.13 thf(fact_6095_numeral__neq__neg__one,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( numeral_numeral_real @ N )
% 4.71/5.13 != ( uminus_uminus_real @ one_one_real ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_neq_neg_one
% 4.71/5.13 thf(fact_6096_numeral__neq__neg__one,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( numeral_numeral_rat @ N )
% 4.71/5.13 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_neq_neg_one
% 4.71/5.13 thf(fact_6097_numeral__neq__neg__one,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( numera6690914467698888265omplex @ N )
% 4.71/5.13 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_neq_neg_one
% 4.71/5.13 thf(fact_6098_atLeastatMost__psubset__iff,axiom,
% 4.71/5.13 ! [A: set_int,B: set_int,C: set_int,D: set_int] :
% 4.71/5.13 ( ( ord_less_set_set_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 4.71/5.13 = ( ( ~ ( ord_less_eq_set_int @ A @ B )
% 4.71/5.13 | ( ( ord_less_eq_set_int @ C @ A )
% 4.71/5.13 & ( ord_less_eq_set_int @ B @ D )
% 4.71/5.13 & ( ( ord_less_set_int @ C @ A )
% 4.71/5.13 | ( ord_less_set_int @ B @ D ) ) ) )
% 4.71/5.13 & ( ord_less_eq_set_int @ C @ D ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_psubset_iff
% 4.71/5.13 thf(fact_6099_atLeastatMost__psubset__iff,axiom,
% 4.71/5.13 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.71/5.13 ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 4.71/5.13 = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 4.71/5.13 | ( ( ord_less_eq_rat @ C @ A )
% 4.71/5.13 & ( ord_less_eq_rat @ B @ D )
% 4.71/5.13 & ( ( ord_less_rat @ C @ A )
% 4.71/5.13 | ( ord_less_rat @ B @ D ) ) ) )
% 4.71/5.13 & ( ord_less_eq_rat @ C @ D ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_psubset_iff
% 4.71/5.13 thf(fact_6100_atLeastatMost__psubset__iff,axiom,
% 4.71/5.13 ! [A: num,B: num,C: num,D: num] :
% 4.71/5.13 ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 4.71/5.13 = ( ( ~ ( ord_less_eq_num @ A @ B )
% 4.71/5.13 | ( ( ord_less_eq_num @ C @ A )
% 4.71/5.13 & ( ord_less_eq_num @ B @ D )
% 4.71/5.13 & ( ( ord_less_num @ C @ A )
% 4.71/5.13 | ( ord_less_num @ B @ D ) ) ) )
% 4.71/5.13 & ( ord_less_eq_num @ C @ D ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_psubset_iff
% 4.71/5.13 thf(fact_6101_atLeastatMost__psubset__iff,axiom,
% 4.71/5.13 ! [A: int,B: int,C: int,D: int] :
% 4.71/5.13 ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 4.71/5.13 = ( ( ~ ( ord_less_eq_int @ A @ B )
% 4.71/5.13 | ( ( ord_less_eq_int @ C @ A )
% 4.71/5.13 & ( ord_less_eq_int @ B @ D )
% 4.71/5.13 & ( ( ord_less_int @ C @ A )
% 4.71/5.13 | ( ord_less_int @ B @ D ) ) ) )
% 4.71/5.13 & ( ord_less_eq_int @ C @ D ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_psubset_iff
% 4.71/5.13 thf(fact_6102_atLeastatMost__psubset__iff,axiom,
% 4.71/5.13 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.71/5.13 ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 4.71/5.13 = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 4.71/5.13 | ( ( ord_less_eq_nat @ C @ A )
% 4.71/5.13 & ( ord_less_eq_nat @ B @ D )
% 4.71/5.13 & ( ( ord_less_nat @ C @ A )
% 4.71/5.13 | ( ord_less_nat @ B @ D ) ) ) )
% 4.71/5.13 & ( ord_less_eq_nat @ C @ D ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_psubset_iff
% 4.71/5.13 thf(fact_6103_atLeastatMost__psubset__iff,axiom,
% 4.71/5.13 ! [A: real,B: real,C: real,D: real] :
% 4.71/5.13 ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 4.71/5.13 = ( ( ~ ( ord_less_eq_real @ A @ B )
% 4.71/5.13 | ( ( ord_less_eq_real @ C @ A )
% 4.71/5.13 & ( ord_less_eq_real @ B @ D )
% 4.71/5.13 & ( ( ord_less_real @ C @ A )
% 4.71/5.13 | ( ord_less_real @ B @ D ) ) ) )
% 4.71/5.13 & ( ord_less_eq_real @ C @ D ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastatMost_psubset_iff
% 4.71/5.13 thf(fact_6104_nonzero__norm__divide,axiom,
% 4.71/5.13 ! [B: real,A: real] :
% 4.71/5.13 ( ( B != zero_zero_real )
% 4.71/5.13 => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 4.71/5.13 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % nonzero_norm_divide
% 4.71/5.13 thf(fact_6105_nonzero__norm__divide,axiom,
% 4.71/5.13 ! [B: complex,A: complex] :
% 4.71/5.13 ( ( B != zero_zero_complex )
% 4.71/5.13 => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 4.71/5.13 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % nonzero_norm_divide
% 4.71/5.13 thf(fact_6106_power__eq__imp__eq__norm,axiom,
% 4.71/5.13 ! [W2: real,N: nat,Z: real] :
% 4.71/5.13 ( ( ( power_power_real @ W2 @ N )
% 4.71/5.13 = ( power_power_real @ Z @ N ) )
% 4.71/5.13 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.13 => ( ( real_V7735802525324610683m_real @ W2 )
% 4.71/5.13 = ( real_V7735802525324610683m_real @ Z ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % power_eq_imp_eq_norm
% 4.71/5.13 thf(fact_6107_power__eq__imp__eq__norm,axiom,
% 4.71/5.13 ! [W2: complex,N: nat,Z: complex] :
% 4.71/5.13 ( ( ( power_power_complex @ W2 @ N )
% 4.71/5.13 = ( power_power_complex @ Z @ N ) )
% 4.71/5.13 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.13 => ( ( real_V1022390504157884413omplex @ W2 )
% 4.71/5.13 = ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % power_eq_imp_eq_norm
% 4.71/5.13 thf(fact_6108_norm__mult__ineq,axiom,
% 4.71/5.13 ! [X: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) ) @ ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_mult_ineq
% 4.71/5.13 thf(fact_6109_norm__mult__ineq,axiom,
% 4.71/5.13 ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_mult_ineq
% 4.71/5.13 thf(fact_6110_mod__le__divisor,axiom,
% 4.71/5.13 ! [N: nat,M2: nat] :
% 4.71/5.13 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.13 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M2 @ N ) @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % mod_le_divisor
% 4.71/5.13 thf(fact_6111_atLeastAtMostPlus1__int__conv,axiom,
% 4.71/5.13 ! [M2: int,N: int] :
% 4.71/5.13 ( ( ord_less_eq_int @ M2 @ ( plus_plus_int @ one_one_int @ N ) )
% 4.71/5.13 => ( ( set_or1266510415728281911st_int @ M2 @ ( plus_plus_int @ one_one_int @ N ) )
% 4.71/5.13 = ( insert_int @ ( plus_plus_int @ one_one_int @ N ) @ ( set_or1266510415728281911st_int @ M2 @ N ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % atLeastAtMostPlus1_int_conv
% 4.71/5.13 thf(fact_6112_simp__from__to,axiom,
% 4.71/5.13 ( set_or1266510415728281911st_int
% 4.71/5.13 = ( ^ [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 ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % simp_from_to
% 4.71/5.13 thf(fact_6113_norm__power__ineq,axiom,
% 4.71/5.13 ! [X: real,N: nat] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( power_power_real @ X @ N ) ) @ ( power_power_real @ ( real_V7735802525324610683m_real @ X ) @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_power_ineq
% 4.71/5.13 thf(fact_6114_norm__power__ineq,axiom,
% 4.71/5.13 ! [X: complex,N: nat] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( power_power_complex @ X @ N ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ X ) @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_power_ineq
% 4.71/5.13 thf(fact_6115_norm__triangle__mono,axiom,
% 4.71/5.13 ! [A: real,R2: real,B: real,S: real] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R2 )
% 4.71/5.13 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ S )
% 4.71/5.13 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_triangle_mono
% 4.71/5.13 thf(fact_6116_norm__triangle__mono,axiom,
% 4.71/5.13 ! [A: complex,R2: real,B: complex,S: real] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R2 )
% 4.71/5.13 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ S )
% 4.71/5.13 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_triangle_mono
% 4.71/5.13 thf(fact_6117_norm__triangle__ineq,axiom,
% 4.71/5.13 ! [X: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_triangle_ineq
% 4.71/5.13 thf(fact_6118_norm__triangle__ineq,axiom,
% 4.71/5.13 ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_triangle_ineq
% 4.71/5.13 thf(fact_6119_norm__triangle__le,axiom,
% 4.71/5.13 ! [X: real,Y: real,E2: real] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E2 )
% 4.71/5.13 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ E2 ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_triangle_le
% 4.71/5.13 thf(fact_6120_norm__triangle__le,axiom,
% 4.71/5.13 ! [X: complex,Y: complex,E2: real] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E2 )
% 4.71/5.13 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ E2 ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_triangle_le
% 4.71/5.13 thf(fact_6121_norm__add__leD,axiom,
% 4.71/5.13 ! [A: real,B: real,C: real] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ C )
% 4.71/5.13 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_add_leD
% 4.71/5.13 thf(fact_6122_norm__add__leD,axiom,
% 4.71/5.13 ! [A: complex,B: complex,C: real] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ C )
% 4.71/5.13 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_add_leD
% 4.71/5.13 thf(fact_6123_norm__triangle__le__diff,axiom,
% 4.71/5.13 ! [X: real,Y: real,E2: real] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E2 )
% 4.71/5.13 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) @ E2 ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_triangle_le_diff
% 4.71/5.13 thf(fact_6124_norm__triangle__le__diff,axiom,
% 4.71/5.13 ! [X: complex,Y: complex,E2: real] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E2 )
% 4.71/5.13 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) @ E2 ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_triangle_le_diff
% 4.71/5.13 thf(fact_6125_norm__diff__triangle__le,axiom,
% 4.71/5.13 ! [X: real,Y: real,E1: real,Z: real,E22: real] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) @ E1 )
% 4.71/5.13 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z ) ) @ E22 )
% 4.71/5.13 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_diff_triangle_le
% 4.71/5.13 thf(fact_6126_norm__diff__triangle__le,axiom,
% 4.71/5.13 ! [X: complex,Y: complex,E1: real,Z: complex,E22: real] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) @ E1 )
% 4.71/5.13 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z ) ) @ E22 )
% 4.71/5.13 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_diff_triangle_le
% 4.71/5.13 thf(fact_6127_norm__triangle__ineq4,axiom,
% 4.71/5.13 ! [A: real,B: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_triangle_ineq4
% 4.71/5.13 thf(fact_6128_norm__triangle__ineq4,axiom,
% 4.71/5.13 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_triangle_ineq4
% 4.71/5.13 thf(fact_6129_norm__triangle__sub,axiom,
% 4.71/5.13 ! [X: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ Y ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_triangle_sub
% 4.71/5.13 thf(fact_6130_norm__triangle__sub,axiom,
% 4.71/5.13 ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Y ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_triangle_sub
% 4.71/5.13 thf(fact_6131_div__less__mono,axiom,
% 4.71/5.13 ! [A2: nat,B2: nat,N: nat] :
% 4.71/5.13 ( ( ord_less_nat @ A2 @ B2 )
% 4.71/5.13 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.13 => ( ( ( modulo_modulo_nat @ A2 @ N )
% 4.71/5.13 = zero_zero_nat )
% 4.71/5.13 => ( ( ( modulo_modulo_nat @ B2 @ N )
% 4.71/5.13 = zero_zero_nat )
% 4.71/5.13 => ( ord_less_nat @ ( divide_divide_nat @ A2 @ N ) @ ( divide_divide_nat @ B2 @ N ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % div_less_mono
% 4.71/5.13 thf(fact_6132_neg__numeral__le__zero,axiom,
% 4.71/5.13 ! [N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_le_zero
% 4.71/5.13 thf(fact_6133_neg__numeral__le__zero,axiom,
% 4.71/5.13 ! [N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_le_zero
% 4.71/5.13 thf(fact_6134_neg__numeral__le__zero,axiom,
% 4.71/5.13 ! [N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_le_zero
% 4.71/5.13 thf(fact_6135_neg__numeral__le__zero,axiom,
% 4.71/5.13 ! [N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_le_zero
% 4.71/5.13 thf(fact_6136_not__zero__le__neg__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_zero_le_neg_numeral
% 4.71/5.13 thf(fact_6137_not__zero__le__neg__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_zero_le_neg_numeral
% 4.71/5.13 thf(fact_6138_not__zero__le__neg__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_zero_le_neg_numeral
% 4.71/5.13 thf(fact_6139_not__zero__le__neg__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_zero_le_neg_numeral
% 4.71/5.13 thf(fact_6140_neg__numeral__less__zero,axiom,
% 4.71/5.13 ! [N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_less_zero
% 4.71/5.13 thf(fact_6141_neg__numeral__less__zero,axiom,
% 4.71/5.13 ! [N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_less_zero
% 4.71/5.13 thf(fact_6142_neg__numeral__less__zero,axiom,
% 4.71/5.13 ! [N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_less_zero
% 4.71/5.13 thf(fact_6143_neg__numeral__less__zero,axiom,
% 4.71/5.13 ! [N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_less_zero
% 4.71/5.13 thf(fact_6144_not__zero__less__neg__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_zero_less_neg_numeral
% 4.71/5.13 thf(fact_6145_not__zero__less__neg__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_zero_less_neg_numeral
% 4.71/5.13 thf(fact_6146_not__zero__less__neg__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_zero_less_neg_numeral
% 4.71/5.13 thf(fact_6147_not__zero__less__neg__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_zero_less_neg_numeral
% 4.71/5.13 thf(fact_6148_eq__divide__eq__numeral_I1_J,axiom,
% 4.71/5.13 ! [W2: num,B: rat,C: rat] :
% 4.71/5.13 ( ( ( numeral_numeral_rat @ W2 )
% 4.71/5.13 = ( divide_divide_rat @ B @ C ) )
% 4.71/5.13 = ( ( ( C != zero_zero_rat )
% 4.71/5.13 => ( ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C )
% 4.71/5.13 = B ) )
% 4.71/5.13 & ( ( C = zero_zero_rat )
% 4.71/5.13 => ( ( numeral_numeral_rat @ W2 )
% 4.71/5.13 = zero_zero_rat ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % eq_divide_eq_numeral(1)
% 4.71/5.13 thf(fact_6149_eq__divide__eq__numeral_I1_J,axiom,
% 4.71/5.13 ! [W2: num,B: real,C: real] :
% 4.71/5.13 ( ( ( numeral_numeral_real @ W2 )
% 4.71/5.13 = ( divide_divide_real @ B @ C ) )
% 4.71/5.13 = ( ( ( C != zero_zero_real )
% 4.71/5.13 => ( ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C )
% 4.71/5.13 = B ) )
% 4.71/5.13 & ( ( C = zero_zero_real )
% 4.71/5.13 => ( ( numeral_numeral_real @ W2 )
% 4.71/5.13 = zero_zero_real ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % eq_divide_eq_numeral(1)
% 4.71/5.13 thf(fact_6150_divide__eq__eq__numeral_I1_J,axiom,
% 4.71/5.13 ! [B: rat,C: rat,W2: num] :
% 4.71/5.13 ( ( ( divide_divide_rat @ B @ C )
% 4.71/5.13 = ( numeral_numeral_rat @ W2 ) )
% 4.71/5.13 = ( ( ( C != zero_zero_rat )
% 4.71/5.13 => ( B
% 4.71/5.13 = ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 4.71/5.13 & ( ( C = zero_zero_rat )
% 4.71/5.13 => ( ( numeral_numeral_rat @ W2 )
% 4.71/5.13 = zero_zero_rat ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % divide_eq_eq_numeral(1)
% 4.71/5.13 thf(fact_6151_divide__eq__eq__numeral_I1_J,axiom,
% 4.71/5.13 ! [B: real,C: real,W2: num] :
% 4.71/5.13 ( ( ( divide_divide_real @ B @ C )
% 4.71/5.13 = ( numeral_numeral_real @ W2 ) )
% 4.71/5.13 = ( ( ( C != zero_zero_real )
% 4.71/5.13 => ( B
% 4.71/5.13 = ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 4.71/5.13 & ( ( C = zero_zero_real )
% 4.71/5.13 => ( ( numeral_numeral_real @ W2 )
% 4.71/5.13 = zero_zero_real ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % divide_eq_eq_numeral(1)
% 4.71/5.13 thf(fact_6152_norm__diff__ineq,axiom,
% 4.71/5.13 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_diff_ineq
% 4.71/5.13 thf(fact_6153_norm__diff__ineq,axiom,
% 4.71/5.13 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_diff_ineq
% 4.71/5.13 thf(fact_6154_norm__triangle__ineq2,axiom,
% 4.71/5.13 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_triangle_ineq2
% 4.71/5.13 thf(fact_6155_norm__triangle__ineq2,axiom,
% 4.71/5.13 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_triangle_ineq2
% 4.71/5.13 thf(fact_6156_neg__numeral__le__one,axiom,
% 4.71/5.13 ! [M2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ one_one_Code_integer ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_le_one
% 4.71/5.13 thf(fact_6157_neg__numeral__le__one,axiom,
% 4.71/5.13 ! [M2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ one_one_real ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_le_one
% 4.71/5.13 thf(fact_6158_neg__numeral__le__one,axiom,
% 4.71/5.13 ! [M2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ one_one_rat ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_le_one
% 4.71/5.13 thf(fact_6159_neg__numeral__le__one,axiom,
% 4.71/5.13 ! [M2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_le_one
% 4.71/5.13 thf(fact_6160_neg__one__le__numeral,axiom,
% 4.71/5.13 ! [M2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M2 ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_one_le_numeral
% 4.71/5.13 thf(fact_6161_neg__one__le__numeral,axiom,
% 4.71/5.13 ! [M2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M2 ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_one_le_numeral
% 4.71/5.13 thf(fact_6162_neg__one__le__numeral,axiom,
% 4.71/5.13 ! [M2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M2 ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_one_le_numeral
% 4.71/5.13 thf(fact_6163_neg__one__le__numeral,axiom,
% 4.71/5.13 ! [M2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M2 ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_one_le_numeral
% 4.71/5.13 thf(fact_6164_neg__numeral__le__neg__one,axiom,
% 4.71/5.13 ! [M2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_le_neg_one
% 4.71/5.13 thf(fact_6165_neg__numeral__le__neg__one,axiom,
% 4.71/5.13 ! [M2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_le_neg_one
% 4.71/5.13 thf(fact_6166_neg__numeral__le__neg__one,axiom,
% 4.71/5.13 ! [M2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_le_neg_one
% 4.71/5.13 thf(fact_6167_neg__numeral__le__neg__one,axiom,
% 4.71/5.13 ! [M2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_le_neg_one
% 4.71/5.13 thf(fact_6168_not__numeral__le__neg__one,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_le_neg_one
% 4.71/5.13 thf(fact_6169_not__numeral__le__neg__one,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_le_neg_one
% 4.71/5.13 thf(fact_6170_not__numeral__le__neg__one,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_le_neg_one
% 4.71/5.13 thf(fact_6171_not__numeral__le__neg__one,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_le_neg_one
% 4.71/5.13 thf(fact_6172_not__one__le__neg__numeral,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_one_le_neg_numeral
% 4.71/5.13 thf(fact_6173_not__one__le__neg__numeral,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_one_le_neg_numeral
% 4.71/5.13 thf(fact_6174_not__one__le__neg__numeral,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_one_le_neg_numeral
% 4.71/5.13 thf(fact_6175_not__one__le__neg__numeral,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_one_le_neg_numeral
% 4.71/5.13 thf(fact_6176_mod__eq__nat1E,axiom,
% 4.71/5.13 ! [M2: nat,Q4: nat,N: nat] :
% 4.71/5.13 ( ( ( modulo_modulo_nat @ M2 @ Q4 )
% 4.71/5.13 = ( modulo_modulo_nat @ N @ Q4 ) )
% 4.71/5.13 => ( ( ord_less_eq_nat @ N @ M2 )
% 4.71/5.13 => ~ ! [S3: nat] :
% 4.71/5.13 ( M2
% 4.71/5.13 != ( plus_plus_nat @ N @ ( times_times_nat @ Q4 @ S3 ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % mod_eq_nat1E
% 4.71/5.13 thf(fact_6177_mod__eq__nat2E,axiom,
% 4.71/5.13 ! [M2: nat,Q4: nat,N: nat] :
% 4.71/5.13 ( ( ( modulo_modulo_nat @ M2 @ Q4 )
% 4.71/5.13 = ( modulo_modulo_nat @ N @ Q4 ) )
% 4.71/5.13 => ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.13 => ~ ! [S3: nat] :
% 4.71/5.13 ( N
% 4.71/5.13 != ( plus_plus_nat @ M2 @ ( times_times_nat @ Q4 @ S3 ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % mod_eq_nat2E
% 4.71/5.13 thf(fact_6178_nat__mod__eq__lemma,axiom,
% 4.71/5.13 ! [X: nat,N: nat,Y: nat] :
% 4.71/5.13 ( ( ( modulo_modulo_nat @ X @ N )
% 4.71/5.13 = ( modulo_modulo_nat @ Y @ N ) )
% 4.71/5.13 => ( ( ord_less_eq_nat @ Y @ X )
% 4.71/5.13 => ? [Q5: nat] :
% 4.71/5.13 ( X
% 4.71/5.13 = ( plus_plus_nat @ Y @ ( times_times_nat @ N @ Q5 ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % nat_mod_eq_lemma
% 4.71/5.13 thf(fact_6179_neg__numeral__less__one,axiom,
% 4.71/5.13 ! [M2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ one_one_Code_integer ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_less_one
% 4.71/5.13 thf(fact_6180_neg__numeral__less__one,axiom,
% 4.71/5.13 ! [M2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_less_one
% 4.71/5.13 thf(fact_6181_neg__numeral__less__one,axiom,
% 4.71/5.13 ! [M2: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ one_one_real ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_less_one
% 4.71/5.13 thf(fact_6182_neg__numeral__less__one,axiom,
% 4.71/5.13 ! [M2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ one_one_rat ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_less_one
% 4.71/5.13 thf(fact_6183_neg__one__less__numeral,axiom,
% 4.71/5.13 ! [M2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M2 ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_one_less_numeral
% 4.71/5.13 thf(fact_6184_neg__one__less__numeral,axiom,
% 4.71/5.13 ! [M2: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M2 ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_one_less_numeral
% 4.71/5.13 thf(fact_6185_neg__one__less__numeral,axiom,
% 4.71/5.13 ! [M2: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M2 ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_one_less_numeral
% 4.71/5.13 thf(fact_6186_neg__one__less__numeral,axiom,
% 4.71/5.13 ! [M2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M2 ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_one_less_numeral
% 4.71/5.13 thf(fact_6187_not__numeral__less__neg__one,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_less_neg_one
% 4.71/5.13 thf(fact_6188_not__numeral__less__neg__one,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ~ ( ord_less_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_less_neg_one
% 4.71/5.13 thf(fact_6189_not__numeral__less__neg__one,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ~ ( ord_less_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_less_neg_one
% 4.71/5.13 thf(fact_6190_not__numeral__less__neg__one,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_numeral_less_neg_one
% 4.71/5.13 thf(fact_6191_not__one__less__neg__numeral,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_one_less_neg_numeral
% 4.71/5.13 thf(fact_6192_not__one__less__neg__numeral,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_one_less_neg_numeral
% 4.71/5.13 thf(fact_6193_not__one__less__neg__numeral,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_one_less_neg_numeral
% 4.71/5.13 thf(fact_6194_not__one__less__neg__numeral,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_one_less_neg_numeral
% 4.71/5.13 thf(fact_6195_not__neg__one__less__neg__numeral,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_neg_one_less_neg_numeral
% 4.71/5.13 thf(fact_6196_not__neg__one__less__neg__numeral,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_neg_one_less_neg_numeral
% 4.71/5.13 thf(fact_6197_not__neg__one__less__neg__numeral,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_neg_one_less_neg_numeral
% 4.71/5.13 thf(fact_6198_not__neg__one__less__neg__numeral,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_neg_one_less_neg_numeral
% 4.71/5.13 thf(fact_6199_nonzero__norm__inverse,axiom,
% 4.71/5.13 ! [A: real] :
% 4.71/5.13 ( ( A != zero_zero_real )
% 4.71/5.13 => ( ( real_V7735802525324610683m_real @ ( inverse_inverse_real @ A ) )
% 4.71/5.13 = ( inverse_inverse_real @ ( real_V7735802525324610683m_real @ A ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % nonzero_norm_inverse
% 4.71/5.13 thf(fact_6200_nonzero__norm__inverse,axiom,
% 4.71/5.13 ! [A: complex] :
% 4.71/5.13 ( ( A != zero_zero_complex )
% 4.71/5.13 => ( ( real_V1022390504157884413omplex @ ( invers8013647133539491842omplex @ A ) )
% 4.71/5.13 = ( inverse_inverse_real @ ( real_V1022390504157884413omplex @ A ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % nonzero_norm_inverse
% 4.71/5.13 thf(fact_6201_norm__exp,axiom,
% 4.71/5.13 ! [X: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ X ) ) @ ( exp_real @ ( real_V7735802525324610683m_real @ X ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_exp
% 4.71/5.13 thf(fact_6202_norm__exp,axiom,
% 4.71/5.13 ! [X: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ X ) ) @ ( exp_real @ ( real_V1022390504157884413omplex @ X ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_exp
% 4.71/5.13 thf(fact_6203_power__eq__1__iff,axiom,
% 4.71/5.13 ! [W2: real,N: nat] :
% 4.71/5.13 ( ( ( power_power_real @ W2 @ N )
% 4.71/5.13 = one_one_real )
% 4.71/5.13 => ( ( ( real_V7735802525324610683m_real @ W2 )
% 4.71/5.13 = one_one_real )
% 4.71/5.13 | ( N = zero_zero_nat ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % power_eq_1_iff
% 4.71/5.13 thf(fact_6204_power__eq__1__iff,axiom,
% 4.71/5.13 ! [W2: complex,N: nat] :
% 4.71/5.13 ( ( ( power_power_complex @ W2 @ N )
% 4.71/5.13 = one_one_complex )
% 4.71/5.13 => ( ( ( real_V1022390504157884413omplex @ W2 )
% 4.71/5.13 = one_one_real )
% 4.71/5.13 | ( N = zero_zero_nat ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % power_eq_1_iff
% 4.71/5.13 thf(fact_6205_norm__diff__triangle__ineq,axiom,
% 4.71/5.13 ! [A: real,B: real,C: real,D: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ C ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_diff_triangle_ineq
% 4.71/5.13 thf(fact_6206_norm__diff__triangle__ineq,axiom,
% 4.71/5.13 ! [A: complex,B: complex,C: complex,D: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ ( plus_plus_complex @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ C ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ D ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_diff_triangle_ineq
% 4.71/5.13 thf(fact_6207_norm__sgn,axiom,
% 4.71/5.13 ! [X: real] :
% 4.71/5.13 ( ( ( X = zero_zero_real )
% 4.71/5.13 => ( ( real_V7735802525324610683m_real @ ( sgn_sgn_real @ X ) )
% 4.71/5.13 = zero_zero_real ) )
% 4.71/5.13 & ( ( X != zero_zero_real )
% 4.71/5.13 => ( ( real_V7735802525324610683m_real @ ( sgn_sgn_real @ X ) )
% 4.71/5.13 = one_one_real ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_sgn
% 4.71/5.13 thf(fact_6208_norm__sgn,axiom,
% 4.71/5.13 ! [X: complex] :
% 4.71/5.13 ( ( ( X = zero_zero_complex )
% 4.71/5.13 => ( ( real_V1022390504157884413omplex @ ( sgn_sgn_complex @ X ) )
% 4.71/5.13 = zero_zero_real ) )
% 4.71/5.13 & ( ( X != zero_zero_complex )
% 4.71/5.13 => ( ( real_V1022390504157884413omplex @ ( sgn_sgn_complex @ X ) )
% 4.71/5.13 = one_one_real ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_sgn
% 4.71/5.13 thf(fact_6209_split__mod,axiom,
% 4.71/5.13 ! [P: nat > $o,M2: nat,N: nat] :
% 4.71/5.13 ( ( P @ ( modulo_modulo_nat @ M2 @ N ) )
% 4.71/5.13 = ( ( ( N = zero_zero_nat )
% 4.71/5.13 => ( P @ M2 ) )
% 4.71/5.13 & ( ( N != zero_zero_nat )
% 4.71/5.13 => ! [I4: nat,J3: nat] :
% 4.71/5.13 ( ( ord_less_nat @ J3 @ N )
% 4.71/5.13 => ( ( M2
% 4.71/5.13 = ( plus_plus_nat @ ( times_times_nat @ N @ I4 ) @ J3 ) )
% 4.71/5.13 => ( P @ J3 ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % split_mod
% 4.71/5.13 thf(fact_6210_divide__less__eq__numeral_I1_J,axiom,
% 4.71/5.13 ! [B: rat,C: rat,W2: num] :
% 4.71/5.13 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W2 ) )
% 4.71/5.13 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.13 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 4.71/5.13 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.13 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.13 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 4.71/5.13 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.13 => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % divide_less_eq_numeral(1)
% 4.71/5.13 thf(fact_6211_divide__less__eq__numeral_I1_J,axiom,
% 4.71/5.13 ! [B: real,C: real,W2: num] :
% 4.71/5.13 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W2 ) )
% 4.71/5.13 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.13 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 4.71/5.13 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.13 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.13 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) @ B ) )
% 4.71/5.13 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.13 => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % divide_less_eq_numeral(1)
% 4.71/5.13 thf(fact_6212_less__divide__eq__numeral_I1_J,axiom,
% 4.71/5.13 ! [W2: num,B: rat,C: rat] :
% 4.71/5.13 ( ( ord_less_rat @ ( numeral_numeral_rat @ W2 ) @ ( divide_divide_rat @ B @ C ) )
% 4.71/5.13 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.13 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 4.71/5.13 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.13 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.13 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 4.71/5.13 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.13 => ( ord_less_rat @ ( numeral_numeral_rat @ W2 ) @ zero_zero_rat ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % less_divide_eq_numeral(1)
% 4.71/5.13 thf(fact_6213_less__divide__eq__numeral_I1_J,axiom,
% 4.71/5.13 ! [W2: num,B: real,C: real] :
% 4.71/5.13 ( ( ord_less_real @ ( numeral_numeral_real @ W2 ) @ ( divide_divide_real @ B @ C ) )
% 4.71/5.13 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.13 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) @ B ) )
% 4.71/5.13 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.13 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.13 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 4.71/5.13 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.13 => ( ord_less_real @ ( numeral_numeral_real @ W2 ) @ zero_zero_real ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % less_divide_eq_numeral(1)
% 4.71/5.13 thf(fact_6214_eq__divide__eq__numeral_I2_J,axiom,
% 4.71/5.13 ! [W2: num,B: real,C: real] :
% 4.71/5.13 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 4.71/5.13 = ( divide_divide_real @ B @ C ) )
% 4.71/5.13 = ( ( ( C != zero_zero_real )
% 4.71/5.13 => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C )
% 4.71/5.13 = B ) )
% 4.71/5.13 & ( ( C = zero_zero_real )
% 4.71/5.13 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 4.71/5.13 = zero_zero_real ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % eq_divide_eq_numeral(2)
% 4.71/5.13 thf(fact_6215_eq__divide__eq__numeral_I2_J,axiom,
% 4.71/5.13 ! [W2: num,B: rat,C: rat] :
% 4.71/5.13 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 4.71/5.13 = ( divide_divide_rat @ B @ C ) )
% 4.71/5.13 = ( ( ( C != zero_zero_rat )
% 4.71/5.13 => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C )
% 4.71/5.13 = B ) )
% 4.71/5.13 & ( ( C = zero_zero_rat )
% 4.71/5.13 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 4.71/5.13 = zero_zero_rat ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % eq_divide_eq_numeral(2)
% 4.71/5.13 thf(fact_6216_eq__divide__eq__numeral_I2_J,axiom,
% 4.71/5.13 ! [W2: num,B: complex,C: complex] :
% 4.71/5.13 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 4.71/5.13 = ( divide1717551699836669952omplex @ B @ C ) )
% 4.71/5.13 = ( ( ( C != zero_zero_complex )
% 4.71/5.13 => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) @ C )
% 4.71/5.13 = B ) )
% 4.71/5.13 & ( ( C = zero_zero_complex )
% 4.71/5.13 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 4.71/5.13 = zero_zero_complex ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % eq_divide_eq_numeral(2)
% 4.71/5.13 thf(fact_6217_divide__eq__eq__numeral_I2_J,axiom,
% 4.71/5.13 ! [B: real,C: real,W2: num] :
% 4.71/5.13 ( ( ( divide_divide_real @ B @ C )
% 4.71/5.13 = ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 4.71/5.13 = ( ( ( C != zero_zero_real )
% 4.71/5.13 => ( B
% 4.71/5.13 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 4.71/5.13 & ( ( C = zero_zero_real )
% 4.71/5.13 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 4.71/5.13 = zero_zero_real ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % divide_eq_eq_numeral(2)
% 4.71/5.13 thf(fact_6218_divide__eq__eq__numeral_I2_J,axiom,
% 4.71/5.13 ! [B: rat,C: rat,W2: num] :
% 4.71/5.13 ( ( ( divide_divide_rat @ B @ C )
% 4.71/5.13 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 4.71/5.13 = ( ( ( C != zero_zero_rat )
% 4.71/5.13 => ( B
% 4.71/5.13 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 4.71/5.13 & ( ( C = zero_zero_rat )
% 4.71/5.13 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 4.71/5.13 = zero_zero_rat ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % divide_eq_eq_numeral(2)
% 4.71/5.13 thf(fact_6219_divide__eq__eq__numeral_I2_J,axiom,
% 4.71/5.13 ! [B: complex,C: complex,W2: num] :
% 4.71/5.13 ( ( ( divide1717551699836669952omplex @ B @ C )
% 4.71/5.13 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 4.71/5.13 = ( ( ( C != zero_zero_complex )
% 4.71/5.13 => ( B
% 4.71/5.13 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) @ C ) ) )
% 4.71/5.13 & ( ( C = zero_zero_complex )
% 4.71/5.13 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 4.71/5.13 = zero_zero_complex ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % divide_eq_eq_numeral(2)
% 4.71/5.13 thf(fact_6220_count__le__length,axiom,
% 4.71/5.13 ! [Xs: list_VEBT_VEBT,X: vEBT_VEBT] : ( ord_less_eq_nat @ ( count_list_VEBT_VEBT @ Xs @ X ) @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 4.71/5.13
% 4.71/5.13 % count_le_length
% 4.71/5.13 thf(fact_6221_count__le__length,axiom,
% 4.71/5.13 ! [Xs: list_nat,X: nat] : ( ord_less_eq_nat @ ( count_list_nat @ Xs @ X ) @ ( size_size_list_nat @ Xs ) ) ).
% 4.71/5.13
% 4.71/5.13 % count_le_length
% 4.71/5.13 thf(fact_6222_norm__triangle__ineq3,axiom,
% 4.71/5.13 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_triangle_ineq3
% 4.71/5.13 thf(fact_6223_norm__triangle__ineq3,axiom,
% 4.71/5.13 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_triangle_ineq3
% 4.71/5.13 thf(fact_6224_real__of__nat__div__aux,axiom,
% 4.71/5.13 ! [X: nat,D: nat] :
% 4.71/5.13 ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ D ) )
% 4.71/5.13 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X @ D ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X @ D ) ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % real_of_nat_div_aux
% 4.71/5.13 thf(fact_6225_nat__mod__distrib,axiom,
% 4.71/5.13 ! [X: int,Y: int] :
% 4.71/5.13 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 4.71/5.13 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.71/5.13 => ( ( nat2 @ ( modulo_modulo_int @ X @ Y ) )
% 4.71/5.13 = ( modulo_modulo_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % nat_mod_distrib
% 4.71/5.13 thf(fact_6226_divide__le__eq__numeral_I1_J,axiom,
% 4.71/5.13 ! [B: real,C: real,W2: num] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W2 ) )
% 4.71/5.13 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.13 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 4.71/5.13 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.13 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.13 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) @ B ) )
% 4.71/5.13 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.13 => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % divide_le_eq_numeral(1)
% 4.71/5.13 thf(fact_6227_divide__le__eq__numeral_I1_J,axiom,
% 4.71/5.13 ! [B: rat,C: rat,W2: num] :
% 4.71/5.13 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W2 ) )
% 4.71/5.13 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.13 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 4.71/5.13 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.13 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.13 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 4.71/5.13 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.13 => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % divide_le_eq_numeral(1)
% 4.71/5.13 thf(fact_6228_le__divide__eq__numeral_I1_J,axiom,
% 4.71/5.13 ! [W2: num,B: real,C: real] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( numeral_numeral_real @ W2 ) @ ( divide_divide_real @ B @ C ) )
% 4.71/5.13 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.13 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) @ B ) )
% 4.71/5.13 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.13 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.13 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C ) ) )
% 4.71/5.13 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.13 => ( ord_less_eq_real @ ( numeral_numeral_real @ W2 ) @ zero_zero_real ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % le_divide_eq_numeral(1)
% 4.71/5.13 thf(fact_6229_le__divide__eq__numeral_I1_J,axiom,
% 4.71/5.13 ! [W2: num,B: rat,C: rat] :
% 4.71/5.13 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W2 ) @ ( divide_divide_rat @ B @ C ) )
% 4.71/5.13 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.13 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 4.71/5.13 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.13 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.13 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 4.71/5.13 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.13 => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W2 ) @ zero_zero_rat ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % le_divide_eq_numeral(1)
% 4.71/5.13 thf(fact_6230_Suc__times__mod__eq,axiom,
% 4.71/5.13 ! [M2: nat,N: nat] :
% 4.71/5.13 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 4.71/5.13 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M2 @ N ) ) @ M2 )
% 4.71/5.13 = one_one_nat ) ) ).
% 4.71/5.13
% 4.71/5.13 % Suc_times_mod_eq
% 4.71/5.13 thf(fact_6231_less__divide__eq__numeral_I2_J,axiom,
% 4.71/5.13 ! [W2: num,B: real,C: real] :
% 4.71/5.13 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ ( divide_divide_real @ B @ C ) )
% 4.71/5.13 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.13 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) @ B ) )
% 4.71/5.13 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.13 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.13 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 4.71/5.13 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.13 => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % less_divide_eq_numeral(2)
% 4.71/5.13 thf(fact_6232_less__divide__eq__numeral_I2_J,axiom,
% 4.71/5.13 ! [W2: num,B: rat,C: rat] :
% 4.71/5.13 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ ( divide_divide_rat @ B @ C ) )
% 4.71/5.13 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.13 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 4.71/5.13 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.13 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.13 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 4.71/5.13 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.13 => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % less_divide_eq_numeral(2)
% 4.71/5.13 thf(fact_6233_divide__less__eq__numeral_I2_J,axiom,
% 4.71/5.13 ! [B: real,C: real,W2: num] :
% 4.71/5.13 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 4.71/5.13 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.13 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) ) )
% 4.71/5.13 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 4.71/5.13 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.13 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C ) @ B ) )
% 4.71/5.13 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 4.71/5.13 => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % divide_less_eq_numeral(2)
% 4.71/5.13 thf(fact_6234_divide__less__eq__numeral_I2_J,axiom,
% 4.71/5.13 ! [B: rat,C: rat,W2: num] :
% 4.71/5.13 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 4.71/5.13 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.13 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 4.71/5.13 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 4.71/5.13 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.13 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 4.71/5.13 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 4.71/5.13 => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % divide_less_eq_numeral(2)
% 4.71/5.13 thf(fact_6235_norm__inverse__le__norm,axiom,
% 4.71/5.13 ! [R2: real,X: real] :
% 4.71/5.13 ( ( ord_less_eq_real @ R2 @ ( real_V7735802525324610683m_real @ X ) )
% 4.71/5.13 => ( ( ord_less_real @ zero_zero_real @ R2 )
% 4.71/5.13 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( inverse_inverse_real @ X ) ) @ ( inverse_inverse_real @ R2 ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_inverse_le_norm
% 4.71/5.13 thf(fact_6236_norm__inverse__le__norm,axiom,
% 4.71/5.13 ! [R2: real,X: complex] :
% 4.71/5.13 ( ( ord_less_eq_real @ R2 @ ( real_V1022390504157884413omplex @ X ) )
% 4.71/5.13 => ( ( ord_less_real @ zero_zero_real @ R2 )
% 4.71/5.13 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( invers8013647133539491842omplex @ X ) ) @ ( inverse_inverse_real @ R2 ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % norm_inverse_le_norm
% 4.71/5.13 thf(fact_6237_CauchyD,axiom,
% 4.71/5.13 ! [X5: nat > complex,E2: real] :
% 4.71/5.13 ( ( topolo6517432010174082258omplex @ X5 )
% 4.71/5.13 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 4.71/5.13 => ? [M9: nat] :
% 4.71/5.13 ! [M: nat] :
% 4.71/5.13 ( ( ord_less_eq_nat @ M9 @ M )
% 4.71/5.13 => ! [N6: nat] :
% 4.71/5.13 ( ( ord_less_eq_nat @ M9 @ N6 )
% 4.71/5.13 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( X5 @ M ) @ ( X5 @ N6 ) ) ) @ E2 ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % CauchyD
% 4.71/5.13 thf(fact_6238_CauchyD,axiom,
% 4.71/5.13 ! [X5: nat > real,E2: real] :
% 4.71/5.13 ( ( topolo4055970368930404560y_real @ X5 )
% 4.71/5.13 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 4.71/5.13 => ? [M9: nat] :
% 4.71/5.13 ! [M: nat] :
% 4.71/5.13 ( ( ord_less_eq_nat @ M9 @ M )
% 4.71/5.13 => ! [N6: nat] :
% 4.71/5.13 ( ( ord_less_eq_nat @ M9 @ N6 )
% 4.71/5.13 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( X5 @ M ) @ ( X5 @ N6 ) ) ) @ E2 ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % CauchyD
% 4.71/5.13 thf(fact_6239_CauchyI,axiom,
% 4.71/5.13 ! [X5: nat > complex] :
% 4.71/5.13 ( ! [E: real] :
% 4.71/5.13 ( ( ord_less_real @ zero_zero_real @ E )
% 4.71/5.13 => ? [M10: nat] :
% 4.71/5.13 ! [M4: nat] :
% 4.71/5.13 ( ( ord_less_eq_nat @ M10 @ M4 )
% 4.71/5.13 => ! [N2: nat] :
% 4.71/5.13 ( ( ord_less_eq_nat @ M10 @ N2 )
% 4.71/5.13 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( X5 @ M4 ) @ ( X5 @ N2 ) ) ) @ E ) ) ) )
% 4.71/5.13 => ( topolo6517432010174082258omplex @ X5 ) ) ).
% 4.71/5.13
% 4.71/5.13 % CauchyI
% 4.71/5.13 thf(fact_6240_CauchyI,axiom,
% 4.71/5.13 ! [X5: nat > real] :
% 4.71/5.13 ( ! [E: real] :
% 4.71/5.13 ( ( ord_less_real @ zero_zero_real @ E )
% 4.71/5.13 => ? [M10: nat] :
% 4.71/5.13 ! [M4: nat] :
% 4.71/5.13 ( ( ord_less_eq_nat @ M10 @ M4 )
% 4.71/5.13 => ! [N2: nat] :
% 4.71/5.13 ( ( ord_less_eq_nat @ M10 @ N2 )
% 4.71/5.13 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( X5 @ M4 ) @ ( X5 @ N2 ) ) ) @ E ) ) ) )
% 4.71/5.13 => ( topolo4055970368930404560y_real @ X5 ) ) ).
% 4.71/5.13
% 4.71/5.13 % CauchyI
% 4.71/5.13 thf(fact_6241_Cauchy__iff,axiom,
% 4.71/5.13 ( topolo6517432010174082258omplex
% 4.71/5.13 = ( ^ [X8: nat > complex] :
% 4.71/5.13 ! [E3: real] :
% 4.71/5.13 ( ( ord_less_real @ zero_zero_real @ E3 )
% 4.71/5.13 => ? [M8: nat] :
% 4.71/5.13 ! [M3: nat] :
% 4.71/5.13 ( ( ord_less_eq_nat @ M8 @ M3 )
% 4.71/5.13 => ! [N4: nat] :
% 4.71/5.13 ( ( ord_less_eq_nat @ M8 @ N4 )
% 4.71/5.13 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( X8 @ M3 ) @ ( X8 @ N4 ) ) ) @ E3 ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % Cauchy_iff
% 4.71/5.13 thf(fact_6242_Cauchy__iff,axiom,
% 4.71/5.13 ( topolo4055970368930404560y_real
% 4.71/5.13 = ( ^ [X8: nat > real] :
% 4.71/5.13 ! [E3: real] :
% 4.71/5.13 ( ( ord_less_real @ zero_zero_real @ E3 )
% 4.71/5.13 => ? [M8: nat] :
% 4.71/5.13 ! [M3: nat] :
% 4.71/5.13 ( ( ord_less_eq_nat @ M8 @ M3 )
% 4.71/5.13 => ! [N4: nat] :
% 4.71/5.13 ( ( ord_less_eq_nat @ M8 @ N4 )
% 4.71/5.13 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( X8 @ M3 ) @ ( X8 @ N4 ) ) ) @ E3 ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % Cauchy_iff
% 4.71/5.13 thf(fact_6243_nth__rotate1,axiom,
% 4.71/5.13 ! [N: nat,Xs: list_int] :
% 4.71/5.13 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 4.71/5.13 => ( ( nth_int @ ( rotate1_int @ Xs ) @ N )
% 4.71/5.13 = ( nth_int @ Xs @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_size_list_int @ Xs ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % nth_rotate1
% 4.71/5.13 thf(fact_6244_nth__rotate1,axiom,
% 4.71/5.13 ! [N: nat,Xs: list_VEBT_VEBT] :
% 4.71/5.13 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.71/5.13 => ( ( nth_VEBT_VEBT @ ( rotate1_VEBT_VEBT @ Xs ) @ N )
% 4.71/5.13 = ( nth_VEBT_VEBT @ Xs @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % nth_rotate1
% 4.71/5.13 thf(fact_6245_nth__rotate1,axiom,
% 4.71/5.13 ! [N: nat,Xs: list_nat] :
% 4.71/5.13 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 4.71/5.13 => ( ( nth_nat @ ( rotate1_nat @ Xs ) @ N )
% 4.71/5.13 = ( nth_nat @ Xs @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_size_list_nat @ Xs ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % nth_rotate1
% 4.71/5.13 thf(fact_6246_bset_I6_J,axiom,
% 4.71/5.13 ! [D4: int,B2: set_int,T: int] :
% 4.71/5.13 ( ( ord_less_int @ zero_zero_int @ D4 )
% 4.71/5.13 => ! [X2: int] :
% 4.71/5.13 ( ! [Xa3: int] :
% 4.71/5.13 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 4.71/5.13 => ! [Xb: int] :
% 4.71/5.13 ( ( member_int @ Xb @ B2 )
% 4.71/5.13 => ( X2
% 4.71/5.13 != ( plus_plus_int @ Xb @ Xa3 ) ) ) )
% 4.71/5.13 => ( ( ord_less_eq_int @ X2 @ T )
% 4.71/5.13 => ( ord_less_eq_int @ ( minus_minus_int @ X2 @ D4 ) @ T ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % bset(6)
% 4.71/5.13 thf(fact_6247_bset_I8_J,axiom,
% 4.71/5.13 ! [D4: int,T: int,B2: set_int] :
% 4.71/5.13 ( ( ord_less_int @ zero_zero_int @ D4 )
% 4.71/5.13 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B2 )
% 4.71/5.13 => ! [X2: int] :
% 4.71/5.13 ( ! [Xa3: int] :
% 4.71/5.13 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 4.71/5.13 => ! [Xb: int] :
% 4.71/5.13 ( ( member_int @ Xb @ B2 )
% 4.71/5.13 => ( X2
% 4.71/5.13 != ( plus_plus_int @ Xb @ Xa3 ) ) ) )
% 4.71/5.13 => ( ( ord_less_eq_int @ T @ X2 )
% 4.71/5.13 => ( ord_less_eq_int @ T @ ( minus_minus_int @ X2 @ D4 ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % bset(8)
% 4.71/5.13 thf(fact_6248_aset_I6_J,axiom,
% 4.71/5.13 ! [D4: int,T: int,A2: set_int] :
% 4.71/5.13 ( ( ord_less_int @ zero_zero_int @ D4 )
% 4.71/5.13 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 4.71/5.13 => ! [X2: int] :
% 4.71/5.13 ( ! [Xa3: int] :
% 4.71/5.13 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 4.71/5.13 => ! [Xb: int] :
% 4.71/5.13 ( ( member_int @ Xb @ A2 )
% 4.71/5.13 => ( X2
% 4.71/5.13 != ( minus_minus_int @ Xb @ Xa3 ) ) ) )
% 4.71/5.13 => ( ( ord_less_eq_int @ X2 @ T )
% 4.71/5.13 => ( ord_less_eq_int @ ( plus_plus_int @ X2 @ D4 ) @ T ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % aset(6)
% 4.71/5.13 thf(fact_6249_product__nth,axiom,
% 4.71/5.13 ! [N: nat,Xs: list_int,Ys2: list_int] :
% 4.71/5.13 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_int @ Ys2 ) ) )
% 4.71/5.13 => ( ( nth_Pr4439495888332055232nt_int @ ( product_int_int @ Xs @ Ys2 ) @ N )
% 4.71/5.13 = ( 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 ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % product_nth
% 4.71/5.13 thf(fact_6250_product__nth,axiom,
% 4.71/5.13 ! [N: nat,Xs: list_int,Ys2: list_VEBT_VEBT] :
% 4.71/5.13 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_int @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) )
% 4.71/5.13 => ( ( nth_Pr3474266648193625910T_VEBT @ ( produc662631939642741121T_VEBT @ Xs @ Ys2 ) @ N )
% 4.71/5.13 = ( 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 ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % product_nth
% 4.71/5.13 thf(fact_6251_product__nth,axiom,
% 4.71/5.13 ! [N: nat,Xs: list_int,Ys2: list_nat] :
% 4.71/5.13 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_nat @ Ys2 ) ) )
% 4.71/5.13 => ( ( nth_Pr8617346907841251940nt_nat @ ( product_int_nat @ Xs @ Ys2 ) @ N )
% 4.71/5.13 = ( 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 ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % product_nth
% 4.71/5.13 thf(fact_6252_product__nth,axiom,
% 4.71/5.13 ! [N: nat,Xs: list_VEBT_VEBT,Ys2: list_int] :
% 4.71/5.13 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys2 ) ) )
% 4.71/5.13 => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys2 ) @ N )
% 4.71/5.13 = ( 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 ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % product_nth
% 4.71/5.13 thf(fact_6253_product__nth,axiom,
% 4.71/5.13 ! [N: nat,Xs: list_VEBT_VEBT,Ys2: list_VEBT_VEBT] :
% 4.71/5.13 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) )
% 4.71/5.13 => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys2 ) @ N )
% 4.71/5.13 = ( 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 ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % product_nth
% 4.71/5.13 thf(fact_6254_product__nth,axiom,
% 4.71/5.13 ! [N: nat,Xs: list_VEBT_VEBT,Ys2: list_nat] :
% 4.71/5.13 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys2 ) ) )
% 4.71/5.13 => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys2 ) @ N )
% 4.71/5.13 = ( 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 ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % product_nth
% 4.71/5.13 thf(fact_6255_product__nth,axiom,
% 4.71/5.13 ! [N: nat,Xs: list_nat,Ys2: list_int] :
% 4.71/5.13 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_int @ Ys2 ) ) )
% 4.71/5.13 => ( ( nth_Pr3440142176431000676at_int @ ( product_nat_int @ Xs @ Ys2 ) @ N )
% 4.71/5.13 = ( product_Pair_nat_int @ ( nth_nat @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys2 ) ) ) @ ( nth_int @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys2 ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % product_nth
% 4.71/5.13 thf(fact_6256_product__nth,axiom,
% 4.71/5.13 ! [N: nat,Xs: list_nat,Ys2: list_VEBT_VEBT] :
% 4.71/5.13 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) )
% 4.71/5.13 => ( ( nth_Pr744662078594809490T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs @ Ys2 ) @ N )
% 4.71/5.13 = ( produc599794634098209291T_VEBT @ ( nth_nat @ Xs @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) @ ( nth_VEBT_VEBT @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % product_nth
% 4.71/5.13 thf(fact_6257_product__nth,axiom,
% 4.71/5.13 ! [N: nat,Xs: list_nat,Ys2: list_nat] :
% 4.71/5.13 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_nat @ Ys2 ) ) )
% 4.71/5.13 => ( ( nth_Pr7617993195940197384at_nat @ ( product_nat_nat @ Xs @ Ys2 ) @ N )
% 4.71/5.13 = ( product_Pair_nat_nat @ ( nth_nat @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys2 ) ) ) @ ( nth_nat @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys2 ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % product_nth
% 4.71/5.13 thf(fact_6258_product__nth,axiom,
% 4.71/5.13 ! [N: nat,Xs: list_P6011104703257516679at_nat,Ys2: list_P6011104703257516679at_nat] :
% 4.71/5.13 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s5460976970255530739at_nat @ Xs ) @ ( size_s5460976970255530739at_nat @ Ys2 ) ) )
% 4.71/5.13 => ( ( nth_Pr6744343527793145070at_nat @ ( produc3544356994491977349at_nat @ Xs @ Ys2 ) @ N )
% 4.71/5.13 = ( produc6161850002892822231at_nat @ ( nth_Pr7617993195940197384at_nat @ Xs @ ( divide_divide_nat @ N @ ( size_s5460976970255530739at_nat @ Ys2 ) ) ) @ ( nth_Pr7617993195940197384at_nat @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_s5460976970255530739at_nat @ Ys2 ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % product_nth
% 4.71/5.13 thf(fact_6259_enat__ord__number_I1_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( numera1916890842035813515d_enat @ N ) )
% 4.71/5.13 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % enat_ord_number(1)
% 4.71/5.13 thf(fact_6260_enat__ord__number_I2_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( numera1916890842035813515d_enat @ N ) )
% 4.71/5.13 = ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % enat_ord_number(2)
% 4.71/5.13 thf(fact_6261_mintlistlength,axiom,
% 4.71/5.13 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 4.71/5.13 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 4.71/5.13 => ( ( Mi != Ma )
% 4.71/5.13 => ( ( ord_less_nat @ Mi @ Ma )
% 4.71/5.13 & ? [M4: nat] :
% 4.71/5.13 ( ( ( some_nat @ M4 )
% 4.71/5.13 = ( vEBT_vebt_mint @ Summary ) )
% 4.71/5.13 & ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % mintlistlength
% 4.71/5.13 thf(fact_6262_lemma__termdiff3,axiom,
% 4.71/5.13 ! [H: real,Z: real,K4: real,N: nat] :
% 4.71/5.13 ( ( H != zero_zero_real )
% 4.71/5.13 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ K4 )
% 4.71/5.13 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z @ H ) ) @ K4 )
% 4.71/5.13 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H ) @ N ) @ ( power_power_real @ Z @ N ) ) @ H ) @ ( 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 @ H ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % lemma_termdiff3
% 4.71/5.13 thf(fact_6263_lemma__termdiff3,axiom,
% 4.71/5.13 ! [H: complex,Z: complex,K4: real,N: nat] :
% 4.71/5.13 ( ( H != zero_zero_complex )
% 4.71/5.13 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ K4 )
% 4.71/5.13 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z @ H ) ) @ K4 )
% 4.71/5.13 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H ) @ N ) @ ( power_power_complex @ Z @ N ) ) @ H ) @ ( 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 @ H ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % lemma_termdiff3
% 4.71/5.13 thf(fact_6264_bounded__linear__axioms__def,axiom,
% 4.71/5.13 ( real_V7139242839884736329omplex
% 4.71/5.13 = ( ^ [F5: complex > complex] :
% 4.71/5.13 ? [K5: real] :
% 4.71/5.13 ! [X3: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F5 @ X3 ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X3 ) @ K5 ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % bounded_linear_axioms_def
% 4.71/5.13 thf(fact_6265_bounded__linear__axioms_Ointro,axiom,
% 4.71/5.13 ! [F: complex > complex] :
% 4.71/5.13 ( ? [K6: real] :
% 4.71/5.13 ! [X4: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X4 ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X4 ) @ K6 ) )
% 4.71/5.13 => ( real_V7139242839884736329omplex @ F ) ) ).
% 4.71/5.13
% 4.71/5.13 % bounded_linear_axioms.intro
% 4.71/5.13 thf(fact_6266_finite__atLeastAtMost,axiom,
% 4.71/5.13 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 4.71/5.13
% 4.71/5.13 % finite_atLeastAtMost
% 4.71/5.13 thf(fact_6267_pow__sum,axiom,
% 4.71/5.13 ! [A: nat,B: nat] :
% 4.71/5.13 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 4.71/5.13 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 4.71/5.13
% 4.71/5.13 % pow_sum
% 4.71/5.13 thf(fact_6268_power__minus__is__div,axiom,
% 4.71/5.13 ! [B: nat,A: nat] :
% 4.71/5.13 ( ( ord_less_eq_nat @ B @ A )
% 4.71/5.13 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ A @ B ) )
% 4.71/5.13 = ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % power_minus_is_div
% 4.71/5.13 thf(fact_6269_member__bound,axiom,
% 4.71/5.13 ! [Tree: vEBT_VEBT,X: nat,N: nat] :
% 4.71/5.13 ( ( vEBT_vebt_member @ Tree @ X )
% 4.71/5.13 => ( ( vEBT_invar_vebt @ Tree @ N )
% 4.71/5.13 => ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % member_bound
% 4.71/5.13 thf(fact_6270_set__n__deg__not__0,axiom,
% 4.71/5.13 ! [TreeList: list_VEBT_VEBT,N: nat,M2: nat] :
% 4.71/5.13 ( ! [X4: vEBT_VEBT] :
% 4.71/5.13 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.71/5.13 => ( vEBT_invar_vebt @ X4 @ N ) )
% 4.71/5.13 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 4.71/5.13 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 4.71/5.13 => ( ord_less_eq_nat @ one_one_nat @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % set_n_deg_not_0
% 4.71/5.13 thf(fact_6271_misiz,axiom,
% 4.71/5.13 ! [T: vEBT_VEBT,N: nat,M2: nat] :
% 4.71/5.13 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.13 => ( ( ( some_nat @ M2 )
% 4.71/5.13 = ( vEBT_vebt_mint @ T ) )
% 4.71/5.13 => ( ord_less_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % misiz
% 4.71/5.13 thf(fact_6272_insert__simp__mima,axiom,
% 4.71/5.13 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 4.71/5.13 ( ( ( X = Mi )
% 4.71/5.13 | ( X = Ma ) )
% 4.71/5.13 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.71/5.13 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.13 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % insert_simp_mima
% 4.71/5.13 thf(fact_6273_helpyd,axiom,
% 4.71/5.13 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 4.71/5.13 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.13 => ( ( ( vEBT_vebt_succ @ T @ X )
% 4.71/5.13 = ( some_nat @ Y ) )
% 4.71/5.13 => ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % helpyd
% 4.71/5.13 thf(fact_6274_helpypredd,axiom,
% 4.71/5.13 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 4.71/5.13 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.13 => ( ( ( vEBT_vebt_pred @ T @ X )
% 4.71/5.13 = ( some_nat @ Y ) )
% 4.71/5.13 => ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % helpypredd
% 4.71/5.13 thf(fact_6275_valid__insert__both__member__options__pres,axiom,
% 4.71/5.13 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 4.71/5.13 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.13 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.71/5.13 => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.71/5.13 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 4.71/5.13 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y ) @ X ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % valid_insert_both_member_options_pres
% 4.71/5.13 thf(fact_6276_valid__insert__both__member__options__add,axiom,
% 4.71/5.13 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 4.71/5.13 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.13 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.71/5.13 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X ) @ X ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % valid_insert_both_member_options_add
% 4.71/5.13 thf(fact_6277_post__member__pre__member,axiom,
% 4.71/5.13 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 4.71/5.13 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.13 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.71/5.13 => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.71/5.13 => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X ) @ Y )
% 4.71/5.13 => ( ( vEBT_vebt_member @ T @ Y )
% 4.71/5.13 | ( X = Y ) ) ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % post_member_pre_member
% 4.71/5.13 thf(fact_6278_semiring__norm_I71_J,axiom,
% 4.71/5.13 ! [M2: num,N: num] :
% 4.71/5.13 ( ( ord_less_eq_num @ ( bit0 @ M2 ) @ ( bit0 @ N ) )
% 4.71/5.13 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % semiring_norm(71)
% 4.71/5.13 thf(fact_6279_semiring__norm_I68_J,axiom,
% 4.71/5.13 ! [N: num] : ( ord_less_eq_num @ one @ N ) ).
% 4.71/5.13
% 4.71/5.13 % semiring_norm(68)
% 4.71/5.13 thf(fact_6280_delt__out__of__range,axiom,
% 4.71/5.13 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 4.71/5.13 ( ( ( ord_less_nat @ X @ Mi )
% 4.71/5.13 | ( ord_less_nat @ Ma @ X ) )
% 4.71/5.13 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.71/5.13 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.13 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % delt_out_of_range
% 4.71/5.13 thf(fact_6281_del__single__cont,axiom,
% 4.71/5.13 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 4.71/5.13 ( ( ( X = Mi )
% 4.71/5.13 & ( X = Ma ) )
% 4.71/5.13 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.71/5.13 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.13 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % del_single_cont
% 4.71/5.13 thf(fact_6282_mi__ma__2__deg,axiom,
% 4.71/5.13 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 4.71/5.13 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 4.71/5.13 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 4.71/5.13 & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % mi_ma_2_deg
% 4.71/5.13 thf(fact_6283_pred__max,axiom,
% 4.71/5.13 ! [Deg: nat,Ma: nat,X: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 4.71/5.13 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.71/5.13 => ( ( ord_less_nat @ Ma @ X )
% 4.71/5.13 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.13 = ( some_nat @ Ma ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % pred_max
% 4.71/5.13 thf(fact_6284_succ__min,axiom,
% 4.71/5.13 ! [Deg: nat,X: nat,Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 4.71/5.13 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.71/5.13 => ( ( ord_less_nat @ X @ Mi )
% 4.71/5.13 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.13 = ( some_nat @ Mi ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % succ_min
% 4.71/5.13 thf(fact_6285_inrange,axiom,
% 4.71/5.13 ! [T: vEBT_VEBT,N: nat] :
% 4.71/5.13 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.13 => ( 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 ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % inrange
% 4.71/5.13 thf(fact_6286_bit__concat__def,axiom,
% 4.71/5.13 ( vEBT_VEBT_bit_concat
% 4.71/5.13 = ( ^ [H3: nat,L3: nat,D5: nat] : ( plus_plus_nat @ ( times_times_nat @ H3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D5 ) ) @ L3 ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % bit_concat_def
% 4.71/5.13 thf(fact_6287_one__eq__numeral__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( one_one_complex
% 4.71/5.13 = ( numera6690914467698888265omplex @ N ) )
% 4.71/5.13 = ( one = N ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_eq_numeral_iff
% 4.71/5.13 thf(fact_6288_one__eq__numeral__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( one_one_rat
% 4.71/5.13 = ( numeral_numeral_rat @ N ) )
% 4.71/5.13 = ( one = N ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_eq_numeral_iff
% 4.71/5.13 thf(fact_6289_one__eq__numeral__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( one_one_real
% 4.71/5.13 = ( numeral_numeral_real @ N ) )
% 4.71/5.13 = ( one = N ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_eq_numeral_iff
% 4.71/5.13 thf(fact_6290_one__eq__numeral__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( one_one_nat
% 4.71/5.13 = ( numeral_numeral_nat @ N ) )
% 4.71/5.13 = ( one = N ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_eq_numeral_iff
% 4.71/5.13 thf(fact_6291_one__eq__numeral__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( one_one_int
% 4.71/5.13 = ( numeral_numeral_int @ N ) )
% 4.71/5.13 = ( one = N ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_eq_numeral_iff
% 4.71/5.13 thf(fact_6292_one__eq__numeral__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( one_on7984719198319812577d_enat
% 4.71/5.13 = ( numera1916890842035813515d_enat @ N ) )
% 4.71/5.13 = ( one = N ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_eq_numeral_iff
% 4.71/5.13 thf(fact_6293_one__eq__numeral__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( one_one_Code_integer
% 4.71/5.13 = ( numera6620942414471956472nteger @ N ) )
% 4.71/5.13 = ( one = N ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_eq_numeral_iff
% 4.71/5.13 thf(fact_6294_numeral__eq__one__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ( numera6690914467698888265omplex @ N )
% 4.71/5.13 = one_one_complex )
% 4.71/5.13 = ( N = one ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_eq_one_iff
% 4.71/5.13 thf(fact_6295_numeral__eq__one__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ( numeral_numeral_rat @ N )
% 4.71/5.13 = one_one_rat )
% 4.71/5.13 = ( N = one ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_eq_one_iff
% 4.71/5.13 thf(fact_6296_numeral__eq__one__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ( numeral_numeral_real @ N )
% 4.71/5.13 = one_one_real )
% 4.71/5.13 = ( N = one ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_eq_one_iff
% 4.71/5.13 thf(fact_6297_numeral__eq__one__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ( numeral_numeral_nat @ N )
% 4.71/5.13 = one_one_nat )
% 4.71/5.13 = ( N = one ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_eq_one_iff
% 4.71/5.13 thf(fact_6298_numeral__eq__one__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ( numeral_numeral_int @ N )
% 4.71/5.13 = one_one_int )
% 4.71/5.13 = ( N = one ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_eq_one_iff
% 4.71/5.13 thf(fact_6299_numeral__eq__one__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ( numera1916890842035813515d_enat @ N )
% 4.71/5.13 = one_on7984719198319812577d_enat )
% 4.71/5.13 = ( N = one ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_eq_one_iff
% 4.71/5.13 thf(fact_6300_numeral__eq__one__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ( numera6620942414471956472nteger @ N )
% 4.71/5.13 = one_one_Code_integer )
% 4.71/5.13 = ( N = one ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_eq_one_iff
% 4.71/5.13 thf(fact_6301_num__double,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( times_times_num @ ( bit0 @ one ) @ N )
% 4.71/5.13 = ( bit0 @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % num_double
% 4.71/5.13 thf(fact_6302_semiring__norm_I69_J,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ~ ( ord_less_eq_num @ ( bit0 @ M2 ) @ one ) ).
% 4.71/5.13
% 4.71/5.13 % semiring_norm(69)
% 4.71/5.13 thf(fact_6303_card__atLeastAtMost,axiom,
% 4.71/5.13 ! [L: nat,U: nat] :
% 4.71/5.13 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 4.71/5.13 = ( minus_minus_nat @ ( suc @ U ) @ L ) ) ).
% 4.71/5.13
% 4.71/5.13 % card_atLeastAtMost
% 4.71/5.13 thf(fact_6304_numeral__eq__neg__one__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) )
% 4.71/5.13 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 4.71/5.13 = ( N = one ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_eq_neg_one_iff
% 4.71/5.13 thf(fact_6305_numeral__eq__neg__one__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N ) )
% 4.71/5.13 = ( uminus_uminus_int @ one_one_int ) )
% 4.71/5.13 = ( N = one ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_eq_neg_one_iff
% 4.71/5.13 thf(fact_6306_numeral__eq__neg__one__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N ) )
% 4.71/5.13 = ( uminus_uminus_real @ one_one_real ) )
% 4.71/5.13 = ( N = one ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_eq_neg_one_iff
% 4.71/5.13 thf(fact_6307_numeral__eq__neg__one__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) )
% 4.71/5.13 = ( uminus_uminus_rat @ one_one_rat ) )
% 4.71/5.13 = ( N = one ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_eq_neg_one_iff
% 4.71/5.13 thf(fact_6308_numeral__eq__neg__one__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) )
% 4.71/5.13 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 4.71/5.13 = ( N = one ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_eq_neg_one_iff
% 4.71/5.13 thf(fact_6309_neg__one__eq__numeral__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 4.71/5.13 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 4.71/5.13 = ( N = one ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_one_eq_numeral_iff
% 4.71/5.13 thf(fact_6310_neg__one__eq__numeral__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ( uminus_uminus_int @ one_one_int )
% 4.71/5.13 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 4.71/5.13 = ( N = one ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_one_eq_numeral_iff
% 4.71/5.13 thf(fact_6311_neg__one__eq__numeral__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ( uminus_uminus_real @ one_one_real )
% 4.71/5.13 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 4.71/5.13 = ( N = one ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_one_eq_numeral_iff
% 4.71/5.13 thf(fact_6312_neg__one__eq__numeral__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ( uminus_uminus_rat @ one_one_rat )
% 4.71/5.13 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 4.71/5.13 = ( N = one ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_one_eq_numeral_iff
% 4.71/5.13 thf(fact_6313_neg__one__eq__numeral__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 4.71/5.13 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 4.71/5.13 = ( N = one ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_one_eq_numeral_iff
% 4.71/5.13 thf(fact_6314_Suc__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( suc @ ( numeral_numeral_nat @ N ) )
% 4.71/5.13 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % Suc_numeral
% 4.71/5.13 thf(fact_6315_not__neg__one__le__neg__numeral__iff,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) )
% 4.71/5.13 = ( M2 != one ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_neg_one_le_neg_numeral_iff
% 4.71/5.13 thf(fact_6316_not__neg__one__le__neg__numeral__iff,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) ) )
% 4.71/5.13 = ( M2 != one ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_neg_one_le_neg_numeral_iff
% 4.71/5.13 thf(fact_6317_not__neg__one__le__neg__numeral__iff,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) )
% 4.71/5.13 = ( M2 != one ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_neg_one_le_neg_numeral_iff
% 4.71/5.13 thf(fact_6318_not__neg__one__le__neg__numeral__iff,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) )
% 4.71/5.13 = ( M2 != one ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_neg_one_le_neg_numeral_iff
% 4.71/5.13 thf(fact_6319_neg__numeral__less__neg__one__iff,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 4.71/5.13 = ( M2 != one ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_less_neg_one_iff
% 4.71/5.13 thf(fact_6320_neg__numeral__less__neg__one__iff,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 4.71/5.13 = ( M2 != one ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_less_neg_one_iff
% 4.71/5.13 thf(fact_6321_neg__numeral__less__neg__one__iff,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 4.71/5.13 = ( M2 != one ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_less_neg_one_iff
% 4.71/5.13 thf(fact_6322_neg__numeral__less__neg__one__iff,axiom,
% 4.71/5.13 ! [M2: num] :
% 4.71/5.13 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 4.71/5.13 = ( M2 != one ) ) ).
% 4.71/5.13
% 4.71/5.13 % neg_numeral_less_neg_one_iff
% 4.71/5.13 thf(fact_6323_one__add__one,axiom,
% 4.71/5.13 ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 4.71/5.13 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_add_one
% 4.71/5.13 thf(fact_6324_one__add__one,axiom,
% 4.71/5.13 ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 4.71/5.13 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_add_one
% 4.71/5.13 thf(fact_6325_one__add__one,axiom,
% 4.71/5.13 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 4.71/5.13 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_add_one
% 4.71/5.13 thf(fact_6326_one__add__one,axiom,
% 4.71/5.13 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 4.71/5.13 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_add_one
% 4.71/5.13 thf(fact_6327_one__add__one,axiom,
% 4.71/5.13 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 4.71/5.13 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_add_one
% 4.71/5.13 thf(fact_6328_one__add__one,axiom,
% 4.71/5.13 ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat )
% 4.71/5.13 = ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_add_one
% 4.71/5.13 thf(fact_6329_one__add__one,axiom,
% 4.71/5.13 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ one_one_Code_integer )
% 4.71/5.13 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_add_one
% 4.71/5.13 thf(fact_6330_zero__eq__power2,axiom,
% 4.71/5.13 ! [A: rat] :
% 4.71/5.13 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.13 = zero_zero_rat )
% 4.71/5.13 = ( A = zero_zero_rat ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_eq_power2
% 4.71/5.13 thf(fact_6331_zero__eq__power2,axiom,
% 4.71/5.13 ! [A: int] :
% 4.71/5.13 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.13 = zero_zero_int )
% 4.71/5.13 = ( A = zero_zero_int ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_eq_power2
% 4.71/5.13 thf(fact_6332_zero__eq__power2,axiom,
% 4.71/5.13 ! [A: nat] :
% 4.71/5.13 ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.13 = zero_zero_nat )
% 4.71/5.13 = ( A = zero_zero_nat ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_eq_power2
% 4.71/5.13 thf(fact_6333_zero__eq__power2,axiom,
% 4.71/5.13 ! [A: real] :
% 4.71/5.13 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.13 = zero_zero_real )
% 4.71/5.13 = ( A = zero_zero_real ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_eq_power2
% 4.71/5.13 thf(fact_6334_zero__eq__power2,axiom,
% 4.71/5.13 ! [A: complex] :
% 4.71/5.13 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.13 = zero_zero_complex )
% 4.71/5.13 = ( A = zero_zero_complex ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_eq_power2
% 4.71/5.13 thf(fact_6335_one__mod__two__eq__one,axiom,
% 4.71/5.13 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 4.71/5.13 = one_one_Code_integer ) ).
% 4.71/5.13
% 4.71/5.13 % one_mod_two_eq_one
% 4.71/5.13 thf(fact_6336_one__mod__two__eq__one,axiom,
% 4.71/5.13 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.71/5.13 = one_one_int ) ).
% 4.71/5.13
% 4.71/5.13 % one_mod_two_eq_one
% 4.71/5.13 thf(fact_6337_one__mod__two__eq__one,axiom,
% 4.71/5.13 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.13 = one_one_nat ) ).
% 4.71/5.13
% 4.71/5.13 % one_mod_two_eq_one
% 4.71/5.13 thf(fact_6338_bits__one__mod__two__eq__one,axiom,
% 4.71/5.13 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 4.71/5.13 = one_one_Code_integer ) ).
% 4.71/5.13
% 4.71/5.13 % bits_one_mod_two_eq_one
% 4.71/5.13 thf(fact_6339_bits__one__mod__two__eq__one,axiom,
% 4.71/5.13 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.71/5.13 = one_one_int ) ).
% 4.71/5.13
% 4.71/5.13 % bits_one_mod_two_eq_one
% 4.71/5.13 thf(fact_6340_bits__one__mod__two__eq__one,axiom,
% 4.71/5.13 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.13 = one_one_nat ) ).
% 4.71/5.13
% 4.71/5.13 % bits_one_mod_two_eq_one
% 4.71/5.13 thf(fact_6341_add__2__eq__Suc_H,axiom,
% 4.71/5.13 ! [N: nat] :
% 4.71/5.13 ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.13 = ( suc @ ( suc @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % add_2_eq_Suc'
% 4.71/5.13 thf(fact_6342_add__2__eq__Suc,axiom,
% 4.71/5.13 ! [N: nat] :
% 4.71/5.13 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 4.71/5.13 = ( suc @ ( suc @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % add_2_eq_Suc
% 4.71/5.13 thf(fact_6343_Suc__1,axiom,
% 4.71/5.13 ( ( suc @ one_one_nat )
% 4.71/5.13 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % Suc_1
% 4.71/5.13 thf(fact_6344_numeral__plus__one,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ one_one_complex )
% 4.71/5.13 = ( numera6690914467698888265omplex @ ( plus_plus_num @ N @ one ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_plus_one
% 4.71/5.13 thf(fact_6345_numeral__plus__one,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 4.71/5.13 = ( numeral_numeral_rat @ ( plus_plus_num @ N @ one ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_plus_one
% 4.71/5.13 thf(fact_6346_numeral__plus__one,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( plus_plus_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 4.71/5.13 = ( numeral_numeral_real @ ( plus_plus_num @ N @ one ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_plus_one
% 4.71/5.13 thf(fact_6347_numeral__plus__one,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 4.71/5.13 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_plus_one
% 4.71/5.13 thf(fact_6348_numeral__plus__one,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( plus_plus_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 4.71/5.13 = ( numeral_numeral_int @ ( plus_plus_num @ N @ one ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_plus_one
% 4.71/5.13 thf(fact_6349_numeral__plus__one,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N ) @ one_on7984719198319812577d_enat )
% 4.71/5.13 = ( numera1916890842035813515d_enat @ ( plus_plus_num @ N @ one ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_plus_one
% 4.71/5.13 thf(fact_6350_numeral__plus__one,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N ) @ one_one_Code_integer )
% 4.71/5.13 = ( numera6620942414471956472nteger @ ( plus_plus_num @ N @ one ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_plus_one
% 4.71/5.13 thf(fact_6351_one__plus__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N ) )
% 4.71/5.13 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_plus_numeral
% 4.71/5.13 thf(fact_6352_one__plus__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 4.71/5.13 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_plus_numeral
% 4.71/5.13 thf(fact_6353_one__plus__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 4.71/5.13 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_plus_numeral
% 4.71/5.13 thf(fact_6354_one__plus__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 4.71/5.13 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_plus_numeral
% 4.71/5.13 thf(fact_6355_one__plus__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 4.71/5.13 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_plus_numeral
% 4.71/5.13 thf(fact_6356_one__plus__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N ) )
% 4.71/5.13 = ( numera1916890842035813515d_enat @ ( plus_plus_num @ one @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_plus_numeral
% 4.71/5.13 thf(fact_6357_one__plus__numeral,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 4.71/5.13 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_plus_numeral
% 4.71/5.13 thf(fact_6358_numeral__le__one__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 4.71/5.13 = ( ord_less_eq_num @ N @ one ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_le_one_iff
% 4.71/5.13 thf(fact_6359_numeral__le__one__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ N ) @ one_on7984719198319812577d_enat )
% 4.71/5.13 = ( ord_less_eq_num @ N @ one ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_le_one_iff
% 4.71/5.13 thf(fact_6360_numeral__le__one__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N ) @ one_one_Code_integer )
% 4.71/5.13 = ( ord_less_eq_num @ N @ one ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_le_one_iff
% 4.71/5.13 thf(fact_6361_numeral__le__one__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 4.71/5.13 = ( ord_less_eq_num @ N @ one ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_le_one_iff
% 4.71/5.13 thf(fact_6362_numeral__le__one__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 4.71/5.13 = ( ord_less_eq_num @ N @ one ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_le_one_iff
% 4.71/5.13 thf(fact_6363_numeral__le__one__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 4.71/5.13 = ( ord_less_eq_num @ N @ one ) ) ).
% 4.71/5.13
% 4.71/5.13 % numeral_le_one_iff
% 4.71/5.13 thf(fact_6364_one__less__numeral__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 4.71/5.13 = ( ord_less_num @ one @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_less_numeral_iff
% 4.71/5.13 thf(fact_6365_one__less__numeral__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 4.71/5.13 = ( ord_less_num @ one @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_less_numeral_iff
% 4.71/5.13 thf(fact_6366_one__less__numeral__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 4.71/5.13 = ( ord_less_num @ one @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_less_numeral_iff
% 4.71/5.13 thf(fact_6367_one__less__numeral__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 4.71/5.13 = ( ord_less_num @ one @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_less_numeral_iff
% 4.71/5.13 thf(fact_6368_one__less__numeral__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ord_le72135733267957522d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N ) )
% 4.71/5.13 = ( ord_less_num @ one @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_less_numeral_iff
% 4.71/5.13 thf(fact_6369_one__less__numeral__iff,axiom,
% 4.71/5.13 ! [N: num] :
% 4.71/5.13 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 4.71/5.13 = ( ord_less_num @ one @ N ) ) ).
% 4.71/5.13
% 4.71/5.13 % one_less_numeral_iff
% 4.71/5.13 thf(fact_6370_one__div__two__eq__zero,axiom,
% 4.71/5.13 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 4.71/5.13 = zero_z3403309356797280102nteger ) ).
% 4.71/5.13
% 4.71/5.13 % one_div_two_eq_zero
% 4.71/5.13 thf(fact_6371_one__div__two__eq__zero,axiom,
% 4.71/5.13 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.71/5.13 = zero_zero_int ) ).
% 4.71/5.13
% 4.71/5.13 % one_div_two_eq_zero
% 4.71/5.13 thf(fact_6372_one__div__two__eq__zero,axiom,
% 4.71/5.13 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.13 = zero_zero_nat ) ).
% 4.71/5.13
% 4.71/5.13 % one_div_two_eq_zero
% 4.71/5.13 thf(fact_6373_bits__1__div__2,axiom,
% 4.71/5.13 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 4.71/5.13 = zero_z3403309356797280102nteger ) ).
% 4.71/5.13
% 4.71/5.13 % bits_1_div_2
% 4.71/5.13 thf(fact_6374_bits__1__div__2,axiom,
% 4.71/5.13 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.71/5.13 = zero_zero_int ) ).
% 4.71/5.13
% 4.71/5.13 % bits_1_div_2
% 4.71/5.13 thf(fact_6375_bits__1__div__2,axiom,
% 4.71/5.13 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.13 = zero_zero_nat ) ).
% 4.71/5.13
% 4.71/5.13 % bits_1_div_2
% 4.71/5.13 thf(fact_6376_power2__less__eq__zero__iff,axiom,
% 4.71/5.13 ! [A: real] :
% 4.71/5.13 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 4.71/5.13 = ( A = zero_zero_real ) ) ).
% 4.71/5.13
% 4.71/5.13 % power2_less_eq_zero_iff
% 4.71/5.13 thf(fact_6377_power2__less__eq__zero__iff,axiom,
% 4.71/5.13 ! [A: rat] :
% 4.71/5.13 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 4.71/5.13 = ( A = zero_zero_rat ) ) ).
% 4.71/5.13
% 4.71/5.13 % power2_less_eq_zero_iff
% 4.71/5.13 thf(fact_6378_power2__less__eq__zero__iff,axiom,
% 4.71/5.13 ! [A: int] :
% 4.71/5.13 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 4.71/5.13 = ( A = zero_zero_int ) ) ).
% 4.71/5.13
% 4.71/5.13 % power2_less_eq_zero_iff
% 4.71/5.13 thf(fact_6379_power2__eq__iff__nonneg,axiom,
% 4.71/5.13 ! [X: real,Y: real] :
% 4.71/5.13 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.13 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.71/5.13 => ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.13 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.13 = ( X = Y ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % power2_eq_iff_nonneg
% 4.71/5.13 thf(fact_6380_power2__eq__iff__nonneg,axiom,
% 4.71/5.13 ! [X: rat,Y: rat] :
% 4.71/5.13 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 4.71/5.13 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 4.71/5.13 => ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.13 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.13 = ( X = Y ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % power2_eq_iff_nonneg
% 4.71/5.13 thf(fact_6381_power2__eq__iff__nonneg,axiom,
% 4.71/5.13 ! [X: nat,Y: nat] :
% 4.71/5.13 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 4.71/5.13 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 4.71/5.13 => ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.13 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.13 = ( X = Y ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % power2_eq_iff_nonneg
% 4.71/5.13 thf(fact_6382_power2__eq__iff__nonneg,axiom,
% 4.71/5.13 ! [X: int,Y: int] :
% 4.71/5.13 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 4.71/5.13 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.71/5.13 => ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.13 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.13 = ( X = Y ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % power2_eq_iff_nonneg
% 4.71/5.13 thf(fact_6383_zero__less__power2,axiom,
% 4.71/5.13 ! [A: real] :
% 4.71/5.13 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.13 = ( A != zero_zero_real ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_less_power2
% 4.71/5.13 thf(fact_6384_zero__less__power2,axiom,
% 4.71/5.13 ! [A: rat] :
% 4.71/5.13 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.13 = ( A != zero_zero_rat ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_less_power2
% 4.71/5.13 thf(fact_6385_zero__less__power2,axiom,
% 4.71/5.13 ! [A: int] :
% 4.71/5.13 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.13 = ( A != zero_zero_int ) ) ).
% 4.71/5.13
% 4.71/5.13 % zero_less_power2
% 4.71/5.13 thf(fact_6386_add__neg__numeral__special_I9_J,axiom,
% 4.71/5.13 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 4.71/5.13 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % add_neg_numeral_special(9)
% 4.71/5.13 thf(fact_6387_add__neg__numeral__special_I9_J,axiom,
% 4.71/5.13 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 4.71/5.13 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % add_neg_numeral_special(9)
% 4.71/5.13 thf(fact_6388_add__neg__numeral__special_I9_J,axiom,
% 4.71/5.13 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 4.71/5.13 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % add_neg_numeral_special(9)
% 4.71/5.13 thf(fact_6389_add__neg__numeral__special_I9_J,axiom,
% 4.71/5.13 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 4.71/5.13 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % add_neg_numeral_special(9)
% 4.71/5.13 thf(fact_6390_add__neg__numeral__special_I9_J,axiom,
% 4.71/5.13 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 4.71/5.13 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % add_neg_numeral_special(9)
% 4.71/5.13 thf(fact_6391_diff__numeral__special_I10_J,axiom,
% 4.71/5.13 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 4.71/5.13 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % diff_numeral_special(10)
% 4.71/5.13 thf(fact_6392_diff__numeral__special_I10_J,axiom,
% 4.71/5.13 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 4.71/5.13 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % diff_numeral_special(10)
% 4.71/5.13 thf(fact_6393_diff__numeral__special_I10_J,axiom,
% 4.71/5.13 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 4.71/5.13 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % diff_numeral_special(10)
% 4.71/5.13 thf(fact_6394_diff__numeral__special_I10_J,axiom,
% 4.71/5.13 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 4.71/5.13 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % diff_numeral_special(10)
% 4.71/5.13 thf(fact_6395_diff__numeral__special_I10_J,axiom,
% 4.71/5.13 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 4.71/5.13 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % diff_numeral_special(10)
% 4.71/5.13 thf(fact_6396_diff__numeral__special_I11_J,axiom,
% 4.71/5.13 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 4.71/5.13 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % diff_numeral_special(11)
% 4.71/5.13 thf(fact_6397_diff__numeral__special_I11_J,axiom,
% 4.71/5.13 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 4.71/5.13 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % diff_numeral_special(11)
% 4.71/5.13 thf(fact_6398_diff__numeral__special_I11_J,axiom,
% 4.71/5.13 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 4.71/5.13 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % diff_numeral_special(11)
% 4.71/5.13 thf(fact_6399_diff__numeral__special_I11_J,axiom,
% 4.71/5.13 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 4.71/5.13 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % diff_numeral_special(11)
% 4.71/5.13 thf(fact_6400_diff__numeral__special_I11_J,axiom,
% 4.71/5.13 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 4.71/5.13 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % diff_numeral_special(11)
% 4.71/5.13 thf(fact_6401_minus__1__div__2__eq,axiom,
% 4.71/5.13 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 4.71/5.13 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 4.71/5.13
% 4.71/5.13 % minus_1_div_2_eq
% 4.71/5.13 thf(fact_6402_minus__1__div__2__eq,axiom,
% 4.71/5.13 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.71/5.13 = ( uminus_uminus_int @ one_one_int ) ) ).
% 4.71/5.13
% 4.71/5.13 % minus_1_div_2_eq
% 4.71/5.13 thf(fact_6403_sum__power2__eq__zero__iff,axiom,
% 4.71/5.13 ! [X: rat,Y: rat] :
% 4.71/5.13 ( ( ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.13 = zero_zero_rat )
% 4.71/5.13 = ( ( X = zero_zero_rat )
% 4.71/5.13 & ( Y = zero_zero_rat ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % sum_power2_eq_zero_iff
% 4.71/5.13 thf(fact_6404_sum__power2__eq__zero__iff,axiom,
% 4.71/5.13 ! [X: int,Y: int] :
% 4.71/5.13 ( ( ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.13 = zero_zero_int )
% 4.71/5.13 = ( ( X = zero_zero_int )
% 4.71/5.13 & ( Y = zero_zero_int ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % sum_power2_eq_zero_iff
% 4.71/5.13 thf(fact_6405_sum__power2__eq__zero__iff,axiom,
% 4.71/5.13 ! [X: real,Y: real] :
% 4.71/5.13 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.13 = zero_zero_real )
% 4.71/5.13 = ( ( X = zero_zero_real )
% 4.71/5.13 & ( Y = zero_zero_real ) ) ) ).
% 4.71/5.13
% 4.71/5.13 % sum_power2_eq_zero_iff
% 4.71/5.13 thf(fact_6406_not__mod__2__eq__0__eq__1,axiom,
% 4.71/5.13 ! [A: code_integer] :
% 4.71/5.13 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 4.71/5.13 != zero_z3403309356797280102nteger )
% 4.71/5.13 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 4.71/5.13 = one_one_Code_integer ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_mod_2_eq_0_eq_1
% 4.71/5.13 thf(fact_6407_not__mod__2__eq__0__eq__1,axiom,
% 4.71/5.13 ! [A: int] :
% 4.71/5.13 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.71/5.13 != zero_zero_int )
% 4.71/5.13 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.71/5.13 = one_one_int ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_mod_2_eq_0_eq_1
% 4.71/5.13 thf(fact_6408_not__mod__2__eq__0__eq__1,axiom,
% 4.71/5.13 ! [A: nat] :
% 4.71/5.13 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.13 != zero_zero_nat )
% 4.71/5.13 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.13 = one_one_nat ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_mod_2_eq_0_eq_1
% 4.71/5.13 thf(fact_6409_not__mod__2__eq__1__eq__0,axiom,
% 4.71/5.13 ! [A: code_integer] :
% 4.71/5.13 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 4.71/5.13 != one_one_Code_integer )
% 4.71/5.13 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 4.71/5.13 = zero_z3403309356797280102nteger ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_mod_2_eq_1_eq_0
% 4.71/5.13 thf(fact_6410_not__mod__2__eq__1__eq__0,axiom,
% 4.71/5.13 ! [A: int] :
% 4.71/5.13 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.71/5.13 != one_one_int )
% 4.71/5.13 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.71/5.13 = zero_zero_int ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_mod_2_eq_1_eq_0
% 4.71/5.13 thf(fact_6411_not__mod__2__eq__1__eq__0,axiom,
% 4.71/5.13 ! [A: nat] :
% 4.71/5.13 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.13 != one_one_nat )
% 4.71/5.13 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.13 = zero_zero_nat ) ) ).
% 4.71/5.13
% 4.71/5.13 % not_mod_2_eq_1_eq_0
% 4.71/5.13 thf(fact_6412_bits__minus__1__mod__2__eq,axiom,
% 4.71/5.13 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 4.71/5.13 = one_one_Code_integer ) ).
% 4.71/5.13
% 4.71/5.13 % bits_minus_1_mod_2_eq
% 4.71/5.13 thf(fact_6413_bits__minus__1__mod__2__eq,axiom,
% 4.71/5.13 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.71/5.13 = one_one_int ) ).
% 4.71/5.14
% 4.71/5.14 % bits_minus_1_mod_2_eq
% 4.71/5.14 thf(fact_6414_minus__1__mod__2__eq,axiom,
% 4.71/5.14 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 4.71/5.14 = one_one_Code_integer ) ).
% 4.71/5.14
% 4.71/5.14 % minus_1_mod_2_eq
% 4.71/5.14 thf(fact_6415_minus__1__mod__2__eq,axiom,
% 4.71/5.14 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.71/5.14 = one_one_int ) ).
% 4.71/5.14
% 4.71/5.14 % minus_1_mod_2_eq
% 4.71/5.14 thf(fact_6416_not__mod2__eq__Suc__0__eq__0,axiom,
% 4.71/5.14 ! [N: nat] :
% 4.71/5.14 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 != ( suc @ zero_zero_nat ) )
% 4.71/5.14 = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = zero_zero_nat ) ) ).
% 4.71/5.14
% 4.71/5.14 % not_mod2_eq_Suc_0_eq_0
% 4.71/5.14 thf(fact_6417_diff__numeral__special_I4_J,axiom,
% 4.71/5.14 ! [M2: num] :
% 4.71/5.14 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ one_one_Code_integer )
% 4.71/5.14 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % diff_numeral_special(4)
% 4.71/5.14 thf(fact_6418_diff__numeral__special_I4_J,axiom,
% 4.71/5.14 ! [M2: num] :
% 4.71/5.14 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int )
% 4.71/5.14 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % diff_numeral_special(4)
% 4.71/5.14 thf(fact_6419_diff__numeral__special_I4_J,axiom,
% 4.71/5.14 ! [M2: num] :
% 4.71/5.14 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ one_one_real )
% 4.71/5.14 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % diff_numeral_special(4)
% 4.71/5.14 thf(fact_6420_diff__numeral__special_I4_J,axiom,
% 4.71/5.14 ! [M2: num] :
% 4.71/5.14 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ one_one_rat )
% 4.71/5.14 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % diff_numeral_special(4)
% 4.71/5.14 thf(fact_6421_diff__numeral__special_I4_J,axiom,
% 4.71/5.14 ! [M2: num] :
% 4.71/5.14 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) ) @ one_one_complex )
% 4.71/5.14 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % diff_numeral_special(4)
% 4.71/5.14 thf(fact_6422_diff__numeral__special_I3_J,axiom,
% 4.71/5.14 ! [N: num] :
% 4.71/5.14 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 4.71/5.14 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % diff_numeral_special(3)
% 4.71/5.14 thf(fact_6423_diff__numeral__special_I3_J,axiom,
% 4.71/5.14 ! [N: num] :
% 4.71/5.14 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 4.71/5.14 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % diff_numeral_special(3)
% 4.71/5.14 thf(fact_6424_diff__numeral__special_I3_J,axiom,
% 4.71/5.14 ! [N: num] :
% 4.71/5.14 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 4.71/5.14 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % diff_numeral_special(3)
% 4.71/5.14 thf(fact_6425_diff__numeral__special_I3_J,axiom,
% 4.71/5.14 ! [N: num] :
% 4.71/5.14 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 4.71/5.14 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % diff_numeral_special(3)
% 4.71/5.14 thf(fact_6426_diff__numeral__special_I3_J,axiom,
% 4.71/5.14 ! [N: num] :
% 4.71/5.14 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 4.71/5.14 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % diff_numeral_special(3)
% 4.71/5.14 thf(fact_6427_add__self__mod__2,axiom,
% 4.71/5.14 ! [M2: nat] :
% 4.71/5.14 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M2 @ M2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = zero_zero_nat ) ).
% 4.71/5.14
% 4.71/5.14 % add_self_mod_2
% 4.71/5.14 thf(fact_6428_half__nonnegative__int__iff,axiom,
% 4.71/5.14 ! [K: int] :
% 4.71/5.14 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 4.71/5.14
% 4.71/5.14 % half_nonnegative_int_iff
% 4.71/5.14 thf(fact_6429_power__minus1__even,axiom,
% 4.71/5.14 ! [N: nat] :
% 4.71/5.14 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.71/5.14 = one_one_int ) ).
% 4.71/5.14
% 4.71/5.14 % power_minus1_even
% 4.71/5.14 thf(fact_6430_power__minus1__even,axiom,
% 4.71/5.14 ! [N: nat] :
% 4.71/5.14 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.71/5.14 = one_one_real ) ).
% 4.71/5.14
% 4.71/5.14 % power_minus1_even
% 4.71/5.14 thf(fact_6431_power__minus1__even,axiom,
% 4.71/5.14 ! [N: nat] :
% 4.71/5.14 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.71/5.14 = one_one_rat ) ).
% 4.71/5.14
% 4.71/5.14 % power_minus1_even
% 4.71/5.14 thf(fact_6432_power__minus1__even,axiom,
% 4.71/5.14 ! [N: nat] :
% 4.71/5.14 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.71/5.14 = one_one_complex ) ).
% 4.71/5.14
% 4.71/5.14 % power_minus1_even
% 4.71/5.14 thf(fact_6433_one__less__floor,axiom,
% 4.71/5.14 ! [X: real] :
% 4.71/5.14 ( ( ord_less_int @ one_one_int @ ( archim6058952711729229775r_real @ X ) )
% 4.71/5.14 = ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ).
% 4.71/5.14
% 4.71/5.14 % one_less_floor
% 4.71/5.14 thf(fact_6434_one__less__floor,axiom,
% 4.71/5.14 ! [X: rat] :
% 4.71/5.14 ( ( ord_less_int @ one_one_int @ ( archim3151403230148437115or_rat @ X ) )
% 4.71/5.14 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) ) ).
% 4.71/5.14
% 4.71/5.14 % one_less_floor
% 4.71/5.14 thf(fact_6435_floor__le__one,axiom,
% 4.71/5.14 ! [X: real] :
% 4.71/5.14 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int )
% 4.71/5.14 = ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % floor_le_one
% 4.71/5.14 thf(fact_6436_floor__le__one,axiom,
% 4.71/5.14 ! [X: rat] :
% 4.71/5.14 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 4.71/5.14 = ( ord_less_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % floor_le_one
% 4.71/5.14 thf(fact_6437_mod2__gr__0,axiom,
% 4.71/5.14 ! [M2: nat] :
% 4.71/5.14 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = one_one_nat ) ) ).
% 4.71/5.14
% 4.71/5.14 % mod2_gr_0
% 4.71/5.14 thf(fact_6438_set__encode__insert,axiom,
% 4.71/5.14 ! [A2: set_nat,N: nat] :
% 4.71/5.14 ( ( finite_finite_nat @ A2 )
% 4.71/5.14 => ( ~ ( member_nat @ N @ A2 )
% 4.71/5.14 => ( ( nat_set_encode @ ( insert_nat @ N @ A2 ) )
% 4.71/5.14 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A2 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % set_encode_insert
% 4.71/5.14 thf(fact_6439_card__2__iff_H,axiom,
% 4.71/5.14 ! [S2: set_complex] :
% 4.71/5.14 ( ( ( finite_card_complex @ S2 )
% 4.71/5.14 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = ( ? [X3: complex] :
% 4.71/5.14 ( ( member_complex @ X3 @ S2 )
% 4.71/5.14 & ? [Y2: complex] :
% 4.71/5.14 ( ( member_complex @ Y2 @ S2 )
% 4.71/5.14 & ( X3 != Y2 )
% 4.71/5.14 & ! [Z2: complex] :
% 4.71/5.14 ( ( member_complex @ Z2 @ S2 )
% 4.71/5.14 => ( ( Z2 = X3 )
% 4.71/5.14 | ( Z2 = Y2 ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % card_2_iff'
% 4.71/5.14 thf(fact_6440_card__2__iff_H,axiom,
% 4.71/5.14 ! [S2: set_list_nat] :
% 4.71/5.14 ( ( ( finite_card_list_nat @ S2 )
% 4.71/5.14 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = ( ? [X3: list_nat] :
% 4.71/5.14 ( ( member_list_nat @ X3 @ S2 )
% 4.71/5.14 & ? [Y2: list_nat] :
% 4.71/5.14 ( ( member_list_nat @ Y2 @ S2 )
% 4.71/5.14 & ( X3 != Y2 )
% 4.71/5.14 & ! [Z2: list_nat] :
% 4.71/5.14 ( ( member_list_nat @ Z2 @ S2 )
% 4.71/5.14 => ( ( Z2 = X3 )
% 4.71/5.14 | ( Z2 = Y2 ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % card_2_iff'
% 4.71/5.14 thf(fact_6441_card__2__iff_H,axiom,
% 4.71/5.14 ! [S2: set_set_nat] :
% 4.71/5.14 ( ( ( finite_card_set_nat @ S2 )
% 4.71/5.14 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = ( ? [X3: set_nat] :
% 4.71/5.14 ( ( member_set_nat @ X3 @ S2 )
% 4.71/5.14 & ? [Y2: set_nat] :
% 4.71/5.14 ( ( member_set_nat @ Y2 @ S2 )
% 4.71/5.14 & ( X3 != Y2 )
% 4.71/5.14 & ! [Z2: set_nat] :
% 4.71/5.14 ( ( member_set_nat @ Z2 @ S2 )
% 4.71/5.14 => ( ( Z2 = X3 )
% 4.71/5.14 | ( Z2 = Y2 ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % card_2_iff'
% 4.71/5.14 thf(fact_6442_card__2__iff_H,axiom,
% 4.71/5.14 ! [S2: set_nat] :
% 4.71/5.14 ( ( ( finite_card_nat @ S2 )
% 4.71/5.14 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = ( ? [X3: nat] :
% 4.71/5.14 ( ( member_nat @ X3 @ S2 )
% 4.71/5.14 & ? [Y2: nat] :
% 4.71/5.14 ( ( member_nat @ Y2 @ S2 )
% 4.71/5.14 & ( X3 != Y2 )
% 4.71/5.14 & ! [Z2: nat] :
% 4.71/5.14 ( ( member_nat @ Z2 @ S2 )
% 4.71/5.14 => ( ( Z2 = X3 )
% 4.71/5.14 | ( Z2 = Y2 ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % card_2_iff'
% 4.71/5.14 thf(fact_6443_card__2__iff_H,axiom,
% 4.71/5.14 ! [S2: set_int] :
% 4.71/5.14 ( ( ( finite_card_int @ S2 )
% 4.71/5.14 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = ( ? [X3: int] :
% 4.71/5.14 ( ( member_int @ X3 @ S2 )
% 4.71/5.14 & ? [Y2: int] :
% 4.71/5.14 ( ( member_int @ Y2 @ S2 )
% 4.71/5.14 & ( X3 != Y2 )
% 4.71/5.14 & ! [Z2: int] :
% 4.71/5.14 ( ( member_int @ Z2 @ S2 )
% 4.71/5.14 => ( ( Z2 = X3 )
% 4.71/5.14 | ( Z2 = Y2 ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % card_2_iff'
% 4.71/5.14 thf(fact_6444_add__diff__assoc__enat,axiom,
% 4.71/5.14 ! [Z: extended_enat,Y: extended_enat,X: extended_enat] :
% 4.71/5.14 ( ( ord_le2932123472753598470d_enat @ Z @ Y )
% 4.71/5.14 => ( ( plus_p3455044024723400733d_enat @ X @ ( minus_3235023915231533773d_enat @ Y @ Z ) )
% 4.71/5.14 = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X @ Y ) @ Z ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % add_diff_assoc_enat
% 4.71/5.14 thf(fact_6445_le__num__One__iff,axiom,
% 4.71/5.14 ! [X: num] :
% 4.71/5.14 ( ( ord_less_eq_num @ X @ one )
% 4.71/5.14 = ( X = one ) ) ).
% 4.71/5.14
% 4.71/5.14 % le_num_One_iff
% 4.71/5.14 thf(fact_6446_ile0__eq,axiom,
% 4.71/5.14 ! [N: extended_enat] :
% 4.71/5.14 ( ( ord_le2932123472753598470d_enat @ N @ zero_z5237406670263579293d_enat )
% 4.71/5.14 = ( N = zero_z5237406670263579293d_enat ) ) ).
% 4.71/5.14
% 4.71/5.14 % ile0_eq
% 4.71/5.14 thf(fact_6447_i0__lb,axiom,
% 4.71/5.14 ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N ) ).
% 4.71/5.14
% 4.71/5.14 % i0_lb
% 4.71/5.14 thf(fact_6448_add__One__commute,axiom,
% 4.71/5.14 ! [N: num] :
% 4.71/5.14 ( ( plus_plus_num @ one @ N )
% 4.71/5.14 = ( plus_plus_num @ N @ one ) ) ).
% 4.71/5.14
% 4.71/5.14 % add_One_commute
% 4.71/5.14 thf(fact_6449_zero__power2,axiom,
% 4.71/5.14 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = zero_zero_rat ) ).
% 4.71/5.14
% 4.71/5.14 % zero_power2
% 4.71/5.14 thf(fact_6450_zero__power2,axiom,
% 4.71/5.14 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = zero_zero_int ) ).
% 4.71/5.14
% 4.71/5.14 % zero_power2
% 4.71/5.14 thf(fact_6451_zero__power2,axiom,
% 4.71/5.14 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = zero_zero_nat ) ).
% 4.71/5.14
% 4.71/5.14 % zero_power2
% 4.71/5.14 thf(fact_6452_zero__power2,axiom,
% 4.71/5.14 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = zero_zero_real ) ).
% 4.71/5.14
% 4.71/5.14 % zero_power2
% 4.71/5.14 thf(fact_6453_zero__power2,axiom,
% 4.71/5.14 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = zero_zero_complex ) ).
% 4.71/5.14
% 4.71/5.14 % zero_power2
% 4.71/5.14 thf(fact_6454_one__power2,axiom,
% 4.71/5.14 ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = one_one_rat ) ).
% 4.71/5.14
% 4.71/5.14 % one_power2
% 4.71/5.14 thf(fact_6455_one__power2,axiom,
% 4.71/5.14 ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = one_one_int ) ).
% 4.71/5.14
% 4.71/5.14 % one_power2
% 4.71/5.14 thf(fact_6456_one__power2,axiom,
% 4.71/5.14 ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = one_one_nat ) ).
% 4.71/5.14
% 4.71/5.14 % one_power2
% 4.71/5.14 thf(fact_6457_one__power2,axiom,
% 4.71/5.14 ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = one_one_real ) ).
% 4.71/5.14
% 4.71/5.14 % one_power2
% 4.71/5.14 thf(fact_6458_one__power2,axiom,
% 4.71/5.14 ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = one_one_complex ) ).
% 4.71/5.14
% 4.71/5.14 % one_power2
% 4.71/5.14 thf(fact_6459_numeral__2__eq__2,axiom,
% 4.71/5.14 ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 4.71/5.14 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % numeral_2_eq_2
% 4.71/5.14 thf(fact_6460_pos2,axiom,
% 4.71/5.14 ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 4.71/5.14
% 4.71/5.14 % pos2
% 4.71/5.14 thf(fact_6461_less__exp,axiom,
% 4.71/5.14 ! [N: nat] : ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 4.71/5.14
% 4.71/5.14 % less_exp
% 4.71/5.14 thf(fact_6462_power2__nat__le__imp__le,axiom,
% 4.71/5.14 ! [M2: nat,N: nat] :
% 4.71/5.14 ( ( ord_less_eq_nat @ ( power_power_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 4.71/5.14 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 4.71/5.14
% 4.71/5.14 % power2_nat_le_imp_le
% 4.71/5.14 thf(fact_6463_power2__nat__le__eq__le,axiom,
% 4.71/5.14 ! [M2: nat,N: nat] :
% 4.71/5.14 ( ( ord_less_eq_nat @ ( power_power_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 4.71/5.14
% 4.71/5.14 % power2_nat_le_eq_le
% 4.71/5.14 thf(fact_6464_self__le__ge2__pow,axiom,
% 4.71/5.14 ! [K: nat,M2: nat] :
% 4.71/5.14 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 4.71/5.14 => ( ord_less_eq_nat @ M2 @ ( power_power_nat @ K @ M2 ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % self_le_ge2_pow
% 4.71/5.14 thf(fact_6465_nat__1__add__1,axiom,
% 4.71/5.14 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 4.71/5.14 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % nat_1_add_1
% 4.71/5.14 thf(fact_6466_num_Osize_I4_J,axiom,
% 4.71/5.14 ( ( size_size_num @ one )
% 4.71/5.14 = zero_zero_nat ) ).
% 4.71/5.14
% 4.71/5.14 % num.size(4)
% 4.71/5.14 thf(fact_6467_numerals_I1_J,axiom,
% 4.71/5.14 ( ( numeral_numeral_nat @ one )
% 4.71/5.14 = one_one_nat ) ).
% 4.71/5.14
% 4.71/5.14 % numerals(1)
% 4.71/5.14 thf(fact_6468_zero__le__power2,axiom,
% 4.71/5.14 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % zero_le_power2
% 4.71/5.14 thf(fact_6469_zero__le__power2,axiom,
% 4.71/5.14 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % zero_le_power2
% 4.71/5.14 thf(fact_6470_zero__le__power2,axiom,
% 4.71/5.14 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % zero_le_power2
% 4.71/5.14 thf(fact_6471_power2__eq__imp__eq,axiom,
% 4.71/5.14 ! [X: real,Y: real] :
% 4.71/5.14 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.14 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.71/5.14 => ( X = Y ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % power2_eq_imp_eq
% 4.71/5.14 thf(fact_6472_power2__eq__imp__eq,axiom,
% 4.71/5.14 ! [X: rat,Y: rat] :
% 4.71/5.14 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 4.71/5.14 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 4.71/5.14 => ( X = Y ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % power2_eq_imp_eq
% 4.71/5.14 thf(fact_6473_power2__eq__imp__eq,axiom,
% 4.71/5.14 ! [X: nat,Y: nat] :
% 4.71/5.14 ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 4.71/5.14 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 4.71/5.14 => ( X = Y ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % power2_eq_imp_eq
% 4.71/5.14 thf(fact_6474_power2__eq__imp__eq,axiom,
% 4.71/5.14 ! [X: int,Y: int] :
% 4.71/5.14 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 4.71/5.14 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.71/5.14 => ( X = Y ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % power2_eq_imp_eq
% 4.71/5.14 thf(fact_6475_power2__le__imp__le,axiom,
% 4.71/5.14 ! [X: real,Y: real] :
% 4.71/5.14 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.71/5.14 => ( ord_less_eq_real @ X @ Y ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % power2_le_imp_le
% 4.71/5.14 thf(fact_6476_power2__le__imp__le,axiom,
% 4.71/5.14 ! [X: rat,Y: rat] :
% 4.71/5.14 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 4.71/5.14 => ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % power2_le_imp_le
% 4.71/5.14 thf(fact_6477_power2__le__imp__le,axiom,
% 4.71/5.14 ! [X: nat,Y: nat] :
% 4.71/5.14 ( ( ord_less_eq_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 4.71/5.14 => ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % power2_le_imp_le
% 4.71/5.14 thf(fact_6478_power2__le__imp__le,axiom,
% 4.71/5.14 ! [X: int,Y: int] :
% 4.71/5.14 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.71/5.14 => ( ord_less_eq_int @ X @ Y ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % power2_le_imp_le
% 4.71/5.14 thf(fact_6479_power2__less__0,axiom,
% 4.71/5.14 ! [A: real] :
% 4.71/5.14 ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 4.71/5.14
% 4.71/5.14 % power2_less_0
% 4.71/5.14 thf(fact_6480_power2__less__0,axiom,
% 4.71/5.14 ! [A: rat] :
% 4.71/5.14 ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 4.71/5.14
% 4.71/5.14 % power2_less_0
% 4.71/5.14 thf(fact_6481_power2__less__0,axiom,
% 4.71/5.14 ! [A: int] :
% 4.71/5.14 ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 4.71/5.14
% 4.71/5.14 % power2_less_0
% 4.71/5.14 thf(fact_6482_mult__2,axiom,
% 4.71/5.14 ! [Z: rat] :
% 4.71/5.14 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 4.71/5.14 = ( plus_plus_rat @ Z @ Z ) ) ).
% 4.71/5.14
% 4.71/5.14 % mult_2
% 4.71/5.14 thf(fact_6483_mult__2,axiom,
% 4.71/5.14 ! [Z: real] :
% 4.71/5.14 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z )
% 4.71/5.14 = ( plus_plus_real @ Z @ Z ) ) ).
% 4.71/5.14
% 4.71/5.14 % mult_2
% 4.71/5.14 thf(fact_6484_mult__2,axiom,
% 4.71/5.14 ! [Z: nat] :
% 4.71/5.14 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 4.71/5.14 = ( plus_plus_nat @ Z @ Z ) ) ).
% 4.71/5.14
% 4.71/5.14 % mult_2
% 4.71/5.14 thf(fact_6485_mult__2,axiom,
% 4.71/5.14 ! [Z: int] :
% 4.71/5.14 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 4.71/5.14 = ( plus_plus_int @ Z @ Z ) ) ).
% 4.71/5.14
% 4.71/5.14 % mult_2
% 4.71/5.14 thf(fact_6486_mult__2,axiom,
% 4.71/5.14 ! [Z: extended_enat] :
% 4.71/5.14 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ Z )
% 4.71/5.14 = ( plus_p3455044024723400733d_enat @ Z @ Z ) ) ).
% 4.71/5.14
% 4.71/5.14 % mult_2
% 4.71/5.14 thf(fact_6487_mult__2,axiom,
% 4.71/5.14 ! [Z: code_integer] :
% 4.71/5.14 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Z )
% 4.71/5.14 = ( plus_p5714425477246183910nteger @ Z @ Z ) ) ).
% 4.71/5.14
% 4.71/5.14 % mult_2
% 4.71/5.14 thf(fact_6488_mult__2__right,axiom,
% 4.71/5.14 ! [Z: rat] :
% 4.71/5.14 ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 4.71/5.14 = ( plus_plus_rat @ Z @ Z ) ) ).
% 4.71/5.14
% 4.71/5.14 % mult_2_right
% 4.71/5.14 thf(fact_6489_mult__2__right,axiom,
% 4.71/5.14 ! [Z: real] :
% 4.71/5.14 ( ( times_times_real @ Z @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 4.71/5.14 = ( plus_plus_real @ Z @ Z ) ) ).
% 4.71/5.14
% 4.71/5.14 % mult_2_right
% 4.71/5.14 thf(fact_6490_mult__2__right,axiom,
% 4.71/5.14 ! [Z: nat] :
% 4.71/5.14 ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = ( plus_plus_nat @ Z @ Z ) ) ).
% 4.71/5.14
% 4.71/5.14 % mult_2_right
% 4.71/5.14 thf(fact_6491_mult__2__right,axiom,
% 4.71/5.14 ! [Z: int] :
% 4.71/5.14 ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.71/5.14 = ( plus_plus_int @ Z @ Z ) ) ).
% 4.71/5.14
% 4.71/5.14 % mult_2_right
% 4.71/5.14 thf(fact_6492_mult__2__right,axiom,
% 4.71/5.14 ! [Z: extended_enat] :
% 4.71/5.14 ( ( times_7803423173614009249d_enat @ Z @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) )
% 4.71/5.14 = ( plus_p3455044024723400733d_enat @ Z @ Z ) ) ).
% 4.71/5.14
% 4.71/5.14 % mult_2_right
% 4.71/5.14 thf(fact_6493_mult__2__right,axiom,
% 4.71/5.14 ! [Z: code_integer] :
% 4.71/5.14 ( ( times_3573771949741848930nteger @ Z @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 4.71/5.14 = ( plus_p5714425477246183910nteger @ Z @ Z ) ) ).
% 4.71/5.14
% 4.71/5.14 % mult_2_right
% 4.71/5.14 thf(fact_6494_left__add__twice,axiom,
% 4.71/5.14 ! [A: rat,B: rat] :
% 4.71/5.14 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 4.71/5.14 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 4.71/5.14
% 4.71/5.14 % left_add_twice
% 4.71/5.14 thf(fact_6495_left__add__twice,axiom,
% 4.71/5.14 ! [A: real,B: real] :
% 4.71/5.14 ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 4.71/5.14 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 4.71/5.14
% 4.71/5.14 % left_add_twice
% 4.71/5.14 thf(fact_6496_left__add__twice,axiom,
% 4.71/5.14 ! [A: nat,B: nat] :
% 4.71/5.14 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 4.71/5.14 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 4.71/5.14
% 4.71/5.14 % left_add_twice
% 4.71/5.14 thf(fact_6497_left__add__twice,axiom,
% 4.71/5.14 ! [A: int,B: int] :
% 4.71/5.14 ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 4.71/5.14 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 4.71/5.14
% 4.71/5.14 % left_add_twice
% 4.71/5.14 thf(fact_6498_left__add__twice,axiom,
% 4.71/5.14 ! [A: extended_enat,B: extended_enat] :
% 4.71/5.14 ( ( plus_p3455044024723400733d_enat @ A @ ( plus_p3455044024723400733d_enat @ A @ B ) )
% 4.71/5.14 = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 4.71/5.14
% 4.71/5.14 % left_add_twice
% 4.71/5.14 thf(fact_6499_left__add__twice,axiom,
% 4.71/5.14 ! [A: code_integer,B: code_integer] :
% 4.71/5.14 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 4.71/5.14 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 4.71/5.14
% 4.71/5.14 % left_add_twice
% 4.71/5.14 thf(fact_6500_field__sum__of__halves,axiom,
% 4.71/5.14 ! [X: rat] :
% 4.71/5.14 ( ( plus_plus_rat @ ( divide_divide_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = X ) ).
% 4.71/5.14
% 4.71/5.14 % field_sum_of_halves
% 4.71/5.14 thf(fact_6501_field__sum__of__halves,axiom,
% 4.71/5.14 ! [X: real] :
% 4.71/5.14 ( ( plus_plus_real @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = X ) ).
% 4.71/5.14
% 4.71/5.14 % field_sum_of_halves
% 4.71/5.14 thf(fact_6502_power2__eq__1__iff,axiom,
% 4.71/5.14 ! [A: int] :
% 4.71/5.14 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = one_one_int )
% 4.71/5.14 = ( ( A = one_one_int )
% 4.71/5.14 | ( A
% 4.71/5.14 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % power2_eq_1_iff
% 4.71/5.14 thf(fact_6503_power2__eq__1__iff,axiom,
% 4.71/5.14 ! [A: real] :
% 4.71/5.14 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = one_one_real )
% 4.71/5.14 = ( ( A = one_one_real )
% 4.71/5.14 | ( A
% 4.71/5.14 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % power2_eq_1_iff
% 4.71/5.14 thf(fact_6504_power2__eq__1__iff,axiom,
% 4.71/5.14 ! [A: rat] :
% 4.71/5.14 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = one_one_rat )
% 4.71/5.14 = ( ( A = one_one_rat )
% 4.71/5.14 | ( A
% 4.71/5.14 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % power2_eq_1_iff
% 4.71/5.14 thf(fact_6505_power2__eq__1__iff,axiom,
% 4.71/5.14 ! [A: complex] :
% 4.71/5.14 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = one_one_complex )
% 4.71/5.14 = ( ( A = one_one_complex )
% 4.71/5.14 | ( A
% 4.71/5.14 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % power2_eq_1_iff
% 4.71/5.14 thf(fact_6506_abs__le__square__iff,axiom,
% 4.71/5.14 ! [X: real,Y: real] :
% 4.71/5.14 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y ) )
% 4.71/5.14 = ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % abs_le_square_iff
% 4.71/5.14 thf(fact_6507_abs__le__square__iff,axiom,
% 4.71/5.14 ! [X: rat,Y: rat] :
% 4.71/5.14 ( ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ ( abs_abs_rat @ Y ) )
% 4.71/5.14 = ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % abs_le_square_iff
% 4.71/5.14 thf(fact_6508_abs__le__square__iff,axiom,
% 4.71/5.14 ! [X: int,Y: int] :
% 4.71/5.14 ( ( ord_less_eq_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y ) )
% 4.71/5.14 = ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % abs_le_square_iff
% 4.71/5.14 thf(fact_6509_less__2__cases,axiom,
% 4.71/5.14 ! [N: nat] :
% 4.71/5.14 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 => ( ( N = zero_zero_nat )
% 4.71/5.14 | ( N
% 4.71/5.14 = ( suc @ zero_zero_nat ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % less_2_cases
% 4.71/5.14 thf(fact_6510_less__2__cases__iff,axiom,
% 4.71/5.14 ! [N: nat] :
% 4.71/5.14 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = ( ( N = zero_zero_nat )
% 4.71/5.14 | ( N
% 4.71/5.14 = ( suc @ zero_zero_nat ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % less_2_cases_iff
% 4.71/5.14 thf(fact_6511_abs__square__eq__1,axiom,
% 4.71/5.14 ! [X: rat] :
% 4.71/5.14 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = one_one_rat )
% 4.71/5.14 = ( ( abs_abs_rat @ X )
% 4.71/5.14 = one_one_rat ) ) ).
% 4.71/5.14
% 4.71/5.14 % abs_square_eq_1
% 4.71/5.14 thf(fact_6512_abs__square__eq__1,axiom,
% 4.71/5.14 ! [X: int] :
% 4.71/5.14 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = one_one_int )
% 4.71/5.14 = ( ( abs_abs_int @ X )
% 4.71/5.14 = one_one_int ) ) ).
% 4.71/5.14
% 4.71/5.14 % abs_square_eq_1
% 4.71/5.14 thf(fact_6513_abs__square__eq__1,axiom,
% 4.71/5.14 ! [X: real] :
% 4.71/5.14 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = one_one_real )
% 4.71/5.14 = ( ( abs_abs_real @ X )
% 4.71/5.14 = one_one_real ) ) ).
% 4.71/5.14
% 4.71/5.14 % abs_square_eq_1
% 4.71/5.14 thf(fact_6514_card__2__iff,axiom,
% 4.71/5.14 ! [S2: set_Pr1261947904930325089at_nat] :
% 4.71/5.14 ( ( ( finite711546835091564841at_nat @ S2 )
% 4.71/5.14 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = ( ? [X3: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 4.71/5.14 ( ( S2
% 4.71/5.14 = ( insert8211810215607154385at_nat @ X3 @ ( insert8211810215607154385at_nat @ Y2 @ bot_bo2099793752762293965at_nat ) ) )
% 4.71/5.14 & ( X3 != Y2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % card_2_iff
% 4.71/5.14 thf(fact_6515_card__2__iff,axiom,
% 4.71/5.14 ! [S2: set_complex] :
% 4.71/5.14 ( ( ( finite_card_complex @ S2 )
% 4.71/5.14 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = ( ? [X3: complex,Y2: complex] :
% 4.71/5.14 ( ( S2
% 4.71/5.14 = ( insert_complex @ X3 @ ( insert_complex @ Y2 @ bot_bot_set_complex ) ) )
% 4.71/5.14 & ( X3 != Y2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % card_2_iff
% 4.71/5.14 thf(fact_6516_card__2__iff,axiom,
% 4.71/5.14 ! [S2: set_list_nat] :
% 4.71/5.14 ( ( ( finite_card_list_nat @ S2 )
% 4.71/5.14 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = ( ? [X3: list_nat,Y2: list_nat] :
% 4.71/5.14 ( ( S2
% 4.71/5.14 = ( insert_list_nat @ X3 @ ( insert_list_nat @ Y2 @ bot_bot_set_list_nat ) ) )
% 4.71/5.14 & ( X3 != Y2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % card_2_iff
% 4.71/5.14 thf(fact_6517_card__2__iff,axiom,
% 4.71/5.14 ! [S2: set_set_nat] :
% 4.71/5.14 ( ( ( finite_card_set_nat @ S2 )
% 4.71/5.14 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = ( ? [X3: set_nat,Y2: set_nat] :
% 4.71/5.14 ( ( S2
% 4.71/5.14 = ( insert_set_nat @ X3 @ ( insert_set_nat @ Y2 @ bot_bot_set_set_nat ) ) )
% 4.71/5.14 & ( X3 != Y2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % card_2_iff
% 4.71/5.14 thf(fact_6518_card__2__iff,axiom,
% 4.71/5.14 ! [S2: set_real] :
% 4.71/5.14 ( ( ( finite_card_real @ S2 )
% 4.71/5.14 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = ( ? [X3: real,Y2: real] :
% 4.71/5.14 ( ( S2
% 4.71/5.14 = ( insert_real @ X3 @ ( insert_real @ Y2 @ bot_bot_set_real ) ) )
% 4.71/5.14 & ( X3 != Y2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % card_2_iff
% 4.71/5.14 thf(fact_6519_card__2__iff,axiom,
% 4.71/5.14 ! [S2: set_o] :
% 4.71/5.14 ( ( ( finite_card_o @ S2 )
% 4.71/5.14 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = ( ? [X3: $o,Y2: $o] :
% 4.71/5.14 ( ( S2
% 4.71/5.14 = ( insert_o @ X3 @ ( insert_o @ Y2 @ bot_bot_set_o ) ) )
% 4.71/5.14 & ( X3 != Y2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % card_2_iff
% 4.71/5.14 thf(fact_6520_card__2__iff,axiom,
% 4.71/5.14 ! [S2: set_nat] :
% 4.71/5.14 ( ( ( finite_card_nat @ S2 )
% 4.71/5.14 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = ( ? [X3: nat,Y2: nat] :
% 4.71/5.14 ( ( S2
% 4.71/5.14 = ( insert_nat @ X3 @ ( insert_nat @ Y2 @ bot_bot_set_nat ) ) )
% 4.71/5.14 & ( X3 != Y2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % card_2_iff
% 4.71/5.14 thf(fact_6521_card__2__iff,axiom,
% 4.71/5.14 ! [S2: set_int] :
% 4.71/5.14 ( ( ( finite_card_int @ S2 )
% 4.71/5.14 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = ( ? [X3: int,Y2: int] :
% 4.71/5.14 ( ( S2
% 4.71/5.14 = ( insert_int @ X3 @ ( insert_int @ Y2 @ bot_bot_set_int ) ) )
% 4.71/5.14 & ( X3 != Y2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % card_2_iff
% 4.71/5.14 thf(fact_6522_nat__2,axiom,
% 4.71/5.14 ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.71/5.14 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % nat_2
% 4.71/5.14 thf(fact_6523_nat__induct2,axiom,
% 4.71/5.14 ! [P: nat > $o,N: nat] :
% 4.71/5.14 ( ( P @ zero_zero_nat )
% 4.71/5.14 => ( ( P @ one_one_nat )
% 4.71/5.14 => ( ! [N2: nat] :
% 4.71/5.14 ( ( P @ N2 )
% 4.71/5.14 => ( P @ ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.71/5.14 => ( P @ N ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % nat_induct2
% 4.71/5.14 thf(fact_6524_square__fact__le__2__fact,axiom,
% 4.71/5.14 ! [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 ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % square_fact_le_2_fact
% 4.71/5.14 thf(fact_6525_two__realpow__ge__one,axiom,
% 4.71/5.14 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 4.71/5.14
% 4.71/5.14 % two_realpow_ge_one
% 4.71/5.14 thf(fact_6526_diff__le__diff__pow,axiom,
% 4.71/5.14 ! [K: nat,M2: nat,N: nat] :
% 4.71/5.14 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 4.71/5.14 => ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M2 ) @ ( power_power_nat @ K @ N ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % diff_le_diff_pow
% 4.71/5.14 thf(fact_6527_realpow__square__minus__le,axiom,
% 4.71/5.14 ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % realpow_square_minus_le
% 4.71/5.14 thf(fact_6528_not__exp__less__eq__0__int,axiom,
% 4.71/5.14 ! [N: nat] :
% 4.71/5.14 ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ zero_zero_int ) ).
% 4.71/5.14
% 4.71/5.14 % not_exp_less_eq_0_int
% 4.71/5.14 thf(fact_6529_power2__less__imp__less,axiom,
% 4.71/5.14 ! [X: real,Y: real] :
% 4.71/5.14 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.71/5.14 => ( ord_less_real @ X @ Y ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % power2_less_imp_less
% 4.71/5.14 thf(fact_6530_power2__less__imp__less,axiom,
% 4.71/5.14 ! [X: rat,Y: rat] :
% 4.71/5.14 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 4.71/5.14 => ( ord_less_rat @ X @ Y ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % power2_less_imp_less
% 4.71/5.14 thf(fact_6531_power2__less__imp__less,axiom,
% 4.71/5.14 ! [X: nat,Y: nat] :
% 4.71/5.14 ( ( ord_less_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 4.71/5.14 => ( ord_less_nat @ X @ Y ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % power2_less_imp_less
% 4.71/5.14 thf(fact_6532_power2__less__imp__less,axiom,
% 4.71/5.14 ! [X: int,Y: int] :
% 4.71/5.14 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.71/5.14 => ( ord_less_int @ X @ Y ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % power2_less_imp_less
% 4.71/5.14 thf(fact_6533_half__gt__zero,axiom,
% 4.71/5.14 ! [A: rat] :
% 4.71/5.14 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.71/5.14 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % half_gt_zero
% 4.71/5.14 thf(fact_6534_half__gt__zero,axiom,
% 4.71/5.14 ! [A: real] :
% 4.71/5.14 ( ( ord_less_real @ zero_zero_real @ A )
% 4.71/5.14 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % half_gt_zero
% 4.71/5.14 thf(fact_6535_half__gt__zero__iff,axiom,
% 4.71/5.14 ! [A: rat] :
% 4.71/5.14 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 4.71/5.14
% 4.71/5.14 % half_gt_zero_iff
% 4.71/5.14 thf(fact_6536_half__gt__zero__iff,axiom,
% 4.71/5.14 ! [A: real] :
% 4.71/5.14 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 4.71/5.14
% 4.71/5.14 % half_gt_zero_iff
% 4.71/5.14 thf(fact_6537_sum__power2__ge__zero,axiom,
% 4.71/5.14 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % sum_power2_ge_zero
% 4.71/5.14 thf(fact_6538_sum__power2__ge__zero,axiom,
% 4.71/5.14 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % sum_power2_ge_zero
% 4.71/5.14 thf(fact_6539_sum__power2__ge__zero,axiom,
% 4.71/5.14 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % sum_power2_ge_zero
% 4.71/5.14 thf(fact_6540_sum__power2__le__zero__iff,axiom,
% 4.71/5.14 ! [X: real,Y: real] :
% 4.71/5.14 ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 4.71/5.14 = ( ( X = zero_zero_real )
% 4.71/5.14 & ( Y = zero_zero_real ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % sum_power2_le_zero_iff
% 4.71/5.14 thf(fact_6541_sum__power2__le__zero__iff,axiom,
% 4.71/5.14 ! [X: rat,Y: rat] :
% 4.71/5.14 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 4.71/5.14 = ( ( X = zero_zero_rat )
% 4.71/5.14 & ( Y = zero_zero_rat ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % sum_power2_le_zero_iff
% 4.71/5.14 thf(fact_6542_sum__power2__le__zero__iff,axiom,
% 4.71/5.14 ! [X: int,Y: int] :
% 4.71/5.14 ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 4.71/5.14 = ( ( X = zero_zero_int )
% 4.71/5.14 & ( Y = zero_zero_int ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % sum_power2_le_zero_iff
% 4.71/5.14 thf(fact_6543_not__sum__power2__lt__zero,axiom,
% 4.71/5.14 ! [X: real,Y: real] :
% 4.71/5.14 ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 4.71/5.14
% 4.71/5.14 % not_sum_power2_lt_zero
% 4.71/5.14 thf(fact_6544_not__sum__power2__lt__zero,axiom,
% 4.71/5.14 ! [X: rat,Y: rat] :
% 4.71/5.14 ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 4.71/5.14
% 4.71/5.14 % not_sum_power2_lt_zero
% 4.71/5.14 thf(fact_6545_not__sum__power2__lt__zero,axiom,
% 4.71/5.14 ! [X: int,Y: int] :
% 4.71/5.14 ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 4.71/5.14
% 4.71/5.14 % not_sum_power2_lt_zero
% 4.71/5.14 thf(fact_6546_sum__power2__gt__zero__iff,axiom,
% 4.71/5.14 ! [X: real,Y: real] :
% 4.71/5.14 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.71/5.14 = ( ( X != zero_zero_real )
% 4.71/5.14 | ( Y != zero_zero_real ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % sum_power2_gt_zero_iff
% 4.71/5.14 thf(fact_6547_sum__power2__gt__zero__iff,axiom,
% 4.71/5.14 ! [X: rat,Y: rat] :
% 4.71/5.14 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.71/5.14 = ( ( X != zero_zero_rat )
% 4.71/5.14 | ( Y != zero_zero_rat ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % sum_power2_gt_zero_iff
% 4.71/5.14 thf(fact_6548_sum__power2__gt__zero__iff,axiom,
% 4.71/5.14 ! [X: int,Y: int] :
% 4.71/5.14 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.71/5.14 = ( ( X != zero_zero_int )
% 4.71/5.14 | ( Y != zero_zero_int ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % sum_power2_gt_zero_iff
% 4.71/5.14 thf(fact_6549_field__less__half__sum,axiom,
% 4.71/5.14 ! [X: rat,Y: rat] :
% 4.71/5.14 ( ( ord_less_rat @ X @ Y )
% 4.71/5.14 => ( ord_less_rat @ X @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % field_less_half_sum
% 4.71/5.14 thf(fact_6550_field__less__half__sum,axiom,
% 4.71/5.14 ! [X: real,Y: real] :
% 4.71/5.14 ( ( ord_less_real @ X @ Y )
% 4.71/5.14 => ( ord_less_real @ X @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % field_less_half_sum
% 4.71/5.14 thf(fact_6551_square__le__1,axiom,
% 4.71/5.14 ! [X: real] :
% 4.71/5.14 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 4.71/5.14 => ( ( ord_less_eq_real @ X @ one_one_real )
% 4.71/5.14 => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % square_le_1
% 4.71/5.14 thf(fact_6552_square__le__1,axiom,
% 4.71/5.14 ! [X: rat] :
% 4.71/5.14 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X )
% 4.71/5.14 => ( ( ord_less_eq_rat @ X @ one_one_rat )
% 4.71/5.14 => ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % square_le_1
% 4.71/5.14 thf(fact_6553_square__le__1,axiom,
% 4.71/5.14 ! [X: int] :
% 4.71/5.14 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 4.71/5.14 => ( ( ord_less_eq_int @ X @ one_one_int )
% 4.71/5.14 => ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % square_le_1
% 4.71/5.14 thf(fact_6554_of__nat__less__two__power,axiom,
% 4.71/5.14 ! [N: nat] : ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ N ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ).
% 4.71/5.14
% 4.71/5.14 % of_nat_less_two_power
% 4.71/5.14 thf(fact_6555_of__nat__less__two__power,axiom,
% 4.71/5.14 ! [N: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 4.71/5.14
% 4.71/5.14 % of_nat_less_two_power
% 4.71/5.14 thf(fact_6556_of__nat__less__two__power,axiom,
% 4.71/5.14 ! [N: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 4.71/5.14
% 4.71/5.14 % of_nat_less_two_power
% 4.71/5.14 thf(fact_6557_of__nat__less__two__power,axiom,
% 4.71/5.14 ! [N: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ).
% 4.71/5.14
% 4.71/5.14 % of_nat_less_two_power
% 4.71/5.14 thf(fact_6558_power2__le__iff__abs__le,axiom,
% 4.71/5.14 ! [Y: real,X: real] :
% 4.71/5.14 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.71/5.14 => ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ Y ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % power2_le_iff_abs_le
% 4.71/5.14 thf(fact_6559_power2__le__iff__abs__le,axiom,
% 4.71/5.14 ! [Y: rat,X: rat] :
% 4.71/5.14 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 4.71/5.14 => ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ Y ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % power2_le_iff_abs_le
% 4.71/5.14 thf(fact_6560_power2__le__iff__abs__le,axiom,
% 4.71/5.14 ! [Y: int,X: int] :
% 4.71/5.14 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.71/5.14 => ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ Y ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % power2_le_iff_abs_le
% 4.71/5.14 thf(fact_6561_exp__add__not__zero__imp__left,axiom,
% 4.71/5.14 ! [M2: nat,N: nat] :
% 4.71/5.14 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N ) )
% 4.71/5.14 != zero_zero_nat )
% 4.71/5.14 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 )
% 4.71/5.14 != zero_zero_nat ) ) ).
% 4.71/5.14
% 4.71/5.14 % exp_add_not_zero_imp_left
% 4.71/5.14 thf(fact_6562_exp__add__not__zero__imp__left,axiom,
% 4.71/5.14 ! [M2: nat,N: nat] :
% 4.71/5.14 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N ) )
% 4.71/5.14 != zero_zero_int )
% 4.71/5.14 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 )
% 4.71/5.14 != zero_zero_int ) ) ).
% 4.71/5.14
% 4.71/5.14 % exp_add_not_zero_imp_left
% 4.71/5.14 thf(fact_6563_exp__add__not__zero__imp__left,axiom,
% 4.71/5.14 ! [M2: nat,N: nat] :
% 4.71/5.14 ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N ) )
% 4.71/5.14 != zero_z3403309356797280102nteger )
% 4.71/5.14 => ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 )
% 4.71/5.14 != zero_z3403309356797280102nteger ) ) ).
% 4.71/5.14
% 4.71/5.14 % exp_add_not_zero_imp_left
% 4.71/5.14 thf(fact_6564_exp__add__not__zero__imp__right,axiom,
% 4.71/5.14 ! [M2: nat,N: nat] :
% 4.71/5.14 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N ) )
% 4.71/5.14 != zero_zero_nat )
% 4.71/5.14 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 4.71/5.14 != zero_zero_nat ) ) ).
% 4.71/5.14
% 4.71/5.14 % exp_add_not_zero_imp_right
% 4.71/5.14 thf(fact_6565_exp__add__not__zero__imp__right,axiom,
% 4.71/5.14 ! [M2: nat,N: nat] :
% 4.71/5.14 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N ) )
% 4.71/5.14 != zero_zero_int )
% 4.71/5.14 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 4.71/5.14 != zero_zero_int ) ) ).
% 4.71/5.14
% 4.71/5.14 % exp_add_not_zero_imp_right
% 4.71/5.14 thf(fact_6566_exp__add__not__zero__imp__right,axiom,
% 4.71/5.14 ! [M2: nat,N: nat] :
% 4.71/5.14 ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N ) )
% 4.71/5.14 != zero_z3403309356797280102nteger )
% 4.71/5.14 => ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 4.71/5.14 != zero_z3403309356797280102nteger ) ) ).
% 4.71/5.14
% 4.71/5.14 % exp_add_not_zero_imp_right
% 4.71/5.14 thf(fact_6567_zero__le__even__power_H,axiom,
% 4.71/5.14 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % zero_le_even_power'
% 4.71/5.14 thf(fact_6568_zero__le__even__power_H,axiom,
% 4.71/5.14 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % zero_le_even_power'
% 4.71/5.14 thf(fact_6569_zero__le__even__power_H,axiom,
% 4.71/5.14 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % zero_le_even_power'
% 4.71/5.14 thf(fact_6570_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 4.71/5.14 ! [N: nat,M2: nat] :
% 4.71/5.14 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 4.71/5.14 != zero_zero_nat )
% 4.71/5.14 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) )
% 4.71/5.14 != zero_zero_nat ) ) ).
% 4.71/5.14
% 4.71/5.14 % exp_not_zero_imp_exp_diff_not_zero
% 4.71/5.14 thf(fact_6571_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 4.71/5.14 ! [N: nat,M2: nat] :
% 4.71/5.14 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 4.71/5.14 != zero_zero_int )
% 4.71/5.14 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) )
% 4.71/5.14 != zero_zero_int ) ) ).
% 4.71/5.14
% 4.71/5.14 % exp_not_zero_imp_exp_diff_not_zero
% 4.71/5.14 thf(fact_6572_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 4.71/5.14 ! [N: nat,M2: nat] :
% 4.71/5.14 ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 4.71/5.14 != zero_z3403309356797280102nteger )
% 4.71/5.14 => ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) )
% 4.71/5.14 != zero_z3403309356797280102nteger ) ) ).
% 4.71/5.14
% 4.71/5.14 % exp_not_zero_imp_exp_diff_not_zero
% 4.71/5.14 thf(fact_6573_abs__square__le__1,axiom,
% 4.71/5.14 ! [X: real] :
% 4.71/5.14 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 4.71/5.14 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 4.71/5.14
% 4.71/5.14 % abs_square_le_1
% 4.71/5.14 thf(fact_6574_abs__square__le__1,axiom,
% 4.71/5.14 ! [X: rat] :
% 4.71/5.14 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 4.71/5.14 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 4.71/5.14
% 4.71/5.14 % abs_square_le_1
% 4.71/5.14 thf(fact_6575_abs__square__le__1,axiom,
% 4.71/5.14 ! [X: int] :
% 4.71/5.14 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 4.71/5.14 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 4.71/5.14
% 4.71/5.14 % abs_square_le_1
% 4.71/5.14 thf(fact_6576_abs__square__less__1,axiom,
% 4.71/5.14 ! [X: real] :
% 4.71/5.14 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 4.71/5.14 = ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 4.71/5.14
% 4.71/5.14 % abs_square_less_1
% 4.71/5.14 thf(fact_6577_abs__square__less__1,axiom,
% 4.71/5.14 ! [X: rat] :
% 4.71/5.14 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 4.71/5.14 = ( ord_less_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 4.71/5.14
% 4.71/5.14 % abs_square_less_1
% 4.71/5.14 thf(fact_6578_abs__square__less__1,axiom,
% 4.71/5.14 ! [X: int] :
% 4.71/5.14 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 4.71/5.14 = ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 4.71/5.14
% 4.71/5.14 % abs_square_less_1
% 4.71/5.14 thf(fact_6579_all__nat__less,axiom,
% 4.71/5.14 ! [N: nat,P: nat > $o] :
% 4.71/5.14 ( ( ! [M3: nat] :
% 4.71/5.14 ( ( ord_less_eq_nat @ M3 @ N )
% 4.71/5.14 => ( P @ M3 ) ) )
% 4.71/5.14 = ( ! [X3: nat] :
% 4.71/5.14 ( ( member_nat @ X3 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 4.71/5.14 => ( P @ X3 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % all_nat_less
% 4.71/5.14 thf(fact_6580_ex__nat__less,axiom,
% 4.71/5.14 ! [N: nat,P: nat > $o] :
% 4.71/5.14 ( ( ? [M3: nat] :
% 4.71/5.14 ( ( ord_less_eq_nat @ M3 @ N )
% 4.71/5.14 & ( P @ M3 ) ) )
% 4.71/5.14 = ( ? [X3: nat] :
% 4.71/5.14 ( ( member_nat @ X3 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 4.71/5.14 & ( P @ X3 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % ex_nat_less
% 4.71/5.14 thf(fact_6581_nat__bit__induct,axiom,
% 4.71/5.14 ! [P: nat > $o,N: nat] :
% 4.71/5.14 ( ( P @ zero_zero_nat )
% 4.71/5.14 => ( ! [N2: nat] :
% 4.71/5.14 ( ( P @ N2 )
% 4.71/5.14 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.71/5.14 => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 4.71/5.14 => ( ! [N2: nat] :
% 4.71/5.14 ( ( P @ N2 )
% 4.71/5.14 => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 4.71/5.14 => ( P @ N ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % nat_bit_induct
% 4.71/5.14 thf(fact_6582_div__2__gt__zero,axiom,
% 4.71/5.14 ! [N: nat] :
% 4.71/5.14 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 4.71/5.14 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % div_2_gt_zero
% 4.71/5.14 thf(fact_6583_Suc__n__div__2__gt__zero,axiom,
% 4.71/5.14 ! [N: nat] :
% 4.71/5.14 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.14 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Suc_n_div_2_gt_zero
% 4.71/5.14 thf(fact_6584_square__norm__one,axiom,
% 4.71/5.14 ! [X: real] :
% 4.71/5.14 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = one_one_real )
% 4.71/5.14 => ( ( real_V7735802525324610683m_real @ X )
% 4.71/5.14 = one_one_real ) ) ).
% 4.71/5.14
% 4.71/5.14 % square_norm_one
% 4.71/5.14 thf(fact_6585_square__norm__one,axiom,
% 4.71/5.14 ! [X: complex] :
% 4.71/5.14 ( ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = one_one_complex )
% 4.71/5.14 => ( ( real_V1022390504157884413omplex @ X )
% 4.71/5.14 = one_one_real ) ) ).
% 4.71/5.14
% 4.71/5.14 % square_norm_one
% 4.71/5.14 thf(fact_6586_L2__set__mult__ineq__lemma,axiom,
% 4.71/5.14 ! [A: real,C: real,B: real,D: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_real @ A @ C ) ) @ ( times_times_real @ B @ D ) ) @ ( plus_plus_real @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ C @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % L2_set_mult_ineq_lemma
% 4.71/5.14 thf(fact_6587_numeral__Bit0,axiom,
% 4.71/5.14 ! [N: num] :
% 4.71/5.14 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 4.71/5.14 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % numeral_Bit0
% 4.71/5.14 thf(fact_6588_numeral__Bit0,axiom,
% 4.71/5.14 ! [N: num] :
% 4.71/5.14 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 4.71/5.14 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % numeral_Bit0
% 4.71/5.14 thf(fact_6589_numeral__Bit0,axiom,
% 4.71/5.14 ! [N: num] :
% 4.71/5.14 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 4.71/5.14 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % numeral_Bit0
% 4.71/5.14 thf(fact_6590_numeral__Bit0,axiom,
% 4.71/5.14 ! [N: num] :
% 4.71/5.14 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 4.71/5.14 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % numeral_Bit0
% 4.71/5.14 thf(fact_6591_numeral__Bit0,axiom,
% 4.71/5.14 ! [N: num] :
% 4.71/5.14 ( ( numera1916890842035813515d_enat @ ( bit0 @ N ) )
% 4.71/5.14 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N ) @ ( numera1916890842035813515d_enat @ N ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % numeral_Bit0
% 4.71/5.14 thf(fact_6592_numeral__Bit0,axiom,
% 4.71/5.14 ! [N: num] :
% 4.71/5.14 ( ( numera6620942414471956472nteger @ ( bit0 @ N ) )
% 4.71/5.14 = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % numeral_Bit0
% 4.71/5.14 thf(fact_6593_exp__half__le2,axiom,
% 4.71/5.14 ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 4.71/5.14
% 4.71/5.14 % exp_half_le2
% 4.71/5.14 thf(fact_6594_exp__plus__inverse__exp,axiom,
% 4.71/5.14 ! [X: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % exp_plus_inverse_exp
% 4.71/5.14 thf(fact_6595_mult__numeral__1__right,axiom,
% 4.71/5.14 ! [A: rat] :
% 4.71/5.14 ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 4.71/5.14 = A ) ).
% 4.71/5.14
% 4.71/5.14 % mult_numeral_1_right
% 4.71/5.14 thf(fact_6596_mult__numeral__1__right,axiom,
% 4.71/5.14 ! [A: real] :
% 4.71/5.14 ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 4.71/5.14 = A ) ).
% 4.71/5.14
% 4.71/5.14 % mult_numeral_1_right
% 4.71/5.14 thf(fact_6597_mult__numeral__1__right,axiom,
% 4.71/5.14 ! [A: nat] :
% 4.71/5.14 ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 4.71/5.14 = A ) ).
% 4.71/5.14
% 4.71/5.14 % mult_numeral_1_right
% 4.71/5.14 thf(fact_6598_mult__numeral__1__right,axiom,
% 4.71/5.14 ! [A: int] :
% 4.71/5.14 ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 4.71/5.14 = A ) ).
% 4.71/5.14
% 4.71/5.14 % mult_numeral_1_right
% 4.71/5.14 thf(fact_6599_mult__numeral__1__right,axiom,
% 4.71/5.14 ! [A: extended_enat] :
% 4.71/5.14 ( ( times_7803423173614009249d_enat @ A @ ( numera1916890842035813515d_enat @ one ) )
% 4.71/5.14 = A ) ).
% 4.71/5.14
% 4.71/5.14 % mult_numeral_1_right
% 4.71/5.14 thf(fact_6600_mult__numeral__1__right,axiom,
% 4.71/5.14 ! [A: code_integer] :
% 4.71/5.14 ( ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ one ) )
% 4.71/5.14 = A ) ).
% 4.71/5.14
% 4.71/5.14 % mult_numeral_1_right
% 4.71/5.14 thf(fact_6601_mult__numeral__1,axiom,
% 4.71/5.14 ! [A: rat] :
% 4.71/5.14 ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 4.71/5.14 = A ) ).
% 4.71/5.14
% 4.71/5.14 % mult_numeral_1
% 4.71/5.14 thf(fact_6602_mult__numeral__1,axiom,
% 4.71/5.14 ! [A: real] :
% 4.71/5.14 ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 4.71/5.14 = A ) ).
% 4.71/5.14
% 4.71/5.14 % mult_numeral_1
% 4.71/5.14 thf(fact_6603_mult__numeral__1,axiom,
% 4.71/5.14 ! [A: nat] :
% 4.71/5.14 ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 4.71/5.14 = A ) ).
% 4.71/5.14
% 4.71/5.14 % mult_numeral_1
% 4.71/5.14 thf(fact_6604_mult__numeral__1,axiom,
% 4.71/5.14 ! [A: int] :
% 4.71/5.14 ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 4.71/5.14 = A ) ).
% 4.71/5.14
% 4.71/5.14 % mult_numeral_1
% 4.71/5.14 thf(fact_6605_mult__numeral__1,axiom,
% 4.71/5.14 ! [A: extended_enat] :
% 4.71/5.14 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ one ) @ A )
% 4.71/5.14 = A ) ).
% 4.71/5.14
% 4.71/5.14 % mult_numeral_1
% 4.71/5.14 thf(fact_6606_mult__numeral__1,axiom,
% 4.71/5.14 ! [A: code_integer] :
% 4.71/5.14 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ one ) @ A )
% 4.71/5.14 = A ) ).
% 4.71/5.14
% 4.71/5.14 % mult_numeral_1
% 4.71/5.14 thf(fact_6607_numeral__One,axiom,
% 4.71/5.14 ( ( numera6690914467698888265omplex @ one )
% 4.71/5.14 = one_one_complex ) ).
% 4.71/5.14
% 4.71/5.14 % numeral_One
% 4.71/5.14 thf(fact_6608_numeral__One,axiom,
% 4.71/5.14 ( ( numeral_numeral_rat @ one )
% 4.71/5.14 = one_one_rat ) ).
% 4.71/5.14
% 4.71/5.14 % numeral_One
% 4.71/5.14 thf(fact_6609_numeral__One,axiom,
% 4.71/5.14 ( ( numeral_numeral_real @ one )
% 4.71/5.14 = one_one_real ) ).
% 4.71/5.14
% 4.71/5.14 % numeral_One
% 4.71/5.14 thf(fact_6610_numeral__One,axiom,
% 4.71/5.14 ( ( numeral_numeral_nat @ one )
% 4.71/5.14 = one_one_nat ) ).
% 4.71/5.14
% 4.71/5.14 % numeral_One
% 4.71/5.14 thf(fact_6611_numeral__One,axiom,
% 4.71/5.14 ( ( numeral_numeral_int @ one )
% 4.71/5.14 = one_one_int ) ).
% 4.71/5.14
% 4.71/5.14 % numeral_One
% 4.71/5.14 thf(fact_6612_numeral__One,axiom,
% 4.71/5.14 ( ( numera1916890842035813515d_enat @ one )
% 4.71/5.14 = one_on7984719198319812577d_enat ) ).
% 4.71/5.14
% 4.71/5.14 % numeral_One
% 4.71/5.14 thf(fact_6613_numeral__One,axiom,
% 4.71/5.14 ( ( numera6620942414471956472nteger @ one )
% 4.71/5.14 = one_one_Code_integer ) ).
% 4.71/5.14
% 4.71/5.14 % numeral_One
% 4.71/5.14 thf(fact_6614_divide__numeral__1,axiom,
% 4.71/5.14 ! [A: real] :
% 4.71/5.14 ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 4.71/5.14 = A ) ).
% 4.71/5.14
% 4.71/5.14 % divide_numeral_1
% 4.71/5.14 thf(fact_6615_numeral__1__eq__Suc__0,axiom,
% 4.71/5.14 ( ( numeral_numeral_nat @ one )
% 4.71/5.14 = ( suc @ zero_zero_nat ) ) ).
% 4.71/5.14
% 4.71/5.14 % numeral_1_eq_Suc_0
% 4.71/5.14 thf(fact_6616_Suc__nat__number__of__add,axiom,
% 4.71/5.14 ! [V: num,N: nat] :
% 4.71/5.14 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 4.71/5.14 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N ) ) ).
% 4.71/5.14
% 4.71/5.14 % Suc_nat_number_of_add
% 4.71/5.14 thf(fact_6617_inverse__numeral__1,axiom,
% 4.71/5.14 ( ( inverse_inverse_real @ ( numeral_numeral_real @ one ) )
% 4.71/5.14 = ( numeral_numeral_real @ one ) ) ).
% 4.71/5.14
% 4.71/5.14 % inverse_numeral_1
% 4.71/5.14 thf(fact_6618_inverse__numeral__1,axiom,
% 4.71/5.14 ( ( inverse_inverse_rat @ ( numeral_numeral_rat @ one ) )
% 4.71/5.14 = ( numeral_numeral_rat @ one ) ) ).
% 4.71/5.14
% 4.71/5.14 % inverse_numeral_1
% 4.71/5.14 thf(fact_6619_sum__squares__bound,axiom,
% 4.71/5.14 ! [X: real,Y: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y ) @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % sum_squares_bound
% 4.71/5.14 thf(fact_6620_sum__squares__bound,axiom,
% 4.71/5.14 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % sum_squares_bound
% 4.71/5.14 thf(fact_6621_divmod__digit__0_I2_J,axiom,
% 4.71/5.14 ! [B: code_integer,A: code_integer] :
% 4.71/5.14 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 4.71/5.14 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 4.71/5.14 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) )
% 4.71/5.14 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % divmod_digit_0(2)
% 4.71/5.14 thf(fact_6622_divmod__digit__0_I2_J,axiom,
% 4.71/5.14 ! [B: int,A: int] :
% 4.71/5.14 ( ( ord_less_int @ zero_zero_int @ B )
% 4.71/5.14 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 4.71/5.14 => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 4.71/5.14 = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % divmod_digit_0(2)
% 4.71/5.14 thf(fact_6623_divmod__digit__0_I2_J,axiom,
% 4.71/5.14 ! [B: nat,A: nat] :
% 4.71/5.14 ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.71/5.14 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 4.71/5.14 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 4.71/5.14 = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % divmod_digit_0(2)
% 4.71/5.14 thf(fact_6624_bits__stable__imp__add__self,axiom,
% 4.71/5.14 ! [A: code_integer] :
% 4.71/5.14 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 4.71/5.14 = A )
% 4.71/5.14 => ( ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = zero_z3403309356797280102nteger ) ) ).
% 4.71/5.14
% 4.71/5.14 % bits_stable_imp_add_self
% 4.71/5.14 thf(fact_6625_bits__stable__imp__add__self,axiom,
% 4.71/5.14 ! [A: int] :
% 4.71/5.14 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.71/5.14 = A )
% 4.71/5.14 => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = zero_zero_int ) ) ).
% 4.71/5.14
% 4.71/5.14 % bits_stable_imp_add_self
% 4.71/5.14 thf(fact_6626_bits__stable__imp__add__self,axiom,
% 4.71/5.14 ! [A: nat] :
% 4.71/5.14 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = A )
% 4.71/5.14 => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = zero_zero_nat ) ) ).
% 4.71/5.14
% 4.71/5.14 % bits_stable_imp_add_self
% 4.71/5.14 thf(fact_6627_odd__0__le__power__imp__0__le,axiom,
% 4.71/5.14 ! [A: real,N: nat] :
% 4.71/5.14 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 4.71/5.14 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 4.71/5.14
% 4.71/5.14 % odd_0_le_power_imp_0_le
% 4.71/5.14 thf(fact_6628_odd__0__le__power__imp__0__le,axiom,
% 4.71/5.14 ! [A: rat,N: nat] :
% 4.71/5.14 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 4.71/5.14 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 4.71/5.14
% 4.71/5.14 % odd_0_le_power_imp_0_le
% 4.71/5.14 thf(fact_6629_odd__0__le__power__imp__0__le,axiom,
% 4.71/5.14 ! [A: int,N: nat] :
% 4.71/5.14 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 4.71/5.14 => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 4.71/5.14
% 4.71/5.14 % odd_0_le_power_imp_0_le
% 4.71/5.14 thf(fact_6630_odd__power__less__zero,axiom,
% 4.71/5.14 ! [A: real,N: nat] :
% 4.71/5.14 ( ( ord_less_real @ A @ zero_zero_real )
% 4.71/5.14 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_real ) ) ).
% 4.71/5.14
% 4.71/5.14 % odd_power_less_zero
% 4.71/5.14 thf(fact_6631_odd__power__less__zero,axiom,
% 4.71/5.14 ! [A: rat,N: nat] :
% 4.71/5.14 ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.71/5.14 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_rat ) ) ).
% 4.71/5.14
% 4.71/5.14 % odd_power_less_zero
% 4.71/5.14 thf(fact_6632_odd__power__less__zero,axiom,
% 4.71/5.14 ! [A: int,N: nat] :
% 4.71/5.14 ( ( ord_less_int @ A @ zero_zero_int )
% 4.71/5.14 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_int ) ) ).
% 4.71/5.14
% 4.71/5.14 % odd_power_less_zero
% 4.71/5.14 thf(fact_6633_power__minus1__odd,axiom,
% 4.71/5.14 ! [N: nat] :
% 4.71/5.14 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 4.71/5.14 = ( uminus_uminus_int @ one_one_int ) ) ).
% 4.71/5.14
% 4.71/5.14 % power_minus1_odd
% 4.71/5.14 thf(fact_6634_power__minus1__odd,axiom,
% 4.71/5.14 ! [N: nat] :
% 4.71/5.14 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 4.71/5.14 = ( uminus_uminus_real @ one_one_real ) ) ).
% 4.71/5.14
% 4.71/5.14 % power_minus1_odd
% 4.71/5.14 thf(fact_6635_power__minus1__odd,axiom,
% 4.71/5.14 ! [N: nat] :
% 4.71/5.14 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 4.71/5.14 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.71/5.14
% 4.71/5.14 % power_minus1_odd
% 4.71/5.14 thf(fact_6636_power__minus1__odd,axiom,
% 4.71/5.14 ! [N: nat] :
% 4.71/5.14 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 4.71/5.14 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 4.71/5.14
% 4.71/5.14 % power_minus1_odd
% 4.71/5.14 thf(fact_6637_ex__power__ivl2,axiom,
% 4.71/5.14 ! [B: nat,K: nat] :
% 4.71/5.14 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 4.71/5.14 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 4.71/5.14 => ? [N2: nat] :
% 4.71/5.14 ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 4.71/5.14 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % ex_power_ivl2
% 4.71/5.14 thf(fact_6638_ex__power__ivl1,axiom,
% 4.71/5.14 ! [B: nat,K: nat] :
% 4.71/5.14 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 4.71/5.14 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 4.71/5.14 => ? [N2: nat] :
% 4.71/5.14 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 4.71/5.14 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % ex_power_ivl1
% 4.71/5.14 thf(fact_6639_plus__inverse__ge__2,axiom,
% 4.71/5.14 ! [X: real] :
% 4.71/5.14 ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.14 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % plus_inverse_ge_2
% 4.71/5.14 thf(fact_6640_exp__bound__half,axiom,
% 4.71/5.14 ! [Z: real] :
% 4.71/5.14 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.71/5.14 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % exp_bound_half
% 4.71/5.14 thf(fact_6641_exp__bound__half,axiom,
% 4.71/5.14 ! [Z: complex] :
% 4.71/5.14 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.71/5.14 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % exp_bound_half
% 4.71/5.14 thf(fact_6642_less__log2__of__power,axiom,
% 4.71/5.14 ! [N: nat,M2: nat] :
% 4.71/5.14 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M2 )
% 4.71/5.14 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % less_log2_of_power
% 4.71/5.14 thf(fact_6643_le__log2__of__power,axiom,
% 4.71/5.14 ! [N: nat,M2: nat] :
% 4.71/5.14 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M2 )
% 4.71/5.14 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % le_log2_of_power
% 4.71/5.14 thf(fact_6644_divmod__digit__0_I1_J,axiom,
% 4.71/5.14 ! [B: code_integer,A: code_integer] :
% 4.71/5.14 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 4.71/5.14 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 4.71/5.14 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 4.71/5.14 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % divmod_digit_0(1)
% 4.71/5.14 thf(fact_6645_divmod__digit__0_I1_J,axiom,
% 4.71/5.14 ! [B: int,A: int] :
% 4.71/5.14 ( ( ord_less_int @ zero_zero_int @ B )
% 4.71/5.14 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 4.71/5.14 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 4.71/5.14 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % divmod_digit_0(1)
% 4.71/5.14 thf(fact_6646_divmod__digit__0_I1_J,axiom,
% 4.71/5.14 ! [B: nat,A: nat] :
% 4.71/5.14 ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.71/5.14 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 4.71/5.14 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 4.71/5.14 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % divmod_digit_0(1)
% 4.71/5.14 thf(fact_6647_mult__exp__mod__exp__eq,axiom,
% 4.71/5.14 ! [M2: nat,N: nat,A: code_integer] :
% 4.71/5.14 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.14 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 4.71/5.14 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % mult_exp_mod_exp_eq
% 4.71/5.14 thf(fact_6648_mult__exp__mod__exp__eq,axiom,
% 4.71/5.14 ! [M2: nat,N: nat,A: int] :
% 4.71/5.14 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.14 => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 4.71/5.14 = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % mult_exp_mod_exp_eq
% 4.71/5.14 thf(fact_6649_mult__exp__mod__exp__eq,axiom,
% 4.71/5.14 ! [M2: nat,N: nat,A: nat] :
% 4.71/5.14 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.14 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.71/5.14 = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % mult_exp_mod_exp_eq
% 4.71/5.14 thf(fact_6650_cong__exp__iff__simps_I2_J,axiom,
% 4.71/5.14 ! [N: num,Q4: num] :
% 4.71/5.14 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q4 ) ) )
% 4.71/5.14 = zero_z3403309356797280102nteger )
% 4.71/5.14 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q4 ) )
% 4.71/5.14 = zero_z3403309356797280102nteger ) ) ).
% 4.71/5.14
% 4.71/5.14 % cong_exp_iff_simps(2)
% 4.71/5.14 thf(fact_6651_cong__exp__iff__simps_I2_J,axiom,
% 4.71/5.14 ! [N: num,Q4: num] :
% 4.71/5.14 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q4 ) ) )
% 4.71/5.14 = zero_zero_int )
% 4.71/5.14 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q4 ) )
% 4.71/5.14 = zero_zero_int ) ) ).
% 4.71/5.14
% 4.71/5.14 % cong_exp_iff_simps(2)
% 4.71/5.14 thf(fact_6652_cong__exp__iff__simps_I2_J,axiom,
% 4.71/5.14 ! [N: num,Q4: num] :
% 4.71/5.14 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q4 ) ) )
% 4.71/5.14 = zero_zero_nat )
% 4.71/5.14 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q4 ) )
% 4.71/5.14 = zero_zero_nat ) ) ).
% 4.71/5.14
% 4.71/5.14 % cong_exp_iff_simps(2)
% 4.71/5.14 thf(fact_6653_atLeast0__atMost__Suc,axiom,
% 4.71/5.14 ! [N: nat] :
% 4.71/5.14 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 4.71/5.14 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % atLeast0_atMost_Suc
% 4.71/5.14 thf(fact_6654_Icc__eq__insert__lb__nat,axiom,
% 4.71/5.14 ! [M2: nat,N: nat] :
% 4.71/5.14 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.14 => ( ( set_or1269000886237332187st_nat @ M2 @ N )
% 4.71/5.14 = ( insert_nat @ M2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Icc_eq_insert_lb_nat
% 4.71/5.14 thf(fact_6655_atLeastAtMostSuc__conv,axiom,
% 4.71/5.14 ! [M2: nat,N: nat] :
% 4.71/5.14 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 4.71/5.14 => ( ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) )
% 4.71/5.14 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % atLeastAtMostSuc_conv
% 4.71/5.14 thf(fact_6656_atLeastAtMost__insertL,axiom,
% 4.71/5.14 ! [M2: nat,N: nat] :
% 4.71/5.14 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.14 => ( ( insert_nat @ M2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) )
% 4.71/5.14 = ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % atLeastAtMost_insertL
% 4.71/5.14 thf(fact_6657_num_Osize_I5_J,axiom,
% 4.71/5.14 ! [X23: num] :
% 4.71/5.14 ( ( size_size_num @ ( bit0 @ X23 ) )
% 4.71/5.14 = ( plus_plus_nat @ ( size_size_num @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % num.size(5)
% 4.71/5.14 thf(fact_6658_log2__of__power__less,axiom,
% 4.71/5.14 ! [M2: nat,N: nat] :
% 4.71/5.14 ( ( ord_less_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.71/5.14 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 4.71/5.14 => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % log2_of_power_less
% 4.71/5.14 thf(fact_6659_exp__bound,axiom,
% 4.71/5.14 ! [X: real] :
% 4.71/5.14 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.14 => ( ( ord_less_eq_real @ X @ one_one_real )
% 4.71/5.14 => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % exp_bound
% 4.71/5.14 thf(fact_6660_neg__zdiv__mult__2,axiom,
% 4.71/5.14 ! [A: int,B: int] :
% 4.71/5.14 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 4.71/5.14 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 4.71/5.14 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % neg_zdiv_mult_2
% 4.71/5.14 thf(fact_6661_pos__zdiv__mult__2,axiom,
% 4.71/5.14 ! [A: int,B: int] :
% 4.71/5.14 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.14 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 4.71/5.14 = ( divide_divide_int @ B @ A ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % pos_zdiv_mult_2
% 4.71/5.14 thf(fact_6662_pos__zmod__mult__2,axiom,
% 4.71/5.14 ! [A: int,B: int] :
% 4.71/5.14 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.14 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 4.71/5.14 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % pos_zmod_mult_2
% 4.71/5.14 thf(fact_6663_real__le__x__sinh,axiom,
% 4.71/5.14 ! [X: real] :
% 4.71/5.14 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.14 => ( ord_less_eq_real @ X @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % real_le_x_sinh
% 4.71/5.14 thf(fact_6664_mult__1s__ring__1_I1_J,axiom,
% 4.71/5.14 ! [B: code_integer] :
% 4.71/5.14 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 4.71/5.14 = ( uminus1351360451143612070nteger @ B ) ) ).
% 4.71/5.14
% 4.71/5.14 % mult_1s_ring_1(1)
% 4.71/5.14 thf(fact_6665_mult__1s__ring__1_I1_J,axiom,
% 4.71/5.14 ! [B: int] :
% 4.71/5.14 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 4.71/5.14 = ( uminus_uminus_int @ B ) ) ).
% 4.71/5.14
% 4.71/5.14 % mult_1s_ring_1(1)
% 4.71/5.14 thf(fact_6666_mult__1s__ring__1_I1_J,axiom,
% 4.71/5.14 ! [B: real] :
% 4.71/5.14 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 4.71/5.14 = ( uminus_uminus_real @ B ) ) ).
% 4.71/5.14
% 4.71/5.14 % mult_1s_ring_1(1)
% 4.71/5.14 thf(fact_6667_mult__1s__ring__1_I1_J,axiom,
% 4.71/5.14 ! [B: rat] :
% 4.71/5.14 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 4.71/5.14 = ( uminus_uminus_rat @ B ) ) ).
% 4.71/5.14
% 4.71/5.14 % mult_1s_ring_1(1)
% 4.71/5.14 thf(fact_6668_mult__1s__ring__1_I1_J,axiom,
% 4.71/5.14 ! [B: complex] :
% 4.71/5.14 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 4.71/5.14 = ( uminus1482373934393186551omplex @ B ) ) ).
% 4.71/5.14
% 4.71/5.14 % mult_1s_ring_1(1)
% 4.71/5.14 thf(fact_6669_mult__1s__ring__1_I2_J,axiom,
% 4.71/5.14 ! [B: code_integer] :
% 4.71/5.14 ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 4.71/5.14 = ( uminus1351360451143612070nteger @ B ) ) ).
% 4.71/5.14
% 4.71/5.14 % mult_1s_ring_1(2)
% 4.71/5.14 thf(fact_6670_mult__1s__ring__1_I2_J,axiom,
% 4.71/5.14 ! [B: int] :
% 4.71/5.14 ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 4.71/5.14 = ( uminus_uminus_int @ B ) ) ).
% 4.71/5.14
% 4.71/5.14 % mult_1s_ring_1(2)
% 4.71/5.14 thf(fact_6671_mult__1s__ring__1_I2_J,axiom,
% 4.71/5.14 ! [B: real] :
% 4.71/5.14 ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 4.71/5.14 = ( uminus_uminus_real @ B ) ) ).
% 4.71/5.14
% 4.71/5.14 % mult_1s_ring_1(2)
% 4.71/5.14 thf(fact_6672_mult__1s__ring__1_I2_J,axiom,
% 4.71/5.14 ! [B: rat] :
% 4.71/5.14 ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 4.71/5.14 = ( uminus_uminus_rat @ B ) ) ).
% 4.71/5.14
% 4.71/5.14 % mult_1s_ring_1(2)
% 4.71/5.14 thf(fact_6673_mult__1s__ring__1_I2_J,axiom,
% 4.71/5.14 ! [B: complex] :
% 4.71/5.14 ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 4.71/5.14 = ( uminus1482373934393186551omplex @ B ) ) ).
% 4.71/5.14
% 4.71/5.14 % mult_1s_ring_1(2)
% 4.71/5.14 thf(fact_6674_uminus__numeral__One,axiom,
% 4.71/5.14 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 4.71/5.14 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 4.71/5.14
% 4.71/5.14 % uminus_numeral_One
% 4.71/5.14 thf(fact_6675_uminus__numeral__One,axiom,
% 4.71/5.14 ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 4.71/5.14 = ( uminus_uminus_int @ one_one_int ) ) ).
% 4.71/5.14
% 4.71/5.14 % uminus_numeral_One
% 4.71/5.14 thf(fact_6676_uminus__numeral__One,axiom,
% 4.71/5.14 ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 4.71/5.14 = ( uminus_uminus_real @ one_one_real ) ) ).
% 4.71/5.14
% 4.71/5.14 % uminus_numeral_One
% 4.71/5.14 thf(fact_6677_uminus__numeral__One,axiom,
% 4.71/5.14 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 4.71/5.14 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.71/5.14
% 4.71/5.14 % uminus_numeral_One
% 4.71/5.14 thf(fact_6678_uminus__numeral__One,axiom,
% 4.71/5.14 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 4.71/5.14 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 4.71/5.14
% 4.71/5.14 % uminus_numeral_One
% 4.71/5.14 thf(fact_6679_real__le__abs__sinh,axiom,
% 4.71/5.14 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % real_le_abs_sinh
% 4.71/5.14 thf(fact_6680_cong__exp__iff__simps_I1_J,axiom,
% 4.71/5.14 ! [N: num] :
% 4.71/5.14 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) )
% 4.71/5.14 = zero_z3403309356797280102nteger ) ).
% 4.71/5.14
% 4.71/5.14 % cong_exp_iff_simps(1)
% 4.71/5.14 thf(fact_6681_cong__exp__iff__simps_I1_J,axiom,
% 4.71/5.14 ! [N: num] :
% 4.71/5.14 ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) )
% 4.71/5.14 = zero_zero_int ) ).
% 4.71/5.14
% 4.71/5.14 % cong_exp_iff_simps(1)
% 4.71/5.14 thf(fact_6682_cong__exp__iff__simps_I1_J,axiom,
% 4.71/5.14 ! [N: num] :
% 4.71/5.14 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) )
% 4.71/5.14 = zero_zero_nat ) ).
% 4.71/5.14
% 4.71/5.14 % cong_exp_iff_simps(1)
% 4.71/5.14 thf(fact_6683_arith__geo__mean,axiom,
% 4.71/5.14 ! [U: real,X: real,Y: real] :
% 4.71/5.14 ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = ( times_times_real @ X @ Y ) )
% 4.71/5.14 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.14 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.71/5.14 => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % arith_geo_mean
% 4.71/5.14 thf(fact_6684_arith__geo__mean,axiom,
% 4.71/5.14 ! [U: rat,X: rat,Y: rat] :
% 4.71/5.14 ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.71/5.14 = ( times_times_rat @ X @ Y ) )
% 4.71/5.14 => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 4.71/5.14 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 4.71/5.14 => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % arith_geo_mean
% 4.71/5.14 thf(fact_6685_mod__double__modulus,axiom,
% 4.71/5.14 ! [M2: code_integer,X: code_integer] :
% 4.71/5.14 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M2 )
% 4.71/5.14 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 4.71/5.14 => ( ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) )
% 4.71/5.14 = ( modulo364778990260209775nteger @ X @ M2 ) )
% 4.71/5.14 | ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) )
% 4.71/5.14 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X @ M2 ) @ M2 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % mod_double_modulus
% 4.71/5.14 thf(fact_6686_mod__double__modulus,axiom,
% 4.71/5.14 ! [M2: nat,X: nat] :
% 4.71/5.14 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 4.71/5.14 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 4.71/5.14 => ( ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 4.71/5.14 = ( modulo_modulo_nat @ X @ M2 ) )
% 4.71/5.14 | ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 4.71/5.14 = ( plus_plus_nat @ ( modulo_modulo_nat @ X @ M2 ) @ M2 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % mod_double_modulus
% 4.71/5.14 thf(fact_6687_mod__double__modulus,axiom,
% 4.71/5.14 ! [M2: int,X: int] :
% 4.71/5.14 ( ( ord_less_int @ zero_zero_int @ M2 )
% 4.71/5.14 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 4.71/5.14 => ( ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) )
% 4.71/5.14 = ( modulo_modulo_int @ X @ M2 ) )
% 4.71/5.14 | ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) )
% 4.71/5.14 = ( plus_plus_int @ ( modulo_modulo_int @ X @ M2 ) @ M2 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % mod_double_modulus
% 4.71/5.14 thf(fact_6688_divmod__digit__1_I2_J,axiom,
% 4.71/5.14 ! [A: code_integer,B: code_integer] :
% 4.71/5.14 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 4.71/5.14 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 4.71/5.14 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 4.71/5.14 => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 4.71/5.14 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % divmod_digit_1(2)
% 4.71/5.14 thf(fact_6689_divmod__digit__1_I2_J,axiom,
% 4.71/5.14 ! [A: nat,B: nat] :
% 4.71/5.14 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.71/5.14 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.71/5.14 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 4.71/5.14 => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 4.71/5.14 = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % divmod_digit_1(2)
% 4.71/5.14 thf(fact_6690_divmod__digit__1_I2_J,axiom,
% 4.71/5.14 ! [A: int,B: int] :
% 4.71/5.14 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.14 => ( ( ord_less_int @ zero_zero_int @ B )
% 4.71/5.14 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 4.71/5.14 => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 4.71/5.14 = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % divmod_digit_1(2)
% 4.71/5.14 thf(fact_6691_subset__eq__atLeast0__atMost__finite,axiom,
% 4.71/5.14 ! [N5: set_nat,N: nat] :
% 4.71/5.14 ( ( ord_less_eq_set_nat @ N5 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 4.71/5.14 => ( finite_finite_nat @ N5 ) ) ).
% 4.71/5.14
% 4.71/5.14 % subset_eq_atLeast0_atMost_finite
% 4.71/5.14 thf(fact_6692_log2__of__power__le,axiom,
% 4.71/5.14 ! [M2: nat,N: nat] :
% 4.71/5.14 ( ( ord_less_eq_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.71/5.14 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 4.71/5.14 => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % log2_of_power_le
% 4.71/5.14 thf(fact_6693_exp__bound__lemma,axiom,
% 4.71/5.14 ! [Z: real] :
% 4.71/5.14 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.71/5.14 => ( 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 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % exp_bound_lemma
% 4.71/5.14 thf(fact_6694_exp__bound__lemma,axiom,
% 4.71/5.14 ! [Z: complex] :
% 4.71/5.14 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.71/5.14 => ( 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 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % exp_bound_lemma
% 4.71/5.14 thf(fact_6695_real__exp__bound__lemma,axiom,
% 4.71/5.14 ! [X: real] :
% 4.71/5.14 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.14 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.71/5.14 => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % real_exp_bound_lemma
% 4.71/5.14 thf(fact_6696_exp__lower__Taylor__quadratic,axiom,
% 4.71/5.14 ! [X: real] :
% 4.71/5.14 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.14 => ( ord_less_eq_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X ) @ ( divide_divide_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( exp_real @ X ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % exp_lower_Taylor_quadratic
% 4.71/5.14 thf(fact_6697_ln__one__plus__pos__lower__bound,axiom,
% 4.71/5.14 ! [X: real] :
% 4.71/5.14 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.14 => ( ( ord_less_eq_real @ X @ one_one_real )
% 4.71/5.14 => ( ord_less_eq_real @ ( minus_minus_real @ X @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % ln_one_plus_pos_lower_bound
% 4.71/5.14 thf(fact_6698_artanh__def,axiom,
% 4.71/5.14 ( artanh_real
% 4.71/5.14 = ( ^ [X3: real] : ( divide_divide_real @ ( ln_ln_real @ ( divide_divide_real @ ( plus_plus_real @ one_one_real @ X3 ) @ ( minus_minus_real @ one_one_real @ X3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % artanh_def
% 4.71/5.14 thf(fact_6699_neg__zmod__mult__2,axiom,
% 4.71/5.14 ! [A: int,B: int] :
% 4.71/5.14 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 4.71/5.14 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 4.71/5.14 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) @ one_one_int ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % neg_zmod_mult_2
% 4.71/5.14 thf(fact_6700_floor__log2__div2,axiom,
% 4.71/5.14 ! [N: nat] :
% 4.71/5.14 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 4.71/5.14 => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 4.71/5.14 = ( 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 ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % floor_log2_div2
% 4.71/5.14 thf(fact_6701_pos__eucl__rel__int__mult__2,axiom,
% 4.71/5.14 ! [B: int,A: int,Q4: int,R2: int] :
% 4.71/5.14 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.71/5.14 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R2 ) )
% 4.71/5.14 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q4 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % pos_eucl_rel_int_mult_2
% 4.71/5.14 thf(fact_6702_invar__vebt_Ointros_I2_J,axiom,
% 4.71/5.14 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M2: nat,Deg: nat] :
% 4.71/5.14 ( ! [X4: vEBT_VEBT] :
% 4.71/5.14 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.71/5.14 => ( vEBT_invar_vebt @ X4 @ N ) )
% 4.71/5.14 => ( ( vEBT_invar_vebt @ Summary @ M2 )
% 4.71/5.14 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 4.71/5.14 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 4.71/5.14 => ( ( M2 = N )
% 4.71/5.14 => ( ( Deg
% 4.71/5.14 = ( plus_plus_nat @ N @ M2 ) )
% 4.71/5.14 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 4.71/5.14 => ( ! [X4: vEBT_VEBT] :
% 4.71/5.14 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.71/5.14 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) )
% 4.71/5.14 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % invar_vebt.intros(2)
% 4.71/5.14 thf(fact_6703_fact__double,axiom,
% 4.71/5.14 ! [N: nat] :
% 4.71/5.14 ( ( semiri5044797733671781792omplex @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.71/5.14 = ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s2602460028002588243omplex @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % fact_double
% 4.71/5.14 thf(fact_6704_fact__double,axiom,
% 4.71/5.14 ! [N: nat] :
% 4.71/5.14 ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.71/5.14 = ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % fact_double
% 4.71/5.14 thf(fact_6705_fact__double,axiom,
% 4.71/5.14 ! [N: nat] :
% 4.71/5.14 ( ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.71/5.14 = ( times_times_real @ ( times_times_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s7457072308508201937r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % fact_double
% 4.71/5.14 thf(fact_6706_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 4.71/5.14 ! [X: real] :
% 4.71/5.14 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.14 => ( ( ord_less_eq_real @ X @ one_one_real )
% 4.71/5.14 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % abs_ln_one_plus_x_minus_x_bound_nonneg
% 4.71/5.14 thf(fact_6707_invar__vebt_Ointros_I3_J,axiom,
% 4.71/5.14 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M2: nat,Deg: nat] :
% 4.71/5.14 ( ! [X4: vEBT_VEBT] :
% 4.71/5.14 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.71/5.14 => ( vEBT_invar_vebt @ X4 @ N ) )
% 4.71/5.14 => ( ( vEBT_invar_vebt @ Summary @ M2 )
% 4.71/5.14 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 4.71/5.14 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 4.71/5.14 => ( ( M2
% 4.71/5.14 = ( suc @ N ) )
% 4.71/5.14 => ( ( Deg
% 4.71/5.14 = ( plus_plus_nat @ N @ M2 ) )
% 4.71/5.14 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 4.71/5.14 => ( ! [X4: vEBT_VEBT] :
% 4.71/5.14 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.71/5.14 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) )
% 4.71/5.14 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % invar_vebt.intros(3)
% 4.71/5.14 thf(fact_6708_neg__eucl__rel__int__mult__2,axiom,
% 4.71/5.14 ! [B: int,A: int,Q4: int,R2: int] :
% 4.71/5.14 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 4.71/5.14 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q4 @ R2 ) )
% 4.71/5.14 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q4 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) @ one_one_int ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % neg_eucl_rel_int_mult_2
% 4.71/5.14 thf(fact_6709_divmod__digit__1_I1_J,axiom,
% 4.71/5.14 ! [A: code_integer,B: code_integer] :
% 4.71/5.14 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 4.71/5.14 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 4.71/5.14 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 4.71/5.14 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 4.71/5.14 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % divmod_digit_1(1)
% 4.71/5.14 thf(fact_6710_divmod__digit__1_I1_J,axiom,
% 4.71/5.14 ! [A: nat,B: nat] :
% 4.71/5.14 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.71/5.14 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.71/5.14 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 4.71/5.14 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_nat )
% 4.71/5.14 = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % divmod_digit_1(1)
% 4.71/5.14 thf(fact_6711_divmod__digit__1_I1_J,axiom,
% 4.71/5.14 ! [A: int,B: int] :
% 4.71/5.14 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.71/5.14 => ( ( ord_less_int @ zero_zero_int @ B )
% 4.71/5.14 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 4.71/5.14 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_int )
% 4.71/5.14 = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % divmod_digit_1(1)
% 4.71/5.14 thf(fact_6712_pochhammer__double,axiom,
% 4.71/5.14 ! [Z: complex,N: nat] :
% 4.71/5.14 ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.71/5.14 = ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s2602460028002588243omplex @ Z @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % pochhammer_double
% 4.71/5.14 thf(fact_6713_pochhammer__double,axiom,
% 4.71/5.14 ! [Z: real,N: nat] :
% 4.71/5.14 ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.71/5.14 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s7457072308508201937r_real @ Z @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % pochhammer_double
% 4.71/5.14 thf(fact_6714_pochhammer__double,axiom,
% 4.71/5.14 ! [Z: rat,N: nat] :
% 4.71/5.14 ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.71/5.14 = ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % pochhammer_double
% 4.71/5.14 thf(fact_6715_ln__one__minus__pos__lower__bound,axiom,
% 4.71/5.14 ! [X: real] :
% 4.71/5.14 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.14 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.71/5.14 => ( ord_less_eq_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % ln_one_minus_pos_lower_bound
% 4.71/5.14 thf(fact_6716_abs__ln__one__plus__x__minus__x__bound,axiom,
% 4.71/5.14 ! [X: real] :
% 4.71/5.14 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.71/5.14 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % abs_ln_one_plus_x_minus_x_bound
% 4.71/5.14 thf(fact_6717_floor__log__nat__eq__if,axiom,
% 4.71/5.14 ! [B: nat,N: nat,K: nat] :
% 4.71/5.14 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 4.71/5.14 => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 4.71/5.14 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 4.71/5.14 => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 4.71/5.14 = ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % floor_log_nat_eq_if
% 4.71/5.14 thf(fact_6718_floor__log__nat__eq__powr__iff,axiom,
% 4.71/5.14 ! [B: nat,K: nat,N: nat] :
% 4.71/5.14 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 4.71/5.14 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.71/5.14 => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 4.71/5.14 = ( semiri1314217659103216013at_int @ N ) )
% 4.71/5.14 = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 4.71/5.14 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % floor_log_nat_eq_powr_iff
% 4.71/5.14 thf(fact_6719_ceiling__log2__div2,axiom,
% 4.71/5.14 ! [N: nat] :
% 4.71/5.14 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 4.71/5.14 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 4.71/5.14 = ( 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 ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % ceiling_log2_div2
% 4.71/5.14 thf(fact_6720_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 4.71/5.14 ! [X: real] :
% 4.71/5.14 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 4.71/5.14 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 4.71/5.14 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % abs_ln_one_plus_x_minus_x_bound_nonpos
% 4.71/5.14 thf(fact_6721_ceiling__log__nat__eq__if,axiom,
% 4.71/5.14 ! [B: nat,N: nat,K: nat] :
% 4.71/5.14 ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 4.71/5.14 => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 4.71/5.14 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 4.71/5.14 => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 4.71/5.14 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % ceiling_log_nat_eq_if
% 4.71/5.14 thf(fact_6722_ceiling__log__nat__eq__powr__iff,axiom,
% 4.71/5.14 ! [B: nat,K: nat,N: nat] :
% 4.71/5.14 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 4.71/5.14 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.71/5.14 => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 4.71/5.14 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) )
% 4.71/5.14 = ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 4.71/5.14 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % ceiling_log_nat_eq_powr_iff
% 4.71/5.14 thf(fact_6723_divmod__step__eq,axiom,
% 4.71/5.14 ! [L: num,R2: nat,Q4: nat] :
% 4.71/5.14 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 4.71/5.14 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q4 @ R2 ) )
% 4.71/5.14 = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ one_one_nat ) @ ( minus_minus_nat @ R2 @ ( numeral_numeral_nat @ L ) ) ) ) )
% 4.71/5.14 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 4.71/5.14 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q4 @ R2 ) )
% 4.71/5.14 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ R2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % divmod_step_eq
% 4.71/5.14 thf(fact_6724_divmod__step__eq,axiom,
% 4.71/5.14 ! [L: num,R2: int,Q4: int] :
% 4.71/5.14 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 4.71/5.14 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q4 @ R2 ) )
% 4.71/5.14 = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ one_one_int ) @ ( minus_minus_int @ R2 @ ( numeral_numeral_int @ L ) ) ) ) )
% 4.71/5.14 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 4.71/5.14 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q4 @ R2 ) )
% 4.71/5.14 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ R2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % divmod_step_eq
% 4.71/5.14 thf(fact_6725_divmod__step__eq,axiom,
% 4.71/5.14 ! [L: num,R2: code_integer,Q4: code_integer] :
% 4.71/5.14 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 4.71/5.14 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q4 @ R2 ) )
% 4.71/5.14 = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R2 @ ( numera6620942414471956472nteger @ L ) ) ) ) )
% 4.71/5.14 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 4.71/5.14 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q4 @ R2 ) )
% 4.71/5.14 = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ R2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % divmod_step_eq
% 4.71/5.14 thf(fact_6726_abs__sqrt__wlog,axiom,
% 4.71/5.14 ! [P: real > real > $o,X: real] :
% 4.71/5.14 ( ! [X4: real] :
% 4.71/5.14 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 4.71/5.14 => ( P @ X4 @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.71/5.14 => ( P @ ( abs_abs_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % abs_sqrt_wlog
% 4.71/5.14 thf(fact_6727_abs__sqrt__wlog,axiom,
% 4.71/5.14 ! [P: rat > rat > $o,X: rat] :
% 4.71/5.14 ( ! [X4: rat] :
% 4.71/5.14 ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 4.71/5.14 => ( P @ X4 @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.71/5.14 => ( P @ ( abs_abs_rat @ X ) @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % abs_sqrt_wlog
% 4.71/5.14 thf(fact_6728_abs__sqrt__wlog,axiom,
% 4.71/5.14 ! [P: int > int > $o,X: int] :
% 4.71/5.14 ( ! [X4: int] :
% 4.71/5.14 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 4.71/5.14 => ( P @ X4 @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.71/5.14 => ( P @ ( abs_abs_int @ X ) @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % abs_sqrt_wlog
% 4.71/5.14 thf(fact_6729_pred__list__to__short,axiom,
% 4.71/5.14 ! [Deg: nat,X: nat,Ma: nat,TreeList: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 4.71/5.14 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.71/5.14 => ( ( ord_less_eq_nat @ X @ Ma )
% 4.71/5.14 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.71/5.14 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.14 = none_nat ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % pred_list_to_short
% 4.71/5.14 thf(fact_6730_succ__list__to__short,axiom,
% 4.71/5.14 ! [Deg: nat,Mi: nat,X: nat,TreeList: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 4.71/5.14 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.71/5.14 => ( ( ord_less_eq_nat @ Mi @ X )
% 4.71/5.14 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.71/5.14 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.14 = none_nat ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % succ_list_to_short
% 4.71/5.14 thf(fact_6731_set__bit__0,axiom,
% 4.71/5.14 ! [A: code_integer] :
% 4.71/5.14 ( ( bit_se2793503036327961859nteger @ zero_zero_nat @ A )
% 4.71/5.14 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % set_bit_0
% 4.71/5.14 thf(fact_6732_set__bit__0,axiom,
% 4.71/5.14 ! [A: int] :
% 4.71/5.14 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 4.71/5.14 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % set_bit_0
% 4.71/5.14 thf(fact_6733_set__bit__0,axiom,
% 4.71/5.14 ! [A: nat] :
% 4.71/5.14 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 4.71/5.14 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % set_bit_0
% 4.71/5.14 thf(fact_6734_unset__bit__0,axiom,
% 4.71/5.14 ! [A: code_integer] :
% 4.71/5.14 ( ( bit_se8260200283734997820nteger @ zero_zero_nat @ A )
% 4.71/5.14 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % unset_bit_0
% 4.71/5.14 thf(fact_6735_unset__bit__0,axiom,
% 4.71/5.14 ! [A: nat] :
% 4.71/5.14 ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 4.71/5.14 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % unset_bit_0
% 4.71/5.14 thf(fact_6736_unset__bit__0,axiom,
% 4.71/5.14 ! [A: int] :
% 4.71/5.14 ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 4.71/5.14 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % unset_bit_0
% 4.71/5.14 thf(fact_6737_high__def,axiom,
% 4.71/5.14 ( vEBT_VEBT_high
% 4.71/5.14 = ( ^ [X3: nat,N4: nat] : ( divide_divide_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % high_def
% 4.71/5.14 thf(fact_6738_high__bound__aux,axiom,
% 4.71/5.14 ! [Ma: nat,N: nat,M2: nat] :
% 4.71/5.14 ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M2 ) ) )
% 4.71/5.14 => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % high_bound_aux
% 4.71/5.14 thf(fact_6739_high__inv,axiom,
% 4.71/5.14 ! [X: nat,N: nat,Y: nat] :
% 4.71/5.14 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.71/5.14 => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 4.71/5.14 = Y ) ) ).
% 4.71/5.14
% 4.71/5.14 % high_inv
% 4.71/5.14 thf(fact_6740_unset__bit__nonnegative__int__iff,axiom,
% 4.71/5.14 ! [N: nat,K: int] :
% 4.71/5.14 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N @ K ) )
% 4.71/5.14 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 4.71/5.14
% 4.71/5.14 % unset_bit_nonnegative_int_iff
% 4.71/5.14 thf(fact_6741_set__bit__nonnegative__int__iff,axiom,
% 4.71/5.14 ! [N: nat,K: int] :
% 4.71/5.14 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N @ K ) )
% 4.71/5.14 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 4.71/5.14
% 4.71/5.14 % set_bit_nonnegative_int_iff
% 4.71/5.14 thf(fact_6742_bot__enat__def,axiom,
% 4.71/5.14 bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 4.71/5.14
% 4.71/5.14 % bot_enat_def
% 4.71/5.14 thf(fact_6743_unset__bit__less__eq,axiom,
% 4.71/5.14 ! [N: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ K ) ).
% 4.71/5.14
% 4.71/5.14 % unset_bit_less_eq
% 4.71/5.14 thf(fact_6744_set__bit__greater__eq,axiom,
% 4.71/5.14 ! [K: int,N: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N @ K ) ) ).
% 4.71/5.14
% 4.71/5.14 % set_bit_greater_eq
% 4.71/5.14 thf(fact_6745_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 4.71/5.14 ! [X: nat,N: nat,M2: nat] :
% 4.71/5.14 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M2 ) ) )
% 4.71/5.14 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.14 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 4.71/5.14 => ( ord_less_nat @ ( vEBT_VEBT_high @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % VEBT_internal.exp_split_high_low(1)
% 4.71/5.14 thf(fact_6746_complex__mod__minus__le__complex__mod,axiom,
% 4.71/5.14 ! [X: complex] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 4.71/5.14
% 4.71/5.14 % complex_mod_minus_le_complex_mod
% 4.71/5.14 thf(fact_6747_complex__mod__triangle__ineq2,axiom,
% 4.71/5.14 ! [B: complex,A: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B @ A ) ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ A ) ) ).
% 4.71/5.14
% 4.71/5.14 % complex_mod_triangle_ineq2
% 4.71/5.14 thf(fact_6748_nested__mint,axiom,
% 4.71/5.14 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,Va2: nat] :
% 4.71/5.14 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 4.71/5.14 => ( ( N
% 4.71/5.14 = ( suc @ ( suc @ Va2 ) ) )
% 4.71/5.14 => ( ~ ( ord_less_nat @ Ma @ Mi )
% 4.71/5.14 => ( ( Ma != Mi )
% 4.71/5.14 => ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Va2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( suc @ ( divide_divide_nat @ Va2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % nested_mint
% 4.71/5.14 thf(fact_6749_both__member__options__from__chilf__to__complete__tree,axiom,
% 4.71/5.14 ! [X: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 4.71/5.14 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.71/5.14 => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 4.71/5.14 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.71/5.14 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % both_member_options_from_chilf_to_complete_tree
% 4.71/5.14 thf(fact_6750_member__inv,axiom,
% 4.71/5.14 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 4.71/5.14 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.14 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.71/5.14 & ( ( X = Mi )
% 4.71/5.14 | ( X = Ma )
% 4.71/5.14 | ( ( ord_less_nat @ X @ Ma )
% 4.71/5.14 & ( ord_less_nat @ Mi @ X )
% 4.71/5.14 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.71/5.14 & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % member_inv
% 4.71/5.14 thf(fact_6751_both__member__options__from__complete__tree__to__child,axiom,
% 4.71/5.14 ! [Deg: nat,Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 4.71/5.14 ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 4.71/5.14 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.14 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.71/5.14 | ( X = Mi )
% 4.71/5.14 | ( X = Ma ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % both_member_options_from_complete_tree_to_child
% 4.71/5.14 thf(fact_6752_summaxma,axiom,
% 4.71/5.14 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 4.71/5.14 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg )
% 4.71/5.14 => ( ( Mi != Ma )
% 4.71/5.14 => ( ( the_nat @ ( vEBT_vebt_maxt @ Summary ) )
% 4.71/5.14 = ( vEBT_VEBT_high @ Ma @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % summaxma
% 4.71/5.14 thf(fact_6753_both__member__options__ding,axiom,
% 4.71/5.14 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 4.71/5.14 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 4.71/5.14 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 4.71/5.14 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.71/5.14 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % both_member_options_ding
% 4.71/5.14 thf(fact_6754_bit__split__inv,axiom,
% 4.71/5.14 ! [X: nat,D: nat] :
% 4.71/5.14 ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X @ D ) @ ( vEBT_VEBT_low @ X @ D ) @ D )
% 4.71/5.14 = X ) ).
% 4.71/5.14
% 4.71/5.14 % bit_split_inv
% 4.71/5.14 thf(fact_6755_low__def,axiom,
% 4.71/5.14 ( vEBT_VEBT_low
% 4.71/5.14 = ( ^ [X3: nat,N4: nat] : ( modulo_modulo_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % low_def
% 4.71/5.14 thf(fact_6756_low__inv,axiom,
% 4.71/5.14 ! [X: nat,N: nat,Y: nat] :
% 4.71/5.14 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.71/5.14 => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 4.71/5.14 = X ) ) ).
% 4.71/5.14
% 4.71/5.14 % low_inv
% 4.71/5.14 thf(fact_6757_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 4.71/5.14 ! [X: nat,N: nat,M2: nat] :
% 4.71/5.14 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M2 ) ) )
% 4.71/5.14 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.14 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 4.71/5.14 => ( ord_less_nat @ ( vEBT_VEBT_low @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % VEBT_internal.exp_split_high_low(2)
% 4.71/5.14 thf(fact_6758_invar__vebt_Ointros_I4_J,axiom,
% 4.71/5.14 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M2: nat,Deg: nat,Mi: nat,Ma: nat] :
% 4.71/5.14 ( ! [X4: vEBT_VEBT] :
% 4.71/5.14 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.71/5.14 => ( vEBT_invar_vebt @ X4 @ N ) )
% 4.71/5.14 => ( ( vEBT_invar_vebt @ Summary @ M2 )
% 4.71/5.14 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 4.71/5.14 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 4.71/5.14 => ( ( M2 = N )
% 4.71/5.14 => ( ( Deg
% 4.71/5.14 = ( plus_plus_nat @ N @ M2 ) )
% 4.71/5.14 => ( ! [I2: nat] :
% 4.71/5.14 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 4.71/5.14 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ X8 ) )
% 4.71/5.14 = ( vEBT_V8194947554948674370ptions @ Summary @ I2 ) ) )
% 4.71/5.14 => ( ( ( Mi = Ma )
% 4.71/5.14 => ! [X4: vEBT_VEBT] :
% 4.71/5.14 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.71/5.14 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) ) )
% 4.71/5.14 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 4.71/5.14 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 4.71/5.14 => ( ( ( Mi != Ma )
% 4.71/5.14 => ! [I2: nat] :
% 4.71/5.14 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 4.71/5.14 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 4.71/5.14 = I2 )
% 4.71/5.14 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 4.71/5.14 & ! [X4: nat] :
% 4.71/5.14 ( ( ( ( vEBT_VEBT_high @ X4 @ N )
% 4.71/5.14 = I2 )
% 4.71/5.14 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ X4 @ N ) ) )
% 4.71/5.14 => ( ( ord_less_nat @ Mi @ X4 )
% 4.71/5.14 & ( ord_less_eq_nat @ X4 @ Ma ) ) ) ) ) )
% 4.71/5.14 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % invar_vebt.intros(4)
% 4.71/5.14 thf(fact_6759_invar__vebt_Ointros_I5_J,axiom,
% 4.71/5.14 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M2: nat,Deg: nat,Mi: nat,Ma: nat] :
% 4.71/5.14 ( ! [X4: vEBT_VEBT] :
% 4.71/5.14 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.71/5.14 => ( vEBT_invar_vebt @ X4 @ N ) )
% 4.71/5.14 => ( ( vEBT_invar_vebt @ Summary @ M2 )
% 4.71/5.14 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 4.71/5.14 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 4.71/5.14 => ( ( M2
% 4.71/5.14 = ( suc @ N ) )
% 4.71/5.14 => ( ( Deg
% 4.71/5.14 = ( plus_plus_nat @ N @ M2 ) )
% 4.71/5.14 => ( ! [I2: nat] :
% 4.71/5.14 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 4.71/5.14 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ X8 ) )
% 4.71/5.14 = ( vEBT_V8194947554948674370ptions @ Summary @ I2 ) ) )
% 4.71/5.14 => ( ( ( Mi = Ma )
% 4.71/5.14 => ! [X4: vEBT_VEBT] :
% 4.71/5.14 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.71/5.14 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) ) )
% 4.71/5.14 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 4.71/5.14 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 4.71/5.14 => ( ( ( Mi != Ma )
% 4.71/5.14 => ! [I2: nat] :
% 4.71/5.14 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 4.71/5.14 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 4.71/5.14 = I2 )
% 4.71/5.14 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 4.71/5.14 & ! [X4: nat] :
% 4.71/5.14 ( ( ( ( vEBT_VEBT_high @ X4 @ N )
% 4.71/5.14 = I2 )
% 4.71/5.14 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ X4 @ N ) ) )
% 4.71/5.14 => ( ( ord_less_nat @ Mi @ X4 )
% 4.71/5.14 & ( ord_less_eq_nat @ X4 @ Ma ) ) ) ) ) )
% 4.71/5.14 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % invar_vebt.intros(5)
% 4.71/5.14 thf(fact_6760_invar__vebt_Ocases,axiom,
% 4.71/5.14 ! [A12: vEBT_VEBT,A23: nat] :
% 4.71/5.14 ( ( vEBT_invar_vebt @ A12 @ A23 )
% 4.71/5.14 => ( ( ? [A5: $o,B5: $o] :
% 4.71/5.14 ( A12
% 4.71/5.14 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.14 => ( A23
% 4.71/5.14 != ( suc @ zero_zero_nat ) ) )
% 4.71/5.14 => ( ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 4.71/5.14 ( ( A12
% 4.71/5.14 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 4.71/5.14 => ( ( A23 = Deg2 )
% 4.71/5.14 => ( ! [X2: vEBT_VEBT] :
% 4.71/5.14 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.71/5.14 => ( vEBT_invar_vebt @ X2 @ N2 ) )
% 4.71/5.14 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 4.71/5.14 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 4.71/5.14 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 4.71/5.14 => ( ( M4 = N2 )
% 4.71/5.14 => ( ( Deg2
% 4.71/5.14 = ( plus_plus_nat @ N2 @ M4 ) )
% 4.71/5.14 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 4.71/5.14 => ~ ! [X2: vEBT_VEBT] :
% 4.71/5.14 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.71/5.14 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X_12 ) ) ) ) ) ) ) ) ) )
% 4.71/5.14 => ( ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 4.71/5.14 ( ( A12
% 4.71/5.14 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 4.71/5.14 => ( ( A23 = Deg2 )
% 4.71/5.14 => ( ! [X2: vEBT_VEBT] :
% 4.71/5.14 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.71/5.14 => ( vEBT_invar_vebt @ X2 @ N2 ) )
% 4.71/5.14 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 4.71/5.14 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 4.71/5.14 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 4.71/5.14 => ( ( M4
% 4.71/5.14 = ( suc @ N2 ) )
% 4.71/5.14 => ( ( Deg2
% 4.71/5.14 = ( plus_plus_nat @ N2 @ M4 ) )
% 4.71/5.14 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 4.71/5.14 => ~ ! [X2: vEBT_VEBT] :
% 4.71/5.14 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.71/5.14 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X_12 ) ) ) ) ) ) ) ) ) )
% 4.71/5.14 => ( ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 4.71/5.14 ( ( A12
% 4.71/5.14 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList2 @ Summary2 ) )
% 4.71/5.14 => ( ( A23 = Deg2 )
% 4.71/5.14 => ( ! [X2: vEBT_VEBT] :
% 4.71/5.14 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.71/5.14 => ( vEBT_invar_vebt @ X2 @ N2 ) )
% 4.71/5.14 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 4.71/5.14 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 4.71/5.14 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 4.71/5.14 => ( ( M4 = N2 )
% 4.71/5.14 => ( ( Deg2
% 4.71/5.14 = ( plus_plus_nat @ N2 @ M4 ) )
% 4.71/5.14 => ( ! [I3: nat] :
% 4.71/5.14 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 4.71/5.14 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X8 ) )
% 4.71/5.14 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 4.71/5.14 => ( ( ( Mi2 = Ma2 )
% 4.71/5.14 => ! [X2: vEBT_VEBT] :
% 4.71/5.14 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.71/5.14 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X_12 ) ) )
% 4.71/5.14 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 4.71/5.14 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 4.71/5.14 => ~ ( ( Mi2 != Ma2 )
% 4.71/5.14 => ! [I3: nat] :
% 4.71/5.14 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 4.71/5.14 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N2 )
% 4.71/5.14 = I3 )
% 4.71/5.14 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma2 @ N2 ) ) )
% 4.71/5.14 & ! [X2: nat] :
% 4.71/5.14 ( ( ( ( vEBT_VEBT_high @ X2 @ N2 )
% 4.71/5.14 = I3 )
% 4.71/5.14 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X2 @ N2 ) ) )
% 4.71/5.14 => ( ( ord_less_nat @ Mi2 @ X2 )
% 4.71/5.14 & ( ord_less_eq_nat @ X2 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 4.71/5.14 => ~ ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 4.71/5.14 ( ( A12
% 4.71/5.14 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList2 @ Summary2 ) )
% 4.71/5.14 => ( ( A23 = Deg2 )
% 4.71/5.14 => ( ! [X2: vEBT_VEBT] :
% 4.71/5.14 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.71/5.14 => ( vEBT_invar_vebt @ X2 @ N2 ) )
% 4.71/5.14 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 4.71/5.14 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 4.71/5.14 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 4.71/5.14 => ( ( M4
% 4.71/5.14 = ( suc @ N2 ) )
% 4.71/5.14 => ( ( Deg2
% 4.71/5.14 = ( plus_plus_nat @ N2 @ M4 ) )
% 4.71/5.14 => ( ! [I3: nat] :
% 4.71/5.14 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 4.71/5.14 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X8 ) )
% 4.71/5.14 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 4.71/5.14 => ( ( ( Mi2 = Ma2 )
% 4.71/5.14 => ! [X2: vEBT_VEBT] :
% 4.71/5.14 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.71/5.14 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X_12 ) ) )
% 4.71/5.14 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 4.71/5.14 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 4.71/5.14 => ~ ( ( Mi2 != Ma2 )
% 4.71/5.14 => ! [I3: nat] :
% 4.71/5.14 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 4.71/5.14 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N2 )
% 4.71/5.14 = I3 )
% 4.71/5.14 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma2 @ N2 ) ) )
% 4.71/5.14 & ! [X2: nat] :
% 4.71/5.14 ( ( ( ( vEBT_VEBT_high @ X2 @ N2 )
% 4.71/5.14 = I3 )
% 4.71/5.14 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X2 @ N2 ) ) )
% 4.71/5.14 => ( ( ord_less_nat @ Mi2 @ X2 )
% 4.71/5.14 & ( ord_less_eq_nat @ X2 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % invar_vebt.cases
% 4.71/5.14 thf(fact_6761_invar__vebt_Osimps,axiom,
% 4.71/5.14 ( vEBT_invar_vebt
% 4.71/5.14 = ( ^ [A13: vEBT_VEBT,A24: nat] :
% 4.71/5.14 ( ( ? [A4: $o,B4: $o] :
% 4.71/5.14 ( A13
% 4.71/5.14 = ( vEBT_Leaf @ A4 @ B4 ) )
% 4.71/5.14 & ( A24
% 4.71/5.14 = ( suc @ zero_zero_nat ) ) )
% 4.71/5.14 | ? [TreeList3: list_VEBT_VEBT,N4: nat,Summary3: vEBT_VEBT] :
% 4.71/5.14 ( ( A13
% 4.71/5.14 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A24 @ TreeList3 @ Summary3 ) )
% 4.71/5.14 & ! [X3: vEBT_VEBT] :
% 4.71/5.14 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 4.71/5.14 => ( vEBT_invar_vebt @ X3 @ N4 ) )
% 4.71/5.14 & ( vEBT_invar_vebt @ Summary3 @ N4 )
% 4.71/5.14 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 4.71/5.14 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 4.71/5.14 & ( A24
% 4.71/5.14 = ( plus_plus_nat @ N4 @ N4 ) )
% 4.71/5.14 & ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X8 )
% 4.71/5.14 & ! [X3: vEBT_VEBT] :
% 4.71/5.14 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 4.71/5.14 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 4.71/5.14 | ? [TreeList3: list_VEBT_VEBT,N4: nat,Summary3: vEBT_VEBT] :
% 4.71/5.14 ( ( A13
% 4.71/5.14 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A24 @ TreeList3 @ Summary3 ) )
% 4.71/5.14 & ! [X3: vEBT_VEBT] :
% 4.71/5.14 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 4.71/5.14 => ( vEBT_invar_vebt @ X3 @ N4 ) )
% 4.71/5.14 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N4 ) )
% 4.71/5.14 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 4.71/5.14 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 4.71/5.14 & ( A24
% 4.71/5.14 = ( plus_plus_nat @ N4 @ ( suc @ N4 ) ) )
% 4.71/5.14 & ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X8 )
% 4.71/5.14 & ! [X3: vEBT_VEBT] :
% 4.71/5.14 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 4.71/5.14 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 4.71/5.14 | ? [TreeList3: list_VEBT_VEBT,N4: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 4.71/5.14 ( ( A13
% 4.71/5.14 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A24 @ TreeList3 @ Summary3 ) )
% 4.71/5.14 & ! [X3: vEBT_VEBT] :
% 4.71/5.14 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 4.71/5.14 => ( vEBT_invar_vebt @ X3 @ N4 ) )
% 4.71/5.14 & ( vEBT_invar_vebt @ Summary3 @ N4 )
% 4.71/5.14 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 4.71/5.14 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 4.71/5.14 & ( A24
% 4.71/5.14 = ( plus_plus_nat @ N4 @ N4 ) )
% 4.71/5.14 & ! [I4: nat] :
% 4.71/5.14 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 4.71/5.14 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X8 ) )
% 4.71/5.14 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I4 ) ) )
% 4.71/5.14 & ( ( Mi3 = Ma3 )
% 4.71/5.14 => ! [X3: vEBT_VEBT] :
% 4.71/5.14 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 4.71/5.14 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 4.71/5.14 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 4.71/5.14 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A24 ) )
% 4.71/5.14 & ( ( Mi3 != Ma3 )
% 4.71/5.14 => ! [I4: nat] :
% 4.71/5.14 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 4.71/5.14 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N4 )
% 4.71/5.14 = I4 )
% 4.71/5.14 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ Ma3 @ N4 ) ) )
% 4.71/5.14 & ! [X3: nat] :
% 4.71/5.14 ( ( ( ( vEBT_VEBT_high @ X3 @ N4 )
% 4.71/5.14 = I4 )
% 4.71/5.14 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ X3 @ N4 ) ) )
% 4.71/5.14 => ( ( ord_less_nat @ Mi3 @ X3 )
% 4.71/5.14 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) )
% 4.71/5.14 | ? [TreeList3: list_VEBT_VEBT,N4: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 4.71/5.14 ( ( A13
% 4.71/5.14 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A24 @ TreeList3 @ Summary3 ) )
% 4.71/5.14 & ! [X3: vEBT_VEBT] :
% 4.71/5.14 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 4.71/5.14 => ( vEBT_invar_vebt @ X3 @ N4 ) )
% 4.71/5.14 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N4 ) )
% 4.71/5.14 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 4.71/5.14 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 4.71/5.14 & ( A24
% 4.71/5.14 = ( plus_plus_nat @ N4 @ ( suc @ N4 ) ) )
% 4.71/5.14 & ! [I4: nat] :
% 4.71/5.14 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 4.71/5.14 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X8 ) )
% 4.71/5.14 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I4 ) ) )
% 4.71/5.14 & ( ( Mi3 = Ma3 )
% 4.71/5.14 => ! [X3: vEBT_VEBT] :
% 4.71/5.14 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 4.71/5.14 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 4.71/5.14 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 4.71/5.14 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A24 ) )
% 4.71/5.14 & ( ( Mi3 != Ma3 )
% 4.71/5.14 => ! [I4: nat] :
% 4.71/5.14 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 4.71/5.14 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N4 )
% 4.71/5.14 = I4 )
% 4.71/5.14 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ Ma3 @ N4 ) ) )
% 4.71/5.14 & ! [X3: nat] :
% 4.71/5.14 ( ( ( ( vEBT_VEBT_high @ X3 @ N4 )
% 4.71/5.14 = I4 )
% 4.71/5.14 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ X3 @ N4 ) ) )
% 4.71/5.14 => ( ( ord_less_nat @ Mi3 @ X3 )
% 4.71/5.14 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % invar_vebt.simps
% 4.71/5.14 thf(fact_6762_in__children__def,axiom,
% 4.71/5.14 ( vEBT_V5917875025757280293ildren
% 4.71/5.14 = ( ^ [N4: nat,TreeList3: list_VEBT_VEBT,X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ X3 @ N4 ) ) @ ( vEBT_VEBT_low @ X3 @ N4 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % in_children_def
% 4.71/5.14 thf(fact_6763_del__x__mi__lets__in__not__minNull,axiom,
% 4.71/5.14 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 4.71/5.14 ( ( ( X = Mi )
% 4.71/5.14 & ( ord_less_nat @ X @ Ma ) )
% 4.71/5.14 => ( ( Mi != Ma )
% 4.71/5.14 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.71/5.14 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = H )
% 4.71/5.14 => ( ( Xn
% 4.71/5.14 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 4.71/5.14 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = L )
% 4.71/5.14 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.71/5.14 => ( ( Newnode
% 4.71/5.14 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H ) @ L ) )
% 4.71/5.14 => ( ( Newlist
% 4.71/5.14 = ( list_u1324408373059187874T_VEBT @ TreeList @ H @ Newnode ) )
% 4.71/5.14 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 4.71/5.14 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.14 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H @ ( 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 @ H ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % del_x_mi_lets_in_not_minNull
% 4.71/5.14 thf(fact_6764_del__x__not__mi__newnode__not__nil,axiom,
% 4.71/5.14 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H: nat,L: nat,Newnode: vEBT_VEBT,TreeList: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 4.71/5.14 ( ( ( ord_less_nat @ Mi @ X )
% 4.71/5.14 & ( ord_less_eq_nat @ X @ Ma ) )
% 4.71/5.14 => ( ( Mi != Ma )
% 4.71/5.14 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.71/5.14 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = H )
% 4.71/5.14 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = L )
% 4.71/5.14 => ( ( Newnode
% 4.71/5.14 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H ) @ L ) )
% 4.71/5.14 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 4.71/5.14 => ( ( Newlist
% 4.71/5.14 = ( list_u1324408373059187874T_VEBT @ TreeList @ H @ Newnode ) )
% 4.71/5.14 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.71/5.14 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.14 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H @ ( 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 @ H ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % del_x_not_mi_newnode_not_nil
% 4.71/5.14 thf(fact_6765_pred__less__length__list,axiom,
% 4.71/5.14 ! [Deg: nat,X: nat,Ma: nat,TreeList: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 4.71/5.14 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.71/5.14 => ( ( ord_less_eq_nat @ X @ Ma )
% 4.71/5.14 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.71/5.14 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.14 = ( if_option_nat
% 4.71/5.14 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.14 != none_nat )
% 4.71/5.14 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 4.71/5.14 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.14 @ ( if_option_nat
% 4.71/5.14 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.71/5.14 = none_nat )
% 4.71/5.14 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 4.71/5.14 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % pred_less_length_list
% 4.71/5.14 thf(fact_6766_pred__lesseq__max,axiom,
% 4.71/5.14 ! [Deg: nat,X: nat,Ma: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 4.71/5.14 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.71/5.14 => ( ( ord_less_eq_nat @ X @ Ma )
% 4.71/5.14 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.14 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.71/5.14 @ ( if_option_nat
% 4.71/5.14 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.14 != none_nat )
% 4.71/5.14 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 4.71/5.14 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.14 @ ( if_option_nat
% 4.71/5.14 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.71/5.14 = none_nat )
% 4.71/5.14 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 4.71/5.14 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 4.71/5.14 @ none_nat ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % pred_lesseq_max
% 4.71/5.14 thf(fact_6767_set__vebt_H__def,axiom,
% 4.71/5.14 ( vEBT_VEBT_set_vebt
% 4.71/5.14 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % set_vebt'_def
% 4.71/5.14 thf(fact_6768_finite__Collect__conjI,axiom,
% 4.71/5.14 ! [P: set_nat > $o,Q: set_nat > $o] :
% 4.71/5.14 ( ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 4.71/5.14 | ( finite1152437895449049373et_nat @ ( collect_set_nat @ Q ) ) )
% 4.71/5.14 => ( finite1152437895449049373et_nat
% 4.71/5.14 @ ( collect_set_nat
% 4.71/5.14 @ ^ [X3: set_nat] :
% 4.71/5.14 ( ( P @ X3 )
% 4.71/5.14 & ( Q @ X3 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_Collect_conjI
% 4.71/5.14 thf(fact_6769_finite__Collect__conjI,axiom,
% 4.71/5.14 ! [P: set_nat_rat > $o,Q: set_nat_rat > $o] :
% 4.71/5.14 ( ( ( finite6430367030675640852at_rat @ ( collect_set_nat_rat @ P ) )
% 4.71/5.14 | ( finite6430367030675640852at_rat @ ( collect_set_nat_rat @ Q ) ) )
% 4.71/5.14 => ( finite6430367030675640852at_rat
% 4.71/5.14 @ ( collect_set_nat_rat
% 4.71/5.14 @ ^ [X3: set_nat_rat] :
% 4.71/5.14 ( ( P @ X3 )
% 4.71/5.14 & ( Q @ X3 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_Collect_conjI
% 4.71/5.14 thf(fact_6770_finite__Collect__conjI,axiom,
% 4.71/5.14 ! [P: ( nat > rat ) > $o,Q: ( nat > rat ) > $o] :
% 4.71/5.14 ( ( ( finite7830837933032798814at_rat @ ( collect_nat_rat @ P ) )
% 4.71/5.14 | ( finite7830837933032798814at_rat @ ( collect_nat_rat @ Q ) ) )
% 4.71/5.14 => ( finite7830837933032798814at_rat
% 4.71/5.14 @ ( collect_nat_rat
% 4.71/5.14 @ ^ [X3: nat > rat] :
% 4.71/5.14 ( ( P @ X3 )
% 4.71/5.14 & ( Q @ X3 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_Collect_conjI
% 4.71/5.14 thf(fact_6771_finite__Collect__conjI,axiom,
% 4.71/5.14 ! [P: nat > $o,Q: nat > $o] :
% 4.71/5.14 ( ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 4.71/5.14 | ( finite_finite_nat @ ( collect_nat @ Q ) ) )
% 4.71/5.14 => ( finite_finite_nat
% 4.71/5.14 @ ( collect_nat
% 4.71/5.14 @ ^ [X3: nat] :
% 4.71/5.14 ( ( P @ X3 )
% 4.71/5.14 & ( Q @ X3 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_Collect_conjI
% 4.71/5.14 thf(fact_6772_finite__Collect__conjI,axiom,
% 4.71/5.14 ! [P: int > $o,Q: int > $o] :
% 4.71/5.14 ( ( ( finite_finite_int @ ( collect_int @ P ) )
% 4.71/5.14 | ( finite_finite_int @ ( collect_int @ Q ) ) )
% 4.71/5.14 => ( finite_finite_int
% 4.71/5.14 @ ( collect_int
% 4.71/5.14 @ ^ [X3: int] :
% 4.71/5.14 ( ( P @ X3 )
% 4.71/5.14 & ( Q @ X3 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_Collect_conjI
% 4.71/5.14 thf(fact_6773_finite__Collect__conjI,axiom,
% 4.71/5.14 ! [P: complex > $o,Q: complex > $o] :
% 4.71/5.14 ( ( ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 4.71/5.14 | ( finite3207457112153483333omplex @ ( collect_complex @ Q ) ) )
% 4.71/5.14 => ( finite3207457112153483333omplex
% 4.71/5.14 @ ( collect_complex
% 4.71/5.14 @ ^ [X3: complex] :
% 4.71/5.14 ( ( P @ X3 )
% 4.71/5.14 & ( Q @ X3 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_Collect_conjI
% 4.71/5.14 thf(fact_6774_finite__Collect__conjI,axiom,
% 4.71/5.14 ! [P: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 4.71/5.14 ( ( ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ P ) )
% 4.71/5.14 | ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ Q ) ) )
% 4.71/5.14 => ( finite6177210948735845034at_nat
% 4.71/5.14 @ ( collec3392354462482085612at_nat
% 4.71/5.14 @ ^ [X3: product_prod_nat_nat] :
% 4.71/5.14 ( ( P @ X3 )
% 4.71/5.14 & ( Q @ X3 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_Collect_conjI
% 4.71/5.14 thf(fact_6775_finite__Collect__conjI,axiom,
% 4.71/5.14 ! [P: extended_enat > $o,Q: extended_enat > $o] :
% 4.71/5.14 ( ( ( finite4001608067531595151d_enat @ ( collec4429806609662206161d_enat @ P ) )
% 4.71/5.14 | ( finite4001608067531595151d_enat @ ( collec4429806609662206161d_enat @ Q ) ) )
% 4.71/5.14 => ( finite4001608067531595151d_enat
% 4.71/5.14 @ ( collec4429806609662206161d_enat
% 4.71/5.14 @ ^ [X3: extended_enat] :
% 4.71/5.14 ( ( P @ X3 )
% 4.71/5.14 & ( Q @ X3 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_Collect_conjI
% 4.71/5.14 thf(fact_6776_finite__Collect__disjI,axiom,
% 4.71/5.14 ! [P: set_nat > $o,Q: set_nat > $o] :
% 4.71/5.14 ( ( finite1152437895449049373et_nat
% 4.71/5.14 @ ( collect_set_nat
% 4.71/5.14 @ ^ [X3: set_nat] :
% 4.71/5.14 ( ( P @ X3 )
% 4.71/5.14 | ( Q @ X3 ) ) ) )
% 4.71/5.14 = ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 4.71/5.14 & ( finite1152437895449049373et_nat @ ( collect_set_nat @ Q ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_Collect_disjI
% 4.71/5.14 thf(fact_6777_finite__Collect__disjI,axiom,
% 4.71/5.14 ! [P: set_nat_rat > $o,Q: set_nat_rat > $o] :
% 4.71/5.14 ( ( finite6430367030675640852at_rat
% 4.71/5.14 @ ( collect_set_nat_rat
% 4.71/5.14 @ ^ [X3: set_nat_rat] :
% 4.71/5.14 ( ( P @ X3 )
% 4.71/5.14 | ( Q @ X3 ) ) ) )
% 4.71/5.14 = ( ( finite6430367030675640852at_rat @ ( collect_set_nat_rat @ P ) )
% 4.71/5.14 & ( finite6430367030675640852at_rat @ ( collect_set_nat_rat @ Q ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_Collect_disjI
% 4.71/5.14 thf(fact_6778_finite__Collect__disjI,axiom,
% 4.71/5.14 ! [P: ( nat > rat ) > $o,Q: ( nat > rat ) > $o] :
% 4.71/5.14 ( ( finite7830837933032798814at_rat
% 4.71/5.14 @ ( collect_nat_rat
% 4.71/5.14 @ ^ [X3: nat > rat] :
% 4.71/5.14 ( ( P @ X3 )
% 4.71/5.14 | ( Q @ X3 ) ) ) )
% 4.71/5.14 = ( ( finite7830837933032798814at_rat @ ( collect_nat_rat @ P ) )
% 4.71/5.14 & ( finite7830837933032798814at_rat @ ( collect_nat_rat @ Q ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_Collect_disjI
% 4.71/5.14 thf(fact_6779_finite__Collect__disjI,axiom,
% 4.71/5.14 ! [P: nat > $o,Q: nat > $o] :
% 4.71/5.14 ( ( finite_finite_nat
% 4.71/5.14 @ ( collect_nat
% 4.71/5.14 @ ^ [X3: nat] :
% 4.71/5.14 ( ( P @ X3 )
% 4.71/5.14 | ( Q @ X3 ) ) ) )
% 4.71/5.14 = ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 4.71/5.14 & ( finite_finite_nat @ ( collect_nat @ Q ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_Collect_disjI
% 4.71/5.14 thf(fact_6780_finite__Collect__disjI,axiom,
% 4.71/5.14 ! [P: int > $o,Q: int > $o] :
% 4.71/5.14 ( ( finite_finite_int
% 4.71/5.14 @ ( collect_int
% 4.71/5.14 @ ^ [X3: int] :
% 4.71/5.14 ( ( P @ X3 )
% 4.71/5.14 | ( Q @ X3 ) ) ) )
% 4.71/5.14 = ( ( finite_finite_int @ ( collect_int @ P ) )
% 4.71/5.14 & ( finite_finite_int @ ( collect_int @ Q ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_Collect_disjI
% 4.71/5.14 thf(fact_6781_finite__Collect__disjI,axiom,
% 4.71/5.14 ! [P: complex > $o,Q: complex > $o] :
% 4.71/5.14 ( ( finite3207457112153483333omplex
% 4.71/5.14 @ ( collect_complex
% 4.71/5.14 @ ^ [X3: complex] :
% 4.71/5.14 ( ( P @ X3 )
% 4.71/5.14 | ( Q @ X3 ) ) ) )
% 4.71/5.14 = ( ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 4.71/5.14 & ( finite3207457112153483333omplex @ ( collect_complex @ Q ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_Collect_disjI
% 4.71/5.14 thf(fact_6782_finite__Collect__disjI,axiom,
% 4.71/5.14 ! [P: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 4.71/5.14 ( ( finite6177210948735845034at_nat
% 4.71/5.14 @ ( collec3392354462482085612at_nat
% 4.71/5.14 @ ^ [X3: product_prod_nat_nat] :
% 4.71/5.14 ( ( P @ X3 )
% 4.71/5.14 | ( Q @ X3 ) ) ) )
% 4.71/5.14 = ( ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ P ) )
% 4.71/5.14 & ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ Q ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_Collect_disjI
% 4.71/5.14 thf(fact_6783_finite__Collect__disjI,axiom,
% 4.71/5.14 ! [P: extended_enat > $o,Q: extended_enat > $o] :
% 4.71/5.14 ( ( finite4001608067531595151d_enat
% 4.71/5.14 @ ( collec4429806609662206161d_enat
% 4.71/5.14 @ ^ [X3: extended_enat] :
% 4.71/5.14 ( ( P @ X3 )
% 4.71/5.14 | ( Q @ X3 ) ) ) )
% 4.71/5.14 = ( ( finite4001608067531595151d_enat @ ( collec4429806609662206161d_enat @ P ) )
% 4.71/5.14 & ( finite4001608067531595151d_enat @ ( collec4429806609662206161d_enat @ Q ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_Collect_disjI
% 4.71/5.14 thf(fact_6784_pred__empty,axiom,
% 4.71/5.14 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 4.71/5.14 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.14 => ( ( ( vEBT_vebt_pred @ T @ X )
% 4.71/5.14 = none_nat )
% 4.71/5.14 = ( ( collect_nat
% 4.71/5.14 @ ^ [Y2: nat] :
% 4.71/5.14 ( ( vEBT_vebt_member @ T @ Y2 )
% 4.71/5.14 & ( ord_less_nat @ Y2 @ X ) ) )
% 4.71/5.14 = bot_bot_set_nat ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % pred_empty
% 4.71/5.14 thf(fact_6785_succ__empty,axiom,
% 4.71/5.14 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 4.71/5.14 ( ( vEBT_invar_vebt @ T @ N )
% 4.71/5.14 => ( ( ( vEBT_vebt_succ @ T @ X )
% 4.71/5.14 = none_nat )
% 4.71/5.14 = ( ( collect_nat
% 4.71/5.14 @ ^ [Y2: nat] :
% 4.71/5.14 ( ( vEBT_vebt_member @ T @ Y2 )
% 4.71/5.14 & ( ord_less_nat @ X @ Y2 ) ) )
% 4.71/5.14 = bot_bot_set_nat ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % succ_empty
% 4.71/5.14 thf(fact_6786_finite__nth__roots,axiom,
% 4.71/5.14 ! [N: nat,C: complex] :
% 4.71/5.14 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.14 => ( finite3207457112153483333omplex
% 4.71/5.14 @ ( collect_complex
% 4.71/5.14 @ ^ [Z2: complex] :
% 4.71/5.14 ( ( power_power_complex @ Z2 @ N )
% 4.71/5.14 = C ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_nth_roots
% 4.71/5.14 thf(fact_6787_finite__Collect__subsets,axiom,
% 4.71/5.14 ! [A2: set_nat_rat] :
% 4.71/5.14 ( ( finite7830837933032798814at_rat @ A2 )
% 4.71/5.14 => ( finite6430367030675640852at_rat
% 4.71/5.14 @ ( collect_set_nat_rat
% 4.71/5.14 @ ^ [B6: set_nat_rat] : ( ord_le2679597024174929757at_rat @ B6 @ A2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_Collect_subsets
% 4.71/5.14 thf(fact_6788_finite__Collect__subsets,axiom,
% 4.71/5.14 ! [A2: set_nat] :
% 4.71/5.14 ( ( finite_finite_nat @ A2 )
% 4.71/5.14 => ( finite1152437895449049373et_nat
% 4.71/5.14 @ ( collect_set_nat
% 4.71/5.14 @ ^ [B6: set_nat] : ( ord_less_eq_set_nat @ B6 @ A2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_Collect_subsets
% 4.71/5.14 thf(fact_6789_finite__Collect__subsets,axiom,
% 4.71/5.14 ! [A2: set_complex] :
% 4.71/5.14 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.14 => ( finite6551019134538273531omplex
% 4.71/5.14 @ ( collect_set_complex
% 4.71/5.14 @ ^ [B6: set_complex] : ( ord_le211207098394363844omplex @ B6 @ A2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_Collect_subsets
% 4.71/5.14 thf(fact_6790_finite__Collect__subsets,axiom,
% 4.71/5.14 ! [A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.14 ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.14 => ( finite9047747110432174090at_nat
% 4.71/5.14 @ ( collec5514110066124741708at_nat
% 4.71/5.14 @ ^ [B6: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ B6 @ A2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_Collect_subsets
% 4.71/5.14 thf(fact_6791_finite__Collect__subsets,axiom,
% 4.71/5.14 ! [A2: set_Extended_enat] :
% 4.71/5.14 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.14 => ( finite5468666774076196335d_enat
% 4.71/5.14 @ ( collec2260605976452661553d_enat
% 4.71/5.14 @ ^ [B6: set_Extended_enat] : ( ord_le7203529160286727270d_enat @ B6 @ A2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_Collect_subsets
% 4.71/5.14 thf(fact_6792_finite__Collect__subsets,axiom,
% 4.71/5.14 ! [A2: set_int] :
% 4.71/5.14 ( ( finite_finite_int @ A2 )
% 4.71/5.14 => ( finite6197958912794628473et_int
% 4.71/5.14 @ ( collect_set_int
% 4.71/5.14 @ ^ [B6: set_int] : ( ord_less_eq_set_int @ B6 @ A2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_Collect_subsets
% 4.71/5.14 thf(fact_6793_singleton__conv,axiom,
% 4.71/5.14 ! [A: product_prod_nat_nat] :
% 4.71/5.14 ( ( collec3392354462482085612at_nat
% 4.71/5.14 @ ^ [X3: product_prod_nat_nat] : ( X3 = A ) )
% 4.71/5.14 = ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ).
% 4.71/5.14
% 4.71/5.14 % singleton_conv
% 4.71/5.14 thf(fact_6794_singleton__conv,axiom,
% 4.71/5.14 ! [A: set_nat] :
% 4.71/5.14 ( ( collect_set_nat
% 4.71/5.14 @ ^ [X3: set_nat] : ( X3 = A ) )
% 4.71/5.14 = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 4.71/5.14
% 4.71/5.14 % singleton_conv
% 4.71/5.14 thf(fact_6795_singleton__conv,axiom,
% 4.71/5.14 ! [A: set_nat_rat] :
% 4.71/5.14 ( ( collect_set_nat_rat
% 4.71/5.14 @ ^ [X3: set_nat_rat] : ( X3 = A ) )
% 4.71/5.14 = ( insert_set_nat_rat @ A @ bot_bo6797373522285170759at_rat ) ) ).
% 4.71/5.14
% 4.71/5.14 % singleton_conv
% 4.71/5.14 thf(fact_6796_singleton__conv,axiom,
% 4.71/5.14 ! [A: nat > rat] :
% 4.71/5.14 ( ( collect_nat_rat
% 4.71/5.14 @ ^ [X3: nat > rat] : ( X3 = A ) )
% 4.71/5.14 = ( insert_nat_rat @ A @ bot_bot_set_nat_rat ) ) ).
% 4.71/5.14
% 4.71/5.14 % singleton_conv
% 4.71/5.14 thf(fact_6797_singleton__conv,axiom,
% 4.71/5.14 ! [A: real] :
% 4.71/5.14 ( ( collect_real
% 4.71/5.14 @ ^ [X3: real] : ( X3 = A ) )
% 4.71/5.14 = ( insert_real @ A @ bot_bot_set_real ) ) ).
% 4.71/5.14
% 4.71/5.14 % singleton_conv
% 4.71/5.14 thf(fact_6798_singleton__conv,axiom,
% 4.71/5.14 ! [A: $o] :
% 4.71/5.14 ( ( collect_o
% 4.71/5.14 @ ^ [X3: $o] : ( X3 = A ) )
% 4.71/5.14 = ( insert_o @ A @ bot_bot_set_o ) ) ).
% 4.71/5.14
% 4.71/5.14 % singleton_conv
% 4.71/5.14 thf(fact_6799_singleton__conv,axiom,
% 4.71/5.14 ! [A: nat] :
% 4.71/5.14 ( ( collect_nat
% 4.71/5.14 @ ^ [X3: nat] : ( X3 = A ) )
% 4.71/5.14 = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 4.71/5.14
% 4.71/5.14 % singleton_conv
% 4.71/5.14 thf(fact_6800_singleton__conv,axiom,
% 4.71/5.14 ! [A: int] :
% 4.71/5.14 ( ( collect_int
% 4.71/5.14 @ ^ [X3: int] : ( X3 = A ) )
% 4.71/5.14 = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 4.71/5.14
% 4.71/5.14 % singleton_conv
% 4.71/5.14 thf(fact_6801_singleton__conv2,axiom,
% 4.71/5.14 ! [A: product_prod_nat_nat] :
% 4.71/5.14 ( ( collec3392354462482085612at_nat
% 4.71/5.14 @ ( ^ [Y5: product_prod_nat_nat,Z4: product_prod_nat_nat] : ( Y5 = Z4 )
% 4.71/5.14 @ A ) )
% 4.71/5.14 = ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ).
% 4.71/5.14
% 4.71/5.14 % singleton_conv2
% 4.71/5.14 thf(fact_6802_singleton__conv2,axiom,
% 4.71/5.14 ! [A: set_nat] :
% 4.71/5.14 ( ( collect_set_nat
% 4.71/5.14 @ ( ^ [Y5: set_nat,Z4: set_nat] : ( Y5 = Z4 )
% 4.71/5.14 @ A ) )
% 4.71/5.14 = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 4.71/5.14
% 4.71/5.14 % singleton_conv2
% 4.71/5.14 thf(fact_6803_singleton__conv2,axiom,
% 4.71/5.14 ! [A: set_nat_rat] :
% 4.71/5.14 ( ( collect_set_nat_rat
% 4.71/5.14 @ ( ^ [Y5: set_nat_rat,Z4: set_nat_rat] : ( Y5 = Z4 )
% 4.71/5.14 @ A ) )
% 4.71/5.14 = ( insert_set_nat_rat @ A @ bot_bo6797373522285170759at_rat ) ) ).
% 4.71/5.14
% 4.71/5.14 % singleton_conv2
% 4.71/5.14 thf(fact_6804_singleton__conv2,axiom,
% 4.71/5.14 ! [A: nat > rat] :
% 4.71/5.14 ( ( collect_nat_rat
% 4.71/5.14 @ ( ^ [Y5: nat > rat,Z4: nat > rat] : ( Y5 = Z4 )
% 4.71/5.14 @ A ) )
% 4.71/5.14 = ( insert_nat_rat @ A @ bot_bot_set_nat_rat ) ) ).
% 4.71/5.14
% 4.71/5.14 % singleton_conv2
% 4.71/5.14 thf(fact_6805_singleton__conv2,axiom,
% 4.71/5.14 ! [A: real] :
% 4.71/5.14 ( ( collect_real
% 4.71/5.14 @ ( ^ [Y5: real,Z4: real] : ( Y5 = Z4 )
% 4.71/5.14 @ A ) )
% 4.71/5.14 = ( insert_real @ A @ bot_bot_set_real ) ) ).
% 4.71/5.14
% 4.71/5.14 % singleton_conv2
% 4.71/5.14 thf(fact_6806_singleton__conv2,axiom,
% 4.71/5.14 ! [A: $o] :
% 4.71/5.14 ( ( collect_o
% 4.71/5.14 @ ( ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 )
% 4.71/5.14 @ A ) )
% 4.71/5.14 = ( insert_o @ A @ bot_bot_set_o ) ) ).
% 4.71/5.14
% 4.71/5.14 % singleton_conv2
% 4.71/5.14 thf(fact_6807_singleton__conv2,axiom,
% 4.71/5.14 ! [A: nat] :
% 4.71/5.14 ( ( collect_nat
% 4.71/5.14 @ ( ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 4.71/5.14 @ A ) )
% 4.71/5.14 = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 4.71/5.14
% 4.71/5.14 % singleton_conv2
% 4.71/5.14 thf(fact_6808_singleton__conv2,axiom,
% 4.71/5.14 ! [A: int] :
% 4.71/5.14 ( ( collect_int
% 4.71/5.14 @ ( ^ [Y5: int,Z4: int] : ( Y5 = Z4 )
% 4.71/5.14 @ A ) )
% 4.71/5.14 = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 4.71/5.14
% 4.71/5.14 % singleton_conv2
% 4.71/5.14 thf(fact_6809_finite__Collect__less__nat,axiom,
% 4.71/5.14 ! [K: nat] :
% 4.71/5.14 ( finite_finite_nat
% 4.71/5.14 @ ( collect_nat
% 4.71/5.14 @ ^ [N4: nat] : ( ord_less_nat @ N4 @ K ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_Collect_less_nat
% 4.71/5.14 thf(fact_6810_finite__Collect__le__nat,axiom,
% 4.71/5.14 ! [K: nat] :
% 4.71/5.14 ( finite_finite_nat
% 4.71/5.14 @ ( collect_nat
% 4.71/5.14 @ ^ [N4: nat] : ( ord_less_eq_nat @ N4 @ K ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_Collect_le_nat
% 4.71/5.14 thf(fact_6811_card__Collect__less__nat,axiom,
% 4.71/5.14 ! [N: nat] :
% 4.71/5.14 ( ( finite_card_nat
% 4.71/5.14 @ ( collect_nat
% 4.71/5.14 @ ^ [I4: nat] : ( ord_less_nat @ I4 @ N ) ) )
% 4.71/5.14 = N ) ).
% 4.71/5.14
% 4.71/5.14 % card_Collect_less_nat
% 4.71/5.14 thf(fact_6812_finite__interval__int1,axiom,
% 4.71/5.14 ! [A: int,B: int] :
% 4.71/5.14 ( finite_finite_int
% 4.71/5.14 @ ( collect_int
% 4.71/5.14 @ ^ [I4: int] :
% 4.71/5.14 ( ( ord_less_eq_int @ A @ I4 )
% 4.71/5.14 & ( ord_less_eq_int @ I4 @ B ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_interval_int1
% 4.71/5.14 thf(fact_6813_list__update__beyond,axiom,
% 4.71/5.14 ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] :
% 4.71/5.14 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ I )
% 4.71/5.14 => ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ X )
% 4.71/5.14 = Xs ) ) ).
% 4.71/5.14
% 4.71/5.14 % list_update_beyond
% 4.71/5.14 thf(fact_6814_list__update__beyond,axiom,
% 4.71/5.14 ! [Xs: list_nat,I: nat,X: nat] :
% 4.71/5.14 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ I )
% 4.71/5.14 => ( ( list_update_nat @ Xs @ I @ X )
% 4.71/5.14 = Xs ) ) ).
% 4.71/5.14
% 4.71/5.14 % list_update_beyond
% 4.71/5.14 thf(fact_6815_card__Collect__le__nat,axiom,
% 4.71/5.14 ! [N: nat] :
% 4.71/5.14 ( ( finite_card_nat
% 4.71/5.14 @ ( collect_nat
% 4.71/5.14 @ ^ [I4: nat] : ( ord_less_eq_nat @ I4 @ N ) ) )
% 4.71/5.14 = ( suc @ N ) ) ).
% 4.71/5.14
% 4.71/5.14 % card_Collect_le_nat
% 4.71/5.14 thf(fact_6816_finite__interval__int3,axiom,
% 4.71/5.14 ! [A: int,B: int] :
% 4.71/5.14 ( finite_finite_int
% 4.71/5.14 @ ( collect_int
% 4.71/5.14 @ ^ [I4: int] :
% 4.71/5.14 ( ( ord_less_int @ A @ I4 )
% 4.71/5.14 & ( ord_less_eq_int @ I4 @ B ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_interval_int3
% 4.71/5.14 thf(fact_6817_finite__interval__int2,axiom,
% 4.71/5.14 ! [A: int,B: int] :
% 4.71/5.14 ( finite_finite_int
% 4.71/5.14 @ ( collect_int
% 4.71/5.14 @ ^ [I4: int] :
% 4.71/5.14 ( ( ord_less_eq_int @ A @ I4 )
% 4.71/5.14 & ( ord_less_int @ I4 @ B ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_interval_int2
% 4.71/5.14 thf(fact_6818_nth__list__update__eq,axiom,
% 4.71/5.14 ! [I: nat,Xs: list_int,X: int] :
% 4.71/5.14 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 4.71/5.14 => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ I )
% 4.71/5.14 = X ) ) ).
% 4.71/5.14
% 4.71/5.14 % nth_list_update_eq
% 4.71/5.14 thf(fact_6819_nth__list__update__eq,axiom,
% 4.71/5.14 ! [I: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 4.71/5.14 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.71/5.14 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ I )
% 4.71/5.14 = X ) ) ).
% 4.71/5.14
% 4.71/5.14 % nth_list_update_eq
% 4.71/5.14 thf(fact_6820_nth__list__update__eq,axiom,
% 4.71/5.14 ! [I: nat,Xs: list_nat,X: nat] :
% 4.71/5.14 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 4.71/5.14 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ I )
% 4.71/5.14 = X ) ) ).
% 4.71/5.14
% 4.71/5.14 % nth_list_update_eq
% 4.71/5.14 thf(fact_6821_set__swap,axiom,
% 4.71/5.14 ! [I: nat,Xs: list_int,J: nat] :
% 4.71/5.14 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 4.71/5.14 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 4.71/5.14 => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs @ I @ ( nth_int @ Xs @ J ) ) @ J @ ( nth_int @ Xs @ I ) ) )
% 4.71/5.14 = ( set_int2 @ Xs ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % set_swap
% 4.71/5.14 thf(fact_6822_set__swap,axiom,
% 4.71/5.14 ! [I: nat,Xs: list_VEBT_VEBT,J: nat] :
% 4.71/5.14 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.71/5.14 => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.71/5.14 => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( nth_VEBT_VEBT @ Xs @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs @ I ) ) )
% 4.71/5.14 = ( set_VEBT_VEBT2 @ Xs ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % set_swap
% 4.71/5.14 thf(fact_6823_set__swap,axiom,
% 4.71/5.14 ! [I: nat,Xs: list_nat,J: nat] :
% 4.71/5.14 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 4.71/5.14 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 4.71/5.14 => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs @ I @ ( nth_nat @ Xs @ J ) ) @ J @ ( nth_nat @ Xs @ I ) ) )
% 4.71/5.14 = ( set_nat2 @ Xs ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % set_swap
% 4.71/5.14 thf(fact_6824_del__x__not__mia,axiom,
% 4.71/5.14 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H: nat,L: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 4.71/5.14 ( ( ( ord_less_nat @ Mi @ X )
% 4.71/5.14 & ( ord_less_eq_nat @ X @ Ma ) )
% 4.71/5.14 => ( ( Mi != Ma )
% 4.71/5.14 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.71/5.14 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = H )
% 4.71/5.14 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = L )
% 4.71/5.14 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.71/5.14 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.14 = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H ) @ L ) )
% 4.71/5.14 @ ( vEBT_Node
% 4.71/5.14 @ ( some_P7363390416028606310at_nat
% 4.71/5.14 @ ( product_Pair_nat_nat @ Mi
% 4.71/5.14 @ ( if_nat @ ( X = Ma )
% 4.71/5.14 @ ( if_nat
% 4.71/5.14 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) )
% 4.71/5.14 = none_nat )
% 4.71/5.14 @ Mi
% 4.71/5.14 @ ( 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 @ H ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H ) @ L ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) ) ) ) ) ) ) )
% 4.71/5.14 @ Ma ) ) )
% 4.71/5.14 @ Deg
% 4.71/5.14 @ ( list_u1324408373059187874T_VEBT @ TreeList @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H ) @ L ) )
% 4.71/5.14 @ ( vEBT_vebt_delete @ Summary @ H ) )
% 4.71/5.14 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H ) @ L ) ) @ H ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H ) @ L ) ) @ Summary ) ) ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % del_x_not_mia
% 4.71/5.14 thf(fact_6825_del__x__not__mi__new__node__nil,axiom,
% 4.71/5.14 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H: nat,L: nat,Newnode: vEBT_VEBT,TreeList: list_VEBT_VEBT,Sn: vEBT_VEBT,Summary: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 4.71/5.14 ( ( ( ord_less_nat @ Mi @ X )
% 4.71/5.14 & ( ord_less_eq_nat @ X @ Ma ) )
% 4.71/5.14 => ( ( Mi != Ma )
% 4.71/5.14 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.71/5.14 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = H )
% 4.71/5.14 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = L )
% 4.71/5.14 => ( ( Newnode
% 4.71/5.14 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H ) @ L ) )
% 4.71/5.14 => ( ( vEBT_VEBT_minNull @ Newnode )
% 4.71/5.14 => ( ( Sn
% 4.71/5.14 = ( vEBT_vebt_delete @ Summary @ H ) )
% 4.71/5.14 => ( ( Newlist
% 4.71/5.14 = ( list_u1324408373059187874T_VEBT @ TreeList @ H @ Newnode ) )
% 4.71/5.14 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.71/5.14 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.14 = ( vEBT_Node
% 4.71/5.14 @ ( some_P7363390416028606310at_nat
% 4.71/5.14 @ ( product_Pair_nat_nat @ Mi
% 4.71/5.14 @ ( if_nat @ ( X = Ma )
% 4.71/5.14 @ ( if_nat
% 4.71/5.14 @ ( ( vEBT_vebt_maxt @ Sn )
% 4.71/5.14 = none_nat )
% 4.71/5.14 @ Mi
% 4.71/5.14 @ ( 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 ) ) ) ) ) ) )
% 4.71/5.14 @ Ma ) ) )
% 4.71/5.14 @ Deg
% 4.71/5.14 @ Newlist
% 4.71/5.14 @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % del_x_not_mi_new_node_nil
% 4.71/5.14 thf(fact_6826_del__x__not__mi,axiom,
% 4.71/5.14 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H: nat,L: nat,Newnode: vEBT_VEBT,TreeList: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 4.71/5.14 ( ( ( ord_less_nat @ Mi @ X )
% 4.71/5.14 & ( ord_less_eq_nat @ X @ Ma ) )
% 4.71/5.14 => ( ( Mi != Ma )
% 4.71/5.14 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.71/5.14 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = H )
% 4.71/5.14 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = L )
% 4.71/5.14 => ( ( Newnode
% 4.71/5.14 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H ) @ L ) )
% 4.71/5.14 => ( ( Newlist
% 4.71/5.14 = ( list_u1324408373059187874T_VEBT @ TreeList @ H @ Newnode ) )
% 4.71/5.14 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.71/5.14 => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 4.71/5.14 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.14 = ( vEBT_Node
% 4.71/5.14 @ ( some_P7363390416028606310at_nat
% 4.71/5.14 @ ( product_Pair_nat_nat @ Mi
% 4.71/5.14 @ ( if_nat @ ( X = Ma )
% 4.71/5.14 @ ( if_nat
% 4.71/5.14 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) )
% 4.71/5.14 = none_nat )
% 4.71/5.14 @ Mi
% 4.71/5.14 @ ( 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 @ H ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) ) ) ) ) ) ) )
% 4.71/5.14 @ Ma ) ) )
% 4.71/5.14 @ Deg
% 4.71/5.14 @ Newlist
% 4.71/5.14 @ ( vEBT_vebt_delete @ Summary @ H ) ) ) )
% 4.71/5.14 & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 4.71/5.14 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.14 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H @ ( 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 @ H ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % del_x_not_mi
% 4.71/5.14 thf(fact_6827_del__x__mia,axiom,
% 4.71/5.14 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 4.71/5.14 ( ( ( X = Mi )
% 4.71/5.14 & ( ord_less_nat @ X @ Ma ) )
% 4.71/5.14 => ( ( Mi != Ma )
% 4.71/5.14 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.71/5.14 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.14 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.71/5.14 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.14 @ ( vEBT_Node
% 4.71/5.14 @ ( some_P7363390416028606310at_nat
% 4.71/5.14 @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 4.71/5.14 @ ( if_nat
% 4.71/5.14 @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 4.71/5.14 = Ma )
% 4.71/5.14 @ ( if_nat
% 4.71/5.14 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.14 = none_nat )
% 4.71/5.14 @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 4.71/5.14 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 4.71/5.14 @ Ma ) ) )
% 4.71/5.14 @ Deg
% 4.71/5.14 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.14 @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.14 @ ( vEBT_Node
% 4.71/5.14 @ ( some_P7363390416028606310at_nat
% 4.71/5.14 @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 4.71/5.14 @ ( if_nat
% 4.71/5.14 @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 4.71/5.14 = Ma )
% 4.71/5.14 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 4.71/5.14 @ Ma ) ) )
% 4.71/5.14 @ Deg
% 4.71/5.14 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.14 @ Summary ) )
% 4.71/5.14 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % del_x_mia
% 4.71/5.14 thf(fact_6828_del__x__mi__lets__in__minNull,axiom,
% 4.71/5.14 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT,Sn: vEBT_VEBT] :
% 4.71/5.14 ( ( ( X = Mi )
% 4.71/5.14 & ( ord_less_nat @ X @ Ma ) )
% 4.71/5.14 => ( ( Mi != Ma )
% 4.71/5.14 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.71/5.14 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = H )
% 4.71/5.14 => ( ( Xn
% 4.71/5.14 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 4.71/5.14 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = L )
% 4.71/5.14 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.71/5.14 => ( ( Newnode
% 4.71/5.14 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H ) @ L ) )
% 4.71/5.14 => ( ( Newlist
% 4.71/5.14 = ( list_u1324408373059187874T_VEBT @ TreeList @ H @ Newnode ) )
% 4.71/5.14 => ( ( vEBT_VEBT_minNull @ Newnode )
% 4.71/5.14 => ( ( Sn
% 4.71/5.14 = ( vEBT_vebt_delete @ Summary @ H ) )
% 4.71/5.14 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.14 = ( vEBT_Node
% 4.71/5.14 @ ( some_P7363390416028606310at_nat
% 4.71/5.14 @ ( product_Pair_nat_nat @ Xn
% 4.71/5.14 @ ( if_nat @ ( Xn = Ma )
% 4.71/5.14 @ ( if_nat
% 4.71/5.14 @ ( ( vEBT_vebt_maxt @ Sn )
% 4.71/5.14 = none_nat )
% 4.71/5.14 @ Xn
% 4.71/5.14 @ ( 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 ) ) ) ) ) ) )
% 4.71/5.14 @ Ma ) ) )
% 4.71/5.14 @ Deg
% 4.71/5.14 @ Newlist
% 4.71/5.14 @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % del_x_mi_lets_in_minNull
% 4.71/5.14 thf(fact_6829_del__x__mi__lets__in,axiom,
% 4.71/5.14 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 4.71/5.14 ( ( ( X = Mi )
% 4.71/5.14 & ( ord_less_nat @ X @ Ma ) )
% 4.71/5.14 => ( ( Mi != Ma )
% 4.71/5.14 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.71/5.14 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = H )
% 4.71/5.14 => ( ( Xn
% 4.71/5.14 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 4.71/5.14 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = L )
% 4.71/5.14 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.71/5.14 => ( ( Newnode
% 4.71/5.14 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H ) @ L ) )
% 4.71/5.14 => ( ( Newlist
% 4.71/5.14 = ( list_u1324408373059187874T_VEBT @ TreeList @ H @ Newnode ) )
% 4.71/5.14 => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 4.71/5.14 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.14 = ( vEBT_Node
% 4.71/5.14 @ ( some_P7363390416028606310at_nat
% 4.71/5.14 @ ( product_Pair_nat_nat @ Xn
% 4.71/5.14 @ ( if_nat @ ( Xn = Ma )
% 4.71/5.14 @ ( if_nat
% 4.71/5.14 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) )
% 4.71/5.14 = none_nat )
% 4.71/5.14 @ Xn
% 4.71/5.14 @ ( 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 @ H ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) ) ) ) ) ) ) )
% 4.71/5.14 @ Ma ) ) )
% 4.71/5.14 @ Deg
% 4.71/5.14 @ Newlist
% 4.71/5.14 @ ( vEBT_vebt_delete @ Summary @ H ) ) ) )
% 4.71/5.14 & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 4.71/5.14 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.14 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H @ ( 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 @ H ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % del_x_mi_lets_in
% 4.71/5.14 thf(fact_6830_del__x__mi,axiom,
% 4.71/5.14 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L: nat] :
% 4.71/5.14 ( ( ( X = Mi )
% 4.71/5.14 & ( ord_less_nat @ X @ Ma ) )
% 4.71/5.14 => ( ( Mi != Ma )
% 4.71/5.14 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.71/5.14 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = H )
% 4.71/5.14 => ( ( Xn
% 4.71/5.14 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 4.71/5.14 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.71/5.14 = L )
% 4.71/5.14 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.71/5.14 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.14 = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H ) @ L ) )
% 4.71/5.14 @ ( vEBT_Node
% 4.71/5.14 @ ( some_P7363390416028606310at_nat
% 4.71/5.14 @ ( product_Pair_nat_nat @ Xn
% 4.71/5.14 @ ( if_nat @ ( Xn = Ma )
% 4.71/5.14 @ ( if_nat
% 4.71/5.14 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) )
% 4.71/5.14 = none_nat )
% 4.71/5.14 @ Xn
% 4.71/5.14 @ ( 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 @ H ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H ) @ L ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) ) ) ) ) ) ) )
% 4.71/5.14 @ Ma ) ) )
% 4.71/5.14 @ Deg
% 4.71/5.14 @ ( list_u1324408373059187874T_VEBT @ TreeList @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H ) @ L ) )
% 4.71/5.14 @ ( vEBT_vebt_delete @ Summary @ H ) )
% 4.71/5.14 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H ) @ L ) ) @ H ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H ) @ L ) ) @ Summary ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % del_x_mi
% 4.71/5.14 thf(fact_6831_del__in__range,axiom,
% 4.71/5.14 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 4.71/5.14 ( ( ( ord_less_eq_nat @ Mi @ X )
% 4.71/5.14 & ( ord_less_eq_nat @ X @ Ma ) )
% 4.71/5.14 => ( ( Mi != Ma )
% 4.71/5.14 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.71/5.14 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.14 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.71/5.14 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.14 @ ( vEBT_Node
% 4.71/5.14 @ ( some_P7363390416028606310at_nat
% 4.71/5.14 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 4.71/5.14 @ ( if_nat
% 4.71/5.14 @ ( ( ( X = Mi )
% 4.71/5.14 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 4.71/5.14 = Ma ) )
% 4.71/5.14 & ( ( X != Mi )
% 4.71/5.14 => ( X = Ma ) ) )
% 4.71/5.14 @ ( if_nat
% 4.71/5.14 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.14 = none_nat )
% 4.71/5.14 @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 4.71/5.14 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 4.71/5.14 @ Ma ) ) )
% 4.71/5.14 @ Deg
% 4.71/5.14 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.14 @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.14 @ ( vEBT_Node
% 4.71/5.14 @ ( some_P7363390416028606310at_nat
% 4.71/5.14 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 4.71/5.14 @ ( if_nat
% 4.71/5.14 @ ( ( ( X = Mi )
% 4.71/5.14 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 4.71/5.14 = Ma ) )
% 4.71/5.14 & ( ( X != Mi )
% 4.71/5.14 => ( X = Ma ) ) )
% 4.71/5.14 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 4.71/5.14 @ Ma ) ) )
% 4.71/5.14 @ Deg
% 4.71/5.14 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.14 @ Summary ) )
% 4.71/5.14 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % del_in_range
% 4.71/5.14 thf(fact_6832_succ__less__length__list,axiom,
% 4.71/5.14 ! [Deg: nat,Mi: nat,X: nat,TreeList: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 4.71/5.14 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.71/5.14 => ( ( ord_less_eq_nat @ Mi @ X )
% 4.71/5.14 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.71/5.14 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.14 = ( if_option_nat
% 4.71/5.14 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.14 != none_nat )
% 4.71/5.14 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 4.71/5.14 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.14 @ ( if_option_nat
% 4.71/5.14 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.71/5.14 = none_nat )
% 4.71/5.14 @ none_nat
% 4.71/5.14 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % succ_less_length_list
% 4.71/5.14 thf(fact_6833_succ__greatereq__min,axiom,
% 4.71/5.14 ! [Deg: nat,Mi: nat,X: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 4.71/5.14 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.71/5.14 => ( ( ord_less_eq_nat @ Mi @ X )
% 4.71/5.14 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.14 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.71/5.14 @ ( if_option_nat
% 4.71/5.14 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.14 != none_nat )
% 4.71/5.14 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 4.71/5.14 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.14 @ ( if_option_nat
% 4.71/5.14 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.71/5.14 = none_nat )
% 4.71/5.14 @ none_nat
% 4.71/5.14 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 4.71/5.14 @ none_nat ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % succ_greatereq_min
% 4.71/5.14 thf(fact_6834_bot__empty__eq2,axiom,
% 4.71/5.14 ( bot_bo4898103413517107610_nat_o
% 4.71/5.14 = ( ^ [X3: product_prod_nat_nat,Y2: product_prod_nat_nat] : ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y2 ) @ bot_bo5327735625951526323at_nat ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % bot_empty_eq2
% 4.71/5.14 thf(fact_6835_bot__empty__eq2,axiom,
% 4.71/5.14 ( bot_bo3364206721330744218_nat_o
% 4.71/5.14 = ( ^ [X3: set_Pr4329608150637261639at_nat,Y2: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X3 @ Y2 ) @ bot_bo4948859079157340979at_nat ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % bot_empty_eq2
% 4.71/5.14 thf(fact_6836_bot__empty__eq2,axiom,
% 4.71/5.14 ( bot_bo394778441745866138_nat_o
% 4.71/5.14 = ( ^ [X3: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y2 ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % bot_empty_eq2
% 4.71/5.14 thf(fact_6837_bot__empty__eq2,axiom,
% 4.71/5.14 ( bot_bot_nat_nat_o
% 4.71/5.14 = ( ^ [X3: nat,Y2: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y2 ) @ bot_bo2099793752762293965at_nat ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % bot_empty_eq2
% 4.71/5.14 thf(fact_6838_bot__empty__eq2,axiom,
% 4.71/5.14 ( bot_bot_int_int_o
% 4.71/5.14 = ( ^ [X3: int,Y2: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y2 ) @ bot_bo1796632182523588997nt_int ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % bot_empty_eq2
% 4.71/5.14 thf(fact_6839_Collect__conv__if,axiom,
% 4.71/5.14 ! [P: product_prod_nat_nat > $o,A: product_prod_nat_nat] :
% 4.71/5.14 ( ( ( P @ A )
% 4.71/5.14 => ( ( collec3392354462482085612at_nat
% 4.71/5.14 @ ^ [X3: product_prod_nat_nat] :
% 4.71/5.14 ( ( X3 = A )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 4.71/5.14 & ( ~ ( P @ A )
% 4.71/5.14 => ( ( collec3392354462482085612at_nat
% 4.71/5.14 @ ^ [X3: product_prod_nat_nat] :
% 4.71/5.14 ( ( X3 = A )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = bot_bo2099793752762293965at_nat ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_conv_if
% 4.71/5.14 thf(fact_6840_Collect__conv__if,axiom,
% 4.71/5.14 ! [P: set_nat > $o,A: set_nat] :
% 4.71/5.14 ( ( ( P @ A )
% 4.71/5.14 => ( ( collect_set_nat
% 4.71/5.14 @ ^ [X3: set_nat] :
% 4.71/5.14 ( ( X3 = A )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 4.71/5.14 & ( ~ ( P @ A )
% 4.71/5.14 => ( ( collect_set_nat
% 4.71/5.14 @ ^ [X3: set_nat] :
% 4.71/5.14 ( ( X3 = A )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = bot_bot_set_set_nat ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_conv_if
% 4.71/5.14 thf(fact_6841_Collect__conv__if,axiom,
% 4.71/5.14 ! [P: set_nat_rat > $o,A: set_nat_rat] :
% 4.71/5.14 ( ( ( P @ A )
% 4.71/5.14 => ( ( collect_set_nat_rat
% 4.71/5.14 @ ^ [X3: set_nat_rat] :
% 4.71/5.14 ( ( X3 = A )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = ( insert_set_nat_rat @ A @ bot_bo6797373522285170759at_rat ) ) )
% 4.71/5.14 & ( ~ ( P @ A )
% 4.71/5.14 => ( ( collect_set_nat_rat
% 4.71/5.14 @ ^ [X3: set_nat_rat] :
% 4.71/5.14 ( ( X3 = A )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = bot_bo6797373522285170759at_rat ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_conv_if
% 4.71/5.14 thf(fact_6842_Collect__conv__if,axiom,
% 4.71/5.14 ! [P: ( nat > rat ) > $o,A: nat > rat] :
% 4.71/5.14 ( ( ( P @ A )
% 4.71/5.14 => ( ( collect_nat_rat
% 4.71/5.14 @ ^ [X3: nat > rat] :
% 4.71/5.14 ( ( X3 = A )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = ( insert_nat_rat @ A @ bot_bot_set_nat_rat ) ) )
% 4.71/5.14 & ( ~ ( P @ A )
% 4.71/5.14 => ( ( collect_nat_rat
% 4.71/5.14 @ ^ [X3: nat > rat] :
% 4.71/5.14 ( ( X3 = A )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = bot_bot_set_nat_rat ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_conv_if
% 4.71/5.14 thf(fact_6843_Collect__conv__if,axiom,
% 4.71/5.14 ! [P: real > $o,A: real] :
% 4.71/5.14 ( ( ( P @ A )
% 4.71/5.14 => ( ( collect_real
% 4.71/5.14 @ ^ [X3: real] :
% 4.71/5.14 ( ( X3 = A )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = ( insert_real @ A @ bot_bot_set_real ) ) )
% 4.71/5.14 & ( ~ ( P @ A )
% 4.71/5.14 => ( ( collect_real
% 4.71/5.14 @ ^ [X3: real] :
% 4.71/5.14 ( ( X3 = A )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = bot_bot_set_real ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_conv_if
% 4.71/5.14 thf(fact_6844_Collect__conv__if,axiom,
% 4.71/5.14 ! [P: $o > $o,A: $o] :
% 4.71/5.14 ( ( ( P @ A )
% 4.71/5.14 => ( ( collect_o
% 4.71/5.14 @ ^ [X3: $o] :
% 4.71/5.14 ( ( X3 = A )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = ( insert_o @ A @ bot_bot_set_o ) ) )
% 4.71/5.14 & ( ~ ( P @ A )
% 4.71/5.14 => ( ( collect_o
% 4.71/5.14 @ ^ [X3: $o] :
% 4.71/5.14 ( ( X3 = A )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = bot_bot_set_o ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_conv_if
% 4.71/5.14 thf(fact_6845_Collect__conv__if,axiom,
% 4.71/5.14 ! [P: nat > $o,A: nat] :
% 4.71/5.14 ( ( ( P @ A )
% 4.71/5.14 => ( ( collect_nat
% 4.71/5.14 @ ^ [X3: nat] :
% 4.71/5.14 ( ( X3 = A )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 4.71/5.14 & ( ~ ( P @ A )
% 4.71/5.14 => ( ( collect_nat
% 4.71/5.14 @ ^ [X3: nat] :
% 4.71/5.14 ( ( X3 = A )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = bot_bot_set_nat ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_conv_if
% 4.71/5.14 thf(fact_6846_Collect__conv__if,axiom,
% 4.71/5.14 ! [P: int > $o,A: int] :
% 4.71/5.14 ( ( ( P @ A )
% 4.71/5.14 => ( ( collect_int
% 4.71/5.14 @ ^ [X3: int] :
% 4.71/5.14 ( ( X3 = A )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = ( insert_int @ A @ bot_bot_set_int ) ) )
% 4.71/5.14 & ( ~ ( P @ A )
% 4.71/5.14 => ( ( collect_int
% 4.71/5.14 @ ^ [X3: int] :
% 4.71/5.14 ( ( X3 = A )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = bot_bot_set_int ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_conv_if
% 4.71/5.14 thf(fact_6847_Collect__conv__if2,axiom,
% 4.71/5.14 ! [P: product_prod_nat_nat > $o,A: product_prod_nat_nat] :
% 4.71/5.14 ( ( ( P @ A )
% 4.71/5.14 => ( ( collec3392354462482085612at_nat
% 4.71/5.14 @ ^ [X3: product_prod_nat_nat] :
% 4.71/5.14 ( ( A = X3 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 4.71/5.14 & ( ~ ( P @ A )
% 4.71/5.14 => ( ( collec3392354462482085612at_nat
% 4.71/5.14 @ ^ [X3: product_prod_nat_nat] :
% 4.71/5.14 ( ( A = X3 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = bot_bo2099793752762293965at_nat ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_conv_if2
% 4.71/5.14 thf(fact_6848_Collect__conv__if2,axiom,
% 4.71/5.14 ! [P: set_nat > $o,A: set_nat] :
% 4.71/5.14 ( ( ( P @ A )
% 4.71/5.14 => ( ( collect_set_nat
% 4.71/5.14 @ ^ [X3: set_nat] :
% 4.71/5.14 ( ( A = X3 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 4.71/5.14 & ( ~ ( P @ A )
% 4.71/5.14 => ( ( collect_set_nat
% 4.71/5.14 @ ^ [X3: set_nat] :
% 4.71/5.14 ( ( A = X3 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = bot_bot_set_set_nat ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_conv_if2
% 4.71/5.14 thf(fact_6849_Collect__conv__if2,axiom,
% 4.71/5.14 ! [P: set_nat_rat > $o,A: set_nat_rat] :
% 4.71/5.14 ( ( ( P @ A )
% 4.71/5.14 => ( ( collect_set_nat_rat
% 4.71/5.14 @ ^ [X3: set_nat_rat] :
% 4.71/5.14 ( ( A = X3 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = ( insert_set_nat_rat @ A @ bot_bo6797373522285170759at_rat ) ) )
% 4.71/5.14 & ( ~ ( P @ A )
% 4.71/5.14 => ( ( collect_set_nat_rat
% 4.71/5.14 @ ^ [X3: set_nat_rat] :
% 4.71/5.14 ( ( A = X3 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = bot_bo6797373522285170759at_rat ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_conv_if2
% 4.71/5.14 thf(fact_6850_Collect__conv__if2,axiom,
% 4.71/5.14 ! [P: ( nat > rat ) > $o,A: nat > rat] :
% 4.71/5.14 ( ( ( P @ A )
% 4.71/5.14 => ( ( collect_nat_rat
% 4.71/5.14 @ ^ [X3: nat > rat] :
% 4.71/5.14 ( ( A = X3 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = ( insert_nat_rat @ A @ bot_bot_set_nat_rat ) ) )
% 4.71/5.14 & ( ~ ( P @ A )
% 4.71/5.14 => ( ( collect_nat_rat
% 4.71/5.14 @ ^ [X3: nat > rat] :
% 4.71/5.14 ( ( A = X3 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = bot_bot_set_nat_rat ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_conv_if2
% 4.71/5.14 thf(fact_6851_Collect__conv__if2,axiom,
% 4.71/5.14 ! [P: real > $o,A: real] :
% 4.71/5.14 ( ( ( P @ A )
% 4.71/5.14 => ( ( collect_real
% 4.71/5.14 @ ^ [X3: real] :
% 4.71/5.14 ( ( A = X3 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = ( insert_real @ A @ bot_bot_set_real ) ) )
% 4.71/5.14 & ( ~ ( P @ A )
% 4.71/5.14 => ( ( collect_real
% 4.71/5.14 @ ^ [X3: real] :
% 4.71/5.14 ( ( A = X3 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = bot_bot_set_real ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_conv_if2
% 4.71/5.14 thf(fact_6852_Collect__conv__if2,axiom,
% 4.71/5.14 ! [P: $o > $o,A: $o] :
% 4.71/5.14 ( ( ( P @ A )
% 4.71/5.14 => ( ( collect_o
% 4.71/5.14 @ ^ [X3: $o] :
% 4.71/5.14 ( ( A = X3 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = ( insert_o @ A @ bot_bot_set_o ) ) )
% 4.71/5.14 & ( ~ ( P @ A )
% 4.71/5.14 => ( ( collect_o
% 4.71/5.14 @ ^ [X3: $o] :
% 4.71/5.14 ( ( A = X3 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = bot_bot_set_o ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_conv_if2
% 4.71/5.14 thf(fact_6853_Collect__conv__if2,axiom,
% 4.71/5.14 ! [P: nat > $o,A: nat] :
% 4.71/5.14 ( ( ( P @ A )
% 4.71/5.14 => ( ( collect_nat
% 4.71/5.14 @ ^ [X3: nat] :
% 4.71/5.14 ( ( A = X3 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 4.71/5.14 & ( ~ ( P @ A )
% 4.71/5.14 => ( ( collect_nat
% 4.71/5.14 @ ^ [X3: nat] :
% 4.71/5.14 ( ( A = X3 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = bot_bot_set_nat ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_conv_if2
% 4.71/5.14 thf(fact_6854_Collect__conv__if2,axiom,
% 4.71/5.14 ! [P: int > $o,A: int] :
% 4.71/5.14 ( ( ( P @ A )
% 4.71/5.14 => ( ( collect_int
% 4.71/5.14 @ ^ [X3: int] :
% 4.71/5.14 ( ( A = X3 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = ( insert_int @ A @ bot_bot_set_int ) ) )
% 4.71/5.14 & ( ~ ( P @ A )
% 4.71/5.14 => ( ( collect_int
% 4.71/5.14 @ ^ [X3: int] :
% 4.71/5.14 ( ( A = X3 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 = bot_bot_set_int ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_conv_if2
% 4.71/5.14 thf(fact_6855_empty__def,axiom,
% 4.71/5.14 ( bot_bot_set_set_nat
% 4.71/5.14 = ( collect_set_nat
% 4.71/5.14 @ ^ [X3: set_nat] : $false ) ) ).
% 4.71/5.14
% 4.71/5.14 % empty_def
% 4.71/5.14 thf(fact_6856_empty__def,axiom,
% 4.71/5.14 ( bot_bo6797373522285170759at_rat
% 4.71/5.14 = ( collect_set_nat_rat
% 4.71/5.14 @ ^ [X3: set_nat_rat] : $false ) ) ).
% 4.71/5.14
% 4.71/5.14 % empty_def
% 4.71/5.14 thf(fact_6857_empty__def,axiom,
% 4.71/5.14 ( bot_bot_set_nat_rat
% 4.71/5.14 = ( collect_nat_rat
% 4.71/5.14 @ ^ [X3: nat > rat] : $false ) ) ).
% 4.71/5.14
% 4.71/5.14 % empty_def
% 4.71/5.14 thf(fact_6858_empty__def,axiom,
% 4.71/5.14 ( bot_bot_set_real
% 4.71/5.14 = ( collect_real
% 4.71/5.14 @ ^ [X3: real] : $false ) ) ).
% 4.71/5.14
% 4.71/5.14 % empty_def
% 4.71/5.14 thf(fact_6859_empty__def,axiom,
% 4.71/5.14 ( bot_bot_set_o
% 4.71/5.14 = ( collect_o
% 4.71/5.14 @ ^ [X3: $o] : $false ) ) ).
% 4.71/5.14
% 4.71/5.14 % empty_def
% 4.71/5.14 thf(fact_6860_empty__def,axiom,
% 4.71/5.14 ( bot_bot_set_nat
% 4.71/5.14 = ( collect_nat
% 4.71/5.14 @ ^ [X3: nat] : $false ) ) ).
% 4.71/5.14
% 4.71/5.14 % empty_def
% 4.71/5.14 thf(fact_6861_empty__def,axiom,
% 4.71/5.14 ( bot_bot_set_int
% 4.71/5.14 = ( collect_int
% 4.71/5.14 @ ^ [X3: int] : $false ) ) ).
% 4.71/5.14
% 4.71/5.14 % empty_def
% 4.71/5.14 thf(fact_6862_lambda__one,axiom,
% 4.71/5.14 ( ( ^ [X3: complex] : X3 )
% 4.71/5.14 = ( times_times_complex @ one_one_complex ) ) ).
% 4.71/5.14
% 4.71/5.14 % lambda_one
% 4.71/5.14 thf(fact_6863_lambda__one,axiom,
% 4.71/5.14 ( ( ^ [X3: real] : X3 )
% 4.71/5.14 = ( times_times_real @ one_one_real ) ) ).
% 4.71/5.14
% 4.71/5.14 % lambda_one
% 4.71/5.14 thf(fact_6864_lambda__one,axiom,
% 4.71/5.14 ( ( ^ [X3: rat] : X3 )
% 4.71/5.14 = ( times_times_rat @ one_one_rat ) ) ).
% 4.71/5.14
% 4.71/5.14 % lambda_one
% 4.71/5.14 thf(fact_6865_lambda__one,axiom,
% 4.71/5.14 ( ( ^ [X3: nat] : X3 )
% 4.71/5.14 = ( times_times_nat @ one_one_nat ) ) ).
% 4.71/5.14
% 4.71/5.14 % lambda_one
% 4.71/5.14 thf(fact_6866_lambda__one,axiom,
% 4.71/5.14 ( ( ^ [X3: int] : X3 )
% 4.71/5.14 = ( times_times_int @ one_one_int ) ) ).
% 4.71/5.14
% 4.71/5.14 % lambda_one
% 4.71/5.14 thf(fact_6867_pred__subset__eq,axiom,
% 4.71/5.14 ! [R: set_o,S2: set_o] :
% 4.71/5.14 ( ( ord_less_eq_o_o
% 4.71/5.14 @ ^ [X3: $o] : ( member_o @ X3 @ R )
% 4.71/5.14 @ ^ [X3: $o] : ( member_o @ X3 @ S2 ) )
% 4.71/5.14 = ( ord_less_eq_set_o @ R @ S2 ) ) ).
% 4.71/5.14
% 4.71/5.14 % pred_subset_eq
% 4.71/5.14 thf(fact_6868_pred__subset__eq,axiom,
% 4.71/5.14 ! [R: set_set_nat,S2: set_set_nat] :
% 4.71/5.14 ( ( ord_le3964352015994296041_nat_o
% 4.71/5.14 @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ R )
% 4.71/5.14 @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ S2 ) )
% 4.71/5.14 = ( ord_le6893508408891458716et_nat @ R @ S2 ) ) ).
% 4.71/5.14
% 4.71/5.14 % pred_subset_eq
% 4.71/5.14 thf(fact_6869_pred__subset__eq,axiom,
% 4.71/5.14 ! [R: set_set_nat_rat,S2: set_set_nat_rat] :
% 4.71/5.14 ( ( ord_le4100815579384348210_rat_o
% 4.71/5.14 @ ^ [X3: set_nat_rat] : ( member_set_nat_rat @ X3 @ R )
% 4.71/5.14 @ ^ [X3: set_nat_rat] : ( member_set_nat_rat @ X3 @ S2 ) )
% 4.71/5.14 = ( ord_le4375437777232675859at_rat @ R @ S2 ) ) ).
% 4.71/5.14
% 4.71/5.14 % pred_subset_eq
% 4.71/5.14 thf(fact_6870_pred__subset__eq,axiom,
% 4.71/5.14 ! [R: set_nat,S2: set_nat] :
% 4.71/5.14 ( ( ord_less_eq_nat_o
% 4.71/5.14 @ ^ [X3: nat] : ( member_nat @ X3 @ R )
% 4.71/5.14 @ ^ [X3: nat] : ( member_nat @ X3 @ S2 ) )
% 4.71/5.14 = ( ord_less_eq_set_nat @ R @ S2 ) ) ).
% 4.71/5.14
% 4.71/5.14 % pred_subset_eq
% 4.71/5.14 thf(fact_6871_pred__subset__eq,axiom,
% 4.71/5.14 ! [R: set_int,S2: set_int] :
% 4.71/5.14 ( ( ord_less_eq_int_o
% 4.71/5.14 @ ^ [X3: int] : ( member_int @ X3 @ R )
% 4.71/5.14 @ ^ [X3: int] : ( member_int @ X3 @ S2 ) )
% 4.71/5.14 = ( ord_less_eq_set_int @ R @ S2 ) ) ).
% 4.71/5.14
% 4.71/5.14 % pred_subset_eq
% 4.71/5.14 thf(fact_6872_Collect__subset,axiom,
% 4.71/5.14 ! [A2: set_o,P: $o > $o] :
% 4.71/5.14 ( ord_less_eq_set_o
% 4.71/5.14 @ ( collect_o
% 4.71/5.14 @ ^ [X3: $o] :
% 4.71/5.14 ( ( member_o @ X3 @ A2 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 @ A2 ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_subset
% 4.71/5.14 thf(fact_6873_Collect__subset,axiom,
% 4.71/5.14 ! [A2: set_set_nat,P: set_nat > $o] :
% 4.71/5.14 ( ord_le6893508408891458716et_nat
% 4.71/5.14 @ ( collect_set_nat
% 4.71/5.14 @ ^ [X3: set_nat] :
% 4.71/5.14 ( ( member_set_nat @ X3 @ A2 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 @ A2 ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_subset
% 4.71/5.14 thf(fact_6874_Collect__subset,axiom,
% 4.71/5.14 ! [A2: set_set_nat_rat,P: set_nat_rat > $o] :
% 4.71/5.14 ( ord_le4375437777232675859at_rat
% 4.71/5.14 @ ( collect_set_nat_rat
% 4.71/5.14 @ ^ [X3: set_nat_rat] :
% 4.71/5.14 ( ( member_set_nat_rat @ X3 @ A2 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 @ A2 ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_subset
% 4.71/5.14 thf(fact_6875_Collect__subset,axiom,
% 4.71/5.14 ! [A2: set_nat,P: nat > $o] :
% 4.71/5.14 ( ord_less_eq_set_nat
% 4.71/5.14 @ ( collect_nat
% 4.71/5.14 @ ^ [X3: nat] :
% 4.71/5.14 ( ( member_nat @ X3 @ A2 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 @ A2 ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_subset
% 4.71/5.14 thf(fact_6876_Collect__subset,axiom,
% 4.71/5.14 ! [A2: set_nat_rat,P: ( nat > rat ) > $o] :
% 4.71/5.14 ( ord_le2679597024174929757at_rat
% 4.71/5.14 @ ( collect_nat_rat
% 4.71/5.14 @ ^ [X3: nat > rat] :
% 4.71/5.14 ( ( member_nat_rat @ X3 @ A2 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 @ A2 ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_subset
% 4.71/5.14 thf(fact_6877_Collect__subset,axiom,
% 4.71/5.14 ! [A2: set_int,P: int > $o] :
% 4.71/5.14 ( ord_less_eq_set_int
% 4.71/5.14 @ ( collect_int
% 4.71/5.14 @ ^ [X3: int] :
% 4.71/5.14 ( ( member_int @ X3 @ A2 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 @ A2 ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_subset
% 4.71/5.14 thf(fact_6878_less__eq__set__def,axiom,
% 4.71/5.14 ( ord_less_eq_set_o
% 4.71/5.14 = ( ^ [A6: set_o,B6: set_o] :
% 4.71/5.14 ( ord_less_eq_o_o
% 4.71/5.14 @ ^ [X3: $o] : ( member_o @ X3 @ A6 )
% 4.71/5.14 @ ^ [X3: $o] : ( member_o @ X3 @ B6 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % less_eq_set_def
% 4.71/5.14 thf(fact_6879_less__eq__set__def,axiom,
% 4.71/5.14 ( ord_le6893508408891458716et_nat
% 4.71/5.14 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 4.71/5.14 ( ord_le3964352015994296041_nat_o
% 4.71/5.14 @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A6 )
% 4.71/5.14 @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ B6 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % less_eq_set_def
% 4.71/5.14 thf(fact_6880_less__eq__set__def,axiom,
% 4.71/5.14 ( ord_le4375437777232675859at_rat
% 4.71/5.14 = ( ^ [A6: set_set_nat_rat,B6: set_set_nat_rat] :
% 4.71/5.14 ( ord_le4100815579384348210_rat_o
% 4.71/5.14 @ ^ [X3: set_nat_rat] : ( member_set_nat_rat @ X3 @ A6 )
% 4.71/5.14 @ ^ [X3: set_nat_rat] : ( member_set_nat_rat @ X3 @ B6 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % less_eq_set_def
% 4.71/5.14 thf(fact_6881_less__eq__set__def,axiom,
% 4.71/5.14 ( ord_less_eq_set_nat
% 4.71/5.14 = ( ^ [A6: set_nat,B6: set_nat] :
% 4.71/5.14 ( ord_less_eq_nat_o
% 4.71/5.14 @ ^ [X3: nat] : ( member_nat @ X3 @ A6 )
% 4.71/5.14 @ ^ [X3: nat] : ( member_nat @ X3 @ B6 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % less_eq_set_def
% 4.71/5.14 thf(fact_6882_less__eq__set__def,axiom,
% 4.71/5.14 ( ord_less_eq_set_int
% 4.71/5.14 = ( ^ [A6: set_int,B6: set_int] :
% 4.71/5.14 ( ord_less_eq_int_o
% 4.71/5.14 @ ^ [X3: int] : ( member_int @ X3 @ A6 )
% 4.71/5.14 @ ^ [X3: int] : ( member_int @ X3 @ B6 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % less_eq_set_def
% 4.71/5.14 thf(fact_6883_Collect__restrict,axiom,
% 4.71/5.14 ! [X5: set_o,P: $o > $o] :
% 4.71/5.14 ( ord_less_eq_set_o
% 4.71/5.14 @ ( collect_o
% 4.71/5.14 @ ^ [X3: $o] :
% 4.71/5.14 ( ( member_o @ X3 @ X5 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 @ X5 ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_restrict
% 4.71/5.14 thf(fact_6884_Collect__restrict,axiom,
% 4.71/5.14 ! [X5: set_set_nat,P: set_nat > $o] :
% 4.71/5.14 ( ord_le6893508408891458716et_nat
% 4.71/5.14 @ ( collect_set_nat
% 4.71/5.14 @ ^ [X3: set_nat] :
% 4.71/5.14 ( ( member_set_nat @ X3 @ X5 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 @ X5 ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_restrict
% 4.71/5.14 thf(fact_6885_Collect__restrict,axiom,
% 4.71/5.14 ! [X5: set_set_nat_rat,P: set_nat_rat > $o] :
% 4.71/5.14 ( ord_le4375437777232675859at_rat
% 4.71/5.14 @ ( collect_set_nat_rat
% 4.71/5.14 @ ^ [X3: set_nat_rat] :
% 4.71/5.14 ( ( member_set_nat_rat @ X3 @ X5 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 @ X5 ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_restrict
% 4.71/5.14 thf(fact_6886_Collect__restrict,axiom,
% 4.71/5.14 ! [X5: set_nat,P: nat > $o] :
% 4.71/5.14 ( ord_less_eq_set_nat
% 4.71/5.14 @ ( collect_nat
% 4.71/5.14 @ ^ [X3: nat] :
% 4.71/5.14 ( ( member_nat @ X3 @ X5 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 @ X5 ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_restrict
% 4.71/5.14 thf(fact_6887_Collect__restrict,axiom,
% 4.71/5.14 ! [X5: set_nat_rat,P: ( nat > rat ) > $o] :
% 4.71/5.14 ( ord_le2679597024174929757at_rat
% 4.71/5.14 @ ( collect_nat_rat
% 4.71/5.14 @ ^ [X3: nat > rat] :
% 4.71/5.14 ( ( member_nat_rat @ X3 @ X5 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 @ X5 ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_restrict
% 4.71/5.14 thf(fact_6888_Collect__restrict,axiom,
% 4.71/5.14 ! [X5: set_int,P: int > $o] :
% 4.71/5.14 ( ord_less_eq_set_int
% 4.71/5.14 @ ( collect_int
% 4.71/5.14 @ ^ [X3: int] :
% 4.71/5.14 ( ( member_int @ X3 @ X5 )
% 4.71/5.14 & ( P @ X3 ) ) )
% 4.71/5.14 @ X5 ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_restrict
% 4.71/5.14 thf(fact_6889_prop__restrict,axiom,
% 4.71/5.14 ! [X: $o,Z7: set_o,X5: set_o,P: $o > $o] :
% 4.71/5.14 ( ( member_o @ X @ Z7 )
% 4.71/5.14 => ( ( ord_less_eq_set_o @ Z7
% 4.71/5.14 @ ( collect_o
% 4.71/5.14 @ ^ [X3: $o] :
% 4.71/5.14 ( ( member_o @ X3 @ X5 )
% 4.71/5.14 & ( P @ X3 ) ) ) )
% 4.71/5.14 => ( P @ X ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % prop_restrict
% 4.71/5.14 thf(fact_6890_prop__restrict,axiom,
% 4.71/5.14 ! [X: set_nat,Z7: set_set_nat,X5: set_set_nat,P: set_nat > $o] :
% 4.71/5.14 ( ( member_set_nat @ X @ Z7 )
% 4.71/5.14 => ( ( ord_le6893508408891458716et_nat @ Z7
% 4.71/5.14 @ ( collect_set_nat
% 4.71/5.14 @ ^ [X3: set_nat] :
% 4.71/5.14 ( ( member_set_nat @ X3 @ X5 )
% 4.71/5.14 & ( P @ X3 ) ) ) )
% 4.71/5.14 => ( P @ X ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % prop_restrict
% 4.71/5.14 thf(fact_6891_prop__restrict,axiom,
% 4.71/5.14 ! [X: set_nat_rat,Z7: set_set_nat_rat,X5: set_set_nat_rat,P: set_nat_rat > $o] :
% 4.71/5.14 ( ( member_set_nat_rat @ X @ Z7 )
% 4.71/5.14 => ( ( ord_le4375437777232675859at_rat @ Z7
% 4.71/5.14 @ ( collect_set_nat_rat
% 4.71/5.14 @ ^ [X3: set_nat_rat] :
% 4.71/5.14 ( ( member_set_nat_rat @ X3 @ X5 )
% 4.71/5.14 & ( P @ X3 ) ) ) )
% 4.71/5.14 => ( P @ X ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % prop_restrict
% 4.71/5.14 thf(fact_6892_prop__restrict,axiom,
% 4.71/5.14 ! [X: nat,Z7: set_nat,X5: set_nat,P: nat > $o] :
% 4.71/5.14 ( ( member_nat @ X @ Z7 )
% 4.71/5.14 => ( ( ord_less_eq_set_nat @ Z7
% 4.71/5.14 @ ( collect_nat
% 4.71/5.14 @ ^ [X3: nat] :
% 4.71/5.14 ( ( member_nat @ X3 @ X5 )
% 4.71/5.14 & ( P @ X3 ) ) ) )
% 4.71/5.14 => ( P @ X ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % prop_restrict
% 4.71/5.14 thf(fact_6893_prop__restrict,axiom,
% 4.71/5.14 ! [X: nat > rat,Z7: set_nat_rat,X5: set_nat_rat,P: ( nat > rat ) > $o] :
% 4.71/5.14 ( ( member_nat_rat @ X @ Z7 )
% 4.71/5.14 => ( ( ord_le2679597024174929757at_rat @ Z7
% 4.71/5.14 @ ( collect_nat_rat
% 4.71/5.14 @ ^ [X3: nat > rat] :
% 4.71/5.14 ( ( member_nat_rat @ X3 @ X5 )
% 4.71/5.14 & ( P @ X3 ) ) ) )
% 4.71/5.14 => ( P @ X ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % prop_restrict
% 4.71/5.14 thf(fact_6894_prop__restrict,axiom,
% 4.71/5.14 ! [X: int,Z7: set_int,X5: set_int,P: int > $o] :
% 4.71/5.14 ( ( member_int @ X @ Z7 )
% 4.71/5.14 => ( ( ord_less_eq_set_int @ Z7
% 4.71/5.14 @ ( collect_int
% 4.71/5.14 @ ^ [X3: int] :
% 4.71/5.14 ( ( member_int @ X3 @ X5 )
% 4.71/5.14 & ( P @ X3 ) ) ) )
% 4.71/5.14 => ( P @ X ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % prop_restrict
% 4.71/5.14 thf(fact_6895_less__set__def,axiom,
% 4.71/5.14 ( ord_less_set_o
% 4.71/5.14 = ( ^ [A6: set_o,B6: set_o] :
% 4.71/5.14 ( ord_less_o_o
% 4.71/5.14 @ ^ [X3: $o] : ( member_o @ X3 @ A6 )
% 4.71/5.14 @ ^ [X3: $o] : ( member_o @ X3 @ B6 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % less_set_def
% 4.71/5.14 thf(fact_6896_less__set__def,axiom,
% 4.71/5.14 ( ord_less_set_set_nat
% 4.71/5.14 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 4.71/5.14 ( ord_less_set_nat_o
% 4.71/5.14 @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A6 )
% 4.71/5.14 @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ B6 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % less_set_def
% 4.71/5.14 thf(fact_6897_less__set__def,axiom,
% 4.71/5.14 ( ord_le1311537459589289991at_rat
% 4.71/5.14 = ( ^ [A6: set_set_nat_rat,B6: set_set_nat_rat] :
% 4.71/5.14 ( ord_le6823063569548456766_rat_o
% 4.71/5.14 @ ^ [X3: set_nat_rat] : ( member_set_nat_rat @ X3 @ A6 )
% 4.71/5.14 @ ^ [X3: set_nat_rat] : ( member_set_nat_rat @ X3 @ B6 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % less_set_def
% 4.71/5.14 thf(fact_6898_less__set__def,axiom,
% 4.71/5.14 ( ord_less_set_nat
% 4.71/5.14 = ( ^ [A6: set_nat,B6: set_nat] :
% 4.71/5.14 ( ord_less_nat_o
% 4.71/5.14 @ ^ [X3: nat] : ( member_nat @ X3 @ A6 )
% 4.71/5.14 @ ^ [X3: nat] : ( member_nat @ X3 @ B6 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % less_set_def
% 4.71/5.14 thf(fact_6899_less__set__def,axiom,
% 4.71/5.14 ( ord_less_set_int
% 4.71/5.14 = ( ^ [A6: set_int,B6: set_int] :
% 4.71/5.14 ( ord_less_int_o
% 4.71/5.14 @ ^ [X3: int] : ( member_int @ X3 @ A6 )
% 4.71/5.14 @ ^ [X3: int] : ( member_int @ X3 @ B6 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % less_set_def
% 4.71/5.14 thf(fact_6900_insert__compr,axiom,
% 4.71/5.14 ( insert8211810215607154385at_nat
% 4.71/5.14 = ( ^ [A4: product_prod_nat_nat,B6: set_Pr1261947904930325089at_nat] :
% 4.71/5.14 ( collec3392354462482085612at_nat
% 4.71/5.14 @ ^ [X3: product_prod_nat_nat] :
% 4.71/5.14 ( ( X3 = A4 )
% 4.71/5.14 | ( member8440522571783428010at_nat @ X3 @ B6 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % insert_compr
% 4.71/5.14 thf(fact_6901_insert__compr,axiom,
% 4.71/5.14 ( insert_real
% 4.71/5.14 = ( ^ [A4: real,B6: set_real] :
% 4.71/5.14 ( collect_real
% 4.71/5.14 @ ^ [X3: real] :
% 4.71/5.14 ( ( X3 = A4 )
% 4.71/5.14 | ( member_real @ X3 @ B6 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % insert_compr
% 4.71/5.14 thf(fact_6902_insert__compr,axiom,
% 4.71/5.14 ( insert_o
% 4.71/5.14 = ( ^ [A4: $o,B6: set_o] :
% 4.71/5.14 ( collect_o
% 4.71/5.14 @ ^ [X3: $o] :
% 4.71/5.14 ( ( X3 = A4 )
% 4.71/5.14 | ( member_o @ X3 @ B6 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % insert_compr
% 4.71/5.14 thf(fact_6903_insert__compr,axiom,
% 4.71/5.14 ( insert_set_nat
% 4.71/5.14 = ( ^ [A4: set_nat,B6: set_set_nat] :
% 4.71/5.14 ( collect_set_nat
% 4.71/5.14 @ ^ [X3: set_nat] :
% 4.71/5.14 ( ( X3 = A4 )
% 4.71/5.14 | ( member_set_nat @ X3 @ B6 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % insert_compr
% 4.71/5.14 thf(fact_6904_insert__compr,axiom,
% 4.71/5.14 ( insert_set_nat_rat
% 4.71/5.14 = ( ^ [A4: set_nat_rat,B6: set_set_nat_rat] :
% 4.71/5.14 ( collect_set_nat_rat
% 4.71/5.14 @ ^ [X3: set_nat_rat] :
% 4.71/5.14 ( ( X3 = A4 )
% 4.71/5.14 | ( member_set_nat_rat @ X3 @ B6 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % insert_compr
% 4.71/5.14 thf(fact_6905_insert__compr,axiom,
% 4.71/5.14 ( insert_nat
% 4.71/5.14 = ( ^ [A4: nat,B6: set_nat] :
% 4.71/5.14 ( collect_nat
% 4.71/5.14 @ ^ [X3: nat] :
% 4.71/5.14 ( ( X3 = A4 )
% 4.71/5.14 | ( member_nat @ X3 @ B6 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % insert_compr
% 4.71/5.14 thf(fact_6906_insert__compr,axiom,
% 4.71/5.14 ( insert_int
% 4.71/5.14 = ( ^ [A4: int,B6: set_int] :
% 4.71/5.14 ( collect_int
% 4.71/5.14 @ ^ [X3: int] :
% 4.71/5.14 ( ( X3 = A4 )
% 4.71/5.14 | ( member_int @ X3 @ B6 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % insert_compr
% 4.71/5.14 thf(fact_6907_insert__compr,axiom,
% 4.71/5.14 ( insert_nat_rat
% 4.71/5.14 = ( ^ [A4: nat > rat,B6: set_nat_rat] :
% 4.71/5.14 ( collect_nat_rat
% 4.71/5.14 @ ^ [X3: nat > rat] :
% 4.71/5.14 ( ( X3 = A4 )
% 4.71/5.14 | ( member_nat_rat @ X3 @ B6 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % insert_compr
% 4.71/5.14 thf(fact_6908_insert__Collect,axiom,
% 4.71/5.14 ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 4.71/5.14 ( ( insert8211810215607154385at_nat @ A @ ( collec3392354462482085612at_nat @ P ) )
% 4.71/5.14 = ( collec3392354462482085612at_nat
% 4.71/5.14 @ ^ [U2: product_prod_nat_nat] :
% 4.71/5.14 ( ( U2 != A )
% 4.71/5.14 => ( P @ U2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % insert_Collect
% 4.71/5.14 thf(fact_6909_insert__Collect,axiom,
% 4.71/5.14 ! [A: real,P: real > $o] :
% 4.71/5.14 ( ( insert_real @ A @ ( collect_real @ P ) )
% 4.71/5.14 = ( collect_real
% 4.71/5.14 @ ^ [U2: real] :
% 4.71/5.14 ( ( U2 != A )
% 4.71/5.14 => ( P @ U2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % insert_Collect
% 4.71/5.14 thf(fact_6910_insert__Collect,axiom,
% 4.71/5.14 ! [A: $o,P: $o > $o] :
% 4.71/5.14 ( ( insert_o @ A @ ( collect_o @ P ) )
% 4.71/5.14 = ( collect_o
% 4.71/5.14 @ ^ [U2: $o] :
% 4.71/5.14 ( ( U2 != A )
% 4.71/5.14 => ( P @ U2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % insert_Collect
% 4.71/5.14 thf(fact_6911_insert__Collect,axiom,
% 4.71/5.14 ! [A: set_nat,P: set_nat > $o] :
% 4.71/5.14 ( ( insert_set_nat @ A @ ( collect_set_nat @ P ) )
% 4.71/5.14 = ( collect_set_nat
% 4.71/5.14 @ ^ [U2: set_nat] :
% 4.71/5.14 ( ( U2 != A )
% 4.71/5.14 => ( P @ U2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % insert_Collect
% 4.71/5.14 thf(fact_6912_insert__Collect,axiom,
% 4.71/5.14 ! [A: set_nat_rat,P: set_nat_rat > $o] :
% 4.71/5.14 ( ( insert_set_nat_rat @ A @ ( collect_set_nat_rat @ P ) )
% 4.71/5.14 = ( collect_set_nat_rat
% 4.71/5.14 @ ^ [U2: set_nat_rat] :
% 4.71/5.14 ( ( U2 != A )
% 4.71/5.14 => ( P @ U2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % insert_Collect
% 4.71/5.14 thf(fact_6913_insert__Collect,axiom,
% 4.71/5.14 ! [A: nat,P: nat > $o] :
% 4.71/5.14 ( ( insert_nat @ A @ ( collect_nat @ P ) )
% 4.71/5.14 = ( collect_nat
% 4.71/5.14 @ ^ [U2: nat] :
% 4.71/5.14 ( ( U2 != A )
% 4.71/5.14 => ( P @ U2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % insert_Collect
% 4.71/5.14 thf(fact_6914_insert__Collect,axiom,
% 4.71/5.14 ! [A: int,P: int > $o] :
% 4.71/5.14 ( ( insert_int @ A @ ( collect_int @ P ) )
% 4.71/5.14 = ( collect_int
% 4.71/5.14 @ ^ [U2: int] :
% 4.71/5.14 ( ( U2 != A )
% 4.71/5.14 => ( P @ U2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % insert_Collect
% 4.71/5.14 thf(fact_6915_insert__Collect,axiom,
% 4.71/5.14 ! [A: nat > rat,P: ( nat > rat ) > $o] :
% 4.71/5.14 ( ( insert_nat_rat @ A @ ( collect_nat_rat @ P ) )
% 4.71/5.14 = ( collect_nat_rat
% 4.71/5.14 @ ^ [U2: nat > rat] :
% 4.71/5.14 ( ( U2 != A )
% 4.71/5.14 => ( P @ U2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % insert_Collect
% 4.71/5.14 thf(fact_6916_pred__subset__eq2,axiom,
% 4.71/5.14 ! [R: set_Pr8693737435421807431at_nat,S2: set_Pr8693737435421807431at_nat] :
% 4.71/5.14 ( ( ord_le5604493270027003598_nat_o
% 4.71/5.14 @ ^ [X3: product_prod_nat_nat,Y2: product_prod_nat_nat] : ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y2 ) @ R )
% 4.71/5.14 @ ^ [X3: product_prod_nat_nat,Y2: product_prod_nat_nat] : ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y2 ) @ S2 ) )
% 4.71/5.14 = ( ord_le3000389064537975527at_nat @ R @ S2 ) ) ).
% 4.71/5.14
% 4.71/5.14 % pred_subset_eq2
% 4.71/5.14 thf(fact_6917_pred__subset__eq2,axiom,
% 4.71/5.14 ! [R: set_Pr7459493094073627847at_nat,S2: set_Pr7459493094073627847at_nat] :
% 4.71/5.14 ( ( ord_le3072208448688395470_nat_o
% 4.71/5.14 @ ^ [X3: set_Pr4329608150637261639at_nat,Y2: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X3 @ Y2 ) @ R )
% 4.71/5.14 @ ^ [X3: set_Pr4329608150637261639at_nat,Y2: set_Pr4329608150637261639at_nat] : ( member1466754251312161552at_nat @ ( produc9060074326276436823at_nat @ X3 @ Y2 ) @ S2 ) )
% 4.71/5.14 = ( ord_le5997549366648089703at_nat @ R @ S2 ) ) ).
% 4.71/5.14
% 4.71/5.14 % pred_subset_eq2
% 4.71/5.14 thf(fact_6918_pred__subset__eq2,axiom,
% 4.71/5.14 ! [R: set_Pr4329608150637261639at_nat,S2: set_Pr4329608150637261639at_nat] :
% 4.71/5.14 ( ( ord_le3935385432712749774_nat_o
% 4.71/5.14 @ ^ [X3: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y2 ) @ R )
% 4.71/5.14 @ ^ [X3: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y2 ) @ S2 ) )
% 4.71/5.14 = ( ord_le1268244103169919719at_nat @ R @ S2 ) ) ).
% 4.71/5.14
% 4.71/5.14 % pred_subset_eq2
% 4.71/5.14 thf(fact_6919_pred__subset__eq2,axiom,
% 4.71/5.14 ! [R: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 4.71/5.14 ( ( ord_le2646555220125990790_nat_o
% 4.71/5.14 @ ^ [X3: nat,Y2: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y2 ) @ R )
% 4.71/5.14 @ ^ [X3: nat,Y2: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y2 ) @ S2 ) )
% 4.71/5.14 = ( ord_le3146513528884898305at_nat @ R @ S2 ) ) ).
% 4.71/5.14
% 4.71/5.14 % pred_subset_eq2
% 4.71/5.14 thf(fact_6920_pred__subset__eq2,axiom,
% 4.71/5.14 ! [R: set_Pr958786334691620121nt_int,S2: set_Pr958786334691620121nt_int] :
% 4.71/5.14 ( ( ord_le6741204236512500942_int_o
% 4.71/5.14 @ ^ [X3: int,Y2: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y2 ) @ R )
% 4.71/5.14 @ ^ [X3: int,Y2: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y2 ) @ S2 ) )
% 4.71/5.14 = ( ord_le2843351958646193337nt_int @ R @ S2 ) ) ).
% 4.71/5.14
% 4.71/5.14 % pred_subset_eq2
% 4.71/5.14 thf(fact_6921_uminus__set__def,axiom,
% 4.71/5.14 ( uminus_uminus_set_o
% 4.71/5.14 = ( ^ [A6: set_o] :
% 4.71/5.14 ( collect_o
% 4.71/5.14 @ ( uminus_uminus_o_o
% 4.71/5.14 @ ^ [X3: $o] : ( member_o @ X3 @ A6 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % uminus_set_def
% 4.71/5.14 thf(fact_6922_uminus__set__def,axiom,
% 4.71/5.14 ( uminus613421341184616069et_nat
% 4.71/5.14 = ( ^ [A6: set_set_nat] :
% 4.71/5.14 ( collect_set_nat
% 4.71/5.14 @ ( uminus6401447641752708672_nat_o
% 4.71/5.14 @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A6 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % uminus_set_def
% 4.71/5.14 thf(fact_6923_uminus__set__def,axiom,
% 4.71/5.14 ( uminus3098529973357106300at_rat
% 4.71/5.14 = ( ^ [A6: set_set_nat_rat] :
% 4.71/5.14 ( collect_set_nat_rat
% 4.71/5.14 @ ( uminus6216118484121566985_rat_o
% 4.71/5.14 @ ^ [X3: set_nat_rat] : ( member_set_nat_rat @ X3 @ A6 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % uminus_set_def
% 4.71/5.14 thf(fact_6924_uminus__set__def,axiom,
% 4.71/5.14 ( uminus5710092332889474511et_nat
% 4.71/5.14 = ( ^ [A6: set_nat] :
% 4.71/5.14 ( collect_nat
% 4.71/5.14 @ ( uminus_uminus_nat_o
% 4.71/5.14 @ ^ [X3: nat] : ( member_nat @ X3 @ A6 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % uminus_set_def
% 4.71/5.14 thf(fact_6925_uminus__set__def,axiom,
% 4.71/5.14 ( uminus1532241313380277803et_int
% 4.71/5.14 = ( ^ [A6: set_int] :
% 4.71/5.14 ( collect_int
% 4.71/5.14 @ ( uminus_uminus_int_o
% 4.71/5.14 @ ^ [X3: int] : ( member_int @ X3 @ A6 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % uminus_set_def
% 4.71/5.14 thf(fact_6926_uminus__set__def,axiom,
% 4.71/5.14 ( uminus6988975074191911878at_rat
% 4.71/5.14 = ( ^ [A6: set_nat_rat] :
% 4.71/5.14 ( collect_nat_rat
% 4.71/5.14 @ ( uminus8974390361584276543_rat_o
% 4.71/5.14 @ ^ [X3: nat > rat] : ( member_nat_rat @ X3 @ A6 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % uminus_set_def
% 4.71/5.14 thf(fact_6927_Collect__neg__eq,axiom,
% 4.71/5.14 ! [P: set_nat > $o] :
% 4.71/5.14 ( ( collect_set_nat
% 4.71/5.14 @ ^ [X3: set_nat] :
% 4.71/5.14 ~ ( P @ X3 ) )
% 4.71/5.14 = ( uminus613421341184616069et_nat @ ( collect_set_nat @ P ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_neg_eq
% 4.71/5.14 thf(fact_6928_Collect__neg__eq,axiom,
% 4.71/5.14 ! [P: set_nat_rat > $o] :
% 4.71/5.14 ( ( collect_set_nat_rat
% 4.71/5.14 @ ^ [X3: set_nat_rat] :
% 4.71/5.14 ~ ( P @ X3 ) )
% 4.71/5.14 = ( uminus3098529973357106300at_rat @ ( collect_set_nat_rat @ P ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_neg_eq
% 4.71/5.14 thf(fact_6929_Collect__neg__eq,axiom,
% 4.71/5.14 ! [P: nat > $o] :
% 4.71/5.14 ( ( collect_nat
% 4.71/5.14 @ ^ [X3: nat] :
% 4.71/5.14 ~ ( P @ X3 ) )
% 4.71/5.14 = ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_neg_eq
% 4.71/5.14 thf(fact_6930_Collect__neg__eq,axiom,
% 4.71/5.14 ! [P: int > $o] :
% 4.71/5.14 ( ( collect_int
% 4.71/5.14 @ ^ [X3: int] :
% 4.71/5.14 ~ ( P @ X3 ) )
% 4.71/5.14 = ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_neg_eq
% 4.71/5.14 thf(fact_6931_Collect__neg__eq,axiom,
% 4.71/5.14 ! [P: ( nat > rat ) > $o] :
% 4.71/5.14 ( ( collect_nat_rat
% 4.71/5.14 @ ^ [X3: nat > rat] :
% 4.71/5.14 ~ ( P @ X3 ) )
% 4.71/5.14 = ( uminus6988975074191911878at_rat @ ( collect_nat_rat @ P ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Collect_neg_eq
% 4.71/5.14 thf(fact_6932_Compl__eq,axiom,
% 4.71/5.14 ( uminus_uminus_set_o
% 4.71/5.14 = ( ^ [A6: set_o] :
% 4.71/5.14 ( collect_o
% 4.71/5.14 @ ^ [X3: $o] :
% 4.71/5.14 ~ ( member_o @ X3 @ A6 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Compl_eq
% 4.71/5.14 thf(fact_6933_Compl__eq,axiom,
% 4.71/5.14 ( uminus613421341184616069et_nat
% 4.71/5.14 = ( ^ [A6: set_set_nat] :
% 4.71/5.14 ( collect_set_nat
% 4.71/5.14 @ ^ [X3: set_nat] :
% 4.71/5.14 ~ ( member_set_nat @ X3 @ A6 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Compl_eq
% 4.71/5.14 thf(fact_6934_Compl__eq,axiom,
% 4.71/5.14 ( uminus3098529973357106300at_rat
% 4.71/5.14 = ( ^ [A6: set_set_nat_rat] :
% 4.71/5.14 ( collect_set_nat_rat
% 4.71/5.14 @ ^ [X3: set_nat_rat] :
% 4.71/5.14 ~ ( member_set_nat_rat @ X3 @ A6 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Compl_eq
% 4.71/5.14 thf(fact_6935_Compl__eq,axiom,
% 4.71/5.14 ( uminus5710092332889474511et_nat
% 4.71/5.14 = ( ^ [A6: set_nat] :
% 4.71/5.14 ( collect_nat
% 4.71/5.14 @ ^ [X3: nat] :
% 4.71/5.14 ~ ( member_nat @ X3 @ A6 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Compl_eq
% 4.71/5.14 thf(fact_6936_Compl__eq,axiom,
% 4.71/5.14 ( uminus1532241313380277803et_int
% 4.71/5.14 = ( ^ [A6: set_int] :
% 4.71/5.14 ( collect_int
% 4.71/5.14 @ ^ [X3: int] :
% 4.71/5.14 ~ ( member_int @ X3 @ A6 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Compl_eq
% 4.71/5.14 thf(fact_6937_Compl__eq,axiom,
% 4.71/5.14 ( uminus6988975074191911878at_rat
% 4.71/5.14 = ( ^ [A6: set_nat_rat] :
% 4.71/5.14 ( collect_nat_rat
% 4.71/5.14 @ ^ [X3: nat > rat] :
% 4.71/5.14 ~ ( member_nat_rat @ X3 @ A6 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % Compl_eq
% 4.71/5.14 thf(fact_6938_not__finite__existsD,axiom,
% 4.71/5.14 ! [P: set_nat > $o] :
% 4.71/5.14 ( ~ ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 4.71/5.14 => ? [X_1: set_nat] : ( P @ X_1 ) ) ).
% 4.71/5.14
% 4.71/5.14 % not_finite_existsD
% 4.71/5.14 thf(fact_6939_not__finite__existsD,axiom,
% 4.71/5.14 ! [P: set_nat_rat > $o] :
% 4.71/5.14 ( ~ ( finite6430367030675640852at_rat @ ( collect_set_nat_rat @ P ) )
% 4.71/5.14 => ? [X_1: set_nat_rat] : ( P @ X_1 ) ) ).
% 4.71/5.14
% 4.71/5.14 % not_finite_existsD
% 4.71/5.14 thf(fact_6940_not__finite__existsD,axiom,
% 4.71/5.14 ! [P: ( nat > rat ) > $o] :
% 4.71/5.14 ( ~ ( finite7830837933032798814at_rat @ ( collect_nat_rat @ P ) )
% 4.71/5.14 => ? [X_1: nat > rat] : ( P @ X_1 ) ) ).
% 4.71/5.14
% 4.71/5.14 % not_finite_existsD
% 4.71/5.14 thf(fact_6941_not__finite__existsD,axiom,
% 4.71/5.14 ! [P: nat > $o] :
% 4.71/5.14 ( ~ ( finite_finite_nat @ ( collect_nat @ P ) )
% 4.71/5.14 => ? [X_1: nat] : ( P @ X_1 ) ) ).
% 4.71/5.14
% 4.71/5.14 % not_finite_existsD
% 4.71/5.14 thf(fact_6942_not__finite__existsD,axiom,
% 4.71/5.14 ! [P: int > $o] :
% 4.71/5.14 ( ~ ( finite_finite_int @ ( collect_int @ P ) )
% 4.71/5.14 => ? [X_1: int] : ( P @ X_1 ) ) ).
% 4.71/5.14
% 4.71/5.14 % not_finite_existsD
% 4.71/5.14 thf(fact_6943_not__finite__existsD,axiom,
% 4.71/5.14 ! [P: complex > $o] :
% 4.71/5.14 ( ~ ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 4.71/5.14 => ? [X_1: complex] : ( P @ X_1 ) ) ).
% 4.71/5.14
% 4.71/5.14 % not_finite_existsD
% 4.71/5.14 thf(fact_6944_not__finite__existsD,axiom,
% 4.71/5.14 ! [P: product_prod_nat_nat > $o] :
% 4.71/5.14 ( ~ ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ P ) )
% 4.71/5.14 => ? [X_1: product_prod_nat_nat] : ( P @ X_1 ) ) ).
% 4.71/5.14
% 4.71/5.14 % not_finite_existsD
% 4.71/5.14 thf(fact_6945_not__finite__existsD,axiom,
% 4.71/5.14 ! [P: extended_enat > $o] :
% 4.71/5.14 ( ~ ( finite4001608067531595151d_enat @ ( collec4429806609662206161d_enat @ P ) )
% 4.71/5.14 => ? [X_1: extended_enat] : ( P @ X_1 ) ) ).
% 4.71/5.14
% 4.71/5.14 % not_finite_existsD
% 4.71/5.14 thf(fact_6946_pigeonhole__infinite__rel,axiom,
% 4.71/5.14 ! [A2: set_o,B2: set_nat,R: $o > nat > $o] :
% 4.71/5.14 ( ~ ( finite_finite_o @ A2 )
% 4.71/5.14 => ( ( finite_finite_nat @ B2 )
% 4.71/5.14 => ( ! [X4: $o] :
% 4.71/5.14 ( ( member_o @ X4 @ A2 )
% 4.71/5.14 => ? [Xa: nat] :
% 4.71/5.14 ( ( member_nat @ Xa @ B2 )
% 4.71/5.14 & ( R @ X4 @ Xa ) ) )
% 4.71/5.14 => ? [X4: nat] :
% 4.71/5.14 ( ( member_nat @ X4 @ B2 )
% 4.71/5.14 & ~ ( finite_finite_o
% 4.71/5.14 @ ( collect_o
% 4.71/5.14 @ ^ [A4: $o] :
% 4.71/5.14 ( ( member_o @ A4 @ A2 )
% 4.71/5.14 & ( R @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % pigeonhole_infinite_rel
% 4.71/5.14 thf(fact_6947_pigeonhole__infinite__rel,axiom,
% 4.71/5.14 ! [A2: set_o,B2: set_int,R: $o > int > $o] :
% 4.71/5.14 ( ~ ( finite_finite_o @ A2 )
% 4.71/5.14 => ( ( finite_finite_int @ B2 )
% 4.71/5.14 => ( ! [X4: $o] :
% 4.71/5.14 ( ( member_o @ X4 @ A2 )
% 4.71/5.14 => ? [Xa: int] :
% 4.71/5.14 ( ( member_int @ Xa @ B2 )
% 4.71/5.14 & ( R @ X4 @ Xa ) ) )
% 4.71/5.14 => ? [X4: int] :
% 4.71/5.14 ( ( member_int @ X4 @ B2 )
% 4.71/5.14 & ~ ( finite_finite_o
% 4.71/5.14 @ ( collect_o
% 4.71/5.14 @ ^ [A4: $o] :
% 4.71/5.14 ( ( member_o @ A4 @ A2 )
% 4.71/5.14 & ( R @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % pigeonhole_infinite_rel
% 4.71/5.14 thf(fact_6948_pigeonhole__infinite__rel,axiom,
% 4.71/5.14 ! [A2: set_o,B2: set_complex,R: $o > complex > $o] :
% 4.71/5.14 ( ~ ( finite_finite_o @ A2 )
% 4.71/5.14 => ( ( finite3207457112153483333omplex @ B2 )
% 4.71/5.14 => ( ! [X4: $o] :
% 4.71/5.14 ( ( member_o @ X4 @ A2 )
% 4.71/5.14 => ? [Xa: complex] :
% 4.71/5.14 ( ( member_complex @ Xa @ B2 )
% 4.71/5.14 & ( R @ X4 @ Xa ) ) )
% 4.71/5.14 => ? [X4: complex] :
% 4.71/5.14 ( ( member_complex @ X4 @ B2 )
% 4.71/5.14 & ~ ( finite_finite_o
% 4.71/5.14 @ ( collect_o
% 4.71/5.14 @ ^ [A4: $o] :
% 4.71/5.14 ( ( member_o @ A4 @ A2 )
% 4.71/5.14 & ( R @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % pigeonhole_infinite_rel
% 4.71/5.14 thf(fact_6949_pigeonhole__infinite__rel,axiom,
% 4.71/5.14 ! [A2: set_o,B2: set_Extended_enat,R: $o > extended_enat > $o] :
% 4.71/5.14 ( ~ ( finite_finite_o @ A2 )
% 4.71/5.14 => ( ( finite4001608067531595151d_enat @ B2 )
% 4.71/5.14 => ( ! [X4: $o] :
% 4.71/5.14 ( ( member_o @ X4 @ A2 )
% 4.71/5.14 => ? [Xa: extended_enat] :
% 4.71/5.14 ( ( member_Extended_enat @ Xa @ B2 )
% 4.71/5.14 & ( R @ X4 @ Xa ) ) )
% 4.71/5.14 => ? [X4: extended_enat] :
% 4.71/5.14 ( ( member_Extended_enat @ X4 @ B2 )
% 4.71/5.14 & ~ ( finite_finite_o
% 4.71/5.14 @ ( collect_o
% 4.71/5.14 @ ^ [A4: $o] :
% 4.71/5.14 ( ( member_o @ A4 @ A2 )
% 4.71/5.14 & ( R @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % pigeonhole_infinite_rel
% 4.71/5.14 thf(fact_6950_pigeonhole__infinite__rel,axiom,
% 4.71/5.14 ! [A2: set_nat,B2: set_nat,R: nat > nat > $o] :
% 4.71/5.14 ( ~ ( finite_finite_nat @ A2 )
% 4.71/5.14 => ( ( finite_finite_nat @ B2 )
% 4.71/5.14 => ( ! [X4: nat] :
% 4.71/5.14 ( ( member_nat @ X4 @ A2 )
% 4.71/5.14 => ? [Xa: nat] :
% 4.71/5.14 ( ( member_nat @ Xa @ B2 )
% 4.71/5.14 & ( R @ X4 @ Xa ) ) )
% 4.71/5.14 => ? [X4: nat] :
% 4.71/5.14 ( ( member_nat @ X4 @ B2 )
% 4.71/5.14 & ~ ( finite_finite_nat
% 4.71/5.14 @ ( collect_nat
% 4.71/5.14 @ ^ [A4: nat] :
% 4.71/5.14 ( ( member_nat @ A4 @ A2 )
% 4.71/5.14 & ( R @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % pigeonhole_infinite_rel
% 4.71/5.14 thf(fact_6951_pigeonhole__infinite__rel,axiom,
% 4.71/5.14 ! [A2: set_nat,B2: set_int,R: nat > int > $o] :
% 4.71/5.14 ( ~ ( finite_finite_nat @ A2 )
% 4.71/5.14 => ( ( finite_finite_int @ B2 )
% 4.71/5.14 => ( ! [X4: nat] :
% 4.71/5.14 ( ( member_nat @ X4 @ A2 )
% 4.71/5.14 => ? [Xa: int] :
% 4.71/5.14 ( ( member_int @ Xa @ B2 )
% 4.71/5.14 & ( R @ X4 @ Xa ) ) )
% 4.71/5.14 => ? [X4: int] :
% 4.71/5.14 ( ( member_int @ X4 @ B2 )
% 4.71/5.14 & ~ ( finite_finite_nat
% 4.71/5.14 @ ( collect_nat
% 4.71/5.14 @ ^ [A4: nat] :
% 4.71/5.14 ( ( member_nat @ A4 @ A2 )
% 4.71/5.14 & ( R @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % pigeonhole_infinite_rel
% 4.71/5.14 thf(fact_6952_pigeonhole__infinite__rel,axiom,
% 4.71/5.14 ! [A2: set_nat,B2: set_complex,R: nat > complex > $o] :
% 4.71/5.14 ( ~ ( finite_finite_nat @ A2 )
% 4.71/5.14 => ( ( finite3207457112153483333omplex @ B2 )
% 4.71/5.14 => ( ! [X4: nat] :
% 4.71/5.14 ( ( member_nat @ X4 @ A2 )
% 4.71/5.14 => ? [Xa: complex] :
% 4.71/5.14 ( ( member_complex @ Xa @ B2 )
% 4.71/5.14 & ( R @ X4 @ Xa ) ) )
% 4.71/5.14 => ? [X4: complex] :
% 4.71/5.14 ( ( member_complex @ X4 @ B2 )
% 4.71/5.14 & ~ ( finite_finite_nat
% 4.71/5.14 @ ( collect_nat
% 4.71/5.14 @ ^ [A4: nat] :
% 4.71/5.14 ( ( member_nat @ A4 @ A2 )
% 4.71/5.14 & ( R @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % pigeonhole_infinite_rel
% 4.71/5.14 thf(fact_6953_pigeonhole__infinite__rel,axiom,
% 4.71/5.14 ! [A2: set_nat,B2: set_Extended_enat,R: nat > extended_enat > $o] :
% 4.71/5.14 ( ~ ( finite_finite_nat @ A2 )
% 4.71/5.14 => ( ( finite4001608067531595151d_enat @ B2 )
% 4.71/5.14 => ( ! [X4: nat] :
% 4.71/5.14 ( ( member_nat @ X4 @ A2 )
% 4.71/5.14 => ? [Xa: extended_enat] :
% 4.71/5.14 ( ( member_Extended_enat @ Xa @ B2 )
% 4.71/5.14 & ( R @ X4 @ Xa ) ) )
% 4.71/5.14 => ? [X4: extended_enat] :
% 4.71/5.14 ( ( member_Extended_enat @ X4 @ B2 )
% 4.71/5.14 & ~ ( finite_finite_nat
% 4.71/5.14 @ ( collect_nat
% 4.71/5.14 @ ^ [A4: nat] :
% 4.71/5.14 ( ( member_nat @ A4 @ A2 )
% 4.71/5.14 & ( R @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % pigeonhole_infinite_rel
% 4.71/5.14 thf(fact_6954_pigeonhole__infinite__rel,axiom,
% 4.71/5.14 ! [A2: set_int,B2: set_nat,R: int > nat > $o] :
% 4.71/5.14 ( ~ ( finite_finite_int @ A2 )
% 4.71/5.14 => ( ( finite_finite_nat @ B2 )
% 4.71/5.14 => ( ! [X4: int] :
% 4.71/5.14 ( ( member_int @ X4 @ A2 )
% 4.71/5.14 => ? [Xa: nat] :
% 4.71/5.14 ( ( member_nat @ Xa @ B2 )
% 4.71/5.14 & ( R @ X4 @ Xa ) ) )
% 4.71/5.14 => ? [X4: nat] :
% 4.71/5.14 ( ( member_nat @ X4 @ B2 )
% 4.71/5.14 & ~ ( finite_finite_int
% 4.71/5.14 @ ( collect_int
% 4.71/5.14 @ ^ [A4: int] :
% 4.71/5.14 ( ( member_int @ A4 @ A2 )
% 4.71/5.14 & ( R @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % pigeonhole_infinite_rel
% 4.71/5.14 thf(fact_6955_pigeonhole__infinite__rel,axiom,
% 4.71/5.14 ! [A2: set_int,B2: set_int,R: int > int > $o] :
% 4.71/5.14 ( ~ ( finite_finite_int @ A2 )
% 4.71/5.14 => ( ( finite_finite_int @ B2 )
% 4.71/5.14 => ( ! [X4: int] :
% 4.71/5.14 ( ( member_int @ X4 @ A2 )
% 4.71/5.14 => ? [Xa: int] :
% 4.71/5.14 ( ( member_int @ Xa @ B2 )
% 4.71/5.14 & ( R @ X4 @ Xa ) ) )
% 4.71/5.14 => ? [X4: int] :
% 4.71/5.14 ( ( member_int @ X4 @ B2 )
% 4.71/5.14 & ~ ( finite_finite_int
% 4.71/5.14 @ ( collect_int
% 4.71/5.14 @ ^ [A4: int] :
% 4.71/5.14 ( ( member_int @ A4 @ A2 )
% 4.71/5.14 & ( R @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % pigeonhole_infinite_rel
% 4.71/5.14 thf(fact_6956_finite__less__ub,axiom,
% 4.71/5.14 ! [F: nat > nat,U: nat] :
% 4.71/5.14 ( ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( F @ N2 ) )
% 4.71/5.14 => ( finite_finite_nat
% 4.71/5.14 @ ( collect_nat
% 4.71/5.14 @ ^ [N4: nat] : ( ord_less_eq_nat @ ( F @ N4 ) @ U ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_less_ub
% 4.71/5.14 thf(fact_6957_finite__M__bounded__by__nat,axiom,
% 4.71/5.14 ! [P: nat > $o,I: nat] :
% 4.71/5.14 ( finite_finite_nat
% 4.71/5.14 @ ( collect_nat
% 4.71/5.14 @ ^ [K3: nat] :
% 4.71/5.14 ( ( P @ K3 )
% 4.71/5.14 & ( ord_less_nat @ K3 @ I ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % finite_M_bounded_by_nat
% 4.71/5.14 thf(fact_6958_minus__set__def,axiom,
% 4.71/5.14 ( minus_minus_set_o
% 4.71/5.14 = ( ^ [A6: set_o,B6: set_o] :
% 4.71/5.14 ( collect_o
% 4.71/5.14 @ ( minus_minus_o_o
% 4.71/5.14 @ ^ [X3: $o] : ( member_o @ X3 @ A6 )
% 4.71/5.14 @ ^ [X3: $o] : ( member_o @ X3 @ B6 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % minus_set_def
% 4.71/5.14 thf(fact_6959_minus__set__def,axiom,
% 4.71/5.14 ( minus_2163939370556025621et_nat
% 4.71/5.14 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 4.71/5.14 ( collect_set_nat
% 4.71/5.14 @ ( minus_6910147592129066416_nat_o
% 4.71/5.14 @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A6 )
% 4.71/5.14 @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ B6 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % minus_set_def
% 4.71/5.14 thf(fact_6960_minus__set__def,axiom,
% 4.71/5.14 ( minus_1626877696091177228at_rat
% 4.71/5.14 = ( ^ [A6: set_set_nat_rat,B6: set_set_nat_rat] :
% 4.71/5.14 ( collect_set_nat_rat
% 4.71/5.14 @ ( minus_7664381017404958329_rat_o
% 4.71/5.14 @ ^ [X3: set_nat_rat] : ( member_set_nat_rat @ X3 @ A6 )
% 4.71/5.14 @ ^ [X3: set_nat_rat] : ( member_set_nat_rat @ X3 @ B6 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % minus_set_def
% 4.71/5.14 thf(fact_6961_minus__set__def,axiom,
% 4.71/5.14 ( minus_minus_set_int
% 4.71/5.14 = ( ^ [A6: set_int,B6: set_int] :
% 4.71/5.14 ( collect_int
% 4.71/5.14 @ ( minus_minus_int_o
% 4.71/5.14 @ ^ [X3: int] : ( member_int @ X3 @ A6 )
% 4.71/5.14 @ ^ [X3: int] : ( member_int @ X3 @ B6 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % minus_set_def
% 4.71/5.14 thf(fact_6962_minus__set__def,axiom,
% 4.71/5.14 ( minus_1741603841019369558at_rat
% 4.71/5.14 = ( ^ [A6: set_nat_rat,B6: set_nat_rat] :
% 4.71/5.14 ( collect_nat_rat
% 4.71/5.14 @ ( minus_8641456556474268591_rat_o
% 4.71/5.14 @ ^ [X3: nat > rat] : ( member_nat_rat @ X3 @ A6 )
% 4.71/5.14 @ ^ [X3: nat > rat] : ( member_nat_rat @ X3 @ B6 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % minus_set_def
% 4.71/5.14 thf(fact_6963_minus__set__def,axiom,
% 4.71/5.14 ( minus_minus_set_nat
% 4.71/5.14 = ( ^ [A6: set_nat,B6: set_nat] :
% 4.71/5.14 ( collect_nat
% 4.71/5.14 @ ( minus_minus_nat_o
% 4.71/5.14 @ ^ [X3: nat] : ( member_nat @ X3 @ A6 )
% 4.71/5.14 @ ^ [X3: nat] : ( member_nat @ X3 @ B6 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % minus_set_def
% 4.71/5.14 thf(fact_6964_set__diff__eq,axiom,
% 4.71/5.14 ( minus_minus_set_o
% 4.71/5.14 = ( ^ [A6: set_o,B6: set_o] :
% 4.71/5.14 ( collect_o
% 4.71/5.14 @ ^ [X3: $o] :
% 4.71/5.14 ( ( member_o @ X3 @ A6 )
% 4.71/5.14 & ~ ( member_o @ X3 @ B6 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % set_diff_eq
% 4.71/5.14 thf(fact_6965_set__diff__eq,axiom,
% 4.71/5.14 ( minus_2163939370556025621et_nat
% 4.71/5.14 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 4.71/5.14 ( collect_set_nat
% 4.71/5.14 @ ^ [X3: set_nat] :
% 4.71/5.14 ( ( member_set_nat @ X3 @ A6 )
% 4.71/5.14 & ~ ( member_set_nat @ X3 @ B6 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % set_diff_eq
% 4.71/5.14 thf(fact_6966_set__diff__eq,axiom,
% 4.71/5.14 ( minus_1626877696091177228at_rat
% 4.71/5.14 = ( ^ [A6: set_set_nat_rat,B6: set_set_nat_rat] :
% 4.71/5.14 ( collect_set_nat_rat
% 4.71/5.14 @ ^ [X3: set_nat_rat] :
% 4.71/5.14 ( ( member_set_nat_rat @ X3 @ A6 )
% 4.71/5.14 & ~ ( member_set_nat_rat @ X3 @ B6 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % set_diff_eq
% 4.71/5.14 thf(fact_6967_set__diff__eq,axiom,
% 4.71/5.14 ( minus_minus_set_int
% 4.71/5.14 = ( ^ [A6: set_int,B6: set_int] :
% 4.71/5.14 ( collect_int
% 4.71/5.14 @ ^ [X3: int] :
% 4.71/5.14 ( ( member_int @ X3 @ A6 )
% 4.71/5.14 & ~ ( member_int @ X3 @ B6 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % set_diff_eq
% 4.71/5.14 thf(fact_6968_set__diff__eq,axiom,
% 4.71/5.14 ( minus_1741603841019369558at_rat
% 4.71/5.14 = ( ^ [A6: set_nat_rat,B6: set_nat_rat] :
% 4.71/5.14 ( collect_nat_rat
% 4.71/5.14 @ ^ [X3: nat > rat] :
% 4.71/5.14 ( ( member_nat_rat @ X3 @ A6 )
% 4.71/5.14 & ~ ( member_nat_rat @ X3 @ B6 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % set_diff_eq
% 4.71/5.14 thf(fact_6969_set__diff__eq,axiom,
% 4.71/5.14 ( minus_minus_set_nat
% 4.71/5.14 = ( ^ [A6: set_nat,B6: set_nat] :
% 4.71/5.14 ( collect_nat
% 4.71/5.14 @ ^ [X3: nat] :
% 4.71/5.14 ( ( member_nat @ X3 @ A6 )
% 4.71/5.14 & ~ ( member_nat @ X3 @ B6 ) ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % set_diff_eq
% 4.71/5.14 thf(fact_6970_card__roots__unity__eq,axiom,
% 4.71/5.14 ! [N: nat] :
% 4.71/5.14 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.14 => ( ( finite_card_complex
% 4.71/5.14 @ ( collect_complex
% 4.71/5.14 @ ^ [Z2: complex] :
% 4.71/5.14 ( ( power_power_complex @ Z2 @ N )
% 4.71/5.14 = one_one_complex ) ) )
% 4.71/5.14 = N ) ) ).
% 4.71/5.14
% 4.71/5.14 % card_roots_unity_eq
% 4.71/5.14 thf(fact_6971_card__nth__roots,axiom,
% 4.71/5.14 ! [C: complex,N: nat] :
% 4.71/5.14 ( ( C != zero_zero_complex )
% 4.71/5.14 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.71/5.14 => ( ( finite_card_complex
% 4.71/5.14 @ ( collect_complex
% 4.71/5.14 @ ^ [Z2: complex] :
% 4.71/5.14 ( ( power_power_complex @ Z2 @ N )
% 4.71/5.14 = C ) ) )
% 4.71/5.14 = N ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % card_nth_roots
% 4.71/5.14 thf(fact_6972_lambda__zero,axiom,
% 4.71/5.14 ( ( ^ [H3: real] : zero_zero_real )
% 4.71/5.14 = ( times_times_real @ zero_zero_real ) ) ).
% 4.71/5.14
% 4.71/5.14 % lambda_zero
% 4.71/5.14 thf(fact_6973_lambda__zero,axiom,
% 4.71/5.14 ( ( ^ [H3: rat] : zero_zero_rat )
% 4.71/5.14 = ( times_times_rat @ zero_zero_rat ) ) ).
% 4.71/5.14
% 4.71/5.14 % lambda_zero
% 4.71/5.14 thf(fact_6974_lambda__zero,axiom,
% 4.71/5.14 ( ( ^ [H3: nat] : zero_zero_nat )
% 4.71/5.14 = ( times_times_nat @ zero_zero_nat ) ) ).
% 4.71/5.14
% 4.71/5.14 % lambda_zero
% 4.71/5.14 thf(fact_6975_lambda__zero,axiom,
% 4.71/5.14 ( ( ^ [H3: int] : zero_zero_int )
% 4.71/5.14 = ( times_times_int @ zero_zero_int ) ) ).
% 4.71/5.14
% 4.71/5.14 % lambda_zero
% 4.71/5.14 thf(fact_6976_set__vebt__def,axiom,
% 4.71/5.14 ( vEBT_set_vebt
% 4.71/5.14 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 4.71/5.14
% 4.71/5.14 % set_vebt_def
% 4.71/5.14 thf(fact_6977_numeral__code_I2_J,axiom,
% 4.71/5.14 ! [N: num] :
% 4.71/5.14 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 4.71/5.15 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % numeral_code(2)
% 4.71/5.15 thf(fact_6978_numeral__code_I2_J,axiom,
% 4.71/5.15 ! [N: num] :
% 4.71/5.15 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 4.71/5.15 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % numeral_code(2)
% 4.71/5.15 thf(fact_6979_numeral__code_I2_J,axiom,
% 4.71/5.15 ! [N: num] :
% 4.71/5.15 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 4.71/5.15 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % numeral_code(2)
% 4.71/5.15 thf(fact_6980_numeral__code_I2_J,axiom,
% 4.71/5.15 ! [N: num] :
% 4.71/5.15 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 4.71/5.15 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % numeral_code(2)
% 4.71/5.15 thf(fact_6981_numeral__code_I2_J,axiom,
% 4.71/5.15 ! [N: num] :
% 4.71/5.15 ( ( numera1916890842035813515d_enat @ ( bit0 @ N ) )
% 4.71/5.15 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N ) @ ( numera1916890842035813515d_enat @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % numeral_code(2)
% 4.71/5.15 thf(fact_6982_numeral__code_I2_J,axiom,
% 4.71/5.15 ! [N: num] :
% 4.71/5.15 ( ( numera6620942414471956472nteger @ ( bit0 @ N ) )
% 4.71/5.15 = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % numeral_code(2)
% 4.71/5.15 thf(fact_6983_finite__int__segment,axiom,
% 4.71/5.15 ! [A: rat,B: rat] :
% 4.71/5.15 ( finite_finite_rat
% 4.71/5.15 @ ( collect_rat
% 4.71/5.15 @ ^ [X3: rat] :
% 4.71/5.15 ( ( member_rat @ X3 @ ring_1_Ints_rat )
% 4.71/5.15 & ( ord_less_eq_rat @ A @ X3 )
% 4.71/5.15 & ( ord_less_eq_rat @ X3 @ B ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % finite_int_segment
% 4.71/5.15 thf(fact_6984_nat__less__as__int,axiom,
% 4.71/5.15 ( ord_less_nat
% 4.71/5.15 = ( ^ [A4: nat,B4: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % nat_less_as_int
% 4.71/5.15 thf(fact_6985_nat__leq__as__int,axiom,
% 4.71/5.15 ( ord_less_eq_nat
% 4.71/5.15 = ( ^ [A4: nat,B4: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % nat_leq_as_int
% 4.71/5.15 thf(fact_6986_finite__abs__int__segment,axiom,
% 4.71/5.15 ! [A: real] :
% 4.71/5.15 ( finite_finite_real
% 4.71/5.15 @ ( collect_real
% 4.71/5.15 @ ^ [K3: real] :
% 4.71/5.15 ( ( member_real @ K3 @ ring_1_Ints_real )
% 4.71/5.15 & ( ord_less_eq_real @ ( abs_abs_real @ K3 ) @ A ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % finite_abs_int_segment
% 4.71/5.15 thf(fact_6987_finite__abs__int__segment,axiom,
% 4.71/5.15 ! [A: rat] :
% 4.71/5.15 ( finite_finite_rat
% 4.71/5.15 @ ( collect_rat
% 4.71/5.15 @ ^ [K3: rat] :
% 4.71/5.15 ( ( member_rat @ K3 @ ring_1_Ints_rat )
% 4.71/5.15 & ( ord_less_eq_rat @ ( abs_abs_rat @ K3 ) @ A ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % finite_abs_int_segment
% 4.71/5.15 thf(fact_6988_card__less__Suc2,axiom,
% 4.71/5.15 ! [M5: set_nat,I: nat] :
% 4.71/5.15 ( ~ ( member_nat @ zero_zero_nat @ M5 )
% 4.71/5.15 => ( ( finite_card_nat
% 4.71/5.15 @ ( collect_nat
% 4.71/5.15 @ ^ [K3: nat] :
% 4.71/5.15 ( ( member_nat @ ( suc @ K3 ) @ M5 )
% 4.71/5.15 & ( ord_less_nat @ K3 @ I ) ) ) )
% 4.71/5.15 = ( finite_card_nat
% 4.71/5.15 @ ( collect_nat
% 4.71/5.15 @ ^ [K3: nat] :
% 4.71/5.15 ( ( member_nat @ K3 @ M5 )
% 4.71/5.15 & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % card_less_Suc2
% 4.71/5.15 thf(fact_6989_card__less__Suc,axiom,
% 4.71/5.15 ! [M5: set_nat,I: nat] :
% 4.71/5.15 ( ( member_nat @ zero_zero_nat @ M5 )
% 4.71/5.15 => ( ( suc
% 4.71/5.15 @ ( finite_card_nat
% 4.71/5.15 @ ( collect_nat
% 4.71/5.15 @ ^ [K3: nat] :
% 4.71/5.15 ( ( member_nat @ ( suc @ K3 ) @ M5 )
% 4.71/5.15 & ( ord_less_nat @ K3 @ I ) ) ) ) )
% 4.71/5.15 = ( finite_card_nat
% 4.71/5.15 @ ( collect_nat
% 4.71/5.15 @ ^ [K3: nat] :
% 4.71/5.15 ( ( member_nat @ K3 @ M5 )
% 4.71/5.15 & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % card_less_Suc
% 4.71/5.15 thf(fact_6990_card__less,axiom,
% 4.71/5.15 ! [M5: set_nat,I: nat] :
% 4.71/5.15 ( ( member_nat @ zero_zero_nat @ M5 )
% 4.71/5.15 => ( ( finite_card_nat
% 4.71/5.15 @ ( collect_nat
% 4.71/5.15 @ ^ [K3: nat] :
% 4.71/5.15 ( ( member_nat @ K3 @ M5 )
% 4.71/5.15 & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) )
% 4.71/5.15 != zero_zero_nat ) ) ).
% 4.71/5.15
% 4.71/5.15 % card_less
% 4.71/5.15 thf(fact_6991_list__update__code_I2_J,axiom,
% 4.71/5.15 ! [X: int,Xs: list_int,Y: int] :
% 4.71/5.15 ( ( list_update_int @ ( cons_int @ X @ Xs ) @ zero_zero_nat @ Y )
% 4.71/5.15 = ( cons_int @ Y @ Xs ) ) ).
% 4.71/5.15
% 4.71/5.15 % list_update_code(2)
% 4.71/5.15 thf(fact_6992_list__update__code_I2_J,axiom,
% 4.71/5.15 ! [X: nat,Xs: list_nat,Y: nat] :
% 4.71/5.15 ( ( list_update_nat @ ( cons_nat @ X @ Xs ) @ zero_zero_nat @ Y )
% 4.71/5.15 = ( cons_nat @ Y @ Xs ) ) ).
% 4.71/5.15
% 4.71/5.15 % list_update_code(2)
% 4.71/5.15 thf(fact_6993_list__update__code_I2_J,axiom,
% 4.71/5.15 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT,Y: vEBT_VEBT] :
% 4.71/5.15 ( ( list_u1324408373059187874T_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ zero_zero_nat @ Y )
% 4.71/5.15 = ( cons_VEBT_VEBT @ Y @ Xs ) ) ).
% 4.71/5.15
% 4.71/5.15 % list_update_code(2)
% 4.71/5.15 thf(fact_6994_set__update__subsetI,axiom,
% 4.71/5.15 ! [Xs: list_o,A2: set_o,X: $o,I: nat] :
% 4.71/5.15 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A2 )
% 4.71/5.15 => ( ( member_o @ X @ A2 )
% 4.71/5.15 => ( ord_less_eq_set_o @ ( set_o2 @ ( list_update_o @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % set_update_subsetI
% 4.71/5.15 thf(fact_6995_set__update__subsetI,axiom,
% 4.71/5.15 ! [Xs: list_set_nat,A2: set_set_nat,X: set_nat,I: nat] :
% 4.71/5.15 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ A2 )
% 4.71/5.15 => ( ( member_set_nat @ X @ A2 )
% 4.71/5.15 => ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ ( list_update_set_nat @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % set_update_subsetI
% 4.71/5.15 thf(fact_6996_set__update__subsetI,axiom,
% 4.71/5.15 ! [Xs: list_set_nat_rat,A2: set_set_nat_rat,X: set_nat_rat,I: nat] :
% 4.71/5.15 ( ( ord_le4375437777232675859at_rat @ ( set_set_nat_rat2 @ Xs ) @ A2 )
% 4.71/5.15 => ( ( member_set_nat_rat @ X @ A2 )
% 4.71/5.15 => ( ord_le4375437777232675859at_rat @ ( set_set_nat_rat2 @ ( list_u886106648575569423at_rat @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % set_update_subsetI
% 4.71/5.15 thf(fact_6997_set__update__subsetI,axiom,
% 4.71/5.15 ! [Xs: list_nat,A2: set_nat,X: nat,I: nat] :
% 4.71/5.15 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 4.71/5.15 => ( ( member_nat @ X @ A2 )
% 4.71/5.15 => ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % set_update_subsetI
% 4.71/5.15 thf(fact_6998_set__update__subsetI,axiom,
% 4.71/5.15 ! [Xs: list_VEBT_VEBT,A2: set_VEBT_VEBT,X: vEBT_VEBT,I: nat] :
% 4.71/5.15 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 4.71/5.15 => ( ( member_VEBT_VEBT @ X @ A2 )
% 4.71/5.15 => ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % set_update_subsetI
% 4.71/5.15 thf(fact_6999_set__update__subsetI,axiom,
% 4.71/5.15 ! [Xs: list_int,A2: set_int,X: int,I: nat] :
% 4.71/5.15 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 4.71/5.15 => ( ( member_int @ X @ A2 )
% 4.71/5.15 => ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % set_update_subsetI
% 4.71/5.15 thf(fact_7000_finite__roots__unity,axiom,
% 4.71/5.15 ! [N: nat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 4.71/5.15 => ( finite_finite_real
% 4.71/5.15 @ ( collect_real
% 4.71/5.15 @ ^ [Z2: real] :
% 4.71/5.15 ( ( power_power_real @ Z2 @ N )
% 4.71/5.15 = one_one_real ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % finite_roots_unity
% 4.71/5.15 thf(fact_7001_finite__roots__unity,axiom,
% 4.71/5.15 ! [N: nat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 4.71/5.15 => ( finite3207457112153483333omplex
% 4.71/5.15 @ ( collect_complex
% 4.71/5.15 @ ^ [Z2: complex] :
% 4.71/5.15 ( ( power_power_complex @ Z2 @ N )
% 4.71/5.15 = one_one_complex ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % finite_roots_unity
% 4.71/5.15 thf(fact_7002_card__roots__unity,axiom,
% 4.71/5.15 ! [N: nat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 4.71/5.15 => ( ord_less_eq_nat
% 4.71/5.15 @ ( finite_card_real
% 4.71/5.15 @ ( collect_real
% 4.71/5.15 @ ^ [Z2: real] :
% 4.71/5.15 ( ( power_power_real @ Z2 @ N )
% 4.71/5.15 = one_one_real ) ) )
% 4.71/5.15 @ N ) ) ).
% 4.71/5.15
% 4.71/5.15 % card_roots_unity
% 4.71/5.15 thf(fact_7003_card__roots__unity,axiom,
% 4.71/5.15 ! [N: nat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 4.71/5.15 => ( ord_less_eq_nat
% 4.71/5.15 @ ( finite_card_complex
% 4.71/5.15 @ ( collect_complex
% 4.71/5.15 @ ^ [Z2: complex] :
% 4.71/5.15 ( ( power_power_complex @ Z2 @ N )
% 4.71/5.15 = one_one_complex ) ) )
% 4.71/5.15 @ N ) ) ).
% 4.71/5.15
% 4.71/5.15 % card_roots_unity
% 4.71/5.15 thf(fact_7004_finite__lists__length__eq,axiom,
% 4.71/5.15 ! [A2: set_complex,N: nat] :
% 4.71/5.15 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.15 => ( finite8712137658972009173omplex
% 4.71/5.15 @ ( collect_list_complex
% 4.71/5.15 @ ^ [Xs2: list_complex] :
% 4.71/5.15 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A2 )
% 4.71/5.15 & ( ( size_s3451745648224563538omplex @ Xs2 )
% 4.71/5.15 = N ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % finite_lists_length_eq
% 4.71/5.15 thf(fact_7005_finite__lists__length__eq,axiom,
% 4.71/5.15 ! [A2: set_Pr1261947904930325089at_nat,N: nat] :
% 4.71/5.15 ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.15 => ( finite500796754983035824at_nat
% 4.71/5.15 @ ( collec3343600615725829874at_nat
% 4.71/5.15 @ ^ [Xs2: list_P6011104703257516679at_nat] :
% 4.71/5.15 ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs2 ) @ A2 )
% 4.71/5.15 & ( ( size_s5460976970255530739at_nat @ Xs2 )
% 4.71/5.15 = N ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % finite_lists_length_eq
% 4.71/5.15 thf(fact_7006_finite__lists__length__eq,axiom,
% 4.71/5.15 ! [A2: set_Extended_enat,N: nat] :
% 4.71/5.15 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.15 => ( finite1862508098717546133d_enat
% 4.71/5.15 @ ( collec8433460942617342167d_enat
% 4.71/5.15 @ ^ [Xs2: list_Extended_enat] :
% 4.71/5.15 ( ( ord_le7203529160286727270d_enat @ ( set_Extended_enat2 @ Xs2 ) @ A2 )
% 4.71/5.15 & ( ( size_s3941691890525107288d_enat @ Xs2 )
% 4.71/5.15 = N ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % finite_lists_length_eq
% 4.71/5.15 thf(fact_7007_finite__lists__length__eq,axiom,
% 4.71/5.15 ! [A2: set_VEBT_VEBT,N: nat] :
% 4.71/5.15 ( ( finite5795047828879050333T_VEBT @ A2 )
% 4.71/5.15 => ( finite3004134309566078307T_VEBT
% 4.71/5.15 @ ( collec5608196760682091941T_VEBT
% 4.71/5.15 @ ^ [Xs2: list_VEBT_VEBT] :
% 4.71/5.15 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A2 )
% 4.71/5.15 & ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 4.71/5.15 = N ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % finite_lists_length_eq
% 4.71/5.15 thf(fact_7008_finite__lists__length__eq,axiom,
% 4.71/5.15 ! [A2: set_nat,N: nat] :
% 4.71/5.15 ( ( finite_finite_nat @ A2 )
% 4.71/5.15 => ( finite8100373058378681591st_nat
% 4.71/5.15 @ ( collect_list_nat
% 4.71/5.15 @ ^ [Xs2: list_nat] :
% 4.71/5.15 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A2 )
% 4.71/5.15 & ( ( size_size_list_nat @ Xs2 )
% 4.71/5.15 = N ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % finite_lists_length_eq
% 4.71/5.15 thf(fact_7009_finite__lists__length__eq,axiom,
% 4.71/5.15 ! [A2: set_int,N: nat] :
% 4.71/5.15 ( ( finite_finite_int @ A2 )
% 4.71/5.15 => ( finite3922522038869484883st_int
% 4.71/5.15 @ ( collect_list_int
% 4.71/5.15 @ ^ [Xs2: list_int] :
% 4.71/5.15 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A2 )
% 4.71/5.15 & ( ( size_size_list_int @ Xs2 )
% 4.71/5.15 = N ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % finite_lists_length_eq
% 4.71/5.15 thf(fact_7010_card__lists__length__eq,axiom,
% 4.71/5.15 ! [A2: set_list_nat,N: nat] :
% 4.71/5.15 ( ( finite8100373058378681591st_nat @ A2 )
% 4.71/5.15 => ( ( finite7325466520557071688st_nat
% 4.71/5.15 @ ( collec5989764272469232197st_nat
% 4.71/5.15 @ ^ [Xs2: list_list_nat] :
% 4.71/5.15 ( ( ord_le6045566169113846134st_nat @ ( set_list_nat2 @ Xs2 ) @ A2 )
% 4.71/5.15 & ( ( size_s3023201423986296836st_nat @ Xs2 )
% 4.71/5.15 = N ) ) ) )
% 4.71/5.15 = ( power_power_nat @ ( finite_card_list_nat @ A2 ) @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % card_lists_length_eq
% 4.71/5.15 thf(fact_7011_card__lists__length__eq,axiom,
% 4.71/5.15 ! [A2: set_set_nat,N: nat] :
% 4.71/5.15 ( ( finite1152437895449049373et_nat @ A2 )
% 4.71/5.15 => ( ( finite5631907774883551598et_nat
% 4.71/5.15 @ ( collect_list_set_nat
% 4.71/5.15 @ ^ [Xs2: list_set_nat] :
% 4.71/5.15 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs2 ) @ A2 )
% 4.71/5.15 & ( ( size_s3254054031482475050et_nat @ Xs2 )
% 4.71/5.15 = N ) ) ) )
% 4.71/5.15 = ( power_power_nat @ ( finite_card_set_nat @ A2 ) @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % card_lists_length_eq
% 4.71/5.15 thf(fact_7012_card__lists__length__eq,axiom,
% 4.71/5.15 ! [A2: set_complex,N: nat] :
% 4.71/5.15 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.15 => ( ( finite5120063068150530198omplex
% 4.71/5.15 @ ( collect_list_complex
% 4.71/5.15 @ ^ [Xs2: list_complex] :
% 4.71/5.15 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A2 )
% 4.71/5.15 & ( ( size_s3451745648224563538omplex @ Xs2 )
% 4.71/5.15 = N ) ) ) )
% 4.71/5.15 = ( power_power_nat @ ( finite_card_complex @ A2 ) @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % card_lists_length_eq
% 4.71/5.15 thf(fact_7013_card__lists__length__eq,axiom,
% 4.71/5.15 ! [A2: set_Pr1261947904930325089at_nat,N: nat] :
% 4.71/5.15 ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.15 => ( ( finite249151656366948015at_nat
% 4.71/5.15 @ ( collec3343600615725829874at_nat
% 4.71/5.15 @ ^ [Xs2: list_P6011104703257516679at_nat] :
% 4.71/5.15 ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs2 ) @ A2 )
% 4.71/5.15 & ( ( size_s5460976970255530739at_nat @ Xs2 )
% 4.71/5.15 = N ) ) ) )
% 4.71/5.15 = ( power_power_nat @ ( finite711546835091564841at_nat @ A2 ) @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % card_lists_length_eq
% 4.71/5.15 thf(fact_7014_card__lists__length__eq,axiom,
% 4.71/5.15 ! [A2: set_Extended_enat,N: nat] :
% 4.71/5.15 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.15 => ( ( finite7441382602597825044d_enat
% 4.71/5.15 @ ( collec8433460942617342167d_enat
% 4.71/5.15 @ ^ [Xs2: list_Extended_enat] :
% 4.71/5.15 ( ( ord_le7203529160286727270d_enat @ ( set_Extended_enat2 @ Xs2 ) @ A2 )
% 4.71/5.15 & ( ( size_s3941691890525107288d_enat @ Xs2 )
% 4.71/5.15 = N ) ) ) )
% 4.71/5.15 = ( power_power_nat @ ( finite121521170596916366d_enat @ A2 ) @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % card_lists_length_eq
% 4.71/5.15 thf(fact_7015_card__lists__length__eq,axiom,
% 4.71/5.15 ! [A2: set_VEBT_VEBT,N: nat] :
% 4.71/5.15 ( ( finite5795047828879050333T_VEBT @ A2 )
% 4.71/5.15 => ( ( finite5915292604075114978T_VEBT
% 4.71/5.15 @ ( collec5608196760682091941T_VEBT
% 4.71/5.15 @ ^ [Xs2: list_VEBT_VEBT] :
% 4.71/5.15 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A2 )
% 4.71/5.15 & ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 4.71/5.15 = N ) ) ) )
% 4.71/5.15 = ( power_power_nat @ ( finite7802652506058667612T_VEBT @ A2 ) @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % card_lists_length_eq
% 4.71/5.15 thf(fact_7016_card__lists__length__eq,axiom,
% 4.71/5.15 ! [A2: set_nat,N: nat] :
% 4.71/5.15 ( ( finite_finite_nat @ A2 )
% 4.71/5.15 => ( ( finite_card_list_nat
% 4.71/5.15 @ ( collect_list_nat
% 4.71/5.15 @ ^ [Xs2: list_nat] :
% 4.71/5.15 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A2 )
% 4.71/5.15 & ( ( size_size_list_nat @ Xs2 )
% 4.71/5.15 = N ) ) ) )
% 4.71/5.15 = ( power_power_nat @ ( finite_card_nat @ A2 ) @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % card_lists_length_eq
% 4.71/5.15 thf(fact_7017_card__lists__length__eq,axiom,
% 4.71/5.15 ! [A2: set_int,N: nat] :
% 4.71/5.15 ( ( finite_finite_int @ A2 )
% 4.71/5.15 => ( ( finite_card_list_int
% 4.71/5.15 @ ( collect_list_int
% 4.71/5.15 @ ^ [Xs2: list_int] :
% 4.71/5.15 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A2 )
% 4.71/5.15 & ( ( size_size_list_int @ Xs2 )
% 4.71/5.15 = N ) ) ) )
% 4.71/5.15 = ( power_power_nat @ ( finite_card_int @ A2 ) @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % card_lists_length_eq
% 4.71/5.15 thf(fact_7018_diff__nat__eq__if,axiom,
% 4.71/5.15 ! [Z6: int,Z: int] :
% 4.71/5.15 ( ( ( ord_less_int @ Z6 @ zero_zero_int )
% 4.71/5.15 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) )
% 4.71/5.15 = ( nat2 @ Z ) ) )
% 4.71/5.15 & ( ~ ( ord_less_int @ Z6 @ zero_zero_int )
% 4.71/5.15 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) )
% 4.71/5.15 = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z6 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z6 ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % diff_nat_eq_if
% 4.71/5.15 thf(fact_7019_finite__lists__length__le,axiom,
% 4.71/5.15 ! [A2: set_complex,N: nat] :
% 4.71/5.15 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.15 => ( finite8712137658972009173omplex
% 4.71/5.15 @ ( collect_list_complex
% 4.71/5.15 @ ^ [Xs2: list_complex] :
% 4.71/5.15 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A2 )
% 4.71/5.15 & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs2 ) @ N ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % finite_lists_length_le
% 4.71/5.15 thf(fact_7020_finite__lists__length__le,axiom,
% 4.71/5.15 ! [A2: set_Pr1261947904930325089at_nat,N: nat] :
% 4.71/5.15 ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.15 => ( finite500796754983035824at_nat
% 4.71/5.15 @ ( collec3343600615725829874at_nat
% 4.71/5.15 @ ^ [Xs2: list_P6011104703257516679at_nat] :
% 4.71/5.15 ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs2 ) @ A2 )
% 4.71/5.15 & ( ord_less_eq_nat @ ( size_s5460976970255530739at_nat @ Xs2 ) @ N ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % finite_lists_length_le
% 4.71/5.15 thf(fact_7021_finite__lists__length__le,axiom,
% 4.71/5.15 ! [A2: set_Extended_enat,N: nat] :
% 4.71/5.15 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.15 => ( finite1862508098717546133d_enat
% 4.71/5.15 @ ( collec8433460942617342167d_enat
% 4.71/5.15 @ ^ [Xs2: list_Extended_enat] :
% 4.71/5.15 ( ( ord_le7203529160286727270d_enat @ ( set_Extended_enat2 @ Xs2 ) @ A2 )
% 4.71/5.15 & ( ord_less_eq_nat @ ( size_s3941691890525107288d_enat @ Xs2 ) @ N ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % finite_lists_length_le
% 4.71/5.15 thf(fact_7022_finite__lists__length__le,axiom,
% 4.71/5.15 ! [A2: set_VEBT_VEBT,N: nat] :
% 4.71/5.15 ( ( finite5795047828879050333T_VEBT @ A2 )
% 4.71/5.15 => ( finite3004134309566078307T_VEBT
% 4.71/5.15 @ ( collec5608196760682091941T_VEBT
% 4.71/5.15 @ ^ [Xs2: list_VEBT_VEBT] :
% 4.71/5.15 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A2 )
% 4.71/5.15 & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ N ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % finite_lists_length_le
% 4.71/5.15 thf(fact_7023_finite__lists__length__le,axiom,
% 4.71/5.15 ! [A2: set_nat,N: nat] :
% 4.71/5.15 ( ( finite_finite_nat @ A2 )
% 4.71/5.15 => ( finite8100373058378681591st_nat
% 4.71/5.15 @ ( collect_list_nat
% 4.71/5.15 @ ^ [Xs2: list_nat] :
% 4.71/5.15 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A2 )
% 4.71/5.15 & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ N ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % finite_lists_length_le
% 4.71/5.15 thf(fact_7024_finite__lists__length__le,axiom,
% 4.71/5.15 ! [A2: set_int,N: nat] :
% 4.71/5.15 ( ( finite_finite_int @ A2 )
% 4.71/5.15 => ( finite3922522038869484883st_int
% 4.71/5.15 @ ( collect_list_int
% 4.71/5.15 @ ^ [Xs2: list_int] :
% 4.71/5.15 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A2 )
% 4.71/5.15 & ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ N ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % finite_lists_length_le
% 4.71/5.15 thf(fact_7025_set__update__subset__insert,axiom,
% 4.71/5.15 ! [Xs: list_P6011104703257516679at_nat,I: nat,X: product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ Xs @ I @ X ) ) @ ( insert8211810215607154385at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % set_update_subset_insert
% 4.71/5.15 thf(fact_7026_set__update__subset__insert,axiom,
% 4.71/5.15 ! [Xs: list_real,I: nat,X: real] : ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs @ I @ X ) ) @ ( insert_real @ X @ ( set_real2 @ Xs ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % set_update_subset_insert
% 4.71/5.15 thf(fact_7027_set__update__subset__insert,axiom,
% 4.71/5.15 ! [Xs: list_o,I: nat,X: $o] : ( ord_less_eq_set_o @ ( set_o2 @ ( list_update_o @ Xs @ I @ X ) ) @ ( insert_o @ X @ ( set_o2 @ Xs ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % set_update_subset_insert
% 4.71/5.15 thf(fact_7028_set__update__subset__insert,axiom,
% 4.71/5.15 ! [Xs: list_nat,I: nat,X: nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs @ I @ X ) ) @ ( insert_nat @ X @ ( set_nat2 @ Xs ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % set_update_subset_insert
% 4.71/5.15 thf(fact_7029_set__update__subset__insert,axiom,
% 4.71/5.15 ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) ) @ ( insert_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % set_update_subset_insert
% 4.71/5.15 thf(fact_7030_set__update__subset__insert,axiom,
% 4.71/5.15 ! [Xs: list_int,I: nat,X: int] : ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs @ I @ X ) ) @ ( insert_int @ X @ ( set_int2 @ Xs ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % set_update_subset_insert
% 4.71/5.15 thf(fact_7031_set__update__memI,axiom,
% 4.71/5.15 ! [N: nat,Xs: list_o,X: $o] :
% 4.71/5.15 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 4.71/5.15 => ( member_o @ X @ ( set_o2 @ ( list_update_o @ Xs @ N @ X ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % set_update_memI
% 4.71/5.15 thf(fact_7032_set__update__memI,axiom,
% 4.71/5.15 ! [N: nat,Xs: list_set_nat,X: set_nat] :
% 4.71/5.15 ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 4.71/5.15 => ( member_set_nat @ X @ ( set_set_nat2 @ ( list_update_set_nat @ Xs @ N @ X ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % set_update_memI
% 4.71/5.15 thf(fact_7033_set__update__memI,axiom,
% 4.71/5.15 ! [N: nat,Xs: list_set_nat_rat,X: set_nat_rat] :
% 4.71/5.15 ( ( ord_less_nat @ N @ ( size_s3959913991096427681at_rat @ Xs ) )
% 4.71/5.15 => ( member_set_nat_rat @ X @ ( set_set_nat_rat2 @ ( list_u886106648575569423at_rat @ Xs @ N @ X ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % set_update_memI
% 4.71/5.15 thf(fact_7034_set__update__memI,axiom,
% 4.71/5.15 ! [N: nat,Xs: list_int,X: int] :
% 4.71/5.15 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 4.71/5.15 => ( member_int @ X @ ( set_int2 @ ( list_update_int @ Xs @ N @ X ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % set_update_memI
% 4.71/5.15 thf(fact_7035_set__update__memI,axiom,
% 4.71/5.15 ! [N: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 4.71/5.15 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.71/5.15 => ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ N @ X ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % set_update_memI
% 4.71/5.15 thf(fact_7036_set__update__memI,axiom,
% 4.71/5.15 ! [N: nat,Xs: list_nat,X: nat] :
% 4.71/5.15 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 4.71/5.15 => ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ Xs @ N @ X ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % set_update_memI
% 4.71/5.15 thf(fact_7037_list__update__same__conv,axiom,
% 4.71/5.15 ! [I: nat,Xs: list_int,X: int] :
% 4.71/5.15 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 4.71/5.15 => ( ( ( list_update_int @ Xs @ I @ X )
% 4.71/5.15 = Xs )
% 4.71/5.15 = ( ( nth_int @ Xs @ I )
% 4.71/5.15 = X ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % list_update_same_conv
% 4.71/5.15 thf(fact_7038_list__update__same__conv,axiom,
% 4.71/5.15 ! [I: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 4.71/5.15 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.71/5.15 => ( ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ X )
% 4.71/5.15 = Xs )
% 4.71/5.15 = ( ( nth_VEBT_VEBT @ Xs @ I )
% 4.71/5.15 = X ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % list_update_same_conv
% 4.71/5.15 thf(fact_7039_list__update__same__conv,axiom,
% 4.71/5.15 ! [I: nat,Xs: list_nat,X: nat] :
% 4.71/5.15 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 4.71/5.15 => ( ( ( list_update_nat @ Xs @ I @ X )
% 4.71/5.15 = Xs )
% 4.71/5.15 = ( ( nth_nat @ Xs @ I )
% 4.71/5.15 = X ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % list_update_same_conv
% 4.71/5.15 thf(fact_7040_nth__list__update,axiom,
% 4.71/5.15 ! [I: nat,Xs: list_int,J: nat,X: int] :
% 4.71/5.15 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 4.71/5.15 => ( ( ( I = J )
% 4.71/5.15 => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ J )
% 4.71/5.15 = X ) )
% 4.71/5.15 & ( ( I != J )
% 4.71/5.15 => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ J )
% 4.71/5.15 = ( nth_int @ Xs @ J ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % nth_list_update
% 4.71/5.15 thf(fact_7041_nth__list__update,axiom,
% 4.71/5.15 ! [I: nat,Xs: list_VEBT_VEBT,J: nat,X: vEBT_VEBT] :
% 4.71/5.15 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.71/5.15 => ( ( ( I = J )
% 4.71/5.15 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ J )
% 4.71/5.15 = X ) )
% 4.71/5.15 & ( ( I != J )
% 4.71/5.15 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ J )
% 4.71/5.15 = ( nth_VEBT_VEBT @ Xs @ J ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % nth_list_update
% 4.71/5.15 thf(fact_7042_nth__list__update,axiom,
% 4.71/5.15 ! [I: nat,Xs: list_nat,J: nat,X: nat] :
% 4.71/5.15 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 4.71/5.15 => ( ( ( I = J )
% 4.71/5.15 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ J )
% 4.71/5.15 = X ) )
% 4.71/5.15 & ( ( I != J )
% 4.71/5.15 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ J )
% 4.71/5.15 = ( nth_nat @ Xs @ J ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % nth_list_update
% 4.71/5.15 thf(fact_7043_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 4.71/5.15 ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 4.71/5.15 ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) @ X )
% 4.71/5.15 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.71/5.15 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % VEBT_internal.naive_member.simps(3)
% 4.71/5.15 thf(fact_7044_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 4.71/5.15 ! [V: nat,TreeList: list_VEBT_VEBT,Vd: vEBT_VEBT,X: nat] :
% 4.71/5.15 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) @ X )
% 4.71/5.15 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.71/5.15 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % VEBT_internal.membermima.simps(5)
% 4.71/5.15 thf(fact_7045_vebt__member_Osimps_I5_J,axiom,
% 4.71/5.15 ! [Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 4.71/5.15 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 4.71/5.15 = ( ( X != Mi )
% 4.71/5.15 => ( ( X != Ma )
% 4.71/5.15 => ( ~ ( ord_less_nat @ X @ Mi )
% 4.71/5.15 & ( ~ ( ord_less_nat @ X @ Mi )
% 4.71/5.15 => ( ~ ( ord_less_nat @ Ma @ X )
% 4.71/5.15 & ( ~ ( ord_less_nat @ Ma @ X )
% 4.71/5.15 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.71/5.15 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % vebt_member.simps(5)
% 4.71/5.15 thf(fact_7046_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 4.71/5.15 ! [Mi: nat,Ma: nat,V: nat,TreeList: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 4.71/5.15 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList @ Vc ) @ X )
% 4.71/5.15 = ( ( X = Mi )
% 4.71/5.15 | ( X = Ma )
% 4.71/5.15 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.71/5.15 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % VEBT_internal.membermima.simps(4)
% 4.71/5.15 thf(fact_7047_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 4.71/5.15 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 4.71/5.15 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 4.71/5.15 = Y )
% 4.71/5.15 => ( ! [A5: $o,B5: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 4.71/5.15 => A5 )
% 4.71/5.15 & ( ( Xa2 != zero_zero_nat )
% 4.71/5.15 => ( ( ( Xa2 = one_one_nat )
% 4.71/5.15 => B5 )
% 4.71/5.15 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 4.71/5.15 => ( ( ? [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 4.71/5.15 => Y )
% 4.71/5.15 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 4.71/5.15 ( ? [S3: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % VEBT_internal.naive_member.elims(1)
% 4.71/5.15 thf(fact_7048_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 4.71/5.15 ! [X: vEBT_VEBT,Xa2: nat] :
% 4.71/5.15 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 4.71/5.15 => ( ! [A5: $o,B5: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.15 => ~ ( ( ( Xa2 = zero_zero_nat )
% 4.71/5.15 => A5 )
% 4.71/5.15 & ( ( Xa2 != zero_zero_nat )
% 4.71/5.15 => ( ( ( Xa2 = one_one_nat )
% 4.71/5.15 => B5 )
% 4.71/5.15 & ( Xa2 = one_one_nat ) ) ) ) )
% 4.71/5.15 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 4.71/5.15 ( ? [S3: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) )
% 4.71/5.15 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % VEBT_internal.naive_member.elims(2)
% 4.71/5.15 thf(fact_7049_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 4.71/5.15 ! [X: vEBT_VEBT,Xa2: nat] :
% 4.71/5.15 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 4.71/5.15 => ( ! [A5: $o,B5: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.15 => ( ( ( Xa2 = zero_zero_nat )
% 4.71/5.15 => A5 )
% 4.71/5.15 & ( ( Xa2 != zero_zero_nat )
% 4.71/5.15 => ( ( ( Xa2 = one_one_nat )
% 4.71/5.15 => B5 )
% 4.71/5.15 & ( Xa2 = one_one_nat ) ) ) ) )
% 4.71/5.15 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 != ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 4.71/5.15 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 4.71/5.15 ( ? [S3: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) )
% 4.71/5.15 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % VEBT_internal.naive_member.elims(3)
% 4.71/5.15 thf(fact_7050_vebt__delete_Osimps_I7_J,axiom,
% 4.71/5.15 ! [X: nat,Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 4.71/5.15 ( ( ( ( ord_less_nat @ X @ Mi )
% 4.71/5.15 | ( ord_less_nat @ Ma @ X ) )
% 4.71/5.15 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) ) )
% 4.71/5.15 & ( ~ ( ( ord_less_nat @ X @ Mi )
% 4.71/5.15 | ( ord_less_nat @ Ma @ X ) )
% 4.71/5.15 => ( ( ( ( X = Mi )
% 4.71/5.15 & ( X = Ma ) )
% 4.71/5.15 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 4.71/5.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) ) )
% 4.71/5.15 & ( ~ ( ( X = Mi )
% 4.71/5.15 & ( X = Ma ) )
% 4.71/5.15 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 4.71/5.15 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.71/5.15 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 @ ( vEBT_Node
% 4.71/5.15 @ ( some_P7363390416028606310at_nat
% 4.71/5.15 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 4.71/5.15 @ ( if_nat
% 4.71/5.15 @ ( ( ( X = Mi )
% 4.71/5.15 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 4.71/5.15 = Ma ) )
% 4.71/5.15 & ( ( X != Mi )
% 4.71/5.15 => ( X = Ma ) ) )
% 4.71/5.15 @ ( if_nat
% 4.71/5.15 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 = none_nat )
% 4.71/5.15 @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 4.71/5.15 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 4.71/5.15 @ Ma ) ) )
% 4.71/5.15 @ ( suc @ ( suc @ Va2 ) )
% 4.71/5.15 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 @ ( vEBT_Node
% 4.71/5.15 @ ( some_P7363390416028606310at_nat
% 4.71/5.15 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 4.71/5.15 @ ( if_nat
% 4.71/5.15 @ ( ( ( X = Mi )
% 4.71/5.15 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 4.71/5.15 = Ma ) )
% 4.71/5.15 & ( ( X != Mi )
% 4.71/5.15 => ( X = Ma ) ) )
% 4.71/5.15 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 4.71/5.15 @ Ma ) ) )
% 4.71/5.15 @ ( suc @ ( suc @ Va2 ) )
% 4.71/5.15 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 @ Summary ) )
% 4.71/5.15 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % vebt_delete.simps(7)
% 4.71/5.15 thf(fact_7051_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 4.71/5.15 ! [X: vEBT_VEBT,Xa2: nat] :
% 4.71/5.15 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 4.71/5.15 => ( ! [Mi2: nat,Ma2: nat] :
% 4.71/5.15 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 4.71/5.15 => ~ ( ( Xa2 = Mi2 )
% 4.71/5.15 | ( Xa2 = Ma2 ) ) )
% 4.71/5.15 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 4.71/5.15 ( ? [Vc2: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 4.71/5.15 => ~ ( ( Xa2 = Mi2 )
% 4.71/5.15 | ( Xa2 = Ma2 )
% 4.71/5.15 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 4.71/5.15 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT] :
% 4.71/5.15 ( ? [Vd2: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 4.71/5.15 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % VEBT_internal.membermima.elims(2)
% 4.71/5.15 thf(fact_7052_vebt__member_Oelims_I2_J,axiom,
% 4.71/5.15 ! [X: vEBT_VEBT,Xa2: nat] :
% 4.71/5.15 ( ( vEBT_vebt_member @ X @ Xa2 )
% 4.71/5.15 => ( ! [A5: $o,B5: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.15 => ~ ( ( ( Xa2 = zero_zero_nat )
% 4.71/5.15 => A5 )
% 4.71/5.15 & ( ( Xa2 != zero_zero_nat )
% 4.71/5.15 => ( ( ( Xa2 = one_one_nat )
% 4.71/5.15 => B5 )
% 4.71/5.15 & ( Xa2 = one_one_nat ) ) ) ) )
% 4.71/5.15 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT] :
% 4.71/5.15 ( ? [Summary2: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 4.71/5.15 => ~ ( ( Xa2 != Mi2 )
% 4.71/5.15 => ( ( Xa2 != Ma2 )
% 4.71/5.15 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 4.71/5.15 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 4.71/5.15 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 4.71/5.15 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 4.71/5.15 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % vebt_member.elims(2)
% 4.71/5.15 thf(fact_7053_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 4.71/5.15 ! [X: vEBT_VEBT,Xa2: nat] :
% 4.71/5.15 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 4.71/5.15 => ( ! [Uu2: $o,Uv2: $o] :
% 4.71/5.15 ( X
% 4.71/5.15 != ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 4.71/5.15 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 4.71/5.15 => ( ! [Mi2: nat,Ma2: nat] :
% 4.71/5.15 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 4.71/5.15 => ( ( Xa2 = Mi2 )
% 4.71/5.15 | ( Xa2 = Ma2 ) ) )
% 4.71/5.15 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 4.71/5.15 ( ? [Vc2: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 4.71/5.15 => ( ( Xa2 = Mi2 )
% 4.71/5.15 | ( Xa2 = Ma2 )
% 4.71/5.15 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 4.71/5.15 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT] :
% 4.71/5.15 ( ? [Vd2: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 4.71/5.15 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % VEBT_internal.membermima.elims(3)
% 4.71/5.15 thf(fact_7054_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 4.71/5.15 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 4.71/5.15 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 4.71/5.15 = Y )
% 4.71/5.15 => ( ( ? [Uu2: $o,Uv2: $o] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 4.71/5.15 => Y )
% 4.71/5.15 => ( ( ? [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 4.71/5.15 => Y )
% 4.71/5.15 => ( ! [Mi2: nat,Ma2: nat] :
% 4.71/5.15 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( ~ ( ( Xa2 = Mi2 )
% 4.71/5.15 | ( Xa2 = Ma2 ) ) ) ) )
% 4.71/5.15 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 4.71/5.15 ( ? [Vc2: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( ~ ( ( Xa2 = Mi2 )
% 4.71/5.15 | ( Xa2 = Ma2 )
% 4.71/5.15 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) )
% 4.71/5.15 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT] :
% 4.71/5.15 ( ? [Vd2: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % VEBT_internal.membermima.elims(1)
% 4.71/5.15 thf(fact_7055_vebt__delete_Oelims,axiom,
% 4.71/5.15 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 4.71/5.15 ( ( ( vEBT_vebt_delete @ X @ Xa2 )
% 4.71/5.15 = Y )
% 4.71/5.15 => ( ! [A5: $o,B5: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.15 => ( ( Xa2 = zero_zero_nat )
% 4.71/5.15 => ( Y
% 4.71/5.15 != ( vEBT_Leaf @ $false @ B5 ) ) ) )
% 4.71/5.15 => ( ! [A5: $o] :
% 4.71/5.15 ( ? [B5: $o] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.15 => ( ( Xa2
% 4.71/5.15 = ( suc @ zero_zero_nat ) )
% 4.71/5.15 => ( Y
% 4.71/5.15 != ( vEBT_Leaf @ A5 @ $false ) ) ) )
% 4.71/5.15 => ( ! [A5: $o,B5: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.15 => ( ? [N2: nat] :
% 4.71/5.15 ( Xa2
% 4.71/5.15 = ( suc @ ( suc @ N2 ) ) )
% 4.71/5.15 => ( Y
% 4.71/5.15 != ( vEBT_Leaf @ A5 @ B5 ) ) ) )
% 4.71/5.15 => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 4.71/5.15 => ( Y
% 4.71/5.15 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) ) )
% 4.71/5.15 => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 4.71/5.15 => ( Y
% 4.71/5.15 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) ) )
% 4.71/5.15 => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 4.71/5.15 => ( Y
% 4.71/5.15 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) ) )
% 4.71/5.15 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 4.71/5.15 => ~ ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 4.71/5.15 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) )
% 4.71/5.15 & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 4.71/5.15 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 4.71/5.15 => ( ( ( ( Xa2 = Mi2 )
% 4.71/5.15 & ( Xa2 = Ma2 ) )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) )
% 4.71/5.15 & ( ~ ( ( Xa2 = Mi2 )
% 4.71/5.15 & ( Xa2 = Ma2 ) )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 @ ( vEBT_Node
% 4.71/5.15 @ ( some_P7363390416028606310at_nat
% 4.71/5.15 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 4.71/5.15 @ ( if_nat
% 4.71/5.15 @ ( ( ( Xa2 = Mi2 )
% 4.71/5.15 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 4.71/5.15 = Ma2 ) )
% 4.71/5.15 & ( ( Xa2 != Mi2 )
% 4.71/5.15 => ( Xa2 = Ma2 ) ) )
% 4.71/5.15 @ ( if_nat
% 4.71/5.15 @ ( ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 = none_nat )
% 4.71/5.15 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 4.71/5.15 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( 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 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 4.71/5.15 @ Ma2 ) ) )
% 4.71/5.15 @ ( suc @ ( suc @ Va ) )
% 4.71/5.15 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 @ ( vEBT_Node
% 4.71/5.15 @ ( some_P7363390416028606310at_nat
% 4.71/5.15 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 4.71/5.15 @ ( if_nat
% 4.71/5.15 @ ( ( ( Xa2 = Mi2 )
% 4.71/5.15 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 4.71/5.15 = Ma2 ) )
% 4.71/5.15 & ( ( Xa2 != Mi2 )
% 4.71/5.15 => ( Xa2 = Ma2 ) ) )
% 4.71/5.15 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( 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 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 4.71/5.15 @ Ma2 ) ) )
% 4.71/5.15 @ ( suc @ ( suc @ Va ) )
% 4.71/5.15 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 @ Summary2 ) )
% 4.71/5.15 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % vebt_delete.elims
% 4.71/5.15 thf(fact_7056_vebt__member_Oelims_I1_J,axiom,
% 4.71/5.15 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 4.71/5.15 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 4.71/5.15 = Y )
% 4.71/5.15 => ( ! [A5: $o,B5: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 4.71/5.15 => A5 )
% 4.71/5.15 & ( ( Xa2 != zero_zero_nat )
% 4.71/5.15 => ( ( ( Xa2 = one_one_nat )
% 4.71/5.15 => B5 )
% 4.71/5.15 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 4.71/5.15 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 4.71/5.15 => Y )
% 4.71/5.15 => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 4.71/5.15 => Y )
% 4.71/5.15 => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 4.71/5.15 => Y )
% 4.71/5.15 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT] :
% 4.71/5.15 ( ? [Summary2: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( ~ ( ( Xa2 != Mi2 )
% 4.71/5.15 => ( ( Xa2 != Ma2 )
% 4.71/5.15 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 4.71/5.15 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 4.71/5.15 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 4.71/5.15 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 4.71/5.15 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % vebt_member.elims(1)
% 4.71/5.15 thf(fact_7057_vebt__member_Oelims_I3_J,axiom,
% 4.71/5.15 ! [X: vEBT_VEBT,Xa2: nat] :
% 4.71/5.15 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 4.71/5.15 => ( ! [A5: $o,B5: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.15 => ( ( ( Xa2 = zero_zero_nat )
% 4.71/5.15 => A5 )
% 4.71/5.15 & ( ( Xa2 != zero_zero_nat )
% 4.71/5.15 => ( ( ( Xa2 = one_one_nat )
% 4.71/5.15 => B5 )
% 4.71/5.15 & ( Xa2 = one_one_nat ) ) ) ) )
% 4.71/5.15 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 4.71/5.15 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 4.71/5.15 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 4.71/5.15 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT] :
% 4.71/5.15 ( ? [Summary2: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 4.71/5.15 => ( ( Xa2 != Mi2 )
% 4.71/5.15 => ( ( Xa2 != Ma2 )
% 4.71/5.15 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 4.71/5.15 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 4.71/5.15 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 4.71/5.15 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 4.71/5.15 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % vebt_member.elims(3)
% 4.71/5.15 thf(fact_7058_vebt__succ_Osimps_I6_J,axiom,
% 4.71/5.15 ! [X: nat,Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 4.71/5.15 ( ( ( ord_less_nat @ X @ Mi )
% 4.71/5.15 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 4.71/5.15 = ( some_nat @ Mi ) ) )
% 4.71/5.15 & ( ~ ( ord_less_nat @ X @ Mi )
% 4.71/5.15 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 4.71/5.15 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.71/5.15 @ ( if_option_nat
% 4.71/5.15 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 != none_nat )
% 4.71/5.15 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 4.71/5.15 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 @ ( if_option_nat
% 4.71/5.15 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.71/5.15 = none_nat )
% 4.71/5.15 @ none_nat
% 4.71/5.15 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 4.71/5.15 @ none_nat ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % vebt_succ.simps(6)
% 4.71/5.15 thf(fact_7059_vebt__pred_Osimps_I7_J,axiom,
% 4.71/5.15 ! [Ma: nat,X: nat,Mi: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 4.71/5.15 ( ( ( ord_less_nat @ Ma @ X )
% 4.71/5.15 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 4.71/5.15 = ( some_nat @ Ma ) ) )
% 4.71/5.15 & ( ~ ( ord_less_nat @ Ma @ X )
% 4.71/5.15 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 4.71/5.15 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.71/5.15 @ ( if_option_nat
% 4.71/5.15 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 != none_nat )
% 4.71/5.15 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 4.71/5.15 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 @ ( if_option_nat
% 4.71/5.15 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.71/5.15 = none_nat )
% 4.71/5.15 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 4.71/5.15 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 4.71/5.15 @ none_nat ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % vebt_pred.simps(7)
% 4.71/5.15 thf(fact_7060_vebt__pred_Oelims,axiom,
% 4.71/5.15 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 4.71/5.15 ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 4.71/5.15 = Y )
% 4.71/5.15 => ( ( ? [Uu2: $o,Uv2: $o] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 4.71/5.15 => ( ( Xa2 = zero_zero_nat )
% 4.71/5.15 => ( Y != none_nat ) ) )
% 4.71/5.15 => ( ! [A5: $o] :
% 4.71/5.15 ( ? [Uw2: $o] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ Uw2 ) )
% 4.71/5.15 => ( ( Xa2
% 4.71/5.15 = ( suc @ zero_zero_nat ) )
% 4.71/5.15 => ~ ( ( A5
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( some_nat @ zero_zero_nat ) ) )
% 4.71/5.15 & ( ~ A5
% 4.71/5.15 => ( Y = none_nat ) ) ) ) )
% 4.71/5.15 => ( ! [A5: $o,B5: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.15 => ( ? [Va: nat] :
% 4.71/5.15 ( Xa2
% 4.71/5.15 = ( suc @ ( suc @ Va ) ) )
% 4.71/5.15 => ~ ( ( B5
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( some_nat @ one_one_nat ) ) )
% 4.71/5.15 & ( ~ B5
% 4.71/5.15 => ( ( A5
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( some_nat @ zero_zero_nat ) ) )
% 4.71/5.15 & ( ~ A5
% 4.71/5.15 => ( Y = none_nat ) ) ) ) ) ) )
% 4.71/5.15 => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 4.71/5.15 => ( Y != none_nat ) )
% 4.71/5.15 => ( ( ? [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 4.71/5.15 => ( Y != none_nat ) )
% 4.71/5.15 => ( ( ? [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 4.71/5.15 => ( Y != none_nat ) )
% 4.71/5.15 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 4.71/5.15 => ~ ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( some_nat @ Ma2 ) ) )
% 4.71/5.15 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 @ ( if_option_nat
% 4.71/5.15 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 != none_nat )
% 4.71/5.15 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 4.71/5.15 @ ( 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 @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 @ ( if_option_nat
% 4.71/5.15 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.71/5.15 = none_nat )
% 4.71/5.15 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 4.71/5.15 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 4.71/5.15 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % vebt_pred.elims
% 4.71/5.15 thf(fact_7061_vebt__succ_Oelims,axiom,
% 4.71/5.15 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 4.71/5.15 ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 4.71/5.15 = Y )
% 4.71/5.15 => ( ! [Uu2: $o,B5: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ Uu2 @ B5 ) )
% 4.71/5.15 => ( ( Xa2 = zero_zero_nat )
% 4.71/5.15 => ~ ( ( B5
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( some_nat @ one_one_nat ) ) )
% 4.71/5.15 & ( ~ B5
% 4.71/5.15 => ( Y = none_nat ) ) ) ) )
% 4.71/5.15 => ( ( ? [Uv2: $o,Uw2: $o] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 4.71/5.15 => ( ? [N2: nat] :
% 4.71/5.15 ( Xa2
% 4.71/5.15 = ( suc @ N2 ) )
% 4.71/5.15 => ( Y != none_nat ) ) )
% 4.71/5.15 => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 4.71/5.15 => ( Y != none_nat ) )
% 4.71/5.15 => ( ( ? [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 4.71/5.15 => ( Y != none_nat ) )
% 4.71/5.15 => ( ( ? [V2: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 4.71/5.15 ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 4.71/5.15 => ( Y != none_nat ) )
% 4.71/5.15 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 4.71/5.15 => ~ ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( some_nat @ Mi2 ) ) )
% 4.71/5.15 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 @ ( if_option_nat
% 4.71/5.15 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 != none_nat )
% 4.71/5.15 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 4.71/5.15 @ ( 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 @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 @ ( if_option_nat
% 4.71/5.15 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.71/5.15 = none_nat )
% 4.71/5.15 @ none_nat
% 4.71/5.15 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 4.71/5.15 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % vebt_succ.elims
% 4.71/5.15 thf(fact_7062_of__int__code__if,axiom,
% 4.71/5.15 ( ring_18347121197199848620nteger
% 4.71/5.15 = ( ^ [K3: int] :
% 4.71/5.15 ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 4.71/5.15 @ ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ K3 ) ) )
% 4.71/5.15 @ ( if_Code_integer
% 4.71/5.15 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.71/5.15 = zero_zero_int )
% 4.71/5.15 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 4.71/5.15 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % of_int_code_if
% 4.71/5.15 thf(fact_7063_of__int__code__if,axiom,
% 4.71/5.15 ( ring_1_of_int_int
% 4.71/5.15 = ( ^ [K3: int] :
% 4.71/5.15 ( if_int @ ( K3 = zero_zero_int ) @ zero_zero_int
% 4.71/5.15 @ ( if_int @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K3 ) ) )
% 4.71/5.15 @ ( if_int
% 4.71/5.15 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.71/5.15 = zero_zero_int )
% 4.71/5.15 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 4.71/5.15 @ ( 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 ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % of_int_code_if
% 4.71/5.15 thf(fact_7064_of__int__code__if,axiom,
% 4.71/5.15 ( ring_1_of_int_real
% 4.71/5.15 = ( ^ [K3: int] :
% 4.71/5.15 ( if_real @ ( K3 = zero_zero_int ) @ zero_zero_real
% 4.71/5.15 @ ( if_real @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K3 ) ) )
% 4.71/5.15 @ ( if_real
% 4.71/5.15 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.71/5.15 = zero_zero_int )
% 4.71/5.15 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 4.71/5.15 @ ( 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 ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % of_int_code_if
% 4.71/5.15 thf(fact_7065_of__int__code__if,axiom,
% 4.71/5.15 ( ring_1_of_int_rat
% 4.71/5.15 = ( ^ [K3: int] :
% 4.71/5.15 ( if_rat @ ( K3 = zero_zero_int ) @ zero_zero_rat
% 4.71/5.15 @ ( if_rat @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ ( uminus_uminus_int @ K3 ) ) )
% 4.71/5.15 @ ( if_rat
% 4.71/5.15 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.71/5.15 = zero_zero_int )
% 4.71/5.15 @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 4.71/5.15 @ ( 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 ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % of_int_code_if
% 4.71/5.15 thf(fact_7066_of__int__code__if,axiom,
% 4.71/5.15 ( ring_17405671764205052669omplex
% 4.71/5.15 = ( ^ [K3: int] :
% 4.71/5.15 ( if_complex @ ( K3 = zero_zero_int ) @ zero_zero_complex
% 4.71/5.15 @ ( if_complex @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K3 ) ) )
% 4.71/5.15 @ ( if_complex
% 4.71/5.15 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.71/5.15 = zero_zero_int )
% 4.71/5.15 @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 4.71/5.15 @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % of_int_code_if
% 4.71/5.15 thf(fact_7067_insert__simp__excp,axiom,
% 4.71/5.15 ! [Mi: nat,Deg: nat,TreeList: list_VEBT_VEBT,X: nat,Ma: nat,Summary: vEBT_VEBT] :
% 4.71/5.15 ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.71/5.15 => ( ( ord_less_nat @ X @ Mi )
% 4.71/5.15 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.71/5.15 => ( ( X != Ma )
% 4.71/5.15 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ ( ord_max_nat @ Mi @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % insert_simp_excp
% 4.71/5.15 thf(fact_7068_insert__simp__norm,axiom,
% 4.71/5.15 ! [X: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 4.71/5.15 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.71/5.15 => ( ( ord_less_nat @ Mi @ X )
% 4.71/5.15 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.71/5.15 => ( ( X != Ma )
% 4.71/5.15 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( ord_max_nat @ X @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % insert_simp_norm
% 4.71/5.15 thf(fact_7069_vebt__insert_Oelims,axiom,
% 4.71/5.15 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 4.71/5.15 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 4.71/5.15 = Y )
% 4.71/5.15 => ( ! [A5: $o,B5: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.15 => ~ ( ( ( Xa2 = zero_zero_nat )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( vEBT_Leaf @ $true @ B5 ) ) )
% 4.71/5.15 & ( ( Xa2 != zero_zero_nat )
% 4.71/5.15 => ( ( ( Xa2 = one_one_nat )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ $true ) ) )
% 4.71/5.15 & ( ( Xa2 != one_one_nat )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ) ) )
% 4.71/5.15 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) )
% 4.71/5.15 => ( Y
% 4.71/5.15 != ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) ) )
% 4.71/5.15 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) )
% 4.71/5.15 => ( Y
% 4.71/5.15 != ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) ) )
% 4.71/5.15 => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 4.71/5.15 => ( Y
% 4.71/5.15 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) ) )
% 4.71/5.15 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 4.71/5.15 => ( Y
% 4.71/5.15 != ( if_VEBT_VEBT
% 4.71/5.15 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 & ~ ( ( Xa2 = Mi2 )
% 4.71/5.15 | ( Xa2 = Ma2 ) ) )
% 4.71/5.15 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 4.71/5.15 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % vebt_insert.elims
% 4.71/5.15 thf(fact_7070_vebt__succ_Opelims,axiom,
% 4.71/5.15 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 4.71/5.15 ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 4.71/5.15 = Y )
% 4.71/5.15 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 4.71/5.15 => ( ! [Uu2: $o,B5: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ Uu2 @ B5 ) )
% 4.71/5.15 => ( ( Xa2 = zero_zero_nat )
% 4.71/5.15 => ( ( ( B5
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( some_nat @ one_one_nat ) ) )
% 4.71/5.15 & ( ~ B5
% 4.71/5.15 => ( Y = none_nat ) ) )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B5 ) @ zero_zero_nat ) ) ) ) )
% 4.71/5.15 => ( ! [Uv2: $o,Uw2: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 4.71/5.15 => ! [N2: nat] :
% 4.71/5.15 ( ( Xa2
% 4.71/5.15 = ( suc @ N2 ) )
% 4.71/5.15 => ( ( Y = none_nat )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N2 ) ) ) ) ) )
% 4.71/5.15 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 4.71/5.15 => ( ( Y = none_nat )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 4.71/5.15 => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 4.71/5.15 => ( ( Y = none_nat )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa2 ) ) ) )
% 4.71/5.15 => ( ! [V2: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 4.71/5.15 => ( ( Y = none_nat )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Xa2 ) ) ) )
% 4.71/5.15 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 4.71/5.15 => ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( some_nat @ Mi2 ) ) )
% 4.71/5.15 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 @ ( if_option_nat
% 4.71/5.15 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 != none_nat )
% 4.71/5.15 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 4.71/5.15 @ ( 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 @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 @ ( if_option_nat
% 4.71/5.15 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.71/5.15 = none_nat )
% 4.71/5.15 @ none_nat
% 4.71/5.15 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 4.71/5.15 @ none_nat ) ) ) )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % vebt_succ.pelims
% 4.71/5.15 thf(fact_7071_vebt__pred_Opelims,axiom,
% 4.71/5.15 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 4.71/5.15 ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 4.71/5.15 = Y )
% 4.71/5.15 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 4.71/5.15 => ( ! [Uu2: $o,Uv2: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 4.71/5.15 => ( ( Xa2 = zero_zero_nat )
% 4.71/5.15 => ( ( Y = none_nat )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) ) ) ) )
% 4.71/5.15 => ( ! [A5: $o,Uw2: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ Uw2 ) )
% 4.71/5.15 => ( ( Xa2
% 4.71/5.15 = ( suc @ zero_zero_nat ) )
% 4.71/5.15 => ( ( ( A5
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( some_nat @ zero_zero_nat ) ) )
% 4.71/5.15 & ( ~ A5
% 4.71/5.15 => ( Y = none_nat ) ) )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 4.71/5.15 => ( ! [A5: $o,B5: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.15 => ! [Va: nat] :
% 4.71/5.15 ( ( Xa2
% 4.71/5.15 = ( suc @ ( suc @ Va ) ) )
% 4.71/5.15 => ( ( ( B5
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( some_nat @ one_one_nat ) ) )
% 4.71/5.15 & ( ~ B5
% 4.71/5.15 => ( ( A5
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( some_nat @ zero_zero_nat ) ) )
% 4.71/5.15 & ( ~ A5
% 4.71/5.15 => ( Y = none_nat ) ) ) ) )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ ( suc @ Va ) ) ) ) ) ) )
% 4.71/5.15 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 4.71/5.15 => ( ( Y = none_nat )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Xa2 ) ) ) )
% 4.71/5.15 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 4.71/5.15 => ( ( Y = none_nat )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Xa2 ) ) ) )
% 4.71/5.15 => ( ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 4.71/5.15 => ( ( Y = none_nat )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Xa2 ) ) ) )
% 4.71/5.15 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 4.71/5.15 => ( ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( some_nat @ Ma2 ) ) )
% 4.71/5.15 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 @ ( if_option_nat
% 4.71/5.15 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 != none_nat )
% 4.71/5.15 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 4.71/5.15 @ ( 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 @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 @ ( if_option_nat
% 4.71/5.15 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.71/5.15 = none_nat )
% 4.71/5.15 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 4.71/5.15 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 4.71/5.15 @ none_nat ) ) ) )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % vebt_pred.pelims
% 4.71/5.15 thf(fact_7072_max__bot2,axiom,
% 4.71/5.15 ! [X: set_real] :
% 4.71/5.15 ( ( ord_max_set_real @ X @ bot_bot_set_real )
% 4.71/5.15 = X ) ).
% 4.71/5.15
% 4.71/5.15 % max_bot2
% 4.71/5.15 thf(fact_7073_max__bot2,axiom,
% 4.71/5.15 ! [X: set_o] :
% 4.71/5.15 ( ( ord_max_set_o @ X @ bot_bot_set_o )
% 4.71/5.15 = X ) ).
% 4.71/5.15
% 4.71/5.15 % max_bot2
% 4.71/5.15 thf(fact_7074_max__bot2,axiom,
% 4.71/5.15 ! [X: set_nat] :
% 4.71/5.15 ( ( ord_max_set_nat @ X @ bot_bot_set_nat )
% 4.71/5.15 = X ) ).
% 4.71/5.15
% 4.71/5.15 % max_bot2
% 4.71/5.15 thf(fact_7075_max__bot2,axiom,
% 4.71/5.15 ! [X: set_int] :
% 4.71/5.15 ( ( ord_max_set_int @ X @ bot_bot_set_int )
% 4.71/5.15 = X ) ).
% 4.71/5.15
% 4.71/5.15 % max_bot2
% 4.71/5.15 thf(fact_7076_max__bot2,axiom,
% 4.71/5.15 ! [X: nat] :
% 4.71/5.15 ( ( ord_max_nat @ X @ bot_bot_nat )
% 4.71/5.15 = X ) ).
% 4.71/5.15
% 4.71/5.15 % max_bot2
% 4.71/5.15 thf(fact_7077_max__bot,axiom,
% 4.71/5.15 ! [X: set_real] :
% 4.71/5.15 ( ( ord_max_set_real @ bot_bot_set_real @ X )
% 4.71/5.15 = X ) ).
% 4.71/5.15
% 4.71/5.15 % max_bot
% 4.71/5.15 thf(fact_7078_max__bot,axiom,
% 4.71/5.15 ! [X: set_o] :
% 4.71/5.15 ( ( ord_max_set_o @ bot_bot_set_o @ X )
% 4.71/5.15 = X ) ).
% 4.71/5.15
% 4.71/5.15 % max_bot
% 4.71/5.15 thf(fact_7079_max__bot,axiom,
% 4.71/5.15 ! [X: set_nat] :
% 4.71/5.15 ( ( ord_max_set_nat @ bot_bot_set_nat @ X )
% 4.71/5.15 = X ) ).
% 4.71/5.15
% 4.71/5.15 % max_bot
% 4.71/5.15 thf(fact_7080_max__bot,axiom,
% 4.71/5.15 ! [X: set_int] :
% 4.71/5.15 ( ( ord_max_set_int @ bot_bot_set_int @ X )
% 4.71/5.15 = X ) ).
% 4.71/5.15
% 4.71/5.15 % max_bot
% 4.71/5.15 thf(fact_7081_max__bot,axiom,
% 4.71/5.15 ! [X: nat] :
% 4.71/5.15 ( ( ord_max_nat @ bot_bot_nat @ X )
% 4.71/5.15 = X ) ).
% 4.71/5.15
% 4.71/5.15 % max_bot
% 4.71/5.15 thf(fact_7082_max__Suc__Suc,axiom,
% 4.71/5.15 ! [M2: nat,N: nat] :
% 4.71/5.15 ( ( ord_max_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 4.71/5.15 = ( suc @ ( ord_max_nat @ M2 @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_Suc_Suc
% 4.71/5.15 thf(fact_7083_max__0R,axiom,
% 4.71/5.15 ! [N: nat] :
% 4.71/5.15 ( ( ord_max_nat @ N @ zero_zero_nat )
% 4.71/5.15 = N ) ).
% 4.71/5.15
% 4.71/5.15 % max_0R
% 4.71/5.15 thf(fact_7084_max__0L,axiom,
% 4.71/5.15 ! [N: nat] :
% 4.71/5.15 ( ( ord_max_nat @ zero_zero_nat @ N )
% 4.71/5.15 = N ) ).
% 4.71/5.15
% 4.71/5.15 % max_0L
% 4.71/5.15 thf(fact_7085_max__nat_Oright__neutral,axiom,
% 4.71/5.15 ! [A: nat] :
% 4.71/5.15 ( ( ord_max_nat @ A @ zero_zero_nat )
% 4.71/5.15 = A ) ).
% 4.71/5.15
% 4.71/5.15 % max_nat.right_neutral
% 4.71/5.15 thf(fact_7086_max__nat_Oneutr__eq__iff,axiom,
% 4.71/5.15 ! [A: nat,B: nat] :
% 4.71/5.15 ( ( zero_zero_nat
% 4.71/5.15 = ( ord_max_nat @ A @ B ) )
% 4.71/5.15 = ( ( A = zero_zero_nat )
% 4.71/5.15 & ( B = zero_zero_nat ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_nat.neutr_eq_iff
% 4.71/5.15 thf(fact_7087_max__nat_Oleft__neutral,axiom,
% 4.71/5.15 ! [A: nat] :
% 4.71/5.15 ( ( ord_max_nat @ zero_zero_nat @ A )
% 4.71/5.15 = A ) ).
% 4.71/5.15
% 4.71/5.15 % max_nat.left_neutral
% 4.71/5.15 thf(fact_7088_max__nat_Oeq__neutr__iff,axiom,
% 4.71/5.15 ! [A: nat,B: nat] :
% 4.71/5.15 ( ( ( ord_max_nat @ A @ B )
% 4.71/5.15 = zero_zero_nat )
% 4.71/5.15 = ( ( A = zero_zero_nat )
% 4.71/5.15 & ( B = zero_zero_nat ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_nat.eq_neutr_iff
% 4.71/5.15 thf(fact_7089_max__number__of_I1_J,axiom,
% 4.71/5.15 ! [U: num,V: num] :
% 4.71/5.15 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 4.71/5.15 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 4.71/5.15 = ( numeral_numeral_real @ V ) ) )
% 4.71/5.15 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 4.71/5.15 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 4.71/5.15 = ( numeral_numeral_real @ U ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_number_of(1)
% 4.71/5.15 thf(fact_7090_max__number__of_I1_J,axiom,
% 4.71/5.15 ! [U: num,V: num] :
% 4.71/5.15 ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 4.71/5.15 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 4.71/5.15 = ( numera1916890842035813515d_enat @ V ) ) )
% 4.71/5.15 & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 4.71/5.15 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 4.71/5.15 = ( numera1916890842035813515d_enat @ U ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_number_of(1)
% 4.71/5.15 thf(fact_7091_max__number__of_I1_J,axiom,
% 4.71/5.15 ! [U: num,V: num] :
% 4.71/5.15 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 4.71/5.15 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 4.71/5.15 = ( numera6620942414471956472nteger @ V ) ) )
% 4.71/5.15 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 4.71/5.15 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 4.71/5.15 = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_number_of(1)
% 4.71/5.15 thf(fact_7092_max__number__of_I1_J,axiom,
% 4.71/5.15 ! [U: num,V: num] :
% 4.71/5.15 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 4.71/5.15 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 4.71/5.15 = ( numeral_numeral_rat @ V ) ) )
% 4.71/5.15 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 4.71/5.15 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 4.71/5.15 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_number_of(1)
% 4.71/5.15 thf(fact_7093_max__number__of_I1_J,axiom,
% 4.71/5.15 ! [U: num,V: num] :
% 4.71/5.15 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 4.71/5.15 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 4.71/5.15 = ( numeral_numeral_nat @ V ) ) )
% 4.71/5.15 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 4.71/5.15 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 4.71/5.15 = ( numeral_numeral_nat @ U ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_number_of(1)
% 4.71/5.15 thf(fact_7094_max__number__of_I1_J,axiom,
% 4.71/5.15 ! [U: num,V: num] :
% 4.71/5.15 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 4.71/5.15 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 4.71/5.15 = ( numeral_numeral_int @ V ) ) )
% 4.71/5.15 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 4.71/5.15 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 4.71/5.15 = ( numeral_numeral_int @ U ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_number_of(1)
% 4.71/5.15 thf(fact_7095_max__0__1_I3_J,axiom,
% 4.71/5.15 ! [X: num] :
% 4.71/5.15 ( ( ord_max_rat @ zero_zero_rat @ ( numeral_numeral_rat @ X ) )
% 4.71/5.15 = ( numeral_numeral_rat @ X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(3)
% 4.71/5.15 thf(fact_7096_max__0__1_I3_J,axiom,
% 4.71/5.15 ! [X: num] :
% 4.71/5.15 ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X ) )
% 4.71/5.15 = ( numeral_numeral_real @ X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(3)
% 4.71/5.15 thf(fact_7097_max__0__1_I3_J,axiom,
% 4.71/5.15 ! [X: num] :
% 4.71/5.15 ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X ) )
% 4.71/5.15 = ( numeral_numeral_nat @ X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(3)
% 4.71/5.15 thf(fact_7098_max__0__1_I3_J,axiom,
% 4.71/5.15 ! [X: num] :
% 4.71/5.15 ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X ) )
% 4.71/5.15 = ( numeral_numeral_int @ X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(3)
% 4.71/5.15 thf(fact_7099_max__0__1_I3_J,axiom,
% 4.71/5.15 ! [X: num] :
% 4.71/5.15 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 4.71/5.15 = ( numera1916890842035813515d_enat @ X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(3)
% 4.71/5.15 thf(fact_7100_max__0__1_I3_J,axiom,
% 4.71/5.15 ! [X: num] :
% 4.71/5.15 ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ X ) )
% 4.71/5.15 = ( numera6620942414471956472nteger @ X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(3)
% 4.71/5.15 thf(fact_7101_max__0__1_I4_J,axiom,
% 4.71/5.15 ! [X: num] :
% 4.71/5.15 ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ zero_zero_rat )
% 4.71/5.15 = ( numeral_numeral_rat @ X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(4)
% 4.71/5.15 thf(fact_7102_max__0__1_I4_J,axiom,
% 4.71/5.15 ! [X: num] :
% 4.71/5.15 ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ zero_zero_real )
% 4.71/5.15 = ( numeral_numeral_real @ X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(4)
% 4.71/5.15 thf(fact_7103_max__0__1_I4_J,axiom,
% 4.71/5.15 ! [X: num] :
% 4.71/5.15 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ zero_zero_nat )
% 4.71/5.15 = ( numeral_numeral_nat @ X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(4)
% 4.71/5.15 thf(fact_7104_max__0__1_I4_J,axiom,
% 4.71/5.15 ! [X: num] :
% 4.71/5.15 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ zero_zero_int )
% 4.71/5.15 = ( numeral_numeral_int @ X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(4)
% 4.71/5.15 thf(fact_7105_max__0__1_I4_J,axiom,
% 4.71/5.15 ! [X: num] :
% 4.71/5.15 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ zero_z5237406670263579293d_enat )
% 4.71/5.15 = ( numera1916890842035813515d_enat @ X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(4)
% 4.71/5.15 thf(fact_7106_max__0__1_I4_J,axiom,
% 4.71/5.15 ! [X: num] :
% 4.71/5.15 ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X ) @ zero_z3403309356797280102nteger )
% 4.71/5.15 = ( numera6620942414471956472nteger @ X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(4)
% 4.71/5.15 thf(fact_7107_max__0__1_I1_J,axiom,
% 4.71/5.15 ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 4.71/5.15 = one_one_real ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(1)
% 4.71/5.15 thf(fact_7108_max__0__1_I1_J,axiom,
% 4.71/5.15 ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 4.71/5.15 = one_one_rat ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(1)
% 4.71/5.15 thf(fact_7109_max__0__1_I1_J,axiom,
% 4.71/5.15 ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 4.71/5.15 = one_one_int ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(1)
% 4.71/5.15 thf(fact_7110_max__0__1_I1_J,axiom,
% 4.71/5.15 ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 4.71/5.15 = one_one_nat ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(1)
% 4.71/5.15 thf(fact_7111_max__0__1_I2_J,axiom,
% 4.71/5.15 ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 4.71/5.15 = one_one_real ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(2)
% 4.71/5.15 thf(fact_7112_max__0__1_I2_J,axiom,
% 4.71/5.15 ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 4.71/5.15 = one_one_rat ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(2)
% 4.71/5.15 thf(fact_7113_max__0__1_I2_J,axiom,
% 4.71/5.15 ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 4.71/5.15 = one_one_int ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(2)
% 4.71/5.15 thf(fact_7114_max__0__1_I2_J,axiom,
% 4.71/5.15 ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 4.71/5.15 = one_one_nat ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(2)
% 4.71/5.15 thf(fact_7115_max__0__1_I5_J,axiom,
% 4.71/5.15 ! [X: num] :
% 4.71/5.15 ( ( ord_max_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 4.71/5.15 = ( numeral_numeral_rat @ X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(5)
% 4.71/5.15 thf(fact_7116_max__0__1_I5_J,axiom,
% 4.71/5.15 ! [X: num] :
% 4.71/5.15 ( ( ord_max_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 4.71/5.15 = ( numeral_numeral_real @ X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(5)
% 4.71/5.15 thf(fact_7117_max__0__1_I5_J,axiom,
% 4.71/5.15 ! [X: num] :
% 4.71/5.15 ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 4.71/5.15 = ( numeral_numeral_nat @ X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(5)
% 4.71/5.15 thf(fact_7118_max__0__1_I5_J,axiom,
% 4.71/5.15 ! [X: num] :
% 4.71/5.15 ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 4.71/5.15 = ( numeral_numeral_int @ X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(5)
% 4.71/5.15 thf(fact_7119_max__0__1_I5_J,axiom,
% 4.71/5.15 ! [X: num] :
% 4.71/5.15 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 4.71/5.15 = ( numera1916890842035813515d_enat @ X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(5)
% 4.71/5.15 thf(fact_7120_max__0__1_I5_J,axiom,
% 4.71/5.15 ! [X: num] :
% 4.71/5.15 ( ( ord_max_Code_integer @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X ) )
% 4.71/5.15 = ( numera6620942414471956472nteger @ X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(5)
% 4.71/5.15 thf(fact_7121_max__0__1_I6_J,axiom,
% 4.71/5.15 ! [X: num] :
% 4.71/5.15 ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat )
% 4.71/5.15 = ( numeral_numeral_rat @ X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(6)
% 4.71/5.15 thf(fact_7122_max__0__1_I6_J,axiom,
% 4.71/5.15 ! [X: num] :
% 4.71/5.15 ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ one_one_real )
% 4.71/5.15 = ( numeral_numeral_real @ X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(6)
% 4.71/5.15 thf(fact_7123_max__0__1_I6_J,axiom,
% 4.71/5.15 ! [X: num] :
% 4.71/5.15 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat )
% 4.71/5.15 = ( numeral_numeral_nat @ X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(6)
% 4.71/5.15 thf(fact_7124_max__0__1_I6_J,axiom,
% 4.71/5.15 ! [X: num] :
% 4.71/5.15 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ one_one_int )
% 4.71/5.15 = ( numeral_numeral_int @ X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(6)
% 4.71/5.15 thf(fact_7125_max__0__1_I6_J,axiom,
% 4.71/5.15 ! [X: num] :
% 4.71/5.15 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ one_on7984719198319812577d_enat )
% 4.71/5.15 = ( numera1916890842035813515d_enat @ X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(6)
% 4.71/5.15 thf(fact_7126_max__0__1_I6_J,axiom,
% 4.71/5.15 ! [X: num] :
% 4.71/5.15 ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer )
% 4.71/5.15 = ( numera6620942414471956472nteger @ X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_0_1(6)
% 4.71/5.15 thf(fact_7127_max__number__of_I4_J,axiom,
% 4.71/5.15 ! [U: num,V: num] :
% 4.71/5.15 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 4.71/5.15 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 4.71/5.15 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 4.71/5.15 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 4.71/5.15 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 4.71/5.15 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_number_of(4)
% 4.71/5.15 thf(fact_7128_max__number__of_I4_J,axiom,
% 4.71/5.15 ! [U: num,V: num] :
% 4.71/5.15 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 4.71/5.15 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 4.71/5.15 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 4.71/5.15 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 4.71/5.15 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 4.71/5.15 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_number_of(4)
% 4.71/5.15 thf(fact_7129_max__number__of_I4_J,axiom,
% 4.71/5.15 ! [U: num,V: num] :
% 4.71/5.15 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 4.71/5.15 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 4.71/5.15 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 4.71/5.15 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 4.71/5.15 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 4.71/5.15 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_number_of(4)
% 4.71/5.15 thf(fact_7130_max__number__of_I4_J,axiom,
% 4.71/5.15 ! [U: num,V: num] :
% 4.71/5.15 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 4.71/5.15 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 4.71/5.15 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 4.71/5.15 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 4.71/5.15 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 4.71/5.15 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_number_of(4)
% 4.71/5.15 thf(fact_7131_max__number__of_I3_J,axiom,
% 4.71/5.15 ! [U: num,V: num] :
% 4.71/5.15 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 4.71/5.15 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 4.71/5.15 = ( numera6620942414471956472nteger @ V ) ) )
% 4.71/5.15 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 4.71/5.15 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 4.71/5.15 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_number_of(3)
% 4.71/5.15 thf(fact_7132_max__number__of_I3_J,axiom,
% 4.71/5.15 ! [U: num,V: num] :
% 4.71/5.15 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 4.71/5.15 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 4.71/5.15 = ( numeral_numeral_real @ V ) ) )
% 4.71/5.15 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 4.71/5.15 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 4.71/5.15 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_number_of(3)
% 4.71/5.15 thf(fact_7133_max__number__of_I3_J,axiom,
% 4.71/5.15 ! [U: num,V: num] :
% 4.71/5.15 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 4.71/5.15 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 4.71/5.15 = ( numeral_numeral_rat @ V ) ) )
% 4.71/5.15 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 4.71/5.15 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 4.71/5.15 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_number_of(3)
% 4.71/5.15 thf(fact_7134_max__number__of_I3_J,axiom,
% 4.71/5.15 ! [U: num,V: num] :
% 4.71/5.15 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 4.71/5.15 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 4.71/5.15 = ( numeral_numeral_int @ V ) ) )
% 4.71/5.15 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 4.71/5.15 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 4.71/5.15 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_number_of(3)
% 4.71/5.15 thf(fact_7135_max__number__of_I2_J,axiom,
% 4.71/5.15 ! [U: num,V: num] :
% 4.71/5.15 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 4.71/5.15 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 4.71/5.15 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 4.71/5.15 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 4.71/5.15 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 4.71/5.15 = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_number_of(2)
% 4.71/5.15 thf(fact_7136_max__number__of_I2_J,axiom,
% 4.71/5.15 ! [U: num,V: num] :
% 4.71/5.15 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 4.71/5.15 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 4.71/5.15 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 4.71/5.15 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 4.71/5.15 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 4.71/5.15 = ( numeral_numeral_real @ U ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_number_of(2)
% 4.71/5.15 thf(fact_7137_max__number__of_I2_J,axiom,
% 4.71/5.15 ! [U: num,V: num] :
% 4.71/5.15 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 4.71/5.15 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 4.71/5.15 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 4.71/5.15 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 4.71/5.15 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 4.71/5.15 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_number_of(2)
% 4.71/5.15 thf(fact_7138_max__number__of_I2_J,axiom,
% 4.71/5.15 ! [U: num,V: num] :
% 4.71/5.15 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 4.71/5.15 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 4.71/5.15 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 4.71/5.15 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 4.71/5.15 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 4.71/5.15 = ( numeral_numeral_int @ U ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_number_of(2)
% 4.71/5.15 thf(fact_7139_of__nat__max,axiom,
% 4.71/5.15 ! [X: nat,Y: nat] :
% 4.71/5.15 ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X @ Y ) )
% 4.71/5.15 = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( semiri1316708129612266289at_nat @ Y ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % of_nat_max
% 4.71/5.15 thf(fact_7140_of__nat__max,axiom,
% 4.71/5.15 ! [X: nat,Y: nat] :
% 4.71/5.15 ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X @ Y ) )
% 4.71/5.15 = ( ord_max_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % of_nat_max
% 4.71/5.15 thf(fact_7141_of__nat__max,axiom,
% 4.71/5.15 ! [X: nat,Y: nat] :
% 4.71/5.15 ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X @ Y ) )
% 4.71/5.15 = ( ord_max_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ Y ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % of_nat_max
% 4.71/5.15 thf(fact_7142_of__nat__max,axiom,
% 4.71/5.15 ! [X: nat,Y: nat] :
% 4.71/5.15 ( ( semiri681578069525770553at_rat @ ( ord_max_nat @ X @ Y ) )
% 4.71/5.15 = ( ord_max_rat @ ( semiri681578069525770553at_rat @ X ) @ ( semiri681578069525770553at_rat @ Y ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % of_nat_max
% 4.71/5.15 thf(fact_7143_max__absorb2,axiom,
% 4.71/5.15 ! [X: set_int,Y: set_int] :
% 4.71/5.15 ( ( ord_less_eq_set_int @ X @ Y )
% 4.71/5.15 => ( ( ord_max_set_int @ X @ Y )
% 4.71/5.15 = Y ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_absorb2
% 4.71/5.15 thf(fact_7144_max__absorb2,axiom,
% 4.71/5.15 ! [X: rat,Y: rat] :
% 4.71/5.15 ( ( ord_less_eq_rat @ X @ Y )
% 4.71/5.15 => ( ( ord_max_rat @ X @ Y )
% 4.71/5.15 = Y ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_absorb2
% 4.71/5.15 thf(fact_7145_max__absorb2,axiom,
% 4.71/5.15 ! [X: num,Y: num] :
% 4.71/5.15 ( ( ord_less_eq_num @ X @ Y )
% 4.71/5.15 => ( ( ord_max_num @ X @ Y )
% 4.71/5.15 = Y ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_absorb2
% 4.71/5.15 thf(fact_7146_max__absorb2,axiom,
% 4.71/5.15 ! [X: nat,Y: nat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ X @ Y )
% 4.71/5.15 => ( ( ord_max_nat @ X @ Y )
% 4.71/5.15 = Y ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_absorb2
% 4.71/5.15 thf(fact_7147_max__absorb2,axiom,
% 4.71/5.15 ! [X: int,Y: int] :
% 4.71/5.15 ( ( ord_less_eq_int @ X @ Y )
% 4.71/5.15 => ( ( ord_max_int @ X @ Y )
% 4.71/5.15 = Y ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_absorb2
% 4.71/5.15 thf(fact_7148_max__absorb1,axiom,
% 4.71/5.15 ! [Y: set_int,X: set_int] :
% 4.71/5.15 ( ( ord_less_eq_set_int @ Y @ X )
% 4.71/5.15 => ( ( ord_max_set_int @ X @ Y )
% 4.71/5.15 = X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_absorb1
% 4.71/5.15 thf(fact_7149_max__absorb1,axiom,
% 4.71/5.15 ! [Y: rat,X: rat] :
% 4.71/5.15 ( ( ord_less_eq_rat @ Y @ X )
% 4.71/5.15 => ( ( ord_max_rat @ X @ Y )
% 4.71/5.15 = X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_absorb1
% 4.71/5.15 thf(fact_7150_max__absorb1,axiom,
% 4.71/5.15 ! [Y: num,X: num] :
% 4.71/5.15 ( ( ord_less_eq_num @ Y @ X )
% 4.71/5.15 => ( ( ord_max_num @ X @ Y )
% 4.71/5.15 = X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_absorb1
% 4.71/5.15 thf(fact_7151_max__absorb1,axiom,
% 4.71/5.15 ! [Y: nat,X: nat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ Y @ X )
% 4.71/5.15 => ( ( ord_max_nat @ X @ Y )
% 4.71/5.15 = X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_absorb1
% 4.71/5.15 thf(fact_7152_max__absorb1,axiom,
% 4.71/5.15 ! [Y: int,X: int] :
% 4.71/5.15 ( ( ord_less_eq_int @ Y @ X )
% 4.71/5.15 => ( ( ord_max_int @ X @ Y )
% 4.71/5.15 = X ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_absorb1
% 4.71/5.15 thf(fact_7153_max__def,axiom,
% 4.71/5.15 ( ord_max_set_int
% 4.71/5.15 = ( ^ [A4: set_int,B4: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_def
% 4.71/5.15 thf(fact_7154_max__def,axiom,
% 4.71/5.15 ( ord_max_rat
% 4.71/5.15 = ( ^ [A4: rat,B4: rat] : ( if_rat @ ( ord_less_eq_rat @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_def
% 4.71/5.15 thf(fact_7155_max__def,axiom,
% 4.71/5.15 ( ord_max_num
% 4.71/5.15 = ( ^ [A4: num,B4: num] : ( if_num @ ( ord_less_eq_num @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_def
% 4.71/5.15 thf(fact_7156_max__def,axiom,
% 4.71/5.15 ( ord_max_nat
% 4.71/5.15 = ( ^ [A4: nat,B4: nat] : ( if_nat @ ( ord_less_eq_nat @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_def
% 4.71/5.15 thf(fact_7157_max__def,axiom,
% 4.71/5.15 ( ord_max_int
% 4.71/5.15 = ( ^ [A4: int,B4: int] : ( if_int @ ( ord_less_eq_int @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_def
% 4.71/5.15 thf(fact_7158_max__add__distrib__left,axiom,
% 4.71/5.15 ! [X: real,Y: real,Z: real] :
% 4.71/5.15 ( ( plus_plus_real @ ( ord_max_real @ X @ Y ) @ Z )
% 4.71/5.15 = ( ord_max_real @ ( plus_plus_real @ X @ Z ) @ ( plus_plus_real @ Y @ Z ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_add_distrib_left
% 4.71/5.15 thf(fact_7159_max__add__distrib__left,axiom,
% 4.71/5.15 ! [X: rat,Y: rat,Z: rat] :
% 4.71/5.15 ( ( plus_plus_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 4.71/5.15 = ( ord_max_rat @ ( plus_plus_rat @ X @ Z ) @ ( plus_plus_rat @ Y @ Z ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_add_distrib_left
% 4.71/5.15 thf(fact_7160_max__add__distrib__left,axiom,
% 4.71/5.15 ! [X: int,Y: int,Z: int] :
% 4.71/5.15 ( ( plus_plus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 4.71/5.15 = ( ord_max_int @ ( plus_plus_int @ X @ Z ) @ ( plus_plus_int @ Y @ Z ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_add_distrib_left
% 4.71/5.15 thf(fact_7161_max__add__distrib__left,axiom,
% 4.71/5.15 ! [X: nat,Y: nat,Z: nat] :
% 4.71/5.15 ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y ) @ Z )
% 4.71/5.15 = ( ord_max_nat @ ( plus_plus_nat @ X @ Z ) @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_add_distrib_left
% 4.71/5.15 thf(fact_7162_max__add__distrib__right,axiom,
% 4.71/5.15 ! [X: real,Y: real,Z: real] :
% 4.71/5.15 ( ( plus_plus_real @ X @ ( ord_max_real @ Y @ Z ) )
% 4.71/5.15 = ( ord_max_real @ ( plus_plus_real @ X @ Y ) @ ( plus_plus_real @ X @ Z ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_add_distrib_right
% 4.71/5.15 thf(fact_7163_max__add__distrib__right,axiom,
% 4.71/5.15 ! [X: rat,Y: rat,Z: rat] :
% 4.71/5.15 ( ( plus_plus_rat @ X @ ( ord_max_rat @ Y @ Z ) )
% 4.71/5.15 = ( ord_max_rat @ ( plus_plus_rat @ X @ Y ) @ ( plus_plus_rat @ X @ Z ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_add_distrib_right
% 4.71/5.15 thf(fact_7164_max__add__distrib__right,axiom,
% 4.71/5.15 ! [X: int,Y: int,Z: int] :
% 4.71/5.15 ( ( plus_plus_int @ X @ ( ord_max_int @ Y @ Z ) )
% 4.71/5.15 = ( ord_max_int @ ( plus_plus_int @ X @ Y ) @ ( plus_plus_int @ X @ Z ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_add_distrib_right
% 4.71/5.15 thf(fact_7165_max__add__distrib__right,axiom,
% 4.71/5.15 ! [X: nat,Y: nat,Z: nat] :
% 4.71/5.15 ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y @ Z ) )
% 4.71/5.15 = ( ord_max_nat @ ( plus_plus_nat @ X @ Y ) @ ( plus_plus_nat @ X @ Z ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_add_distrib_right
% 4.71/5.15 thf(fact_7166_max__diff__distrib__left,axiom,
% 4.71/5.15 ! [X: real,Y: real,Z: real] :
% 4.71/5.15 ( ( minus_minus_real @ ( ord_max_real @ X @ Y ) @ Z )
% 4.71/5.15 = ( ord_max_real @ ( minus_minus_real @ X @ Z ) @ ( minus_minus_real @ Y @ Z ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_diff_distrib_left
% 4.71/5.15 thf(fact_7167_max__diff__distrib__left,axiom,
% 4.71/5.15 ! [X: rat,Y: rat,Z: rat] :
% 4.71/5.15 ( ( minus_minus_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 4.71/5.15 = ( ord_max_rat @ ( minus_minus_rat @ X @ Z ) @ ( minus_minus_rat @ Y @ Z ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_diff_distrib_left
% 4.71/5.15 thf(fact_7168_max__diff__distrib__left,axiom,
% 4.71/5.15 ! [X: int,Y: int,Z: int] :
% 4.71/5.15 ( ( minus_minus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 4.71/5.15 = ( ord_max_int @ ( minus_minus_int @ X @ Z ) @ ( minus_minus_int @ Y @ Z ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_diff_distrib_left
% 4.71/5.15 thf(fact_7169_nat__add__max__right,axiom,
% 4.71/5.15 ! [M2: nat,N: nat,Q4: nat] :
% 4.71/5.15 ( ( plus_plus_nat @ M2 @ ( ord_max_nat @ N @ Q4 ) )
% 4.71/5.15 = ( ord_max_nat @ ( plus_plus_nat @ M2 @ N ) @ ( plus_plus_nat @ M2 @ Q4 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % nat_add_max_right
% 4.71/5.15 thf(fact_7170_nat__add__max__left,axiom,
% 4.71/5.15 ! [M2: nat,N: nat,Q4: nat] :
% 4.71/5.15 ( ( plus_plus_nat @ ( ord_max_nat @ M2 @ N ) @ Q4 )
% 4.71/5.15 = ( ord_max_nat @ ( plus_plus_nat @ M2 @ Q4 ) @ ( plus_plus_nat @ N @ Q4 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % nat_add_max_left
% 4.71/5.15 thf(fact_7171_nat__mult__max__left,axiom,
% 4.71/5.15 ! [M2: nat,N: nat,Q4: nat] :
% 4.71/5.15 ( ( times_times_nat @ ( ord_max_nat @ M2 @ N ) @ Q4 )
% 4.71/5.15 = ( ord_max_nat @ ( times_times_nat @ M2 @ Q4 ) @ ( times_times_nat @ N @ Q4 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % nat_mult_max_left
% 4.71/5.15 thf(fact_7172_nat__mult__max__right,axiom,
% 4.71/5.15 ! [M2: nat,N: nat,Q4: nat] :
% 4.71/5.15 ( ( times_times_nat @ M2 @ ( ord_max_nat @ N @ Q4 ) )
% 4.71/5.15 = ( ord_max_nat @ ( times_times_nat @ M2 @ N ) @ ( times_times_nat @ M2 @ Q4 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % nat_mult_max_right
% 4.71/5.15 thf(fact_7173_max__def__raw,axiom,
% 4.71/5.15 ( ord_max_set_int
% 4.71/5.15 = ( ^ [A4: set_int,B4: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_def_raw
% 4.71/5.15 thf(fact_7174_max__def__raw,axiom,
% 4.71/5.15 ( ord_max_rat
% 4.71/5.15 = ( ^ [A4: rat,B4: rat] : ( if_rat @ ( ord_less_eq_rat @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_def_raw
% 4.71/5.15 thf(fact_7175_max__def__raw,axiom,
% 4.71/5.15 ( ord_max_num
% 4.71/5.15 = ( ^ [A4: num,B4: num] : ( if_num @ ( ord_less_eq_num @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_def_raw
% 4.71/5.15 thf(fact_7176_max__def__raw,axiom,
% 4.71/5.15 ( ord_max_nat
% 4.71/5.15 = ( ^ [A4: nat,B4: nat] : ( if_nat @ ( ord_less_eq_nat @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_def_raw
% 4.71/5.15 thf(fact_7177_max__def__raw,axiom,
% 4.71/5.15 ( ord_max_int
% 4.71/5.15 = ( ^ [A4: int,B4: int] : ( if_int @ ( ord_less_eq_int @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_def_raw
% 4.71/5.15 thf(fact_7178_nat__minus__add__max,axiom,
% 4.71/5.15 ! [N: nat,M2: nat] :
% 4.71/5.15 ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M2 ) @ M2 )
% 4.71/5.15 = ( ord_max_nat @ N @ M2 ) ) ).
% 4.71/5.15
% 4.71/5.15 % nat_minus_add_max
% 4.71/5.15 thf(fact_7179_vebt__insert_Osimps_I5_J,axiom,
% 4.71/5.15 ! [Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 4.71/5.15 ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 4.71/5.15 = ( if_VEBT_VEBT
% 4.71/5.15 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.71/5.15 & ~ ( ( X = Mi )
% 4.71/5.15 | ( X = Ma ) ) )
% 4.71/5.15 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ X @ Mi ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ Ma ) ) ) @ ( suc @ ( suc @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 4.71/5.15 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % vebt_insert.simps(5)
% 4.71/5.15 thf(fact_7180_vebt__delete_Opelims,axiom,
% 4.71/5.15 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 4.71/5.15 ( ( ( vEBT_vebt_delete @ X @ Xa2 )
% 4.71/5.15 = Y )
% 4.71/5.15 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 4.71/5.15 => ( ! [A5: $o,B5: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.15 => ( ( Xa2 = zero_zero_nat )
% 4.71/5.15 => ( ( Y
% 4.71/5.15 = ( vEBT_Leaf @ $false @ B5 ) )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ zero_zero_nat ) ) ) ) )
% 4.71/5.15 => ( ! [A5: $o,B5: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.15 => ( ( Xa2
% 4.71/5.15 = ( suc @ zero_zero_nat ) )
% 4.71/5.15 => ( ( Y
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ $false ) )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 4.71/5.15 => ( ! [A5: $o,B5: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.15 => ! [N2: nat] :
% 4.71/5.15 ( ( Xa2
% 4.71/5.15 = ( suc @ ( suc @ N2 ) ) )
% 4.71/5.15 => ( ( Y
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ ( suc @ N2 ) ) ) ) ) ) )
% 4.71/5.15 => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 4.71/5.15 => ( ( Y
% 4.71/5.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 4.71/5.15 => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 4.71/5.15 => ( ( Y
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 4.71/5.15 => ~ ( 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 ) ) ) )
% 4.71/5.15 => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 4.71/5.15 => ( ( Y
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 4.71/5.15 => ~ ( 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 ) ) ) )
% 4.71/5.15 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 4.71/5.15 => ( ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 4.71/5.15 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) )
% 4.71/5.15 & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 4.71/5.15 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 4.71/5.15 => ( ( ( ( Xa2 = Mi2 )
% 4.71/5.15 & ( Xa2 = Ma2 ) )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) )
% 4.71/5.15 & ( ~ ( ( Xa2 = Mi2 )
% 4.71/5.15 & ( Xa2 = Ma2 ) )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 @ ( vEBT_Node
% 4.71/5.15 @ ( some_P7363390416028606310at_nat
% 4.71/5.15 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 4.71/5.15 @ ( if_nat
% 4.71/5.15 @ ( ( ( Xa2 = Mi2 )
% 4.71/5.15 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 4.71/5.15 = Ma2 ) )
% 4.71/5.15 & ( ( Xa2 != Mi2 )
% 4.71/5.15 => ( Xa2 = Ma2 ) ) )
% 4.71/5.15 @ ( if_nat
% 4.71/5.15 @ ( ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 = none_nat )
% 4.71/5.15 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 4.71/5.15 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( 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 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 4.71/5.15 @ Ma2 ) ) )
% 4.71/5.15 @ ( suc @ ( suc @ Va ) )
% 4.71/5.15 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 @ ( vEBT_Node
% 4.71/5.15 @ ( some_P7363390416028606310at_nat
% 4.71/5.15 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 4.71/5.15 @ ( if_nat
% 4.71/5.15 @ ( ( ( Xa2 = Mi2 )
% 4.71/5.15 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 4.71/5.15 = Ma2 ) )
% 4.71/5.15 & ( ( Xa2 != Mi2 )
% 4.71/5.15 => ( Xa2 = Ma2 ) ) )
% 4.71/5.15 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( 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 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 4.71/5.15 @ Ma2 ) ) )
% 4.71/5.15 @ ( suc @ ( suc @ Va ) )
% 4.71/5.15 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( 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 @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 @ Summary2 ) )
% 4.71/5.15 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) ) ) ) ) )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % vebt_delete.pelims
% 4.71/5.15 thf(fact_7181_vebt__insert_Opelims,axiom,
% 4.71/5.15 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 4.71/5.15 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 4.71/5.15 = Y )
% 4.71/5.15 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 4.71/5.15 => ( ! [A5: $o,B5: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.15 => ( ( ( ( Xa2 = zero_zero_nat )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( vEBT_Leaf @ $true @ B5 ) ) )
% 4.71/5.15 & ( ( Xa2 != zero_zero_nat )
% 4.71/5.15 => ( ( ( Xa2 = one_one_nat )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ $true ) ) )
% 4.71/5.15 & ( ( Xa2 != one_one_nat )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ) )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 4.71/5.15 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) )
% 4.71/5.15 => ( ( Y
% 4.71/5.15 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S3 ) @ Xa2 ) ) ) )
% 4.71/5.15 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) )
% 4.71/5.15 => ( ( Y
% 4.71/5.15 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S3 ) @ Xa2 ) ) ) )
% 4.71/5.15 => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 4.71/5.15 => ( ( Y
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 4.71/5.15 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 4.71/5.15 => ( ( Y
% 4.71/5.15 = ( if_VEBT_VEBT
% 4.71/5.15 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 & ~ ( ( Xa2 = Mi2 )
% 4.71/5.15 | ( Xa2 = Ma2 ) ) )
% 4.71/5.15 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 4.71/5.15 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % vebt_insert.pelims
% 4.71/5.15 thf(fact_7182_vebt__member_Opelims_I1_J,axiom,
% 4.71/5.15 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 4.71/5.15 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 4.71/5.15 = Y )
% 4.71/5.15 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 4.71/5.15 => ( ! [A5: $o,B5: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.15 => ( ( Y
% 4.71/5.15 = ( ( ( Xa2 = zero_zero_nat )
% 4.71/5.15 => A5 )
% 4.71/5.15 & ( ( Xa2 != zero_zero_nat )
% 4.71/5.15 => ( ( ( Xa2 = one_one_nat )
% 4.71/5.15 => B5 )
% 4.71/5.15 & ( Xa2 = one_one_nat ) ) ) ) )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 4.71/5.15 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 4.71/5.15 => ( ~ Y
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 4.71/5.15 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 4.71/5.15 => ( ~ Y
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 4.71/5.15 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 4.71/5.15 => ( ~ Y
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 4.71/5.15 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 4.71/5.15 => ( ( Y
% 4.71/5.15 = ( ( Xa2 != Mi2 )
% 4.71/5.15 => ( ( Xa2 != Ma2 )
% 4.71/5.15 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 4.71/5.15 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 4.71/5.15 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 4.71/5.15 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 4.71/5.15 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % vebt_member.pelims(1)
% 4.71/5.15 thf(fact_7183_vebt__member_Opelims_I3_J,axiom,
% 4.71/5.15 ! [X: vEBT_VEBT,Xa2: nat] :
% 4.71/5.15 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 4.71/5.15 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 4.71/5.15 => ( ! [A5: $o,B5: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.15 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 4.71/5.15 => ( ( ( Xa2 = zero_zero_nat )
% 4.71/5.15 => A5 )
% 4.71/5.15 & ( ( Xa2 != zero_zero_nat )
% 4.71/5.15 => ( ( ( Xa2 = one_one_nat )
% 4.71/5.15 => B5 )
% 4.71/5.15 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 4.71/5.15 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 4.71/5.15 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) )
% 4.71/5.15 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) )
% 4.71/5.15 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 4.71/5.15 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 4.71/5.15 => ( ( Xa2 != Mi2 )
% 4.71/5.15 => ( ( Xa2 != Ma2 )
% 4.71/5.15 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 4.71/5.15 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 4.71/5.15 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 4.71/5.15 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 4.71/5.15 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % vebt_member.pelims(3)
% 4.71/5.15 thf(fact_7184_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 4.71/5.15 ! [X: vEBT_VEBT,Xa2: nat] :
% 4.71/5.15 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 4.71/5.15 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 4.71/5.15 => ( ! [A5: $o,B5: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.15 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 4.71/5.15 => ( ( ( Xa2 = zero_zero_nat )
% 4.71/5.15 => A5 )
% 4.71/5.15 & ( ( Xa2 != zero_zero_nat )
% 4.71/5.15 => ( ( ( Xa2 = one_one_nat )
% 4.71/5.15 => B5 )
% 4.71/5.15 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 4.71/5.15 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 4.71/5.15 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) )
% 4.71/5.15 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) @ Xa2 ) )
% 4.71/5.15 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % VEBT_internal.naive_member.pelims(3)
% 4.71/5.15 thf(fact_7185_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 4.71/5.15 ! [X: vEBT_VEBT,Xa2: nat] :
% 4.71/5.15 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 4.71/5.15 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 4.71/5.15 => ( ! [A5: $o,B5: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.15 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 4.71/5.15 => ~ ( ( ( Xa2 = zero_zero_nat )
% 4.71/5.15 => A5 )
% 4.71/5.15 & ( ( Xa2 != zero_zero_nat )
% 4.71/5.15 => ( ( ( Xa2 = one_one_nat )
% 4.71/5.15 => B5 )
% 4.71/5.15 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 4.71/5.15 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) )
% 4.71/5.15 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) @ Xa2 ) )
% 4.71/5.15 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % VEBT_internal.naive_member.pelims(2)
% 4.71/5.15 thf(fact_7186_vebt__member_Opelims_I2_J,axiom,
% 4.71/5.15 ! [X: vEBT_VEBT,Xa2: nat] :
% 4.71/5.15 ( ( vEBT_vebt_member @ X @ Xa2 )
% 4.71/5.15 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 4.71/5.15 => ( ! [A5: $o,B5: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.15 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 4.71/5.15 => ~ ( ( ( Xa2 = zero_zero_nat )
% 4.71/5.15 => A5 )
% 4.71/5.15 & ( ( Xa2 != zero_zero_nat )
% 4.71/5.15 => ( ( ( Xa2 = one_one_nat )
% 4.71/5.15 => B5 )
% 4.71/5.15 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 4.71/5.15 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 4.71/5.15 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 4.71/5.15 => ~ ( ( Xa2 != Mi2 )
% 4.71/5.15 => ( ( Xa2 != Ma2 )
% 4.71/5.15 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 4.71/5.15 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 4.71/5.15 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 4.71/5.15 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 4.71/5.15 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % vebt_member.pelims(2)
% 4.71/5.15 thf(fact_7187_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 4.71/5.15 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 4.71/5.15 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 4.71/5.15 = Y )
% 4.71/5.15 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 4.71/5.15 => ( ! [A5: $o,B5: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.71/5.15 => ( ( Y
% 4.71/5.15 = ( ( ( Xa2 = zero_zero_nat )
% 4.71/5.15 => A5 )
% 4.71/5.15 & ( ( Xa2 != zero_zero_nat )
% 4.71/5.15 => ( ( ( Xa2 = one_one_nat )
% 4.71/5.15 => B5 )
% 4.71/5.15 & ( Xa2 = one_one_nat ) ) ) ) )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 4.71/5.15 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 4.71/5.15 => ( ~ Y
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 4.71/5.15 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) )
% 4.71/5.15 => ( ( Y
% 4.71/5.15 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S3 ) @ Xa2 ) ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % VEBT_internal.naive_member.pelims(1)
% 4.71/5.15 thf(fact_7188_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 4.71/5.15 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 4.71/5.15 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 4.71/5.15 = Y )
% 4.71/5.15 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 4.71/5.15 => ( ! [Uu2: $o,Uv2: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 4.71/5.15 => ( ~ Y
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 4.71/5.15 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 4.71/5.15 => ( ~ Y
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) ) )
% 4.71/5.15 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 4.71/5.15 => ( ( Y
% 4.71/5.15 = ( ( Xa2 = Mi2 )
% 4.71/5.15 | ( Xa2 = Ma2 ) ) )
% 4.71/5.15 => ~ ( 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 ) ) ) )
% 4.71/5.15 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 4.71/5.15 => ( ( Y
% 4.71/5.15 = ( ( Xa2 = Mi2 )
% 4.71/5.15 | ( Xa2 = Ma2 )
% 4.71/5.15 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ Xa2 ) ) ) )
% 4.71/5.15 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 4.71/5.15 => ( ( Y
% 4.71/5.15 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % VEBT_internal.membermima.pelims(1)
% 4.71/5.15 thf(fact_7189_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 4.71/5.15 ! [X: vEBT_VEBT,Xa2: nat] :
% 4.71/5.15 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 4.71/5.15 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 4.71/5.15 => ( ! [Uu2: $o,Uv2: $o] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) )
% 4.71/5.15 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 4.71/5.15 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) )
% 4.71/5.15 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 4.71/5.15 => ( ( 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 ) )
% 4.71/5.15 => ( ( Xa2 = Mi2 )
% 4.71/5.15 | ( Xa2 = Ma2 ) ) ) )
% 4.71/5.15 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 4.71/5.15 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ Xa2 ) )
% 4.71/5.15 => ( ( Xa2 = Mi2 )
% 4.71/5.15 | ( Xa2 = Ma2 )
% 4.71/5.15 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) )
% 4.71/5.15 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 4.71/5.15 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ Xa2 ) )
% 4.71/5.15 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % VEBT_internal.membermima.pelims(3)
% 4.71/5.15 thf(fact_7190_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 4.71/5.15 ! [X: vEBT_VEBT,Xa2: nat] :
% 4.71/5.15 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 4.71/5.15 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 4.71/5.15 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 4.71/5.15 => ( ( 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 ) )
% 4.71/5.15 => ~ ( ( Xa2 = Mi2 )
% 4.71/5.15 | ( Xa2 = Ma2 ) ) ) )
% 4.71/5.15 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 4.71/5.15 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ Xa2 ) )
% 4.71/5.15 => ~ ( ( Xa2 = Mi2 )
% 4.71/5.15 | ( Xa2 = Ma2 )
% 4.71/5.15 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) )
% 4.71/5.15 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 4.71/5.15 ( ( X
% 4.71/5.15 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 4.71/5.15 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ Xa2 ) )
% 4.71/5.15 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.71/5.15 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.71/5.15 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % VEBT_internal.membermima.pelims(2)
% 4.71/5.15 thf(fact_7191_max_Oabsorb3,axiom,
% 4.71/5.15 ! [B: real,A: real] :
% 4.71/5.15 ( ( ord_less_real @ B @ A )
% 4.71/5.15 => ( ( ord_max_real @ A @ B )
% 4.71/5.15 = A ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.absorb3
% 4.71/5.15 thf(fact_7192_max_Oabsorb3,axiom,
% 4.71/5.15 ! [B: rat,A: rat] :
% 4.71/5.15 ( ( ord_less_rat @ B @ A )
% 4.71/5.15 => ( ( ord_max_rat @ A @ B )
% 4.71/5.15 = A ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.absorb3
% 4.71/5.15 thf(fact_7193_max_Oabsorb3,axiom,
% 4.71/5.15 ! [B: num,A: num] :
% 4.71/5.15 ( ( ord_less_num @ B @ A )
% 4.71/5.15 => ( ( ord_max_num @ A @ B )
% 4.71/5.15 = A ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.absorb3
% 4.71/5.15 thf(fact_7194_max_Oabsorb3,axiom,
% 4.71/5.15 ! [B: nat,A: nat] :
% 4.71/5.15 ( ( ord_less_nat @ B @ A )
% 4.71/5.15 => ( ( ord_max_nat @ A @ B )
% 4.71/5.15 = A ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.absorb3
% 4.71/5.15 thf(fact_7195_max_Oabsorb3,axiom,
% 4.71/5.15 ! [B: int,A: int] :
% 4.71/5.15 ( ( ord_less_int @ B @ A )
% 4.71/5.15 => ( ( ord_max_int @ A @ B )
% 4.71/5.15 = A ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.absorb3
% 4.71/5.15 thf(fact_7196_max_Oabsorb4,axiom,
% 4.71/5.15 ! [A: real,B: real] :
% 4.71/5.15 ( ( ord_less_real @ A @ B )
% 4.71/5.15 => ( ( ord_max_real @ A @ B )
% 4.71/5.15 = B ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.absorb4
% 4.71/5.15 thf(fact_7197_max_Oabsorb4,axiom,
% 4.71/5.15 ! [A: rat,B: rat] :
% 4.71/5.15 ( ( ord_less_rat @ A @ B )
% 4.71/5.15 => ( ( ord_max_rat @ A @ B )
% 4.71/5.15 = B ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.absorb4
% 4.71/5.15 thf(fact_7198_max_Oabsorb4,axiom,
% 4.71/5.15 ! [A: num,B: num] :
% 4.71/5.15 ( ( ord_less_num @ A @ B )
% 4.71/5.15 => ( ( ord_max_num @ A @ B )
% 4.71/5.15 = B ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.absorb4
% 4.71/5.15 thf(fact_7199_max_Oabsorb4,axiom,
% 4.71/5.15 ! [A: nat,B: nat] :
% 4.71/5.15 ( ( ord_less_nat @ A @ B )
% 4.71/5.15 => ( ( ord_max_nat @ A @ B )
% 4.71/5.15 = B ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.absorb4
% 4.71/5.15 thf(fact_7200_max_Oabsorb4,axiom,
% 4.71/5.15 ! [A: int,B: int] :
% 4.71/5.15 ( ( ord_less_int @ A @ B )
% 4.71/5.15 => ( ( ord_max_int @ A @ B )
% 4.71/5.15 = B ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.absorb4
% 4.71/5.15 thf(fact_7201_max__less__iff__conj,axiom,
% 4.71/5.15 ! [X: real,Y: real,Z: real] :
% 4.71/5.15 ( ( ord_less_real @ ( ord_max_real @ X @ Y ) @ Z )
% 4.71/5.15 = ( ( ord_less_real @ X @ Z )
% 4.71/5.15 & ( ord_less_real @ Y @ Z ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_less_iff_conj
% 4.71/5.15 thf(fact_7202_max__less__iff__conj,axiom,
% 4.71/5.15 ! [X: rat,Y: rat,Z: rat] :
% 4.71/5.15 ( ( ord_less_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 4.71/5.15 = ( ( ord_less_rat @ X @ Z )
% 4.71/5.15 & ( ord_less_rat @ Y @ Z ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_less_iff_conj
% 4.71/5.15 thf(fact_7203_max__less__iff__conj,axiom,
% 4.71/5.15 ! [X: num,Y: num,Z: num] :
% 4.71/5.15 ( ( ord_less_num @ ( ord_max_num @ X @ Y ) @ Z )
% 4.71/5.15 = ( ( ord_less_num @ X @ Z )
% 4.71/5.15 & ( ord_less_num @ Y @ Z ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_less_iff_conj
% 4.71/5.15 thf(fact_7204_max__less__iff__conj,axiom,
% 4.71/5.15 ! [X: nat,Y: nat,Z: nat] :
% 4.71/5.15 ( ( ord_less_nat @ ( ord_max_nat @ X @ Y ) @ Z )
% 4.71/5.15 = ( ( ord_less_nat @ X @ Z )
% 4.71/5.15 & ( ord_less_nat @ Y @ Z ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_less_iff_conj
% 4.71/5.15 thf(fact_7205_max__less__iff__conj,axiom,
% 4.71/5.15 ! [X: int,Y: int,Z: int] :
% 4.71/5.15 ( ( ord_less_int @ ( ord_max_int @ X @ Y ) @ Z )
% 4.71/5.15 = ( ( ord_less_int @ X @ Z )
% 4.71/5.15 & ( ord_less_int @ Y @ Z ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max_less_iff_conj
% 4.71/5.15 thf(fact_7206_max_Oabsorb1,axiom,
% 4.71/5.15 ! [B: rat,A: rat] :
% 4.71/5.15 ( ( ord_less_eq_rat @ B @ A )
% 4.71/5.15 => ( ( ord_max_rat @ A @ B )
% 4.71/5.15 = A ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.absorb1
% 4.71/5.15 thf(fact_7207_max_Oabsorb1,axiom,
% 4.71/5.15 ! [B: num,A: num] :
% 4.71/5.15 ( ( ord_less_eq_num @ B @ A )
% 4.71/5.15 => ( ( ord_max_num @ A @ B )
% 4.71/5.15 = A ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.absorb1
% 4.71/5.15 thf(fact_7208_max_Oabsorb1,axiom,
% 4.71/5.15 ! [B: nat,A: nat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ B @ A )
% 4.71/5.15 => ( ( ord_max_nat @ A @ B )
% 4.71/5.15 = A ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.absorb1
% 4.71/5.15 thf(fact_7209_max_Oabsorb1,axiom,
% 4.71/5.15 ! [B: int,A: int] :
% 4.71/5.15 ( ( ord_less_eq_int @ B @ A )
% 4.71/5.15 => ( ( ord_max_int @ A @ B )
% 4.71/5.15 = A ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.absorb1
% 4.71/5.15 thf(fact_7210_max_Oabsorb2,axiom,
% 4.71/5.15 ! [A: rat,B: rat] :
% 4.71/5.15 ( ( ord_less_eq_rat @ A @ B )
% 4.71/5.15 => ( ( ord_max_rat @ A @ B )
% 4.71/5.15 = B ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.absorb2
% 4.71/5.15 thf(fact_7211_max_Oabsorb2,axiom,
% 4.71/5.15 ! [A: num,B: num] :
% 4.71/5.15 ( ( ord_less_eq_num @ A @ B )
% 4.71/5.15 => ( ( ord_max_num @ A @ B )
% 4.71/5.15 = B ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.absorb2
% 4.71/5.15 thf(fact_7212_max_Oabsorb2,axiom,
% 4.71/5.15 ! [A: nat,B: nat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ A @ B )
% 4.71/5.15 => ( ( ord_max_nat @ A @ B )
% 4.71/5.15 = B ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.absorb2
% 4.71/5.15 thf(fact_7213_max_Oabsorb2,axiom,
% 4.71/5.15 ! [A: int,B: int] :
% 4.71/5.15 ( ( ord_less_eq_int @ A @ B )
% 4.71/5.15 => ( ( ord_max_int @ A @ B )
% 4.71/5.15 = B ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.absorb2
% 4.71/5.15 thf(fact_7214_max_Obounded__iff,axiom,
% 4.71/5.15 ! [B: rat,C: rat,A: rat] :
% 4.71/5.15 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 4.71/5.15 = ( ( ord_less_eq_rat @ B @ A )
% 4.71/5.15 & ( ord_less_eq_rat @ C @ A ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.bounded_iff
% 4.71/5.15 thf(fact_7215_max_Obounded__iff,axiom,
% 4.71/5.15 ! [B: num,C: num,A: num] :
% 4.71/5.15 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 4.71/5.15 = ( ( ord_less_eq_num @ B @ A )
% 4.71/5.15 & ( ord_less_eq_num @ C @ A ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.bounded_iff
% 4.71/5.15 thf(fact_7216_max_Obounded__iff,axiom,
% 4.71/5.15 ! [B: nat,C: nat,A: nat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 4.71/5.15 = ( ( ord_less_eq_nat @ B @ A )
% 4.71/5.15 & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.bounded_iff
% 4.71/5.15 thf(fact_7217_max_Obounded__iff,axiom,
% 4.71/5.15 ! [B: int,C: int,A: int] :
% 4.71/5.15 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 4.71/5.15 = ( ( ord_less_eq_int @ B @ A )
% 4.71/5.15 & ( ord_less_eq_int @ C @ A ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.bounded_iff
% 4.71/5.15 thf(fact_7218_max_Omono,axiom,
% 4.71/5.15 ! [C: rat,A: rat,D: rat,B: rat] :
% 4.71/5.15 ( ( ord_less_eq_rat @ C @ A )
% 4.71/5.15 => ( ( ord_less_eq_rat @ D @ B )
% 4.71/5.15 => ( ord_less_eq_rat @ ( ord_max_rat @ C @ D ) @ ( ord_max_rat @ A @ B ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.mono
% 4.71/5.15 thf(fact_7219_max_Omono,axiom,
% 4.71/5.15 ! [C: num,A: num,D: num,B: num] :
% 4.71/5.15 ( ( ord_less_eq_num @ C @ A )
% 4.71/5.15 => ( ( ord_less_eq_num @ D @ B )
% 4.71/5.15 => ( ord_less_eq_num @ ( ord_max_num @ C @ D ) @ ( ord_max_num @ A @ B ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.mono
% 4.71/5.15 thf(fact_7220_max_Omono,axiom,
% 4.71/5.15 ! [C: nat,A: nat,D: nat,B: nat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ C @ A )
% 4.71/5.15 => ( ( ord_less_eq_nat @ D @ B )
% 4.71/5.15 => ( ord_less_eq_nat @ ( ord_max_nat @ C @ D ) @ ( ord_max_nat @ A @ B ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.mono
% 4.71/5.15 thf(fact_7221_max_Omono,axiom,
% 4.71/5.15 ! [C: int,A: int,D: int,B: int] :
% 4.71/5.15 ( ( ord_less_eq_int @ C @ A )
% 4.71/5.15 => ( ( ord_less_eq_int @ D @ B )
% 4.71/5.15 => ( ord_less_eq_int @ ( ord_max_int @ C @ D ) @ ( ord_max_int @ A @ B ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.mono
% 4.71/5.15 thf(fact_7222_max_OorderE,axiom,
% 4.71/5.15 ! [B: rat,A: rat] :
% 4.71/5.15 ( ( ord_less_eq_rat @ B @ A )
% 4.71/5.15 => ( A
% 4.71/5.15 = ( ord_max_rat @ A @ B ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.orderE
% 4.71/5.15 thf(fact_7223_max_OorderE,axiom,
% 4.71/5.15 ! [B: num,A: num] :
% 4.71/5.15 ( ( ord_less_eq_num @ B @ A )
% 4.71/5.15 => ( A
% 4.71/5.15 = ( ord_max_num @ A @ B ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.orderE
% 4.71/5.15 thf(fact_7224_max_OorderE,axiom,
% 4.71/5.15 ! [B: nat,A: nat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ B @ A )
% 4.71/5.15 => ( A
% 4.71/5.15 = ( ord_max_nat @ A @ B ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.orderE
% 4.71/5.15 thf(fact_7225_max_OorderE,axiom,
% 4.71/5.15 ! [B: int,A: int] :
% 4.71/5.15 ( ( ord_less_eq_int @ B @ A )
% 4.71/5.15 => ( A
% 4.71/5.15 = ( ord_max_int @ A @ B ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.orderE
% 4.71/5.15 thf(fact_7226_max_OorderI,axiom,
% 4.71/5.15 ! [A: rat,B: rat] :
% 4.71/5.15 ( ( A
% 4.71/5.15 = ( ord_max_rat @ A @ B ) )
% 4.71/5.15 => ( ord_less_eq_rat @ B @ A ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.orderI
% 4.71/5.15 thf(fact_7227_max_OorderI,axiom,
% 4.71/5.15 ! [A: num,B: num] :
% 4.71/5.15 ( ( A
% 4.71/5.15 = ( ord_max_num @ A @ B ) )
% 4.71/5.15 => ( ord_less_eq_num @ B @ A ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.orderI
% 4.71/5.15 thf(fact_7228_max_OorderI,axiom,
% 4.71/5.15 ! [A: nat,B: nat] :
% 4.71/5.15 ( ( A
% 4.71/5.15 = ( ord_max_nat @ A @ B ) )
% 4.71/5.15 => ( ord_less_eq_nat @ B @ A ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.orderI
% 4.71/5.15 thf(fact_7229_max_OorderI,axiom,
% 4.71/5.15 ! [A: int,B: int] :
% 4.71/5.15 ( ( A
% 4.71/5.15 = ( ord_max_int @ A @ B ) )
% 4.71/5.15 => ( ord_less_eq_int @ B @ A ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.orderI
% 4.71/5.15 thf(fact_7230_max_OboundedE,axiom,
% 4.71/5.15 ! [B: rat,C: rat,A: rat] :
% 4.71/5.15 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 4.71/5.15 => ~ ( ( ord_less_eq_rat @ B @ A )
% 4.71/5.15 => ~ ( ord_less_eq_rat @ C @ A ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.boundedE
% 4.71/5.15 thf(fact_7231_max_OboundedE,axiom,
% 4.71/5.15 ! [B: num,C: num,A: num] :
% 4.71/5.15 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 4.71/5.15 => ~ ( ( ord_less_eq_num @ B @ A )
% 4.71/5.15 => ~ ( ord_less_eq_num @ C @ A ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.boundedE
% 4.71/5.15 thf(fact_7232_max_OboundedE,axiom,
% 4.71/5.15 ! [B: nat,C: nat,A: nat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 4.71/5.15 => ~ ( ( ord_less_eq_nat @ B @ A )
% 4.71/5.15 => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.boundedE
% 4.71/5.15 thf(fact_7233_max_OboundedE,axiom,
% 4.71/5.15 ! [B: int,C: int,A: int] :
% 4.71/5.15 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 4.71/5.15 => ~ ( ( ord_less_eq_int @ B @ A )
% 4.71/5.15 => ~ ( ord_less_eq_int @ C @ A ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.boundedE
% 4.71/5.15 thf(fact_7234_max_OboundedI,axiom,
% 4.71/5.15 ! [B: rat,A: rat,C: rat] :
% 4.71/5.15 ( ( ord_less_eq_rat @ B @ A )
% 4.71/5.15 => ( ( ord_less_eq_rat @ C @ A )
% 4.71/5.15 => ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.boundedI
% 4.71/5.15 thf(fact_7235_max_OboundedI,axiom,
% 4.71/5.15 ! [B: num,A: num,C: num] :
% 4.71/5.15 ( ( ord_less_eq_num @ B @ A )
% 4.71/5.15 => ( ( ord_less_eq_num @ C @ A )
% 4.71/5.15 => ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.boundedI
% 4.71/5.15 thf(fact_7236_max_OboundedI,axiom,
% 4.71/5.15 ! [B: nat,A: nat,C: nat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ B @ A )
% 4.71/5.15 => ( ( ord_less_eq_nat @ C @ A )
% 4.71/5.15 => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.boundedI
% 4.71/5.15 thf(fact_7237_max_OboundedI,axiom,
% 4.71/5.15 ! [B: int,A: int,C: int] :
% 4.71/5.15 ( ( ord_less_eq_int @ B @ A )
% 4.71/5.15 => ( ( ord_less_eq_int @ C @ A )
% 4.71/5.15 => ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.boundedI
% 4.71/5.15 thf(fact_7238_max_Oorder__iff,axiom,
% 4.71/5.15 ( ord_less_eq_rat
% 4.71/5.15 = ( ^ [B4: rat,A4: rat] :
% 4.71/5.15 ( A4
% 4.71/5.15 = ( ord_max_rat @ A4 @ B4 ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.order_iff
% 4.71/5.15 thf(fact_7239_max_Oorder__iff,axiom,
% 4.71/5.15 ( ord_less_eq_num
% 4.71/5.15 = ( ^ [B4: num,A4: num] :
% 4.71/5.15 ( A4
% 4.71/5.15 = ( ord_max_num @ A4 @ B4 ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.order_iff
% 4.71/5.15 thf(fact_7240_max_Oorder__iff,axiom,
% 4.71/5.15 ( ord_less_eq_nat
% 4.71/5.15 = ( ^ [B4: nat,A4: nat] :
% 4.71/5.15 ( A4
% 4.71/5.15 = ( ord_max_nat @ A4 @ B4 ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.order_iff
% 4.71/5.15 thf(fact_7241_max_Oorder__iff,axiom,
% 4.71/5.15 ( ord_less_eq_int
% 4.71/5.15 = ( ^ [B4: int,A4: int] :
% 4.71/5.15 ( A4
% 4.71/5.15 = ( ord_max_int @ A4 @ B4 ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.order_iff
% 4.71/5.15 thf(fact_7242_max_Ocobounded1,axiom,
% 4.71/5.15 ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( ord_max_rat @ A @ B ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.cobounded1
% 4.71/5.15 thf(fact_7243_max_Ocobounded1,axiom,
% 4.71/5.15 ! [A: num,B: num] : ( ord_less_eq_num @ A @ ( ord_max_num @ A @ B ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.cobounded1
% 4.71/5.15 thf(fact_7244_max_Ocobounded1,axiom,
% 4.71/5.15 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.cobounded1
% 4.71/5.15 thf(fact_7245_max_Ocobounded1,axiom,
% 4.71/5.15 ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.cobounded1
% 4.71/5.15 thf(fact_7246_max_Ocobounded2,axiom,
% 4.71/5.15 ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( ord_max_rat @ A @ B ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.cobounded2
% 4.71/5.15 thf(fact_7247_max_Ocobounded2,axiom,
% 4.71/5.15 ! [B: num,A: num] : ( ord_less_eq_num @ B @ ( ord_max_num @ A @ B ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.cobounded2
% 4.71/5.15 thf(fact_7248_max_Ocobounded2,axiom,
% 4.71/5.15 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.cobounded2
% 4.71/5.15 thf(fact_7249_max_Ocobounded2,axiom,
% 4.71/5.15 ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.cobounded2
% 4.71/5.15 thf(fact_7250_le__max__iff__disj,axiom,
% 4.71/5.15 ! [Z: rat,X: rat,Y: rat] :
% 4.71/5.15 ( ( ord_less_eq_rat @ Z @ ( ord_max_rat @ X @ Y ) )
% 4.71/5.15 = ( ( ord_less_eq_rat @ Z @ X )
% 4.71/5.15 | ( ord_less_eq_rat @ Z @ Y ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % le_max_iff_disj
% 4.71/5.15 thf(fact_7251_le__max__iff__disj,axiom,
% 4.71/5.15 ! [Z: num,X: num,Y: num] :
% 4.71/5.15 ( ( ord_less_eq_num @ Z @ ( ord_max_num @ X @ Y ) )
% 4.71/5.15 = ( ( ord_less_eq_num @ Z @ X )
% 4.71/5.15 | ( ord_less_eq_num @ Z @ Y ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % le_max_iff_disj
% 4.71/5.15 thf(fact_7252_le__max__iff__disj,axiom,
% 4.71/5.15 ! [Z: nat,X: nat,Y: nat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ Z @ ( ord_max_nat @ X @ Y ) )
% 4.71/5.15 = ( ( ord_less_eq_nat @ Z @ X )
% 4.71/5.15 | ( ord_less_eq_nat @ Z @ Y ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % le_max_iff_disj
% 4.71/5.15 thf(fact_7253_le__max__iff__disj,axiom,
% 4.71/5.15 ! [Z: int,X: int,Y: int] :
% 4.71/5.15 ( ( ord_less_eq_int @ Z @ ( ord_max_int @ X @ Y ) )
% 4.71/5.15 = ( ( ord_less_eq_int @ Z @ X )
% 4.71/5.15 | ( ord_less_eq_int @ Z @ Y ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % le_max_iff_disj
% 4.71/5.15 thf(fact_7254_max_Oabsorb__iff1,axiom,
% 4.71/5.15 ( ord_less_eq_rat
% 4.71/5.15 = ( ^ [B4: rat,A4: rat] :
% 4.71/5.15 ( ( ord_max_rat @ A4 @ B4 )
% 4.71/5.15 = A4 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.absorb_iff1
% 4.71/5.15 thf(fact_7255_max_Oabsorb__iff1,axiom,
% 4.71/5.15 ( ord_less_eq_num
% 4.71/5.15 = ( ^ [B4: num,A4: num] :
% 4.71/5.15 ( ( ord_max_num @ A4 @ B4 )
% 4.71/5.15 = A4 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.absorb_iff1
% 4.71/5.15 thf(fact_7256_max_Oabsorb__iff1,axiom,
% 4.71/5.15 ( ord_less_eq_nat
% 4.71/5.15 = ( ^ [B4: nat,A4: nat] :
% 4.71/5.15 ( ( ord_max_nat @ A4 @ B4 )
% 4.71/5.15 = A4 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.absorb_iff1
% 4.71/5.15 thf(fact_7257_max_Oabsorb__iff1,axiom,
% 4.71/5.15 ( ord_less_eq_int
% 4.71/5.15 = ( ^ [B4: int,A4: int] :
% 4.71/5.15 ( ( ord_max_int @ A4 @ B4 )
% 4.71/5.15 = A4 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.absorb_iff1
% 4.71/5.15 thf(fact_7258_max_Oabsorb__iff2,axiom,
% 4.71/5.15 ( ord_less_eq_rat
% 4.71/5.15 = ( ^ [A4: rat,B4: rat] :
% 4.71/5.15 ( ( ord_max_rat @ A4 @ B4 )
% 4.71/5.15 = B4 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.absorb_iff2
% 4.71/5.15 thf(fact_7259_max_Oabsorb__iff2,axiom,
% 4.71/5.15 ( ord_less_eq_num
% 4.71/5.15 = ( ^ [A4: num,B4: num] :
% 4.71/5.15 ( ( ord_max_num @ A4 @ B4 )
% 4.71/5.15 = B4 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.absorb_iff2
% 4.71/5.15 thf(fact_7260_max_Oabsorb__iff2,axiom,
% 4.71/5.15 ( ord_less_eq_nat
% 4.71/5.15 = ( ^ [A4: nat,B4: nat] :
% 4.71/5.15 ( ( ord_max_nat @ A4 @ B4 )
% 4.71/5.15 = B4 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.absorb_iff2
% 4.71/5.15 thf(fact_7261_max_Oabsorb__iff2,axiom,
% 4.71/5.15 ( ord_less_eq_int
% 4.71/5.15 = ( ^ [A4: int,B4: int] :
% 4.71/5.15 ( ( ord_max_int @ A4 @ B4 )
% 4.71/5.15 = B4 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.absorb_iff2
% 4.71/5.15 thf(fact_7262_max_OcoboundedI1,axiom,
% 4.71/5.15 ! [C: rat,A: rat,B: rat] :
% 4.71/5.15 ( ( ord_less_eq_rat @ C @ A )
% 4.71/5.15 => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.coboundedI1
% 4.71/5.15 thf(fact_7263_max_OcoboundedI1,axiom,
% 4.71/5.15 ! [C: num,A: num,B: num] :
% 4.71/5.15 ( ( ord_less_eq_num @ C @ A )
% 4.71/5.15 => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.coboundedI1
% 4.71/5.15 thf(fact_7264_max_OcoboundedI1,axiom,
% 4.71/5.15 ! [C: nat,A: nat,B: nat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ C @ A )
% 4.71/5.15 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.coboundedI1
% 4.71/5.15 thf(fact_7265_max_OcoboundedI1,axiom,
% 4.71/5.15 ! [C: int,A: int,B: int] :
% 4.71/5.15 ( ( ord_less_eq_int @ C @ A )
% 4.71/5.15 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.coboundedI1
% 4.71/5.15 thf(fact_7266_max_OcoboundedI2,axiom,
% 4.71/5.15 ! [C: rat,B: rat,A: rat] :
% 4.71/5.15 ( ( ord_less_eq_rat @ C @ B )
% 4.71/5.15 => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.coboundedI2
% 4.71/5.15 thf(fact_7267_max_OcoboundedI2,axiom,
% 4.71/5.15 ! [C: num,B: num,A: num] :
% 4.71/5.15 ( ( ord_less_eq_num @ C @ B )
% 4.71/5.15 => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.coboundedI2
% 4.71/5.15 thf(fact_7268_max_OcoboundedI2,axiom,
% 4.71/5.15 ! [C: nat,B: nat,A: nat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ C @ B )
% 4.71/5.15 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.coboundedI2
% 4.71/5.15 thf(fact_7269_max_OcoboundedI2,axiom,
% 4.71/5.15 ! [C: int,B: int,A: int] :
% 4.71/5.15 ( ( ord_less_eq_int @ C @ B )
% 4.71/5.15 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.coboundedI2
% 4.71/5.15 thf(fact_7270_less__max__iff__disj,axiom,
% 4.71/5.15 ! [Z: real,X: real,Y: real] :
% 4.71/5.15 ( ( ord_less_real @ Z @ ( ord_max_real @ X @ Y ) )
% 4.71/5.15 = ( ( ord_less_real @ Z @ X )
% 4.71/5.15 | ( ord_less_real @ Z @ Y ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % less_max_iff_disj
% 4.71/5.15 thf(fact_7271_less__max__iff__disj,axiom,
% 4.71/5.15 ! [Z: rat,X: rat,Y: rat] :
% 4.71/5.15 ( ( ord_less_rat @ Z @ ( ord_max_rat @ X @ Y ) )
% 4.71/5.15 = ( ( ord_less_rat @ Z @ X )
% 4.71/5.15 | ( ord_less_rat @ Z @ Y ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % less_max_iff_disj
% 4.71/5.15 thf(fact_7272_less__max__iff__disj,axiom,
% 4.71/5.15 ! [Z: num,X: num,Y: num] :
% 4.71/5.15 ( ( ord_less_num @ Z @ ( ord_max_num @ X @ Y ) )
% 4.71/5.15 = ( ( ord_less_num @ Z @ X )
% 4.71/5.15 | ( ord_less_num @ Z @ Y ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % less_max_iff_disj
% 4.71/5.15 thf(fact_7273_less__max__iff__disj,axiom,
% 4.71/5.15 ! [Z: nat,X: nat,Y: nat] :
% 4.71/5.15 ( ( ord_less_nat @ Z @ ( ord_max_nat @ X @ Y ) )
% 4.71/5.15 = ( ( ord_less_nat @ Z @ X )
% 4.71/5.15 | ( ord_less_nat @ Z @ Y ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % less_max_iff_disj
% 4.71/5.15 thf(fact_7274_less__max__iff__disj,axiom,
% 4.71/5.15 ! [Z: int,X: int,Y: int] :
% 4.71/5.15 ( ( ord_less_int @ Z @ ( ord_max_int @ X @ Y ) )
% 4.71/5.15 = ( ( ord_less_int @ Z @ X )
% 4.71/5.15 | ( ord_less_int @ Z @ Y ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % less_max_iff_disj
% 4.71/5.15 thf(fact_7275_max_Ostrict__boundedE,axiom,
% 4.71/5.15 ! [B: real,C: real,A: real] :
% 4.71/5.15 ( ( ord_less_real @ ( ord_max_real @ B @ C ) @ A )
% 4.71/5.15 => ~ ( ( ord_less_real @ B @ A )
% 4.71/5.15 => ~ ( ord_less_real @ C @ A ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.strict_boundedE
% 4.71/5.15 thf(fact_7276_max_Ostrict__boundedE,axiom,
% 4.71/5.15 ! [B: rat,C: rat,A: rat] :
% 4.71/5.15 ( ( ord_less_rat @ ( ord_max_rat @ B @ C ) @ A )
% 4.71/5.15 => ~ ( ( ord_less_rat @ B @ A )
% 4.71/5.15 => ~ ( ord_less_rat @ C @ A ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.strict_boundedE
% 4.71/5.15 thf(fact_7277_max_Ostrict__boundedE,axiom,
% 4.71/5.15 ! [B: num,C: num,A: num] :
% 4.71/5.15 ( ( ord_less_num @ ( ord_max_num @ B @ C ) @ A )
% 4.71/5.15 => ~ ( ( ord_less_num @ B @ A )
% 4.71/5.15 => ~ ( ord_less_num @ C @ A ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.strict_boundedE
% 4.71/5.15 thf(fact_7278_max_Ostrict__boundedE,axiom,
% 4.71/5.15 ! [B: nat,C: nat,A: nat] :
% 4.71/5.15 ( ( ord_less_nat @ ( ord_max_nat @ B @ C ) @ A )
% 4.71/5.15 => ~ ( ( ord_less_nat @ B @ A )
% 4.71/5.15 => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.strict_boundedE
% 4.71/5.15 thf(fact_7279_max_Ostrict__boundedE,axiom,
% 4.71/5.15 ! [B: int,C: int,A: int] :
% 4.71/5.15 ( ( ord_less_int @ ( ord_max_int @ B @ C ) @ A )
% 4.71/5.15 => ~ ( ( ord_less_int @ B @ A )
% 4.71/5.15 => ~ ( ord_less_int @ C @ A ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.strict_boundedE
% 4.71/5.15 thf(fact_7280_max_Ostrict__order__iff,axiom,
% 4.71/5.15 ( ord_less_real
% 4.71/5.15 = ( ^ [B4: real,A4: real] :
% 4.71/5.15 ( ( A4
% 4.71/5.15 = ( ord_max_real @ A4 @ B4 ) )
% 4.71/5.15 & ( A4 != B4 ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.strict_order_iff
% 4.71/5.15 thf(fact_7281_max_Ostrict__order__iff,axiom,
% 4.71/5.15 ( ord_less_rat
% 4.71/5.15 = ( ^ [B4: rat,A4: rat] :
% 4.71/5.15 ( ( A4
% 4.71/5.15 = ( ord_max_rat @ A4 @ B4 ) )
% 4.71/5.15 & ( A4 != B4 ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.strict_order_iff
% 4.71/5.15 thf(fact_7282_max_Ostrict__order__iff,axiom,
% 4.71/5.15 ( ord_less_num
% 4.71/5.15 = ( ^ [B4: num,A4: num] :
% 4.71/5.15 ( ( A4
% 4.71/5.15 = ( ord_max_num @ A4 @ B4 ) )
% 4.71/5.15 & ( A4 != B4 ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.strict_order_iff
% 4.71/5.15 thf(fact_7283_max_Ostrict__order__iff,axiom,
% 4.71/5.15 ( ord_less_nat
% 4.71/5.15 = ( ^ [B4: nat,A4: nat] :
% 4.71/5.15 ( ( A4
% 4.71/5.15 = ( ord_max_nat @ A4 @ B4 ) )
% 4.71/5.15 & ( A4 != B4 ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.strict_order_iff
% 4.71/5.15 thf(fact_7284_max_Ostrict__order__iff,axiom,
% 4.71/5.15 ( ord_less_int
% 4.71/5.15 = ( ^ [B4: int,A4: int] :
% 4.71/5.15 ( ( A4
% 4.71/5.15 = ( ord_max_int @ A4 @ B4 ) )
% 4.71/5.15 & ( A4 != B4 ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.strict_order_iff
% 4.71/5.15 thf(fact_7285_max_Ostrict__coboundedI1,axiom,
% 4.71/5.15 ! [C: real,A: real,B: real] :
% 4.71/5.15 ( ( ord_less_real @ C @ A )
% 4.71/5.15 => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.strict_coboundedI1
% 4.71/5.15 thf(fact_7286_max_Ostrict__coboundedI1,axiom,
% 4.71/5.15 ! [C: rat,A: rat,B: rat] :
% 4.71/5.15 ( ( ord_less_rat @ C @ A )
% 4.71/5.15 => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.strict_coboundedI1
% 4.71/5.15 thf(fact_7287_max_Ostrict__coboundedI1,axiom,
% 4.71/5.15 ! [C: num,A: num,B: num] :
% 4.71/5.15 ( ( ord_less_num @ C @ A )
% 4.71/5.15 => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.strict_coboundedI1
% 4.71/5.15 thf(fact_7288_max_Ostrict__coboundedI1,axiom,
% 4.71/5.15 ! [C: nat,A: nat,B: nat] :
% 4.71/5.15 ( ( ord_less_nat @ C @ A )
% 4.71/5.15 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.strict_coboundedI1
% 4.71/5.15 thf(fact_7289_max_Ostrict__coboundedI1,axiom,
% 4.71/5.15 ! [C: int,A: int,B: int] :
% 4.71/5.15 ( ( ord_less_int @ C @ A )
% 4.71/5.15 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.strict_coboundedI1
% 4.71/5.15 thf(fact_7290_max_Ostrict__coboundedI2,axiom,
% 4.71/5.15 ! [C: real,B: real,A: real] :
% 4.71/5.15 ( ( ord_less_real @ C @ B )
% 4.71/5.15 => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.strict_coboundedI2
% 4.71/5.15 thf(fact_7291_max_Ostrict__coboundedI2,axiom,
% 4.71/5.15 ! [C: rat,B: rat,A: rat] :
% 4.71/5.15 ( ( ord_less_rat @ C @ B )
% 4.71/5.15 => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.strict_coboundedI2
% 4.71/5.15 thf(fact_7292_max_Ostrict__coboundedI2,axiom,
% 4.71/5.15 ! [C: num,B: num,A: num] :
% 4.71/5.15 ( ( ord_less_num @ C @ B )
% 4.71/5.15 => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.strict_coboundedI2
% 4.71/5.15 thf(fact_7293_max_Ostrict__coboundedI2,axiom,
% 4.71/5.15 ! [C: nat,B: nat,A: nat] :
% 4.71/5.15 ( ( ord_less_nat @ C @ B )
% 4.71/5.15 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.strict_coboundedI2
% 4.71/5.15 thf(fact_7294_max_Ostrict__coboundedI2,axiom,
% 4.71/5.15 ! [C: int,B: int,A: int] :
% 4.71/5.15 ( ( ord_less_int @ C @ B )
% 4.71/5.15 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % max.strict_coboundedI2
% 4.71/5.15 thf(fact_7295_monoseq__arctan__series,axiom,
% 4.71/5.15 ! [X: real] :
% 4.71/5.15 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 4.71/5.15 => ( topolo6980174941875973593q_real
% 4.71/5.15 @ ^ [N4: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % monoseq_arctan_series
% 4.71/5.15 thf(fact_7296_gbinomial__code,axiom,
% 4.71/5.15 ( gbinomial_complex
% 4.71/5.15 = ( ^ [A4: complex,K3: nat] :
% 4.71/5.15 ( if_complex @ ( K3 = zero_zero_nat ) @ one_one_complex
% 4.71/5.15 @ ( divide1717551699836669952omplex
% 4.71/5.15 @ ( set_fo1517530859248394432omplex
% 4.71/5.15 @ ^ [L3: nat] : ( times_times_complex @ ( minus_minus_complex @ A4 @ ( semiri8010041392384452111omplex @ L3 ) ) )
% 4.71/5.15 @ zero_zero_nat
% 4.71/5.15 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 4.71/5.15 @ one_one_complex )
% 4.71/5.15 @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % gbinomial_code
% 4.71/5.15 thf(fact_7297_gbinomial__code,axiom,
% 4.71/5.15 ( gbinomial_rat
% 4.71/5.15 = ( ^ [A4: rat,K3: nat] :
% 4.71/5.15 ( if_rat @ ( K3 = zero_zero_nat ) @ one_one_rat
% 4.71/5.15 @ ( divide_divide_rat
% 4.71/5.15 @ ( set_fo1949268297981939178at_rat
% 4.71/5.15 @ ^ [L3: nat] : ( times_times_rat @ ( minus_minus_rat @ A4 @ ( semiri681578069525770553at_rat @ L3 ) ) )
% 4.71/5.15 @ zero_zero_nat
% 4.71/5.15 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 4.71/5.15 @ one_one_rat )
% 4.71/5.15 @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % gbinomial_code
% 4.71/5.15 thf(fact_7298_gbinomial__code,axiom,
% 4.71/5.15 ( gbinomial_real
% 4.71/5.15 = ( ^ [A4: real,K3: nat] :
% 4.71/5.15 ( if_real @ ( K3 = zero_zero_nat ) @ one_one_real
% 4.71/5.15 @ ( divide_divide_real
% 4.71/5.15 @ ( set_fo3111899725591712190t_real
% 4.71/5.15 @ ^ [L3: nat] : ( times_times_real @ ( minus_minus_real @ A4 @ ( semiri5074537144036343181t_real @ L3 ) ) )
% 4.71/5.15 @ zero_zero_nat
% 4.71/5.15 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 4.71/5.15 @ one_one_real )
% 4.71/5.15 @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % gbinomial_code
% 4.71/5.15 thf(fact_7299_pochhammer__times__pochhammer__half,axiom,
% 4.71/5.15 ! [Z: complex,N: nat] :
% 4.71/5.15 ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ ( suc @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 4.71/5.15 = ( groups6464643781859351333omplex
% 4.71/5.15 @ ^ [K3: nat] : ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % pochhammer_times_pochhammer_half
% 4.71/5.15 thf(fact_7300_pochhammer__times__pochhammer__half,axiom,
% 4.71/5.15 ! [Z: real,N: nat] :
% 4.71/5.15 ( ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ ( suc @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 4.71/5.15 = ( groups129246275422532515t_real
% 4.71/5.15 @ ^ [K3: nat] : ( plus_plus_real @ Z @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % pochhammer_times_pochhammer_half
% 4.71/5.15 thf(fact_7301_pochhammer__times__pochhammer__half,axiom,
% 4.71/5.15 ! [Z: rat,N: nat] :
% 4.71/5.15 ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 4.71/5.15 = ( groups73079841787564623at_rat
% 4.71/5.15 @ ^ [K3: nat] : ( plus_plus_rat @ Z @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % pochhammer_times_pochhammer_half
% 4.71/5.15 thf(fact_7302_ln__series,axiom,
% 4.71/5.15 ! [X: real] :
% 4.71/5.15 ( ( ord_less_real @ zero_zero_real @ X )
% 4.71/5.15 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 4.71/5.15 => ( ( ln_ln_real @ X )
% 4.71/5.15 = ( suminf_real
% 4.71/5.15 @ ^ [N4: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N4 @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X @ one_one_real ) @ ( suc @ N4 ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % ln_series
% 4.71/5.15 thf(fact_7303_signed__take__bit__rec,axiom,
% 4.71/5.15 ( bit_ri6519982836138164636nteger
% 4.71/5.15 = ( ^ [N4: nat,A4: code_integer] : ( if_Code_integer @ ( N4 = 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 @ N4 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % signed_take_bit_rec
% 4.71/5.15 thf(fact_7304_signed__take__bit__rec,axiom,
% 4.71/5.15 ( bit_ri631733984087533419it_int
% 4.71/5.15 = ( ^ [N4: nat,A4: int] : ( if_int @ ( N4 = 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 @ N4 @ one_one_nat ) @ ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % signed_take_bit_rec
% 4.71/5.15 thf(fact_7305_arctan__series,axiom,
% 4.71/5.15 ! [X: real] :
% 4.71/5.15 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 4.71/5.15 => ( ( arctan @ X )
% 4.71/5.15 = ( suminf_real
% 4.71/5.15 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % arctan_series
% 4.71/5.15 thf(fact_7306_signed__take__bit__of__0,axiom,
% 4.71/5.15 ! [N: nat] :
% 4.71/5.15 ( ( bit_ri631733984087533419it_int @ N @ zero_zero_int )
% 4.71/5.15 = zero_zero_int ) ).
% 4.71/5.15
% 4.71/5.15 % signed_take_bit_of_0
% 4.71/5.15 thf(fact_7307_signed__take__bit__Suc__1,axiom,
% 4.71/5.15 ! [N: nat] :
% 4.71/5.15 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ one_one_int )
% 4.71/5.15 = one_one_int ) ).
% 4.71/5.15
% 4.71/5.15 % signed_take_bit_Suc_1
% 4.71/5.15 thf(fact_7308_signed__take__bit__of__minus__1,axiom,
% 4.71/5.15 ! [N: nat] :
% 4.71/5.15 ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 4.71/5.15 = ( uminus_uminus_int @ one_one_int ) ) ).
% 4.71/5.15
% 4.71/5.15 % signed_take_bit_of_minus_1
% 4.71/5.15 thf(fact_7309_signed__take__bit__numeral__of__1,axiom,
% 4.71/5.15 ! [K: num] :
% 4.71/5.15 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 4.71/5.15 = one_one_int ) ).
% 4.71/5.15
% 4.71/5.15 % signed_take_bit_numeral_of_1
% 4.71/5.15 thf(fact_7310_powser__zero,axiom,
% 4.71/5.15 ! [F: nat > complex] :
% 4.71/5.15 ( ( suminf_complex
% 4.71/5.15 @ ^ [N4: nat] : ( times_times_complex @ ( F @ N4 ) @ ( power_power_complex @ zero_zero_complex @ N4 ) ) )
% 4.71/5.15 = ( F @ zero_zero_nat ) ) ).
% 4.71/5.15
% 4.71/5.15 % powser_zero
% 4.71/5.15 thf(fact_7311_powser__zero,axiom,
% 4.71/5.15 ! [F: nat > real] :
% 4.71/5.15 ( ( suminf_real
% 4.71/5.15 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ ( power_power_real @ zero_zero_real @ N4 ) ) )
% 4.71/5.15 = ( F @ zero_zero_nat ) ) ).
% 4.71/5.15
% 4.71/5.15 % powser_zero
% 4.71/5.15 thf(fact_7312_prod_Ocl__ivl__Suc,axiom,
% 4.71/5.15 ! [N: nat,M2: nat,G2: nat > complex] :
% 4.71/5.15 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 4.71/5.15 => ( ( groups6464643781859351333omplex @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 4.71/5.15 = one_one_complex ) )
% 4.71/5.15 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 4.71/5.15 => ( ( groups6464643781859351333omplex @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 4.71/5.15 = ( times_times_complex @ ( groups6464643781859351333omplex @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.cl_ivl_Suc
% 4.71/5.15 thf(fact_7313_prod_Ocl__ivl__Suc,axiom,
% 4.71/5.15 ! [N: nat,M2: nat,G2: nat > real] :
% 4.71/5.15 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 4.71/5.15 => ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 4.71/5.15 = one_one_real ) )
% 4.71/5.15 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 4.71/5.15 => ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 4.71/5.15 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.cl_ivl_Suc
% 4.71/5.15 thf(fact_7314_prod_Ocl__ivl__Suc,axiom,
% 4.71/5.15 ! [N: nat,M2: nat,G2: nat > rat] :
% 4.71/5.15 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 4.71/5.15 => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 4.71/5.15 = one_one_rat ) )
% 4.71/5.15 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 4.71/5.15 => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 4.71/5.15 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.cl_ivl_Suc
% 4.71/5.15 thf(fact_7315_prod_Ocl__ivl__Suc,axiom,
% 4.71/5.15 ! [N: nat,M2: nat,G2: nat > nat] :
% 4.71/5.15 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 4.71/5.15 => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 4.71/5.15 = one_one_nat ) )
% 4.71/5.15 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 4.71/5.15 => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 4.71/5.15 = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.cl_ivl_Suc
% 4.71/5.15 thf(fact_7316_prod_Ocl__ivl__Suc,axiom,
% 4.71/5.15 ! [N: nat,M2: nat,G2: nat > int] :
% 4.71/5.15 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 4.71/5.15 => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 4.71/5.15 = one_one_int ) )
% 4.71/5.15 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 4.71/5.15 => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 4.71/5.15 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.cl_ivl_Suc
% 4.71/5.15 thf(fact_7317_signed__take__bit__0,axiom,
% 4.71/5.15 ! [A: code_integer] :
% 4.71/5.15 ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 4.71/5.15 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % signed_take_bit_0
% 4.71/5.15 thf(fact_7318_signed__take__bit__0,axiom,
% 4.71/5.15 ! [A: int] :
% 4.71/5.15 ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 4.71/5.15 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % signed_take_bit_0
% 4.71/5.15 thf(fact_7319_prod__atLeastAtMost__code,axiom,
% 4.71/5.15 ! [F: nat > complex,A: nat,B: nat] :
% 4.71/5.15 ( ( groups6464643781859351333omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 4.71/5.15 = ( set_fo1517530859248394432omplex
% 4.71/5.15 @ ^ [A4: nat] : ( times_times_complex @ ( F @ A4 ) )
% 4.71/5.15 @ A
% 4.71/5.15 @ B
% 4.71/5.15 @ one_one_complex ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod_atLeastAtMost_code
% 4.71/5.15 thf(fact_7320_prod__atLeastAtMost__code,axiom,
% 4.71/5.15 ! [F: nat > real,A: nat,B: nat] :
% 4.71/5.15 ( ( groups129246275422532515t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 4.71/5.15 = ( set_fo3111899725591712190t_real
% 4.71/5.15 @ ^ [A4: nat] : ( times_times_real @ ( F @ A4 ) )
% 4.71/5.15 @ A
% 4.71/5.15 @ B
% 4.71/5.15 @ one_one_real ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod_atLeastAtMost_code
% 4.71/5.15 thf(fact_7321_prod__atLeastAtMost__code,axiom,
% 4.71/5.15 ! [F: nat > rat,A: nat,B: nat] :
% 4.71/5.15 ( ( groups73079841787564623at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 4.71/5.15 = ( set_fo1949268297981939178at_rat
% 4.71/5.15 @ ^ [A4: nat] : ( times_times_rat @ ( F @ A4 ) )
% 4.71/5.15 @ A
% 4.71/5.15 @ B
% 4.71/5.15 @ one_one_rat ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod_atLeastAtMost_code
% 4.71/5.15 thf(fact_7322_prod__atLeastAtMost__code,axiom,
% 4.71/5.15 ! [F: nat > nat,A: nat,B: nat] :
% 4.71/5.15 ( ( groups708209901874060359at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 4.71/5.15 = ( set_fo2584398358068434914at_nat
% 4.71/5.15 @ ^ [A4: nat] : ( times_times_nat @ ( F @ A4 ) )
% 4.71/5.15 @ A
% 4.71/5.15 @ B
% 4.71/5.15 @ one_one_nat ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod_atLeastAtMost_code
% 4.71/5.15 thf(fact_7323_prod__atLeastAtMost__code,axiom,
% 4.71/5.15 ! [F: nat > int,A: nat,B: nat] :
% 4.71/5.15 ( ( groups705719431365010083at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 4.71/5.15 = ( set_fo2581907887559384638at_int
% 4.71/5.15 @ ^ [A4: nat] : ( times_times_int @ ( F @ A4 ) )
% 4.71/5.15 @ A
% 4.71/5.15 @ B
% 4.71/5.15 @ one_one_int ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod_atLeastAtMost_code
% 4.71/5.15 thf(fact_7324_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 4.71/5.15 ! [G2: nat > nat,M2: nat,N: nat] :
% 4.71/5.15 ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N ) ) )
% 4.71/5.15 = ( groups708209901874060359at_nat
% 4.71/5.15 @ ^ [I4: nat] : ( G2 @ ( suc @ I4 ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.shift_bounds_cl_Suc_ivl
% 4.71/5.15 thf(fact_7325_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 4.71/5.15 ! [G2: nat > int,M2: nat,N: nat] :
% 4.71/5.15 ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N ) ) )
% 4.71/5.15 = ( groups705719431365010083at_int
% 4.71/5.15 @ ^ [I4: nat] : ( G2 @ ( suc @ I4 ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.shift_bounds_cl_Suc_ivl
% 4.71/5.15 thf(fact_7326_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 4.71/5.15 ! [G2: nat > nat,M2: nat,K: nat,N: nat] :
% 4.71/5.15 ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 4.71/5.15 = ( groups708209901874060359at_nat
% 4.71/5.15 @ ^ [I4: nat] : ( G2 @ ( plus_plus_nat @ I4 @ K ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.shift_bounds_cl_nat_ivl
% 4.71/5.15 thf(fact_7327_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 4.71/5.15 ! [G2: nat > int,M2: nat,K: nat,N: nat] :
% 4.71/5.15 ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 4.71/5.15 = ( groups705719431365010083at_int
% 4.71/5.15 @ ^ [I4: nat] : ( G2 @ ( plus_plus_nat @ I4 @ K ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.shift_bounds_cl_nat_ivl
% 4.71/5.15 thf(fact_7328_prod_OatLeastAtMost__rev,axiom,
% 4.71/5.15 ! [G2: nat > nat,N: nat,M2: nat] :
% 4.71/5.15 ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ N @ M2 ) )
% 4.71/5.15 = ( groups708209901874060359at_nat
% 4.71/5.15 @ ^ [I4: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N ) @ I4 ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ N @ M2 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.atLeastAtMost_rev
% 4.71/5.15 thf(fact_7329_prod_OatLeastAtMost__rev,axiom,
% 4.71/5.15 ! [G2: nat > int,N: nat,M2: nat] :
% 4.71/5.15 ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ N @ M2 ) )
% 4.71/5.15 = ( groups705719431365010083at_int
% 4.71/5.15 @ ^ [I4: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N ) @ I4 ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ N @ M2 ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.atLeastAtMost_rev
% 4.71/5.15 thf(fact_7330_prod_OatLeast0__atMost__Suc,axiom,
% 4.71/5.15 ! [G2: nat > real,N: nat] :
% 4.71/5.15 ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 4.71/5.15 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.atLeast0_atMost_Suc
% 4.71/5.15 thf(fact_7331_prod_OatLeast0__atMost__Suc,axiom,
% 4.71/5.15 ! [G2: nat > rat,N: nat] :
% 4.71/5.15 ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 4.71/5.15 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.atLeast0_atMost_Suc
% 4.71/5.15 thf(fact_7332_prod_OatLeast0__atMost__Suc,axiom,
% 4.71/5.15 ! [G2: nat > nat,N: nat] :
% 4.71/5.15 ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 4.71/5.15 = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.atLeast0_atMost_Suc
% 4.71/5.15 thf(fact_7333_prod_OatLeast0__atMost__Suc,axiom,
% 4.71/5.15 ! [G2: nat > int,N: nat] :
% 4.71/5.15 ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 4.71/5.15 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.atLeast0_atMost_Suc
% 4.71/5.15 thf(fact_7334_prod_OatLeast__Suc__atMost,axiom,
% 4.71/5.15 ! [M2: nat,N: nat,G2: nat > real] :
% 4.71/5.15 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.15 => ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 4.71/5.15 = ( times_times_real @ ( G2 @ M2 ) @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.atLeast_Suc_atMost
% 4.71/5.15 thf(fact_7335_prod_OatLeast__Suc__atMost,axiom,
% 4.71/5.15 ! [M2: nat,N: nat,G2: nat > rat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.15 => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 4.71/5.15 = ( times_times_rat @ ( G2 @ M2 ) @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.atLeast_Suc_atMost
% 4.71/5.15 thf(fact_7336_prod_OatLeast__Suc__atMost,axiom,
% 4.71/5.15 ! [M2: nat,N: nat,G2: nat > nat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.15 => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 4.71/5.15 = ( times_times_nat @ ( G2 @ M2 ) @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.atLeast_Suc_atMost
% 4.71/5.15 thf(fact_7337_prod_OatLeast__Suc__atMost,axiom,
% 4.71/5.15 ! [M2: nat,N: nat,G2: nat > int] :
% 4.71/5.15 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.15 => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 4.71/5.15 = ( times_times_int @ ( G2 @ M2 ) @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.atLeast_Suc_atMost
% 4.71/5.15 thf(fact_7338_prod_Onat__ivl__Suc_H,axiom,
% 4.71/5.15 ! [M2: nat,N: nat,G2: nat > real] :
% 4.71/5.15 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 4.71/5.15 => ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 4.71/5.15 = ( times_times_real @ ( G2 @ ( suc @ N ) ) @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.nat_ivl_Suc'
% 4.71/5.15 thf(fact_7339_prod_Onat__ivl__Suc_H,axiom,
% 4.71/5.15 ! [M2: nat,N: nat,G2: nat > rat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 4.71/5.15 => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 4.71/5.15 = ( times_times_rat @ ( G2 @ ( suc @ N ) ) @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.nat_ivl_Suc'
% 4.71/5.15 thf(fact_7340_prod_Onat__ivl__Suc_H,axiom,
% 4.71/5.15 ! [M2: nat,N: nat,G2: nat > nat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 4.71/5.15 => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 4.71/5.15 = ( times_times_nat @ ( G2 @ ( suc @ N ) ) @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.nat_ivl_Suc'
% 4.71/5.15 thf(fact_7341_prod_Onat__ivl__Suc_H,axiom,
% 4.71/5.15 ! [M2: nat,N: nat,G2: nat > int] :
% 4.71/5.15 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 4.71/5.15 => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 4.71/5.15 = ( times_times_int @ ( G2 @ ( suc @ N ) ) @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.nat_ivl_Suc'
% 4.71/5.15 thf(fact_7342_prod_OSuc__reindex__ivl,axiom,
% 4.71/5.15 ! [M2: nat,N: nat,G2: nat > real] :
% 4.71/5.15 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.15 => ( ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 4.71/5.15 = ( times_times_real @ ( G2 @ M2 )
% 4.71/5.15 @ ( groups129246275422532515t_real
% 4.71/5.15 @ ^ [I4: nat] : ( G2 @ ( suc @ I4 ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.Suc_reindex_ivl
% 4.71/5.15 thf(fact_7343_prod_OSuc__reindex__ivl,axiom,
% 4.71/5.15 ! [M2: nat,N: nat,G2: nat > rat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.15 => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 4.71/5.15 = ( times_times_rat @ ( G2 @ M2 )
% 4.71/5.15 @ ( groups73079841787564623at_rat
% 4.71/5.15 @ ^ [I4: nat] : ( G2 @ ( suc @ I4 ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.Suc_reindex_ivl
% 4.71/5.15 thf(fact_7344_prod_OSuc__reindex__ivl,axiom,
% 4.71/5.15 ! [M2: nat,N: nat,G2: nat > nat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.15 => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 4.71/5.15 = ( times_times_nat @ ( G2 @ M2 )
% 4.71/5.15 @ ( groups708209901874060359at_nat
% 4.71/5.15 @ ^ [I4: nat] : ( G2 @ ( suc @ I4 ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.Suc_reindex_ivl
% 4.71/5.15 thf(fact_7345_prod_OSuc__reindex__ivl,axiom,
% 4.71/5.15 ! [M2: nat,N: nat,G2: nat > int] :
% 4.71/5.15 ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.15 => ( ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 4.71/5.15 = ( times_times_int @ ( G2 @ M2 )
% 4.71/5.15 @ ( groups705719431365010083at_int
% 4.71/5.15 @ ^ [I4: nat] : ( G2 @ ( suc @ I4 ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.Suc_reindex_ivl
% 4.71/5.15 thf(fact_7346_fact__prod,axiom,
% 4.71/5.15 ( semiri1406184849735516958ct_int
% 4.71/5.15 = ( ^ [N4: nat] :
% 4.71/5.15 ( semiri1314217659103216013at_int
% 4.71/5.15 @ ( groups708209901874060359at_nat
% 4.71/5.15 @ ^ [X3: nat] : X3
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % fact_prod
% 4.71/5.15 thf(fact_7347_fact__prod,axiom,
% 4.71/5.15 ( semiri773545260158071498ct_rat
% 4.71/5.15 = ( ^ [N4: nat] :
% 4.71/5.15 ( semiri681578069525770553at_rat
% 4.71/5.15 @ ( groups708209901874060359at_nat
% 4.71/5.15 @ ^ [X3: nat] : X3
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % fact_prod
% 4.71/5.15 thf(fact_7348_fact__prod,axiom,
% 4.71/5.15 ( semiri1408675320244567234ct_nat
% 4.71/5.15 = ( ^ [N4: nat] :
% 4.71/5.15 ( semiri1316708129612266289at_nat
% 4.71/5.15 @ ( groups708209901874060359at_nat
% 4.71/5.15 @ ^ [X3: nat] : X3
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % fact_prod
% 4.71/5.15 thf(fact_7349_fact__prod,axiom,
% 4.71/5.15 ( semiri2265585572941072030t_real
% 4.71/5.15 = ( ^ [N4: nat] :
% 4.71/5.15 ( semiri5074537144036343181t_real
% 4.71/5.15 @ ( groups708209901874060359at_nat
% 4.71/5.15 @ ^ [X3: nat] : X3
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % fact_prod
% 4.71/5.15 thf(fact_7350_prod_Oub__add__nat,axiom,
% 4.71/5.15 ! [M2: nat,N: nat,G2: nat > real,P6: nat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 4.71/5.15 => ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P6 ) ) )
% 4.71/5.15 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.ub_add_nat
% 4.71/5.15 thf(fact_7351_prod_Oub__add__nat,axiom,
% 4.71/5.15 ! [M2: nat,N: nat,G2: nat > rat,P6: nat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 4.71/5.15 => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P6 ) ) )
% 4.71/5.15 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.ub_add_nat
% 4.71/5.15 thf(fact_7352_prod_Oub__add__nat,axiom,
% 4.71/5.15 ! [M2: nat,N: nat,G2: nat > nat,P6: nat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 4.71/5.15 => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P6 ) ) )
% 4.71/5.15 = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.ub_add_nat
% 4.71/5.15 thf(fact_7353_prod_Oub__add__nat,axiom,
% 4.71/5.15 ! [M2: nat,N: nat,G2: nat > int,P6: nat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 4.71/5.15 => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P6 ) ) )
% 4.71/5.15 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P6 ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.ub_add_nat
% 4.71/5.15 thf(fact_7354_fold__atLeastAtMost__nat_Oelims,axiom,
% 4.71/5.15 ! [X: nat > nat > nat,Xa2: nat,Xb2: nat,Xc: nat,Y: nat] :
% 4.71/5.15 ( ( ( set_fo2584398358068434914at_nat @ X @ Xa2 @ Xb2 @ Xc )
% 4.71/5.15 = Y )
% 4.71/5.15 => ( ( ( ord_less_nat @ Xb2 @ Xa2 )
% 4.71/5.15 => ( Y = Xc ) )
% 4.71/5.15 & ( ~ ( ord_less_nat @ Xb2 @ Xa2 )
% 4.71/5.15 => ( Y
% 4.71/5.15 = ( set_fo2584398358068434914at_nat @ X @ ( plus_plus_nat @ Xa2 @ one_one_nat ) @ Xb2 @ ( X @ Xa2 @ Xc ) ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % fold_atLeastAtMost_nat.elims
% 4.71/5.15 thf(fact_7355_fold__atLeastAtMost__nat_Osimps,axiom,
% 4.71/5.15 ( set_fo2584398358068434914at_nat
% 4.71/5.15 = ( ^ [F5: nat > nat > nat,A4: nat,B4: nat,Acc2: nat] : ( if_nat @ ( ord_less_nat @ B4 @ A4 ) @ Acc2 @ ( set_fo2584398358068434914at_nat @ F5 @ ( plus_plus_nat @ A4 @ one_one_nat ) @ B4 @ ( F5 @ A4 @ Acc2 ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % fold_atLeastAtMost_nat.simps
% 4.71/5.15 thf(fact_7356_fact__eq__fact__times,axiom,
% 4.71/5.15 ! [N: nat,M2: nat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ N @ M2 )
% 4.71/5.15 => ( ( semiri1408675320244567234ct_nat @ M2 )
% 4.71/5.15 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 4.71/5.15 @ ( groups708209901874060359at_nat
% 4.71/5.15 @ ^ [X3: nat] : X3
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M2 ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % fact_eq_fact_times
% 4.71/5.15 thf(fact_7357_monoseq__realpow,axiom,
% 4.71/5.15 ! [X: real] :
% 4.71/5.15 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.71/5.15 => ( ( ord_less_eq_real @ X @ one_one_real )
% 4.71/5.15 => ( topolo6980174941875973593q_real @ ( power_power_real @ X ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % monoseq_realpow
% 4.71/5.15 thf(fact_7358_pochhammer__Suc__prod,axiom,
% 4.71/5.15 ! [A: real,N: nat] :
% 4.71/5.15 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 4.71/5.15 = ( groups129246275422532515t_real
% 4.71/5.15 @ ^ [I4: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ I4 ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % pochhammer_Suc_prod
% 4.71/5.15 thf(fact_7359_pochhammer__Suc__prod,axiom,
% 4.71/5.15 ! [A: rat,N: nat] :
% 4.71/5.15 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 4.71/5.15 = ( groups73079841787564623at_rat
% 4.71/5.15 @ ^ [I4: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ I4 ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % pochhammer_Suc_prod
% 4.71/5.15 thf(fact_7360_pochhammer__Suc__prod,axiom,
% 4.71/5.15 ! [A: nat,N: nat] :
% 4.71/5.15 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 4.71/5.15 = ( groups708209901874060359at_nat
% 4.71/5.15 @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ I4 ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % pochhammer_Suc_prod
% 4.71/5.15 thf(fact_7361_pochhammer__Suc__prod,axiom,
% 4.71/5.15 ! [A: int,N: nat] :
% 4.71/5.15 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 4.71/5.15 = ( groups705719431365010083at_int
% 4.71/5.15 @ ^ [I4: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ I4 ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % pochhammer_Suc_prod
% 4.71/5.15 thf(fact_7362_signed__take__bit__int__greater__eq__self__iff,axiom,
% 4.71/5.15 ! [K: int,N: nat] :
% 4.71/5.15 ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 4.71/5.15 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % signed_take_bit_int_greater_eq_self_iff
% 4.71/5.15 thf(fact_7363_signed__take__bit__int__less__self__iff,axiom,
% 4.71/5.15 ! [N: nat,K: int] :
% 4.71/5.15 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 4.71/5.15 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 4.71/5.15
% 4.71/5.15 % signed_take_bit_int_less_self_iff
% 4.71/5.15 thf(fact_7364_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 4.71/5.15 ! [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 ) ) ).
% 4.71/5.15
% 4.71/5.15 % signed_take_bit_int_greater_eq_minus_exp
% 4.71/5.15 thf(fact_7365_signed__take__bit__int__less__eq__self__iff,axiom,
% 4.71/5.15 ! [N: nat,K: int] :
% 4.71/5.15 ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 4.71/5.15 = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 4.71/5.15
% 4.71/5.15 % signed_take_bit_int_less_eq_self_iff
% 4.71/5.15 thf(fact_7366_pochhammer__prod__rev,axiom,
% 4.71/5.15 ( comm_s7457072308508201937r_real
% 4.71/5.15 = ( ^ [A4: real,N4: nat] :
% 4.71/5.15 ( groups129246275422532515t_real
% 4.71/5.15 @ ^ [I4: nat] : ( plus_plus_real @ A4 @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N4 @ I4 ) ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % pochhammer_prod_rev
% 4.71/5.15 thf(fact_7367_pochhammer__prod__rev,axiom,
% 4.71/5.15 ( comm_s4028243227959126397er_rat
% 4.71/5.15 = ( ^ [A4: rat,N4: nat] :
% 4.71/5.15 ( groups73079841787564623at_rat
% 4.71/5.15 @ ^ [I4: nat] : ( plus_plus_rat @ A4 @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N4 @ I4 ) ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % pochhammer_prod_rev
% 4.71/5.15 thf(fact_7368_pochhammer__prod__rev,axiom,
% 4.71/5.15 ( comm_s4663373288045622133er_nat
% 4.71/5.15 = ( ^ [A4: nat,N4: nat] :
% 4.71/5.15 ( groups708209901874060359at_nat
% 4.71/5.15 @ ^ [I4: nat] : ( plus_plus_nat @ A4 @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N4 @ I4 ) ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % pochhammer_prod_rev
% 4.71/5.15 thf(fact_7369_pochhammer__prod__rev,axiom,
% 4.71/5.15 ( comm_s4660882817536571857er_int
% 4.71/5.15 = ( ^ [A4: int,N4: nat] :
% 4.71/5.15 ( groups705719431365010083at_int
% 4.71/5.15 @ ^ [I4: nat] : ( plus_plus_int @ A4 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N4 @ I4 ) ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N4 ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % pochhammer_prod_rev
% 4.71/5.15 thf(fact_7370_fact__div__fact,axiom,
% 4.71/5.15 ! [N: nat,M2: nat] :
% 4.71/5.15 ( ( ord_less_eq_nat @ N @ M2 )
% 4.71/5.15 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 4.71/5.15 = ( groups708209901874060359at_nat
% 4.71/5.15 @ ^ [X3: nat] : X3
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M2 ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % fact_div_fact
% 4.71/5.15 thf(fact_7371_prod_Oin__pairs,axiom,
% 4.71/5.15 ! [G2: nat > real,M2: nat,N: nat] :
% 4.71/5.15 ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 4.71/5.15 = ( groups129246275422532515t_real
% 4.71/5.15 @ ^ [I4: nat] : ( times_times_real @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.in_pairs
% 4.71/5.15 thf(fact_7372_prod_Oin__pairs,axiom,
% 4.71/5.15 ! [G2: nat > rat,M2: nat,N: nat] :
% 4.71/5.15 ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 4.71/5.15 = ( groups73079841787564623at_rat
% 4.71/5.15 @ ^ [I4: nat] : ( times_times_rat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.in_pairs
% 4.71/5.15 thf(fact_7373_prod_Oin__pairs,axiom,
% 4.71/5.15 ! [G2: nat > nat,M2: nat,N: nat] :
% 4.71/5.15 ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 4.71/5.15 = ( groups708209901874060359at_nat
% 4.71/5.15 @ ^ [I4: nat] : ( times_times_nat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.in_pairs
% 4.71/5.15 thf(fact_7374_prod_Oin__pairs,axiom,
% 4.71/5.15 ! [G2: nat > int,M2: nat,N: nat] :
% 4.71/5.15 ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 4.71/5.15 = ( groups705719431365010083at_int
% 4.71/5.15 @ ^ [I4: nat] : ( times_times_int @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.in_pairs
% 4.71/5.15 thf(fact_7375_pochhammer__Suc__prod__rev,axiom,
% 4.71/5.15 ! [A: real,N: nat] :
% 4.71/5.15 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 4.71/5.15 = ( groups129246275422532515t_real
% 4.71/5.15 @ ^ [I4: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ I4 ) ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % pochhammer_Suc_prod_rev
% 4.71/5.15 thf(fact_7376_pochhammer__Suc__prod__rev,axiom,
% 4.71/5.15 ! [A: rat,N: nat] :
% 4.71/5.15 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 4.71/5.15 = ( groups73079841787564623at_rat
% 4.71/5.15 @ ^ [I4: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N @ I4 ) ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % pochhammer_Suc_prod_rev
% 4.71/5.15 thf(fact_7377_pochhammer__Suc__prod__rev,axiom,
% 4.71/5.15 ! [A: nat,N: nat] :
% 4.71/5.15 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 4.71/5.15 = ( groups708209901874060359at_nat
% 4.71/5.15 @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N @ I4 ) ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % pochhammer_Suc_prod_rev
% 4.71/5.15 thf(fact_7378_pochhammer__Suc__prod__rev,axiom,
% 4.71/5.15 ! [A: int,N: nat] :
% 4.71/5.15 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 4.71/5.15 = ( groups705719431365010083at_int
% 4.71/5.15 @ ^ [I4: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ I4 ) ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % pochhammer_Suc_prod_rev
% 4.71/5.15 thf(fact_7379_signed__take__bit__int__less__eq,axiom,
% 4.71/5.15 ! [N: nat,K: int] :
% 4.71/5.15 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 4.71/5.15 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % signed_take_bit_int_less_eq
% 4.71/5.15 thf(fact_7380_signed__take__bit__int__eq__self__iff,axiom,
% 4.71/5.15 ! [N: nat,K: int] :
% 4.71/5.15 ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 4.71/5.15 = K )
% 4.71/5.15 = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 4.71/5.15 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % signed_take_bit_int_eq_self_iff
% 4.71/5.15 thf(fact_7381_signed__take__bit__int__eq__self,axiom,
% 4.71/5.15 ! [N: nat,K: int] :
% 4.71/5.15 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 4.71/5.15 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 4.71/5.15 => ( ( bit_ri631733984087533419it_int @ N @ K )
% 4.71/5.15 = K ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % signed_take_bit_int_eq_self
% 4.71/5.15 thf(fact_7382_gbinomial__Suc,axiom,
% 4.71/5.15 ! [A: rat,K: nat] :
% 4.71/5.15 ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 4.71/5.15 = ( divide_divide_rat
% 4.71/5.15 @ ( groups73079841787564623at_rat
% 4.71/5.15 @ ^ [I4: nat] : ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ I4 ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 4.71/5.15 @ ( semiri773545260158071498ct_rat @ ( suc @ K ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % gbinomial_Suc
% 4.71/5.15 thf(fact_7383_gbinomial__Suc,axiom,
% 4.71/5.15 ! [A: real,K: nat] :
% 4.71/5.15 ( ( gbinomial_real @ A @ ( suc @ K ) )
% 4.71/5.15 = ( divide_divide_real
% 4.71/5.15 @ ( groups129246275422532515t_real
% 4.71/5.15 @ ^ [I4: nat] : ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ I4 ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 4.71/5.15 @ ( semiri2265585572941072030t_real @ ( suc @ K ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % gbinomial_Suc
% 4.71/5.15 thf(fact_7384_gbinomial__Suc,axiom,
% 4.71/5.15 ! [A: nat,K: nat] :
% 4.71/5.15 ( ( gbinomial_nat @ A @ ( suc @ K ) )
% 4.71/5.15 = ( divide_divide_nat
% 4.71/5.15 @ ( groups708209901874060359at_nat
% 4.71/5.15 @ ^ [I4: nat] : ( minus_minus_nat @ A @ ( semiri1316708129612266289at_nat @ I4 ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 4.71/5.15 @ ( semiri1408675320244567234ct_nat @ ( suc @ K ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % gbinomial_Suc
% 4.71/5.15 thf(fact_7385_gbinomial__Suc,axiom,
% 4.71/5.15 ! [A: int,K: nat] :
% 4.71/5.15 ( ( gbinomial_int @ A @ ( suc @ K ) )
% 4.71/5.15 = ( divide_divide_int
% 4.71/5.15 @ ( groups705719431365010083at_int
% 4.71/5.15 @ ^ [I4: nat] : ( minus_minus_int @ A @ ( semiri1314217659103216013at_int @ I4 ) )
% 4.71/5.15 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 4.71/5.15 @ ( semiri1406184849735516958ct_int @ ( suc @ K ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % gbinomial_Suc
% 4.71/5.15 thf(fact_7386_signed__take__bit__int__greater__eq,axiom,
% 4.71/5.15 ! [K: int,N: nat] :
% 4.71/5.15 ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 4.71/5.15 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % signed_take_bit_int_greater_eq
% 4.71/5.15 thf(fact_7387_fact__code,axiom,
% 4.71/5.15 ( semiri1406184849735516958ct_int
% 4.71/5.15 = ( ^ [N4: nat] : ( semiri1314217659103216013at_int @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % fact_code
% 4.71/5.15 thf(fact_7388_fact__code,axiom,
% 4.71/5.15 ( semiri773545260158071498ct_rat
% 4.71/5.15 = ( ^ [N4: nat] : ( semiri681578069525770553at_rat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % fact_code
% 4.71/5.15 thf(fact_7389_fact__code,axiom,
% 4.71/5.15 ( semiri1408675320244567234ct_nat
% 4.71/5.15 = ( ^ [N4: nat] : ( semiri1316708129612266289at_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % fact_code
% 4.71/5.15 thf(fact_7390_fact__code,axiom,
% 4.71/5.15 ( semiri2265585572941072030t_real
% 4.71/5.15 = ( ^ [N4: nat] : ( semiri5074537144036343181t_real @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % fact_code
% 4.71/5.15 thf(fact_7391_pochhammer__code,axiom,
% 4.71/5.15 ( comm_s2602460028002588243omplex
% 4.71/5.15 = ( ^ [A4: complex,N4: nat] :
% 4.71/5.15 ( if_complex @ ( N4 = zero_zero_nat ) @ one_one_complex
% 4.71/5.15 @ ( set_fo1517530859248394432omplex
% 4.71/5.15 @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A4 @ ( semiri8010041392384452111omplex @ O ) ) )
% 4.71/5.15 @ zero_zero_nat
% 4.71/5.15 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 4.71/5.15 @ one_one_complex ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % pochhammer_code
% 4.71/5.15 thf(fact_7392_pochhammer__code,axiom,
% 4.71/5.15 ( comm_s4660882817536571857er_int
% 4.71/5.15 = ( ^ [A4: int,N4: nat] :
% 4.71/5.15 ( if_int @ ( N4 = zero_zero_nat ) @ one_one_int
% 4.71/5.15 @ ( set_fo2581907887559384638at_int
% 4.71/5.15 @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A4 @ ( semiri1314217659103216013at_int @ O ) ) )
% 4.71/5.15 @ zero_zero_nat
% 4.71/5.15 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 4.71/5.15 @ one_one_int ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % pochhammer_code
% 4.71/5.15 thf(fact_7393_pochhammer__code,axiom,
% 4.71/5.15 ( comm_s7457072308508201937r_real
% 4.71/5.15 = ( ^ [A4: real,N4: nat] :
% 4.71/5.15 ( if_real @ ( N4 = zero_zero_nat ) @ one_one_real
% 4.71/5.15 @ ( set_fo3111899725591712190t_real
% 4.71/5.15 @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A4 @ ( semiri5074537144036343181t_real @ O ) ) )
% 4.71/5.15 @ zero_zero_nat
% 4.71/5.15 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 4.71/5.15 @ one_one_real ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % pochhammer_code
% 4.71/5.15 thf(fact_7394_pochhammer__code,axiom,
% 4.71/5.15 ( comm_s4028243227959126397er_rat
% 4.71/5.15 = ( ^ [A4: rat,N4: nat] :
% 4.71/5.15 ( if_rat @ ( N4 = zero_zero_nat ) @ one_one_rat
% 4.71/5.15 @ ( set_fo1949268297981939178at_rat
% 4.71/5.15 @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A4 @ ( semiri681578069525770553at_rat @ O ) ) )
% 4.71/5.15 @ zero_zero_nat
% 4.71/5.15 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 4.71/5.15 @ one_one_rat ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % pochhammer_code
% 4.71/5.15 thf(fact_7395_pochhammer__code,axiom,
% 4.71/5.15 ( comm_s4663373288045622133er_nat
% 4.71/5.15 = ( ^ [A4: nat,N4: nat] :
% 4.71/5.15 ( if_nat @ ( N4 = zero_zero_nat ) @ one_one_nat
% 4.71/5.15 @ ( set_fo2584398358068434914at_nat
% 4.71/5.15 @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A4 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 4.71/5.15 @ zero_zero_nat
% 4.71/5.15 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 4.71/5.15 @ one_one_nat ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % pochhammer_code
% 4.71/5.15 thf(fact_7396_prod_Oinsert,axiom,
% 4.71/5.15 ! [A2: set_real,X: real,G2: real > real] :
% 4.71/5.15 ( ( finite_finite_real @ A2 )
% 4.71/5.15 => ( ~ ( member_real @ X @ A2 )
% 4.71/5.15 => ( ( groups1681761925125756287l_real @ G2 @ ( insert_real @ X @ A2 ) )
% 4.71/5.15 = ( times_times_real @ ( G2 @ X ) @ ( groups1681761925125756287l_real @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.insert
% 4.71/5.15 thf(fact_7397_prod_Oinsert,axiom,
% 4.71/5.15 ! [A2: set_o,X: $o,G2: $o > real] :
% 4.71/5.15 ( ( finite_finite_o @ A2 )
% 4.71/5.15 => ( ~ ( member_o @ X @ A2 )
% 4.71/5.15 => ( ( groups234877984723959775o_real @ G2 @ ( insert_o @ X @ A2 ) )
% 4.71/5.15 = ( times_times_real @ ( G2 @ X ) @ ( groups234877984723959775o_real @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.insert
% 4.71/5.15 thf(fact_7398_prod_Oinsert,axiom,
% 4.71/5.15 ! [A2: set_nat,X: nat,G2: nat > real] :
% 4.71/5.15 ( ( finite_finite_nat @ A2 )
% 4.71/5.15 => ( ~ ( member_nat @ X @ A2 )
% 4.71/5.15 => ( ( groups129246275422532515t_real @ G2 @ ( insert_nat @ X @ A2 ) )
% 4.71/5.15 = ( times_times_real @ ( G2 @ X ) @ ( groups129246275422532515t_real @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.insert
% 4.71/5.15 thf(fact_7399_prod_Oinsert,axiom,
% 4.71/5.15 ! [A2: set_int,X: int,G2: int > real] :
% 4.71/5.15 ( ( finite_finite_int @ A2 )
% 4.71/5.15 => ( ~ ( member_int @ X @ A2 )
% 4.71/5.15 => ( ( groups2316167850115554303t_real @ G2 @ ( insert_int @ X @ A2 ) )
% 4.71/5.15 = ( times_times_real @ ( G2 @ X ) @ ( groups2316167850115554303t_real @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.insert
% 4.71/5.15 thf(fact_7400_prod_Oinsert,axiom,
% 4.71/5.15 ! [A2: set_complex,X: complex,G2: complex > real] :
% 4.71/5.15 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.15 => ( ~ ( member_complex @ X @ A2 )
% 4.71/5.15 => ( ( groups766887009212190081x_real @ G2 @ ( insert_complex @ X @ A2 ) )
% 4.71/5.15 = ( times_times_real @ ( G2 @ X ) @ ( groups766887009212190081x_real @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.insert
% 4.71/5.15 thf(fact_7401_prod_Oinsert,axiom,
% 4.71/5.15 ! [A2: set_Extended_enat,X: extended_enat,G2: extended_enat > real] :
% 4.71/5.15 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.15 => ( ~ ( member_Extended_enat @ X @ A2 )
% 4.71/5.15 => ( ( groups97031904164794029t_real @ G2 @ ( insert_Extended_enat @ X @ A2 ) )
% 4.71/5.15 = ( times_times_real @ ( G2 @ X ) @ ( groups97031904164794029t_real @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.insert
% 4.71/5.15 thf(fact_7402_prod_Oinsert,axiom,
% 4.71/5.15 ! [A2: set_real,X: real,G2: real > rat] :
% 4.71/5.15 ( ( finite_finite_real @ A2 )
% 4.71/5.15 => ( ~ ( member_real @ X @ A2 )
% 4.71/5.15 => ( ( groups4061424788464935467al_rat @ G2 @ ( insert_real @ X @ A2 ) )
% 4.71/5.15 = ( times_times_rat @ ( G2 @ X ) @ ( groups4061424788464935467al_rat @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.insert
% 4.71/5.15 thf(fact_7403_prod_Oinsert,axiom,
% 4.71/5.15 ! [A2: set_o,X: $o,G2: $o > rat] :
% 4.71/5.15 ( ( finite_finite_o @ A2 )
% 4.71/5.15 => ( ~ ( member_o @ X @ A2 )
% 4.71/5.15 => ( ( groups2869687844427037835_o_rat @ G2 @ ( insert_o @ X @ A2 ) )
% 4.71/5.15 = ( times_times_rat @ ( G2 @ X ) @ ( groups2869687844427037835_o_rat @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.insert
% 4.71/5.15 thf(fact_7404_prod_Oinsert,axiom,
% 4.71/5.15 ! [A2: set_nat,X: nat,G2: nat > rat] :
% 4.71/5.15 ( ( finite_finite_nat @ A2 )
% 4.71/5.15 => ( ~ ( member_nat @ X @ A2 )
% 4.71/5.15 => ( ( groups73079841787564623at_rat @ G2 @ ( insert_nat @ X @ A2 ) )
% 4.71/5.15 = ( times_times_rat @ ( G2 @ X ) @ ( groups73079841787564623at_rat @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.insert
% 4.71/5.15 thf(fact_7405_prod_Oinsert,axiom,
% 4.71/5.15 ! [A2: set_int,X: int,G2: int > rat] :
% 4.71/5.15 ( ( finite_finite_int @ A2 )
% 4.71/5.15 => ( ~ ( member_int @ X @ A2 )
% 4.71/5.15 => ( ( groups1072433553688619179nt_rat @ G2 @ ( insert_int @ X @ A2 ) )
% 4.71/5.15 = ( times_times_rat @ ( G2 @ X ) @ ( groups1072433553688619179nt_rat @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.insert
% 4.71/5.15 thf(fact_7406_prod_Odelta,axiom,
% 4.71/5.15 ! [S2: set_o,A: $o,B: $o > complex] :
% 4.71/5.15 ( ( finite_finite_o @ S2 )
% 4.71/5.15 => ( ( ( member_o @ A @ S2 )
% 4.71/5.15 => ( ( groups4859619685533338977omplex
% 4.71/5.15 @ ^ [K3: $o] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = ( B @ A ) ) )
% 4.71/5.15 & ( ~ ( member_o @ A @ S2 )
% 4.71/5.15 => ( ( groups4859619685533338977omplex
% 4.71/5.15 @ ^ [K3: $o] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = one_one_complex ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.delta
% 4.71/5.15 thf(fact_7407_prod_Odelta,axiom,
% 4.71/5.15 ! [S2: set_nat,A: nat,B: nat > complex] :
% 4.71/5.15 ( ( finite_finite_nat @ S2 )
% 4.71/5.15 => ( ( ( member_nat @ A @ S2 )
% 4.71/5.15 => ( ( groups6464643781859351333omplex
% 4.71/5.15 @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = ( B @ A ) ) )
% 4.71/5.15 & ( ~ ( member_nat @ A @ S2 )
% 4.71/5.15 => ( ( groups6464643781859351333omplex
% 4.71/5.15 @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = one_one_complex ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.delta
% 4.71/5.15 thf(fact_7408_prod_Odelta,axiom,
% 4.71/5.15 ! [S2: set_int,A: int,B: int > complex] :
% 4.71/5.15 ( ( finite_finite_int @ S2 )
% 4.71/5.15 => ( ( ( member_int @ A @ S2 )
% 4.71/5.15 => ( ( groups7440179247065528705omplex
% 4.71/5.15 @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = ( B @ A ) ) )
% 4.71/5.15 & ( ~ ( member_int @ A @ S2 )
% 4.71/5.15 => ( ( groups7440179247065528705omplex
% 4.71/5.15 @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = one_one_complex ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.delta
% 4.71/5.15 thf(fact_7409_prod_Odelta,axiom,
% 4.71/5.15 ! [S2: set_complex,A: complex,B: complex > complex] :
% 4.71/5.15 ( ( finite3207457112153483333omplex @ S2 )
% 4.71/5.15 => ( ( ( member_complex @ A @ S2 )
% 4.71/5.15 => ( ( groups3708469109370488835omplex
% 4.71/5.15 @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = ( B @ A ) ) )
% 4.71/5.15 & ( ~ ( member_complex @ A @ S2 )
% 4.71/5.15 => ( ( groups3708469109370488835omplex
% 4.71/5.15 @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = one_one_complex ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.delta
% 4.71/5.15 thf(fact_7410_prod_Odelta,axiom,
% 4.71/5.15 ! [S2: set_Extended_enat,A: extended_enat,B: extended_enat > complex] :
% 4.71/5.15 ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.15 => ( ( ( member_Extended_enat @ A @ S2 )
% 4.71/5.15 => ( ( groups4622424608036095791omplex
% 4.71/5.15 @ ^ [K3: extended_enat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = ( B @ A ) ) )
% 4.71/5.15 & ( ~ ( member_Extended_enat @ A @ S2 )
% 4.71/5.15 => ( ( groups4622424608036095791omplex
% 4.71/5.15 @ ^ [K3: extended_enat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ one_one_complex )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = one_one_complex ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.delta
% 4.71/5.15 thf(fact_7411_prod_Odelta,axiom,
% 4.71/5.15 ! [S2: set_o,A: $o,B: $o > real] :
% 4.71/5.15 ( ( finite_finite_o @ S2 )
% 4.71/5.15 => ( ( ( member_o @ A @ S2 )
% 4.71/5.15 => ( ( groups234877984723959775o_real
% 4.71/5.15 @ ^ [K3: $o] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = ( B @ A ) ) )
% 4.71/5.15 & ( ~ ( member_o @ A @ S2 )
% 4.71/5.15 => ( ( groups234877984723959775o_real
% 4.71/5.15 @ ^ [K3: $o] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = one_one_real ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.delta
% 4.71/5.15 thf(fact_7412_prod_Odelta,axiom,
% 4.71/5.15 ! [S2: set_nat,A: nat,B: nat > real] :
% 4.71/5.15 ( ( finite_finite_nat @ S2 )
% 4.71/5.15 => ( ( ( member_nat @ A @ S2 )
% 4.71/5.15 => ( ( groups129246275422532515t_real
% 4.71/5.15 @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = ( B @ A ) ) )
% 4.71/5.15 & ( ~ ( member_nat @ A @ S2 )
% 4.71/5.15 => ( ( groups129246275422532515t_real
% 4.71/5.15 @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = one_one_real ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.delta
% 4.71/5.15 thf(fact_7413_prod_Odelta,axiom,
% 4.71/5.15 ! [S2: set_int,A: int,B: int > real] :
% 4.71/5.15 ( ( finite_finite_int @ S2 )
% 4.71/5.15 => ( ( ( member_int @ A @ S2 )
% 4.71/5.15 => ( ( groups2316167850115554303t_real
% 4.71/5.15 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = ( B @ A ) ) )
% 4.71/5.15 & ( ~ ( member_int @ A @ S2 )
% 4.71/5.15 => ( ( groups2316167850115554303t_real
% 4.71/5.15 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = one_one_real ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.delta
% 4.71/5.15 thf(fact_7414_prod_Odelta,axiom,
% 4.71/5.15 ! [S2: set_complex,A: complex,B: complex > real] :
% 4.71/5.15 ( ( finite3207457112153483333omplex @ S2 )
% 4.71/5.15 => ( ( ( member_complex @ A @ S2 )
% 4.71/5.15 => ( ( groups766887009212190081x_real
% 4.71/5.15 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = ( B @ A ) ) )
% 4.71/5.15 & ( ~ ( member_complex @ A @ S2 )
% 4.71/5.15 => ( ( groups766887009212190081x_real
% 4.71/5.15 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = one_one_real ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.delta
% 4.71/5.15 thf(fact_7415_prod_Odelta,axiom,
% 4.71/5.15 ! [S2: set_Extended_enat,A: extended_enat,B: extended_enat > real] :
% 4.71/5.15 ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.15 => ( ( ( member_Extended_enat @ A @ S2 )
% 4.71/5.15 => ( ( groups97031904164794029t_real
% 4.71/5.15 @ ^ [K3: extended_enat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = ( B @ A ) ) )
% 4.71/5.15 & ( ~ ( member_Extended_enat @ A @ S2 )
% 4.71/5.15 => ( ( groups97031904164794029t_real
% 4.71/5.15 @ ^ [K3: extended_enat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = one_one_real ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.delta
% 4.71/5.15 thf(fact_7416_prod_Odelta_H,axiom,
% 4.71/5.15 ! [S2: set_o,A: $o,B: $o > complex] :
% 4.71/5.15 ( ( finite_finite_o @ S2 )
% 4.71/5.15 => ( ( ( member_o @ A @ S2 )
% 4.71/5.15 => ( ( groups4859619685533338977omplex
% 4.71/5.15 @ ^ [K3: $o] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = ( B @ A ) ) )
% 4.71/5.15 & ( ~ ( member_o @ A @ S2 )
% 4.71/5.15 => ( ( groups4859619685533338977omplex
% 4.71/5.15 @ ^ [K3: $o] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = one_one_complex ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.delta'
% 4.71/5.15 thf(fact_7417_prod_Odelta_H,axiom,
% 4.71/5.15 ! [S2: set_nat,A: nat,B: nat > complex] :
% 4.71/5.15 ( ( finite_finite_nat @ S2 )
% 4.71/5.15 => ( ( ( member_nat @ A @ S2 )
% 4.71/5.15 => ( ( groups6464643781859351333omplex
% 4.71/5.15 @ ^ [K3: nat] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = ( B @ A ) ) )
% 4.71/5.15 & ( ~ ( member_nat @ A @ S2 )
% 4.71/5.15 => ( ( groups6464643781859351333omplex
% 4.71/5.15 @ ^ [K3: nat] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = one_one_complex ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.delta'
% 4.71/5.15 thf(fact_7418_prod_Odelta_H,axiom,
% 4.71/5.15 ! [S2: set_int,A: int,B: int > complex] :
% 4.71/5.15 ( ( finite_finite_int @ S2 )
% 4.71/5.15 => ( ( ( member_int @ A @ S2 )
% 4.71/5.15 => ( ( groups7440179247065528705omplex
% 4.71/5.15 @ ^ [K3: int] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = ( B @ A ) ) )
% 4.71/5.15 & ( ~ ( member_int @ A @ S2 )
% 4.71/5.15 => ( ( groups7440179247065528705omplex
% 4.71/5.15 @ ^ [K3: int] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = one_one_complex ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.delta'
% 4.71/5.15 thf(fact_7419_prod_Odelta_H,axiom,
% 4.71/5.15 ! [S2: set_complex,A: complex,B: complex > complex] :
% 4.71/5.15 ( ( finite3207457112153483333omplex @ S2 )
% 4.71/5.15 => ( ( ( member_complex @ A @ S2 )
% 4.71/5.15 => ( ( groups3708469109370488835omplex
% 4.71/5.15 @ ^ [K3: complex] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = ( B @ A ) ) )
% 4.71/5.15 & ( ~ ( member_complex @ A @ S2 )
% 4.71/5.15 => ( ( groups3708469109370488835omplex
% 4.71/5.15 @ ^ [K3: complex] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = one_one_complex ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.delta'
% 4.71/5.15 thf(fact_7420_prod_Odelta_H,axiom,
% 4.71/5.15 ! [S2: set_Extended_enat,A: extended_enat,B: extended_enat > complex] :
% 4.71/5.15 ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.15 => ( ( ( member_Extended_enat @ A @ S2 )
% 4.71/5.15 => ( ( groups4622424608036095791omplex
% 4.71/5.15 @ ^ [K3: extended_enat] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = ( B @ A ) ) )
% 4.71/5.15 & ( ~ ( member_Extended_enat @ A @ S2 )
% 4.71/5.15 => ( ( groups4622424608036095791omplex
% 4.71/5.15 @ ^ [K3: extended_enat] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ one_one_complex )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = one_one_complex ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.delta'
% 4.71/5.15 thf(fact_7421_prod_Odelta_H,axiom,
% 4.71/5.15 ! [S2: set_o,A: $o,B: $o > real] :
% 4.71/5.15 ( ( finite_finite_o @ S2 )
% 4.71/5.15 => ( ( ( member_o @ A @ S2 )
% 4.71/5.15 => ( ( groups234877984723959775o_real
% 4.71/5.15 @ ^ [K3: $o] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = ( B @ A ) ) )
% 4.71/5.15 & ( ~ ( member_o @ A @ S2 )
% 4.71/5.15 => ( ( groups234877984723959775o_real
% 4.71/5.15 @ ^ [K3: $o] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = one_one_real ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.delta'
% 4.71/5.15 thf(fact_7422_prod_Odelta_H,axiom,
% 4.71/5.15 ! [S2: set_nat,A: nat,B: nat > real] :
% 4.71/5.15 ( ( finite_finite_nat @ S2 )
% 4.71/5.15 => ( ( ( member_nat @ A @ S2 )
% 4.71/5.15 => ( ( groups129246275422532515t_real
% 4.71/5.15 @ ^ [K3: nat] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = ( B @ A ) ) )
% 4.71/5.15 & ( ~ ( member_nat @ A @ S2 )
% 4.71/5.15 => ( ( groups129246275422532515t_real
% 4.71/5.15 @ ^ [K3: nat] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = one_one_real ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.delta'
% 4.71/5.15 thf(fact_7423_prod_Odelta_H,axiom,
% 4.71/5.15 ! [S2: set_int,A: int,B: int > real] :
% 4.71/5.15 ( ( finite_finite_int @ S2 )
% 4.71/5.15 => ( ( ( member_int @ A @ S2 )
% 4.71/5.15 => ( ( groups2316167850115554303t_real
% 4.71/5.15 @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = ( B @ A ) ) )
% 4.71/5.15 & ( ~ ( member_int @ A @ S2 )
% 4.71/5.15 => ( ( groups2316167850115554303t_real
% 4.71/5.15 @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = one_one_real ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.delta'
% 4.71/5.15 thf(fact_7424_prod_Odelta_H,axiom,
% 4.71/5.15 ! [S2: set_complex,A: complex,B: complex > real] :
% 4.71/5.15 ( ( finite3207457112153483333omplex @ S2 )
% 4.71/5.15 => ( ( ( member_complex @ A @ S2 )
% 4.71/5.15 => ( ( groups766887009212190081x_real
% 4.71/5.15 @ ^ [K3: complex] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = ( B @ A ) ) )
% 4.71/5.15 & ( ~ ( member_complex @ A @ S2 )
% 4.71/5.15 => ( ( groups766887009212190081x_real
% 4.71/5.15 @ ^ [K3: complex] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = one_one_real ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.delta'
% 4.71/5.15 thf(fact_7425_prod_Odelta_H,axiom,
% 4.71/5.15 ! [S2: set_Extended_enat,A: extended_enat,B: extended_enat > real] :
% 4.71/5.15 ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.15 => ( ( ( member_Extended_enat @ A @ S2 )
% 4.71/5.15 => ( ( groups97031904164794029t_real
% 4.71/5.15 @ ^ [K3: extended_enat] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = ( B @ A ) ) )
% 4.71/5.15 & ( ~ ( member_Extended_enat @ A @ S2 )
% 4.71/5.15 => ( ( groups97031904164794029t_real
% 4.71/5.15 @ ^ [K3: extended_enat] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 4.71/5.15 @ S2 )
% 4.71/5.15 = one_one_real ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.delta'
% 4.71/5.15 thf(fact_7426_suminf__geometric,axiom,
% 4.71/5.15 ! [C: real] :
% 4.71/5.15 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 4.71/5.15 => ( ( suminf_real @ ( power_power_real @ C ) )
% 4.71/5.15 = ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % suminf_geometric
% 4.71/5.15 thf(fact_7427_suminf__geometric,axiom,
% 4.71/5.15 ! [C: complex] :
% 4.71/5.15 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 4.71/5.15 => ( ( suminf_complex @ ( power_power_complex @ C ) )
% 4.71/5.15 = ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % suminf_geometric
% 4.71/5.15 thf(fact_7428_prod_Oinfinite,axiom,
% 4.71/5.15 ! [A2: set_nat,G2: nat > complex] :
% 4.71/5.15 ( ~ ( finite_finite_nat @ A2 )
% 4.71/5.15 => ( ( groups6464643781859351333omplex @ G2 @ A2 )
% 4.71/5.15 = one_one_complex ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.infinite
% 4.71/5.15 thf(fact_7429_prod_Oinfinite,axiom,
% 4.71/5.15 ! [A2: set_int,G2: int > complex] :
% 4.71/5.15 ( ~ ( finite_finite_int @ A2 )
% 4.71/5.15 => ( ( groups7440179247065528705omplex @ G2 @ A2 )
% 4.71/5.15 = one_one_complex ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.infinite
% 4.71/5.15 thf(fact_7430_prod_Oinfinite,axiom,
% 4.71/5.15 ! [A2: set_complex,G2: complex > complex] :
% 4.71/5.15 ( ~ ( finite3207457112153483333omplex @ A2 )
% 4.71/5.15 => ( ( groups3708469109370488835omplex @ G2 @ A2 )
% 4.71/5.15 = one_one_complex ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.infinite
% 4.71/5.15 thf(fact_7431_prod_Oinfinite,axiom,
% 4.71/5.15 ! [A2: set_Extended_enat,G2: extended_enat > complex] :
% 4.71/5.15 ( ~ ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.15 => ( ( groups4622424608036095791omplex @ G2 @ A2 )
% 4.71/5.15 = one_one_complex ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.infinite
% 4.71/5.15 thf(fact_7432_prod_Oinfinite,axiom,
% 4.71/5.15 ! [A2: set_nat,G2: nat > real] :
% 4.71/5.15 ( ~ ( finite_finite_nat @ A2 )
% 4.71/5.15 => ( ( groups129246275422532515t_real @ G2 @ A2 )
% 4.71/5.15 = one_one_real ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.infinite
% 4.71/5.15 thf(fact_7433_prod_Oinfinite,axiom,
% 4.71/5.15 ! [A2: set_int,G2: int > real] :
% 4.71/5.15 ( ~ ( finite_finite_int @ A2 )
% 4.71/5.15 => ( ( groups2316167850115554303t_real @ G2 @ A2 )
% 4.71/5.15 = one_one_real ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.infinite
% 4.71/5.15 thf(fact_7434_prod_Oinfinite,axiom,
% 4.71/5.15 ! [A2: set_complex,G2: complex > real] :
% 4.71/5.15 ( ~ ( finite3207457112153483333omplex @ A2 )
% 4.71/5.15 => ( ( groups766887009212190081x_real @ G2 @ A2 )
% 4.71/5.15 = one_one_real ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.infinite
% 4.71/5.15 thf(fact_7435_prod_Oinfinite,axiom,
% 4.71/5.15 ! [A2: set_Extended_enat,G2: extended_enat > real] :
% 4.71/5.15 ( ~ ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.15 => ( ( groups97031904164794029t_real @ G2 @ A2 )
% 4.71/5.15 = one_one_real ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.infinite
% 4.71/5.15 thf(fact_7436_prod_Oinfinite,axiom,
% 4.71/5.15 ! [A2: set_nat,G2: nat > rat] :
% 4.71/5.15 ( ~ ( finite_finite_nat @ A2 )
% 4.71/5.15 => ( ( groups73079841787564623at_rat @ G2 @ A2 )
% 4.71/5.15 = one_one_rat ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.infinite
% 4.71/5.15 thf(fact_7437_prod_Oinfinite,axiom,
% 4.71/5.15 ! [A2: set_int,G2: int > rat] :
% 4.71/5.15 ( ~ ( finite_finite_int @ A2 )
% 4.71/5.15 => ( ( groups1072433553688619179nt_rat @ G2 @ A2 )
% 4.71/5.15 = one_one_rat ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod.infinite
% 4.71/5.15 thf(fact_7438_prod_Oempty,axiom,
% 4.71/5.15 ! [G2: real > complex] :
% 4.71/5.15 ( ( groups713298508707869441omplex @ G2 @ bot_bot_set_real )
% 4.71/5.15 = one_one_complex ) ).
% 4.71/5.15
% 4.71/5.15 % prod.empty
% 4.71/5.15 thf(fact_7439_prod_Oempty,axiom,
% 4.71/5.15 ! [G2: real > real] :
% 4.71/5.15 ( ( groups1681761925125756287l_real @ G2 @ bot_bot_set_real )
% 4.71/5.15 = one_one_real ) ).
% 4.71/5.15
% 4.71/5.15 % prod.empty
% 4.71/5.15 thf(fact_7440_prod_Oempty,axiom,
% 4.71/5.15 ! [G2: real > rat] :
% 4.71/5.15 ( ( groups4061424788464935467al_rat @ G2 @ bot_bot_set_real )
% 4.71/5.15 = one_one_rat ) ).
% 4.71/5.15
% 4.71/5.15 % prod.empty
% 4.71/5.15 thf(fact_7441_prod_Oempty,axiom,
% 4.71/5.15 ! [G2: real > nat] :
% 4.71/5.15 ( ( groups4696554848551431203al_nat @ G2 @ bot_bot_set_real )
% 4.71/5.15 = one_one_nat ) ).
% 4.71/5.15
% 4.71/5.15 % prod.empty
% 4.71/5.15 thf(fact_7442_prod_Oempty,axiom,
% 4.71/5.15 ! [G2: real > int] :
% 4.71/5.15 ( ( groups4694064378042380927al_int @ G2 @ bot_bot_set_real )
% 4.71/5.15 = one_one_int ) ).
% 4.71/5.15
% 4.71/5.15 % prod.empty
% 4.71/5.15 thf(fact_7443_prod_Oempty,axiom,
% 4.71/5.15 ! [G2: $o > complex] :
% 4.71/5.15 ( ( groups4859619685533338977omplex @ G2 @ bot_bot_set_o )
% 4.71/5.15 = one_one_complex ) ).
% 4.71/5.15
% 4.71/5.15 % prod.empty
% 4.71/5.15 thf(fact_7444_prod_Oempty,axiom,
% 4.71/5.15 ! [G2: $o > real] :
% 4.71/5.15 ( ( groups234877984723959775o_real @ G2 @ bot_bot_set_o )
% 4.71/5.15 = one_one_real ) ).
% 4.71/5.15
% 4.71/5.15 % prod.empty
% 4.71/5.15 thf(fact_7445_prod_Oempty,axiom,
% 4.71/5.15 ! [G2: $o > rat] :
% 4.71/5.15 ( ( groups2869687844427037835_o_rat @ G2 @ bot_bot_set_o )
% 4.71/5.15 = one_one_rat ) ).
% 4.71/5.15
% 4.71/5.15 % prod.empty
% 4.71/5.15 thf(fact_7446_prod_Oempty,axiom,
% 4.71/5.15 ! [G2: $o > nat] :
% 4.71/5.15 ( ( groups3504817904513533571_o_nat @ G2 @ bot_bot_set_o )
% 4.71/5.15 = one_one_nat ) ).
% 4.71/5.15
% 4.71/5.15 % prod.empty
% 4.71/5.15 thf(fact_7447_prod_Oempty,axiom,
% 4.71/5.15 ! [G2: $o > int] :
% 4.71/5.15 ( ( groups3502327434004483295_o_int @ G2 @ bot_bot_set_o )
% 4.71/5.15 = one_one_int ) ).
% 4.71/5.15
% 4.71/5.15 % prod.empty
% 4.71/5.15 thf(fact_7448_prod_Oneutral__const,axiom,
% 4.71/5.15 ! [A2: set_nat] :
% 4.71/5.15 ( ( groups708209901874060359at_nat
% 4.71/5.15 @ ^ [Uu3: nat] : one_one_nat
% 4.71/5.15 @ A2 )
% 4.71/5.15 = one_one_nat ) ).
% 4.71/5.15
% 4.71/5.15 % prod.neutral_const
% 4.71/5.15 thf(fact_7449_prod_Oneutral__const,axiom,
% 4.71/5.15 ! [A2: set_nat] :
% 4.71/5.15 ( ( groups705719431365010083at_int
% 4.71/5.15 @ ^ [Uu3: nat] : one_one_int
% 4.71/5.15 @ A2 )
% 4.71/5.15 = one_one_int ) ).
% 4.71/5.15
% 4.71/5.15 % prod.neutral_const
% 4.71/5.15 thf(fact_7450_prod_Oneutral__const,axiom,
% 4.71/5.15 ! [A2: set_int] :
% 4.71/5.15 ( ( groups1705073143266064639nt_int
% 4.71/5.15 @ ^ [Uu3: int] : one_one_int
% 4.71/5.15 @ A2 )
% 4.71/5.15 = one_one_int ) ).
% 4.71/5.15
% 4.71/5.15 % prod.neutral_const
% 4.71/5.15 thf(fact_7451_suminf__zero,axiom,
% 4.71/5.15 ( ( suminf_real
% 4.71/5.15 @ ^ [N4: nat] : zero_zero_real )
% 4.71/5.15 = zero_zero_real ) ).
% 4.71/5.15
% 4.71/5.15 % suminf_zero
% 4.71/5.15 thf(fact_7452_suminf__zero,axiom,
% 4.71/5.15 ( ( suminf_nat
% 4.71/5.15 @ ^ [N4: nat] : zero_zero_nat )
% 4.71/5.15 = zero_zero_nat ) ).
% 4.71/5.15
% 4.71/5.15 % suminf_zero
% 4.71/5.15 thf(fact_7453_suminf__zero,axiom,
% 4.71/5.15 ( ( suminf_int
% 4.71/5.15 @ ^ [N4: nat] : zero_zero_int )
% 4.71/5.15 = zero_zero_int ) ).
% 4.71/5.15
% 4.71/5.15 % suminf_zero
% 4.71/5.15 thf(fact_7454_prod__zero__iff,axiom,
% 4.71/5.15 ! [A2: set_nat,F: nat > real] :
% 4.71/5.15 ( ( finite_finite_nat @ A2 )
% 4.71/5.15 => ( ( ( groups129246275422532515t_real @ F @ A2 )
% 4.71/5.15 = zero_zero_real )
% 4.71/5.15 = ( ? [X3: nat] :
% 4.71/5.15 ( ( member_nat @ X3 @ A2 )
% 4.71/5.15 & ( ( F @ X3 )
% 4.71/5.15 = zero_zero_real ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod_zero_iff
% 4.71/5.15 thf(fact_7455_prod__zero__iff,axiom,
% 4.71/5.15 ! [A2: set_int,F: int > real] :
% 4.71/5.15 ( ( finite_finite_int @ A2 )
% 4.71/5.15 => ( ( ( groups2316167850115554303t_real @ F @ A2 )
% 4.71/5.15 = zero_zero_real )
% 4.71/5.15 = ( ? [X3: int] :
% 4.71/5.15 ( ( member_int @ X3 @ A2 )
% 4.71/5.15 & ( ( F @ X3 )
% 4.71/5.15 = zero_zero_real ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod_zero_iff
% 4.71/5.15 thf(fact_7456_prod__zero__iff,axiom,
% 4.71/5.15 ! [A2: set_complex,F: complex > real] :
% 4.71/5.15 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.15 => ( ( ( groups766887009212190081x_real @ F @ A2 )
% 4.71/5.15 = zero_zero_real )
% 4.71/5.15 = ( ? [X3: complex] :
% 4.71/5.15 ( ( member_complex @ X3 @ A2 )
% 4.71/5.15 & ( ( F @ X3 )
% 4.71/5.15 = zero_zero_real ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod_zero_iff
% 4.71/5.15 thf(fact_7457_prod__zero__iff,axiom,
% 4.71/5.15 ! [A2: set_Extended_enat,F: extended_enat > real] :
% 4.71/5.15 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.15 => ( ( ( groups97031904164794029t_real @ F @ A2 )
% 4.71/5.15 = zero_zero_real )
% 4.71/5.15 = ( ? [X3: extended_enat] :
% 4.71/5.15 ( ( member_Extended_enat @ X3 @ A2 )
% 4.71/5.15 & ( ( F @ X3 )
% 4.71/5.15 = zero_zero_real ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod_zero_iff
% 4.71/5.15 thf(fact_7458_prod__zero__iff,axiom,
% 4.71/5.15 ! [A2: set_nat,F: nat > rat] :
% 4.71/5.15 ( ( finite_finite_nat @ A2 )
% 4.71/5.15 => ( ( ( groups73079841787564623at_rat @ F @ A2 )
% 4.71/5.15 = zero_zero_rat )
% 4.71/5.15 = ( ? [X3: nat] :
% 4.71/5.15 ( ( member_nat @ X3 @ A2 )
% 4.71/5.15 & ( ( F @ X3 )
% 4.71/5.15 = zero_zero_rat ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod_zero_iff
% 4.71/5.15 thf(fact_7459_prod__zero__iff,axiom,
% 4.71/5.15 ! [A2: set_int,F: int > rat] :
% 4.71/5.15 ( ( finite_finite_int @ A2 )
% 4.71/5.15 => ( ( ( groups1072433553688619179nt_rat @ F @ A2 )
% 4.71/5.15 = zero_zero_rat )
% 4.71/5.15 = ( ? [X3: int] :
% 4.71/5.15 ( ( member_int @ X3 @ A2 )
% 4.71/5.15 & ( ( F @ X3 )
% 4.71/5.15 = zero_zero_rat ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod_zero_iff
% 4.71/5.15 thf(fact_7460_prod__zero__iff,axiom,
% 4.71/5.15 ! [A2: set_complex,F: complex > rat] :
% 4.71/5.15 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.15 => ( ( ( groups225925009352817453ex_rat @ F @ A2 )
% 4.71/5.15 = zero_zero_rat )
% 4.71/5.15 = ( ? [X3: complex] :
% 4.71/5.15 ( ( member_complex @ X3 @ A2 )
% 4.71/5.15 & ( ( F @ X3 )
% 4.71/5.15 = zero_zero_rat ) ) ) ) ) ).
% 4.71/5.15
% 4.71/5.15 % prod_zero_iff
% 4.71/5.15 thf(fact_7461_prod__zero__iff,axiom,
% 4.71/5.15 ! [A2: set_Extended_enat,F: extended_enat > rat] :
% 4.71/5.15 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.15 => ( ( ( groups2245840878043517529at_rat @ F @ A2 )
% 4.71/5.16 = zero_zero_rat )
% 4.71/5.16 = ( ? [X3: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X3 @ A2 )
% 4.71/5.16 & ( ( F @ X3 )
% 4.71/5.16 = zero_zero_rat ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_zero_iff
% 4.71/5.16 thf(fact_7462_prod__zero__iff,axiom,
% 4.71/5.16 ! [A2: set_int,F: int > nat] :
% 4.71/5.16 ( ( finite_finite_int @ A2 )
% 4.71/5.16 => ( ( ( groups1707563613775114915nt_nat @ F @ A2 )
% 4.71/5.16 = zero_zero_nat )
% 4.71/5.16 = ( ? [X3: int] :
% 4.71/5.16 ( ( member_int @ X3 @ A2 )
% 4.71/5.16 & ( ( F @ X3 )
% 4.71/5.16 = zero_zero_nat ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_zero_iff
% 4.71/5.16 thf(fact_7463_prod__zero__iff,axiom,
% 4.71/5.16 ! [A2: set_complex,F: complex > nat] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.16 => ( ( ( groups861055069439313189ex_nat @ F @ A2 )
% 4.71/5.16 = zero_zero_nat )
% 4.71/5.16 = ( ? [X3: complex] :
% 4.71/5.16 ( ( member_complex @ X3 @ A2 )
% 4.71/5.16 & ( ( F @ X3 )
% 4.71/5.16 = zero_zero_nat ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_zero_iff
% 4.71/5.16 thf(fact_7464_prod__eq__1__iff,axiom,
% 4.71/5.16 ! [A2: set_int,F: int > nat] :
% 4.71/5.16 ( ( finite_finite_int @ A2 )
% 4.71/5.16 => ( ( ( groups1707563613775114915nt_nat @ F @ A2 )
% 4.71/5.16 = one_one_nat )
% 4.71/5.16 = ( ! [X3: int] :
% 4.71/5.16 ( ( member_int @ X3 @ A2 )
% 4.71/5.16 => ( ( F @ X3 )
% 4.71/5.16 = one_one_nat ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_eq_1_iff
% 4.71/5.16 thf(fact_7465_prod__eq__1__iff,axiom,
% 4.71/5.16 ! [A2: set_complex,F: complex > nat] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.16 => ( ( ( groups861055069439313189ex_nat @ F @ A2 )
% 4.71/5.16 = one_one_nat )
% 4.71/5.16 = ( ! [X3: complex] :
% 4.71/5.16 ( ( member_complex @ X3 @ A2 )
% 4.71/5.16 => ( ( F @ X3 )
% 4.71/5.16 = one_one_nat ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_eq_1_iff
% 4.71/5.16 thf(fact_7466_prod__eq__1__iff,axiom,
% 4.71/5.16 ! [A2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 4.71/5.16 ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.16 => ( ( ( groups4077766827762148844at_nat @ F @ A2 )
% 4.71/5.16 = one_one_nat )
% 4.71/5.16 = ( ! [X3: product_prod_nat_nat] :
% 4.71/5.16 ( ( member8440522571783428010at_nat @ X3 @ A2 )
% 4.71/5.16 => ( ( F @ X3 )
% 4.71/5.16 = one_one_nat ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_eq_1_iff
% 4.71/5.16 thf(fact_7467_prod__eq__1__iff,axiom,
% 4.71/5.16 ! [A2: set_Extended_enat,F: extended_enat > nat] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.16 => ( ( ( groups2880970938130013265at_nat @ F @ A2 )
% 4.71/5.16 = one_one_nat )
% 4.71/5.16 = ( ! [X3: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X3 @ A2 )
% 4.71/5.16 => ( ( F @ X3 )
% 4.71/5.16 = one_one_nat ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_eq_1_iff
% 4.71/5.16 thf(fact_7468_prod__eq__1__iff,axiom,
% 4.71/5.16 ! [A2: set_nat,F: nat > nat] :
% 4.71/5.16 ( ( finite_finite_nat @ A2 )
% 4.71/5.16 => ( ( ( groups708209901874060359at_nat @ F @ A2 )
% 4.71/5.16 = one_one_nat )
% 4.71/5.16 = ( ! [X3: nat] :
% 4.71/5.16 ( ( member_nat @ X3 @ A2 )
% 4.71/5.16 => ( ( F @ X3 )
% 4.71/5.16 = one_one_nat ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_eq_1_iff
% 4.71/5.16 thf(fact_7469_prod__pos__nat__iff,axiom,
% 4.71/5.16 ! [A2: set_int,F: int > nat] :
% 4.71/5.16 ( ( finite_finite_int @ A2 )
% 4.71/5.16 => ( ( ord_less_nat @ zero_zero_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) )
% 4.71/5.16 = ( ! [X3: int] :
% 4.71/5.16 ( ( member_int @ X3 @ A2 )
% 4.71/5.16 => ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_pos_nat_iff
% 4.71/5.16 thf(fact_7470_prod__pos__nat__iff,axiom,
% 4.71/5.16 ! [A2: set_complex,F: complex > nat] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.16 => ( ( ord_less_nat @ zero_zero_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) )
% 4.71/5.16 = ( ! [X3: complex] :
% 4.71/5.16 ( ( member_complex @ X3 @ A2 )
% 4.71/5.16 => ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_pos_nat_iff
% 4.71/5.16 thf(fact_7471_prod__pos__nat__iff,axiom,
% 4.71/5.16 ! [A2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 4.71/5.16 ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.16 => ( ( ord_less_nat @ zero_zero_nat @ ( groups4077766827762148844at_nat @ F @ A2 ) )
% 4.71/5.16 = ( ! [X3: product_prod_nat_nat] :
% 4.71/5.16 ( ( member8440522571783428010at_nat @ X3 @ A2 )
% 4.71/5.16 => ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_pos_nat_iff
% 4.71/5.16 thf(fact_7472_prod__pos__nat__iff,axiom,
% 4.71/5.16 ! [A2: set_Extended_enat,F: extended_enat > nat] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.16 => ( ( ord_less_nat @ zero_zero_nat @ ( groups2880970938130013265at_nat @ F @ A2 ) )
% 4.71/5.16 = ( ! [X3: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X3 @ A2 )
% 4.71/5.16 => ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_pos_nat_iff
% 4.71/5.16 thf(fact_7473_prod__pos__nat__iff,axiom,
% 4.71/5.16 ! [A2: set_nat,F: nat > nat] :
% 4.71/5.16 ( ( finite_finite_nat @ A2 )
% 4.71/5.16 => ( ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 4.71/5.16 = ( ! [X3: nat] :
% 4.71/5.16 ( ( member_nat @ X3 @ A2 )
% 4.71/5.16 => ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_pos_nat_iff
% 4.71/5.16 thf(fact_7474_prod__int__eq,axiom,
% 4.71/5.16 ! [I: nat,J: nat] :
% 4.71/5.16 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 4.71/5.16 = ( groups1705073143266064639nt_int
% 4.71/5.16 @ ^ [X3: int] : X3
% 4.71/5.16 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_int_eq
% 4.71/5.16 thf(fact_7475_prod__int__plus__eq,axiom,
% 4.71/5.16 ! [I: nat,J: nat] :
% 4.71/5.16 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ ( plus_plus_nat @ I @ J ) ) )
% 4.71/5.16 = ( groups1705073143266064639nt_int
% 4.71/5.16 @ ^ [X3: int] : X3
% 4.71/5.16 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I @ J ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_int_plus_eq
% 4.71/5.16 thf(fact_7476_prod_Oneutral,axiom,
% 4.71/5.16 ! [A2: set_nat,G2: nat > nat] :
% 4.71/5.16 ( ! [X4: nat] :
% 4.71/5.16 ( ( member_nat @ X4 @ A2 )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_nat ) )
% 4.71/5.16 => ( ( groups708209901874060359at_nat @ G2 @ A2 )
% 4.71/5.16 = one_one_nat ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.neutral
% 4.71/5.16 thf(fact_7477_prod_Oneutral,axiom,
% 4.71/5.16 ! [A2: set_nat,G2: nat > int] :
% 4.71/5.16 ( ! [X4: nat] :
% 4.71/5.16 ( ( member_nat @ X4 @ A2 )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_int ) )
% 4.71/5.16 => ( ( groups705719431365010083at_int @ G2 @ A2 )
% 4.71/5.16 = one_one_int ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.neutral
% 4.71/5.16 thf(fact_7478_prod_Oneutral,axiom,
% 4.71/5.16 ! [A2: set_int,G2: int > int] :
% 4.71/5.16 ( ! [X4: int] :
% 4.71/5.16 ( ( member_int @ X4 @ A2 )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_int ) )
% 4.71/5.16 => ( ( groups1705073143266064639nt_int @ G2 @ A2 )
% 4.71/5.16 = one_one_int ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.neutral
% 4.71/5.16 thf(fact_7479_prod_Onot__neutral__contains__not__neutral,axiom,
% 4.71/5.16 ! [G2: $o > complex,A2: set_o] :
% 4.71/5.16 ( ( ( groups4859619685533338977omplex @ G2 @ A2 )
% 4.71/5.16 != one_one_complex )
% 4.71/5.16 => ~ ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ A2 )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_complex ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.not_neutral_contains_not_neutral
% 4.71/5.16 thf(fact_7480_prod_Onot__neutral__contains__not__neutral,axiom,
% 4.71/5.16 ! [G2: nat > complex,A2: set_nat] :
% 4.71/5.16 ( ( ( groups6464643781859351333omplex @ G2 @ A2 )
% 4.71/5.16 != one_one_complex )
% 4.71/5.16 => ~ ! [A5: nat] :
% 4.71/5.16 ( ( member_nat @ A5 @ A2 )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_complex ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.not_neutral_contains_not_neutral
% 4.71/5.16 thf(fact_7481_prod_Onot__neutral__contains__not__neutral,axiom,
% 4.71/5.16 ! [G2: int > complex,A2: set_int] :
% 4.71/5.16 ( ( ( groups7440179247065528705omplex @ G2 @ A2 )
% 4.71/5.16 != one_one_complex )
% 4.71/5.16 => ~ ! [A5: int] :
% 4.71/5.16 ( ( member_int @ A5 @ A2 )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_complex ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.not_neutral_contains_not_neutral
% 4.71/5.16 thf(fact_7482_prod_Onot__neutral__contains__not__neutral,axiom,
% 4.71/5.16 ! [G2: $o > real,A2: set_o] :
% 4.71/5.16 ( ( ( groups234877984723959775o_real @ G2 @ A2 )
% 4.71/5.16 != one_one_real )
% 4.71/5.16 => ~ ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ A2 )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_real ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.not_neutral_contains_not_neutral
% 4.71/5.16 thf(fact_7483_prod_Onot__neutral__contains__not__neutral,axiom,
% 4.71/5.16 ! [G2: nat > real,A2: set_nat] :
% 4.71/5.16 ( ( ( groups129246275422532515t_real @ G2 @ A2 )
% 4.71/5.16 != one_one_real )
% 4.71/5.16 => ~ ! [A5: nat] :
% 4.71/5.16 ( ( member_nat @ A5 @ A2 )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_real ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.not_neutral_contains_not_neutral
% 4.71/5.16 thf(fact_7484_prod_Onot__neutral__contains__not__neutral,axiom,
% 4.71/5.16 ! [G2: int > real,A2: set_int] :
% 4.71/5.16 ( ( ( groups2316167850115554303t_real @ G2 @ A2 )
% 4.71/5.16 != one_one_real )
% 4.71/5.16 => ~ ! [A5: int] :
% 4.71/5.16 ( ( member_int @ A5 @ A2 )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_real ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.not_neutral_contains_not_neutral
% 4.71/5.16 thf(fact_7485_prod_Onot__neutral__contains__not__neutral,axiom,
% 4.71/5.16 ! [G2: $o > rat,A2: set_o] :
% 4.71/5.16 ( ( ( groups2869687844427037835_o_rat @ G2 @ A2 )
% 4.71/5.16 != one_one_rat )
% 4.71/5.16 => ~ ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ A2 )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_rat ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.not_neutral_contains_not_neutral
% 4.71/5.16 thf(fact_7486_prod_Onot__neutral__contains__not__neutral,axiom,
% 4.71/5.16 ! [G2: nat > rat,A2: set_nat] :
% 4.71/5.16 ( ( ( groups73079841787564623at_rat @ G2 @ A2 )
% 4.71/5.16 != one_one_rat )
% 4.71/5.16 => ~ ! [A5: nat] :
% 4.71/5.16 ( ( member_nat @ A5 @ A2 )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_rat ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.not_neutral_contains_not_neutral
% 4.71/5.16 thf(fact_7487_prod_Onot__neutral__contains__not__neutral,axiom,
% 4.71/5.16 ! [G2: int > rat,A2: set_int] :
% 4.71/5.16 ( ( ( groups1072433553688619179nt_rat @ G2 @ A2 )
% 4.71/5.16 != one_one_rat )
% 4.71/5.16 => ~ ! [A5: int] :
% 4.71/5.16 ( ( member_int @ A5 @ A2 )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_rat ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.not_neutral_contains_not_neutral
% 4.71/5.16 thf(fact_7488_prod_Onot__neutral__contains__not__neutral,axiom,
% 4.71/5.16 ! [G2: $o > nat,A2: set_o] :
% 4.71/5.16 ( ( ( groups3504817904513533571_o_nat @ G2 @ A2 )
% 4.71/5.16 != one_one_nat )
% 4.71/5.16 => ~ ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ A2 )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_nat ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.not_neutral_contains_not_neutral
% 4.71/5.16 thf(fact_7489_prod_Oswap__restrict,axiom,
% 4.71/5.16 ! [A2: set_o,B2: set_nat,G2: $o > nat > nat,R: $o > nat > $o] :
% 4.71/5.16 ( ( finite_finite_o @ A2 )
% 4.71/5.16 => ( ( finite_finite_nat @ B2 )
% 4.71/5.16 => ( ( groups3504817904513533571_o_nat
% 4.71/5.16 @ ^ [X3: $o] :
% 4.71/5.16 ( groups708209901874060359at_nat @ ( G2 @ X3 )
% 4.71/5.16 @ ( collect_nat
% 4.71/5.16 @ ^ [Y2: nat] :
% 4.71/5.16 ( ( member_nat @ Y2 @ B2 )
% 4.71/5.16 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.16 @ A2 )
% 4.71/5.16 = ( groups708209901874060359at_nat
% 4.71/5.16 @ ^ [Y2: nat] :
% 4.71/5.16 ( groups3504817904513533571_o_nat
% 4.71/5.16 @ ^ [X3: $o] : ( G2 @ X3 @ Y2 )
% 4.71/5.16 @ ( collect_o
% 4.71/5.16 @ ^ [X3: $o] :
% 4.71/5.16 ( ( member_o @ X3 @ A2 )
% 4.71/5.16 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.16 @ B2 ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.swap_restrict
% 4.71/5.16 thf(fact_7490_prod_Oswap__restrict,axiom,
% 4.71/5.16 ! [A2: set_int,B2: set_nat,G2: int > nat > nat,R: int > nat > $o] :
% 4.71/5.16 ( ( finite_finite_int @ A2 )
% 4.71/5.16 => ( ( finite_finite_nat @ B2 )
% 4.71/5.16 => ( ( groups1707563613775114915nt_nat
% 4.71/5.16 @ ^ [X3: int] :
% 4.71/5.16 ( groups708209901874060359at_nat @ ( G2 @ X3 )
% 4.71/5.16 @ ( collect_nat
% 4.71/5.16 @ ^ [Y2: nat] :
% 4.71/5.16 ( ( member_nat @ Y2 @ B2 )
% 4.71/5.16 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.16 @ A2 )
% 4.71/5.16 = ( groups708209901874060359at_nat
% 4.71/5.16 @ ^ [Y2: nat] :
% 4.71/5.16 ( groups1707563613775114915nt_nat
% 4.71/5.16 @ ^ [X3: int] : ( G2 @ X3 @ Y2 )
% 4.71/5.16 @ ( collect_int
% 4.71/5.16 @ ^ [X3: int] :
% 4.71/5.16 ( ( member_int @ X3 @ A2 )
% 4.71/5.16 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.16 @ B2 ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.swap_restrict
% 4.71/5.16 thf(fact_7491_prod_Oswap__restrict,axiom,
% 4.71/5.16 ! [A2: set_complex,B2: set_nat,G2: complex > nat > nat,R: complex > nat > $o] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.16 => ( ( finite_finite_nat @ B2 )
% 4.71/5.16 => ( ( groups861055069439313189ex_nat
% 4.71/5.16 @ ^ [X3: complex] :
% 4.71/5.16 ( groups708209901874060359at_nat @ ( G2 @ X3 )
% 4.71/5.16 @ ( collect_nat
% 4.71/5.16 @ ^ [Y2: nat] :
% 4.71/5.16 ( ( member_nat @ Y2 @ B2 )
% 4.71/5.16 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.16 @ A2 )
% 4.71/5.16 = ( groups708209901874060359at_nat
% 4.71/5.16 @ ^ [Y2: nat] :
% 4.71/5.16 ( groups861055069439313189ex_nat
% 4.71/5.16 @ ^ [X3: complex] : ( G2 @ X3 @ Y2 )
% 4.71/5.16 @ ( collect_complex
% 4.71/5.16 @ ^ [X3: complex] :
% 4.71/5.16 ( ( member_complex @ X3 @ A2 )
% 4.71/5.16 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.16 @ B2 ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.swap_restrict
% 4.71/5.16 thf(fact_7492_prod_Oswap__restrict,axiom,
% 4.71/5.16 ! [A2: set_Extended_enat,B2: set_nat,G2: extended_enat > nat > nat,R: extended_enat > nat > $o] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.16 => ( ( finite_finite_nat @ B2 )
% 4.71/5.16 => ( ( groups2880970938130013265at_nat
% 4.71/5.16 @ ^ [X3: extended_enat] :
% 4.71/5.16 ( groups708209901874060359at_nat @ ( G2 @ X3 )
% 4.71/5.16 @ ( collect_nat
% 4.71/5.16 @ ^ [Y2: nat] :
% 4.71/5.16 ( ( member_nat @ Y2 @ B2 )
% 4.71/5.16 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.16 @ A2 )
% 4.71/5.16 = ( groups708209901874060359at_nat
% 4.71/5.16 @ ^ [Y2: nat] :
% 4.71/5.16 ( groups2880970938130013265at_nat
% 4.71/5.16 @ ^ [X3: extended_enat] : ( G2 @ X3 @ Y2 )
% 4.71/5.16 @ ( collec4429806609662206161d_enat
% 4.71/5.16 @ ^ [X3: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X3 @ A2 )
% 4.71/5.16 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.16 @ B2 ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.swap_restrict
% 4.71/5.16 thf(fact_7493_prod_Oswap__restrict,axiom,
% 4.71/5.16 ! [A2: set_o,B2: set_nat,G2: $o > nat > int,R: $o > nat > $o] :
% 4.71/5.16 ( ( finite_finite_o @ A2 )
% 4.71/5.16 => ( ( finite_finite_nat @ B2 )
% 4.71/5.16 => ( ( groups3502327434004483295_o_int
% 4.71/5.16 @ ^ [X3: $o] :
% 4.71/5.16 ( groups705719431365010083at_int @ ( G2 @ X3 )
% 4.71/5.16 @ ( collect_nat
% 4.71/5.16 @ ^ [Y2: nat] :
% 4.71/5.16 ( ( member_nat @ Y2 @ B2 )
% 4.71/5.16 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.16 @ A2 )
% 4.71/5.16 = ( groups705719431365010083at_int
% 4.71/5.16 @ ^ [Y2: nat] :
% 4.71/5.16 ( groups3502327434004483295_o_int
% 4.71/5.16 @ ^ [X3: $o] : ( G2 @ X3 @ Y2 )
% 4.71/5.16 @ ( collect_o
% 4.71/5.16 @ ^ [X3: $o] :
% 4.71/5.16 ( ( member_o @ X3 @ A2 )
% 4.71/5.16 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.16 @ B2 ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.swap_restrict
% 4.71/5.16 thf(fact_7494_prod_Oswap__restrict,axiom,
% 4.71/5.16 ! [A2: set_complex,B2: set_nat,G2: complex > nat > int,R: complex > nat > $o] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.16 => ( ( finite_finite_nat @ B2 )
% 4.71/5.16 => ( ( groups858564598930262913ex_int
% 4.71/5.16 @ ^ [X3: complex] :
% 4.71/5.16 ( groups705719431365010083at_int @ ( G2 @ X3 )
% 4.71/5.16 @ ( collect_nat
% 4.71/5.16 @ ^ [Y2: nat] :
% 4.71/5.16 ( ( member_nat @ Y2 @ B2 )
% 4.71/5.16 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.16 @ A2 )
% 4.71/5.16 = ( groups705719431365010083at_int
% 4.71/5.16 @ ^ [Y2: nat] :
% 4.71/5.16 ( groups858564598930262913ex_int
% 4.71/5.16 @ ^ [X3: complex] : ( G2 @ X3 @ Y2 )
% 4.71/5.16 @ ( collect_complex
% 4.71/5.16 @ ^ [X3: complex] :
% 4.71/5.16 ( ( member_complex @ X3 @ A2 )
% 4.71/5.16 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.16 @ B2 ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.swap_restrict
% 4.71/5.16 thf(fact_7495_prod_Oswap__restrict,axiom,
% 4.71/5.16 ! [A2: set_Extended_enat,B2: set_nat,G2: extended_enat > nat > int,R: extended_enat > nat > $o] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.16 => ( ( finite_finite_nat @ B2 )
% 4.71/5.16 => ( ( groups2878480467620962989at_int
% 4.71/5.16 @ ^ [X3: extended_enat] :
% 4.71/5.16 ( groups705719431365010083at_int @ ( G2 @ X3 )
% 4.71/5.16 @ ( collect_nat
% 4.71/5.16 @ ^ [Y2: nat] :
% 4.71/5.16 ( ( member_nat @ Y2 @ B2 )
% 4.71/5.16 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.16 @ A2 )
% 4.71/5.16 = ( groups705719431365010083at_int
% 4.71/5.16 @ ^ [Y2: nat] :
% 4.71/5.16 ( groups2878480467620962989at_int
% 4.71/5.16 @ ^ [X3: extended_enat] : ( G2 @ X3 @ Y2 )
% 4.71/5.16 @ ( collec4429806609662206161d_enat
% 4.71/5.16 @ ^ [X3: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X3 @ A2 )
% 4.71/5.16 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.16 @ B2 ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.swap_restrict
% 4.71/5.16 thf(fact_7496_prod_Oswap__restrict,axiom,
% 4.71/5.16 ! [A2: set_o,B2: set_int,G2: $o > int > int,R: $o > int > $o] :
% 4.71/5.16 ( ( finite_finite_o @ A2 )
% 4.71/5.16 => ( ( finite_finite_int @ B2 )
% 4.71/5.16 => ( ( groups3502327434004483295_o_int
% 4.71/5.16 @ ^ [X3: $o] :
% 4.71/5.16 ( groups1705073143266064639nt_int @ ( G2 @ X3 )
% 4.71/5.16 @ ( collect_int
% 4.71/5.16 @ ^ [Y2: int] :
% 4.71/5.16 ( ( member_int @ Y2 @ B2 )
% 4.71/5.16 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.16 @ A2 )
% 4.71/5.16 = ( groups1705073143266064639nt_int
% 4.71/5.16 @ ^ [Y2: int] :
% 4.71/5.16 ( groups3502327434004483295_o_int
% 4.71/5.16 @ ^ [X3: $o] : ( G2 @ X3 @ Y2 )
% 4.71/5.16 @ ( collect_o
% 4.71/5.16 @ ^ [X3: $o] :
% 4.71/5.16 ( ( member_o @ X3 @ A2 )
% 4.71/5.16 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.16 @ B2 ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.swap_restrict
% 4.71/5.16 thf(fact_7497_prod_Oswap__restrict,axiom,
% 4.71/5.16 ! [A2: set_complex,B2: set_int,G2: complex > int > int,R: complex > int > $o] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.16 => ( ( finite_finite_int @ B2 )
% 4.71/5.16 => ( ( groups858564598930262913ex_int
% 4.71/5.16 @ ^ [X3: complex] :
% 4.71/5.16 ( groups1705073143266064639nt_int @ ( G2 @ X3 )
% 4.71/5.16 @ ( collect_int
% 4.71/5.16 @ ^ [Y2: int] :
% 4.71/5.16 ( ( member_int @ Y2 @ B2 )
% 4.71/5.16 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.16 @ A2 )
% 4.71/5.16 = ( groups1705073143266064639nt_int
% 4.71/5.16 @ ^ [Y2: int] :
% 4.71/5.16 ( groups858564598930262913ex_int
% 4.71/5.16 @ ^ [X3: complex] : ( G2 @ X3 @ Y2 )
% 4.71/5.16 @ ( collect_complex
% 4.71/5.16 @ ^ [X3: complex] :
% 4.71/5.16 ( ( member_complex @ X3 @ A2 )
% 4.71/5.16 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.16 @ B2 ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.swap_restrict
% 4.71/5.16 thf(fact_7498_prod_Oswap__restrict,axiom,
% 4.71/5.16 ! [A2: set_Extended_enat,B2: set_int,G2: extended_enat > int > int,R: extended_enat > int > $o] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.16 => ( ( finite_finite_int @ B2 )
% 4.71/5.16 => ( ( groups2878480467620962989at_int
% 4.71/5.16 @ ^ [X3: extended_enat] :
% 4.71/5.16 ( groups1705073143266064639nt_int @ ( G2 @ X3 )
% 4.71/5.16 @ ( collect_int
% 4.71/5.16 @ ^ [Y2: int] :
% 4.71/5.16 ( ( member_int @ Y2 @ B2 )
% 4.71/5.16 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.16 @ A2 )
% 4.71/5.16 = ( groups1705073143266064639nt_int
% 4.71/5.16 @ ^ [Y2: int] :
% 4.71/5.16 ( groups2878480467620962989at_int
% 4.71/5.16 @ ^ [X3: extended_enat] : ( G2 @ X3 @ Y2 )
% 4.71/5.16 @ ( collec4429806609662206161d_enat
% 4.71/5.16 @ ^ [X3: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X3 @ A2 )
% 4.71/5.16 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.16 @ B2 ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.swap_restrict
% 4.71/5.16 thf(fact_7499_prod__nonneg,axiom,
% 4.71/5.16 ! [A2: set_nat,F: nat > nat] :
% 4.71/5.16 ( ! [X4: nat] :
% 4.71/5.16 ( ( member_nat @ X4 @ A2 )
% 4.71/5.16 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 4.71/5.16 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_nonneg
% 4.71/5.16 thf(fact_7500_prod__nonneg,axiom,
% 4.71/5.16 ! [A2: set_nat,F: nat > int] :
% 4.71/5.16 ( ! [X4: nat] :
% 4.71/5.16 ( ( member_nat @ X4 @ A2 )
% 4.71/5.16 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 4.71/5.16 => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_nonneg
% 4.71/5.16 thf(fact_7501_prod__nonneg,axiom,
% 4.71/5.16 ! [A2: set_int,F: int > int] :
% 4.71/5.16 ( ! [X4: int] :
% 4.71/5.16 ( ( member_int @ X4 @ A2 )
% 4.71/5.16 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 4.71/5.16 => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_nonneg
% 4.71/5.16 thf(fact_7502_prod__mono,axiom,
% 4.71/5.16 ! [A2: set_o,F: $o > real,G2: $o > real] :
% 4.71/5.16 ( ! [I2: $o] :
% 4.71/5.16 ( ( member_o @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_eq_real @ ( F @ I2 ) @ ( G2 @ I2 ) ) ) )
% 4.71/5.16 => ( ord_less_eq_real @ ( groups234877984723959775o_real @ F @ A2 ) @ ( groups234877984723959775o_real @ G2 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono
% 4.71/5.16 thf(fact_7503_prod__mono,axiom,
% 4.71/5.16 ! [A2: set_nat,F: nat > real,G2: nat > real] :
% 4.71/5.16 ( ! [I2: nat] :
% 4.71/5.16 ( ( member_nat @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_eq_real @ ( F @ I2 ) @ ( G2 @ I2 ) ) ) )
% 4.71/5.16 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ G2 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono
% 4.71/5.16 thf(fact_7504_prod__mono,axiom,
% 4.71/5.16 ! [A2: set_int,F: int > real,G2: int > real] :
% 4.71/5.16 ( ! [I2: int] :
% 4.71/5.16 ( ( member_int @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_eq_real @ ( F @ I2 ) @ ( G2 @ I2 ) ) ) )
% 4.71/5.16 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ G2 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono
% 4.71/5.16 thf(fact_7505_prod__mono,axiom,
% 4.71/5.16 ! [A2: set_o,F: $o > rat,G2: $o > rat] :
% 4.71/5.16 ( ! [I2: $o] :
% 4.71/5.16 ( ( member_o @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_eq_rat @ ( F @ I2 ) @ ( G2 @ I2 ) ) ) )
% 4.71/5.16 => ( ord_less_eq_rat @ ( groups2869687844427037835_o_rat @ F @ A2 ) @ ( groups2869687844427037835_o_rat @ G2 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono
% 4.71/5.16 thf(fact_7506_prod__mono,axiom,
% 4.71/5.16 ! [A2: set_nat,F: nat > rat,G2: nat > rat] :
% 4.71/5.16 ( ! [I2: nat] :
% 4.71/5.16 ( ( member_nat @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_eq_rat @ ( F @ I2 ) @ ( G2 @ I2 ) ) ) )
% 4.71/5.16 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ G2 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono
% 4.71/5.16 thf(fact_7507_prod__mono,axiom,
% 4.71/5.16 ! [A2: set_int,F: int > rat,G2: int > rat] :
% 4.71/5.16 ( ! [I2: int] :
% 4.71/5.16 ( ( member_int @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_eq_rat @ ( F @ I2 ) @ ( G2 @ I2 ) ) ) )
% 4.71/5.16 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( groups1072433553688619179nt_rat @ G2 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono
% 4.71/5.16 thf(fact_7508_prod__mono,axiom,
% 4.71/5.16 ! [A2: set_o,F: $o > nat,G2: $o > nat] :
% 4.71/5.16 ( ! [I2: $o] :
% 4.71/5.16 ( ( member_o @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_eq_nat @ ( F @ I2 ) @ ( G2 @ I2 ) ) ) )
% 4.71/5.16 => ( ord_less_eq_nat @ ( groups3504817904513533571_o_nat @ F @ A2 ) @ ( groups3504817904513533571_o_nat @ G2 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono
% 4.71/5.16 thf(fact_7509_prod__mono,axiom,
% 4.71/5.16 ! [A2: set_int,F: int > nat,G2: int > nat] :
% 4.71/5.16 ( ! [I2: int] :
% 4.71/5.16 ( ( member_int @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_eq_nat @ ( F @ I2 ) @ ( G2 @ I2 ) ) ) )
% 4.71/5.16 => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( groups1707563613775114915nt_nat @ G2 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono
% 4.71/5.16 thf(fact_7510_prod__mono,axiom,
% 4.71/5.16 ! [A2: set_o,F: $o > int,G2: $o > int] :
% 4.71/5.16 ( ! [I2: $o] :
% 4.71/5.16 ( ( member_o @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_eq_int @ ( F @ I2 ) @ ( G2 @ I2 ) ) ) )
% 4.71/5.16 => ( ord_less_eq_int @ ( groups3502327434004483295_o_int @ F @ A2 ) @ ( groups3502327434004483295_o_int @ G2 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono
% 4.71/5.16 thf(fact_7511_prod__mono,axiom,
% 4.71/5.16 ! [A2: set_nat,F: nat > nat,G2: nat > nat] :
% 4.71/5.16 ( ! [I2: nat] :
% 4.71/5.16 ( ( member_nat @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_eq_nat @ ( F @ I2 ) @ ( G2 @ I2 ) ) ) )
% 4.71/5.16 => ( ord_less_eq_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ ( groups708209901874060359at_nat @ G2 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono
% 4.71/5.16 thf(fact_7512_prod__pos,axiom,
% 4.71/5.16 ! [A2: set_nat,F: nat > nat] :
% 4.71/5.16 ( ! [X4: nat] :
% 4.71/5.16 ( ( member_nat @ X4 @ A2 )
% 4.71/5.16 => ( ord_less_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 4.71/5.16 => ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_pos
% 4.71/5.16 thf(fact_7513_prod__pos,axiom,
% 4.71/5.16 ! [A2: set_nat,F: nat > int] :
% 4.71/5.16 ( ! [X4: nat] :
% 4.71/5.16 ( ( member_nat @ X4 @ A2 )
% 4.71/5.16 => ( ord_less_int @ zero_zero_int @ ( F @ X4 ) ) )
% 4.71/5.16 => ( ord_less_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_pos
% 4.71/5.16 thf(fact_7514_prod__pos,axiom,
% 4.71/5.16 ! [A2: set_int,F: int > int] :
% 4.71/5.16 ( ! [X4: int] :
% 4.71/5.16 ( ( member_int @ X4 @ A2 )
% 4.71/5.16 => ( ord_less_int @ zero_zero_int @ ( F @ X4 ) ) )
% 4.71/5.16 => ( ord_less_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_pos
% 4.71/5.16 thf(fact_7515_prod__ge__1,axiom,
% 4.71/5.16 ! [A2: set_o,F: $o > real] :
% 4.71/5.16 ( ! [X4: $o] :
% 4.71/5.16 ( ( member_o @ X4 @ A2 )
% 4.71/5.16 => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 4.71/5.16 => ( ord_less_eq_real @ one_one_real @ ( groups234877984723959775o_real @ F @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_ge_1
% 4.71/5.16 thf(fact_7516_prod__ge__1,axiom,
% 4.71/5.16 ! [A2: set_nat,F: nat > real] :
% 4.71/5.16 ( ! [X4: nat] :
% 4.71/5.16 ( ( member_nat @ X4 @ A2 )
% 4.71/5.16 => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 4.71/5.16 => ( ord_less_eq_real @ one_one_real @ ( groups129246275422532515t_real @ F @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_ge_1
% 4.71/5.16 thf(fact_7517_prod__ge__1,axiom,
% 4.71/5.16 ! [A2: set_int,F: int > real] :
% 4.71/5.16 ( ! [X4: int] :
% 4.71/5.16 ( ( member_int @ X4 @ A2 )
% 4.71/5.16 => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 4.71/5.16 => ( ord_less_eq_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_ge_1
% 4.71/5.16 thf(fact_7518_prod__ge__1,axiom,
% 4.71/5.16 ! [A2: set_o,F: $o > rat] :
% 4.71/5.16 ( ! [X4: $o] :
% 4.71/5.16 ( ( member_o @ X4 @ A2 )
% 4.71/5.16 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 4.71/5.16 => ( ord_less_eq_rat @ one_one_rat @ ( groups2869687844427037835_o_rat @ F @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_ge_1
% 4.71/5.16 thf(fact_7519_prod__ge__1,axiom,
% 4.71/5.16 ! [A2: set_nat,F: nat > rat] :
% 4.71/5.16 ( ! [X4: nat] :
% 4.71/5.16 ( ( member_nat @ X4 @ A2 )
% 4.71/5.16 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 4.71/5.16 => ( ord_less_eq_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_ge_1
% 4.71/5.16 thf(fact_7520_prod__ge__1,axiom,
% 4.71/5.16 ! [A2: set_int,F: int > rat] :
% 4.71/5.16 ( ! [X4: int] :
% 4.71/5.16 ( ( member_int @ X4 @ A2 )
% 4.71/5.16 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 4.71/5.16 => ( ord_less_eq_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_ge_1
% 4.71/5.16 thf(fact_7521_prod__ge__1,axiom,
% 4.71/5.16 ! [A2: set_o,F: $o > nat] :
% 4.71/5.16 ( ! [X4: $o] :
% 4.71/5.16 ( ( member_o @ X4 @ A2 )
% 4.71/5.16 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X4 ) ) )
% 4.71/5.16 => ( ord_less_eq_nat @ one_one_nat @ ( groups3504817904513533571_o_nat @ F @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_ge_1
% 4.71/5.16 thf(fact_7522_prod__ge__1,axiom,
% 4.71/5.16 ! [A2: set_int,F: int > nat] :
% 4.71/5.16 ( ! [X4: int] :
% 4.71/5.16 ( ( member_int @ X4 @ A2 )
% 4.71/5.16 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X4 ) ) )
% 4.71/5.16 => ( ord_less_eq_nat @ one_one_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_ge_1
% 4.71/5.16 thf(fact_7523_prod__ge__1,axiom,
% 4.71/5.16 ! [A2: set_o,F: $o > int] :
% 4.71/5.16 ( ! [X4: $o] :
% 4.71/5.16 ( ( member_o @ X4 @ A2 )
% 4.71/5.16 => ( ord_less_eq_int @ one_one_int @ ( F @ X4 ) ) )
% 4.71/5.16 => ( ord_less_eq_int @ one_one_int @ ( groups3502327434004483295_o_int @ F @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_ge_1
% 4.71/5.16 thf(fact_7524_prod__ge__1,axiom,
% 4.71/5.16 ! [A2: set_nat,F: nat > nat] :
% 4.71/5.16 ( ! [X4: nat] :
% 4.71/5.16 ( ( member_nat @ X4 @ A2 )
% 4.71/5.16 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X4 ) ) )
% 4.71/5.16 => ( ord_less_eq_nat @ one_one_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_ge_1
% 4.71/5.16 thf(fact_7525_prod__zero,axiom,
% 4.71/5.16 ! [A2: set_nat,F: nat > real] :
% 4.71/5.16 ( ( finite_finite_nat @ A2 )
% 4.71/5.16 => ( ? [X2: nat] :
% 4.71/5.16 ( ( member_nat @ X2 @ A2 )
% 4.71/5.16 & ( ( F @ X2 )
% 4.71/5.16 = zero_zero_real ) )
% 4.71/5.16 => ( ( groups129246275422532515t_real @ F @ A2 )
% 4.71/5.16 = zero_zero_real ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_zero
% 4.71/5.16 thf(fact_7526_prod__zero,axiom,
% 4.71/5.16 ! [A2: set_int,F: int > real] :
% 4.71/5.16 ( ( finite_finite_int @ A2 )
% 4.71/5.16 => ( ? [X2: int] :
% 4.71/5.16 ( ( member_int @ X2 @ A2 )
% 4.71/5.16 & ( ( F @ X2 )
% 4.71/5.16 = zero_zero_real ) )
% 4.71/5.16 => ( ( groups2316167850115554303t_real @ F @ A2 )
% 4.71/5.16 = zero_zero_real ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_zero
% 4.71/5.16 thf(fact_7527_prod__zero,axiom,
% 4.71/5.16 ! [A2: set_complex,F: complex > real] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.16 => ( ? [X2: complex] :
% 4.71/5.16 ( ( member_complex @ X2 @ A2 )
% 4.71/5.16 & ( ( F @ X2 )
% 4.71/5.16 = zero_zero_real ) )
% 4.71/5.16 => ( ( groups766887009212190081x_real @ F @ A2 )
% 4.71/5.16 = zero_zero_real ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_zero
% 4.71/5.16 thf(fact_7528_prod__zero,axiom,
% 4.71/5.16 ! [A2: set_Extended_enat,F: extended_enat > real] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.16 => ( ? [X2: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X2 @ A2 )
% 4.71/5.16 & ( ( F @ X2 )
% 4.71/5.16 = zero_zero_real ) )
% 4.71/5.16 => ( ( groups97031904164794029t_real @ F @ A2 )
% 4.71/5.16 = zero_zero_real ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_zero
% 4.71/5.16 thf(fact_7529_prod__zero,axiom,
% 4.71/5.16 ! [A2: set_nat,F: nat > rat] :
% 4.71/5.16 ( ( finite_finite_nat @ A2 )
% 4.71/5.16 => ( ? [X2: nat] :
% 4.71/5.16 ( ( member_nat @ X2 @ A2 )
% 4.71/5.16 & ( ( F @ X2 )
% 4.71/5.16 = zero_zero_rat ) )
% 4.71/5.16 => ( ( groups73079841787564623at_rat @ F @ A2 )
% 4.71/5.16 = zero_zero_rat ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_zero
% 4.71/5.16 thf(fact_7530_prod__zero,axiom,
% 4.71/5.16 ! [A2: set_int,F: int > rat] :
% 4.71/5.16 ( ( finite_finite_int @ A2 )
% 4.71/5.16 => ( ? [X2: int] :
% 4.71/5.16 ( ( member_int @ X2 @ A2 )
% 4.71/5.16 & ( ( F @ X2 )
% 4.71/5.16 = zero_zero_rat ) )
% 4.71/5.16 => ( ( groups1072433553688619179nt_rat @ F @ A2 )
% 4.71/5.16 = zero_zero_rat ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_zero
% 4.71/5.16 thf(fact_7531_prod__zero,axiom,
% 4.71/5.16 ! [A2: set_complex,F: complex > rat] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.16 => ( ? [X2: complex] :
% 4.71/5.16 ( ( member_complex @ X2 @ A2 )
% 4.71/5.16 & ( ( F @ X2 )
% 4.71/5.16 = zero_zero_rat ) )
% 4.71/5.16 => ( ( groups225925009352817453ex_rat @ F @ A2 )
% 4.71/5.16 = zero_zero_rat ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_zero
% 4.71/5.16 thf(fact_7532_prod__zero,axiom,
% 4.71/5.16 ! [A2: set_Extended_enat,F: extended_enat > rat] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.16 => ( ? [X2: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X2 @ A2 )
% 4.71/5.16 & ( ( F @ X2 )
% 4.71/5.16 = zero_zero_rat ) )
% 4.71/5.16 => ( ( groups2245840878043517529at_rat @ F @ A2 )
% 4.71/5.16 = zero_zero_rat ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_zero
% 4.71/5.16 thf(fact_7533_prod__zero,axiom,
% 4.71/5.16 ! [A2: set_int,F: int > nat] :
% 4.71/5.16 ( ( finite_finite_int @ A2 )
% 4.71/5.16 => ( ? [X2: int] :
% 4.71/5.16 ( ( member_int @ X2 @ A2 )
% 4.71/5.16 & ( ( F @ X2 )
% 4.71/5.16 = zero_zero_nat ) )
% 4.71/5.16 => ( ( groups1707563613775114915nt_nat @ F @ A2 )
% 4.71/5.16 = zero_zero_nat ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_zero
% 4.71/5.16 thf(fact_7534_prod__zero,axiom,
% 4.71/5.16 ! [A2: set_complex,F: complex > nat] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.16 => ( ? [X2: complex] :
% 4.71/5.16 ( ( member_complex @ X2 @ A2 )
% 4.71/5.16 & ( ( F @ X2 )
% 4.71/5.16 = zero_zero_nat ) )
% 4.71/5.16 => ( ( groups861055069439313189ex_nat @ F @ A2 )
% 4.71/5.16 = zero_zero_nat ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_zero
% 4.71/5.16 thf(fact_7535_sum_Ofinite__Collect__op,axiom,
% 4.71/5.16 ! [I5: set_o,X: $o > real,Y: $o > real] :
% 4.71/5.16 ( ( finite_finite_o
% 4.71/5.16 @ ( collect_o
% 4.71/5.16 @ ^ [I4: $o] :
% 4.71/5.16 ( ( member_o @ I4 @ I5 )
% 4.71/5.16 & ( ( X @ I4 )
% 4.71/5.16 != zero_zero_real ) ) ) )
% 4.71/5.16 => ( ( finite_finite_o
% 4.71/5.16 @ ( collect_o
% 4.71/5.16 @ ^ [I4: $o] :
% 4.71/5.16 ( ( member_o @ I4 @ I5 )
% 4.71/5.16 & ( ( Y @ I4 )
% 4.71/5.16 != zero_zero_real ) ) ) )
% 4.71/5.16 => ( finite_finite_o
% 4.71/5.16 @ ( collect_o
% 4.71/5.16 @ ^ [I4: $o] :
% 4.71/5.16 ( ( member_o @ I4 @ I5 )
% 4.71/5.16 & ( ( plus_plus_real @ ( X @ I4 ) @ ( Y @ I4 ) )
% 4.71/5.16 != zero_zero_real ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % sum.finite_Collect_op
% 4.71/5.16 thf(fact_7536_sum_Ofinite__Collect__op,axiom,
% 4.71/5.16 ! [I5: set_nat,X: nat > real,Y: nat > real] :
% 4.71/5.16 ( ( finite_finite_nat
% 4.71/5.16 @ ( collect_nat
% 4.71/5.16 @ ^ [I4: nat] :
% 4.71/5.16 ( ( member_nat @ I4 @ I5 )
% 4.71/5.16 & ( ( X @ I4 )
% 4.71/5.16 != zero_zero_real ) ) ) )
% 4.71/5.16 => ( ( finite_finite_nat
% 4.71/5.16 @ ( collect_nat
% 4.71/5.16 @ ^ [I4: nat] :
% 4.71/5.16 ( ( member_nat @ I4 @ I5 )
% 4.71/5.16 & ( ( Y @ I4 )
% 4.71/5.16 != zero_zero_real ) ) ) )
% 4.71/5.16 => ( finite_finite_nat
% 4.71/5.16 @ ( collect_nat
% 4.71/5.16 @ ^ [I4: nat] :
% 4.71/5.16 ( ( member_nat @ I4 @ I5 )
% 4.71/5.16 & ( ( plus_plus_real @ ( X @ I4 ) @ ( Y @ I4 ) )
% 4.71/5.16 != zero_zero_real ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % sum.finite_Collect_op
% 4.71/5.16 thf(fact_7537_sum_Ofinite__Collect__op,axiom,
% 4.71/5.16 ! [I5: set_int,X: int > real,Y: int > real] :
% 4.71/5.16 ( ( finite_finite_int
% 4.71/5.16 @ ( collect_int
% 4.71/5.16 @ ^ [I4: int] :
% 4.71/5.16 ( ( member_int @ I4 @ I5 )
% 4.71/5.16 & ( ( X @ I4 )
% 4.71/5.16 != zero_zero_real ) ) ) )
% 4.71/5.16 => ( ( finite_finite_int
% 4.71/5.16 @ ( collect_int
% 4.71/5.16 @ ^ [I4: int] :
% 4.71/5.16 ( ( member_int @ I4 @ I5 )
% 4.71/5.16 & ( ( Y @ I4 )
% 4.71/5.16 != zero_zero_real ) ) ) )
% 4.71/5.16 => ( finite_finite_int
% 4.71/5.16 @ ( collect_int
% 4.71/5.16 @ ^ [I4: int] :
% 4.71/5.16 ( ( member_int @ I4 @ I5 )
% 4.71/5.16 & ( ( plus_plus_real @ ( X @ I4 ) @ ( Y @ I4 ) )
% 4.71/5.16 != zero_zero_real ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % sum.finite_Collect_op
% 4.71/5.16 thf(fact_7538_sum_Ofinite__Collect__op,axiom,
% 4.71/5.16 ! [I5: set_complex,X: complex > real,Y: complex > real] :
% 4.71/5.16 ( ( finite3207457112153483333omplex
% 4.71/5.16 @ ( collect_complex
% 4.71/5.16 @ ^ [I4: complex] :
% 4.71/5.16 ( ( member_complex @ I4 @ I5 )
% 4.71/5.16 & ( ( X @ I4 )
% 4.71/5.16 != zero_zero_real ) ) ) )
% 4.71/5.16 => ( ( finite3207457112153483333omplex
% 4.71/5.16 @ ( collect_complex
% 4.71/5.16 @ ^ [I4: complex] :
% 4.71/5.16 ( ( member_complex @ I4 @ I5 )
% 4.71/5.16 & ( ( Y @ I4 )
% 4.71/5.16 != zero_zero_real ) ) ) )
% 4.71/5.16 => ( finite3207457112153483333omplex
% 4.71/5.16 @ ( collect_complex
% 4.71/5.16 @ ^ [I4: complex] :
% 4.71/5.16 ( ( member_complex @ I4 @ I5 )
% 4.71/5.16 & ( ( plus_plus_real @ ( X @ I4 ) @ ( Y @ I4 ) )
% 4.71/5.16 != zero_zero_real ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % sum.finite_Collect_op
% 4.71/5.16 thf(fact_7539_sum_Ofinite__Collect__op,axiom,
% 4.71/5.16 ! [I5: set_Extended_enat,X: extended_enat > real,Y: extended_enat > real] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat
% 4.71/5.16 @ ( collec4429806609662206161d_enat
% 4.71/5.16 @ ^ [I4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ I4 @ I5 )
% 4.71/5.16 & ( ( X @ I4 )
% 4.71/5.16 != zero_zero_real ) ) ) )
% 4.71/5.16 => ( ( finite4001608067531595151d_enat
% 4.71/5.16 @ ( collec4429806609662206161d_enat
% 4.71/5.16 @ ^ [I4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ I4 @ I5 )
% 4.71/5.16 & ( ( Y @ I4 )
% 4.71/5.16 != zero_zero_real ) ) ) )
% 4.71/5.16 => ( finite4001608067531595151d_enat
% 4.71/5.16 @ ( collec4429806609662206161d_enat
% 4.71/5.16 @ ^ [I4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ I4 @ I5 )
% 4.71/5.16 & ( ( plus_plus_real @ ( X @ I4 ) @ ( Y @ I4 ) )
% 4.71/5.16 != zero_zero_real ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % sum.finite_Collect_op
% 4.71/5.16 thf(fact_7540_sum_Ofinite__Collect__op,axiom,
% 4.71/5.16 ! [I5: set_o,X: $o > rat,Y: $o > rat] :
% 4.71/5.16 ( ( finite_finite_o
% 4.71/5.16 @ ( collect_o
% 4.71/5.16 @ ^ [I4: $o] :
% 4.71/5.16 ( ( member_o @ I4 @ I5 )
% 4.71/5.16 & ( ( X @ I4 )
% 4.71/5.16 != zero_zero_rat ) ) ) )
% 4.71/5.16 => ( ( finite_finite_o
% 4.71/5.16 @ ( collect_o
% 4.71/5.16 @ ^ [I4: $o] :
% 4.71/5.16 ( ( member_o @ I4 @ I5 )
% 4.71/5.16 & ( ( Y @ I4 )
% 4.71/5.16 != zero_zero_rat ) ) ) )
% 4.71/5.16 => ( finite_finite_o
% 4.71/5.16 @ ( collect_o
% 4.71/5.16 @ ^ [I4: $o] :
% 4.71/5.16 ( ( member_o @ I4 @ I5 )
% 4.71/5.16 & ( ( plus_plus_rat @ ( X @ I4 ) @ ( Y @ I4 ) )
% 4.71/5.16 != zero_zero_rat ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % sum.finite_Collect_op
% 4.71/5.16 thf(fact_7541_sum_Ofinite__Collect__op,axiom,
% 4.71/5.16 ! [I5: set_nat,X: nat > rat,Y: nat > rat] :
% 4.71/5.16 ( ( finite_finite_nat
% 4.71/5.16 @ ( collect_nat
% 4.71/5.16 @ ^ [I4: nat] :
% 4.71/5.16 ( ( member_nat @ I4 @ I5 )
% 4.71/5.16 & ( ( X @ I4 )
% 4.71/5.16 != zero_zero_rat ) ) ) )
% 4.71/5.16 => ( ( finite_finite_nat
% 4.71/5.16 @ ( collect_nat
% 4.71/5.16 @ ^ [I4: nat] :
% 4.71/5.16 ( ( member_nat @ I4 @ I5 )
% 4.71/5.16 & ( ( Y @ I4 )
% 4.71/5.16 != zero_zero_rat ) ) ) )
% 4.71/5.16 => ( finite_finite_nat
% 4.71/5.16 @ ( collect_nat
% 4.71/5.16 @ ^ [I4: nat] :
% 4.71/5.16 ( ( member_nat @ I4 @ I5 )
% 4.71/5.16 & ( ( plus_plus_rat @ ( X @ I4 ) @ ( Y @ I4 ) )
% 4.71/5.16 != zero_zero_rat ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % sum.finite_Collect_op
% 4.71/5.16 thf(fact_7542_sum_Ofinite__Collect__op,axiom,
% 4.71/5.16 ! [I5: set_int,X: int > rat,Y: int > rat] :
% 4.71/5.16 ( ( finite_finite_int
% 4.71/5.16 @ ( collect_int
% 4.71/5.16 @ ^ [I4: int] :
% 4.71/5.16 ( ( member_int @ I4 @ I5 )
% 4.71/5.16 & ( ( X @ I4 )
% 4.71/5.16 != zero_zero_rat ) ) ) )
% 4.71/5.16 => ( ( finite_finite_int
% 4.71/5.16 @ ( collect_int
% 4.71/5.16 @ ^ [I4: int] :
% 4.71/5.16 ( ( member_int @ I4 @ I5 )
% 4.71/5.16 & ( ( Y @ I4 )
% 4.71/5.16 != zero_zero_rat ) ) ) )
% 4.71/5.16 => ( finite_finite_int
% 4.71/5.16 @ ( collect_int
% 4.71/5.16 @ ^ [I4: int] :
% 4.71/5.16 ( ( member_int @ I4 @ I5 )
% 4.71/5.16 & ( ( plus_plus_rat @ ( X @ I4 ) @ ( Y @ I4 ) )
% 4.71/5.16 != zero_zero_rat ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % sum.finite_Collect_op
% 4.71/5.16 thf(fact_7543_sum_Ofinite__Collect__op,axiom,
% 4.71/5.16 ! [I5: set_complex,X: complex > rat,Y: complex > rat] :
% 4.71/5.16 ( ( finite3207457112153483333omplex
% 4.71/5.16 @ ( collect_complex
% 4.71/5.16 @ ^ [I4: complex] :
% 4.71/5.16 ( ( member_complex @ I4 @ I5 )
% 4.71/5.16 & ( ( X @ I4 )
% 4.71/5.16 != zero_zero_rat ) ) ) )
% 4.71/5.16 => ( ( finite3207457112153483333omplex
% 4.71/5.16 @ ( collect_complex
% 4.71/5.16 @ ^ [I4: complex] :
% 4.71/5.16 ( ( member_complex @ I4 @ I5 )
% 4.71/5.16 & ( ( Y @ I4 )
% 4.71/5.16 != zero_zero_rat ) ) ) )
% 4.71/5.16 => ( finite3207457112153483333omplex
% 4.71/5.16 @ ( collect_complex
% 4.71/5.16 @ ^ [I4: complex] :
% 4.71/5.16 ( ( member_complex @ I4 @ I5 )
% 4.71/5.16 & ( ( plus_plus_rat @ ( X @ I4 ) @ ( Y @ I4 ) )
% 4.71/5.16 != zero_zero_rat ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % sum.finite_Collect_op
% 4.71/5.16 thf(fact_7544_sum_Ofinite__Collect__op,axiom,
% 4.71/5.16 ! [I5: set_Extended_enat,X: extended_enat > rat,Y: extended_enat > rat] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat
% 4.71/5.16 @ ( collec4429806609662206161d_enat
% 4.71/5.16 @ ^ [I4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ I4 @ I5 )
% 4.71/5.16 & ( ( X @ I4 )
% 4.71/5.16 != zero_zero_rat ) ) ) )
% 4.71/5.16 => ( ( finite4001608067531595151d_enat
% 4.71/5.16 @ ( collec4429806609662206161d_enat
% 4.71/5.16 @ ^ [I4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ I4 @ I5 )
% 4.71/5.16 & ( ( Y @ I4 )
% 4.71/5.16 != zero_zero_rat ) ) ) )
% 4.71/5.16 => ( finite4001608067531595151d_enat
% 4.71/5.16 @ ( collec4429806609662206161d_enat
% 4.71/5.16 @ ^ [I4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ I4 @ I5 )
% 4.71/5.16 & ( ( plus_plus_rat @ ( X @ I4 ) @ ( Y @ I4 ) )
% 4.71/5.16 != zero_zero_rat ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % sum.finite_Collect_op
% 4.71/5.16 thf(fact_7545_prod_Ofinite__Collect__op,axiom,
% 4.71/5.16 ! [I5: set_o,X: $o > complex,Y: $o > complex] :
% 4.71/5.16 ( ( finite_finite_o
% 4.71/5.16 @ ( collect_o
% 4.71/5.16 @ ^ [I4: $o] :
% 4.71/5.16 ( ( member_o @ I4 @ I5 )
% 4.71/5.16 & ( ( X @ I4 )
% 4.71/5.16 != one_one_complex ) ) ) )
% 4.71/5.16 => ( ( finite_finite_o
% 4.71/5.16 @ ( collect_o
% 4.71/5.16 @ ^ [I4: $o] :
% 4.71/5.16 ( ( member_o @ I4 @ I5 )
% 4.71/5.16 & ( ( Y @ I4 )
% 4.71/5.16 != one_one_complex ) ) ) )
% 4.71/5.16 => ( finite_finite_o
% 4.71/5.16 @ ( collect_o
% 4.71/5.16 @ ^ [I4: $o] :
% 4.71/5.16 ( ( member_o @ I4 @ I5 )
% 4.71/5.16 & ( ( times_times_complex @ ( X @ I4 ) @ ( Y @ I4 ) )
% 4.71/5.16 != one_one_complex ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.finite_Collect_op
% 4.71/5.16 thf(fact_7546_prod_Ofinite__Collect__op,axiom,
% 4.71/5.16 ! [I5: set_nat,X: nat > complex,Y: nat > complex] :
% 4.71/5.16 ( ( finite_finite_nat
% 4.71/5.16 @ ( collect_nat
% 4.71/5.16 @ ^ [I4: nat] :
% 4.71/5.16 ( ( member_nat @ I4 @ I5 )
% 4.71/5.16 & ( ( X @ I4 )
% 4.71/5.16 != one_one_complex ) ) ) )
% 4.71/5.16 => ( ( finite_finite_nat
% 4.71/5.16 @ ( collect_nat
% 4.71/5.16 @ ^ [I4: nat] :
% 4.71/5.16 ( ( member_nat @ I4 @ I5 )
% 4.71/5.16 & ( ( Y @ I4 )
% 4.71/5.16 != one_one_complex ) ) ) )
% 4.71/5.16 => ( finite_finite_nat
% 4.71/5.16 @ ( collect_nat
% 4.71/5.16 @ ^ [I4: nat] :
% 4.71/5.16 ( ( member_nat @ I4 @ I5 )
% 4.71/5.16 & ( ( times_times_complex @ ( X @ I4 ) @ ( Y @ I4 ) )
% 4.71/5.16 != one_one_complex ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.finite_Collect_op
% 4.71/5.16 thf(fact_7547_prod_Ofinite__Collect__op,axiom,
% 4.71/5.16 ! [I5: set_int,X: int > complex,Y: int > complex] :
% 4.71/5.16 ( ( finite_finite_int
% 4.71/5.16 @ ( collect_int
% 4.71/5.16 @ ^ [I4: int] :
% 4.71/5.16 ( ( member_int @ I4 @ I5 )
% 4.71/5.16 & ( ( X @ I4 )
% 4.71/5.16 != one_one_complex ) ) ) )
% 4.71/5.16 => ( ( finite_finite_int
% 4.71/5.16 @ ( collect_int
% 4.71/5.16 @ ^ [I4: int] :
% 4.71/5.16 ( ( member_int @ I4 @ I5 )
% 4.71/5.16 & ( ( Y @ I4 )
% 4.71/5.16 != one_one_complex ) ) ) )
% 4.71/5.16 => ( finite_finite_int
% 4.71/5.16 @ ( collect_int
% 4.71/5.16 @ ^ [I4: int] :
% 4.71/5.16 ( ( member_int @ I4 @ I5 )
% 4.71/5.16 & ( ( times_times_complex @ ( X @ I4 ) @ ( Y @ I4 ) )
% 4.71/5.16 != one_one_complex ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.finite_Collect_op
% 4.71/5.16 thf(fact_7548_prod_Ofinite__Collect__op,axiom,
% 4.71/5.16 ! [I5: set_complex,X: complex > complex,Y: complex > complex] :
% 4.71/5.16 ( ( finite3207457112153483333omplex
% 4.71/5.16 @ ( collect_complex
% 4.71/5.16 @ ^ [I4: complex] :
% 4.71/5.16 ( ( member_complex @ I4 @ I5 )
% 4.71/5.16 & ( ( X @ I4 )
% 4.71/5.16 != one_one_complex ) ) ) )
% 4.71/5.16 => ( ( finite3207457112153483333omplex
% 4.71/5.16 @ ( collect_complex
% 4.71/5.16 @ ^ [I4: complex] :
% 4.71/5.16 ( ( member_complex @ I4 @ I5 )
% 4.71/5.16 & ( ( Y @ I4 )
% 4.71/5.16 != one_one_complex ) ) ) )
% 4.71/5.16 => ( finite3207457112153483333omplex
% 4.71/5.16 @ ( collect_complex
% 4.71/5.16 @ ^ [I4: complex] :
% 4.71/5.16 ( ( member_complex @ I4 @ I5 )
% 4.71/5.16 & ( ( times_times_complex @ ( X @ I4 ) @ ( Y @ I4 ) )
% 4.71/5.16 != one_one_complex ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.finite_Collect_op
% 4.71/5.16 thf(fact_7549_prod_Ofinite__Collect__op,axiom,
% 4.71/5.16 ! [I5: set_Extended_enat,X: extended_enat > complex,Y: extended_enat > complex] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat
% 4.71/5.16 @ ( collec4429806609662206161d_enat
% 4.71/5.16 @ ^ [I4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ I4 @ I5 )
% 4.71/5.16 & ( ( X @ I4 )
% 4.71/5.16 != one_one_complex ) ) ) )
% 4.71/5.16 => ( ( finite4001608067531595151d_enat
% 4.71/5.16 @ ( collec4429806609662206161d_enat
% 4.71/5.16 @ ^ [I4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ I4 @ I5 )
% 4.71/5.16 & ( ( Y @ I4 )
% 4.71/5.16 != one_one_complex ) ) ) )
% 4.71/5.16 => ( finite4001608067531595151d_enat
% 4.71/5.16 @ ( collec4429806609662206161d_enat
% 4.71/5.16 @ ^ [I4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ I4 @ I5 )
% 4.71/5.16 & ( ( times_times_complex @ ( X @ I4 ) @ ( Y @ I4 ) )
% 4.71/5.16 != one_one_complex ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.finite_Collect_op
% 4.71/5.16 thf(fact_7550_prod_Ofinite__Collect__op,axiom,
% 4.71/5.16 ! [I5: set_o,X: $o > real,Y: $o > real] :
% 4.71/5.16 ( ( finite_finite_o
% 4.71/5.16 @ ( collect_o
% 4.71/5.16 @ ^ [I4: $o] :
% 4.71/5.16 ( ( member_o @ I4 @ I5 )
% 4.71/5.16 & ( ( X @ I4 )
% 4.71/5.16 != one_one_real ) ) ) )
% 4.71/5.16 => ( ( finite_finite_o
% 4.71/5.16 @ ( collect_o
% 4.71/5.16 @ ^ [I4: $o] :
% 4.71/5.16 ( ( member_o @ I4 @ I5 )
% 4.71/5.16 & ( ( Y @ I4 )
% 4.71/5.16 != one_one_real ) ) ) )
% 4.71/5.16 => ( finite_finite_o
% 4.71/5.16 @ ( collect_o
% 4.71/5.16 @ ^ [I4: $o] :
% 4.71/5.16 ( ( member_o @ I4 @ I5 )
% 4.71/5.16 & ( ( times_times_real @ ( X @ I4 ) @ ( Y @ I4 ) )
% 4.71/5.16 != one_one_real ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.finite_Collect_op
% 4.71/5.16 thf(fact_7551_prod_Ofinite__Collect__op,axiom,
% 4.71/5.16 ! [I5: set_nat,X: nat > real,Y: nat > real] :
% 4.71/5.16 ( ( finite_finite_nat
% 4.71/5.16 @ ( collect_nat
% 4.71/5.16 @ ^ [I4: nat] :
% 4.71/5.16 ( ( member_nat @ I4 @ I5 )
% 4.71/5.16 & ( ( X @ I4 )
% 4.71/5.16 != one_one_real ) ) ) )
% 4.71/5.16 => ( ( finite_finite_nat
% 4.71/5.16 @ ( collect_nat
% 4.71/5.16 @ ^ [I4: nat] :
% 4.71/5.16 ( ( member_nat @ I4 @ I5 )
% 4.71/5.16 & ( ( Y @ I4 )
% 4.71/5.16 != one_one_real ) ) ) )
% 4.71/5.16 => ( finite_finite_nat
% 4.71/5.16 @ ( collect_nat
% 4.71/5.16 @ ^ [I4: nat] :
% 4.71/5.16 ( ( member_nat @ I4 @ I5 )
% 4.71/5.16 & ( ( times_times_real @ ( X @ I4 ) @ ( Y @ I4 ) )
% 4.71/5.16 != one_one_real ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.finite_Collect_op
% 4.71/5.16 thf(fact_7552_prod_Ofinite__Collect__op,axiom,
% 4.71/5.16 ! [I5: set_int,X: int > real,Y: int > real] :
% 4.71/5.16 ( ( finite_finite_int
% 4.71/5.16 @ ( collect_int
% 4.71/5.16 @ ^ [I4: int] :
% 4.71/5.16 ( ( member_int @ I4 @ I5 )
% 4.71/5.16 & ( ( X @ I4 )
% 4.71/5.16 != one_one_real ) ) ) )
% 4.71/5.16 => ( ( finite_finite_int
% 4.71/5.16 @ ( collect_int
% 4.71/5.16 @ ^ [I4: int] :
% 4.71/5.16 ( ( member_int @ I4 @ I5 )
% 4.71/5.16 & ( ( Y @ I4 )
% 4.71/5.16 != one_one_real ) ) ) )
% 4.71/5.16 => ( finite_finite_int
% 4.71/5.16 @ ( collect_int
% 4.71/5.16 @ ^ [I4: int] :
% 4.71/5.16 ( ( member_int @ I4 @ I5 )
% 4.71/5.16 & ( ( times_times_real @ ( X @ I4 ) @ ( Y @ I4 ) )
% 4.71/5.16 != one_one_real ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.finite_Collect_op
% 4.71/5.16 thf(fact_7553_prod_Ofinite__Collect__op,axiom,
% 4.71/5.16 ! [I5: set_complex,X: complex > real,Y: complex > real] :
% 4.71/5.16 ( ( finite3207457112153483333omplex
% 4.71/5.16 @ ( collect_complex
% 4.71/5.16 @ ^ [I4: complex] :
% 4.71/5.16 ( ( member_complex @ I4 @ I5 )
% 4.71/5.16 & ( ( X @ I4 )
% 4.71/5.16 != one_one_real ) ) ) )
% 4.71/5.16 => ( ( finite3207457112153483333omplex
% 4.71/5.16 @ ( collect_complex
% 4.71/5.16 @ ^ [I4: complex] :
% 4.71/5.16 ( ( member_complex @ I4 @ I5 )
% 4.71/5.16 & ( ( Y @ I4 )
% 4.71/5.16 != one_one_real ) ) ) )
% 4.71/5.16 => ( finite3207457112153483333omplex
% 4.71/5.16 @ ( collect_complex
% 4.71/5.16 @ ^ [I4: complex] :
% 4.71/5.16 ( ( member_complex @ I4 @ I5 )
% 4.71/5.16 & ( ( times_times_real @ ( X @ I4 ) @ ( Y @ I4 ) )
% 4.71/5.16 != one_one_real ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.finite_Collect_op
% 4.71/5.16 thf(fact_7554_prod_Ofinite__Collect__op,axiom,
% 4.71/5.16 ! [I5: set_Extended_enat,X: extended_enat > real,Y: extended_enat > real] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat
% 4.71/5.16 @ ( collec4429806609662206161d_enat
% 4.71/5.16 @ ^ [I4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ I4 @ I5 )
% 4.71/5.16 & ( ( X @ I4 )
% 4.71/5.16 != one_one_real ) ) ) )
% 4.71/5.16 => ( ( finite4001608067531595151d_enat
% 4.71/5.16 @ ( collec4429806609662206161d_enat
% 4.71/5.16 @ ^ [I4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ I4 @ I5 )
% 4.71/5.16 & ( ( Y @ I4 )
% 4.71/5.16 != one_one_real ) ) ) )
% 4.71/5.16 => ( finite4001608067531595151d_enat
% 4.71/5.16 @ ( collec4429806609662206161d_enat
% 4.71/5.16 @ ^ [I4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ I4 @ I5 )
% 4.71/5.16 & ( ( times_times_real @ ( X @ I4 ) @ ( Y @ I4 ) )
% 4.71/5.16 != one_one_real ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.finite_Collect_op
% 4.71/5.16 thf(fact_7555_prod_Ointer__filter,axiom,
% 4.71/5.16 ! [A2: set_o,G2: $o > complex,P: $o > $o] :
% 4.71/5.16 ( ( finite_finite_o @ A2 )
% 4.71/5.16 => ( ( groups4859619685533338977omplex @ G2
% 4.71/5.16 @ ( collect_o
% 4.71/5.16 @ ^ [X3: $o] :
% 4.71/5.16 ( ( member_o @ X3 @ A2 )
% 4.71/5.16 & ( P @ X3 ) ) ) )
% 4.71/5.16 = ( groups4859619685533338977omplex
% 4.71/5.16 @ ^ [X3: $o] : ( if_complex @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_complex )
% 4.71/5.16 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.inter_filter
% 4.71/5.16 thf(fact_7556_prod_Ointer__filter,axiom,
% 4.71/5.16 ! [A2: set_nat,G2: nat > complex,P: nat > $o] :
% 4.71/5.16 ( ( finite_finite_nat @ A2 )
% 4.71/5.16 => ( ( groups6464643781859351333omplex @ G2
% 4.71/5.16 @ ( collect_nat
% 4.71/5.16 @ ^ [X3: nat] :
% 4.71/5.16 ( ( member_nat @ X3 @ A2 )
% 4.71/5.16 & ( P @ X3 ) ) ) )
% 4.71/5.16 = ( groups6464643781859351333omplex
% 4.71/5.16 @ ^ [X3: nat] : ( if_complex @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_complex )
% 4.71/5.16 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.inter_filter
% 4.71/5.16 thf(fact_7557_prod_Ointer__filter,axiom,
% 4.71/5.16 ! [A2: set_int,G2: int > complex,P: int > $o] :
% 4.71/5.16 ( ( finite_finite_int @ A2 )
% 4.71/5.16 => ( ( groups7440179247065528705omplex @ G2
% 4.71/5.16 @ ( collect_int
% 4.71/5.16 @ ^ [X3: int] :
% 4.71/5.16 ( ( member_int @ X3 @ A2 )
% 4.71/5.16 & ( P @ X3 ) ) ) )
% 4.71/5.16 = ( groups7440179247065528705omplex
% 4.71/5.16 @ ^ [X3: int] : ( if_complex @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_complex )
% 4.71/5.16 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.inter_filter
% 4.71/5.16 thf(fact_7558_prod_Ointer__filter,axiom,
% 4.71/5.16 ! [A2: set_complex,G2: complex > complex,P: complex > $o] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.16 => ( ( groups3708469109370488835omplex @ G2
% 4.71/5.16 @ ( collect_complex
% 4.71/5.16 @ ^ [X3: complex] :
% 4.71/5.16 ( ( member_complex @ X3 @ A2 )
% 4.71/5.16 & ( P @ X3 ) ) ) )
% 4.71/5.16 = ( groups3708469109370488835omplex
% 4.71/5.16 @ ^ [X3: complex] : ( if_complex @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_complex )
% 4.71/5.16 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.inter_filter
% 4.71/5.16 thf(fact_7559_prod_Ointer__filter,axiom,
% 4.71/5.16 ! [A2: set_Extended_enat,G2: extended_enat > complex,P: extended_enat > $o] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.16 => ( ( groups4622424608036095791omplex @ G2
% 4.71/5.16 @ ( collec4429806609662206161d_enat
% 4.71/5.16 @ ^ [X3: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X3 @ A2 )
% 4.71/5.16 & ( P @ X3 ) ) ) )
% 4.71/5.16 = ( groups4622424608036095791omplex
% 4.71/5.16 @ ^ [X3: extended_enat] : ( if_complex @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_complex )
% 4.71/5.16 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.inter_filter
% 4.71/5.16 thf(fact_7560_prod_Ointer__filter,axiom,
% 4.71/5.16 ! [A2: set_o,G2: $o > real,P: $o > $o] :
% 4.71/5.16 ( ( finite_finite_o @ A2 )
% 4.71/5.16 => ( ( groups234877984723959775o_real @ G2
% 4.71/5.16 @ ( collect_o
% 4.71/5.16 @ ^ [X3: $o] :
% 4.71/5.16 ( ( member_o @ X3 @ A2 )
% 4.71/5.16 & ( P @ X3 ) ) ) )
% 4.71/5.16 = ( groups234877984723959775o_real
% 4.71/5.16 @ ^ [X3: $o] : ( if_real @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_real )
% 4.71/5.16 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.inter_filter
% 4.71/5.16 thf(fact_7561_prod_Ointer__filter,axiom,
% 4.71/5.16 ! [A2: set_nat,G2: nat > real,P: nat > $o] :
% 4.71/5.16 ( ( finite_finite_nat @ A2 )
% 4.71/5.16 => ( ( groups129246275422532515t_real @ G2
% 4.71/5.16 @ ( collect_nat
% 4.71/5.16 @ ^ [X3: nat] :
% 4.71/5.16 ( ( member_nat @ X3 @ A2 )
% 4.71/5.16 & ( P @ X3 ) ) ) )
% 4.71/5.16 = ( groups129246275422532515t_real
% 4.71/5.16 @ ^ [X3: nat] : ( if_real @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_real )
% 4.71/5.16 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.inter_filter
% 4.71/5.16 thf(fact_7562_prod_Ointer__filter,axiom,
% 4.71/5.16 ! [A2: set_int,G2: int > real,P: int > $o] :
% 4.71/5.16 ( ( finite_finite_int @ A2 )
% 4.71/5.16 => ( ( groups2316167850115554303t_real @ G2
% 4.71/5.16 @ ( collect_int
% 4.71/5.16 @ ^ [X3: int] :
% 4.71/5.16 ( ( member_int @ X3 @ A2 )
% 4.71/5.16 & ( P @ X3 ) ) ) )
% 4.71/5.16 = ( groups2316167850115554303t_real
% 4.71/5.16 @ ^ [X3: int] : ( if_real @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_real )
% 4.71/5.16 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.inter_filter
% 4.71/5.16 thf(fact_7563_prod_Ointer__filter,axiom,
% 4.71/5.16 ! [A2: set_complex,G2: complex > real,P: complex > $o] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.16 => ( ( groups766887009212190081x_real @ G2
% 4.71/5.16 @ ( collect_complex
% 4.71/5.16 @ ^ [X3: complex] :
% 4.71/5.16 ( ( member_complex @ X3 @ A2 )
% 4.71/5.16 & ( P @ X3 ) ) ) )
% 4.71/5.16 = ( groups766887009212190081x_real
% 4.71/5.16 @ ^ [X3: complex] : ( if_real @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_real )
% 4.71/5.16 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.inter_filter
% 4.71/5.16 thf(fact_7564_prod_Ointer__filter,axiom,
% 4.71/5.16 ! [A2: set_Extended_enat,G2: extended_enat > real,P: extended_enat > $o] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.16 => ( ( groups97031904164794029t_real @ G2
% 4.71/5.16 @ ( collec4429806609662206161d_enat
% 4.71/5.16 @ ^ [X3: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X3 @ A2 )
% 4.71/5.16 & ( P @ X3 ) ) ) )
% 4.71/5.16 = ( groups97031904164794029t_real
% 4.71/5.16 @ ^ [X3: extended_enat] : ( if_real @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_real )
% 4.71/5.16 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.inter_filter
% 4.71/5.16 thf(fact_7565_prod__le__1,axiom,
% 4.71/5.16 ! [A2: set_o,F: $o > real] :
% 4.71/5.16 ( ! [X4: $o] :
% 4.71/5.16 ( ( member_o @ X4 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 4.71/5.16 & ( ord_less_eq_real @ ( F @ X4 ) @ one_one_real ) ) )
% 4.71/5.16 => ( ord_less_eq_real @ ( groups234877984723959775o_real @ F @ A2 ) @ one_one_real ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_le_1
% 4.71/5.16 thf(fact_7566_prod__le__1,axiom,
% 4.71/5.16 ! [A2: set_nat,F: nat > real] :
% 4.71/5.16 ( ! [X4: nat] :
% 4.71/5.16 ( ( member_nat @ X4 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 4.71/5.16 & ( ord_less_eq_real @ ( F @ X4 ) @ one_one_real ) ) )
% 4.71/5.16 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ one_one_real ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_le_1
% 4.71/5.16 thf(fact_7567_prod__le__1,axiom,
% 4.71/5.16 ! [A2: set_int,F: int > real] :
% 4.71/5.16 ( ! [X4: int] :
% 4.71/5.16 ( ( member_int @ X4 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 4.71/5.16 & ( ord_less_eq_real @ ( F @ X4 ) @ one_one_real ) ) )
% 4.71/5.16 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ one_one_real ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_le_1
% 4.71/5.16 thf(fact_7568_prod__le__1,axiom,
% 4.71/5.16 ! [A2: set_o,F: $o > rat] :
% 4.71/5.16 ( ! [X4: $o] :
% 4.71/5.16 ( ( member_o @ X4 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 4.71/5.16 & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 4.71/5.16 => ( ord_less_eq_rat @ ( groups2869687844427037835_o_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_le_1
% 4.71/5.16 thf(fact_7569_prod__le__1,axiom,
% 4.71/5.16 ! [A2: set_nat,F: nat > rat] :
% 4.71/5.16 ( ! [X4: nat] :
% 4.71/5.16 ( ( member_nat @ X4 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 4.71/5.16 & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 4.71/5.16 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_le_1
% 4.71/5.16 thf(fact_7570_prod__le__1,axiom,
% 4.71/5.16 ! [A2: set_int,F: int > rat] :
% 4.71/5.16 ( ! [X4: int] :
% 4.71/5.16 ( ( member_int @ X4 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 4.71/5.16 & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 4.71/5.16 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_le_1
% 4.71/5.16 thf(fact_7571_prod__le__1,axiom,
% 4.71/5.16 ! [A2: set_o,F: $o > nat] :
% 4.71/5.16 ( ! [X4: $o] :
% 4.71/5.16 ( ( member_o @ X4 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) )
% 4.71/5.16 & ( ord_less_eq_nat @ ( F @ X4 ) @ one_one_nat ) ) )
% 4.71/5.16 => ( ord_less_eq_nat @ ( groups3504817904513533571_o_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_le_1
% 4.71/5.16 thf(fact_7572_prod__le__1,axiom,
% 4.71/5.16 ! [A2: set_int,F: int > nat] :
% 4.71/5.16 ( ! [X4: int] :
% 4.71/5.16 ( ( member_int @ X4 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) )
% 4.71/5.16 & ( ord_less_eq_nat @ ( F @ X4 ) @ one_one_nat ) ) )
% 4.71/5.16 => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_le_1
% 4.71/5.16 thf(fact_7573_prod__le__1,axiom,
% 4.71/5.16 ! [A2: set_o,F: $o > int] :
% 4.71/5.16 ( ! [X4: $o] :
% 4.71/5.16 ( ( member_o @ X4 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) )
% 4.71/5.16 & ( ord_less_eq_int @ ( F @ X4 ) @ one_one_int ) ) )
% 4.71/5.16 => ( ord_less_eq_int @ ( groups3502327434004483295_o_int @ F @ A2 ) @ one_one_int ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_le_1
% 4.71/5.16 thf(fact_7574_prod__le__1,axiom,
% 4.71/5.16 ! [A2: set_nat,F: nat > nat] :
% 4.71/5.16 ( ! [X4: nat] :
% 4.71/5.16 ( ( member_nat @ X4 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) )
% 4.71/5.16 & ( ord_less_eq_nat @ ( F @ X4 ) @ one_one_nat ) ) )
% 4.71/5.16 => ( ord_less_eq_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ one_one_nat ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_le_1
% 4.71/5.16 thf(fact_7575_prod_Orelated,axiom,
% 4.71/5.16 ! [R: complex > complex > $o,S2: set_nat,H: nat > complex,G2: nat > complex] :
% 4.71/5.16 ( ( R @ one_one_complex @ one_one_complex )
% 4.71/5.16 => ( ! [X1: complex,Y1: complex,X24: complex,Y24: complex] :
% 4.71/5.16 ( ( ( R @ X1 @ X24 )
% 4.71/5.16 & ( R @ Y1 @ Y24 ) )
% 4.71/5.16 => ( R @ ( times_times_complex @ X1 @ Y1 ) @ ( times_times_complex @ X24 @ Y24 ) ) )
% 4.71/5.16 => ( ( finite_finite_nat @ S2 )
% 4.71/5.16 => ( ! [X4: nat] :
% 4.71/5.16 ( ( member_nat @ X4 @ S2 )
% 4.71/5.16 => ( R @ ( H @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.16 => ( R @ ( groups6464643781859351333omplex @ H @ S2 ) @ ( groups6464643781859351333omplex @ G2 @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.related
% 4.71/5.16 thf(fact_7576_prod_Orelated,axiom,
% 4.71/5.16 ! [R: complex > complex > $o,S2: set_int,H: int > complex,G2: int > complex] :
% 4.71/5.16 ( ( R @ one_one_complex @ one_one_complex )
% 4.71/5.16 => ( ! [X1: complex,Y1: complex,X24: complex,Y24: complex] :
% 4.71/5.16 ( ( ( R @ X1 @ X24 )
% 4.71/5.16 & ( R @ Y1 @ Y24 ) )
% 4.71/5.16 => ( R @ ( times_times_complex @ X1 @ Y1 ) @ ( times_times_complex @ X24 @ Y24 ) ) )
% 4.71/5.16 => ( ( finite_finite_int @ S2 )
% 4.71/5.16 => ( ! [X4: int] :
% 4.71/5.16 ( ( member_int @ X4 @ S2 )
% 4.71/5.16 => ( R @ ( H @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.16 => ( R @ ( groups7440179247065528705omplex @ H @ S2 ) @ ( groups7440179247065528705omplex @ G2 @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.related
% 4.71/5.16 thf(fact_7577_prod_Orelated,axiom,
% 4.71/5.16 ! [R: complex > complex > $o,S2: set_complex,H: complex > complex,G2: complex > complex] :
% 4.71/5.16 ( ( R @ one_one_complex @ one_one_complex )
% 4.71/5.16 => ( ! [X1: complex,Y1: complex,X24: complex,Y24: complex] :
% 4.71/5.16 ( ( ( R @ X1 @ X24 )
% 4.71/5.16 & ( R @ Y1 @ Y24 ) )
% 4.71/5.16 => ( R @ ( times_times_complex @ X1 @ Y1 ) @ ( times_times_complex @ X24 @ Y24 ) ) )
% 4.71/5.16 => ( ( finite3207457112153483333omplex @ S2 )
% 4.71/5.16 => ( ! [X4: complex] :
% 4.71/5.16 ( ( member_complex @ X4 @ S2 )
% 4.71/5.16 => ( R @ ( H @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.16 => ( R @ ( groups3708469109370488835omplex @ H @ S2 ) @ ( groups3708469109370488835omplex @ G2 @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.related
% 4.71/5.16 thf(fact_7578_prod_Orelated,axiom,
% 4.71/5.16 ! [R: complex > complex > $o,S2: set_Extended_enat,H: extended_enat > complex,G2: extended_enat > complex] :
% 4.71/5.16 ( ( R @ one_one_complex @ one_one_complex )
% 4.71/5.16 => ( ! [X1: complex,Y1: complex,X24: complex,Y24: complex] :
% 4.71/5.16 ( ( ( R @ X1 @ X24 )
% 4.71/5.16 & ( R @ Y1 @ Y24 ) )
% 4.71/5.16 => ( R @ ( times_times_complex @ X1 @ Y1 ) @ ( times_times_complex @ X24 @ Y24 ) ) )
% 4.71/5.16 => ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.16 => ( ! [X4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X4 @ S2 )
% 4.71/5.16 => ( R @ ( H @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.16 => ( R @ ( groups4622424608036095791omplex @ H @ S2 ) @ ( groups4622424608036095791omplex @ G2 @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.related
% 4.71/5.16 thf(fact_7579_prod_Orelated,axiom,
% 4.71/5.16 ! [R: real > real > $o,S2: set_nat,H: nat > real,G2: nat > real] :
% 4.71/5.16 ( ( R @ one_one_real @ one_one_real )
% 4.71/5.16 => ( ! [X1: real,Y1: real,X24: real,Y24: real] :
% 4.71/5.16 ( ( ( R @ X1 @ X24 )
% 4.71/5.16 & ( R @ Y1 @ Y24 ) )
% 4.71/5.16 => ( R @ ( times_times_real @ X1 @ Y1 ) @ ( times_times_real @ X24 @ Y24 ) ) )
% 4.71/5.16 => ( ( finite_finite_nat @ S2 )
% 4.71/5.16 => ( ! [X4: nat] :
% 4.71/5.16 ( ( member_nat @ X4 @ S2 )
% 4.71/5.16 => ( R @ ( H @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.16 => ( R @ ( groups129246275422532515t_real @ H @ S2 ) @ ( groups129246275422532515t_real @ G2 @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.related
% 4.71/5.16 thf(fact_7580_prod_Orelated,axiom,
% 4.71/5.16 ! [R: real > real > $o,S2: set_int,H: int > real,G2: int > real] :
% 4.71/5.16 ( ( R @ one_one_real @ one_one_real )
% 4.71/5.16 => ( ! [X1: real,Y1: real,X24: real,Y24: real] :
% 4.71/5.16 ( ( ( R @ X1 @ X24 )
% 4.71/5.16 & ( R @ Y1 @ Y24 ) )
% 4.71/5.16 => ( R @ ( times_times_real @ X1 @ Y1 ) @ ( times_times_real @ X24 @ Y24 ) ) )
% 4.71/5.16 => ( ( finite_finite_int @ S2 )
% 4.71/5.16 => ( ! [X4: int] :
% 4.71/5.16 ( ( member_int @ X4 @ S2 )
% 4.71/5.16 => ( R @ ( H @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.16 => ( R @ ( groups2316167850115554303t_real @ H @ S2 ) @ ( groups2316167850115554303t_real @ G2 @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.related
% 4.71/5.16 thf(fact_7581_prod_Orelated,axiom,
% 4.71/5.16 ! [R: real > real > $o,S2: set_complex,H: complex > real,G2: complex > real] :
% 4.71/5.16 ( ( R @ one_one_real @ one_one_real )
% 4.71/5.16 => ( ! [X1: real,Y1: real,X24: real,Y24: real] :
% 4.71/5.16 ( ( ( R @ X1 @ X24 )
% 4.71/5.16 & ( R @ Y1 @ Y24 ) )
% 4.71/5.16 => ( R @ ( times_times_real @ X1 @ Y1 ) @ ( times_times_real @ X24 @ Y24 ) ) )
% 4.71/5.16 => ( ( finite3207457112153483333omplex @ S2 )
% 4.71/5.16 => ( ! [X4: complex] :
% 4.71/5.16 ( ( member_complex @ X4 @ S2 )
% 4.71/5.16 => ( R @ ( H @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.16 => ( R @ ( groups766887009212190081x_real @ H @ S2 ) @ ( groups766887009212190081x_real @ G2 @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.related
% 4.71/5.16 thf(fact_7582_prod_Orelated,axiom,
% 4.71/5.16 ! [R: real > real > $o,S2: set_Extended_enat,H: extended_enat > real,G2: extended_enat > real] :
% 4.71/5.16 ( ( R @ one_one_real @ one_one_real )
% 4.71/5.16 => ( ! [X1: real,Y1: real,X24: real,Y24: real] :
% 4.71/5.16 ( ( ( R @ X1 @ X24 )
% 4.71/5.16 & ( R @ Y1 @ Y24 ) )
% 4.71/5.16 => ( R @ ( times_times_real @ X1 @ Y1 ) @ ( times_times_real @ X24 @ Y24 ) ) )
% 4.71/5.16 => ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.16 => ( ! [X4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X4 @ S2 )
% 4.71/5.16 => ( R @ ( H @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.16 => ( R @ ( groups97031904164794029t_real @ H @ S2 ) @ ( groups97031904164794029t_real @ G2 @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.related
% 4.71/5.16 thf(fact_7583_prod_Orelated,axiom,
% 4.71/5.16 ! [R: rat > rat > $o,S2: set_nat,H: nat > rat,G2: nat > rat] :
% 4.71/5.16 ( ( R @ one_one_rat @ one_one_rat )
% 4.71/5.16 => ( ! [X1: rat,Y1: rat,X24: rat,Y24: rat] :
% 4.71/5.16 ( ( ( R @ X1 @ X24 )
% 4.71/5.16 & ( R @ Y1 @ Y24 ) )
% 4.71/5.16 => ( R @ ( times_times_rat @ X1 @ Y1 ) @ ( times_times_rat @ X24 @ Y24 ) ) )
% 4.71/5.16 => ( ( finite_finite_nat @ S2 )
% 4.71/5.16 => ( ! [X4: nat] :
% 4.71/5.16 ( ( member_nat @ X4 @ S2 )
% 4.71/5.16 => ( R @ ( H @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.16 => ( R @ ( groups73079841787564623at_rat @ H @ S2 ) @ ( groups73079841787564623at_rat @ G2 @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.related
% 4.71/5.16 thf(fact_7584_prod_Orelated,axiom,
% 4.71/5.16 ! [R: rat > rat > $o,S2: set_int,H: int > rat,G2: int > rat] :
% 4.71/5.16 ( ( R @ one_one_rat @ one_one_rat )
% 4.71/5.16 => ( ! [X1: rat,Y1: rat,X24: rat,Y24: rat] :
% 4.71/5.16 ( ( ( R @ X1 @ X24 )
% 4.71/5.16 & ( R @ Y1 @ Y24 ) )
% 4.71/5.16 => ( R @ ( times_times_rat @ X1 @ Y1 ) @ ( times_times_rat @ X24 @ Y24 ) ) )
% 4.71/5.16 => ( ( finite_finite_int @ S2 )
% 4.71/5.16 => ( ! [X4: int] :
% 4.71/5.16 ( ( member_int @ X4 @ S2 )
% 4.71/5.16 => ( R @ ( H @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.16 => ( R @ ( groups1072433553688619179nt_rat @ H @ S2 ) @ ( groups1072433553688619179nt_rat @ G2 @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.related
% 4.71/5.16 thf(fact_7585_prod_Oinsert__if,axiom,
% 4.71/5.16 ! [A2: set_real,X: real,G2: real > real] :
% 4.71/5.16 ( ( finite_finite_real @ A2 )
% 4.71/5.16 => ( ( ( member_real @ X @ A2 )
% 4.71/5.16 => ( ( groups1681761925125756287l_real @ G2 @ ( insert_real @ X @ A2 ) )
% 4.71/5.16 = ( groups1681761925125756287l_real @ G2 @ A2 ) ) )
% 4.71/5.16 & ( ~ ( member_real @ X @ A2 )
% 4.71/5.16 => ( ( groups1681761925125756287l_real @ G2 @ ( insert_real @ X @ A2 ) )
% 4.71/5.16 = ( times_times_real @ ( G2 @ X ) @ ( groups1681761925125756287l_real @ G2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.insert_if
% 4.71/5.16 thf(fact_7586_prod_Oinsert__if,axiom,
% 4.71/5.16 ! [A2: set_o,X: $o,G2: $o > real] :
% 4.71/5.16 ( ( finite_finite_o @ A2 )
% 4.71/5.16 => ( ( ( member_o @ X @ A2 )
% 4.71/5.16 => ( ( groups234877984723959775o_real @ G2 @ ( insert_o @ X @ A2 ) )
% 4.71/5.16 = ( groups234877984723959775o_real @ G2 @ A2 ) ) )
% 4.71/5.16 & ( ~ ( member_o @ X @ A2 )
% 4.71/5.16 => ( ( groups234877984723959775o_real @ G2 @ ( insert_o @ X @ A2 ) )
% 4.71/5.16 = ( times_times_real @ ( G2 @ X ) @ ( groups234877984723959775o_real @ G2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.insert_if
% 4.71/5.16 thf(fact_7587_prod_Oinsert__if,axiom,
% 4.71/5.16 ! [A2: set_nat,X: nat,G2: nat > real] :
% 4.71/5.16 ( ( finite_finite_nat @ A2 )
% 4.71/5.16 => ( ( ( member_nat @ X @ A2 )
% 4.71/5.16 => ( ( groups129246275422532515t_real @ G2 @ ( insert_nat @ X @ A2 ) )
% 4.71/5.16 = ( groups129246275422532515t_real @ G2 @ A2 ) ) )
% 4.71/5.16 & ( ~ ( member_nat @ X @ A2 )
% 4.71/5.16 => ( ( groups129246275422532515t_real @ G2 @ ( insert_nat @ X @ A2 ) )
% 4.71/5.16 = ( times_times_real @ ( G2 @ X ) @ ( groups129246275422532515t_real @ G2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.insert_if
% 4.71/5.16 thf(fact_7588_prod_Oinsert__if,axiom,
% 4.71/5.16 ! [A2: set_int,X: int,G2: int > real] :
% 4.71/5.16 ( ( finite_finite_int @ A2 )
% 4.71/5.16 => ( ( ( member_int @ X @ A2 )
% 4.71/5.16 => ( ( groups2316167850115554303t_real @ G2 @ ( insert_int @ X @ A2 ) )
% 4.71/5.16 = ( groups2316167850115554303t_real @ G2 @ A2 ) ) )
% 4.71/5.16 & ( ~ ( member_int @ X @ A2 )
% 4.71/5.16 => ( ( groups2316167850115554303t_real @ G2 @ ( insert_int @ X @ A2 ) )
% 4.71/5.16 = ( times_times_real @ ( G2 @ X ) @ ( groups2316167850115554303t_real @ G2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.insert_if
% 4.71/5.16 thf(fact_7589_prod_Oinsert__if,axiom,
% 4.71/5.16 ! [A2: set_complex,X: complex,G2: complex > real] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.16 => ( ( ( member_complex @ X @ A2 )
% 4.71/5.16 => ( ( groups766887009212190081x_real @ G2 @ ( insert_complex @ X @ A2 ) )
% 4.71/5.16 = ( groups766887009212190081x_real @ G2 @ A2 ) ) )
% 4.71/5.16 & ( ~ ( member_complex @ X @ A2 )
% 4.71/5.16 => ( ( groups766887009212190081x_real @ G2 @ ( insert_complex @ X @ A2 ) )
% 4.71/5.16 = ( times_times_real @ ( G2 @ X ) @ ( groups766887009212190081x_real @ G2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.insert_if
% 4.71/5.16 thf(fact_7590_prod_Oinsert__if,axiom,
% 4.71/5.16 ! [A2: set_Extended_enat,X: extended_enat,G2: extended_enat > real] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.16 => ( ( ( member_Extended_enat @ X @ A2 )
% 4.71/5.16 => ( ( groups97031904164794029t_real @ G2 @ ( insert_Extended_enat @ X @ A2 ) )
% 4.71/5.16 = ( groups97031904164794029t_real @ G2 @ A2 ) ) )
% 4.71/5.16 & ( ~ ( member_Extended_enat @ X @ A2 )
% 4.71/5.16 => ( ( groups97031904164794029t_real @ G2 @ ( insert_Extended_enat @ X @ A2 ) )
% 4.71/5.16 = ( times_times_real @ ( G2 @ X ) @ ( groups97031904164794029t_real @ G2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.insert_if
% 4.71/5.16 thf(fact_7591_prod_Oinsert__if,axiom,
% 4.71/5.16 ! [A2: set_real,X: real,G2: real > rat] :
% 4.71/5.16 ( ( finite_finite_real @ A2 )
% 4.71/5.16 => ( ( ( member_real @ X @ A2 )
% 4.71/5.16 => ( ( groups4061424788464935467al_rat @ G2 @ ( insert_real @ X @ A2 ) )
% 4.71/5.16 = ( groups4061424788464935467al_rat @ G2 @ A2 ) ) )
% 4.71/5.16 & ( ~ ( member_real @ X @ A2 )
% 4.71/5.16 => ( ( groups4061424788464935467al_rat @ G2 @ ( insert_real @ X @ A2 ) )
% 4.71/5.16 = ( times_times_rat @ ( G2 @ X ) @ ( groups4061424788464935467al_rat @ G2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.insert_if
% 4.71/5.16 thf(fact_7592_prod_Oinsert__if,axiom,
% 4.71/5.16 ! [A2: set_o,X: $o,G2: $o > rat] :
% 4.71/5.16 ( ( finite_finite_o @ A2 )
% 4.71/5.16 => ( ( ( member_o @ X @ A2 )
% 4.71/5.16 => ( ( groups2869687844427037835_o_rat @ G2 @ ( insert_o @ X @ A2 ) )
% 4.71/5.16 = ( groups2869687844427037835_o_rat @ G2 @ A2 ) ) )
% 4.71/5.16 & ( ~ ( member_o @ X @ A2 )
% 4.71/5.16 => ( ( groups2869687844427037835_o_rat @ G2 @ ( insert_o @ X @ A2 ) )
% 4.71/5.16 = ( times_times_rat @ ( G2 @ X ) @ ( groups2869687844427037835_o_rat @ G2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.insert_if
% 4.71/5.16 thf(fact_7593_prod_Oinsert__if,axiom,
% 4.71/5.16 ! [A2: set_nat,X: nat,G2: nat > rat] :
% 4.71/5.16 ( ( finite_finite_nat @ A2 )
% 4.71/5.16 => ( ( ( member_nat @ X @ A2 )
% 4.71/5.16 => ( ( groups73079841787564623at_rat @ G2 @ ( insert_nat @ X @ A2 ) )
% 4.71/5.16 = ( groups73079841787564623at_rat @ G2 @ A2 ) ) )
% 4.71/5.16 & ( ~ ( member_nat @ X @ A2 )
% 4.71/5.16 => ( ( groups73079841787564623at_rat @ G2 @ ( insert_nat @ X @ A2 ) )
% 4.71/5.16 = ( times_times_rat @ ( G2 @ X ) @ ( groups73079841787564623at_rat @ G2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.insert_if
% 4.71/5.16 thf(fact_7594_prod_Oinsert__if,axiom,
% 4.71/5.16 ! [A2: set_int,X: int,G2: int > rat] :
% 4.71/5.16 ( ( finite_finite_int @ A2 )
% 4.71/5.16 => ( ( ( member_int @ X @ A2 )
% 4.71/5.16 => ( ( groups1072433553688619179nt_rat @ G2 @ ( insert_int @ X @ A2 ) )
% 4.71/5.16 = ( groups1072433553688619179nt_rat @ G2 @ A2 ) ) )
% 4.71/5.16 & ( ~ ( member_int @ X @ A2 )
% 4.71/5.16 => ( ( groups1072433553688619179nt_rat @ G2 @ ( insert_int @ X @ A2 ) )
% 4.71/5.16 = ( times_times_rat @ ( G2 @ X ) @ ( groups1072433553688619179nt_rat @ G2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.insert_if
% 4.71/5.16 thf(fact_7595_prod_Oreindex__bij__witness__not__neutral,axiom,
% 4.71/5.16 ! [S5: set_o,T5: set_o,S2: set_o,I: $o > $o,J: $o > $o,T3: set_o,G2: $o > complex,H: $o > complex] :
% 4.71/5.16 ( ( finite_finite_o @ S5 )
% 4.71/5.16 => ( ( finite_finite_o @ T5 )
% 4.71/5.16 => ( ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ ( minus_minus_set_o @ S2 @ S5 ) )
% 4.71/5.16 => ( ( I @ ( J @ A5 ) )
% 4.71/5.16 = A5 ) )
% 4.71/5.16 => ( ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ ( minus_minus_set_o @ S2 @ S5 ) )
% 4.71/5.16 => ( member_o @ ( J @ A5 ) @ ( minus_minus_set_o @ T3 @ T5 ) ) )
% 4.71/5.16 => ( ! [B5: $o] :
% 4.71/5.16 ( ( member_o @ B5 @ ( minus_minus_set_o @ T3 @ T5 ) )
% 4.71/5.16 => ( ( J @ ( I @ B5 ) )
% 4.71/5.16 = B5 ) )
% 4.71/5.16 => ( ! [B5: $o] :
% 4.71/5.16 ( ( member_o @ B5 @ ( minus_minus_set_o @ T3 @ T5 ) )
% 4.71/5.16 => ( member_o @ ( I @ B5 ) @ ( minus_minus_set_o @ S2 @ S5 ) ) )
% 4.71/5.16 => ( ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ S5 )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [B5: $o] :
% 4.71/5.16 ( ( member_o @ B5 @ T5 )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ S2 )
% 4.71/5.16 => ( ( H @ ( J @ A5 ) )
% 4.71/5.16 = ( G2 @ A5 ) ) )
% 4.71/5.16 => ( ( groups4859619685533338977omplex @ G2 @ S2 )
% 4.71/5.16 = ( groups4859619685533338977omplex @ H @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.reindex_bij_witness_not_neutral
% 4.71/5.16 thf(fact_7596_prod_Oreindex__bij__witness__not__neutral,axiom,
% 4.71/5.16 ! [S5: set_o,T5: set_int,S2: set_o,I: int > $o,J: $o > int,T3: set_int,G2: $o > complex,H: int > complex] :
% 4.71/5.16 ( ( finite_finite_o @ S5 )
% 4.71/5.16 => ( ( finite_finite_int @ T5 )
% 4.71/5.16 => ( ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ ( minus_minus_set_o @ S2 @ S5 ) )
% 4.71/5.16 => ( ( I @ ( J @ A5 ) )
% 4.71/5.16 = A5 ) )
% 4.71/5.16 => ( ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ ( minus_minus_set_o @ S2 @ S5 ) )
% 4.71/5.16 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T3 @ T5 ) ) )
% 4.71/5.16 => ( ! [B5: int] :
% 4.71/5.16 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 4.71/5.16 => ( ( J @ ( I @ B5 ) )
% 4.71/5.16 = B5 ) )
% 4.71/5.16 => ( ! [B5: int] :
% 4.71/5.16 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 4.71/5.16 => ( member_o @ ( I @ B5 ) @ ( minus_minus_set_o @ S2 @ S5 ) ) )
% 4.71/5.16 => ( ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ S5 )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [B5: int] :
% 4.71/5.16 ( ( member_int @ B5 @ T5 )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ S2 )
% 4.71/5.16 => ( ( H @ ( J @ A5 ) )
% 4.71/5.16 = ( G2 @ A5 ) ) )
% 4.71/5.16 => ( ( groups4859619685533338977omplex @ G2 @ S2 )
% 4.71/5.16 = ( groups7440179247065528705omplex @ H @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.reindex_bij_witness_not_neutral
% 4.71/5.16 thf(fact_7597_prod_Oreindex__bij__witness__not__neutral,axiom,
% 4.71/5.16 ! [S5: set_o,T5: set_complex,S2: set_o,I: complex > $o,J: $o > complex,T3: set_complex,G2: $o > complex,H: complex > complex] :
% 4.71/5.16 ( ( finite_finite_o @ S5 )
% 4.71/5.16 => ( ( finite3207457112153483333omplex @ T5 )
% 4.71/5.16 => ( ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ ( minus_minus_set_o @ S2 @ S5 ) )
% 4.71/5.16 => ( ( I @ ( J @ A5 ) )
% 4.71/5.16 = A5 ) )
% 4.71/5.16 => ( ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ ( minus_minus_set_o @ S2 @ S5 ) )
% 4.71/5.16 => ( member_complex @ ( J @ A5 ) @ ( minus_811609699411566653omplex @ T3 @ T5 ) ) )
% 4.71/5.16 => ( ! [B5: complex] :
% 4.71/5.16 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 4.71/5.16 => ( ( J @ ( I @ B5 ) )
% 4.71/5.16 = B5 ) )
% 4.71/5.16 => ( ! [B5: complex] :
% 4.71/5.16 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 4.71/5.16 => ( member_o @ ( I @ B5 ) @ ( minus_minus_set_o @ S2 @ S5 ) ) )
% 4.71/5.16 => ( ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ S5 )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [B5: complex] :
% 4.71/5.16 ( ( member_complex @ B5 @ T5 )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ S2 )
% 4.71/5.16 => ( ( H @ ( J @ A5 ) )
% 4.71/5.16 = ( G2 @ A5 ) ) )
% 4.71/5.16 => ( ( groups4859619685533338977omplex @ G2 @ S2 )
% 4.71/5.16 = ( groups3708469109370488835omplex @ H @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.reindex_bij_witness_not_neutral
% 4.71/5.16 thf(fact_7598_prod_Oreindex__bij__witness__not__neutral,axiom,
% 4.71/5.16 ! [S5: set_o,T5: set_Extended_enat,S2: set_o,I: extended_enat > $o,J: $o > extended_enat,T3: set_Extended_enat,G2: $o > complex,H: extended_enat > complex] :
% 4.71/5.16 ( ( finite_finite_o @ S5 )
% 4.71/5.16 => ( ( finite4001608067531595151d_enat @ T5 )
% 4.71/5.16 => ( ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ ( minus_minus_set_o @ S2 @ S5 ) )
% 4.71/5.16 => ( ( I @ ( J @ A5 ) )
% 4.71/5.16 = A5 ) )
% 4.71/5.16 => ( ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ ( minus_minus_set_o @ S2 @ S5 ) )
% 4.71/5.16 => ( member_Extended_enat @ ( J @ A5 ) @ ( minus_925952699566721837d_enat @ T3 @ T5 ) ) )
% 4.71/5.16 => ( ! [B5: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ B5 @ ( minus_925952699566721837d_enat @ T3 @ T5 ) )
% 4.71/5.16 => ( ( J @ ( I @ B5 ) )
% 4.71/5.16 = B5 ) )
% 4.71/5.16 => ( ! [B5: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ B5 @ ( minus_925952699566721837d_enat @ T3 @ T5 ) )
% 4.71/5.16 => ( member_o @ ( I @ B5 ) @ ( minus_minus_set_o @ S2 @ S5 ) ) )
% 4.71/5.16 => ( ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ S5 )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [B5: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ B5 @ T5 )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ S2 )
% 4.71/5.16 => ( ( H @ ( J @ A5 ) )
% 4.71/5.16 = ( G2 @ A5 ) ) )
% 4.71/5.16 => ( ( groups4859619685533338977omplex @ G2 @ S2 )
% 4.71/5.16 = ( groups4622424608036095791omplex @ H @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.reindex_bij_witness_not_neutral
% 4.71/5.16 thf(fact_7599_prod_Oreindex__bij__witness__not__neutral,axiom,
% 4.71/5.16 ! [S5: set_int,T5: set_o,S2: set_int,I: $o > int,J: int > $o,T3: set_o,G2: int > complex,H: $o > complex] :
% 4.71/5.16 ( ( finite_finite_int @ S5 )
% 4.71/5.16 => ( ( finite_finite_o @ T5 )
% 4.71/5.16 => ( ! [A5: int] :
% 4.71/5.16 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 4.71/5.16 => ( ( I @ ( J @ A5 ) )
% 4.71/5.16 = A5 ) )
% 4.71/5.16 => ( ! [A5: int] :
% 4.71/5.16 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 4.71/5.16 => ( member_o @ ( J @ A5 ) @ ( minus_minus_set_o @ T3 @ T5 ) ) )
% 4.71/5.16 => ( ! [B5: $o] :
% 4.71/5.16 ( ( member_o @ B5 @ ( minus_minus_set_o @ T3 @ T5 ) )
% 4.71/5.16 => ( ( J @ ( I @ B5 ) )
% 4.71/5.16 = B5 ) )
% 4.71/5.16 => ( ! [B5: $o] :
% 4.71/5.16 ( ( member_o @ B5 @ ( minus_minus_set_o @ T3 @ T5 ) )
% 4.71/5.16 => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 4.71/5.16 => ( ! [A5: int] :
% 4.71/5.16 ( ( member_int @ A5 @ S5 )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [B5: $o] :
% 4.71/5.16 ( ( member_o @ B5 @ T5 )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [A5: int] :
% 4.71/5.16 ( ( member_int @ A5 @ S2 )
% 4.71/5.16 => ( ( H @ ( J @ A5 ) )
% 4.71/5.16 = ( G2 @ A5 ) ) )
% 4.71/5.16 => ( ( groups7440179247065528705omplex @ G2 @ S2 )
% 4.71/5.16 = ( groups4859619685533338977omplex @ H @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.reindex_bij_witness_not_neutral
% 4.71/5.16 thf(fact_7600_prod_Oreindex__bij__witness__not__neutral,axiom,
% 4.71/5.16 ! [S5: set_int,T5: set_int,S2: set_int,I: int > int,J: int > int,T3: set_int,G2: int > complex,H: int > complex] :
% 4.71/5.16 ( ( finite_finite_int @ S5 )
% 4.71/5.16 => ( ( finite_finite_int @ T5 )
% 4.71/5.16 => ( ! [A5: int] :
% 4.71/5.16 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 4.71/5.16 => ( ( I @ ( J @ A5 ) )
% 4.71/5.16 = A5 ) )
% 4.71/5.16 => ( ! [A5: int] :
% 4.71/5.16 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 4.71/5.16 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T3 @ T5 ) ) )
% 4.71/5.16 => ( ! [B5: int] :
% 4.71/5.16 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 4.71/5.16 => ( ( J @ ( I @ B5 ) )
% 4.71/5.16 = B5 ) )
% 4.71/5.16 => ( ! [B5: int] :
% 4.71/5.16 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 4.71/5.16 => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 4.71/5.16 => ( ! [A5: int] :
% 4.71/5.16 ( ( member_int @ A5 @ S5 )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [B5: int] :
% 4.71/5.16 ( ( member_int @ B5 @ T5 )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [A5: int] :
% 4.71/5.16 ( ( member_int @ A5 @ S2 )
% 4.71/5.16 => ( ( H @ ( J @ A5 ) )
% 4.71/5.16 = ( G2 @ A5 ) ) )
% 4.71/5.16 => ( ( groups7440179247065528705omplex @ G2 @ S2 )
% 4.71/5.16 = ( groups7440179247065528705omplex @ H @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.reindex_bij_witness_not_neutral
% 4.71/5.16 thf(fact_7601_prod_Oreindex__bij__witness__not__neutral,axiom,
% 4.71/5.16 ! [S5: set_int,T5: set_complex,S2: set_int,I: complex > int,J: int > complex,T3: set_complex,G2: int > complex,H: complex > complex] :
% 4.71/5.16 ( ( finite_finite_int @ S5 )
% 4.71/5.16 => ( ( finite3207457112153483333omplex @ T5 )
% 4.71/5.16 => ( ! [A5: int] :
% 4.71/5.16 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 4.71/5.16 => ( ( I @ ( J @ A5 ) )
% 4.71/5.16 = A5 ) )
% 4.71/5.16 => ( ! [A5: int] :
% 4.71/5.16 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 4.71/5.16 => ( member_complex @ ( J @ A5 ) @ ( minus_811609699411566653omplex @ T3 @ T5 ) ) )
% 4.71/5.16 => ( ! [B5: complex] :
% 4.71/5.16 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 4.71/5.16 => ( ( J @ ( I @ B5 ) )
% 4.71/5.16 = B5 ) )
% 4.71/5.16 => ( ! [B5: complex] :
% 4.71/5.16 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 4.71/5.16 => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 4.71/5.16 => ( ! [A5: int] :
% 4.71/5.16 ( ( member_int @ A5 @ S5 )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [B5: complex] :
% 4.71/5.16 ( ( member_complex @ B5 @ T5 )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [A5: int] :
% 4.71/5.16 ( ( member_int @ A5 @ S2 )
% 4.71/5.16 => ( ( H @ ( J @ A5 ) )
% 4.71/5.16 = ( G2 @ A5 ) ) )
% 4.71/5.16 => ( ( groups7440179247065528705omplex @ G2 @ S2 )
% 4.71/5.16 = ( groups3708469109370488835omplex @ H @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.reindex_bij_witness_not_neutral
% 4.71/5.16 thf(fact_7602_prod_Oreindex__bij__witness__not__neutral,axiom,
% 4.71/5.16 ! [S5: set_int,T5: set_Extended_enat,S2: set_int,I: extended_enat > int,J: int > extended_enat,T3: set_Extended_enat,G2: int > complex,H: extended_enat > complex] :
% 4.71/5.16 ( ( finite_finite_int @ S5 )
% 4.71/5.16 => ( ( finite4001608067531595151d_enat @ T5 )
% 4.71/5.16 => ( ! [A5: int] :
% 4.71/5.16 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 4.71/5.16 => ( ( I @ ( J @ A5 ) )
% 4.71/5.16 = A5 ) )
% 4.71/5.16 => ( ! [A5: int] :
% 4.71/5.16 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 4.71/5.16 => ( member_Extended_enat @ ( J @ A5 ) @ ( minus_925952699566721837d_enat @ T3 @ T5 ) ) )
% 4.71/5.16 => ( ! [B5: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ B5 @ ( minus_925952699566721837d_enat @ T3 @ T5 ) )
% 4.71/5.16 => ( ( J @ ( I @ B5 ) )
% 4.71/5.16 = B5 ) )
% 4.71/5.16 => ( ! [B5: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ B5 @ ( minus_925952699566721837d_enat @ T3 @ T5 ) )
% 4.71/5.16 => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 4.71/5.16 => ( ! [A5: int] :
% 4.71/5.16 ( ( member_int @ A5 @ S5 )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [B5: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ B5 @ T5 )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [A5: int] :
% 4.71/5.16 ( ( member_int @ A5 @ S2 )
% 4.71/5.16 => ( ( H @ ( J @ A5 ) )
% 4.71/5.16 = ( G2 @ A5 ) ) )
% 4.71/5.16 => ( ( groups7440179247065528705omplex @ G2 @ S2 )
% 4.71/5.16 = ( groups4622424608036095791omplex @ H @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.reindex_bij_witness_not_neutral
% 4.71/5.16 thf(fact_7603_prod_Oreindex__bij__witness__not__neutral,axiom,
% 4.71/5.16 ! [S5: set_complex,T5: set_o,S2: set_complex,I: $o > complex,J: complex > $o,T3: set_o,G2: complex > complex,H: $o > complex] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ S5 )
% 4.71/5.16 => ( ( finite_finite_o @ T5 )
% 4.71/5.16 => ( ! [A5: complex] :
% 4.71/5.16 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 4.71/5.16 => ( ( I @ ( J @ A5 ) )
% 4.71/5.16 = A5 ) )
% 4.71/5.16 => ( ! [A5: complex] :
% 4.71/5.16 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 4.71/5.16 => ( member_o @ ( J @ A5 ) @ ( minus_minus_set_o @ T3 @ T5 ) ) )
% 4.71/5.16 => ( ! [B5: $o] :
% 4.71/5.16 ( ( member_o @ B5 @ ( minus_minus_set_o @ T3 @ T5 ) )
% 4.71/5.16 => ( ( J @ ( I @ B5 ) )
% 4.71/5.16 = B5 ) )
% 4.71/5.16 => ( ! [B5: $o] :
% 4.71/5.16 ( ( member_o @ B5 @ ( minus_minus_set_o @ T3 @ T5 ) )
% 4.71/5.16 => ( member_complex @ ( I @ B5 ) @ ( minus_811609699411566653omplex @ S2 @ S5 ) ) )
% 4.71/5.16 => ( ! [A5: complex] :
% 4.71/5.16 ( ( member_complex @ A5 @ S5 )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [B5: $o] :
% 4.71/5.16 ( ( member_o @ B5 @ T5 )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [A5: complex] :
% 4.71/5.16 ( ( member_complex @ A5 @ S2 )
% 4.71/5.16 => ( ( H @ ( J @ A5 ) )
% 4.71/5.16 = ( G2 @ A5 ) ) )
% 4.71/5.16 => ( ( groups3708469109370488835omplex @ G2 @ S2 )
% 4.71/5.16 = ( groups4859619685533338977omplex @ H @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.reindex_bij_witness_not_neutral
% 4.71/5.16 thf(fact_7604_prod_Oreindex__bij__witness__not__neutral,axiom,
% 4.71/5.16 ! [S5: set_complex,T5: set_int,S2: set_complex,I: int > complex,J: complex > int,T3: set_int,G2: complex > complex,H: int > complex] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ S5 )
% 4.71/5.16 => ( ( finite_finite_int @ T5 )
% 4.71/5.16 => ( ! [A5: complex] :
% 4.71/5.16 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 4.71/5.16 => ( ( I @ ( J @ A5 ) )
% 4.71/5.16 = A5 ) )
% 4.71/5.16 => ( ! [A5: complex] :
% 4.71/5.16 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 4.71/5.16 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T3 @ T5 ) ) )
% 4.71/5.16 => ( ! [B5: int] :
% 4.71/5.16 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 4.71/5.16 => ( ( J @ ( I @ B5 ) )
% 4.71/5.16 = B5 ) )
% 4.71/5.16 => ( ! [B5: int] :
% 4.71/5.16 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 4.71/5.16 => ( member_complex @ ( I @ B5 ) @ ( minus_811609699411566653omplex @ S2 @ S5 ) ) )
% 4.71/5.16 => ( ! [A5: complex] :
% 4.71/5.16 ( ( member_complex @ A5 @ S5 )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [B5: int] :
% 4.71/5.16 ( ( member_int @ B5 @ T5 )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [A5: complex] :
% 4.71/5.16 ( ( member_complex @ A5 @ S2 )
% 4.71/5.16 => ( ( H @ ( J @ A5 ) )
% 4.71/5.16 = ( G2 @ A5 ) ) )
% 4.71/5.16 => ( ( groups3708469109370488835omplex @ G2 @ S2 )
% 4.71/5.16 = ( groups7440179247065528705omplex @ H @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.reindex_bij_witness_not_neutral
% 4.71/5.16 thf(fact_7605_prod_Osetdiff__irrelevant,axiom,
% 4.71/5.16 ! [A2: set_int,G2: int > complex] :
% 4.71/5.16 ( ( finite_finite_int @ A2 )
% 4.71/5.16 => ( ( groups7440179247065528705omplex @ G2
% 4.71/5.16 @ ( minus_minus_set_int @ A2
% 4.71/5.16 @ ( collect_int
% 4.71/5.16 @ ^ [X3: int] :
% 4.71/5.16 ( ( G2 @ X3 )
% 4.71/5.16 = one_one_complex ) ) ) )
% 4.71/5.16 = ( groups7440179247065528705omplex @ G2 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.setdiff_irrelevant
% 4.71/5.16 thf(fact_7606_prod_Osetdiff__irrelevant,axiom,
% 4.71/5.16 ! [A2: set_complex,G2: complex > complex] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.16 => ( ( groups3708469109370488835omplex @ G2
% 4.71/5.16 @ ( minus_811609699411566653omplex @ A2
% 4.71/5.16 @ ( collect_complex
% 4.71/5.16 @ ^ [X3: complex] :
% 4.71/5.16 ( ( G2 @ X3 )
% 4.71/5.16 = one_one_complex ) ) ) )
% 4.71/5.16 = ( groups3708469109370488835omplex @ G2 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.setdiff_irrelevant
% 4.71/5.16 thf(fact_7607_prod_Osetdiff__irrelevant,axiom,
% 4.71/5.16 ! [A2: set_Extended_enat,G2: extended_enat > complex] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.16 => ( ( groups4622424608036095791omplex @ G2
% 4.71/5.16 @ ( minus_925952699566721837d_enat @ A2
% 4.71/5.16 @ ( collec4429806609662206161d_enat
% 4.71/5.16 @ ^ [X3: extended_enat] :
% 4.71/5.16 ( ( G2 @ X3 )
% 4.71/5.16 = one_one_complex ) ) ) )
% 4.71/5.16 = ( groups4622424608036095791omplex @ G2 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.setdiff_irrelevant
% 4.71/5.16 thf(fact_7608_prod_Osetdiff__irrelevant,axiom,
% 4.71/5.16 ! [A2: set_int,G2: int > real] :
% 4.71/5.16 ( ( finite_finite_int @ A2 )
% 4.71/5.16 => ( ( groups2316167850115554303t_real @ G2
% 4.71/5.16 @ ( minus_minus_set_int @ A2
% 4.71/5.16 @ ( collect_int
% 4.71/5.16 @ ^ [X3: int] :
% 4.71/5.16 ( ( G2 @ X3 )
% 4.71/5.16 = one_one_real ) ) ) )
% 4.71/5.16 = ( groups2316167850115554303t_real @ G2 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.setdiff_irrelevant
% 4.71/5.16 thf(fact_7609_prod_Osetdiff__irrelevant,axiom,
% 4.71/5.16 ! [A2: set_complex,G2: complex > real] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.16 => ( ( groups766887009212190081x_real @ G2
% 4.71/5.16 @ ( minus_811609699411566653omplex @ A2
% 4.71/5.16 @ ( collect_complex
% 4.71/5.16 @ ^ [X3: complex] :
% 4.71/5.16 ( ( G2 @ X3 )
% 4.71/5.16 = one_one_real ) ) ) )
% 4.71/5.16 = ( groups766887009212190081x_real @ G2 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.setdiff_irrelevant
% 4.71/5.16 thf(fact_7610_prod_Osetdiff__irrelevant,axiom,
% 4.71/5.16 ! [A2: set_Extended_enat,G2: extended_enat > real] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.16 => ( ( groups97031904164794029t_real @ G2
% 4.71/5.16 @ ( minus_925952699566721837d_enat @ A2
% 4.71/5.16 @ ( collec4429806609662206161d_enat
% 4.71/5.16 @ ^ [X3: extended_enat] :
% 4.71/5.16 ( ( G2 @ X3 )
% 4.71/5.16 = one_one_real ) ) ) )
% 4.71/5.16 = ( groups97031904164794029t_real @ G2 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.setdiff_irrelevant
% 4.71/5.16 thf(fact_7611_prod_Osetdiff__irrelevant,axiom,
% 4.71/5.16 ! [A2: set_int,G2: int > rat] :
% 4.71/5.16 ( ( finite_finite_int @ A2 )
% 4.71/5.16 => ( ( groups1072433553688619179nt_rat @ G2
% 4.71/5.16 @ ( minus_minus_set_int @ A2
% 4.71/5.16 @ ( collect_int
% 4.71/5.16 @ ^ [X3: int] :
% 4.71/5.16 ( ( G2 @ X3 )
% 4.71/5.16 = one_one_rat ) ) ) )
% 4.71/5.16 = ( groups1072433553688619179nt_rat @ G2 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.setdiff_irrelevant
% 4.71/5.16 thf(fact_7612_prod_Osetdiff__irrelevant,axiom,
% 4.71/5.16 ! [A2: set_complex,G2: complex > rat] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.16 => ( ( groups225925009352817453ex_rat @ G2
% 4.71/5.16 @ ( minus_811609699411566653omplex @ A2
% 4.71/5.16 @ ( collect_complex
% 4.71/5.16 @ ^ [X3: complex] :
% 4.71/5.16 ( ( G2 @ X3 )
% 4.71/5.16 = one_one_rat ) ) ) )
% 4.71/5.16 = ( groups225925009352817453ex_rat @ G2 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.setdiff_irrelevant
% 4.71/5.16 thf(fact_7613_prod_Osetdiff__irrelevant,axiom,
% 4.71/5.16 ! [A2: set_Extended_enat,G2: extended_enat > rat] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.16 => ( ( groups2245840878043517529at_rat @ G2
% 4.71/5.16 @ ( minus_925952699566721837d_enat @ A2
% 4.71/5.16 @ ( collec4429806609662206161d_enat
% 4.71/5.16 @ ^ [X3: extended_enat] :
% 4.71/5.16 ( ( G2 @ X3 )
% 4.71/5.16 = one_one_rat ) ) ) )
% 4.71/5.16 = ( groups2245840878043517529at_rat @ G2 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.setdiff_irrelevant
% 4.71/5.16 thf(fact_7614_prod_Osetdiff__irrelevant,axiom,
% 4.71/5.16 ! [A2: set_int,G2: int > nat] :
% 4.71/5.16 ( ( finite_finite_int @ A2 )
% 4.71/5.16 => ( ( groups1707563613775114915nt_nat @ G2
% 4.71/5.16 @ ( minus_minus_set_int @ A2
% 4.71/5.16 @ ( collect_int
% 4.71/5.16 @ ^ [X3: int] :
% 4.71/5.16 ( ( G2 @ X3 )
% 4.71/5.16 = one_one_nat ) ) ) )
% 4.71/5.16 = ( groups1707563613775114915nt_nat @ G2 @ A2 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.setdiff_irrelevant
% 4.71/5.16 thf(fact_7615_less__1__prod2,axiom,
% 4.71/5.16 ! [I5: set_o,I: $o,F: $o > real] :
% 4.71/5.16 ( ( finite_finite_o @ I5 )
% 4.71/5.16 => ( ( member_o @ I @ I5 )
% 4.71/5.16 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 4.71/5.16 => ( ! [I2: $o] :
% 4.71/5.16 ( ( member_o @ I2 @ I5 )
% 4.71/5.16 => ( ord_less_eq_real @ one_one_real @ ( F @ I2 ) ) )
% 4.71/5.16 => ( ord_less_real @ one_one_real @ ( groups234877984723959775o_real @ F @ I5 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % less_1_prod2
% 4.71/5.16 thf(fact_7616_less__1__prod2,axiom,
% 4.71/5.16 ! [I5: set_nat,I: nat,F: nat > real] :
% 4.71/5.16 ( ( finite_finite_nat @ I5 )
% 4.71/5.16 => ( ( member_nat @ I @ I5 )
% 4.71/5.16 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 4.71/5.16 => ( ! [I2: nat] :
% 4.71/5.16 ( ( member_nat @ I2 @ I5 )
% 4.71/5.16 => ( ord_less_eq_real @ one_one_real @ ( F @ I2 ) ) )
% 4.71/5.16 => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I5 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % less_1_prod2
% 4.71/5.16 thf(fact_7617_less__1__prod2,axiom,
% 4.71/5.16 ! [I5: set_int,I: int,F: int > real] :
% 4.71/5.16 ( ( finite_finite_int @ I5 )
% 4.71/5.16 => ( ( member_int @ I @ I5 )
% 4.71/5.16 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 4.71/5.16 => ( ! [I2: int] :
% 4.71/5.16 ( ( member_int @ I2 @ I5 )
% 4.71/5.16 => ( ord_less_eq_real @ one_one_real @ ( F @ I2 ) ) )
% 4.71/5.16 => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I5 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % less_1_prod2
% 4.71/5.16 thf(fact_7618_less__1__prod2,axiom,
% 4.71/5.16 ! [I5: set_complex,I: complex,F: complex > real] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ I5 )
% 4.71/5.16 => ( ( member_complex @ I @ I5 )
% 4.71/5.16 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 4.71/5.16 => ( ! [I2: complex] :
% 4.71/5.16 ( ( member_complex @ I2 @ I5 )
% 4.71/5.16 => ( ord_less_eq_real @ one_one_real @ ( F @ I2 ) ) )
% 4.71/5.16 => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I5 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % less_1_prod2
% 4.71/5.16 thf(fact_7619_less__1__prod2,axiom,
% 4.71/5.16 ! [I5: set_Extended_enat,I: extended_enat,F: extended_enat > real] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ I5 )
% 4.71/5.16 => ( ( member_Extended_enat @ I @ I5 )
% 4.71/5.16 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 4.71/5.16 => ( ! [I2: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ I2 @ I5 )
% 4.71/5.16 => ( ord_less_eq_real @ one_one_real @ ( F @ I2 ) ) )
% 4.71/5.16 => ( ord_less_real @ one_one_real @ ( groups97031904164794029t_real @ F @ I5 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % less_1_prod2
% 4.71/5.16 thf(fact_7620_less__1__prod2,axiom,
% 4.71/5.16 ! [I5: set_o,I: $o,F: $o > rat] :
% 4.71/5.16 ( ( finite_finite_o @ I5 )
% 4.71/5.16 => ( ( member_o @ I @ I5 )
% 4.71/5.16 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 4.71/5.16 => ( ! [I2: $o] :
% 4.71/5.16 ( ( member_o @ I2 @ I5 )
% 4.71/5.16 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I2 ) ) )
% 4.71/5.16 => ( ord_less_rat @ one_one_rat @ ( groups2869687844427037835_o_rat @ F @ I5 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % less_1_prod2
% 4.71/5.16 thf(fact_7621_less__1__prod2,axiom,
% 4.71/5.16 ! [I5: set_nat,I: nat,F: nat > rat] :
% 4.71/5.16 ( ( finite_finite_nat @ I5 )
% 4.71/5.16 => ( ( member_nat @ I @ I5 )
% 4.71/5.16 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 4.71/5.16 => ( ! [I2: nat] :
% 4.71/5.16 ( ( member_nat @ I2 @ I5 )
% 4.71/5.16 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I2 ) ) )
% 4.71/5.16 => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I5 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % less_1_prod2
% 4.71/5.16 thf(fact_7622_less__1__prod2,axiom,
% 4.71/5.16 ! [I5: set_int,I: int,F: int > rat] :
% 4.71/5.16 ( ( finite_finite_int @ I5 )
% 4.71/5.16 => ( ( member_int @ I @ I5 )
% 4.71/5.16 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 4.71/5.16 => ( ! [I2: int] :
% 4.71/5.16 ( ( member_int @ I2 @ I5 )
% 4.71/5.16 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I2 ) ) )
% 4.71/5.16 => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I5 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % less_1_prod2
% 4.71/5.16 thf(fact_7623_less__1__prod2,axiom,
% 4.71/5.16 ! [I5: set_complex,I: complex,F: complex > rat] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ I5 )
% 4.71/5.16 => ( ( member_complex @ I @ I5 )
% 4.71/5.16 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 4.71/5.16 => ( ! [I2: complex] :
% 4.71/5.16 ( ( member_complex @ I2 @ I5 )
% 4.71/5.16 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I2 ) ) )
% 4.71/5.16 => ( ord_less_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ I5 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % less_1_prod2
% 4.71/5.16 thf(fact_7624_less__1__prod2,axiom,
% 4.71/5.16 ! [I5: set_Extended_enat,I: extended_enat,F: extended_enat > rat] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ I5 )
% 4.71/5.16 => ( ( member_Extended_enat @ I @ I5 )
% 4.71/5.16 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 4.71/5.16 => ( ! [I2: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ I2 @ I5 )
% 4.71/5.16 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I2 ) ) )
% 4.71/5.16 => ( ord_less_rat @ one_one_rat @ ( groups2245840878043517529at_rat @ F @ I5 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % less_1_prod2
% 4.71/5.16 thf(fact_7625_less__1__prod,axiom,
% 4.71/5.16 ! [I5: set_complex,F: complex > real] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ I5 )
% 4.71/5.16 => ( ( I5 != bot_bot_set_complex )
% 4.71/5.16 => ( ! [I2: complex] :
% 4.71/5.16 ( ( member_complex @ I2 @ I5 )
% 4.71/5.16 => ( ord_less_real @ one_one_real @ ( F @ I2 ) ) )
% 4.71/5.16 => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I5 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % less_1_prod
% 4.71/5.16 thf(fact_7626_less__1__prod,axiom,
% 4.71/5.16 ! [I5: set_Extended_enat,F: extended_enat > real] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ I5 )
% 4.71/5.16 => ( ( I5 != bot_bo7653980558646680370d_enat )
% 4.71/5.16 => ( ! [I2: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ I2 @ I5 )
% 4.71/5.16 => ( ord_less_real @ one_one_real @ ( F @ I2 ) ) )
% 4.71/5.16 => ( ord_less_real @ one_one_real @ ( groups97031904164794029t_real @ F @ I5 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % less_1_prod
% 4.71/5.16 thf(fact_7627_less__1__prod,axiom,
% 4.71/5.16 ! [I5: set_real,F: real > real] :
% 4.71/5.16 ( ( finite_finite_real @ I5 )
% 4.71/5.16 => ( ( I5 != bot_bot_set_real )
% 4.71/5.16 => ( ! [I2: real] :
% 4.71/5.16 ( ( member_real @ I2 @ I5 )
% 4.71/5.16 => ( ord_less_real @ one_one_real @ ( F @ I2 ) ) )
% 4.71/5.16 => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I5 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % less_1_prod
% 4.71/5.16 thf(fact_7628_less__1__prod,axiom,
% 4.71/5.16 ! [I5: set_o,F: $o > real] :
% 4.71/5.16 ( ( finite_finite_o @ I5 )
% 4.71/5.16 => ( ( I5 != bot_bot_set_o )
% 4.71/5.16 => ( ! [I2: $o] :
% 4.71/5.16 ( ( member_o @ I2 @ I5 )
% 4.71/5.16 => ( ord_less_real @ one_one_real @ ( F @ I2 ) ) )
% 4.71/5.16 => ( ord_less_real @ one_one_real @ ( groups234877984723959775o_real @ F @ I5 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % less_1_prod
% 4.71/5.16 thf(fact_7629_less__1__prod,axiom,
% 4.71/5.16 ! [I5: set_nat,F: nat > real] :
% 4.71/5.16 ( ( finite_finite_nat @ I5 )
% 4.71/5.16 => ( ( I5 != bot_bot_set_nat )
% 4.71/5.16 => ( ! [I2: nat] :
% 4.71/5.16 ( ( member_nat @ I2 @ I5 )
% 4.71/5.16 => ( ord_less_real @ one_one_real @ ( F @ I2 ) ) )
% 4.71/5.16 => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I5 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % less_1_prod
% 4.71/5.16 thf(fact_7630_less__1__prod,axiom,
% 4.71/5.16 ! [I5: set_int,F: int > real] :
% 4.71/5.16 ( ( finite_finite_int @ I5 )
% 4.71/5.16 => ( ( I5 != bot_bot_set_int )
% 4.71/5.16 => ( ! [I2: int] :
% 4.71/5.16 ( ( member_int @ I2 @ I5 )
% 4.71/5.16 => ( ord_less_real @ one_one_real @ ( F @ I2 ) ) )
% 4.71/5.16 => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I5 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % less_1_prod
% 4.71/5.16 thf(fact_7631_less__1__prod,axiom,
% 4.71/5.16 ! [I5: set_complex,F: complex > rat] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ I5 )
% 4.71/5.16 => ( ( I5 != bot_bot_set_complex )
% 4.71/5.16 => ( ! [I2: complex] :
% 4.71/5.16 ( ( member_complex @ I2 @ I5 )
% 4.71/5.16 => ( ord_less_rat @ one_one_rat @ ( F @ I2 ) ) )
% 4.71/5.16 => ( ord_less_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ I5 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % less_1_prod
% 4.71/5.16 thf(fact_7632_less__1__prod,axiom,
% 4.71/5.16 ! [I5: set_Extended_enat,F: extended_enat > rat] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ I5 )
% 4.71/5.16 => ( ( I5 != bot_bo7653980558646680370d_enat )
% 4.71/5.16 => ( ! [I2: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ I2 @ I5 )
% 4.71/5.16 => ( ord_less_rat @ one_one_rat @ ( F @ I2 ) ) )
% 4.71/5.16 => ( ord_less_rat @ one_one_rat @ ( groups2245840878043517529at_rat @ F @ I5 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % less_1_prod
% 4.71/5.16 thf(fact_7633_less__1__prod,axiom,
% 4.71/5.16 ! [I5: set_real,F: real > rat] :
% 4.71/5.16 ( ( finite_finite_real @ I5 )
% 4.71/5.16 => ( ( I5 != bot_bot_set_real )
% 4.71/5.16 => ( ! [I2: real] :
% 4.71/5.16 ( ( member_real @ I2 @ I5 )
% 4.71/5.16 => ( ord_less_rat @ one_one_rat @ ( F @ I2 ) ) )
% 4.71/5.16 => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ I5 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % less_1_prod
% 4.71/5.16 thf(fact_7634_less__1__prod,axiom,
% 4.71/5.16 ! [I5: set_o,F: $o > rat] :
% 4.71/5.16 ( ( finite_finite_o @ I5 )
% 4.71/5.16 => ( ( I5 != bot_bot_set_o )
% 4.71/5.16 => ( ! [I2: $o] :
% 4.71/5.16 ( ( member_o @ I2 @ I5 )
% 4.71/5.16 => ( ord_less_rat @ one_one_rat @ ( F @ I2 ) ) )
% 4.71/5.16 => ( ord_less_rat @ one_one_rat @ ( groups2869687844427037835_o_rat @ F @ I5 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % less_1_prod
% 4.71/5.16 thf(fact_7635_prod_Osubset__diff,axiom,
% 4.71/5.16 ! [B2: set_complex,A2: set_complex,G2: complex > real] :
% 4.71/5.16 ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 4.71/5.16 => ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.16 => ( ( groups766887009212190081x_real @ G2 @ A2 )
% 4.71/5.16 = ( times_times_real @ ( groups766887009212190081x_real @ G2 @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups766887009212190081x_real @ G2 @ B2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.subset_diff
% 4.71/5.16 thf(fact_7636_prod_Osubset__diff,axiom,
% 4.71/5.16 ! [B2: set_Extended_enat,A2: set_Extended_enat,G2: extended_enat > real] :
% 4.71/5.16 ( ( ord_le7203529160286727270d_enat @ B2 @ A2 )
% 4.71/5.16 => ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.16 => ( ( groups97031904164794029t_real @ G2 @ A2 )
% 4.71/5.16 = ( times_times_real @ ( groups97031904164794029t_real @ G2 @ ( minus_925952699566721837d_enat @ A2 @ B2 ) ) @ ( groups97031904164794029t_real @ G2 @ B2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.subset_diff
% 4.71/5.16 thf(fact_7637_prod_Osubset__diff,axiom,
% 4.71/5.16 ! [B2: set_nat,A2: set_nat,G2: nat > real] :
% 4.71/5.16 ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 4.71/5.16 => ( ( finite_finite_nat @ A2 )
% 4.71/5.16 => ( ( groups129246275422532515t_real @ G2 @ A2 )
% 4.71/5.16 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups129246275422532515t_real @ G2 @ B2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.subset_diff
% 4.71/5.16 thf(fact_7638_prod_Osubset__diff,axiom,
% 4.71/5.16 ! [B2: set_complex,A2: set_complex,G2: complex > rat] :
% 4.71/5.16 ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 4.71/5.16 => ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.16 => ( ( groups225925009352817453ex_rat @ G2 @ A2 )
% 4.71/5.16 = ( times_times_rat @ ( groups225925009352817453ex_rat @ G2 @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups225925009352817453ex_rat @ G2 @ B2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.subset_diff
% 4.71/5.16 thf(fact_7639_prod_Osubset__diff,axiom,
% 4.71/5.16 ! [B2: set_Extended_enat,A2: set_Extended_enat,G2: extended_enat > rat] :
% 4.71/5.16 ( ( ord_le7203529160286727270d_enat @ B2 @ A2 )
% 4.71/5.16 => ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.16 => ( ( groups2245840878043517529at_rat @ G2 @ A2 )
% 4.71/5.16 = ( times_times_rat @ ( groups2245840878043517529at_rat @ G2 @ ( minus_925952699566721837d_enat @ A2 @ B2 ) ) @ ( groups2245840878043517529at_rat @ G2 @ B2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.subset_diff
% 4.71/5.16 thf(fact_7640_prod_Osubset__diff,axiom,
% 4.71/5.16 ! [B2: set_nat,A2: set_nat,G2: nat > rat] :
% 4.71/5.16 ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 4.71/5.16 => ( ( finite_finite_nat @ A2 )
% 4.71/5.16 => ( ( groups73079841787564623at_rat @ G2 @ A2 )
% 4.71/5.16 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups73079841787564623at_rat @ G2 @ B2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.subset_diff
% 4.71/5.16 thf(fact_7641_prod_Osubset__diff,axiom,
% 4.71/5.16 ! [B2: set_complex,A2: set_complex,G2: complex > nat] :
% 4.71/5.16 ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 4.71/5.16 => ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.16 => ( ( groups861055069439313189ex_nat @ G2 @ A2 )
% 4.71/5.16 = ( times_times_nat @ ( groups861055069439313189ex_nat @ G2 @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups861055069439313189ex_nat @ G2 @ B2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.subset_diff
% 4.71/5.16 thf(fact_7642_prod_Osubset__diff,axiom,
% 4.71/5.16 ! [B2: set_Extended_enat,A2: set_Extended_enat,G2: extended_enat > nat] :
% 4.71/5.16 ( ( ord_le7203529160286727270d_enat @ B2 @ A2 )
% 4.71/5.16 => ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.16 => ( ( groups2880970938130013265at_nat @ G2 @ A2 )
% 4.71/5.16 = ( times_times_nat @ ( groups2880970938130013265at_nat @ G2 @ ( minus_925952699566721837d_enat @ A2 @ B2 ) ) @ ( groups2880970938130013265at_nat @ G2 @ B2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.subset_diff
% 4.71/5.16 thf(fact_7643_prod_Osubset__diff,axiom,
% 4.71/5.16 ! [B2: set_complex,A2: set_complex,G2: complex > int] :
% 4.71/5.16 ( ( ord_le211207098394363844omplex @ B2 @ A2 )
% 4.71/5.16 => ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.16 => ( ( groups858564598930262913ex_int @ G2 @ A2 )
% 4.71/5.16 = ( times_times_int @ ( groups858564598930262913ex_int @ G2 @ ( minus_811609699411566653omplex @ A2 @ B2 ) ) @ ( groups858564598930262913ex_int @ G2 @ B2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.subset_diff
% 4.71/5.16 thf(fact_7644_prod_Osubset__diff,axiom,
% 4.71/5.16 ! [B2: set_Extended_enat,A2: set_Extended_enat,G2: extended_enat > int] :
% 4.71/5.16 ( ( ord_le7203529160286727270d_enat @ B2 @ A2 )
% 4.71/5.16 => ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.16 => ( ( groups2878480467620962989at_int @ G2 @ A2 )
% 4.71/5.16 = ( times_times_int @ ( groups2878480467620962989at_int @ G2 @ ( minus_925952699566721837d_enat @ A2 @ B2 ) ) @ ( groups2878480467620962989at_int @ G2 @ B2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.subset_diff
% 4.71/5.16 thf(fact_7645_prod_Osame__carrier,axiom,
% 4.71/5.16 ! [C2: set_o,A2: set_o,B2: set_o,G2: $o > complex,H: $o > complex] :
% 4.71/5.16 ( ( finite_finite_o @ C2 )
% 4.71/5.16 => ( ( ord_less_eq_set_o @ A2 @ C2 )
% 4.71/5.16 => ( ( ord_less_eq_set_o @ B2 @ C2 )
% 4.71/5.16 => ( ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ ( minus_minus_set_o @ C2 @ A2 ) )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [B5: $o] :
% 4.71/5.16 ( ( member_o @ B5 @ ( minus_minus_set_o @ C2 @ B2 ) )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ( ( groups4859619685533338977omplex @ G2 @ A2 )
% 4.71/5.16 = ( groups4859619685533338977omplex @ H @ B2 ) )
% 4.71/5.16 = ( ( groups4859619685533338977omplex @ G2 @ C2 )
% 4.71/5.16 = ( groups4859619685533338977omplex @ H @ C2 ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.same_carrier
% 4.71/5.16 thf(fact_7646_prod_Osame__carrier,axiom,
% 4.71/5.16 ! [C2: set_complex,A2: set_complex,B2: set_complex,G2: complex > complex,H: complex > complex] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ C2 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ A2 @ C2 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ B2 @ C2 )
% 4.71/5.16 => ( ! [A5: complex] :
% 4.71/5.16 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C2 @ A2 ) )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [B5: complex] :
% 4.71/5.16 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C2 @ B2 ) )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ( ( groups3708469109370488835omplex @ G2 @ A2 )
% 4.71/5.16 = ( groups3708469109370488835omplex @ H @ B2 ) )
% 4.71/5.16 = ( ( groups3708469109370488835omplex @ G2 @ C2 )
% 4.71/5.16 = ( groups3708469109370488835omplex @ H @ C2 ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.same_carrier
% 4.71/5.16 thf(fact_7647_prod_Osame__carrier,axiom,
% 4.71/5.16 ! [C2: set_Extended_enat,A2: set_Extended_enat,B2: set_Extended_enat,G2: extended_enat > complex,H: extended_enat > complex] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ C2 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ A2 @ C2 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ B2 @ C2 )
% 4.71/5.16 => ( ! [A5: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ A5 @ ( minus_925952699566721837d_enat @ C2 @ A2 ) )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [B5: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ B5 @ ( minus_925952699566721837d_enat @ C2 @ B2 ) )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ( ( groups4622424608036095791omplex @ G2 @ A2 )
% 4.71/5.16 = ( groups4622424608036095791omplex @ H @ B2 ) )
% 4.71/5.16 = ( ( groups4622424608036095791omplex @ G2 @ C2 )
% 4.71/5.16 = ( groups4622424608036095791omplex @ H @ C2 ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.same_carrier
% 4.71/5.16 thf(fact_7648_prod_Osame__carrier,axiom,
% 4.71/5.16 ! [C2: set_o,A2: set_o,B2: set_o,G2: $o > real,H: $o > real] :
% 4.71/5.16 ( ( finite_finite_o @ C2 )
% 4.71/5.16 => ( ( ord_less_eq_set_o @ A2 @ C2 )
% 4.71/5.16 => ( ( ord_less_eq_set_o @ B2 @ C2 )
% 4.71/5.16 => ( ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ ( minus_minus_set_o @ C2 @ A2 ) )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_real ) )
% 4.71/5.16 => ( ! [B5: $o] :
% 4.71/5.16 ( ( member_o @ B5 @ ( minus_minus_set_o @ C2 @ B2 ) )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_real ) )
% 4.71/5.16 => ( ( ( groups234877984723959775o_real @ G2 @ A2 )
% 4.71/5.16 = ( groups234877984723959775o_real @ H @ B2 ) )
% 4.71/5.16 = ( ( groups234877984723959775o_real @ G2 @ C2 )
% 4.71/5.16 = ( groups234877984723959775o_real @ H @ C2 ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.same_carrier
% 4.71/5.16 thf(fact_7649_prod_Osame__carrier,axiom,
% 4.71/5.16 ! [C2: set_complex,A2: set_complex,B2: set_complex,G2: complex > real,H: complex > real] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ C2 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ A2 @ C2 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ B2 @ C2 )
% 4.71/5.16 => ( ! [A5: complex] :
% 4.71/5.16 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C2 @ A2 ) )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_real ) )
% 4.71/5.16 => ( ! [B5: complex] :
% 4.71/5.16 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C2 @ B2 ) )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_real ) )
% 4.71/5.16 => ( ( ( groups766887009212190081x_real @ G2 @ A2 )
% 4.71/5.16 = ( groups766887009212190081x_real @ H @ B2 ) )
% 4.71/5.16 = ( ( groups766887009212190081x_real @ G2 @ C2 )
% 4.71/5.16 = ( groups766887009212190081x_real @ H @ C2 ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.same_carrier
% 4.71/5.16 thf(fact_7650_prod_Osame__carrier,axiom,
% 4.71/5.16 ! [C2: set_Extended_enat,A2: set_Extended_enat,B2: set_Extended_enat,G2: extended_enat > real,H: extended_enat > real] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ C2 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ A2 @ C2 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ B2 @ C2 )
% 4.71/5.16 => ( ! [A5: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ A5 @ ( minus_925952699566721837d_enat @ C2 @ A2 ) )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_real ) )
% 4.71/5.16 => ( ! [B5: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ B5 @ ( minus_925952699566721837d_enat @ C2 @ B2 ) )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_real ) )
% 4.71/5.16 => ( ( ( groups97031904164794029t_real @ G2 @ A2 )
% 4.71/5.16 = ( groups97031904164794029t_real @ H @ B2 ) )
% 4.71/5.16 = ( ( groups97031904164794029t_real @ G2 @ C2 )
% 4.71/5.16 = ( groups97031904164794029t_real @ H @ C2 ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.same_carrier
% 4.71/5.16 thf(fact_7651_prod_Osame__carrier,axiom,
% 4.71/5.16 ! [C2: set_o,A2: set_o,B2: set_o,G2: $o > rat,H: $o > rat] :
% 4.71/5.16 ( ( finite_finite_o @ C2 )
% 4.71/5.16 => ( ( ord_less_eq_set_o @ A2 @ C2 )
% 4.71/5.16 => ( ( ord_less_eq_set_o @ B2 @ C2 )
% 4.71/5.16 => ( ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ ( minus_minus_set_o @ C2 @ A2 ) )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_rat ) )
% 4.71/5.16 => ( ! [B5: $o] :
% 4.71/5.16 ( ( member_o @ B5 @ ( minus_minus_set_o @ C2 @ B2 ) )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_rat ) )
% 4.71/5.16 => ( ( ( groups2869687844427037835_o_rat @ G2 @ A2 )
% 4.71/5.16 = ( groups2869687844427037835_o_rat @ H @ B2 ) )
% 4.71/5.16 = ( ( groups2869687844427037835_o_rat @ G2 @ C2 )
% 4.71/5.16 = ( groups2869687844427037835_o_rat @ H @ C2 ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.same_carrier
% 4.71/5.16 thf(fact_7652_prod_Osame__carrier,axiom,
% 4.71/5.16 ! [C2: set_complex,A2: set_complex,B2: set_complex,G2: complex > rat,H: complex > rat] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ C2 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ A2 @ C2 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ B2 @ C2 )
% 4.71/5.16 => ( ! [A5: complex] :
% 4.71/5.16 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C2 @ A2 ) )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_rat ) )
% 4.71/5.16 => ( ! [B5: complex] :
% 4.71/5.16 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C2 @ B2 ) )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_rat ) )
% 4.71/5.16 => ( ( ( groups225925009352817453ex_rat @ G2 @ A2 )
% 4.71/5.16 = ( groups225925009352817453ex_rat @ H @ B2 ) )
% 4.71/5.16 = ( ( groups225925009352817453ex_rat @ G2 @ C2 )
% 4.71/5.16 = ( groups225925009352817453ex_rat @ H @ C2 ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.same_carrier
% 4.71/5.16 thf(fact_7653_prod_Osame__carrier,axiom,
% 4.71/5.16 ! [C2: set_Extended_enat,A2: set_Extended_enat,B2: set_Extended_enat,G2: extended_enat > rat,H: extended_enat > rat] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ C2 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ A2 @ C2 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ B2 @ C2 )
% 4.71/5.16 => ( ! [A5: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ A5 @ ( minus_925952699566721837d_enat @ C2 @ A2 ) )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_rat ) )
% 4.71/5.16 => ( ! [B5: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ B5 @ ( minus_925952699566721837d_enat @ C2 @ B2 ) )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_rat ) )
% 4.71/5.16 => ( ( ( groups2245840878043517529at_rat @ G2 @ A2 )
% 4.71/5.16 = ( groups2245840878043517529at_rat @ H @ B2 ) )
% 4.71/5.16 = ( ( groups2245840878043517529at_rat @ G2 @ C2 )
% 4.71/5.16 = ( groups2245840878043517529at_rat @ H @ C2 ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.same_carrier
% 4.71/5.16 thf(fact_7654_prod_Osame__carrier,axiom,
% 4.71/5.16 ! [C2: set_o,A2: set_o,B2: set_o,G2: $o > nat,H: $o > nat] :
% 4.71/5.16 ( ( finite_finite_o @ C2 )
% 4.71/5.16 => ( ( ord_less_eq_set_o @ A2 @ C2 )
% 4.71/5.16 => ( ( ord_less_eq_set_o @ B2 @ C2 )
% 4.71/5.16 => ( ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ ( minus_minus_set_o @ C2 @ A2 ) )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_nat ) )
% 4.71/5.16 => ( ! [B5: $o] :
% 4.71/5.16 ( ( member_o @ B5 @ ( minus_minus_set_o @ C2 @ B2 ) )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_nat ) )
% 4.71/5.16 => ( ( ( groups3504817904513533571_o_nat @ G2 @ A2 )
% 4.71/5.16 = ( groups3504817904513533571_o_nat @ H @ B2 ) )
% 4.71/5.16 = ( ( groups3504817904513533571_o_nat @ G2 @ C2 )
% 4.71/5.16 = ( groups3504817904513533571_o_nat @ H @ C2 ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.same_carrier
% 4.71/5.16 thf(fact_7655_prod_Osame__carrierI,axiom,
% 4.71/5.16 ! [C2: set_o,A2: set_o,B2: set_o,G2: $o > complex,H: $o > complex] :
% 4.71/5.16 ( ( finite_finite_o @ C2 )
% 4.71/5.16 => ( ( ord_less_eq_set_o @ A2 @ C2 )
% 4.71/5.16 => ( ( ord_less_eq_set_o @ B2 @ C2 )
% 4.71/5.16 => ( ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ ( minus_minus_set_o @ C2 @ A2 ) )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [B5: $o] :
% 4.71/5.16 ( ( member_o @ B5 @ ( minus_minus_set_o @ C2 @ B2 ) )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ( ( groups4859619685533338977omplex @ G2 @ C2 )
% 4.71/5.16 = ( groups4859619685533338977omplex @ H @ C2 ) )
% 4.71/5.16 => ( ( groups4859619685533338977omplex @ G2 @ A2 )
% 4.71/5.16 = ( groups4859619685533338977omplex @ H @ B2 ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.same_carrierI
% 4.71/5.16 thf(fact_7656_prod_Osame__carrierI,axiom,
% 4.71/5.16 ! [C2: set_complex,A2: set_complex,B2: set_complex,G2: complex > complex,H: complex > complex] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ C2 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ A2 @ C2 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ B2 @ C2 )
% 4.71/5.16 => ( ! [A5: complex] :
% 4.71/5.16 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C2 @ A2 ) )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [B5: complex] :
% 4.71/5.16 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C2 @ B2 ) )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ( ( groups3708469109370488835omplex @ G2 @ C2 )
% 4.71/5.16 = ( groups3708469109370488835omplex @ H @ C2 ) )
% 4.71/5.16 => ( ( groups3708469109370488835omplex @ G2 @ A2 )
% 4.71/5.16 = ( groups3708469109370488835omplex @ H @ B2 ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.same_carrierI
% 4.71/5.16 thf(fact_7657_prod_Osame__carrierI,axiom,
% 4.71/5.16 ! [C2: set_Extended_enat,A2: set_Extended_enat,B2: set_Extended_enat,G2: extended_enat > complex,H: extended_enat > complex] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ C2 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ A2 @ C2 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ B2 @ C2 )
% 4.71/5.16 => ( ! [A5: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ A5 @ ( minus_925952699566721837d_enat @ C2 @ A2 ) )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [B5: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ B5 @ ( minus_925952699566721837d_enat @ C2 @ B2 ) )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ( ( groups4622424608036095791omplex @ G2 @ C2 )
% 4.71/5.16 = ( groups4622424608036095791omplex @ H @ C2 ) )
% 4.71/5.16 => ( ( groups4622424608036095791omplex @ G2 @ A2 )
% 4.71/5.16 = ( groups4622424608036095791omplex @ H @ B2 ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.same_carrierI
% 4.71/5.16 thf(fact_7658_prod_Osame__carrierI,axiom,
% 4.71/5.16 ! [C2: set_o,A2: set_o,B2: set_o,G2: $o > real,H: $o > real] :
% 4.71/5.16 ( ( finite_finite_o @ C2 )
% 4.71/5.16 => ( ( ord_less_eq_set_o @ A2 @ C2 )
% 4.71/5.16 => ( ( ord_less_eq_set_o @ B2 @ C2 )
% 4.71/5.16 => ( ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ ( minus_minus_set_o @ C2 @ A2 ) )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_real ) )
% 4.71/5.16 => ( ! [B5: $o] :
% 4.71/5.16 ( ( member_o @ B5 @ ( minus_minus_set_o @ C2 @ B2 ) )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_real ) )
% 4.71/5.16 => ( ( ( groups234877984723959775o_real @ G2 @ C2 )
% 4.71/5.16 = ( groups234877984723959775o_real @ H @ C2 ) )
% 4.71/5.16 => ( ( groups234877984723959775o_real @ G2 @ A2 )
% 4.71/5.16 = ( groups234877984723959775o_real @ H @ B2 ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.same_carrierI
% 4.71/5.16 thf(fact_7659_prod_Osame__carrierI,axiom,
% 4.71/5.16 ! [C2: set_complex,A2: set_complex,B2: set_complex,G2: complex > real,H: complex > real] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ C2 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ A2 @ C2 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ B2 @ C2 )
% 4.71/5.16 => ( ! [A5: complex] :
% 4.71/5.16 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C2 @ A2 ) )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_real ) )
% 4.71/5.16 => ( ! [B5: complex] :
% 4.71/5.16 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C2 @ B2 ) )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_real ) )
% 4.71/5.16 => ( ( ( groups766887009212190081x_real @ G2 @ C2 )
% 4.71/5.16 = ( groups766887009212190081x_real @ H @ C2 ) )
% 4.71/5.16 => ( ( groups766887009212190081x_real @ G2 @ A2 )
% 4.71/5.16 = ( groups766887009212190081x_real @ H @ B2 ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.same_carrierI
% 4.71/5.16 thf(fact_7660_prod_Osame__carrierI,axiom,
% 4.71/5.16 ! [C2: set_Extended_enat,A2: set_Extended_enat,B2: set_Extended_enat,G2: extended_enat > real,H: extended_enat > real] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ C2 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ A2 @ C2 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ B2 @ C2 )
% 4.71/5.16 => ( ! [A5: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ A5 @ ( minus_925952699566721837d_enat @ C2 @ A2 ) )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_real ) )
% 4.71/5.16 => ( ! [B5: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ B5 @ ( minus_925952699566721837d_enat @ C2 @ B2 ) )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_real ) )
% 4.71/5.16 => ( ( ( groups97031904164794029t_real @ G2 @ C2 )
% 4.71/5.16 = ( groups97031904164794029t_real @ H @ C2 ) )
% 4.71/5.16 => ( ( groups97031904164794029t_real @ G2 @ A2 )
% 4.71/5.16 = ( groups97031904164794029t_real @ H @ B2 ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.same_carrierI
% 4.71/5.16 thf(fact_7661_prod_Osame__carrierI,axiom,
% 4.71/5.16 ! [C2: set_o,A2: set_o,B2: set_o,G2: $o > rat,H: $o > rat] :
% 4.71/5.16 ( ( finite_finite_o @ C2 )
% 4.71/5.16 => ( ( ord_less_eq_set_o @ A2 @ C2 )
% 4.71/5.16 => ( ( ord_less_eq_set_o @ B2 @ C2 )
% 4.71/5.16 => ( ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ ( minus_minus_set_o @ C2 @ A2 ) )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_rat ) )
% 4.71/5.16 => ( ! [B5: $o] :
% 4.71/5.16 ( ( member_o @ B5 @ ( minus_minus_set_o @ C2 @ B2 ) )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_rat ) )
% 4.71/5.16 => ( ( ( groups2869687844427037835_o_rat @ G2 @ C2 )
% 4.71/5.16 = ( groups2869687844427037835_o_rat @ H @ C2 ) )
% 4.71/5.16 => ( ( groups2869687844427037835_o_rat @ G2 @ A2 )
% 4.71/5.16 = ( groups2869687844427037835_o_rat @ H @ B2 ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.same_carrierI
% 4.71/5.16 thf(fact_7662_prod_Osame__carrierI,axiom,
% 4.71/5.16 ! [C2: set_complex,A2: set_complex,B2: set_complex,G2: complex > rat,H: complex > rat] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ C2 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ A2 @ C2 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ B2 @ C2 )
% 4.71/5.16 => ( ! [A5: complex] :
% 4.71/5.16 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C2 @ A2 ) )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_rat ) )
% 4.71/5.16 => ( ! [B5: complex] :
% 4.71/5.16 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C2 @ B2 ) )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_rat ) )
% 4.71/5.16 => ( ( ( groups225925009352817453ex_rat @ G2 @ C2 )
% 4.71/5.16 = ( groups225925009352817453ex_rat @ H @ C2 ) )
% 4.71/5.16 => ( ( groups225925009352817453ex_rat @ G2 @ A2 )
% 4.71/5.16 = ( groups225925009352817453ex_rat @ H @ B2 ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.same_carrierI
% 4.71/5.16 thf(fact_7663_prod_Osame__carrierI,axiom,
% 4.71/5.16 ! [C2: set_Extended_enat,A2: set_Extended_enat,B2: set_Extended_enat,G2: extended_enat > rat,H: extended_enat > rat] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ C2 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ A2 @ C2 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ B2 @ C2 )
% 4.71/5.16 => ( ! [A5: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ A5 @ ( minus_925952699566721837d_enat @ C2 @ A2 ) )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_rat ) )
% 4.71/5.16 => ( ! [B5: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ B5 @ ( minus_925952699566721837d_enat @ C2 @ B2 ) )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_rat ) )
% 4.71/5.16 => ( ( ( groups2245840878043517529at_rat @ G2 @ C2 )
% 4.71/5.16 = ( groups2245840878043517529at_rat @ H @ C2 ) )
% 4.71/5.16 => ( ( groups2245840878043517529at_rat @ G2 @ A2 )
% 4.71/5.16 = ( groups2245840878043517529at_rat @ H @ B2 ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.same_carrierI
% 4.71/5.16 thf(fact_7664_prod_Osame__carrierI,axiom,
% 4.71/5.16 ! [C2: set_o,A2: set_o,B2: set_o,G2: $o > nat,H: $o > nat] :
% 4.71/5.16 ( ( finite_finite_o @ C2 )
% 4.71/5.16 => ( ( ord_less_eq_set_o @ A2 @ C2 )
% 4.71/5.16 => ( ( ord_less_eq_set_o @ B2 @ C2 )
% 4.71/5.16 => ( ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ ( minus_minus_set_o @ C2 @ A2 ) )
% 4.71/5.16 => ( ( G2 @ A5 )
% 4.71/5.16 = one_one_nat ) )
% 4.71/5.16 => ( ! [B5: $o] :
% 4.71/5.16 ( ( member_o @ B5 @ ( minus_minus_set_o @ C2 @ B2 ) )
% 4.71/5.16 => ( ( H @ B5 )
% 4.71/5.16 = one_one_nat ) )
% 4.71/5.16 => ( ( ( groups3504817904513533571_o_nat @ G2 @ C2 )
% 4.71/5.16 = ( groups3504817904513533571_o_nat @ H @ C2 ) )
% 4.71/5.16 => ( ( groups3504817904513533571_o_nat @ G2 @ A2 )
% 4.71/5.16 = ( groups3504817904513533571_o_nat @ H @ B2 ) ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.same_carrierI
% 4.71/5.16 thf(fact_7665_prod_Omono__neutral__left,axiom,
% 4.71/5.16 ! [T3: set_complex,S2: set_complex,G2: complex > complex] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ T3 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: complex] :
% 4.71/5.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ( groups3708469109370488835omplex @ G2 @ S2 )
% 4.71/5.16 = ( groups3708469109370488835omplex @ G2 @ T3 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_left
% 4.71/5.16 thf(fact_7666_prod_Omono__neutral__left,axiom,
% 4.71/5.16 ! [T3: set_Extended_enat,S2: set_Extended_enat,G2: extended_enat > complex] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ T3 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ( groups4622424608036095791omplex @ G2 @ S2 )
% 4.71/5.16 = ( groups4622424608036095791omplex @ G2 @ T3 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_left
% 4.71/5.16 thf(fact_7667_prod_Omono__neutral__left,axiom,
% 4.71/5.16 ! [T3: set_complex,S2: set_complex,G2: complex > real] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ T3 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: complex] :
% 4.71/5.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_real ) )
% 4.71/5.16 => ( ( groups766887009212190081x_real @ G2 @ S2 )
% 4.71/5.16 = ( groups766887009212190081x_real @ G2 @ T3 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_left
% 4.71/5.16 thf(fact_7668_prod_Omono__neutral__left,axiom,
% 4.71/5.16 ! [T3: set_Extended_enat,S2: set_Extended_enat,G2: extended_enat > real] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ T3 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_real ) )
% 4.71/5.16 => ( ( groups97031904164794029t_real @ G2 @ S2 )
% 4.71/5.16 = ( groups97031904164794029t_real @ G2 @ T3 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_left
% 4.71/5.16 thf(fact_7669_prod_Omono__neutral__left,axiom,
% 4.71/5.16 ! [T3: set_complex,S2: set_complex,G2: complex > rat] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ T3 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: complex] :
% 4.71/5.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_rat ) )
% 4.71/5.16 => ( ( groups225925009352817453ex_rat @ G2 @ S2 )
% 4.71/5.16 = ( groups225925009352817453ex_rat @ G2 @ T3 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_left
% 4.71/5.16 thf(fact_7670_prod_Omono__neutral__left,axiom,
% 4.71/5.16 ! [T3: set_Extended_enat,S2: set_Extended_enat,G2: extended_enat > rat] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ T3 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_rat ) )
% 4.71/5.16 => ( ( groups2245840878043517529at_rat @ G2 @ S2 )
% 4.71/5.16 = ( groups2245840878043517529at_rat @ G2 @ T3 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_left
% 4.71/5.16 thf(fact_7671_prod_Omono__neutral__left,axiom,
% 4.71/5.16 ! [T3: set_complex,S2: set_complex,G2: complex > nat] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ T3 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: complex] :
% 4.71/5.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_nat ) )
% 4.71/5.16 => ( ( groups861055069439313189ex_nat @ G2 @ S2 )
% 4.71/5.16 = ( groups861055069439313189ex_nat @ G2 @ T3 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_left
% 4.71/5.16 thf(fact_7672_prod_Omono__neutral__left,axiom,
% 4.71/5.16 ! [T3: set_Extended_enat,S2: set_Extended_enat,G2: extended_enat > nat] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ T3 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_nat ) )
% 4.71/5.16 => ( ( groups2880970938130013265at_nat @ G2 @ S2 )
% 4.71/5.16 = ( groups2880970938130013265at_nat @ G2 @ T3 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_left
% 4.71/5.16 thf(fact_7673_prod_Omono__neutral__left,axiom,
% 4.71/5.16 ! [T3: set_complex,S2: set_complex,G2: complex > int] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ T3 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: complex] :
% 4.71/5.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_int ) )
% 4.71/5.16 => ( ( groups858564598930262913ex_int @ G2 @ S2 )
% 4.71/5.16 = ( groups858564598930262913ex_int @ G2 @ T3 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_left
% 4.71/5.16 thf(fact_7674_prod_Omono__neutral__left,axiom,
% 4.71/5.16 ! [T3: set_Extended_enat,S2: set_Extended_enat,G2: extended_enat > int] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ T3 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_int ) )
% 4.71/5.16 => ( ( groups2878480467620962989at_int @ G2 @ S2 )
% 4.71/5.16 = ( groups2878480467620962989at_int @ G2 @ T3 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_left
% 4.71/5.16 thf(fact_7675_prod_Omono__neutral__right,axiom,
% 4.71/5.16 ! [T3: set_complex,S2: set_complex,G2: complex > complex] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ T3 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: complex] :
% 4.71/5.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ( groups3708469109370488835omplex @ G2 @ T3 )
% 4.71/5.16 = ( groups3708469109370488835omplex @ G2 @ S2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_right
% 4.71/5.16 thf(fact_7676_prod_Omono__neutral__right,axiom,
% 4.71/5.16 ! [T3: set_Extended_enat,S2: set_Extended_enat,G2: extended_enat > complex] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ T3 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ( groups4622424608036095791omplex @ G2 @ T3 )
% 4.71/5.16 = ( groups4622424608036095791omplex @ G2 @ S2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_right
% 4.71/5.16 thf(fact_7677_prod_Omono__neutral__right,axiom,
% 4.71/5.16 ! [T3: set_complex,S2: set_complex,G2: complex > real] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ T3 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: complex] :
% 4.71/5.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_real ) )
% 4.71/5.16 => ( ( groups766887009212190081x_real @ G2 @ T3 )
% 4.71/5.16 = ( groups766887009212190081x_real @ G2 @ S2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_right
% 4.71/5.16 thf(fact_7678_prod_Omono__neutral__right,axiom,
% 4.71/5.16 ! [T3: set_Extended_enat,S2: set_Extended_enat,G2: extended_enat > real] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ T3 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_real ) )
% 4.71/5.16 => ( ( groups97031904164794029t_real @ G2 @ T3 )
% 4.71/5.16 = ( groups97031904164794029t_real @ G2 @ S2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_right
% 4.71/5.16 thf(fact_7679_prod_Omono__neutral__right,axiom,
% 4.71/5.16 ! [T3: set_complex,S2: set_complex,G2: complex > rat] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ T3 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: complex] :
% 4.71/5.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_rat ) )
% 4.71/5.16 => ( ( groups225925009352817453ex_rat @ G2 @ T3 )
% 4.71/5.16 = ( groups225925009352817453ex_rat @ G2 @ S2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_right
% 4.71/5.16 thf(fact_7680_prod_Omono__neutral__right,axiom,
% 4.71/5.16 ! [T3: set_Extended_enat,S2: set_Extended_enat,G2: extended_enat > rat] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ T3 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_rat ) )
% 4.71/5.16 => ( ( groups2245840878043517529at_rat @ G2 @ T3 )
% 4.71/5.16 = ( groups2245840878043517529at_rat @ G2 @ S2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_right
% 4.71/5.16 thf(fact_7681_prod_Omono__neutral__right,axiom,
% 4.71/5.16 ! [T3: set_complex,S2: set_complex,G2: complex > nat] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ T3 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: complex] :
% 4.71/5.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_nat ) )
% 4.71/5.16 => ( ( groups861055069439313189ex_nat @ G2 @ T3 )
% 4.71/5.16 = ( groups861055069439313189ex_nat @ G2 @ S2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_right
% 4.71/5.16 thf(fact_7682_prod_Omono__neutral__right,axiom,
% 4.71/5.16 ! [T3: set_Extended_enat,S2: set_Extended_enat,G2: extended_enat > nat] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ T3 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_nat ) )
% 4.71/5.16 => ( ( groups2880970938130013265at_nat @ G2 @ T3 )
% 4.71/5.16 = ( groups2880970938130013265at_nat @ G2 @ S2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_right
% 4.71/5.16 thf(fact_7683_prod_Omono__neutral__right,axiom,
% 4.71/5.16 ! [T3: set_complex,S2: set_complex,G2: complex > int] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ T3 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: complex] :
% 4.71/5.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_int ) )
% 4.71/5.16 => ( ( groups858564598930262913ex_int @ G2 @ T3 )
% 4.71/5.16 = ( groups858564598930262913ex_int @ G2 @ S2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_right
% 4.71/5.16 thf(fact_7684_prod_Omono__neutral__right,axiom,
% 4.71/5.16 ! [T3: set_Extended_enat,S2: set_Extended_enat,G2: extended_enat > int] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ T3 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_int ) )
% 4.71/5.16 => ( ( groups2878480467620962989at_int @ G2 @ T3 )
% 4.71/5.16 = ( groups2878480467620962989at_int @ G2 @ S2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_right
% 4.71/5.16 thf(fact_7685_prod_Omono__neutral__cong__left,axiom,
% 4.71/5.16 ! [T3: set_o,S2: set_o,H: $o > complex,G2: $o > complex] :
% 4.71/5.16 ( ( finite_finite_o @ T3 )
% 4.71/5.16 => ( ( ord_less_eq_set_o @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: $o] :
% 4.71/5.16 ( ( member_o @ X4 @ ( minus_minus_set_o @ T3 @ S2 ) )
% 4.71/5.16 => ( ( H @ X4 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [X4: $o] :
% 4.71/5.16 ( ( member_o @ X4 @ S2 )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = ( H @ X4 ) ) )
% 4.71/5.16 => ( ( groups4859619685533338977omplex @ G2 @ S2 )
% 4.71/5.16 = ( groups4859619685533338977omplex @ H @ T3 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_cong_left
% 4.71/5.16 thf(fact_7686_prod_Omono__neutral__cong__left,axiom,
% 4.71/5.16 ! [T3: set_complex,S2: set_complex,H: complex > complex,G2: complex > complex] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ T3 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: complex] :
% 4.71/5.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 4.71/5.16 => ( ( H @ X4 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [X4: complex] :
% 4.71/5.16 ( ( member_complex @ X4 @ S2 )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = ( H @ X4 ) ) )
% 4.71/5.16 => ( ( groups3708469109370488835omplex @ G2 @ S2 )
% 4.71/5.16 = ( groups3708469109370488835omplex @ H @ T3 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_cong_left
% 4.71/5.16 thf(fact_7687_prod_Omono__neutral__cong__left,axiom,
% 4.71/5.16 ! [T3: set_Extended_enat,S2: set_Extended_enat,H: extended_enat > complex,G2: extended_enat > complex] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ T3 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 4.71/5.16 => ( ( H @ X4 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [X4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X4 @ S2 )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = ( H @ X4 ) ) )
% 4.71/5.16 => ( ( groups4622424608036095791omplex @ G2 @ S2 )
% 4.71/5.16 = ( groups4622424608036095791omplex @ H @ T3 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_cong_left
% 4.71/5.16 thf(fact_7688_prod_Omono__neutral__cong__left,axiom,
% 4.71/5.16 ! [T3: set_o,S2: set_o,H: $o > real,G2: $o > real] :
% 4.71/5.16 ( ( finite_finite_o @ T3 )
% 4.71/5.16 => ( ( ord_less_eq_set_o @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: $o] :
% 4.71/5.16 ( ( member_o @ X4 @ ( minus_minus_set_o @ T3 @ S2 ) )
% 4.71/5.16 => ( ( H @ X4 )
% 4.71/5.16 = one_one_real ) )
% 4.71/5.16 => ( ! [X4: $o] :
% 4.71/5.16 ( ( member_o @ X4 @ S2 )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = ( H @ X4 ) ) )
% 4.71/5.16 => ( ( groups234877984723959775o_real @ G2 @ S2 )
% 4.71/5.16 = ( groups234877984723959775o_real @ H @ T3 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_cong_left
% 4.71/5.16 thf(fact_7689_prod_Omono__neutral__cong__left,axiom,
% 4.71/5.16 ! [T3: set_complex,S2: set_complex,H: complex > real,G2: complex > real] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ T3 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: complex] :
% 4.71/5.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 4.71/5.16 => ( ( H @ X4 )
% 4.71/5.16 = one_one_real ) )
% 4.71/5.16 => ( ! [X4: complex] :
% 4.71/5.16 ( ( member_complex @ X4 @ S2 )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = ( H @ X4 ) ) )
% 4.71/5.16 => ( ( groups766887009212190081x_real @ G2 @ S2 )
% 4.71/5.16 = ( groups766887009212190081x_real @ H @ T3 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_cong_left
% 4.71/5.16 thf(fact_7690_prod_Omono__neutral__cong__left,axiom,
% 4.71/5.16 ! [T3: set_Extended_enat,S2: set_Extended_enat,H: extended_enat > real,G2: extended_enat > real] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ T3 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 4.71/5.16 => ( ( H @ X4 )
% 4.71/5.16 = one_one_real ) )
% 4.71/5.16 => ( ! [X4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X4 @ S2 )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = ( H @ X4 ) ) )
% 4.71/5.16 => ( ( groups97031904164794029t_real @ G2 @ S2 )
% 4.71/5.16 = ( groups97031904164794029t_real @ H @ T3 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_cong_left
% 4.71/5.16 thf(fact_7691_prod_Omono__neutral__cong__left,axiom,
% 4.71/5.16 ! [T3: set_o,S2: set_o,H: $o > rat,G2: $o > rat] :
% 4.71/5.16 ( ( finite_finite_o @ T3 )
% 4.71/5.16 => ( ( ord_less_eq_set_o @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: $o] :
% 4.71/5.16 ( ( member_o @ X4 @ ( minus_minus_set_o @ T3 @ S2 ) )
% 4.71/5.16 => ( ( H @ X4 )
% 4.71/5.16 = one_one_rat ) )
% 4.71/5.16 => ( ! [X4: $o] :
% 4.71/5.16 ( ( member_o @ X4 @ S2 )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = ( H @ X4 ) ) )
% 4.71/5.16 => ( ( groups2869687844427037835_o_rat @ G2 @ S2 )
% 4.71/5.16 = ( groups2869687844427037835_o_rat @ H @ T3 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_cong_left
% 4.71/5.16 thf(fact_7692_prod_Omono__neutral__cong__left,axiom,
% 4.71/5.16 ! [T3: set_complex,S2: set_complex,H: complex > rat,G2: complex > rat] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ T3 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: complex] :
% 4.71/5.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 4.71/5.16 => ( ( H @ X4 )
% 4.71/5.16 = one_one_rat ) )
% 4.71/5.16 => ( ! [X4: complex] :
% 4.71/5.16 ( ( member_complex @ X4 @ S2 )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = ( H @ X4 ) ) )
% 4.71/5.16 => ( ( groups225925009352817453ex_rat @ G2 @ S2 )
% 4.71/5.16 = ( groups225925009352817453ex_rat @ H @ T3 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_cong_left
% 4.71/5.16 thf(fact_7693_prod_Omono__neutral__cong__left,axiom,
% 4.71/5.16 ! [T3: set_Extended_enat,S2: set_Extended_enat,H: extended_enat > rat,G2: extended_enat > rat] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ T3 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 4.71/5.16 => ( ( H @ X4 )
% 4.71/5.16 = one_one_rat ) )
% 4.71/5.16 => ( ! [X4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X4 @ S2 )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = ( H @ X4 ) ) )
% 4.71/5.16 => ( ( groups2245840878043517529at_rat @ G2 @ S2 )
% 4.71/5.16 = ( groups2245840878043517529at_rat @ H @ T3 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_cong_left
% 4.71/5.16 thf(fact_7694_prod_Omono__neutral__cong__left,axiom,
% 4.71/5.16 ! [T3: set_o,S2: set_o,H: $o > nat,G2: $o > nat] :
% 4.71/5.16 ( ( finite_finite_o @ T3 )
% 4.71/5.16 => ( ( ord_less_eq_set_o @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: $o] :
% 4.71/5.16 ( ( member_o @ X4 @ ( minus_minus_set_o @ T3 @ S2 ) )
% 4.71/5.16 => ( ( H @ X4 )
% 4.71/5.16 = one_one_nat ) )
% 4.71/5.16 => ( ! [X4: $o] :
% 4.71/5.16 ( ( member_o @ X4 @ S2 )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = ( H @ X4 ) ) )
% 4.71/5.16 => ( ( groups3504817904513533571_o_nat @ G2 @ S2 )
% 4.71/5.16 = ( groups3504817904513533571_o_nat @ H @ T3 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_cong_left
% 4.71/5.16 thf(fact_7695_prod_Omono__neutral__cong__right,axiom,
% 4.71/5.16 ! [T3: set_o,S2: set_o,G2: $o > complex,H: $o > complex] :
% 4.71/5.16 ( ( finite_finite_o @ T3 )
% 4.71/5.16 => ( ( ord_less_eq_set_o @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: $o] :
% 4.71/5.16 ( ( member_o @ X4 @ ( minus_minus_set_o @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [X4: $o] :
% 4.71/5.16 ( ( member_o @ X4 @ S2 )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = ( H @ X4 ) ) )
% 4.71/5.16 => ( ( groups4859619685533338977omplex @ G2 @ T3 )
% 4.71/5.16 = ( groups4859619685533338977omplex @ H @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_cong_right
% 4.71/5.16 thf(fact_7696_prod_Omono__neutral__cong__right,axiom,
% 4.71/5.16 ! [T3: set_complex,S2: set_complex,G2: complex > complex,H: complex > complex] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ T3 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: complex] :
% 4.71/5.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [X4: complex] :
% 4.71/5.16 ( ( member_complex @ X4 @ S2 )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = ( H @ X4 ) ) )
% 4.71/5.16 => ( ( groups3708469109370488835omplex @ G2 @ T3 )
% 4.71/5.16 = ( groups3708469109370488835omplex @ H @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_cong_right
% 4.71/5.16 thf(fact_7697_prod_Omono__neutral__cong__right,axiom,
% 4.71/5.16 ! [T3: set_Extended_enat,S2: set_Extended_enat,G2: extended_enat > complex,H: extended_enat > complex] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ T3 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_complex ) )
% 4.71/5.16 => ( ! [X4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X4 @ S2 )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = ( H @ X4 ) ) )
% 4.71/5.16 => ( ( groups4622424608036095791omplex @ G2 @ T3 )
% 4.71/5.16 = ( groups4622424608036095791omplex @ H @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_cong_right
% 4.71/5.16 thf(fact_7698_prod_Omono__neutral__cong__right,axiom,
% 4.71/5.16 ! [T3: set_o,S2: set_o,G2: $o > real,H: $o > real] :
% 4.71/5.16 ( ( finite_finite_o @ T3 )
% 4.71/5.16 => ( ( ord_less_eq_set_o @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: $o] :
% 4.71/5.16 ( ( member_o @ X4 @ ( minus_minus_set_o @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_real ) )
% 4.71/5.16 => ( ! [X4: $o] :
% 4.71/5.16 ( ( member_o @ X4 @ S2 )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = ( H @ X4 ) ) )
% 4.71/5.16 => ( ( groups234877984723959775o_real @ G2 @ T3 )
% 4.71/5.16 = ( groups234877984723959775o_real @ H @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_cong_right
% 4.71/5.16 thf(fact_7699_prod_Omono__neutral__cong__right,axiom,
% 4.71/5.16 ! [T3: set_complex,S2: set_complex,G2: complex > real,H: complex > real] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ T3 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: complex] :
% 4.71/5.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_real ) )
% 4.71/5.16 => ( ! [X4: complex] :
% 4.71/5.16 ( ( member_complex @ X4 @ S2 )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = ( H @ X4 ) ) )
% 4.71/5.16 => ( ( groups766887009212190081x_real @ G2 @ T3 )
% 4.71/5.16 = ( groups766887009212190081x_real @ H @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_cong_right
% 4.71/5.16 thf(fact_7700_prod_Omono__neutral__cong__right,axiom,
% 4.71/5.16 ! [T3: set_Extended_enat,S2: set_Extended_enat,G2: extended_enat > real,H: extended_enat > real] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ T3 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_real ) )
% 4.71/5.16 => ( ! [X4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X4 @ S2 )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = ( H @ X4 ) ) )
% 4.71/5.16 => ( ( groups97031904164794029t_real @ G2 @ T3 )
% 4.71/5.16 = ( groups97031904164794029t_real @ H @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_cong_right
% 4.71/5.16 thf(fact_7701_prod_Omono__neutral__cong__right,axiom,
% 4.71/5.16 ! [T3: set_o,S2: set_o,G2: $o > rat,H: $o > rat] :
% 4.71/5.16 ( ( finite_finite_o @ T3 )
% 4.71/5.16 => ( ( ord_less_eq_set_o @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: $o] :
% 4.71/5.16 ( ( member_o @ X4 @ ( minus_minus_set_o @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_rat ) )
% 4.71/5.16 => ( ! [X4: $o] :
% 4.71/5.16 ( ( member_o @ X4 @ S2 )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = ( H @ X4 ) ) )
% 4.71/5.16 => ( ( groups2869687844427037835_o_rat @ G2 @ T3 )
% 4.71/5.16 = ( groups2869687844427037835_o_rat @ H @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_cong_right
% 4.71/5.16 thf(fact_7702_prod_Omono__neutral__cong__right,axiom,
% 4.71/5.16 ! [T3: set_complex,S2: set_complex,G2: complex > rat,H: complex > rat] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ T3 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: complex] :
% 4.71/5.16 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_rat ) )
% 4.71/5.16 => ( ! [X4: complex] :
% 4.71/5.16 ( ( member_complex @ X4 @ S2 )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = ( H @ X4 ) ) )
% 4.71/5.16 => ( ( groups225925009352817453ex_rat @ G2 @ T3 )
% 4.71/5.16 = ( groups225925009352817453ex_rat @ H @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_cong_right
% 4.71/5.16 thf(fact_7703_prod_Omono__neutral__cong__right,axiom,
% 4.71/5.16 ! [T3: set_Extended_enat,S2: set_Extended_enat,G2: extended_enat > rat,H: extended_enat > rat] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ T3 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X4 @ ( minus_925952699566721837d_enat @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_rat ) )
% 4.71/5.16 => ( ! [X4: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ X4 @ S2 )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = ( H @ X4 ) ) )
% 4.71/5.16 => ( ( groups2245840878043517529at_rat @ G2 @ T3 )
% 4.71/5.16 = ( groups2245840878043517529at_rat @ H @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_cong_right
% 4.71/5.16 thf(fact_7704_prod_Omono__neutral__cong__right,axiom,
% 4.71/5.16 ! [T3: set_o,S2: set_o,G2: $o > nat,H: $o > nat] :
% 4.71/5.16 ( ( finite_finite_o @ T3 )
% 4.71/5.16 => ( ( ord_less_eq_set_o @ S2 @ T3 )
% 4.71/5.16 => ( ! [X4: $o] :
% 4.71/5.16 ( ( member_o @ X4 @ ( minus_minus_set_o @ T3 @ S2 ) )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = one_one_nat ) )
% 4.71/5.16 => ( ! [X4: $o] :
% 4.71/5.16 ( ( member_o @ X4 @ S2 )
% 4.71/5.16 => ( ( G2 @ X4 )
% 4.71/5.16 = ( H @ X4 ) ) )
% 4.71/5.16 => ( ( groups3504817904513533571_o_nat @ G2 @ T3 )
% 4.71/5.16 = ( groups3504817904513533571_o_nat @ H @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.mono_neutral_cong_right
% 4.71/5.16 thf(fact_7705_prod__mono__strict,axiom,
% 4.71/5.16 ! [A2: set_complex,F: complex > real,G2: complex > real] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.16 => ( ! [I2: complex] :
% 4.71/5.16 ( ( member_complex @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_real @ ( F @ I2 ) @ ( G2 @ I2 ) ) ) )
% 4.71/5.16 => ( ( A2 != bot_bot_set_complex )
% 4.71/5.16 => ( ord_less_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono_strict
% 4.71/5.16 thf(fact_7706_prod__mono__strict,axiom,
% 4.71/5.16 ! [A2: set_Extended_enat,F: extended_enat > real,G2: extended_enat > real] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.16 => ( ! [I2: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_real @ ( F @ I2 ) @ ( G2 @ I2 ) ) ) )
% 4.71/5.16 => ( ( A2 != bot_bo7653980558646680370d_enat )
% 4.71/5.16 => ( ord_less_real @ ( groups97031904164794029t_real @ F @ A2 ) @ ( groups97031904164794029t_real @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono_strict
% 4.71/5.16 thf(fact_7707_prod__mono__strict,axiom,
% 4.71/5.16 ! [A2: set_real,F: real > real,G2: real > real] :
% 4.71/5.16 ( ( finite_finite_real @ A2 )
% 4.71/5.16 => ( ! [I2: real] :
% 4.71/5.16 ( ( member_real @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_real @ ( F @ I2 ) @ ( G2 @ I2 ) ) ) )
% 4.71/5.16 => ( ( A2 != bot_bot_set_real )
% 4.71/5.16 => ( ord_less_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono_strict
% 4.71/5.16 thf(fact_7708_prod__mono__strict,axiom,
% 4.71/5.16 ! [A2: set_o,F: $o > real,G2: $o > real] :
% 4.71/5.16 ( ( finite_finite_o @ A2 )
% 4.71/5.16 => ( ! [I2: $o] :
% 4.71/5.16 ( ( member_o @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_real @ ( F @ I2 ) @ ( G2 @ I2 ) ) ) )
% 4.71/5.16 => ( ( A2 != bot_bot_set_o )
% 4.71/5.16 => ( ord_less_real @ ( groups234877984723959775o_real @ F @ A2 ) @ ( groups234877984723959775o_real @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono_strict
% 4.71/5.16 thf(fact_7709_prod__mono__strict,axiom,
% 4.71/5.16 ! [A2: set_nat,F: nat > real,G2: nat > real] :
% 4.71/5.16 ( ( finite_finite_nat @ A2 )
% 4.71/5.16 => ( ! [I2: nat] :
% 4.71/5.16 ( ( member_nat @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_real @ ( F @ I2 ) @ ( G2 @ I2 ) ) ) )
% 4.71/5.16 => ( ( A2 != bot_bot_set_nat )
% 4.71/5.16 => ( ord_less_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono_strict
% 4.71/5.16 thf(fact_7710_prod__mono__strict,axiom,
% 4.71/5.16 ! [A2: set_int,F: int > real,G2: int > real] :
% 4.71/5.16 ( ( finite_finite_int @ A2 )
% 4.71/5.16 => ( ! [I2: int] :
% 4.71/5.16 ( ( member_int @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_real @ ( F @ I2 ) @ ( G2 @ I2 ) ) ) )
% 4.71/5.16 => ( ( A2 != bot_bot_set_int )
% 4.71/5.16 => ( ord_less_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono_strict
% 4.71/5.16 thf(fact_7711_prod__mono__strict,axiom,
% 4.71/5.16 ! [A2: set_complex,F: complex > rat,G2: complex > rat] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.16 => ( ! [I2: complex] :
% 4.71/5.16 ( ( member_complex @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_rat @ ( F @ I2 ) @ ( G2 @ I2 ) ) ) )
% 4.71/5.16 => ( ( A2 != bot_bot_set_complex )
% 4.71/5.16 => ( ord_less_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( groups225925009352817453ex_rat @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono_strict
% 4.71/5.16 thf(fact_7712_prod__mono__strict,axiom,
% 4.71/5.16 ! [A2: set_Extended_enat,F: extended_enat > rat,G2: extended_enat > rat] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.16 => ( ! [I2: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_rat @ ( F @ I2 ) @ ( G2 @ I2 ) ) ) )
% 4.71/5.16 => ( ( A2 != bot_bo7653980558646680370d_enat )
% 4.71/5.16 => ( ord_less_rat @ ( groups2245840878043517529at_rat @ F @ A2 ) @ ( groups2245840878043517529at_rat @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono_strict
% 4.71/5.16 thf(fact_7713_prod__mono__strict,axiom,
% 4.71/5.16 ! [A2: set_real,F: real > rat,G2: real > rat] :
% 4.71/5.16 ( ( finite_finite_real @ A2 )
% 4.71/5.16 => ( ! [I2: real] :
% 4.71/5.16 ( ( member_real @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_rat @ ( F @ I2 ) @ ( G2 @ I2 ) ) ) )
% 4.71/5.16 => ( ( A2 != bot_bot_set_real )
% 4.71/5.16 => ( ord_less_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono_strict
% 4.71/5.16 thf(fact_7714_prod__mono__strict,axiom,
% 4.71/5.16 ! [A2: set_o,F: $o > rat,G2: $o > rat] :
% 4.71/5.16 ( ( finite_finite_o @ A2 )
% 4.71/5.16 => ( ! [I2: $o] :
% 4.71/5.16 ( ( member_o @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_rat @ ( F @ I2 ) @ ( G2 @ I2 ) ) ) )
% 4.71/5.16 => ( ( A2 != bot_bot_set_o )
% 4.71/5.16 => ( ord_less_rat @ ( groups2869687844427037835_o_rat @ F @ A2 ) @ ( groups2869687844427037835_o_rat @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono_strict
% 4.71/5.16 thf(fact_7715_prod_Oinsert__remove,axiom,
% 4.71/5.16 ! [A2: set_complex,G2: complex > real,X: complex] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.16 => ( ( groups766887009212190081x_real @ G2 @ ( insert_complex @ X @ A2 ) )
% 4.71/5.16 = ( times_times_real @ ( G2 @ X ) @ ( groups766887009212190081x_real @ G2 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.insert_remove
% 4.71/5.16 thf(fact_7716_prod_Oinsert__remove,axiom,
% 4.71/5.16 ! [A2: set_Extended_enat,G2: extended_enat > real,X: extended_enat] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.16 => ( ( groups97031904164794029t_real @ G2 @ ( insert_Extended_enat @ X @ A2 ) )
% 4.71/5.16 = ( times_times_real @ ( G2 @ X ) @ ( groups97031904164794029t_real @ G2 @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.insert_remove
% 4.71/5.16 thf(fact_7717_prod_Oinsert__remove,axiom,
% 4.71/5.16 ! [A2: set_real,G2: real > real,X: real] :
% 4.71/5.16 ( ( finite_finite_real @ A2 )
% 4.71/5.16 => ( ( groups1681761925125756287l_real @ G2 @ ( insert_real @ X @ A2 ) )
% 4.71/5.16 = ( times_times_real @ ( G2 @ X ) @ ( groups1681761925125756287l_real @ G2 @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.insert_remove
% 4.71/5.16 thf(fact_7718_prod_Oinsert__remove,axiom,
% 4.71/5.16 ! [A2: set_o,G2: $o > real,X: $o] :
% 4.71/5.16 ( ( finite_finite_o @ A2 )
% 4.71/5.16 => ( ( groups234877984723959775o_real @ G2 @ ( insert_o @ X @ A2 ) )
% 4.71/5.16 = ( times_times_real @ ( G2 @ X ) @ ( groups234877984723959775o_real @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.insert_remove
% 4.71/5.16 thf(fact_7719_prod_Oinsert__remove,axiom,
% 4.71/5.16 ! [A2: set_int,G2: int > real,X: int] :
% 4.71/5.16 ( ( finite_finite_int @ A2 )
% 4.71/5.16 => ( ( groups2316167850115554303t_real @ G2 @ ( insert_int @ X @ A2 ) )
% 4.71/5.16 = ( times_times_real @ ( G2 @ X ) @ ( groups2316167850115554303t_real @ G2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.insert_remove
% 4.71/5.16 thf(fact_7720_prod_Oinsert__remove,axiom,
% 4.71/5.16 ! [A2: set_nat,G2: nat > real,X: nat] :
% 4.71/5.16 ( ( finite_finite_nat @ A2 )
% 4.71/5.16 => ( ( groups129246275422532515t_real @ G2 @ ( insert_nat @ X @ A2 ) )
% 4.71/5.16 = ( times_times_real @ ( G2 @ X ) @ ( groups129246275422532515t_real @ G2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.insert_remove
% 4.71/5.16 thf(fact_7721_prod_Oinsert__remove,axiom,
% 4.71/5.16 ! [A2: set_complex,G2: complex > rat,X: complex] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.16 => ( ( groups225925009352817453ex_rat @ G2 @ ( insert_complex @ X @ A2 ) )
% 4.71/5.16 = ( times_times_rat @ ( G2 @ X ) @ ( groups225925009352817453ex_rat @ G2 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.insert_remove
% 4.71/5.16 thf(fact_7722_prod_Oinsert__remove,axiom,
% 4.71/5.16 ! [A2: set_Extended_enat,G2: extended_enat > rat,X: extended_enat] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.16 => ( ( groups2245840878043517529at_rat @ G2 @ ( insert_Extended_enat @ X @ A2 ) )
% 4.71/5.16 = ( times_times_rat @ ( G2 @ X ) @ ( groups2245840878043517529at_rat @ G2 @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.insert_remove
% 4.71/5.16 thf(fact_7723_prod_Oinsert__remove,axiom,
% 4.71/5.16 ! [A2: set_real,G2: real > rat,X: real] :
% 4.71/5.16 ( ( finite_finite_real @ A2 )
% 4.71/5.16 => ( ( groups4061424788464935467al_rat @ G2 @ ( insert_real @ X @ A2 ) )
% 4.71/5.16 = ( times_times_rat @ ( G2 @ X ) @ ( groups4061424788464935467al_rat @ G2 @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.insert_remove
% 4.71/5.16 thf(fact_7724_prod_Oinsert__remove,axiom,
% 4.71/5.16 ! [A2: set_o,G2: $o > rat,X: $o] :
% 4.71/5.16 ( ( finite_finite_o @ A2 )
% 4.71/5.16 => ( ( groups2869687844427037835_o_rat @ G2 @ ( insert_o @ X @ A2 ) )
% 4.71/5.16 = ( times_times_rat @ ( G2 @ X ) @ ( groups2869687844427037835_o_rat @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.insert_remove
% 4.71/5.16 thf(fact_7725_prod_Oremove,axiom,
% 4.71/5.16 ! [A2: set_complex,X: complex,G2: complex > real] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.16 => ( ( member_complex @ X @ A2 )
% 4.71/5.16 => ( ( groups766887009212190081x_real @ G2 @ A2 )
% 4.71/5.16 = ( times_times_real @ ( G2 @ X ) @ ( groups766887009212190081x_real @ G2 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.remove
% 4.71/5.16 thf(fact_7726_prod_Oremove,axiom,
% 4.71/5.16 ! [A2: set_Extended_enat,X: extended_enat,G2: extended_enat > real] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.16 => ( ( member_Extended_enat @ X @ A2 )
% 4.71/5.16 => ( ( groups97031904164794029t_real @ G2 @ A2 )
% 4.71/5.16 = ( times_times_real @ ( G2 @ X ) @ ( groups97031904164794029t_real @ G2 @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.remove
% 4.71/5.16 thf(fact_7727_prod_Oremove,axiom,
% 4.71/5.16 ! [A2: set_real,X: real,G2: real > real] :
% 4.71/5.16 ( ( finite_finite_real @ A2 )
% 4.71/5.16 => ( ( member_real @ X @ A2 )
% 4.71/5.16 => ( ( groups1681761925125756287l_real @ G2 @ A2 )
% 4.71/5.16 = ( times_times_real @ ( G2 @ X ) @ ( groups1681761925125756287l_real @ G2 @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.remove
% 4.71/5.16 thf(fact_7728_prod_Oremove,axiom,
% 4.71/5.16 ! [A2: set_o,X: $o,G2: $o > real] :
% 4.71/5.16 ( ( finite_finite_o @ A2 )
% 4.71/5.16 => ( ( member_o @ X @ A2 )
% 4.71/5.16 => ( ( groups234877984723959775o_real @ G2 @ A2 )
% 4.71/5.16 = ( times_times_real @ ( G2 @ X ) @ ( groups234877984723959775o_real @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.remove
% 4.71/5.16 thf(fact_7729_prod_Oremove,axiom,
% 4.71/5.16 ! [A2: set_int,X: int,G2: int > real] :
% 4.71/5.16 ( ( finite_finite_int @ A2 )
% 4.71/5.16 => ( ( member_int @ X @ A2 )
% 4.71/5.16 => ( ( groups2316167850115554303t_real @ G2 @ A2 )
% 4.71/5.16 = ( times_times_real @ ( G2 @ X ) @ ( groups2316167850115554303t_real @ G2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.remove
% 4.71/5.16 thf(fact_7730_prod_Oremove,axiom,
% 4.71/5.16 ! [A2: set_nat,X: nat,G2: nat > real] :
% 4.71/5.16 ( ( finite_finite_nat @ A2 )
% 4.71/5.16 => ( ( member_nat @ X @ A2 )
% 4.71/5.16 => ( ( groups129246275422532515t_real @ G2 @ A2 )
% 4.71/5.16 = ( times_times_real @ ( G2 @ X ) @ ( groups129246275422532515t_real @ G2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.remove
% 4.71/5.16 thf(fact_7731_prod_Oremove,axiom,
% 4.71/5.16 ! [A2: set_complex,X: complex,G2: complex > rat] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.16 => ( ( member_complex @ X @ A2 )
% 4.71/5.16 => ( ( groups225925009352817453ex_rat @ G2 @ A2 )
% 4.71/5.16 = ( times_times_rat @ ( G2 @ X ) @ ( groups225925009352817453ex_rat @ G2 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.remove
% 4.71/5.16 thf(fact_7732_prod_Oremove,axiom,
% 4.71/5.16 ! [A2: set_Extended_enat,X: extended_enat,G2: extended_enat > rat] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.16 => ( ( member_Extended_enat @ X @ A2 )
% 4.71/5.16 => ( ( groups2245840878043517529at_rat @ G2 @ A2 )
% 4.71/5.16 = ( times_times_rat @ ( G2 @ X ) @ ( groups2245840878043517529at_rat @ G2 @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ X @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.remove
% 4.71/5.16 thf(fact_7733_prod_Oremove,axiom,
% 4.71/5.16 ! [A2: set_real,X: real,G2: real > rat] :
% 4.71/5.16 ( ( finite_finite_real @ A2 )
% 4.71/5.16 => ( ( member_real @ X @ A2 )
% 4.71/5.16 => ( ( groups4061424788464935467al_rat @ G2 @ A2 )
% 4.71/5.16 = ( times_times_rat @ ( G2 @ X ) @ ( groups4061424788464935467al_rat @ G2 @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.remove
% 4.71/5.16 thf(fact_7734_prod_Oremove,axiom,
% 4.71/5.16 ! [A2: set_o,X: $o,G2: $o > rat] :
% 4.71/5.16 ( ( finite_finite_o @ A2 )
% 4.71/5.16 => ( ( member_o @ X @ A2 )
% 4.71/5.16 => ( ( groups2869687844427037835_o_rat @ G2 @ A2 )
% 4.71/5.16 = ( times_times_rat @ ( G2 @ X ) @ ( groups2869687844427037835_o_rat @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.remove
% 4.71/5.16 thf(fact_7735_prod_Odelta__remove,axiom,
% 4.71/5.16 ! [S2: set_complex,A: complex,B: complex > real,C: complex > real] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ S2 )
% 4.71/5.16 => ( ( ( member_complex @ A @ S2 )
% 4.71/5.16 => ( ( groups766887009212190081x_real
% 4.71/5.16 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( times_times_real @ ( B @ A ) @ ( groups766887009212190081x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 4.71/5.16 & ( ~ ( member_complex @ A @ S2 )
% 4.71/5.16 => ( ( groups766887009212190081x_real
% 4.71/5.16 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( groups766887009212190081x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.delta_remove
% 4.71/5.16 thf(fact_7736_prod_Odelta__remove,axiom,
% 4.71/5.16 ! [S2: set_Extended_enat,A: extended_enat,B: extended_enat > real,C: extended_enat > real] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.16 => ( ( ( member_Extended_enat @ A @ S2 )
% 4.71/5.16 => ( ( groups97031904164794029t_real
% 4.71/5.16 @ ^ [K3: extended_enat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( times_times_real @ ( B @ A ) @ ( groups97031904164794029t_real @ C @ ( minus_925952699566721837d_enat @ S2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ) ) ) )
% 4.71/5.16 & ( ~ ( member_Extended_enat @ A @ S2 )
% 4.71/5.16 => ( ( groups97031904164794029t_real
% 4.71/5.16 @ ^ [K3: extended_enat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( groups97031904164794029t_real @ C @ ( minus_925952699566721837d_enat @ S2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.delta_remove
% 4.71/5.16 thf(fact_7737_prod_Odelta__remove,axiom,
% 4.71/5.16 ! [S2: set_real,A: real,B: real > real,C: real > real] :
% 4.71/5.16 ( ( finite_finite_real @ S2 )
% 4.71/5.16 => ( ( ( member_real @ A @ S2 )
% 4.71/5.16 => ( ( groups1681761925125756287l_real
% 4.71/5.16 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( times_times_real @ ( B @ A ) @ ( groups1681761925125756287l_real @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 4.71/5.16 & ( ~ ( member_real @ A @ S2 )
% 4.71/5.16 => ( ( groups1681761925125756287l_real
% 4.71/5.16 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( groups1681761925125756287l_real @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.delta_remove
% 4.71/5.16 thf(fact_7738_prod_Odelta__remove,axiom,
% 4.71/5.16 ! [S2: set_o,A: $o,B: $o > real,C: $o > real] :
% 4.71/5.16 ( ( finite_finite_o @ S2 )
% 4.71/5.16 => ( ( ( member_o @ A @ S2 )
% 4.71/5.16 => ( ( groups234877984723959775o_real
% 4.71/5.16 @ ^ [K3: $o] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( times_times_real @ ( B @ A ) @ ( groups234877984723959775o_real @ C @ ( minus_minus_set_o @ S2 @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 4.71/5.16 & ( ~ ( member_o @ A @ S2 )
% 4.71/5.16 => ( ( groups234877984723959775o_real
% 4.71/5.16 @ ^ [K3: $o] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( groups234877984723959775o_real @ C @ ( minus_minus_set_o @ S2 @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.delta_remove
% 4.71/5.16 thf(fact_7739_prod_Odelta__remove,axiom,
% 4.71/5.16 ! [S2: set_int,A: int,B: int > real,C: int > real] :
% 4.71/5.16 ( ( finite_finite_int @ S2 )
% 4.71/5.16 => ( ( ( member_int @ A @ S2 )
% 4.71/5.16 => ( ( groups2316167850115554303t_real
% 4.71/5.16 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( times_times_real @ ( B @ A ) @ ( groups2316167850115554303t_real @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 4.71/5.16 & ( ~ ( member_int @ A @ S2 )
% 4.71/5.16 => ( ( groups2316167850115554303t_real
% 4.71/5.16 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( groups2316167850115554303t_real @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.delta_remove
% 4.71/5.16 thf(fact_7740_prod_Odelta__remove,axiom,
% 4.71/5.16 ! [S2: set_nat,A: nat,B: nat > real,C: nat > real] :
% 4.71/5.16 ( ( finite_finite_nat @ S2 )
% 4.71/5.16 => ( ( ( member_nat @ A @ S2 )
% 4.71/5.16 => ( ( groups129246275422532515t_real
% 4.71/5.16 @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( times_times_real @ ( B @ A ) @ ( groups129246275422532515t_real @ C @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 4.71/5.16 & ( ~ ( member_nat @ A @ S2 )
% 4.71/5.16 => ( ( groups129246275422532515t_real
% 4.71/5.16 @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( groups129246275422532515t_real @ C @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.delta_remove
% 4.71/5.16 thf(fact_7741_prod_Odelta__remove,axiom,
% 4.71/5.16 ! [S2: set_complex,A: complex,B: complex > rat,C: complex > rat] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ S2 )
% 4.71/5.16 => ( ( ( member_complex @ A @ S2 )
% 4.71/5.16 => ( ( groups225925009352817453ex_rat
% 4.71/5.16 @ ^ [K3: complex] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( times_times_rat @ ( B @ A ) @ ( groups225925009352817453ex_rat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 4.71/5.16 & ( ~ ( member_complex @ A @ S2 )
% 4.71/5.16 => ( ( groups225925009352817453ex_rat
% 4.71/5.16 @ ^ [K3: complex] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( groups225925009352817453ex_rat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.delta_remove
% 4.71/5.16 thf(fact_7742_prod_Odelta__remove,axiom,
% 4.71/5.16 ! [S2: set_Extended_enat,A: extended_enat,B: extended_enat > rat,C: extended_enat > rat] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.16 => ( ( ( member_Extended_enat @ A @ S2 )
% 4.71/5.16 => ( ( groups2245840878043517529at_rat
% 4.71/5.16 @ ^ [K3: extended_enat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( times_times_rat @ ( B @ A ) @ ( groups2245840878043517529at_rat @ C @ ( minus_925952699566721837d_enat @ S2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ) ) ) )
% 4.71/5.16 & ( ~ ( member_Extended_enat @ A @ S2 )
% 4.71/5.16 => ( ( groups2245840878043517529at_rat
% 4.71/5.16 @ ^ [K3: extended_enat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( groups2245840878043517529at_rat @ C @ ( minus_925952699566721837d_enat @ S2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.delta_remove
% 4.71/5.16 thf(fact_7743_prod_Odelta__remove,axiom,
% 4.71/5.16 ! [S2: set_real,A: real,B: real > rat,C: real > rat] :
% 4.71/5.16 ( ( finite_finite_real @ S2 )
% 4.71/5.16 => ( ( ( member_real @ A @ S2 )
% 4.71/5.16 => ( ( groups4061424788464935467al_rat
% 4.71/5.16 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( times_times_rat @ ( B @ A ) @ ( groups4061424788464935467al_rat @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 4.71/5.16 & ( ~ ( member_real @ A @ S2 )
% 4.71/5.16 => ( ( groups4061424788464935467al_rat
% 4.71/5.16 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( groups4061424788464935467al_rat @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.delta_remove
% 4.71/5.16 thf(fact_7744_prod_Odelta__remove,axiom,
% 4.71/5.16 ! [S2: set_o,A: $o,B: $o > rat,C: $o > rat] :
% 4.71/5.16 ( ( finite_finite_o @ S2 )
% 4.71/5.16 => ( ( ( member_o @ A @ S2 )
% 4.71/5.16 => ( ( groups2869687844427037835_o_rat
% 4.71/5.16 @ ^ [K3: $o] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( times_times_rat @ ( B @ A ) @ ( groups2869687844427037835_o_rat @ C @ ( minus_minus_set_o @ S2 @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 4.71/5.16 & ( ~ ( member_o @ A @ S2 )
% 4.71/5.16 => ( ( groups2869687844427037835_o_rat
% 4.71/5.16 @ ^ [K3: $o] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( groups2869687844427037835_o_rat @ C @ ( minus_minus_set_o @ S2 @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod.delta_remove
% 4.71/5.16 thf(fact_7745_prod__mono2,axiom,
% 4.71/5.16 ! [B2: set_o,A2: set_o,F: $o > real] :
% 4.71/5.16 ( ( finite_finite_o @ B2 )
% 4.71/5.16 => ( ( ord_less_eq_set_o @ A2 @ B2 )
% 4.71/5.16 => ( ! [B5: $o] :
% 4.71/5.16 ( ( member_o @ B5 @ ( minus_minus_set_o @ B2 @ A2 ) )
% 4.71/5.16 => ( ord_less_eq_real @ one_one_real @ ( F @ B5 ) ) )
% 4.71/5.16 => ( ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ A2 )
% 4.71/5.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A5 ) ) )
% 4.71/5.16 => ( ord_less_eq_real @ ( groups234877984723959775o_real @ F @ A2 ) @ ( groups234877984723959775o_real @ F @ B2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono2
% 4.71/5.16 thf(fact_7746_prod__mono2,axiom,
% 4.71/5.16 ! [B2: set_complex,A2: set_complex,F: complex > real] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ B2 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 4.71/5.16 => ( ! [B5: complex] :
% 4.71/5.16 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 4.71/5.16 => ( ord_less_eq_real @ one_one_real @ ( F @ B5 ) ) )
% 4.71/5.16 => ( ! [A5: complex] :
% 4.71/5.16 ( ( member_complex @ A5 @ A2 )
% 4.71/5.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A5 ) ) )
% 4.71/5.16 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ F @ B2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono2
% 4.71/5.16 thf(fact_7747_prod__mono2,axiom,
% 4.71/5.16 ! [B2: set_Extended_enat,A2: set_Extended_enat,F: extended_enat > real] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ B2 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ A2 @ B2 )
% 4.71/5.16 => ( ! [B5: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ B5 @ ( minus_925952699566721837d_enat @ B2 @ A2 ) )
% 4.71/5.16 => ( ord_less_eq_real @ one_one_real @ ( F @ B5 ) ) )
% 4.71/5.16 => ( ! [A5: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ A5 @ A2 )
% 4.71/5.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A5 ) ) )
% 4.71/5.16 => ( ord_less_eq_real @ ( groups97031904164794029t_real @ F @ A2 ) @ ( groups97031904164794029t_real @ F @ B2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono2
% 4.71/5.16 thf(fact_7748_prod__mono2,axiom,
% 4.71/5.16 ! [B2: set_nat,A2: set_nat,F: nat > real] :
% 4.71/5.16 ( ( finite_finite_nat @ B2 )
% 4.71/5.16 => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 4.71/5.16 => ( ! [B5: nat] :
% 4.71/5.16 ( ( member_nat @ B5 @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 4.71/5.16 => ( ord_less_eq_real @ one_one_real @ ( F @ B5 ) ) )
% 4.71/5.16 => ( ! [A5: nat] :
% 4.71/5.16 ( ( member_nat @ A5 @ A2 )
% 4.71/5.16 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A5 ) ) )
% 4.71/5.16 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ F @ B2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono2
% 4.71/5.16 thf(fact_7749_prod__mono2,axiom,
% 4.71/5.16 ! [B2: set_o,A2: set_o,F: $o > rat] :
% 4.71/5.16 ( ( finite_finite_o @ B2 )
% 4.71/5.16 => ( ( ord_less_eq_set_o @ A2 @ B2 )
% 4.71/5.16 => ( ! [B5: $o] :
% 4.71/5.16 ( ( member_o @ B5 @ ( minus_minus_set_o @ B2 @ A2 ) )
% 4.71/5.16 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B5 ) ) )
% 4.71/5.16 => ( ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ A2 )
% 4.71/5.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A5 ) ) )
% 4.71/5.16 => ( ord_less_eq_rat @ ( groups2869687844427037835_o_rat @ F @ A2 ) @ ( groups2869687844427037835_o_rat @ F @ B2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono2
% 4.71/5.16 thf(fact_7750_prod__mono2,axiom,
% 4.71/5.16 ! [B2: set_complex,A2: set_complex,F: complex > rat] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ B2 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 4.71/5.16 => ( ! [B5: complex] :
% 4.71/5.16 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 4.71/5.16 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B5 ) ) )
% 4.71/5.16 => ( ! [A5: complex] :
% 4.71/5.16 ( ( member_complex @ A5 @ A2 )
% 4.71/5.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A5 ) ) )
% 4.71/5.16 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( groups225925009352817453ex_rat @ F @ B2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono2
% 4.71/5.16 thf(fact_7751_prod__mono2,axiom,
% 4.71/5.16 ! [B2: set_Extended_enat,A2: set_Extended_enat,F: extended_enat > rat] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ B2 )
% 4.71/5.16 => ( ( ord_le7203529160286727270d_enat @ A2 @ B2 )
% 4.71/5.16 => ( ! [B5: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ B5 @ ( minus_925952699566721837d_enat @ B2 @ A2 ) )
% 4.71/5.16 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B5 ) ) )
% 4.71/5.16 => ( ! [A5: extended_enat] :
% 4.71/5.16 ( ( member_Extended_enat @ A5 @ A2 )
% 4.71/5.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A5 ) ) )
% 4.71/5.16 => ( ord_less_eq_rat @ ( groups2245840878043517529at_rat @ F @ A2 ) @ ( groups2245840878043517529at_rat @ F @ B2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono2
% 4.71/5.16 thf(fact_7752_prod__mono2,axiom,
% 4.71/5.16 ! [B2: set_nat,A2: set_nat,F: nat > rat] :
% 4.71/5.16 ( ( finite_finite_nat @ B2 )
% 4.71/5.16 => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 4.71/5.16 => ( ! [B5: nat] :
% 4.71/5.16 ( ( member_nat @ B5 @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 4.71/5.16 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B5 ) ) )
% 4.71/5.16 => ( ! [A5: nat] :
% 4.71/5.16 ( ( member_nat @ A5 @ A2 )
% 4.71/5.16 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A5 ) ) )
% 4.71/5.16 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ F @ B2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono2
% 4.71/5.16 thf(fact_7753_prod__mono2,axiom,
% 4.71/5.16 ! [B2: set_o,A2: set_o,F: $o > int] :
% 4.71/5.16 ( ( finite_finite_o @ B2 )
% 4.71/5.16 => ( ( ord_less_eq_set_o @ A2 @ B2 )
% 4.71/5.16 => ( ! [B5: $o] :
% 4.71/5.16 ( ( member_o @ B5 @ ( minus_minus_set_o @ B2 @ A2 ) )
% 4.71/5.16 => ( ord_less_eq_int @ one_one_int @ ( F @ B5 ) ) )
% 4.71/5.16 => ( ! [A5: $o] :
% 4.71/5.16 ( ( member_o @ A5 @ A2 )
% 4.71/5.16 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A5 ) ) )
% 4.71/5.16 => ( ord_less_eq_int @ ( groups3502327434004483295_o_int @ F @ A2 ) @ ( groups3502327434004483295_o_int @ F @ B2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono2
% 4.71/5.16 thf(fact_7754_prod__mono2,axiom,
% 4.71/5.16 ! [B2: set_complex,A2: set_complex,F: complex > int] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ B2 )
% 4.71/5.16 => ( ( ord_le211207098394363844omplex @ A2 @ B2 )
% 4.71/5.16 => ( ! [B5: complex] :
% 4.71/5.16 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B2 @ A2 ) )
% 4.71/5.16 => ( ord_less_eq_int @ one_one_int @ ( F @ B5 ) ) )
% 4.71/5.16 => ( ! [A5: complex] :
% 4.71/5.16 ( ( member_complex @ A5 @ A2 )
% 4.71/5.16 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A5 ) ) )
% 4.71/5.16 => ( ord_less_eq_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( groups858564598930262913ex_int @ F @ B2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_mono2
% 4.71/5.16 thf(fact_7755_prod__le__power,axiom,
% 4.71/5.16 ! [A2: set_o,F: $o > real,N: real,K: nat] :
% 4.71/5.16 ( ! [I2: $o] :
% 4.71/5.16 ( ( member_o @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_eq_real @ ( F @ I2 ) @ N ) ) )
% 4.71/5.16 => ( ( ord_less_eq_nat @ ( finite_card_o @ A2 ) @ K )
% 4.71/5.16 => ( ( ord_less_eq_real @ one_one_real @ N )
% 4.71/5.16 => ( ord_less_eq_real @ ( groups234877984723959775o_real @ F @ A2 ) @ ( power_power_real @ N @ K ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_le_power
% 4.71/5.16 thf(fact_7756_prod__le__power,axiom,
% 4.71/5.16 ! [A2: set_complex,F: complex > real,N: real,K: nat] :
% 4.71/5.16 ( ! [I2: complex] :
% 4.71/5.16 ( ( member_complex @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_eq_real @ ( F @ I2 ) @ N ) ) )
% 4.71/5.16 => ( ( ord_less_eq_nat @ ( finite_card_complex @ A2 ) @ K )
% 4.71/5.16 => ( ( ord_less_eq_real @ one_one_real @ N )
% 4.71/5.16 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( power_power_real @ N @ K ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_le_power
% 4.71/5.16 thf(fact_7757_prod__le__power,axiom,
% 4.71/5.16 ! [A2: set_nat,F: nat > real,N: real,K: nat] :
% 4.71/5.16 ( ! [I2: nat] :
% 4.71/5.16 ( ( member_nat @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_eq_real @ ( F @ I2 ) @ N ) ) )
% 4.71/5.16 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A2 ) @ K )
% 4.71/5.16 => ( ( ord_less_eq_real @ one_one_real @ N )
% 4.71/5.16 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( power_power_real @ N @ K ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_le_power
% 4.71/5.16 thf(fact_7758_prod__le__power,axiom,
% 4.71/5.16 ! [A2: set_int,F: int > real,N: real,K: nat] :
% 4.71/5.16 ( ! [I2: int] :
% 4.71/5.16 ( ( member_int @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_eq_real @ ( F @ I2 ) @ N ) ) )
% 4.71/5.16 => ( ( ord_less_eq_nat @ ( finite_card_int @ A2 ) @ K )
% 4.71/5.16 => ( ( ord_less_eq_real @ one_one_real @ N )
% 4.71/5.16 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( power_power_real @ N @ K ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_le_power
% 4.71/5.16 thf(fact_7759_prod__le__power,axiom,
% 4.71/5.16 ! [A2: set_o,F: $o > rat,N: rat,K: nat] :
% 4.71/5.16 ( ! [I2: $o] :
% 4.71/5.16 ( ( member_o @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_eq_rat @ ( F @ I2 ) @ N ) ) )
% 4.71/5.16 => ( ( ord_less_eq_nat @ ( finite_card_o @ A2 ) @ K )
% 4.71/5.16 => ( ( ord_less_eq_rat @ one_one_rat @ N )
% 4.71/5.16 => ( ord_less_eq_rat @ ( groups2869687844427037835_o_rat @ F @ A2 ) @ ( power_power_rat @ N @ K ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_le_power
% 4.71/5.16 thf(fact_7760_prod__le__power,axiom,
% 4.71/5.16 ! [A2: set_complex,F: complex > rat,N: rat,K: nat] :
% 4.71/5.16 ( ! [I2: complex] :
% 4.71/5.16 ( ( member_complex @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_eq_rat @ ( F @ I2 ) @ N ) ) )
% 4.71/5.16 => ( ( ord_less_eq_nat @ ( finite_card_complex @ A2 ) @ K )
% 4.71/5.16 => ( ( ord_less_eq_rat @ one_one_rat @ N )
% 4.71/5.16 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( power_power_rat @ N @ K ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_le_power
% 4.71/5.16 thf(fact_7761_prod__le__power,axiom,
% 4.71/5.16 ! [A2: set_nat,F: nat > rat,N: rat,K: nat] :
% 4.71/5.16 ( ! [I2: nat] :
% 4.71/5.16 ( ( member_nat @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_eq_rat @ ( F @ I2 ) @ N ) ) )
% 4.71/5.16 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A2 ) @ K )
% 4.71/5.16 => ( ( ord_less_eq_rat @ one_one_rat @ N )
% 4.71/5.16 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( power_power_rat @ N @ K ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_le_power
% 4.71/5.16 thf(fact_7762_prod__le__power,axiom,
% 4.71/5.16 ! [A2: set_int,F: int > rat,N: rat,K: nat] :
% 4.71/5.16 ( ! [I2: int] :
% 4.71/5.16 ( ( member_int @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_eq_rat @ ( F @ I2 ) @ N ) ) )
% 4.71/5.16 => ( ( ord_less_eq_nat @ ( finite_card_int @ A2 ) @ K )
% 4.71/5.16 => ( ( ord_less_eq_rat @ one_one_rat @ N )
% 4.71/5.16 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( power_power_rat @ N @ K ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_le_power
% 4.71/5.16 thf(fact_7763_prod__le__power,axiom,
% 4.71/5.16 ! [A2: set_o,F: $o > nat,N: nat,K: nat] :
% 4.71/5.16 ( ! [I2: $o] :
% 4.71/5.16 ( ( member_o @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_eq_nat @ ( F @ I2 ) @ N ) ) )
% 4.71/5.16 => ( ( ord_less_eq_nat @ ( finite_card_o @ A2 ) @ K )
% 4.71/5.16 => ( ( ord_less_eq_nat @ one_one_nat @ N )
% 4.71/5.16 => ( ord_less_eq_nat @ ( groups3504817904513533571_o_nat @ F @ A2 ) @ ( power_power_nat @ N @ K ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_le_power
% 4.71/5.16 thf(fact_7764_prod__le__power,axiom,
% 4.71/5.16 ! [A2: set_complex,F: complex > nat,N: nat,K: nat] :
% 4.71/5.16 ( ! [I2: complex] :
% 4.71/5.16 ( ( member_complex @ I2 @ A2 )
% 4.71/5.16 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) )
% 4.71/5.16 & ( ord_less_eq_nat @ ( F @ I2 ) @ N ) ) )
% 4.71/5.16 => ( ( ord_less_eq_nat @ ( finite_card_complex @ A2 ) @ K )
% 4.71/5.16 => ( ( ord_less_eq_nat @ one_one_nat @ N )
% 4.71/5.16 => ( ord_less_eq_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ ( power_power_nat @ N @ K ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_le_power
% 4.71/5.16 thf(fact_7765_prod__diff1,axiom,
% 4.71/5.16 ! [A2: set_complex,F: complex > rat,A: complex] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.16 => ( ( ( F @ A )
% 4.71/5.16 != zero_zero_rat )
% 4.71/5.16 => ( ( ( member_complex @ A @ A2 )
% 4.71/5.16 => ( ( groups225925009352817453ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 4.71/5.16 = ( divide_divide_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 4.71/5.16 & ( ~ ( member_complex @ A @ A2 )
% 4.71/5.16 => ( ( groups225925009352817453ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 4.71/5.16 = ( groups225925009352817453ex_rat @ F @ A2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_diff1
% 4.71/5.16 thf(fact_7766_prod__diff1,axiom,
% 4.71/5.16 ! [A2: set_Extended_enat,F: extended_enat > rat,A: extended_enat] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.16 => ( ( ( F @ A )
% 4.71/5.16 != zero_zero_rat )
% 4.71/5.16 => ( ( ( member_Extended_enat @ A @ A2 )
% 4.71/5.16 => ( ( groups2245840878043517529at_rat @ F @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 4.71/5.16 = ( divide_divide_rat @ ( groups2245840878043517529at_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 4.71/5.16 & ( ~ ( member_Extended_enat @ A @ A2 )
% 4.71/5.16 => ( ( groups2245840878043517529at_rat @ F @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 4.71/5.16 = ( groups2245840878043517529at_rat @ F @ A2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_diff1
% 4.71/5.16 thf(fact_7767_prod__diff1,axiom,
% 4.71/5.16 ! [A2: set_real,F: real > rat,A: real] :
% 4.71/5.16 ( ( finite_finite_real @ A2 )
% 4.71/5.16 => ( ( ( F @ A )
% 4.71/5.16 != zero_zero_rat )
% 4.71/5.16 => ( ( ( member_real @ A @ A2 )
% 4.71/5.16 => ( ( groups4061424788464935467al_rat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 4.71/5.16 = ( divide_divide_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 4.71/5.16 & ( ~ ( member_real @ A @ A2 )
% 4.71/5.16 => ( ( groups4061424788464935467al_rat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 4.71/5.16 = ( groups4061424788464935467al_rat @ F @ A2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_diff1
% 4.71/5.16 thf(fact_7768_prod__diff1,axiom,
% 4.71/5.16 ! [A2: set_o,F: $o > rat,A: $o] :
% 4.71/5.16 ( ( finite_finite_o @ A2 )
% 4.71/5.16 => ( ( ( F @ A )
% 4.71/5.16 != zero_zero_rat )
% 4.71/5.16 => ( ( ( member_o @ A @ A2 )
% 4.71/5.16 => ( ( groups2869687844427037835_o_rat @ F @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 4.71/5.16 = ( divide_divide_rat @ ( groups2869687844427037835_o_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 4.71/5.16 & ( ~ ( member_o @ A @ A2 )
% 4.71/5.16 => ( ( groups2869687844427037835_o_rat @ F @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 4.71/5.16 = ( groups2869687844427037835_o_rat @ F @ A2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_diff1
% 4.71/5.16 thf(fact_7769_prod__diff1,axiom,
% 4.71/5.16 ! [A2: set_int,F: int > rat,A: int] :
% 4.71/5.16 ( ( finite_finite_int @ A2 )
% 4.71/5.16 => ( ( ( F @ A )
% 4.71/5.16 != zero_zero_rat )
% 4.71/5.16 => ( ( ( member_int @ A @ A2 )
% 4.71/5.16 => ( ( groups1072433553688619179nt_rat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 4.71/5.16 = ( divide_divide_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 4.71/5.16 & ( ~ ( member_int @ A @ A2 )
% 4.71/5.16 => ( ( groups1072433553688619179nt_rat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 4.71/5.16 = ( groups1072433553688619179nt_rat @ F @ A2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_diff1
% 4.71/5.16 thf(fact_7770_prod__diff1,axiom,
% 4.71/5.16 ! [A2: set_nat,F: nat > rat,A: nat] :
% 4.71/5.16 ( ( finite_finite_nat @ A2 )
% 4.71/5.16 => ( ( ( F @ A )
% 4.71/5.16 != zero_zero_rat )
% 4.71/5.16 => ( ( ( member_nat @ A @ A2 )
% 4.71/5.16 => ( ( groups73079841787564623at_rat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 4.71/5.16 = ( divide_divide_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 4.71/5.16 & ( ~ ( member_nat @ A @ A2 )
% 4.71/5.16 => ( ( groups73079841787564623at_rat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 4.71/5.16 = ( groups73079841787564623at_rat @ F @ A2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_diff1
% 4.71/5.16 thf(fact_7771_prod__diff1,axiom,
% 4.71/5.16 ! [A2: set_complex,F: complex > int,A: complex] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.16 => ( ( ( F @ A )
% 4.71/5.16 != zero_zero_int )
% 4.71/5.16 => ( ( ( member_complex @ A @ A2 )
% 4.71/5.16 => ( ( groups858564598930262913ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 4.71/5.16 = ( divide_divide_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 4.71/5.16 & ( ~ ( member_complex @ A @ A2 )
% 4.71/5.16 => ( ( groups858564598930262913ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 4.71/5.16 = ( groups858564598930262913ex_int @ F @ A2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_diff1
% 4.71/5.16 thf(fact_7772_prod__diff1,axiom,
% 4.71/5.16 ! [A2: set_Extended_enat,F: extended_enat > int,A: extended_enat] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.16 => ( ( ( F @ A )
% 4.71/5.16 != zero_zero_int )
% 4.71/5.16 => ( ( ( member_Extended_enat @ A @ A2 )
% 4.71/5.16 => ( ( groups2878480467620962989at_int @ F @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 4.71/5.16 = ( divide_divide_int @ ( groups2878480467620962989at_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 4.71/5.16 & ( ~ ( member_Extended_enat @ A @ A2 )
% 4.71/5.16 => ( ( groups2878480467620962989at_int @ F @ ( minus_925952699566721837d_enat @ A2 @ ( insert_Extended_enat @ A @ bot_bo7653980558646680370d_enat ) ) )
% 4.71/5.16 = ( groups2878480467620962989at_int @ F @ A2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_diff1
% 4.71/5.16 thf(fact_7773_prod__diff1,axiom,
% 4.71/5.16 ! [A2: set_real,F: real > int,A: real] :
% 4.71/5.16 ( ( finite_finite_real @ A2 )
% 4.71/5.16 => ( ( ( F @ A )
% 4.71/5.16 != zero_zero_int )
% 4.71/5.16 => ( ( ( member_real @ A @ A2 )
% 4.71/5.16 => ( ( groups4694064378042380927al_int @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 4.71/5.16 = ( divide_divide_int @ ( groups4694064378042380927al_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 4.71/5.16 & ( ~ ( member_real @ A @ A2 )
% 4.71/5.16 => ( ( groups4694064378042380927al_int @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 4.71/5.16 = ( groups4694064378042380927al_int @ F @ A2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_diff1
% 4.71/5.16 thf(fact_7774_prod__diff1,axiom,
% 4.71/5.16 ! [A2: set_o,F: $o > int,A: $o] :
% 4.71/5.16 ( ( finite_finite_o @ A2 )
% 4.71/5.16 => ( ( ( F @ A )
% 4.71/5.16 != zero_zero_int )
% 4.71/5.16 => ( ( ( member_o @ A @ A2 )
% 4.71/5.16 => ( ( groups3502327434004483295_o_int @ F @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 4.71/5.16 = ( divide_divide_int @ ( groups3502327434004483295_o_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 4.71/5.16 & ( ~ ( member_o @ A @ A2 )
% 4.71/5.16 => ( ( groups3502327434004483295_o_int @ F @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 4.71/5.16 = ( groups3502327434004483295_o_int @ F @ A2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_diff1
% 4.71/5.16 thf(fact_7775_prod__gen__delta,axiom,
% 4.71/5.16 ! [S2: set_o,A: $o,B: $o > complex,C: complex] :
% 4.71/5.16 ( ( finite_finite_o @ S2 )
% 4.71/5.16 => ( ( ( member_o @ A @ S2 )
% 4.71/5.16 => ( ( groups4859619685533338977omplex
% 4.71/5.16 @ ^ [K3: $o] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( times_times_complex @ ( B @ A ) @ ( power_power_complex @ C @ ( minus_minus_nat @ ( finite_card_o @ S2 ) @ one_one_nat ) ) ) ) )
% 4.71/5.16 & ( ~ ( member_o @ A @ S2 )
% 4.71/5.16 => ( ( groups4859619685533338977omplex
% 4.71/5.16 @ ^ [K3: $o] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( power_power_complex @ C @ ( finite_card_o @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_gen_delta
% 4.71/5.16 thf(fact_7776_prod__gen__delta,axiom,
% 4.71/5.16 ! [S2: set_nat,A: nat,B: nat > complex,C: complex] :
% 4.71/5.16 ( ( finite_finite_nat @ S2 )
% 4.71/5.16 => ( ( ( member_nat @ A @ S2 )
% 4.71/5.16 => ( ( groups6464643781859351333omplex
% 4.71/5.16 @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( times_times_complex @ ( B @ A ) @ ( power_power_complex @ C @ ( minus_minus_nat @ ( finite_card_nat @ S2 ) @ one_one_nat ) ) ) ) )
% 4.71/5.16 & ( ~ ( member_nat @ A @ S2 )
% 4.71/5.16 => ( ( groups6464643781859351333omplex
% 4.71/5.16 @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( power_power_complex @ C @ ( finite_card_nat @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_gen_delta
% 4.71/5.16 thf(fact_7777_prod__gen__delta,axiom,
% 4.71/5.16 ! [S2: set_int,A: int,B: int > complex,C: complex] :
% 4.71/5.16 ( ( finite_finite_int @ S2 )
% 4.71/5.16 => ( ( ( member_int @ A @ S2 )
% 4.71/5.16 => ( ( groups7440179247065528705omplex
% 4.71/5.16 @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( times_times_complex @ ( B @ A ) @ ( power_power_complex @ C @ ( minus_minus_nat @ ( finite_card_int @ S2 ) @ one_one_nat ) ) ) ) )
% 4.71/5.16 & ( ~ ( member_int @ A @ S2 )
% 4.71/5.16 => ( ( groups7440179247065528705omplex
% 4.71/5.16 @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( power_power_complex @ C @ ( finite_card_int @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_gen_delta
% 4.71/5.16 thf(fact_7778_prod__gen__delta,axiom,
% 4.71/5.16 ! [S2: set_complex,A: complex,B: complex > complex,C: complex] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ S2 )
% 4.71/5.16 => ( ( ( member_complex @ A @ S2 )
% 4.71/5.16 => ( ( groups3708469109370488835omplex
% 4.71/5.16 @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( times_times_complex @ ( B @ A ) @ ( power_power_complex @ C @ ( minus_minus_nat @ ( finite_card_complex @ S2 ) @ one_one_nat ) ) ) ) )
% 4.71/5.16 & ( ~ ( member_complex @ A @ S2 )
% 4.71/5.16 => ( ( groups3708469109370488835omplex
% 4.71/5.16 @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( power_power_complex @ C @ ( finite_card_complex @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_gen_delta
% 4.71/5.16 thf(fact_7779_prod__gen__delta,axiom,
% 4.71/5.16 ! [S2: set_Extended_enat,A: extended_enat,B: extended_enat > complex,C: complex] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.16 => ( ( ( member_Extended_enat @ A @ S2 )
% 4.71/5.16 => ( ( groups4622424608036095791omplex
% 4.71/5.16 @ ^ [K3: extended_enat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( times_times_complex @ ( B @ A ) @ ( power_power_complex @ C @ ( minus_minus_nat @ ( finite121521170596916366d_enat @ S2 ) @ one_one_nat ) ) ) ) )
% 4.71/5.16 & ( ~ ( member_Extended_enat @ A @ S2 )
% 4.71/5.16 => ( ( groups4622424608036095791omplex
% 4.71/5.16 @ ^ [K3: extended_enat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( power_power_complex @ C @ ( finite121521170596916366d_enat @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_gen_delta
% 4.71/5.16 thf(fact_7780_prod__gen__delta,axiom,
% 4.71/5.16 ! [S2: set_o,A: $o,B: $o > real,C: real] :
% 4.71/5.16 ( ( finite_finite_o @ S2 )
% 4.71/5.16 => ( ( ( member_o @ A @ S2 )
% 4.71/5.16 => ( ( groups234877984723959775o_real
% 4.71/5.16 @ ^ [K3: $o] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( times_times_real @ ( B @ A ) @ ( power_power_real @ C @ ( minus_minus_nat @ ( finite_card_o @ S2 ) @ one_one_nat ) ) ) ) )
% 4.71/5.16 & ( ~ ( member_o @ A @ S2 )
% 4.71/5.16 => ( ( groups234877984723959775o_real
% 4.71/5.16 @ ^ [K3: $o] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( power_power_real @ C @ ( finite_card_o @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_gen_delta
% 4.71/5.16 thf(fact_7781_prod__gen__delta,axiom,
% 4.71/5.16 ! [S2: set_nat,A: nat,B: nat > real,C: real] :
% 4.71/5.16 ( ( finite_finite_nat @ S2 )
% 4.71/5.16 => ( ( ( member_nat @ A @ S2 )
% 4.71/5.16 => ( ( groups129246275422532515t_real
% 4.71/5.16 @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( times_times_real @ ( B @ A ) @ ( power_power_real @ C @ ( minus_minus_nat @ ( finite_card_nat @ S2 ) @ one_one_nat ) ) ) ) )
% 4.71/5.16 & ( ~ ( member_nat @ A @ S2 )
% 4.71/5.16 => ( ( groups129246275422532515t_real
% 4.71/5.16 @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( power_power_real @ C @ ( finite_card_nat @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_gen_delta
% 4.71/5.16 thf(fact_7782_prod__gen__delta,axiom,
% 4.71/5.16 ! [S2: set_int,A: int,B: int > real,C: real] :
% 4.71/5.16 ( ( finite_finite_int @ S2 )
% 4.71/5.16 => ( ( ( member_int @ A @ S2 )
% 4.71/5.16 => ( ( groups2316167850115554303t_real
% 4.71/5.16 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( times_times_real @ ( B @ A ) @ ( power_power_real @ C @ ( minus_minus_nat @ ( finite_card_int @ S2 ) @ one_one_nat ) ) ) ) )
% 4.71/5.16 & ( ~ ( member_int @ A @ S2 )
% 4.71/5.16 => ( ( groups2316167850115554303t_real
% 4.71/5.16 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( power_power_real @ C @ ( finite_card_int @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_gen_delta
% 4.71/5.16 thf(fact_7783_prod__gen__delta,axiom,
% 4.71/5.16 ! [S2: set_complex,A: complex,B: complex > real,C: real] :
% 4.71/5.16 ( ( finite3207457112153483333omplex @ S2 )
% 4.71/5.16 => ( ( ( member_complex @ A @ S2 )
% 4.71/5.16 => ( ( groups766887009212190081x_real
% 4.71/5.16 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( times_times_real @ ( B @ A ) @ ( power_power_real @ C @ ( minus_minus_nat @ ( finite_card_complex @ S2 ) @ one_one_nat ) ) ) ) )
% 4.71/5.16 & ( ~ ( member_complex @ A @ S2 )
% 4.71/5.16 => ( ( groups766887009212190081x_real
% 4.71/5.16 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( power_power_real @ C @ ( finite_card_complex @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_gen_delta
% 4.71/5.16 thf(fact_7784_prod__gen__delta,axiom,
% 4.71/5.16 ! [S2: set_Extended_enat,A: extended_enat,B: extended_enat > real,C: real] :
% 4.71/5.16 ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.16 => ( ( ( member_Extended_enat @ A @ S2 )
% 4.71/5.16 => ( ( groups97031904164794029t_real
% 4.71/5.16 @ ^ [K3: extended_enat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( times_times_real @ ( B @ A ) @ ( power_power_real @ C @ ( minus_minus_nat @ ( finite121521170596916366d_enat @ S2 ) @ one_one_nat ) ) ) ) )
% 4.71/5.16 & ( ~ ( member_Extended_enat @ A @ S2 )
% 4.71/5.16 => ( ( groups97031904164794029t_real
% 4.71/5.16 @ ^ [K3: extended_enat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C )
% 4.71/5.16 @ S2 )
% 4.71/5.16 = ( power_power_real @ C @ ( finite121521170596916366d_enat @ S2 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % prod_gen_delta
% 4.71/5.16 thf(fact_7785_pi__series,axiom,
% 4.71/5.16 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 4.71/5.16 = ( suminf_real
% 4.71/5.16 @ ^ [K3: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % pi_series
% 4.71/5.16 thf(fact_7786_round__unique,axiom,
% 4.71/5.16 ! [X: real,Y: int] :
% 4.71/5.16 ( ( ord_less_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y ) )
% 4.71/5.16 => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y ) @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 4.71/5.16 => ( ( archim8280529875227126926d_real @ X )
% 4.71/5.16 = Y ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % round_unique
% 4.71/5.16 thf(fact_7787_round__unique,axiom,
% 4.71/5.16 ! [X: rat,Y: int] :
% 4.71/5.16 ( ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y ) )
% 4.71/5.16 => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 4.71/5.16 => ( ( archim7778729529865785530nd_rat @ X )
% 4.71/5.16 = Y ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % round_unique
% 4.71/5.16 thf(fact_7788_dbl__simps_I4_J,axiom,
% 4.71/5.16 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 4.71/5.16 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % dbl_simps(4)
% 4.71/5.16 thf(fact_7789_dbl__simps_I4_J,axiom,
% 4.71/5.16 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 4.71/5.16 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % dbl_simps(4)
% 4.71/5.16 thf(fact_7790_dbl__simps_I4_J,axiom,
% 4.71/5.16 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 4.71/5.16 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % dbl_simps(4)
% 4.71/5.16 thf(fact_7791_dbl__simps_I4_J,axiom,
% 4.71/5.16 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 4.71/5.16 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % dbl_simps(4)
% 4.71/5.16 thf(fact_7792_dbl__simps_I4_J,axiom,
% 4.71/5.16 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 4.71/5.16 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % dbl_simps(4)
% 4.71/5.16 thf(fact_7793_summable__arctan__series,axiom,
% 4.71/5.16 ! [X: real] :
% 4.71/5.16 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 4.71/5.16 => ( summable_real
% 4.71/5.16 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_arctan_series
% 4.71/5.16 thf(fact_7794_round__altdef,axiom,
% 4.71/5.16 ( archim8280529875227126926d_real
% 4.71/5.16 = ( ^ [X3: real] : ( if_int @ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( archim2898591450579166408c_real @ X3 ) ) @ ( archim7802044766580827645g_real @ X3 ) @ ( archim6058952711729229775r_real @ X3 ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % round_altdef
% 4.71/5.16 thf(fact_7795_round__altdef,axiom,
% 4.71/5.16 ( archim7778729529865785530nd_rat
% 4.71/5.16 = ( ^ [X3: rat] : ( if_int @ ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( archimedean_frac_rat @ X3 ) ) @ ( archim2889992004027027881ng_rat @ X3 ) @ ( archim3151403230148437115or_rat @ X3 ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % round_altdef
% 4.71/5.16 thf(fact_7796_round__unique_H,axiom,
% 4.71/5.16 ! [X: rat,N: int] :
% 4.71/5.16 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ N ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 4.71/5.16 => ( ( archim7778729529865785530nd_rat @ X )
% 4.71/5.16 = N ) ) ).
% 4.71/5.16
% 4.71/5.16 % round_unique'
% 4.71/5.16 thf(fact_7797_round__unique_H,axiom,
% 4.71/5.16 ! [X: real,N: int] :
% 4.71/5.16 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ ( ring_1_of_int_real @ N ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.71/5.16 => ( ( archim8280529875227126926d_real @ X )
% 4.71/5.16 = N ) ) ).
% 4.71/5.16
% 4.71/5.16 % round_unique'
% 4.71/5.16 thf(fact_7798_dbl__simps_I2_J,axiom,
% 4.71/5.16 ( ( neg_numeral_dbl_real @ zero_zero_real )
% 4.71/5.16 = zero_zero_real ) ).
% 4.71/5.16
% 4.71/5.16 % dbl_simps(2)
% 4.71/5.16 thf(fact_7799_dbl__simps_I2_J,axiom,
% 4.71/5.16 ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 4.71/5.16 = zero_zero_rat ) ).
% 4.71/5.16
% 4.71/5.16 % dbl_simps(2)
% 4.71/5.16 thf(fact_7800_dbl__simps_I2_J,axiom,
% 4.71/5.16 ( ( neg_numeral_dbl_int @ zero_zero_int )
% 4.71/5.16 = zero_zero_int ) ).
% 4.71/5.16
% 4.71/5.16 % dbl_simps(2)
% 4.71/5.16 thf(fact_7801_summable__single,axiom,
% 4.71/5.16 ! [I: nat,F: nat > real] :
% 4.71/5.16 ( summable_real
% 4.71/5.16 @ ^ [R5: nat] : ( if_real @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_real ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_single
% 4.71/5.16 thf(fact_7802_summable__single,axiom,
% 4.71/5.16 ! [I: nat,F: nat > nat] :
% 4.71/5.16 ( summable_nat
% 4.71/5.16 @ ^ [R5: nat] : ( if_nat @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_nat ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_single
% 4.71/5.16 thf(fact_7803_summable__single,axiom,
% 4.71/5.16 ! [I: nat,F: nat > int] :
% 4.71/5.16 ( summable_int
% 4.71/5.16 @ ^ [R5: nat] : ( if_int @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_int ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_single
% 4.71/5.16 thf(fact_7804_summable__zero,axiom,
% 4.71/5.16 ( summable_real
% 4.71/5.16 @ ^ [N4: nat] : zero_zero_real ) ).
% 4.71/5.16
% 4.71/5.16 % summable_zero
% 4.71/5.16 thf(fact_7805_summable__zero,axiom,
% 4.71/5.16 ( summable_nat
% 4.71/5.16 @ ^ [N4: nat] : zero_zero_nat ) ).
% 4.71/5.16
% 4.71/5.16 % summable_zero
% 4.71/5.16 thf(fact_7806_summable__zero,axiom,
% 4.71/5.16 ( summable_int
% 4.71/5.16 @ ^ [N4: nat] : zero_zero_int ) ).
% 4.71/5.16
% 4.71/5.16 % summable_zero
% 4.71/5.16 thf(fact_7807_round__0,axiom,
% 4.71/5.16 ( ( archim8280529875227126926d_real @ zero_zero_real )
% 4.71/5.16 = zero_zero_int ) ).
% 4.71/5.16
% 4.71/5.16 % round_0
% 4.71/5.16 thf(fact_7808_round__0,axiom,
% 4.71/5.16 ( ( archim7778729529865785530nd_rat @ zero_zero_rat )
% 4.71/5.16 = zero_zero_int ) ).
% 4.71/5.16
% 4.71/5.16 % round_0
% 4.71/5.16 thf(fact_7809_round__1,axiom,
% 4.71/5.16 ( ( archim8280529875227126926d_real @ one_one_real )
% 4.71/5.16 = one_one_int ) ).
% 4.71/5.16
% 4.71/5.16 % round_1
% 4.71/5.16 thf(fact_7810_round__1,axiom,
% 4.71/5.16 ( ( archim7778729529865785530nd_rat @ one_one_rat )
% 4.71/5.16 = one_one_int ) ).
% 4.71/5.16
% 4.71/5.16 % round_1
% 4.71/5.16 thf(fact_7811_summable__cmult__iff,axiom,
% 4.71/5.16 ! [C: real,F: nat > real] :
% 4.71/5.16 ( ( summable_real
% 4.71/5.16 @ ^ [N4: nat] : ( times_times_real @ C @ ( F @ N4 ) ) )
% 4.71/5.16 = ( ( C = zero_zero_real )
% 4.71/5.16 | ( summable_real @ F ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_cmult_iff
% 4.71/5.16 thf(fact_7812_dbl__simps_I5_J,axiom,
% 4.71/5.16 ! [K: num] :
% 4.71/5.16 ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 4.71/5.16 = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % dbl_simps(5)
% 4.71/5.16 thf(fact_7813_dbl__simps_I5_J,axiom,
% 4.71/5.16 ! [K: num] :
% 4.71/5.16 ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) )
% 4.71/5.16 = ( numeral_numeral_int @ ( bit0 @ K ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % dbl_simps(5)
% 4.71/5.16 thf(fact_7814_dbl__simps_I5_J,axiom,
% 4.71/5.16 ! [K: num] :
% 4.71/5.16 ( ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) )
% 4.71/5.16 = ( numera6620942414471956472nteger @ ( bit0 @ K ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % dbl_simps(5)
% 4.71/5.16 thf(fact_7815_summable__divide__iff,axiom,
% 4.71/5.16 ! [F: nat > real,C: real] :
% 4.71/5.16 ( ( summable_real
% 4.71/5.16 @ ^ [N4: nat] : ( divide_divide_real @ ( F @ N4 ) @ C ) )
% 4.71/5.16 = ( ( C = zero_zero_real )
% 4.71/5.16 | ( summable_real @ F ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_divide_iff
% 4.71/5.16 thf(fact_7816_dbl__simps_I1_J,axiom,
% 4.71/5.16 ! [K: num] :
% 4.71/5.16 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 4.71/5.16 = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % dbl_simps(1)
% 4.71/5.16 thf(fact_7817_dbl__simps_I1_J,axiom,
% 4.71/5.16 ! [K: num] :
% 4.71/5.16 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 4.71/5.16 = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % dbl_simps(1)
% 4.71/5.16 thf(fact_7818_dbl__simps_I1_J,axiom,
% 4.71/5.16 ! [K: num] :
% 4.71/5.16 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 4.71/5.16 = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % dbl_simps(1)
% 4.71/5.16 thf(fact_7819_dbl__simps_I1_J,axiom,
% 4.71/5.16 ! [K: num] :
% 4.71/5.16 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 4.71/5.16 = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % dbl_simps(1)
% 4.71/5.16 thf(fact_7820_dbl__simps_I1_J,axiom,
% 4.71/5.16 ! [K: num] :
% 4.71/5.16 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 4.71/5.16 = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % dbl_simps(1)
% 4.71/5.16 thf(fact_7821_summable__If__finite,axiom,
% 4.71/5.16 ! [P: nat > $o,F: nat > real] :
% 4.71/5.16 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 4.71/5.16 => ( summable_real
% 4.71/5.16 @ ^ [R5: nat] : ( if_real @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_real ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_If_finite
% 4.71/5.16 thf(fact_7822_summable__If__finite,axiom,
% 4.71/5.16 ! [P: nat > $o,F: nat > nat] :
% 4.71/5.16 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 4.71/5.16 => ( summable_nat
% 4.71/5.16 @ ^ [R5: nat] : ( if_nat @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_nat ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_If_finite
% 4.71/5.16 thf(fact_7823_summable__If__finite,axiom,
% 4.71/5.16 ! [P: nat > $o,F: nat > int] :
% 4.71/5.16 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 4.71/5.16 => ( summable_int
% 4.71/5.16 @ ^ [R5: nat] : ( if_int @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_int ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_If_finite
% 4.71/5.16 thf(fact_7824_summable__If__finite__set,axiom,
% 4.71/5.16 ! [A2: set_nat,F: nat > real] :
% 4.71/5.16 ( ( finite_finite_nat @ A2 )
% 4.71/5.16 => ( summable_real
% 4.71/5.16 @ ^ [R5: nat] : ( if_real @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_real ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_If_finite_set
% 4.71/5.16 thf(fact_7825_summable__If__finite__set,axiom,
% 4.71/5.16 ! [A2: set_nat,F: nat > nat] :
% 4.71/5.16 ( ( finite_finite_nat @ A2 )
% 4.71/5.16 => ( summable_nat
% 4.71/5.16 @ ^ [R5: nat] : ( if_nat @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_nat ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_If_finite_set
% 4.71/5.16 thf(fact_7826_summable__If__finite__set,axiom,
% 4.71/5.16 ! [A2: set_nat,F: nat > int] :
% 4.71/5.16 ( ( finite_finite_nat @ A2 )
% 4.71/5.16 => ( summable_int
% 4.71/5.16 @ ^ [R5: nat] : ( if_int @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_int ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_If_finite_set
% 4.71/5.16 thf(fact_7827_dbl__simps_I3_J,axiom,
% 4.71/5.16 ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 4.71/5.16 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % dbl_simps(3)
% 4.71/5.16 thf(fact_7828_dbl__simps_I3_J,axiom,
% 4.71/5.16 ( ( neg_numeral_dbl_rat @ one_one_rat )
% 4.71/5.16 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % dbl_simps(3)
% 4.71/5.16 thf(fact_7829_dbl__simps_I3_J,axiom,
% 4.71/5.16 ( ( neg_numeral_dbl_real @ one_one_real )
% 4.71/5.16 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % dbl_simps(3)
% 4.71/5.16 thf(fact_7830_dbl__simps_I3_J,axiom,
% 4.71/5.16 ( ( neg_numeral_dbl_int @ one_one_int )
% 4.71/5.16 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % dbl_simps(3)
% 4.71/5.16 thf(fact_7831_dbl__simps_I3_J,axiom,
% 4.71/5.16 ( ( neg_nu8804712462038260780nteger @ one_one_Code_integer )
% 4.71/5.16 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % dbl_simps(3)
% 4.71/5.16 thf(fact_7832_summable__comparison__test,axiom,
% 4.71/5.16 ! [F: nat > real,G2: nat > real] :
% 4.71/5.16 ( ? [N8: nat] :
% 4.71/5.16 ! [N2: nat] :
% 4.71/5.16 ( ( ord_less_eq_nat @ N8 @ N2 )
% 4.71/5.16 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N2 ) ) @ ( G2 @ N2 ) ) )
% 4.71/5.16 => ( ( summable_real @ G2 )
% 4.71/5.16 => ( summable_real @ F ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_comparison_test
% 4.71/5.16 thf(fact_7833_summable__comparison__test,axiom,
% 4.71/5.16 ! [F: nat > complex,G2: nat > real] :
% 4.71/5.16 ( ? [N8: nat] :
% 4.71/5.16 ! [N2: nat] :
% 4.71/5.16 ( ( ord_less_eq_nat @ N8 @ N2 )
% 4.71/5.16 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N2 ) ) @ ( G2 @ N2 ) ) )
% 4.71/5.16 => ( ( summable_real @ G2 )
% 4.71/5.16 => ( summable_complex @ F ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_comparison_test
% 4.71/5.16 thf(fact_7834_summable__comparison__test_H,axiom,
% 4.71/5.16 ! [G2: nat > real,N5: nat,F: nat > real] :
% 4.71/5.16 ( ( summable_real @ G2 )
% 4.71/5.16 => ( ! [N2: nat] :
% 4.71/5.16 ( ( ord_less_eq_nat @ N5 @ N2 )
% 4.71/5.16 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N2 ) ) @ ( G2 @ N2 ) ) )
% 4.71/5.16 => ( summable_real @ F ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_comparison_test'
% 4.71/5.16 thf(fact_7835_summable__comparison__test_H,axiom,
% 4.71/5.16 ! [G2: nat > real,N5: nat,F: nat > complex] :
% 4.71/5.16 ( ( summable_real @ G2 )
% 4.71/5.16 => ( ! [N2: nat] :
% 4.71/5.16 ( ( ord_less_eq_nat @ N5 @ N2 )
% 4.71/5.16 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N2 ) ) @ ( G2 @ N2 ) ) )
% 4.71/5.16 => ( summable_complex @ F ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_comparison_test'
% 4.71/5.16 thf(fact_7836_summable__const__iff,axiom,
% 4.71/5.16 ! [C: real] :
% 4.71/5.16 ( ( summable_real
% 4.71/5.16 @ ^ [Uu3: nat] : C )
% 4.71/5.16 = ( C = zero_zero_real ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_const_iff
% 4.71/5.16 thf(fact_7837_suminf__le,axiom,
% 4.71/5.16 ! [F: nat > real,G2: nat > real] :
% 4.71/5.16 ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( G2 @ N2 ) )
% 4.71/5.16 => ( ( summable_real @ F )
% 4.71/5.16 => ( ( summable_real @ G2 )
% 4.71/5.16 => ( ord_less_eq_real @ ( suminf_real @ F ) @ ( suminf_real @ G2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % suminf_le
% 4.71/5.16 thf(fact_7838_suminf__le,axiom,
% 4.71/5.16 ! [F: nat > nat,G2: nat > nat] :
% 4.71/5.16 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( G2 @ N2 ) )
% 4.71/5.16 => ( ( summable_nat @ F )
% 4.71/5.16 => ( ( summable_nat @ G2 )
% 4.71/5.16 => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % suminf_le
% 4.71/5.16 thf(fact_7839_suminf__le,axiom,
% 4.71/5.16 ! [F: nat > int,G2: nat > int] :
% 4.71/5.16 ( ! [N2: nat] : ( ord_less_eq_int @ ( F @ N2 ) @ ( G2 @ N2 ) )
% 4.71/5.16 => ( ( summable_int @ F )
% 4.71/5.16 => ( ( summable_int @ G2 )
% 4.71/5.16 => ( ord_less_eq_int @ ( suminf_int @ F ) @ ( suminf_int @ G2 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % suminf_le
% 4.71/5.16 thf(fact_7840_summable__finite,axiom,
% 4.71/5.16 ! [N5: set_nat,F: nat > real] :
% 4.71/5.16 ( ( finite_finite_nat @ N5 )
% 4.71/5.16 => ( ! [N2: nat] :
% 4.71/5.16 ( ~ ( member_nat @ N2 @ N5 )
% 4.71/5.16 => ( ( F @ N2 )
% 4.71/5.16 = zero_zero_real ) )
% 4.71/5.16 => ( summable_real @ F ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_finite
% 4.71/5.16 thf(fact_7841_summable__finite,axiom,
% 4.71/5.16 ! [N5: set_nat,F: nat > nat] :
% 4.71/5.16 ( ( finite_finite_nat @ N5 )
% 4.71/5.16 => ( ! [N2: nat] :
% 4.71/5.16 ( ~ ( member_nat @ N2 @ N5 )
% 4.71/5.16 => ( ( F @ N2 )
% 4.71/5.16 = zero_zero_nat ) )
% 4.71/5.16 => ( summable_nat @ F ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_finite
% 4.71/5.16 thf(fact_7842_summable__finite,axiom,
% 4.71/5.16 ! [N5: set_nat,F: nat > int] :
% 4.71/5.16 ( ( finite_finite_nat @ N5 )
% 4.71/5.16 => ( ! [N2: nat] :
% 4.71/5.16 ( ~ ( member_nat @ N2 @ N5 )
% 4.71/5.16 => ( ( F @ N2 )
% 4.71/5.16 = zero_zero_int ) )
% 4.71/5.16 => ( summable_int @ F ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_finite
% 4.71/5.16 thf(fact_7843_summable__mult__D,axiom,
% 4.71/5.16 ! [C: real,F: nat > real] :
% 4.71/5.16 ( ( summable_real
% 4.71/5.16 @ ^ [N4: nat] : ( times_times_real @ C @ ( F @ N4 ) ) )
% 4.71/5.16 => ( ( C != zero_zero_real )
% 4.71/5.16 => ( summable_real @ F ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_mult_D
% 4.71/5.16 thf(fact_7844_summable__zero__power,axiom,
% 4.71/5.16 summable_int @ ( power_power_int @ zero_zero_int ) ).
% 4.71/5.16
% 4.71/5.16 % summable_zero_power
% 4.71/5.16 thf(fact_7845_summable__zero__power,axiom,
% 4.71/5.16 summable_real @ ( power_power_real @ zero_zero_real ) ).
% 4.71/5.16
% 4.71/5.16 % summable_zero_power
% 4.71/5.16 thf(fact_7846_summable__zero__power,axiom,
% 4.71/5.16 summable_complex @ ( power_power_complex @ zero_zero_complex ) ).
% 4.71/5.16
% 4.71/5.16 % summable_zero_power
% 4.71/5.16 thf(fact_7847_pi__ge__zero,axiom,
% 4.71/5.16 ord_less_eq_real @ zero_zero_real @ pi ).
% 4.71/5.16
% 4.71/5.16 % pi_ge_zero
% 4.71/5.16 thf(fact_7848_dbl__def,axiom,
% 4.71/5.16 ( neg_numeral_dbl_real
% 4.71/5.16 = ( ^ [X3: real] : ( plus_plus_real @ X3 @ X3 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % dbl_def
% 4.71/5.16 thf(fact_7849_dbl__def,axiom,
% 4.71/5.16 ( neg_numeral_dbl_rat
% 4.71/5.16 = ( ^ [X3: rat] : ( plus_plus_rat @ X3 @ X3 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % dbl_def
% 4.71/5.16 thf(fact_7850_dbl__def,axiom,
% 4.71/5.16 ( neg_numeral_dbl_int
% 4.71/5.16 = ( ^ [X3: int] : ( plus_plus_int @ X3 @ X3 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % dbl_def
% 4.71/5.16 thf(fact_7851_suminf__eq__zero__iff,axiom,
% 4.71/5.16 ! [F: nat > real] :
% 4.71/5.16 ( ( summable_real @ F )
% 4.71/5.16 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N2 ) )
% 4.71/5.16 => ( ( ( suminf_real @ F )
% 4.71/5.16 = zero_zero_real )
% 4.71/5.16 = ( ! [N4: nat] :
% 4.71/5.16 ( ( F @ N4 )
% 4.71/5.16 = zero_zero_real ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % suminf_eq_zero_iff
% 4.71/5.16 thf(fact_7852_suminf__eq__zero__iff,axiom,
% 4.71/5.16 ! [F: nat > nat] :
% 4.71/5.16 ( ( summable_nat @ F )
% 4.71/5.16 => ( ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N2 ) )
% 4.71/5.16 => ( ( ( suminf_nat @ F )
% 4.71/5.16 = zero_zero_nat )
% 4.71/5.16 = ( ! [N4: nat] :
% 4.71/5.16 ( ( F @ N4 )
% 4.71/5.16 = zero_zero_nat ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % suminf_eq_zero_iff
% 4.71/5.16 thf(fact_7853_suminf__eq__zero__iff,axiom,
% 4.71/5.16 ! [F: nat > int] :
% 4.71/5.16 ( ( summable_int @ F )
% 4.71/5.16 => ( ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N2 ) )
% 4.71/5.16 => ( ( ( suminf_int @ F )
% 4.71/5.16 = zero_zero_int )
% 4.71/5.16 = ( ! [N4: nat] :
% 4.71/5.16 ( ( F @ N4 )
% 4.71/5.16 = zero_zero_int ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % suminf_eq_zero_iff
% 4.71/5.16 thf(fact_7854_suminf__nonneg,axiom,
% 4.71/5.16 ! [F: nat > real] :
% 4.71/5.16 ( ( summable_real @ F )
% 4.71/5.16 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N2 ) )
% 4.71/5.16 => ( ord_less_eq_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % suminf_nonneg
% 4.71/5.16 thf(fact_7855_suminf__nonneg,axiom,
% 4.71/5.16 ! [F: nat > nat] :
% 4.71/5.16 ( ( summable_nat @ F )
% 4.71/5.16 => ( ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N2 ) )
% 4.71/5.16 => ( ord_less_eq_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % suminf_nonneg
% 4.71/5.16 thf(fact_7856_suminf__nonneg,axiom,
% 4.71/5.16 ! [F: nat > int] :
% 4.71/5.16 ( ( summable_int @ F )
% 4.71/5.16 => ( ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N2 ) )
% 4.71/5.16 => ( ord_less_eq_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % suminf_nonneg
% 4.71/5.16 thf(fact_7857_suminf__pos,axiom,
% 4.71/5.16 ! [F: nat > real] :
% 4.71/5.16 ( ( summable_real @ F )
% 4.71/5.16 => ( ! [N2: nat] : ( ord_less_real @ zero_zero_real @ ( F @ N2 ) )
% 4.71/5.16 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % suminf_pos
% 4.71/5.16 thf(fact_7858_suminf__pos,axiom,
% 4.71/5.16 ! [F: nat > nat] :
% 4.71/5.16 ( ( summable_nat @ F )
% 4.71/5.16 => ( ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ N2 ) )
% 4.71/5.16 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % suminf_pos
% 4.71/5.16 thf(fact_7859_suminf__pos,axiom,
% 4.71/5.16 ! [F: nat > int] :
% 4.71/5.16 ( ( summable_int @ F )
% 4.71/5.16 => ( ! [N2: nat] : ( ord_less_int @ zero_zero_int @ ( F @ N2 ) )
% 4.71/5.16 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % suminf_pos
% 4.71/5.16 thf(fact_7860_summable__zero__power_H,axiom,
% 4.71/5.16 ! [F: nat > complex] :
% 4.71/5.16 ( summable_complex
% 4.71/5.16 @ ^ [N4: nat] : ( times_times_complex @ ( F @ N4 ) @ ( power_power_complex @ zero_zero_complex @ N4 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_zero_power'
% 4.71/5.16 thf(fact_7861_summable__zero__power_H,axiom,
% 4.71/5.16 ! [F: nat > real] :
% 4.71/5.16 ( summable_real
% 4.71/5.16 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ ( power_power_real @ zero_zero_real @ N4 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_zero_power'
% 4.71/5.16 thf(fact_7862_summable__zero__power_H,axiom,
% 4.71/5.16 ! [F: nat > int] :
% 4.71/5.16 ( summable_int
% 4.71/5.16 @ ^ [N4: nat] : ( times_times_int @ ( F @ N4 ) @ ( power_power_int @ zero_zero_int @ N4 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_zero_power'
% 4.71/5.16 thf(fact_7863_summable__0__powser,axiom,
% 4.71/5.16 ! [F: nat > complex] :
% 4.71/5.16 ( summable_complex
% 4.71/5.16 @ ^ [N4: nat] : ( times_times_complex @ ( F @ N4 ) @ ( power_power_complex @ zero_zero_complex @ N4 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_0_powser
% 4.71/5.16 thf(fact_7864_summable__0__powser,axiom,
% 4.71/5.16 ! [F: nat > real] :
% 4.71/5.16 ( summable_real
% 4.71/5.16 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ ( power_power_real @ zero_zero_real @ N4 ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_0_powser
% 4.71/5.16 thf(fact_7865_round__mono,axiom,
% 4.71/5.16 ! [X: rat,Y: rat] :
% 4.71/5.16 ( ( ord_less_eq_rat @ X @ Y )
% 4.71/5.16 => ( ord_less_eq_int @ ( archim7778729529865785530nd_rat @ X ) @ ( archim7778729529865785530nd_rat @ Y ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % round_mono
% 4.71/5.16 thf(fact_7866_summable__norm__comparison__test,axiom,
% 4.71/5.16 ! [F: nat > complex,G2: nat > real] :
% 4.71/5.16 ( ? [N8: nat] :
% 4.71/5.16 ! [N2: nat] :
% 4.71/5.16 ( ( ord_less_eq_nat @ N8 @ N2 )
% 4.71/5.16 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N2 ) ) @ ( G2 @ N2 ) ) )
% 4.71/5.16 => ( ( summable_real @ G2 )
% 4.71/5.16 => ( summable_real
% 4.71/5.16 @ ^ [N4: nat] : ( real_V1022390504157884413omplex @ ( F @ N4 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_norm_comparison_test
% 4.71/5.16 thf(fact_7867_summable__rabs__comparison__test,axiom,
% 4.71/5.16 ! [F: nat > real,G2: nat > real] :
% 4.71/5.16 ( ? [N8: nat] :
% 4.71/5.16 ! [N2: nat] :
% 4.71/5.16 ( ( ord_less_eq_nat @ N8 @ N2 )
% 4.71/5.16 => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N2 ) ) @ ( G2 @ N2 ) ) )
% 4.71/5.16 => ( ( summable_real @ G2 )
% 4.71/5.16 => ( summable_real
% 4.71/5.16 @ ^ [N4: nat] : ( abs_abs_real @ ( F @ N4 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_rabs_comparison_test
% 4.71/5.16 thf(fact_7868_floor__le__round,axiom,
% 4.71/5.16 ! [X: real] : ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( archim8280529875227126926d_real @ X ) ) ).
% 4.71/5.16
% 4.71/5.16 % floor_le_round
% 4.71/5.16 thf(fact_7869_floor__le__round,axiom,
% 4.71/5.16 ! [X: rat] : ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim7778729529865785530nd_rat @ X ) ) ).
% 4.71/5.16
% 4.71/5.16 % floor_le_round
% 4.71/5.16 thf(fact_7870_ceiling__ge__round,axiom,
% 4.71/5.16 ! [X: real] : ( ord_less_eq_int @ ( archim8280529875227126926d_real @ X ) @ ( archim7802044766580827645g_real @ X ) ) ).
% 4.71/5.16
% 4.71/5.16 % ceiling_ge_round
% 4.71/5.16 thf(fact_7871_summable__rabs,axiom,
% 4.71/5.16 ! [F: nat > real] :
% 4.71/5.16 ( ( summable_real
% 4.71/5.16 @ ^ [N4: nat] : ( abs_abs_real @ ( F @ N4 ) ) )
% 4.71/5.16 => ( ord_less_eq_real @ ( abs_abs_real @ ( suminf_real @ F ) )
% 4.71/5.16 @ ( suminf_real
% 4.71/5.16 @ ^ [N4: nat] : ( abs_abs_real @ ( F @ N4 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_rabs
% 4.71/5.16 thf(fact_7872_suminf__pos__iff,axiom,
% 4.71/5.16 ! [F: nat > real] :
% 4.71/5.16 ( ( summable_real @ F )
% 4.71/5.16 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N2 ) )
% 4.71/5.16 => ( ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) )
% 4.71/5.16 = ( ? [I4: nat] : ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % suminf_pos_iff
% 4.71/5.16 thf(fact_7873_suminf__pos__iff,axiom,
% 4.71/5.16 ! [F: nat > nat] :
% 4.71/5.16 ( ( summable_nat @ F )
% 4.71/5.16 => ( ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N2 ) )
% 4.71/5.16 => ( ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) )
% 4.71/5.16 = ( ? [I4: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % suminf_pos_iff
% 4.71/5.16 thf(fact_7874_suminf__pos__iff,axiom,
% 4.71/5.16 ! [F: nat > int] :
% 4.71/5.16 ( ( summable_int @ F )
% 4.71/5.16 => ( ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N2 ) )
% 4.71/5.16 => ( ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) )
% 4.71/5.16 = ( ? [I4: nat] : ( ord_less_int @ zero_zero_int @ ( F @ I4 ) ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % suminf_pos_iff
% 4.71/5.16 thf(fact_7875_suminf__pos2,axiom,
% 4.71/5.16 ! [F: nat > real,I: nat] :
% 4.71/5.16 ( ( summable_real @ F )
% 4.71/5.16 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N2 ) )
% 4.71/5.16 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 4.71/5.16 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % suminf_pos2
% 4.71/5.16 thf(fact_7876_suminf__pos2,axiom,
% 4.71/5.16 ! [F: nat > nat,I: nat] :
% 4.71/5.16 ( ( summable_nat @ F )
% 4.71/5.16 => ( ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N2 ) )
% 4.71/5.16 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 4.71/5.16 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % suminf_pos2
% 4.71/5.16 thf(fact_7877_suminf__pos2,axiom,
% 4.71/5.16 ! [F: nat > int,I: nat] :
% 4.71/5.16 ( ( summable_int @ F )
% 4.71/5.16 => ( ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N2 ) )
% 4.71/5.16 => ( ( ord_less_int @ zero_zero_int @ ( F @ I ) )
% 4.71/5.16 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % suminf_pos2
% 4.71/5.16 thf(fact_7878_suminf__split__head,axiom,
% 4.71/5.16 ! [F: nat > real] :
% 4.71/5.16 ( ( summable_real @ F )
% 4.71/5.16 => ( ( suminf_real
% 4.71/5.16 @ ^ [N4: nat] : ( F @ ( suc @ N4 ) ) )
% 4.71/5.16 = ( minus_minus_real @ ( suminf_real @ F ) @ ( F @ zero_zero_nat ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % suminf_split_head
% 4.71/5.16 thf(fact_7879_pi__ge__two,axiom,
% 4.71/5.16 ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 4.71/5.16
% 4.71/5.16 % pi_ge_two
% 4.71/5.16 thf(fact_7880_summable__norm,axiom,
% 4.71/5.16 ! [F: nat > real] :
% 4.71/5.16 ( ( summable_real
% 4.71/5.16 @ ^ [N4: nat] : ( real_V7735802525324610683m_real @ ( F @ N4 ) ) )
% 4.71/5.16 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( suminf_real @ F ) )
% 4.71/5.16 @ ( suminf_real
% 4.71/5.16 @ ^ [N4: nat] : ( real_V7735802525324610683m_real @ ( F @ N4 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_norm
% 4.71/5.16 thf(fact_7881_summable__norm,axiom,
% 4.71/5.16 ! [F: nat > complex] :
% 4.71/5.16 ( ( summable_real
% 4.71/5.16 @ ^ [N4: nat] : ( real_V1022390504157884413omplex @ ( F @ N4 ) ) )
% 4.71/5.16 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( suminf_complex @ F ) )
% 4.71/5.16 @ ( suminf_real
% 4.71/5.16 @ ^ [N4: nat] : ( real_V1022390504157884413omplex @ ( F @ N4 ) ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % summable_norm
% 4.71/5.16 thf(fact_7882_pi__half__le__two,axiom,
% 4.71/5.16 ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 4.71/5.16
% 4.71/5.16 % pi_half_le_two
% 4.71/5.16 thf(fact_7883_powser__split__head_I1_J,axiom,
% 4.71/5.16 ! [F: nat > complex,Z: complex] :
% 4.71/5.16 ( ( summable_complex
% 4.71/5.16 @ ^ [N4: nat] : ( times_times_complex @ ( F @ N4 ) @ ( power_power_complex @ Z @ N4 ) ) )
% 4.71/5.16 => ( ( suminf_complex
% 4.71/5.16 @ ^ [N4: nat] : ( times_times_complex @ ( F @ N4 ) @ ( power_power_complex @ Z @ N4 ) ) )
% 4.71/5.16 = ( plus_plus_complex @ ( F @ zero_zero_nat )
% 4.71/5.16 @ ( times_times_complex
% 4.71/5.16 @ ( suminf_complex
% 4.71/5.16 @ ^ [N4: nat] : ( times_times_complex @ ( F @ ( suc @ N4 ) ) @ ( power_power_complex @ Z @ N4 ) ) )
% 4.71/5.16 @ Z ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % powser_split_head(1)
% 4.71/5.16 thf(fact_7884_powser__split__head_I1_J,axiom,
% 4.71/5.16 ! [F: nat > real,Z: real] :
% 4.71/5.16 ( ( summable_real
% 4.71/5.16 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ ( power_power_real @ Z @ N4 ) ) )
% 4.71/5.16 => ( ( suminf_real
% 4.71/5.16 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ ( power_power_real @ Z @ N4 ) ) )
% 4.71/5.16 = ( plus_plus_real @ ( F @ zero_zero_nat )
% 4.71/5.16 @ ( times_times_real
% 4.71/5.16 @ ( suminf_real
% 4.71/5.16 @ ^ [N4: nat] : ( times_times_real @ ( F @ ( suc @ N4 ) ) @ ( power_power_real @ Z @ N4 ) ) )
% 4.71/5.16 @ Z ) ) ) ) ).
% 4.71/5.16
% 4.71/5.16 % powser_split_head(1)
% 4.71/5.16 thf(fact_7885_powser__split__head_I2_J,axiom,
% 4.71/5.16 ! [F: nat > complex,Z: complex] :
% 4.71/5.16 ( ( summable_complex
% 4.71/5.16 @ ^ [N4: nat] : ( times_times_complex @ ( F @ N4 ) @ ( power_power_complex @ Z @ N4 ) ) )
% 4.71/5.16 => ( ( times_times_complex
% 4.71/5.16 @ ( suminf_complex
% 4.71/5.16 @ ^ [N4: nat] : ( times_times_complex @ ( F @ ( suc @ N4 ) ) @ ( power_power_complex @ Z @ N4 ) ) )
% 4.71/5.16 @ Z )
% 4.71/5.16 = ( minus_minus_complex
% 4.71/5.16 @ ( suminf_complex
% 4.71/5.16 @ ^ [N4: nat] : ( times_times_complex @ ( F @ N4 ) @ ( power_power_complex @ Z @ N4 ) ) )
% 4.71/5.17 @ ( F @ zero_zero_nat ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % powser_split_head(2)
% 4.71/5.17 thf(fact_7886_powser__split__head_I2_J,axiom,
% 4.71/5.17 ! [F: nat > real,Z: real] :
% 4.71/5.17 ( ( summable_real
% 4.71/5.17 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ ( power_power_real @ Z @ N4 ) ) )
% 4.71/5.17 => ( ( times_times_real
% 4.71/5.17 @ ( suminf_real
% 4.71/5.17 @ ^ [N4: nat] : ( times_times_real @ ( F @ ( suc @ N4 ) ) @ ( power_power_real @ Z @ N4 ) ) )
% 4.71/5.17 @ Z )
% 4.71/5.17 = ( minus_minus_real
% 4.71/5.17 @ ( suminf_real
% 4.71/5.17 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ ( power_power_real @ Z @ N4 ) ) )
% 4.71/5.17 @ ( F @ zero_zero_nat ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % powser_split_head(2)
% 4.71/5.17 thf(fact_7887_suminf__exist__split,axiom,
% 4.71/5.17 ! [R2: real,F: nat > real] :
% 4.71/5.17 ( ( ord_less_real @ zero_zero_real @ R2 )
% 4.71/5.17 => ( ( summable_real @ F )
% 4.71/5.17 => ? [N9: nat] :
% 4.71/5.17 ! [N6: nat] :
% 4.71/5.17 ( ( ord_less_eq_nat @ N9 @ N6 )
% 4.71/5.17 => ( ord_less_real
% 4.71/5.17 @ ( real_V7735802525324610683m_real
% 4.71/5.17 @ ( suminf_real
% 4.71/5.17 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N6 ) ) ) )
% 4.71/5.17 @ R2 ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % suminf_exist_split
% 4.71/5.17 thf(fact_7888_suminf__exist__split,axiom,
% 4.71/5.17 ! [R2: real,F: nat > complex] :
% 4.71/5.17 ( ( ord_less_real @ zero_zero_real @ R2 )
% 4.71/5.17 => ( ( summable_complex @ F )
% 4.71/5.17 => ? [N9: nat] :
% 4.71/5.17 ! [N6: nat] :
% 4.71/5.17 ( ( ord_less_eq_nat @ N9 @ N6 )
% 4.71/5.17 => ( ord_less_real
% 4.71/5.17 @ ( real_V1022390504157884413omplex
% 4.71/5.17 @ ( suminf_complex
% 4.71/5.17 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N6 ) ) ) )
% 4.71/5.17 @ R2 ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % suminf_exist_split
% 4.71/5.17 thf(fact_7889_round__diff__minimal,axiom,
% 4.71/5.17 ! [Z: real,M2: 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 @ M2 ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % round_diff_minimal
% 4.71/5.17 thf(fact_7890_round__diff__minimal,axiom,
% 4.71/5.17 ! [Z: rat,M2: 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 @ M2 ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % round_diff_minimal
% 4.71/5.17 thf(fact_7891_summable__power__series,axiom,
% 4.71/5.17 ! [F: nat > real,Z: real] :
% 4.71/5.17 ( ! [I2: nat] : ( ord_less_eq_real @ ( F @ I2 ) @ one_one_real )
% 4.71/5.17 => ( ! [I2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 4.71/5.17 => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 4.71/5.17 => ( ( ord_less_real @ Z @ one_one_real )
% 4.71/5.17 => ( summable_real
% 4.71/5.17 @ ^ [I4: nat] : ( times_times_real @ ( F @ I4 ) @ ( power_power_real @ Z @ I4 ) ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % summable_power_series
% 4.71/5.17 thf(fact_7892_Abel__lemma,axiom,
% 4.71/5.17 ! [R2: real,R0: real,A: nat > complex,M5: real] :
% 4.71/5.17 ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 4.71/5.17 => ( ( ord_less_real @ R2 @ R0 )
% 4.71/5.17 => ( ! [N2: nat] : ( ord_less_eq_real @ ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N2 ) ) @ ( power_power_real @ R0 @ N2 ) ) @ M5 )
% 4.71/5.17 => ( summable_real
% 4.71/5.17 @ ^ [N4: nat] : ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N4 ) ) @ ( power_power_real @ R2 @ N4 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % Abel_lemma
% 4.71/5.17 thf(fact_7893_pi__half__ge__zero,axiom,
% 4.71/5.17 ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % pi_half_ge_zero
% 4.71/5.17 thf(fact_7894_summable__ratio__test,axiom,
% 4.71/5.17 ! [C: real,N5: nat,F: nat > real] :
% 4.71/5.17 ( ( ord_less_real @ C @ one_one_real )
% 4.71/5.17 => ( ! [N2: nat] :
% 4.71/5.17 ( ( ord_less_eq_nat @ N5 @ N2 )
% 4.71/5.17 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ ( suc @ N2 ) ) ) @ ( times_times_real @ C @ ( real_V7735802525324610683m_real @ ( F @ N2 ) ) ) ) )
% 4.71/5.17 => ( summable_real @ F ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % summable_ratio_test
% 4.71/5.17 thf(fact_7895_summable__ratio__test,axiom,
% 4.71/5.17 ! [C: real,N5: nat,F: nat > complex] :
% 4.71/5.17 ( ( ord_less_real @ C @ one_one_real )
% 4.71/5.17 => ( ! [N2: nat] :
% 4.71/5.17 ( ( ord_less_eq_nat @ N5 @ N2 )
% 4.71/5.17 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ ( suc @ N2 ) ) ) @ ( times_times_real @ C @ ( real_V1022390504157884413omplex @ ( F @ N2 ) ) ) ) )
% 4.71/5.17 => ( summable_complex @ F ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % summable_ratio_test
% 4.71/5.17 thf(fact_7896_round__def,axiom,
% 4.71/5.17 ( archim8280529875227126926d_real
% 4.71/5.17 = ( ^ [X3: real] : ( archim6058952711729229775r_real @ ( plus_plus_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % round_def
% 4.71/5.17 thf(fact_7897_round__def,axiom,
% 4.71/5.17 ( archim7778729529865785530nd_rat
% 4.71/5.17 = ( ^ [X3: rat] : ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % round_def
% 4.71/5.17 thf(fact_7898_of__int__round__le,axiom,
% 4.71/5.17 ! [X: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % of_int_round_le
% 4.71/5.17 thf(fact_7899_of__int__round__le,axiom,
% 4.71/5.17 ! [X: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % of_int_round_le
% 4.71/5.17 thf(fact_7900_of__int__round__ge,axiom,
% 4.71/5.17 ! [X: real] : ( ord_less_eq_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % of_int_round_ge
% 4.71/5.17 thf(fact_7901_of__int__round__ge,axiom,
% 4.71/5.17 ! [X: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % of_int_round_ge
% 4.71/5.17 thf(fact_7902_of__int__round__gt,axiom,
% 4.71/5.17 ! [X: rat] : ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % of_int_round_gt
% 4.71/5.17 thf(fact_7903_of__int__round__gt,axiom,
% 4.71/5.17 ! [X: real] : ( ord_less_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % of_int_round_gt
% 4.71/5.17 thf(fact_7904_of__int__round__abs__le,axiom,
% 4.71/5.17 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) @ X ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % of_int_round_abs_le
% 4.71/5.17 thf(fact_7905_of__int__round__abs__le,axiom,
% 4.71/5.17 ! [X: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ X ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % of_int_round_abs_le
% 4.71/5.17 thf(fact_7906_card__lists__distinct__length__eq,axiom,
% 4.71/5.17 ! [A2: set_list_nat,K: nat] :
% 4.71/5.17 ( ( finite8100373058378681591st_nat @ A2 )
% 4.71/5.17 => ( ( ord_less_eq_nat @ K @ ( finite_card_list_nat @ A2 ) )
% 4.71/5.17 => ( ( finite7325466520557071688st_nat
% 4.71/5.17 @ ( collec5989764272469232197st_nat
% 4.71/5.17 @ ^ [Xs2: list_list_nat] :
% 4.71/5.17 ( ( ( size_s3023201423986296836st_nat @ Xs2 )
% 4.71/5.17 = K )
% 4.71/5.17 & ( distinct_list_nat @ Xs2 )
% 4.71/5.17 & ( ord_le6045566169113846134st_nat @ ( set_list_nat2 @ Xs2 ) @ A2 ) ) ) )
% 4.71/5.17 = ( groups708209901874060359at_nat
% 4.71/5.17 @ ^ [X3: nat] : X3
% 4.71/5.17 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_list_nat @ A2 ) @ K ) @ one_one_nat ) @ ( finite_card_list_nat @ A2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % card_lists_distinct_length_eq
% 4.71/5.17 thf(fact_7907_card__lists__distinct__length__eq,axiom,
% 4.71/5.17 ! [A2: set_set_nat,K: nat] :
% 4.71/5.17 ( ( finite1152437895449049373et_nat @ A2 )
% 4.71/5.17 => ( ( ord_less_eq_nat @ K @ ( finite_card_set_nat @ A2 ) )
% 4.71/5.17 => ( ( finite5631907774883551598et_nat
% 4.71/5.17 @ ( collect_list_set_nat
% 4.71/5.17 @ ^ [Xs2: list_set_nat] :
% 4.71/5.17 ( ( ( size_s3254054031482475050et_nat @ Xs2 )
% 4.71/5.17 = K )
% 4.71/5.17 & ( distinct_set_nat @ Xs2 )
% 4.71/5.17 & ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs2 ) @ A2 ) ) ) )
% 4.71/5.17 = ( groups708209901874060359at_nat
% 4.71/5.17 @ ^ [X3: nat] : X3
% 4.71/5.17 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_set_nat @ A2 ) @ K ) @ one_one_nat ) @ ( finite_card_set_nat @ A2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % card_lists_distinct_length_eq
% 4.71/5.17 thf(fact_7908_card__lists__distinct__length__eq,axiom,
% 4.71/5.17 ! [A2: set_complex,K: nat] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.17 => ( ( ord_less_eq_nat @ K @ ( finite_card_complex @ A2 ) )
% 4.71/5.17 => ( ( finite5120063068150530198omplex
% 4.71/5.17 @ ( collect_list_complex
% 4.71/5.17 @ ^ [Xs2: list_complex] :
% 4.71/5.17 ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 4.71/5.17 = K )
% 4.71/5.17 & ( distinct_complex @ Xs2 )
% 4.71/5.17 & ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A2 ) ) ) )
% 4.71/5.17 = ( groups708209901874060359at_nat
% 4.71/5.17 @ ^ [X3: nat] : X3
% 4.71/5.17 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_complex @ A2 ) @ K ) @ one_one_nat ) @ ( finite_card_complex @ A2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % card_lists_distinct_length_eq
% 4.71/5.17 thf(fact_7909_card__lists__distinct__length__eq,axiom,
% 4.71/5.17 ! [A2: set_Pr1261947904930325089at_nat,K: nat] :
% 4.71/5.17 ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.17 => ( ( ord_less_eq_nat @ K @ ( finite711546835091564841at_nat @ A2 ) )
% 4.71/5.17 => ( ( finite249151656366948015at_nat
% 4.71/5.17 @ ( collec3343600615725829874at_nat
% 4.71/5.17 @ ^ [Xs2: list_P6011104703257516679at_nat] :
% 4.71/5.17 ( ( ( size_s5460976970255530739at_nat @ Xs2 )
% 4.71/5.17 = K )
% 4.71/5.17 & ( distin6923225563576452346at_nat @ Xs2 )
% 4.71/5.17 & ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs2 ) @ A2 ) ) ) )
% 4.71/5.17 = ( groups708209901874060359at_nat
% 4.71/5.17 @ ^ [X3: nat] : X3
% 4.71/5.17 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite711546835091564841at_nat @ A2 ) @ K ) @ one_one_nat ) @ ( finite711546835091564841at_nat @ A2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % card_lists_distinct_length_eq
% 4.71/5.17 thf(fact_7910_card__lists__distinct__length__eq,axiom,
% 4.71/5.17 ! [A2: set_Extended_enat,K: nat] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.17 => ( ( ord_less_eq_nat @ K @ ( finite121521170596916366d_enat @ A2 ) )
% 4.71/5.17 => ( ( finite7441382602597825044d_enat
% 4.71/5.17 @ ( collec8433460942617342167d_enat
% 4.71/5.17 @ ^ [Xs2: list_Extended_enat] :
% 4.71/5.17 ( ( ( size_s3941691890525107288d_enat @ Xs2 )
% 4.71/5.17 = K )
% 4.71/5.17 & ( distin4523846830085650399d_enat @ Xs2 )
% 4.71/5.17 & ( ord_le7203529160286727270d_enat @ ( set_Extended_enat2 @ Xs2 ) @ A2 ) ) ) )
% 4.71/5.17 = ( groups708209901874060359at_nat
% 4.71/5.17 @ ^ [X3: nat] : X3
% 4.71/5.17 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite121521170596916366d_enat @ A2 ) @ K ) @ one_one_nat ) @ ( finite121521170596916366d_enat @ A2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % card_lists_distinct_length_eq
% 4.71/5.17 thf(fact_7911_card__lists__distinct__length__eq,axiom,
% 4.71/5.17 ! [A2: set_VEBT_VEBT,K: nat] :
% 4.71/5.17 ( ( finite5795047828879050333T_VEBT @ A2 )
% 4.71/5.17 => ( ( ord_less_eq_nat @ K @ ( finite7802652506058667612T_VEBT @ A2 ) )
% 4.71/5.17 => ( ( finite5915292604075114978T_VEBT
% 4.71/5.17 @ ( collec5608196760682091941T_VEBT
% 4.71/5.17 @ ^ [Xs2: list_VEBT_VEBT] :
% 4.71/5.17 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 4.71/5.17 = K )
% 4.71/5.17 & ( distinct_VEBT_VEBT @ Xs2 )
% 4.71/5.17 & ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A2 ) ) ) )
% 4.71/5.17 = ( groups708209901874060359at_nat
% 4.71/5.17 @ ^ [X3: nat] : X3
% 4.71/5.17 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite7802652506058667612T_VEBT @ A2 ) @ K ) @ one_one_nat ) @ ( finite7802652506058667612T_VEBT @ A2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % card_lists_distinct_length_eq
% 4.71/5.17 thf(fact_7912_card__lists__distinct__length__eq,axiom,
% 4.71/5.17 ! [A2: set_nat,K: nat] :
% 4.71/5.17 ( ( finite_finite_nat @ A2 )
% 4.71/5.17 => ( ( ord_less_eq_nat @ K @ ( finite_card_nat @ A2 ) )
% 4.71/5.17 => ( ( finite_card_list_nat
% 4.71/5.17 @ ( collect_list_nat
% 4.71/5.17 @ ^ [Xs2: list_nat] :
% 4.71/5.17 ( ( ( size_size_list_nat @ Xs2 )
% 4.71/5.17 = K )
% 4.71/5.17 & ( distinct_nat @ Xs2 )
% 4.71/5.17 & ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A2 ) ) ) )
% 4.71/5.17 = ( groups708209901874060359at_nat
% 4.71/5.17 @ ^ [X3: nat] : X3
% 4.71/5.17 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_nat @ A2 ) @ K ) @ one_one_nat ) @ ( finite_card_nat @ A2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % card_lists_distinct_length_eq
% 4.71/5.17 thf(fact_7913_card__lists__distinct__length__eq,axiom,
% 4.71/5.17 ! [A2: set_int,K: nat] :
% 4.71/5.17 ( ( finite_finite_int @ A2 )
% 4.71/5.17 => ( ( ord_less_eq_nat @ K @ ( finite_card_int @ A2 ) )
% 4.71/5.17 => ( ( finite_card_list_int
% 4.71/5.17 @ ( collect_list_int
% 4.71/5.17 @ ^ [Xs2: list_int] :
% 4.71/5.17 ( ( ( size_size_list_int @ Xs2 )
% 4.71/5.17 = K )
% 4.71/5.17 & ( distinct_int @ Xs2 )
% 4.71/5.17 & ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A2 ) ) ) )
% 4.71/5.17 = ( groups708209901874060359at_nat
% 4.71/5.17 @ ^ [X3: nat] : X3
% 4.71/5.17 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_int @ A2 ) @ K ) @ one_one_nat ) @ ( finite_card_int @ A2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % card_lists_distinct_length_eq
% 4.71/5.17 thf(fact_7914_arcosh__def,axiom,
% 4.71/5.17 ( arcosh_real
% 4.71/5.17 = ( ^ [X3: real] : ( ln_ln_real @ ( plus_plus_real @ X3 @ ( powr_real @ ( minus_minus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % arcosh_def
% 4.71/5.17 thf(fact_7915_binomial__code,axiom,
% 4.71/5.17 ( binomial
% 4.71/5.17 = ( ^ [N4: nat,K3: nat] : ( if_nat @ ( ord_less_nat @ N4 @ K3 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K3 ) ) @ ( binomial @ N4 @ ( minus_minus_nat @ N4 @ K3 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N4 @ K3 ) @ one_one_nat ) @ N4 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K3 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % binomial_code
% 4.71/5.17 thf(fact_7916_accp__subset,axiom,
% 4.71/5.17 ! [R1: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o,R22: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o] :
% 4.71/5.17 ( ( ord_le1077754993875142464_nat_o @ R1 @ R22 )
% 4.71/5.17 => ( ord_le7812727212727832188_nat_o @ ( accp_P2887432264394892906BT_nat @ R22 ) @ ( accp_P2887432264394892906BT_nat @ R1 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % accp_subset
% 4.71/5.17 thf(fact_7917_accp__subset,axiom,
% 4.71/5.17 ! [R1: product_prod_nat_nat > product_prod_nat_nat > $o,R22: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 4.71/5.17 ( ( ord_le5604493270027003598_nat_o @ R1 @ R22 )
% 4.71/5.17 => ( ord_le704812498762024988_nat_o @ ( accp_P4275260045618599050at_nat @ R22 ) @ ( accp_P4275260045618599050at_nat @ R1 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % accp_subset
% 4.71/5.17 thf(fact_7918_accp__subset,axiom,
% 4.71/5.17 ! [R1: product_prod_int_int > product_prod_int_int > $o,R22: product_prod_int_int > product_prod_int_int > $o] :
% 4.71/5.17 ( ( ord_le1598226405681992910_int_o @ R1 @ R22 )
% 4.71/5.17 => ( ord_le8369615600986905444_int_o @ ( accp_P1096762738010456898nt_int @ R22 ) @ ( accp_P1096762738010456898nt_int @ R1 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % accp_subset
% 4.71/5.17 thf(fact_7919_accp__subset,axiom,
% 4.71/5.17 ! [R1: list_nat > list_nat > $o,R22: list_nat > list_nat > $o] :
% 4.71/5.17 ( ( ord_le6558929396352911974_nat_o @ R1 @ R22 )
% 4.71/5.17 => ( ord_le1520216061033275535_nat_o @ ( accp_list_nat @ R22 ) @ ( accp_list_nat @ R1 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % accp_subset
% 4.71/5.17 thf(fact_7920_accp__subset,axiom,
% 4.71/5.17 ! [R1: nat > nat > $o,R22: nat > nat > $o] :
% 4.71/5.17 ( ( ord_le2646555220125990790_nat_o @ R1 @ R22 )
% 4.71/5.17 => ( ord_less_eq_nat_o @ ( accp_nat @ R22 ) @ ( accp_nat @ R1 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % accp_subset
% 4.71/5.17 thf(fact_7921_sum__gp,axiom,
% 4.71/5.17 ! [N: nat,M2: nat,X: complex] :
% 4.71/5.17 ( ( ( ord_less_nat @ N @ M2 )
% 4.71/5.17 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 4.71/5.17 = zero_zero_complex ) )
% 4.71/5.17 & ( ~ ( ord_less_nat @ N @ M2 )
% 4.71/5.17 => ( ( ( X = one_one_complex )
% 4.71/5.17 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 4.71/5.17 = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M2 ) ) ) )
% 4.71/5.17 & ( ( X != one_one_complex )
% 4.71/5.17 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 4.71/5.17 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ M2 ) @ ( power_power_complex @ X @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_gp
% 4.71/5.17 thf(fact_7922_sum__gp,axiom,
% 4.71/5.17 ! [N: nat,M2: nat,X: rat] :
% 4.71/5.17 ( ( ( ord_less_nat @ N @ M2 )
% 4.71/5.17 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 4.71/5.17 = zero_zero_rat ) )
% 4.71/5.17 & ( ~ ( ord_less_nat @ N @ M2 )
% 4.71/5.17 => ( ( ( X = one_one_rat )
% 4.71/5.17 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 4.71/5.17 = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M2 ) ) ) )
% 4.71/5.17 & ( ( X != one_one_rat )
% 4.71/5.17 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 4.71/5.17 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ M2 ) @ ( power_power_rat @ X @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_gp
% 4.71/5.17 thf(fact_7923_sum__gp,axiom,
% 4.71/5.17 ! [N: nat,M2: nat,X: real] :
% 4.71/5.17 ( ( ( ord_less_nat @ N @ M2 )
% 4.71/5.17 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 4.71/5.17 = zero_zero_real ) )
% 4.71/5.17 & ( ~ ( ord_less_nat @ N @ M2 )
% 4.71/5.17 => ( ( ( X = one_one_real )
% 4.71/5.17 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 4.71/5.17 = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M2 ) ) ) )
% 4.71/5.17 & ( ( X != one_one_real )
% 4.71/5.17 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 4.71/5.17 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ M2 ) @ ( power_power_real @ X @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_gp
% 4.71/5.17 thf(fact_7924_binomial__n__n,axiom,
% 4.71/5.17 ! [N: nat] :
% 4.71/5.17 ( ( binomial @ N @ N )
% 4.71/5.17 = one_one_nat ) ).
% 4.71/5.17
% 4.71/5.17 % binomial_n_n
% 4.71/5.17 thf(fact_7925_sum_Oneutral__const,axiom,
% 4.71/5.17 ! [A2: set_nat] :
% 4.71/5.17 ( ( groups3542108847815614940at_nat
% 4.71/5.17 @ ^ [Uu3: nat] : zero_zero_nat
% 4.71/5.17 @ A2 )
% 4.71/5.17 = zero_zero_nat ) ).
% 4.71/5.17
% 4.71/5.17 % sum.neutral_const
% 4.71/5.17 thf(fact_7926_sum_Oneutral__const,axiom,
% 4.71/5.17 ! [A2: set_complex] :
% 4.71/5.17 ( ( groups7754918857620584856omplex
% 4.71/5.17 @ ^ [Uu3: complex] : zero_zero_complex
% 4.71/5.17 @ A2 )
% 4.71/5.17 = zero_zero_complex ) ).
% 4.71/5.17
% 4.71/5.17 % sum.neutral_const
% 4.71/5.17 thf(fact_7927_sum_Oneutral__const,axiom,
% 4.71/5.17 ! [A2: set_int] :
% 4.71/5.17 ( ( groups4538972089207619220nt_int
% 4.71/5.17 @ ^ [Uu3: int] : zero_zero_int
% 4.71/5.17 @ A2 )
% 4.71/5.17 = zero_zero_int ) ).
% 4.71/5.17
% 4.71/5.17 % sum.neutral_const
% 4.71/5.17 thf(fact_7928_sum_Oneutral__const,axiom,
% 4.71/5.17 ! [A2: set_nat] :
% 4.71/5.17 ( ( groups6591440286371151544t_real
% 4.71/5.17 @ ^ [Uu3: nat] : zero_zero_real
% 4.71/5.17 @ A2 )
% 4.71/5.17 = zero_zero_real ) ).
% 4.71/5.17
% 4.71/5.17 % sum.neutral_const
% 4.71/5.17 thf(fact_7929_sum_Oempty,axiom,
% 4.71/5.17 ! [G2: real > real] :
% 4.71/5.17 ( ( groups8097168146408367636l_real @ G2 @ bot_bot_set_real )
% 4.71/5.17 = zero_zero_real ) ).
% 4.71/5.17
% 4.71/5.17 % sum.empty
% 4.71/5.17 thf(fact_7930_sum_Oempty,axiom,
% 4.71/5.17 ! [G2: real > rat] :
% 4.71/5.17 ( ( groups1300246762558778688al_rat @ G2 @ bot_bot_set_real )
% 4.71/5.17 = zero_zero_rat ) ).
% 4.71/5.17
% 4.71/5.17 % sum.empty
% 4.71/5.17 thf(fact_7931_sum_Oempty,axiom,
% 4.71/5.17 ! [G2: real > nat] :
% 4.71/5.17 ( ( groups1935376822645274424al_nat @ G2 @ bot_bot_set_real )
% 4.71/5.17 = zero_zero_nat ) ).
% 4.71/5.17
% 4.71/5.17 % sum.empty
% 4.71/5.17 thf(fact_7932_sum_Oempty,axiom,
% 4.71/5.17 ! [G2: real > int] :
% 4.71/5.17 ( ( groups1932886352136224148al_int @ G2 @ bot_bot_set_real )
% 4.71/5.17 = zero_zero_int ) ).
% 4.71/5.17
% 4.71/5.17 % sum.empty
% 4.71/5.17 thf(fact_7933_sum_Oempty,axiom,
% 4.71/5.17 ! [G2: $o > real] :
% 4.71/5.17 ( ( groups8691415230153176458o_real @ G2 @ bot_bot_set_o )
% 4.71/5.17 = zero_zero_real ) ).
% 4.71/5.17
% 4.71/5.17 % sum.empty
% 4.71/5.17 thf(fact_7934_sum_Oempty,axiom,
% 4.71/5.17 ! [G2: $o > rat] :
% 4.71/5.17 ( ( groups7872700643590313910_o_rat @ G2 @ bot_bot_set_o )
% 4.71/5.17 = zero_zero_rat ) ).
% 4.71/5.17
% 4.71/5.17 % sum.empty
% 4.71/5.17 thf(fact_7935_sum_Oempty,axiom,
% 4.71/5.17 ! [G2: $o > nat] :
% 4.71/5.17 ( ( groups8507830703676809646_o_nat @ G2 @ bot_bot_set_o )
% 4.71/5.17 = zero_zero_nat ) ).
% 4.71/5.17
% 4.71/5.17 % sum.empty
% 4.71/5.17 thf(fact_7936_sum_Oempty,axiom,
% 4.71/5.17 ! [G2: $o > int] :
% 4.71/5.17 ( ( groups8505340233167759370_o_int @ G2 @ bot_bot_set_o )
% 4.71/5.17 = zero_zero_int ) ).
% 4.71/5.17
% 4.71/5.17 % sum.empty
% 4.71/5.17 thf(fact_7937_sum_Oempty,axiom,
% 4.71/5.17 ! [G2: nat > rat] :
% 4.71/5.17 ( ( groups2906978787729119204at_rat @ G2 @ bot_bot_set_nat )
% 4.71/5.17 = zero_zero_rat ) ).
% 4.71/5.17
% 4.71/5.17 % sum.empty
% 4.71/5.17 thf(fact_7938_sum_Oempty,axiom,
% 4.71/5.17 ! [G2: nat > int] :
% 4.71/5.17 ( ( groups3539618377306564664at_int @ G2 @ bot_bot_set_nat )
% 4.71/5.17 = zero_zero_int ) ).
% 4.71/5.17
% 4.71/5.17 % sum.empty
% 4.71/5.17 thf(fact_7939_sum__eq__0__iff,axiom,
% 4.71/5.17 ! [F2: set_int,F: int > nat] :
% 4.71/5.17 ( ( finite_finite_int @ F2 )
% 4.71/5.17 => ( ( ( groups4541462559716669496nt_nat @ F @ F2 )
% 4.71/5.17 = zero_zero_nat )
% 4.71/5.17 = ( ! [X3: int] :
% 4.71/5.17 ( ( member_int @ X3 @ F2 )
% 4.71/5.17 => ( ( F @ X3 )
% 4.71/5.17 = zero_zero_nat ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_eq_0_iff
% 4.71/5.17 thf(fact_7940_sum__eq__0__iff,axiom,
% 4.71/5.17 ! [F2: set_complex,F: complex > nat] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ F2 )
% 4.71/5.17 => ( ( ( groups5693394587270226106ex_nat @ F @ F2 )
% 4.71/5.17 = zero_zero_nat )
% 4.71/5.17 = ( ! [X3: complex] :
% 4.71/5.17 ( ( member_complex @ X3 @ F2 )
% 4.71/5.17 => ( ( F @ X3 )
% 4.71/5.17 = zero_zero_nat ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_eq_0_iff
% 4.71/5.17 thf(fact_7941_sum__eq__0__iff,axiom,
% 4.71/5.17 ! [F2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 4.71/5.17 ( ( finite6177210948735845034at_nat @ F2 )
% 4.71/5.17 => ( ( ( groups977919841031483927at_nat @ F @ F2 )
% 4.71/5.17 = zero_zero_nat )
% 4.71/5.17 = ( ! [X3: product_prod_nat_nat] :
% 4.71/5.17 ( ( member8440522571783428010at_nat @ X3 @ F2 )
% 4.71/5.17 => ( ( F @ X3 )
% 4.71/5.17 = zero_zero_nat ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_eq_0_iff
% 4.71/5.17 thf(fact_7942_sum__eq__0__iff,axiom,
% 4.71/5.17 ! [F2: set_Extended_enat,F: extended_enat > nat] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ F2 )
% 4.71/5.17 => ( ( ( groups2027974829824023292at_nat @ F @ F2 )
% 4.71/5.17 = zero_zero_nat )
% 4.71/5.17 = ( ! [X3: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ X3 @ F2 )
% 4.71/5.17 => ( ( F @ X3 )
% 4.71/5.17 = zero_zero_nat ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_eq_0_iff
% 4.71/5.17 thf(fact_7943_sum__eq__0__iff,axiom,
% 4.71/5.17 ! [F2: set_nat,F: nat > nat] :
% 4.71/5.17 ( ( finite_finite_nat @ F2 )
% 4.71/5.17 => ( ( ( groups3542108847815614940at_nat @ F @ F2 )
% 4.71/5.17 = zero_zero_nat )
% 4.71/5.17 = ( ! [X3: nat] :
% 4.71/5.17 ( ( member_nat @ X3 @ F2 )
% 4.71/5.17 => ( ( F @ X3 )
% 4.71/5.17 = zero_zero_nat ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_eq_0_iff
% 4.71/5.17 thf(fact_7944_sum_Oinfinite,axiom,
% 4.71/5.17 ! [A2: set_int,G2: int > real] :
% 4.71/5.17 ( ~ ( finite_finite_int @ A2 )
% 4.71/5.17 => ( ( groups8778361861064173332t_real @ G2 @ A2 )
% 4.71/5.17 = zero_zero_real ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.infinite
% 4.71/5.17 thf(fact_7945_sum_Oinfinite,axiom,
% 4.71/5.17 ! [A2: set_complex,G2: complex > real] :
% 4.71/5.17 ( ~ ( finite3207457112153483333omplex @ A2 )
% 4.71/5.17 => ( ( groups5808333547571424918x_real @ G2 @ A2 )
% 4.71/5.17 = zero_zero_real ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.infinite
% 4.71/5.17 thf(fact_7946_sum_Oinfinite,axiom,
% 4.71/5.17 ! [A2: set_Extended_enat,G2: extended_enat > real] :
% 4.71/5.17 ( ~ ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.17 => ( ( groups4148127829035722712t_real @ G2 @ A2 )
% 4.71/5.17 = zero_zero_real ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.infinite
% 4.71/5.17 thf(fact_7947_sum_Oinfinite,axiom,
% 4.71/5.17 ! [A2: set_nat,G2: nat > rat] :
% 4.71/5.17 ( ~ ( finite_finite_nat @ A2 )
% 4.71/5.17 => ( ( groups2906978787729119204at_rat @ G2 @ A2 )
% 4.71/5.17 = zero_zero_rat ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.infinite
% 4.71/5.17 thf(fact_7948_sum_Oinfinite,axiom,
% 4.71/5.17 ! [A2: set_int,G2: int > rat] :
% 4.71/5.17 ( ~ ( finite_finite_int @ A2 )
% 4.71/5.17 => ( ( groups3906332499630173760nt_rat @ G2 @ A2 )
% 4.71/5.17 = zero_zero_rat ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.infinite
% 4.71/5.17 thf(fact_7949_sum_Oinfinite,axiom,
% 4.71/5.17 ! [A2: set_complex,G2: complex > rat] :
% 4.71/5.17 ( ~ ( finite3207457112153483333omplex @ A2 )
% 4.71/5.17 => ( ( groups5058264527183730370ex_rat @ G2 @ A2 )
% 4.71/5.17 = zero_zero_rat ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.infinite
% 4.71/5.17 thf(fact_7950_sum_Oinfinite,axiom,
% 4.71/5.17 ! [A2: set_Extended_enat,G2: extended_enat > rat] :
% 4.71/5.17 ( ~ ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.17 => ( ( groups1392844769737527556at_rat @ G2 @ A2 )
% 4.71/5.17 = zero_zero_rat ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.infinite
% 4.71/5.17 thf(fact_7951_sum_Oinfinite,axiom,
% 4.71/5.17 ! [A2: set_int,G2: int > nat] :
% 4.71/5.17 ( ~ ( finite_finite_int @ A2 )
% 4.71/5.17 => ( ( groups4541462559716669496nt_nat @ G2 @ A2 )
% 4.71/5.17 = zero_zero_nat ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.infinite
% 4.71/5.17 thf(fact_7952_sum_Oinfinite,axiom,
% 4.71/5.17 ! [A2: set_complex,G2: complex > nat] :
% 4.71/5.17 ( ~ ( finite3207457112153483333omplex @ A2 )
% 4.71/5.17 => ( ( groups5693394587270226106ex_nat @ G2 @ A2 )
% 4.71/5.17 = zero_zero_nat ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.infinite
% 4.71/5.17 thf(fact_7953_sum_Oinfinite,axiom,
% 4.71/5.17 ! [A2: set_Extended_enat,G2: extended_enat > nat] :
% 4.71/5.17 ( ~ ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.17 => ( ( groups2027974829824023292at_nat @ G2 @ A2 )
% 4.71/5.17 = zero_zero_nat ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.infinite
% 4.71/5.17 thf(fact_7954_of__real__eq__0__iff,axiom,
% 4.71/5.17 ! [X: real] :
% 4.71/5.17 ( ( ( real_V1803761363581548252l_real @ X )
% 4.71/5.17 = zero_zero_real )
% 4.71/5.17 = ( X = zero_zero_real ) ) ).
% 4.71/5.17
% 4.71/5.17 % of_real_eq_0_iff
% 4.71/5.17 thf(fact_7955_of__real__eq__0__iff,axiom,
% 4.71/5.17 ! [X: real] :
% 4.71/5.17 ( ( ( real_V4546457046886955230omplex @ X )
% 4.71/5.17 = zero_zero_complex )
% 4.71/5.17 = ( X = zero_zero_real ) ) ).
% 4.71/5.17
% 4.71/5.17 % of_real_eq_0_iff
% 4.71/5.17 thf(fact_7956_of__real__0,axiom,
% 4.71/5.17 ( ( real_V1803761363581548252l_real @ zero_zero_real )
% 4.71/5.17 = zero_zero_real ) ).
% 4.71/5.17
% 4.71/5.17 % of_real_0
% 4.71/5.17 thf(fact_7957_of__real__0,axiom,
% 4.71/5.17 ( ( real_V4546457046886955230omplex @ zero_zero_real )
% 4.71/5.17 = zero_zero_complex ) ).
% 4.71/5.17
% 4.71/5.17 % of_real_0
% 4.71/5.17 thf(fact_7958_of__real__eq__1__iff,axiom,
% 4.71/5.17 ! [X: real] :
% 4.71/5.17 ( ( ( real_V1803761363581548252l_real @ X )
% 4.71/5.17 = one_one_real )
% 4.71/5.17 = ( X = one_one_real ) ) ).
% 4.71/5.17
% 4.71/5.17 % of_real_eq_1_iff
% 4.71/5.17 thf(fact_7959_of__real__eq__1__iff,axiom,
% 4.71/5.17 ! [X: real] :
% 4.71/5.17 ( ( ( real_V4546457046886955230omplex @ X )
% 4.71/5.17 = one_one_complex )
% 4.71/5.17 = ( X = one_one_real ) ) ).
% 4.71/5.17
% 4.71/5.17 % of_real_eq_1_iff
% 4.71/5.17 thf(fact_7960_of__real__1,axiom,
% 4.71/5.17 ( ( real_V1803761363581548252l_real @ one_one_real )
% 4.71/5.17 = one_one_real ) ).
% 4.71/5.17
% 4.71/5.17 % of_real_1
% 4.71/5.17 thf(fact_7961_of__real__1,axiom,
% 4.71/5.17 ( ( real_V4546457046886955230omplex @ one_one_real )
% 4.71/5.17 = one_one_complex ) ).
% 4.71/5.17
% 4.71/5.17 % of_real_1
% 4.71/5.17 thf(fact_7962_binomial__0__Suc,axiom,
% 4.71/5.17 ! [K: nat] :
% 4.71/5.17 ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 4.71/5.17 = zero_zero_nat ) ).
% 4.71/5.17
% 4.71/5.17 % binomial_0_Suc
% 4.71/5.17 thf(fact_7963_binomial__1,axiom,
% 4.71/5.17 ! [N: nat] :
% 4.71/5.17 ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 4.71/5.17 = N ) ).
% 4.71/5.17
% 4.71/5.17 % binomial_1
% 4.71/5.17 thf(fact_7964_binomial__eq__0__iff,axiom,
% 4.71/5.17 ! [N: nat,K: nat] :
% 4.71/5.17 ( ( ( binomial @ N @ K )
% 4.71/5.17 = zero_zero_nat )
% 4.71/5.17 = ( ord_less_nat @ N @ K ) ) ).
% 4.71/5.17
% 4.71/5.17 % binomial_eq_0_iff
% 4.71/5.17 thf(fact_7965_binomial__n__0,axiom,
% 4.71/5.17 ! [N: nat] :
% 4.71/5.17 ( ( binomial @ N @ zero_zero_nat )
% 4.71/5.17 = one_one_nat ) ).
% 4.71/5.17
% 4.71/5.17 % binomial_n_0
% 4.71/5.17 thf(fact_7966_sum_Odelta,axiom,
% 4.71/5.17 ! [S2: set_o,A: $o,B: $o > real] :
% 4.71/5.17 ( ( finite_finite_o @ S2 )
% 4.71/5.17 => ( ( ( member_o @ A @ S2 )
% 4.71/5.17 => ( ( groups8691415230153176458o_real
% 4.71/5.17 @ ^ [K3: $o] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = ( B @ A ) ) )
% 4.71/5.17 & ( ~ ( member_o @ A @ S2 )
% 4.71/5.17 => ( ( groups8691415230153176458o_real
% 4.71/5.17 @ ^ [K3: $o] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = zero_zero_real ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.delta
% 4.71/5.17 thf(fact_7967_sum_Odelta,axiom,
% 4.71/5.17 ! [S2: set_int,A: int,B: int > real] :
% 4.71/5.17 ( ( finite_finite_int @ S2 )
% 4.71/5.17 => ( ( ( member_int @ A @ S2 )
% 4.71/5.17 => ( ( groups8778361861064173332t_real
% 4.71/5.17 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = ( B @ A ) ) )
% 4.71/5.17 & ( ~ ( member_int @ A @ S2 )
% 4.71/5.17 => ( ( groups8778361861064173332t_real
% 4.71/5.17 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = zero_zero_real ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.delta
% 4.71/5.17 thf(fact_7968_sum_Odelta,axiom,
% 4.71/5.17 ! [S2: set_complex,A: complex,B: complex > real] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ S2 )
% 4.71/5.17 => ( ( ( member_complex @ A @ S2 )
% 4.71/5.17 => ( ( groups5808333547571424918x_real
% 4.71/5.17 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = ( B @ A ) ) )
% 4.71/5.17 & ( ~ ( member_complex @ A @ S2 )
% 4.71/5.17 => ( ( groups5808333547571424918x_real
% 4.71/5.17 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = zero_zero_real ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.delta
% 4.71/5.17 thf(fact_7969_sum_Odelta,axiom,
% 4.71/5.17 ! [S2: set_Extended_enat,A: extended_enat,B: extended_enat > real] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.17 => ( ( ( member_Extended_enat @ A @ S2 )
% 4.71/5.17 => ( ( groups4148127829035722712t_real
% 4.71/5.17 @ ^ [K3: extended_enat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = ( B @ A ) ) )
% 4.71/5.17 & ( ~ ( member_Extended_enat @ A @ S2 )
% 4.71/5.17 => ( ( groups4148127829035722712t_real
% 4.71/5.17 @ ^ [K3: extended_enat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = zero_zero_real ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.delta
% 4.71/5.17 thf(fact_7970_sum_Odelta,axiom,
% 4.71/5.17 ! [S2: set_o,A: $o,B: $o > rat] :
% 4.71/5.17 ( ( finite_finite_o @ S2 )
% 4.71/5.17 => ( ( ( member_o @ A @ S2 )
% 4.71/5.17 => ( ( groups7872700643590313910_o_rat
% 4.71/5.17 @ ^ [K3: $o] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = ( B @ A ) ) )
% 4.71/5.17 & ( ~ ( member_o @ A @ S2 )
% 4.71/5.17 => ( ( groups7872700643590313910_o_rat
% 4.71/5.17 @ ^ [K3: $o] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = zero_zero_rat ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.delta
% 4.71/5.17 thf(fact_7971_sum_Odelta,axiom,
% 4.71/5.17 ! [S2: set_nat,A: nat,B: nat > rat] :
% 4.71/5.17 ( ( finite_finite_nat @ S2 )
% 4.71/5.17 => ( ( ( member_nat @ A @ S2 )
% 4.71/5.17 => ( ( groups2906978787729119204at_rat
% 4.71/5.17 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = ( B @ A ) ) )
% 4.71/5.17 & ( ~ ( member_nat @ A @ S2 )
% 4.71/5.17 => ( ( groups2906978787729119204at_rat
% 4.71/5.17 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = zero_zero_rat ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.delta
% 4.71/5.17 thf(fact_7972_sum_Odelta,axiom,
% 4.71/5.17 ! [S2: set_int,A: int,B: int > rat] :
% 4.71/5.17 ( ( finite_finite_int @ S2 )
% 4.71/5.17 => ( ( ( member_int @ A @ S2 )
% 4.71/5.17 => ( ( groups3906332499630173760nt_rat
% 4.71/5.17 @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = ( B @ A ) ) )
% 4.71/5.17 & ( ~ ( member_int @ A @ S2 )
% 4.71/5.17 => ( ( groups3906332499630173760nt_rat
% 4.71/5.17 @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = zero_zero_rat ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.delta
% 4.71/5.17 thf(fact_7973_sum_Odelta,axiom,
% 4.71/5.17 ! [S2: set_complex,A: complex,B: complex > rat] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ S2 )
% 4.71/5.17 => ( ( ( member_complex @ A @ S2 )
% 4.71/5.17 => ( ( groups5058264527183730370ex_rat
% 4.71/5.17 @ ^ [K3: complex] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = ( B @ A ) ) )
% 4.71/5.17 & ( ~ ( member_complex @ A @ S2 )
% 4.71/5.17 => ( ( groups5058264527183730370ex_rat
% 4.71/5.17 @ ^ [K3: complex] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = zero_zero_rat ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.delta
% 4.71/5.17 thf(fact_7974_sum_Odelta,axiom,
% 4.71/5.17 ! [S2: set_Extended_enat,A: extended_enat,B: extended_enat > rat] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.17 => ( ( ( member_Extended_enat @ A @ S2 )
% 4.71/5.17 => ( ( groups1392844769737527556at_rat
% 4.71/5.17 @ ^ [K3: extended_enat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = ( B @ A ) ) )
% 4.71/5.17 & ( ~ ( member_Extended_enat @ A @ S2 )
% 4.71/5.17 => ( ( groups1392844769737527556at_rat
% 4.71/5.17 @ ^ [K3: extended_enat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = zero_zero_rat ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.delta
% 4.71/5.17 thf(fact_7975_sum_Odelta,axiom,
% 4.71/5.17 ! [S2: set_o,A: $o,B: $o > nat] :
% 4.71/5.17 ( ( finite_finite_o @ S2 )
% 4.71/5.17 => ( ( ( member_o @ A @ S2 )
% 4.71/5.17 => ( ( groups8507830703676809646_o_nat
% 4.71/5.17 @ ^ [K3: $o] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_nat )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = ( B @ A ) ) )
% 4.71/5.17 & ( ~ ( member_o @ A @ S2 )
% 4.71/5.17 => ( ( groups8507830703676809646_o_nat
% 4.71/5.17 @ ^ [K3: $o] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_nat )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = zero_zero_nat ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.delta
% 4.71/5.17 thf(fact_7976_sum_Odelta_H,axiom,
% 4.71/5.17 ! [S2: set_o,A: $o,B: $o > real] :
% 4.71/5.17 ( ( finite_finite_o @ S2 )
% 4.71/5.17 => ( ( ( member_o @ A @ S2 )
% 4.71/5.17 => ( ( groups8691415230153176458o_real
% 4.71/5.17 @ ^ [K3: $o] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = ( B @ A ) ) )
% 4.71/5.17 & ( ~ ( member_o @ A @ S2 )
% 4.71/5.17 => ( ( groups8691415230153176458o_real
% 4.71/5.17 @ ^ [K3: $o] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = zero_zero_real ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.delta'
% 4.71/5.17 thf(fact_7977_sum_Odelta_H,axiom,
% 4.71/5.17 ! [S2: set_int,A: int,B: int > real] :
% 4.71/5.17 ( ( finite_finite_int @ S2 )
% 4.71/5.17 => ( ( ( member_int @ A @ S2 )
% 4.71/5.17 => ( ( groups8778361861064173332t_real
% 4.71/5.17 @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = ( B @ A ) ) )
% 4.71/5.17 & ( ~ ( member_int @ A @ S2 )
% 4.71/5.17 => ( ( groups8778361861064173332t_real
% 4.71/5.17 @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = zero_zero_real ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.delta'
% 4.71/5.17 thf(fact_7978_sum_Odelta_H,axiom,
% 4.71/5.17 ! [S2: set_complex,A: complex,B: complex > real] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ S2 )
% 4.71/5.17 => ( ( ( member_complex @ A @ S2 )
% 4.71/5.17 => ( ( groups5808333547571424918x_real
% 4.71/5.17 @ ^ [K3: complex] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = ( B @ A ) ) )
% 4.71/5.17 & ( ~ ( member_complex @ A @ S2 )
% 4.71/5.17 => ( ( groups5808333547571424918x_real
% 4.71/5.17 @ ^ [K3: complex] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = zero_zero_real ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.delta'
% 4.71/5.17 thf(fact_7979_sum_Odelta_H,axiom,
% 4.71/5.17 ! [S2: set_Extended_enat,A: extended_enat,B: extended_enat > real] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.17 => ( ( ( member_Extended_enat @ A @ S2 )
% 4.71/5.17 => ( ( groups4148127829035722712t_real
% 4.71/5.17 @ ^ [K3: extended_enat] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = ( B @ A ) ) )
% 4.71/5.17 & ( ~ ( member_Extended_enat @ A @ S2 )
% 4.71/5.17 => ( ( groups4148127829035722712t_real
% 4.71/5.17 @ ^ [K3: extended_enat] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = zero_zero_real ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.delta'
% 4.71/5.17 thf(fact_7980_sum_Odelta_H,axiom,
% 4.71/5.17 ! [S2: set_o,A: $o,B: $o > rat] :
% 4.71/5.17 ( ( finite_finite_o @ S2 )
% 4.71/5.17 => ( ( ( member_o @ A @ S2 )
% 4.71/5.17 => ( ( groups7872700643590313910_o_rat
% 4.71/5.17 @ ^ [K3: $o] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = ( B @ A ) ) )
% 4.71/5.17 & ( ~ ( member_o @ A @ S2 )
% 4.71/5.17 => ( ( groups7872700643590313910_o_rat
% 4.71/5.17 @ ^ [K3: $o] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = zero_zero_rat ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.delta'
% 4.71/5.17 thf(fact_7981_sum_Odelta_H,axiom,
% 4.71/5.17 ! [S2: set_nat,A: nat,B: nat > rat] :
% 4.71/5.17 ( ( finite_finite_nat @ S2 )
% 4.71/5.17 => ( ( ( member_nat @ A @ S2 )
% 4.71/5.17 => ( ( groups2906978787729119204at_rat
% 4.71/5.17 @ ^ [K3: nat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = ( B @ A ) ) )
% 4.71/5.17 & ( ~ ( member_nat @ A @ S2 )
% 4.71/5.17 => ( ( groups2906978787729119204at_rat
% 4.71/5.17 @ ^ [K3: nat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = zero_zero_rat ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.delta'
% 4.71/5.17 thf(fact_7982_sum_Odelta_H,axiom,
% 4.71/5.17 ! [S2: set_int,A: int,B: int > rat] :
% 4.71/5.17 ( ( finite_finite_int @ S2 )
% 4.71/5.17 => ( ( ( member_int @ A @ S2 )
% 4.71/5.17 => ( ( groups3906332499630173760nt_rat
% 4.71/5.17 @ ^ [K3: int] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = ( B @ A ) ) )
% 4.71/5.17 & ( ~ ( member_int @ A @ S2 )
% 4.71/5.17 => ( ( groups3906332499630173760nt_rat
% 4.71/5.17 @ ^ [K3: int] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = zero_zero_rat ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.delta'
% 4.71/5.17 thf(fact_7983_sum_Odelta_H,axiom,
% 4.71/5.17 ! [S2: set_complex,A: complex,B: complex > rat] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ S2 )
% 4.71/5.17 => ( ( ( member_complex @ A @ S2 )
% 4.71/5.17 => ( ( groups5058264527183730370ex_rat
% 4.71/5.17 @ ^ [K3: complex] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = ( B @ A ) ) )
% 4.71/5.17 & ( ~ ( member_complex @ A @ S2 )
% 4.71/5.17 => ( ( groups5058264527183730370ex_rat
% 4.71/5.17 @ ^ [K3: complex] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = zero_zero_rat ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.delta'
% 4.71/5.17 thf(fact_7984_sum_Odelta_H,axiom,
% 4.71/5.17 ! [S2: set_Extended_enat,A: extended_enat,B: extended_enat > rat] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.17 => ( ( ( member_Extended_enat @ A @ S2 )
% 4.71/5.17 => ( ( groups1392844769737527556at_rat
% 4.71/5.17 @ ^ [K3: extended_enat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = ( B @ A ) ) )
% 4.71/5.17 & ( ~ ( member_Extended_enat @ A @ S2 )
% 4.71/5.17 => ( ( groups1392844769737527556at_rat
% 4.71/5.17 @ ^ [K3: extended_enat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = zero_zero_rat ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.delta'
% 4.71/5.17 thf(fact_7985_sum_Odelta_H,axiom,
% 4.71/5.17 ! [S2: set_o,A: $o,B: $o > nat] :
% 4.71/5.17 ( ( finite_finite_o @ S2 )
% 4.71/5.17 => ( ( ( member_o @ A @ S2 )
% 4.71/5.17 => ( ( groups8507830703676809646_o_nat
% 4.71/5.17 @ ^ [K3: $o] : ( if_nat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_nat )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = ( B @ A ) ) )
% 4.71/5.17 & ( ~ ( member_o @ A @ S2 )
% 4.71/5.17 => ( ( groups8507830703676809646_o_nat
% 4.71/5.17 @ ^ [K3: $o] : ( if_nat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_nat )
% 4.71/5.17 @ S2 )
% 4.71/5.17 = zero_zero_nat ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.delta'
% 4.71/5.17 thf(fact_7986_sum__abs,axiom,
% 4.71/5.17 ! [F: int > int,A2: set_int] :
% 4.71/5.17 ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 4.71/5.17 @ ( groups4538972089207619220nt_int
% 4.71/5.17 @ ^ [I4: int] : ( abs_abs_int @ ( F @ I4 ) )
% 4.71/5.17 @ A2 ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_abs
% 4.71/5.17 thf(fact_7987_sum__abs,axiom,
% 4.71/5.17 ! [F: nat > real,A2: set_nat] :
% 4.71/5.17 ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 4.71/5.17 @ ( groups6591440286371151544t_real
% 4.71/5.17 @ ^ [I4: nat] : ( abs_abs_real @ ( F @ I4 ) )
% 4.71/5.17 @ A2 ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_abs
% 4.71/5.17 thf(fact_7988_sum_Oinsert,axiom,
% 4.71/5.17 ! [A2: set_real,X: real,G2: real > real] :
% 4.71/5.17 ( ( finite_finite_real @ A2 )
% 4.71/5.17 => ( ~ ( member_real @ X @ A2 )
% 4.71/5.17 => ( ( groups8097168146408367636l_real @ G2 @ ( insert_real @ X @ A2 ) )
% 4.71/5.17 = ( plus_plus_real @ ( G2 @ X ) @ ( groups8097168146408367636l_real @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.insert
% 4.71/5.17 thf(fact_7989_sum_Oinsert,axiom,
% 4.71/5.17 ! [A2: set_o,X: $o,G2: $o > real] :
% 4.71/5.17 ( ( finite_finite_o @ A2 )
% 4.71/5.17 => ( ~ ( member_o @ X @ A2 )
% 4.71/5.17 => ( ( groups8691415230153176458o_real @ G2 @ ( insert_o @ X @ A2 ) )
% 4.71/5.17 = ( plus_plus_real @ ( G2 @ X ) @ ( groups8691415230153176458o_real @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.insert
% 4.71/5.17 thf(fact_7990_sum_Oinsert,axiom,
% 4.71/5.17 ! [A2: set_int,X: int,G2: int > real] :
% 4.71/5.17 ( ( finite_finite_int @ A2 )
% 4.71/5.17 => ( ~ ( member_int @ X @ A2 )
% 4.71/5.17 => ( ( groups8778361861064173332t_real @ G2 @ ( insert_int @ X @ A2 ) )
% 4.71/5.17 = ( plus_plus_real @ ( G2 @ X ) @ ( groups8778361861064173332t_real @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.insert
% 4.71/5.17 thf(fact_7991_sum_Oinsert,axiom,
% 4.71/5.17 ! [A2: set_complex,X: complex,G2: complex > real] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.17 => ( ~ ( member_complex @ X @ A2 )
% 4.71/5.17 => ( ( groups5808333547571424918x_real @ G2 @ ( insert_complex @ X @ A2 ) )
% 4.71/5.17 = ( plus_plus_real @ ( G2 @ X ) @ ( groups5808333547571424918x_real @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.insert
% 4.71/5.17 thf(fact_7992_sum_Oinsert,axiom,
% 4.71/5.17 ! [A2: set_Extended_enat,X: extended_enat,G2: extended_enat > real] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.17 => ( ~ ( member_Extended_enat @ X @ A2 )
% 4.71/5.17 => ( ( groups4148127829035722712t_real @ G2 @ ( insert_Extended_enat @ X @ A2 ) )
% 4.71/5.17 = ( plus_plus_real @ ( G2 @ X ) @ ( groups4148127829035722712t_real @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.insert
% 4.71/5.17 thf(fact_7993_sum_Oinsert,axiom,
% 4.71/5.17 ! [A2: set_real,X: real,G2: real > rat] :
% 4.71/5.17 ( ( finite_finite_real @ A2 )
% 4.71/5.17 => ( ~ ( member_real @ X @ A2 )
% 4.71/5.17 => ( ( groups1300246762558778688al_rat @ G2 @ ( insert_real @ X @ A2 ) )
% 4.71/5.17 = ( plus_plus_rat @ ( G2 @ X ) @ ( groups1300246762558778688al_rat @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.insert
% 4.71/5.17 thf(fact_7994_sum_Oinsert,axiom,
% 4.71/5.17 ! [A2: set_o,X: $o,G2: $o > rat] :
% 4.71/5.17 ( ( finite_finite_o @ A2 )
% 4.71/5.17 => ( ~ ( member_o @ X @ A2 )
% 4.71/5.17 => ( ( groups7872700643590313910_o_rat @ G2 @ ( insert_o @ X @ A2 ) )
% 4.71/5.17 = ( plus_plus_rat @ ( G2 @ X ) @ ( groups7872700643590313910_o_rat @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.insert
% 4.71/5.17 thf(fact_7995_sum_Oinsert,axiom,
% 4.71/5.17 ! [A2: set_nat,X: nat,G2: nat > rat] :
% 4.71/5.17 ( ( finite_finite_nat @ A2 )
% 4.71/5.17 => ( ~ ( member_nat @ X @ A2 )
% 4.71/5.17 => ( ( groups2906978787729119204at_rat @ G2 @ ( insert_nat @ X @ A2 ) )
% 4.71/5.17 = ( plus_plus_rat @ ( G2 @ X ) @ ( groups2906978787729119204at_rat @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.insert
% 4.71/5.17 thf(fact_7996_sum_Oinsert,axiom,
% 4.71/5.17 ! [A2: set_int,X: int,G2: int > rat] :
% 4.71/5.17 ( ( finite_finite_int @ A2 )
% 4.71/5.17 => ( ~ ( member_int @ X @ A2 )
% 4.71/5.17 => ( ( groups3906332499630173760nt_rat @ G2 @ ( insert_int @ X @ A2 ) )
% 4.71/5.17 = ( plus_plus_rat @ ( G2 @ X ) @ ( groups3906332499630173760nt_rat @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.insert
% 4.71/5.17 thf(fact_7997_sum_Oinsert,axiom,
% 4.71/5.17 ! [A2: set_complex,X: complex,G2: complex > rat] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.17 => ( ~ ( member_complex @ X @ A2 )
% 4.71/5.17 => ( ( groups5058264527183730370ex_rat @ G2 @ ( insert_complex @ X @ A2 ) )
% 4.71/5.17 = ( plus_plus_rat @ ( G2 @ X ) @ ( groups5058264527183730370ex_rat @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.insert
% 4.71/5.17 thf(fact_7998_zero__less__binomial__iff,axiom,
% 4.71/5.17 ! [N: nat,K: nat] :
% 4.71/5.17 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) )
% 4.71/5.17 = ( ord_less_eq_nat @ K @ N ) ) ).
% 4.71/5.17
% 4.71/5.17 % zero_less_binomial_iff
% 4.71/5.17 thf(fact_7999_sum__abs__ge__zero,axiom,
% 4.71/5.17 ! [F: int > int,A2: set_int] :
% 4.71/5.17 ( ord_less_eq_int @ zero_zero_int
% 4.71/5.17 @ ( groups4538972089207619220nt_int
% 4.71/5.17 @ ^ [I4: int] : ( abs_abs_int @ ( F @ I4 ) )
% 4.71/5.17 @ A2 ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_abs_ge_zero
% 4.71/5.17 thf(fact_8000_sum__abs__ge__zero,axiom,
% 4.71/5.17 ! [F: nat > real,A2: set_nat] :
% 4.71/5.17 ( ord_less_eq_real @ zero_zero_real
% 4.71/5.17 @ ( groups6591440286371151544t_real
% 4.71/5.17 @ ^ [I4: nat] : ( abs_abs_real @ ( F @ I4 ) )
% 4.71/5.17 @ A2 ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_abs_ge_zero
% 4.71/5.17 thf(fact_8001_distinct__swap,axiom,
% 4.71/5.17 ! [I: nat,Xs: list_int,J: nat] :
% 4.71/5.17 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 4.71/5.17 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 4.71/5.17 => ( ( distinct_int @ ( list_update_int @ ( list_update_int @ Xs @ I @ ( nth_int @ Xs @ J ) ) @ J @ ( nth_int @ Xs @ I ) ) )
% 4.71/5.17 = ( distinct_int @ Xs ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % distinct_swap
% 4.71/5.17 thf(fact_8002_distinct__swap,axiom,
% 4.71/5.17 ! [I: nat,Xs: list_VEBT_VEBT,J: nat] :
% 4.71/5.17 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.71/5.17 => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.71/5.17 => ( ( distinct_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( nth_VEBT_VEBT @ Xs @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs @ I ) ) )
% 4.71/5.17 = ( distinct_VEBT_VEBT @ Xs ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % distinct_swap
% 4.71/5.17 thf(fact_8003_distinct__swap,axiom,
% 4.71/5.17 ! [I: nat,Xs: list_nat,J: nat] :
% 4.71/5.17 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 4.71/5.17 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 4.71/5.17 => ( ( distinct_nat @ ( list_update_nat @ ( list_update_nat @ Xs @ I @ ( nth_nat @ Xs @ J ) ) @ J @ ( nth_nat @ Xs @ I ) ) )
% 4.71/5.17 = ( distinct_nat @ Xs ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % distinct_swap
% 4.71/5.17 thf(fact_8004_sum_Ocl__ivl__Suc,axiom,
% 4.71/5.17 ! [N: nat,M2: nat,G2: nat > rat] :
% 4.71/5.17 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 4.71/5.17 => ( ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 4.71/5.17 = zero_zero_rat ) )
% 4.71/5.17 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 4.71/5.17 => ( ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 4.71/5.17 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.cl_ivl_Suc
% 4.71/5.17 thf(fact_8005_sum_Ocl__ivl__Suc,axiom,
% 4.71/5.17 ! [N: nat,M2: nat,G2: nat > int] :
% 4.71/5.17 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 4.71/5.17 => ( ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 4.71/5.17 = zero_zero_int ) )
% 4.71/5.17 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 4.71/5.17 => ( ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 4.71/5.17 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.cl_ivl_Suc
% 4.71/5.17 thf(fact_8006_sum_Ocl__ivl__Suc,axiom,
% 4.71/5.17 ! [N: nat,M2: nat,G2: nat > nat] :
% 4.71/5.17 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 4.71/5.17 => ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 4.71/5.17 = zero_zero_nat ) )
% 4.71/5.17 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 4.71/5.17 => ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 4.71/5.17 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.cl_ivl_Suc
% 4.71/5.17 thf(fact_8007_sum_Ocl__ivl__Suc,axiom,
% 4.71/5.17 ! [N: nat,M2: nat,G2: nat > real] :
% 4.71/5.17 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 4.71/5.17 => ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 4.71/5.17 = zero_zero_real ) )
% 4.71/5.17 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 4.71/5.17 => ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 4.71/5.17 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.cl_ivl_Suc
% 4.71/5.17 thf(fact_8008_sum__zero__power,axiom,
% 4.71/5.17 ! [A2: set_nat,C: nat > complex] :
% 4.71/5.17 ( ( ( ( finite_finite_nat @ A2 )
% 4.71/5.17 & ( member_nat @ zero_zero_nat @ A2 ) )
% 4.71/5.17 => ( ( groups2073611262835488442omplex
% 4.71/5.17 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) )
% 4.71/5.17 @ A2 )
% 4.71/5.17 = ( C @ zero_zero_nat ) ) )
% 4.71/5.17 & ( ~ ( ( finite_finite_nat @ A2 )
% 4.71/5.17 & ( member_nat @ zero_zero_nat @ A2 ) )
% 4.71/5.17 => ( ( groups2073611262835488442omplex
% 4.71/5.17 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) )
% 4.71/5.17 @ A2 )
% 4.71/5.17 = zero_zero_complex ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_zero_power
% 4.71/5.17 thf(fact_8009_sum__zero__power,axiom,
% 4.71/5.17 ! [A2: set_nat,C: nat > rat] :
% 4.71/5.17 ( ( ( ( finite_finite_nat @ A2 )
% 4.71/5.17 & ( member_nat @ zero_zero_nat @ A2 ) )
% 4.71/5.17 => ( ( groups2906978787729119204at_rat
% 4.71/5.17 @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) )
% 4.71/5.17 @ A2 )
% 4.71/5.17 = ( C @ zero_zero_nat ) ) )
% 4.71/5.17 & ( ~ ( ( finite_finite_nat @ A2 )
% 4.71/5.17 & ( member_nat @ zero_zero_nat @ A2 ) )
% 4.71/5.17 => ( ( groups2906978787729119204at_rat
% 4.71/5.17 @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) )
% 4.71/5.17 @ A2 )
% 4.71/5.17 = zero_zero_rat ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_zero_power
% 4.71/5.17 thf(fact_8010_sum__zero__power,axiom,
% 4.71/5.17 ! [A2: set_nat,C: nat > real] :
% 4.71/5.17 ( ( ( ( finite_finite_nat @ A2 )
% 4.71/5.17 & ( member_nat @ zero_zero_nat @ A2 ) )
% 4.71/5.17 => ( ( groups6591440286371151544t_real
% 4.71/5.17 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) )
% 4.71/5.17 @ A2 )
% 4.71/5.17 = ( C @ zero_zero_nat ) ) )
% 4.71/5.17 & ( ~ ( ( finite_finite_nat @ A2 )
% 4.71/5.17 & ( member_nat @ zero_zero_nat @ A2 ) )
% 4.71/5.17 => ( ( groups6591440286371151544t_real
% 4.71/5.17 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) )
% 4.71/5.17 @ A2 )
% 4.71/5.17 = zero_zero_real ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_zero_power
% 4.71/5.17 thf(fact_8011_finite__lists__distinct__length__eq,axiom,
% 4.71/5.17 ! [A2: set_complex,N: nat] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.17 => ( finite8712137658972009173omplex
% 4.71/5.17 @ ( collect_list_complex
% 4.71/5.17 @ ^ [Xs2: list_complex] :
% 4.71/5.17 ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 4.71/5.17 = N )
% 4.71/5.17 & ( distinct_complex @ Xs2 )
% 4.71/5.17 & ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % finite_lists_distinct_length_eq
% 4.71/5.17 thf(fact_8012_finite__lists__distinct__length__eq,axiom,
% 4.71/5.17 ! [A2: set_Pr1261947904930325089at_nat,N: nat] :
% 4.71/5.17 ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.17 => ( finite500796754983035824at_nat
% 4.71/5.17 @ ( collec3343600615725829874at_nat
% 4.71/5.17 @ ^ [Xs2: list_P6011104703257516679at_nat] :
% 4.71/5.17 ( ( ( size_s5460976970255530739at_nat @ Xs2 )
% 4.71/5.17 = N )
% 4.71/5.17 & ( distin6923225563576452346at_nat @ Xs2 )
% 4.71/5.17 & ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs2 ) @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % finite_lists_distinct_length_eq
% 4.71/5.17 thf(fact_8013_finite__lists__distinct__length__eq,axiom,
% 4.71/5.17 ! [A2: set_Extended_enat,N: nat] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.17 => ( finite1862508098717546133d_enat
% 4.71/5.17 @ ( collec8433460942617342167d_enat
% 4.71/5.17 @ ^ [Xs2: list_Extended_enat] :
% 4.71/5.17 ( ( ( size_s3941691890525107288d_enat @ Xs2 )
% 4.71/5.17 = N )
% 4.71/5.17 & ( distin4523846830085650399d_enat @ Xs2 )
% 4.71/5.17 & ( ord_le7203529160286727270d_enat @ ( set_Extended_enat2 @ Xs2 ) @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % finite_lists_distinct_length_eq
% 4.71/5.17 thf(fact_8014_finite__lists__distinct__length__eq,axiom,
% 4.71/5.17 ! [A2: set_VEBT_VEBT,N: nat] :
% 4.71/5.17 ( ( finite5795047828879050333T_VEBT @ A2 )
% 4.71/5.17 => ( finite3004134309566078307T_VEBT
% 4.71/5.17 @ ( collec5608196760682091941T_VEBT
% 4.71/5.17 @ ^ [Xs2: list_VEBT_VEBT] :
% 4.71/5.17 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 4.71/5.17 = N )
% 4.71/5.17 & ( distinct_VEBT_VEBT @ Xs2 )
% 4.71/5.17 & ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % finite_lists_distinct_length_eq
% 4.71/5.17 thf(fact_8015_finite__lists__distinct__length__eq,axiom,
% 4.71/5.17 ! [A2: set_nat,N: nat] :
% 4.71/5.17 ( ( finite_finite_nat @ A2 )
% 4.71/5.17 => ( finite8100373058378681591st_nat
% 4.71/5.17 @ ( collect_list_nat
% 4.71/5.17 @ ^ [Xs2: list_nat] :
% 4.71/5.17 ( ( ( size_size_list_nat @ Xs2 )
% 4.71/5.17 = N )
% 4.71/5.17 & ( distinct_nat @ Xs2 )
% 4.71/5.17 & ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % finite_lists_distinct_length_eq
% 4.71/5.17 thf(fact_8016_finite__lists__distinct__length__eq,axiom,
% 4.71/5.17 ! [A2: set_int,N: nat] :
% 4.71/5.17 ( ( finite_finite_int @ A2 )
% 4.71/5.17 => ( finite3922522038869484883st_int
% 4.71/5.17 @ ( collect_list_int
% 4.71/5.17 @ ^ [Xs2: list_int] :
% 4.71/5.17 ( ( ( size_size_list_int @ Xs2 )
% 4.71/5.17 = N )
% 4.71/5.17 & ( distinct_int @ Xs2 )
% 4.71/5.17 & ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % finite_lists_distinct_length_eq
% 4.71/5.17 thf(fact_8017_norm__of__real__add1,axiom,
% 4.71/5.17 ! [X: real] :
% 4.71/5.17 ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X ) @ one_one_real ) )
% 4.71/5.17 = ( abs_abs_real @ ( plus_plus_real @ X @ one_one_real ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % norm_of_real_add1
% 4.71/5.17 thf(fact_8018_norm__of__real__add1,axiom,
% 4.71/5.17 ! [X: real] :
% 4.71/5.17 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X ) @ one_one_complex ) )
% 4.71/5.17 = ( abs_abs_real @ ( plus_plus_real @ X @ one_one_real ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % norm_of_real_add1
% 4.71/5.17 thf(fact_8019_sum__zero__power_H,axiom,
% 4.71/5.17 ! [A2: set_nat,C: nat > complex,D: nat > complex] :
% 4.71/5.17 ( ( ( ( finite_finite_nat @ A2 )
% 4.71/5.17 & ( member_nat @ zero_zero_nat @ A2 ) )
% 4.71/5.17 => ( ( groups2073611262835488442omplex
% 4.71/5.17 @ ^ [I4: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) ) @ ( D @ I4 ) )
% 4.71/5.17 @ A2 )
% 4.71/5.17 = ( divide1717551699836669952omplex @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 4.71/5.17 & ( ~ ( ( finite_finite_nat @ A2 )
% 4.71/5.17 & ( member_nat @ zero_zero_nat @ A2 ) )
% 4.71/5.17 => ( ( groups2073611262835488442omplex
% 4.71/5.17 @ ^ [I4: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) ) @ ( D @ I4 ) )
% 4.71/5.17 @ A2 )
% 4.71/5.17 = zero_zero_complex ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_zero_power'
% 4.71/5.17 thf(fact_8020_sum__zero__power_H,axiom,
% 4.71/5.17 ! [A2: set_nat,C: nat > rat,D: nat > rat] :
% 4.71/5.17 ( ( ( ( finite_finite_nat @ A2 )
% 4.71/5.17 & ( member_nat @ zero_zero_nat @ A2 ) )
% 4.71/5.17 => ( ( groups2906978787729119204at_rat
% 4.71/5.17 @ ^ [I4: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) ) @ ( D @ I4 ) )
% 4.71/5.17 @ A2 )
% 4.71/5.17 = ( divide_divide_rat @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 4.71/5.17 & ( ~ ( ( finite_finite_nat @ A2 )
% 4.71/5.17 & ( member_nat @ zero_zero_nat @ A2 ) )
% 4.71/5.17 => ( ( groups2906978787729119204at_rat
% 4.71/5.17 @ ^ [I4: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) ) @ ( D @ I4 ) )
% 4.71/5.17 @ A2 )
% 4.71/5.17 = zero_zero_rat ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_zero_power'
% 4.71/5.17 thf(fact_8021_sum__zero__power_H,axiom,
% 4.71/5.17 ! [A2: set_nat,C: nat > real,D: nat > real] :
% 4.71/5.17 ( ( ( ( finite_finite_nat @ A2 )
% 4.71/5.17 & ( member_nat @ zero_zero_nat @ A2 ) )
% 4.71/5.17 => ( ( groups6591440286371151544t_real
% 4.71/5.17 @ ^ [I4: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) ) @ ( D @ I4 ) )
% 4.71/5.17 @ A2 )
% 4.71/5.17 = ( divide_divide_real @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 4.71/5.17 & ( ~ ( ( finite_finite_nat @ A2 )
% 4.71/5.17 & ( member_nat @ zero_zero_nat @ A2 ) )
% 4.71/5.17 => ( ( groups6591440286371151544t_real
% 4.71/5.17 @ ^ [I4: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) ) @ ( D @ I4 ) )
% 4.71/5.17 @ A2 )
% 4.71/5.17 = zero_zero_real ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_zero_power'
% 4.71/5.17 thf(fact_8022_sum__norm__le,axiom,
% 4.71/5.17 ! [S2: set_o,F: $o > complex,G2: $o > real] :
% 4.71/5.17 ( ! [X4: $o] :
% 4.71/5.17 ( ( member_o @ X4 @ S2 )
% 4.71/5.17 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X4 ) ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups5328290441151304332omplex @ F @ S2 ) ) @ ( groups8691415230153176458o_real @ G2 @ S2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_norm_le
% 4.71/5.17 thf(fact_8023_sum__norm__le,axiom,
% 4.71/5.17 ! [S2: set_set_nat,F: set_nat > complex,G2: set_nat > real] :
% 4.71/5.17 ( ! [X4: set_nat] :
% 4.71/5.17 ( ( member_set_nat @ X4 @ S2 )
% 4.71/5.17 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X4 ) ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups8255218700646806128omplex @ F @ S2 ) ) @ ( groups5107569545109728110t_real @ G2 @ S2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_norm_le
% 4.71/5.17 thf(fact_8024_sum__norm__le,axiom,
% 4.71/5.17 ! [S2: set_set_nat_rat,F: set_nat_rat > complex,G2: set_nat_rat > real] :
% 4.71/5.17 ( ! [X4: set_nat_rat] :
% 4.71/5.17 ( ( member_set_nat_rat @ X4 @ S2 )
% 4.71/5.17 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X4 ) ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups6246630355582004071omplex @ F @ S2 ) ) @ ( groups4357547368389691109t_real @ G2 @ S2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_norm_le
% 4.71/5.17 thf(fact_8025_sum__norm__le,axiom,
% 4.71/5.17 ! [S2: set_int,F: int > complex,G2: int > real] :
% 4.71/5.17 ( ! [X4: int] :
% 4.71/5.17 ( ( member_int @ X4 @ S2 )
% 4.71/5.17 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X4 ) ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups3049146728041665814omplex @ F @ S2 ) ) @ ( groups8778361861064173332t_real @ G2 @ S2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_norm_le
% 4.71/5.17 thf(fact_8026_sum__norm__le,axiom,
% 4.71/5.17 ! [S2: set_nat,F: nat > complex,G2: nat > real] :
% 4.71/5.17 ( ! [X4: nat] :
% 4.71/5.17 ( ( member_nat @ X4 @ S2 )
% 4.71/5.17 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X4 ) ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ S2 ) ) @ ( groups6591440286371151544t_real @ G2 @ S2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_norm_le
% 4.71/5.17 thf(fact_8027_sum__norm__le,axiom,
% 4.71/5.17 ! [S2: set_complex,F: complex > complex,G2: complex > real] :
% 4.71/5.17 ( ! [X4: complex] :
% 4.71/5.17 ( ( member_complex @ X4 @ S2 )
% 4.71/5.17 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X4 ) ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ S2 ) ) @ ( groups5808333547571424918x_real @ G2 @ S2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_norm_le
% 4.71/5.17 thf(fact_8028_sum__norm__le,axiom,
% 4.71/5.17 ! [S2: set_nat,F: nat > real,G2: nat > real] :
% 4.71/5.17 ( ! [X4: nat] :
% 4.71/5.17 ( ( member_nat @ X4 @ S2 )
% 4.71/5.17 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ X4 ) ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ S2 ) ) @ ( groups6591440286371151544t_real @ G2 @ S2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_norm_le
% 4.71/5.17 thf(fact_8029_sum_Oneutral,axiom,
% 4.71/5.17 ! [A2: set_nat,G2: nat > nat] :
% 4.71/5.17 ( ! [X4: nat] :
% 4.71/5.17 ( ( member_nat @ X4 @ A2 )
% 4.71/5.17 => ( ( G2 @ X4 )
% 4.71/5.17 = zero_zero_nat ) )
% 4.71/5.17 => ( ( groups3542108847815614940at_nat @ G2 @ A2 )
% 4.71/5.17 = zero_zero_nat ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.neutral
% 4.71/5.17 thf(fact_8030_sum_Oneutral,axiom,
% 4.71/5.17 ! [A2: set_complex,G2: complex > complex] :
% 4.71/5.17 ( ! [X4: complex] :
% 4.71/5.17 ( ( member_complex @ X4 @ A2 )
% 4.71/5.17 => ( ( G2 @ X4 )
% 4.71/5.17 = zero_zero_complex ) )
% 4.71/5.17 => ( ( groups7754918857620584856omplex @ G2 @ A2 )
% 4.71/5.17 = zero_zero_complex ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.neutral
% 4.71/5.17 thf(fact_8031_sum_Oneutral,axiom,
% 4.71/5.17 ! [A2: set_int,G2: int > int] :
% 4.71/5.17 ( ! [X4: int] :
% 4.71/5.17 ( ( member_int @ X4 @ A2 )
% 4.71/5.17 => ( ( G2 @ X4 )
% 4.71/5.17 = zero_zero_int ) )
% 4.71/5.17 => ( ( groups4538972089207619220nt_int @ G2 @ A2 )
% 4.71/5.17 = zero_zero_int ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.neutral
% 4.71/5.17 thf(fact_8032_sum_Oneutral,axiom,
% 4.71/5.17 ! [A2: set_nat,G2: nat > real] :
% 4.71/5.17 ( ! [X4: nat] :
% 4.71/5.17 ( ( member_nat @ X4 @ A2 )
% 4.71/5.17 => ( ( G2 @ X4 )
% 4.71/5.17 = zero_zero_real ) )
% 4.71/5.17 => ( ( groups6591440286371151544t_real @ G2 @ A2 )
% 4.71/5.17 = zero_zero_real ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.neutral
% 4.71/5.17 thf(fact_8033_sum_Onot__neutral__contains__not__neutral,axiom,
% 4.71/5.17 ! [G2: $o > real,A2: set_o] :
% 4.71/5.17 ( ( ( groups8691415230153176458o_real @ G2 @ A2 )
% 4.71/5.17 != zero_zero_real )
% 4.71/5.17 => ~ ! [A5: $o] :
% 4.71/5.17 ( ( member_o @ A5 @ A2 )
% 4.71/5.17 => ( ( G2 @ A5 )
% 4.71/5.17 = zero_zero_real ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.not_neutral_contains_not_neutral
% 4.71/5.17 thf(fact_8034_sum_Onot__neutral__contains__not__neutral,axiom,
% 4.71/5.17 ! [G2: int > real,A2: set_int] :
% 4.71/5.17 ( ( ( groups8778361861064173332t_real @ G2 @ A2 )
% 4.71/5.17 != zero_zero_real )
% 4.71/5.17 => ~ ! [A5: int] :
% 4.71/5.17 ( ( member_int @ A5 @ A2 )
% 4.71/5.17 => ( ( G2 @ A5 )
% 4.71/5.17 = zero_zero_real ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.not_neutral_contains_not_neutral
% 4.71/5.17 thf(fact_8035_sum_Onot__neutral__contains__not__neutral,axiom,
% 4.71/5.17 ! [G2: $o > rat,A2: set_o] :
% 4.71/5.17 ( ( ( groups7872700643590313910_o_rat @ G2 @ A2 )
% 4.71/5.17 != zero_zero_rat )
% 4.71/5.17 => ~ ! [A5: $o] :
% 4.71/5.17 ( ( member_o @ A5 @ A2 )
% 4.71/5.17 => ( ( G2 @ A5 )
% 4.71/5.17 = zero_zero_rat ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.not_neutral_contains_not_neutral
% 4.71/5.17 thf(fact_8036_sum_Onot__neutral__contains__not__neutral,axiom,
% 4.71/5.17 ! [G2: nat > rat,A2: set_nat] :
% 4.71/5.17 ( ( ( groups2906978787729119204at_rat @ G2 @ A2 )
% 4.71/5.17 != zero_zero_rat )
% 4.71/5.17 => ~ ! [A5: nat] :
% 4.71/5.17 ( ( member_nat @ A5 @ A2 )
% 4.71/5.17 => ( ( G2 @ A5 )
% 4.71/5.17 = zero_zero_rat ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.not_neutral_contains_not_neutral
% 4.71/5.17 thf(fact_8037_sum_Onot__neutral__contains__not__neutral,axiom,
% 4.71/5.17 ! [G2: int > rat,A2: set_int] :
% 4.71/5.17 ( ( ( groups3906332499630173760nt_rat @ G2 @ A2 )
% 4.71/5.17 != zero_zero_rat )
% 4.71/5.17 => ~ ! [A5: int] :
% 4.71/5.17 ( ( member_int @ A5 @ A2 )
% 4.71/5.17 => ( ( G2 @ A5 )
% 4.71/5.17 = zero_zero_rat ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.not_neutral_contains_not_neutral
% 4.71/5.17 thf(fact_8038_sum_Onot__neutral__contains__not__neutral,axiom,
% 4.71/5.17 ! [G2: $o > nat,A2: set_o] :
% 4.71/5.17 ( ( ( groups8507830703676809646_o_nat @ G2 @ A2 )
% 4.71/5.17 != zero_zero_nat )
% 4.71/5.17 => ~ ! [A5: $o] :
% 4.71/5.17 ( ( member_o @ A5 @ A2 )
% 4.71/5.17 => ( ( G2 @ A5 )
% 4.71/5.17 = zero_zero_nat ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.not_neutral_contains_not_neutral
% 4.71/5.17 thf(fact_8039_sum_Onot__neutral__contains__not__neutral,axiom,
% 4.71/5.17 ! [G2: int > nat,A2: set_int] :
% 4.71/5.17 ( ( ( groups4541462559716669496nt_nat @ G2 @ A2 )
% 4.71/5.17 != zero_zero_nat )
% 4.71/5.17 => ~ ! [A5: int] :
% 4.71/5.17 ( ( member_int @ A5 @ A2 )
% 4.71/5.17 => ( ( G2 @ A5 )
% 4.71/5.17 = zero_zero_nat ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.not_neutral_contains_not_neutral
% 4.71/5.17 thf(fact_8040_sum_Onot__neutral__contains__not__neutral,axiom,
% 4.71/5.17 ! [G2: $o > int,A2: set_o] :
% 4.71/5.17 ( ( ( groups8505340233167759370_o_int @ G2 @ A2 )
% 4.71/5.17 != zero_zero_int )
% 4.71/5.17 => ~ ! [A5: $o] :
% 4.71/5.17 ( ( member_o @ A5 @ A2 )
% 4.71/5.17 => ( ( G2 @ A5 )
% 4.71/5.17 = zero_zero_int ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.not_neutral_contains_not_neutral
% 4.71/5.17 thf(fact_8041_sum_Onot__neutral__contains__not__neutral,axiom,
% 4.71/5.17 ! [G2: nat > int,A2: set_nat] :
% 4.71/5.17 ( ( ( groups3539618377306564664at_int @ G2 @ A2 )
% 4.71/5.17 != zero_zero_int )
% 4.71/5.17 => ~ ! [A5: nat] :
% 4.71/5.17 ( ( member_nat @ A5 @ A2 )
% 4.71/5.17 => ( ( G2 @ A5 )
% 4.71/5.17 = zero_zero_int ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.not_neutral_contains_not_neutral
% 4.71/5.17 thf(fact_8042_sum_Onot__neutral__contains__not__neutral,axiom,
% 4.71/5.17 ! [G2: nat > nat,A2: set_nat] :
% 4.71/5.17 ( ( ( groups3542108847815614940at_nat @ G2 @ A2 )
% 4.71/5.17 != zero_zero_nat )
% 4.71/5.17 => ~ ! [A5: nat] :
% 4.71/5.17 ( ( member_nat @ A5 @ A2 )
% 4.71/5.17 => ( ( G2 @ A5 )
% 4.71/5.17 = zero_zero_nat ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.not_neutral_contains_not_neutral
% 4.71/5.17 thf(fact_8043_norm__sum,axiom,
% 4.71/5.17 ! [F: nat > complex,A2: set_nat] :
% 4.71/5.17 ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ A2 ) )
% 4.71/5.17 @ ( groups6591440286371151544t_real
% 4.71/5.17 @ ^ [I4: nat] : ( real_V1022390504157884413omplex @ ( F @ I4 ) )
% 4.71/5.17 @ A2 ) ) ).
% 4.71/5.17
% 4.71/5.17 % norm_sum
% 4.71/5.17 thf(fact_8044_norm__sum,axiom,
% 4.71/5.17 ! [F: complex > complex,A2: set_complex] :
% 4.71/5.17 ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 4.71/5.17 @ ( groups5808333547571424918x_real
% 4.71/5.17 @ ^ [I4: complex] : ( real_V1022390504157884413omplex @ ( F @ I4 ) )
% 4.71/5.17 @ A2 ) ) ).
% 4.71/5.17
% 4.71/5.17 % norm_sum
% 4.71/5.17 thf(fact_8045_norm__sum,axiom,
% 4.71/5.17 ! [F: nat > real,A2: set_nat] :
% 4.71/5.17 ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 4.71/5.17 @ ( groups6591440286371151544t_real
% 4.71/5.17 @ ^ [I4: nat] : ( real_V7735802525324610683m_real @ ( F @ I4 ) )
% 4.71/5.17 @ A2 ) ) ).
% 4.71/5.17
% 4.71/5.17 % norm_sum
% 4.71/5.17 thf(fact_8046_choose__one,axiom,
% 4.71/5.17 ! [N: nat] :
% 4.71/5.17 ( ( binomial @ N @ one_one_nat )
% 4.71/5.17 = N ) ).
% 4.71/5.17
% 4.71/5.17 % choose_one
% 4.71/5.17 thf(fact_8047_sum__mono,axiom,
% 4.71/5.17 ! [K4: set_o,F: $o > rat,G2: $o > rat] :
% 4.71/5.17 ( ! [I2: $o] :
% 4.71/5.17 ( ( member_o @ I2 @ K4 )
% 4.71/5.17 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G2 @ I2 ) ) )
% 4.71/5.17 => ( ord_less_eq_rat @ ( groups7872700643590313910_o_rat @ F @ K4 ) @ ( groups7872700643590313910_o_rat @ G2 @ K4 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_mono
% 4.71/5.17 thf(fact_8048_sum__mono,axiom,
% 4.71/5.17 ! [K4: set_nat,F: nat > rat,G2: nat > rat] :
% 4.71/5.17 ( ! [I2: nat] :
% 4.71/5.17 ( ( member_nat @ I2 @ K4 )
% 4.71/5.17 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G2 @ I2 ) ) )
% 4.71/5.17 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ K4 ) @ ( groups2906978787729119204at_rat @ G2 @ K4 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_mono
% 4.71/5.17 thf(fact_8049_sum__mono,axiom,
% 4.71/5.17 ! [K4: set_int,F: int > rat,G2: int > rat] :
% 4.71/5.17 ( ! [I2: int] :
% 4.71/5.17 ( ( member_int @ I2 @ K4 )
% 4.71/5.17 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G2 @ I2 ) ) )
% 4.71/5.17 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ K4 ) @ ( groups3906332499630173760nt_rat @ G2 @ K4 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_mono
% 4.71/5.17 thf(fact_8050_sum__mono,axiom,
% 4.71/5.17 ! [K4: set_o,F: $o > nat,G2: $o > nat] :
% 4.71/5.17 ( ! [I2: $o] :
% 4.71/5.17 ( ( member_o @ I2 @ K4 )
% 4.71/5.17 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G2 @ I2 ) ) )
% 4.71/5.17 => ( ord_less_eq_nat @ ( groups8507830703676809646_o_nat @ F @ K4 ) @ ( groups8507830703676809646_o_nat @ G2 @ K4 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_mono
% 4.71/5.17 thf(fact_8051_sum__mono,axiom,
% 4.71/5.17 ! [K4: set_int,F: int > nat,G2: int > nat] :
% 4.71/5.17 ( ! [I2: int] :
% 4.71/5.17 ( ( member_int @ I2 @ K4 )
% 4.71/5.17 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G2 @ I2 ) ) )
% 4.71/5.17 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K4 ) @ ( groups4541462559716669496nt_nat @ G2 @ K4 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_mono
% 4.71/5.17 thf(fact_8052_sum__mono,axiom,
% 4.71/5.17 ! [K4: set_o,F: $o > int,G2: $o > int] :
% 4.71/5.17 ( ! [I2: $o] :
% 4.71/5.17 ( ( member_o @ I2 @ K4 )
% 4.71/5.17 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G2 @ I2 ) ) )
% 4.71/5.17 => ( ord_less_eq_int @ ( groups8505340233167759370_o_int @ F @ K4 ) @ ( groups8505340233167759370_o_int @ G2 @ K4 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_mono
% 4.71/5.17 thf(fact_8053_sum__mono,axiom,
% 4.71/5.17 ! [K4: set_nat,F: nat > int,G2: nat > int] :
% 4.71/5.17 ( ! [I2: nat] :
% 4.71/5.17 ( ( member_nat @ I2 @ K4 )
% 4.71/5.17 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G2 @ I2 ) ) )
% 4.71/5.17 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K4 ) @ ( groups3539618377306564664at_int @ G2 @ K4 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_mono
% 4.71/5.17 thf(fact_8054_sum__mono,axiom,
% 4.71/5.17 ! [K4: set_nat,F: nat > nat,G2: nat > nat] :
% 4.71/5.17 ( ! [I2: nat] :
% 4.71/5.17 ( ( member_nat @ I2 @ K4 )
% 4.71/5.17 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G2 @ I2 ) ) )
% 4.71/5.17 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ K4 ) @ ( groups3542108847815614940at_nat @ G2 @ K4 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_mono
% 4.71/5.17 thf(fact_8055_sum__mono,axiom,
% 4.71/5.17 ! [K4: set_int,F: int > int,G2: int > int] :
% 4.71/5.17 ( ! [I2: int] :
% 4.71/5.17 ( ( member_int @ I2 @ K4 )
% 4.71/5.17 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G2 @ I2 ) ) )
% 4.71/5.17 => ( ord_less_eq_int @ ( groups4538972089207619220nt_int @ F @ K4 ) @ ( groups4538972089207619220nt_int @ G2 @ K4 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_mono
% 4.71/5.17 thf(fact_8056_sum__mono,axiom,
% 4.71/5.17 ! [K4: set_nat,F: nat > real,G2: nat > real] :
% 4.71/5.17 ( ! [I2: nat] :
% 4.71/5.17 ( ( member_nat @ I2 @ K4 )
% 4.71/5.17 => ( ord_less_eq_real @ ( F @ I2 ) @ ( G2 @ I2 ) ) )
% 4.71/5.17 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ K4 ) @ ( groups6591440286371151544t_real @ G2 @ K4 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_mono
% 4.71/5.17 thf(fact_8057_sum_Oswap__restrict,axiom,
% 4.71/5.17 ! [A2: set_o,B2: set_nat,G2: $o > nat > nat,R: $o > nat > $o] :
% 4.71/5.17 ( ( finite_finite_o @ A2 )
% 4.71/5.17 => ( ( finite_finite_nat @ B2 )
% 4.71/5.17 => ( ( groups8507830703676809646_o_nat
% 4.71/5.17 @ ^ [X3: $o] :
% 4.71/5.17 ( groups3542108847815614940at_nat @ ( G2 @ X3 )
% 4.71/5.17 @ ( collect_nat
% 4.71/5.17 @ ^ [Y2: nat] :
% 4.71/5.17 ( ( member_nat @ Y2 @ B2 )
% 4.71/5.17 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.17 @ A2 )
% 4.71/5.17 = ( groups3542108847815614940at_nat
% 4.71/5.17 @ ^ [Y2: nat] :
% 4.71/5.17 ( groups8507830703676809646_o_nat
% 4.71/5.17 @ ^ [X3: $o] : ( G2 @ X3 @ Y2 )
% 4.71/5.17 @ ( collect_o
% 4.71/5.17 @ ^ [X3: $o] :
% 4.71/5.17 ( ( member_o @ X3 @ A2 )
% 4.71/5.17 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.17 @ B2 ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.swap_restrict
% 4.71/5.17 thf(fact_8058_sum_Oswap__restrict,axiom,
% 4.71/5.17 ! [A2: set_int,B2: set_nat,G2: int > nat > nat,R: int > nat > $o] :
% 4.71/5.17 ( ( finite_finite_int @ A2 )
% 4.71/5.17 => ( ( finite_finite_nat @ B2 )
% 4.71/5.17 => ( ( groups4541462559716669496nt_nat
% 4.71/5.17 @ ^ [X3: int] :
% 4.71/5.17 ( groups3542108847815614940at_nat @ ( G2 @ X3 )
% 4.71/5.17 @ ( collect_nat
% 4.71/5.17 @ ^ [Y2: nat] :
% 4.71/5.17 ( ( member_nat @ Y2 @ B2 )
% 4.71/5.17 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.17 @ A2 )
% 4.71/5.17 = ( groups3542108847815614940at_nat
% 4.71/5.17 @ ^ [Y2: nat] :
% 4.71/5.17 ( groups4541462559716669496nt_nat
% 4.71/5.17 @ ^ [X3: int] : ( G2 @ X3 @ Y2 )
% 4.71/5.17 @ ( collect_int
% 4.71/5.17 @ ^ [X3: int] :
% 4.71/5.17 ( ( member_int @ X3 @ A2 )
% 4.71/5.17 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.17 @ B2 ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.swap_restrict
% 4.71/5.17 thf(fact_8059_sum_Oswap__restrict,axiom,
% 4.71/5.17 ! [A2: set_complex,B2: set_nat,G2: complex > nat > nat,R: complex > nat > $o] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.17 => ( ( finite_finite_nat @ B2 )
% 4.71/5.17 => ( ( groups5693394587270226106ex_nat
% 4.71/5.17 @ ^ [X3: complex] :
% 4.71/5.17 ( groups3542108847815614940at_nat @ ( G2 @ X3 )
% 4.71/5.17 @ ( collect_nat
% 4.71/5.17 @ ^ [Y2: nat] :
% 4.71/5.17 ( ( member_nat @ Y2 @ B2 )
% 4.71/5.17 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.17 @ A2 )
% 4.71/5.17 = ( groups3542108847815614940at_nat
% 4.71/5.17 @ ^ [Y2: nat] :
% 4.71/5.17 ( groups5693394587270226106ex_nat
% 4.71/5.17 @ ^ [X3: complex] : ( G2 @ X3 @ Y2 )
% 4.71/5.17 @ ( collect_complex
% 4.71/5.17 @ ^ [X3: complex] :
% 4.71/5.17 ( ( member_complex @ X3 @ A2 )
% 4.71/5.17 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.17 @ B2 ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.swap_restrict
% 4.71/5.17 thf(fact_8060_sum_Oswap__restrict,axiom,
% 4.71/5.17 ! [A2: set_Extended_enat,B2: set_nat,G2: extended_enat > nat > nat,R: extended_enat > nat > $o] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.17 => ( ( finite_finite_nat @ B2 )
% 4.71/5.17 => ( ( groups2027974829824023292at_nat
% 4.71/5.17 @ ^ [X3: extended_enat] :
% 4.71/5.17 ( groups3542108847815614940at_nat @ ( G2 @ X3 )
% 4.71/5.17 @ ( collect_nat
% 4.71/5.17 @ ^ [Y2: nat] :
% 4.71/5.17 ( ( member_nat @ Y2 @ B2 )
% 4.71/5.17 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.17 @ A2 )
% 4.71/5.17 = ( groups3542108847815614940at_nat
% 4.71/5.17 @ ^ [Y2: nat] :
% 4.71/5.17 ( groups2027974829824023292at_nat
% 4.71/5.17 @ ^ [X3: extended_enat] : ( G2 @ X3 @ Y2 )
% 4.71/5.17 @ ( collec4429806609662206161d_enat
% 4.71/5.17 @ ^ [X3: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ X3 @ A2 )
% 4.71/5.17 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.17 @ B2 ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.swap_restrict
% 4.71/5.17 thf(fact_8061_sum_Oswap__restrict,axiom,
% 4.71/5.17 ! [A2: set_o,B2: set_complex,G2: $o > complex > complex,R: $o > complex > $o] :
% 4.71/5.17 ( ( finite_finite_o @ A2 )
% 4.71/5.17 => ( ( finite3207457112153483333omplex @ B2 )
% 4.71/5.17 => ( ( groups5328290441151304332omplex
% 4.71/5.17 @ ^ [X3: $o] :
% 4.71/5.17 ( groups7754918857620584856omplex @ ( G2 @ X3 )
% 4.71/5.17 @ ( collect_complex
% 4.71/5.17 @ ^ [Y2: complex] :
% 4.71/5.17 ( ( member_complex @ Y2 @ B2 )
% 4.71/5.17 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.17 @ A2 )
% 4.71/5.17 = ( groups7754918857620584856omplex
% 4.71/5.17 @ ^ [Y2: complex] :
% 4.71/5.17 ( groups5328290441151304332omplex
% 4.71/5.17 @ ^ [X3: $o] : ( G2 @ X3 @ Y2 )
% 4.71/5.17 @ ( collect_o
% 4.71/5.17 @ ^ [X3: $o] :
% 4.71/5.17 ( ( member_o @ X3 @ A2 )
% 4.71/5.17 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.17 @ B2 ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.swap_restrict
% 4.71/5.17 thf(fact_8062_sum_Oswap__restrict,axiom,
% 4.71/5.17 ! [A2: set_nat,B2: set_complex,G2: nat > complex > complex,R: nat > complex > $o] :
% 4.71/5.17 ( ( finite_finite_nat @ A2 )
% 4.71/5.17 => ( ( finite3207457112153483333omplex @ B2 )
% 4.71/5.17 => ( ( groups2073611262835488442omplex
% 4.71/5.17 @ ^ [X3: nat] :
% 4.71/5.17 ( groups7754918857620584856omplex @ ( G2 @ X3 )
% 4.71/5.17 @ ( collect_complex
% 4.71/5.17 @ ^ [Y2: complex] :
% 4.71/5.17 ( ( member_complex @ Y2 @ B2 )
% 4.71/5.17 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.17 @ A2 )
% 4.71/5.17 = ( groups7754918857620584856omplex
% 4.71/5.17 @ ^ [Y2: complex] :
% 4.71/5.17 ( groups2073611262835488442omplex
% 4.71/5.17 @ ^ [X3: nat] : ( G2 @ X3 @ Y2 )
% 4.71/5.17 @ ( collect_nat
% 4.71/5.17 @ ^ [X3: nat] :
% 4.71/5.17 ( ( member_nat @ X3 @ A2 )
% 4.71/5.17 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.17 @ B2 ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.swap_restrict
% 4.71/5.17 thf(fact_8063_sum_Oswap__restrict,axiom,
% 4.71/5.17 ! [A2: set_int,B2: set_complex,G2: int > complex > complex,R: int > complex > $o] :
% 4.71/5.17 ( ( finite_finite_int @ A2 )
% 4.71/5.17 => ( ( finite3207457112153483333omplex @ B2 )
% 4.71/5.17 => ( ( groups3049146728041665814omplex
% 4.71/5.17 @ ^ [X3: int] :
% 4.71/5.17 ( groups7754918857620584856omplex @ ( G2 @ X3 )
% 4.71/5.17 @ ( collect_complex
% 4.71/5.17 @ ^ [Y2: complex] :
% 4.71/5.17 ( ( member_complex @ Y2 @ B2 )
% 4.71/5.17 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.17 @ A2 )
% 4.71/5.17 = ( groups7754918857620584856omplex
% 4.71/5.17 @ ^ [Y2: complex] :
% 4.71/5.17 ( groups3049146728041665814omplex
% 4.71/5.17 @ ^ [X3: int] : ( G2 @ X3 @ Y2 )
% 4.71/5.17 @ ( collect_int
% 4.71/5.17 @ ^ [X3: int] :
% 4.71/5.17 ( ( member_int @ X3 @ A2 )
% 4.71/5.17 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.17 @ B2 ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.swap_restrict
% 4.71/5.17 thf(fact_8064_sum_Oswap__restrict,axiom,
% 4.71/5.17 ! [A2: set_Extended_enat,B2: set_complex,G2: extended_enat > complex > complex,R: extended_enat > complex > $o] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.17 => ( ( finite3207457112153483333omplex @ B2 )
% 4.71/5.17 => ( ( groups6818542070133387226omplex
% 4.71/5.17 @ ^ [X3: extended_enat] :
% 4.71/5.17 ( groups7754918857620584856omplex @ ( G2 @ X3 )
% 4.71/5.17 @ ( collect_complex
% 4.71/5.17 @ ^ [Y2: complex] :
% 4.71/5.17 ( ( member_complex @ Y2 @ B2 )
% 4.71/5.17 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.17 @ A2 )
% 4.71/5.17 = ( groups7754918857620584856omplex
% 4.71/5.17 @ ^ [Y2: complex] :
% 4.71/5.17 ( groups6818542070133387226omplex
% 4.71/5.17 @ ^ [X3: extended_enat] : ( G2 @ X3 @ Y2 )
% 4.71/5.17 @ ( collec4429806609662206161d_enat
% 4.71/5.17 @ ^ [X3: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ X3 @ A2 )
% 4.71/5.17 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.17 @ B2 ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.swap_restrict
% 4.71/5.17 thf(fact_8065_sum_Oswap__restrict,axiom,
% 4.71/5.17 ! [A2: set_o,B2: set_int,G2: $o > int > int,R: $o > int > $o] :
% 4.71/5.17 ( ( finite_finite_o @ A2 )
% 4.71/5.17 => ( ( finite_finite_int @ B2 )
% 4.71/5.17 => ( ( groups8505340233167759370_o_int
% 4.71/5.17 @ ^ [X3: $o] :
% 4.71/5.17 ( groups4538972089207619220nt_int @ ( G2 @ X3 )
% 4.71/5.17 @ ( collect_int
% 4.71/5.17 @ ^ [Y2: int] :
% 4.71/5.17 ( ( member_int @ Y2 @ B2 )
% 4.71/5.17 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.17 @ A2 )
% 4.71/5.17 = ( groups4538972089207619220nt_int
% 4.71/5.17 @ ^ [Y2: int] :
% 4.71/5.17 ( groups8505340233167759370_o_int
% 4.71/5.17 @ ^ [X3: $o] : ( G2 @ X3 @ Y2 )
% 4.71/5.17 @ ( collect_o
% 4.71/5.17 @ ^ [X3: $o] :
% 4.71/5.17 ( ( member_o @ X3 @ A2 )
% 4.71/5.17 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.17 @ B2 ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.swap_restrict
% 4.71/5.17 thf(fact_8066_sum_Oswap__restrict,axiom,
% 4.71/5.17 ! [A2: set_nat,B2: set_int,G2: nat > int > int,R: nat > int > $o] :
% 4.71/5.17 ( ( finite_finite_nat @ A2 )
% 4.71/5.17 => ( ( finite_finite_int @ B2 )
% 4.71/5.17 => ( ( groups3539618377306564664at_int
% 4.71/5.17 @ ^ [X3: nat] :
% 4.71/5.17 ( groups4538972089207619220nt_int @ ( G2 @ X3 )
% 4.71/5.17 @ ( collect_int
% 4.71/5.17 @ ^ [Y2: int] :
% 4.71/5.17 ( ( member_int @ Y2 @ B2 )
% 4.71/5.17 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.17 @ A2 )
% 4.71/5.17 = ( groups4538972089207619220nt_int
% 4.71/5.17 @ ^ [Y2: int] :
% 4.71/5.17 ( groups3539618377306564664at_int
% 4.71/5.17 @ ^ [X3: nat] : ( G2 @ X3 @ Y2 )
% 4.71/5.17 @ ( collect_nat
% 4.71/5.17 @ ^ [X3: nat] :
% 4.71/5.17 ( ( member_nat @ X3 @ A2 )
% 4.71/5.17 & ( R @ X3 @ Y2 ) ) ) )
% 4.71/5.17 @ B2 ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.swap_restrict
% 4.71/5.17 thf(fact_8067_sum__nonpos,axiom,
% 4.71/5.17 ! [A2: set_o,F: $o > real] :
% 4.71/5.17 ( ! [X4: $o] :
% 4.71/5.17 ( ( member_o @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_real @ ( F @ X4 ) @ zero_zero_real ) )
% 4.71/5.17 => ( ord_less_eq_real @ ( groups8691415230153176458o_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonpos
% 4.71/5.17 thf(fact_8068_sum__nonpos,axiom,
% 4.71/5.17 ! [A2: set_int,F: int > real] :
% 4.71/5.17 ( ! [X4: int] :
% 4.71/5.17 ( ( member_int @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_real @ ( F @ X4 ) @ zero_zero_real ) )
% 4.71/5.17 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonpos
% 4.71/5.17 thf(fact_8069_sum__nonpos,axiom,
% 4.71/5.17 ! [A2: set_o,F: $o > rat] :
% 4.71/5.17 ( ! [X4: $o] :
% 4.71/5.17 ( ( member_o @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 4.71/5.17 => ( ord_less_eq_rat @ ( groups7872700643590313910_o_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonpos
% 4.71/5.17 thf(fact_8070_sum__nonpos,axiom,
% 4.71/5.17 ! [A2: set_nat,F: nat > rat] :
% 4.71/5.17 ( ! [X4: nat] :
% 4.71/5.17 ( ( member_nat @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 4.71/5.17 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonpos
% 4.71/5.17 thf(fact_8071_sum__nonpos,axiom,
% 4.71/5.17 ! [A2: set_int,F: int > rat] :
% 4.71/5.17 ( ! [X4: int] :
% 4.71/5.17 ( ( member_int @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 4.71/5.17 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonpos
% 4.71/5.17 thf(fact_8072_sum__nonpos,axiom,
% 4.71/5.17 ! [A2: set_o,F: $o > nat] :
% 4.71/5.17 ( ! [X4: $o] :
% 4.71/5.17 ( ( member_o @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_nat @ ( F @ X4 ) @ zero_zero_nat ) )
% 4.71/5.17 => ( ord_less_eq_nat @ ( groups8507830703676809646_o_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonpos
% 4.71/5.17 thf(fact_8073_sum__nonpos,axiom,
% 4.71/5.17 ! [A2: set_int,F: int > nat] :
% 4.71/5.17 ( ! [X4: int] :
% 4.71/5.17 ( ( member_int @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_nat @ ( F @ X4 ) @ zero_zero_nat ) )
% 4.71/5.17 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonpos
% 4.71/5.17 thf(fact_8074_sum__nonpos,axiom,
% 4.71/5.17 ! [A2: set_o,F: $o > int] :
% 4.71/5.17 ( ! [X4: $o] :
% 4.71/5.17 ( ( member_o @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_int @ ( F @ X4 ) @ zero_zero_int ) )
% 4.71/5.17 => ( ord_less_eq_int @ ( groups8505340233167759370_o_int @ F @ A2 ) @ zero_zero_int ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonpos
% 4.71/5.17 thf(fact_8075_sum__nonpos,axiom,
% 4.71/5.17 ! [A2: set_nat,F: nat > int] :
% 4.71/5.17 ( ! [X4: nat] :
% 4.71/5.17 ( ( member_nat @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_int @ ( F @ X4 ) @ zero_zero_int ) )
% 4.71/5.17 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ zero_zero_int ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonpos
% 4.71/5.17 thf(fact_8076_sum__nonpos,axiom,
% 4.71/5.17 ! [A2: set_nat,F: nat > nat] :
% 4.71/5.17 ( ! [X4: nat] :
% 4.71/5.17 ( ( member_nat @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_nat @ ( F @ X4 ) @ zero_zero_nat ) )
% 4.71/5.17 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonpos
% 4.71/5.17 thf(fact_8077_sum__nonneg,axiom,
% 4.71/5.17 ! [A2: set_o,F: $o > real] :
% 4.71/5.17 ( ! [X4: $o] :
% 4.71/5.17 ( ( member_o @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( groups8691415230153176458o_real @ F @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg
% 4.71/5.17 thf(fact_8078_sum__nonneg,axiom,
% 4.71/5.17 ! [A2: set_int,F: int > real] :
% 4.71/5.17 ( ! [X4: int] :
% 4.71/5.17 ( ( member_int @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg
% 4.71/5.17 thf(fact_8079_sum__nonneg,axiom,
% 4.71/5.17 ! [A2: set_o,F: $o > rat] :
% 4.71/5.17 ( ! [X4: $o] :
% 4.71/5.17 ( ( member_o @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 4.71/5.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups7872700643590313910_o_rat @ F @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg
% 4.71/5.17 thf(fact_8080_sum__nonneg,axiom,
% 4.71/5.17 ! [A2: set_nat,F: nat > rat] :
% 4.71/5.17 ( ! [X4: nat] :
% 4.71/5.17 ( ( member_nat @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 4.71/5.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg
% 4.71/5.17 thf(fact_8081_sum__nonneg,axiom,
% 4.71/5.17 ! [A2: set_int,F: int > rat] :
% 4.71/5.17 ( ! [X4: int] :
% 4.71/5.17 ( ( member_int @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 4.71/5.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg
% 4.71/5.17 thf(fact_8082_sum__nonneg,axiom,
% 4.71/5.17 ! [A2: set_o,F: $o > nat] :
% 4.71/5.17 ( ! [X4: $o] :
% 4.71/5.17 ( ( member_o @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 4.71/5.17 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups8507830703676809646_o_nat @ F @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg
% 4.71/5.17 thf(fact_8083_sum__nonneg,axiom,
% 4.71/5.17 ! [A2: set_int,F: int > nat] :
% 4.71/5.17 ( ! [X4: int] :
% 4.71/5.17 ( ( member_int @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 4.71/5.17 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg
% 4.71/5.17 thf(fact_8084_sum__nonneg,axiom,
% 4.71/5.17 ! [A2: set_o,F: $o > int] :
% 4.71/5.17 ( ! [X4: $o] :
% 4.71/5.17 ( ( member_o @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 4.71/5.17 => ( ord_less_eq_int @ zero_zero_int @ ( groups8505340233167759370_o_int @ F @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg
% 4.71/5.17 thf(fact_8085_sum__nonneg,axiom,
% 4.71/5.17 ! [A2: set_nat,F: nat > int] :
% 4.71/5.17 ( ! [X4: nat] :
% 4.71/5.17 ( ( member_nat @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 4.71/5.17 => ( ord_less_eq_int @ zero_zero_int @ ( groups3539618377306564664at_int @ F @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg
% 4.71/5.17 thf(fact_8086_sum__nonneg,axiom,
% 4.71/5.17 ! [A2: set_nat,F: nat > nat] :
% 4.71/5.17 ( ! [X4: nat] :
% 4.71/5.17 ( ( member_nat @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 4.71/5.17 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg
% 4.71/5.17 thf(fact_8087_sum__mono__inv,axiom,
% 4.71/5.17 ! [F: $o > rat,I5: set_o,G2: $o > rat,I: $o] :
% 4.71/5.17 ( ( ( groups7872700643590313910_o_rat @ F @ I5 )
% 4.71/5.17 = ( groups7872700643590313910_o_rat @ G2 @ I5 ) )
% 4.71/5.17 => ( ! [I2: $o] :
% 4.71/5.17 ( ( member_o @ I2 @ I5 )
% 4.71/5.17 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G2 @ I2 ) ) )
% 4.71/5.17 => ( ( member_o @ I @ I5 )
% 4.71/5.17 => ( ( finite_finite_o @ I5 )
% 4.71/5.17 => ( ( F @ I )
% 4.71/5.17 = ( G2 @ I ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_mono_inv
% 4.71/5.17 thf(fact_8088_sum__mono__inv,axiom,
% 4.71/5.17 ! [F: nat > rat,I5: set_nat,G2: nat > rat,I: nat] :
% 4.71/5.17 ( ( ( groups2906978787729119204at_rat @ F @ I5 )
% 4.71/5.17 = ( groups2906978787729119204at_rat @ G2 @ I5 ) )
% 4.71/5.17 => ( ! [I2: nat] :
% 4.71/5.17 ( ( member_nat @ I2 @ I5 )
% 4.71/5.17 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G2 @ I2 ) ) )
% 4.71/5.17 => ( ( member_nat @ I @ I5 )
% 4.71/5.17 => ( ( finite_finite_nat @ I5 )
% 4.71/5.17 => ( ( F @ I )
% 4.71/5.17 = ( G2 @ I ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_mono_inv
% 4.71/5.17 thf(fact_8089_sum__mono__inv,axiom,
% 4.71/5.17 ! [F: int > rat,I5: set_int,G2: int > rat,I: int] :
% 4.71/5.17 ( ( ( groups3906332499630173760nt_rat @ F @ I5 )
% 4.71/5.17 = ( groups3906332499630173760nt_rat @ G2 @ I5 ) )
% 4.71/5.17 => ( ! [I2: int] :
% 4.71/5.17 ( ( member_int @ I2 @ I5 )
% 4.71/5.17 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G2 @ I2 ) ) )
% 4.71/5.17 => ( ( member_int @ I @ I5 )
% 4.71/5.17 => ( ( finite_finite_int @ I5 )
% 4.71/5.17 => ( ( F @ I )
% 4.71/5.17 = ( G2 @ I ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_mono_inv
% 4.71/5.17 thf(fact_8090_sum__mono__inv,axiom,
% 4.71/5.17 ! [F: complex > rat,I5: set_complex,G2: complex > rat,I: complex] :
% 4.71/5.17 ( ( ( groups5058264527183730370ex_rat @ F @ I5 )
% 4.71/5.17 = ( groups5058264527183730370ex_rat @ G2 @ I5 ) )
% 4.71/5.17 => ( ! [I2: complex] :
% 4.71/5.17 ( ( member_complex @ I2 @ I5 )
% 4.71/5.17 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G2 @ I2 ) ) )
% 4.71/5.17 => ( ( member_complex @ I @ I5 )
% 4.71/5.17 => ( ( finite3207457112153483333omplex @ I5 )
% 4.71/5.17 => ( ( F @ I )
% 4.71/5.17 = ( G2 @ I ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_mono_inv
% 4.71/5.17 thf(fact_8091_sum__mono__inv,axiom,
% 4.71/5.17 ! [F: extended_enat > rat,I5: set_Extended_enat,G2: extended_enat > rat,I: extended_enat] :
% 4.71/5.17 ( ( ( groups1392844769737527556at_rat @ F @ I5 )
% 4.71/5.17 = ( groups1392844769737527556at_rat @ G2 @ I5 ) )
% 4.71/5.17 => ( ! [I2: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ I2 @ I5 )
% 4.71/5.17 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G2 @ I2 ) ) )
% 4.71/5.17 => ( ( member_Extended_enat @ I @ I5 )
% 4.71/5.17 => ( ( finite4001608067531595151d_enat @ I5 )
% 4.71/5.17 => ( ( F @ I )
% 4.71/5.17 = ( G2 @ I ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_mono_inv
% 4.71/5.17 thf(fact_8092_sum__mono__inv,axiom,
% 4.71/5.17 ! [F: $o > nat,I5: set_o,G2: $o > nat,I: $o] :
% 4.71/5.17 ( ( ( groups8507830703676809646_o_nat @ F @ I5 )
% 4.71/5.17 = ( groups8507830703676809646_o_nat @ G2 @ I5 ) )
% 4.71/5.17 => ( ! [I2: $o] :
% 4.71/5.17 ( ( member_o @ I2 @ I5 )
% 4.71/5.17 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G2 @ I2 ) ) )
% 4.71/5.17 => ( ( member_o @ I @ I5 )
% 4.71/5.17 => ( ( finite_finite_o @ I5 )
% 4.71/5.17 => ( ( F @ I )
% 4.71/5.17 = ( G2 @ I ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_mono_inv
% 4.71/5.17 thf(fact_8093_sum__mono__inv,axiom,
% 4.71/5.17 ! [F: int > nat,I5: set_int,G2: int > nat,I: int] :
% 4.71/5.17 ( ( ( groups4541462559716669496nt_nat @ F @ I5 )
% 4.71/5.17 = ( groups4541462559716669496nt_nat @ G2 @ I5 ) )
% 4.71/5.17 => ( ! [I2: int] :
% 4.71/5.17 ( ( member_int @ I2 @ I5 )
% 4.71/5.17 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G2 @ I2 ) ) )
% 4.71/5.17 => ( ( member_int @ I @ I5 )
% 4.71/5.17 => ( ( finite_finite_int @ I5 )
% 4.71/5.17 => ( ( F @ I )
% 4.71/5.17 = ( G2 @ I ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_mono_inv
% 4.71/5.17 thf(fact_8094_sum__mono__inv,axiom,
% 4.71/5.17 ! [F: complex > nat,I5: set_complex,G2: complex > nat,I: complex] :
% 4.71/5.17 ( ( ( groups5693394587270226106ex_nat @ F @ I5 )
% 4.71/5.17 = ( groups5693394587270226106ex_nat @ G2 @ I5 ) )
% 4.71/5.17 => ( ! [I2: complex] :
% 4.71/5.17 ( ( member_complex @ I2 @ I5 )
% 4.71/5.17 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G2 @ I2 ) ) )
% 4.71/5.17 => ( ( member_complex @ I @ I5 )
% 4.71/5.17 => ( ( finite3207457112153483333omplex @ I5 )
% 4.71/5.17 => ( ( F @ I )
% 4.71/5.17 = ( G2 @ I ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_mono_inv
% 4.71/5.17 thf(fact_8095_sum__mono__inv,axiom,
% 4.71/5.17 ! [F: extended_enat > nat,I5: set_Extended_enat,G2: extended_enat > nat,I: extended_enat] :
% 4.71/5.17 ( ( ( groups2027974829824023292at_nat @ F @ I5 )
% 4.71/5.17 = ( groups2027974829824023292at_nat @ G2 @ I5 ) )
% 4.71/5.17 => ( ! [I2: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ I2 @ I5 )
% 4.71/5.17 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G2 @ I2 ) ) )
% 4.71/5.17 => ( ( member_Extended_enat @ I @ I5 )
% 4.71/5.17 => ( ( finite4001608067531595151d_enat @ I5 )
% 4.71/5.17 => ( ( F @ I )
% 4.71/5.17 = ( G2 @ I ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_mono_inv
% 4.71/5.17 thf(fact_8096_sum__mono__inv,axiom,
% 4.71/5.17 ! [F: $o > int,I5: set_o,G2: $o > int,I: $o] :
% 4.71/5.17 ( ( ( groups8505340233167759370_o_int @ F @ I5 )
% 4.71/5.17 = ( groups8505340233167759370_o_int @ G2 @ I5 ) )
% 4.71/5.17 => ( ! [I2: $o] :
% 4.71/5.17 ( ( member_o @ I2 @ I5 )
% 4.71/5.17 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G2 @ I2 ) ) )
% 4.71/5.17 => ( ( member_o @ I @ I5 )
% 4.71/5.17 => ( ( finite_finite_o @ I5 )
% 4.71/5.17 => ( ( F @ I )
% 4.71/5.17 = ( G2 @ I ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_mono_inv
% 4.71/5.17 thf(fact_8097_binomial__eq__0,axiom,
% 4.71/5.17 ! [N: nat,K: nat] :
% 4.71/5.17 ( ( ord_less_nat @ N @ K )
% 4.71/5.17 => ( ( binomial @ N @ K )
% 4.71/5.17 = zero_zero_nat ) ) ).
% 4.71/5.17
% 4.71/5.17 % binomial_eq_0
% 4.71/5.17 thf(fact_8098_binomial__symmetric,axiom,
% 4.71/5.17 ! [K: nat,N: nat] :
% 4.71/5.17 ( ( ord_less_eq_nat @ K @ N )
% 4.71/5.17 => ( ( binomial @ N @ K )
% 4.71/5.17 = ( binomial @ N @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % binomial_symmetric
% 4.71/5.17 thf(fact_8099_finite__distinct__list,axiom,
% 4.71/5.17 ! [A2: set_VEBT_VEBT] :
% 4.71/5.17 ( ( finite5795047828879050333T_VEBT @ A2 )
% 4.71/5.17 => ? [Xs3: list_VEBT_VEBT] :
% 4.71/5.17 ( ( ( set_VEBT_VEBT2 @ Xs3 )
% 4.71/5.17 = A2 )
% 4.71/5.17 & ( distinct_VEBT_VEBT @ Xs3 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % finite_distinct_list
% 4.71/5.17 thf(fact_8100_finite__distinct__list,axiom,
% 4.71/5.17 ! [A2: set_nat] :
% 4.71/5.17 ( ( finite_finite_nat @ A2 )
% 4.71/5.17 => ? [Xs3: list_nat] :
% 4.71/5.17 ( ( ( set_nat2 @ Xs3 )
% 4.71/5.17 = A2 )
% 4.71/5.17 & ( distinct_nat @ Xs3 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % finite_distinct_list
% 4.71/5.17 thf(fact_8101_finite__distinct__list,axiom,
% 4.71/5.17 ! [A2: set_int] :
% 4.71/5.17 ( ( finite_finite_int @ A2 )
% 4.71/5.17 => ? [Xs3: list_int] :
% 4.71/5.17 ( ( ( set_int2 @ Xs3 )
% 4.71/5.17 = A2 )
% 4.71/5.17 & ( distinct_int @ Xs3 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % finite_distinct_list
% 4.71/5.17 thf(fact_8102_finite__distinct__list,axiom,
% 4.71/5.17 ! [A2: set_complex] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.17 => ? [Xs3: list_complex] :
% 4.71/5.17 ( ( ( set_complex2 @ Xs3 )
% 4.71/5.17 = A2 )
% 4.71/5.17 & ( distinct_complex @ Xs3 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % finite_distinct_list
% 4.71/5.17 thf(fact_8103_finite__distinct__list,axiom,
% 4.71/5.17 ! [A2: set_Pr1261947904930325089at_nat] :
% 4.71/5.17 ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.17 => ? [Xs3: list_P6011104703257516679at_nat] :
% 4.71/5.17 ( ( ( set_Pr5648618587558075414at_nat @ Xs3 )
% 4.71/5.17 = A2 )
% 4.71/5.17 & ( distin6923225563576452346at_nat @ Xs3 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % finite_distinct_list
% 4.71/5.17 thf(fact_8104_finite__distinct__list,axiom,
% 4.71/5.17 ! [A2: set_Extended_enat] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.17 => ? [Xs3: list_Extended_enat] :
% 4.71/5.17 ( ( ( set_Extended_enat2 @ Xs3 )
% 4.71/5.17 = A2 )
% 4.71/5.17 & ( distin4523846830085650399d_enat @ Xs3 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % finite_distinct_list
% 4.71/5.17 thf(fact_8105_binomial__le__pow,axiom,
% 4.71/5.17 ! [R2: nat,N: nat] :
% 4.71/5.17 ( ( ord_less_eq_nat @ R2 @ N )
% 4.71/5.17 => ( ord_less_eq_nat @ ( binomial @ N @ R2 ) @ ( power_power_nat @ N @ R2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % binomial_le_pow
% 4.71/5.17 thf(fact_8106_sum__cong__Suc,axiom,
% 4.71/5.17 ! [A2: set_nat,F: nat > nat,G2: nat > nat] :
% 4.71/5.17 ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 4.71/5.17 => ( ! [X4: nat] :
% 4.71/5.17 ( ( member_nat @ ( suc @ X4 ) @ A2 )
% 4.71/5.17 => ( ( F @ ( suc @ X4 ) )
% 4.71/5.17 = ( G2 @ ( suc @ X4 ) ) ) )
% 4.71/5.17 => ( ( groups3542108847815614940at_nat @ F @ A2 )
% 4.71/5.17 = ( groups3542108847815614940at_nat @ G2 @ A2 ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_cong_Suc
% 4.71/5.17 thf(fact_8107_sum__cong__Suc,axiom,
% 4.71/5.17 ! [A2: set_nat,F: nat > real,G2: nat > real] :
% 4.71/5.17 ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 4.71/5.17 => ( ! [X4: nat] :
% 4.71/5.17 ( ( member_nat @ ( suc @ X4 ) @ A2 )
% 4.71/5.17 => ( ( F @ ( suc @ X4 ) )
% 4.71/5.17 = ( G2 @ ( suc @ X4 ) ) ) )
% 4.71/5.17 => ( ( groups6591440286371151544t_real @ F @ A2 )
% 4.71/5.17 = ( groups6591440286371151544t_real @ G2 @ A2 ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_cong_Suc
% 4.71/5.17 thf(fact_8108_sum_Ointer__filter,axiom,
% 4.71/5.17 ! [A2: set_o,G2: $o > real,P: $o > $o] :
% 4.71/5.17 ( ( finite_finite_o @ A2 )
% 4.71/5.17 => ( ( groups8691415230153176458o_real @ G2
% 4.71/5.17 @ ( collect_o
% 4.71/5.17 @ ^ [X3: $o] :
% 4.71/5.17 ( ( member_o @ X3 @ A2 )
% 4.71/5.17 & ( P @ X3 ) ) ) )
% 4.71/5.17 = ( groups8691415230153176458o_real
% 4.71/5.17 @ ^ [X3: $o] : ( if_real @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_zero_real )
% 4.71/5.17 @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.inter_filter
% 4.71/5.17 thf(fact_8109_sum_Ointer__filter,axiom,
% 4.71/5.17 ! [A2: set_int,G2: int > real,P: int > $o] :
% 4.71/5.17 ( ( finite_finite_int @ A2 )
% 4.71/5.17 => ( ( groups8778361861064173332t_real @ G2
% 4.71/5.17 @ ( collect_int
% 4.71/5.17 @ ^ [X3: int] :
% 4.71/5.17 ( ( member_int @ X3 @ A2 )
% 4.71/5.17 & ( P @ X3 ) ) ) )
% 4.71/5.17 = ( groups8778361861064173332t_real
% 4.71/5.17 @ ^ [X3: int] : ( if_real @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_zero_real )
% 4.71/5.17 @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.inter_filter
% 4.71/5.17 thf(fact_8110_sum_Ointer__filter,axiom,
% 4.71/5.17 ! [A2: set_complex,G2: complex > real,P: complex > $o] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.17 => ( ( groups5808333547571424918x_real @ G2
% 4.71/5.17 @ ( collect_complex
% 4.71/5.17 @ ^ [X3: complex] :
% 4.71/5.17 ( ( member_complex @ X3 @ A2 )
% 4.71/5.17 & ( P @ X3 ) ) ) )
% 4.71/5.17 = ( groups5808333547571424918x_real
% 4.71/5.17 @ ^ [X3: complex] : ( if_real @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_zero_real )
% 4.71/5.17 @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.inter_filter
% 4.71/5.17 thf(fact_8111_sum_Ointer__filter,axiom,
% 4.71/5.17 ! [A2: set_Extended_enat,G2: extended_enat > real,P: extended_enat > $o] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.17 => ( ( groups4148127829035722712t_real @ G2
% 4.71/5.17 @ ( collec4429806609662206161d_enat
% 4.71/5.17 @ ^ [X3: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ X3 @ A2 )
% 4.71/5.17 & ( P @ X3 ) ) ) )
% 4.71/5.17 = ( groups4148127829035722712t_real
% 4.71/5.17 @ ^ [X3: extended_enat] : ( if_real @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_zero_real )
% 4.71/5.17 @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.inter_filter
% 4.71/5.17 thf(fact_8112_sum_Ointer__filter,axiom,
% 4.71/5.17 ! [A2: set_o,G2: $o > rat,P: $o > $o] :
% 4.71/5.17 ( ( finite_finite_o @ A2 )
% 4.71/5.17 => ( ( groups7872700643590313910_o_rat @ G2
% 4.71/5.17 @ ( collect_o
% 4.71/5.17 @ ^ [X3: $o] :
% 4.71/5.17 ( ( member_o @ X3 @ A2 )
% 4.71/5.17 & ( P @ X3 ) ) ) )
% 4.71/5.17 = ( groups7872700643590313910_o_rat
% 4.71/5.17 @ ^ [X3: $o] : ( if_rat @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_zero_rat )
% 4.71/5.17 @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.inter_filter
% 4.71/5.17 thf(fact_8113_sum_Ointer__filter,axiom,
% 4.71/5.17 ! [A2: set_nat,G2: nat > rat,P: nat > $o] :
% 4.71/5.17 ( ( finite_finite_nat @ A2 )
% 4.71/5.17 => ( ( groups2906978787729119204at_rat @ G2
% 4.71/5.17 @ ( collect_nat
% 4.71/5.17 @ ^ [X3: nat] :
% 4.71/5.17 ( ( member_nat @ X3 @ A2 )
% 4.71/5.17 & ( P @ X3 ) ) ) )
% 4.71/5.17 = ( groups2906978787729119204at_rat
% 4.71/5.17 @ ^ [X3: nat] : ( if_rat @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_zero_rat )
% 4.71/5.17 @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.inter_filter
% 4.71/5.17 thf(fact_8114_sum_Ointer__filter,axiom,
% 4.71/5.17 ! [A2: set_int,G2: int > rat,P: int > $o] :
% 4.71/5.17 ( ( finite_finite_int @ A2 )
% 4.71/5.17 => ( ( groups3906332499630173760nt_rat @ G2
% 4.71/5.17 @ ( collect_int
% 4.71/5.17 @ ^ [X3: int] :
% 4.71/5.17 ( ( member_int @ X3 @ A2 )
% 4.71/5.17 & ( P @ X3 ) ) ) )
% 4.71/5.17 = ( groups3906332499630173760nt_rat
% 4.71/5.17 @ ^ [X3: int] : ( if_rat @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_zero_rat )
% 4.71/5.17 @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.inter_filter
% 4.71/5.17 thf(fact_8115_sum_Ointer__filter,axiom,
% 4.71/5.17 ! [A2: set_complex,G2: complex > rat,P: complex > $o] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.17 => ( ( groups5058264527183730370ex_rat @ G2
% 4.71/5.17 @ ( collect_complex
% 4.71/5.17 @ ^ [X3: complex] :
% 4.71/5.17 ( ( member_complex @ X3 @ A2 )
% 4.71/5.17 & ( P @ X3 ) ) ) )
% 4.71/5.17 = ( groups5058264527183730370ex_rat
% 4.71/5.17 @ ^ [X3: complex] : ( if_rat @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_zero_rat )
% 4.71/5.17 @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.inter_filter
% 4.71/5.17 thf(fact_8116_sum_Ointer__filter,axiom,
% 4.71/5.17 ! [A2: set_Extended_enat,G2: extended_enat > rat,P: extended_enat > $o] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.17 => ( ( groups1392844769737527556at_rat @ G2
% 4.71/5.17 @ ( collec4429806609662206161d_enat
% 4.71/5.17 @ ^ [X3: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ X3 @ A2 )
% 4.71/5.17 & ( P @ X3 ) ) ) )
% 4.71/5.17 = ( groups1392844769737527556at_rat
% 4.71/5.17 @ ^ [X3: extended_enat] : ( if_rat @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_zero_rat )
% 4.71/5.17 @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.inter_filter
% 4.71/5.17 thf(fact_8117_sum_Ointer__filter,axiom,
% 4.71/5.17 ! [A2: set_o,G2: $o > nat,P: $o > $o] :
% 4.71/5.17 ( ( finite_finite_o @ A2 )
% 4.71/5.17 => ( ( groups8507830703676809646_o_nat @ G2
% 4.71/5.17 @ ( collect_o
% 4.71/5.17 @ ^ [X3: $o] :
% 4.71/5.17 ( ( member_o @ X3 @ A2 )
% 4.71/5.17 & ( P @ X3 ) ) ) )
% 4.71/5.17 = ( groups8507830703676809646_o_nat
% 4.71/5.17 @ ^ [X3: $o] : ( if_nat @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_zero_nat )
% 4.71/5.17 @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.inter_filter
% 4.71/5.17 thf(fact_8118_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 4.71/5.17 ! [G2: nat > nat,M2: nat,N: nat] :
% 4.71/5.17 ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N ) ) )
% 4.71/5.17 = ( groups3542108847815614940at_nat
% 4.71/5.17 @ ^ [I4: nat] : ( G2 @ ( suc @ I4 ) )
% 4.71/5.17 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.shift_bounds_cl_Suc_ivl
% 4.71/5.17 thf(fact_8119_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 4.71/5.17 ! [G2: nat > real,M2: nat,N: nat] :
% 4.71/5.17 ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N ) ) )
% 4.71/5.17 = ( groups6591440286371151544t_real
% 4.71/5.17 @ ^ [I4: nat] : ( G2 @ ( suc @ I4 ) )
% 4.71/5.17 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.shift_bounds_cl_Suc_ivl
% 4.71/5.17 thf(fact_8120_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 4.71/5.17 ! [G2: nat > nat,M2: nat,K: nat,N: nat] :
% 4.71/5.17 ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 4.71/5.17 = ( groups3542108847815614940at_nat
% 4.71/5.17 @ ^ [I4: nat] : ( G2 @ ( plus_plus_nat @ I4 @ K ) )
% 4.71/5.17 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.shift_bounds_cl_nat_ivl
% 4.71/5.17 thf(fact_8121_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 4.71/5.17 ! [G2: nat > real,M2: nat,K: nat,N: nat] :
% 4.71/5.17 ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 4.71/5.17 = ( groups6591440286371151544t_real
% 4.71/5.17 @ ^ [I4: nat] : ( G2 @ ( plus_plus_nat @ I4 @ K ) )
% 4.71/5.17 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.shift_bounds_cl_nat_ivl
% 4.71/5.17 thf(fact_8122_sum__nonneg__eq__0__iff,axiom,
% 4.71/5.17 ! [A2: set_o,F: $o > real] :
% 4.71/5.17 ( ( finite_finite_o @ A2 )
% 4.71/5.17 => ( ! [X4: $o] :
% 4.71/5.17 ( ( member_o @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 4.71/5.17 => ( ( ( groups8691415230153176458o_real @ F @ A2 )
% 4.71/5.17 = zero_zero_real )
% 4.71/5.17 = ( ! [X3: $o] :
% 4.71/5.17 ( ( member_o @ X3 @ A2 )
% 4.71/5.17 => ( ( F @ X3 )
% 4.71/5.17 = zero_zero_real ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_eq_0_iff
% 4.71/5.17 thf(fact_8123_sum__nonneg__eq__0__iff,axiom,
% 4.71/5.17 ! [A2: set_int,F: int > real] :
% 4.71/5.17 ( ( finite_finite_int @ A2 )
% 4.71/5.17 => ( ! [X4: int] :
% 4.71/5.17 ( ( member_int @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 4.71/5.17 => ( ( ( groups8778361861064173332t_real @ F @ A2 )
% 4.71/5.17 = zero_zero_real )
% 4.71/5.17 = ( ! [X3: int] :
% 4.71/5.17 ( ( member_int @ X3 @ A2 )
% 4.71/5.17 => ( ( F @ X3 )
% 4.71/5.17 = zero_zero_real ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_eq_0_iff
% 4.71/5.17 thf(fact_8124_sum__nonneg__eq__0__iff,axiom,
% 4.71/5.17 ! [A2: set_complex,F: complex > real] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.17 => ( ! [X4: complex] :
% 4.71/5.17 ( ( member_complex @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 4.71/5.17 => ( ( ( groups5808333547571424918x_real @ F @ A2 )
% 4.71/5.17 = zero_zero_real )
% 4.71/5.17 = ( ! [X3: complex] :
% 4.71/5.17 ( ( member_complex @ X3 @ A2 )
% 4.71/5.17 => ( ( F @ X3 )
% 4.71/5.17 = zero_zero_real ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_eq_0_iff
% 4.71/5.17 thf(fact_8125_sum__nonneg__eq__0__iff,axiom,
% 4.71/5.17 ! [A2: set_Extended_enat,F: extended_enat > real] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.17 => ( ! [X4: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 4.71/5.17 => ( ( ( groups4148127829035722712t_real @ F @ A2 )
% 4.71/5.17 = zero_zero_real )
% 4.71/5.17 = ( ! [X3: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ X3 @ A2 )
% 4.71/5.17 => ( ( F @ X3 )
% 4.71/5.17 = zero_zero_real ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_eq_0_iff
% 4.71/5.17 thf(fact_8126_sum__nonneg__eq__0__iff,axiom,
% 4.71/5.17 ! [A2: set_o,F: $o > rat] :
% 4.71/5.17 ( ( finite_finite_o @ A2 )
% 4.71/5.17 => ( ! [X4: $o] :
% 4.71/5.17 ( ( member_o @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 4.71/5.17 => ( ( ( groups7872700643590313910_o_rat @ F @ A2 )
% 4.71/5.17 = zero_zero_rat )
% 4.71/5.17 = ( ! [X3: $o] :
% 4.71/5.17 ( ( member_o @ X3 @ A2 )
% 4.71/5.17 => ( ( F @ X3 )
% 4.71/5.17 = zero_zero_rat ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_eq_0_iff
% 4.71/5.17 thf(fact_8127_sum__nonneg__eq__0__iff,axiom,
% 4.71/5.17 ! [A2: set_nat,F: nat > rat] :
% 4.71/5.17 ( ( finite_finite_nat @ A2 )
% 4.71/5.17 => ( ! [X4: nat] :
% 4.71/5.17 ( ( member_nat @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 4.71/5.17 => ( ( ( groups2906978787729119204at_rat @ F @ A2 )
% 4.71/5.17 = zero_zero_rat )
% 4.71/5.17 = ( ! [X3: nat] :
% 4.71/5.17 ( ( member_nat @ X3 @ A2 )
% 4.71/5.17 => ( ( F @ X3 )
% 4.71/5.17 = zero_zero_rat ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_eq_0_iff
% 4.71/5.17 thf(fact_8128_sum__nonneg__eq__0__iff,axiom,
% 4.71/5.17 ! [A2: set_int,F: int > rat] :
% 4.71/5.17 ( ( finite_finite_int @ A2 )
% 4.71/5.17 => ( ! [X4: int] :
% 4.71/5.17 ( ( member_int @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 4.71/5.17 => ( ( ( groups3906332499630173760nt_rat @ F @ A2 )
% 4.71/5.17 = zero_zero_rat )
% 4.71/5.17 = ( ! [X3: int] :
% 4.71/5.17 ( ( member_int @ X3 @ A2 )
% 4.71/5.17 => ( ( F @ X3 )
% 4.71/5.17 = zero_zero_rat ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_eq_0_iff
% 4.71/5.17 thf(fact_8129_sum__nonneg__eq__0__iff,axiom,
% 4.71/5.17 ! [A2: set_complex,F: complex > rat] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.17 => ( ! [X4: complex] :
% 4.71/5.17 ( ( member_complex @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 4.71/5.17 => ( ( ( groups5058264527183730370ex_rat @ F @ A2 )
% 4.71/5.17 = zero_zero_rat )
% 4.71/5.17 = ( ! [X3: complex] :
% 4.71/5.17 ( ( member_complex @ X3 @ A2 )
% 4.71/5.17 => ( ( F @ X3 )
% 4.71/5.17 = zero_zero_rat ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_eq_0_iff
% 4.71/5.17 thf(fact_8130_sum__nonneg__eq__0__iff,axiom,
% 4.71/5.17 ! [A2: set_Extended_enat,F: extended_enat > rat] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.17 => ( ! [X4: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 4.71/5.17 => ( ( ( groups1392844769737527556at_rat @ F @ A2 )
% 4.71/5.17 = zero_zero_rat )
% 4.71/5.17 = ( ! [X3: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ X3 @ A2 )
% 4.71/5.17 => ( ( F @ X3 )
% 4.71/5.17 = zero_zero_rat ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_eq_0_iff
% 4.71/5.17 thf(fact_8131_sum__nonneg__eq__0__iff,axiom,
% 4.71/5.17 ! [A2: set_o,F: $o > nat] :
% 4.71/5.17 ( ( finite_finite_o @ A2 )
% 4.71/5.17 => ( ! [X4: $o] :
% 4.71/5.17 ( ( member_o @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 4.71/5.17 => ( ( ( groups8507830703676809646_o_nat @ F @ A2 )
% 4.71/5.17 = zero_zero_nat )
% 4.71/5.17 = ( ! [X3: $o] :
% 4.71/5.17 ( ( member_o @ X3 @ A2 )
% 4.71/5.17 => ( ( F @ X3 )
% 4.71/5.17 = zero_zero_nat ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_eq_0_iff
% 4.71/5.17 thf(fact_8132_sum__le__included,axiom,
% 4.71/5.17 ! [S: set_int,T: set_int,G2: int > real,I: int > int,F: int > real] :
% 4.71/5.17 ( ( finite_finite_int @ S )
% 4.71/5.17 => ( ( finite_finite_int @ T )
% 4.71/5.17 => ( ! [X4: int] :
% 4.71/5.17 ( ( member_int @ X4 @ T )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ! [X4: int] :
% 4.71/5.17 ( ( member_int @ X4 @ S )
% 4.71/5.17 => ? [Xa: int] :
% 4.71/5.17 ( ( member_int @ Xa @ T )
% 4.71/5.17 & ( ( I @ Xa )
% 4.71/5.17 = X4 )
% 4.71/5.17 & ( ord_less_eq_real @ ( F @ X4 ) @ ( G2 @ Xa ) ) ) )
% 4.71/5.17 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups8778361861064173332t_real @ G2 @ T ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_le_included
% 4.71/5.17 thf(fact_8133_sum__le__included,axiom,
% 4.71/5.17 ! [S: set_int,T: set_complex,G2: complex > real,I: complex > int,F: int > real] :
% 4.71/5.17 ( ( finite_finite_int @ S )
% 4.71/5.17 => ( ( finite3207457112153483333omplex @ T )
% 4.71/5.17 => ( ! [X4: complex] :
% 4.71/5.17 ( ( member_complex @ X4 @ T )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ! [X4: int] :
% 4.71/5.17 ( ( member_int @ X4 @ S )
% 4.71/5.17 => ? [Xa: complex] :
% 4.71/5.17 ( ( member_complex @ Xa @ T )
% 4.71/5.17 & ( ( I @ Xa )
% 4.71/5.17 = X4 )
% 4.71/5.17 & ( ord_less_eq_real @ ( F @ X4 ) @ ( G2 @ Xa ) ) ) )
% 4.71/5.17 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups5808333547571424918x_real @ G2 @ T ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_le_included
% 4.71/5.17 thf(fact_8134_sum__le__included,axiom,
% 4.71/5.17 ! [S: set_int,T: set_Extended_enat,G2: extended_enat > real,I: extended_enat > int,F: int > real] :
% 4.71/5.17 ( ( finite_finite_int @ S )
% 4.71/5.17 => ( ( finite4001608067531595151d_enat @ T )
% 4.71/5.17 => ( ! [X4: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ X4 @ T )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ! [X4: int] :
% 4.71/5.17 ( ( member_int @ X4 @ S )
% 4.71/5.17 => ? [Xa: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ Xa @ T )
% 4.71/5.17 & ( ( I @ Xa )
% 4.71/5.17 = X4 )
% 4.71/5.17 & ( ord_less_eq_real @ ( F @ X4 ) @ ( G2 @ Xa ) ) ) )
% 4.71/5.17 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups4148127829035722712t_real @ G2 @ T ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_le_included
% 4.71/5.17 thf(fact_8135_sum__le__included,axiom,
% 4.71/5.17 ! [S: set_complex,T: set_int,G2: int > real,I: int > complex,F: complex > real] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ S )
% 4.71/5.17 => ( ( finite_finite_int @ T )
% 4.71/5.17 => ( ! [X4: int] :
% 4.71/5.17 ( ( member_int @ X4 @ T )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ! [X4: complex] :
% 4.71/5.17 ( ( member_complex @ X4 @ S )
% 4.71/5.17 => ? [Xa: int] :
% 4.71/5.17 ( ( member_int @ Xa @ T )
% 4.71/5.17 & ( ( I @ Xa )
% 4.71/5.17 = X4 )
% 4.71/5.17 & ( ord_less_eq_real @ ( F @ X4 ) @ ( G2 @ Xa ) ) ) )
% 4.71/5.17 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups8778361861064173332t_real @ G2 @ T ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_le_included
% 4.71/5.17 thf(fact_8136_sum__le__included,axiom,
% 4.71/5.17 ! [S: set_complex,T: set_complex,G2: complex > real,I: complex > complex,F: complex > real] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ S )
% 4.71/5.17 => ( ( finite3207457112153483333omplex @ T )
% 4.71/5.17 => ( ! [X4: complex] :
% 4.71/5.17 ( ( member_complex @ X4 @ T )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ! [X4: complex] :
% 4.71/5.17 ( ( member_complex @ X4 @ S )
% 4.71/5.17 => ? [Xa: complex] :
% 4.71/5.17 ( ( member_complex @ Xa @ T )
% 4.71/5.17 & ( ( I @ Xa )
% 4.71/5.17 = X4 )
% 4.71/5.17 & ( ord_less_eq_real @ ( F @ X4 ) @ ( G2 @ Xa ) ) ) )
% 4.71/5.17 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups5808333547571424918x_real @ G2 @ T ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_le_included
% 4.71/5.17 thf(fact_8137_sum__le__included,axiom,
% 4.71/5.17 ! [S: set_complex,T: set_Extended_enat,G2: extended_enat > real,I: extended_enat > complex,F: complex > real] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ S )
% 4.71/5.17 => ( ( finite4001608067531595151d_enat @ T )
% 4.71/5.17 => ( ! [X4: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ X4 @ T )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ! [X4: complex] :
% 4.71/5.17 ( ( member_complex @ X4 @ S )
% 4.71/5.17 => ? [Xa: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ Xa @ T )
% 4.71/5.17 & ( ( I @ Xa )
% 4.71/5.17 = X4 )
% 4.71/5.17 & ( ord_less_eq_real @ ( F @ X4 ) @ ( G2 @ Xa ) ) ) )
% 4.71/5.17 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups4148127829035722712t_real @ G2 @ T ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_le_included
% 4.71/5.17 thf(fact_8138_sum__le__included,axiom,
% 4.71/5.17 ! [S: set_Extended_enat,T: set_int,G2: int > real,I: int > extended_enat,F: extended_enat > real] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ S )
% 4.71/5.17 => ( ( finite_finite_int @ T )
% 4.71/5.17 => ( ! [X4: int] :
% 4.71/5.17 ( ( member_int @ X4 @ T )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ! [X4: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ X4 @ S )
% 4.71/5.17 => ? [Xa: int] :
% 4.71/5.17 ( ( member_int @ Xa @ T )
% 4.71/5.17 & ( ( I @ Xa )
% 4.71/5.17 = X4 )
% 4.71/5.17 & ( ord_less_eq_real @ ( F @ X4 ) @ ( G2 @ Xa ) ) ) )
% 4.71/5.17 => ( ord_less_eq_real @ ( groups4148127829035722712t_real @ F @ S ) @ ( groups8778361861064173332t_real @ G2 @ T ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_le_included
% 4.71/5.17 thf(fact_8139_sum__le__included,axiom,
% 4.71/5.17 ! [S: set_Extended_enat,T: set_complex,G2: complex > real,I: complex > extended_enat,F: extended_enat > real] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ S )
% 4.71/5.17 => ( ( finite3207457112153483333omplex @ T )
% 4.71/5.17 => ( ! [X4: complex] :
% 4.71/5.17 ( ( member_complex @ X4 @ T )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ! [X4: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ X4 @ S )
% 4.71/5.17 => ? [Xa: complex] :
% 4.71/5.17 ( ( member_complex @ Xa @ T )
% 4.71/5.17 & ( ( I @ Xa )
% 4.71/5.17 = X4 )
% 4.71/5.17 & ( ord_less_eq_real @ ( F @ X4 ) @ ( G2 @ Xa ) ) ) )
% 4.71/5.17 => ( ord_less_eq_real @ ( groups4148127829035722712t_real @ F @ S ) @ ( groups5808333547571424918x_real @ G2 @ T ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_le_included
% 4.71/5.17 thf(fact_8140_sum__le__included,axiom,
% 4.71/5.17 ! [S: set_Extended_enat,T: set_Extended_enat,G2: extended_enat > real,I: extended_enat > extended_enat,F: extended_enat > real] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ S )
% 4.71/5.17 => ( ( finite4001608067531595151d_enat @ T )
% 4.71/5.17 => ( ! [X4: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ X4 @ T )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ! [X4: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ X4 @ S )
% 4.71/5.17 => ? [Xa: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ Xa @ T )
% 4.71/5.17 & ( ( I @ Xa )
% 4.71/5.17 = X4 )
% 4.71/5.17 & ( ord_less_eq_real @ ( F @ X4 ) @ ( G2 @ Xa ) ) ) )
% 4.71/5.17 => ( ord_less_eq_real @ ( groups4148127829035722712t_real @ F @ S ) @ ( groups4148127829035722712t_real @ G2 @ T ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_le_included
% 4.71/5.17 thf(fact_8141_sum__le__included,axiom,
% 4.71/5.17 ! [S: set_nat,T: set_nat,G2: nat > rat,I: nat > nat,F: nat > rat] :
% 4.71/5.17 ( ( finite_finite_nat @ S )
% 4.71/5.17 => ( ( finite_finite_nat @ T )
% 4.71/5.17 => ( ! [X4: nat] :
% 4.71/5.17 ( ( member_nat @ X4 @ T )
% 4.71/5.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ! [X4: nat] :
% 4.71/5.17 ( ( member_nat @ X4 @ S )
% 4.71/5.17 => ? [Xa: nat] :
% 4.71/5.17 ( ( member_nat @ Xa @ T )
% 4.71/5.17 & ( ( I @ Xa )
% 4.71/5.17 = X4 )
% 4.71/5.17 & ( ord_less_eq_rat @ ( F @ X4 ) @ ( G2 @ Xa ) ) ) )
% 4.71/5.17 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S ) @ ( groups2906978787729119204at_rat @ G2 @ T ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_le_included
% 4.71/5.17 thf(fact_8142_sum__strict__mono__ex1,axiom,
% 4.71/5.17 ! [A2: set_int,F: int > real,G2: int > real] :
% 4.71/5.17 ( ( finite_finite_int @ A2 )
% 4.71/5.17 => ( ! [X4: int] :
% 4.71/5.17 ( ( member_int @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_real @ ( F @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ? [X2: int] :
% 4.71/5.17 ( ( member_int @ X2 @ A2 )
% 4.71/5.17 & ( ord_less_real @ ( F @ X2 ) @ ( G2 @ X2 ) ) )
% 4.71/5.17 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_strict_mono_ex1
% 4.71/5.17 thf(fact_8143_sum__strict__mono__ex1,axiom,
% 4.71/5.17 ! [A2: set_complex,F: complex > real,G2: complex > real] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.17 => ( ! [X4: complex] :
% 4.71/5.17 ( ( member_complex @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_real @ ( F @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ? [X2: complex] :
% 4.71/5.17 ( ( member_complex @ X2 @ A2 )
% 4.71/5.17 & ( ord_less_real @ ( F @ X2 ) @ ( G2 @ X2 ) ) )
% 4.71/5.17 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_strict_mono_ex1
% 4.71/5.17 thf(fact_8144_sum__strict__mono__ex1,axiom,
% 4.71/5.17 ! [A2: set_Extended_enat,F: extended_enat > real,G2: extended_enat > real] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.17 => ( ! [X4: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_real @ ( F @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ? [X2: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ X2 @ A2 )
% 4.71/5.17 & ( ord_less_real @ ( F @ X2 ) @ ( G2 @ X2 ) ) )
% 4.71/5.17 => ( ord_less_real @ ( groups4148127829035722712t_real @ F @ A2 ) @ ( groups4148127829035722712t_real @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_strict_mono_ex1
% 4.71/5.17 thf(fact_8145_sum__strict__mono__ex1,axiom,
% 4.71/5.17 ! [A2: set_nat,F: nat > rat,G2: nat > rat] :
% 4.71/5.17 ( ( finite_finite_nat @ A2 )
% 4.71/5.17 => ( ! [X4: nat] :
% 4.71/5.17 ( ( member_nat @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ? [X2: nat] :
% 4.71/5.17 ( ( member_nat @ X2 @ A2 )
% 4.71/5.17 & ( ord_less_rat @ ( F @ X2 ) @ ( G2 @ X2 ) ) )
% 4.71/5.17 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_strict_mono_ex1
% 4.71/5.17 thf(fact_8146_sum__strict__mono__ex1,axiom,
% 4.71/5.17 ! [A2: set_int,F: int > rat,G2: int > rat] :
% 4.71/5.17 ( ( finite_finite_int @ A2 )
% 4.71/5.17 => ( ! [X4: int] :
% 4.71/5.17 ( ( member_int @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ? [X2: int] :
% 4.71/5.17 ( ( member_int @ X2 @ A2 )
% 4.71/5.17 & ( ord_less_rat @ ( F @ X2 ) @ ( G2 @ X2 ) ) )
% 4.71/5.17 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_strict_mono_ex1
% 4.71/5.17 thf(fact_8147_sum__strict__mono__ex1,axiom,
% 4.71/5.17 ! [A2: set_complex,F: complex > rat,G2: complex > rat] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.17 => ( ! [X4: complex] :
% 4.71/5.17 ( ( member_complex @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ? [X2: complex] :
% 4.71/5.17 ( ( member_complex @ X2 @ A2 )
% 4.71/5.17 & ( ord_less_rat @ ( F @ X2 ) @ ( G2 @ X2 ) ) )
% 4.71/5.17 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_strict_mono_ex1
% 4.71/5.17 thf(fact_8148_sum__strict__mono__ex1,axiom,
% 4.71/5.17 ! [A2: set_Extended_enat,F: extended_enat > rat,G2: extended_enat > rat] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.17 => ( ! [X4: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ? [X2: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ X2 @ A2 )
% 4.71/5.17 & ( ord_less_rat @ ( F @ X2 ) @ ( G2 @ X2 ) ) )
% 4.71/5.17 => ( ord_less_rat @ ( groups1392844769737527556at_rat @ F @ A2 ) @ ( groups1392844769737527556at_rat @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_strict_mono_ex1
% 4.71/5.17 thf(fact_8149_sum__strict__mono__ex1,axiom,
% 4.71/5.17 ! [A2: set_int,F: int > nat,G2: int > nat] :
% 4.71/5.17 ( ( finite_finite_int @ A2 )
% 4.71/5.17 => ( ! [X4: int] :
% 4.71/5.17 ( ( member_int @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ? [X2: int] :
% 4.71/5.17 ( ( member_int @ X2 @ A2 )
% 4.71/5.17 & ( ord_less_nat @ ( F @ X2 ) @ ( G2 @ X2 ) ) )
% 4.71/5.17 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_strict_mono_ex1
% 4.71/5.17 thf(fact_8150_sum__strict__mono__ex1,axiom,
% 4.71/5.17 ! [A2: set_complex,F: complex > nat,G2: complex > nat] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.17 => ( ! [X4: complex] :
% 4.71/5.17 ( ( member_complex @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ? [X2: complex] :
% 4.71/5.17 ( ( member_complex @ X2 @ A2 )
% 4.71/5.17 & ( ord_less_nat @ ( F @ X2 ) @ ( G2 @ X2 ) ) )
% 4.71/5.17 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_strict_mono_ex1
% 4.71/5.17 thf(fact_8151_sum__strict__mono__ex1,axiom,
% 4.71/5.17 ! [A2: set_Extended_enat,F: extended_enat > nat,G2: extended_enat > nat] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.17 => ( ! [X4: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ? [X2: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ X2 @ A2 )
% 4.71/5.17 & ( ord_less_nat @ ( F @ X2 ) @ ( G2 @ X2 ) ) )
% 4.71/5.17 => ( ord_less_nat @ ( groups2027974829824023292at_nat @ F @ A2 ) @ ( groups2027974829824023292at_nat @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_strict_mono_ex1
% 4.71/5.17 thf(fact_8152_sum_Orelated,axiom,
% 4.71/5.17 ! [R: real > real > $o,S2: set_int,H: int > real,G2: int > real] :
% 4.71/5.17 ( ( R @ zero_zero_real @ zero_zero_real )
% 4.71/5.17 => ( ! [X1: real,Y1: real,X24: real,Y24: real] :
% 4.71/5.17 ( ( ( R @ X1 @ X24 )
% 4.71/5.17 & ( R @ Y1 @ Y24 ) )
% 4.71/5.17 => ( R @ ( plus_plus_real @ X1 @ Y1 ) @ ( plus_plus_real @ X24 @ Y24 ) ) )
% 4.71/5.17 => ( ( finite_finite_int @ S2 )
% 4.71/5.17 => ( ! [X4: int] :
% 4.71/5.17 ( ( member_int @ X4 @ S2 )
% 4.71/5.17 => ( R @ ( H @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( R @ ( groups8778361861064173332t_real @ H @ S2 ) @ ( groups8778361861064173332t_real @ G2 @ S2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.related
% 4.71/5.17 thf(fact_8153_sum_Orelated,axiom,
% 4.71/5.17 ! [R: real > real > $o,S2: set_complex,H: complex > real,G2: complex > real] :
% 4.71/5.17 ( ( R @ zero_zero_real @ zero_zero_real )
% 4.71/5.17 => ( ! [X1: real,Y1: real,X24: real,Y24: real] :
% 4.71/5.17 ( ( ( R @ X1 @ X24 )
% 4.71/5.17 & ( R @ Y1 @ Y24 ) )
% 4.71/5.17 => ( R @ ( plus_plus_real @ X1 @ Y1 ) @ ( plus_plus_real @ X24 @ Y24 ) ) )
% 4.71/5.17 => ( ( finite3207457112153483333omplex @ S2 )
% 4.71/5.17 => ( ! [X4: complex] :
% 4.71/5.17 ( ( member_complex @ X4 @ S2 )
% 4.71/5.17 => ( R @ ( H @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( R @ ( groups5808333547571424918x_real @ H @ S2 ) @ ( groups5808333547571424918x_real @ G2 @ S2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.related
% 4.71/5.17 thf(fact_8154_sum_Orelated,axiom,
% 4.71/5.17 ! [R: real > real > $o,S2: set_Extended_enat,H: extended_enat > real,G2: extended_enat > real] :
% 4.71/5.17 ( ( R @ zero_zero_real @ zero_zero_real )
% 4.71/5.17 => ( ! [X1: real,Y1: real,X24: real,Y24: real] :
% 4.71/5.17 ( ( ( R @ X1 @ X24 )
% 4.71/5.17 & ( R @ Y1 @ Y24 ) )
% 4.71/5.17 => ( R @ ( plus_plus_real @ X1 @ Y1 ) @ ( plus_plus_real @ X24 @ Y24 ) ) )
% 4.71/5.17 => ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.17 => ( ! [X4: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ X4 @ S2 )
% 4.71/5.17 => ( R @ ( H @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( R @ ( groups4148127829035722712t_real @ H @ S2 ) @ ( groups4148127829035722712t_real @ G2 @ S2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.related
% 4.71/5.17 thf(fact_8155_sum_Orelated,axiom,
% 4.71/5.17 ! [R: rat > rat > $o,S2: set_nat,H: nat > rat,G2: nat > rat] :
% 4.71/5.17 ( ( R @ zero_zero_rat @ zero_zero_rat )
% 4.71/5.17 => ( ! [X1: rat,Y1: rat,X24: rat,Y24: rat] :
% 4.71/5.17 ( ( ( R @ X1 @ X24 )
% 4.71/5.17 & ( R @ Y1 @ Y24 ) )
% 4.71/5.17 => ( R @ ( plus_plus_rat @ X1 @ Y1 ) @ ( plus_plus_rat @ X24 @ Y24 ) ) )
% 4.71/5.17 => ( ( finite_finite_nat @ S2 )
% 4.71/5.17 => ( ! [X4: nat] :
% 4.71/5.17 ( ( member_nat @ X4 @ S2 )
% 4.71/5.17 => ( R @ ( H @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( R @ ( groups2906978787729119204at_rat @ H @ S2 ) @ ( groups2906978787729119204at_rat @ G2 @ S2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.related
% 4.71/5.17 thf(fact_8156_sum_Orelated,axiom,
% 4.71/5.17 ! [R: rat > rat > $o,S2: set_int,H: int > rat,G2: int > rat] :
% 4.71/5.17 ( ( R @ zero_zero_rat @ zero_zero_rat )
% 4.71/5.17 => ( ! [X1: rat,Y1: rat,X24: rat,Y24: rat] :
% 4.71/5.17 ( ( ( R @ X1 @ X24 )
% 4.71/5.17 & ( R @ Y1 @ Y24 ) )
% 4.71/5.17 => ( R @ ( plus_plus_rat @ X1 @ Y1 ) @ ( plus_plus_rat @ X24 @ Y24 ) ) )
% 4.71/5.17 => ( ( finite_finite_int @ S2 )
% 4.71/5.17 => ( ! [X4: int] :
% 4.71/5.17 ( ( member_int @ X4 @ S2 )
% 4.71/5.17 => ( R @ ( H @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( R @ ( groups3906332499630173760nt_rat @ H @ S2 ) @ ( groups3906332499630173760nt_rat @ G2 @ S2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.related
% 4.71/5.17 thf(fact_8157_sum_Orelated,axiom,
% 4.71/5.17 ! [R: rat > rat > $o,S2: set_complex,H: complex > rat,G2: complex > rat] :
% 4.71/5.17 ( ( R @ zero_zero_rat @ zero_zero_rat )
% 4.71/5.17 => ( ! [X1: rat,Y1: rat,X24: rat,Y24: rat] :
% 4.71/5.17 ( ( ( R @ X1 @ X24 )
% 4.71/5.17 & ( R @ Y1 @ Y24 ) )
% 4.71/5.17 => ( R @ ( plus_plus_rat @ X1 @ Y1 ) @ ( plus_plus_rat @ X24 @ Y24 ) ) )
% 4.71/5.17 => ( ( finite3207457112153483333omplex @ S2 )
% 4.71/5.17 => ( ! [X4: complex] :
% 4.71/5.17 ( ( member_complex @ X4 @ S2 )
% 4.71/5.17 => ( R @ ( H @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( R @ ( groups5058264527183730370ex_rat @ H @ S2 ) @ ( groups5058264527183730370ex_rat @ G2 @ S2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.related
% 4.71/5.17 thf(fact_8158_sum_Orelated,axiom,
% 4.71/5.17 ! [R: rat > rat > $o,S2: set_Extended_enat,H: extended_enat > rat,G2: extended_enat > rat] :
% 4.71/5.17 ( ( R @ zero_zero_rat @ zero_zero_rat )
% 4.71/5.17 => ( ! [X1: rat,Y1: rat,X24: rat,Y24: rat] :
% 4.71/5.17 ( ( ( R @ X1 @ X24 )
% 4.71/5.17 & ( R @ Y1 @ Y24 ) )
% 4.71/5.17 => ( R @ ( plus_plus_rat @ X1 @ Y1 ) @ ( plus_plus_rat @ X24 @ Y24 ) ) )
% 4.71/5.17 => ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.17 => ( ! [X4: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ X4 @ S2 )
% 4.71/5.17 => ( R @ ( H @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( R @ ( groups1392844769737527556at_rat @ H @ S2 ) @ ( groups1392844769737527556at_rat @ G2 @ S2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.related
% 4.71/5.17 thf(fact_8159_sum_Orelated,axiom,
% 4.71/5.17 ! [R: nat > nat > $o,S2: set_int,H: int > nat,G2: int > nat] :
% 4.71/5.17 ( ( R @ zero_zero_nat @ zero_zero_nat )
% 4.71/5.17 => ( ! [X1: nat,Y1: nat,X24: nat,Y24: nat] :
% 4.71/5.17 ( ( ( R @ X1 @ X24 )
% 4.71/5.17 & ( R @ Y1 @ Y24 ) )
% 4.71/5.17 => ( R @ ( plus_plus_nat @ X1 @ Y1 ) @ ( plus_plus_nat @ X24 @ Y24 ) ) )
% 4.71/5.17 => ( ( finite_finite_int @ S2 )
% 4.71/5.17 => ( ! [X4: int] :
% 4.71/5.17 ( ( member_int @ X4 @ S2 )
% 4.71/5.17 => ( R @ ( H @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( R @ ( groups4541462559716669496nt_nat @ H @ S2 ) @ ( groups4541462559716669496nt_nat @ G2 @ S2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.related
% 4.71/5.17 thf(fact_8160_sum_Orelated,axiom,
% 4.71/5.17 ! [R: nat > nat > $o,S2: set_complex,H: complex > nat,G2: complex > nat] :
% 4.71/5.17 ( ( R @ zero_zero_nat @ zero_zero_nat )
% 4.71/5.17 => ( ! [X1: nat,Y1: nat,X24: nat,Y24: nat] :
% 4.71/5.17 ( ( ( R @ X1 @ X24 )
% 4.71/5.17 & ( R @ Y1 @ Y24 ) )
% 4.71/5.17 => ( R @ ( plus_plus_nat @ X1 @ Y1 ) @ ( plus_plus_nat @ X24 @ Y24 ) ) )
% 4.71/5.17 => ( ( finite3207457112153483333omplex @ S2 )
% 4.71/5.17 => ( ! [X4: complex] :
% 4.71/5.17 ( ( member_complex @ X4 @ S2 )
% 4.71/5.17 => ( R @ ( H @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( R @ ( groups5693394587270226106ex_nat @ H @ S2 ) @ ( groups5693394587270226106ex_nat @ G2 @ S2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.related
% 4.71/5.17 thf(fact_8161_sum_Orelated,axiom,
% 4.71/5.17 ! [R: nat > nat > $o,S2: set_Extended_enat,H: extended_enat > nat,G2: extended_enat > nat] :
% 4.71/5.17 ( ( R @ zero_zero_nat @ zero_zero_nat )
% 4.71/5.17 => ( ! [X1: nat,Y1: nat,X24: nat,Y24: nat] :
% 4.71/5.17 ( ( ( R @ X1 @ X24 )
% 4.71/5.17 & ( R @ Y1 @ Y24 ) )
% 4.71/5.17 => ( R @ ( plus_plus_nat @ X1 @ Y1 ) @ ( plus_plus_nat @ X24 @ Y24 ) ) )
% 4.71/5.17 => ( ( finite4001608067531595151d_enat @ S2 )
% 4.71/5.17 => ( ! [X4: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ X4 @ S2 )
% 4.71/5.17 => ( R @ ( H @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( R @ ( groups2027974829824023292at_nat @ H @ S2 ) @ ( groups2027974829824023292at_nat @ G2 @ S2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.related
% 4.71/5.17 thf(fact_8162_sum__strict__mono,axiom,
% 4.71/5.17 ! [A2: set_complex,F: complex > real,G2: complex > real] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.17 => ( ( A2 != bot_bot_set_complex )
% 4.71/5.17 => ( ! [X4: complex] :
% 4.71/5.17 ( ( member_complex @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_real @ ( F @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_strict_mono
% 4.71/5.17 thf(fact_8163_sum__strict__mono,axiom,
% 4.71/5.17 ! [A2: set_Extended_enat,F: extended_enat > real,G2: extended_enat > real] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.17 => ( ( A2 != bot_bo7653980558646680370d_enat )
% 4.71/5.17 => ( ! [X4: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_real @ ( F @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ord_less_real @ ( groups4148127829035722712t_real @ F @ A2 ) @ ( groups4148127829035722712t_real @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_strict_mono
% 4.71/5.17 thf(fact_8164_sum__strict__mono,axiom,
% 4.71/5.17 ! [A2: set_real,F: real > real,G2: real > real] :
% 4.71/5.17 ( ( finite_finite_real @ A2 )
% 4.71/5.17 => ( ( A2 != bot_bot_set_real )
% 4.71/5.17 => ( ! [X4: real] :
% 4.71/5.17 ( ( member_real @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_real @ ( F @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_strict_mono
% 4.71/5.17 thf(fact_8165_sum__strict__mono,axiom,
% 4.71/5.17 ! [A2: set_o,F: $o > real,G2: $o > real] :
% 4.71/5.17 ( ( finite_finite_o @ A2 )
% 4.71/5.17 => ( ( A2 != bot_bot_set_o )
% 4.71/5.17 => ( ! [X4: $o] :
% 4.71/5.17 ( ( member_o @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_real @ ( F @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ord_less_real @ ( groups8691415230153176458o_real @ F @ A2 ) @ ( groups8691415230153176458o_real @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_strict_mono
% 4.71/5.17 thf(fact_8166_sum__strict__mono,axiom,
% 4.71/5.17 ! [A2: set_int,F: int > real,G2: int > real] :
% 4.71/5.17 ( ( finite_finite_int @ A2 )
% 4.71/5.17 => ( ( A2 != bot_bot_set_int )
% 4.71/5.17 => ( ! [X4: int] :
% 4.71/5.17 ( ( member_int @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_real @ ( F @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_strict_mono
% 4.71/5.17 thf(fact_8167_sum__strict__mono,axiom,
% 4.71/5.17 ! [A2: set_complex,F: complex > rat,G2: complex > rat] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.17 => ( ( A2 != bot_bot_set_complex )
% 4.71/5.17 => ( ! [X4: complex] :
% 4.71/5.17 ( ( member_complex @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_rat @ ( F @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_strict_mono
% 4.71/5.17 thf(fact_8168_sum__strict__mono,axiom,
% 4.71/5.17 ! [A2: set_Extended_enat,F: extended_enat > rat,G2: extended_enat > rat] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.17 => ( ( A2 != bot_bo7653980558646680370d_enat )
% 4.71/5.17 => ( ! [X4: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_rat @ ( F @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ord_less_rat @ ( groups1392844769737527556at_rat @ F @ A2 ) @ ( groups1392844769737527556at_rat @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_strict_mono
% 4.71/5.17 thf(fact_8169_sum__strict__mono,axiom,
% 4.71/5.17 ! [A2: set_real,F: real > rat,G2: real > rat] :
% 4.71/5.17 ( ( finite_finite_real @ A2 )
% 4.71/5.17 => ( ( A2 != bot_bot_set_real )
% 4.71/5.17 => ( ! [X4: real] :
% 4.71/5.17 ( ( member_real @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_rat @ ( F @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_strict_mono
% 4.71/5.17 thf(fact_8170_sum__strict__mono,axiom,
% 4.71/5.17 ! [A2: set_o,F: $o > rat,G2: $o > rat] :
% 4.71/5.17 ( ( finite_finite_o @ A2 )
% 4.71/5.17 => ( ( A2 != bot_bot_set_o )
% 4.71/5.17 => ( ! [X4: $o] :
% 4.71/5.17 ( ( member_o @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_rat @ ( F @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ord_less_rat @ ( groups7872700643590313910_o_rat @ F @ A2 ) @ ( groups7872700643590313910_o_rat @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_strict_mono
% 4.71/5.17 thf(fact_8171_sum__strict__mono,axiom,
% 4.71/5.17 ! [A2: set_nat,F: nat > rat,G2: nat > rat] :
% 4.71/5.17 ( ( finite_finite_nat @ A2 )
% 4.71/5.17 => ( ( A2 != bot_bot_set_nat )
% 4.71/5.17 => ( ! [X4: nat] :
% 4.71/5.17 ( ( member_nat @ X4 @ A2 )
% 4.71/5.17 => ( ord_less_rat @ ( F @ X4 ) @ ( G2 @ X4 ) ) )
% 4.71/5.17 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G2 @ A2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_strict_mono
% 4.71/5.17 thf(fact_8172_zero__less__binomial,axiom,
% 4.71/5.17 ! [K: nat,N: nat] :
% 4.71/5.17 ( ( ord_less_eq_nat @ K @ N )
% 4.71/5.17 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % zero_less_binomial
% 4.71/5.17 thf(fact_8173_sum_Oinsert__if,axiom,
% 4.71/5.17 ! [A2: set_real,X: real,G2: real > real] :
% 4.71/5.17 ( ( finite_finite_real @ A2 )
% 4.71/5.17 => ( ( ( member_real @ X @ A2 )
% 4.71/5.17 => ( ( groups8097168146408367636l_real @ G2 @ ( insert_real @ X @ A2 ) )
% 4.71/5.17 = ( groups8097168146408367636l_real @ G2 @ A2 ) ) )
% 4.71/5.17 & ( ~ ( member_real @ X @ A2 )
% 4.71/5.17 => ( ( groups8097168146408367636l_real @ G2 @ ( insert_real @ X @ A2 ) )
% 4.71/5.17 = ( plus_plus_real @ ( G2 @ X ) @ ( groups8097168146408367636l_real @ G2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.insert_if
% 4.71/5.17 thf(fact_8174_sum_Oinsert__if,axiom,
% 4.71/5.17 ! [A2: set_o,X: $o,G2: $o > real] :
% 4.71/5.17 ( ( finite_finite_o @ A2 )
% 4.71/5.17 => ( ( ( member_o @ X @ A2 )
% 4.71/5.17 => ( ( groups8691415230153176458o_real @ G2 @ ( insert_o @ X @ A2 ) )
% 4.71/5.17 = ( groups8691415230153176458o_real @ G2 @ A2 ) ) )
% 4.71/5.17 & ( ~ ( member_o @ X @ A2 )
% 4.71/5.17 => ( ( groups8691415230153176458o_real @ G2 @ ( insert_o @ X @ A2 ) )
% 4.71/5.17 = ( plus_plus_real @ ( G2 @ X ) @ ( groups8691415230153176458o_real @ G2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.insert_if
% 4.71/5.17 thf(fact_8175_sum_Oinsert__if,axiom,
% 4.71/5.17 ! [A2: set_int,X: int,G2: int > real] :
% 4.71/5.17 ( ( finite_finite_int @ A2 )
% 4.71/5.17 => ( ( ( member_int @ X @ A2 )
% 4.71/5.17 => ( ( groups8778361861064173332t_real @ G2 @ ( insert_int @ X @ A2 ) )
% 4.71/5.17 = ( groups8778361861064173332t_real @ G2 @ A2 ) ) )
% 4.71/5.17 & ( ~ ( member_int @ X @ A2 )
% 4.71/5.17 => ( ( groups8778361861064173332t_real @ G2 @ ( insert_int @ X @ A2 ) )
% 4.71/5.17 = ( plus_plus_real @ ( G2 @ X ) @ ( groups8778361861064173332t_real @ G2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.insert_if
% 4.71/5.17 thf(fact_8176_sum_Oinsert__if,axiom,
% 4.71/5.17 ! [A2: set_complex,X: complex,G2: complex > real] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.17 => ( ( ( member_complex @ X @ A2 )
% 4.71/5.17 => ( ( groups5808333547571424918x_real @ G2 @ ( insert_complex @ X @ A2 ) )
% 4.71/5.17 = ( groups5808333547571424918x_real @ G2 @ A2 ) ) )
% 4.71/5.17 & ( ~ ( member_complex @ X @ A2 )
% 4.71/5.17 => ( ( groups5808333547571424918x_real @ G2 @ ( insert_complex @ X @ A2 ) )
% 4.71/5.17 = ( plus_plus_real @ ( G2 @ X ) @ ( groups5808333547571424918x_real @ G2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.insert_if
% 4.71/5.17 thf(fact_8177_sum_Oinsert__if,axiom,
% 4.71/5.17 ! [A2: set_Extended_enat,X: extended_enat,G2: extended_enat > real] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.17 => ( ( ( member_Extended_enat @ X @ A2 )
% 4.71/5.17 => ( ( groups4148127829035722712t_real @ G2 @ ( insert_Extended_enat @ X @ A2 ) )
% 4.71/5.17 = ( groups4148127829035722712t_real @ G2 @ A2 ) ) )
% 4.71/5.17 & ( ~ ( member_Extended_enat @ X @ A2 )
% 4.71/5.17 => ( ( groups4148127829035722712t_real @ G2 @ ( insert_Extended_enat @ X @ A2 ) )
% 4.71/5.17 = ( plus_plus_real @ ( G2 @ X ) @ ( groups4148127829035722712t_real @ G2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.insert_if
% 4.71/5.17 thf(fact_8178_sum_Oinsert__if,axiom,
% 4.71/5.17 ! [A2: set_real,X: real,G2: real > rat] :
% 4.71/5.17 ( ( finite_finite_real @ A2 )
% 4.71/5.17 => ( ( ( member_real @ X @ A2 )
% 4.71/5.17 => ( ( groups1300246762558778688al_rat @ G2 @ ( insert_real @ X @ A2 ) )
% 4.71/5.17 = ( groups1300246762558778688al_rat @ G2 @ A2 ) ) )
% 4.71/5.17 & ( ~ ( member_real @ X @ A2 )
% 4.71/5.17 => ( ( groups1300246762558778688al_rat @ G2 @ ( insert_real @ X @ A2 ) )
% 4.71/5.17 = ( plus_plus_rat @ ( G2 @ X ) @ ( groups1300246762558778688al_rat @ G2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.insert_if
% 4.71/5.17 thf(fact_8179_sum_Oinsert__if,axiom,
% 4.71/5.17 ! [A2: set_o,X: $o,G2: $o > rat] :
% 4.71/5.17 ( ( finite_finite_o @ A2 )
% 4.71/5.17 => ( ( ( member_o @ X @ A2 )
% 4.71/5.17 => ( ( groups7872700643590313910_o_rat @ G2 @ ( insert_o @ X @ A2 ) )
% 4.71/5.17 = ( groups7872700643590313910_o_rat @ G2 @ A2 ) ) )
% 4.71/5.17 & ( ~ ( member_o @ X @ A2 )
% 4.71/5.17 => ( ( groups7872700643590313910_o_rat @ G2 @ ( insert_o @ X @ A2 ) )
% 4.71/5.17 = ( plus_plus_rat @ ( G2 @ X ) @ ( groups7872700643590313910_o_rat @ G2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.insert_if
% 4.71/5.17 thf(fact_8180_sum_Oinsert__if,axiom,
% 4.71/5.17 ! [A2: set_nat,X: nat,G2: nat > rat] :
% 4.71/5.17 ( ( finite_finite_nat @ A2 )
% 4.71/5.17 => ( ( ( member_nat @ X @ A2 )
% 4.71/5.17 => ( ( groups2906978787729119204at_rat @ G2 @ ( insert_nat @ X @ A2 ) )
% 4.71/5.17 = ( groups2906978787729119204at_rat @ G2 @ A2 ) ) )
% 4.71/5.17 & ( ~ ( member_nat @ X @ A2 )
% 4.71/5.17 => ( ( groups2906978787729119204at_rat @ G2 @ ( insert_nat @ X @ A2 ) )
% 4.71/5.17 = ( plus_plus_rat @ ( G2 @ X ) @ ( groups2906978787729119204at_rat @ G2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.insert_if
% 4.71/5.17 thf(fact_8181_sum_Oinsert__if,axiom,
% 4.71/5.17 ! [A2: set_int,X: int,G2: int > rat] :
% 4.71/5.17 ( ( finite_finite_int @ A2 )
% 4.71/5.17 => ( ( ( member_int @ X @ A2 )
% 4.71/5.17 => ( ( groups3906332499630173760nt_rat @ G2 @ ( insert_int @ X @ A2 ) )
% 4.71/5.17 = ( groups3906332499630173760nt_rat @ G2 @ A2 ) ) )
% 4.71/5.17 & ( ~ ( member_int @ X @ A2 )
% 4.71/5.17 => ( ( groups3906332499630173760nt_rat @ G2 @ ( insert_int @ X @ A2 ) )
% 4.71/5.17 = ( plus_plus_rat @ ( G2 @ X ) @ ( groups3906332499630173760nt_rat @ G2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.insert_if
% 4.71/5.17 thf(fact_8182_sum_Oinsert__if,axiom,
% 4.71/5.17 ! [A2: set_complex,X: complex,G2: complex > rat] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.17 => ( ( ( member_complex @ X @ A2 )
% 4.71/5.17 => ( ( groups5058264527183730370ex_rat @ G2 @ ( insert_complex @ X @ A2 ) )
% 4.71/5.17 = ( groups5058264527183730370ex_rat @ G2 @ A2 ) ) )
% 4.71/5.17 & ( ~ ( member_complex @ X @ A2 )
% 4.71/5.17 => ( ( groups5058264527183730370ex_rat @ G2 @ ( insert_complex @ X @ A2 ) )
% 4.71/5.17 = ( plus_plus_rat @ ( G2 @ X ) @ ( groups5058264527183730370ex_rat @ G2 @ A2 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.insert_if
% 4.71/5.17 thf(fact_8183_sum_Oreindex__bij__witness__not__neutral,axiom,
% 4.71/5.17 ! [S5: set_o,T5: set_o,S2: set_o,I: $o > $o,J: $o > $o,T3: set_o,G2: $o > real,H: $o > real] :
% 4.71/5.17 ( ( finite_finite_o @ S5 )
% 4.71/5.17 => ( ( finite_finite_o @ T5 )
% 4.71/5.17 => ( ! [A5: $o] :
% 4.71/5.17 ( ( member_o @ A5 @ ( minus_minus_set_o @ S2 @ S5 ) )
% 4.71/5.17 => ( ( I @ ( J @ A5 ) )
% 4.71/5.17 = A5 ) )
% 4.71/5.17 => ( ! [A5: $o] :
% 4.71/5.17 ( ( member_o @ A5 @ ( minus_minus_set_o @ S2 @ S5 ) )
% 4.71/5.17 => ( member_o @ ( J @ A5 ) @ ( minus_minus_set_o @ T3 @ T5 ) ) )
% 4.71/5.17 => ( ! [B5: $o] :
% 4.71/5.17 ( ( member_o @ B5 @ ( minus_minus_set_o @ T3 @ T5 ) )
% 4.71/5.17 => ( ( J @ ( I @ B5 ) )
% 4.71/5.17 = B5 ) )
% 4.71/5.17 => ( ! [B5: $o] :
% 4.71/5.17 ( ( member_o @ B5 @ ( minus_minus_set_o @ T3 @ T5 ) )
% 4.71/5.17 => ( member_o @ ( I @ B5 ) @ ( minus_minus_set_o @ S2 @ S5 ) ) )
% 4.71/5.17 => ( ! [A5: $o] :
% 4.71/5.17 ( ( member_o @ A5 @ S5 )
% 4.71/5.17 => ( ( G2 @ A5 )
% 4.71/5.17 = zero_zero_real ) )
% 4.71/5.17 => ( ! [B5: $o] :
% 4.71/5.17 ( ( member_o @ B5 @ T5 )
% 4.71/5.17 => ( ( H @ B5 )
% 4.71/5.17 = zero_zero_real ) )
% 4.71/5.17 => ( ! [A5: $o] :
% 4.71/5.17 ( ( member_o @ A5 @ S2 )
% 4.71/5.17 => ( ( H @ ( J @ A5 ) )
% 4.71/5.17 = ( G2 @ A5 ) ) )
% 4.71/5.17 => ( ( groups8691415230153176458o_real @ G2 @ S2 )
% 4.71/5.17 = ( groups8691415230153176458o_real @ H @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.reindex_bij_witness_not_neutral
% 4.71/5.17 thf(fact_8184_sum_Oreindex__bij__witness__not__neutral,axiom,
% 4.71/5.17 ! [S5: set_o,T5: set_int,S2: set_o,I: int > $o,J: $o > int,T3: set_int,G2: $o > real,H: int > real] :
% 4.71/5.17 ( ( finite_finite_o @ S5 )
% 4.71/5.17 => ( ( finite_finite_int @ T5 )
% 4.71/5.17 => ( ! [A5: $o] :
% 4.71/5.17 ( ( member_o @ A5 @ ( minus_minus_set_o @ S2 @ S5 ) )
% 4.71/5.17 => ( ( I @ ( J @ A5 ) )
% 4.71/5.17 = A5 ) )
% 4.71/5.17 => ( ! [A5: $o] :
% 4.71/5.17 ( ( member_o @ A5 @ ( minus_minus_set_o @ S2 @ S5 ) )
% 4.71/5.17 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T3 @ T5 ) ) )
% 4.71/5.17 => ( ! [B5: int] :
% 4.71/5.17 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 4.71/5.17 => ( ( J @ ( I @ B5 ) )
% 4.71/5.17 = B5 ) )
% 4.71/5.17 => ( ! [B5: int] :
% 4.71/5.17 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 4.71/5.17 => ( member_o @ ( I @ B5 ) @ ( minus_minus_set_o @ S2 @ S5 ) ) )
% 4.71/5.17 => ( ! [A5: $o] :
% 4.71/5.17 ( ( member_o @ A5 @ S5 )
% 4.71/5.17 => ( ( G2 @ A5 )
% 4.71/5.17 = zero_zero_real ) )
% 4.71/5.17 => ( ! [B5: int] :
% 4.71/5.17 ( ( member_int @ B5 @ T5 )
% 4.71/5.17 => ( ( H @ B5 )
% 4.71/5.17 = zero_zero_real ) )
% 4.71/5.17 => ( ! [A5: $o] :
% 4.71/5.17 ( ( member_o @ A5 @ S2 )
% 4.71/5.17 => ( ( H @ ( J @ A5 ) )
% 4.71/5.17 = ( G2 @ A5 ) ) )
% 4.71/5.17 => ( ( groups8691415230153176458o_real @ G2 @ S2 )
% 4.71/5.17 = ( groups8778361861064173332t_real @ H @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.reindex_bij_witness_not_neutral
% 4.71/5.17 thf(fact_8185_sum_Oreindex__bij__witness__not__neutral,axiom,
% 4.71/5.17 ! [S5: set_o,T5: set_complex,S2: set_o,I: complex > $o,J: $o > complex,T3: set_complex,G2: $o > real,H: complex > real] :
% 4.71/5.17 ( ( finite_finite_o @ S5 )
% 4.71/5.17 => ( ( finite3207457112153483333omplex @ T5 )
% 4.71/5.17 => ( ! [A5: $o] :
% 4.71/5.17 ( ( member_o @ A5 @ ( minus_minus_set_o @ S2 @ S5 ) )
% 4.71/5.17 => ( ( I @ ( J @ A5 ) )
% 4.71/5.17 = A5 ) )
% 4.71/5.17 => ( ! [A5: $o] :
% 4.71/5.17 ( ( member_o @ A5 @ ( minus_minus_set_o @ S2 @ S5 ) )
% 4.71/5.17 => ( member_complex @ ( J @ A5 ) @ ( minus_811609699411566653omplex @ T3 @ T5 ) ) )
% 4.71/5.17 => ( ! [B5: complex] :
% 4.71/5.17 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 4.71/5.17 => ( ( J @ ( I @ B5 ) )
% 4.71/5.17 = B5 ) )
% 4.71/5.17 => ( ! [B5: complex] :
% 4.71/5.17 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 4.71/5.17 => ( member_o @ ( I @ B5 ) @ ( minus_minus_set_o @ S2 @ S5 ) ) )
% 4.71/5.17 => ( ! [A5: $o] :
% 4.71/5.17 ( ( member_o @ A5 @ S5 )
% 4.71/5.17 => ( ( G2 @ A5 )
% 4.71/5.17 = zero_zero_real ) )
% 4.71/5.17 => ( ! [B5: complex] :
% 4.71/5.17 ( ( member_complex @ B5 @ T5 )
% 4.71/5.17 => ( ( H @ B5 )
% 4.71/5.17 = zero_zero_real ) )
% 4.71/5.17 => ( ! [A5: $o] :
% 4.71/5.17 ( ( member_o @ A5 @ S2 )
% 4.71/5.17 => ( ( H @ ( J @ A5 ) )
% 4.71/5.17 = ( G2 @ A5 ) ) )
% 4.71/5.17 => ( ( groups8691415230153176458o_real @ G2 @ S2 )
% 4.71/5.17 = ( groups5808333547571424918x_real @ H @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.reindex_bij_witness_not_neutral
% 4.71/5.17 thf(fact_8186_sum_Oreindex__bij__witness__not__neutral,axiom,
% 4.71/5.17 ! [S5: set_o,T5: set_Extended_enat,S2: set_o,I: extended_enat > $o,J: $o > extended_enat,T3: set_Extended_enat,G2: $o > real,H: extended_enat > real] :
% 4.71/5.17 ( ( finite_finite_o @ S5 )
% 4.71/5.17 => ( ( finite4001608067531595151d_enat @ T5 )
% 4.71/5.17 => ( ! [A5: $o] :
% 4.71/5.17 ( ( member_o @ A5 @ ( minus_minus_set_o @ S2 @ S5 ) )
% 4.71/5.17 => ( ( I @ ( J @ A5 ) )
% 4.71/5.17 = A5 ) )
% 4.71/5.17 => ( ! [A5: $o] :
% 4.71/5.17 ( ( member_o @ A5 @ ( minus_minus_set_o @ S2 @ S5 ) )
% 4.71/5.17 => ( member_Extended_enat @ ( J @ A5 ) @ ( minus_925952699566721837d_enat @ T3 @ T5 ) ) )
% 4.71/5.17 => ( ! [B5: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ B5 @ ( minus_925952699566721837d_enat @ T3 @ T5 ) )
% 4.71/5.17 => ( ( J @ ( I @ B5 ) )
% 4.71/5.17 = B5 ) )
% 4.71/5.17 => ( ! [B5: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ B5 @ ( minus_925952699566721837d_enat @ T3 @ T5 ) )
% 4.71/5.17 => ( member_o @ ( I @ B5 ) @ ( minus_minus_set_o @ S2 @ S5 ) ) )
% 4.71/5.17 => ( ! [A5: $o] :
% 4.71/5.17 ( ( member_o @ A5 @ S5 )
% 4.71/5.17 => ( ( G2 @ A5 )
% 4.71/5.17 = zero_zero_real ) )
% 4.71/5.17 => ( ! [B5: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ B5 @ T5 )
% 4.71/5.17 => ( ( H @ B5 )
% 4.71/5.17 = zero_zero_real ) )
% 4.71/5.17 => ( ! [A5: $o] :
% 4.71/5.17 ( ( member_o @ A5 @ S2 )
% 4.71/5.17 => ( ( H @ ( J @ A5 ) )
% 4.71/5.17 = ( G2 @ A5 ) ) )
% 4.71/5.17 => ( ( groups8691415230153176458o_real @ G2 @ S2 )
% 4.71/5.17 = ( groups4148127829035722712t_real @ H @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.reindex_bij_witness_not_neutral
% 4.71/5.17 thf(fact_8187_sum_Oreindex__bij__witness__not__neutral,axiom,
% 4.71/5.17 ! [S5: set_int,T5: set_o,S2: set_int,I: $o > int,J: int > $o,T3: set_o,G2: int > real,H: $o > real] :
% 4.71/5.17 ( ( finite_finite_int @ S5 )
% 4.71/5.17 => ( ( finite_finite_o @ T5 )
% 4.71/5.17 => ( ! [A5: int] :
% 4.71/5.17 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 4.71/5.17 => ( ( I @ ( J @ A5 ) )
% 4.71/5.17 = A5 ) )
% 4.71/5.17 => ( ! [A5: int] :
% 4.71/5.17 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 4.71/5.17 => ( member_o @ ( J @ A5 ) @ ( minus_minus_set_o @ T3 @ T5 ) ) )
% 4.71/5.17 => ( ! [B5: $o] :
% 4.71/5.17 ( ( member_o @ B5 @ ( minus_minus_set_o @ T3 @ T5 ) )
% 4.71/5.17 => ( ( J @ ( I @ B5 ) )
% 4.71/5.17 = B5 ) )
% 4.71/5.17 => ( ! [B5: $o] :
% 4.71/5.17 ( ( member_o @ B5 @ ( minus_minus_set_o @ T3 @ T5 ) )
% 4.71/5.17 => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 4.71/5.17 => ( ! [A5: int] :
% 4.71/5.17 ( ( member_int @ A5 @ S5 )
% 4.71/5.17 => ( ( G2 @ A5 )
% 4.71/5.17 = zero_zero_real ) )
% 4.71/5.17 => ( ! [B5: $o] :
% 4.71/5.17 ( ( member_o @ B5 @ T5 )
% 4.71/5.17 => ( ( H @ B5 )
% 4.71/5.17 = zero_zero_real ) )
% 4.71/5.17 => ( ! [A5: int] :
% 4.71/5.17 ( ( member_int @ A5 @ S2 )
% 4.71/5.17 => ( ( H @ ( J @ A5 ) )
% 4.71/5.17 = ( G2 @ A5 ) ) )
% 4.71/5.17 => ( ( groups8778361861064173332t_real @ G2 @ S2 )
% 4.71/5.17 = ( groups8691415230153176458o_real @ H @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.reindex_bij_witness_not_neutral
% 4.71/5.17 thf(fact_8188_sum_Oreindex__bij__witness__not__neutral,axiom,
% 4.71/5.17 ! [S5: set_int,T5: set_int,S2: set_int,I: int > int,J: int > int,T3: set_int,G2: int > real,H: int > real] :
% 4.71/5.17 ( ( finite_finite_int @ S5 )
% 4.71/5.17 => ( ( finite_finite_int @ T5 )
% 4.71/5.17 => ( ! [A5: int] :
% 4.71/5.17 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 4.71/5.17 => ( ( I @ ( J @ A5 ) )
% 4.71/5.17 = A5 ) )
% 4.71/5.17 => ( ! [A5: int] :
% 4.71/5.17 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 4.71/5.17 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T3 @ T5 ) ) )
% 4.71/5.17 => ( ! [B5: int] :
% 4.71/5.17 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 4.71/5.17 => ( ( J @ ( I @ B5 ) )
% 4.71/5.17 = B5 ) )
% 4.71/5.17 => ( ! [B5: int] :
% 4.71/5.17 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 4.71/5.17 => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 4.71/5.17 => ( ! [A5: int] :
% 4.71/5.17 ( ( member_int @ A5 @ S5 )
% 4.71/5.17 => ( ( G2 @ A5 )
% 4.71/5.17 = zero_zero_real ) )
% 4.71/5.17 => ( ! [B5: int] :
% 4.71/5.17 ( ( member_int @ B5 @ T5 )
% 4.71/5.17 => ( ( H @ B5 )
% 4.71/5.17 = zero_zero_real ) )
% 4.71/5.17 => ( ! [A5: int] :
% 4.71/5.17 ( ( member_int @ A5 @ S2 )
% 4.71/5.17 => ( ( H @ ( J @ A5 ) )
% 4.71/5.17 = ( G2 @ A5 ) ) )
% 4.71/5.17 => ( ( groups8778361861064173332t_real @ G2 @ S2 )
% 4.71/5.17 = ( groups8778361861064173332t_real @ H @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.reindex_bij_witness_not_neutral
% 4.71/5.17 thf(fact_8189_sum_Oreindex__bij__witness__not__neutral,axiom,
% 4.71/5.17 ! [S5: set_int,T5: set_complex,S2: set_int,I: complex > int,J: int > complex,T3: set_complex,G2: int > real,H: complex > real] :
% 4.71/5.17 ( ( finite_finite_int @ S5 )
% 4.71/5.17 => ( ( finite3207457112153483333omplex @ T5 )
% 4.71/5.17 => ( ! [A5: int] :
% 4.71/5.17 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 4.71/5.17 => ( ( I @ ( J @ A5 ) )
% 4.71/5.17 = A5 ) )
% 4.71/5.17 => ( ! [A5: int] :
% 4.71/5.17 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 4.71/5.17 => ( member_complex @ ( J @ A5 ) @ ( minus_811609699411566653omplex @ T3 @ T5 ) ) )
% 4.71/5.17 => ( ! [B5: complex] :
% 4.71/5.17 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 4.71/5.17 => ( ( J @ ( I @ B5 ) )
% 4.71/5.17 = B5 ) )
% 4.71/5.17 => ( ! [B5: complex] :
% 4.71/5.17 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 4.71/5.17 => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 4.71/5.17 => ( ! [A5: int] :
% 4.71/5.17 ( ( member_int @ A5 @ S5 )
% 4.71/5.17 => ( ( G2 @ A5 )
% 4.71/5.17 = zero_zero_real ) )
% 4.71/5.17 => ( ! [B5: complex] :
% 4.71/5.17 ( ( member_complex @ B5 @ T5 )
% 4.71/5.17 => ( ( H @ B5 )
% 4.71/5.17 = zero_zero_real ) )
% 4.71/5.17 => ( ! [A5: int] :
% 4.71/5.17 ( ( member_int @ A5 @ S2 )
% 4.71/5.17 => ( ( H @ ( J @ A5 ) )
% 4.71/5.17 = ( G2 @ A5 ) ) )
% 4.71/5.17 => ( ( groups8778361861064173332t_real @ G2 @ S2 )
% 4.71/5.17 = ( groups5808333547571424918x_real @ H @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.reindex_bij_witness_not_neutral
% 4.71/5.17 thf(fact_8190_sum_Oreindex__bij__witness__not__neutral,axiom,
% 4.71/5.17 ! [S5: set_int,T5: set_Extended_enat,S2: set_int,I: extended_enat > int,J: int > extended_enat,T3: set_Extended_enat,G2: int > real,H: extended_enat > real] :
% 4.71/5.17 ( ( finite_finite_int @ S5 )
% 4.71/5.17 => ( ( finite4001608067531595151d_enat @ T5 )
% 4.71/5.17 => ( ! [A5: int] :
% 4.71/5.17 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 4.71/5.17 => ( ( I @ ( J @ A5 ) )
% 4.71/5.17 = A5 ) )
% 4.71/5.17 => ( ! [A5: int] :
% 4.71/5.17 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S5 ) )
% 4.71/5.17 => ( member_Extended_enat @ ( J @ A5 ) @ ( minus_925952699566721837d_enat @ T3 @ T5 ) ) )
% 4.71/5.17 => ( ! [B5: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ B5 @ ( minus_925952699566721837d_enat @ T3 @ T5 ) )
% 4.71/5.17 => ( ( J @ ( I @ B5 ) )
% 4.71/5.17 = B5 ) )
% 4.71/5.17 => ( ! [B5: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ B5 @ ( minus_925952699566721837d_enat @ T3 @ T5 ) )
% 4.71/5.17 => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S5 ) ) )
% 4.71/5.17 => ( ! [A5: int] :
% 4.71/5.17 ( ( member_int @ A5 @ S5 )
% 4.71/5.17 => ( ( G2 @ A5 )
% 4.71/5.17 = zero_zero_real ) )
% 4.71/5.17 => ( ! [B5: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ B5 @ T5 )
% 4.71/5.17 => ( ( H @ B5 )
% 4.71/5.17 = zero_zero_real ) )
% 4.71/5.17 => ( ! [A5: int] :
% 4.71/5.17 ( ( member_int @ A5 @ S2 )
% 4.71/5.17 => ( ( H @ ( J @ A5 ) )
% 4.71/5.17 = ( G2 @ A5 ) ) )
% 4.71/5.17 => ( ( groups8778361861064173332t_real @ G2 @ S2 )
% 4.71/5.17 = ( groups4148127829035722712t_real @ H @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.reindex_bij_witness_not_neutral
% 4.71/5.17 thf(fact_8191_sum_Oreindex__bij__witness__not__neutral,axiom,
% 4.71/5.17 ! [S5: set_complex,T5: set_o,S2: set_complex,I: $o > complex,J: complex > $o,T3: set_o,G2: complex > real,H: $o > real] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ S5 )
% 4.71/5.17 => ( ( finite_finite_o @ T5 )
% 4.71/5.17 => ( ! [A5: complex] :
% 4.71/5.17 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 4.71/5.17 => ( ( I @ ( J @ A5 ) )
% 4.71/5.17 = A5 ) )
% 4.71/5.17 => ( ! [A5: complex] :
% 4.71/5.17 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 4.71/5.17 => ( member_o @ ( J @ A5 ) @ ( minus_minus_set_o @ T3 @ T5 ) ) )
% 4.71/5.17 => ( ! [B5: $o] :
% 4.71/5.17 ( ( member_o @ B5 @ ( minus_minus_set_o @ T3 @ T5 ) )
% 4.71/5.17 => ( ( J @ ( I @ B5 ) )
% 4.71/5.17 = B5 ) )
% 4.71/5.17 => ( ! [B5: $o] :
% 4.71/5.17 ( ( member_o @ B5 @ ( minus_minus_set_o @ T3 @ T5 ) )
% 4.71/5.17 => ( member_complex @ ( I @ B5 ) @ ( minus_811609699411566653omplex @ S2 @ S5 ) ) )
% 4.71/5.17 => ( ! [A5: complex] :
% 4.71/5.17 ( ( member_complex @ A5 @ S5 )
% 4.71/5.17 => ( ( G2 @ A5 )
% 4.71/5.17 = zero_zero_real ) )
% 4.71/5.17 => ( ! [B5: $o] :
% 4.71/5.17 ( ( member_o @ B5 @ T5 )
% 4.71/5.17 => ( ( H @ B5 )
% 4.71/5.17 = zero_zero_real ) )
% 4.71/5.17 => ( ! [A5: complex] :
% 4.71/5.17 ( ( member_complex @ A5 @ S2 )
% 4.71/5.17 => ( ( H @ ( J @ A5 ) )
% 4.71/5.17 = ( G2 @ A5 ) ) )
% 4.71/5.17 => ( ( groups5808333547571424918x_real @ G2 @ S2 )
% 4.71/5.17 = ( groups8691415230153176458o_real @ H @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.reindex_bij_witness_not_neutral
% 4.71/5.17 thf(fact_8192_sum_Oreindex__bij__witness__not__neutral,axiom,
% 4.71/5.17 ! [S5: set_complex,T5: set_int,S2: set_complex,I: int > complex,J: complex > int,T3: set_int,G2: complex > real,H: int > real] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ S5 )
% 4.71/5.17 => ( ( finite_finite_int @ T5 )
% 4.71/5.17 => ( ! [A5: complex] :
% 4.71/5.17 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 4.71/5.17 => ( ( I @ ( J @ A5 ) )
% 4.71/5.17 = A5 ) )
% 4.71/5.17 => ( ! [A5: complex] :
% 4.71/5.17 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ S2 @ S5 ) )
% 4.71/5.17 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T3 @ T5 ) ) )
% 4.71/5.17 => ( ! [B5: int] :
% 4.71/5.17 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 4.71/5.17 => ( ( J @ ( I @ B5 ) )
% 4.71/5.17 = B5 ) )
% 4.71/5.17 => ( ! [B5: int] :
% 4.71/5.17 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 4.71/5.17 => ( member_complex @ ( I @ B5 ) @ ( minus_811609699411566653omplex @ S2 @ S5 ) ) )
% 4.71/5.17 => ( ! [A5: complex] :
% 4.71/5.17 ( ( member_complex @ A5 @ S5 )
% 4.71/5.17 => ( ( G2 @ A5 )
% 4.71/5.17 = zero_zero_real ) )
% 4.71/5.17 => ( ! [B5: int] :
% 4.71/5.17 ( ( member_int @ B5 @ T5 )
% 4.71/5.17 => ( ( H @ B5 )
% 4.71/5.17 = zero_zero_real ) )
% 4.71/5.17 => ( ! [A5: complex] :
% 4.71/5.17 ( ( member_complex @ A5 @ S2 )
% 4.71/5.17 => ( ( H @ ( J @ A5 ) )
% 4.71/5.17 = ( G2 @ A5 ) ) )
% 4.71/5.17 => ( ( groups5808333547571424918x_real @ G2 @ S2 )
% 4.71/5.17 = ( groups8778361861064173332t_real @ H @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.reindex_bij_witness_not_neutral
% 4.71/5.17 thf(fact_8193_choose__mult,axiom,
% 4.71/5.17 ! [K: nat,M2: nat,N: nat] :
% 4.71/5.17 ( ( ord_less_eq_nat @ K @ M2 )
% 4.71/5.17 => ( ( ord_less_eq_nat @ M2 @ N )
% 4.71/5.17 => ( ( times_times_nat @ ( binomial @ N @ M2 ) @ ( binomial @ M2 @ K ) )
% 4.71/5.17 = ( times_times_nat @ ( binomial @ N @ K ) @ ( binomial @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M2 @ K ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % choose_mult
% 4.71/5.17 thf(fact_8194_binomial__absorb__comp,axiom,
% 4.71/5.17 ! [N: nat,K: nat] :
% 4.71/5.17 ( ( times_times_nat @ ( minus_minus_nat @ N @ K ) @ ( binomial @ N @ K ) )
% 4.71/5.17 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % binomial_absorb_comp
% 4.71/5.17 thf(fact_8195_distinct__conv__nth,axiom,
% 4.71/5.17 ( distinct_int
% 4.71/5.17 = ( ^ [Xs2: list_int] :
% 4.71/5.17 ! [I4: nat] :
% 4.71/5.17 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs2 ) )
% 4.71/5.17 => ! [J3: nat] :
% 4.71/5.17 ( ( ord_less_nat @ J3 @ ( size_size_list_int @ Xs2 ) )
% 4.71/5.17 => ( ( I4 != J3 )
% 4.71/5.17 => ( ( nth_int @ Xs2 @ I4 )
% 4.71/5.17 != ( nth_int @ Xs2 @ J3 ) ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % distinct_conv_nth
% 4.71/5.17 thf(fact_8196_distinct__conv__nth,axiom,
% 4.71/5.17 ( distinct_VEBT_VEBT
% 4.71/5.17 = ( ^ [Xs2: list_VEBT_VEBT] :
% 4.71/5.17 ! [I4: nat] :
% 4.71/5.17 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 4.71/5.17 => ! [J3: nat] :
% 4.71/5.17 ( ( ord_less_nat @ J3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 4.71/5.17 => ( ( I4 != J3 )
% 4.71/5.17 => ( ( nth_VEBT_VEBT @ Xs2 @ I4 )
% 4.71/5.17 != ( nth_VEBT_VEBT @ Xs2 @ J3 ) ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % distinct_conv_nth
% 4.71/5.17 thf(fact_8197_distinct__conv__nth,axiom,
% 4.71/5.17 ( distinct_nat
% 4.71/5.17 = ( ^ [Xs2: list_nat] :
% 4.71/5.17 ! [I4: nat] :
% 4.71/5.17 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs2 ) )
% 4.71/5.17 => ! [J3: nat] :
% 4.71/5.17 ( ( ord_less_nat @ J3 @ ( size_size_list_nat @ Xs2 ) )
% 4.71/5.17 => ( ( I4 != J3 )
% 4.71/5.17 => ( ( nth_nat @ Xs2 @ I4 )
% 4.71/5.17 != ( nth_nat @ Xs2 @ J3 ) ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % distinct_conv_nth
% 4.71/5.17 thf(fact_8198_nth__eq__iff__index__eq,axiom,
% 4.71/5.17 ! [Xs: list_int,I: nat,J: nat] :
% 4.71/5.17 ( ( distinct_int @ Xs )
% 4.71/5.17 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 4.71/5.17 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 4.71/5.17 => ( ( ( nth_int @ Xs @ I )
% 4.71/5.17 = ( nth_int @ Xs @ J ) )
% 4.71/5.17 = ( I = J ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % nth_eq_iff_index_eq
% 4.71/5.17 thf(fact_8199_nth__eq__iff__index__eq,axiom,
% 4.71/5.17 ! [Xs: list_VEBT_VEBT,I: nat,J: nat] :
% 4.71/5.17 ( ( distinct_VEBT_VEBT @ Xs )
% 4.71/5.17 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.71/5.17 => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.71/5.17 => ( ( ( nth_VEBT_VEBT @ Xs @ I )
% 4.71/5.17 = ( nth_VEBT_VEBT @ Xs @ J ) )
% 4.71/5.17 = ( I = J ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % nth_eq_iff_index_eq
% 4.71/5.17 thf(fact_8200_nth__eq__iff__index__eq,axiom,
% 4.71/5.17 ! [Xs: list_nat,I: nat,J: nat] :
% 4.71/5.17 ( ( distinct_nat @ Xs )
% 4.71/5.17 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 4.71/5.17 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 4.71/5.17 => ( ( ( nth_nat @ Xs @ I )
% 4.71/5.17 = ( nth_nat @ Xs @ J ) )
% 4.71/5.17 = ( I = J ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % nth_eq_iff_index_eq
% 4.71/5.17 thf(fact_8201_sum__nonneg__0,axiom,
% 4.71/5.17 ! [S: set_o,F: $o > real,I: $o] :
% 4.71/5.17 ( ( finite_finite_o @ S )
% 4.71/5.17 => ( ! [I2: $o] :
% 4.71/5.17 ( ( member_o @ I2 @ S )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ( ( groups8691415230153176458o_real @ F @ S )
% 4.71/5.17 = zero_zero_real )
% 4.71/5.17 => ( ( member_o @ I @ S )
% 4.71/5.17 => ( ( F @ I )
% 4.71/5.17 = zero_zero_real ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_0
% 4.71/5.17 thf(fact_8202_sum__nonneg__0,axiom,
% 4.71/5.17 ! [S: set_int,F: int > real,I: int] :
% 4.71/5.17 ( ( finite_finite_int @ S )
% 4.71/5.17 => ( ! [I2: int] :
% 4.71/5.17 ( ( member_int @ I2 @ S )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ( ( groups8778361861064173332t_real @ F @ S )
% 4.71/5.17 = zero_zero_real )
% 4.71/5.17 => ( ( member_int @ I @ S )
% 4.71/5.17 => ( ( F @ I )
% 4.71/5.17 = zero_zero_real ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_0
% 4.71/5.17 thf(fact_8203_sum__nonneg__0,axiom,
% 4.71/5.17 ! [S: set_complex,F: complex > real,I: complex] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ S )
% 4.71/5.17 => ( ! [I2: complex] :
% 4.71/5.17 ( ( member_complex @ I2 @ S )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ( ( groups5808333547571424918x_real @ F @ S )
% 4.71/5.17 = zero_zero_real )
% 4.71/5.17 => ( ( member_complex @ I @ S )
% 4.71/5.17 => ( ( F @ I )
% 4.71/5.17 = zero_zero_real ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_0
% 4.71/5.17 thf(fact_8204_sum__nonneg__0,axiom,
% 4.71/5.17 ! [S: set_Extended_enat,F: extended_enat > real,I: extended_enat] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ S )
% 4.71/5.17 => ( ! [I2: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ I2 @ S )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ( ( groups4148127829035722712t_real @ F @ S )
% 4.71/5.17 = zero_zero_real )
% 4.71/5.17 => ( ( member_Extended_enat @ I @ S )
% 4.71/5.17 => ( ( F @ I )
% 4.71/5.17 = zero_zero_real ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_0
% 4.71/5.17 thf(fact_8205_sum__nonneg__0,axiom,
% 4.71/5.17 ! [S: set_o,F: $o > rat,I: $o] :
% 4.71/5.17 ( ( finite_finite_o @ S )
% 4.71/5.17 => ( ! [I2: $o] :
% 4.71/5.17 ( ( member_o @ I2 @ S )
% 4.71/5.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ( ( groups7872700643590313910_o_rat @ F @ S )
% 4.71/5.17 = zero_zero_rat )
% 4.71/5.17 => ( ( member_o @ I @ S )
% 4.71/5.17 => ( ( F @ I )
% 4.71/5.17 = zero_zero_rat ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_0
% 4.71/5.17 thf(fact_8206_sum__nonneg__0,axiom,
% 4.71/5.17 ! [S: set_nat,F: nat > rat,I: nat] :
% 4.71/5.17 ( ( finite_finite_nat @ S )
% 4.71/5.17 => ( ! [I2: nat] :
% 4.71/5.17 ( ( member_nat @ I2 @ S )
% 4.71/5.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ( ( groups2906978787729119204at_rat @ F @ S )
% 4.71/5.17 = zero_zero_rat )
% 4.71/5.17 => ( ( member_nat @ I @ S )
% 4.71/5.17 => ( ( F @ I )
% 4.71/5.17 = zero_zero_rat ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_0
% 4.71/5.17 thf(fact_8207_sum__nonneg__0,axiom,
% 4.71/5.17 ! [S: set_int,F: int > rat,I: int] :
% 4.71/5.17 ( ( finite_finite_int @ S )
% 4.71/5.17 => ( ! [I2: int] :
% 4.71/5.17 ( ( member_int @ I2 @ S )
% 4.71/5.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ( ( groups3906332499630173760nt_rat @ F @ S )
% 4.71/5.17 = zero_zero_rat )
% 4.71/5.17 => ( ( member_int @ I @ S )
% 4.71/5.17 => ( ( F @ I )
% 4.71/5.17 = zero_zero_rat ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_0
% 4.71/5.17 thf(fact_8208_sum__nonneg__0,axiom,
% 4.71/5.17 ! [S: set_complex,F: complex > rat,I: complex] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ S )
% 4.71/5.17 => ( ! [I2: complex] :
% 4.71/5.17 ( ( member_complex @ I2 @ S )
% 4.71/5.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ( ( groups5058264527183730370ex_rat @ F @ S )
% 4.71/5.17 = zero_zero_rat )
% 4.71/5.17 => ( ( member_complex @ I @ S )
% 4.71/5.17 => ( ( F @ I )
% 4.71/5.17 = zero_zero_rat ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_0
% 4.71/5.17 thf(fact_8209_sum__nonneg__0,axiom,
% 4.71/5.17 ! [S: set_Extended_enat,F: extended_enat > rat,I: extended_enat] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ S )
% 4.71/5.17 => ( ! [I2: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ I2 @ S )
% 4.71/5.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ( ( groups1392844769737527556at_rat @ F @ S )
% 4.71/5.17 = zero_zero_rat )
% 4.71/5.17 => ( ( member_Extended_enat @ I @ S )
% 4.71/5.17 => ( ( F @ I )
% 4.71/5.17 = zero_zero_rat ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_0
% 4.71/5.17 thf(fact_8210_sum__nonneg__0,axiom,
% 4.71/5.17 ! [S: set_o,F: $o > nat,I: $o] :
% 4.71/5.17 ( ( finite_finite_o @ S )
% 4.71/5.17 => ( ! [I2: $o] :
% 4.71/5.17 ( ( member_o @ I2 @ S )
% 4.71/5.17 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ( ( groups8507830703676809646_o_nat @ F @ S )
% 4.71/5.17 = zero_zero_nat )
% 4.71/5.17 => ( ( member_o @ I @ S )
% 4.71/5.17 => ( ( F @ I )
% 4.71/5.17 = zero_zero_nat ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_0
% 4.71/5.17 thf(fact_8211_sum__nonneg__leq__bound,axiom,
% 4.71/5.17 ! [S: set_o,F: $o > real,B2: real,I: $o] :
% 4.71/5.17 ( ( finite_finite_o @ S )
% 4.71/5.17 => ( ! [I2: $o] :
% 4.71/5.17 ( ( member_o @ I2 @ S )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ( ( groups8691415230153176458o_real @ F @ S )
% 4.71/5.17 = B2 )
% 4.71/5.17 => ( ( member_o @ I @ S )
% 4.71/5.17 => ( ord_less_eq_real @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_leq_bound
% 4.71/5.17 thf(fact_8212_sum__nonneg__leq__bound,axiom,
% 4.71/5.17 ! [S: set_int,F: int > real,B2: real,I: int] :
% 4.71/5.17 ( ( finite_finite_int @ S )
% 4.71/5.17 => ( ! [I2: int] :
% 4.71/5.17 ( ( member_int @ I2 @ S )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ( ( groups8778361861064173332t_real @ F @ S )
% 4.71/5.17 = B2 )
% 4.71/5.17 => ( ( member_int @ I @ S )
% 4.71/5.17 => ( ord_less_eq_real @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_leq_bound
% 4.71/5.17 thf(fact_8213_sum__nonneg__leq__bound,axiom,
% 4.71/5.17 ! [S: set_complex,F: complex > real,B2: real,I: complex] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ S )
% 4.71/5.17 => ( ! [I2: complex] :
% 4.71/5.17 ( ( member_complex @ I2 @ S )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ( ( groups5808333547571424918x_real @ F @ S )
% 4.71/5.17 = B2 )
% 4.71/5.17 => ( ( member_complex @ I @ S )
% 4.71/5.17 => ( ord_less_eq_real @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_leq_bound
% 4.71/5.17 thf(fact_8214_sum__nonneg__leq__bound,axiom,
% 4.71/5.17 ! [S: set_Extended_enat,F: extended_enat > real,B2: real,I: extended_enat] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ S )
% 4.71/5.17 => ( ! [I2: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ I2 @ S )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ( ( groups4148127829035722712t_real @ F @ S )
% 4.71/5.17 = B2 )
% 4.71/5.17 => ( ( member_Extended_enat @ I @ S )
% 4.71/5.17 => ( ord_less_eq_real @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_leq_bound
% 4.71/5.17 thf(fact_8215_sum__nonneg__leq__bound,axiom,
% 4.71/5.17 ! [S: set_o,F: $o > rat,B2: rat,I: $o] :
% 4.71/5.17 ( ( finite_finite_o @ S )
% 4.71/5.17 => ( ! [I2: $o] :
% 4.71/5.17 ( ( member_o @ I2 @ S )
% 4.71/5.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ( ( groups7872700643590313910_o_rat @ F @ S )
% 4.71/5.17 = B2 )
% 4.71/5.17 => ( ( member_o @ I @ S )
% 4.71/5.17 => ( ord_less_eq_rat @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_leq_bound
% 4.71/5.17 thf(fact_8216_sum__nonneg__leq__bound,axiom,
% 4.71/5.17 ! [S: set_nat,F: nat > rat,B2: rat,I: nat] :
% 4.71/5.17 ( ( finite_finite_nat @ S )
% 4.71/5.17 => ( ! [I2: nat] :
% 4.71/5.17 ( ( member_nat @ I2 @ S )
% 4.71/5.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ( ( groups2906978787729119204at_rat @ F @ S )
% 4.71/5.17 = B2 )
% 4.71/5.17 => ( ( member_nat @ I @ S )
% 4.71/5.17 => ( ord_less_eq_rat @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_leq_bound
% 4.71/5.17 thf(fact_8217_sum__nonneg__leq__bound,axiom,
% 4.71/5.17 ! [S: set_int,F: int > rat,B2: rat,I: int] :
% 4.71/5.17 ( ( finite_finite_int @ S )
% 4.71/5.17 => ( ! [I2: int] :
% 4.71/5.17 ( ( member_int @ I2 @ S )
% 4.71/5.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ( ( groups3906332499630173760nt_rat @ F @ S )
% 4.71/5.17 = B2 )
% 4.71/5.17 => ( ( member_int @ I @ S )
% 4.71/5.17 => ( ord_less_eq_rat @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_leq_bound
% 4.71/5.17 thf(fact_8218_sum__nonneg__leq__bound,axiom,
% 4.71/5.17 ! [S: set_complex,F: complex > rat,B2: rat,I: complex] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ S )
% 4.71/5.17 => ( ! [I2: complex] :
% 4.71/5.17 ( ( member_complex @ I2 @ S )
% 4.71/5.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ( ( groups5058264527183730370ex_rat @ F @ S )
% 4.71/5.17 = B2 )
% 4.71/5.17 => ( ( member_complex @ I @ S )
% 4.71/5.17 => ( ord_less_eq_rat @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_leq_bound
% 4.71/5.17 thf(fact_8219_sum__nonneg__leq__bound,axiom,
% 4.71/5.17 ! [S: set_Extended_enat,F: extended_enat > rat,B2: rat,I: extended_enat] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ S )
% 4.71/5.17 => ( ! [I2: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ I2 @ S )
% 4.71/5.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ( ( groups1392844769737527556at_rat @ F @ S )
% 4.71/5.17 = B2 )
% 4.71/5.17 => ( ( member_Extended_enat @ I @ S )
% 4.71/5.17 => ( ord_less_eq_rat @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_leq_bound
% 4.71/5.17 thf(fact_8220_sum__nonneg__leq__bound,axiom,
% 4.71/5.17 ! [S: set_o,F: $o > nat,B2: nat,I: $o] :
% 4.71/5.17 ( ( finite_finite_o @ S )
% 4.71/5.17 => ( ! [I2: $o] :
% 4.71/5.17 ( ( member_o @ I2 @ S )
% 4.71/5.17 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ( ( groups8507830703676809646_o_nat @ F @ S )
% 4.71/5.17 = B2 )
% 4.71/5.17 => ( ( member_o @ I @ S )
% 4.71/5.17 => ( ord_less_eq_nat @ ( F @ I ) @ B2 ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_nonneg_leq_bound
% 4.71/5.17 thf(fact_8221_n__subsets,axiom,
% 4.71/5.17 ! [A2: set_nat_rat,K: nat] :
% 4.71/5.17 ( ( finite7830837933032798814at_rat @ A2 )
% 4.71/5.17 => ( ( finite8736671560171388117at_rat
% 4.71/5.17 @ ( collect_set_nat_rat
% 4.71/5.17 @ ^ [B6: set_nat_rat] :
% 4.71/5.17 ( ( ord_le2679597024174929757at_rat @ B6 @ A2 )
% 4.71/5.17 & ( ( finite_card_nat_rat @ B6 )
% 4.71/5.17 = K ) ) ) )
% 4.71/5.17 = ( binomial @ ( finite_card_nat_rat @ A2 ) @ K ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % n_subsets
% 4.71/5.17 thf(fact_8222_n__subsets,axiom,
% 4.71/5.17 ! [A2: set_list_nat,K: nat] :
% 4.71/5.17 ( ( finite8100373058378681591st_nat @ A2 )
% 4.71/5.17 => ( ( finite2364142230527598318st_nat
% 4.71/5.17 @ ( collect_set_list_nat
% 4.71/5.17 @ ^ [B6: set_list_nat] :
% 4.71/5.17 ( ( ord_le6045566169113846134st_nat @ B6 @ A2 )
% 4.71/5.17 & ( ( finite_card_list_nat @ B6 )
% 4.71/5.17 = K ) ) ) )
% 4.71/5.17 = ( binomial @ ( finite_card_list_nat @ A2 ) @ K ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % n_subsets
% 4.71/5.17 thf(fact_8223_n__subsets,axiom,
% 4.71/5.17 ! [A2: set_set_nat,K: nat] :
% 4.71/5.17 ( ( finite1152437895449049373et_nat @ A2 )
% 4.71/5.17 => ( ( finite1149291290879098388et_nat
% 4.71/5.17 @ ( collect_set_set_nat
% 4.71/5.17 @ ^ [B6: set_set_nat] :
% 4.71/5.17 ( ( ord_le6893508408891458716et_nat @ B6 @ A2 )
% 4.71/5.17 & ( ( finite_card_set_nat @ B6 )
% 4.71/5.17 = K ) ) ) )
% 4.71/5.17 = ( binomial @ ( finite_card_set_nat @ A2 ) @ K ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % n_subsets
% 4.71/5.17 thf(fact_8224_n__subsets,axiom,
% 4.71/5.17 ! [A2: set_nat,K: nat] :
% 4.71/5.17 ( ( finite_finite_nat @ A2 )
% 4.71/5.17 => ( ( finite_card_set_nat
% 4.71/5.17 @ ( collect_set_nat
% 4.71/5.17 @ ^ [B6: set_nat] :
% 4.71/5.17 ( ( ord_less_eq_set_nat @ B6 @ A2 )
% 4.71/5.17 & ( ( finite_card_nat @ B6 )
% 4.71/5.17 = K ) ) ) )
% 4.71/5.17 = ( binomial @ ( finite_card_nat @ A2 ) @ K ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % n_subsets
% 4.71/5.17 thf(fact_8225_n__subsets,axiom,
% 4.71/5.17 ! [A2: set_complex,K: nat] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.17 => ( ( finite903997441450111292omplex
% 4.71/5.17 @ ( collect_set_complex
% 4.71/5.17 @ ^ [B6: set_complex] :
% 4.71/5.17 ( ( ord_le211207098394363844omplex @ B6 @ A2 )
% 4.71/5.17 & ( ( finite_card_complex @ B6 )
% 4.71/5.17 = K ) ) ) )
% 4.71/5.17 = ( binomial @ ( finite_card_complex @ A2 ) @ K ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % n_subsets
% 4.71/5.17 thf(fact_8226_n__subsets,axiom,
% 4.71/5.17 ! [A2: set_Pr1261947904930325089at_nat,K: nat] :
% 4.71/5.17 ( ( finite6177210948735845034at_nat @ A2 )
% 4.71/5.17 => ( ( finite4356350796350151305at_nat
% 4.71/5.17 @ ( collec5514110066124741708at_nat
% 4.71/5.17 @ ^ [B6: set_Pr1261947904930325089at_nat] :
% 4.71/5.17 ( ( ord_le3146513528884898305at_nat @ B6 @ A2 )
% 4.71/5.17 & ( ( finite711546835091564841at_nat @ B6 )
% 4.71/5.17 = K ) ) ) )
% 4.71/5.17 = ( binomial @ ( finite711546835091564841at_nat @ A2 ) @ K ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % n_subsets
% 4.71/5.17 thf(fact_8227_n__subsets,axiom,
% 4.71/5.17 ! [A2: set_Extended_enat,K: nat] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.17 => ( ( finite3719263829065406702d_enat
% 4.71/5.17 @ ( collec2260605976452661553d_enat
% 4.71/5.17 @ ^ [B6: set_Extended_enat] :
% 4.71/5.17 ( ( ord_le7203529160286727270d_enat @ B6 @ A2 )
% 4.71/5.17 & ( ( finite121521170596916366d_enat @ B6 )
% 4.71/5.17 = K ) ) ) )
% 4.71/5.17 = ( binomial @ ( finite121521170596916366d_enat @ A2 ) @ K ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % n_subsets
% 4.71/5.17 thf(fact_8228_n__subsets,axiom,
% 4.71/5.17 ! [A2: set_int,K: nat] :
% 4.71/5.17 ( ( finite_finite_int @ A2 )
% 4.71/5.17 => ( ( finite_card_set_int
% 4.71/5.17 @ ( collect_set_int
% 4.71/5.17 @ ^ [B6: set_int] :
% 4.71/5.17 ( ( ord_less_eq_set_int @ B6 @ A2 )
% 4.71/5.17 & ( ( finite_card_int @ B6 )
% 4.71/5.17 = K ) ) ) )
% 4.71/5.17 = ( binomial @ ( finite_card_int @ A2 ) @ K ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % n_subsets
% 4.71/5.17 thf(fact_8229_sum_Osetdiff__irrelevant,axiom,
% 4.71/5.17 ! [A2: set_int,G2: int > real] :
% 4.71/5.17 ( ( finite_finite_int @ A2 )
% 4.71/5.17 => ( ( groups8778361861064173332t_real @ G2
% 4.71/5.17 @ ( minus_minus_set_int @ A2
% 4.71/5.17 @ ( collect_int
% 4.71/5.17 @ ^ [X3: int] :
% 4.71/5.17 ( ( G2 @ X3 )
% 4.71/5.17 = zero_zero_real ) ) ) )
% 4.71/5.17 = ( groups8778361861064173332t_real @ G2 @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.setdiff_irrelevant
% 4.71/5.17 thf(fact_8230_sum_Osetdiff__irrelevant,axiom,
% 4.71/5.17 ! [A2: set_complex,G2: complex > real] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.17 => ( ( groups5808333547571424918x_real @ G2
% 4.71/5.17 @ ( minus_811609699411566653omplex @ A2
% 4.71/5.17 @ ( collect_complex
% 4.71/5.17 @ ^ [X3: complex] :
% 4.71/5.17 ( ( G2 @ X3 )
% 4.71/5.17 = zero_zero_real ) ) ) )
% 4.71/5.17 = ( groups5808333547571424918x_real @ G2 @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.setdiff_irrelevant
% 4.71/5.17 thf(fact_8231_sum_Osetdiff__irrelevant,axiom,
% 4.71/5.17 ! [A2: set_Extended_enat,G2: extended_enat > real] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.17 => ( ( groups4148127829035722712t_real @ G2
% 4.71/5.17 @ ( minus_925952699566721837d_enat @ A2
% 4.71/5.17 @ ( collec4429806609662206161d_enat
% 4.71/5.17 @ ^ [X3: extended_enat] :
% 4.71/5.17 ( ( G2 @ X3 )
% 4.71/5.17 = zero_zero_real ) ) ) )
% 4.71/5.17 = ( groups4148127829035722712t_real @ G2 @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.setdiff_irrelevant
% 4.71/5.17 thf(fact_8232_sum_Osetdiff__irrelevant,axiom,
% 4.71/5.17 ! [A2: set_int,G2: int > rat] :
% 4.71/5.17 ( ( finite_finite_int @ A2 )
% 4.71/5.17 => ( ( groups3906332499630173760nt_rat @ G2
% 4.71/5.17 @ ( minus_minus_set_int @ A2
% 4.71/5.17 @ ( collect_int
% 4.71/5.17 @ ^ [X3: int] :
% 4.71/5.17 ( ( G2 @ X3 )
% 4.71/5.17 = zero_zero_rat ) ) ) )
% 4.71/5.17 = ( groups3906332499630173760nt_rat @ G2 @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.setdiff_irrelevant
% 4.71/5.17 thf(fact_8233_sum_Osetdiff__irrelevant,axiom,
% 4.71/5.17 ! [A2: set_complex,G2: complex > rat] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.17 => ( ( groups5058264527183730370ex_rat @ G2
% 4.71/5.17 @ ( minus_811609699411566653omplex @ A2
% 4.71/5.17 @ ( collect_complex
% 4.71/5.17 @ ^ [X3: complex] :
% 4.71/5.17 ( ( G2 @ X3 )
% 4.71/5.17 = zero_zero_rat ) ) ) )
% 4.71/5.17 = ( groups5058264527183730370ex_rat @ G2 @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.setdiff_irrelevant
% 4.71/5.17 thf(fact_8234_sum_Osetdiff__irrelevant,axiom,
% 4.71/5.17 ! [A2: set_Extended_enat,G2: extended_enat > rat] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.17 => ( ( groups1392844769737527556at_rat @ G2
% 4.71/5.17 @ ( minus_925952699566721837d_enat @ A2
% 4.71/5.17 @ ( collec4429806609662206161d_enat
% 4.71/5.17 @ ^ [X3: extended_enat] :
% 4.71/5.17 ( ( G2 @ X3 )
% 4.71/5.17 = zero_zero_rat ) ) ) )
% 4.71/5.17 = ( groups1392844769737527556at_rat @ G2 @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.setdiff_irrelevant
% 4.71/5.17 thf(fact_8235_sum_Osetdiff__irrelevant,axiom,
% 4.71/5.17 ! [A2: set_int,G2: int > nat] :
% 4.71/5.17 ( ( finite_finite_int @ A2 )
% 4.71/5.17 => ( ( groups4541462559716669496nt_nat @ G2
% 4.71/5.17 @ ( minus_minus_set_int @ A2
% 4.71/5.17 @ ( collect_int
% 4.71/5.17 @ ^ [X3: int] :
% 4.71/5.17 ( ( G2 @ X3 )
% 4.71/5.17 = zero_zero_nat ) ) ) )
% 4.71/5.17 = ( groups4541462559716669496nt_nat @ G2 @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.setdiff_irrelevant
% 4.71/5.17 thf(fact_8236_sum_Osetdiff__irrelevant,axiom,
% 4.71/5.17 ! [A2: set_complex,G2: complex > nat] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.17 => ( ( groups5693394587270226106ex_nat @ G2
% 4.71/5.17 @ ( minus_811609699411566653omplex @ A2
% 4.71/5.17 @ ( collect_complex
% 4.71/5.17 @ ^ [X3: complex] :
% 4.71/5.17 ( ( G2 @ X3 )
% 4.71/5.17 = zero_zero_nat ) ) ) )
% 4.71/5.17 = ( groups5693394587270226106ex_nat @ G2 @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.setdiff_irrelevant
% 4.71/5.17 thf(fact_8237_sum_Osetdiff__irrelevant,axiom,
% 4.71/5.17 ! [A2: set_Extended_enat,G2: extended_enat > nat] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ A2 )
% 4.71/5.17 => ( ( groups2027974829824023292at_nat @ G2
% 4.71/5.17 @ ( minus_925952699566721837d_enat @ A2
% 4.71/5.17 @ ( collec4429806609662206161d_enat
% 4.71/5.17 @ ^ [X3: extended_enat] :
% 4.71/5.17 ( ( G2 @ X3 )
% 4.71/5.17 = zero_zero_nat ) ) ) )
% 4.71/5.17 = ( groups2027974829824023292at_nat @ G2 @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.setdiff_irrelevant
% 4.71/5.17 thf(fact_8238_sum_Osetdiff__irrelevant,axiom,
% 4.71/5.17 ! [A2: set_complex,G2: complex > int] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ A2 )
% 4.71/5.17 => ( ( groups5690904116761175830ex_int @ G2
% 4.71/5.17 @ ( minus_811609699411566653omplex @ A2
% 4.71/5.17 @ ( collect_complex
% 4.71/5.17 @ ^ [X3: complex] :
% 4.71/5.17 ( ( G2 @ X3 )
% 4.71/5.17 = zero_zero_int ) ) ) )
% 4.71/5.17 = ( groups5690904116761175830ex_int @ G2 @ A2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.setdiff_irrelevant
% 4.71/5.17 thf(fact_8239_sum__power__add,axiom,
% 4.71/5.17 ! [X: complex,M2: nat,I5: set_nat] :
% 4.71/5.17 ( ( groups2073611262835488442omplex
% 4.71/5.17 @ ^ [I4: nat] : ( power_power_complex @ X @ ( plus_plus_nat @ M2 @ I4 ) )
% 4.71/5.17 @ I5 )
% 4.71/5.17 = ( times_times_complex @ ( power_power_complex @ X @ M2 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ I5 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_power_add
% 4.71/5.17 thf(fact_8240_sum__power__add,axiom,
% 4.71/5.17 ! [X: rat,M2: nat,I5: set_nat] :
% 4.71/5.17 ( ( groups2906978787729119204at_rat
% 4.71/5.17 @ ^ [I4: nat] : ( power_power_rat @ X @ ( plus_plus_nat @ M2 @ I4 ) )
% 4.71/5.17 @ I5 )
% 4.71/5.17 = ( times_times_rat @ ( power_power_rat @ X @ M2 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ I5 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_power_add
% 4.71/5.17 thf(fact_8241_sum__power__add,axiom,
% 4.71/5.17 ! [X: int,M2: nat,I5: set_nat] :
% 4.71/5.17 ( ( groups3539618377306564664at_int
% 4.71/5.17 @ ^ [I4: nat] : ( power_power_int @ X @ ( plus_plus_nat @ M2 @ I4 ) )
% 4.71/5.17 @ I5 )
% 4.71/5.17 = ( times_times_int @ ( power_power_int @ X @ M2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ I5 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_power_add
% 4.71/5.17 thf(fact_8242_sum__power__add,axiom,
% 4.71/5.17 ! [X: real,M2: nat,I5: set_nat] :
% 4.71/5.17 ( ( groups6591440286371151544t_real
% 4.71/5.17 @ ^ [I4: nat] : ( power_power_real @ X @ ( plus_plus_nat @ M2 @ I4 ) )
% 4.71/5.17 @ I5 )
% 4.71/5.17 = ( times_times_real @ ( power_power_real @ X @ M2 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ I5 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_power_add
% 4.71/5.17 thf(fact_8243_exp__sum,axiom,
% 4.71/5.17 ! [I5: set_int,F: int > real] :
% 4.71/5.17 ( ( finite_finite_int @ I5 )
% 4.71/5.17 => ( ( exp_real @ ( groups8778361861064173332t_real @ F @ I5 ) )
% 4.71/5.17 = ( groups2316167850115554303t_real
% 4.71/5.17 @ ^ [X3: int] : ( exp_real @ ( F @ X3 ) )
% 4.71/5.17 @ I5 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % exp_sum
% 4.71/5.17 thf(fact_8244_exp__sum,axiom,
% 4.71/5.17 ! [I5: set_complex,F: complex > real] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ I5 )
% 4.71/5.17 => ( ( exp_real @ ( groups5808333547571424918x_real @ F @ I5 ) )
% 4.71/5.17 = ( groups766887009212190081x_real
% 4.71/5.17 @ ^ [X3: complex] : ( exp_real @ ( F @ X3 ) )
% 4.71/5.17 @ I5 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % exp_sum
% 4.71/5.17 thf(fact_8245_exp__sum,axiom,
% 4.71/5.17 ! [I5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > real] :
% 4.71/5.17 ( ( finite6177210948735845034at_nat @ I5 )
% 4.71/5.17 => ( ( exp_real @ ( groups4567486121110086003t_real @ F @ I5 ) )
% 4.71/5.17 = ( groups6036352826371341000t_real
% 4.71/5.17 @ ^ [X3: product_prod_nat_nat] : ( exp_real @ ( F @ X3 ) )
% 4.71/5.17 @ I5 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % exp_sum
% 4.71/5.17 thf(fact_8246_exp__sum,axiom,
% 4.71/5.17 ! [I5: set_Extended_enat,F: extended_enat > real] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ I5 )
% 4.71/5.17 => ( ( exp_real @ ( groups4148127829035722712t_real @ F @ I5 ) )
% 4.71/5.17 = ( groups97031904164794029t_real
% 4.71/5.17 @ ^ [X3: extended_enat] : ( exp_real @ ( F @ X3 ) )
% 4.71/5.17 @ I5 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % exp_sum
% 4.71/5.17 thf(fact_8247_exp__sum,axiom,
% 4.71/5.17 ! [I5: set_complex,F: complex > complex] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ I5 )
% 4.71/5.17 => ( ( exp_complex @ ( groups7754918857620584856omplex @ F @ I5 ) )
% 4.71/5.17 = ( groups3708469109370488835omplex
% 4.71/5.17 @ ^ [X3: complex] : ( exp_complex @ ( F @ X3 ) )
% 4.71/5.17 @ I5 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % exp_sum
% 4.71/5.17 thf(fact_8248_exp__sum,axiom,
% 4.71/5.17 ! [I5: set_nat,F: nat > real] :
% 4.71/5.17 ( ( finite_finite_nat @ I5 )
% 4.71/5.17 => ( ( exp_real @ ( groups6591440286371151544t_real @ F @ I5 ) )
% 4.71/5.17 = ( groups129246275422532515t_real
% 4.71/5.17 @ ^ [X3: nat] : ( exp_real @ ( F @ X3 ) )
% 4.71/5.17 @ I5 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % exp_sum
% 4.71/5.17 thf(fact_8249_sum_OatLeastAtMost__rev,axiom,
% 4.71/5.17 ! [G2: nat > nat,N: nat,M2: nat] :
% 4.71/5.17 ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ N @ M2 ) )
% 4.71/5.17 = ( groups3542108847815614940at_nat
% 4.71/5.17 @ ^ [I4: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N ) @ I4 ) )
% 4.71/5.17 @ ( set_or1269000886237332187st_nat @ N @ M2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.atLeastAtMost_rev
% 4.71/5.17 thf(fact_8250_sum_OatLeastAtMost__rev,axiom,
% 4.71/5.17 ! [G2: nat > real,N: nat,M2: nat] :
% 4.71/5.17 ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ N @ M2 ) )
% 4.71/5.17 = ( groups6591440286371151544t_real
% 4.71/5.17 @ ^ [I4: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N ) @ I4 ) )
% 4.71/5.17 @ ( set_or1269000886237332187st_nat @ N @ M2 ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum.atLeastAtMost_rev
% 4.71/5.17 thf(fact_8251_suminf__finite,axiom,
% 4.71/5.17 ! [N5: set_nat,F: nat > int] :
% 4.71/5.17 ( ( finite_finite_nat @ N5 )
% 4.71/5.17 => ( ! [N2: nat] :
% 4.71/5.17 ( ~ ( member_nat @ N2 @ N5 )
% 4.71/5.17 => ( ( F @ N2 )
% 4.71/5.17 = zero_zero_int ) )
% 4.71/5.17 => ( ( suminf_int @ F )
% 4.71/5.17 = ( groups3539618377306564664at_int @ F @ N5 ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % suminf_finite
% 4.71/5.17 thf(fact_8252_suminf__finite,axiom,
% 4.71/5.17 ! [N5: set_nat,F: nat > nat] :
% 4.71/5.17 ( ( finite_finite_nat @ N5 )
% 4.71/5.17 => ( ! [N2: nat] :
% 4.71/5.17 ( ~ ( member_nat @ N2 @ N5 )
% 4.71/5.17 => ( ( F @ N2 )
% 4.71/5.17 = zero_zero_nat ) )
% 4.71/5.17 => ( ( suminf_nat @ F )
% 4.71/5.17 = ( groups3542108847815614940at_nat @ F @ N5 ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % suminf_finite
% 4.71/5.17 thf(fact_8253_suminf__finite,axiom,
% 4.71/5.17 ! [N5: set_nat,F: nat > real] :
% 4.71/5.17 ( ( finite_finite_nat @ N5 )
% 4.71/5.17 => ( ! [N2: nat] :
% 4.71/5.17 ( ~ ( member_nat @ N2 @ N5 )
% 4.71/5.17 => ( ( F @ N2 )
% 4.71/5.17 = zero_zero_real ) )
% 4.71/5.17 => ( ( suminf_real @ F )
% 4.71/5.17 = ( groups6591440286371151544t_real @ F @ N5 ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % suminf_finite
% 4.71/5.17 thf(fact_8254_sum__pos2,axiom,
% 4.71/5.17 ! [I5: set_o,I: $o,F: $o > real] :
% 4.71/5.17 ( ( finite_finite_o @ I5 )
% 4.71/5.17 => ( ( member_o @ I @ I5 )
% 4.71/5.17 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 4.71/5.17 => ( ! [I2: $o] :
% 4.71/5.17 ( ( member_o @ I2 @ I5 )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ord_less_real @ zero_zero_real @ ( groups8691415230153176458o_real @ F @ I5 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_pos2
% 4.71/5.17 thf(fact_8255_sum__pos2,axiom,
% 4.71/5.17 ! [I5: set_int,I: int,F: int > real] :
% 4.71/5.17 ( ( finite_finite_int @ I5 )
% 4.71/5.17 => ( ( member_int @ I @ I5 )
% 4.71/5.17 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 4.71/5.17 => ( ! [I2: int] :
% 4.71/5.17 ( ( member_int @ I2 @ I5 )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I5 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_pos2
% 4.71/5.17 thf(fact_8256_sum__pos2,axiom,
% 4.71/5.17 ! [I5: set_complex,I: complex,F: complex > real] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ I5 )
% 4.71/5.17 => ( ( member_complex @ I @ I5 )
% 4.71/5.17 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 4.71/5.17 => ( ! [I2: complex] :
% 4.71/5.17 ( ( member_complex @ I2 @ I5 )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I5 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_pos2
% 4.71/5.17 thf(fact_8257_sum__pos2,axiom,
% 4.71/5.17 ! [I5: set_Extended_enat,I: extended_enat,F: extended_enat > real] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ I5 )
% 4.71/5.17 => ( ( member_Extended_enat @ I @ I5 )
% 4.71/5.17 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 4.71/5.17 => ( ! [I2: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ I2 @ I5 )
% 4.71/5.17 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ord_less_real @ zero_zero_real @ ( groups4148127829035722712t_real @ F @ I5 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_pos2
% 4.71/5.17 thf(fact_8258_sum__pos2,axiom,
% 4.71/5.17 ! [I5: set_o,I: $o,F: $o > rat] :
% 4.71/5.17 ( ( finite_finite_o @ I5 )
% 4.71/5.17 => ( ( member_o @ I @ I5 )
% 4.71/5.17 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 4.71/5.17 => ( ! [I2: $o] :
% 4.71/5.17 ( ( member_o @ I2 @ I5 )
% 4.71/5.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ord_less_rat @ zero_zero_rat @ ( groups7872700643590313910_o_rat @ F @ I5 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_pos2
% 4.71/5.17 thf(fact_8259_sum__pos2,axiom,
% 4.71/5.17 ! [I5: set_nat,I: nat,F: nat > rat] :
% 4.71/5.17 ( ( finite_finite_nat @ I5 )
% 4.71/5.17 => ( ( member_nat @ I @ I5 )
% 4.71/5.17 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 4.71/5.17 => ( ! [I2: nat] :
% 4.71/5.17 ( ( member_nat @ I2 @ I5 )
% 4.71/5.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I5 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_pos2
% 4.71/5.17 thf(fact_8260_sum__pos2,axiom,
% 4.71/5.17 ! [I5: set_int,I: int,F: int > rat] :
% 4.71/5.17 ( ( finite_finite_int @ I5 )
% 4.71/5.17 => ( ( member_int @ I @ I5 )
% 4.71/5.17 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 4.71/5.17 => ( ! [I2: int] :
% 4.71/5.17 ( ( member_int @ I2 @ I5 )
% 4.71/5.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I5 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_pos2
% 4.71/5.17 thf(fact_8261_sum__pos2,axiom,
% 4.71/5.17 ! [I5: set_complex,I: complex,F: complex > rat] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ I5 )
% 4.71/5.17 => ( ( member_complex @ I @ I5 )
% 4.71/5.17 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 4.71/5.17 => ( ! [I2: complex] :
% 4.71/5.17 ( ( member_complex @ I2 @ I5 )
% 4.71/5.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I5 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_pos2
% 4.71/5.17 thf(fact_8262_sum__pos2,axiom,
% 4.71/5.17 ! [I5: set_Extended_enat,I: extended_enat,F: extended_enat > rat] :
% 4.71/5.17 ( ( finite4001608067531595151d_enat @ I5 )
% 4.71/5.17 => ( ( member_Extended_enat @ I @ I5 )
% 4.71/5.17 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 4.71/5.17 => ( ! [I2: extended_enat] :
% 4.71/5.17 ( ( member_Extended_enat @ I2 @ I5 )
% 4.71/5.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ord_less_rat @ zero_zero_rat @ ( groups1392844769737527556at_rat @ F @ I5 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_pos2
% 4.71/5.17 thf(fact_8263_sum__pos2,axiom,
% 4.71/5.17 ! [I5: set_o,I: $o,F: $o > nat] :
% 4.71/5.17 ( ( finite_finite_o @ I5 )
% 4.71/5.17 => ( ( member_o @ I @ I5 )
% 4.71/5.17 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 4.71/5.17 => ( ! [I2: $o] :
% 4.71/5.17 ( ( member_o @ I2 @ I5 )
% 4.71/5.17 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ord_less_nat @ zero_zero_nat @ ( groups8507830703676809646_o_nat @ F @ I5 ) ) ) ) ) ) ).
% 4.71/5.17
% 4.71/5.17 % sum_pos2
% 4.71/5.17 thf(fact_8264_sum__pos,axiom,
% 4.71/5.17 ! [I5: set_complex,F: complex > real] :
% 4.71/5.17 ( ( finite3207457112153483333omplex @ I5 )
% 4.71/5.17 => ( ( I5 != bot_bot_set_complex )
% 4.71/5.17 => ( ! [I2: complex] :
% 4.71/5.17 ( ( member_complex @ I2 @ I5 )
% 4.71/5.17 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 4.71/5.17 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I5 ) ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % sum_pos
% 4.88/5.17 thf(fact_8265_sum__pos,axiom,
% 4.88/5.17 ! [I5: set_Extended_enat,F: extended_enat > real] :
% 4.88/5.17 ( ( finite4001608067531595151d_enat @ I5 )
% 4.88/5.17 => ( ( I5 != bot_bo7653980558646680370d_enat )
% 4.88/5.17 => ( ! [I2: extended_enat] :
% 4.88/5.17 ( ( member_Extended_enat @ I2 @ I5 )
% 4.88/5.17 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 4.88/5.17 => ( ord_less_real @ zero_zero_real @ ( groups4148127829035722712t_real @ F @ I5 ) ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % sum_pos
% 4.88/5.17 thf(fact_8266_sum__pos,axiom,
% 4.88/5.17 ! [I5: set_real,F: real > real] :
% 4.88/5.17 ( ( finite_finite_real @ I5 )
% 4.88/5.17 => ( ( I5 != bot_bot_set_real )
% 4.88/5.17 => ( ! [I2: real] :
% 4.88/5.17 ( ( member_real @ I2 @ I5 )
% 4.88/5.17 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 4.88/5.17 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I5 ) ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % sum_pos
% 4.88/5.17 thf(fact_8267_sum__pos,axiom,
% 4.88/5.17 ! [I5: set_o,F: $o > real] :
% 4.88/5.17 ( ( finite_finite_o @ I5 )
% 4.88/5.17 => ( ( I5 != bot_bot_set_o )
% 4.88/5.17 => ( ! [I2: $o] :
% 4.88/5.17 ( ( member_o @ I2 @ I5 )
% 4.88/5.17 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 4.88/5.17 => ( ord_less_real @ zero_zero_real @ ( groups8691415230153176458o_real @ F @ I5 ) ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % sum_pos
% 4.88/5.17 thf(fact_8268_sum__pos,axiom,
% 4.88/5.17 ! [I5: set_int,F: int > real] :
% 4.88/5.17 ( ( finite_finite_int @ I5 )
% 4.88/5.17 => ( ( I5 != bot_bot_set_int )
% 4.88/5.17 => ( ! [I2: int] :
% 4.88/5.17 ( ( member_int @ I2 @ I5 )
% 4.88/5.17 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 4.88/5.17 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I5 ) ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % sum_pos
% 4.88/5.17 thf(fact_8269_sum__pos,axiom,
% 4.88/5.17 ! [I5: set_complex,F: complex > rat] :
% 4.88/5.17 ( ( finite3207457112153483333omplex @ I5 )
% 4.88/5.17 => ( ( I5 != bot_bot_set_complex )
% 4.88/5.17 => ( ! [I2: complex] :
% 4.88/5.17 ( ( member_complex @ I2 @ I5 )
% 4.88/5.17 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 4.88/5.17 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I5 ) ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % sum_pos
% 4.88/5.17 thf(fact_8270_sum__pos,axiom,
% 4.88/5.17 ! [I5: set_Extended_enat,F: extended_enat > rat] :
% 4.88/5.17 ( ( finite4001608067531595151d_enat @ I5 )
% 4.88/5.17 => ( ( I5 != bot_bo7653980558646680370d_enat )
% 4.88/5.17 => ( ! [I2: extended_enat] :
% 4.88/5.17 ( ( member_Extended_enat @ I2 @ I5 )
% 4.88/5.17 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 4.88/5.17 => ( ord_less_rat @ zero_zero_rat @ ( groups1392844769737527556at_rat @ F @ I5 ) ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % sum_pos
% 4.88/5.17 thf(fact_8271_sum__pos,axiom,
% 4.88/5.17 ! [I5: set_real,F: real > rat] :
% 4.88/5.17 ( ( finite_finite_real @ I5 )
% 4.88/5.17 => ( ( I5 != bot_bot_set_real )
% 4.88/5.17 => ( ! [I2: real] :
% 4.88/5.17 ( ( member_real @ I2 @ I5 )
% 4.88/5.17 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 4.88/5.17 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I5 ) ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % sum_pos
% 4.88/5.17 thf(fact_8272_sum__pos,axiom,
% 4.88/5.17 ! [I5: set_o,F: $o > rat] :
% 4.88/5.17 ( ( finite_finite_o @ I5 )
% 4.88/5.17 => ( ( I5 != bot_bot_set_o )
% 4.88/5.17 => ( ! [I2: $o] :
% 4.88/5.17 ( ( member_o @ I2 @ I5 )
% 4.88/5.17 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 4.88/5.17 => ( ord_less_rat @ zero_zero_rat @ ( groups7872700643590313910_o_rat @ F @ I5 ) ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % sum_pos
% 4.88/5.17 thf(fact_8273_sum__pos,axiom,
% 4.88/5.17 ! [I5: set_nat,F: nat > rat] :
% 4.88/5.17 ( ( finite_finite_nat @ I5 )
% 4.88/5.17 => ( ( I5 != bot_bot_set_nat )
% 4.88/5.17 => ( ! [I2: nat] :
% 4.88/5.17 ( ( member_nat @ I2 @ I5 )
% 4.88/5.17 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 4.88/5.17 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I5 ) ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % sum_pos
% 4.88/5.17 thf(fact_8274_norm__less__p1,axiom,
% 4.88/5.17 ! [X: real] : ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ ( real_V7735802525324610683m_real @ X ) ) @ one_one_real ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % norm_less_p1
% 4.88/5.17 thf(fact_8275_norm__less__p1,axiom,
% 4.88/5.17 ! [X: complex] : ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( real_V1022390504157884413omplex @ X ) ) @ one_one_complex ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % norm_less_p1
% 4.88/5.17 thf(fact_8276_sum__bounded__above,axiom,
% 4.88/5.17 ! [A2: set_o,F: $o > rat,K4: rat] :
% 4.88/5.17 ( ! [I2: $o] :
% 4.88/5.17 ( ( member_o @ I2 @ A2 )
% 4.88/5.17 => ( ord_less_eq_rat @ ( F @ I2 ) @ K4 ) )
% 4.88/5.17 => ( ord_less_eq_rat @ ( groups7872700643590313910_o_rat @ F @ A2 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_o @ A2 ) ) @ K4 ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % sum_bounded_above
% 4.88/5.17 thf(fact_8277_sum__bounded__above,axiom,
% 4.88/5.17 ! [A2: set_complex,F: complex > rat,K4: rat] :
% 4.88/5.17 ( ! [I2: complex] :
% 4.88/5.17 ( ( member_complex @ I2 @ A2 )
% 4.88/5.17 => ( ord_less_eq_rat @ ( F @ I2 ) @ K4 ) )
% 4.88/5.17 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_complex @ A2 ) ) @ K4 ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % sum_bounded_above
% 4.88/5.17 thf(fact_8278_sum__bounded__above,axiom,
% 4.88/5.17 ! [A2: set_nat,F: nat > rat,K4: rat] :
% 4.88/5.17 ( ! [I2: nat] :
% 4.88/5.17 ( ( member_nat @ I2 @ A2 )
% 4.88/5.17 => ( ord_less_eq_rat @ ( F @ I2 ) @ K4 ) )
% 4.88/5.17 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A2 ) ) @ K4 ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % sum_bounded_above
% 4.88/5.17 thf(fact_8279_sum__bounded__above,axiom,
% 4.88/5.17 ! [A2: set_int,F: int > rat,K4: rat] :
% 4.88/5.17 ( ! [I2: int] :
% 4.88/5.17 ( ( member_int @ I2 @ A2 )
% 4.88/5.17 => ( ord_less_eq_rat @ ( F @ I2 ) @ K4 ) )
% 4.88/5.17 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_int @ A2 ) ) @ K4 ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % sum_bounded_above
% 4.88/5.17 thf(fact_8280_sum__bounded__above,axiom,
% 4.88/5.17 ! [A2: set_o,F: $o > nat,K4: nat] :
% 4.88/5.17 ( ! [I2: $o] :
% 4.88/5.17 ( ( member_o @ I2 @ A2 )
% 4.88/5.17 => ( ord_less_eq_nat @ ( F @ I2 ) @ K4 ) )
% 4.88/5.17 => ( ord_less_eq_nat @ ( groups8507830703676809646_o_nat @ F @ A2 ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_o @ A2 ) ) @ K4 ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % sum_bounded_above
% 4.88/5.17 thf(fact_8281_sum__bounded__above,axiom,
% 4.88/5.17 ! [A2: set_complex,F: complex > nat,K4: nat] :
% 4.88/5.17 ( ! [I2: complex] :
% 4.88/5.17 ( ( member_complex @ I2 @ A2 )
% 4.88/5.17 => ( ord_less_eq_nat @ ( F @ I2 ) @ K4 ) )
% 4.88/5.17 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_complex @ A2 ) ) @ K4 ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % sum_bounded_above
% 4.88/5.17 thf(fact_8282_sum__bounded__above,axiom,
% 4.88/5.17 ! [A2: set_int,F: int > nat,K4: nat] :
% 4.88/5.17 ( ! [I2: int] :
% 4.88/5.17 ( ( member_int @ I2 @ A2 )
% 4.88/5.17 => ( ord_less_eq_nat @ ( F @ I2 ) @ K4 ) )
% 4.88/5.17 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_int @ A2 ) ) @ K4 ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % sum_bounded_above
% 4.88/5.17 thf(fact_8283_sum__bounded__above,axiom,
% 4.88/5.17 ! [A2: set_o,F: $o > int,K4: int] :
% 4.88/5.17 ( ! [I2: $o] :
% 4.88/5.17 ( ( member_o @ I2 @ A2 )
% 4.88/5.17 => ( ord_less_eq_int @ ( F @ I2 ) @ K4 ) )
% 4.88/5.17 => ( ord_less_eq_int @ ( groups8505340233167759370_o_int @ F @ A2 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_o @ A2 ) ) @ K4 ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % sum_bounded_above
% 4.88/5.17 thf(fact_8284_sum__bounded__above,axiom,
% 4.88/5.17 ! [A2: set_complex,F: complex > int,K4: int] :
% 4.88/5.17 ( ! [I2: complex] :
% 4.88/5.17 ( ( member_complex @ I2 @ A2 )
% 4.88/5.17 => ( ord_less_eq_int @ ( F @ I2 ) @ K4 ) )
% 4.88/5.17 => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_complex @ A2 ) ) @ K4 ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % sum_bounded_above
% 4.88/5.17 thf(fact_8285_sum__bounded__above,axiom,
% 4.88/5.17 ! [A2: set_nat,F: nat > int,K4: int] :
% 4.88/5.17 ( ! [I2: nat] :
% 4.88/5.17 ( ( member_nat @ I2 @ A2 )
% 4.88/5.17 => ( ord_less_eq_int @ ( F @ I2 ) @ K4 ) )
% 4.88/5.17 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_nat @ A2 ) ) @ K4 ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % sum_bounded_above
% 4.88/5.17 thf(fact_8286_binomial__absorption,axiom,
% 4.88/5.17 ! [K: nat,N: nat] :
% 4.88/5.17 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N @ ( suc @ K ) ) )
% 4.88/5.17 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % binomial_absorption
% 4.88/5.17 thf(fact_8287_binomial__fact__lemma,axiom,
% 4.88/5.17 ! [K: nat,N: nat] :
% 4.88/5.17 ( ( ord_less_eq_nat @ K @ N )
% 4.88/5.17 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( binomial @ N @ K ) )
% 4.88/5.17 = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % binomial_fact_lemma
% 4.88/5.17 thf(fact_8288_binomial__mono,axiom,
% 4.88/5.17 ! [K: nat,K7: nat,N: nat] :
% 4.88/5.17 ( ( ord_less_eq_nat @ K @ K7 )
% 4.88/5.17 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K7 ) @ N )
% 4.88/5.17 => ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K7 ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % binomial_mono
% 4.88/5.17 thf(fact_8289_binomial__maximum_H,axiom,
% 4.88/5.17 ! [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 ) ) ).
% 4.88/5.17
% 4.88/5.17 % binomial_maximum'
% 4.88/5.17 thf(fact_8290_binomial__maximum,axiom,
% 4.88/5.17 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % binomial_maximum
% 4.88/5.17 thf(fact_8291_binomial__antimono,axiom,
% 4.88/5.17 ! [K: nat,K7: nat,N: nat] :
% 4.88/5.17 ( ( ord_less_eq_nat @ K @ K7 )
% 4.88/5.17 => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 4.88/5.17 => ( ( ord_less_eq_nat @ K7 @ N )
% 4.88/5.17 => ( ord_less_eq_nat @ ( binomial @ N @ K7 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % binomial_antimono
% 4.88/5.17 thf(fact_8292_binomial__le__pow2,axiom,
% 4.88/5.17 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 4.88/5.17
% 4.88/5.17 % binomial_le_pow2
% 4.88/5.17 thf(fact_8293_choose__reduce__nat,axiom,
% 4.88/5.17 ! [N: nat,K: nat] :
% 4.88/5.17 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.17 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.88/5.17 => ( ( binomial @ N @ K )
% 4.88/5.17 = ( 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 ) ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % choose_reduce_nat
% 4.88/5.17 thf(fact_8294_times__binomial__minus1__eq,axiom,
% 4.88/5.17 ! [K: nat,N: nat] :
% 4.88/5.17 ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.88/5.17 => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 4.88/5.17 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % times_binomial_minus1_eq
% 4.88/5.17 thf(fact_8295_binomial__altdef__nat,axiom,
% 4.88/5.17 ! [K: nat,N: nat] :
% 4.88/5.17 ( ( ord_less_eq_nat @ K @ N )
% 4.88/5.17 => ( ( binomial @ N @ K )
% 4.88/5.17 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % binomial_altdef_nat
% 4.88/5.17 thf(fact_8296_binomial__less__binomial__Suc,axiom,
% 4.88/5.17 ! [K: nat,N: nat] :
% 4.88/5.17 ( ( ord_less_nat @ K @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.88/5.17 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % binomial_less_binomial_Suc
% 4.88/5.17 thf(fact_8297_binomial__strict__antimono,axiom,
% 4.88/5.17 ! [K: nat,K7: nat,N: nat] :
% 4.88/5.17 ( ( ord_less_nat @ K @ K7 )
% 4.88/5.17 => ( ( ord_less_eq_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 4.88/5.17 => ( ( ord_less_eq_nat @ K7 @ N )
% 4.88/5.17 => ( ord_less_nat @ ( binomial @ N @ K7 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % binomial_strict_antimono
% 4.88/5.17 thf(fact_8298_binomial__strict__mono,axiom,
% 4.88/5.17 ! [K: nat,K7: nat,N: nat] :
% 4.88/5.17 ( ( ord_less_nat @ K @ K7 )
% 4.88/5.17 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K7 ) @ N )
% 4.88/5.17 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K7 ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % binomial_strict_mono
% 4.88/5.17 thf(fact_8299_binomial__addition__formula,axiom,
% 4.88/5.17 ! [N: nat,K: nat] :
% 4.88/5.17 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.17 => ( ( binomial @ N @ ( suc @ K ) )
% 4.88/5.17 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % binomial_addition_formula
% 4.88/5.17 thf(fact_8300_choose__two,axiom,
% 4.88/5.17 ! [N: nat] :
% 4.88/5.17 ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.88/5.17 = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % choose_two
% 4.88/5.17 thf(fact_8301_mask__eq__sum__exp__nat,axiom,
% 4.88/5.17 ! [N: nat] :
% 4.88/5.17 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 4.88/5.17 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.88/5.17 @ ( collect_nat
% 4.88/5.17 @ ^ [Q3: nat] : ( ord_less_nat @ Q3 @ N ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % mask_eq_sum_exp_nat
% 4.88/5.17 thf(fact_8302_gauss__sum__nat,axiom,
% 4.88/5.17 ! [N: nat] :
% 4.88/5.17 ( ( groups3542108847815614940at_nat
% 4.88/5.17 @ ^ [X3: nat] : X3
% 4.88/5.17 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 4.88/5.17 = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % gauss_sum_nat
% 4.88/5.17 thf(fact_8303_arith__series__nat,axiom,
% 4.88/5.17 ! [A: nat,D: nat,N: nat] :
% 4.88/5.17 ( ( groups3542108847815614940at_nat
% 4.88/5.17 @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I4 @ D ) )
% 4.88/5.17 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 4.88/5.17 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % arith_series_nat
% 4.88/5.17 thf(fact_8304_Sum__Icc__nat,axiom,
% 4.88/5.17 ! [M2: nat,N: nat] :
% 4.88/5.17 ( ( groups3542108847815614940at_nat
% 4.88/5.17 @ ^ [X3: nat] : X3
% 4.88/5.17 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 4.88/5.17 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( plus_plus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M2 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % Sum_Icc_nat
% 4.88/5.17 thf(fact_8305_central__binomial__lower__bound,axiom,
% 4.88/5.17 ! [N: nat] :
% 4.88/5.17 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.17 => ( 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 ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % central_binomial_lower_bound
% 4.88/5.17 thf(fact_8306_and__int_Opinduct,axiom,
% 4.88/5.17 ! [A0: int,A12: int,P: int > int > $o] :
% 4.88/5.17 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 4.88/5.17 => ( ! [K2: int,L4: int] :
% 4.88/5.17 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L4 ) )
% 4.88/5.17 => ( ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 4.88/5.17 & ( member_int @ L4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 4.88/5.17 => ( P @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 4.88/5.17 => ( P @ K2 @ L4 ) ) )
% 4.88/5.17 => ( P @ A0 @ A12 ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % and_int.pinduct
% 4.88/5.17 thf(fact_8307_prod__decode__aux_Opelims,axiom,
% 4.88/5.17 ! [X: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 4.88/5.17 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 4.88/5.17 = Y )
% 4.88/5.17 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 4.88/5.17 => ~ ( ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 4.88/5.17 => ( Y
% 4.88/5.17 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 4.88/5.17 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 4.88/5.17 => ( Y
% 4.88/5.17 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) )
% 4.88/5.17 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % prod_decode_aux.pelims
% 4.88/5.17 thf(fact_8308_sum__nth__roots,axiom,
% 4.88/5.17 ! [N: nat,C: complex] :
% 4.88/5.17 ( ( ord_less_nat @ one_one_nat @ N )
% 4.88/5.17 => ( ( groups7754918857620584856omplex
% 4.88/5.17 @ ^ [X3: complex] : X3
% 4.88/5.17 @ ( collect_complex
% 4.88/5.17 @ ^ [Z2: complex] :
% 4.88/5.17 ( ( power_power_complex @ Z2 @ N )
% 4.88/5.17 = C ) ) )
% 4.88/5.17 = zero_zero_complex ) ) ).
% 4.88/5.17
% 4.88/5.17 % sum_nth_roots
% 4.88/5.17 thf(fact_8309_sum__roots__unity,axiom,
% 4.88/5.17 ! [N: nat] :
% 4.88/5.17 ( ( ord_less_nat @ one_one_nat @ N )
% 4.88/5.17 => ( ( groups7754918857620584856omplex
% 4.88/5.17 @ ^ [X3: complex] : X3
% 4.88/5.17 @ ( collect_complex
% 4.88/5.17 @ ^ [Z2: complex] :
% 4.88/5.17 ( ( power_power_complex @ Z2 @ N )
% 4.88/5.17 = one_one_complex ) ) )
% 4.88/5.17 = zero_zero_complex ) ) ).
% 4.88/5.17
% 4.88/5.17 % sum_roots_unity
% 4.88/5.17 thf(fact_8310_Sum__Icc__int,axiom,
% 4.88/5.17 ! [M2: int,N: int] :
% 4.88/5.17 ( ( ord_less_eq_int @ M2 @ N )
% 4.88/5.17 => ( ( groups4538972089207619220nt_int
% 4.88/5.17 @ ^ [X3: int] : X3
% 4.88/5.17 @ ( set_or1266510415728281911st_int @ M2 @ N ) )
% 4.88/5.17 = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N @ ( plus_plus_int @ N @ one_one_int ) ) @ ( times_times_int @ M2 @ ( minus_minus_int @ M2 @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % Sum_Icc_int
% 4.88/5.17 thf(fact_8311_upto_Opinduct,axiom,
% 4.88/5.17 ! [A0: int,A12: int,P: int > int > $o] :
% 4.88/5.17 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 4.88/5.17 => ( ! [I2: int,J2: int] :
% 4.88/5.17 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I2 @ J2 ) )
% 4.88/5.17 => ( ( ( ord_less_eq_int @ I2 @ J2 )
% 4.88/5.17 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) @ J2 ) )
% 4.88/5.17 => ( P @ I2 @ J2 ) ) )
% 4.88/5.17 => ( P @ A0 @ A12 ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % upto.pinduct
% 4.88/5.17 thf(fact_8312_finite__lessThan,axiom,
% 4.88/5.17 ! [K: nat] : ( finite_finite_nat @ ( set_ord_lessThan_nat @ K ) ) ).
% 4.88/5.17
% 4.88/5.17 % finite_lessThan
% 4.88/5.17 thf(fact_8313_finite__atMost,axiom,
% 4.88/5.17 ! [K: nat] : ( finite_finite_nat @ ( set_ord_atMost_nat @ K ) ) ).
% 4.88/5.17
% 4.88/5.17 % finite_atMost
% 4.88/5.17 thf(fact_8314_card__lessThan,axiom,
% 4.88/5.17 ! [U: nat] :
% 4.88/5.17 ( ( finite_card_nat @ ( set_ord_lessThan_nat @ U ) )
% 4.88/5.17 = U ) ).
% 4.88/5.17
% 4.88/5.17 % card_lessThan
% 4.88/5.17 thf(fact_8315_lessThan__0,axiom,
% 4.88/5.17 ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 4.88/5.17 = bot_bot_set_nat ) ).
% 4.88/5.17
% 4.88/5.17 % lessThan_0
% 4.88/5.17 thf(fact_8316_card__atMost,axiom,
% 4.88/5.17 ! [U: nat] :
% 4.88/5.17 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 4.88/5.17 = ( suc @ U ) ) ).
% 4.88/5.17
% 4.88/5.17 % card_atMost
% 4.88/5.17 thf(fact_8317_atMost__0,axiom,
% 4.88/5.17 ( ( set_ord_atMost_nat @ zero_zero_nat )
% 4.88/5.17 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 4.88/5.17
% 4.88/5.17 % atMost_0
% 4.88/5.17 thf(fact_8318_lessThan__Suc__atMost,axiom,
% 4.88/5.17 ! [K: nat] :
% 4.88/5.17 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 4.88/5.17 = ( set_ord_atMost_nat @ K ) ) ).
% 4.88/5.17
% 4.88/5.17 % lessThan_Suc_atMost
% 4.88/5.17 thf(fact_8319_atMost__atLeast0,axiom,
% 4.88/5.17 ( set_ord_atMost_nat
% 4.88/5.17 = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 4.88/5.17
% 4.88/5.17 % atMost_atLeast0
% 4.88/5.17 thf(fact_8320_atMost__Suc,axiom,
% 4.88/5.17 ! [K: nat] :
% 4.88/5.17 ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 4.88/5.17 = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % atMost_Suc
% 4.88/5.17 thf(fact_8321_lessThan__Suc,axiom,
% 4.88/5.17 ! [K: nat] :
% 4.88/5.17 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 4.88/5.17 = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % lessThan_Suc
% 4.88/5.17 thf(fact_8322_lessThan__empty__iff,axiom,
% 4.88/5.17 ! [N: nat] :
% 4.88/5.17 ( ( ( set_ord_lessThan_nat @ N )
% 4.88/5.17 = bot_bot_set_nat )
% 4.88/5.17 = ( N = zero_zero_nat ) ) ).
% 4.88/5.17
% 4.88/5.17 % lessThan_empty_iff
% 4.88/5.17 thf(fact_8323_finite__nat__iff__bounded__le,axiom,
% 4.88/5.17 ( finite_finite_nat
% 4.88/5.17 = ( ^ [S6: set_nat] :
% 4.88/5.17 ? [K3: nat] : ( ord_less_eq_set_nat @ S6 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % finite_nat_iff_bounded_le
% 4.88/5.17 thf(fact_8324_finite__nat__iff__bounded,axiom,
% 4.88/5.17 ( finite_finite_nat
% 4.88/5.17 = ( ^ [S6: set_nat] :
% 4.88/5.17 ? [K3: nat] : ( ord_less_eq_set_nat @ S6 @ ( set_ord_lessThan_nat @ K3 ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % finite_nat_iff_bounded
% 4.88/5.17 thf(fact_8325_finite__nat__bounded,axiom,
% 4.88/5.17 ! [S2: set_nat] :
% 4.88/5.17 ( ( finite_finite_nat @ S2 )
% 4.88/5.17 => ? [K2: nat] : ( ord_less_eq_set_nat @ S2 @ ( set_ord_lessThan_nat @ K2 ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % finite_nat_bounded
% 4.88/5.17 thf(fact_8326_choose__rising__sum_I1_J,axiom,
% 4.88/5.17 ! [N: nat,M2: nat] :
% 4.88/5.17 ( ( groups3542108847815614940at_nat
% 4.88/5.17 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 4.88/5.17 @ ( set_ord_atMost_nat @ M2 ) )
% 4.88/5.17 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M2 ) @ one_one_nat ) @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % choose_rising_sum(1)
% 4.88/5.17 thf(fact_8327_choose__rising__sum_I2_J,axiom,
% 4.88/5.17 ! [N: nat,M2: nat] :
% 4.88/5.17 ( ( groups3542108847815614940at_nat
% 4.88/5.17 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 4.88/5.17 @ ( set_ord_atMost_nat @ M2 ) )
% 4.88/5.17 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M2 ) @ one_one_nat ) @ M2 ) ) ).
% 4.88/5.17
% 4.88/5.17 % choose_rising_sum(2)
% 4.88/5.17 thf(fact_8328_sum__choose__diagonal,axiom,
% 4.88/5.17 ! [M2: nat,N: nat] :
% 4.88/5.17 ( ( ord_less_eq_nat @ M2 @ N )
% 4.88/5.17 => ( ( groups3542108847815614940at_nat
% 4.88/5.17 @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N @ K3 ) @ ( minus_minus_nat @ M2 @ K3 ) )
% 4.88/5.17 @ ( set_ord_atMost_nat @ M2 ) )
% 4.88/5.17 = ( binomial @ ( suc @ N ) @ M2 ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % sum_choose_diagonal
% 4.88/5.17 thf(fact_8329_atLeast1__atMost__eq__remove0,axiom,
% 4.88/5.17 ! [N: nat] :
% 4.88/5.17 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 4.88/5.17 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % atLeast1_atMost_eq_remove0
% 4.88/5.17 thf(fact_8330_polynomial__product__nat,axiom,
% 4.88/5.17 ! [M2: nat,A: nat > nat,N: nat,B: nat > nat,X: nat] :
% 4.88/5.17 ( ! [I2: nat] :
% 4.88/5.17 ( ( ord_less_nat @ M2 @ I2 )
% 4.88/5.17 => ( ( A @ I2 )
% 4.88/5.17 = zero_zero_nat ) )
% 4.88/5.17 => ( ! [J2: nat] :
% 4.88/5.17 ( ( ord_less_nat @ N @ J2 )
% 4.88/5.17 => ( ( B @ J2 )
% 4.88/5.17 = zero_zero_nat ) )
% 4.88/5.17 => ( ( times_times_nat
% 4.88/5.17 @ ( groups3542108847815614940at_nat
% 4.88/5.17 @ ^ [I4: nat] : ( times_times_nat @ ( A @ I4 ) @ ( power_power_nat @ X @ I4 ) )
% 4.88/5.17 @ ( set_ord_atMost_nat @ M2 ) )
% 4.88/5.17 @ ( groups3542108847815614940at_nat
% 4.88/5.17 @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X @ J3 ) )
% 4.88/5.17 @ ( set_ord_atMost_nat @ N ) ) )
% 4.88/5.17 = ( groups3542108847815614940at_nat
% 4.88/5.17 @ ^ [R5: nat] :
% 4.88/5.17 ( times_times_nat
% 4.88/5.17 @ ( groups3542108847815614940at_nat
% 4.88/5.17 @ ^ [K3: nat] : ( times_times_nat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 4.88/5.17 @ ( set_ord_atMost_nat @ R5 ) )
% 4.88/5.17 @ ( power_power_nat @ X @ R5 ) )
% 4.88/5.17 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % polynomial_product_nat
% 4.88/5.17 thf(fact_8331_Maclaurin__exp__le,axiom,
% 4.88/5.17 ! [X: real,N: nat] :
% 4.88/5.17 ? [T6: real] :
% 4.88/5.17 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 4.88/5.17 & ( ( exp_real @ X )
% 4.88/5.17 = ( plus_plus_real
% 4.88/5.17 @ ( groups6591440286371151544t_real
% 4.88/5.17 @ ^ [M3: nat] : ( divide_divide_real @ ( power_power_real @ X @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) )
% 4.88/5.17 @ ( set_ord_lessThan_nat @ N ) )
% 4.88/5.17 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % Maclaurin_exp_le
% 4.88/5.17 thf(fact_8332_binomial__r__part__sum,axiom,
% 4.88/5.17 ! [M2: nat] :
% 4.88/5.17 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M2 ) )
% 4.88/5.17 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % binomial_r_part_sum
% 4.88/5.17 thf(fact_8333_choose__linear__sum,axiom,
% 4.88/5.17 ! [N: nat] :
% 4.88/5.17 ( ( groups3542108847815614940at_nat
% 4.88/5.17 @ ^ [I4: nat] : ( times_times_nat @ I4 @ ( binomial @ N @ I4 ) )
% 4.88/5.17 @ ( set_ord_atMost_nat @ N ) )
% 4.88/5.17 = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % choose_linear_sum
% 4.88/5.17 thf(fact_8334_sum__pos__lt__pair,axiom,
% 4.88/5.17 ! [F: nat > real,K: nat] :
% 4.88/5.17 ( ( summable_real @ F )
% 4.88/5.17 => ( ! [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 ) ) ) ) )
% 4.88/5.17 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % sum_pos_lt_pair
% 4.88/5.17 thf(fact_8335_Maclaurin__exp__lt,axiom,
% 4.88/5.17 ! [X: real,N: nat] :
% 4.88/5.17 ( ( X != zero_zero_real )
% 4.88/5.17 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.17 => ? [T6: real] :
% 4.88/5.17 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 4.88/5.17 & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 4.88/5.17 & ( ( exp_real @ X )
% 4.88/5.17 = ( plus_plus_real
% 4.88/5.17 @ ( groups6591440286371151544t_real
% 4.88/5.17 @ ^ [M3: nat] : ( divide_divide_real @ ( power_power_real @ X @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) )
% 4.88/5.17 @ ( set_ord_lessThan_nat @ N ) )
% 4.88/5.17 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % Maclaurin_exp_lt
% 4.88/5.17 thf(fact_8336_nat__dvd__1__iff__1,axiom,
% 4.88/5.17 ! [M2: nat] :
% 4.88/5.17 ( ( dvd_dvd_nat @ M2 @ one_one_nat )
% 4.88/5.17 = ( M2 = one_one_nat ) ) ).
% 4.88/5.17
% 4.88/5.17 % nat_dvd_1_iff_1
% 4.88/5.17 thf(fact_8337_dvd__1__iff__1,axiom,
% 4.88/5.17 ! [M2: nat] :
% 4.88/5.17 ( ( dvd_dvd_nat @ M2 @ ( suc @ zero_zero_nat ) )
% 4.88/5.17 = ( M2
% 4.88/5.17 = ( suc @ zero_zero_nat ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % dvd_1_iff_1
% 4.88/5.17 thf(fact_8338_dvd__1__left,axiom,
% 4.88/5.17 ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 4.88/5.17
% 4.88/5.17 % dvd_1_left
% 4.88/5.17 thf(fact_8339_nat__mult__dvd__cancel__disj,axiom,
% 4.88/5.17 ! [K: nat,M2: nat,N: nat] :
% 4.88/5.17 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N ) )
% 4.88/5.17 = ( ( K = zero_zero_nat )
% 4.88/5.17 | ( dvd_dvd_nat @ M2 @ N ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % nat_mult_dvd_cancel_disj
% 4.88/5.17 thf(fact_8340_set__decode__0,axiom,
% 4.88/5.17 ! [X: nat] :
% 4.88/5.17 ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X ) )
% 4.88/5.17 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % set_decode_0
% 4.88/5.17 thf(fact_8341_odd__Suc__minus__one,axiom,
% 4.88/5.17 ! [N: nat] :
% 4.88/5.17 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 4.88/5.17 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 4.88/5.17 = N ) ) ).
% 4.88/5.17
% 4.88/5.17 % odd_Suc_minus_one
% 4.88/5.17 thf(fact_8342_even__diff__nat,axiom,
% 4.88/5.17 ! [M2: nat,N: nat] :
% 4.88/5.17 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M2 @ N ) )
% 4.88/5.17 = ( ( ord_less_nat @ M2 @ N )
% 4.88/5.17 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % even_diff_nat
% 4.88/5.17 thf(fact_8343_odd__two__times__div__two__nat,axiom,
% 4.88/5.17 ! [N: nat] :
% 4.88/5.17 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 4.88/5.17 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.88/5.17 = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % odd_two_times_div_two_nat
% 4.88/5.17 thf(fact_8344_dvd__antisym,axiom,
% 4.88/5.17 ! [M2: nat,N: nat] :
% 4.88/5.17 ( ( dvd_dvd_nat @ M2 @ N )
% 4.88/5.17 => ( ( dvd_dvd_nat @ N @ M2 )
% 4.88/5.17 => ( M2 = N ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % dvd_antisym
% 4.88/5.17 thf(fact_8345_gcd__nat_Oextremum__uniqueI,axiom,
% 4.88/5.17 ! [A: nat] :
% 4.88/5.17 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 4.88/5.17 => ( A = zero_zero_nat ) ) ).
% 4.88/5.17
% 4.88/5.17 % gcd_nat.extremum_uniqueI
% 4.88/5.17 thf(fact_8346_gcd__nat_Onot__eq__extremum,axiom,
% 4.88/5.17 ! [A: nat] :
% 4.88/5.17 ( ( A != zero_zero_nat )
% 4.88/5.17 = ( ( dvd_dvd_nat @ A @ zero_zero_nat )
% 4.88/5.17 & ( A != zero_zero_nat ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % gcd_nat.not_eq_extremum
% 4.88/5.17 thf(fact_8347_gcd__nat_Oextremum__unique,axiom,
% 4.88/5.17 ! [A: nat] :
% 4.88/5.17 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 4.88/5.17 = ( A = zero_zero_nat ) ) ).
% 4.88/5.17
% 4.88/5.17 % gcd_nat.extremum_unique
% 4.88/5.17 thf(fact_8348_gcd__nat_Oextremum__strict,axiom,
% 4.88/5.17 ! [A: nat] :
% 4.88/5.17 ~ ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 4.88/5.17 & ( zero_zero_nat != A ) ) ).
% 4.88/5.17
% 4.88/5.17 % gcd_nat.extremum_strict
% 4.88/5.17 thf(fact_8349_gcd__nat_Oextremum,axiom,
% 4.88/5.17 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 4.88/5.17
% 4.88/5.17 % gcd_nat.extremum
% 4.88/5.17 thf(fact_8350_dvd__diff__nat,axiom,
% 4.88/5.17 ! [K: nat,M2: nat,N: nat] :
% 4.88/5.17 ( ( dvd_dvd_nat @ K @ M2 )
% 4.88/5.17 => ( ( dvd_dvd_nat @ K @ N )
% 4.88/5.17 => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % dvd_diff_nat
% 4.88/5.17 thf(fact_8351_nat__dvd__not__less,axiom,
% 4.88/5.17 ! [M2: nat,N: nat] :
% 4.88/5.17 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 4.88/5.17 => ( ( ord_less_nat @ M2 @ N )
% 4.88/5.17 => ~ ( dvd_dvd_nat @ N @ M2 ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % nat_dvd_not_less
% 4.88/5.17 thf(fact_8352_dvd__pos__nat,axiom,
% 4.88/5.17 ! [N: nat,M2: nat] :
% 4.88/5.17 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.17 => ( ( dvd_dvd_nat @ M2 @ N )
% 4.88/5.17 => ( ord_less_nat @ zero_zero_nat @ M2 ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % dvd_pos_nat
% 4.88/5.17 thf(fact_8353_dvd__minus__self,axiom,
% 4.88/5.17 ! [M2: nat,N: nat] :
% 4.88/5.17 ( ( dvd_dvd_nat @ M2 @ ( minus_minus_nat @ N @ M2 ) )
% 4.88/5.17 = ( ( ord_less_nat @ N @ M2 )
% 4.88/5.17 | ( dvd_dvd_nat @ M2 @ N ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % dvd_minus_self
% 4.88/5.17 thf(fact_8354_less__eq__dvd__minus,axiom,
% 4.88/5.17 ! [M2: nat,N: nat] :
% 4.88/5.17 ( ( ord_less_eq_nat @ M2 @ N )
% 4.88/5.17 => ( ( dvd_dvd_nat @ M2 @ N )
% 4.88/5.17 = ( dvd_dvd_nat @ M2 @ ( minus_minus_nat @ N @ M2 ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % less_eq_dvd_minus
% 4.88/5.17 thf(fact_8355_dvd__diffD1,axiom,
% 4.88/5.17 ! [K: nat,M2: nat,N: nat] :
% 4.88/5.17 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M2 @ N ) )
% 4.88/5.17 => ( ( dvd_dvd_nat @ K @ M2 )
% 4.88/5.17 => ( ( ord_less_eq_nat @ N @ M2 )
% 4.88/5.17 => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % dvd_diffD1
% 4.88/5.17 thf(fact_8356_dvd__diffD,axiom,
% 4.88/5.17 ! [K: nat,M2: nat,N: nat] :
% 4.88/5.17 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M2 @ N ) )
% 4.88/5.17 => ( ( dvd_dvd_nat @ K @ N )
% 4.88/5.17 => ( ( ord_less_eq_nat @ N @ M2 )
% 4.88/5.17 => ( dvd_dvd_nat @ K @ M2 ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % dvd_diffD
% 4.88/5.17 thf(fact_8357_dvd__imp__le,axiom,
% 4.88/5.17 ! [K: nat,N: nat] :
% 4.88/5.17 ( ( dvd_dvd_nat @ K @ N )
% 4.88/5.17 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.17 => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % dvd_imp_le
% 4.88/5.17 thf(fact_8358_dvd__mult__cancel,axiom,
% 4.88/5.17 ! [K: nat,M2: nat,N: nat] :
% 4.88/5.17 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N ) )
% 4.88/5.17 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.88/5.17 => ( dvd_dvd_nat @ M2 @ N ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % dvd_mult_cancel
% 4.88/5.17 thf(fact_8359_nat__mult__dvd__cancel1,axiom,
% 4.88/5.17 ! [K: nat,M2: nat,N: nat] :
% 4.88/5.17 ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.88/5.17 => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M2 ) @ ( times_times_nat @ K @ N ) )
% 4.88/5.17 = ( dvd_dvd_nat @ M2 @ N ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % nat_mult_dvd_cancel1
% 4.88/5.17 thf(fact_8360_bezout__add__strong__nat,axiom,
% 4.88/5.17 ! [A: nat,B: nat] :
% 4.88/5.17 ( ( A != zero_zero_nat )
% 4.88/5.17 => ? [D6: nat,X4: nat,Y3: nat] :
% 4.88/5.17 ( ( dvd_dvd_nat @ D6 @ A )
% 4.88/5.17 & ( dvd_dvd_nat @ D6 @ B )
% 4.88/5.17 & ( ( times_times_nat @ A @ X4 )
% 4.88/5.17 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D6 ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % bezout_add_strong_nat
% 4.88/5.17 thf(fact_8361_mod__greater__zero__iff__not__dvd,axiom,
% 4.88/5.17 ! [M2: nat,N: nat] :
% 4.88/5.17 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M2 @ N ) )
% 4.88/5.17 = ( ~ ( dvd_dvd_nat @ N @ M2 ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % mod_greater_zero_iff_not_dvd
% 4.88/5.17 thf(fact_8362_mod__eq__dvd__iff__nat,axiom,
% 4.88/5.17 ! [N: nat,M2: nat,Q4: nat] :
% 4.88/5.17 ( ( ord_less_eq_nat @ N @ M2 )
% 4.88/5.17 => ( ( ( modulo_modulo_nat @ M2 @ Q4 )
% 4.88/5.17 = ( modulo_modulo_nat @ N @ Q4 ) )
% 4.88/5.17 = ( dvd_dvd_nat @ Q4 @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % mod_eq_dvd_iff_nat
% 4.88/5.17 thf(fact_8363_real__of__nat__div,axiom,
% 4.88/5.17 ! [D: nat,N: nat] :
% 4.88/5.17 ( ( dvd_dvd_nat @ D @ N )
% 4.88/5.17 => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ D ) )
% 4.88/5.17 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % real_of_nat_div
% 4.88/5.17 thf(fact_8364_sums__if_H,axiom,
% 4.88/5.17 ! [G2: nat > real,X: real] :
% 4.88/5.17 ( ( sums_real @ G2 @ X )
% 4.88/5.17 => ( sums_real
% 4.88/5.17 @ ^ [N4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ zero_zero_real @ ( G2 @ ( divide_divide_nat @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.88/5.17 @ X ) ) ).
% 4.88/5.17
% 4.88/5.17 % sums_if'
% 4.88/5.17 thf(fact_8365_sums__if,axiom,
% 4.88/5.17 ! [G2: nat > real,X: real,F: nat > real,Y: real] :
% 4.88/5.17 ( ( sums_real @ G2 @ X )
% 4.88/5.17 => ( ( sums_real @ F @ Y )
% 4.88/5.17 => ( sums_real
% 4.88/5.17 @ ^ [N4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ ( F @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( G2 @ ( divide_divide_nat @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.88/5.17 @ ( plus_plus_real @ X @ Y ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % sums_if
% 4.88/5.17 thf(fact_8366_dvd__fact,axiom,
% 4.88/5.17 ! [M2: nat,N: nat] :
% 4.88/5.17 ( ( ord_less_eq_nat @ one_one_nat @ M2 )
% 4.88/5.17 => ( ( ord_less_eq_nat @ M2 @ N )
% 4.88/5.17 => ( dvd_dvd_nat @ M2 @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % dvd_fact
% 4.88/5.17 thf(fact_8367_finite__divisors__nat,axiom,
% 4.88/5.17 ! [M2: nat] :
% 4.88/5.17 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 4.88/5.17 => ( finite_finite_nat
% 4.88/5.17 @ ( collect_nat
% 4.88/5.17 @ ^ [D5: nat] : ( dvd_dvd_nat @ D5 @ M2 ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % finite_divisors_nat
% 4.88/5.17 thf(fact_8368_dvd__mult__cancel1,axiom,
% 4.88/5.17 ! [M2: nat,N: nat] :
% 4.88/5.17 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 4.88/5.17 => ( ( dvd_dvd_nat @ ( times_times_nat @ M2 @ N ) @ M2 )
% 4.88/5.17 = ( N = one_one_nat ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % dvd_mult_cancel1
% 4.88/5.17 thf(fact_8369_dvd__mult__cancel2,axiom,
% 4.88/5.17 ! [M2: nat,N: nat] :
% 4.88/5.17 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 4.88/5.17 => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M2 ) @ M2 )
% 4.88/5.17 = ( N = one_one_nat ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % dvd_mult_cancel2
% 4.88/5.17 thf(fact_8370_dvd__minus__add,axiom,
% 4.88/5.17 ! [Q4: nat,N: nat,R2: nat,M2: nat] :
% 4.88/5.17 ( ( ord_less_eq_nat @ Q4 @ N )
% 4.88/5.17 => ( ( ord_less_eq_nat @ Q4 @ ( times_times_nat @ R2 @ M2 ) )
% 4.88/5.17 => ( ( dvd_dvd_nat @ M2 @ ( minus_minus_nat @ N @ Q4 ) )
% 4.88/5.17 = ( dvd_dvd_nat @ M2 @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R2 @ M2 ) @ Q4 ) ) ) ) ) ) ).
% 4.88/5.17
% 4.88/5.17 % dvd_minus_add
% 4.88/5.17 thf(fact_8371_power__dvd__imp__le,axiom,
% 4.88/5.18 ! [I: nat,M2: nat,N: nat] :
% 4.88/5.18 ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M2 ) @ ( power_power_nat @ I @ N ) )
% 4.88/5.18 => ( ( ord_less_nat @ one_one_nat @ I )
% 4.88/5.18 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % power_dvd_imp_le
% 4.88/5.18 thf(fact_8372_mod__nat__eqI,axiom,
% 4.88/5.18 ! [R2: nat,N: nat,M2: nat] :
% 4.88/5.18 ( ( ord_less_nat @ R2 @ N )
% 4.88/5.18 => ( ( ord_less_eq_nat @ R2 @ M2 )
% 4.88/5.18 => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M2 @ R2 ) )
% 4.88/5.18 => ( ( modulo_modulo_nat @ M2 @ N )
% 4.88/5.18 = R2 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % mod_nat_eqI
% 4.88/5.18 thf(fact_8373_odd__pos,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 4.88/5.18 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % odd_pos
% 4.88/5.18 thf(fact_8374_dvd__power__iff__le,axiom,
% 4.88/5.18 ! [K: nat,M2: nat,N: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 4.88/5.18 => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M2 ) @ ( power_power_nat @ K @ N ) )
% 4.88/5.18 = ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % dvd_power_iff_le
% 4.88/5.18 thf(fact_8375_even__set__encode__iff,axiom,
% 4.88/5.18 ! [A2: set_nat] :
% 4.88/5.18 ( ( finite_finite_nat @ A2 )
% 4.88/5.18 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A2 ) )
% 4.88/5.18 = ( ~ ( member_nat @ zero_zero_nat @ A2 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % even_set_encode_iff
% 4.88/5.18 thf(fact_8376_even__mod__4__div__2,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 4.88/5.18 = ( suc @ zero_zero_nat ) )
% 4.88/5.18 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % even_mod_4_div_2
% 4.88/5.18 thf(fact_8377_sum__split__even__odd,axiom,
% 4.88/5.18 ! [F: nat > real,G2: nat > real,N: nat] :
% 4.88/5.18 ( ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [I4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( F @ I4 ) @ ( G2 @ I4 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 4.88/5.18 = ( plus_plus_real
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [I4: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ N ) )
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [I4: nat] : ( G2 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ one_one_nat ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sum_split_even_odd
% 4.88/5.18 thf(fact_8378_Bernoulli__inequality__even,axiom,
% 4.88/5.18 ! [N: nat,X: real] :
% 4.88/5.18 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 4.88/5.18 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Bernoulli_inequality_even
% 4.88/5.18 thf(fact_8379_sin__coeff__def,axiom,
% 4.88/5.18 ( sin_coeff
% 4.88/5.18 = ( ^ [N4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N4 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N4 ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sin_coeff_def
% 4.88/5.18 thf(fact_8380_vebt__buildup_Oelims,axiom,
% 4.88/5.18 ! [X: nat,Y: vEBT_VEBT] :
% 4.88/5.18 ( ( ( vEBT_vebt_buildup @ X )
% 4.88/5.18 = Y )
% 4.88/5.18 => ( ( ( X = zero_zero_nat )
% 4.88/5.18 => ( Y
% 4.88/5.18 != ( vEBT_Leaf @ $false @ $false ) ) )
% 4.88/5.18 => ( ( ( X
% 4.88/5.18 = ( suc @ zero_zero_nat ) )
% 4.88/5.18 => ( Y
% 4.88/5.18 != ( vEBT_Leaf @ $false @ $false ) ) )
% 4.88/5.18 => ~ ! [Va: nat] :
% 4.88/5.18 ( ( X
% 4.88/5.18 = ( suc @ ( suc @ Va ) ) )
% 4.88/5.18 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 4.88/5.18 => ( Y
% 4.88/5.18 = ( 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 ) ) ) ) ) ) )
% 4.88/5.18 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 4.88/5.18 => ( Y
% 4.88/5.18 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % vebt_buildup.elims
% 4.88/5.18 thf(fact_8381_sin__paired,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( sums_real
% 4.88/5.18 @ ^ [N4: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 4.88/5.18 @ ( sin_real @ X ) ) ).
% 4.88/5.18
% 4.88/5.18 % sin_paired
% 4.88/5.18 thf(fact_8382_sin__coeff__0,axiom,
% 4.88/5.18 ( ( sin_coeff @ zero_zero_nat )
% 4.88/5.18 = zero_zero_real ) ).
% 4.88/5.18
% 4.88/5.18 % sin_coeff_0
% 4.88/5.18 thf(fact_8383_sin__x__le__x,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ord_less_eq_real @ ( sin_real @ X ) @ X ) ) ).
% 4.88/5.18
% 4.88/5.18 % sin_x_le_x
% 4.88/5.18 thf(fact_8384_sin__le__one,axiom,
% 4.88/5.18 ! [X: real] : ( ord_less_eq_real @ ( sin_real @ X ) @ one_one_real ) ).
% 4.88/5.18
% 4.88/5.18 % sin_le_one
% 4.88/5.18 thf(fact_8385_abs__sin__x__le__abs__x,axiom,
% 4.88/5.18 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ ( abs_abs_real @ X ) ) ).
% 4.88/5.18
% 4.88/5.18 % abs_sin_x_le_abs_x
% 4.88/5.18 thf(fact_8386_zdvd__antisym__nonneg,axiom,
% 4.88/5.18 ! [M2: int,N: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ zero_zero_int @ M2 )
% 4.88/5.18 => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 4.88/5.18 => ( ( dvd_dvd_int @ M2 @ N )
% 4.88/5.18 => ( ( dvd_dvd_int @ N @ M2 )
% 4.88/5.18 => ( M2 = N ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % zdvd_antisym_nonneg
% 4.88/5.18 thf(fact_8387_sin__x__ge__neg__x,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ ( sin_real @ X ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sin_x_ge_neg_x
% 4.88/5.18 thf(fact_8388_sin__ge__zero,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ pi )
% 4.88/5.18 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sin_ge_zero
% 4.88/5.18 thf(fact_8389_sin__ge__minus__one,axiom,
% 4.88/5.18 ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X ) ) ).
% 4.88/5.18
% 4.88/5.18 % sin_ge_minus_one
% 4.88/5.18 thf(fact_8390_abs__sin__le__one,axiom,
% 4.88/5.18 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ one_one_real ) ).
% 4.88/5.18
% 4.88/5.18 % abs_sin_le_one
% 4.88/5.18 thf(fact_8391_zdvd__imp__le,axiom,
% 4.88/5.18 ! [Z: int,N: int] :
% 4.88/5.18 ( ( dvd_dvd_int @ Z @ N )
% 4.88/5.18 => ( ( ord_less_int @ zero_zero_int @ N )
% 4.88/5.18 => ( ord_less_eq_int @ Z @ N ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % zdvd_imp_le
% 4.88/5.18 thf(fact_8392_dvd__imp__le__int,axiom,
% 4.88/5.18 ! [I: int,D: int] :
% 4.88/5.18 ( ( I != zero_zero_int )
% 4.88/5.18 => ( ( dvd_dvd_int @ D @ I )
% 4.88/5.18 => ( ord_less_eq_int @ ( abs_abs_int @ D ) @ ( abs_abs_int @ I ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % dvd_imp_le_int
% 4.88/5.18 thf(fact_8393_real__of__int__div,axiom,
% 4.88/5.18 ! [D: int,N: int] :
% 4.88/5.18 ( ( dvd_dvd_int @ D @ N )
% 4.88/5.18 => ( ( ring_1_of_int_real @ ( divide_divide_int @ N @ D ) )
% 4.88/5.18 = ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % real_of_int_div
% 4.88/5.18 thf(fact_8394_mod__int__pos__iff,axiom,
% 4.88/5.18 ! [K: int,L: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) )
% 4.88/5.18 = ( ( dvd_dvd_int @ L @ K )
% 4.88/5.18 | ( ( L = zero_zero_int )
% 4.88/5.18 & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 4.88/5.18 | ( ord_less_int @ zero_zero_int @ L ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % mod_int_pos_iff
% 4.88/5.18 thf(fact_8395_Maclaurin__sin__bound,axiom,
% 4.88/5.18 ! [X: real,N: nat] :
% 4.88/5.18 ( ord_less_eq_real
% 4.88/5.18 @ ( abs_abs_real
% 4.88/5.18 @ ( minus_minus_real @ ( sin_real @ X )
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ N ) ) ) )
% 4.88/5.18 @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( abs_abs_real @ X ) @ N ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Maclaurin_sin_bound
% 4.88/5.18 thf(fact_8396_sin__pi__divide__n__ge__0,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( N != zero_zero_nat )
% 4.88/5.18 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sin_pi_divide_n_ge_0
% 4.88/5.18 thf(fact_8397_nat__dvd__iff,axiom,
% 4.88/5.18 ! [Z: int,M2: nat] :
% 4.88/5.18 ( ( dvd_dvd_nat @ ( nat2 @ Z ) @ M2 )
% 4.88/5.18 = ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 4.88/5.18 => ( dvd_dvd_int @ Z @ ( semiri1314217659103216013at_int @ M2 ) ) )
% 4.88/5.18 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 4.88/5.18 => ( M2 = zero_zero_nat ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % nat_dvd_iff
% 4.88/5.18 thf(fact_8398_sin__inj__pi,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.88/5.18 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.88/5.18 => ( ( ( sin_real @ X )
% 4.88/5.18 = ( sin_real @ Y ) )
% 4.88/5.18 => ( X = Y ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sin_inj_pi
% 4.88/5.18 thf(fact_8399_sin__mono__le__eq,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.88/5.18 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.88/5.18 => ( ( ord_less_eq_real @ ( sin_real @ X ) @ ( sin_real @ Y ) )
% 4.88/5.18 = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sin_mono_le_eq
% 4.88/5.18 thf(fact_8400_sin__monotone__2pi__le,axiom,
% 4.88/5.18 ! [Y: real,X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.88/5.18 => ( ord_less_eq_real @ ( sin_real @ Y ) @ ( sin_real @ X ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sin_monotone_2pi_le
% 4.88/5.18 thf(fact_8401_sin__le__zero,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ pi @ X )
% 4.88/5.18 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 4.88/5.18 => ( ord_less_eq_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sin_le_zero
% 4.88/5.18 thf(fact_8402_sin__mono__less__eq,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.88/5.18 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.88/5.18 => ( ( ord_less_real @ ( sin_real @ X ) @ ( sin_real @ Y ) )
% 4.88/5.18 = ( ord_less_real @ X @ Y ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sin_mono_less_eq
% 4.88/5.18 thf(fact_8403_sin__monotone__2pi,axiom,
% 4.88/5.18 ! [Y: real,X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 4.88/5.18 => ( ( ord_less_real @ Y @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.88/5.18 => ( ord_less_real @ ( sin_real @ Y ) @ ( sin_real @ X ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sin_monotone_2pi
% 4.88/5.18 thf(fact_8404_sin__total,axiom,
% 4.88/5.18 ! [Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 4.88/5.18 => ? [X4: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 4.88/5.18 & ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.88/5.18 & ( ( sin_real @ X4 )
% 4.88/5.18 = Y )
% 4.88/5.18 & ! [Y4: real] :
% 4.88/5.18 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 4.88/5.18 & ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.88/5.18 & ( ( sin_real @ Y4 )
% 4.88/5.18 = Y ) )
% 4.88/5.18 => ( Y4 = X4 ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sin_total
% 4.88/5.18 thf(fact_8405_even__nat__iff,axiom,
% 4.88/5.18 ! [K: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 4.88/5.18 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 4.88/5.18 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % even_nat_iff
% 4.88/5.18 thf(fact_8406_sin__pi__divide__n__gt__0,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 4.88/5.18 => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sin_pi_divide_n_gt_0
% 4.88/5.18 thf(fact_8407_Maclaurin__sin__expansion2,axiom,
% 4.88/5.18 ! [X: real,N: nat] :
% 4.88/5.18 ? [T6: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 4.88/5.18 & ( ( sin_real @ X )
% 4.88/5.18 = ( plus_plus_real
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ N ) )
% 4.88/5.18 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Maclaurin_sin_expansion2
% 4.88/5.18 thf(fact_8408_Maclaurin__sin__expansion4,axiom,
% 4.88/5.18 ! [X: real,N: nat] :
% 4.88/5.18 ( ( ord_less_real @ zero_zero_real @ X )
% 4.88/5.18 => ? [T6: real] :
% 4.88/5.18 ( ( ord_less_real @ zero_zero_real @ T6 )
% 4.88/5.18 & ( ord_less_eq_real @ T6 @ X )
% 4.88/5.18 & ( ( sin_real @ X )
% 4.88/5.18 = ( plus_plus_real
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ N ) )
% 4.88/5.18 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Maclaurin_sin_expansion4
% 4.88/5.18 thf(fact_8409_Maclaurin__sin__expansion3,axiom,
% 4.88/5.18 ! [N: nat,X: real] :
% 4.88/5.18 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.18 => ( ( ord_less_real @ zero_zero_real @ X )
% 4.88/5.18 => ? [T6: real] :
% 4.88/5.18 ( ( ord_less_real @ zero_zero_real @ T6 )
% 4.88/5.18 & ( ord_less_real @ T6 @ X )
% 4.88/5.18 & ( ( sin_real @ X )
% 4.88/5.18 = ( plus_plus_real
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ N ) )
% 4.88/5.18 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Maclaurin_sin_expansion3
% 4.88/5.18 thf(fact_8410_vebt__buildup_Osimps_I3_J,axiom,
% 4.88/5.18 ! [Va2: nat] :
% 4.88/5.18 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 4.88/5.18 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va2 ) ) )
% 4.88/5.18 = ( 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 ) ) ) ) ) ) )
% 4.88/5.18 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 4.88/5.18 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va2 ) ) )
% 4.88/5.18 = ( 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 ) ) ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % vebt_buildup.simps(3)
% 4.88/5.18 thf(fact_8411_sin__zero__lemma,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( ( sin_real @ X )
% 4.88/5.18 = zero_zero_real )
% 4.88/5.18 => ? [N2: nat] :
% 4.88/5.18 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 4.88/5.18 & ( X
% 4.88/5.18 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sin_zero_lemma
% 4.88/5.18 thf(fact_8412_vebt__buildup_Opelims,axiom,
% 4.88/5.18 ! [X: nat,Y: vEBT_VEBT] :
% 4.88/5.18 ( ( ( vEBT_vebt_buildup @ X )
% 4.88/5.18 = Y )
% 4.88/5.18 => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X )
% 4.88/5.18 => ( ( ( X = zero_zero_nat )
% 4.88/5.18 => ( ( Y
% 4.88/5.18 = ( vEBT_Leaf @ $false @ $false ) )
% 4.88/5.18 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 4.88/5.18 => ( ( ( X
% 4.88/5.18 = ( suc @ zero_zero_nat ) )
% 4.88/5.18 => ( ( Y
% 4.88/5.18 = ( vEBT_Leaf @ $false @ $false ) )
% 4.88/5.18 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 4.88/5.18 => ~ ! [Va: nat] :
% 4.88/5.18 ( ( X
% 4.88/5.18 = ( suc @ ( suc @ Va ) ) )
% 4.88/5.18 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 4.88/5.18 => ( Y
% 4.88/5.18 = ( 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 ) ) ) ) ) ) )
% 4.88/5.18 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 4.88/5.18 => ( Y
% 4.88/5.18 = ( 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 ) ) ) ) ) ) ) ) )
% 4.88/5.18 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va ) ) ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % vebt_buildup.pelims
% 4.88/5.18 thf(fact_8413_sincos__total__2pi,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.88/5.18 = one_one_real )
% 4.88/5.18 => ~ ! [T6: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 4.88/5.18 => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 4.88/5.18 => ( ( X
% 4.88/5.18 = ( cos_real @ T6 ) )
% 4.88/5.18 => ( Y
% 4.88/5.18 != ( sin_real @ T6 ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sincos_total_2pi
% 4.88/5.18 thf(fact_8414_cos__le__one,axiom,
% 4.88/5.18 ! [X: real] : ( ord_less_eq_real @ ( cos_real @ X ) @ one_one_real ) ).
% 4.88/5.18
% 4.88/5.18 % cos_le_one
% 4.88/5.18 thf(fact_8415_arcosh__cosh__real,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( arcosh_real @ ( cosh_real @ X ) )
% 4.88/5.18 = X ) ) ).
% 4.88/5.18
% 4.88/5.18 % arcosh_cosh_real
% 4.88/5.18 thf(fact_8416_cosh__real__nonneg,axiom,
% 4.88/5.18 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 4.88/5.18
% 4.88/5.18 % cosh_real_nonneg
% 4.88/5.18 thf(fact_8417_cosh__real__nonneg__le__iff,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 4.88/5.18 = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % cosh_real_nonneg_le_iff
% 4.88/5.18 thf(fact_8418_cosh__real__nonpos__le__iff,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 4.88/5.18 => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 4.88/5.18 = ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % cosh_real_nonpos_le_iff
% 4.88/5.18 thf(fact_8419_cosh__real__ge__1,axiom,
% 4.88/5.18 ! [X: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X ) ) ).
% 4.88/5.18
% 4.88/5.18 % cosh_real_ge_1
% 4.88/5.18 thf(fact_8420_sinh__le__cosh__real,axiom,
% 4.88/5.18 ! [X: real] : ( ord_less_eq_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) ) ).
% 4.88/5.18
% 4.88/5.18 % sinh_le_cosh_real
% 4.88/5.18 thf(fact_8421_cos__inj__pi,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ pi )
% 4.88/5.18 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ pi )
% 4.88/5.18 => ( ( ( cos_real @ X )
% 4.88/5.18 = ( cos_real @ Y ) )
% 4.88/5.18 => ( X = Y ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % cos_inj_pi
% 4.88/5.18 thf(fact_8422_cos__mono__le__eq,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ pi )
% 4.88/5.18 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ pi )
% 4.88/5.18 => ( ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y ) )
% 4.88/5.18 = ( ord_less_eq_real @ Y @ X ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % cos_mono_le_eq
% 4.88/5.18 thf(fact_8423_cos__monotone__0__pi__le,axiom,
% 4.88/5.18 ! [Y: real,X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ pi )
% 4.88/5.18 => ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % cos_monotone_0_pi_le
% 4.88/5.18 thf(fact_8424_cos__ge__minus__one,axiom,
% 4.88/5.18 ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X ) ) ).
% 4.88/5.18
% 4.88/5.18 % cos_ge_minus_one
% 4.88/5.18 thf(fact_8425_abs__cos__le__one,axiom,
% 4.88/5.18 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X ) ) @ one_one_real ) ).
% 4.88/5.18
% 4.88/5.18 % abs_cos_le_one
% 4.88/5.18 thf(fact_8426_cosh__real__strict__mono,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( ord_less_real @ X @ Y )
% 4.88/5.18 => ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % cosh_real_strict_mono
% 4.88/5.18 thf(fact_8427_cosh__real__nonneg__less__iff,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.88/5.18 => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 4.88/5.18 = ( ord_less_real @ X @ Y ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % cosh_real_nonneg_less_iff
% 4.88/5.18 thf(fact_8428_cosh__real__nonpos__less__iff,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 4.88/5.18 => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 4.88/5.18 = ( ord_less_real @ Y @ X ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % cosh_real_nonpos_less_iff
% 4.88/5.18 thf(fact_8429_cos__mono__less__eq,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ pi )
% 4.88/5.18 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ pi )
% 4.88/5.18 => ( ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y ) )
% 4.88/5.18 = ( ord_less_real @ Y @ X ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % cos_mono_less_eq
% 4.88/5.18 thf(fact_8430_cos__monotone__0__pi,axiom,
% 4.88/5.18 ! [Y: real,X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.88/5.18 => ( ( ord_less_real @ Y @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ pi )
% 4.88/5.18 => ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % cos_monotone_0_pi
% 4.88/5.18 thf(fact_8431_cos__monotone__minus__pi__0_H,axiom,
% 4.88/5.18 ! [Y: real,X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 4.88/5.18 => ( ord_less_eq_real @ ( cos_real @ Y ) @ ( cos_real @ X ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % cos_monotone_minus_pi_0'
% 4.88/5.18 thf(fact_8432_cos__is__zero,axiom,
% 4.88/5.18 ? [X4: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 4.88/5.18 & ( ord_less_eq_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 4.88/5.18 & ( ( cos_real @ X4 )
% 4.88/5.18 = zero_zero_real )
% 4.88/5.18 & ! [Y4: real] :
% 4.88/5.18 ( ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 4.88/5.18 & ( ord_less_eq_real @ Y4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 4.88/5.18 & ( ( cos_real @ Y4 )
% 4.88/5.18 = zero_zero_real ) )
% 4.88/5.18 => ( Y4 = X4 ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % cos_is_zero
% 4.88/5.18 thf(fact_8433_cos__two__le__zero,axiom,
% 4.88/5.18 ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 4.88/5.18
% 4.88/5.18 % cos_two_le_zero
% 4.88/5.18 thf(fact_8434_cos__monotone__minus__pi__0,axiom,
% 4.88/5.18 ! [Y: real,X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 4.88/5.18 => ( ( ord_less_real @ Y @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 4.88/5.18 => ( ord_less_real @ ( cos_real @ Y ) @ ( cos_real @ X ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % cos_monotone_minus_pi_0
% 4.88/5.18 thf(fact_8435_cos__total,axiom,
% 4.88/5.18 ! [Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 4.88/5.18 => ? [X4: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 4.88/5.18 & ( ord_less_eq_real @ X4 @ pi )
% 4.88/5.18 & ( ( cos_real @ X4 )
% 4.88/5.18 = Y )
% 4.88/5.18 & ! [Y4: real] :
% 4.88/5.18 ( ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 4.88/5.18 & ( ord_less_eq_real @ Y4 @ pi )
% 4.88/5.18 & ( ( cos_real @ Y4 )
% 4.88/5.18 = Y ) )
% 4.88/5.18 => ( Y4 = X4 ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % cos_total
% 4.88/5.18 thf(fact_8436_sincos__principal__value,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ? [Y3: real] :
% 4.88/5.18 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 4.88/5.18 & ( ord_less_eq_real @ Y3 @ pi )
% 4.88/5.18 & ( ( sin_real @ Y3 )
% 4.88/5.18 = ( sin_real @ X ) )
% 4.88/5.18 & ( ( cos_real @ Y3 )
% 4.88/5.18 = ( cos_real @ X ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sincos_principal_value
% 4.88/5.18 thf(fact_8437_sin__cos__le1,axiom,
% 4.88/5.18 ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) @ one_one_real ) ).
% 4.88/5.18
% 4.88/5.18 % sin_cos_le1
% 4.88/5.18 thf(fact_8438_cos__ge__zero,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.88/5.18 => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % cos_ge_zero
% 4.88/5.18 thf(fact_8439_sincos__total__pi,axiom,
% 4.88/5.18 ! [Y: real,X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.88/5.18 => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.88/5.18 = one_one_real )
% 4.88/5.18 => ? [T6: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 4.88/5.18 & ( ord_less_eq_real @ T6 @ pi )
% 4.88/5.18 & ( X
% 4.88/5.18 = ( cos_real @ T6 ) )
% 4.88/5.18 & ( Y
% 4.88/5.18 = ( sin_real @ T6 ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sincos_total_pi
% 4.88/5.18 thf(fact_8440_cos__zero__lemma,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( ( cos_real @ X )
% 4.88/5.18 = zero_zero_real )
% 4.88/5.18 => ? [N2: nat] :
% 4.88/5.18 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 4.88/5.18 & ( X
% 4.88/5.18 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % cos_zero_lemma
% 4.88/5.18 thf(fact_8441_sincos__total__pi__half,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.88/5.18 => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.88/5.18 = one_one_real )
% 4.88/5.18 => ? [T6: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 4.88/5.18 & ( ord_less_eq_real @ T6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.88/5.18 & ( X
% 4.88/5.18 = ( cos_real @ T6 ) )
% 4.88/5.18 & ( Y
% 4.88/5.18 = ( sin_real @ T6 ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sincos_total_pi_half
% 4.88/5.18 thf(fact_8442_sincos__total__2pi__le,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.88/5.18 = one_one_real )
% 4.88/5.18 => ? [T6: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 4.88/5.18 & ( ord_less_eq_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 4.88/5.18 & ( X
% 4.88/5.18 = ( cos_real @ T6 ) )
% 4.88/5.18 & ( Y
% 4.88/5.18 = ( sin_real @ T6 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sincos_total_2pi_le
% 4.88/5.18 thf(fact_8443_Maclaurin__cos__expansion2,axiom,
% 4.88/5.18 ! [X: real,N: nat] :
% 4.88/5.18 ( ( ord_less_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.18 => ? [T6: real] :
% 4.88/5.18 ( ( ord_less_real @ zero_zero_real @ T6 )
% 4.88/5.18 & ( ord_less_real @ T6 @ X )
% 4.88/5.18 & ( ( cos_real @ X )
% 4.88/5.18 = ( plus_plus_real
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ N ) )
% 4.88/5.18 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Maclaurin_cos_expansion2
% 4.88/5.18 thf(fact_8444_Maclaurin__minus__cos__expansion,axiom,
% 4.88/5.18 ! [N: nat,X: real] :
% 4.88/5.18 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.18 => ( ( ord_less_real @ X @ zero_zero_real )
% 4.88/5.18 => ? [T6: real] :
% 4.88/5.18 ( ( ord_less_real @ X @ T6 )
% 4.88/5.18 & ( ord_less_real @ T6 @ zero_zero_real )
% 4.88/5.18 & ( ( cos_real @ X )
% 4.88/5.18 = ( plus_plus_real
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ N ) )
% 4.88/5.18 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Maclaurin_minus_cos_expansion
% 4.88/5.18 thf(fact_8445_Maclaurin__cos__expansion,axiom,
% 4.88/5.18 ! [X: real,N: nat] :
% 4.88/5.18 ? [T6: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 4.88/5.18 & ( ( cos_real @ X )
% 4.88/5.18 = ( plus_plus_real
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ N ) )
% 4.88/5.18 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Maclaurin_cos_expansion
% 4.88/5.18 thf(fact_8446_complex__unimodular__polar,axiom,
% 4.88/5.18 ! [Z: complex] :
% 4.88/5.18 ( ( ( real_V1022390504157884413omplex @ Z )
% 4.88/5.18 = one_one_real )
% 4.88/5.18 => ~ ! [T6: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 4.88/5.18 => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 4.88/5.18 => ( Z
% 4.88/5.18 != ( complex2 @ ( cos_real @ T6 ) @ ( sin_real @ T6 ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % complex_unimodular_polar
% 4.88/5.18 thf(fact_8447_cos__coeff__0,axiom,
% 4.88/5.18 ( ( cos_coeff @ zero_zero_nat )
% 4.88/5.18 = one_one_real ) ).
% 4.88/5.18
% 4.88/5.18 % cos_coeff_0
% 4.88/5.18 thf(fact_8448_tan__pos__pi2__le,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.88/5.18 => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % tan_pos_pi2_le
% 4.88/5.18 thf(fact_8449_tan__total__pos,axiom,
% 4.88/5.18 ! [Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.88/5.18 => ? [X4: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 4.88/5.18 & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.88/5.18 & ( ( tan_real @ X4 )
% 4.88/5.18 = Y ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % tan_total_pos
% 4.88/5.18 thf(fact_8450_tan__mono__le,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ Y )
% 4.88/5.18 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.88/5.18 => ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % tan_mono_le
% 4.88/5.18 thf(fact_8451_tan__mono__le__eq,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 4.88/5.18 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.88/5.18 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 4.88/5.18 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.88/5.18 => ( ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y ) )
% 4.88/5.18 = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % tan_mono_le_eq
% 4.88/5.18 thf(fact_8452_arcsin,axiom,
% 4.88/5.18 ! [Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 4.88/5.18 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 4.88/5.18 & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.88/5.18 & ( ( sin_real @ ( arcsin @ Y ) )
% 4.88/5.18 = Y ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arcsin
% 4.88/5.18 thf(fact_8453_arcsin__pi,axiom,
% 4.88/5.18 ! [Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 4.88/5.18 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 4.88/5.18 & ( ord_less_eq_real @ ( arcsin @ Y ) @ pi )
% 4.88/5.18 & ( ( sin_real @ ( arcsin @ Y ) )
% 4.88/5.18 = Y ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arcsin_pi
% 4.88/5.18 thf(fact_8454_arcsin__le__iff,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ one_one_real )
% 4.88/5.18 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.88/5.18 => ( ( ord_less_eq_real @ ( arcsin @ X ) @ Y )
% 4.88/5.18 = ( ord_less_eq_real @ X @ ( sin_real @ Y ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arcsin_le_iff
% 4.88/5.18 thf(fact_8455_le__arcsin__iff,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ one_one_real )
% 4.88/5.18 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ ( arcsin @ X ) )
% 4.88/5.18 = ( ord_less_eq_real @ ( sin_real @ Y ) @ X ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % le_arcsin_iff
% 4.88/5.18 thf(fact_8456_sin__arcsin,axiom,
% 4.88/5.18 ! [Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 4.88/5.18 => ( ( sin_real @ ( arcsin @ Y ) )
% 4.88/5.18 = Y ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sin_arcsin
% 4.88/5.18 thf(fact_8457_arcsin__minus,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ one_one_real )
% 4.88/5.18 => ( ( arcsin @ ( uminus_uminus_real @ X ) )
% 4.88/5.18 = ( uminus_uminus_real @ ( arcsin @ X ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arcsin_minus
% 4.88/5.18 thf(fact_8458_arcsin__le__arcsin,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 4.88/5.18 => ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arcsin_le_arcsin
% 4.88/5.18 thf(fact_8459_arcsin__eq__iff,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 4.88/5.18 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 4.88/5.18 => ( ( ( arcsin @ X )
% 4.88/5.18 = ( arcsin @ Y ) )
% 4.88/5.18 = ( X = Y ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arcsin_eq_iff
% 4.88/5.18 thf(fact_8460_arcsin__le__mono,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 4.88/5.18 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 4.88/5.18 => ( ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y ) )
% 4.88/5.18 = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arcsin_le_mono
% 4.88/5.18 thf(fact_8461_arcsin__less__arcsin,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 4.88/5.18 => ( ( ord_less_real @ X @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 4.88/5.18 => ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arcsin_less_arcsin
% 4.88/5.18 thf(fact_8462_arcsin__less__mono,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 4.88/5.18 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 4.88/5.18 => ( ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y ) )
% 4.88/5.18 = ( ord_less_real @ X @ Y ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arcsin_less_mono
% 4.88/5.18 thf(fact_8463_arcsin__bounded,axiom,
% 4.88/5.18 ! [Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 4.88/5.18 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 4.88/5.18 & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arcsin_bounded
% 4.88/5.18 thf(fact_8464_arcsin__ubound,axiom,
% 4.88/5.18 ! [Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 4.88/5.18 => ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arcsin_ubound
% 4.88/5.18 thf(fact_8465_arcsin__lbound,axiom,
% 4.88/5.18 ! [Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 4.88/5.18 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arcsin_lbound
% 4.88/5.18 thf(fact_8466_arcsin__sin,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.88/5.18 => ( ( arcsin @ ( sin_real @ X ) )
% 4.88/5.18 = X ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arcsin_sin
% 4.88/5.18 thf(fact_8467_arcsin__def,axiom,
% 4.88/5.18 ( arcsin
% 4.88/5.18 = ( ^ [Y2: real] :
% 4.88/5.18 ( the_real
% 4.88/5.18 @ ^ [X3: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 4.88/5.18 & ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.88/5.18 & ( ( sin_real @ X3 )
% 4.88/5.18 = Y2 ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arcsin_def
% 4.88/5.18 thf(fact_8468_arcosh__real__def,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ one_one_real @ X )
% 4.88/5.18 => ( ( arcosh_real @ X )
% 4.88/5.18 = ( ln_ln_real @ ( plus_plus_real @ X @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arcosh_real_def
% 4.88/5.18 thf(fact_8469_num_Osize__gen_I2_J,axiom,
% 4.88/5.18 ! [X23: num] :
% 4.88/5.18 ( ( size_num @ ( bit0 @ X23 ) )
% 4.88/5.18 = ( plus_plus_nat @ ( size_num @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % num.size_gen(2)
% 4.88/5.18 thf(fact_8470_real__sqrt__le__iff,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y ) )
% 4.88/5.18 = ( ord_less_eq_real @ X @ Y ) ) ).
% 4.88/5.18
% 4.88/5.18 % real_sqrt_le_iff
% 4.88/5.18 thf(fact_8471_real__sqrt__ge__0__iff,axiom,
% 4.88/5.18 ! [Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ Y ) )
% 4.88/5.18 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ).
% 4.88/5.18
% 4.88/5.18 % real_sqrt_ge_0_iff
% 4.88/5.18 thf(fact_8472_real__sqrt__le__0__iff,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( sqrt @ X ) @ zero_zero_real )
% 4.88/5.18 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 4.88/5.18
% 4.88/5.18 % real_sqrt_le_0_iff
% 4.88/5.18 thf(fact_8473_real__sqrt__ge__1__iff,axiom,
% 4.88/5.18 ! [Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y ) )
% 4.88/5.18 = ( ord_less_eq_real @ one_one_real @ Y ) ) ).
% 4.88/5.18
% 4.88/5.18 % real_sqrt_ge_1_iff
% 4.88/5.18 thf(fact_8474_real__sqrt__le__1__iff,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( sqrt @ X ) @ one_one_real )
% 4.88/5.18 = ( ord_less_eq_real @ X @ one_one_real ) ) ).
% 4.88/5.18
% 4.88/5.18 % real_sqrt_le_1_iff
% 4.88/5.18 thf(fact_8475_real__sqrt__pow2,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.88/5.18 = X ) ) ).
% 4.88/5.18
% 4.88/5.18 % real_sqrt_pow2
% 4.88/5.18 thf(fact_8476_real__sqrt__pow2__iff,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.88/5.18 = X )
% 4.88/5.18 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 4.88/5.18
% 4.88/5.18 % real_sqrt_pow2_iff
% 4.88/5.18 thf(fact_8477_take__bit__nat__less__eq__self,axiom,
% 4.88/5.18 ! [N: nat,M2: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M2 ) @ M2 ) ).
% 4.88/5.18
% 4.88/5.18 % take_bit_nat_less_eq_self
% 4.88/5.18 thf(fact_8478_take__bit__tightened__less__eq__nat,axiom,
% 4.88/5.18 ! [M2: nat,N: nat,Q4: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ M2 @ N )
% 4.88/5.18 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M2 @ Q4 ) @ ( bit_se2925701944663578781it_nat @ N @ Q4 ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % take_bit_tightened_less_eq_nat
% 4.88/5.18 thf(fact_8479_real__sqrt__le__mono,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ X @ Y )
% 4.88/5.18 => ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % real_sqrt_le_mono
% 4.88/5.18 thf(fact_8480_nat__take__bit__eq,axiom,
% 4.88/5.18 ! [K: int,N: nat] :
% 4.88/5.18 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 4.88/5.18 => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 4.88/5.18 = ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % nat_take_bit_eq
% 4.88/5.18 thf(fact_8481_take__bit__nat__eq,axiom,
% 4.88/5.18 ! [K: int,N: nat] :
% 4.88/5.18 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 4.88/5.18 => ( ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) )
% 4.88/5.18 = ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % take_bit_nat_eq
% 4.88/5.18 thf(fact_8482_real__sqrt__ge__zero,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % real_sqrt_ge_zero
% 4.88/5.18 thf(fact_8483_real__sqrt__eq__zero__cancel,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( ( sqrt @ X )
% 4.88/5.18 = zero_zero_real )
% 4.88/5.18 => ( X = zero_zero_real ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % real_sqrt_eq_zero_cancel
% 4.88/5.18 thf(fact_8484_real__sqrt__ge__one,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ one_one_real @ X )
% 4.88/5.18 => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % real_sqrt_ge_one
% 4.88/5.18 thf(fact_8485_take__bit__tightened__less__eq__int,axiom,
% 4.88/5.18 ! [M2: nat,N: nat,K: int] :
% 4.88/5.18 ( ( ord_less_eq_nat @ M2 @ N )
% 4.88/5.18 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M2 @ K ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % take_bit_tightened_less_eq_int
% 4.88/5.18 thf(fact_8486_take__bit__int__less__eq__self__iff,axiom,
% 4.88/5.18 ! [N: nat,K: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 4.88/5.18 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 4.88/5.18
% 4.88/5.18 % take_bit_int_less_eq_self_iff
% 4.88/5.18 thf(fact_8487_take__bit__nonnegative,axiom,
% 4.88/5.18 ! [N: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 4.88/5.18
% 4.88/5.18 % take_bit_nonnegative
% 4.88/5.18 thf(fact_8488_real__div__sqrt,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( divide_divide_real @ X @ ( sqrt @ X ) )
% 4.88/5.18 = ( sqrt @ X ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % real_div_sqrt
% 4.88/5.18 thf(fact_8489_sqrt__add__le__add__sqrt,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.88/5.18 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sqrt_add_le_add_sqrt
% 4.88/5.18 thf(fact_8490_le__real__sqrt__sumsq,axiom,
% 4.88/5.18 ! [X: real,Y: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % le_real_sqrt_sumsq
% 4.88/5.18 thf(fact_8491_ln__neg__is__const,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 4.88/5.18 => ( ( ln_ln_real @ X )
% 4.88/5.18 = ( the_real
% 4.88/5.18 @ ^ [X3: real] : $false ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % ln_neg_is_const
% 4.88/5.18 thf(fact_8492_sqrt__divide__self__eq,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( divide_divide_real @ ( sqrt @ X ) @ X )
% 4.88/5.18 = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sqrt_divide_self_eq
% 4.88/5.18 thf(fact_8493_take__bit__nat__eq__self__iff,axiom,
% 4.88/5.18 ! [N: nat,M2: nat] :
% 4.88/5.18 ( ( ( bit_se2925701944663578781it_nat @ N @ M2 )
% 4.88/5.18 = M2 )
% 4.88/5.18 = ( ord_less_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % take_bit_nat_eq_self_iff
% 4.88/5.18 thf(fact_8494_take__bit__nat__less__exp,axiom,
% 4.88/5.18 ! [N: nat,M2: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % take_bit_nat_less_exp
% 4.88/5.18 thf(fact_8495_take__bit__nat__eq__self,axiom,
% 4.88/5.18 ! [M2: nat,N: nat] :
% 4.88/5.18 ( ( ord_less_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.88/5.18 => ( ( bit_se2925701944663578781it_nat @ N @ M2 )
% 4.88/5.18 = M2 ) ) ).
% 4.88/5.18
% 4.88/5.18 % take_bit_nat_eq_self
% 4.88/5.18 thf(fact_8496_real__le__rsqrt,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 4.88/5.18 => ( ord_less_eq_real @ X @ ( sqrt @ Y ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % real_le_rsqrt
% 4.88/5.18 thf(fact_8497_sqrt__le__D,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( sqrt @ X ) @ Y )
% 4.88/5.18 => ( ord_less_eq_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sqrt_le_D
% 4.88/5.18 thf(fact_8498_num_Osize__gen_I1_J,axiom,
% 4.88/5.18 ( ( size_num @ one )
% 4.88/5.18 = zero_zero_nat ) ).
% 4.88/5.18
% 4.88/5.18 % num.size_gen(1)
% 4.88/5.18 thf(fact_8499_take__bit__nat__less__self__iff,axiom,
% 4.88/5.18 ! [N: nat,M2: nat] :
% 4.88/5.18 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M2 ) @ M2 )
% 4.88/5.18 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M2 ) ) ).
% 4.88/5.18
% 4.88/5.18 % take_bit_nat_less_self_iff
% 4.88/5.18 thf(fact_8500_real__le__lsqrt,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.88/5.18 => ( ord_less_eq_real @ ( sqrt @ X ) @ Y ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % real_le_lsqrt
% 4.88/5.18 thf(fact_8501_real__sqrt__unique,axiom,
% 4.88/5.18 ! [Y: real,X: real] :
% 4.88/5.18 ( ( ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.88/5.18 = X )
% 4.88/5.18 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.88/5.18 => ( ( sqrt @ X )
% 4.88/5.18 = Y ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % real_sqrt_unique
% 4.88/5.18 thf(fact_8502_real__sqrt__sum__squares__ge1,axiom,
% 4.88/5.18 ! [X: real,Y: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % real_sqrt_sum_squares_ge1
% 4.88/5.18 thf(fact_8503_real__sqrt__sum__squares__ge2,axiom,
% 4.88/5.18 ! [Y: real,X: real] : ( ord_less_eq_real @ Y @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % real_sqrt_sum_squares_ge2
% 4.88/5.18 thf(fact_8504_real__sqrt__sum__squares__triangle__ineq,axiom,
% 4.88/5.18 ! [A: real,C: real,B: real,D: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( plus_plus_real @ A @ C ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( plus_plus_real @ B @ D ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ C @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % real_sqrt_sum_squares_triangle_ineq
% 4.88/5.18 thf(fact_8505_sqrt__ge__absD,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ Y ) )
% 4.88/5.18 => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) ).
% 4.88/5.18
% 4.88/5.18 % sqrt_ge_absD
% 4.88/5.18 thf(fact_8506_take__bit__int__less__self__iff,axiom,
% 4.88/5.18 ! [N: nat,K: int] :
% 4.88/5.18 ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 4.88/5.18 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 4.88/5.18
% 4.88/5.18 % take_bit_int_less_self_iff
% 4.88/5.18 thf(fact_8507_take__bit__int__greater__eq__self__iff,axiom,
% 4.88/5.18 ! [K: int,N: nat] :
% 4.88/5.18 ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 4.88/5.18 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % take_bit_int_greater_eq_self_iff
% 4.88/5.18 thf(fact_8508_real__less__lsqrt,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.88/5.18 => ( ( ord_less_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.88/5.18 => ( ord_less_real @ ( sqrt @ X ) @ Y ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % real_less_lsqrt
% 4.88/5.18 thf(fact_8509_sqrt__sum__squares__le__sum,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.88/5.18 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X @ Y ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sqrt_sum_squares_le_sum
% 4.88/5.18 thf(fact_8510_real__sqrt__ge__abs1,axiom,
% 4.88/5.18 ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % real_sqrt_ge_abs1
% 4.88/5.18 thf(fact_8511_real__sqrt__ge__abs2,axiom,
% 4.88/5.18 ! [Y: real,X: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % real_sqrt_ge_abs2
% 4.88/5.18 thf(fact_8512_sqrt__sum__squares__le__sum__abs,axiom,
% 4.88/5.18 ! [X: real,Y: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sqrt_sum_squares_le_sum_abs
% 4.88/5.18 thf(fact_8513_take__bit__int__eq__self,axiom,
% 4.88/5.18 ! [K: int,N: nat] :
% 4.88/5.18 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 4.88/5.18 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 4.88/5.18 => ( ( bit_se2923211474154528505it_int @ N @ K )
% 4.88/5.18 = K ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % take_bit_int_eq_self
% 4.88/5.18 thf(fact_8514_take__bit__int__eq__self__iff,axiom,
% 4.88/5.18 ! [N: nat,K: int] :
% 4.88/5.18 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 4.88/5.18 = K )
% 4.88/5.18 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 4.88/5.18 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % take_bit_int_eq_self_iff
% 4.88/5.18 thf(fact_8515_real__sqrt__power__even,axiom,
% 4.88/5.18 ! [N: nat,X: real] :
% 4.88/5.18 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 4.88/5.18 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( power_power_real @ ( sqrt @ X ) @ N )
% 4.88/5.18 = ( power_power_real @ X @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % real_sqrt_power_even
% 4.88/5.18 thf(fact_8516_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 4.88/5.18 ! [X: real,Y: real,Xa2: real,Ya: real] : ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % real_sqrt_sum_squares_mult_ge_zero
% 4.88/5.18 thf(fact_8517_arith__geo__mean__sqrt,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.88/5.18 => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X @ Y ) ) @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arith_geo_mean_sqrt
% 4.88/5.18 thf(fact_8518_powr__half__sqrt,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.88/5.18 = ( sqrt @ X ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % powr_half_sqrt
% 4.88/5.18 thf(fact_8519_take__bit__int__less__eq,axiom,
% 4.88/5.18 ! [N: nat,K: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 4.88/5.18 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.18 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % take_bit_int_less_eq
% 4.88/5.18 thf(fact_8520_take__bit__int__greater__eq,axiom,
% 4.88/5.18 ! [K: int,N: nat] :
% 4.88/5.18 ( ( ord_less_int @ K @ zero_zero_int )
% 4.88/5.18 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % take_bit_int_greater_eq
% 4.88/5.18 thf(fact_8521_divmod__step__nat__def,axiom,
% 4.88/5.18 ( unique5026877609467782581ep_nat
% 4.88/5.18 = ( ^ [L3: num] :
% 4.88/5.18 ( produc2626176000494625587at_nat
% 4.88/5.18 @ ^ [Q3: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L3 ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L3 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ R5 ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % divmod_step_nat_def
% 4.88/5.18 thf(fact_8522_cos__x__y__le__one,axiom,
% 4.88/5.18 ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 4.88/5.18
% 4.88/5.18 % cos_x_y_le_one
% 4.88/5.18 thf(fact_8523_take__bit__minus__small__eq,axiom,
% 4.88/5.18 ! [K: int,N: nat] :
% 4.88/5.18 ( ( ord_less_int @ zero_zero_int @ K )
% 4.88/5.18 => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 4.88/5.18 => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 4.88/5.18 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % take_bit_minus_small_eq
% 4.88/5.18 thf(fact_8524_divmod__step__int__def,axiom,
% 4.88/5.18 ( unique5024387138958732305ep_int
% 4.88/5.18 = ( ^ [L3: num] :
% 4.88/5.18 ( produc4245557441103728435nt_int
% 4.88/5.18 @ ^ [Q3: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L3 ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L3 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ R5 ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % divmod_step_int_def
% 4.88/5.18 thf(fact_8525_pi__half,axiom,
% 4.88/5.18 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 4.88/5.18 = ( the_real
% 4.88/5.18 @ ^ [X3: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 4.88/5.18 & ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 4.88/5.18 & ( ( cos_real @ X3 )
% 4.88/5.18 = zero_zero_real ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % pi_half
% 4.88/5.18 thf(fact_8526_pi__def,axiom,
% 4.88/5.18 ( pi
% 4.88/5.18 = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 4.88/5.18 @ ( the_real
% 4.88/5.18 @ ^ [X3: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 4.88/5.18 & ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 4.88/5.18 & ( ( cos_real @ X3 )
% 4.88/5.18 = zero_zero_real ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % pi_def
% 4.88/5.18 thf(fact_8527_sqrt__sum__squares__half__less,axiom,
% 4.88/5.18 ! [X: real,U: real,Y: real] :
% 4.88/5.18 ( ( ord_less_real @ X @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.88/5.18 => ( ( ord_less_real @ Y @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.88/5.18 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.88/5.18 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sqrt_sum_squares_half_less
% 4.88/5.18 thf(fact_8528_sin__cos__sqrt,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) )
% 4.88/5.18 => ( ( sin_real @ X )
% 4.88/5.18 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sin_cos_sqrt
% 4.88/5.18 thf(fact_8529_cos__arcsin,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ one_one_real )
% 4.88/5.18 => ( ( cos_real @ ( arcsin @ X ) )
% 4.88/5.18 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % cos_arcsin
% 4.88/5.18 thf(fact_8530_sin__arccos__abs,axiom,
% 4.88/5.18 ! [Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 4.88/5.18 => ( ( sin_real @ ( arccos @ Y ) )
% 4.88/5.18 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sin_arccos_abs
% 4.88/5.18 thf(fact_8531_sin__arccos,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ one_one_real )
% 4.88/5.18 => ( ( sin_real @ ( arccos @ X ) )
% 4.88/5.18 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sin_arccos
% 4.88/5.18 thf(fact_8532_divmod__nat__if,axiom,
% 4.88/5.18 ( divmod_nat
% 4.88/5.18 = ( ^ [M3: nat,N4: nat] :
% 4.88/5.18 ( if_Pro6206227464963214023at_nat
% 4.88/5.18 @ ( ( N4 = zero_zero_nat )
% 4.88/5.18 | ( ord_less_nat @ M3 @ N4 ) )
% 4.88/5.18 @ ( product_Pair_nat_nat @ zero_zero_nat @ M3 )
% 4.88/5.18 @ ( produc2626176000494625587at_nat
% 4.88/5.18 @ ^ [Q3: nat] : ( product_Pair_nat_nat @ ( suc @ Q3 ) )
% 4.88/5.18 @ ( divmod_nat @ ( minus_minus_nat @ M3 @ N4 ) @ N4 ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % divmod_nat_if
% 4.88/5.18 thf(fact_8533_flip__bit__nonnegative__int__iff,axiom,
% 4.88/5.18 ! [N: nat,K: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N @ K ) )
% 4.88/5.18 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 4.88/5.18
% 4.88/5.18 % flip_bit_nonnegative_int_iff
% 4.88/5.18 thf(fact_8534_cos__arccos,axiom,
% 4.88/5.18 ! [Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 4.88/5.18 => ( ( cos_real @ ( arccos @ Y ) )
% 4.88/5.18 = Y ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % cos_arccos
% 4.88/5.18 thf(fact_8535_arccos__le__arccos,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 4.88/5.18 => ( ord_less_eq_real @ ( arccos @ Y ) @ ( arccos @ X ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arccos_le_arccos
% 4.88/5.18 thf(fact_8536_arccos__eq__iff,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 4.88/5.18 & ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real ) )
% 4.88/5.18 => ( ( ( arccos @ X )
% 4.88/5.18 = ( arccos @ Y ) )
% 4.88/5.18 = ( X = Y ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arccos_eq_iff
% 4.88/5.18 thf(fact_8537_arccos__le__mono,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 4.88/5.18 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 4.88/5.18 => ( ( ord_less_eq_real @ ( arccos @ X ) @ ( arccos @ Y ) )
% 4.88/5.18 = ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arccos_le_mono
% 4.88/5.18 thf(fact_8538_arccos__lbound,axiom,
% 4.88/5.18 ! [Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 4.88/5.18 => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arccos_lbound
% 4.88/5.18 thf(fact_8539_arccos__less__arccos,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 4.88/5.18 => ( ( ord_less_real @ X @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 4.88/5.18 => ( ord_less_real @ ( arccos @ Y ) @ ( arccos @ X ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arccos_less_arccos
% 4.88/5.18 thf(fact_8540_arccos__less__mono,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 4.88/5.18 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 4.88/5.18 => ( ( ord_less_real @ ( arccos @ X ) @ ( arccos @ Y ) )
% 4.88/5.18 = ( ord_less_real @ Y @ X ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arccos_less_mono
% 4.88/5.18 thf(fact_8541_arccos__ubound,axiom,
% 4.88/5.18 ! [Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 4.88/5.18 => ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arccos_ubound
% 4.88/5.18 thf(fact_8542_arccos__cos,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ pi )
% 4.88/5.18 => ( ( arccos @ ( cos_real @ X ) )
% 4.88/5.18 = X ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arccos_cos
% 4.88/5.18 thf(fact_8543_cos__arccos__abs,axiom,
% 4.88/5.18 ! [Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 4.88/5.18 => ( ( cos_real @ ( arccos @ Y ) )
% 4.88/5.18 = Y ) ) ).
% 4.88/5.18
% 4.88/5.18 % cos_arccos_abs
% 4.88/5.18 thf(fact_8544_arccos__cos__eq__abs,axiom,
% 4.88/5.18 ! [Theta: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( abs_abs_real @ Theta ) @ pi )
% 4.88/5.18 => ( ( arccos @ ( cos_real @ Theta ) )
% 4.88/5.18 = ( abs_abs_real @ Theta ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arccos_cos_eq_abs
% 4.88/5.18 thf(fact_8545_arccos__bounded,axiom,
% 4.88/5.18 ! [Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 4.88/5.18 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 4.88/5.18 & ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arccos_bounded
% 4.88/5.18 thf(fact_8546_arccos__cos2,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 4.88/5.18 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ X )
% 4.88/5.18 => ( ( arccos @ ( cos_real @ X ) )
% 4.88/5.18 = ( uminus_uminus_real @ X ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arccos_cos2
% 4.88/5.18 thf(fact_8547_arccos__minus,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ one_one_real )
% 4.88/5.18 => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 4.88/5.18 = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arccos_minus
% 4.88/5.18 thf(fact_8548_arccos__def,axiom,
% 4.88/5.18 ( arccos
% 4.88/5.18 = ( ^ [Y2: real] :
% 4.88/5.18 ( the_real
% 4.88/5.18 @ ^ [X3: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 4.88/5.18 & ( ord_less_eq_real @ X3 @ pi )
% 4.88/5.18 & ( ( cos_real @ X3 )
% 4.88/5.18 = Y2 ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arccos_def
% 4.88/5.18 thf(fact_8549_arccos,axiom,
% 4.88/5.18 ! [Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 4.88/5.18 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 4.88/5.18 & ( ord_less_eq_real @ ( arccos @ Y ) @ pi )
% 4.88/5.18 & ( ( cos_real @ ( arccos @ Y ) )
% 4.88/5.18 = Y ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arccos
% 4.88/5.18 thf(fact_8550_arccos__minus__abs,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 4.88/5.18 => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 4.88/5.18 = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arccos_minus_abs
% 4.88/5.18 thf(fact_8551_floor__real__def,axiom,
% 4.88/5.18 ( archim6058952711729229775r_real
% 4.88/5.18 = ( ^ [X3: real] :
% 4.88/5.18 ( the_int
% 4.88/5.18 @ ^ [Z2: int] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ X3 )
% 4.88/5.18 & ( ord_less_real @ X3 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % floor_real_def
% 4.88/5.18 thf(fact_8552_arccos__le__pi2,axiom,
% 4.88/5.18 ! [Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.88/5.18 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 4.88/5.18 => ( ord_less_eq_real @ ( arccos @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % arccos_le_pi2
% 4.88/5.18 thf(fact_8553_int__ge__less__than__def,axiom,
% 4.88/5.18 ( int_ge_less_than
% 4.88/5.18 = ( ^ [D5: int] :
% 4.88/5.18 ( collec213857154873943460nt_int
% 4.88/5.18 @ ( produc4947309494688390418_int_o
% 4.88/5.18 @ ^ [Z8: int,Z2: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ D5 @ Z8 )
% 4.88/5.18 & ( ord_less_int @ Z8 @ Z2 ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % int_ge_less_than_def
% 4.88/5.18 thf(fact_8554_int__ge__less__than2__def,axiom,
% 4.88/5.18 ( int_ge_less_than2
% 4.88/5.18 = ( ^ [D5: int] :
% 4.88/5.18 ( collec213857154873943460nt_int
% 4.88/5.18 @ ( produc4947309494688390418_int_o
% 4.88/5.18 @ ^ [Z8: int,Z2: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ D5 @ Z2 )
% 4.88/5.18 & ( ord_less_int @ Z8 @ Z2 ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % int_ge_less_than2_def
% 4.88/5.18 thf(fact_8555_Suc__0__mod__eq,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 4.88/5.18 = ( zero_n2687167440665602831ol_nat
% 4.88/5.18 @ ( N
% 4.88/5.18 != ( suc @ zero_zero_nat ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Suc_0_mod_eq
% 4.88/5.18 thf(fact_8556_take__bit__of__Suc__0,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 4.88/5.18 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % take_bit_of_Suc_0
% 4.88/5.18 thf(fact_8557_divide__int__unfold,axiom,
% 4.88/5.18 ! [L: int,K: int,N: nat,M2: nat] :
% 4.88/5.18 ( ( ( ( ( sgn_sgn_int @ L )
% 4.88/5.18 = zero_zero_int )
% 4.88/5.18 | ( ( sgn_sgn_int @ K )
% 4.88/5.18 = zero_zero_int )
% 4.88/5.18 | ( N = zero_zero_nat ) )
% 4.88/5.18 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 4.88/5.18 = zero_zero_int ) )
% 4.88/5.18 & ( ~ ( ( ( sgn_sgn_int @ L )
% 4.88/5.18 = zero_zero_int )
% 4.88/5.18 | ( ( sgn_sgn_int @ K )
% 4.88/5.18 = zero_zero_int )
% 4.88/5.18 | ( N = zero_zero_nat ) )
% 4.88/5.18 => ( ( ( ( sgn_sgn_int @ K )
% 4.88/5.18 = ( sgn_sgn_int @ L ) )
% 4.88/5.18 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 4.88/5.18 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M2 @ N ) ) ) )
% 4.88/5.18 & ( ( ( sgn_sgn_int @ K )
% 4.88/5.18 != ( sgn_sgn_int @ L ) )
% 4.88/5.18 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 4.88/5.18 = ( uminus_uminus_int
% 4.88/5.18 @ ( semiri1314217659103216013at_int
% 4.88/5.18 @ ( plus_plus_nat @ ( divide_divide_nat @ M2 @ N )
% 4.88/5.18 @ ( zero_n2687167440665602831ol_nat
% 4.88/5.18 @ ~ ( dvd_dvd_nat @ N @ M2 ) ) ) ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % divide_int_unfold
% 4.88/5.18 thf(fact_8558_modulo__int__unfold,axiom,
% 4.88/5.18 ! [L: int,K: int,N: nat,M2: nat] :
% 4.88/5.18 ( ( ( ( ( sgn_sgn_int @ L )
% 4.88/5.18 = zero_zero_int )
% 4.88/5.18 | ( ( sgn_sgn_int @ K )
% 4.88/5.18 = zero_zero_int )
% 4.88/5.18 | ( N = zero_zero_nat ) )
% 4.88/5.18 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 4.88/5.18 = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M2 ) ) ) )
% 4.88/5.18 & ( ~ ( ( ( sgn_sgn_int @ L )
% 4.88/5.18 = zero_zero_int )
% 4.88/5.18 | ( ( sgn_sgn_int @ K )
% 4.88/5.18 = zero_zero_int )
% 4.88/5.18 | ( N = zero_zero_nat ) )
% 4.88/5.18 => ( ( ( ( sgn_sgn_int @ K )
% 4.88/5.18 = ( sgn_sgn_int @ L ) )
% 4.88/5.18 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 4.88/5.18 = ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M2 @ N ) ) ) ) )
% 4.88/5.18 & ( ( ( sgn_sgn_int @ K )
% 4.88/5.18 != ( sgn_sgn_int @ L ) )
% 4.88/5.18 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 4.88/5.18 = ( times_times_int @ ( sgn_sgn_int @ L )
% 4.88/5.18 @ ( minus_minus_int
% 4.88/5.18 @ ( semiri1314217659103216013at_int
% 4.88/5.18 @ ( times_times_nat @ N
% 4.88/5.18 @ ( zero_n2687167440665602831ol_nat
% 4.88/5.18 @ ~ ( dvd_dvd_nat @ N @ M2 ) ) ) )
% 4.88/5.18 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M2 @ N ) ) ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % modulo_int_unfold
% 4.88/5.18 thf(fact_8559_and__int_Opsimps,axiom,
% 4.88/5.18 ! [K: int,L: int] :
% 4.88/5.18 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L ) )
% 4.88/5.18 => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 4.88/5.18 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 4.88/5.18 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 4.88/5.18 = ( uminus_uminus_int
% 4.88/5.18 @ ( zero_n2684676970156552555ol_int
% 4.88/5.18 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 4.88/5.18 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 4.88/5.18 & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 4.88/5.18 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 4.88/5.18 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 4.88/5.18 = ( plus_plus_int
% 4.88/5.18 @ ( zero_n2684676970156552555ol_int
% 4.88/5.18 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 4.88/5.18 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 4.88/5.18 @ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % and_int.psimps
% 4.88/5.18 thf(fact_8560_and__int_Opelims,axiom,
% 4.88/5.18 ! [X: int,Xa2: int,Y: int] :
% 4.88/5.18 ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 4.88/5.18 = Y )
% 4.88/5.18 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 4.88/5.18 => ~ ( ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 4.88/5.18 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 4.88/5.18 => ( Y
% 4.88/5.18 = ( uminus_uminus_int
% 4.88/5.18 @ ( zero_n2684676970156552555ol_int
% 4.88/5.18 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 4.88/5.18 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 4.88/5.18 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 4.88/5.18 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 4.88/5.18 => ( Y
% 4.88/5.18 = ( plus_plus_int
% 4.88/5.18 @ ( zero_n2684676970156552555ol_int
% 4.88/5.18 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 4.88/5.18 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 4.88/5.18 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 4.88/5.18 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % and_int.pelims
% 4.88/5.18 thf(fact_8561_floor__rat__def,axiom,
% 4.88/5.18 ( archim3151403230148437115or_rat
% 4.88/5.18 = ( ^ [X3: rat] :
% 4.88/5.18 ( the_int
% 4.88/5.18 @ ^ [Z2: int] :
% 4.88/5.18 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ X3 )
% 4.88/5.18 & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % floor_rat_def
% 4.88/5.18 thf(fact_8562_and__int_Oelims,axiom,
% 4.88/5.18 ! [X: int,Xa2: int,Y: int] :
% 4.88/5.18 ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 4.88/5.18 = Y )
% 4.88/5.18 => ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 4.88/5.18 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 4.88/5.18 => ( Y
% 4.88/5.18 = ( uminus_uminus_int
% 4.88/5.18 @ ( zero_n2684676970156552555ol_int
% 4.88/5.18 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 4.88/5.18 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 4.88/5.18 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 4.88/5.18 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 4.88/5.18 => ( Y
% 4.88/5.18 = ( plus_plus_int
% 4.88/5.18 @ ( zero_n2684676970156552555ol_int
% 4.88/5.18 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 4.88/5.18 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 4.88/5.18 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % and_int.elims
% 4.88/5.18 thf(fact_8563_and__nonnegative__int__iff,axiom,
% 4.88/5.18 ! [K: int,L: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 4.88/5.18 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 4.88/5.18 | ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % and_nonnegative_int_iff
% 4.88/5.18 thf(fact_8564_less__eq__rat__def,axiom,
% 4.88/5.18 ( ord_less_eq_rat
% 4.88/5.18 = ( ^ [X3: rat,Y2: rat] :
% 4.88/5.18 ( ( ord_less_rat @ X3 @ Y2 )
% 4.88/5.18 | ( X3 = Y2 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % less_eq_rat_def
% 4.88/5.18 thf(fact_8565_obtain__pos__sum,axiom,
% 4.88/5.18 ! [R2: rat] :
% 4.88/5.18 ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 4.88/5.18 => ~ ! [S3: rat] :
% 4.88/5.18 ( ( ord_less_rat @ zero_zero_rat @ S3 )
% 4.88/5.18 => ! [T6: rat] :
% 4.88/5.18 ( ( ord_less_rat @ zero_zero_rat @ T6 )
% 4.88/5.18 => ( R2
% 4.88/5.18 != ( plus_plus_rat @ S3 @ T6 ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % obtain_pos_sum
% 4.88/5.18 thf(fact_8566_AND__lower,axiom,
% 4.88/5.18 ! [X: int,Y: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 4.88/5.18 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X @ Y ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % AND_lower
% 4.88/5.18 thf(fact_8567_AND__upper1,axiom,
% 4.88/5.18 ! [X: int,Y: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 4.88/5.18 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ X ) ) ).
% 4.88/5.18
% 4.88/5.18 % AND_upper1
% 4.88/5.18 thf(fact_8568_AND__upper2,axiom,
% 4.88/5.18 ! [Y: int,X: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.88/5.18 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Y ) ) ).
% 4.88/5.18
% 4.88/5.18 % AND_upper2
% 4.88/5.18 thf(fact_8569_AND__upper1_H,axiom,
% 4.88/5.18 ! [Y: int,Z: int,Ya: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.88/5.18 => ( ( ord_less_eq_int @ Y @ Z )
% 4.88/5.18 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % AND_upper1'
% 4.88/5.18 thf(fact_8570_AND__upper2_H,axiom,
% 4.88/5.18 ! [Y: int,Z: int,X: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.88/5.18 => ( ( ord_less_eq_int @ Y @ Z )
% 4.88/5.18 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Z ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % AND_upper2'
% 4.88/5.18 thf(fact_8571_AND__upper2_H_H,axiom,
% 4.88/5.18 ! [Y: int,Z: int,X: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.88/5.18 => ( ( ord_less_int @ Y @ Z )
% 4.88/5.18 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Z ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % AND_upper2''
% 4.88/5.18 thf(fact_8572_AND__upper1_H_H,axiom,
% 4.88/5.18 ! [Y: int,Z: int,Ya: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.88/5.18 => ( ( ord_less_int @ Y @ Z )
% 4.88/5.18 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % AND_upper1''
% 4.88/5.18 thf(fact_8573_and__less__eq,axiom,
% 4.88/5.18 ! [L: int,K: int] :
% 4.88/5.18 ( ( ord_less_int @ L @ zero_zero_int )
% 4.88/5.18 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ K ) ) ).
% 4.88/5.18
% 4.88/5.18 % and_less_eq
% 4.88/5.18 thf(fact_8574_and__int_Osimps,axiom,
% 4.88/5.18 ( bit_se725231765392027082nd_int
% 4.88/5.18 = ( ^ [K3: int,L3: int] :
% 4.88/5.18 ( if_int
% 4.88/5.18 @ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 4.88/5.18 & ( member_int @ L3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 4.88/5.18 @ ( uminus_uminus_int
% 4.88/5.18 @ ( zero_n2684676970156552555ol_int
% 4.88/5.18 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 4.88/5.18 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L3 ) ) ) )
% 4.88/5.18 @ ( plus_plus_int
% 4.88/5.18 @ ( zero_n2684676970156552555ol_int
% 4.88/5.18 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 4.88/5.18 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L3 ) ) )
% 4.88/5.18 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % and_int.simps
% 4.88/5.18 thf(fact_8575_odd__mod__4__div__2,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 4.88/5.18 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 4.88/5.18 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % odd_mod_4_div_2
% 4.88/5.18 thf(fact_8576_Suc__0__xor__eq,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 4.88/5.18 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 4.88/5.18 @ ( zero_n2687167440665602831ol_nat
% 4.88/5.18 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Suc_0_xor_eq
% 4.88/5.18 thf(fact_8577_semiring__norm_I73_J,axiom,
% 4.88/5.18 ! [M2: num,N: num] :
% 4.88/5.18 ( ( ord_less_eq_num @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 4.88/5.18 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % semiring_norm(73)
% 4.88/5.18 thf(fact_8578_semiring__norm_I72_J,axiom,
% 4.88/5.18 ! [M2: num,N: num] :
% 4.88/5.18 ( ( ord_less_eq_num @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 4.88/5.18 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % semiring_norm(72)
% 4.88/5.18 thf(fact_8579_semiring__norm_I70_J,axiom,
% 4.88/5.18 ! [M2: num] :
% 4.88/5.18 ~ ( ord_less_eq_num @ ( bit1 @ M2 ) @ one ) ).
% 4.88/5.18
% 4.88/5.18 % semiring_norm(70)
% 4.88/5.18 thf(fact_8580_and__nat__numerals_I3_J,axiom,
% 4.88/5.18 ! [X: num] :
% 4.88/5.18 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 4.88/5.18 = zero_zero_nat ) ).
% 4.88/5.18
% 4.88/5.18 % and_nat_numerals(3)
% 4.88/5.18 thf(fact_8581_and__nat__numerals_I1_J,axiom,
% 4.88/5.18 ! [Y: num] :
% 4.88/5.18 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 4.88/5.18 = zero_zero_nat ) ).
% 4.88/5.18
% 4.88/5.18 % and_nat_numerals(1)
% 4.88/5.18 thf(fact_8582_semiring__norm_I79_J,axiom,
% 4.88/5.18 ! [M2: num,N: num] :
% 4.88/5.18 ( ( ord_less_num @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 4.88/5.18 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % semiring_norm(79)
% 4.88/5.18 thf(fact_8583_semiring__norm_I74_J,axiom,
% 4.88/5.18 ! [M2: num,N: num] :
% 4.88/5.18 ( ( ord_less_eq_num @ ( bit1 @ M2 ) @ ( bit0 @ N ) )
% 4.88/5.18 = ( ord_less_num @ M2 @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % semiring_norm(74)
% 4.88/5.18 thf(fact_8584_and__nat__numerals_I2_J,axiom,
% 4.88/5.18 ! [Y: num] :
% 4.88/5.18 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 4.88/5.18 = one_one_nat ) ).
% 4.88/5.18
% 4.88/5.18 % and_nat_numerals(2)
% 4.88/5.18 thf(fact_8585_and__nat__numerals_I4_J,axiom,
% 4.88/5.18 ! [X: num] :
% 4.88/5.18 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 4.88/5.18 = one_one_nat ) ).
% 4.88/5.18
% 4.88/5.18 % and_nat_numerals(4)
% 4.88/5.18 thf(fact_8586_Suc__0__and__eq,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 4.88/5.18 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Suc_0_and_eq
% 4.88/5.18 thf(fact_8587_and__Suc__0__eq,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 4.88/5.18 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % and_Suc_0_eq
% 4.88/5.18 thf(fact_8588_xor__nat__numerals_I4_J,axiom,
% 4.88/5.18 ! [X: num] :
% 4.88/5.18 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 4.88/5.18 = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % xor_nat_numerals(4)
% 4.88/5.18 thf(fact_8589_xor__nat__numerals_I3_J,axiom,
% 4.88/5.18 ! [X: num] :
% 4.88/5.18 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 4.88/5.18 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % xor_nat_numerals(3)
% 4.88/5.18 thf(fact_8590_xor__nat__numerals_I2_J,axiom,
% 4.88/5.18 ! [Y: num] :
% 4.88/5.18 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 4.88/5.18 = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % xor_nat_numerals(2)
% 4.88/5.18 thf(fact_8591_xor__nat__numerals_I1_J,axiom,
% 4.88/5.18 ! [Y: num] :
% 4.88/5.18 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 4.88/5.18 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % xor_nat_numerals(1)
% 4.88/5.18 thf(fact_8592_num_Oexhaust,axiom,
% 4.88/5.18 ! [Y: num] :
% 4.88/5.18 ( ( Y != one )
% 4.88/5.18 => ( ! [X24: num] :
% 4.88/5.18 ( Y
% 4.88/5.18 != ( bit0 @ X24 ) )
% 4.88/5.18 => ~ ! [X32: num] :
% 4.88/5.18 ( Y
% 4.88/5.18 != ( bit1 @ X32 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % num.exhaust
% 4.88/5.18 thf(fact_8593_eval__nat__numeral_I3_J,axiom,
% 4.88/5.18 ! [N: num] :
% 4.88/5.18 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 4.88/5.18 = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % eval_nat_numeral(3)
% 4.88/5.18 thf(fact_8594_numeral__3__eq__3,axiom,
% 4.88/5.18 ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 4.88/5.18 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % numeral_3_eq_3
% 4.88/5.18 thf(fact_8595_Suc3__eq__add__3,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( suc @ ( suc @ ( suc @ N ) ) )
% 4.88/5.18 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % Suc3_eq_add_3
% 4.88/5.18 thf(fact_8596_num_Osize__gen_I3_J,axiom,
% 4.88/5.18 ! [X33: num] :
% 4.88/5.18 ( ( size_num @ ( bit1 @ X33 ) )
% 4.88/5.18 = ( plus_plus_nat @ ( size_num @ X33 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % num.size_gen(3)
% 4.88/5.18 thf(fact_8597_num_Osize_I6_J,axiom,
% 4.88/5.18 ! [X33: num] :
% 4.88/5.18 ( ( size_size_num @ ( bit1 @ X33 ) )
% 4.88/5.18 = ( plus_plus_nat @ ( size_size_num @ X33 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % num.size(6)
% 4.88/5.18 thf(fact_8598_exp__le,axiom,
% 4.88/5.18 ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 4.88/5.18
% 4.88/5.18 % exp_le
% 4.88/5.18 thf(fact_8599_mod__exhaust__less__4,axiom,
% 4.88/5.18 ! [M2: nat] :
% 4.88/5.18 ( ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 4.88/5.18 = zero_zero_nat )
% 4.88/5.18 | ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 4.88/5.18 = one_one_nat )
% 4.88/5.18 | ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 4.88/5.18 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.88/5.18 | ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 4.88/5.18 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % mod_exhaust_less_4
% 4.88/5.18 thf(fact_8600_and__nat__unfold,axiom,
% 4.88/5.18 ( bit_se727722235901077358nd_nat
% 4.88/5.18 = ( ^ [M3: nat,N4: nat] :
% 4.88/5.18 ( if_nat
% 4.88/5.18 @ ( ( M3 = zero_zero_nat )
% 4.88/5.18 | ( N4 = zero_zero_nat ) )
% 4.88/5.18 @ zero_zero_nat
% 4.88/5.18 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % and_nat_unfold
% 4.88/5.18 thf(fact_8601_xor__nat__unfold,axiom,
% 4.88/5.18 ( bit_se6528837805403552850or_nat
% 4.88/5.18 = ( ^ [M3: nat,N4: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N4 @ ( if_nat @ ( N4 = zero_zero_nat ) @ M3 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % xor_nat_unfold
% 4.88/5.18 thf(fact_8602_xor__Suc__0__eq,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 4.88/5.18 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 4.88/5.18 @ ( zero_n2687167440665602831ol_nat
% 4.88/5.18 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % xor_Suc_0_eq
% 4.88/5.18 thf(fact_8603_tanh__real__le__iff,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( tanh_real @ X ) @ ( tanh_real @ Y ) )
% 4.88/5.18 = ( ord_less_eq_real @ X @ Y ) ) ).
% 4.88/5.18
% 4.88/5.18 % tanh_real_le_iff
% 4.88/5.18 thf(fact_8604_tanh__real__nonneg__iff,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ ( tanh_real @ X ) )
% 4.88/5.18 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 4.88/5.18
% 4.88/5.18 % tanh_real_nonneg_iff
% 4.88/5.18 thf(fact_8605_tanh__real__nonpos__iff,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( tanh_real @ X ) @ zero_zero_real )
% 4.88/5.18 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 4.88/5.18
% 4.88/5.18 % tanh_real_nonpos_iff
% 4.88/5.18 thf(fact_8606_xor__nonnegative__int__iff,axiom,
% 4.88/5.18 ! [K: int,L: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L ) )
% 4.88/5.18 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 4.88/5.18 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % xor_nonnegative_int_iff
% 4.88/5.18 thf(fact_8607_push__bit__nonnegative__int__iff,axiom,
% 4.88/5.18 ! [N: nat,K: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N @ K ) )
% 4.88/5.18 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 4.88/5.18
% 4.88/5.18 % push_bit_nonnegative_int_iff
% 4.88/5.18 thf(fact_8608_pred__numeral__simps_I1_J,axiom,
% 4.88/5.18 ( ( pred_numeral @ one )
% 4.88/5.18 = zero_zero_nat ) ).
% 4.88/5.18
% 4.88/5.18 % pred_numeral_simps(1)
% 4.88/5.18 thf(fact_8609_Suc__eq__numeral,axiom,
% 4.88/5.18 ! [N: nat,K: num] :
% 4.88/5.18 ( ( ( suc @ N )
% 4.88/5.18 = ( numeral_numeral_nat @ K ) )
% 4.88/5.18 = ( N
% 4.88/5.18 = ( pred_numeral @ K ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Suc_eq_numeral
% 4.88/5.18 thf(fact_8610_eq__numeral__Suc,axiom,
% 4.88/5.18 ! [K: num,N: nat] :
% 4.88/5.18 ( ( ( numeral_numeral_nat @ K )
% 4.88/5.18 = ( suc @ N ) )
% 4.88/5.18 = ( ( pred_numeral @ K )
% 4.88/5.18 = N ) ) ).
% 4.88/5.18
% 4.88/5.18 % eq_numeral_Suc
% 4.88/5.18 thf(fact_8611_less__Suc__numeral,axiom,
% 4.88/5.18 ! [N: nat,K: num] :
% 4.88/5.18 ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 4.88/5.18 = ( ord_less_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % less_Suc_numeral
% 4.88/5.18 thf(fact_8612_less__numeral__Suc,axiom,
% 4.88/5.18 ! [K: num,N: nat] :
% 4.88/5.18 ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 4.88/5.18 = ( ord_less_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % less_numeral_Suc
% 4.88/5.18 thf(fact_8613_pred__numeral__simps_I3_J,axiom,
% 4.88/5.18 ! [K: num] :
% 4.88/5.18 ( ( pred_numeral @ ( bit1 @ K ) )
% 4.88/5.18 = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % pred_numeral_simps(3)
% 4.88/5.18 thf(fact_8614_le__numeral__Suc,axiom,
% 4.88/5.18 ! [K: num,N: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 4.88/5.18 = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % le_numeral_Suc
% 4.88/5.18 thf(fact_8615_le__Suc__numeral,axiom,
% 4.88/5.18 ! [N: nat,K: num] :
% 4.88/5.18 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 4.88/5.18 = ( ord_less_eq_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % le_Suc_numeral
% 4.88/5.18 thf(fact_8616_diff__Suc__numeral,axiom,
% 4.88/5.18 ! [N: nat,K: num] :
% 4.88/5.18 ( ( minus_minus_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 4.88/5.18 = ( minus_minus_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % diff_Suc_numeral
% 4.88/5.18 thf(fact_8617_diff__numeral__Suc,axiom,
% 4.88/5.18 ! [K: num,N: nat] :
% 4.88/5.18 ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 4.88/5.18 = ( minus_minus_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % diff_numeral_Suc
% 4.88/5.18 thf(fact_8618_max__numeral__Suc,axiom,
% 4.88/5.18 ! [K: num,N: nat] :
% 4.88/5.18 ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 4.88/5.18 = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % max_numeral_Suc
% 4.88/5.18 thf(fact_8619_max__Suc__numeral,axiom,
% 4.88/5.18 ! [N: nat,K: num] :
% 4.88/5.18 ( ( ord_max_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 4.88/5.18 = ( suc @ ( ord_max_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % max_Suc_numeral
% 4.88/5.18 thf(fact_8620_push__bit__of__Suc__0,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 4.88/5.18 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % push_bit_of_Suc_0
% 4.88/5.18 thf(fact_8621_XOR__lower,axiom,
% 4.88/5.18 ! [X: int,Y: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 4.88/5.18 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.88/5.18 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X @ Y ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % XOR_lower
% 4.88/5.18 thf(fact_8622_numeral__eq__Suc,axiom,
% 4.88/5.18 ( numeral_numeral_nat
% 4.88/5.18 = ( ^ [K3: num] : ( suc @ ( pred_numeral @ K3 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % numeral_eq_Suc
% 4.88/5.18 thf(fact_8623_flip__bit__nat__def,axiom,
% 4.88/5.18 ( bit_se2161824704523386999it_nat
% 4.88/5.18 = ( ^ [M3: nat,N4: nat] : ( bit_se6528837805403552850or_nat @ N4 @ ( bit_se547839408752420682it_nat @ M3 @ one_one_nat ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % flip_bit_nat_def
% 4.88/5.18 thf(fact_8624_pred__numeral__def,axiom,
% 4.88/5.18 ( pred_numeral
% 4.88/5.18 = ( ^ [K3: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K3 ) @ one_one_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % pred_numeral_def
% 4.88/5.18 thf(fact_8625_lessThan__nat__numeral,axiom,
% 4.88/5.18 ! [K: num] :
% 4.88/5.18 ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 4.88/5.18 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % lessThan_nat_numeral
% 4.88/5.18 thf(fact_8626_atMost__nat__numeral,axiom,
% 4.88/5.18 ! [K: num] :
% 4.88/5.18 ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 4.88/5.18 = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % atMost_nat_numeral
% 4.88/5.18 thf(fact_8627_XOR__upper,axiom,
% 4.88/5.18 ! [X: int,N: nat,Y: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 4.88/5.18 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 4.88/5.18 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 4.88/5.18 => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % XOR_upper
% 4.88/5.18 thf(fact_8628_or__nat__unfold,axiom,
% 4.88/5.18 ( bit_se1412395901928357646or_nat
% 4.88/5.18 = ( ^ [M3: nat,N4: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N4 @ ( if_nat @ ( N4 = zero_zero_nat ) @ M3 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % or_nat_unfold
% 4.88/5.18 thf(fact_8629_Sum__Ico__nat,axiom,
% 4.88/5.18 ! [M2: nat,N: nat] :
% 4.88/5.18 ( ( groups3542108847815614940at_nat
% 4.88/5.18 @ ^ [X3: nat] : X3
% 4.88/5.18 @ ( set_or4665077453230672383an_nat @ M2 @ N ) )
% 4.88/5.18 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M2 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Sum_Ico_nat
% 4.88/5.18 thf(fact_8630_Least__eq__0,axiom,
% 4.88/5.18 ! [P: nat > $o] :
% 4.88/5.18 ( ( P @ zero_zero_nat )
% 4.88/5.18 => ( ( ord_Least_nat @ P )
% 4.88/5.18 = zero_zero_nat ) ) ).
% 4.88/5.18
% 4.88/5.18 % Least_eq_0
% 4.88/5.18 thf(fact_8631_mask__nat__positive__iff,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 4.88/5.18 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % mask_nat_positive_iff
% 4.88/5.18 thf(fact_8632_finite__atLeastLessThan,axiom,
% 4.88/5.18 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or4665077453230672383an_nat @ L @ U ) ) ).
% 4.88/5.18
% 4.88/5.18 % finite_atLeastLessThan
% 4.88/5.18 thf(fact_8633_card__atLeastLessThan,axiom,
% 4.88/5.18 ! [L: nat,U: nat] :
% 4.88/5.18 ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 4.88/5.18 = ( minus_minus_nat @ U @ L ) ) ).
% 4.88/5.18
% 4.88/5.18 % card_atLeastLessThan
% 4.88/5.18 thf(fact_8634_atLeastLessThan__singleton,axiom,
% 4.88/5.18 ! [M2: nat] :
% 4.88/5.18 ( ( set_or4665077453230672383an_nat @ M2 @ ( suc @ M2 ) )
% 4.88/5.18 = ( insert_nat @ M2 @ bot_bot_set_nat ) ) ).
% 4.88/5.18
% 4.88/5.18 % atLeastLessThan_singleton
% 4.88/5.18 thf(fact_8635_or__nat__numerals_I4_J,axiom,
% 4.88/5.18 ! [X: num] :
% 4.88/5.18 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 4.88/5.18 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % or_nat_numerals(4)
% 4.88/5.18 thf(fact_8636_or__nat__numerals_I2_J,axiom,
% 4.88/5.18 ! [Y: num] :
% 4.88/5.18 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 4.88/5.18 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % or_nat_numerals(2)
% 4.88/5.18 thf(fact_8637_or__nat__numerals_I3_J,axiom,
% 4.88/5.18 ! [X: num] :
% 4.88/5.18 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 4.88/5.18 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % or_nat_numerals(3)
% 4.88/5.18 thf(fact_8638_or__nat__numerals_I1_J,axiom,
% 4.88/5.18 ! [Y: num] :
% 4.88/5.18 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 4.88/5.18 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % or_nat_numerals(1)
% 4.88/5.18 thf(fact_8639_set__bit__nat__def,axiom,
% 4.88/5.18 ( bit_se7882103937844011126it_nat
% 4.88/5.18 = ( ^ [M3: nat,N4: nat] : ( bit_se1412395901928357646or_nat @ N4 @ ( bit_se547839408752420682it_nat @ M3 @ one_one_nat ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % set_bit_nat_def
% 4.88/5.18 thf(fact_8640_less__eq__mask,axiom,
% 4.88/5.18 ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % less_eq_mask
% 4.88/5.18 thf(fact_8641_all__nat__less__eq,axiom,
% 4.88/5.18 ! [N: nat,P: nat > $o] :
% 4.88/5.18 ( ( ! [M3: nat] :
% 4.88/5.18 ( ( ord_less_nat @ M3 @ N )
% 4.88/5.18 => ( P @ M3 ) ) )
% 4.88/5.18 = ( ! [X3: nat] :
% 4.88/5.18 ( ( member_nat @ X3 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 4.88/5.18 => ( P @ X3 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % all_nat_less_eq
% 4.88/5.18 thf(fact_8642_ex__nat__less__eq,axiom,
% 4.88/5.18 ! [N: nat,P: nat > $o] :
% 4.88/5.18 ( ( ? [M3: nat] :
% 4.88/5.18 ( ( ord_less_nat @ M3 @ N )
% 4.88/5.18 & ( P @ M3 ) ) )
% 4.88/5.18 = ( ? [X3: nat] :
% 4.88/5.18 ( ( member_nat @ X3 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 4.88/5.18 & ( P @ X3 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % ex_nat_less_eq
% 4.88/5.18 thf(fact_8643_atLeastLessThanSuc__atLeastAtMost,axiom,
% 4.88/5.18 ! [L: nat,U: nat] :
% 4.88/5.18 ( ( set_or4665077453230672383an_nat @ L @ ( suc @ U ) )
% 4.88/5.18 = ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 4.88/5.18
% 4.88/5.18 % atLeastLessThanSuc_atLeastAtMost
% 4.88/5.18 thf(fact_8644_lessThan__atLeast0,axiom,
% 4.88/5.18 ( set_ord_lessThan_nat
% 4.88/5.18 = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 4.88/5.18
% 4.88/5.18 % lessThan_atLeast0
% 4.88/5.18 thf(fact_8645_atLeastLessThan0,axiom,
% 4.88/5.18 ! [M2: nat] :
% 4.88/5.18 ( ( set_or4665077453230672383an_nat @ M2 @ zero_zero_nat )
% 4.88/5.18 = bot_bot_set_nat ) ).
% 4.88/5.18
% 4.88/5.18 % atLeastLessThan0
% 4.88/5.18 thf(fact_8646_mask__nonnegative__int,axiom,
% 4.88/5.18 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % mask_nonnegative_int
% 4.88/5.18 thf(fact_8647_Least__Suc2,axiom,
% 4.88/5.18 ! [P: nat > $o,N: nat,Q: nat > $o,M2: nat] :
% 4.88/5.18 ( ( P @ N )
% 4.88/5.18 => ( ( Q @ M2 )
% 4.88/5.18 => ( ~ ( P @ zero_zero_nat )
% 4.88/5.18 => ( ! [K2: nat] :
% 4.88/5.18 ( ( P @ ( suc @ K2 ) )
% 4.88/5.18 = ( Q @ K2 ) )
% 4.88/5.18 => ( ( ord_Least_nat @ P )
% 4.88/5.18 = ( suc @ ( ord_Least_nat @ Q ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Least_Suc2
% 4.88/5.18 thf(fact_8648_Least__Suc,axiom,
% 4.88/5.18 ! [P: nat > $o,N: nat] :
% 4.88/5.18 ( ( P @ N )
% 4.88/5.18 => ( ~ ( P @ zero_zero_nat )
% 4.88/5.18 => ( ( ord_Least_nat @ P )
% 4.88/5.18 = ( suc
% 4.88/5.18 @ ( ord_Least_nat
% 4.88/5.18 @ ^ [M3: nat] : ( P @ ( suc @ M3 ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Least_Suc
% 4.88/5.18 thf(fact_8649_atLeast0__lessThan__Suc,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 4.88/5.18 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % atLeast0_lessThan_Suc
% 4.88/5.18 thf(fact_8650_less__mask,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 4.88/5.18 => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % less_mask
% 4.88/5.18 thf(fact_8651_subset__eq__atLeast0__lessThan__finite,axiom,
% 4.88/5.18 ! [N5: set_nat,N: nat] :
% 4.88/5.18 ( ( ord_less_eq_set_nat @ N5 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 4.88/5.18 => ( finite_finite_nat @ N5 ) ) ).
% 4.88/5.18
% 4.88/5.18 % subset_eq_atLeast0_lessThan_finite
% 4.88/5.18 thf(fact_8652_subset__card__intvl__is__intvl,axiom,
% 4.88/5.18 ! [A2: set_nat,K: nat] :
% 4.88/5.18 ( ( ord_less_eq_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) )
% 4.88/5.18 => ( A2
% 4.88/5.18 = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % subset_card_intvl_is_intvl
% 4.88/5.18 thf(fact_8653_atLeastLessThanSuc,axiom,
% 4.88/5.18 ! [M2: nat,N: nat] :
% 4.88/5.18 ( ( ( ord_less_eq_nat @ M2 @ N )
% 4.88/5.18 => ( ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N ) )
% 4.88/5.18 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M2 @ N ) ) ) )
% 4.88/5.18 & ( ~ ( ord_less_eq_nat @ M2 @ N )
% 4.88/5.18 => ( ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N ) )
% 4.88/5.18 = bot_bot_set_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % atLeastLessThanSuc
% 4.88/5.18 thf(fact_8654_prod__Suc__Suc__fact,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 4.88/5.18 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % prod_Suc_Suc_fact
% 4.88/5.18 thf(fact_8655_prod__Suc__fact,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 4.88/5.18 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % prod_Suc_fact
% 4.88/5.18 thf(fact_8656_subset__eq__atLeast0__lessThan__card,axiom,
% 4.88/5.18 ! [N5: set_nat,N: nat] :
% 4.88/5.18 ( ( ord_less_eq_set_nat @ N5 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 4.88/5.18 => ( ord_less_eq_nat @ ( finite_card_nat @ N5 ) @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % subset_eq_atLeast0_lessThan_card
% 4.88/5.18 thf(fact_8657_card__sum__le__nat__sum,axiom,
% 4.88/5.18 ! [S2: set_nat] :
% 4.88/5.18 ( ord_less_eq_nat
% 4.88/5.18 @ ( groups3542108847815614940at_nat
% 4.88/5.18 @ ^ [X3: nat] : X3
% 4.88/5.18 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S2 ) ) )
% 4.88/5.18 @ ( groups3542108847815614940at_nat
% 4.88/5.18 @ ^ [X3: nat] : X3
% 4.88/5.18 @ S2 ) ) ).
% 4.88/5.18
% 4.88/5.18 % card_sum_le_nat_sum
% 4.88/5.18 thf(fact_8658_atLeastLessThan__nat__numeral,axiom,
% 4.88/5.18 ! [M2: nat,K: num] :
% 4.88/5.18 ( ( ( ord_less_eq_nat @ M2 @ ( pred_numeral @ K ) )
% 4.88/5.18 => ( ( set_or4665077453230672383an_nat @ M2 @ ( numeral_numeral_nat @ K ) )
% 4.88/5.18 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M2 @ ( pred_numeral @ K ) ) ) ) )
% 4.88/5.18 & ( ~ ( ord_less_eq_nat @ M2 @ ( pred_numeral @ K ) )
% 4.88/5.18 => ( ( set_or4665077453230672383an_nat @ M2 @ ( numeral_numeral_nat @ K ) )
% 4.88/5.18 = bot_bot_set_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % atLeastLessThan_nat_numeral
% 4.88/5.18 thf(fact_8659_mask__nat__less__exp,axiom,
% 4.88/5.18 ! [N: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % mask_nat_less_exp
% 4.88/5.18 thf(fact_8660_mask__nat__def,axiom,
% 4.88/5.18 ( bit_se2002935070580805687sk_nat
% 4.88/5.18 = ( ^ [N4: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % mask_nat_def
% 4.88/5.18 thf(fact_8661_mask__half__int,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.88/5.18 = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % mask_half_int
% 4.88/5.18 thf(fact_8662_atLeast1__lessThan__eq__remove0,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 4.88/5.18 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % atLeast1_lessThan_eq_remove0
% 4.88/5.18 thf(fact_8663_Suc__0__or__eq,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 4.88/5.18 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Suc_0_or_eq
% 4.88/5.18 thf(fact_8664_or__Suc__0__eq,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 4.88/5.18 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % or_Suc_0_eq
% 4.88/5.18 thf(fact_8665_sum__power2,axiom,
% 4.88/5.18 ! [K: nat] :
% 4.88/5.18 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 4.88/5.18 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 4.88/5.18
% 4.88/5.18 % sum_power2
% 4.88/5.18 thf(fact_8666_Chebyshev__sum__upper__nat,axiom,
% 4.88/5.18 ! [N: nat,A: nat > nat,B: nat > nat] :
% 4.88/5.18 ( ! [I2: nat,J2: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ I2 @ J2 )
% 4.88/5.18 => ( ( ord_less_nat @ J2 @ N )
% 4.88/5.18 => ( ord_less_eq_nat @ ( A @ I2 ) @ ( A @ J2 ) ) ) )
% 4.88/5.18 => ( ! [I2: nat,J2: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ I2 @ J2 )
% 4.88/5.18 => ( ( ord_less_nat @ J2 @ N )
% 4.88/5.18 => ( ord_less_eq_nat @ ( B @ J2 ) @ ( B @ I2 ) ) ) )
% 4.88/5.18 => ( ord_less_eq_nat
% 4.88/5.18 @ ( times_times_nat @ N
% 4.88/5.18 @ ( groups3542108847815614940at_nat
% 4.88/5.18 @ ^ [I4: nat] : ( times_times_nat @ ( A @ I4 ) @ ( B @ I4 ) )
% 4.88/5.18 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 4.88/5.18 @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Chebyshev_sum_upper_nat
% 4.88/5.18 thf(fact_8667_VEBT_Osize__gen_I1_J,axiom,
% 4.88/5.18 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 4.88/5.18 ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 4.88/5.18 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % VEBT.size_gen(1)
% 4.88/5.18 thf(fact_8668_VEBT_Osize_I3_J,axiom,
% 4.88/5.18 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 4.88/5.18 ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 4.88/5.18 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % VEBT.size(3)
% 4.88/5.18 thf(fact_8669_finite__atLeastLessThan__int,axiom,
% 4.88/5.18 ! [L: int,U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 4.88/5.18
% 4.88/5.18 % finite_atLeastLessThan_int
% 4.88/5.18 thf(fact_8670_or__nonnegative__int__iff,axiom,
% 4.88/5.18 ! [K: int,L: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L ) )
% 4.88/5.18 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 4.88/5.18 & ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % or_nonnegative_int_iff
% 4.88/5.18 thf(fact_8671_card__atLeastLessThan__int,axiom,
% 4.88/5.18 ! [L: int,U: int] :
% 4.88/5.18 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L @ U ) )
% 4.88/5.18 = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % card_atLeastLessThan_int
% 4.88/5.18 thf(fact_8672_OR__lower,axiom,
% 4.88/5.18 ! [X: int,Y: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 4.88/5.18 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.88/5.18 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X @ Y ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % OR_lower
% 4.88/5.18 thf(fact_8673_or__greater__eq,axiom,
% 4.88/5.18 ! [L: int,K: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 4.88/5.18 => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % or_greater_eq
% 4.88/5.18 thf(fact_8674_finite__atLeastZeroLessThan__int,axiom,
% 4.88/5.18 ! [U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) ) ).
% 4.88/5.18
% 4.88/5.18 % finite_atLeastZeroLessThan_int
% 4.88/5.18 thf(fact_8675_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 4.88/5.18 ! [L: int,U: int] :
% 4.88/5.18 ( ( set_or4662586982721622107an_int @ L @ ( plus_plus_int @ U @ one_one_int ) )
% 4.88/5.18 = ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 4.88/5.18
% 4.88/5.18 % atLeastLessThanPlusOne_atLeastAtMost_int
% 4.88/5.18 thf(fact_8676_card__atLeastZeroLessThan__int,axiom,
% 4.88/5.18 ! [U: int] :
% 4.88/5.18 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) )
% 4.88/5.18 = ( nat2 @ U ) ) ).
% 4.88/5.18
% 4.88/5.18 % card_atLeastZeroLessThan_int
% 4.88/5.18 thf(fact_8677_OR__upper,axiom,
% 4.88/5.18 ! [X: int,N: nat,Y: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 4.88/5.18 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 4.88/5.18 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 4.88/5.18 => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % OR_upper
% 4.88/5.18 thf(fact_8678_divmod__step__integer__def,axiom,
% 4.88/5.18 ( unique4921790084139445826nteger
% 4.88/5.18 = ( ^ [L3: num] :
% 4.88/5.18 ( produc6916734918728496179nteger
% 4.88/5.18 @ ^ [Q3: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L3 ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L3 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ R5 ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % divmod_step_integer_def
% 4.88/5.18 thf(fact_8679_less__eq__integer__code_I1_J,axiom,
% 4.88/5.18 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 4.88/5.18
% 4.88/5.18 % less_eq_integer_code(1)
% 4.88/5.18 thf(fact_8680_zero__natural_Orsp,axiom,
% 4.88/5.18 zero_zero_nat = zero_zero_nat ).
% 4.88/5.18
% 4.88/5.18 % zero_natural.rsp
% 4.88/5.18 thf(fact_8681_one__natural_Orsp,axiom,
% 4.88/5.18 one_one_nat = one_one_nat ).
% 4.88/5.18
% 4.88/5.18 % one_natural.rsp
% 4.88/5.18 thf(fact_8682_binomial__def,axiom,
% 4.88/5.18 ( binomial
% 4.88/5.18 = ( ^ [N4: nat,K3: nat] :
% 4.88/5.18 ( finite_card_set_nat
% 4.88/5.18 @ ( collect_set_nat
% 4.88/5.18 @ ^ [K5: set_nat] :
% 4.88/5.18 ( ( member_set_nat @ K5 @ ( pow_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N4 ) ) )
% 4.88/5.18 & ( ( finite_card_nat @ K5 )
% 4.88/5.18 = K3 ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % binomial_def
% 4.88/5.18 thf(fact_8683_finite__enumerate,axiom,
% 4.88/5.18 ! [S2: set_nat] :
% 4.88/5.18 ( ( finite_finite_nat @ S2 )
% 4.88/5.18 => ? [R4: nat > nat] :
% 4.88/5.18 ( ( strict1292158309912662752at_nat @ R4 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S2 ) ) )
% 4.88/5.18 & ! [N6: nat] :
% 4.88/5.18 ( ( ord_less_nat @ N6 @ ( finite_card_nat @ S2 ) )
% 4.88/5.18 => ( member_nat @ ( R4 @ N6 ) @ S2 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % finite_enumerate
% 4.88/5.18 thf(fact_8684_nat_Odisc__eq__case_I1_J,axiom,
% 4.88/5.18 ! [Nat: nat] :
% 4.88/5.18 ( ( Nat = zero_zero_nat )
% 4.88/5.18 = ( case_nat_o @ $true
% 4.88/5.18 @ ^ [Uu3: nat] : $false
% 4.88/5.18 @ Nat ) ) ).
% 4.88/5.18
% 4.88/5.18 % nat.disc_eq_case(1)
% 4.88/5.18 thf(fact_8685_nat_Odisc__eq__case_I2_J,axiom,
% 4.88/5.18 ! [Nat: nat] :
% 4.88/5.18 ( ( Nat != zero_zero_nat )
% 4.88/5.18 = ( case_nat_o @ $false
% 4.88/5.18 @ ^ [Uu3: nat] : $true
% 4.88/5.18 @ Nat ) ) ).
% 4.88/5.18
% 4.88/5.18 % nat.disc_eq_case(2)
% 4.88/5.18 thf(fact_8686_less__eq__nat_Osimps_I2_J,axiom,
% 4.88/5.18 ! [M2: nat,N: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 4.88/5.18 = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M2 ) @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % less_eq_nat.simps(2)
% 4.88/5.18 thf(fact_8687_max__Suc2,axiom,
% 4.88/5.18 ! [M2: nat,N: nat] :
% 4.88/5.18 ( ( ord_max_nat @ M2 @ ( suc @ N ) )
% 4.88/5.18 = ( case_nat_nat @ ( suc @ N )
% 4.88/5.18 @ ^ [M6: nat] : ( suc @ ( ord_max_nat @ M6 @ N ) )
% 4.88/5.18 @ M2 ) ) ).
% 4.88/5.18
% 4.88/5.18 % max_Suc2
% 4.88/5.18 thf(fact_8688_max__Suc1,axiom,
% 4.88/5.18 ! [N: nat,M2: nat] :
% 4.88/5.18 ( ( ord_max_nat @ ( suc @ N ) @ M2 )
% 4.88/5.18 = ( case_nat_nat @ ( suc @ N )
% 4.88/5.18 @ ^ [M6: nat] : ( suc @ ( ord_max_nat @ N @ M6 ) )
% 4.88/5.18 @ M2 ) ) ).
% 4.88/5.18
% 4.88/5.18 % max_Suc1
% 4.88/5.18 thf(fact_8689_diff__Suc,axiom,
% 4.88/5.18 ! [M2: nat,N: nat] :
% 4.88/5.18 ( ( minus_minus_nat @ M2 @ ( suc @ N ) )
% 4.88/5.18 = ( case_nat_nat @ zero_zero_nat
% 4.88/5.18 @ ^ [K3: nat] : K3
% 4.88/5.18 @ ( minus_minus_nat @ M2 @ N ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % diff_Suc
% 4.88/5.18 thf(fact_8690_num__of__integer__code,axiom,
% 4.88/5.18 ( code_num_of_integer
% 4.88/5.18 = ( ^ [K3: code_integer] :
% 4.88/5.18 ( if_num @ ( ord_le3102999989581377725nteger @ K3 @ one_one_Code_integer ) @ one
% 4.88/5.18 @ ( produc7336495610019696514er_num
% 4.88/5.18 @ ^ [L3: code_integer,J3: code_integer] : ( if_num @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L3 ) @ ( code_num_of_integer @ L3 ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L3 ) @ ( code_num_of_integer @ L3 ) ) @ one ) )
% 4.88/5.18 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % num_of_integer_code
% 4.88/5.18 thf(fact_8691_pred__def,axiom,
% 4.88/5.18 ( pred
% 4.88/5.18 = ( case_nat_nat @ zero_zero_nat
% 4.88/5.18 @ ^ [X25: nat] : X25 ) ) ).
% 4.88/5.18
% 4.88/5.18 % pred_def
% 4.88/5.18 thf(fact_8692_Sup__nat__empty,axiom,
% 4.88/5.18 ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 4.88/5.18 = zero_zero_nat ) ).
% 4.88/5.18
% 4.88/5.18 % Sup_nat_empty
% 4.88/5.18 thf(fact_8693_Inf__nat__def1,axiom,
% 4.88/5.18 ! [K4: set_nat] :
% 4.88/5.18 ( ( K4 != bot_bot_set_nat )
% 4.88/5.18 => ( member_nat @ ( complete_Inf_Inf_nat @ K4 ) @ K4 ) ) ).
% 4.88/5.18
% 4.88/5.18 % Inf_nat_def1
% 4.88/5.18 thf(fact_8694_nat__of__integer__code,axiom,
% 4.88/5.18 ( code_nat_of_integer
% 4.88/5.18 = ( ^ [K3: code_integer] :
% 4.88/5.18 ( if_nat @ ( ord_le3102999989581377725nteger @ K3 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 4.88/5.18 @ ( produc1555791787009142072er_nat
% 4.88/5.18 @ ^ [L3: code_integer,J3: code_integer] : ( if_nat @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L3 ) @ ( code_nat_of_integer @ L3 ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L3 ) @ ( code_nat_of_integer @ L3 ) ) @ one_one_nat ) )
% 4.88/5.18 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % nat_of_integer_code
% 4.88/5.18 thf(fact_8695_drop__bit__nonnegative__int__iff,axiom,
% 4.88/5.18 ! [N: nat,K: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N @ K ) )
% 4.88/5.18 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 4.88/5.18
% 4.88/5.18 % drop_bit_nonnegative_int_iff
% 4.88/5.18 thf(fact_8696_drop__bit__of__Suc__0,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 4.88/5.18 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % drop_bit_of_Suc_0
% 4.88/5.18 thf(fact_8697_nat__of__integer__non__positive,axiom,
% 4.88/5.18 ! [K: code_integer] :
% 4.88/5.18 ( ( ord_le3102999989581377725nteger @ K @ zero_z3403309356797280102nteger )
% 4.88/5.18 => ( ( code_nat_of_integer @ K )
% 4.88/5.18 = zero_zero_nat ) ) ).
% 4.88/5.18
% 4.88/5.18 % nat_of_integer_non_positive
% 4.88/5.18 thf(fact_8698_nat__of__integer__code__post_I1_J,axiom,
% 4.88/5.18 ( ( code_nat_of_integer @ zero_z3403309356797280102nteger )
% 4.88/5.18 = zero_zero_nat ) ).
% 4.88/5.18
% 4.88/5.18 % nat_of_integer_code_post(1)
% 4.88/5.18 thf(fact_8699_nat__of__integer__code__post_I2_J,axiom,
% 4.88/5.18 ( ( code_nat_of_integer @ one_one_Code_integer )
% 4.88/5.18 = one_one_nat ) ).
% 4.88/5.18
% 4.88/5.18 % nat_of_integer_code_post(2)
% 4.88/5.18 thf(fact_8700_card__greaterThanLessThan__int,axiom,
% 4.88/5.18 ! [L: int,U: int] :
% 4.88/5.18 ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L @ U ) )
% 4.88/5.18 = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L @ one_one_int ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % card_greaterThanLessThan_int
% 4.88/5.18 thf(fact_8701_finite__greaterThanLessThan__int,axiom,
% 4.88/5.18 ! [L: int,U: int] : ( finite_finite_int @ ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 4.88/5.18
% 4.88/5.18 % finite_greaterThanLessThan_int
% 4.88/5.18 thf(fact_8702_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 4.88/5.18 ! [L: int,U: int] :
% 4.88/5.18 ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 4.88/5.18 = ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 4.88/5.18
% 4.88/5.18 % atLeastPlusOneLessThan_greaterThanLessThan_int
% 4.88/5.18 thf(fact_8703_finite__greaterThanLessThan,axiom,
% 4.88/5.18 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 4.88/5.18
% 4.88/5.18 % finite_greaterThanLessThan
% 4.88/5.18 thf(fact_8704_Suc__funpow,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( compow_nat_nat @ N @ suc )
% 4.88/5.18 = ( plus_plus_nat @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % Suc_funpow
% 4.88/5.18 thf(fact_8705_signed__take__bit__nonnegative__iff,axiom,
% 4.88/5.18 ! [N: nat,K: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 4.88/5.18 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % signed_take_bit_nonnegative_iff
% 4.88/5.18 thf(fact_8706_card__greaterThanLessThan,axiom,
% 4.88/5.18 ! [L: nat,U: nat] :
% 4.88/5.18 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 4.88/5.18 = ( minus_minus_nat @ U @ ( suc @ L ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % card_greaterThanLessThan
% 4.88/5.18 thf(fact_8707_bit__nat__iff,axiom,
% 4.88/5.18 ! [K: int,N: nat] :
% 4.88/5.18 ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N )
% 4.88/5.18 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 4.88/5.18 & ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % bit_nat_iff
% 4.88/5.18 thf(fact_8708_bit__Suc__0__iff,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 4.88/5.18 = ( N = zero_zero_nat ) ) ).
% 4.88/5.18
% 4.88/5.18 % bit_Suc_0_iff
% 4.88/5.18 thf(fact_8709_not__bit__Suc__0__Suc,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % not_bit_Suc_0_Suc
% 4.88/5.18 thf(fact_8710_atLeastSucLessThan__greaterThanLessThan,axiom,
% 4.88/5.18 ! [L: nat,U: nat] :
% 4.88/5.18 ( ( set_or4665077453230672383an_nat @ ( suc @ L ) @ U )
% 4.88/5.18 = ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 4.88/5.18
% 4.88/5.18 % atLeastSucLessThan_greaterThanLessThan
% 4.88/5.18 thf(fact_8711_not__bit__Suc__0__numeral,axiom,
% 4.88/5.18 ! [N: num] :
% 4.88/5.18 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % not_bit_Suc_0_numeral
% 4.88/5.18 thf(fact_8712_bit__push__bit__iff__int,axiom,
% 4.88/5.18 ! [M2: nat,K: int,N: nat] :
% 4.88/5.18 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M2 @ K ) @ N )
% 4.88/5.18 = ( ( ord_less_eq_nat @ M2 @ N )
% 4.88/5.18 & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ M2 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % bit_push_bit_iff_int
% 4.88/5.18 thf(fact_8713_bit__push__bit__iff__nat,axiom,
% 4.88/5.18 ! [M2: nat,Q4: nat,N: nat] :
% 4.88/5.18 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M2 @ Q4 ) @ N )
% 4.88/5.18 = ( ( ord_less_eq_nat @ M2 @ N )
% 4.88/5.18 & ( bit_se1148574629649215175it_nat @ Q4 @ ( minus_minus_nat @ N @ M2 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % bit_push_bit_iff_nat
% 4.88/5.18 thf(fact_8714_bit__imp__take__bit__positive,axiom,
% 4.88/5.18 ! [N: nat,M2: nat,K: int] :
% 4.88/5.18 ( ( ord_less_nat @ N @ M2 )
% 4.88/5.18 => ( ( bit_se1146084159140164899it_int @ K @ N )
% 4.88/5.18 => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M2 @ K ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % bit_imp_take_bit_positive
% 4.88/5.18 thf(fact_8715_int__bit__bound,axiom,
% 4.88/5.18 ! [K: int] :
% 4.88/5.18 ~ ! [N2: nat] :
% 4.88/5.18 ( ! [M: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ N2 @ M )
% 4.88/5.18 => ( ( bit_se1146084159140164899it_int @ K @ M )
% 4.88/5.18 = ( bit_se1146084159140164899it_int @ K @ N2 ) ) )
% 4.88/5.18 => ~ ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.88/5.18 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 4.88/5.18 = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % int_bit_bound
% 4.88/5.18 thf(fact_8716_upto_Opelims,axiom,
% 4.88/5.18 ! [X: int,Xa2: int,Y: list_int] :
% 4.88/5.18 ( ( ( upto @ X @ Xa2 )
% 4.88/5.18 = Y )
% 4.88/5.18 => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 4.88/5.18 => ~ ( ( ( ( ord_less_eq_int @ X @ Xa2 )
% 4.88/5.18 => ( Y
% 4.88/5.18 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa2 ) ) ) )
% 4.88/5.18 & ( ~ ( ord_less_eq_int @ X @ Xa2 )
% 4.88/5.18 => ( Y = nil_int ) ) )
% 4.88/5.18 => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % upto.pelims
% 4.88/5.18 thf(fact_8717_upto_Opsimps,axiom,
% 4.88/5.18 ! [I: int,J: int] :
% 4.88/5.18 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I @ J ) )
% 4.88/5.18 => ( ( ( ord_less_eq_int @ I @ J )
% 4.88/5.18 => ( ( upto @ I @ J )
% 4.88/5.18 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) )
% 4.88/5.18 & ( ~ ( ord_less_eq_int @ I @ J )
% 4.88/5.18 => ( ( upto @ I @ J )
% 4.88/5.18 = nil_int ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % upto.psimps
% 4.88/5.18 thf(fact_8718_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 4.88/5.18 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 4.88/5.18 @ ^ [X3: nat,Y2: nat] : ( ord_less_eq_nat @ Y2 @ X3 )
% 4.88/5.18 @ ^ [X3: nat,Y2: nat] : ( ord_less_nat @ Y2 @ X3 ) ) ).
% 4.88/5.18
% 4.88/5.18 % max_nat.semilattice_neutr_order_axioms
% 4.88/5.18 thf(fact_8719_nth__upto,axiom,
% 4.88/5.18 ! [I: int,K: nat,J: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 4.88/5.18 => ( ( nth_int @ ( upto @ I @ J ) @ K )
% 4.88/5.18 = ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % nth_upto
% 4.88/5.18 thf(fact_8720_upto__rec__numeral_I1_J,axiom,
% 4.88/5.18 ! [M2: num,N: num] :
% 4.88/5.18 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 4.88/5.18 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 4.88/5.18 = ( cons_int @ ( numeral_numeral_int @ M2 ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 4.88/5.18 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 4.88/5.18 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 4.88/5.18 = nil_int ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % upto_rec_numeral(1)
% 4.88/5.18 thf(fact_8721_upto__rec__numeral_I2_J,axiom,
% 4.88/5.18 ! [M2: num,N: num] :
% 4.88/5.18 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 4.88/5.18 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 4.88/5.18 = ( cons_int @ ( numeral_numeral_int @ M2 ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 4.88/5.18 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 4.88/5.18 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 4.88/5.18 = nil_int ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % upto_rec_numeral(2)
% 4.88/5.18 thf(fact_8722_upto__rec__numeral_I3_J,axiom,
% 4.88/5.18 ! [M2: num,N: num] :
% 4.88/5.18 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 4.88/5.18 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 4.88/5.18 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 4.88/5.18 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 4.88/5.18 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 4.88/5.18 = nil_int ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % upto_rec_numeral(3)
% 4.88/5.18 thf(fact_8723_upto__rec__numeral_I4_J,axiom,
% 4.88/5.18 ! [M2: num,N: num] :
% 4.88/5.18 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 4.88/5.18 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 4.88/5.18 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 4.88/5.18 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 4.88/5.18 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 4.88/5.18 = nil_int ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % upto_rec_numeral(4)
% 4.88/5.18 thf(fact_8724_upto__split2,axiom,
% 4.88/5.18 ! [I: int,J: int,K: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ I @ J )
% 4.88/5.18 => ( ( ord_less_eq_int @ J @ K )
% 4.88/5.18 => ( ( upto @ I @ K )
% 4.88/5.18 = ( append_int @ ( upto @ I @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % upto_split2
% 4.88/5.18 thf(fact_8725_upto__rec1,axiom,
% 4.88/5.18 ! [I: int,J: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ I @ J )
% 4.88/5.18 => ( ( upto @ I @ J )
% 4.88/5.18 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % upto_rec1
% 4.88/5.18 thf(fact_8726_upto_Oelims,axiom,
% 4.88/5.18 ! [X: int,Xa2: int,Y: list_int] :
% 4.88/5.18 ( ( ( upto @ X @ Xa2 )
% 4.88/5.18 = Y )
% 4.88/5.18 => ( ( ( ord_less_eq_int @ X @ Xa2 )
% 4.88/5.18 => ( Y
% 4.88/5.18 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa2 ) ) ) )
% 4.88/5.18 & ( ~ ( ord_less_eq_int @ X @ Xa2 )
% 4.88/5.18 => ( Y = nil_int ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % upto.elims
% 4.88/5.18 thf(fact_8727_upto_Osimps,axiom,
% 4.88/5.18 ( upto
% 4.88/5.18 = ( ^ [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 ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % upto.simps
% 4.88/5.18 thf(fact_8728_upto__rec2,axiom,
% 4.88/5.18 ! [I: int,J: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ I @ J )
% 4.88/5.18 => ( ( upto @ I @ J )
% 4.88/5.18 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % upto_rec2
% 4.88/5.18 thf(fact_8729_upto__split1,axiom,
% 4.88/5.18 ! [I: int,J: int,K: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ I @ J )
% 4.88/5.18 => ( ( ord_less_eq_int @ J @ K )
% 4.88/5.18 => ( ( upto @ I @ K )
% 4.88/5.18 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % upto_split1
% 4.88/5.18 thf(fact_8730_upto__split3,axiom,
% 4.88/5.18 ! [I: int,J: int,K: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ I @ J )
% 4.88/5.18 => ( ( ord_less_eq_int @ J @ K )
% 4.88/5.18 => ( ( upto @ I @ K )
% 4.88/5.18 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % upto_split3
% 4.88/5.18 thf(fact_8731_pred__numeral__simps_I2_J,axiom,
% 4.88/5.18 ! [K: num] :
% 4.88/5.18 ( ( pred_numeral @ ( bit0 @ K ) )
% 4.88/5.18 = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % pred_numeral_simps(2)
% 4.88/5.18 thf(fact_8732_eval__nat__numeral_I2_J,axiom,
% 4.88/5.18 ! [N: num] :
% 4.88/5.18 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 4.88/5.18 = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % eval_nat_numeral(2)
% 4.88/5.18 thf(fact_8733_one__plus__BitM,axiom,
% 4.88/5.18 ! [N: num] :
% 4.88/5.18 ( ( plus_plus_num @ one @ ( bitM @ N ) )
% 4.88/5.18 = ( bit0 @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % one_plus_BitM
% 4.88/5.18 thf(fact_8734_BitM__plus__one,axiom,
% 4.88/5.18 ! [N: num] :
% 4.88/5.18 ( ( plus_plus_num @ ( bitM @ N ) @ one )
% 4.88/5.18 = ( bit0 @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % BitM_plus_one
% 4.88/5.18 thf(fact_8735_rat__floor__lemma,axiom,
% 4.88/5.18 ! [A: int,B: int] :
% 4.88/5.18 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 4.88/5.18 & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % rat_floor_lemma
% 4.88/5.18 thf(fact_8736_image__minus__const__atLeastLessThan__nat,axiom,
% 4.88/5.18 ! [C: nat,Y: nat,X: nat] :
% 4.88/5.18 ( ( ( ord_less_nat @ C @ Y )
% 4.88/5.18 => ( ( image_nat_nat
% 4.88/5.18 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 4.88/5.18 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 4.88/5.18 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C ) @ ( minus_minus_nat @ Y @ C ) ) ) )
% 4.88/5.18 & ( ~ ( ord_less_nat @ C @ Y )
% 4.88/5.18 => ( ( ( ord_less_nat @ X @ Y )
% 4.88/5.18 => ( ( image_nat_nat
% 4.88/5.18 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 4.88/5.18 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 4.88/5.18 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 4.88/5.18 & ( ~ ( ord_less_nat @ X @ Y )
% 4.88/5.18 => ( ( image_nat_nat
% 4.88/5.18 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 4.88/5.18 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 4.88/5.18 = bot_bot_set_nat ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % image_minus_const_atLeastLessThan_nat
% 4.88/5.18 thf(fact_8737_image__Suc__atLeastAtMost,axiom,
% 4.88/5.18 ! [I: nat,J: nat] :
% 4.88/5.18 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 4.88/5.18 = ( set_or1269000886237332187st_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % image_Suc_atLeastAtMost
% 4.88/5.18 thf(fact_8738_image__Suc__atLeastLessThan,axiom,
% 4.88/5.18 ! [I: nat,J: nat] :
% 4.88/5.18 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I @ J ) )
% 4.88/5.18 = ( set_or4665077453230672383an_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % image_Suc_atLeastLessThan
% 4.88/5.18 thf(fact_8739_le__rat,axiom,
% 4.88/5.18 ! [B: int,D: int,A: int,C: int] :
% 4.88/5.18 ( ( B != zero_zero_int )
% 4.88/5.18 => ( ( D != zero_zero_int )
% 4.88/5.18 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 4.88/5.18 = ( ord_less_eq_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % le_rat
% 4.88/5.18 thf(fact_8740_zero__notin__Suc__image,axiom,
% 4.88/5.18 ! [A2: set_nat] :
% 4.88/5.18 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A2 ) ) ).
% 4.88/5.18
% 4.88/5.18 % zero_notin_Suc_image
% 4.88/5.18 thf(fact_8741_image__Suc__lessThan,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 4.88/5.18 = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % image_Suc_lessThan
% 4.88/5.18 thf(fact_8742_image__Suc__atMost,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 4.88/5.18 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % image_Suc_atMost
% 4.88/5.18 thf(fact_8743_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 4.88/5.18 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % atLeast0_atMost_Suc_eq_insert_0
% 4.88/5.18 thf(fact_8744_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 4.88/5.18 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % atLeast0_lessThan_Suc_eq_insert_0
% 4.88/5.18 thf(fact_8745_lessThan__Suc__eq__insert__0,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 4.88/5.18 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % lessThan_Suc_eq_insert_0
% 4.88/5.18 thf(fact_8746_atMost__Suc__eq__insert__0,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 4.88/5.18 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % atMost_Suc_eq_insert_0
% 4.88/5.18 thf(fact_8747_sorted__list__of__set__greaterThanLessThan,axiom,
% 4.88/5.18 ! [I: nat,J: nat] :
% 4.88/5.18 ( ( ord_less_nat @ ( suc @ I ) @ J )
% 4.88/5.18 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) )
% 4.88/5.18 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sorted_list_of_set_greaterThanLessThan
% 4.88/5.18 thf(fact_8748_one__le__Fract__iff,axiom,
% 4.88/5.18 ! [B: int,A: int] :
% 4.88/5.18 ( ( ord_less_int @ zero_zero_int @ B )
% 4.88/5.18 => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 4.88/5.18 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % one_le_Fract_iff
% 4.88/5.18 thf(fact_8749_Fract__le__one__iff,axiom,
% 4.88/5.18 ! [B: int,A: int] :
% 4.88/5.18 ( ( ord_less_int @ zero_zero_int @ B )
% 4.88/5.18 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 4.88/5.18 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Fract_le_one_iff
% 4.88/5.18 thf(fact_8750_zero__le__Fract__iff,axiom,
% 4.88/5.18 ! [B: int,A: int] :
% 4.88/5.18 ( ( ord_less_int @ zero_zero_int @ B )
% 4.88/5.18 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 4.88/5.18 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % zero_le_Fract_iff
% 4.88/5.18 thf(fact_8751_Fract__le__zero__iff,axiom,
% 4.88/5.18 ! [B: int,A: int] :
% 4.88/5.18 ( ( ord_less_int @ zero_zero_int @ B )
% 4.88/5.18 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 4.88/5.18 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Fract_le_zero_iff
% 4.88/5.18 thf(fact_8752_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 4.88/5.18 ! [N: nat,J: nat,I: nat] :
% 4.88/5.18 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ ( suc @ I ) ) )
% 4.88/5.18 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) ) @ N )
% 4.88/5.18 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % nth_sorted_list_of_set_greaterThanLessThan
% 4.88/5.18 thf(fact_8753_Inf__real__def,axiom,
% 4.88/5.18 ( comple4887499456419720421f_real
% 4.88/5.18 = ( ^ [X8: set_real] : ( uminus_uminus_real @ ( comple1385675409528146559p_real @ ( image_real_real @ uminus_uminus_real @ X8 ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Inf_real_def
% 4.88/5.18 thf(fact_8754_finite__int__iff__bounded__le,axiom,
% 4.88/5.18 ( finite_finite_int
% 4.88/5.18 = ( ^ [S6: set_int] :
% 4.88/5.18 ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S6 ) @ ( set_ord_atMost_int @ K3 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % finite_int_iff_bounded_le
% 4.88/5.18 thf(fact_8755_finite__int__iff__bounded,axiom,
% 4.88/5.18 ( finite_finite_int
% 4.88/5.18 = ( ^ [S6: set_int] :
% 4.88/5.18 ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S6 ) @ ( set_ord_lessThan_int @ K3 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % finite_int_iff_bounded
% 4.88/5.18 thf(fact_8756_image__int__atLeastAtMost,axiom,
% 4.88/5.18 ! [A: nat,B: nat] :
% 4.88/5.18 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 4.88/5.18 = ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % image_int_atLeastAtMost
% 4.88/5.18 thf(fact_8757_image__int__atLeastLessThan,axiom,
% 4.88/5.18 ! [A: nat,B: nat] :
% 4.88/5.18 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 4.88/5.18 = ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % image_int_atLeastLessThan
% 4.88/5.18 thf(fact_8758_image__add__int__atLeastLessThan,axiom,
% 4.88/5.18 ! [L: int,U: int] :
% 4.88/5.18 ( ( image_int_int
% 4.88/5.18 @ ^ [X3: int] : ( plus_plus_int @ X3 @ L )
% 4.88/5.18 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 4.88/5.18 = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 4.88/5.18
% 4.88/5.18 % image_add_int_atLeastLessThan
% 4.88/5.18 thf(fact_8759_image__atLeastZeroLessThan__int,axiom,
% 4.88/5.18 ! [U: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ zero_zero_int @ U )
% 4.88/5.18 => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 4.88/5.18 = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % image_atLeastZeroLessThan_int
% 4.88/5.18 thf(fact_8760_suminf__eq__SUP__real,axiom,
% 4.88/5.18 ! [X5: nat > real] :
% 4.88/5.18 ( ( summable_real @ X5 )
% 4.88/5.18 => ( ! [I2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( X5 @ I2 ) )
% 4.88/5.18 => ( ( suminf_real @ X5 )
% 4.88/5.18 = ( comple1385675409528146559p_real
% 4.88/5.18 @ ( image_nat_real
% 4.88/5.18 @ ^ [I4: nat] : ( groups6591440286371151544t_real @ X5 @ ( set_ord_lessThan_nat @ I4 ) )
% 4.88/5.18 @ top_top_set_nat ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % suminf_eq_SUP_real
% 4.88/5.18 thf(fact_8761_nat__not__finite,axiom,
% 4.88/5.18 ~ ( finite_finite_nat @ top_top_set_nat ) ).
% 4.88/5.18
% 4.88/5.18 % nat_not_finite
% 4.88/5.18 thf(fact_8762_infinite__UNIV__nat,axiom,
% 4.88/5.18 ~ ( finite_finite_nat @ top_top_set_nat ) ).
% 4.88/5.18
% 4.88/5.18 % infinite_UNIV_nat
% 4.88/5.18 thf(fact_8763_UN__lessThan__UNIV,axiom,
% 4.88/5.18 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 4.88/5.18 = top_top_set_nat ) ).
% 4.88/5.18
% 4.88/5.18 % UN_lessThan_UNIV
% 4.88/5.18 thf(fact_8764_UN__atMost__UNIV,axiom,
% 4.88/5.18 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 4.88/5.18 = top_top_set_nat ) ).
% 4.88/5.18
% 4.88/5.18 % UN_atMost_UNIV
% 4.88/5.18 thf(fact_8765_range__enumerate,axiom,
% 4.88/5.18 ! [S2: set_nat] :
% 4.88/5.18 ( ~ ( finite_finite_nat @ S2 )
% 4.88/5.18 => ( ( image_nat_nat @ ( infini8530281810654367211te_nat @ S2 ) @ top_top_set_nat )
% 4.88/5.18 = S2 ) ) ).
% 4.88/5.18
% 4.88/5.18 % range_enumerate
% 4.88/5.18 thf(fact_8766_UNIV__nat__eq,axiom,
% 4.88/5.18 ( top_top_set_nat
% 4.88/5.18 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % UNIV_nat_eq
% 4.88/5.18 thf(fact_8767_range__mod,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.18 => ( ( image_nat_nat
% 4.88/5.18 @ ^ [M3: nat] : ( modulo_modulo_nat @ M3 @ N )
% 4.88/5.18 @ top_top_set_nat )
% 4.88/5.18 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % range_mod
% 4.88/5.18 thf(fact_8768_card__UNIV__unit,axiom,
% 4.88/5.18 ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 4.88/5.18 = one_one_nat ) ).
% 4.88/5.18
% 4.88/5.18 % card_UNIV_unit
% 4.88/5.18 thf(fact_8769_range__mult,axiom,
% 4.88/5.18 ! [A: real] :
% 4.88/5.18 ( ( ( A = zero_zero_real )
% 4.88/5.18 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 4.88/5.18 = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 4.88/5.18 & ( ( A != zero_zero_real )
% 4.88/5.18 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 4.88/5.18 = top_top_set_real ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % range_mult
% 4.88/5.18 thf(fact_8770_sup__nat__def,axiom,
% 4.88/5.18 sup_sup_nat = ord_max_nat ).
% 4.88/5.18
% 4.88/5.18 % sup_nat_def
% 4.88/5.18 thf(fact_8771_atLeastLessThan__add__Un,axiom,
% 4.88/5.18 ! [I: nat,J: nat,K: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ I @ J )
% 4.88/5.18 => ( ( set_or4665077453230672383an_nat @ I @ ( plus_plus_nat @ J @ K ) )
% 4.88/5.18 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % atLeastLessThan_add_Un
% 4.88/5.18 thf(fact_8772_root__def,axiom,
% 4.88/5.18 ( root
% 4.88/5.18 = ( ^ [N4: nat,X3: real] :
% 4.88/5.18 ( if_real @ ( N4 = zero_zero_nat ) @ zero_zero_real
% 4.88/5.18 @ ( the_in5290026491893676941l_real @ top_top_set_real
% 4.88/5.18 @ ^ [Y2: real] : ( times_times_real @ ( sgn_sgn_real @ Y2 ) @ ( power_power_real @ ( abs_abs_real @ Y2 ) @ N4 ) )
% 4.88/5.18 @ X3 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % root_def
% 4.88/5.18 thf(fact_8773_DERIV__real__root__generic,axiom,
% 4.88/5.18 ! [N: nat,X: real,D4: real] :
% 4.88/5.18 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.18 => ( ( X != zero_zero_real )
% 4.88/5.18 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 4.88/5.18 => ( ( ord_less_real @ zero_zero_real @ X )
% 4.88/5.18 => ( D4
% 4.88/5.18 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 4.88/5.18 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 4.88/5.18 => ( ( ord_less_real @ X @ zero_zero_real )
% 4.88/5.18 => ( D4
% 4.88/5.18 = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 4.88/5.18 => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 4.88/5.18 => ( D4
% 4.88/5.18 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 4.88/5.18 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ D4 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % DERIV_real_root_generic
% 4.88/5.18 thf(fact_8774_DERIV__even__real__root,axiom,
% 4.88/5.18 ! [N: nat,X: real] :
% 4.88/5.18 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.18 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 4.88/5.18 => ( ( ord_less_real @ X @ zero_zero_real )
% 4.88/5.18 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % DERIV_even_real_root
% 4.88/5.18 thf(fact_8775_DERIV__arctan__series,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 4.88/5.18 => ( has_fi5821293074295781190e_real
% 4.88/5.18 @ ^ [X9: real] :
% 4.88/5.18 ( suminf_real
% 4.88/5.18 @ ^ [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 ) ) ) ) )
% 4.88/5.18 @ ( suminf_real
% 4.88/5.18 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( power_power_real @ X @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.88/5.18 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % DERIV_arctan_series
% 4.88/5.18 thf(fact_8776_deriv__nonneg__imp__mono,axiom,
% 4.88/5.18 ! [A: real,B: real,G2: real > real,G3: real > real] :
% 4.88/5.18 ( ! [X4: real] :
% 4.88/5.18 ( ( member_real @ X4 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 4.88/5.18 => ( has_fi5821293074295781190e_real @ G2 @ ( G3 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 4.88/5.18 => ( ! [X4: real] :
% 4.88/5.18 ( ( member_real @ X4 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 4.88/5.18 => ( ord_less_eq_real @ zero_zero_real @ ( G3 @ X4 ) ) )
% 4.88/5.18 => ( ( ord_less_eq_real @ A @ B )
% 4.88/5.18 => ( ord_less_eq_real @ ( G2 @ A ) @ ( G2 @ B ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % deriv_nonneg_imp_mono
% 4.88/5.18 thf(fact_8777_DERIV__nonneg__imp__nondecreasing,axiom,
% 4.88/5.18 ! [A: real,B: real,F: real > real] :
% 4.88/5.18 ( ( ord_less_eq_real @ A @ B )
% 4.88/5.18 => ( ! [X4: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ A @ X4 )
% 4.88/5.18 => ( ( ord_less_eq_real @ X4 @ B )
% 4.88/5.18 => ? [Y4: real] :
% 4.88/5.18 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 4.88/5.18 & ( ord_less_eq_real @ zero_zero_real @ Y4 ) ) ) )
% 4.88/5.18 => ( ord_less_eq_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % DERIV_nonneg_imp_nondecreasing
% 4.88/5.18 thf(fact_8778_DERIV__nonpos__imp__nonincreasing,axiom,
% 4.88/5.18 ! [A: real,B: real,F: real > real] :
% 4.88/5.18 ( ( ord_less_eq_real @ A @ B )
% 4.88/5.18 => ( ! [X4: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ A @ X4 )
% 4.88/5.18 => ( ( ord_less_eq_real @ X4 @ B )
% 4.88/5.18 => ? [Y4: real] :
% 4.88/5.18 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 4.88/5.18 & ( ord_less_eq_real @ Y4 @ zero_zero_real ) ) ) )
% 4.88/5.18 => ( ord_less_eq_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % DERIV_nonpos_imp_nonincreasing
% 4.88/5.18 thf(fact_8779_DERIV__pos__imp__increasing,axiom,
% 4.88/5.18 ! [A: real,B: real,F: real > real] :
% 4.88/5.18 ( ( ord_less_real @ A @ B )
% 4.88/5.18 => ( ! [X4: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ A @ X4 )
% 4.88/5.18 => ( ( ord_less_eq_real @ X4 @ B )
% 4.88/5.18 => ? [Y4: real] :
% 4.88/5.18 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 4.88/5.18 & ( ord_less_real @ zero_zero_real @ Y4 ) ) ) )
% 4.88/5.18 => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % DERIV_pos_imp_increasing
% 4.88/5.18 thf(fact_8780_DERIV__neg__imp__decreasing,axiom,
% 4.88/5.18 ! [A: real,B: real,F: real > real] :
% 4.88/5.18 ( ( ord_less_real @ A @ B )
% 4.88/5.18 => ( ! [X4: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ A @ X4 )
% 4.88/5.18 => ( ( ord_less_eq_real @ X4 @ B )
% 4.88/5.18 => ? [Y4: real] :
% 4.88/5.18 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 4.88/5.18 & ( ord_less_real @ Y4 @ zero_zero_real ) ) ) )
% 4.88/5.18 => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % DERIV_neg_imp_decreasing
% 4.88/5.18 thf(fact_8781_MVT2,axiom,
% 4.88/5.18 ! [A: real,B: real,F: real > real,F6: real > real] :
% 4.88/5.18 ( ( ord_less_real @ A @ B )
% 4.88/5.18 => ( ! [X4: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ A @ X4 )
% 4.88/5.18 => ( ( ord_less_eq_real @ X4 @ B )
% 4.88/5.18 => ( has_fi5821293074295781190e_real @ F @ ( F6 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 4.88/5.18 => ? [Z3: real] :
% 4.88/5.18 ( ( ord_less_real @ A @ Z3 )
% 4.88/5.18 & ( ord_less_real @ Z3 @ B )
% 4.88/5.18 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 4.88/5.18 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F6 @ Z3 ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % MVT2
% 4.88/5.18 thf(fact_8782_DERIV__local__min,axiom,
% 4.88/5.18 ! [F: real > real,L: real,X: real,D: real] :
% 4.88/5.18 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 4.88/5.18 => ( ( ord_less_real @ zero_zero_real @ D )
% 4.88/5.18 => ( ! [Y3: real] :
% 4.88/5.18 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D )
% 4.88/5.18 => ( ord_less_eq_real @ ( F @ X ) @ ( F @ Y3 ) ) )
% 4.88/5.18 => ( L = zero_zero_real ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % DERIV_local_min
% 4.88/5.18 thf(fact_8783_DERIV__local__max,axiom,
% 4.88/5.18 ! [F: real > real,L: real,X: real,D: real] :
% 4.88/5.18 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 4.88/5.18 => ( ( ord_less_real @ zero_zero_real @ D )
% 4.88/5.18 => ( ! [Y3: real] :
% 4.88/5.18 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D )
% 4.88/5.18 => ( ord_less_eq_real @ ( F @ Y3 ) @ ( F @ X ) ) )
% 4.88/5.18 => ( L = zero_zero_real ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % DERIV_local_max
% 4.88/5.18 thf(fact_8784_DERIV__pow,axiom,
% 4.88/5.18 ! [N: nat,X: real,S: set_real] :
% 4.88/5.18 ( has_fi5821293074295781190e_real
% 4.88/5.18 @ ^ [X3: real] : ( power_power_real @ X3 @ N )
% 4.88/5.18 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 4.88/5.18 @ ( topolo2177554685111907308n_real @ X @ S ) ) ).
% 4.88/5.18
% 4.88/5.18 % DERIV_pow
% 4.88/5.18 thf(fact_8785_DERIV__fun__pow,axiom,
% 4.88/5.18 ! [G2: real > real,M2: real,X: real,N: nat] :
% 4.88/5.18 ( ( has_fi5821293074295781190e_real @ G2 @ M2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 4.88/5.18 => ( has_fi5821293074295781190e_real
% 4.88/5.18 @ ^ [X3: real] : ( power_power_real @ ( G2 @ X3 ) @ N )
% 4.88/5.18 @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( G2 @ X ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) @ M2 )
% 4.88/5.18 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % DERIV_fun_pow
% 4.88/5.18 thf(fact_8786_DERIV__series_H,axiom,
% 4.88/5.18 ! [F: real > nat > real,F6: real > nat > real,X0: real,A: real,B: real,L5: nat > real] :
% 4.88/5.18 ( ! [N2: nat] :
% 4.88/5.18 ( has_fi5821293074295781190e_real
% 4.88/5.18 @ ^ [X3: real] : ( F @ X3 @ N2 )
% 4.88/5.18 @ ( F6 @ X0 @ N2 )
% 4.88/5.18 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 4.88/5.18 => ( ! [X4: real] :
% 4.88/5.18 ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 4.88/5.18 => ( summable_real @ ( F @ X4 ) ) )
% 4.88/5.18 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 4.88/5.18 => ( ( summable_real @ ( F6 @ X0 ) )
% 4.88/5.18 => ( ( summable_real @ L5 )
% 4.88/5.18 => ( ! [N2: nat,X4: real,Y3: real] :
% 4.88/5.18 ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 4.88/5.18 => ( ( member_real @ Y3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 4.88/5.18 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X4 @ N2 ) @ ( F @ Y3 @ N2 ) ) ) @ ( times_times_real @ ( L5 @ N2 ) @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y3 ) ) ) ) ) )
% 4.88/5.18 => ( has_fi5821293074295781190e_real
% 4.88/5.18 @ ^ [X3: real] : ( suminf_real @ ( F @ X3 ) )
% 4.88/5.18 @ ( suminf_real @ ( F6 @ X0 ) )
% 4.88/5.18 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % DERIV_series'
% 4.88/5.18 thf(fact_8787_DERIV__fun__powr,axiom,
% 4.88/5.18 ! [G2: real > real,M2: real,X: real,R2: real] :
% 4.88/5.18 ( ( has_fi5821293074295781190e_real @ G2 @ M2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 4.88/5.18 => ( ( ord_less_real @ zero_zero_real @ ( G2 @ X ) )
% 4.88/5.18 => ( has_fi5821293074295781190e_real
% 4.88/5.18 @ ^ [X3: real] : ( powr_real @ ( G2 @ X3 ) @ R2 )
% 4.88/5.18 @ ( times_times_real @ ( times_times_real @ R2 @ ( powr_real @ ( G2 @ X ) @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M2 )
% 4.88/5.18 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % DERIV_fun_powr
% 4.88/5.18 thf(fact_8788_DERIV__real__root,axiom,
% 4.88/5.18 ! [N: nat,X: real] :
% 4.88/5.18 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.18 => ( ( ord_less_real @ zero_zero_real @ X )
% 4.88/5.18 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % DERIV_real_root
% 4.88/5.18 thf(fact_8789_Maclaurin__all__le__objl,axiom,
% 4.88/5.18 ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 4.88/5.18 ( ( ( ( Diff @ zero_zero_nat )
% 4.88/5.18 = F )
% 4.88/5.18 & ! [M4: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 4.88/5.18 => ? [T6: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 4.88/5.18 & ( ( F @ X )
% 4.88/5.18 = ( plus_plus_real
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X @ M3 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ N ) )
% 4.88/5.18 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Maclaurin_all_le_objl
% 4.88/5.18 thf(fact_8790_Maclaurin__all__le,axiom,
% 4.88/5.18 ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 4.88/5.18 ( ( ( Diff @ zero_zero_nat )
% 4.88/5.18 = F )
% 4.88/5.18 => ( ! [M4: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 4.88/5.18 => ? [T6: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 4.88/5.18 & ( ( F @ X )
% 4.88/5.18 = ( plus_plus_real
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X @ M3 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ N ) )
% 4.88/5.18 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Maclaurin_all_le
% 4.88/5.18 thf(fact_8791_DERIV__odd__real__root,axiom,
% 4.88/5.18 ! [N: nat,X: real] :
% 4.88/5.18 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 4.88/5.18 => ( ( X != zero_zero_real )
% 4.88/5.18 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % DERIV_odd_real_root
% 4.88/5.18 thf(fact_8792_Maclaurin,axiom,
% 4.88/5.18 ! [H: real,N: nat,Diff: nat > real > real,F: real > real] :
% 4.88/5.18 ( ( ord_less_real @ zero_zero_real @ H )
% 4.88/5.18 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.18 => ( ( ( Diff @ zero_zero_nat )
% 4.88/5.18 = F )
% 4.88/5.18 => ( ! [M4: nat,T6: real] :
% 4.88/5.18 ( ( ( ord_less_nat @ M4 @ N )
% 4.88/5.18 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 4.88/5.18 & ( ord_less_eq_real @ T6 @ H ) )
% 4.88/5.18 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 4.88/5.18 => ? [T6: real] :
% 4.88/5.18 ( ( ord_less_real @ zero_zero_real @ T6 )
% 4.88/5.18 & ( ord_less_real @ T6 @ H )
% 4.88/5.18 & ( ( F @ H )
% 4.88/5.18 = ( plus_plus_real
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H @ M3 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ N ) )
% 4.88/5.18 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H @ N ) ) ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Maclaurin
% 4.88/5.18 thf(fact_8793_Maclaurin2,axiom,
% 4.88/5.18 ! [H: real,Diff: nat > real > real,F: real > real,N: nat] :
% 4.88/5.18 ( ( ord_less_real @ zero_zero_real @ H )
% 4.88/5.18 => ( ( ( Diff @ zero_zero_nat )
% 4.88/5.18 = F )
% 4.88/5.18 => ( ! [M4: nat,T6: real] :
% 4.88/5.18 ( ( ( ord_less_nat @ M4 @ N )
% 4.88/5.18 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 4.88/5.18 & ( ord_less_eq_real @ T6 @ H ) )
% 4.88/5.18 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 4.88/5.18 => ? [T6: real] :
% 4.88/5.18 ( ( ord_less_real @ zero_zero_real @ T6 )
% 4.88/5.18 & ( ord_less_eq_real @ T6 @ H )
% 4.88/5.18 & ( ( F @ H )
% 4.88/5.18 = ( plus_plus_real
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H @ M3 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ N ) )
% 4.88/5.18 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H @ N ) ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Maclaurin2
% 4.88/5.18 thf(fact_8794_Maclaurin__minus,axiom,
% 4.88/5.18 ! [H: real,N: nat,Diff: nat > real > real,F: real > real] :
% 4.88/5.18 ( ( ord_less_real @ H @ zero_zero_real )
% 4.88/5.18 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.18 => ( ( ( Diff @ zero_zero_nat )
% 4.88/5.18 = F )
% 4.88/5.18 => ( ! [M4: nat,T6: real] :
% 4.88/5.18 ( ( ( ord_less_nat @ M4 @ N )
% 4.88/5.18 & ( ord_less_eq_real @ H @ T6 )
% 4.88/5.18 & ( ord_less_eq_real @ T6 @ zero_zero_real ) )
% 4.88/5.18 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 4.88/5.18 => ? [T6: real] :
% 4.88/5.18 ( ( ord_less_real @ H @ T6 )
% 4.88/5.18 & ( ord_less_real @ T6 @ zero_zero_real )
% 4.88/5.18 & ( ( F @ H )
% 4.88/5.18 = ( plus_plus_real
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H @ M3 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ N ) )
% 4.88/5.18 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H @ N ) ) ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Maclaurin_minus
% 4.88/5.18 thf(fact_8795_Maclaurin__all__lt,axiom,
% 4.88/5.18 ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 4.88/5.18 ( ( ( Diff @ zero_zero_nat )
% 4.88/5.18 = F )
% 4.88/5.18 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.18 => ( ( X != zero_zero_real )
% 4.88/5.18 => ( ! [M4: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 4.88/5.18 => ? [T6: real] :
% 4.88/5.18 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 4.88/5.18 & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 4.88/5.18 & ( ( F @ X )
% 4.88/5.18 = ( plus_plus_real
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X @ M3 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ N ) )
% 4.88/5.18 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Maclaurin_all_lt
% 4.88/5.18 thf(fact_8796_Maclaurin__bi__le,axiom,
% 4.88/5.18 ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 4.88/5.18 ( ( ( Diff @ zero_zero_nat )
% 4.88/5.18 = F )
% 4.88/5.18 => ( ! [M4: nat,T6: real] :
% 4.88/5.18 ( ( ( ord_less_nat @ M4 @ N )
% 4.88/5.18 & ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) ) )
% 4.88/5.18 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 4.88/5.18 => ? [T6: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 4.88/5.18 & ( ( F @ X )
% 4.88/5.18 = ( plus_plus_real
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X @ M3 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ N ) )
% 4.88/5.18 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Maclaurin_bi_le
% 4.88/5.18 thf(fact_8797_Taylor__down,axiom,
% 4.88/5.18 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 4.88/5.18 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.18 => ( ( ( Diff @ zero_zero_nat )
% 4.88/5.18 = F )
% 4.88/5.18 => ( ! [M4: nat,T6: real] :
% 4.88/5.18 ( ( ( ord_less_nat @ M4 @ N )
% 4.88/5.18 & ( ord_less_eq_real @ A @ T6 )
% 4.88/5.18 & ( ord_less_eq_real @ T6 @ B ) )
% 4.88/5.18 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 4.88/5.18 => ( ( ord_less_real @ A @ C )
% 4.88/5.18 => ( ( ord_less_eq_real @ C @ B )
% 4.88/5.18 => ? [T6: real] :
% 4.88/5.18 ( ( ord_less_real @ A @ T6 )
% 4.88/5.18 & ( ord_less_real @ T6 @ C )
% 4.88/5.18 & ( ( F @ A )
% 4.88/5.18 = ( plus_plus_real
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M3 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ N ) )
% 4.88/5.18 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Taylor_down
% 4.88/5.18 thf(fact_8798_Taylor__up,axiom,
% 4.88/5.18 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 4.88/5.18 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.18 => ( ( ( Diff @ zero_zero_nat )
% 4.88/5.18 = F )
% 4.88/5.18 => ( ! [M4: nat,T6: real] :
% 4.88/5.18 ( ( ( ord_less_nat @ M4 @ N )
% 4.88/5.18 & ( ord_less_eq_real @ A @ T6 )
% 4.88/5.18 & ( ord_less_eq_real @ T6 @ B ) )
% 4.88/5.18 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 4.88/5.18 => ( ( ord_less_eq_real @ A @ C )
% 4.88/5.18 => ( ( ord_less_real @ C @ B )
% 4.88/5.18 => ? [T6: real] :
% 4.88/5.18 ( ( ord_less_real @ C @ T6 )
% 4.88/5.18 & ( ord_less_real @ T6 @ B )
% 4.88/5.18 & ( ( F @ B )
% 4.88/5.18 = ( plus_plus_real
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M3 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ N ) )
% 4.88/5.18 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Taylor_up
% 4.88/5.18 thf(fact_8799_Taylor,axiom,
% 4.88/5.18 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X: real] :
% 4.88/5.18 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.18 => ( ( ( Diff @ zero_zero_nat )
% 4.88/5.18 = F )
% 4.88/5.18 => ( ! [M4: nat,T6: real] :
% 4.88/5.18 ( ( ( ord_less_nat @ M4 @ N )
% 4.88/5.18 & ( ord_less_eq_real @ A @ T6 )
% 4.88/5.18 & ( ord_less_eq_real @ T6 @ B ) )
% 4.88/5.18 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 4.88/5.18 => ( ( ord_less_eq_real @ A @ C )
% 4.88/5.18 => ( ( ord_less_eq_real @ C @ B )
% 4.88/5.18 => ( ( ord_less_eq_real @ A @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ B )
% 4.88/5.18 => ( ( X != C )
% 4.88/5.18 => ? [T6: real] :
% 4.88/5.18 ( ( ( ord_less_real @ X @ C )
% 4.88/5.18 => ( ( ord_less_real @ X @ T6 )
% 4.88/5.18 & ( ord_less_real @ T6 @ C ) ) )
% 4.88/5.18 & ( ~ ( ord_less_real @ X @ C )
% 4.88/5.18 => ( ( ord_less_real @ C @ T6 )
% 4.88/5.18 & ( ord_less_real @ T6 @ X ) ) )
% 4.88/5.18 & ( ( F @ X )
% 4.88/5.18 = ( plus_plus_real
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ M3 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ N ) )
% 4.88/5.18 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Taylor
% 4.88/5.18 thf(fact_8800_Maclaurin__lemma2,axiom,
% 4.88/5.18 ! [N: nat,H: real,Diff: nat > real > real,K: nat,B2: real] :
% 4.88/5.18 ( ! [M4: nat,T6: real] :
% 4.88/5.18 ( ( ( ord_less_nat @ M4 @ N )
% 4.88/5.18 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 4.88/5.18 & ( ord_less_eq_real @ T6 @ H ) )
% 4.88/5.18 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 4.88/5.18 => ( ( N
% 4.88/5.18 = ( suc @ K ) )
% 4.88/5.18 => ! [M: nat,T7: real] :
% 4.88/5.18 ( ( ( ord_less_nat @ M @ N )
% 4.88/5.18 & ( ord_less_eq_real @ zero_zero_real @ T7 )
% 4.88/5.18 & ( ord_less_eq_real @ T7 @ H ) )
% 4.88/5.18 => ( has_fi5821293074295781190e_real
% 4.88/5.18 @ ^ [U2: real] :
% 4.88/5.18 ( minus_minus_real @ ( Diff @ M @ U2 )
% 4.88/5.18 @ ( plus_plus_real
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ U2 @ P5 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ M ) ) )
% 4.88/5.18 @ ( times_times_real @ B2 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N @ M ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ M ) ) ) ) ) )
% 4.88/5.18 @ ( minus_minus_real @ ( Diff @ ( suc @ M ) @ T7 )
% 4.88/5.18 @ ( plus_plus_real
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M ) @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ T7 @ P5 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ M ) ) ) )
% 4.88/5.18 @ ( times_times_real @ B2 @ ( divide_divide_real @ ( power_power_real @ T7 @ ( minus_minus_nat @ N @ ( suc @ M ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ ( suc @ M ) ) ) ) ) ) )
% 4.88/5.18 @ ( topolo2177554685111907308n_real @ T7 @ top_top_set_real ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Maclaurin_lemma2
% 4.88/5.18 thf(fact_8801_summable__Leibniz_I3_J,axiom,
% 4.88/5.18 ! [A: nat > real] :
% 4.88/5.18 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 4.88/5.18 => ( ( topolo6980174941875973593q_real @ A )
% 4.88/5.18 => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 4.88/5.18 => ! [N6: nat] :
% 4.88/5.18 ( member_real
% 4.88/5.18 @ ( suminf_real
% 4.88/5.18 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) )
% 4.88/5.18 @ ( set_or1222579329274155063t_real
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) )
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % summable_Leibniz(3)
% 4.88/5.18 thf(fact_8802_summable__Leibniz_I2_J,axiom,
% 4.88/5.18 ! [A: nat > real] :
% 4.88/5.18 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 4.88/5.18 => ( ( topolo6980174941875973593q_real @ A )
% 4.88/5.18 => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 4.88/5.18 => ! [N6: nat] :
% 4.88/5.18 ( member_real
% 4.88/5.18 @ ( suminf_real
% 4.88/5.18 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) )
% 4.88/5.18 @ ( set_or1222579329274155063t_real
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) )
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % summable_Leibniz(2)
% 4.88/5.18 thf(fact_8803_summable__Leibniz_H_I5_J,axiom,
% 4.88/5.18 ! [A: nat > real] :
% 4.88/5.18 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 4.88/5.18 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 4.88/5.18 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 4.88/5.18 => ( filterlim_nat_real
% 4.88/5.18 @ ^ [N4: nat] :
% 4.88/5.18 ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 4.88/5.18 @ ( topolo2815343760600316023s_real
% 4.88/5.18 @ ( suminf_real
% 4.88/5.18 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 4.88/5.18 @ at_top_nat ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % summable_Leibniz'(5)
% 4.88/5.18 thf(fact_8804_trivial__limit__sequentially,axiom,
% 4.88/5.18 at_top_nat != bot_bot_filter_nat ).
% 4.88/5.18
% 4.88/5.18 % trivial_limit_sequentially
% 4.88/5.18 thf(fact_8805_mult__nat__right__at__top,axiom,
% 4.88/5.18 ! [C: nat] :
% 4.88/5.18 ( ( ord_less_nat @ zero_zero_nat @ C )
% 4.88/5.18 => ( filterlim_nat_nat
% 4.88/5.18 @ ^ [X3: nat] : ( times_times_nat @ X3 @ C )
% 4.88/5.18 @ at_top_nat
% 4.88/5.18 @ at_top_nat ) ) ).
% 4.88/5.18
% 4.88/5.18 % mult_nat_right_at_top
% 4.88/5.18 thf(fact_8806_mult__nat__left__at__top,axiom,
% 4.88/5.18 ! [C: nat] :
% 4.88/5.18 ( ( ord_less_nat @ zero_zero_nat @ C )
% 4.88/5.18 => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 4.88/5.18
% 4.88/5.18 % mult_nat_left_at_top
% 4.88/5.18 thf(fact_8807_monoseq__convergent,axiom,
% 4.88/5.18 ! [X5: nat > real,B2: real] :
% 4.88/5.18 ( ( topolo6980174941875973593q_real @ X5 )
% 4.88/5.18 => ( ! [I2: nat] : ( ord_less_eq_real @ ( abs_abs_real @ ( X5 @ I2 ) ) @ B2 )
% 4.88/5.18 => ~ ! [L6: real] :
% 4.88/5.18 ~ ( filterlim_nat_real @ X5 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % monoseq_convergent
% 4.88/5.18 thf(fact_8808_nested__sequence__unique,axiom,
% 4.88/5.18 ! [F: nat > real,G2: nat > real] :
% 4.88/5.18 ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 4.88/5.18 => ( ! [N2: nat] : ( ord_less_eq_real @ ( G2 @ ( suc @ N2 ) ) @ ( G2 @ N2 ) )
% 4.88/5.18 => ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( G2 @ N2 ) )
% 4.88/5.18 => ( ( filterlim_nat_real
% 4.88/5.18 @ ^ [N4: nat] : ( minus_minus_real @ ( F @ N4 ) @ ( G2 @ N4 ) )
% 4.88/5.18 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 4.88/5.18 @ at_top_nat )
% 4.88/5.18 => ? [L4: real] :
% 4.88/5.18 ( ! [N6: nat] : ( ord_less_eq_real @ ( F @ N6 ) @ L4 )
% 4.88/5.18 & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat )
% 4.88/5.18 & ! [N6: nat] : ( ord_less_eq_real @ L4 @ ( G2 @ N6 ) )
% 4.88/5.18 & ( filterlim_nat_real @ G2 @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % nested_sequence_unique
% 4.88/5.18 thf(fact_8809_LIMSEQ__inverse__zero,axiom,
% 4.88/5.18 ! [X5: nat > real] :
% 4.88/5.18 ( ! [R4: real] :
% 4.88/5.18 ? [N8: nat] :
% 4.88/5.18 ! [N2: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ N8 @ N2 )
% 4.88/5.18 => ( ord_less_real @ R4 @ ( X5 @ N2 ) ) )
% 4.88/5.18 => ( filterlim_nat_real
% 4.88/5.18 @ ^ [N4: nat] : ( inverse_inverse_real @ ( X5 @ N4 ) )
% 4.88/5.18 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 4.88/5.18 @ at_top_nat ) ) ).
% 4.88/5.18
% 4.88/5.18 % LIMSEQ_inverse_zero
% 4.88/5.18 thf(fact_8810_increasing__LIMSEQ,axiom,
% 4.88/5.18 ! [F: nat > real,L: real] :
% 4.88/5.18 ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 4.88/5.18 => ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ L )
% 4.88/5.18 => ( ! [E: real] :
% 4.88/5.18 ( ( ord_less_real @ zero_zero_real @ E )
% 4.88/5.18 => ? [N6: nat] : ( ord_less_eq_real @ L @ ( plus_plus_real @ ( F @ N6 ) @ E ) ) )
% 4.88/5.18 => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L ) @ at_top_nat ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % increasing_LIMSEQ
% 4.88/5.18 thf(fact_8811_LIMSEQ__realpow__zero,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( ord_less_real @ X @ one_one_real )
% 4.88/5.18 => ( filterlim_nat_real @ ( power_power_real @ X ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % LIMSEQ_realpow_zero
% 4.88/5.18 thf(fact_8812_summable,axiom,
% 4.88/5.18 ! [A: nat > real] :
% 4.88/5.18 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 4.88/5.18 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 4.88/5.18 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 4.88/5.18 => ( summable_real
% 4.88/5.18 @ ^ [N4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( A @ N4 ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % summable
% 4.88/5.18 thf(fact_8813_zeroseq__arctan__series,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 4.88/5.18 => ( filterlim_nat_real
% 4.88/5.18 @ ^ [N4: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 4.88/5.18 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 4.88/5.18 @ at_top_nat ) ) ).
% 4.88/5.18
% 4.88/5.18 % zeroseq_arctan_series
% 4.88/5.18 thf(fact_8814_summable__Leibniz_H_I3_J,axiom,
% 4.88/5.18 ! [A: nat > real] :
% 4.88/5.18 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 4.88/5.18 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 4.88/5.18 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 4.88/5.18 => ( filterlim_nat_real
% 4.88/5.18 @ ^ [N4: nat] :
% 4.88/5.18 ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 4.88/5.18 @ ( topolo2815343760600316023s_real
% 4.88/5.18 @ ( suminf_real
% 4.88/5.18 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 4.88/5.18 @ at_top_nat ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % summable_Leibniz'(3)
% 4.88/5.18 thf(fact_8815_summable__Leibniz_H_I2_J,axiom,
% 4.88/5.18 ! [A: nat > real,N: nat] :
% 4.88/5.18 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 4.88/5.18 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 4.88/5.18 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 4.88/5.18 => ( ord_less_eq_real
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 4.88/5.18 @ ( suminf_real
% 4.88/5.18 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % summable_Leibniz'(2)
% 4.88/5.18 thf(fact_8816_sums__alternating__upper__lower,axiom,
% 4.88/5.18 ! [A: nat > real] :
% 4.88/5.18 ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 4.88/5.18 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 4.88/5.18 => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 4.88/5.18 => ? [L4: real] :
% 4.88/5.18 ( ! [N6: nat] :
% 4.88/5.18 ( ord_less_eq_real
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) )
% 4.88/5.18 @ L4 )
% 4.88/5.18 & ( filterlim_nat_real
% 4.88/5.18 @ ^ [N4: nat] :
% 4.88/5.18 ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 4.88/5.18 @ ( topolo2815343760600316023s_real @ L4 )
% 4.88/5.18 @ at_top_nat )
% 4.88/5.18 & ! [N6: nat] :
% 4.88/5.18 ( ord_less_eq_real @ L4
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) ) )
% 4.88/5.18 & ( filterlim_nat_real
% 4.88/5.18 @ ^ [N4: nat] :
% 4.88/5.18 ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 4.88/5.18 @ ( topolo2815343760600316023s_real @ L4 )
% 4.88/5.18 @ at_top_nat ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sums_alternating_upper_lower
% 4.88/5.18 thf(fact_8817_summable__Leibniz_I5_J,axiom,
% 4.88/5.18 ! [A: nat > real] :
% 4.88/5.18 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 4.88/5.18 => ( ( topolo6980174941875973593q_real @ A )
% 4.88/5.18 => ( filterlim_nat_real
% 4.88/5.18 @ ^ [N4: nat] :
% 4.88/5.18 ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 4.88/5.18 @ ( topolo2815343760600316023s_real
% 4.88/5.18 @ ( suminf_real
% 4.88/5.18 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 4.88/5.18 @ at_top_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % summable_Leibniz(5)
% 4.88/5.18 thf(fact_8818_summable__Leibniz_H_I4_J,axiom,
% 4.88/5.18 ! [A: nat > real,N: nat] :
% 4.88/5.18 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 4.88/5.18 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 4.88/5.18 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 4.88/5.18 => ( ord_less_eq_real
% 4.88/5.18 @ ( suminf_real
% 4.88/5.18 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) )
% 4.88/5.18 @ ( groups6591440286371151544t_real
% 4.88/5.18 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % summable_Leibniz'(4)
% 4.88/5.18 thf(fact_8819_Bseq__eq__bounded,axiom,
% 4.88/5.18 ! [F: nat > real,A: real,B: real] :
% 4.88/5.18 ( ( ord_less_eq_set_real @ ( image_nat_real @ F @ top_top_set_nat ) @ ( set_or1222579329274155063t_real @ A @ B ) )
% 4.88/5.18 => ( bfun_nat_real @ F @ at_top_nat ) ) ).
% 4.88/5.18
% 4.88/5.18 % Bseq_eq_bounded
% 4.88/5.18 thf(fact_8820_Bseq__realpow,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ one_one_real )
% 4.88/5.18 => ( bfun_nat_real @ ( power_power_real @ X ) @ at_top_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Bseq_realpow
% 4.88/5.18 thf(fact_8821_DERIV__neg__imp__decreasing__at__top,axiom,
% 4.88/5.18 ! [B: real,F: real > real,Flim: real] :
% 4.88/5.18 ( ! [X4: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ B @ X4 )
% 4.88/5.18 => ? [Y4: real] :
% 4.88/5.18 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 4.88/5.18 & ( ord_less_real @ Y4 @ zero_zero_real ) ) )
% 4.88/5.18 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 4.88/5.18 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % DERIV_neg_imp_decreasing_at_top
% 4.88/5.18 thf(fact_8822_filterlim__pow__at__bot__even,axiom,
% 4.88/5.18 ! [N: nat,F: real > real,F2: filter_real] :
% 4.88/5.18 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.18 => ( ( filterlim_real_real @ F @ at_bot_real @ F2 )
% 4.88/5.18 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 4.88/5.18 => ( filterlim_real_real
% 4.88/5.18 @ ^ [X3: real] : ( power_power_real @ ( F @ X3 ) @ N )
% 4.88/5.18 @ at_top_real
% 4.88/5.18 @ F2 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % filterlim_pow_at_bot_even
% 4.88/5.18 thf(fact_8823_at__top__le__at__infinity,axiom,
% 4.88/5.18 ord_le4104064031414453916r_real @ at_top_real @ at_infinity_real ).
% 4.88/5.18
% 4.88/5.18 % at_top_le_at_infinity
% 4.88/5.18 thf(fact_8824_at__bot__le__at__infinity,axiom,
% 4.88/5.18 ord_le4104064031414453916r_real @ at_bot_real @ at_infinity_real ).
% 4.88/5.18
% 4.88/5.18 % at_bot_le_at_infinity
% 4.88/5.18 thf(fact_8825_eventually__sequentiallyI,axiom,
% 4.88/5.18 ! [C: nat,P: nat > $o] :
% 4.88/5.18 ( ! [X4: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ C @ X4 )
% 4.88/5.18 => ( P @ X4 ) )
% 4.88/5.18 => ( eventually_nat @ P @ at_top_nat ) ) ).
% 4.88/5.18
% 4.88/5.18 % eventually_sequentiallyI
% 4.88/5.18 thf(fact_8826_eventually__sequentially,axiom,
% 4.88/5.18 ! [P: nat > $o] :
% 4.88/5.18 ( ( eventually_nat @ P @ at_top_nat )
% 4.88/5.18 = ( ? [N3: nat] :
% 4.88/5.18 ! [N4: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ N3 @ N4 )
% 4.88/5.18 => ( P @ N4 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % eventually_sequentially
% 4.88/5.18 thf(fact_8827_le__sequentially,axiom,
% 4.88/5.18 ! [F2: filter_nat] :
% 4.88/5.18 ( ( ord_le2510731241096832064er_nat @ F2 @ at_top_nat )
% 4.88/5.18 = ( ! [N3: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N3 ) @ F2 ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % le_sequentially
% 4.88/5.18 thf(fact_8828_DERIV__pos__imp__increasing__at__bot,axiom,
% 4.88/5.18 ! [B: real,F: real > real,Flim: real] :
% 4.88/5.18 ( ! [X4: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ X4 @ B )
% 4.88/5.18 => ? [Y4: real] :
% 4.88/5.18 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 4.88/5.18 & ( ord_less_real @ zero_zero_real @ Y4 ) ) )
% 4.88/5.18 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 4.88/5.18 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % DERIV_pos_imp_increasing_at_bot
% 4.88/5.18 thf(fact_8829_filterlim__pow__at__bot__odd,axiom,
% 4.88/5.18 ! [N: nat,F: real > real,F2: filter_real] :
% 4.88/5.18 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.18 => ( ( filterlim_real_real @ F @ at_bot_real @ F2 )
% 4.88/5.18 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 4.88/5.18 => ( filterlim_real_real
% 4.88/5.18 @ ^ [X3: real] : ( power_power_real @ ( F @ X3 ) @ N )
% 4.88/5.18 @ at_bot_real
% 4.88/5.18 @ F2 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % filterlim_pow_at_bot_odd
% 4.88/5.18 thf(fact_8830_finite__greaterThanAtMost,axiom,
% 4.88/5.18 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 4.88/5.18
% 4.88/5.18 % finite_greaterThanAtMost
% 4.88/5.18 thf(fact_8831_card__greaterThanAtMost,axiom,
% 4.88/5.18 ! [L: nat,U: nat] :
% 4.88/5.18 ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L @ U ) )
% 4.88/5.18 = ( minus_minus_nat @ U @ L ) ) ).
% 4.88/5.18
% 4.88/5.18 % card_greaterThanAtMost
% 4.88/5.18 thf(fact_8832_atLeastSucAtMost__greaterThanAtMost,axiom,
% 4.88/5.18 ! [L: nat,U: nat] :
% 4.88/5.18 ( ( set_or1269000886237332187st_nat @ ( suc @ L ) @ U )
% 4.88/5.18 = ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 4.88/5.18
% 4.88/5.18 % atLeastSucAtMost_greaterThanAtMost
% 4.88/5.18 thf(fact_8833_GreatestI__ex__nat,axiom,
% 4.88/5.18 ! [P: nat > $o,B: nat] :
% 4.88/5.18 ( ? [X_12: nat] : ( P @ X_12 )
% 4.88/5.18 => ( ! [Y3: nat] :
% 4.88/5.18 ( ( P @ Y3 )
% 4.88/5.18 => ( ord_less_eq_nat @ Y3 @ B ) )
% 4.88/5.18 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % GreatestI_ex_nat
% 4.88/5.18 thf(fact_8834_Greatest__le__nat,axiom,
% 4.88/5.18 ! [P: nat > $o,K: nat,B: nat] :
% 4.88/5.18 ( ( P @ K )
% 4.88/5.18 => ( ! [Y3: nat] :
% 4.88/5.18 ( ( P @ Y3 )
% 4.88/5.18 => ( ord_less_eq_nat @ Y3 @ B ) )
% 4.88/5.18 => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Greatest_le_nat
% 4.88/5.18 thf(fact_8835_GreatestI__nat,axiom,
% 4.88/5.18 ! [P: nat > $o,K: nat,B: nat] :
% 4.88/5.18 ( ( P @ K )
% 4.88/5.18 => ( ! [Y3: nat] :
% 4.88/5.18 ( ( P @ Y3 )
% 4.88/5.18 => ( ord_less_eq_nat @ Y3 @ B ) )
% 4.88/5.18 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % GreatestI_nat
% 4.88/5.18 thf(fact_8836_sorted__list__of__set__greaterThanAtMost,axiom,
% 4.88/5.18 ! [I: nat,J: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ ( suc @ I ) @ J )
% 4.88/5.18 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) )
% 4.88/5.18 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sorted_list_of_set_greaterThanAtMost
% 4.88/5.18 thf(fact_8837_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 4.88/5.18 ! [N: nat,J: nat,I: nat] :
% 4.88/5.18 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ I ) )
% 4.88/5.18 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) ) @ N )
% 4.88/5.18 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % nth_sorted_list_of_set_greaterThanAtMost
% 4.88/5.18 thf(fact_8838_finite__greaterThanAtMost__int,axiom,
% 4.88/5.18 ! [L: int,U: int] : ( finite_finite_int @ ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 4.88/5.18
% 4.88/5.18 % finite_greaterThanAtMost_int
% 4.88/5.18 thf(fact_8839_card__greaterThanAtMost__int,axiom,
% 4.88/5.18 ! [L: int,U: int] :
% 4.88/5.18 ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L @ U ) )
% 4.88/5.18 = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % card_greaterThanAtMost_int
% 4.88/5.18 thf(fact_8840_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 4.88/5.18 ! [L: int,U: int] :
% 4.88/5.18 ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 4.88/5.18 = ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 4.88/5.18
% 4.88/5.18 % atLeastPlusOneAtMost_greaterThanAtMost_int
% 4.88/5.18 thf(fact_8841_Gcd__eq__Max,axiom,
% 4.88/5.18 ! [M5: set_nat] :
% 4.88/5.18 ( ( finite_finite_nat @ M5 )
% 4.88/5.18 => ( ( M5 != bot_bot_set_nat )
% 4.88/5.18 => ( ~ ( member_nat @ zero_zero_nat @ M5 )
% 4.88/5.18 => ( ( gcd_Gcd_nat @ M5 )
% 4.88/5.18 = ( lattic8265883725875713057ax_nat
% 4.88/5.18 @ ( comple7806235888213564991et_nat
% 4.88/5.18 @ ( image_nat_set_nat
% 4.88/5.18 @ ^ [M3: nat] :
% 4.88/5.18 ( collect_nat
% 4.88/5.18 @ ^ [D5: nat] : ( dvd_dvd_nat @ D5 @ M3 ) )
% 4.88/5.18 @ M5 ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Gcd_eq_Max
% 4.88/5.18 thf(fact_8842_Max__divisors__self__nat,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( N != zero_zero_nat )
% 4.88/5.18 => ( ( lattic8265883725875713057ax_nat
% 4.88/5.18 @ ( collect_nat
% 4.88/5.18 @ ^ [D5: nat] : ( dvd_dvd_nat @ D5 @ N ) ) )
% 4.88/5.18 = N ) ) ).
% 4.88/5.18
% 4.88/5.18 % Max_divisors_self_nat
% 4.88/5.18 thf(fact_8843_card__le__Suc__Max,axiom,
% 4.88/5.18 ! [S2: set_nat] :
% 4.88/5.18 ( ( finite_finite_nat @ S2 )
% 4.88/5.18 => ( ord_less_eq_nat @ ( finite_card_nat @ S2 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S2 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % card_le_Suc_Max
% 4.88/5.18 thf(fact_8844_Sup__nat__def,axiom,
% 4.88/5.18 ( complete_Sup_Sup_nat
% 4.88/5.18 = ( ^ [X8: set_nat] : ( if_nat @ ( X8 = bot_bot_set_nat ) @ zero_zero_nat @ ( lattic8265883725875713057ax_nat @ X8 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Sup_nat_def
% 4.88/5.18 thf(fact_8845_divide__nat__def,axiom,
% 4.88/5.18 ( divide_divide_nat
% 4.88/5.18 = ( ^ [M3: nat,N4: nat] :
% 4.88/5.18 ( if_nat @ ( N4 = zero_zero_nat ) @ zero_zero_nat
% 4.88/5.18 @ ( lattic8265883725875713057ax_nat
% 4.88/5.18 @ ( collect_nat
% 4.88/5.18 @ ^ [K3: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K3 @ N4 ) @ M3 ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % divide_nat_def
% 4.88/5.18 thf(fact_8846_greaterThan__0,axiom,
% 4.88/5.18 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 4.88/5.18 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 4.88/5.18
% 4.88/5.18 % greaterThan_0
% 4.88/5.18 thf(fact_8847_greaterThan__Suc,axiom,
% 4.88/5.18 ! [K: nat] :
% 4.88/5.18 ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 4.88/5.18 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % greaterThan_Suc
% 4.88/5.18 thf(fact_8848_INT__greaterThan__UNIV,axiom,
% 4.88/5.18 ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 4.88/5.18 = bot_bot_set_nat ) ).
% 4.88/5.18
% 4.88/5.18 % INT_greaterThan_UNIV
% 4.88/5.18 thf(fact_8849_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 4.88/5.18 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 4.88/5.18 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 4.88/5.18 = Y )
% 4.88/5.18 => ( ( ? [Uu2: $o,Uv2: $o] :
% 4.88/5.18 ( X
% 4.88/5.18 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 4.88/5.18 => ( Y
% 4.88/5.18 = ( Xa2 != one_one_nat ) ) )
% 4.88/5.18 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.88/5.18 ( ( X
% 4.88/5.18 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 4.88/5.18 => ( Y
% 4.88/5.18 = ( ~ ( ( Deg2 = Xa2 )
% 4.88/5.18 & ! [X3: vEBT_VEBT] :
% 4.88/5.18 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.88/5.18 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.88/5.18 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.88/5.18 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 4.88/5.18 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.88/5.18 & ( case_o184042715313410164at_nat
% 4.88/5.18 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 4.88/5.18 & ! [X3: vEBT_VEBT] :
% 4.88/5.18 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.88/5.18 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 4.88/5.18 @ ( produc6081775807080527818_nat_o
% 4.88/5.18 @ ^ [Mi3: nat,Ma3: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 4.88/5.18 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 4.88/5.18 & ! [I4: nat] :
% 4.88/5.18 ( ( 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 ) ) ) ) ) )
% 4.88/5.18 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X8 ) )
% 4.88/5.18 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 4.88/5.18 & ( ( Mi3 = Ma3 )
% 4.88/5.18 => ! [X3: vEBT_VEBT] :
% 4.88/5.18 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.88/5.18 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 4.88/5.18 & ( ( Mi3 != Ma3 )
% 4.88/5.18 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 4.88/5.18 & ! [X3: nat] :
% 4.88/5.18 ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 4.88/5.18 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X3 )
% 4.88/5.18 => ( ( ord_less_nat @ Mi3 @ X3 )
% 4.88/5.18 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 4.88/5.18 @ Mima ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % VEBT_internal.valid'.elims(1)
% 4.88/5.18 thf(fact_8850_atLeast__0,axiom,
% 4.88/5.18 ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 4.88/5.18 = top_top_set_nat ) ).
% 4.88/5.18
% 4.88/5.18 % atLeast_0
% 4.88/5.18 thf(fact_8851_atLeast__Suc__greaterThan,axiom,
% 4.88/5.18 ! [K: nat] :
% 4.88/5.18 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 4.88/5.18 = ( set_or1210151606488870762an_nat @ K ) ) ).
% 4.88/5.18
% 4.88/5.18 % atLeast_Suc_greaterThan
% 4.88/5.18 thf(fact_8852_decseq__bounded,axiom,
% 4.88/5.18 ! [X5: nat > real,B2: real] :
% 4.88/5.18 ( ( order_9091379641038594480t_real @ X5 )
% 4.88/5.18 => ( ! [I2: nat] : ( ord_less_eq_real @ B2 @ ( X5 @ I2 ) )
% 4.88/5.18 => ( bfun_nat_real @ X5 @ at_top_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % decseq_bounded
% 4.88/5.18 thf(fact_8853_decseq__convergent,axiom,
% 4.88/5.18 ! [X5: nat > real,B2: real] :
% 4.88/5.18 ( ( order_9091379641038594480t_real @ X5 )
% 4.88/5.18 => ( ! [I2: nat] : ( ord_less_eq_real @ B2 @ ( X5 @ I2 ) )
% 4.88/5.18 => ~ ! [L6: real] :
% 4.88/5.18 ( ( filterlim_nat_real @ X5 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 4.88/5.18 => ~ ! [I3: nat] : ( ord_less_eq_real @ L6 @ ( X5 @ I3 ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % decseq_convergent
% 4.88/5.18 thf(fact_8854_UN__atLeast__UNIV,axiom,
% 4.88/5.18 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 4.88/5.18 = top_top_set_nat ) ).
% 4.88/5.18
% 4.88/5.18 % UN_atLeast_UNIV
% 4.88/5.18 thf(fact_8855_atLeast__Suc,axiom,
% 4.88/5.18 ! [K: nat] :
% 4.88/5.18 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 4.88/5.18 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % atLeast_Suc
% 4.88/5.18 thf(fact_8856_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 4.88/5.18 ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg4: nat] :
% 4.88/5.18 ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList @ Summary ) @ Deg4 )
% 4.88/5.18 = ( ( Deg = Deg4 )
% 4.88/5.18 & ! [X3: vEBT_VEBT] :
% 4.88/5.18 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.88/5.18 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.88/5.18 & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.88/5.18 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 4.88/5.18 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.88/5.18 & ( case_o184042715313410164at_nat
% 4.88/5.18 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X8 )
% 4.88/5.18 & ! [X3: vEBT_VEBT] :
% 4.88/5.18 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.88/5.18 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 4.88/5.18 @ ( produc6081775807080527818_nat_o
% 4.88/5.18 @ ^ [Mi3: nat,Ma3: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 4.88/5.18 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 4.88/5.18 & ! [I4: nat] :
% 4.88/5.18 ( ( 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 ) ) ) ) ) )
% 4.88/5.18 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X8 ) )
% 4.88/5.18 = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 4.88/5.18 & ( ( Mi3 = Ma3 )
% 4.88/5.18 => ! [X3: vEBT_VEBT] :
% 4.88/5.18 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.88/5.18 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 4.88/5.18 & ( ( Mi3 != Ma3 )
% 4.88/5.18 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 4.88/5.18 & ! [X3: nat] :
% 4.88/5.18 ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 4.88/5.18 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X3 )
% 4.88/5.18 => ( ( ord_less_nat @ Mi3 @ X3 )
% 4.88/5.18 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 4.88/5.18 @ Mima2 ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % VEBT_internal.valid'.simps(2)
% 4.88/5.18 thf(fact_8857_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 4.88/5.18 ! [X: vEBT_VEBT,Xa2: nat] :
% 4.88/5.18 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 4.88/5.18 => ( ( ? [Uu2: $o,Uv2: $o] :
% 4.88/5.18 ( X
% 4.88/5.18 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 4.88/5.18 => ( Xa2 = one_one_nat ) )
% 4.88/5.18 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.88/5.18 ( ( X
% 4.88/5.18 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 4.88/5.18 => ( ( Deg2 = Xa2 )
% 4.88/5.18 & ! [X4: vEBT_VEBT] :
% 4.88/5.18 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.88/5.18 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.88/5.18 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.88/5.18 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 4.88/5.18 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.88/5.18 & ( case_o184042715313410164at_nat
% 4.88/5.18 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 4.88/5.18 & ! [X3: vEBT_VEBT] :
% 4.88/5.18 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.88/5.18 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 4.88/5.18 @ ( produc6081775807080527818_nat_o
% 4.88/5.18 @ ^ [Mi3: nat,Ma3: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 4.88/5.18 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 4.88/5.18 & ! [I4: nat] :
% 4.88/5.18 ( ( 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 ) ) ) ) ) )
% 4.88/5.18 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X8 ) )
% 4.88/5.18 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 4.88/5.18 & ( ( Mi3 = Ma3 )
% 4.88/5.18 => ! [X3: vEBT_VEBT] :
% 4.88/5.18 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.88/5.18 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 4.88/5.18 & ( ( Mi3 != Ma3 )
% 4.88/5.18 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 4.88/5.18 & ! [X3: nat] :
% 4.88/5.18 ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 4.88/5.18 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X3 )
% 4.88/5.18 => ( ( ord_less_nat @ Mi3 @ X3 )
% 4.88/5.18 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 4.88/5.18 @ Mima ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % VEBT_internal.valid'.elims(3)
% 4.88/5.18 thf(fact_8858_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 4.88/5.18 ! [X: vEBT_VEBT,Xa2: nat] :
% 4.88/5.18 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 4.88/5.18 => ( ( ? [Uu2: $o,Uv2: $o] :
% 4.88/5.18 ( X
% 4.88/5.18 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 4.88/5.18 => ( Xa2 != one_one_nat ) )
% 4.88/5.18 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.88/5.18 ( ( X
% 4.88/5.18 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 4.88/5.18 => ~ ( ( Deg2 = Xa2 )
% 4.88/5.18 & ! [X2: vEBT_VEBT] :
% 4.88/5.18 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.88/5.18 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.88/5.18 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.88/5.18 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 4.88/5.18 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.88/5.18 & ( case_o184042715313410164at_nat
% 4.88/5.18 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 4.88/5.18 & ! [X3: vEBT_VEBT] :
% 4.88/5.18 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.88/5.18 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 4.88/5.18 @ ( produc6081775807080527818_nat_o
% 4.88/5.18 @ ^ [Mi3: nat,Ma3: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 4.88/5.18 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 4.88/5.18 & ! [I4: nat] :
% 4.88/5.18 ( ( 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 ) ) ) ) ) )
% 4.88/5.18 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X8 ) )
% 4.88/5.18 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 4.88/5.18 & ( ( Mi3 = Ma3 )
% 4.88/5.18 => ! [X3: vEBT_VEBT] :
% 4.88/5.18 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.88/5.18 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 4.88/5.18 & ( ( Mi3 != Ma3 )
% 4.88/5.18 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 4.88/5.18 & ! [X3: nat] :
% 4.88/5.18 ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 4.88/5.18 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X3 )
% 4.88/5.18 => ( ( ord_less_nat @ Mi3 @ X3 )
% 4.88/5.18 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 4.88/5.18 @ Mima ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % VEBT_internal.valid'.elims(2)
% 4.88/5.18 thf(fact_8859_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 4.88/5.18 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 4.88/5.18 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 4.88/5.18 = Y )
% 4.88/5.18 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 4.88/5.18 => ( ! [Uu2: $o,Uv2: $o] :
% 4.88/5.18 ( ( X
% 4.88/5.18 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 4.88/5.18 => ( ( Y
% 4.88/5.18 = ( Xa2 = one_one_nat ) )
% 4.88/5.18 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 4.88/5.18 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.88/5.18 ( ( X
% 4.88/5.18 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 4.88/5.18 => ( ( Y
% 4.88/5.18 = ( ( Deg2 = Xa2 )
% 4.88/5.18 & ! [X3: vEBT_VEBT] :
% 4.88/5.18 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.88/5.18 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.88/5.18 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.88/5.18 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 4.88/5.18 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.88/5.18 & ( case_o184042715313410164at_nat
% 4.88/5.18 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 4.88/5.18 & ! [X3: vEBT_VEBT] :
% 4.88/5.18 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.88/5.18 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 4.88/5.18 @ ( produc6081775807080527818_nat_o
% 4.88/5.18 @ ^ [Mi3: nat,Ma3: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 4.88/5.18 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 4.88/5.18 & ! [I4: nat] :
% 4.88/5.18 ( ( 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 ) ) ) ) ) )
% 4.88/5.18 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X8 ) )
% 4.88/5.18 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 4.88/5.18 & ( ( Mi3 = Ma3 )
% 4.88/5.18 => ! [X3: vEBT_VEBT] :
% 4.88/5.18 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.88/5.18 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 4.88/5.18 & ( ( Mi3 != Ma3 )
% 4.88/5.18 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 4.88/5.18 & ! [X3: nat] :
% 4.88/5.18 ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 4.88/5.18 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X3 )
% 4.88/5.18 => ( ( ord_less_nat @ Mi3 @ X3 )
% 4.88/5.18 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 4.88/5.18 @ Mima ) ) )
% 4.88/5.18 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % VEBT_internal.valid'.pelims(1)
% 4.88/5.18 thf(fact_8860_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 4.88/5.18 ! [X: vEBT_VEBT,Xa2: nat] :
% 4.88/5.18 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 4.88/5.18 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 4.88/5.18 => ( ! [Uu2: $o,Uv2: $o] :
% 4.88/5.18 ( ( X
% 4.88/5.18 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 4.88/5.18 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 4.88/5.18 => ( Xa2 != one_one_nat ) ) )
% 4.88/5.18 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.88/5.18 ( ( X
% 4.88/5.18 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 4.88/5.18 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 4.88/5.18 => ~ ( ( Deg2 = Xa2 )
% 4.88/5.18 & ! [X2: vEBT_VEBT] :
% 4.88/5.18 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.88/5.18 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.88/5.18 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.88/5.18 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 4.88/5.18 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.88/5.18 & ( case_o184042715313410164at_nat
% 4.88/5.18 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 4.88/5.18 & ! [X3: vEBT_VEBT] :
% 4.88/5.18 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.88/5.18 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 4.88/5.18 @ ( produc6081775807080527818_nat_o
% 4.88/5.18 @ ^ [Mi3: nat,Ma3: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 4.88/5.18 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 4.88/5.18 & ! [I4: nat] :
% 4.88/5.18 ( ( 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 ) ) ) ) ) )
% 4.88/5.18 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X8 ) )
% 4.88/5.18 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 4.88/5.18 & ( ( Mi3 = Ma3 )
% 4.88/5.18 => ! [X3: vEBT_VEBT] :
% 4.88/5.18 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.88/5.18 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 4.88/5.18 & ( ( Mi3 != Ma3 )
% 4.88/5.18 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 4.88/5.18 & ! [X3: nat] :
% 4.88/5.18 ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 4.88/5.18 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X3 )
% 4.88/5.18 => ( ( ord_less_nat @ Mi3 @ X3 )
% 4.88/5.18 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 4.88/5.18 @ Mima ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % VEBT_internal.valid'.pelims(2)
% 4.88/5.18 thf(fact_8861_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 4.88/5.18 ! [X: vEBT_VEBT,Xa2: nat] :
% 4.88/5.18 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 4.88/5.18 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 4.88/5.18 => ( ! [Uu2: $o,Uv2: $o] :
% 4.88/5.18 ( ( X
% 4.88/5.18 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 4.88/5.18 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 4.88/5.18 => ( Xa2 = one_one_nat ) ) )
% 4.88/5.18 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.88/5.18 ( ( X
% 4.88/5.18 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 4.88/5.18 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 4.88/5.18 => ( ( Deg2 = Xa2 )
% 4.88/5.18 & ! [X4: vEBT_VEBT] :
% 4.88/5.18 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.88/5.18 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.88/5.18 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.88/5.18 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 4.88/5.18 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.88/5.18 & ( case_o184042715313410164at_nat
% 4.88/5.18 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 4.88/5.18 & ! [X3: vEBT_VEBT] :
% 4.88/5.18 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.88/5.18 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 4.88/5.18 @ ( produc6081775807080527818_nat_o
% 4.88/5.18 @ ^ [Mi3: nat,Ma3: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 4.88/5.18 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 4.88/5.18 & ! [I4: nat] :
% 4.88/5.18 ( ( 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 ) ) ) ) ) )
% 4.88/5.18 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X8 ) )
% 4.88/5.18 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 4.88/5.18 & ( ( Mi3 = Ma3 )
% 4.88/5.18 => ! [X3: vEBT_VEBT] :
% 4.88/5.18 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.88/5.18 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 4.88/5.18 & ( ( Mi3 != Ma3 )
% 4.88/5.18 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 4.88/5.18 & ! [X3: nat] :
% 4.88/5.18 ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 4.88/5.18 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X3 )
% 4.88/5.18 => ( ( ord_less_nat @ Mi3 @ X3 )
% 4.88/5.18 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 4.88/5.18 @ Mima ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % VEBT_internal.valid'.pelims(3)
% 4.88/5.18 thf(fact_8862_Sup__real__def,axiom,
% 4.88/5.18 ( comple1385675409528146559p_real
% 4.88/5.18 = ( ^ [X8: set_real] :
% 4.88/5.18 ( ord_Least_real
% 4.88/5.18 @ ^ [Z2: real] :
% 4.88/5.18 ! [X3: real] :
% 4.88/5.18 ( ( member_real @ X3 @ X8 )
% 4.88/5.18 => ( ord_less_eq_real @ X3 @ Z2 ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Sup_real_def
% 4.88/5.18 thf(fact_8863_Sup__int__def,axiom,
% 4.88/5.18 ( complete_Sup_Sup_int
% 4.88/5.18 = ( ^ [X8: set_int] :
% 4.88/5.18 ( the_int
% 4.88/5.18 @ ^ [X3: int] :
% 4.88/5.18 ( ( member_int @ X3 @ X8 )
% 4.88/5.18 & ! [Y2: int] :
% 4.88/5.18 ( ( member_int @ Y2 @ X8 )
% 4.88/5.18 => ( ord_less_eq_int @ Y2 @ X3 ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Sup_int_def
% 4.88/5.18 thf(fact_8864_card_Ocomp__fun__commute__on,axiom,
% 4.88/5.18 ( ( comp_nat_nat_nat @ suc @ suc )
% 4.88/5.18 = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 4.88/5.18
% 4.88/5.18 % card.comp_fun_commute_on
% 4.88/5.18 thf(fact_8865_mono__Suc,axiom,
% 4.88/5.18 order_mono_nat_nat @ suc ).
% 4.88/5.18
% 4.88/5.18 % mono_Suc
% 4.88/5.18 thf(fact_8866_mono__times__nat,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.18 => ( order_mono_nat_nat @ ( times_times_nat @ N ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % mono_times_nat
% 4.88/5.18 thf(fact_8867_incseq__bounded,axiom,
% 4.88/5.18 ! [X5: nat > real,B2: real] :
% 4.88/5.18 ( ( order_mono_nat_real @ X5 )
% 4.88/5.18 => ( ! [I2: nat] : ( ord_less_eq_real @ ( X5 @ I2 ) @ B2 )
% 4.88/5.18 => ( bfun_nat_real @ X5 @ at_top_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % incseq_bounded
% 4.88/5.18 thf(fact_8868_incseq__convergent,axiom,
% 4.88/5.18 ! [X5: nat > real,B2: real] :
% 4.88/5.18 ( ( order_mono_nat_real @ X5 )
% 4.88/5.18 => ( ! [I2: nat] : ( ord_less_eq_real @ ( X5 @ I2 ) @ B2 )
% 4.88/5.18 => ~ ! [L6: real] :
% 4.88/5.18 ( ( filterlim_nat_real @ X5 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 4.88/5.18 => ~ ! [I3: nat] : ( ord_less_eq_real @ ( X5 @ I3 ) @ L6 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % incseq_convergent
% 4.88/5.18 thf(fact_8869_infinite__int__iff__infinite__nat__abs,axiom,
% 4.88/5.18 ! [S2: set_int] :
% 4.88/5.18 ( ( ~ ( finite_finite_int @ S2 ) )
% 4.88/5.18 = ( ~ ( finite_finite_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ S2 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % infinite_int_iff_infinite_nat_abs
% 4.88/5.18 thf(fact_8870_mono__ge2__power__minus__self,axiom,
% 4.88/5.18 ! [K: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 4.88/5.18 => ( order_mono_nat_nat
% 4.88/5.18 @ ^ [M3: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M3 ) @ M3 ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % mono_ge2_power_minus_self
% 4.88/5.18 thf(fact_8871_take__bit__num__simps_I1_J,axiom,
% 4.88/5.18 ! [M2: num] :
% 4.88/5.18 ( ( bit_take_bit_num @ zero_zero_nat @ M2 )
% 4.88/5.18 = none_num ) ).
% 4.88/5.18
% 4.88/5.18 % take_bit_num_simps(1)
% 4.88/5.18 thf(fact_8872_nonneg__incseq__Bseq__subseq__iff,axiom,
% 4.88/5.18 ! [F: nat > real,G2: nat > nat] :
% 4.88/5.18 ( ! [X4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 4.88/5.18 => ( ( order_mono_nat_real @ F )
% 4.88/5.18 => ( ( order_5726023648592871131at_nat @ G2 )
% 4.88/5.18 => ( ( bfun_nat_real
% 4.88/5.18 @ ^ [X3: nat] : ( F @ ( G2 @ X3 ) )
% 4.88/5.18 @ at_top_nat )
% 4.88/5.18 = ( bfun_nat_real @ F @ at_top_nat ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % nonneg_incseq_Bseq_subseq_iff
% 4.88/5.18 thf(fact_8873_strict__mono__imp__increasing,axiom,
% 4.88/5.18 ! [F: nat > nat,N: nat] :
% 4.88/5.18 ( ( order_5726023648592871131at_nat @ F )
% 4.88/5.18 => ( ord_less_eq_nat @ N @ ( F @ N ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % strict_mono_imp_increasing
% 4.88/5.18 thf(fact_8874_infinite__enumerate,axiom,
% 4.88/5.18 ! [S2: set_nat] :
% 4.88/5.18 ( ~ ( finite_finite_nat @ S2 )
% 4.88/5.18 => ? [R4: nat > nat] :
% 4.88/5.18 ( ( order_5726023648592871131at_nat @ R4 )
% 4.88/5.18 & ! [N6: nat] : ( member_nat @ ( R4 @ N6 ) @ S2 ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % infinite_enumerate
% 4.88/5.18 thf(fact_8875_strict__mono__enumerate,axiom,
% 4.88/5.18 ! [S2: set_nat] :
% 4.88/5.18 ( ~ ( finite_finite_nat @ S2 )
% 4.88/5.18 => ( order_5726023648592871131at_nat @ ( infini8530281810654367211te_nat @ S2 ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % strict_mono_enumerate
% 4.88/5.18 thf(fact_8876_take__bit__num__def,axiom,
% 4.88/5.18 ( bit_take_bit_num
% 4.88/5.18 = ( ^ [N4: nat,M3: num] :
% 4.88/5.18 ( if_option_num
% 4.88/5.18 @ ( ( bit_se2925701944663578781it_nat @ N4 @ ( numeral_numeral_nat @ M3 ) )
% 4.88/5.18 = zero_zero_nat )
% 4.88/5.18 @ none_num
% 4.88/5.18 @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N4 @ ( numeral_numeral_nat @ M3 ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % take_bit_num_def
% 4.88/5.18 thf(fact_8877_num__of__nat__numeral__eq,axiom,
% 4.88/5.18 ! [Q4: num] :
% 4.88/5.18 ( ( num_of_nat @ ( numeral_numeral_nat @ Q4 ) )
% 4.88/5.18 = Q4 ) ).
% 4.88/5.18
% 4.88/5.18 % num_of_nat_numeral_eq
% 4.88/5.18 thf(fact_8878_num__of__nat_Osimps_I1_J,axiom,
% 4.88/5.18 ( ( num_of_nat @ zero_zero_nat )
% 4.88/5.18 = one ) ).
% 4.88/5.18
% 4.88/5.18 % num_of_nat.simps(1)
% 4.88/5.18 thf(fact_8879_numeral__num__of__nat,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.18 => ( ( numeral_numeral_nat @ ( num_of_nat @ N ) )
% 4.88/5.18 = N ) ) ).
% 4.88/5.18
% 4.88/5.18 % numeral_num_of_nat
% 4.88/5.18 thf(fact_8880_num__of__nat__One,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ N @ one_one_nat )
% 4.88/5.18 => ( ( num_of_nat @ N )
% 4.88/5.18 = one ) ) ).
% 4.88/5.18
% 4.88/5.18 % num_of_nat_One
% 4.88/5.18 thf(fact_8881_num__of__nat__double,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.18 => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
% 4.88/5.18 = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % num_of_nat_double
% 4.88/5.18 thf(fact_8882_num__of__nat__plus__distrib,axiom,
% 4.88/5.18 ! [M2: nat,N: nat] :
% 4.88/5.18 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 4.88/5.18 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.18 => ( ( num_of_nat @ ( plus_plus_nat @ M2 @ N ) )
% 4.88/5.18 = ( plus_plus_num @ ( num_of_nat @ M2 ) @ ( num_of_nat @ N ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % num_of_nat_plus_distrib
% 4.88/5.18 thf(fact_8883_inj__sgn__power,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.18 => ( inj_on_real_real
% 4.88/5.18 @ ^ [Y2: real] : ( times_times_real @ ( sgn_sgn_real @ Y2 ) @ ( power_power_real @ ( abs_abs_real @ Y2 ) @ N ) )
% 4.88/5.18 @ top_top_set_real ) ) ).
% 4.88/5.18
% 4.88/5.18 % inj_sgn_power
% 4.88/5.18 thf(fact_8884_min__Suc__Suc,axiom,
% 4.88/5.18 ! [M2: nat,N: nat] :
% 4.88/5.18 ( ( ord_min_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 4.88/5.18 = ( suc @ ( ord_min_nat @ M2 @ N ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % min_Suc_Suc
% 4.88/5.18 thf(fact_8885_min__0R,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( ord_min_nat @ N @ zero_zero_nat )
% 4.88/5.18 = zero_zero_nat ) ).
% 4.88/5.18
% 4.88/5.18 % min_0R
% 4.88/5.18 thf(fact_8886_min__0L,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( ord_min_nat @ zero_zero_nat @ N )
% 4.88/5.18 = zero_zero_nat ) ).
% 4.88/5.18
% 4.88/5.18 % min_0L
% 4.88/5.18 thf(fact_8887_min__Suc__numeral,axiom,
% 4.88/5.18 ! [N: nat,K: num] :
% 4.88/5.18 ( ( ord_min_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 4.88/5.18 = ( suc @ ( ord_min_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % min_Suc_numeral
% 4.88/5.18 thf(fact_8888_min__numeral__Suc,axiom,
% 4.88/5.18 ! [K: num,N: nat] :
% 4.88/5.18 ( ( ord_min_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 4.88/5.18 = ( suc @ ( ord_min_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % min_numeral_Suc
% 4.88/5.18 thf(fact_8889_inf__nat__def,axiom,
% 4.88/5.18 inf_inf_nat = ord_min_nat ).
% 4.88/5.18
% 4.88/5.18 % inf_nat_def
% 4.88/5.18 thf(fact_8890_min__diff,axiom,
% 4.88/5.18 ! [M2: nat,I: nat,N: nat] :
% 4.88/5.18 ( ( ord_min_nat @ ( minus_minus_nat @ M2 @ I ) @ ( minus_minus_nat @ N @ I ) )
% 4.88/5.18 = ( minus_minus_nat @ ( ord_min_nat @ M2 @ N ) @ I ) ) ).
% 4.88/5.18
% 4.88/5.18 % min_diff
% 4.88/5.18 thf(fact_8891_nat__mult__min__right,axiom,
% 4.88/5.18 ! [M2: nat,N: nat,Q4: nat] :
% 4.88/5.18 ( ( times_times_nat @ M2 @ ( ord_min_nat @ N @ Q4 ) )
% 4.88/5.18 = ( ord_min_nat @ ( times_times_nat @ M2 @ N ) @ ( times_times_nat @ M2 @ Q4 ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % nat_mult_min_right
% 4.88/5.18 thf(fact_8892_nat__mult__min__left,axiom,
% 4.88/5.18 ! [M2: nat,N: nat,Q4: nat] :
% 4.88/5.18 ( ( times_times_nat @ ( ord_min_nat @ M2 @ N ) @ Q4 )
% 4.88/5.18 = ( ord_min_nat @ ( times_times_nat @ M2 @ Q4 ) @ ( times_times_nat @ N @ Q4 ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % nat_mult_min_left
% 4.88/5.18 thf(fact_8893_min__Suc1,axiom,
% 4.88/5.18 ! [N: nat,M2: nat] :
% 4.88/5.18 ( ( ord_min_nat @ ( suc @ N ) @ M2 )
% 4.88/5.18 = ( case_nat_nat @ zero_zero_nat
% 4.88/5.18 @ ^ [M6: nat] : ( suc @ ( ord_min_nat @ N @ M6 ) )
% 4.88/5.18 @ M2 ) ) ).
% 4.88/5.18
% 4.88/5.18 % min_Suc1
% 4.88/5.18 thf(fact_8894_min__Suc2,axiom,
% 4.88/5.18 ! [M2: nat,N: nat] :
% 4.88/5.18 ( ( ord_min_nat @ M2 @ ( suc @ N ) )
% 4.88/5.18 = ( case_nat_nat @ zero_zero_nat
% 4.88/5.18 @ ^ [M6: nat] : ( suc @ ( ord_min_nat @ M6 @ N ) )
% 4.88/5.18 @ M2 ) ) ).
% 4.88/5.18
% 4.88/5.18 % min_Suc2
% 4.88/5.18 thf(fact_8895_inj__Suc,axiom,
% 4.88/5.18 ! [N5: set_nat] : ( inj_on_nat_nat @ suc @ N5 ) ).
% 4.88/5.18
% 4.88/5.18 % inj_Suc
% 4.88/5.18 thf(fact_8896_inj__on__diff__nat,axiom,
% 4.88/5.18 ! [N5: set_nat,K: nat] :
% 4.88/5.18 ( ! [N2: nat] :
% 4.88/5.18 ( ( member_nat @ N2 @ N5 )
% 4.88/5.18 => ( ord_less_eq_nat @ K @ N2 ) )
% 4.88/5.18 => ( inj_on_nat_nat
% 4.88/5.18 @ ^ [N4: nat] : ( minus_minus_nat @ N4 @ K )
% 4.88/5.18 @ N5 ) ) ).
% 4.88/5.18
% 4.88/5.18 % inj_on_diff_nat
% 4.88/5.18 thf(fact_8897_inj__on__set__encode,axiom,
% 4.88/5.18 inj_on_set_nat_nat @ nat_set_encode @ ( collect_set_nat @ finite_finite_nat ) ).
% 4.88/5.18
% 4.88/5.18 % inj_on_set_encode
% 4.88/5.18 thf(fact_8898_summable__reindex,axiom,
% 4.88/5.18 ! [F: nat > real,G2: nat > nat] :
% 4.88/5.18 ( ( summable_real @ F )
% 4.88/5.18 => ( ( inj_on_nat_nat @ G2 @ top_top_set_nat )
% 4.88/5.18 => ( ! [X4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 4.88/5.18 => ( summable_real @ ( comp_nat_real_nat @ F @ G2 ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % summable_reindex
% 4.88/5.18 thf(fact_8899_suminf__reindex__mono,axiom,
% 4.88/5.18 ! [F: nat > real,G2: nat > nat] :
% 4.88/5.18 ( ( summable_real @ F )
% 4.88/5.18 => ( ( inj_on_nat_nat @ G2 @ top_top_set_nat )
% 4.88/5.18 => ( ! [X4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 4.88/5.18 => ( ord_less_eq_real @ ( suminf_real @ ( comp_nat_real_nat @ F @ G2 ) ) @ ( suminf_real @ F ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % suminf_reindex_mono
% 4.88/5.18 thf(fact_8900_suminf__reindex,axiom,
% 4.88/5.18 ! [F: nat > real,G2: nat > nat] :
% 4.88/5.18 ( ( summable_real @ F )
% 4.88/5.18 => ( ( inj_on_nat_nat @ G2 @ top_top_set_nat )
% 4.88/5.18 => ( ! [X4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 4.88/5.18 => ( ! [X4: nat] :
% 4.88/5.18 ( ~ ( member_nat @ X4 @ ( image_nat_nat @ G2 @ top_top_set_nat ) )
% 4.88/5.18 => ( ( F @ X4 )
% 4.88/5.18 = zero_zero_real ) )
% 4.88/5.18 => ( ( suminf_real @ ( comp_nat_real_nat @ F @ G2 ) )
% 4.88/5.18 = ( suminf_real @ F ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % suminf_reindex
% 4.88/5.18 thf(fact_8901_continuous__on__arcosh_H,axiom,
% 4.88/5.18 ! [A2: set_real,F: real > real] :
% 4.88/5.18 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 4.88/5.18 => ( ! [X4: real] :
% 4.88/5.18 ( ( member_real @ X4 @ A2 )
% 4.88/5.18 => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 4.88/5.18 => ( topolo5044208981011980120l_real @ A2
% 4.88/5.18 @ ^ [X3: real] : ( arcosh_real @ ( F @ X3 ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % continuous_on_arcosh'
% 4.88/5.18 thf(fact_8902_continuous__image__closed__interval,axiom,
% 4.88/5.18 ! [A: real,B: real,F: real > real] :
% 4.88/5.18 ( ( ord_less_eq_real @ A @ B )
% 4.88/5.18 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 4.88/5.18 => ? [C3: real,D6: real] :
% 4.88/5.18 ( ( ( image_real_real @ F @ ( set_or1222579329274155063t_real @ A @ B ) )
% 4.88/5.18 = ( set_or1222579329274155063t_real @ C3 @ D6 ) )
% 4.88/5.18 & ( ord_less_eq_real @ C3 @ D6 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % continuous_image_closed_interval
% 4.88/5.18 thf(fact_8903_continuous__on__arcosh,axiom,
% 4.88/5.18 ! [A2: set_real] :
% 4.88/5.18 ( ( ord_less_eq_set_real @ A2 @ ( set_ord_atLeast_real @ one_one_real ) )
% 4.88/5.18 => ( topolo5044208981011980120l_real @ A2 @ arcosh_real ) ) ).
% 4.88/5.18
% 4.88/5.18 % continuous_on_arcosh
% 4.88/5.18 thf(fact_8904_continuous__on__artanh,axiom,
% 4.88/5.18 ! [A2: set_real] :
% 4.88/5.18 ( ( ord_less_eq_set_real @ A2 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) )
% 4.88/5.18 => ( topolo5044208981011980120l_real @ A2 @ artanh_real ) ) ).
% 4.88/5.18
% 4.88/5.18 % continuous_on_artanh
% 4.88/5.18 thf(fact_8905_DERIV__isconst2,axiom,
% 4.88/5.18 ! [A: real,B: real,F: real > real,X: real] :
% 4.88/5.18 ( ( ord_less_real @ A @ B )
% 4.88/5.18 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 4.88/5.18 => ( ! [X4: real] :
% 4.88/5.18 ( ( ord_less_real @ A @ X4 )
% 4.88/5.18 => ( ( ord_less_real @ X4 @ B )
% 4.88/5.18 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 4.88/5.18 => ( ( ord_less_eq_real @ A @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ B )
% 4.88/5.18 => ( ( F @ X )
% 4.88/5.18 = ( F @ A ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % DERIV_isconst2
% 4.88/5.18 thf(fact_8906_powr__real__of__int_H,axiom,
% 4.88/5.18 ! [X: real,N: int] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( ( X != zero_zero_real )
% 4.88/5.18 | ( ord_less_int @ zero_zero_int @ N ) )
% 4.88/5.18 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 4.88/5.18 = ( power_int_real @ X @ N ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % powr_real_of_int'
% 4.88/5.18 thf(fact_8907_isCont__Lb__Ub,axiom,
% 4.88/5.18 ! [A: real,B: real,F: real > real] :
% 4.88/5.18 ( ( ord_less_eq_real @ A @ B )
% 4.88/5.18 => ( ! [X4: real] :
% 4.88/5.18 ( ( ( ord_less_eq_real @ A @ X4 )
% 4.88/5.18 & ( ord_less_eq_real @ X4 @ B ) )
% 4.88/5.18 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ F ) )
% 4.88/5.18 => ? [L6: real,M9: real] :
% 4.88/5.18 ( ! [X2: real] :
% 4.88/5.18 ( ( ( ord_less_eq_real @ A @ X2 )
% 4.88/5.18 & ( ord_less_eq_real @ X2 @ B ) )
% 4.88/5.18 => ( ( ord_less_eq_real @ L6 @ ( F @ X2 ) )
% 4.88/5.18 & ( ord_less_eq_real @ ( F @ X2 ) @ M9 ) ) )
% 4.88/5.18 & ! [Y4: real] :
% 4.88/5.18 ( ( ( ord_less_eq_real @ L6 @ Y4 )
% 4.88/5.18 & ( ord_less_eq_real @ Y4 @ M9 ) )
% 4.88/5.18 => ? [X4: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ A @ X4 )
% 4.88/5.18 & ( ord_less_eq_real @ X4 @ B )
% 4.88/5.18 & ( ( F @ X4 )
% 4.88/5.18 = Y4 ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % isCont_Lb_Ub
% 4.88/5.18 thf(fact_8908_isCont__inverse__function2,axiom,
% 4.88/5.18 ! [A: real,X: real,B: real,G2: real > real,F: real > real] :
% 4.88/5.18 ( ( ord_less_real @ A @ X )
% 4.88/5.18 => ( ( ord_less_real @ X @ B )
% 4.88/5.18 => ( ! [Z3: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ A @ Z3 )
% 4.88/5.18 => ( ( ord_less_eq_real @ Z3 @ B )
% 4.88/5.18 => ( ( G2 @ ( F @ Z3 ) )
% 4.88/5.18 = Z3 ) ) )
% 4.88/5.18 => ( ! [Z3: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ A @ Z3 )
% 4.88/5.18 => ( ( ord_less_eq_real @ Z3 @ B )
% 4.88/5.18 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) ) )
% 4.88/5.18 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X ) @ top_top_set_real ) @ G2 ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % isCont_inverse_function2
% 4.88/5.18 thf(fact_8909_LIM__less__bound,axiom,
% 4.88/5.18 ! [B: real,X: real,F: real > real] :
% 4.88/5.18 ( ( ord_less_real @ B @ X )
% 4.88/5.18 => ( ! [X4: real] :
% 4.88/5.18 ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ B @ X ) )
% 4.88/5.18 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 4.88/5.18 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ F )
% 4.88/5.18 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % LIM_less_bound
% 4.88/5.18 thf(fact_8910_isCont__inverse__function,axiom,
% 4.88/5.18 ! [D: real,X: real,G2: real > real,F: real > real] :
% 4.88/5.18 ( ( ord_less_real @ zero_zero_real @ D )
% 4.88/5.18 => ( ! [Z3: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ X ) ) @ D )
% 4.88/5.18 => ( ( G2 @ ( F @ Z3 ) )
% 4.88/5.18 = Z3 ) )
% 4.88/5.18 => ( ! [Z3: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ X ) ) @ D )
% 4.88/5.18 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) )
% 4.88/5.18 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X ) @ top_top_set_real ) @ G2 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % isCont_inverse_function
% 4.88/5.18 thf(fact_8911_GMVT_H,axiom,
% 4.88/5.18 ! [A: real,B: real,F: real > real,G2: real > real,G3: real > real,F6: real > real] :
% 4.88/5.18 ( ( ord_less_real @ A @ B )
% 4.88/5.18 => ( ! [Z3: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ A @ Z3 )
% 4.88/5.18 => ( ( ord_less_eq_real @ Z3 @ B )
% 4.88/5.18 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) ) )
% 4.88/5.18 => ( ! [Z3: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ A @ Z3 )
% 4.88/5.18 => ( ( ord_less_eq_real @ Z3 @ B )
% 4.88/5.18 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ G2 ) ) )
% 4.88/5.18 => ( ! [Z3: real] :
% 4.88/5.18 ( ( ord_less_real @ A @ Z3 )
% 4.88/5.18 => ( ( ord_less_real @ Z3 @ B )
% 4.88/5.18 => ( has_fi5821293074295781190e_real @ G2 @ ( G3 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 4.88/5.18 => ( ! [Z3: real] :
% 4.88/5.18 ( ( ord_less_real @ A @ Z3 )
% 4.88/5.18 => ( ( ord_less_real @ Z3 @ B )
% 4.88/5.18 => ( has_fi5821293074295781190e_real @ F @ ( F6 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 4.88/5.18 => ? [C3: real] :
% 4.88/5.18 ( ( ord_less_real @ A @ C3 )
% 4.88/5.18 & ( ord_less_real @ C3 @ B )
% 4.88/5.18 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G3 @ C3 ) )
% 4.88/5.18 = ( times_times_real @ ( minus_minus_real @ ( G2 @ B ) @ ( G2 @ A ) ) @ ( F6 @ C3 ) ) ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % GMVT'
% 4.88/5.18 thf(fact_8912_bdd__above__nat,axiom,
% 4.88/5.18 condit2214826472909112428ve_nat = finite_finite_nat ).
% 4.88/5.18
% 4.88/5.18 % bdd_above_nat
% 4.88/5.18 thf(fact_8913_GMVT,axiom,
% 4.88/5.18 ! [A: real,B: real,F: real > real,G2: real > real] :
% 4.88/5.18 ( ( ord_less_real @ A @ B )
% 4.88/5.18 => ( ! [X4: real] :
% 4.88/5.18 ( ( ( ord_less_eq_real @ A @ X4 )
% 4.88/5.18 & ( ord_less_eq_real @ X4 @ B ) )
% 4.88/5.18 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ F ) )
% 4.88/5.18 => ( ! [X4: real] :
% 4.88/5.18 ( ( ( ord_less_real @ A @ X4 )
% 4.88/5.18 & ( ord_less_real @ X4 @ B ) )
% 4.88/5.18 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 4.88/5.18 => ( ! [X4: real] :
% 4.88/5.18 ( ( ( ord_less_eq_real @ A @ X4 )
% 4.88/5.18 & ( ord_less_eq_real @ X4 @ B ) )
% 4.88/5.18 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ G2 ) )
% 4.88/5.18 => ( ! [X4: real] :
% 4.88/5.18 ( ( ( ord_less_real @ A @ X4 )
% 4.88/5.18 & ( ord_less_real @ X4 @ B ) )
% 4.88/5.18 => ( differ6690327859849518006l_real @ G2 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 4.88/5.18 => ? [G_c: real,F_c: real,C3: real] :
% 4.88/5.18 ( ( has_fi5821293074295781190e_real @ G2 @ G_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 4.88/5.18 & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 4.88/5.18 & ( ord_less_real @ A @ C3 )
% 4.88/5.18 & ( ord_less_real @ C3 @ B )
% 4.88/5.18 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ G_c )
% 4.88/5.18 = ( times_times_real @ ( minus_minus_real @ ( G2 @ B ) @ ( G2 @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % GMVT
% 4.88/5.18 thf(fact_8914_num__of__nat_Osimps_I2_J,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.18 => ( ( num_of_nat @ ( suc @ N ) )
% 4.88/5.18 = ( inc @ ( num_of_nat @ N ) ) ) )
% 4.88/5.18 & ( ~ ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.18 => ( ( num_of_nat @ ( suc @ N ) )
% 4.88/5.18 = one ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % num_of_nat.simps(2)
% 4.88/5.18 thf(fact_8915_pred__numeral__inc,axiom,
% 4.88/5.18 ! [K: num] :
% 4.88/5.18 ( ( pred_numeral @ ( inc @ K ) )
% 4.88/5.18 = ( numeral_numeral_nat @ K ) ) ).
% 4.88/5.18
% 4.88/5.18 % pred_numeral_inc
% 4.88/5.18 thf(fact_8916_add__inc,axiom,
% 4.88/5.18 ! [X: num,Y: num] :
% 4.88/5.18 ( ( plus_plus_num @ X @ ( inc @ Y ) )
% 4.88/5.18 = ( inc @ ( plus_plus_num @ X @ Y ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % add_inc
% 4.88/5.18 thf(fact_8917_num__induct,axiom,
% 4.88/5.18 ! [P: num > $o,X: num] :
% 4.88/5.18 ( ( P @ one )
% 4.88/5.18 => ( ! [X4: num] :
% 4.88/5.18 ( ( P @ X4 )
% 4.88/5.18 => ( P @ ( inc @ X4 ) ) )
% 4.88/5.18 => ( P @ X ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % num_induct
% 4.88/5.18 thf(fact_8918_inc_Osimps_I1_J,axiom,
% 4.88/5.18 ( ( inc @ one )
% 4.88/5.18 = ( bit0 @ one ) ) ).
% 4.88/5.18
% 4.88/5.18 % inc.simps(1)
% 4.88/5.18 thf(fact_8919_inc_Osimps_I2_J,axiom,
% 4.88/5.18 ! [X: num] :
% 4.88/5.18 ( ( inc @ ( bit0 @ X ) )
% 4.88/5.18 = ( bit1 @ X ) ) ).
% 4.88/5.18
% 4.88/5.18 % inc.simps(2)
% 4.88/5.18 thf(fact_8920_inc_Osimps_I3_J,axiom,
% 4.88/5.18 ! [X: num] :
% 4.88/5.18 ( ( inc @ ( bit1 @ X ) )
% 4.88/5.18 = ( bit0 @ ( inc @ X ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % inc.simps(3)
% 4.88/5.18 thf(fact_8921_add__One,axiom,
% 4.88/5.18 ! [X: num] :
% 4.88/5.18 ( ( plus_plus_num @ X @ one )
% 4.88/5.18 = ( inc @ X ) ) ).
% 4.88/5.18
% 4.88/5.18 % add_One
% 4.88/5.18 thf(fact_8922_inc__BitM__eq,axiom,
% 4.88/5.18 ! [N: num] :
% 4.88/5.18 ( ( inc @ ( bitM @ N ) )
% 4.88/5.18 = ( bit0 @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % inc_BitM_eq
% 4.88/5.18 thf(fact_8923_BitM__inc__eq,axiom,
% 4.88/5.18 ! [N: num] :
% 4.88/5.18 ( ( bitM @ ( inc @ N ) )
% 4.88/5.18 = ( bit1 @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % BitM_inc_eq
% 4.88/5.18 thf(fact_8924_mult__inc,axiom,
% 4.88/5.18 ! [X: num,Y: num] :
% 4.88/5.18 ( ( times_times_num @ X @ ( inc @ Y ) )
% 4.88/5.18 = ( plus_plus_num @ ( times_times_num @ X @ Y ) @ X ) ) ).
% 4.88/5.18
% 4.88/5.18 % mult_inc
% 4.88/5.18 thf(fact_8925_Rats__eq__int__div__nat,axiom,
% 4.88/5.18 ( field_5140801741446780682s_real
% 4.88/5.18 = ( collect_real
% 4.88/5.18 @ ^ [Uu3: real] :
% 4.88/5.18 ? [I4: int,N4: nat] :
% 4.88/5.18 ( ( Uu3
% 4.88/5.18 = ( divide_divide_real @ ( ring_1_of_int_real @ I4 ) @ ( semiri5074537144036343181t_real @ N4 ) ) )
% 4.88/5.18 & ( N4 != zero_zero_nat ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Rats_eq_int_div_nat
% 4.88/5.18 thf(fact_8926_Rats__abs__iff,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( member_real @ ( abs_abs_real @ X ) @ field_5140801741446780682s_real )
% 4.88/5.18 = ( member_real @ X @ field_5140801741446780682s_real ) ) ).
% 4.88/5.18
% 4.88/5.18 % Rats_abs_iff
% 4.88/5.18 thf(fact_8927_Rats__no__bot__less,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ? [X4: real] :
% 4.88/5.18 ( ( member_real @ X4 @ field_5140801741446780682s_real )
% 4.88/5.18 & ( ord_less_real @ X4 @ X ) ) ).
% 4.88/5.18
% 4.88/5.18 % Rats_no_bot_less
% 4.88/5.18 thf(fact_8928_Rats__dense__in__real,axiom,
% 4.88/5.18 ! [X: real,Y: real] :
% 4.88/5.18 ( ( ord_less_real @ X @ Y )
% 4.88/5.18 => ? [X4: real] :
% 4.88/5.18 ( ( member_real @ X4 @ field_5140801741446780682s_real )
% 4.88/5.18 & ( ord_less_real @ X @ X4 )
% 4.88/5.18 & ( ord_less_real @ X4 @ Y ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Rats_dense_in_real
% 4.88/5.18 thf(fact_8929_Rats__no__top__le,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ? [X4: real] :
% 4.88/5.18 ( ( member_real @ X4 @ field_5140801741446780682s_real )
% 4.88/5.18 & ( ord_less_eq_real @ X @ X4 ) ) ).
% 4.88/5.18
% 4.88/5.18 % Rats_no_top_le
% 4.88/5.18 thf(fact_8930_Rats__eq__int__div__int,axiom,
% 4.88/5.18 ( field_5140801741446780682s_real
% 4.88/5.18 = ( collect_real
% 4.88/5.18 @ ^ [Uu3: real] :
% 4.88/5.18 ? [I4: int,J3: int] :
% 4.88/5.18 ( ( Uu3
% 4.88/5.18 = ( divide_divide_real @ ( ring_1_of_int_real @ I4 ) @ ( ring_1_of_int_real @ J3 ) ) )
% 4.88/5.18 & ( J3 != zero_zero_int ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Rats_eq_int_div_int
% 4.88/5.18 thf(fact_8931_Arg__bounded,axiom,
% 4.88/5.18 ! [Z: complex] :
% 4.88/5.18 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 4.88/5.18 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ).
% 4.88/5.18
% 4.88/5.18 % Arg_bounded
% 4.88/5.18 thf(fact_8932_bij__betw__roots__unity,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.18 => ( bij_betw_nat_complex
% 4.88/5.18 @ ^ [K3: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K3 ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 4.88/5.18 @ ( set_ord_lessThan_nat @ N )
% 4.88/5.18 @ ( collect_complex
% 4.88/5.18 @ ^ [Z2: complex] :
% 4.88/5.18 ( ( power_power_complex @ Z2 @ N )
% 4.88/5.18 = one_one_complex ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % bij_betw_roots_unity
% 4.88/5.18 thf(fact_8933_cis__Arg__unique,axiom,
% 4.88/5.18 ! [Z: complex,X: real] :
% 4.88/5.18 ( ( ( sgn_sgn_complex @ Z )
% 4.88/5.18 = ( cis @ X ) )
% 4.88/5.18 => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X )
% 4.88/5.18 => ( ( ord_less_eq_real @ X @ pi )
% 4.88/5.18 => ( ( arg @ Z )
% 4.88/5.18 = X ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % cis_Arg_unique
% 4.88/5.18 thf(fact_8934_Arg__correct,axiom,
% 4.88/5.18 ! [Z: complex] :
% 4.88/5.18 ( ( Z != zero_zero_complex )
% 4.88/5.18 => ( ( ( sgn_sgn_complex @ Z )
% 4.88/5.18 = ( cis @ ( arg @ Z ) ) )
% 4.88/5.18 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 4.88/5.18 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Arg_correct
% 4.88/5.18 thf(fact_8935_bij__betw__nth__root__unity,axiom,
% 4.88/5.18 ! [C: complex,N: nat] :
% 4.88/5.18 ( ( C != zero_zero_complex )
% 4.88/5.18 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.18 => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 4.88/5.18 @ ( collect_complex
% 4.88/5.18 @ ^ [Z2: complex] :
% 4.88/5.18 ( ( power_power_complex @ Z2 @ N )
% 4.88/5.18 = one_one_complex ) )
% 4.88/5.18 @ ( collect_complex
% 4.88/5.18 @ ^ [Z2: complex] :
% 4.88/5.18 ( ( power_power_complex @ Z2 @ N )
% 4.88/5.18 = C ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % bij_betw_nth_root_unity
% 4.88/5.18 thf(fact_8936_bij__betw__Suc,axiom,
% 4.88/5.18 ! [M5: set_nat,N5: set_nat] :
% 4.88/5.18 ( ( bij_betw_nat_nat @ suc @ M5 @ N5 )
% 4.88/5.18 = ( ( image_nat_nat @ suc @ M5 )
% 4.88/5.18 = N5 ) ) ).
% 4.88/5.18
% 4.88/5.18 % bij_betw_Suc
% 4.88/5.18 thf(fact_8937_bij__enumerate,axiom,
% 4.88/5.18 ! [S2: set_nat] :
% 4.88/5.18 ( ~ ( finite_finite_nat @ S2 )
% 4.88/5.18 => ( bij_betw_nat_nat @ ( infini8530281810654367211te_nat @ S2 ) @ top_top_set_nat @ S2 ) ) ).
% 4.88/5.18
% 4.88/5.18 % bij_enumerate
% 4.88/5.18 thf(fact_8938_Arg__def,axiom,
% 4.88/5.18 ( arg
% 4.88/5.18 = ( ^ [Z2: complex] :
% 4.88/5.18 ( if_real @ ( Z2 = zero_zero_complex ) @ zero_zero_real
% 4.88/5.18 @ ( fChoice_real
% 4.88/5.18 @ ^ [A4: real] :
% 4.88/5.18 ( ( ( sgn_sgn_complex @ Z2 )
% 4.88/5.18 = ( cis @ A4 ) )
% 4.88/5.18 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A4 )
% 4.88/5.18 & ( ord_less_eq_real @ A4 @ pi ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Arg_def
% 4.88/5.18 thf(fact_8939_less__eq__int_Orep__eq,axiom,
% 4.88/5.18 ( ord_less_eq_int
% 4.88/5.18 = ( ^ [X3: int,Xa4: int] :
% 4.88/5.18 ( produc8739625826339149834_nat_o
% 4.88/5.18 @ ^ [Y2: nat,Z2: nat] :
% 4.88/5.18 ( produc6081775807080527818_nat_o
% 4.88/5.18 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y2 @ V3 ) @ ( plus_plus_nat @ U2 @ Z2 ) ) )
% 4.88/5.18 @ ( rep_Integ @ X3 )
% 4.88/5.18 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % less_eq_int.rep_eq
% 4.88/5.18 thf(fact_8940_less__int_Orep__eq,axiom,
% 4.88/5.18 ( ord_less_int
% 4.88/5.18 = ( ^ [X3: int,Xa4: int] :
% 4.88/5.18 ( produc8739625826339149834_nat_o
% 4.88/5.18 @ ^ [Y2: nat,Z2: nat] :
% 4.88/5.18 ( produc6081775807080527818_nat_o
% 4.88/5.18 @ ^ [U2: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y2 @ V3 ) @ ( plus_plus_nat @ U2 @ Z2 ) ) )
% 4.88/5.18 @ ( rep_Integ @ X3 )
% 4.88/5.18 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % less_int.rep_eq
% 4.88/5.18 thf(fact_8941_less__eq__int_Oabs__eq,axiom,
% 4.88/5.18 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 4.88/5.18 ( ( ord_less_eq_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 4.88/5.18 = ( produc8739625826339149834_nat_o
% 4.88/5.18 @ ^ [X3: nat,Y2: nat] :
% 4.88/5.18 ( produc6081775807080527818_nat_o
% 4.88/5.18 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V3 ) @ ( plus_plus_nat @ U2 @ Y2 ) ) )
% 4.88/5.18 @ Xa2
% 4.88/5.18 @ X ) ) ).
% 4.88/5.18
% 4.88/5.18 % less_eq_int.abs_eq
% 4.88/5.18 thf(fact_8942_zero__int__def,axiom,
% 4.88/5.18 ( zero_zero_int
% 4.88/5.18 = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % zero_int_def
% 4.88/5.18 thf(fact_8943_int__def,axiom,
% 4.88/5.18 ( semiri1314217659103216013at_int
% 4.88/5.18 = ( ^ [N4: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N4 @ zero_zero_nat ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % int_def
% 4.88/5.18 thf(fact_8944_one__int__def,axiom,
% 4.88/5.18 ( one_one_int
% 4.88/5.18 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % one_int_def
% 4.88/5.18 thf(fact_8945_less__int_Oabs__eq,axiom,
% 4.88/5.18 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 4.88/5.18 ( ( ord_less_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 4.88/5.18 = ( produc8739625826339149834_nat_o
% 4.88/5.18 @ ^ [X3: nat,Y2: nat] :
% 4.88/5.18 ( produc6081775807080527818_nat_o
% 4.88/5.18 @ ^ [U2: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V3 ) @ ( plus_plus_nat @ U2 @ Y2 ) ) )
% 4.88/5.18 @ Xa2
% 4.88/5.18 @ X ) ) ).
% 4.88/5.18
% 4.88/5.18 % less_int.abs_eq
% 4.88/5.18 thf(fact_8946_card__length__sum__list__rec,axiom,
% 4.88/5.18 ! [M2: nat,N5: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ one_one_nat @ M2 )
% 4.88/5.18 => ( ( finite_card_list_nat
% 4.88/5.18 @ ( collect_list_nat
% 4.88/5.18 @ ^ [L3: list_nat] :
% 4.88/5.18 ( ( ( size_size_list_nat @ L3 )
% 4.88/5.18 = M2 )
% 4.88/5.18 & ( ( groups4561878855575611511st_nat @ L3 )
% 4.88/5.18 = N5 ) ) ) )
% 4.88/5.18 = ( plus_plus_nat
% 4.88/5.18 @ ( finite_card_list_nat
% 4.88/5.18 @ ( collect_list_nat
% 4.88/5.18 @ ^ [L3: list_nat] :
% 4.88/5.18 ( ( ( size_size_list_nat @ L3 )
% 4.88/5.18 = ( minus_minus_nat @ M2 @ one_one_nat ) )
% 4.88/5.18 & ( ( groups4561878855575611511st_nat @ L3 )
% 4.88/5.18 = N5 ) ) ) )
% 4.88/5.18 @ ( finite_card_list_nat
% 4.88/5.18 @ ( collect_list_nat
% 4.88/5.18 @ ^ [L3: list_nat] :
% 4.88/5.18 ( ( ( size_size_list_nat @ L3 )
% 4.88/5.18 = M2 )
% 4.88/5.18 & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L3 ) @ one_one_nat )
% 4.88/5.18 = N5 ) ) ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % card_length_sum_list_rec
% 4.88/5.18 thf(fact_8947_card__length__sum__list,axiom,
% 4.88/5.18 ! [M2: nat,N5: nat] :
% 4.88/5.18 ( ( finite_card_list_nat
% 4.88/5.18 @ ( collect_list_nat
% 4.88/5.18 @ ^ [L3: list_nat] :
% 4.88/5.18 ( ( ( size_size_list_nat @ L3 )
% 4.88/5.18 = M2 )
% 4.88/5.18 & ( ( groups4561878855575611511st_nat @ L3 )
% 4.88/5.18 = N5 ) ) ) )
% 4.88/5.18 = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N5 @ M2 ) @ one_one_nat ) @ N5 ) ) ).
% 4.88/5.18
% 4.88/5.18 % card_length_sum_list
% 4.88/5.18 thf(fact_8948_hd__upt,axiom,
% 4.88/5.18 ! [I: nat,J: nat] :
% 4.88/5.18 ( ( ord_less_nat @ I @ J )
% 4.88/5.18 => ( ( hd_nat @ ( upt @ I @ J ) )
% 4.88/5.18 = I ) ) ).
% 4.88/5.18
% 4.88/5.18 % hd_upt
% 4.88/5.18 thf(fact_8949_upt__conv__Nil,axiom,
% 4.88/5.18 ! [J: nat,I: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ J @ I )
% 4.88/5.18 => ( ( upt @ I @ J )
% 4.88/5.18 = nil_nat ) ) ).
% 4.88/5.18
% 4.88/5.18 % upt_conv_Nil
% 4.88/5.18 thf(fact_8950_upt__eq__Nil__conv,axiom,
% 4.88/5.18 ! [I: nat,J: nat] :
% 4.88/5.18 ( ( ( upt @ I @ J )
% 4.88/5.18 = nil_nat )
% 4.88/5.18 = ( ( J = zero_zero_nat )
% 4.88/5.18 | ( ord_less_eq_nat @ J @ I ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % upt_eq_Nil_conv
% 4.88/5.18 thf(fact_8951_take__upt,axiom,
% 4.88/5.18 ! [I: nat,M2: nat,N: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ M2 ) @ N )
% 4.88/5.18 => ( ( take_nat @ M2 @ ( upt @ I @ N ) )
% 4.88/5.18 = ( upt @ I @ ( plus_plus_nat @ I @ M2 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % take_upt
% 4.88/5.18 thf(fact_8952_nth__upt,axiom,
% 4.88/5.18 ! [I: nat,K: nat,J: nat] :
% 4.88/5.18 ( ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J )
% 4.88/5.18 => ( ( nth_nat @ ( upt @ I @ J ) @ K )
% 4.88/5.18 = ( plus_plus_nat @ I @ K ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % nth_upt
% 4.88/5.18 thf(fact_8953_upt__rec__numeral,axiom,
% 4.88/5.18 ! [M2: num,N: num] :
% 4.88/5.18 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 4.88/5.18 => ( ( upt @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 4.88/5.18 = ( cons_nat @ ( numeral_numeral_nat @ M2 ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M2 ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 4.88/5.18 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 4.88/5.18 => ( ( upt @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 4.88/5.18 = nil_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % upt_rec_numeral
% 4.88/5.18 thf(fact_8954_sum__list__upt,axiom,
% 4.88/5.18 ! [M2: nat,N: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ M2 @ N )
% 4.88/5.18 => ( ( groups4561878855575611511st_nat @ ( upt @ M2 @ N ) )
% 4.88/5.18 = ( groups3542108847815614940at_nat
% 4.88/5.18 @ ^ [X3: nat] : X3
% 4.88/5.18 @ ( set_or4665077453230672383an_nat @ M2 @ N ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sum_list_upt
% 4.88/5.18 thf(fact_8955_map__add__upt,axiom,
% 4.88/5.18 ! [N: nat,M2: nat] :
% 4.88/5.18 ( ( map_nat_nat
% 4.88/5.18 @ ^ [I4: nat] : ( plus_plus_nat @ I4 @ N )
% 4.88/5.18 @ ( upt @ zero_zero_nat @ M2 ) )
% 4.88/5.18 = ( upt @ N @ ( plus_plus_nat @ M2 @ N ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % map_add_upt
% 4.88/5.18 thf(fact_8956_atLeast__upt,axiom,
% 4.88/5.18 ( set_ord_lessThan_nat
% 4.88/5.18 = ( ^ [N4: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N4 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % atLeast_upt
% 4.88/5.18 thf(fact_8957_upt__0,axiom,
% 4.88/5.18 ! [I: nat] :
% 4.88/5.18 ( ( upt @ I @ zero_zero_nat )
% 4.88/5.18 = nil_nat ) ).
% 4.88/5.18
% 4.88/5.18 % upt_0
% 4.88/5.18 thf(fact_8958_sorted__wrt__upt,axiom,
% 4.88/5.18 ! [M2: nat,N: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M2 @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % sorted_wrt_upt
% 4.88/5.18 thf(fact_8959_sorted__upt,axiom,
% 4.88/5.18 ! [M2: nat,N: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M2 @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % sorted_upt
% 4.88/5.18 thf(fact_8960_upt__add__eq__append,axiom,
% 4.88/5.18 ! [I: nat,J: nat,K: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ I @ J )
% 4.88/5.18 => ( ( upt @ I @ ( plus_plus_nat @ J @ K ) )
% 4.88/5.18 = ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % upt_add_eq_append
% 4.88/5.18 thf(fact_8961_atMost__upto,axiom,
% 4.88/5.18 ( set_ord_atMost_nat
% 4.88/5.18 = ( ^ [N4: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N4 ) ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % atMost_upto
% 4.88/5.18 thf(fact_8962_upt__rec,axiom,
% 4.88/5.18 ( upt
% 4.88/5.18 = ( ^ [I4: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I4 @ J3 ) @ ( cons_nat @ I4 @ ( upt @ ( suc @ I4 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % upt_rec
% 4.88/5.18 thf(fact_8963_upt__conv__Cons,axiom,
% 4.88/5.18 ! [I: nat,J: nat] :
% 4.88/5.18 ( ( ord_less_nat @ I @ J )
% 4.88/5.18 => ( ( upt @ I @ J )
% 4.88/5.18 = ( cons_nat @ I @ ( upt @ ( suc @ I ) @ J ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % upt_conv_Cons
% 4.88/5.18 thf(fact_8964_upt__Suc,axiom,
% 4.88/5.18 ! [I: nat,J: nat] :
% 4.88/5.18 ( ( ( ord_less_eq_nat @ I @ J )
% 4.88/5.18 => ( ( upt @ I @ ( suc @ J ) )
% 4.88/5.18 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 4.88/5.18 & ( ~ ( ord_less_eq_nat @ I @ J )
% 4.88/5.18 => ( ( upt @ I @ ( suc @ J ) )
% 4.88/5.18 = nil_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % upt_Suc
% 4.88/5.18 thf(fact_8965_upt__Suc__append,axiom,
% 4.88/5.18 ! [I: nat,J: nat] :
% 4.88/5.18 ( ( ord_less_eq_nat @ I @ J )
% 4.88/5.18 => ( ( upt @ I @ ( suc @ J ) )
% 4.88/5.18 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % upt_Suc_append
% 4.88/5.18 thf(fact_8966_map__decr__upt,axiom,
% 4.88/5.18 ! [M2: nat,N: nat] :
% 4.88/5.18 ( ( map_nat_nat
% 4.88/5.18 @ ^ [N4: nat] : ( minus_minus_nat @ N4 @ ( suc @ zero_zero_nat ) )
% 4.88/5.18 @ ( upt @ ( suc @ M2 ) @ ( suc @ N ) ) )
% 4.88/5.18 = ( upt @ M2 @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % map_decr_upt
% 4.88/5.18 thf(fact_8967_upt__eq__Cons__conv,axiom,
% 4.88/5.18 ! [I: nat,J: nat,X: nat,Xs: list_nat] :
% 4.88/5.18 ( ( ( upt @ I @ J )
% 4.88/5.18 = ( cons_nat @ X @ Xs ) )
% 4.88/5.18 = ( ( ord_less_nat @ I @ J )
% 4.88/5.18 & ( I = X )
% 4.88/5.18 & ( ( upt @ ( plus_plus_nat @ I @ one_one_nat ) @ J )
% 4.88/5.18 = Xs ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % upt_eq_Cons_conv
% 4.88/5.18 thf(fact_8968_sorted__wrt__less__idx,axiom,
% 4.88/5.18 ! [Ns: list_nat,I: nat] :
% 4.88/5.18 ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 4.88/5.18 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Ns ) )
% 4.88/5.18 => ( ord_less_eq_nat @ I @ ( nth_nat @ Ns @ I ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sorted_wrt_less_idx
% 4.88/5.18 thf(fact_8969_sorted__upto,axiom,
% 4.88/5.18 ! [M2: int,N: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( upto @ M2 @ N ) ) ).
% 4.88/5.18
% 4.88/5.18 % sorted_upto
% 4.88/5.18 thf(fact_8970_Field__natLeq__on,axiom,
% 4.88/5.18 ! [N: nat] :
% 4.88/5.18 ( ( field_nat
% 4.88/5.18 @ ( collec3392354462482085612at_nat
% 4.88/5.18 @ ( produc6081775807080527818_nat_o
% 4.88/5.18 @ ^ [X3: nat,Y2: nat] :
% 4.88/5.18 ( ( ord_less_nat @ X3 @ N )
% 4.88/5.18 & ( ord_less_nat @ Y2 @ N )
% 4.88/5.18 & ( ord_less_eq_nat @ X3 @ Y2 ) ) ) ) )
% 4.88/5.18 = ( collect_nat
% 4.88/5.18 @ ^ [X3: nat] : ( ord_less_nat @ X3 @ N ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % Field_natLeq_on
% 4.88/5.18 thf(fact_8971_natLess__def,axiom,
% 4.88/5.18 ( bNF_Ca8459412986667044542atLess
% 4.88/5.18 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % natLess_def
% 4.88/5.18 thf(fact_8972_wf__less,axiom,
% 4.88/5.18 wf_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ).
% 4.88/5.18
% 4.88/5.18 % wf_less
% 4.88/5.18 thf(fact_8973_rat__less__eq__code,axiom,
% 4.88/5.18 ( ord_less_eq_rat
% 4.88/5.18 = ( ^ [P5: rat,Q3: rat] :
% 4.88/5.18 ( produc4947309494688390418_int_o
% 4.88/5.18 @ ^ [A4: int,C5: int] :
% 4.88/5.18 ( produc4947309494688390418_int_o
% 4.88/5.18 @ ^ [B4: int,D5: int] : ( ord_less_eq_int @ ( times_times_int @ A4 @ D5 ) @ ( times_times_int @ C5 @ B4 ) )
% 4.88/5.18 @ ( quotient_of @ Q3 ) )
% 4.88/5.18 @ ( quotient_of @ P5 ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % rat_less_eq_code
% 4.88/5.18 thf(fact_8974_of__real__sqrt,axiom,
% 4.88/5.18 ! [X: real] :
% 4.88/5.18 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.18 => ( ( real_V4546457046886955230omplex @ ( sqrt @ X ) )
% 4.88/5.18 = ( csqrt @ ( real_V4546457046886955230omplex @ X ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % of_real_sqrt
% 4.88/5.18 thf(fact_8975_last__upt,axiom,
% 4.88/5.18 ! [I: nat,J: nat] :
% 4.88/5.18 ( ( ord_less_nat @ I @ J )
% 4.88/5.18 => ( ( last_nat @ ( upt @ I @ J ) )
% 4.88/5.18 = ( minus_minus_nat @ J @ one_one_nat ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % last_upt
% 4.88/5.18 thf(fact_8976_sqr_Osimps_I3_J,axiom,
% 4.88/5.18 ! [N: num] :
% 4.88/5.18 ( ( sqr @ ( bit1 @ N ) )
% 4.88/5.18 = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N ) @ N ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sqr.simps(3)
% 4.88/5.18 thf(fact_8977_not__nonnegative__int__iff,axiom,
% 4.88/5.18 ! [K: int] :
% 4.88/5.18 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 4.88/5.18 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 4.88/5.18
% 4.88/5.18 % not_nonnegative_int_iff
% 4.88/5.18 thf(fact_8978_not__negative__int__iff,axiom,
% 4.88/5.18 ! [K: int] :
% 4.88/5.18 ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 4.88/5.18 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 4.88/5.18
% 4.88/5.18 % not_negative_int_iff
% 4.88/5.18 thf(fact_8979_sqr_Osimps_I2_J,axiom,
% 4.88/5.18 ! [N: num] :
% 4.88/5.18 ( ( sqr @ ( bit0 @ N ) )
% 4.88/5.18 = ( bit0 @ ( bit0 @ ( sqr @ N ) ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sqr.simps(2)
% 4.88/5.18 thf(fact_8980_sqr_Osimps_I1_J,axiom,
% 4.88/5.18 ( ( sqr @ one )
% 4.88/5.18 = one ) ).
% 4.88/5.18
% 4.88/5.18 % sqr.simps(1)
% 4.88/5.18 thf(fact_8981_sqr__conv__mult,axiom,
% 4.88/5.18 ( sqr
% 4.88/5.18 = ( ^ [X3: num] : ( times_times_num @ X3 @ X3 ) ) ) ).
% 4.88/5.18
% 4.88/5.18 % sqr_conv_mult
% 4.88/5.18 thf(fact_8982_pow_Osimps_I3_J,axiom,
% 4.88/5.18 ! [X: num,Y: num] :
% 4.88/5.18 ( ( pow @ X @ ( bit1 @ Y ) )
% 4.88/5.18 = ( times_times_num @ ( sqr @ ( pow @ X @ Y ) ) @ X ) ) ).
% 4.88/5.18
% 4.88/5.18 % pow.simps(3)
% 4.88/5.19 thf(fact_8983_pow_Osimps_I1_J,axiom,
% 4.88/5.19 ! [X: num] :
% 4.88/5.19 ( ( pow @ X @ one )
% 4.88/5.19 = X ) ).
% 4.88/5.19
% 4.88/5.19 % pow.simps(1)
% 4.88/5.19 thf(fact_8984_pow_Osimps_I2_J,axiom,
% 4.88/5.19 ! [X: num,Y: num] :
% 4.88/5.19 ( ( pow @ X @ ( bit0 @ Y ) )
% 4.88/5.19 = ( sqr @ ( pow @ X @ Y ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % pow.simps(2)
% 4.88/5.19 thf(fact_8985_Suc__0__mod__numeral,axiom,
% 4.88/5.19 ! [K: num] :
% 4.88/5.19 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 4.88/5.19 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Suc_0_mod_numeral
% 4.88/5.19 thf(fact_8986_bezw_Osimps,axiom,
% 4.88/5.19 ( bezw
% 4.88/5.19 = ( ^ [X3: nat,Y2: nat] : ( if_Pro3027730157355071871nt_int @ ( Y2 = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X3 @ Y2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X3 @ Y2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X3 @ Y2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X3 @ Y2 ) ) ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % bezw.simps
% 4.88/5.19 thf(fact_8987_bezw_Oelims,axiom,
% 4.88/5.19 ! [X: nat,Xa2: nat,Y: product_prod_int_int] :
% 4.88/5.19 ( ( ( bezw @ X @ Xa2 )
% 4.88/5.19 = Y )
% 4.88/5.19 => ( ( ( Xa2 = zero_zero_nat )
% 4.88/5.19 => ( Y
% 4.88/5.19 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 4.88/5.19 & ( ( Xa2 != zero_zero_nat )
% 4.88/5.19 => ( Y
% 4.88/5.19 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa2 ) ) ) ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % bezw.elims
% 4.88/5.19 thf(fact_8988_bezw__non__0,axiom,
% 4.88/5.19 ! [Y: nat,X: nat] :
% 4.88/5.19 ( ( ord_less_nat @ zero_zero_nat @ Y )
% 4.88/5.19 => ( ( bezw @ X @ Y )
% 4.88/5.19 = ( 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 ) ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % bezw_non_0
% 4.88/5.19 thf(fact_8989_bezw_Opelims,axiom,
% 4.88/5.19 ! [X: nat,Xa2: nat,Y: product_prod_int_int] :
% 4.88/5.19 ( ( ( bezw @ X @ Xa2 )
% 4.88/5.19 = Y )
% 4.88/5.19 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 4.88/5.19 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 4.88/5.19 => ( Y
% 4.88/5.19 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 4.88/5.19 & ( ( Xa2 != zero_zero_nat )
% 4.88/5.19 => ( Y
% 4.88/5.19 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa2 ) ) ) ) ) ) ) )
% 4.88/5.19 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % bezw.pelims
% 4.88/5.19 thf(fact_8990_Suc__0__div__numeral,axiom,
% 4.88/5.19 ! [K: num] :
% 4.88/5.19 ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 4.88/5.19 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Suc_0_div_numeral
% 4.88/5.19 thf(fact_8991_finite__vimage__Suc__iff,axiom,
% 4.88/5.19 ! [F2: set_nat] :
% 4.88/5.19 ( ( finite_finite_nat @ ( vimage_nat_nat @ suc @ F2 ) )
% 4.88/5.19 = ( finite_finite_nat @ F2 ) ) ).
% 4.88/5.19
% 4.88/5.19 % finite_vimage_Suc_iff
% 4.88/5.19 thf(fact_8992_vimage__Suc__insert__0,axiom,
% 4.88/5.19 ! [A2: set_nat] :
% 4.88/5.19 ( ( vimage_nat_nat @ suc @ ( insert_nat @ zero_zero_nat @ A2 ) )
% 4.88/5.19 = ( vimage_nat_nat @ suc @ A2 ) ) ).
% 4.88/5.19
% 4.88/5.19 % vimage_Suc_insert_0
% 4.88/5.19 thf(fact_8993_natLeq__on__wo__rel,axiom,
% 4.88/5.19 ! [N: nat] :
% 4.88/5.19 ( bNF_We3818239936649020644el_nat
% 4.88/5.19 @ ( collec3392354462482085612at_nat
% 4.88/5.19 @ ( produc6081775807080527818_nat_o
% 4.88/5.19 @ ^ [X3: nat,Y2: nat] :
% 4.88/5.19 ( ( ord_less_nat @ X3 @ N )
% 4.88/5.19 & ( ord_less_nat @ Y2 @ N )
% 4.88/5.19 & ( ord_less_eq_nat @ X3 @ Y2 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % natLeq_on_wo_rel
% 4.88/5.19 thf(fact_8994_pred__nat__trancl__eq__le,axiom,
% 4.88/5.19 ! [M2: nat,N: nat] :
% 4.88/5.19 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M2 @ N ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 4.88/5.19 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 4.88/5.19
% 4.88/5.19 % pred_nat_trancl_eq_le
% 4.88/5.19 thf(fact_8995_pairs__le__eq__Sigma,axiom,
% 4.88/5.19 ! [M2: nat] :
% 4.88/5.19 ( ( collec3392354462482085612at_nat
% 4.88/5.19 @ ( produc6081775807080527818_nat_o
% 4.88/5.19 @ ^ [I4: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I4 @ J3 ) @ M2 ) ) )
% 4.88/5.19 = ( produc457027306803732586at_nat @ ( set_ord_atMost_nat @ M2 )
% 4.88/5.19 @ ^ [R5: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M2 @ R5 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % pairs_le_eq_Sigma
% 4.88/5.19 thf(fact_8996_less__eq,axiom,
% 4.88/5.19 ! [M2: nat,N: nat] :
% 4.88/5.19 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M2 @ N ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 4.88/5.19 = ( ord_less_nat @ M2 @ N ) ) ).
% 4.88/5.19
% 4.88/5.19 % less_eq
% 4.88/5.19 thf(fact_8997_Bseq__monoseq__convergent_H__inc,axiom,
% 4.88/5.19 ! [F: nat > real,M5: nat] :
% 4.88/5.19 ( ( bfun_nat_real
% 4.88/5.19 @ ^ [N4: nat] : ( F @ ( plus_plus_nat @ N4 @ M5 ) )
% 4.88/5.19 @ at_top_nat )
% 4.88/5.19 => ( ! [M4: nat,N2: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ M5 @ M4 )
% 4.88/5.19 => ( ( ord_less_eq_nat @ M4 @ N2 )
% 4.88/5.19 => ( ord_less_eq_real @ ( F @ M4 ) @ ( F @ N2 ) ) ) )
% 4.88/5.19 => ( topolo7531315842566124627t_real @ F ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Bseq_monoseq_convergent'_inc
% 4.88/5.19 thf(fact_8998_Bseq__mono__convergent,axiom,
% 4.88/5.19 ! [X5: nat > real] :
% 4.88/5.19 ( ( bfun_nat_real @ X5 @ at_top_nat )
% 4.88/5.19 => ( ! [M4: nat,N2: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ M4 @ N2 )
% 4.88/5.19 => ( ord_less_eq_real @ ( X5 @ M4 ) @ ( X5 @ N2 ) ) )
% 4.88/5.19 => ( topolo7531315842566124627t_real @ X5 ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Bseq_mono_convergent
% 4.88/5.19 thf(fact_8999_convergent__realpow,axiom,
% 4.88/5.19 ! [X: real] :
% 4.88/5.19 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 4.88/5.19 => ( ( ord_less_eq_real @ X @ one_one_real )
% 4.88/5.19 => ( topolo7531315842566124627t_real @ ( power_power_real @ X ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % convergent_realpow
% 4.88/5.19 thf(fact_9000_Bseq__monoseq__convergent_H__dec,axiom,
% 4.88/5.19 ! [F: nat > real,M5: nat] :
% 4.88/5.19 ( ( bfun_nat_real
% 4.88/5.19 @ ^ [N4: nat] : ( F @ ( plus_plus_nat @ N4 @ M5 ) )
% 4.88/5.19 @ at_top_nat )
% 4.88/5.19 => ( ! [M4: nat,N2: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ M5 @ M4 )
% 4.88/5.19 => ( ( ord_less_eq_nat @ M4 @ N2 )
% 4.88/5.19 => ( ord_less_eq_real @ ( F @ N2 ) @ ( F @ M4 ) ) ) )
% 4.88/5.19 => ( topolo7531315842566124627t_real @ F ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Bseq_monoseq_convergent'_dec
% 4.88/5.19 thf(fact_9001_Restr__natLeq,axiom,
% 4.88/5.19 ! [N: nat] :
% 4.88/5.19 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 4.88/5.19 @ ( produc457027306803732586at_nat
% 4.88/5.19 @ ( collect_nat
% 4.88/5.19 @ ^ [X3: nat] : ( ord_less_nat @ X3 @ N ) )
% 4.88/5.19 @ ^ [Uu3: nat] :
% 4.88/5.19 ( collect_nat
% 4.88/5.19 @ ^ [X3: nat] : ( ord_less_nat @ X3 @ N ) ) ) )
% 4.88/5.19 = ( collec3392354462482085612at_nat
% 4.88/5.19 @ ( produc6081775807080527818_nat_o
% 4.88/5.19 @ ^ [X3: nat,Y2: nat] :
% 4.88/5.19 ( ( ord_less_nat @ X3 @ N )
% 4.88/5.19 & ( ord_less_nat @ Y2 @ N )
% 4.88/5.19 & ( ord_less_eq_nat @ X3 @ Y2 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Restr_natLeq
% 4.88/5.19 thf(fact_9002_natLeq__def,axiom,
% 4.88/5.19 ( bNF_Ca8665028551170535155natLeq
% 4.88/5.19 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_eq_nat ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % natLeq_def
% 4.88/5.19 thf(fact_9003_Restr__natLeq2,axiom,
% 4.88/5.19 ! [N: nat] :
% 4.88/5.19 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 4.88/5.19 @ ( produc457027306803732586at_nat @ ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 4.88/5.19 @ ^ [Uu3: nat] : ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N ) ) )
% 4.88/5.19 = ( collec3392354462482085612at_nat
% 4.88/5.19 @ ( produc6081775807080527818_nat_o
% 4.88/5.19 @ ^ [X3: nat,Y2: nat] :
% 4.88/5.19 ( ( ord_less_nat @ X3 @ N )
% 4.88/5.19 & ( ord_less_nat @ Y2 @ N )
% 4.88/5.19 & ( ord_less_eq_nat @ X3 @ Y2 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Restr_natLeq2
% 4.88/5.19 thf(fact_9004_natLeq__underS__less,axiom,
% 4.88/5.19 ! [N: nat] :
% 4.88/5.19 ( ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 4.88/5.19 = ( collect_nat
% 4.88/5.19 @ ^ [X3: nat] : ( ord_less_nat @ X3 @ N ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % natLeq_underS_less
% 4.88/5.19 thf(fact_9005_pair__lessI2,axiom,
% 4.88/5.19 ! [A: nat,B: nat,S: nat,T: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ A @ B )
% 4.88/5.19 => ( ( ord_less_nat @ S @ T )
% 4.88/5.19 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_less ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % pair_lessI2
% 4.88/5.19 thf(fact_9006_trans__pair__less,axiom,
% 4.88/5.19 trans_4347625901269045472at_nat @ fun_pair_less ).
% 4.88/5.19
% 4.88/5.19 % trans_pair_less
% 4.88/5.19 thf(fact_9007_total__pair__less,axiom,
% 4.88/5.19 ! [A2: set_Pr1261947904930325089at_nat] : ( total_3592101749530773125at_nat @ A2 @ fun_pair_less ) ).
% 4.88/5.19
% 4.88/5.19 % total_pair_less
% 4.88/5.19 thf(fact_9008_pair__less__iff1,axiom,
% 4.88/5.19 ! [X: nat,Y: nat,Z: nat] :
% 4.88/5.19 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( product_Pair_nat_nat @ X @ Z ) ) @ fun_pair_less )
% 4.88/5.19 = ( ord_less_nat @ Y @ Z ) ) ).
% 4.88/5.19
% 4.88/5.19 % pair_less_iff1
% 4.88/5.19 thf(fact_9009_wf__pair__less,axiom,
% 4.88/5.19 wf_Pro7803398752247294826at_nat @ fun_pair_less ).
% 4.88/5.19
% 4.88/5.19 % wf_pair_less
% 4.88/5.19 thf(fact_9010_pair__lessI1,axiom,
% 4.88/5.19 ! [A: nat,B: nat,S: nat,T: nat] :
% 4.88/5.19 ( ( ord_less_nat @ A @ B )
% 4.88/5.19 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_less ) ) ).
% 4.88/5.19
% 4.88/5.19 % pair_lessI1
% 4.88/5.19 thf(fact_9011_gcd__nat_Oordering__top__axioms,axiom,
% 4.88/5.19 ( ordering_top_nat @ dvd_dvd_nat
% 4.88/5.19 @ ^ [M3: nat,N4: nat] :
% 4.88/5.19 ( ( dvd_dvd_nat @ M3 @ N4 )
% 4.88/5.19 & ( M3 != N4 ) )
% 4.88/5.19 @ zero_zero_nat ) ).
% 4.88/5.19
% 4.88/5.19 % gcd_nat.ordering_top_axioms
% 4.88/5.19 thf(fact_9012_bot__nat__0_Oordering__top__axioms,axiom,
% 4.88/5.19 ( ordering_top_nat
% 4.88/5.19 @ ^ [X3: nat,Y2: nat] : ( ord_less_eq_nat @ Y2 @ X3 )
% 4.88/5.19 @ ^ [X3: nat,Y2: nat] : ( ord_less_nat @ Y2 @ X3 )
% 4.88/5.19 @ zero_zero_nat ) ).
% 4.88/5.19
% 4.88/5.19 % bot_nat_0.ordering_top_axioms
% 4.88/5.19 thf(fact_9013_pair__leqI2,axiom,
% 4.88/5.19 ! [A: nat,B: nat,S: nat,T: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ A @ B )
% 4.88/5.19 => ( ( ord_less_eq_nat @ S @ T )
% 4.88/5.19 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_leq ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % pair_leqI2
% 4.88/5.19 thf(fact_9014_pair__leqI1,axiom,
% 4.88/5.19 ! [A: nat,B: nat,S: nat,T: nat] :
% 4.88/5.19 ( ( ord_less_nat @ A @ B )
% 4.88/5.19 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_leq ) ) ).
% 4.88/5.19
% 4.88/5.19 % pair_leqI1
% 4.88/5.19 thf(fact_9015_pair__leq__def,axiom,
% 4.88/5.19 ( fun_pair_leq
% 4.88/5.19 = ( sup_su718114333110466843at_nat @ fun_pair_less @ id_Pro2258643101195443293at_nat ) ) ).
% 4.88/5.19
% 4.88/5.19 % pair_leq_def
% 4.88/5.19 thf(fact_9016_wmax__insertI,axiom,
% 4.88/5.19 ! [Y: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat] :
% 4.88/5.19 ( ( member8440522571783428010at_nat @ Y @ YS )
% 4.88/5.19 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 4.88/5.19 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_max_weak )
% 4.88/5.19 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( insert8211810215607154385at_nat @ X @ XS ) @ YS ) @ fun_max_weak ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % wmax_insertI
% 4.88/5.19 thf(fact_9017_wmin__insertI,axiom,
% 4.88/5.19 ! [X: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
% 4.88/5.19 ( ( member8440522571783428010at_nat @ X @ XS )
% 4.88/5.19 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 4.88/5.19 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_min_weak )
% 4.88/5.19 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ ( insert8211810215607154385at_nat @ Y @ YS ) ) @ fun_min_weak ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % wmin_insertI
% 4.88/5.19 thf(fact_9018_wmin__emptyI,axiom,
% 4.88/5.19 ! [X5: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X5 @ bot_bo2099793752762293965at_nat ) @ fun_min_weak ) ).
% 4.88/5.19
% 4.88/5.19 % wmin_emptyI
% 4.88/5.19 thf(fact_9019_wmax__emptyI,axiom,
% 4.88/5.19 ! [X5: set_Pr1261947904930325089at_nat] :
% 4.88/5.19 ( ( finite6177210948735845034at_nat @ X5 )
% 4.88/5.19 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ X5 ) @ fun_max_weak ) ) ).
% 4.88/5.19
% 4.88/5.19 % wmax_emptyI
% 4.88/5.19 thf(fact_9020_min__weak__def,axiom,
% 4.88/5.19 ( fun_min_weak
% 4.88/5.19 = ( sup_su5525570899277871387at_nat @ ( min_ex6901939911449802026at_nat @ fun_pair_leq ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ bot_bo2099793752762293965at_nat ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % min_weak_def
% 4.88/5.19 thf(fact_9021_max__weak__def,axiom,
% 4.88/5.19 ( fun_max_weak
% 4.88/5.19 = ( sup_su5525570899277871387at_nat @ ( max_ex8135407076693332796at_nat @ fun_pair_leq ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ bot_bo2099793752762293965at_nat ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % max_weak_def
% 4.88/5.19 thf(fact_9022_smax__insertI,axiom,
% 4.88/5.19 ! [Y: product_prod_nat_nat,Y6: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,X5: set_Pr1261947904930325089at_nat] :
% 4.88/5.19 ( ( member8440522571783428010at_nat @ Y @ Y6 )
% 4.88/5.19 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_less )
% 4.88/5.19 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X5 @ Y6 ) @ fun_max_strict )
% 4.88/5.19 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( insert8211810215607154385at_nat @ X @ X5 ) @ Y6 ) @ fun_max_strict ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % smax_insertI
% 4.88/5.19 thf(fact_9023_smin__insertI,axiom,
% 4.88/5.19 ! [X: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
% 4.88/5.19 ( ( member8440522571783428010at_nat @ X @ XS )
% 4.88/5.19 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_less )
% 4.88/5.19 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_min_strict )
% 4.88/5.19 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ ( insert8211810215607154385at_nat @ Y @ YS ) ) @ fun_min_strict ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % smin_insertI
% 4.88/5.19 thf(fact_9024_smax__emptyI,axiom,
% 4.88/5.19 ! [Y6: set_Pr1261947904930325089at_nat] :
% 4.88/5.19 ( ( finite6177210948735845034at_nat @ Y6 )
% 4.88/5.19 => ( ( Y6 != bot_bo2099793752762293965at_nat )
% 4.88/5.19 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ Y6 ) @ fun_max_strict ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % smax_emptyI
% 4.88/5.19 thf(fact_9025_smin__emptyI,axiom,
% 4.88/5.19 ! [X5: set_Pr1261947904930325089at_nat] :
% 4.88/5.19 ( ( X5 != bot_bo2099793752762293965at_nat )
% 4.88/5.19 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X5 @ bot_bo2099793752762293965at_nat ) @ fun_min_strict ) ) ).
% 4.88/5.19
% 4.88/5.19 % smin_emptyI
% 4.88/5.19 thf(fact_9026_min__strict__def,axiom,
% 4.88/5.19 ( fun_min_strict
% 4.88/5.19 = ( min_ex6901939911449802026at_nat @ fun_pair_less ) ) ).
% 4.88/5.19
% 4.88/5.19 % min_strict_def
% 4.88/5.19 thf(fact_9027_max__strict__def,axiom,
% 4.88/5.19 ( fun_max_strict
% 4.88/5.19 = ( max_ex8135407076693332796at_nat @ fun_pair_less ) ) ).
% 4.88/5.19
% 4.88/5.19 % max_strict_def
% 4.88/5.19 thf(fact_9028_max__rpair__set,axiom,
% 4.88/5.19 fun_re2478310338295953701at_nat @ ( produc9060074326276436823at_nat @ fun_max_strict @ fun_max_weak ) ).
% 4.88/5.19
% 4.88/5.19 % max_rpair_set
% 4.88/5.19 thf(fact_9029_min__rpair__set,axiom,
% 4.88/5.19 fun_re2478310338295953701at_nat @ ( produc9060074326276436823at_nat @ fun_min_strict @ fun_min_weak ) ).
% 4.88/5.19
% 4.88/5.19 % min_rpair_set
% 4.88/5.19 thf(fact_9030_bit__concat__bit__iff,axiom,
% 4.88/5.19 ! [M2: nat,K: int,L: int,N: nat] :
% 4.88/5.19 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M2 @ K @ L ) @ N )
% 4.88/5.19 = ( ( ( ord_less_nat @ N @ M2 )
% 4.88/5.19 & ( bit_se1146084159140164899it_int @ K @ N ) )
% 4.88/5.19 | ( ( ord_less_eq_nat @ M2 @ N )
% 4.88/5.19 & ( bit_se1146084159140164899it_int @ L @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % bit_concat_bit_iff
% 4.88/5.19 thf(fact_9031_concat__bit__0,axiom,
% 4.88/5.19 ! [K: int,L: int] :
% 4.88/5.19 ( ( bit_concat_bit @ zero_zero_nat @ K @ L )
% 4.88/5.19 = L ) ).
% 4.88/5.19
% 4.88/5.19 % concat_bit_0
% 4.88/5.19 thf(fact_9032_concat__bit__nonnegative__iff,axiom,
% 4.88/5.19 ! [N: nat,K: int,L: int] :
% 4.88/5.19 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N @ K @ L ) )
% 4.88/5.19 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ).
% 4.88/5.19
% 4.88/5.19 % concat_bit_nonnegative_iff
% 4.88/5.19 thf(fact_9033_division__segment__nat__def,axiom,
% 4.88/5.19 ( euclid3398187327856392827nt_nat
% 4.88/5.19 = ( ^ [N4: nat] : one_one_nat ) ) ).
% 4.88/5.19
% 4.88/5.19 % division_segment_nat_def
% 4.88/5.19 thf(fact_9034_division__segment__int__def,axiom,
% 4.88/5.19 ( euclid3395696857347342551nt_int
% 4.88/5.19 = ( ^ [K3: int] : ( if_int @ ( ord_less_eq_int @ zero_zero_int @ K3 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % division_segment_int_def
% 4.88/5.19 thf(fact_9035_less__eq__enat__def,axiom,
% 4.88/5.19 ( ord_le2932123472753598470d_enat
% 4.88/5.19 = ( ^ [M3: extended_enat] :
% 4.88/5.19 ( extended_case_enat_o
% 4.88/5.19 @ ^ [N1: nat] :
% 4.88/5.19 ( extended_case_enat_o
% 4.88/5.19 @ ^ [M1: nat] : ( ord_less_eq_nat @ M1 @ N1 )
% 4.88/5.19 @ $false
% 4.88/5.19 @ M3 )
% 4.88/5.19 @ $true ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % less_eq_enat_def
% 4.88/5.19 thf(fact_9036_less__enat__def,axiom,
% 4.88/5.19 ( ord_le72135733267957522d_enat
% 4.88/5.19 = ( ^ [M3: extended_enat,N4: extended_enat] :
% 4.88/5.19 ( extended_case_enat_o
% 4.88/5.19 @ ^ [M1: nat] : ( extended_case_enat_o @ ( ord_less_nat @ M1 ) @ $true @ N4 )
% 4.88/5.19 @ $false
% 4.88/5.19 @ M3 ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % less_enat_def
% 4.88/5.19 thf(fact_9037_of__rat__dense,axiom,
% 4.88/5.19 ! [X: real,Y: real] :
% 4.88/5.19 ( ( ord_less_real @ X @ Y )
% 4.88/5.19 => ? [Q5: rat] :
% 4.88/5.19 ( ( ord_less_real @ X @ ( field_7254667332652039916t_real @ Q5 ) )
% 4.88/5.19 & ( ord_less_real @ ( field_7254667332652039916t_real @ Q5 ) @ Y ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % of_rat_dense
% 4.88/5.19 thf(fact_9038_compute__powr__real,axiom,
% 4.88/5.19 ( powr_real2
% 4.88/5.19 = ( ^ [B4: real,I4: real] :
% 4.88/5.19 ( if_real @ ( ord_less_eq_real @ B4 @ zero_zero_real )
% 4.88/5.19 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 4.88/5.19 @ ^ [Uu3: product_unit] : ( powr_real2 @ B4 @ I4 ) )
% 4.88/5.19 @ ( if_real
% 4.88/5.19 @ ( ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ I4 ) )
% 4.88/5.19 = I4 )
% 4.88/5.19 @ ( 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 ) ) ) ) ) )
% 4.88/5.19 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 4.88/5.19 @ ^ [Uu3: product_unit] : ( powr_real2 @ B4 @ I4 ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % compute_powr_real
% 4.88/5.19 thf(fact_9039_inj__on__char__of__nat,axiom,
% 4.88/5.19 inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % inj_on_char_of_nat
% 4.88/5.19 thf(fact_9040_UNIV__char__of__nat,axiom,
% 4.88/5.19 ( top_top_set_char
% 4.88/5.19 = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % UNIV_char_of_nat
% 4.88/5.19 thf(fact_9041_range__nat__of__char,axiom,
% 4.88/5.19 ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 4.88/5.19 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % range_nat_of_char
% 4.88/5.19 thf(fact_9042_char_Osize_I2_J,axiom,
% 4.88/5.19 ! [X15: $o,X23: $o,X33: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 4.88/5.19 ( ( size_size_char @ ( char2 @ X15 @ X23 @ X33 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 4.88/5.19 = zero_zero_nat ) ).
% 4.88/5.19
% 4.88/5.19 % char.size(2)
% 4.88/5.19 thf(fact_9043_nat__of__char__less__256,axiom,
% 4.88/5.19 ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % nat_of_char_less_256
% 4.88/5.19 thf(fact_9044_char_Osize__gen,axiom,
% 4.88/5.19 ! [X15: $o,X23: $o,X33: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 4.88/5.19 ( ( size_char @ ( char2 @ X15 @ X23 @ X33 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 4.88/5.19 = zero_zero_nat ) ).
% 4.88/5.19
% 4.88/5.19 % char.size_gen
% 4.88/5.19 thf(fact_9045_one__int_Otransfer,axiom,
% 4.88/5.19 pcr_int @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ one_one_int ).
% 4.88/5.19
% 4.88/5.19 % one_int.transfer
% 4.88/5.19 thf(fact_9046_Rats__abs__nat__div__natE,axiom,
% 4.88/5.19 ! [X: real] :
% 4.88/5.19 ( ( member_real @ X @ field_5140801741446780682s_real )
% 4.88/5.19 => ~ ! [M4: nat,N2: nat] :
% 4.88/5.19 ( ( N2 != zero_zero_nat )
% 4.88/5.19 => ( ( ( abs_abs_real @ X )
% 4.88/5.19 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ M4 ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 4.88/5.19 => ~ ( algebr934650988132801477me_nat @ M4 @ N2 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Rats_abs_nat_div_natE
% 4.88/5.19 thf(fact_9047_coprime__common__divisor__nat,axiom,
% 4.88/5.19 ! [A: nat,B: nat,X: nat] :
% 4.88/5.19 ( ( algebr934650988132801477me_nat @ A @ B )
% 4.88/5.19 => ( ( dvd_dvd_nat @ X @ A )
% 4.88/5.19 => ( ( dvd_dvd_nat @ X @ B )
% 4.88/5.19 => ( X = one_one_nat ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % coprime_common_divisor_nat
% 4.88/5.19 thf(fact_9048_coprime__Suc__0__left,axiom,
% 4.88/5.19 ! [N: nat] : ( algebr934650988132801477me_nat @ ( suc @ zero_zero_nat ) @ N ) ).
% 4.88/5.19
% 4.88/5.19 % coprime_Suc_0_left
% 4.88/5.19 thf(fact_9049_coprime__Suc__0__right,axiom,
% 4.88/5.19 ! [N: nat] : ( algebr934650988132801477me_nat @ N @ ( suc @ zero_zero_nat ) ) ).
% 4.88/5.19
% 4.88/5.19 % coprime_Suc_0_right
% 4.88/5.19 thf(fact_9050_coprime__diff__one__left__nat,axiom,
% 4.88/5.19 ! [N: nat] :
% 4.88/5.19 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.19 => ( algebr934650988132801477me_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ N ) ) ).
% 4.88/5.19
% 4.88/5.19 % coprime_diff_one_left_nat
% 4.88/5.19 thf(fact_9051_coprime__diff__one__right__nat,axiom,
% 4.88/5.19 ! [N: nat] :
% 4.88/5.19 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.19 => ( algebr934650988132801477me_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % coprime_diff_one_right_nat
% 4.88/5.19 thf(fact_9052_zero__int_Otransfer,axiom,
% 4.88/5.19 pcr_int @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ zero_zero_int ).
% 4.88/5.19
% 4.88/5.19 % zero_int.transfer
% 4.88/5.19 thf(fact_9053_less__natural_Orsp,axiom,
% 4.88/5.19 ( bNF_re578469030762574527_nat_o
% 4.88/5.19 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 4.88/5.19 @ ( bNF_re4705727531993890431at_o_o
% 4.88/5.19 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 4.88/5.19 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
% 4.88/5.19 @ ord_less_nat
% 4.88/5.19 @ ord_less_nat ) ).
% 4.88/5.19
% 4.88/5.19 % less_natural.rsp
% 4.88/5.19 thf(fact_9054_less__eq__integer_Orsp,axiom,
% 4.88/5.19 ( bNF_re3403563459893282935_int_o
% 4.88/5.19 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 )
% 4.88/5.19 @ ( bNF_re5089333283451836215nt_o_o
% 4.88/5.19 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 )
% 4.88/5.19 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
% 4.88/5.19 @ ord_less_eq_int
% 4.88/5.19 @ ord_less_eq_int ) ).
% 4.88/5.19
% 4.88/5.19 % less_eq_integer.rsp
% 4.88/5.19 thf(fact_9055_less__eq__natural_Orsp,axiom,
% 4.88/5.19 ( bNF_re578469030762574527_nat_o
% 4.88/5.19 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 4.88/5.19 @ ( bNF_re4705727531993890431at_o_o
% 4.88/5.19 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 4.88/5.19 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
% 4.88/5.19 @ ord_less_eq_nat
% 4.88/5.19 @ ord_less_eq_nat ) ).
% 4.88/5.19
% 4.88/5.19 % less_eq_natural.rsp
% 4.88/5.19 thf(fact_9056_less__int_Otransfer,axiom,
% 4.88/5.19 ( bNF_re717283939379294677_int_o @ pcr_int
% 4.88/5.19 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 4.88/5.19 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
% 4.88/5.19 @ ( produc8739625826339149834_nat_o
% 4.88/5.19 @ ^ [X3: nat,Y2: nat] :
% 4.88/5.19 ( produc6081775807080527818_nat_o
% 4.88/5.19 @ ^ [U2: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V3 ) @ ( plus_plus_nat @ U2 @ Y2 ) ) ) )
% 4.88/5.19 @ ord_less_int ) ).
% 4.88/5.19
% 4.88/5.19 % less_int.transfer
% 4.88/5.19 thf(fact_9057_less__eq__int_Otransfer,axiom,
% 4.88/5.19 ( bNF_re717283939379294677_int_o @ pcr_int
% 4.88/5.19 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 4.88/5.19 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
% 4.88/5.19 @ ( produc8739625826339149834_nat_o
% 4.88/5.19 @ ^ [X3: nat,Y2: nat] :
% 4.88/5.19 ( produc6081775807080527818_nat_o
% 4.88/5.19 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V3 ) @ ( plus_plus_nat @ U2 @ Y2 ) ) ) )
% 4.88/5.19 @ ord_less_eq_int ) ).
% 4.88/5.19
% 4.88/5.19 % less_eq_int.transfer
% 4.88/5.19 thf(fact_9058_int__transfer,axiom,
% 4.88/5.19 ( bNF_re6830278522597306478at_int
% 4.88/5.19 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 4.88/5.19 @ pcr_int
% 4.88/5.19 @ ^ [N4: nat] : ( product_Pair_nat_nat @ N4 @ zero_zero_nat )
% 4.88/5.19 @ semiri1314217659103216013at_int ) ).
% 4.88/5.19
% 4.88/5.19 % int_transfer
% 4.88/5.19 thf(fact_9059_Real_Opositive_Orsp,axiom,
% 4.88/5.19 ( bNF_re728719798268516973at_o_o @ realrel
% 4.88/5.19 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 )
% 4.88/5.19 @ ^ [X8: nat > rat] :
% 4.88/5.19 ? [R5: rat] :
% 4.88/5.19 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 4.88/5.19 & ? [K3: nat] :
% 4.88/5.19 ! [N4: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ K3 @ N4 )
% 4.88/5.19 => ( ord_less_rat @ R5 @ ( X8 @ N4 ) ) ) )
% 4.88/5.19 @ ^ [X8: nat > rat] :
% 4.88/5.19 ? [R5: rat] :
% 4.88/5.19 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 4.88/5.19 & ? [K3: nat] :
% 4.88/5.19 ! [N4: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ K3 @ N4 )
% 4.88/5.19 => ( ord_less_rat @ R5 @ ( X8 @ N4 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Real.positive.rsp
% 4.88/5.19 thf(fact_9060_less__eq__int_Orsp,axiom,
% 4.88/5.19 ( bNF_re4202695980764964119_nat_o @ intrel
% 4.88/5.19 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 4.88/5.19 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
% 4.88/5.19 @ ( produc8739625826339149834_nat_o
% 4.88/5.19 @ ^ [X3: nat,Y2: nat] :
% 4.88/5.19 ( produc6081775807080527818_nat_o
% 4.88/5.19 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V3 ) @ ( plus_plus_nat @ U2 @ Y2 ) ) ) )
% 4.88/5.19 @ ( produc8739625826339149834_nat_o
% 4.88/5.19 @ ^ [X3: nat,Y2: nat] :
% 4.88/5.19 ( produc6081775807080527818_nat_o
% 4.88/5.19 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V3 ) @ ( plus_plus_nat @ U2 @ Y2 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % less_eq_int.rsp
% 4.88/5.19 thf(fact_9061_zero__int_Orsp,axiom,
% 4.88/5.19 intrel @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 4.88/5.19
% 4.88/5.19 % zero_int.rsp
% 4.88/5.19 thf(fact_9062_transp__realrel,axiom,
% 4.88/5.19 transp_nat_rat @ realrel ).
% 4.88/5.19
% 4.88/5.19 % transp_realrel
% 4.88/5.19 thf(fact_9063_one__real_Orsp,axiom,
% 4.88/5.19 ( realrel
% 4.88/5.19 @ ^ [N4: nat] : one_one_rat
% 4.88/5.19 @ ^ [N4: nat] : one_one_rat ) ).
% 4.88/5.19
% 4.88/5.19 % one_real.rsp
% 4.88/5.19 thf(fact_9064_zero__real_Orsp,axiom,
% 4.88/5.19 ( realrel
% 4.88/5.19 @ ^ [N4: nat] : zero_zero_rat
% 4.88/5.19 @ ^ [N4: nat] : zero_zero_rat ) ).
% 4.88/5.19
% 4.88/5.19 % zero_real.rsp
% 4.88/5.19 thf(fact_9065_uminus__real_Orsp,axiom,
% 4.88/5.19 ( bNF_re895249473297799549at_rat @ realrel @ realrel
% 4.88/5.19 @ ^ [X8: nat > rat,N4: nat] : ( uminus_uminus_rat @ ( X8 @ N4 ) )
% 4.88/5.19 @ ^ [X8: nat > rat,N4: nat] : ( uminus_uminus_rat @ ( X8 @ N4 ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % uminus_real.rsp
% 4.88/5.19 thf(fact_9066_times__real_Orsp,axiom,
% 4.88/5.19 ( bNF_re1962705104956426057at_rat @ realrel @ ( bNF_re895249473297799549at_rat @ realrel @ realrel )
% 4.88/5.19 @ ^ [X8: nat > rat,Y7: nat > rat,N4: nat] : ( times_times_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) )
% 4.88/5.19 @ ^ [X8: nat > rat,Y7: nat > rat,N4: nat] : ( times_times_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % times_real.rsp
% 4.88/5.19 thf(fact_9067_plus__real_Orsp,axiom,
% 4.88/5.19 ( bNF_re1962705104956426057at_rat @ realrel @ ( bNF_re895249473297799549at_rat @ realrel @ realrel )
% 4.88/5.19 @ ^ [X8: nat > rat,Y7: nat > rat,N4: nat] : ( plus_plus_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) )
% 4.88/5.19 @ ^ [X8: nat > rat,Y7: nat > rat,N4: nat] : ( plus_plus_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % plus_real.rsp
% 4.88/5.19 thf(fact_9068_one__int_Orsp,axiom,
% 4.88/5.19 intrel @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ).
% 4.88/5.19
% 4.88/5.19 % one_int.rsp
% 4.88/5.19 thf(fact_9069_less__int_Orsp,axiom,
% 4.88/5.19 ( bNF_re4202695980764964119_nat_o @ intrel
% 4.88/5.19 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 4.88/5.19 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
% 4.88/5.19 @ ( produc8739625826339149834_nat_o
% 4.88/5.19 @ ^ [X3: nat,Y2: nat] :
% 4.88/5.19 ( produc6081775807080527818_nat_o
% 4.88/5.19 @ ^ [U2: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V3 ) @ ( plus_plus_nat @ U2 @ Y2 ) ) ) )
% 4.88/5.19 @ ( produc8739625826339149834_nat_o
% 4.88/5.19 @ ^ [X3: nat,Y2: nat] :
% 4.88/5.19 ( produc6081775807080527818_nat_o
% 4.88/5.19 @ ^ [U2: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V3 ) @ ( plus_plus_nat @ U2 @ Y2 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % less_int.rsp
% 4.88/5.19 thf(fact_9070_inverse__real_Orsp,axiom,
% 4.88/5.19 ( bNF_re895249473297799549at_rat @ realrel @ realrel
% 4.88/5.19 @ ^ [X8: nat > rat] :
% 4.88/5.19 ( if_nat_rat @ ( vanishes @ X8 )
% 4.88/5.19 @ ^ [N4: nat] : zero_zero_rat
% 4.88/5.19 @ ^ [N4: nat] : ( inverse_inverse_rat @ ( X8 @ N4 ) ) )
% 4.88/5.19 @ ^ [X8: nat > rat] :
% 4.88/5.19 ( if_nat_rat @ ( vanishes @ X8 )
% 4.88/5.19 @ ^ [N4: nat] : zero_zero_rat
% 4.88/5.19 @ ^ [N4: nat] : ( inverse_inverse_rat @ ( X8 @ N4 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % inverse_real.rsp
% 4.88/5.19 thf(fact_9071_vanishes__const,axiom,
% 4.88/5.19 ! [C: rat] :
% 4.88/5.19 ( ( vanishes
% 4.88/5.19 @ ^ [N4: nat] : C )
% 4.88/5.19 = ( C = zero_zero_rat ) ) ).
% 4.88/5.19
% 4.88/5.19 % vanishes_const
% 4.88/5.19 thf(fact_9072_vanishes__minus,axiom,
% 4.88/5.19 ! [X5: nat > rat] :
% 4.88/5.19 ( ( vanishes @ X5 )
% 4.88/5.19 => ( vanishes
% 4.88/5.19 @ ^ [N4: nat] : ( uminus_uminus_rat @ ( X5 @ N4 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % vanishes_minus
% 4.88/5.19 thf(fact_9073_vanishes__diff,axiom,
% 4.88/5.19 ! [X5: nat > rat,Y6: nat > rat] :
% 4.88/5.19 ( ( vanishes @ X5 )
% 4.88/5.19 => ( ( vanishes @ Y6 )
% 4.88/5.19 => ( vanishes
% 4.88/5.19 @ ^ [N4: nat] : ( minus_minus_rat @ ( X5 @ N4 ) @ ( Y6 @ N4 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % vanishes_diff
% 4.88/5.19 thf(fact_9074_vanishes__add,axiom,
% 4.88/5.19 ! [X5: nat > rat,Y6: nat > rat] :
% 4.88/5.19 ( ( vanishes @ X5 )
% 4.88/5.19 => ( ( vanishes @ Y6 )
% 4.88/5.19 => ( vanishes
% 4.88/5.19 @ ^ [N4: nat] : ( plus_plus_rat @ ( X5 @ N4 ) @ ( Y6 @ N4 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % vanishes_add
% 4.88/5.19 thf(fact_9075_vanishesD,axiom,
% 4.88/5.19 ! [X5: nat > rat,R2: rat] :
% 4.88/5.19 ( ( vanishes @ X5 )
% 4.88/5.19 => ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 4.88/5.19 => ? [K2: nat] :
% 4.88/5.19 ! [N6: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ K2 @ N6 )
% 4.88/5.19 => ( ord_less_rat @ ( abs_abs_rat @ ( X5 @ N6 ) ) @ R2 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % vanishesD
% 4.88/5.19 thf(fact_9076_vanishesI,axiom,
% 4.88/5.19 ! [X5: nat > rat] :
% 4.88/5.19 ( ! [R4: rat] :
% 4.88/5.19 ( ( ord_less_rat @ zero_zero_rat @ R4 )
% 4.88/5.19 => ? [K8: nat] :
% 4.88/5.19 ! [N2: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ K8 @ N2 )
% 4.88/5.19 => ( ord_less_rat @ ( abs_abs_rat @ ( X5 @ N2 ) ) @ R4 ) ) )
% 4.88/5.19 => ( vanishes @ X5 ) ) ).
% 4.88/5.19
% 4.88/5.19 % vanishesI
% 4.88/5.19 thf(fact_9077_vanishes__def,axiom,
% 4.88/5.19 ( vanishes
% 4.88/5.19 = ( ^ [X8: nat > rat] :
% 4.88/5.19 ! [R5: rat] :
% 4.88/5.19 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 4.88/5.19 => ? [K3: nat] :
% 4.88/5.19 ! [N4: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ K3 @ N4 )
% 4.88/5.19 => ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N4 ) ) @ R5 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % vanishes_def
% 4.88/5.19 thf(fact_9078_vanishes__mult__bounded,axiom,
% 4.88/5.19 ! [X5: nat > rat,Y6: nat > rat] :
% 4.88/5.19 ( ? [A8: rat] :
% 4.88/5.19 ( ( ord_less_rat @ zero_zero_rat @ A8 )
% 4.88/5.19 & ! [N2: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X5 @ N2 ) ) @ A8 ) )
% 4.88/5.19 => ( ( vanishes @ Y6 )
% 4.88/5.19 => ( vanishes
% 4.88/5.19 @ ^ [N4: nat] : ( times_times_rat @ ( X5 @ N4 ) @ ( Y6 @ N4 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % vanishes_mult_bounded
% 4.88/5.19 thf(fact_9079_inverse__real_Otransfer,axiom,
% 4.88/5.19 ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real
% 4.88/5.19 @ ^ [X8: nat > rat] :
% 4.88/5.19 ( if_nat_rat @ ( vanishes @ X8 )
% 4.88/5.19 @ ^ [N4: nat] : zero_zero_rat
% 4.88/5.19 @ ^ [N4: nat] : ( inverse_inverse_rat @ ( X8 @ N4 ) ) )
% 4.88/5.19 @ inverse_inverse_real ) ).
% 4.88/5.19
% 4.88/5.19 % inverse_real.transfer
% 4.88/5.19 thf(fact_9080_inverse__real_Oabs__eq,axiom,
% 4.88/5.19 ! [X: nat > rat] :
% 4.88/5.19 ( ( realrel @ X @ X )
% 4.88/5.19 => ( ( inverse_inverse_real @ ( real2 @ X ) )
% 4.88/5.19 = ( real2
% 4.88/5.19 @ ( if_nat_rat @ ( vanishes @ X )
% 4.88/5.19 @ ^ [N4: nat] : zero_zero_rat
% 4.88/5.19 @ ^ [N4: nat] : ( inverse_inverse_rat @ ( X @ N4 ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % inverse_real.abs_eq
% 4.88/5.19 thf(fact_9081_real_Oabs__induct,axiom,
% 4.88/5.19 ! [P: real > $o,X: real] :
% 4.88/5.19 ( ! [Y3: nat > rat] :
% 4.88/5.19 ( ( realrel @ Y3 @ Y3 )
% 4.88/5.19 => ( P @ ( real2 @ Y3 ) ) )
% 4.88/5.19 => ( P @ X ) ) ).
% 4.88/5.19
% 4.88/5.19 % real.abs_induct
% 4.88/5.19 thf(fact_9082_zero__real__def,axiom,
% 4.88/5.19 ( zero_zero_real
% 4.88/5.19 = ( real2
% 4.88/5.19 @ ^ [N4: nat] : zero_zero_rat ) ) ).
% 4.88/5.19
% 4.88/5.19 % zero_real_def
% 4.88/5.19 thf(fact_9083_of__nat__Real,axiom,
% 4.88/5.19 ( semiri5074537144036343181t_real
% 4.88/5.19 = ( ^ [X3: nat] :
% 4.88/5.19 ( real2
% 4.88/5.19 @ ^ [N4: nat] : ( semiri681578069525770553at_rat @ X3 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % of_nat_Real
% 4.88/5.19 thf(fact_9084_one__real__def,axiom,
% 4.88/5.19 ( one_one_real
% 4.88/5.19 = ( real2
% 4.88/5.19 @ ^ [N4: nat] : one_one_rat ) ) ).
% 4.88/5.19
% 4.88/5.19 % one_real_def
% 4.88/5.19 thf(fact_9085_of__rat__Real,axiom,
% 4.88/5.19 ( field_7254667332652039916t_real
% 4.88/5.19 = ( ^ [X3: rat] :
% 4.88/5.19 ( real2
% 4.88/5.19 @ ^ [N4: nat] : X3 ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % of_rat_Real
% 4.88/5.19 thf(fact_9086_of__int__Real,axiom,
% 4.88/5.19 ( ring_1_of_int_real
% 4.88/5.19 = ( ^ [X3: int] :
% 4.88/5.19 ( real2
% 4.88/5.19 @ ^ [N4: nat] : ( ring_1_of_int_rat @ X3 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % of_int_Real
% 4.88/5.19 thf(fact_9087_real_Orel__eq__transfer,axiom,
% 4.88/5.19 ( bNF_re4521903465945308077real_o @ pcr_real
% 4.88/5.19 @ ( bNF_re4297313714947099218al_o_o @ pcr_real
% 4.88/5.19 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
% 4.88/5.19 @ realrel
% 4.88/5.19 @ ^ [Y5: real,Z4: real] : ( Y5 = Z4 ) ) ).
% 4.88/5.19
% 4.88/5.19 % real.rel_eq_transfer
% 4.88/5.19 thf(fact_9088_zero__real_Otransfer,axiom,
% 4.88/5.19 ( pcr_real
% 4.88/5.19 @ ^ [N4: nat] : zero_zero_rat
% 4.88/5.19 @ zero_zero_real ) ).
% 4.88/5.19
% 4.88/5.19 % zero_real.transfer
% 4.88/5.19 thf(fact_9089_one__real_Otransfer,axiom,
% 4.88/5.19 ( pcr_real
% 4.88/5.19 @ ^ [N4: nat] : one_one_rat
% 4.88/5.19 @ one_one_real ) ).
% 4.88/5.19
% 4.88/5.19 % one_real.transfer
% 4.88/5.19 thf(fact_9090_uminus__real_Otransfer,axiom,
% 4.88/5.19 ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real
% 4.88/5.19 @ ^ [X8: nat > rat,N4: nat] : ( uminus_uminus_rat @ ( X8 @ N4 ) )
% 4.88/5.19 @ uminus_uminus_real ) ).
% 4.88/5.19
% 4.88/5.19 % uminus_real.transfer
% 4.88/5.19 thf(fact_9091_plus__real_Otransfer,axiom,
% 4.88/5.19 ( bNF_re4695409256820837752l_real @ pcr_real @ ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real )
% 4.88/5.19 @ ^ [X8: nat > rat,Y7: nat > rat,N4: nat] : ( plus_plus_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) )
% 4.88/5.19 @ plus_plus_real ) ).
% 4.88/5.19
% 4.88/5.19 % plus_real.transfer
% 4.88/5.19 thf(fact_9092_uminus__real_Oabs__eq,axiom,
% 4.88/5.19 ! [X: nat > rat] :
% 4.88/5.19 ( ( realrel @ X @ X )
% 4.88/5.19 => ( ( uminus_uminus_real @ ( real2 @ X ) )
% 4.88/5.19 = ( real2
% 4.88/5.19 @ ^ [N4: nat] : ( uminus_uminus_rat @ ( X @ N4 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % uminus_real.abs_eq
% 4.88/5.19 thf(fact_9093_times__real_Otransfer,axiom,
% 4.88/5.19 ( bNF_re4695409256820837752l_real @ pcr_real @ ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real )
% 4.88/5.19 @ ^ [X8: nat > rat,Y7: nat > rat,N4: nat] : ( times_times_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) )
% 4.88/5.19 @ times_times_real ) ).
% 4.88/5.19
% 4.88/5.19 % times_real.transfer
% 4.88/5.19 thf(fact_9094_plus__real_Oabs__eq,axiom,
% 4.88/5.19 ! [Xa2: nat > rat,X: nat > rat] :
% 4.88/5.19 ( ( realrel @ Xa2 @ Xa2 )
% 4.88/5.19 => ( ( realrel @ X @ X )
% 4.88/5.19 => ( ( plus_plus_real @ ( real2 @ Xa2 ) @ ( real2 @ X ) )
% 4.88/5.19 = ( real2
% 4.88/5.19 @ ^ [N4: nat] : ( plus_plus_rat @ ( Xa2 @ N4 ) @ ( X @ N4 ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % plus_real.abs_eq
% 4.88/5.19 thf(fact_9095_times__real_Oabs__eq,axiom,
% 4.88/5.19 ! [Xa2: nat > rat,X: nat > rat] :
% 4.88/5.19 ( ( realrel @ Xa2 @ Xa2 )
% 4.88/5.19 => ( ( realrel @ X @ X )
% 4.88/5.19 => ( ( times_times_real @ ( real2 @ Xa2 ) @ ( real2 @ X ) )
% 4.88/5.19 = ( real2
% 4.88/5.19 @ ^ [N4: nat] : ( times_times_rat @ ( Xa2 @ N4 ) @ ( X @ N4 ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % times_real.abs_eq
% 4.88/5.19 thf(fact_9096_Real_Opositive_Otransfer,axiom,
% 4.88/5.19 ( bNF_re4297313714947099218al_o_o @ pcr_real
% 4.88/5.19 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 )
% 4.88/5.19 @ ^ [X8: nat > rat] :
% 4.88/5.19 ? [R5: rat] :
% 4.88/5.19 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 4.88/5.19 & ? [K3: nat] :
% 4.88/5.19 ! [N4: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ K3 @ N4 )
% 4.88/5.19 => ( ord_less_rat @ R5 @ ( X8 @ N4 ) ) ) )
% 4.88/5.19 @ positive ) ).
% 4.88/5.19
% 4.88/5.19 % Real.positive.transfer
% 4.88/5.19 thf(fact_9097_Real_Opositive_Oabs__eq,axiom,
% 4.88/5.19 ! [X: nat > rat] :
% 4.88/5.19 ( ( realrel @ X @ X )
% 4.88/5.19 => ( ( positive @ ( real2 @ X ) )
% 4.88/5.19 = ( ? [R5: rat] :
% 4.88/5.19 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 4.88/5.19 & ? [K3: nat] :
% 4.88/5.19 ! [N4: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ K3 @ N4 )
% 4.88/5.19 => ( ord_less_rat @ R5 @ ( X @ N4 ) ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Real.positive.abs_eq
% 4.88/5.19 thf(fact_9098_Real_Opositive__mult,axiom,
% 4.88/5.19 ! [X: real,Y: real] :
% 4.88/5.19 ( ( positive @ X )
% 4.88/5.19 => ( ( positive @ Y )
% 4.88/5.19 => ( positive @ ( times_times_real @ X @ Y ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Real.positive_mult
% 4.88/5.19 thf(fact_9099_Real_Opositive__add,axiom,
% 4.88/5.19 ! [X: real,Y: real] :
% 4.88/5.19 ( ( positive @ X )
% 4.88/5.19 => ( ( positive @ Y )
% 4.88/5.19 => ( positive @ ( plus_plus_real @ X @ Y ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Real.positive_add
% 4.88/5.19 thf(fact_9100_Real_Opositive__zero,axiom,
% 4.88/5.19 ~ ( positive @ zero_zero_real ) ).
% 4.88/5.19
% 4.88/5.19 % Real.positive_zero
% 4.88/5.19 thf(fact_9101_Real_Opositive__minus,axiom,
% 4.88/5.19 ! [X: real] :
% 4.88/5.19 ( ~ ( positive @ X )
% 4.88/5.19 => ( ( X != zero_zero_real )
% 4.88/5.19 => ( positive @ ( uminus_uminus_real @ X ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Real.positive_minus
% 4.88/5.19 thf(fact_9102_less__real__def,axiom,
% 4.88/5.19 ( ord_less_real
% 4.88/5.19 = ( ^ [X3: real,Y2: real] : ( positive @ ( minus_minus_real @ Y2 @ X3 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % less_real_def
% 4.88/5.19 thf(fact_9103_le__Real,axiom,
% 4.88/5.19 ! [X5: nat > rat,Y6: nat > rat] :
% 4.88/5.19 ( ( cauchy @ X5 )
% 4.88/5.19 => ( ( cauchy @ Y6 )
% 4.88/5.19 => ( ( ord_less_eq_real @ ( real2 @ X5 ) @ ( real2 @ Y6 ) )
% 4.88/5.19 = ( ! [R5: rat] :
% 4.88/5.19 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 4.88/5.19 => ? [K3: nat] :
% 4.88/5.19 ! [N4: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ K3 @ N4 )
% 4.88/5.19 => ( ord_less_eq_rat @ ( X5 @ N4 ) @ ( plus_plus_rat @ ( Y6 @ N4 ) @ R5 ) ) ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % le_Real
% 4.88/5.19 thf(fact_9104_Real_Opositive_Orep__eq,axiom,
% 4.88/5.19 ( positive
% 4.88/5.19 = ( ^ [X3: real] :
% 4.88/5.19 ? [R5: rat] :
% 4.88/5.19 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 4.88/5.19 & ? [K3: nat] :
% 4.88/5.19 ! [N4: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ K3 @ N4 )
% 4.88/5.19 => ( ord_less_rat @ R5 @ ( rep_real2 @ X3 @ N4 ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Real.positive.rep_eq
% 4.88/5.19 thf(fact_9105_cauchy__inverse,axiom,
% 4.88/5.19 ! [X5: nat > rat] :
% 4.88/5.19 ( ( cauchy @ X5 )
% 4.88/5.19 => ( ~ ( vanishes @ X5 )
% 4.88/5.19 => ( cauchy
% 4.88/5.19 @ ^ [N4: nat] : ( inverse_inverse_rat @ ( X5 @ N4 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % cauchy_inverse
% 4.88/5.19 thf(fact_9106_realrel__refl,axiom,
% 4.88/5.19 ! [X5: nat > rat] :
% 4.88/5.19 ( ( cauchy @ X5 )
% 4.88/5.19 => ( realrel @ X5 @ X5 ) ) ).
% 4.88/5.19
% 4.88/5.19 % realrel_refl
% 4.88/5.19 thf(fact_9107_cauchy__add,axiom,
% 4.88/5.19 ! [X5: nat > rat,Y6: nat > rat] :
% 4.88/5.19 ( ( cauchy @ X5 )
% 4.88/5.19 => ( ( cauchy @ Y6 )
% 4.88/5.19 => ( cauchy
% 4.88/5.19 @ ^ [N4: nat] : ( plus_plus_rat @ ( X5 @ N4 ) @ ( Y6 @ N4 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % cauchy_add
% 4.88/5.19 thf(fact_9108_cauchy__const,axiom,
% 4.88/5.19 ! [X: rat] :
% 4.88/5.19 ( cauchy
% 4.88/5.19 @ ^ [N4: nat] : X ) ).
% 4.88/5.19
% 4.88/5.19 % cauchy_const
% 4.88/5.19 thf(fact_9109_cauchy__minus,axiom,
% 4.88/5.19 ! [X5: nat > rat] :
% 4.88/5.19 ( ( cauchy @ X5 )
% 4.88/5.19 => ( cauchy
% 4.88/5.19 @ ^ [N4: nat] : ( uminus_uminus_rat @ ( X5 @ N4 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % cauchy_minus
% 4.88/5.19 thf(fact_9110_cauchy__mult,axiom,
% 4.88/5.19 ! [X5: nat > rat,Y6: nat > rat] :
% 4.88/5.19 ( ( cauchy @ X5 )
% 4.88/5.19 => ( ( cauchy @ Y6 )
% 4.88/5.19 => ( cauchy
% 4.88/5.19 @ ^ [N4: nat] : ( times_times_rat @ ( X5 @ N4 ) @ ( Y6 @ N4 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % cauchy_mult
% 4.88/5.19 thf(fact_9111_cauchy__diff,axiom,
% 4.88/5.19 ! [X5: nat > rat,Y6: nat > rat] :
% 4.88/5.19 ( ( cauchy @ X5 )
% 4.88/5.19 => ( ( cauchy @ Y6 )
% 4.88/5.19 => ( cauchy
% 4.88/5.19 @ ^ [N4: nat] : ( minus_minus_rat @ ( X5 @ N4 ) @ ( Y6 @ N4 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % cauchy_diff
% 4.88/5.19 thf(fact_9112_Real__induct,axiom,
% 4.88/5.19 ! [P: real > $o,X: real] :
% 4.88/5.19 ( ! [X10: nat > rat] :
% 4.88/5.19 ( ( cauchy @ X10 )
% 4.88/5.19 => ( P @ ( real2 @ X10 ) ) )
% 4.88/5.19 => ( P @ X ) ) ).
% 4.88/5.19
% 4.88/5.19 % Real_induct
% 4.88/5.19 thf(fact_9113_cr__real__eq,axiom,
% 4.88/5.19 ( pcr_real
% 4.88/5.19 = ( ^ [X3: nat > rat,Y2: real] :
% 4.88/5.19 ( ( cauchy @ X3 )
% 4.88/5.19 & ( ( real2 @ X3 )
% 4.88/5.19 = Y2 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % cr_real_eq
% 4.88/5.19 thf(fact_9114_cauchy__imp__bounded,axiom,
% 4.88/5.19 ! [X5: nat > rat] :
% 4.88/5.19 ( ( cauchy @ X5 )
% 4.88/5.19 => ? [B5: rat] :
% 4.88/5.19 ( ( ord_less_rat @ zero_zero_rat @ B5 )
% 4.88/5.19 & ! [N6: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X5 @ N6 ) ) @ B5 ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % cauchy_imp_bounded
% 4.88/5.19 thf(fact_9115_less__RealD,axiom,
% 4.88/5.19 ! [Y6: nat > rat,X: real] :
% 4.88/5.19 ( ( cauchy @ Y6 )
% 4.88/5.19 => ( ( ord_less_real @ X @ ( real2 @ Y6 ) )
% 4.88/5.19 => ? [N2: nat] : ( ord_less_real @ X @ ( field_7254667332652039916t_real @ ( Y6 @ N2 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % less_RealD
% 4.88/5.19 thf(fact_9116_le__RealI,axiom,
% 4.88/5.19 ! [Y6: nat > rat,X: real] :
% 4.88/5.19 ( ( cauchy @ Y6 )
% 4.88/5.19 => ( ! [N2: nat] : ( ord_less_eq_real @ X @ ( field_7254667332652039916t_real @ ( Y6 @ N2 ) ) )
% 4.88/5.19 => ( ord_less_eq_real @ X @ ( real2 @ Y6 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % le_RealI
% 4.88/5.19 thf(fact_9117_Real__leI,axiom,
% 4.88/5.19 ! [X5: nat > rat,Y: real] :
% 4.88/5.19 ( ( cauchy @ X5 )
% 4.88/5.19 => ( ! [N2: nat] : ( ord_less_eq_real @ ( field_7254667332652039916t_real @ ( X5 @ N2 ) ) @ Y )
% 4.88/5.19 => ( ord_less_eq_real @ ( real2 @ X5 ) @ Y ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Real_leI
% 4.88/5.19 thf(fact_9118_minus__Real,axiom,
% 4.88/5.19 ! [X5: nat > rat] :
% 4.88/5.19 ( ( cauchy @ X5 )
% 4.88/5.19 => ( ( uminus_uminus_real @ ( real2 @ X5 ) )
% 4.88/5.19 = ( real2
% 4.88/5.19 @ ^ [N4: nat] : ( uminus_uminus_rat @ ( X5 @ N4 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % minus_Real
% 4.88/5.19 thf(fact_9119_add__Real,axiom,
% 4.88/5.19 ! [X5: nat > rat,Y6: nat > rat] :
% 4.88/5.19 ( ( cauchy @ X5 )
% 4.88/5.19 => ( ( cauchy @ Y6 )
% 4.88/5.19 => ( ( plus_plus_real @ ( real2 @ X5 ) @ ( real2 @ Y6 ) )
% 4.88/5.19 = ( real2
% 4.88/5.19 @ ^ [N4: nat] : ( plus_plus_rat @ ( X5 @ N4 ) @ ( Y6 @ N4 ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % add_Real
% 4.88/5.19 thf(fact_9120_mult__Real,axiom,
% 4.88/5.19 ! [X5: nat > rat,Y6: nat > rat] :
% 4.88/5.19 ( ( cauchy @ X5 )
% 4.88/5.19 => ( ( cauchy @ Y6 )
% 4.88/5.19 => ( ( times_times_real @ ( real2 @ X5 ) @ ( real2 @ Y6 ) )
% 4.88/5.19 = ( real2
% 4.88/5.19 @ ^ [N4: nat] : ( times_times_rat @ ( X5 @ N4 ) @ ( Y6 @ N4 ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % mult_Real
% 4.88/5.19 thf(fact_9121_diff__Real,axiom,
% 4.88/5.19 ! [X5: nat > rat,Y6: nat > rat] :
% 4.88/5.19 ( ( cauchy @ X5 )
% 4.88/5.19 => ( ( cauchy @ Y6 )
% 4.88/5.19 => ( ( minus_minus_real @ ( real2 @ X5 ) @ ( real2 @ Y6 ) )
% 4.88/5.19 = ( real2
% 4.88/5.19 @ ^ [N4: nat] : ( minus_minus_rat @ ( X5 @ N4 ) @ ( Y6 @ N4 ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % diff_Real
% 4.88/5.19 thf(fact_9122_realrelI,axiom,
% 4.88/5.19 ! [X5: nat > rat,Y6: nat > rat] :
% 4.88/5.19 ( ( cauchy @ X5 )
% 4.88/5.19 => ( ( cauchy @ Y6 )
% 4.88/5.19 => ( ( vanishes
% 4.88/5.19 @ ^ [N4: nat] : ( minus_minus_rat @ ( X5 @ N4 ) @ ( Y6 @ N4 ) ) )
% 4.88/5.19 => ( realrel @ X5 @ Y6 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % realrelI
% 4.88/5.19 thf(fact_9123_eq__Real,axiom,
% 4.88/5.19 ! [X5: nat > rat,Y6: nat > rat] :
% 4.88/5.19 ( ( cauchy @ X5 )
% 4.88/5.19 => ( ( cauchy @ Y6 )
% 4.88/5.19 => ( ( ( real2 @ X5 )
% 4.88/5.19 = ( real2 @ Y6 ) )
% 4.88/5.19 = ( vanishes
% 4.88/5.19 @ ^ [N4: nat] : ( minus_minus_rat @ ( X5 @ N4 ) @ ( Y6 @ N4 ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % eq_Real
% 4.88/5.19 thf(fact_9124_vanishes__diff__inverse,axiom,
% 4.88/5.19 ! [X5: nat > rat,Y6: nat > rat] :
% 4.88/5.19 ( ( cauchy @ X5 )
% 4.88/5.19 => ( ~ ( vanishes @ X5 )
% 4.88/5.19 => ( ( cauchy @ Y6 )
% 4.88/5.19 => ( ~ ( vanishes @ Y6 )
% 4.88/5.19 => ( ( vanishes
% 4.88/5.19 @ ^ [N4: nat] : ( minus_minus_rat @ ( X5 @ N4 ) @ ( Y6 @ N4 ) ) )
% 4.88/5.19 => ( vanishes
% 4.88/5.19 @ ^ [N4: nat] : ( minus_minus_rat @ ( inverse_inverse_rat @ ( X5 @ N4 ) ) @ ( inverse_inverse_rat @ ( Y6 @ N4 ) ) ) ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % vanishes_diff_inverse
% 4.88/5.19 thf(fact_9125_realrel__def,axiom,
% 4.88/5.19 ( realrel
% 4.88/5.19 = ( ^ [X8: nat > rat,Y7: nat > rat] :
% 4.88/5.19 ( ( cauchy @ X8 )
% 4.88/5.19 & ( cauchy @ Y7 )
% 4.88/5.19 & ( vanishes
% 4.88/5.19 @ ^ [N4: nat] : ( minus_minus_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % realrel_def
% 4.88/5.19 thf(fact_9126_cauchy__not__vanishes__cases,axiom,
% 4.88/5.19 ! [X5: nat > rat] :
% 4.88/5.19 ( ( cauchy @ X5 )
% 4.88/5.19 => ( ~ ( vanishes @ X5 )
% 4.88/5.19 => ? [B5: rat] :
% 4.88/5.19 ( ( ord_less_rat @ zero_zero_rat @ B5 )
% 4.88/5.19 & ? [K2: nat] :
% 4.88/5.19 ( ! [N6: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ K2 @ N6 )
% 4.88/5.19 => ( ord_less_rat @ B5 @ ( uminus_uminus_rat @ ( X5 @ N6 ) ) ) )
% 4.88/5.19 | ! [N6: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ K2 @ N6 )
% 4.88/5.19 => ( ord_less_rat @ B5 @ ( X5 @ N6 ) ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % cauchy_not_vanishes_cases
% 4.88/5.19 thf(fact_9127_positive__Real,axiom,
% 4.88/5.19 ! [X5: nat > rat] :
% 4.88/5.19 ( ( cauchy @ X5 )
% 4.88/5.19 => ( ( positive @ ( real2 @ X5 ) )
% 4.88/5.19 = ( ? [R5: rat] :
% 4.88/5.19 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 4.88/5.19 & ? [K3: nat] :
% 4.88/5.19 ! [N4: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ K3 @ N4 )
% 4.88/5.19 => ( ord_less_rat @ R5 @ ( X5 @ N4 ) ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % positive_Real
% 4.88/5.19 thf(fact_9128_cauchy__not__vanishes,axiom,
% 4.88/5.19 ! [X5: nat > rat] :
% 4.88/5.19 ( ( cauchy @ X5 )
% 4.88/5.19 => ( ~ ( vanishes @ X5 )
% 4.88/5.19 => ? [B5: rat] :
% 4.88/5.19 ( ( ord_less_rat @ zero_zero_rat @ B5 )
% 4.88/5.19 & ? [K2: nat] :
% 4.88/5.19 ! [N6: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ K2 @ N6 )
% 4.88/5.19 => ( ord_less_rat @ B5 @ ( abs_abs_rat @ ( X5 @ N6 ) ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % cauchy_not_vanishes
% 4.88/5.19 thf(fact_9129_cauchy__def,axiom,
% 4.88/5.19 ( cauchy
% 4.88/5.19 = ( ^ [X8: nat > rat] :
% 4.88/5.19 ! [R5: rat] :
% 4.88/5.19 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 4.88/5.19 => ? [K3: nat] :
% 4.88/5.19 ! [M3: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ K3 @ M3 )
% 4.88/5.19 => ! [N4: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ K3 @ N4 )
% 4.88/5.19 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X8 @ M3 ) @ ( X8 @ N4 ) ) ) @ R5 ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % cauchy_def
% 4.88/5.19 thf(fact_9130_cauchyI,axiom,
% 4.88/5.19 ! [X5: nat > rat] :
% 4.88/5.19 ( ! [R4: rat] :
% 4.88/5.19 ( ( ord_less_rat @ zero_zero_rat @ R4 )
% 4.88/5.19 => ? [K8: nat] :
% 4.88/5.19 ! [M4: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ K8 @ M4 )
% 4.88/5.19 => ! [N2: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ K8 @ N2 )
% 4.88/5.19 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X5 @ M4 ) @ ( X5 @ N2 ) ) ) @ R4 ) ) ) )
% 4.88/5.19 => ( cauchy @ X5 ) ) ).
% 4.88/5.19
% 4.88/5.19 % cauchyI
% 4.88/5.19 thf(fact_9131_cauchyD,axiom,
% 4.88/5.19 ! [X5: nat > rat,R2: rat] :
% 4.88/5.19 ( ( cauchy @ X5 )
% 4.88/5.19 => ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 4.88/5.19 => ? [K2: nat] :
% 4.88/5.19 ! [M: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ K2 @ M )
% 4.88/5.19 => ! [N6: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ K2 @ N6 )
% 4.88/5.19 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X5 @ M ) @ ( X5 @ N6 ) ) ) @ R2 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % cauchyD
% 4.88/5.19 thf(fact_9132_inverse__Real,axiom,
% 4.88/5.19 ! [X5: nat > rat] :
% 4.88/5.19 ( ( cauchy @ X5 )
% 4.88/5.19 => ( ( ( vanishes @ X5 )
% 4.88/5.19 => ( ( inverse_inverse_real @ ( real2 @ X5 ) )
% 4.88/5.19 = zero_zero_real ) )
% 4.88/5.19 & ( ~ ( vanishes @ X5 )
% 4.88/5.19 => ( ( inverse_inverse_real @ ( real2 @ X5 ) )
% 4.88/5.19 = ( real2
% 4.88/5.19 @ ^ [N4: nat] : ( inverse_inverse_rat @ ( X5 @ N4 ) ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % inverse_Real
% 4.88/5.19 thf(fact_9133_not__positive__Real,axiom,
% 4.88/5.19 ! [X5: nat > rat] :
% 4.88/5.19 ( ( cauchy @ X5 )
% 4.88/5.19 => ( ( ~ ( positive @ ( real2 @ X5 ) ) )
% 4.88/5.19 = ( ! [R5: rat] :
% 4.88/5.19 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 4.88/5.19 => ? [K3: nat] :
% 4.88/5.19 ! [N4: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ K3 @ N4 )
% 4.88/5.19 => ( ord_less_eq_rat @ ( X5 @ N4 ) @ R5 ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % not_positive_Real
% 4.88/5.19 thf(fact_9134_inverse__real__def,axiom,
% 4.88/5.19 ( inverse_inverse_real
% 4.88/5.19 = ( map_fu7146612038024189824t_real @ rep_real2 @ real2
% 4.88/5.19 @ ^ [X8: nat > rat] :
% 4.88/5.19 ( if_nat_rat @ ( vanishes @ X8 )
% 4.88/5.19 @ ^ [N4: nat] : zero_zero_rat
% 4.88/5.19 @ ^ [N4: nat] : ( inverse_inverse_rat @ ( X8 @ N4 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % inverse_real_def
% 4.88/5.19 thf(fact_9135_cr__real__def,axiom,
% 4.88/5.19 ( cr_real
% 4.88/5.19 = ( ^ [X3: nat > rat,Y2: real] :
% 4.88/5.19 ( ( realrel @ X3 @ X3 )
% 4.88/5.19 & ( ( real2 @ X3 )
% 4.88/5.19 = Y2 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % cr_real_def
% 4.88/5.19 thf(fact_9136_real_Opcr__cr__eq,axiom,
% 4.88/5.19 pcr_real = cr_real ).
% 4.88/5.19
% 4.88/5.19 % real.pcr_cr_eq
% 4.88/5.19 thf(fact_9137_uminus__real__def,axiom,
% 4.88/5.19 ( uminus_uminus_real
% 4.88/5.19 = ( map_fu7146612038024189824t_real @ rep_real2 @ real2
% 4.88/5.19 @ ^ [X8: nat > rat,N4: nat] : ( uminus_uminus_rat @ ( X8 @ N4 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % uminus_real_def
% 4.88/5.19 thf(fact_9138_times__real__def,axiom,
% 4.88/5.19 ( times_times_real
% 4.88/5.19 = ( map_fu1532550112467129777l_real @ rep_real2 @ ( map_fu7146612038024189824t_real @ rep_real2 @ real2 )
% 4.88/5.19 @ ^ [X8: nat > rat,Y7: nat > rat,N4: nat] : ( times_times_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % times_real_def
% 4.88/5.19 thf(fact_9139_plus__real__def,axiom,
% 4.88/5.19 ( plus_plus_real
% 4.88/5.19 = ( map_fu1532550112467129777l_real @ rep_real2 @ ( map_fu7146612038024189824t_real @ rep_real2 @ real2 )
% 4.88/5.19 @ ^ [X8: nat > rat,Y7: nat > rat,N4: nat] : ( plus_plus_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % plus_real_def
% 4.88/5.19 thf(fact_9140_numeral__le__enat__iff,axiom,
% 4.88/5.19 ! [M2: num,N: nat] :
% 4.88/5.19 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( extended_enat2 @ N ) )
% 4.88/5.19 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M2 ) @ N ) ) ).
% 4.88/5.19
% 4.88/5.19 % numeral_le_enat_iff
% 4.88/5.19 thf(fact_9141_enat__ord__simps_I2_J,axiom,
% 4.88/5.19 ! [M2: nat,N: nat] :
% 4.88/5.19 ( ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M2 ) @ ( extended_enat2 @ N ) )
% 4.88/5.19 = ( ord_less_nat @ M2 @ N ) ) ).
% 4.88/5.19
% 4.88/5.19 % enat_ord_simps(2)
% 4.88/5.19 thf(fact_9142_enat__ord__simps_I1_J,axiom,
% 4.88/5.19 ! [M2: nat,N: nat] :
% 4.88/5.19 ( ( ord_le2932123472753598470d_enat @ ( extended_enat2 @ M2 ) @ ( extended_enat2 @ N ) )
% 4.88/5.19 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 4.88/5.19
% 4.88/5.19 % enat_ord_simps(1)
% 4.88/5.19 thf(fact_9143_idiff__enat__0,axiom,
% 4.88/5.19 ! [N: extended_enat] :
% 4.88/5.19 ( ( minus_3235023915231533773d_enat @ ( extended_enat2 @ zero_zero_nat ) @ N )
% 4.88/5.19 = ( extended_enat2 @ zero_zero_nat ) ) ).
% 4.88/5.19
% 4.88/5.19 % idiff_enat_0
% 4.88/5.19 thf(fact_9144_idiff__enat__0__right,axiom,
% 4.88/5.19 ! [N: extended_enat] :
% 4.88/5.19 ( ( minus_3235023915231533773d_enat @ N @ ( extended_enat2 @ zero_zero_nat ) )
% 4.88/5.19 = N ) ).
% 4.88/5.19
% 4.88/5.19 % idiff_enat_0_right
% 4.88/5.19 thf(fact_9145_numeral__less__enat__iff,axiom,
% 4.88/5.19 ! [M2: num,N: nat] :
% 4.88/5.19 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( extended_enat2 @ N ) )
% 4.88/5.19 = ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ N ) ) ).
% 4.88/5.19
% 4.88/5.19 % numeral_less_enat_iff
% 4.88/5.19 thf(fact_9146_one__enat__def,axiom,
% 4.88/5.19 ( one_on7984719198319812577d_enat
% 4.88/5.19 = ( extended_enat2 @ one_one_nat ) ) ).
% 4.88/5.19
% 4.88/5.19 % one_enat_def
% 4.88/5.19 thf(fact_9147_enat__1__iff_I1_J,axiom,
% 4.88/5.19 ! [X: nat] :
% 4.88/5.19 ( ( ( extended_enat2 @ X )
% 4.88/5.19 = one_on7984719198319812577d_enat )
% 4.88/5.19 = ( X = one_one_nat ) ) ).
% 4.88/5.19
% 4.88/5.19 % enat_1_iff(1)
% 4.88/5.19 thf(fact_9148_enat__1__iff_I2_J,axiom,
% 4.88/5.19 ! [X: nat] :
% 4.88/5.19 ( ( one_on7984719198319812577d_enat
% 4.88/5.19 = ( extended_enat2 @ X ) )
% 4.88/5.19 = ( X = one_one_nat ) ) ).
% 4.88/5.19
% 4.88/5.19 % enat_1_iff(2)
% 4.88/5.19 thf(fact_9149_enat__0__iff_I2_J,axiom,
% 4.88/5.19 ! [X: nat] :
% 4.88/5.19 ( ( zero_z5237406670263579293d_enat
% 4.88/5.19 = ( extended_enat2 @ X ) )
% 4.88/5.19 = ( X = zero_zero_nat ) ) ).
% 4.88/5.19
% 4.88/5.19 % enat_0_iff(2)
% 4.88/5.19 thf(fact_9150_enat__0__iff_I1_J,axiom,
% 4.88/5.19 ! [X: nat] :
% 4.88/5.19 ( ( ( extended_enat2 @ X )
% 4.88/5.19 = zero_z5237406670263579293d_enat )
% 4.88/5.19 = ( X = zero_zero_nat ) ) ).
% 4.88/5.19
% 4.88/5.19 % enat_0_iff(1)
% 4.88/5.19 thf(fact_9151_zero__enat__def,axiom,
% 4.88/5.19 ( zero_z5237406670263579293d_enat
% 4.88/5.19 = ( extended_enat2 @ zero_zero_nat ) ) ).
% 4.88/5.19
% 4.88/5.19 % zero_enat_def
% 4.88/5.19 thf(fact_9152_less__enatE,axiom,
% 4.88/5.19 ! [N: extended_enat,M2: nat] :
% 4.88/5.19 ( ( ord_le72135733267957522d_enat @ N @ ( extended_enat2 @ M2 ) )
% 4.88/5.19 => ~ ! [K2: nat] :
% 4.88/5.19 ( ( N
% 4.88/5.19 = ( extended_enat2 @ K2 ) )
% 4.88/5.19 => ~ ( ord_less_nat @ K2 @ M2 ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % less_enatE
% 4.88/5.19 thf(fact_9153_enat__ile,axiom,
% 4.88/5.19 ! [N: extended_enat,M2: nat] :
% 4.88/5.19 ( ( ord_le2932123472753598470d_enat @ N @ ( extended_enat2 @ M2 ) )
% 4.88/5.19 => ? [K2: nat] :
% 4.88/5.19 ( N
% 4.88/5.19 = ( extended_enat2 @ K2 ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % enat_ile
% 4.88/5.19 thf(fact_9154_finite__enat__bounded,axiom,
% 4.88/5.19 ! [A2: set_Extended_enat,N: nat] :
% 4.88/5.19 ( ! [Y3: extended_enat] :
% 4.88/5.19 ( ( member_Extended_enat @ Y3 @ A2 )
% 4.88/5.19 => ( ord_le2932123472753598470d_enat @ Y3 @ ( extended_enat2 @ N ) ) )
% 4.88/5.19 => ( finite4001608067531595151d_enat @ A2 ) ) ).
% 4.88/5.19
% 4.88/5.19 % finite_enat_bounded
% 4.88/5.19 thf(fact_9155_Suc__ile__eq,axiom,
% 4.88/5.19 ! [M2: nat,N: extended_enat] :
% 4.88/5.19 ( ( ord_le2932123472753598470d_enat @ ( extended_enat2 @ ( suc @ M2 ) ) @ N )
% 4.88/5.19 = ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M2 ) @ N ) ) ).
% 4.88/5.19
% 4.88/5.19 % Suc_ile_eq
% 4.88/5.19 thf(fact_9156_eventually__prod__sequentially,axiom,
% 4.88/5.19 ! [P: product_prod_nat_nat > $o] :
% 4.88/5.19 ( ( eventu1038000079068216329at_nat @ P @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 4.88/5.19 = ( ? [N3: nat] :
% 4.88/5.19 ! [M3: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ N3 @ M3 )
% 4.88/5.19 => ! [N4: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ N3 @ N4 )
% 4.88/5.19 => ( P @ ( product_Pair_nat_nat @ N4 @ M3 ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % eventually_prod_sequentially
% 4.88/5.19 thf(fact_9157_iadd__le__enat__iff,axiom,
% 4.88/5.19 ! [X: extended_enat,Y: extended_enat,N: nat] :
% 4.88/5.19 ( ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ X @ Y ) @ ( extended_enat2 @ N ) )
% 4.88/5.19 = ( ? [Y8: nat,X9: nat] :
% 4.88/5.19 ( ( X
% 4.88/5.19 = ( extended_enat2 @ X9 ) )
% 4.88/5.19 & ( Y
% 4.88/5.19 = ( extended_enat2 @ Y8 ) )
% 4.88/5.19 & ( ord_less_eq_nat @ ( plus_plus_nat @ X9 @ Y8 ) @ N ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % iadd_le_enat_iff
% 4.88/5.19 thf(fact_9158_elimnum,axiom,
% 4.88/5.19 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 4.88/5.19 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 4.88/5.19 => ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 4.88/5.19 = ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % elimnum
% 4.88/5.19 thf(fact_9159_VEBT__internal_Oelim__dead_Osimps_I3_J,axiom,
% 4.88/5.19 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,L: nat] :
% 4.88/5.19 ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ ( extended_enat2 @ L ) )
% 4.88/5.19 = ( vEBT_Node @ Info @ Deg
% 4.88/5.19 @ ( take_VEBT_VEBT @ ( divide_divide_nat @ L @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.88/5.19 @ ( map_VE8901447254227204932T_VEBT
% 4.88/5.19 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.88/5.19 @ TreeList ) )
% 4.88/5.19 @ ( vEBT_VEBT_elim_dead @ Summary @ ( extended_enat2 @ ( divide_divide_nat @ L @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % VEBT_internal.elim_dead.simps(3)
% 4.88/5.19 thf(fact_9160_VEBT__internal_Oelim__dead_Osimps_I1_J,axiom,
% 4.88/5.19 ! [A: $o,B: $o,Uu: extended_enat] :
% 4.88/5.19 ( ( vEBT_VEBT_elim_dead @ ( vEBT_Leaf @ A @ B ) @ Uu )
% 4.88/5.19 = ( vEBT_Leaf @ A @ B ) ) ).
% 4.88/5.19
% 4.88/5.19 % VEBT_internal.elim_dead.simps(1)
% 4.88/5.19 thf(fact_9161_VEBT__internal_Oelim__dead_Oelims,axiom,
% 4.88/5.19 ! [X: vEBT_VEBT,Xa2: extended_enat,Y: vEBT_VEBT] :
% 4.88/5.19 ( ( ( vEBT_VEBT_elim_dead @ X @ Xa2 )
% 4.88/5.19 = Y )
% 4.88/5.19 => ( ! [A5: $o,B5: $o] :
% 4.88/5.19 ( ( X
% 4.88/5.19 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.88/5.19 => ( Y
% 4.88/5.19 != ( vEBT_Leaf @ A5 @ B5 ) ) )
% 4.88/5.19 => ( ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.88/5.19 ( ( X
% 4.88/5.19 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 4.88/5.19 => ( ( Xa2 = extend5688581933313929465d_enat )
% 4.88/5.19 => ( Y
% 4.88/5.19 != ( vEBT_Node @ Info2 @ Deg2
% 4.88/5.19 @ ( map_VE8901447254227204932T_VEBT
% 4.88/5.19 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.88/5.19 @ TreeList2 )
% 4.88/5.19 @ ( vEBT_VEBT_elim_dead @ Summary2 @ extend5688581933313929465d_enat ) ) ) ) )
% 4.88/5.19 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.88/5.19 ( ( X
% 4.88/5.19 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 4.88/5.19 => ! [L4: nat] :
% 4.88/5.19 ( ( Xa2
% 4.88/5.19 = ( extended_enat2 @ L4 ) )
% 4.88/5.19 => ( Y
% 4.88/5.19 != ( vEBT_Node @ Info2 @ Deg2
% 4.88/5.19 @ ( take_VEBT_VEBT @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.88/5.19 @ ( map_VE8901447254227204932T_VEBT
% 4.88/5.19 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.88/5.19 @ TreeList2 ) )
% 4.88/5.19 @ ( vEBT_VEBT_elim_dead @ Summary2 @ ( extended_enat2 @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % VEBT_internal.elim_dead.elims
% 4.88/5.19 thf(fact_9162_VEBT__internal_Oelim__dead_Osimps_I2_J,axiom,
% 4.88/5.19 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 4.88/5.19 ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ extend5688581933313929465d_enat )
% 4.88/5.19 = ( vEBT_Node @ Info @ Deg
% 4.88/5.19 @ ( map_VE8901447254227204932T_VEBT
% 4.88/5.19 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.88/5.19 @ TreeList )
% 4.88/5.19 @ ( vEBT_VEBT_elim_dead @ Summary @ extend5688581933313929465d_enat ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % VEBT_internal.elim_dead.simps(2)
% 4.88/5.19 thf(fact_9163_elimcomplete,axiom,
% 4.88/5.19 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 4.88/5.19 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 4.88/5.19 => ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ extend5688581933313929465d_enat )
% 4.88/5.19 = ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % elimcomplete
% 4.88/5.19 thf(fact_9164_enat__ord__code_I3_J,axiom,
% 4.88/5.19 ! [Q4: extended_enat] : ( ord_le2932123472753598470d_enat @ Q4 @ extend5688581933313929465d_enat ) ).
% 4.88/5.19
% 4.88/5.19 % enat_ord_code(3)
% 4.88/5.19 thf(fact_9165_enat__ord__simps_I5_J,axiom,
% 4.88/5.19 ! [Q4: extended_enat] :
% 4.88/5.19 ( ( ord_le2932123472753598470d_enat @ extend5688581933313929465d_enat @ Q4 )
% 4.88/5.19 = ( Q4 = extend5688581933313929465d_enat ) ) ).
% 4.88/5.19
% 4.88/5.19 % enat_ord_simps(5)
% 4.88/5.19 thf(fact_9166_times__enat__simps_I4_J,axiom,
% 4.88/5.19 ! [M2: nat] :
% 4.88/5.19 ( ( ( M2 = zero_zero_nat )
% 4.88/5.19 => ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M2 ) @ extend5688581933313929465d_enat )
% 4.88/5.19 = zero_z5237406670263579293d_enat ) )
% 4.88/5.19 & ( ( M2 != zero_zero_nat )
% 4.88/5.19 => ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M2 ) @ extend5688581933313929465d_enat )
% 4.88/5.19 = extend5688581933313929465d_enat ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % times_enat_simps(4)
% 4.88/5.19 thf(fact_9167_times__enat__simps_I3_J,axiom,
% 4.88/5.19 ! [N: nat] :
% 4.88/5.19 ( ( ( N = zero_zero_nat )
% 4.88/5.19 => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N ) )
% 4.88/5.19 = zero_z5237406670263579293d_enat ) )
% 4.88/5.19 & ( ( N != zero_zero_nat )
% 4.88/5.19 => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N ) )
% 4.88/5.19 = extend5688581933313929465d_enat ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % times_enat_simps(3)
% 4.88/5.19 thf(fact_9168_enat__ord__code_I5_J,axiom,
% 4.88/5.19 ! [N: nat] :
% 4.88/5.19 ~ ( ord_le2932123472753598470d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N ) ) ).
% 4.88/5.19
% 4.88/5.19 % enat_ord_code(5)
% 4.88/5.19 thf(fact_9169_infinity__ileE,axiom,
% 4.88/5.19 ! [M2: nat] :
% 4.88/5.19 ~ ( ord_le2932123472753598470d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ M2 ) ) ).
% 4.88/5.19
% 4.88/5.19 % infinity_ileE
% 4.88/5.19 thf(fact_9170_enat__add__left__cancel__le,axiom,
% 4.88/5.19 ! [A: extended_enat,B: extended_enat,C: extended_enat] :
% 4.88/5.19 ( ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ A @ B ) @ ( plus_p3455044024723400733d_enat @ A @ C ) )
% 4.88/5.19 = ( ( A = extend5688581933313929465d_enat )
% 4.88/5.19 | ( ord_le2932123472753598470d_enat @ B @ C ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % enat_add_left_cancel_le
% 4.88/5.19 thf(fact_9171_enat__ord__simps_I3_J,axiom,
% 4.88/5.19 ! [Q4: extended_enat] : ( ord_le2932123472753598470d_enat @ Q4 @ extend5688581933313929465d_enat ) ).
% 4.88/5.19
% 4.88/5.19 % enat_ord_simps(3)
% 4.88/5.19 thf(fact_9172_Sup__enat__def,axiom,
% 4.88/5.19 ( comple4398354569131411667d_enat
% 4.88/5.19 = ( ^ [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 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Sup_enat_def
% 4.88/5.19 thf(fact_9173_Inf__enat__def,axiom,
% 4.88/5.19 ( comple2295165028678016749d_enat
% 4.88/5.19 = ( ^ [A6: set_Extended_enat] :
% 4.88/5.19 ( if_Extended_enat @ ( A6 = bot_bo7653980558646680370d_enat ) @ extend5688581933313929465d_enat
% 4.88/5.19 @ ( ord_Le1955565732374568822d_enat
% 4.88/5.19 @ ^ [X3: extended_enat] : ( member_Extended_enat @ X3 @ A6 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Inf_enat_def
% 4.88/5.19 thf(fact_9174_VEBT__internal_Oelim__dead_Ocases,axiom,
% 4.88/5.19 ! [X: produc7272778201969148633d_enat] :
% 4.88/5.19 ( ! [A5: $o,B5: $o,Uu2: extended_enat] :
% 4.88/5.19 ( X
% 4.88/5.19 != ( produc581526299967858633d_enat @ ( vEBT_Leaf @ A5 @ B5 ) @ Uu2 ) )
% 4.88/5.19 => ( ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.88/5.19 ( X
% 4.88/5.19 != ( produc581526299967858633d_enat @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) @ extend5688581933313929465d_enat ) )
% 4.88/5.19 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,L4: nat] :
% 4.88/5.19 ( X
% 4.88/5.19 != ( produc581526299967858633d_enat @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) @ ( extended_enat2 @ L4 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % VEBT_internal.elim_dead.cases
% 4.88/5.19 thf(fact_9175_VEBT__internal_Oelim__dead_Opelims,axiom,
% 4.88/5.19 ! [X: vEBT_VEBT,Xa2: extended_enat,Y: vEBT_VEBT] :
% 4.88/5.19 ( ( ( vEBT_VEBT_elim_dead @ X @ Xa2 )
% 4.88/5.19 = Y )
% 4.88/5.19 => ( ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ X @ Xa2 ) )
% 4.88/5.19 => ( ! [A5: $o,B5: $o] :
% 4.88/5.19 ( ( X
% 4.88/5.19 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.88/5.19 => ( ( Y
% 4.88/5.19 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.88/5.19 => ~ ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 4.88/5.19 => ( ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.88/5.19 ( ( X
% 4.88/5.19 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 4.88/5.19 => ( ( Xa2 = extend5688581933313929465d_enat )
% 4.88/5.19 => ( ( Y
% 4.88/5.19 = ( vEBT_Node @ Info2 @ Deg2
% 4.88/5.19 @ ( map_VE8901447254227204932T_VEBT
% 4.88/5.19 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.88/5.19 @ TreeList2 )
% 4.88/5.19 @ ( vEBT_VEBT_elim_dead @ Summary2 @ extend5688581933313929465d_enat ) ) )
% 4.88/5.19 => ~ ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) @ extend5688581933313929465d_enat ) ) ) ) )
% 4.88/5.19 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.88/5.19 ( ( X
% 4.88/5.19 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 4.88/5.19 => ! [L4: nat] :
% 4.88/5.19 ( ( Xa2
% 4.88/5.19 = ( extended_enat2 @ L4 ) )
% 4.88/5.19 => ( ( Y
% 4.88/5.19 = ( vEBT_Node @ Info2 @ Deg2
% 4.88/5.19 @ ( take_VEBT_VEBT @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.88/5.19 @ ( map_VE8901447254227204932T_VEBT
% 4.88/5.19 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 4.88/5.19 @ TreeList2 ) )
% 4.88/5.19 @ ( vEBT_VEBT_elim_dead @ Summary2 @ ( extended_enat2 @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 4.88/5.19 => ~ ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) @ ( extended_enat2 @ L4 ) ) ) ) ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % VEBT_internal.elim_dead.pelims
% 4.88/5.19 thf(fact_9176_times__enat__def,axiom,
% 4.88/5.19 ( times_7803423173614009249d_enat
% 4.88/5.19 = ( ^ [M3: extended_enat,N4: extended_enat] :
% 4.88/5.19 ( extend3600170679010898289d_enat
% 4.88/5.19 @ ^ [O: nat] :
% 4.88/5.19 ( extend3600170679010898289d_enat
% 4.88/5.19 @ ^ [P5: nat] : ( extended_enat2 @ ( times_times_nat @ O @ P5 ) )
% 4.88/5.19 @ ( if_Extended_enat @ ( O = zero_zero_nat ) @ zero_z5237406670263579293d_enat @ extend5688581933313929465d_enat )
% 4.88/5.19 @ N4 )
% 4.88/5.19 @ ( if_Extended_enat @ ( N4 = zero_z5237406670263579293d_enat ) @ zero_z5237406670263579293d_enat @ extend5688581933313929465d_enat )
% 4.88/5.19 @ M3 ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % times_enat_def
% 4.88/5.19 thf(fact_9177_eSuc__Max,axiom,
% 4.88/5.19 ! [A2: set_Extended_enat] :
% 4.88/5.19 ( ( finite4001608067531595151d_enat @ A2 )
% 4.88/5.19 => ( ( A2 != bot_bo7653980558646680370d_enat )
% 4.88/5.19 => ( ( extended_eSuc @ ( lattic921264341876707157d_enat @ A2 ) )
% 4.88/5.19 = ( lattic921264341876707157d_enat @ ( image_80655429650038917d_enat @ extended_eSuc @ A2 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % eSuc_Max
% 4.88/5.19 thf(fact_9178_eSuc__ile__mono,axiom,
% 4.88/5.19 ! [N: extended_enat,M2: extended_enat] :
% 4.88/5.19 ( ( ord_le2932123472753598470d_enat @ ( extended_eSuc @ N ) @ ( extended_eSuc @ M2 ) )
% 4.88/5.19 = ( ord_le2932123472753598470d_enat @ N @ M2 ) ) ).
% 4.88/5.19
% 4.88/5.19 % eSuc_ile_mono
% 4.88/5.19 thf(fact_9179_iless__Suc__eq,axiom,
% 4.88/5.19 ! [M2: nat,N: extended_enat] :
% 4.88/5.19 ( ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M2 ) @ ( extended_eSuc @ N ) )
% 4.88/5.19 = ( ord_le2932123472753598470d_enat @ ( extended_enat2 @ M2 ) @ N ) ) ).
% 4.88/5.19
% 4.88/5.19 % iless_Suc_eq
% 4.88/5.19 thf(fact_9180_ile__eSuc,axiom,
% 4.88/5.19 ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ N @ ( extended_eSuc @ N ) ) ).
% 4.88/5.19
% 4.88/5.19 % ile_eSuc
% 4.88/5.19 thf(fact_9181_not__eSuc__ilei0,axiom,
% 4.88/5.19 ! [N: extended_enat] :
% 4.88/5.19 ~ ( ord_le2932123472753598470d_enat @ ( extended_eSuc @ N ) @ zero_z5237406670263579293d_enat ) ).
% 4.88/5.19
% 4.88/5.19 % not_eSuc_ilei0
% 4.88/5.19 thf(fact_9182_ileI1,axiom,
% 4.88/5.19 ! [M2: extended_enat,N: extended_enat] :
% 4.88/5.19 ( ( ord_le72135733267957522d_enat @ M2 @ N )
% 4.88/5.19 => ( ord_le2932123472753598470d_enat @ ( extended_eSuc @ M2 ) @ N ) ) ).
% 4.88/5.19
% 4.88/5.19 % ileI1
% 4.88/5.19 thf(fact_9183_eSuc__Sup,axiom,
% 4.88/5.19 ! [A2: set_Extended_enat] :
% 4.88/5.19 ( ( A2 != bot_bo7653980558646680370d_enat )
% 4.88/5.19 => ( ( extended_eSuc @ ( comple4398354569131411667d_enat @ A2 ) )
% 4.88/5.19 = ( comple4398354569131411667d_enat @ ( image_80655429650038917d_enat @ extended_eSuc @ A2 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % eSuc_Sup
% 4.88/5.19 thf(fact_9184_less__than__iff,axiom,
% 4.88/5.19 ! [X: nat,Y: nat] :
% 4.88/5.19 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ less_than )
% 4.88/5.19 = ( ord_less_nat @ X @ Y ) ) ).
% 4.88/5.19
% 4.88/5.19 % less_than_iff
% 4.88/5.19 thf(fact_9185_pair__less__def,axiom,
% 4.88/5.19 ( fun_pair_less
% 4.88/5.19 = ( lex_prod_nat_nat @ less_than @ less_than ) ) ).
% 4.88/5.19
% 4.88/5.19 % pair_less_def
% 4.88/5.19 thf(fact_9186_natLeq__on__well__order__on,axiom,
% 4.88/5.19 ! [N: nat] :
% 4.88/5.19 ( order_2888998067076097458on_nat
% 4.88/5.19 @ ( collect_nat
% 4.88/5.19 @ ^ [X3: nat] : ( ord_less_nat @ X3 @ N ) )
% 4.88/5.19 @ ( collec3392354462482085612at_nat
% 4.88/5.19 @ ( produc6081775807080527818_nat_o
% 4.88/5.19 @ ^ [X3: nat,Y2: nat] :
% 4.88/5.19 ( ( ord_less_nat @ X3 @ N )
% 4.88/5.19 & ( ord_less_nat @ Y2 @ N )
% 4.88/5.19 & ( ord_less_eq_nat @ X3 @ Y2 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % natLeq_on_well_order_on
% 4.88/5.19 thf(fact_9187_natLeq__on__Well__order,axiom,
% 4.88/5.19 ! [N: nat] :
% 4.88/5.19 ( order_2888998067076097458on_nat
% 4.88/5.19 @ ( field_nat
% 4.88/5.19 @ ( collec3392354462482085612at_nat
% 4.88/5.19 @ ( produc6081775807080527818_nat_o
% 4.88/5.19 @ ^ [X3: nat,Y2: nat] :
% 4.88/5.19 ( ( ord_less_nat @ X3 @ N )
% 4.88/5.19 & ( ord_less_nat @ Y2 @ N )
% 4.88/5.19 & ( ord_less_eq_nat @ X3 @ Y2 ) ) ) ) )
% 4.88/5.19 @ ( collec3392354462482085612at_nat
% 4.88/5.19 @ ( produc6081775807080527818_nat_o
% 4.88/5.19 @ ^ [X3: nat,Y2: nat] :
% 4.88/5.19 ( ( ord_less_nat @ X3 @ N )
% 4.88/5.19 & ( ord_less_nat @ Y2 @ N )
% 4.88/5.19 & ( ord_less_eq_nat @ X3 @ Y2 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % natLeq_on_Well_order
% 4.88/5.19 thf(fact_9188_Real_Opositive__def,axiom,
% 4.88/5.19 ( positive
% 4.88/5.19 = ( map_fu1856342031159181835at_o_o @ rep_real2 @ id_o
% 4.88/5.19 @ ^ [X8: nat > rat] :
% 4.88/5.19 ? [R5: rat] :
% 4.88/5.19 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 4.88/5.19 & ? [K3: nat] :
% 4.88/5.19 ! [N4: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ K3 @ N4 )
% 4.88/5.19 => ( ord_less_rat @ R5 @ ( X8 @ N4 ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Real.positive_def
% 4.88/5.19 thf(fact_9189_cmod__plus__Re__le__0__iff,axiom,
% 4.88/5.19 ! [Z: complex] :
% 4.88/5.19 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ zero_zero_real )
% 4.88/5.19 = ( ( re @ Z )
% 4.88/5.19 = ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % cmod_plus_Re_le_0_iff
% 4.88/5.19 thf(fact_9190_Re__csqrt,axiom,
% 4.88/5.19 ! [Z: complex] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Re_csqrt
% 4.88/5.19 thf(fact_9191_abs__Re__le__cmod,axiom,
% 4.88/5.19 ! [X: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 4.88/5.19
% 4.88/5.19 % abs_Re_le_cmod
% 4.88/5.19 thf(fact_9192_complex__Re__le__cmod,axiom,
% 4.88/5.19 ! [X: complex] : ( ord_less_eq_real @ ( re @ X ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 4.88/5.19
% 4.88/5.19 % complex_Re_le_cmod
% 4.88/5.19 thf(fact_9193_complex__abs__le__norm,axiom,
% 4.88/5.19 ! [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 ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % complex_abs_le_norm
% 4.88/5.19 thf(fact_9194_csqrt__of__real__nonneg,axiom,
% 4.88/5.19 ! [X: complex] :
% 4.88/5.19 ( ( ( im @ X )
% 4.88/5.19 = zero_zero_real )
% 4.88/5.19 => ( ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) )
% 4.88/5.19 => ( ( csqrt @ X )
% 4.88/5.19 = ( real_V4546457046886955230omplex @ ( sqrt @ ( re @ X ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % csqrt_of_real_nonneg
% 4.88/5.19 thf(fact_9195_abs__Im__le__cmod,axiom,
% 4.88/5.19 ! [X: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 4.88/5.19
% 4.88/5.19 % abs_Im_le_cmod
% 4.88/5.19 thf(fact_9196_cmod__Im__le__iff,axiom,
% 4.88/5.19 ! [X: complex,Y: complex] :
% 4.88/5.19 ( ( ( re @ X )
% 4.88/5.19 = ( re @ Y ) )
% 4.88/5.19 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) )
% 4.88/5.19 = ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X ) ) @ ( abs_abs_real @ ( im @ Y ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % cmod_Im_le_iff
% 4.88/5.19 thf(fact_9197_cmod__Re__le__iff,axiom,
% 4.88/5.19 ! [X: complex,Y: complex] :
% 4.88/5.19 ( ( ( im @ X )
% 4.88/5.19 = ( im @ Y ) )
% 4.88/5.19 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) )
% 4.88/5.19 = ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X ) ) @ ( abs_abs_real @ ( re @ Y ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % cmod_Re_le_iff
% 4.88/5.19 thf(fact_9198_csqrt__principal,axiom,
% 4.88/5.19 ! [Z: complex] :
% 4.88/5.19 ( ( ord_less_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) )
% 4.88/5.19 | ( ( ( re @ ( csqrt @ Z ) )
% 4.88/5.19 = zero_zero_real )
% 4.88/5.19 & ( ord_less_eq_real @ zero_zero_real @ ( im @ ( csqrt @ Z ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % csqrt_principal
% 4.88/5.19 thf(fact_9199_cmod__le,axiom,
% 4.88/5.19 ! [Z: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % cmod_le
% 4.88/5.19 thf(fact_9200_csqrt__square,axiom,
% 4.88/5.19 ! [B: complex] :
% 4.88/5.19 ( ( ( ord_less_real @ zero_zero_real @ ( re @ B ) )
% 4.88/5.19 | ( ( ( re @ B )
% 4.88/5.19 = zero_zero_real )
% 4.88/5.19 & ( ord_less_eq_real @ zero_zero_real @ ( im @ B ) ) ) )
% 4.88/5.19 => ( ( csqrt @ ( power_power_complex @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.88/5.19 = B ) ) ).
% 4.88/5.19
% 4.88/5.19 % csqrt_square
% 4.88/5.19 thf(fact_9201_csqrt__unique,axiom,
% 4.88/5.19 ! [W2: complex,Z: complex] :
% 4.88/5.19 ( ( ( power_power_complex @ W2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.88/5.19 = Z )
% 4.88/5.19 => ( ( ( ord_less_real @ zero_zero_real @ ( re @ W2 ) )
% 4.88/5.19 | ( ( ( re @ W2 )
% 4.88/5.19 = zero_zero_real )
% 4.88/5.19 & ( ord_less_eq_real @ zero_zero_real @ ( im @ W2 ) ) ) )
% 4.88/5.19 => ( ( csqrt @ Z )
% 4.88/5.19 = W2 ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % csqrt_unique
% 4.88/5.19 thf(fact_9202_csqrt__of__real__nonpos,axiom,
% 4.88/5.19 ! [X: complex] :
% 4.88/5.19 ( ( ( im @ X )
% 4.88/5.19 = zero_zero_real )
% 4.88/5.19 => ( ( ord_less_eq_real @ ( re @ X ) @ zero_zero_real )
% 4.88/5.19 => ( ( csqrt @ X )
% 4.88/5.19 = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X ) ) ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % csqrt_of_real_nonpos
% 4.88/5.19 thf(fact_9203_csqrt__minus,axiom,
% 4.88/5.19 ! [X: complex] :
% 4.88/5.19 ( ( ( ord_less_real @ ( im @ X ) @ zero_zero_real )
% 4.88/5.19 | ( ( ( im @ X )
% 4.88/5.19 = zero_zero_real )
% 4.88/5.19 & ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) ) ) )
% 4.88/5.19 => ( ( csqrt @ ( uminus1482373934393186551omplex @ X ) )
% 4.88/5.19 = ( times_times_complex @ imaginary_unit @ ( csqrt @ X ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % csqrt_minus
% 4.88/5.19 thf(fact_9204_UNIV__bool,axiom,
% 4.88/5.19 ( top_top_set_o
% 4.88/5.19 = ( insert_o @ $false @ ( insert_o @ $true @ bot_bot_set_o ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % UNIV_bool
% 4.88/5.19 thf(fact_9205_Rep__unit__induct,axiom,
% 4.88/5.19 ! [Y: $o,P: $o > $o] :
% 4.88/5.19 ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 4.88/5.19 => ( ! [X4: product_unit] : ( P @ ( product_Rep_unit @ X4 ) )
% 4.88/5.19 => ( P @ Y ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Rep_unit_induct
% 4.88/5.19 thf(fact_9206_Abs__unit__inject,axiom,
% 4.88/5.19 ! [X: $o,Y: $o] :
% 4.88/5.19 ( ( member_o @ X @ ( insert_o @ $true @ bot_bot_set_o ) )
% 4.88/5.19 => ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 4.88/5.19 => ( ( ( product_Abs_unit @ X )
% 4.88/5.19 = ( product_Abs_unit @ Y ) )
% 4.88/5.19 = ( X = Y ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Abs_unit_inject
% 4.88/5.19 thf(fact_9207_Abs__unit__inverse,axiom,
% 4.88/5.19 ! [Y: $o] :
% 4.88/5.19 ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 4.88/5.19 => ( ( product_Rep_unit @ ( product_Abs_unit @ Y ) )
% 4.88/5.19 = Y ) ) ).
% 4.88/5.19
% 4.88/5.19 % Abs_unit_inverse
% 4.88/5.19 thf(fact_9208_Rep__unit,axiom,
% 4.88/5.19 ! [X: product_unit] : ( member_o @ ( product_Rep_unit @ X ) @ ( insert_o @ $true @ bot_bot_set_o ) ) ).
% 4.88/5.19
% 4.88/5.19 % Rep_unit
% 4.88/5.19 thf(fact_9209_Abs__unit__cases,axiom,
% 4.88/5.19 ! [X: product_unit] :
% 4.88/5.19 ~ ! [Y3: $o] :
% 4.88/5.19 ( ( X
% 4.88/5.19 = ( product_Abs_unit @ Y3 ) )
% 4.88/5.19 => ~ ( member_o @ Y3 @ ( insert_o @ $true @ bot_bot_set_o ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Abs_unit_cases
% 4.88/5.19 thf(fact_9210_Rep__unit__cases,axiom,
% 4.88/5.19 ! [Y: $o] :
% 4.88/5.19 ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 4.88/5.19 => ~ ! [X4: product_unit] :
% 4.88/5.19 ( Y
% 4.88/5.19 = ( ~ ( product_Rep_unit @ X4 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Rep_unit_cases
% 4.88/5.19 thf(fact_9211_Abs__unit__induct,axiom,
% 4.88/5.19 ! [P: product_unit > $o,X: product_unit] :
% 4.88/5.19 ( ! [Y3: $o] :
% 4.88/5.19 ( ( member_o @ Y3 @ ( insert_o @ $true @ bot_bot_set_o ) )
% 4.88/5.19 => ( P @ ( product_Abs_unit @ Y3 ) ) )
% 4.88/5.19 => ( P @ X ) ) ).
% 4.88/5.19
% 4.88/5.19 % Abs_unit_induct
% 4.88/5.19 thf(fact_9212_type__definition__unit,axiom,
% 4.88/5.19 type_d6188575255521822967unit_o @ product_Rep_unit @ product_Abs_unit @ ( insert_o @ $true @ bot_bot_set_o ) ).
% 4.88/5.19
% 4.88/5.19 % type_definition_unit
% 4.88/5.19 thf(fact_9213_Quotient__real,axiom,
% 4.88/5.19 quotie3684837364556693515t_real @ realrel @ real2 @ rep_real2 @ cr_real ).
% 4.88/5.19
% 4.88/5.19 % Quotient_real
% 4.88/5.19 thf(fact_9214_gcd__nat_Oeq__neutr__iff,axiom,
% 4.88/5.19 ! [A: nat,B: nat] :
% 4.88/5.19 ( ( ( gcd_gcd_nat @ A @ B )
% 4.88/5.19 = zero_zero_nat )
% 4.88/5.19 = ( ( A = zero_zero_nat )
% 4.88/5.19 & ( B = zero_zero_nat ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % gcd_nat.eq_neutr_iff
% 4.88/5.19 thf(fact_9215_gcd__nat_Oleft__neutral,axiom,
% 4.88/5.19 ! [A: nat] :
% 4.88/5.19 ( ( gcd_gcd_nat @ zero_zero_nat @ A )
% 4.88/5.19 = A ) ).
% 4.88/5.19
% 4.88/5.19 % gcd_nat.left_neutral
% 4.88/5.19 thf(fact_9216_gcd__nat_Oneutr__eq__iff,axiom,
% 4.88/5.19 ! [A: nat,B: nat] :
% 4.88/5.19 ( ( zero_zero_nat
% 4.88/5.19 = ( gcd_gcd_nat @ A @ B ) )
% 4.88/5.19 = ( ( A = zero_zero_nat )
% 4.88/5.19 & ( B = zero_zero_nat ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % gcd_nat.neutr_eq_iff
% 4.88/5.19 thf(fact_9217_gcd__nat_Oright__neutral,axiom,
% 4.88/5.19 ! [A: nat] :
% 4.88/5.19 ( ( gcd_gcd_nat @ A @ zero_zero_nat )
% 4.88/5.19 = A ) ).
% 4.88/5.19
% 4.88/5.19 % gcd_nat.right_neutral
% 4.88/5.19 thf(fact_9218_gcd__0__nat,axiom,
% 4.88/5.19 ! [X: nat] :
% 4.88/5.19 ( ( gcd_gcd_nat @ X @ zero_zero_nat )
% 4.88/5.19 = X ) ).
% 4.88/5.19
% 4.88/5.19 % gcd_0_nat
% 4.88/5.19 thf(fact_9219_gcd__0__left__nat,axiom,
% 4.88/5.19 ! [X: nat] :
% 4.88/5.19 ( ( gcd_gcd_nat @ zero_zero_nat @ X )
% 4.88/5.19 = X ) ).
% 4.88/5.19
% 4.88/5.19 % gcd_0_left_nat
% 4.88/5.19 thf(fact_9220_gcd__1__nat,axiom,
% 4.88/5.19 ! [M2: nat] :
% 4.88/5.19 ( ( gcd_gcd_nat @ M2 @ one_one_nat )
% 4.88/5.19 = one_one_nat ) ).
% 4.88/5.19
% 4.88/5.19 % gcd_1_nat
% 4.88/5.19 thf(fact_9221_gcd__Suc__0,axiom,
% 4.88/5.19 ! [M2: nat] :
% 4.88/5.19 ( ( gcd_gcd_nat @ M2 @ ( suc @ zero_zero_nat ) )
% 4.88/5.19 = ( suc @ zero_zero_nat ) ) ).
% 4.88/5.19
% 4.88/5.19 % gcd_Suc_0
% 4.88/5.19 thf(fact_9222_gcd__pos__nat,axiom,
% 4.88/5.19 ! [M2: nat,N: nat] :
% 4.88/5.19 ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M2 @ N ) )
% 4.88/5.19 = ( ( M2 != zero_zero_nat )
% 4.88/5.19 | ( N != zero_zero_nat ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % gcd_pos_nat
% 4.88/5.19 thf(fact_9223_gcd__non__0__nat,axiom,
% 4.88/5.19 ! [Y: nat,X: nat] :
% 4.88/5.19 ( ( Y != zero_zero_nat )
% 4.88/5.19 => ( ( gcd_gcd_nat @ X @ Y )
% 4.88/5.19 = ( gcd_gcd_nat @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % gcd_non_0_nat
% 4.88/5.19 thf(fact_9224_gcd__nat_Osimps,axiom,
% 4.88/5.19 ( gcd_gcd_nat
% 4.88/5.19 = ( ^ [X3: nat,Y2: nat] : ( if_nat @ ( Y2 = zero_zero_nat ) @ X3 @ ( gcd_gcd_nat @ Y2 @ ( modulo_modulo_nat @ X3 @ Y2 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % gcd_nat.simps
% 4.88/5.19 thf(fact_9225_gcd__nat_Oelims,axiom,
% 4.88/5.19 ! [X: nat,Xa2: nat,Y: nat] :
% 4.88/5.19 ( ( ( gcd_gcd_nat @ X @ Xa2 )
% 4.88/5.19 = Y )
% 4.88/5.19 => ( ( ( Xa2 = zero_zero_nat )
% 4.88/5.19 => ( Y = X ) )
% 4.88/5.19 & ( ( Xa2 != zero_zero_nat )
% 4.88/5.19 => ( Y
% 4.88/5.19 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % gcd_nat.elims
% 4.88/5.19 thf(fact_9226_gcd__diff1__nat,axiom,
% 4.88/5.19 ! [N: nat,M2: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ N @ M2 )
% 4.88/5.19 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M2 @ N ) @ N )
% 4.88/5.19 = ( gcd_gcd_nat @ M2 @ N ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % gcd_diff1_nat
% 4.88/5.19 thf(fact_9227_gcd__diff2__nat,axiom,
% 4.88/5.19 ! [M2: nat,N: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ M2 @ N )
% 4.88/5.19 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N @ M2 ) @ N )
% 4.88/5.19 = ( gcd_gcd_nat @ M2 @ N ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % gcd_diff2_nat
% 4.88/5.19 thf(fact_9228_gcd__le1__nat,axiom,
% 4.88/5.19 ! [A: nat,B: nat] :
% 4.88/5.19 ( ( A != zero_zero_nat )
% 4.88/5.19 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 4.88/5.19
% 4.88/5.19 % gcd_le1_nat
% 4.88/5.19 thf(fact_9229_gcd__le2__nat,axiom,
% 4.88/5.19 ! [B: nat,A: nat] :
% 4.88/5.19 ( ( B != zero_zero_nat )
% 4.88/5.19 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 4.88/5.19
% 4.88/5.19 % gcd_le2_nat
% 4.88/5.19 thf(fact_9230_gcd__ge__0__int,axiom,
% 4.88/5.19 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_gcd_int @ X @ Y ) ) ).
% 4.88/5.19
% 4.88/5.19 % gcd_ge_0_int
% 4.88/5.19 thf(fact_9231_gcd__unique__int,axiom,
% 4.88/5.19 ! [D: int,A: int,B: int] :
% 4.88/5.19 ( ( ( ord_less_eq_int @ zero_zero_int @ D )
% 4.88/5.19 & ( dvd_dvd_int @ D @ A )
% 4.88/5.19 & ( dvd_dvd_int @ D @ B )
% 4.88/5.19 & ! [E3: int] :
% 4.88/5.19 ( ( ( dvd_dvd_int @ E3 @ A )
% 4.88/5.19 & ( dvd_dvd_int @ E3 @ B ) )
% 4.88/5.19 => ( dvd_dvd_int @ E3 @ D ) ) )
% 4.88/5.19 = ( D
% 4.88/5.19 = ( gcd_gcd_int @ A @ B ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % gcd_unique_int
% 4.88/5.19 thf(fact_9232_bezout__gcd__nat_H,axiom,
% 4.88/5.19 ! [B: nat,A: nat] :
% 4.88/5.19 ? [X4: nat,Y3: nat] :
% 4.88/5.19 ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y3 ) @ ( times_times_nat @ A @ X4 ) )
% 4.88/5.19 & ( ( minus_minus_nat @ ( times_times_nat @ A @ X4 ) @ ( times_times_nat @ B @ Y3 ) )
% 4.88/5.19 = ( gcd_gcd_nat @ A @ B ) ) )
% 4.88/5.19 | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y3 ) @ ( times_times_nat @ B @ X4 ) )
% 4.88/5.19 & ( ( minus_minus_nat @ ( times_times_nat @ B @ X4 ) @ ( times_times_nat @ A @ Y3 ) )
% 4.88/5.19 = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % bezout_gcd_nat'
% 4.88/5.19 thf(fact_9233_bezout__nat,axiom,
% 4.88/5.19 ! [A: nat,B: nat] :
% 4.88/5.19 ( ( A != zero_zero_nat )
% 4.88/5.19 => ? [X4: nat,Y3: nat] :
% 4.88/5.19 ( ( times_times_nat @ A @ X4 )
% 4.88/5.19 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % bezout_nat
% 4.88/5.19 thf(fact_9234_gcd__le1__int,axiom,
% 4.88/5.19 ! [A: int,B: int] :
% 4.88/5.19 ( ( ord_less_int @ zero_zero_int @ A )
% 4.88/5.19 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ A ) ) ).
% 4.88/5.19
% 4.88/5.19 % gcd_le1_int
% 4.88/5.19 thf(fact_9235_gcd__le2__int,axiom,
% 4.88/5.19 ! [B: int,A: int] :
% 4.88/5.19 ( ( ord_less_int @ zero_zero_int @ B )
% 4.88/5.19 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ B ) ) ).
% 4.88/5.19
% 4.88/5.19 % gcd_le2_int
% 4.88/5.19 thf(fact_9236_gcd__cases__int,axiom,
% 4.88/5.19 ! [X: int,Y: int,P: int > $o] :
% 4.88/5.19 ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 4.88/5.19 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.88/5.19 => ( P @ ( gcd_gcd_int @ X @ Y ) ) ) )
% 4.88/5.19 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 4.88/5.19 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 4.88/5.19 => ( P @ ( gcd_gcd_int @ X @ ( uminus_uminus_int @ Y ) ) ) ) )
% 4.88/5.19 => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 4.88/5.19 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.88/5.19 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ Y ) ) ) )
% 4.88/5.19 => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 4.88/5.19 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 4.88/5.19 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ ( uminus_uminus_int @ Y ) ) ) ) )
% 4.88/5.19 => ( P @ ( gcd_gcd_int @ X @ Y ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % gcd_cases_int
% 4.88/5.19 thf(fact_9237_Gcd__in,axiom,
% 4.88/5.19 ! [A2: set_nat] :
% 4.88/5.19 ( ! [A5: nat,B5: nat] :
% 4.88/5.19 ( ( member_nat @ A5 @ A2 )
% 4.88/5.19 => ( ( member_nat @ B5 @ A2 )
% 4.88/5.19 => ( member_nat @ ( gcd_gcd_nat @ A5 @ B5 ) @ A2 ) ) )
% 4.88/5.19 => ( ( A2 != bot_bot_set_nat )
% 4.88/5.19 => ( member_nat @ ( gcd_Gcd_nat @ A2 ) @ A2 ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Gcd_in
% 4.88/5.19 thf(fact_9238_Gcd__nat__set__eq__fold,axiom,
% 4.88/5.19 ! [Xs: list_nat] :
% 4.88/5.19 ( ( gcd_Gcd_nat @ ( set_nat2 @ Xs ) )
% 4.88/5.19 = ( fold_nat_nat @ gcd_gcd_nat @ Xs @ zero_zero_nat ) ) ).
% 4.88/5.19
% 4.88/5.19 % Gcd_nat_set_eq_fold
% 4.88/5.19 thf(fact_9239_gcd__nat_Osemilattice__neutr__order__axioms,axiom,
% 4.88/5.19 ( semila1623282765462674594er_nat @ gcd_gcd_nat @ zero_zero_nat @ dvd_dvd_nat
% 4.88/5.19 @ ^ [M3: nat,N4: nat] :
% 4.88/5.19 ( ( dvd_dvd_nat @ M3 @ N4 )
% 4.88/5.19 & ( M3 != N4 ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % gcd_nat.semilattice_neutr_order_axioms
% 4.88/5.19 thf(fact_9240_gcd__is__Max__divisors__nat,axiom,
% 4.88/5.19 ! [N: nat,M2: nat] :
% 4.88/5.19 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.19 => ( ( gcd_gcd_nat @ M2 @ N )
% 4.88/5.19 = ( lattic8265883725875713057ax_nat
% 4.88/5.19 @ ( collect_nat
% 4.88/5.19 @ ^ [D5: nat] :
% 4.88/5.19 ( ( dvd_dvd_nat @ D5 @ M2 )
% 4.88/5.19 & ( dvd_dvd_nat @ D5 @ N ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % gcd_is_Max_divisors_nat
% 4.88/5.19 thf(fact_9241_gcd__nat_Opelims,axiom,
% 4.88/5.19 ! [X: nat,Xa2: nat,Y: nat] :
% 4.88/5.19 ( ( ( gcd_gcd_nat @ X @ Xa2 )
% 4.88/5.19 = Y )
% 4.88/5.19 => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 4.88/5.19 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 4.88/5.19 => ( Y = X ) )
% 4.88/5.19 & ( ( Xa2 != zero_zero_nat )
% 4.88/5.19 => ( Y
% 4.88/5.19 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) ) )
% 4.88/5.19 => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % gcd_nat.pelims
% 4.88/5.19 thf(fact_9242_max__nat_Osemilattice__neutr__axioms,axiom,
% 4.88/5.19 semila9081495762789891438tr_nat @ ord_max_nat @ zero_zero_nat ).
% 4.88/5.19
% 4.88/5.19 % max_nat.semilattice_neutr_axioms
% 4.88/5.19 thf(fact_9243_gcd__nat_Osemilattice__neutr__axioms,axiom,
% 4.88/5.19 semila9081495762789891438tr_nat @ gcd_gcd_nat @ zero_zero_nat ).
% 4.88/5.19
% 4.88/5.19 % gcd_nat.semilattice_neutr_axioms
% 4.88/5.19 thf(fact_9244_less__eq__int__def,axiom,
% 4.88/5.19 ( ord_less_eq_int
% 4.88/5.19 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 4.88/5.19 @ ( produc8739625826339149834_nat_o
% 4.88/5.19 @ ^ [X3: nat,Y2: nat] :
% 4.88/5.19 ( produc6081775807080527818_nat_o
% 4.88/5.19 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V3 ) @ ( plus_plus_nat @ U2 @ Y2 ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % less_eq_int_def
% 4.88/5.19 thf(fact_9245_less__int__def,axiom,
% 4.88/5.19 ( ord_less_int
% 4.88/5.19 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 4.88/5.19 @ ( produc8739625826339149834_nat_o
% 4.88/5.19 @ ^ [X3: nat,Y2: nat] :
% 4.88/5.19 ( produc6081775807080527818_nat_o
% 4.88/5.19 @ ^ [U2: nat,V3: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V3 ) @ ( plus_plus_nat @ U2 @ Y2 ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % less_int_def
% 4.88/5.19 thf(fact_9246_MOST__nat,axiom,
% 4.88/5.19 ! [P: nat > $o] :
% 4.88/5.19 ( ( eventually_nat @ P @ cofinite_nat )
% 4.88/5.19 = ( ? [M3: nat] :
% 4.88/5.19 ! [N4: nat] :
% 4.88/5.19 ( ( ord_less_nat @ M3 @ N4 )
% 4.88/5.19 => ( P @ N4 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % MOST_nat
% 4.88/5.19 thf(fact_9247_MOST__ge__nat,axiom,
% 4.88/5.19 ! [M2: nat] : ( eventually_nat @ ( ord_less_eq_nat @ M2 ) @ cofinite_nat ) ).
% 4.88/5.19
% 4.88/5.19 % MOST_ge_nat
% 4.88/5.19 thf(fact_9248_MOST__nat__le,axiom,
% 4.88/5.19 ! [P: nat > $o] :
% 4.88/5.19 ( ( eventually_nat @ P @ cofinite_nat )
% 4.88/5.19 = ( ? [M3: nat] :
% 4.88/5.19 ! [N4: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ M3 @ N4 )
% 4.88/5.19 => ( P @ N4 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % MOST_nat_le
% 4.88/5.19 thf(fact_9249_MOST__Suc__iff,axiom,
% 4.88/5.19 ! [P: nat > $o] :
% 4.88/5.19 ( ( eventually_nat
% 4.88/5.19 @ ^ [N4: nat] : ( P @ ( suc @ N4 ) )
% 4.88/5.19 @ cofinite_nat )
% 4.88/5.19 = ( eventually_nat @ P @ cofinite_nat ) ) ).
% 4.88/5.19
% 4.88/5.19 % MOST_Suc_iff
% 4.88/5.19 thf(fact_9250_MOST__SucI,axiom,
% 4.88/5.19 ! [P: nat > $o] :
% 4.88/5.19 ( ( eventually_nat @ P @ cofinite_nat )
% 4.88/5.19 => ( eventually_nat
% 4.88/5.19 @ ^ [N4: nat] : ( P @ ( suc @ N4 ) )
% 4.88/5.19 @ cofinite_nat ) ) ).
% 4.88/5.19
% 4.88/5.19 % MOST_SucI
% 4.88/5.19 thf(fact_9251_MOST__SucD,axiom,
% 4.88/5.19 ! [P: nat > $o] :
% 4.88/5.19 ( ( eventually_nat
% 4.88/5.19 @ ^ [N4: nat] : ( P @ ( suc @ N4 ) )
% 4.88/5.19 @ cofinite_nat )
% 4.88/5.19 => ( eventually_nat @ P @ cofinite_nat ) ) ).
% 4.88/5.19
% 4.88/5.19 % MOST_SucD
% 4.88/5.19 thf(fact_9252_gcd__nat_Omonoid__axioms,axiom,
% 4.88/5.19 monoid_nat @ gcd_gcd_nat @ zero_zero_nat ).
% 4.88/5.19
% 4.88/5.19 % gcd_nat.monoid_axioms
% 4.88/5.19 thf(fact_9253_max__nat_Omonoid__axioms,axiom,
% 4.88/5.19 monoid_nat @ ord_max_nat @ zero_zero_nat ).
% 4.88/5.19
% 4.88/5.19 % max_nat.monoid_axioms
% 4.88/5.19 thf(fact_9254_INFM__nat,axiom,
% 4.88/5.19 ! [P: nat > $o] :
% 4.88/5.19 ( ( frequently_nat @ P @ cofinite_nat )
% 4.88/5.19 = ( ! [M3: nat] :
% 4.88/5.19 ? [N4: nat] :
% 4.88/5.19 ( ( ord_less_nat @ M3 @ N4 )
% 4.88/5.19 & ( P @ N4 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % INFM_nat
% 4.88/5.19 thf(fact_9255_INFM__nat__le,axiom,
% 4.88/5.19 ! [P: nat > $o] :
% 4.88/5.19 ( ( frequently_nat @ P @ cofinite_nat )
% 4.88/5.19 = ( ! [M3: nat] :
% 4.88/5.19 ? [N4: nat] :
% 4.88/5.19 ( ( ord_less_eq_nat @ M3 @ N4 )
% 4.88/5.19 & ( P @ N4 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % INFM_nat_le
% 4.88/5.19 thf(fact_9256_list__encode_Oelims,axiom,
% 4.88/5.19 ! [X: list_nat,Y: nat] :
% 4.88/5.19 ( ( ( nat_list_encode @ X )
% 4.88/5.19 = Y )
% 4.88/5.19 => ( ( ( X = nil_nat )
% 4.88/5.19 => ( Y != zero_zero_nat ) )
% 4.88/5.19 => ~ ! [X4: nat,Xs3: list_nat] :
% 4.88/5.19 ( ( X
% 4.88/5.19 = ( cons_nat @ X4 @ Xs3 ) )
% 4.88/5.19 => ( Y
% 4.88/5.19 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X4 @ ( nat_list_encode @ Xs3 ) ) ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % list_encode.elims
% 4.88/5.19 thf(fact_9257_le__prod__encode__1,axiom,
% 4.88/5.19 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % le_prod_encode_1
% 4.88/5.19 thf(fact_9258_le__prod__encode__2,axiom,
% 4.88/5.19 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % le_prod_encode_2
% 4.88/5.19 thf(fact_9259_list__encode_Osimps_I1_J,axiom,
% 4.88/5.19 ( ( nat_list_encode @ nil_nat )
% 4.88/5.19 = zero_zero_nat ) ).
% 4.88/5.19
% 4.88/5.19 % list_encode.simps(1)
% 4.88/5.19 thf(fact_9260_list__encode_Opelims,axiom,
% 4.88/5.19 ! [X: list_nat,Y: nat] :
% 4.88/5.19 ( ( ( nat_list_encode @ X )
% 4.88/5.19 = Y )
% 4.88/5.19 => ( ( accp_list_nat @ nat_list_encode_rel @ X )
% 4.88/5.19 => ( ( ( X = nil_nat )
% 4.88/5.19 => ( ( Y = zero_zero_nat )
% 4.88/5.19 => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 4.88/5.19 => ~ ! [X4: nat,Xs3: list_nat] :
% 4.88/5.19 ( ( X
% 4.88/5.19 = ( cons_nat @ X4 @ Xs3 ) )
% 4.88/5.19 => ( ( Y
% 4.88/5.19 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X4 @ ( nat_list_encode @ Xs3 ) ) ) ) )
% 4.88/5.19 => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X4 @ Xs3 ) ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % list_encode.pelims
% 4.88/5.19 thf(fact_9261_prod__decode__def,axiom,
% 4.88/5.19 ( nat_prod_decode
% 4.88/5.19 = ( nat_prod_decode_aux @ zero_zero_nat ) ) ).
% 4.88/5.19
% 4.88/5.19 % prod_decode_def
% 4.88/5.19 thf(fact_9262_list__decode_Opinduct,axiom,
% 4.88/5.19 ! [A0: nat,P: nat > $o] :
% 4.88/5.19 ( ( accp_nat @ nat_list_decode_rel @ A0 )
% 4.88/5.19 => ( ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 4.88/5.19 => ( P @ zero_zero_nat ) )
% 4.88/5.19 => ( ! [N2: nat] :
% 4.88/5.19 ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N2 ) )
% 4.88/5.19 => ( ! [X2: nat,Y4: nat] :
% 4.88/5.19 ( ( ( product_Pair_nat_nat @ X2 @ Y4 )
% 4.88/5.19 = ( nat_prod_decode @ N2 ) )
% 4.88/5.19 => ( P @ Y4 ) )
% 4.88/5.19 => ( P @ ( suc @ N2 ) ) ) )
% 4.88/5.19 => ( P @ A0 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % list_decode.pinduct
% 4.88/5.19 thf(fact_9263_list__decode_Oelims,axiom,
% 4.88/5.19 ! [X: nat,Y: list_nat] :
% 4.88/5.19 ( ( ( nat_list_decode @ X )
% 4.88/5.19 = Y )
% 4.88/5.19 => ( ( ( X = zero_zero_nat )
% 4.88/5.19 => ( Y != nil_nat ) )
% 4.88/5.19 => ~ ! [N2: nat] :
% 4.88/5.19 ( ( X
% 4.88/5.19 = ( suc @ N2 ) )
% 4.88/5.19 => ( Y
% 4.88/5.19 != ( produc2761476792215241774st_nat
% 4.88/5.19 @ ^ [X3: nat,Y2: nat] : ( cons_nat @ X3 @ ( nat_list_decode @ Y2 ) )
% 4.88/5.19 @ ( nat_prod_decode @ N2 ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % list_decode.elims
% 4.88/5.19 thf(fact_9264_list__decode_Opsimps_I1_J,axiom,
% 4.88/5.19 ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 4.88/5.19 => ( ( nat_list_decode @ zero_zero_nat )
% 4.88/5.19 = nil_nat ) ) ).
% 4.88/5.19
% 4.88/5.19 % list_decode.psimps(1)
% 4.88/5.19 thf(fact_9265_list__decode_Osimps_I1_J,axiom,
% 4.88/5.19 ( ( nat_list_decode @ zero_zero_nat )
% 4.88/5.19 = nil_nat ) ).
% 4.88/5.19
% 4.88/5.19 % list_decode.simps(1)
% 4.88/5.19 thf(fact_9266_list__decode_Opelims,axiom,
% 4.88/5.19 ! [X: nat,Y: list_nat] :
% 4.88/5.19 ( ( ( nat_list_decode @ X )
% 4.88/5.19 = Y )
% 4.88/5.19 => ( ( accp_nat @ nat_list_decode_rel @ X )
% 4.88/5.19 => ( ( ( X = zero_zero_nat )
% 4.88/5.19 => ( ( Y = nil_nat )
% 4.88/5.19 => ~ ( accp_nat @ nat_list_decode_rel @ zero_zero_nat ) ) )
% 4.88/5.19 => ~ ! [N2: nat] :
% 4.88/5.19 ( ( X
% 4.88/5.19 = ( suc @ N2 ) )
% 4.88/5.19 => ( ( Y
% 4.88/5.19 = ( produc2761476792215241774st_nat
% 4.88/5.19 @ ^ [X3: nat,Y2: nat] : ( cons_nat @ X3 @ ( nat_list_decode @ Y2 ) )
% 4.88/5.19 @ ( nat_prod_decode @ N2 ) ) )
% 4.88/5.19 => ~ ( accp_nat @ nat_list_decode_rel @ ( suc @ N2 ) ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % list_decode.pelims
% 4.88/5.19 thf(fact_9267_integer__of__nat__1,axiom,
% 4.88/5.19 ( ( code_integer_of_nat @ one_one_nat )
% 4.88/5.19 = one_one_Code_integer ) ).
% 4.88/5.19
% 4.88/5.19 % integer_of_nat_1
% 4.88/5.19 thf(fact_9268_gcd__nat_Ocomm__monoid__axioms,axiom,
% 4.88/5.19 comm_monoid_nat @ gcd_gcd_nat @ zero_zero_nat ).
% 4.88/5.19
% 4.88/5.19 % gcd_nat.comm_monoid_axioms
% 4.88/5.19 thf(fact_9269_max__nat_Ocomm__monoid__axioms,axiom,
% 4.88/5.19 comm_monoid_nat @ ord_max_nat @ zero_zero_nat ).
% 4.88/5.19
% 4.88/5.19 % max_nat.comm_monoid_axioms
% 4.88/5.19 thf(fact_9270_integer__of__nat__0,axiom,
% 4.88/5.19 ( ( code_integer_of_nat @ zero_zero_nat )
% 4.88/5.19 = zero_z3403309356797280102nteger ) ).
% 4.88/5.19
% 4.88/5.19 % integer_of_nat_0
% 4.88/5.19 thf(fact_9271_times__num__def,axiom,
% 4.88/5.19 ( times_times_num
% 4.88/5.19 = ( ^ [M3: num,N4: num] : ( num_of_nat @ ( times_times_nat @ ( nat_of_num @ M3 ) @ ( nat_of_num @ N4 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % times_num_def
% 4.88/5.19 thf(fact_9272_nat__of__num__neq__0,axiom,
% 4.88/5.19 ! [X: num] :
% 4.88/5.19 ( ( nat_of_num @ X )
% 4.88/5.19 != zero_zero_nat ) ).
% 4.88/5.19
% 4.88/5.19 % nat_of_num_neq_0
% 4.88/5.19 thf(fact_9273_nat__of__num__code_I2_J,axiom,
% 4.88/5.19 ! [N: num] :
% 4.88/5.19 ( ( nat_of_num @ ( bit0 @ N ) )
% 4.88/5.19 = ( plus_plus_nat @ ( nat_of_num @ N ) @ ( nat_of_num @ N ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % nat_of_num_code(2)
% 4.88/5.19 thf(fact_9274_nat__of__num__inc,axiom,
% 4.88/5.19 ! [X: num] :
% 4.88/5.19 ( ( nat_of_num @ ( inc @ X ) )
% 4.88/5.19 = ( suc @ ( nat_of_num @ X ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % nat_of_num_inc
% 4.88/5.19 thf(fact_9275_num__eq__iff,axiom,
% 4.88/5.19 ( ( ^ [Y5: num,Z4: num] : ( Y5 = Z4 ) )
% 4.88/5.19 = ( ^ [X3: num,Y2: num] :
% 4.88/5.19 ( ( nat_of_num @ X3 )
% 4.88/5.19 = ( nat_of_num @ Y2 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % num_eq_iff
% 4.88/5.19 thf(fact_9276_nat__of__num__numeral,axiom,
% 4.88/5.19 nat_of_num = numeral_numeral_nat ).
% 4.88/5.19
% 4.88/5.19 % nat_of_num_numeral
% 4.88/5.19 thf(fact_9277_nat__of__num__inverse,axiom,
% 4.88/5.19 ! [X: num] :
% 4.88/5.19 ( ( num_of_nat @ ( nat_of_num @ X ) )
% 4.88/5.19 = X ) ).
% 4.88/5.19
% 4.88/5.19 % nat_of_num_inverse
% 4.88/5.19 thf(fact_9278_nat__of__num_Osimps_I2_J,axiom,
% 4.88/5.19 ! [X: num] :
% 4.88/5.19 ( ( nat_of_num @ ( bit0 @ X ) )
% 4.88/5.19 = ( plus_plus_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ X ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % nat_of_num.simps(2)
% 4.88/5.19 thf(fact_9279_nat__of__num__add,axiom,
% 4.88/5.19 ! [X: num,Y: num] :
% 4.88/5.19 ( ( nat_of_num @ ( plus_plus_num @ X @ Y ) )
% 4.88/5.19 = ( plus_plus_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ Y ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % nat_of_num_add
% 4.88/5.19 thf(fact_9280_nat__of__num__code_I1_J,axiom,
% 4.88/5.19 ( ( nat_of_num @ one )
% 4.88/5.19 = one_one_nat ) ).
% 4.88/5.19
% 4.88/5.19 % nat_of_num_code(1)
% 4.88/5.19 thf(fact_9281_less__eq__num__def,axiom,
% 4.88/5.19 ( ord_less_eq_num
% 4.88/5.19 = ( ^ [M3: num,N4: num] : ( ord_less_eq_nat @ ( nat_of_num @ M3 ) @ ( nat_of_num @ N4 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % less_eq_num_def
% 4.88/5.19 thf(fact_9282_nat__of__num__mult,axiom,
% 4.88/5.19 ! [X: num,Y: num] :
% 4.88/5.19 ( ( nat_of_num @ ( times_times_num @ X @ Y ) )
% 4.88/5.19 = ( times_times_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ Y ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % nat_of_num_mult
% 4.88/5.19 thf(fact_9283_nat__of__num__sqr,axiom,
% 4.88/5.19 ! [X: num] :
% 4.88/5.19 ( ( nat_of_num @ ( sqr @ X ) )
% 4.88/5.19 = ( times_times_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ X ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % nat_of_num_sqr
% 4.88/5.19 thf(fact_9284_nat__of__num__pos,axiom,
% 4.88/5.19 ! [X: num] : ( ord_less_nat @ zero_zero_nat @ ( nat_of_num @ X ) ) ).
% 4.88/5.19
% 4.88/5.19 % nat_of_num_pos
% 4.88/5.19 thf(fact_9285_less__num__def,axiom,
% 4.88/5.19 ( ord_less_num
% 4.88/5.19 = ( ^ [M3: num,N4: num] : ( ord_less_nat @ ( nat_of_num @ M3 ) @ ( nat_of_num @ N4 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % less_num_def
% 4.88/5.19 thf(fact_9286_nat__of__num_Osimps_I1_J,axiom,
% 4.88/5.19 ( ( nat_of_num @ one )
% 4.88/5.19 = ( suc @ zero_zero_nat ) ) ).
% 4.88/5.19
% 4.88/5.19 % nat_of_num.simps(1)
% 4.88/5.19 thf(fact_9287_nat__of__num_Osimps_I3_J,axiom,
% 4.88/5.19 ! [X: num] :
% 4.88/5.19 ( ( nat_of_num @ ( bit1 @ X ) )
% 4.88/5.19 = ( suc @ ( plus_plus_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ X ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % nat_of_num.simps(3)
% 4.88/5.19 thf(fact_9288_num__of__nat__inverse,axiom,
% 4.88/5.19 ! [N: nat] :
% 4.88/5.19 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.88/5.19 => ( ( nat_of_num @ ( num_of_nat @ N ) )
% 4.88/5.19 = N ) ) ).
% 4.88/5.19
% 4.88/5.19 % num_of_nat_inverse
% 4.88/5.19 thf(fact_9289_nat__of__num__code_I3_J,axiom,
% 4.88/5.19 ! [N: num] :
% 4.88/5.19 ( ( nat_of_num @ ( bit1 @ N ) )
% 4.88/5.19 = ( suc @ ( plus_plus_nat @ ( nat_of_num @ N ) @ ( nat_of_num @ N ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % nat_of_num_code(3)
% 4.88/5.19 thf(fact_9290_plus__num__def,axiom,
% 4.88/5.19 ( plus_plus_num
% 4.88/5.19 = ( ^ [M3: num,N4: num] : ( num_of_nat @ ( plus_plus_nat @ ( nat_of_num @ M3 ) @ ( nat_of_num @ N4 ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % plus_num_def
% 4.88/5.19 thf(fact_9291_pcr__real__def,axiom,
% 4.88/5.19 ( pcr_real
% 4.88/5.19 = ( relcom2856161143838007533t_real
% 4.88/5.19 @ ( bNF_re4702136315717946289at_rat
% 4.88/5.19 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 4.88/5.19 @ ^ [Y5: rat,Z4: rat] : ( Y5 = Z4 ) )
% 4.88/5.19 @ cr_real ) ) ).
% 4.88/5.19
% 4.88/5.19 % pcr_real_def
% 4.88/5.19 thf(fact_9292_real_Odomain,axiom,
% 4.88/5.19 ( ( domainp_nat_rat_real @ pcr_real )
% 4.88/5.19 = ( ^ [X3: nat > rat] :
% 4.88/5.19 ? [Y2: nat > rat] :
% 4.88/5.19 ( ( bNF_re4702136315717946289at_rat
% 4.88/5.19 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 4.88/5.19 @ ^ [Y5: rat,Z4: rat] : ( Y5 = Z4 )
% 4.88/5.19 @ X3
% 4.88/5.19 @ Y2 )
% 4.88/5.19 & ( realrel @ Y2 @ Y2 ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % real.domain
% 4.88/5.19 thf(fact_9293_Domainp__pcr__real,axiom,
% 4.88/5.19 ( ( domainp_nat_rat_real @ pcr_real )
% 4.88/5.19 = cauchy ) ).
% 4.88/5.19
% 4.88/5.19 % Domainp_pcr_real
% 4.88/5.19 thf(fact_9294_real_Odomain__eq,axiom,
% 4.88/5.19 ( ( domainp_nat_rat_real @ pcr_real )
% 4.88/5.19 = ( ^ [X3: nat > rat] : ( realrel @ X3 @ X3 ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % real.domain_eq
% 4.88/5.19 thf(fact_9295_real_Odomain__par__left__total,axiom,
% 4.88/5.19 ! [P4: ( nat > rat ) > $o] :
% 4.88/5.19 ( ( left_t2768085380646472630at_rat
% 4.88/5.19 @ ( bNF_re4702136315717946289at_rat
% 4.88/5.19 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 4.88/5.19 @ ^ [Y5: rat,Z4: rat] : ( Y5 = Z4 ) ) )
% 4.88/5.19 => ( ( bNF_re728719798268516973at_o_o
% 4.88/5.19 @ ( bNF_re4702136315717946289at_rat
% 4.88/5.19 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 4.88/5.19 @ ^ [Y5: rat,Z4: rat] : ( Y5 = Z4 ) )
% 4.88/5.19 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 )
% 4.88/5.19 @ P4
% 4.88/5.19 @ ^ [X3: nat > rat] : ( realrel @ X3 @ X3 ) )
% 4.88/5.19 => ( ( domainp_nat_rat_real @ pcr_real )
% 4.88/5.19 = P4 ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % real.domain_par_left_total
% 4.88/5.19 thf(fact_9296_Rep__real,axiom,
% 4.88/5.19 ! [X: real] :
% 4.88/5.19 ( member_set_nat_rat @ ( rep_real @ X )
% 4.88/5.19 @ ( collect_set_nat_rat
% 4.88/5.19 @ ^ [C5: set_nat_rat] :
% 4.88/5.19 ? [X3: nat > rat] :
% 4.88/5.19 ( ( realrel @ X3 @ X3 )
% 4.88/5.19 & ( C5
% 4.88/5.19 = ( collect_nat_rat @ ( realrel @ X3 ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Rep_real
% 4.88/5.19 thf(fact_9297_Rep__real__cases,axiom,
% 4.88/5.19 ! [Y: set_nat_rat] :
% 4.88/5.19 ( ( member_set_nat_rat @ Y
% 4.88/5.19 @ ( collect_set_nat_rat
% 4.88/5.19 @ ^ [C5: set_nat_rat] :
% 4.88/5.19 ? [X3: nat > rat] :
% 4.88/5.19 ( ( realrel @ X3 @ X3 )
% 4.88/5.19 & ( C5
% 4.88/5.19 = ( collect_nat_rat @ ( realrel @ X3 ) ) ) ) ) )
% 4.88/5.19 => ~ ! [X4: real] :
% 4.88/5.19 ( Y
% 4.88/5.19 != ( rep_real @ X4 ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Rep_real_cases
% 4.88/5.19 thf(fact_9298_Rep__real__inject,axiom,
% 4.88/5.19 ! [X: real,Y: real] :
% 4.88/5.19 ( ( ( rep_real @ X )
% 4.88/5.19 = ( rep_real @ Y ) )
% 4.88/5.19 = ( X = Y ) ) ).
% 4.88/5.19
% 4.88/5.19 % Rep_real_inject
% 4.88/5.19 thf(fact_9299_Rep__real__induct,axiom,
% 4.88/5.19 ! [Y: set_nat_rat,P: set_nat_rat > $o] :
% 4.88/5.19 ( ( member_set_nat_rat @ Y
% 4.88/5.19 @ ( collect_set_nat_rat
% 4.88/5.19 @ ^ [C5: set_nat_rat] :
% 4.88/5.19 ? [X3: nat > rat] :
% 4.88/5.19 ( ( realrel @ X3 @ X3 )
% 4.88/5.19 & ( C5
% 4.88/5.19 = ( collect_nat_rat @ ( realrel @ X3 ) ) ) ) ) )
% 4.88/5.19 => ( ! [X4: real] : ( P @ ( rep_real @ X4 ) )
% 4.88/5.19 => ( P @ Y ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Rep_real_induct
% 4.88/5.19 thf(fact_9300_Abs__real__inverse,axiom,
% 4.88/5.19 ! [Y: set_nat_rat] :
% 4.88/5.19 ( ( member_set_nat_rat @ Y
% 4.88/5.19 @ ( collect_set_nat_rat
% 4.88/5.19 @ ^ [C5: set_nat_rat] :
% 4.88/5.19 ? [X3: nat > rat] :
% 4.88/5.19 ( ( realrel @ X3 @ X3 )
% 4.88/5.19 & ( C5
% 4.88/5.19 = ( collect_nat_rat @ ( realrel @ X3 ) ) ) ) ) )
% 4.88/5.19 => ( ( rep_real @ ( abs_real @ Y ) )
% 4.88/5.19 = Y ) ) ).
% 4.88/5.19
% 4.88/5.19 % Abs_real_inverse
% 4.88/5.19 thf(fact_9301_rep__real__def,axiom,
% 4.88/5.19 ( rep_real2
% 4.88/5.19 = ( quot_r1730120044975580712at_rat @ rep_real ) ) ).
% 4.88/5.19
% 4.88/5.19 % rep_real_def
% 4.88/5.19 thf(fact_9302_Rep__real__inverse,axiom,
% 4.88/5.19 ! [X: real] :
% 4.88/5.19 ( ( abs_real @ ( rep_real @ X ) )
% 4.88/5.19 = X ) ).
% 4.88/5.19
% 4.88/5.19 % Rep_real_inverse
% 4.88/5.19 thf(fact_9303_Abs__real__cases,axiom,
% 4.88/5.19 ! [X: real] :
% 4.88/5.19 ~ ! [Y3: set_nat_rat] :
% 4.88/5.19 ( ( X
% 4.88/5.19 = ( abs_real @ Y3 ) )
% 4.88/5.19 => ~ ( member_set_nat_rat @ Y3
% 4.88/5.19 @ ( collect_set_nat_rat
% 4.88/5.19 @ ^ [C5: set_nat_rat] :
% 4.88/5.19 ? [X3: nat > rat] :
% 4.88/5.19 ( ( realrel @ X3 @ X3 )
% 4.88/5.19 & ( C5
% 4.88/5.19 = ( collect_nat_rat @ ( realrel @ X3 ) ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Abs_real_cases
% 4.88/5.19 thf(fact_9304_Abs__real__induct,axiom,
% 4.88/5.19 ! [P: real > $o,X: real] :
% 4.88/5.19 ( ! [Y3: set_nat_rat] :
% 4.88/5.19 ( ( member_set_nat_rat @ Y3
% 4.88/5.19 @ ( collect_set_nat_rat
% 4.88/5.19 @ ^ [C5: set_nat_rat] :
% 4.88/5.19 ? [X3: nat > rat] :
% 4.88/5.19 ( ( realrel @ X3 @ X3 )
% 4.88/5.19 & ( C5
% 4.88/5.19 = ( collect_nat_rat @ ( realrel @ X3 ) ) ) ) ) )
% 4.88/5.19 => ( P @ ( abs_real @ Y3 ) ) )
% 4.88/5.19 => ( P @ X ) ) ).
% 4.88/5.19
% 4.88/5.19 % Abs_real_induct
% 4.88/5.19 thf(fact_9305_Abs__real__inject,axiom,
% 4.88/5.19 ! [X: set_nat_rat,Y: set_nat_rat] :
% 4.88/5.19 ( ( member_set_nat_rat @ X
% 4.88/5.19 @ ( collect_set_nat_rat
% 4.88/5.19 @ ^ [C5: set_nat_rat] :
% 4.88/5.19 ? [X3: nat > rat] :
% 4.88/5.19 ( ( realrel @ X3 @ X3 )
% 4.88/5.19 & ( C5
% 4.88/5.19 = ( collect_nat_rat @ ( realrel @ X3 ) ) ) ) ) )
% 4.88/5.19 => ( ( member_set_nat_rat @ Y
% 4.88/5.19 @ ( collect_set_nat_rat
% 4.88/5.19 @ ^ [C5: set_nat_rat] :
% 4.88/5.19 ? [X3: nat > rat] :
% 4.88/5.19 ( ( realrel @ X3 @ X3 )
% 4.88/5.19 & ( C5
% 4.88/5.19 = ( collect_nat_rat @ ( realrel @ X3 ) ) ) ) ) )
% 4.88/5.19 => ( ( ( abs_real @ X )
% 4.88/5.19 = ( abs_real @ Y ) )
% 4.88/5.19 = ( X = Y ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % Abs_real_inject
% 4.88/5.19 thf(fact_9306_Real__def,axiom,
% 4.88/5.19 ( real2
% 4.88/5.19 = ( quot_a3129823074075660125t_real @ realrel @ abs_real ) ) ).
% 4.88/5.19
% 4.88/5.19 % Real_def
% 4.88/5.19 thf(fact_9307_type__definition__real,axiom,
% 4.88/5.19 ( type_d8072115097938612567at_rat @ rep_real @ abs_real
% 4.88/5.19 @ ( collect_set_nat_rat
% 4.88/5.19 @ ^ [C5: set_nat_rat] :
% 4.88/5.19 ? [X3: nat > rat] :
% 4.88/5.19 ( ( realrel @ X3 @ X3 )
% 4.88/5.19 & ( C5
% 4.88/5.19 = ( collect_nat_rat @ ( realrel @ X3 ) ) ) ) ) ) ).
% 4.88/5.19
% 4.88/5.19 % type_definition_real
% 4.88/5.19
% 4.88/5.19 % Helper facts (38)
% 4.88/5.19 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 4.88/5.19 ! [X: int,Y: int] :
% 4.88/5.19 ( ( if_int @ $false @ X @ Y )
% 4.88/5.19 = Y ) ).
% 4.88/5.19
% 4.88/5.19 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 4.88/5.19 ! [X: int,Y: int] :
% 4.88/5.19 ( ( if_int @ $true @ X @ Y )
% 4.88/5.19 = X ) ).
% 4.88/5.19
% 4.88/5.19 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 4.88/5.19 ! [X: nat,Y: nat] :
% 4.88/5.19 ( ( if_nat @ $false @ X @ Y )
% 4.88/5.19 = Y ) ).
% 4.88/5.19
% 4.88/5.19 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 4.88/5.19 ! [X: nat,Y: nat] :
% 4.88/5.19 ( ( if_nat @ $true @ X @ Y )
% 4.88/5.19 = X ) ).
% 4.88/5.19
% 4.88/5.19 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 4.88/5.19 ! [X: num,Y: num] :
% 4.88/5.19 ( ( if_num @ $false @ X @ Y )
% 4.88/5.19 = Y ) ).
% 4.88/5.19
% 4.88/5.19 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 4.88/5.19 ! [X: num,Y: num] :
% 4.88/5.19 ( ( if_num @ $true @ X @ Y )
% 4.88/5.19 = X ) ).
% 4.88/5.19
% 4.88/5.19 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 4.88/5.19 ! [X: rat,Y: rat] :
% 4.88/5.19 ( ( if_rat @ $false @ X @ Y )
% 4.88/5.19 = Y ) ).
% 4.88/5.19
% 4.88/5.19 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 4.88/5.19 ! [X: rat,Y: rat] :
% 4.88/5.19 ( ( if_rat @ $true @ X @ Y )
% 4.88/5.19 = X ) ).
% 4.88/5.19
% 4.88/5.19 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 4.88/5.19 ! [X: real,Y: real] :
% 4.88/5.19 ( ( if_real @ $false @ X @ Y )
% 4.88/5.19 = Y ) ).
% 4.88/5.19
% 4.88/5.19 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 4.88/5.19 ! [X: real,Y: real] :
% 4.88/5.19 ( ( if_real @ $true @ X @ Y )
% 4.88/5.19 = X ) ).
% 4.88/5.19
% 4.88/5.19 thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 4.88/5.19 ! [P: real > $o] :
% 4.88/5.19 ( ( P @ ( fChoice_real @ P ) )
% 4.88/5.19 = ( ? [X8: real] : ( P @ X8 ) ) ) ).
% 4.88/5.19
% 4.88/5.19 thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 4.88/5.19 ! [X: complex,Y: complex] :
% 4.88/5.19 ( ( if_complex @ $false @ X @ Y )
% 4.88/5.19 = Y ) ).
% 4.88/5.19
% 4.88/5.19 thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 4.88/5.19 ! [X: complex,Y: complex] :
% 4.88/5.19 ( ( if_complex @ $true @ X @ Y )
% 4.88/5.19 = X ) ).
% 4.88/5.19
% 4.88/5.19 thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 4.88/5.19 ! [X: extended_enat,Y: extended_enat] :
% 4.88/5.19 ( ( if_Extended_enat @ $false @ X @ Y )
% 4.88/5.19 = Y ) ).
% 4.88/5.19
% 4.88/5.19 thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 4.88/5.19 ! [X: extended_enat,Y: extended_enat] :
% 4.88/5.19 ( ( if_Extended_enat @ $true @ X @ Y )
% 4.88/5.19 = X ) ).
% 4.88/5.19
% 4.88/5.19 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 4.88/5.19 ! [X: code_integer,Y: code_integer] :
% 4.88/5.19 ( ( if_Code_integer @ $false @ X @ Y )
% 4.88/5.19 = Y ) ).
% 4.88/5.19
% 4.88/5.19 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 4.88/5.19 ! [X: code_integer,Y: code_integer] :
% 4.88/5.19 ( ( if_Code_integer @ $true @ X @ Y )
% 4.88/5.19 = X ) ).
% 4.88/5.19
% 4.88/5.19 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 4.88/5.19 ! [X: set_int,Y: set_int] :
% 4.88/5.19 ( ( if_set_int @ $false @ X @ Y )
% 4.88/5.19 = Y ) ).
% 4.88/5.19
% 4.88/5.19 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 4.88/5.19 ! [X: set_int,Y: set_int] :
% 5.91/6.25 ( ( if_set_int @ $true @ X @ Y )
% 5.91/6.25 = X ) ).
% 5.91/6.25
% 5.91/6.25 thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.91/6.25 ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 5.91/6.25 ( ( if_VEBT_VEBT @ $false @ X @ Y )
% 5.91/6.25 = Y ) ).
% 5.91/6.25
% 5.91/6.25 thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.91/6.25 ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 5.91/6.25 ( ( if_VEBT_VEBT @ $true @ X @ Y )
% 5.91/6.25 = X ) ).
% 5.91/6.25
% 5.91/6.25 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.91/6.25 ! [X: list_int,Y: list_int] :
% 5.91/6.25 ( ( if_list_int @ $false @ X @ Y )
% 5.91/6.25 = Y ) ).
% 5.91/6.25
% 5.91/6.25 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.91/6.25 ! [X: list_int,Y: list_int] :
% 5.91/6.25 ( ( if_list_int @ $true @ X @ Y )
% 5.91/6.25 = X ) ).
% 5.91/6.25
% 5.91/6.25 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.91/6.25 ! [X: list_nat,Y: list_nat] :
% 5.91/6.25 ( ( if_list_nat @ $false @ X @ Y )
% 5.91/6.25 = Y ) ).
% 5.91/6.25
% 5.91/6.25 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.91/6.25 ! [X: list_nat,Y: list_nat] :
% 5.91/6.25 ( ( if_list_nat @ $true @ X @ Y )
% 5.91/6.25 = X ) ).
% 5.91/6.25
% 5.91/6.25 thf(help_If_2_1_If_001_062_It__Nat__Onat_Mt__Rat__Orat_J_T,axiom,
% 5.91/6.25 ! [X: nat > rat,Y: nat > rat] :
% 5.91/6.25 ( ( if_nat_rat @ $false @ X @ Y )
% 5.91/6.25 = Y ) ).
% 5.91/6.25
% 5.91/6.25 thf(help_If_1_1_If_001_062_It__Nat__Onat_Mt__Rat__Orat_J_T,axiom,
% 5.91/6.25 ! [X: nat > rat,Y: nat > rat] :
% 5.91/6.25 ( ( if_nat_rat @ $true @ X @ Y )
% 5.91/6.25 = X ) ).
% 5.91/6.25
% 5.91/6.25 thf(help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 5.91/6.25 ! [X: option_nat,Y: option_nat] :
% 5.91/6.25 ( ( if_option_nat @ $false @ X @ Y )
% 5.91/6.25 = Y ) ).
% 5.91/6.25
% 5.91/6.25 thf(help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 5.91/6.25 ! [X: option_nat,Y: option_nat] :
% 5.91/6.25 ( ( if_option_nat @ $true @ X @ Y )
% 5.91/6.25 = X ) ).
% 5.91/6.25
% 5.91/6.25 thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.91/6.25 ! [X: option_num,Y: option_num] :
% 5.91/6.25 ( ( if_option_num @ $false @ X @ Y )
% 5.91/6.25 = Y ) ).
% 5.91/6.25
% 5.91/6.25 thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.91/6.25 ! [X: option_num,Y: option_num] :
% 5.91/6.25 ( ( if_option_num @ $true @ X @ Y )
% 5.91/6.25 = X ) ).
% 5.91/6.25
% 5.91/6.25 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.91/6.25 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 5.91/6.25 ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y )
% 5.91/6.25 = Y ) ).
% 5.91/6.25
% 5.91/6.25 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.91/6.25 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 5.91/6.25 ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y )
% 5.91/6.25 = X ) ).
% 5.91/6.25
% 5.91/6.25 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.91/6.25 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 5.91/6.25 ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y )
% 5.91/6.25 = Y ) ).
% 5.91/6.25
% 5.91/6.25 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.91/6.25 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 5.91/6.25 ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y )
% 5.91/6.25 = X ) ).
% 5.91/6.25
% 5.91/6.25 thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.91/6.25 ! [P: $o] :
% 5.91/6.25 ( ( P = $true )
% 5.91/6.25 | ( P = $false ) ) ).
% 5.91/6.25
% 5.91/6.25 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.91/6.25 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 5.91/6.25 ( ( if_Pro6119634080678213985nteger @ $false @ X @ Y )
% 5.91/6.25 = Y ) ).
% 5.91/6.25
% 5.91/6.25 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.91/6.25 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 5.91/6.25 ( ( if_Pro6119634080678213985nteger @ $true @ X @ Y )
% 5.91/6.25 = X ) ).
% 5.91/6.25
% 5.91/6.25 % Conjectures (2)
% 5.91/6.25 thf(conj_0,hypothesis,
% 5.91/6.25 vEBT_invar_vebt @ t @ n ).
% 5.91/6.25
% 5.91/6.25 thf(conj_1,conjecture,
% 5.91/6.25 vEBT_invar_vebt @ ( vEBT_vebt_delete @ t @ x ) @ n ).
% 5.91/6.25
% 5.91/6.25 %------------------------------------------------------------------------------
% 5.91/6.25 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.y7A7xmTbRd/cvc5---1.0.5_24675.p...
% 5.91/6.25 (declare-sort $$unsorted 0)
% 5.91/6.25 (declare-sort tptp.set_Pr7459493094073627847at_nat 0)
% 5.91/6.25 (declare-sort tptp.produc1319942482725812455at_nat 0)
% 5.91/6.25 (declare-sort tptp.set_Pr4329608150637261639at_nat 0)
% 5.91/6.25 (declare-sort tptp.produc4471711990508489141at_nat 0)
% 5.91/6.25 (declare-sort tptp.produc3843707927480180839at_nat 0)
% 5.91/6.25 (declare-sort tptp.list_P8469869581646625389at_nat 0)
% 5.91/6.25 (declare-sort tptp.set_Pr8693737435421807431at_nat 0)
% 5.91/6.25 (declare-sort tptp.produc859450856879609959at_nat 0)
% 5.91/6.25 (declare-sort tptp.list_P7413028617227757229T_VEBT 0)
% 5.91/6.25 (declare-sort tptp.produc7248412053542808358at_nat 0)
% 5.91/6.25 (declare-sort tptp.list_P7037539587688870467BT_nat 0)
% 5.91/6.25 (declare-sort tptp.list_P4547456442757143711BT_int 0)
% 5.91/6.25 (declare-sort tptp.list_P5647936690300460905T_VEBT 0)
% 5.91/6.25 (declare-sort tptp.list_P7524865323317820941T_VEBT 0)
% 5.91/6.25 (declare-sort tptp.set_li5450038453877631591at_nat 0)
% 5.91/6.25 (declare-sort tptp.produc8243902056947475879T_VEBT 0)
% 5.91/6.25 (declare-sort tptp.set_se7855581050983116737at_nat 0)
% 5.91/6.25 (declare-sort tptp.produc8923325533196201883nteger 0)
% 5.91/6.25 (declare-sort tptp.produc7272778201969148633d_enat 0)
% 5.91/6.25 (declare-sort tptp.option4927543243414619207at_nat 0)
% 5.91/6.25 (declare-sort tptp.filter1242075044329608583at_nat 0)
% 5.91/6.25 (declare-sort tptp.list_P6011104703257516679at_nat 0)
% 5.91/6.25 (declare-sort tptp.list_P3521021558325789923at_int 0)
% 5.91/6.25 (declare-sort tptp.list_P8198026277950538467nt_nat 0)
% 5.91/6.25 (declare-sort tptp.list_P5707943133018811711nt_int 0)
% 5.91/6.25 (declare-sort tptp.produc9072475918466114483BT_nat 0)
% 5.91/6.25 (declare-sort tptp.produc4894624898956917775BT_int 0)
% 5.91/6.25 (declare-sort tptp.produc8025551001238799321T_VEBT 0)
% 5.91/6.25 (declare-sort tptp.produc1531783533982839933T_VEBT 0)
% 5.91/6.25 (declare-sort tptp.set_Pr1261947904930325089at_nat 0)
% 5.91/6.25 (declare-sort tptp.set_Pr958786334691620121nt_int 0)
% 5.91/6.25 (declare-sort tptp.list_set_nat_rat 0)
% 5.91/6.25 (declare-sort tptp.set_set_nat_rat 0)
% 5.91/6.25 (declare-sort tptp.list_list_VEBT_VEBT 0)
% 5.91/6.25 (declare-sort tptp.set_list_list_nat 0)
% 5.91/6.25 (declare-sort tptp.set_list_VEBT_VEBT 0)
% 5.91/6.25 (declare-sort tptp.set_set_list_nat 0)
% 5.91/6.25 (declare-sort tptp.set_list_set_nat 0)
% 5.91/6.25 (declare-sort tptp.set_set_set_nat 0)
% 5.91/6.25 (declare-sort tptp.set_li5464603477888414924d_enat 0)
% 5.91/6.25 (declare-sort tptp.set_se7270636423289371942d_enat 0)
% 5.91/6.25 (declare-sort tptp.product_prod_nat_nat 0)
% 5.91/6.25 (declare-sort tptp.product_prod_nat_int 0)
% 5.91/6.25 (declare-sort tptp.product_prod_int_nat 0)
% 5.91/6.25 (declare-sort tptp.product_prod_int_int 0)
% 5.91/6.25 (declare-sort tptp.set_list_complex 0)
% 5.91/6.25 (declare-sort tptp.set_set_complex 0)
% 5.91/6.25 (declare-sort tptp.option_VEBT_VEBT 0)
% 5.91/6.25 (declare-sort tptp.set_nat_rat 0)
% 5.91/6.25 (declare-sort tptp.list_list_nat 0)
% 5.91/6.25 (declare-sort tptp.list_VEBT_VEBT 0)
% 5.91/6.25 (declare-sort tptp.set_list_nat 0)
% 5.91/6.25 (declare-sort tptp.set_list_int 0)
% 5.91/6.25 (declare-sort tptp.list_set_nat 0)
% 5.91/6.25 (declare-sort tptp.set_VEBT_VEBT 0)
% 5.91/6.25 (declare-sort tptp.set_set_nat 0)
% 5.91/6.25 (declare-sort tptp.set_set_int 0)
% 5.91/6.25 (declare-sort tptp.list_Extended_enat 0)
% 5.91/6.25 (declare-sort tptp.set_Product_unit 0)
% 5.91/6.25 (declare-sort tptp.set_Extended_enat 0)
% 5.91/6.25 (declare-sort tptp.list_complex 0)
% 5.91/6.25 (declare-sort tptp.set_complex 0)
% 5.91/6.25 (declare-sort tptp.filter_real 0)
% 5.91/6.25 (declare-sort tptp.option_num 0)
% 5.91/6.25 (declare-sort tptp.option_nat 0)
% 5.91/6.25 (declare-sort tptp.option_int 0)
% 5.91/6.25 (declare-sort tptp.filter_nat 0)
% 5.91/6.25 (declare-sort tptp.set_char 0)
% 5.91/6.25 (declare-sort tptp.list_real 0)
% 5.91/6.25 (declare-sort tptp.set_real 0)
% 5.91/6.25 (declare-sort tptp.list_num 0)
% 5.91/6.25 (declare-sort tptp.list_nat 0)
% 5.91/6.25 (declare-sort tptp.list_int 0)
% 5.91/6.25 (declare-sort tptp.vEBT_VEBT 0)
% 5.91/6.25 (declare-sort tptp.set_rat 0)
% 5.91/6.25 (declare-sort tptp.set_num 0)
% 5.91/6.25 (declare-sort tptp.set_nat 0)
% 5.91/6.25 (declare-sort tptp.set_int 0)
% 5.91/6.25 (declare-sort tptp.code_integer 0)
% 5.91/6.25 (declare-sort tptp.product_unit 0)
% 5.91/6.25 (declare-sort tptp.extended_enat 0)
% 5.91/6.25 (declare-sort tptp.list_o 0)
% 5.91/6.25 (declare-sort tptp.complex 0)
% 5.91/6.25 (declare-sort tptp.literal 0)
% 5.91/6.25 (declare-sort tptp.set_o 0)
% 5.91/6.25 (declare-sort tptp.char 0)
% 5.91/6.25 (declare-sort tptp.real 0)
% 5.91/6.25 (declare-sort tptp.rat 0)
% 5.91/6.25 (declare-sort tptp.num 0)
% 5.91/6.25 (declare-sort tptp.nat 0)
% 5.91/6.25 (declare-sort tptp.int 0)
% 5.91/6.25 (declare-fun tptp.archim2889992004027027881ng_rat (tptp.rat) tptp.int)
% 5.91/6.25 (declare-fun tptp.archim7802044766580827645g_real (tptp.real) tptp.int)
% 5.91/6.25 (declare-fun tptp.archim3151403230148437115or_rat (tptp.rat) tptp.int)
% 5.91/6.25 (declare-fun tptp.archim6058952711729229775r_real (tptp.real) tptp.int)
% 5.91/6.25 (declare-fun tptp.archimedean_frac_rat (tptp.rat) tptp.rat)
% 5.91/6.25 (declare-fun tptp.archim2898591450579166408c_real (tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.archim7778729529865785530nd_rat (tptp.rat) tptp.int)
% 5.91/6.25 (declare-fun tptp.archim8280529875227126926d_real (tptp.real) tptp.int)
% 5.91/6.25 (declare-fun tptp.bNF_Ca8665028551170535155natLeq () tptp.set_Pr1261947904930325089at_nat)
% 5.91/6.25 (declare-fun tptp.bNF_Ca8459412986667044542atLess () tptp.set_Pr1261947904930325089at_nat)
% 5.91/6.25 (declare-fun tptp.bNF_re1962705104956426057at_rat ((-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) Bool) (-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) tptp.nat tptp.rat) (-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) tptp.nat tptp.rat)) Bool)
% 5.91/6.25 (declare-fun tptp.bNF_re895249473297799549at_rat ((-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat)) Bool)
% 5.91/6.25 (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)
% 5.91/6.25 (declare-fun tptp.bNF_re4695409256820837752l_real ((-> (-> tptp.nat tptp.rat) tptp.real Bool) (-> (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) (-> tptp.real tptp.real) Bool) (-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) tptp.nat tptp.rat) (-> tptp.real tptp.real tptp.real)) Bool)
% 5.91/6.25 (declare-fun tptp.bNF_re4521903465945308077real_o ((-> (-> tptp.nat tptp.rat) tptp.real Bool) (-> (-> (-> tptp.nat tptp.rat) Bool) (-> tptp.real Bool) Bool) (-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> tptp.real tptp.real Bool)) Bool)
% 5.91/6.25 (declare-fun tptp.bNF_re3023117138289059399t_real ((-> (-> tptp.nat tptp.rat) tptp.real Bool) (-> (-> tptp.nat tptp.rat) tptp.real Bool) (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) (-> tptp.real tptp.real)) Bool)
% 5.91/6.25 (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)
% 5.91/6.25 (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)
% 5.91/6.25 (declare-fun tptp.bNF_re5089333283451836215nt_o_o ((-> tptp.int tptp.int Bool) (-> Bool Bool Bool) (-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 5.91/6.25 (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)
% 5.91/6.25 (declare-fun tptp.bNF_re4705727531993890431at_o_o ((-> tptp.nat tptp.nat Bool) (-> Bool Bool Bool) (-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 5.91/6.25 (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)
% 5.91/6.25 (declare-fun tptp.bNF_re4702136315717946289at_rat ((-> tptp.nat tptp.nat Bool) (-> tptp.rat tptp.rat Bool) (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat)) Bool)
% 5.91/6.25 (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)
% 5.91/6.25 (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)
% 5.91/6.25 (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)
% 5.91/6.25 (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)
% 5.91/6.25 (declare-fun tptp.bNF_We3818239936649020644el_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 5.91/6.25 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.gbinomial_complex (tptp.complex tptp.nat) tptp.complex)
% 5.91/6.25 (declare-fun tptp.gbinomial_int (tptp.int tptp.nat) tptp.int)
% 5.91/6.25 (declare-fun tptp.gbinomial_nat (tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.gbinomial_rat (tptp.rat tptp.nat) tptp.rat)
% 5.91/6.25 (declare-fun tptp.gbinomial_real (tptp.real tptp.nat) tptp.real)
% 5.91/6.25 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 5.91/6.25 (declare-fun tptp.bit_concat_bit (tptp.nat tptp.int tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.bit_ri7919022796975470100ot_int (tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.bit_ri6519982836138164636nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 5.91/6.25 (declare-fun tptp.bit_ri631733984087533419it_int (tptp.nat tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.bit_se727722235901077358nd_nat (tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.bit_se8568078237143864401it_int (tptp.nat tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.bit_se8570568707652914677it_nat (tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.bit_se2159334234014336723it_int (tptp.nat tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.bit_se2161824704523386999it_nat (tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.bit_se2000444600071755411sk_int (tptp.nat) tptp.int)
% 5.91/6.25 (declare-fun tptp.bit_se2002935070580805687sk_nat (tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.bit_se1409905431419307370or_int (tptp.int tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.bit_se1412395901928357646or_nat (tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.bit_se545348938243370406it_int (tptp.nat tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.bit_se547839408752420682it_nat (tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.bit_se2793503036327961859nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 5.91/6.25 (declare-fun tptp.bit_se7879613467334960850it_int (tptp.nat tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.bit_se7882103937844011126it_nat (tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.bit_se2925701944663578781it_nat (tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.bit_se8260200283734997820nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 5.91/6.25 (declare-fun tptp.bit_se4203085406695923979it_int (tptp.nat tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.bit_se4205575877204974255it_nat (tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.bit_se6526347334894502574or_int (tptp.int tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.bit_se6528837805403552850or_nat (tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.bit_se1148574629649215175it_nat (tptp.nat tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.bit_take_bit_num (tptp.nat tptp.num) tptp.option_num)
% 5.91/6.25 (declare-fun tptp.code_divmod_integer (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 5.91/6.25 (declare-fun tptp.code_integer_of_nat (tptp.nat) tptp.code_integer)
% 5.91/6.25 (declare-fun tptp.code_nat_of_integer (tptp.code_integer) tptp.nat)
% 5.91/6.25 (declare-fun tptp.code_num_of_integer (tptp.code_integer) tptp.num)
% 5.91/6.25 (declare-fun tptp.comple2295165028678016749d_enat (tptp.set_Extended_enat) tptp.extended_enat)
% 5.91/6.25 (declare-fun tptp.complete_Inf_Inf_nat (tptp.set_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.comple4887499456419720421f_real (tptp.set_real) tptp.real)
% 5.91/6.25 (declare-fun tptp.comple7806235888213564991et_nat (tptp.set_set_nat) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.comple4398354569131411667d_enat (tptp.set_Extended_enat) tptp.extended_enat)
% 5.91/6.25 (declare-fun tptp.complete_Sup_Sup_int (tptp.set_int) tptp.int)
% 5.91/6.25 (declare-fun tptp.complete_Sup_Sup_nat (tptp.set_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.comple1385675409528146559p_real (tptp.set_real) tptp.real)
% 5.91/6.25 (declare-fun tptp.comple7399068483239264473et_nat (tptp.set_set_nat) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.arg (tptp.complex) tptp.real)
% 5.91/6.25 (declare-fun tptp.cis (tptp.real) tptp.complex)
% 5.91/6.25 (declare-fun tptp.complex2 (tptp.real tptp.real) tptp.complex)
% 5.91/6.25 (declare-fun tptp.im (tptp.complex) tptp.real)
% 5.91/6.25 (declare-fun tptp.re (tptp.complex) tptp.real)
% 5.91/6.25 (declare-fun tptp.csqrt (tptp.complex) tptp.complex)
% 5.91/6.25 (declare-fun tptp.imaginary_unit () tptp.complex)
% 5.91/6.25 (declare-fun tptp.condit2214826472909112428ve_nat (tptp.set_nat) Bool)
% 5.91/6.25 (declare-fun tptp.differ6690327859849518006l_real ((-> tptp.real tptp.real) tptp.filter_real) Bool)
% 5.91/6.25 (declare-fun tptp.has_fi5821293074295781190e_real ((-> tptp.real tptp.real) tptp.real tptp.filter_real) Bool)
% 5.91/6.25 (declare-fun tptp.divmod_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 5.91/6.25 (declare-fun tptp.eucl_rel_int (tptp.int tptp.int tptp.product_prod_int_int) Bool)
% 5.91/6.25 (declare-fun tptp.unique6319869463603278526ux_int (tptp.product_prod_int_int) Bool)
% 5.91/6.25 (declare-fun tptp.unique6322359934112328802ux_nat (tptp.product_prod_nat_nat) Bool)
% 5.91/6.25 (declare-fun tptp.unique5055182867167087721od_nat (tptp.num tptp.num) tptp.product_prod_nat_nat)
% 5.91/6.25 (declare-fun tptp.unique4921790084139445826nteger (tptp.num tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.91/6.25 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 5.91/6.25 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 5.91/6.25 (declare-fun tptp.euclid3395696857347342551nt_int (tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.euclid3398187327856392827nt_nat (tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.extended_eSuc (tptp.extended_enat) tptp.extended_enat)
% 5.91/6.25 (declare-fun tptp.extended_enat2 (tptp.nat) tptp.extended_enat)
% 5.91/6.25 (declare-fun tptp.extended_case_enat_o ((-> tptp.nat Bool) Bool tptp.extended_enat) Bool)
% 5.91/6.25 (declare-fun tptp.extend3600170679010898289d_enat ((-> tptp.nat tptp.extended_enat) tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 5.91/6.25 (declare-fun tptp.extend5688581933313929465d_enat () tptp.extended_enat)
% 5.91/6.25 (declare-fun tptp.comm_s2602460028002588243omplex (tptp.complex tptp.nat) tptp.complex)
% 5.91/6.25 (declare-fun tptp.comm_s4660882817536571857er_int (tptp.int tptp.nat) tptp.int)
% 5.91/6.25 (declare-fun tptp.comm_s4663373288045622133er_nat (tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.comm_s4028243227959126397er_rat (tptp.rat tptp.nat) tptp.rat)
% 5.91/6.25 (declare-fun tptp.comm_s7457072308508201937r_real (tptp.real tptp.nat) tptp.real)
% 5.91/6.25 (declare-fun tptp.semiri5044797733671781792omplex (tptp.nat) tptp.complex)
% 5.91/6.25 (declare-fun tptp.semiri1406184849735516958ct_int (tptp.nat) tptp.int)
% 5.91/6.25 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.semiri773545260158071498ct_rat (tptp.nat) tptp.rat)
% 5.91/6.25 (declare-fun tptp.semiri2265585572941072030t_real (tptp.nat) tptp.real)
% 5.91/6.25 (declare-fun tptp.invers8013647133539491842omplex (tptp.complex) tptp.complex)
% 5.91/6.25 (declare-fun tptp.inverse_inverse_rat (tptp.rat) tptp.rat)
% 5.91/6.25 (declare-fun tptp.inverse_inverse_real (tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.at_bot_real () tptp.filter_real)
% 5.91/6.25 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 5.91/6.25 (declare-fun tptp.at_top_real () tptp.filter_real)
% 5.91/6.25 (declare-fun tptp.cofinite_nat () tptp.filter_nat)
% 5.91/6.25 (declare-fun tptp.eventually_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 5.91/6.25 (declare-fun tptp.eventu1038000079068216329at_nat ((-> tptp.product_prod_nat_nat Bool) tptp.filter1242075044329608583at_nat) Bool)
% 5.91/6.25 (declare-fun tptp.filterlim_nat_nat ((-> tptp.nat tptp.nat) tptp.filter_nat tptp.filter_nat) Bool)
% 5.91/6.25 (declare-fun tptp.filterlim_nat_real ((-> tptp.nat tptp.real) tptp.filter_real tptp.filter_nat) Bool)
% 5.91/6.25 (declare-fun tptp.filterlim_real_real ((-> tptp.real tptp.real) tptp.filter_real tptp.filter_real) Bool)
% 5.91/6.25 (declare-fun tptp.frequently_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 5.91/6.25 (declare-fun tptp.prod_filter_nat_nat (tptp.filter_nat tptp.filter_nat) tptp.filter1242075044329608583at_nat)
% 5.91/6.25 (declare-fun tptp.finite_card_nat_rat (tptp.set_nat_rat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.finite_card_o (tptp.set_o) tptp.nat)
% 5.91/6.25 (declare-fun tptp.finite_card_complex (tptp.set_complex) tptp.nat)
% 5.91/6.25 (declare-fun tptp.finite121521170596916366d_enat (tptp.set_Extended_enat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.finite_card_int (tptp.set_int) tptp.nat)
% 5.91/6.25 (declare-fun tptp.finite5120063068150530198omplex (tptp.set_list_complex) tptp.nat)
% 5.91/6.25 (declare-fun tptp.finite7441382602597825044d_enat (tptp.set_li5464603477888414924d_enat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.finite_card_list_int (tptp.set_list_int) tptp.nat)
% 5.91/6.25 (declare-fun tptp.finite7325466520557071688st_nat (tptp.set_list_list_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.finite_card_list_nat (tptp.set_list_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.finite249151656366948015at_nat (tptp.set_li5450038453877631591at_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.finite5631907774883551598et_nat (tptp.set_list_set_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.finite5915292604075114978T_VEBT (tptp.set_list_VEBT_VEBT) tptp.nat)
% 5.91/6.25 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.finite711546835091564841at_nat (tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.finite410649719033368117t_unit (tptp.set_Product_unit) tptp.nat)
% 5.91/6.25 (declare-fun tptp.finite_card_real (tptp.set_real) tptp.nat)
% 5.91/6.25 (declare-fun tptp.finite8736671560171388117at_rat (tptp.set_set_nat_rat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.finite903997441450111292omplex (tptp.set_set_complex) tptp.nat)
% 5.91/6.25 (declare-fun tptp.finite3719263829065406702d_enat (tptp.set_se7270636423289371942d_enat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.finite_card_set_int (tptp.set_set_int) tptp.nat)
% 5.91/6.25 (declare-fun tptp.finite2364142230527598318st_nat (tptp.set_set_list_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.finite_card_set_nat (tptp.set_set_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.finite4356350796350151305at_nat (tptp.set_se7855581050983116737at_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.finite1149291290879098388et_nat (tptp.set_set_set_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.finite7802652506058667612T_VEBT (tptp.set_VEBT_VEBT) tptp.nat)
% 5.91/6.25 (declare-fun tptp.finite7830837933032798814at_rat (tptp.set_nat_rat) Bool)
% 5.91/6.25 (declare-fun tptp.finite_finite_o (tptp.set_o) Bool)
% 5.91/6.25 (declare-fun tptp.finite3207457112153483333omplex (tptp.set_complex) Bool)
% 5.91/6.25 (declare-fun tptp.finite4001608067531595151d_enat (tptp.set_Extended_enat) Bool)
% 5.91/6.25 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 5.91/6.25 (declare-fun tptp.finite8712137658972009173omplex (tptp.set_list_complex) Bool)
% 5.91/6.25 (declare-fun tptp.finite1862508098717546133d_enat (tptp.set_li5464603477888414924d_enat) Bool)
% 5.91/6.25 (declare-fun tptp.finite3922522038869484883st_int (tptp.set_list_int) Bool)
% 5.91/6.25 (declare-fun tptp.finite8100373058378681591st_nat (tptp.set_list_nat) Bool)
% 5.91/6.25 (declare-fun tptp.finite500796754983035824at_nat (tptp.set_li5450038453877631591at_nat) Bool)
% 5.91/6.25 (declare-fun tptp.finite3004134309566078307T_VEBT (tptp.set_list_VEBT_VEBT) Bool)
% 5.91/6.25 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 5.91/6.25 (declare-fun tptp.finite_finite_num (tptp.set_num) Bool)
% 5.91/6.25 (declare-fun tptp.finite6177210948735845034at_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 5.91/6.25 (declare-fun tptp.finite_finite_rat (tptp.set_rat) Bool)
% 5.91/6.25 (declare-fun tptp.finite_finite_real (tptp.set_real) Bool)
% 5.91/6.25 (declare-fun tptp.finite6430367030675640852at_rat (tptp.set_set_nat_rat) Bool)
% 5.91/6.25 (declare-fun tptp.finite6551019134538273531omplex (tptp.set_set_complex) Bool)
% 5.91/6.25 (declare-fun tptp.finite5468666774076196335d_enat (tptp.set_se7270636423289371942d_enat) Bool)
% 5.91/6.25 (declare-fun tptp.finite6197958912794628473et_int (tptp.set_set_int) Bool)
% 5.91/6.25 (declare-fun tptp.finite1152437895449049373et_nat (tptp.set_set_nat) Bool)
% 5.91/6.25 (declare-fun tptp.finite9047747110432174090at_nat (tptp.set_se7855581050983116737at_nat) Bool)
% 5.91/6.25 (declare-fun tptp.finite5795047828879050333T_VEBT (tptp.set_VEBT_VEBT) Bool)
% 5.91/6.25 (declare-fun tptp.bij_be1856998921033663316omplex ((-> tptp.complex tptp.complex) tptp.set_complex tptp.set_complex) Bool)
% 5.91/6.25 (declare-fun tptp.bij_betw_nat_complex ((-> tptp.nat tptp.complex) tptp.set_nat tptp.set_complex) Bool)
% 5.91/6.25 (declare-fun tptp.bij_betw_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat tptp.set_nat) Bool)
% 5.91/6.25 (declare-fun tptp.comp_int_nat_int ((-> tptp.int tptp.nat) (-> tptp.int tptp.int) tptp.int) tptp.nat)
% 5.91/6.25 (declare-fun tptp.comp_nat_nat_nat ((-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.comp_nat_real_nat ((-> tptp.nat tptp.real) (-> tptp.nat tptp.nat) tptp.nat) tptp.real)
% 5.91/6.25 (declare-fun tptp.id_o (Bool) Bool)
% 5.91/6.25 (declare-fun tptp.inj_on_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 5.91/6.25 (declare-fun tptp.inj_on_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) Bool)
% 5.91/6.25 (declare-fun tptp.inj_on_real_real ((-> tptp.real tptp.real) tptp.set_real) Bool)
% 5.91/6.25 (declare-fun tptp.inj_on_set_nat_nat ((-> tptp.set_nat tptp.nat) tptp.set_set_nat) Bool)
% 5.91/6.25 (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)
% 5.91/6.25 (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)
% 5.91/6.25 (declare-fun tptp.map_fu1532550112467129777l_real ((-> tptp.real tptp.nat tptp.rat) (-> (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) tptp.real tptp.real) (-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) tptp.nat tptp.rat) tptp.real tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.map_fu7146612038024189824t_real ((-> tptp.real tptp.nat tptp.rat) (-> (-> tptp.nat tptp.rat) tptp.real) (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.map_fu1856342031159181835at_o_o ((-> tptp.real tptp.nat tptp.rat) (-> Bool Bool) (-> (-> tptp.nat tptp.rat) Bool) tptp.real) Bool)
% 5.91/6.25 (declare-fun tptp.strict1292158309912662752at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 5.91/6.25 (declare-fun tptp.the_in5290026491893676941l_real (tptp.set_real (-> tptp.real tptp.real) tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.fun_max_strict () tptp.set_Pr4329608150637261639at_nat)
% 5.91/6.25 (declare-fun tptp.fun_max_weak () tptp.set_Pr4329608150637261639at_nat)
% 5.91/6.25 (declare-fun tptp.fun_min_strict () tptp.set_Pr4329608150637261639at_nat)
% 5.91/6.25 (declare-fun tptp.fun_min_weak () tptp.set_Pr4329608150637261639at_nat)
% 5.91/6.25 (declare-fun tptp.fun_pair_leq () tptp.set_Pr8693737435421807431at_nat)
% 5.91/6.25 (declare-fun tptp.fun_pair_less () tptp.set_Pr8693737435421807431at_nat)
% 5.91/6.25 (declare-fun tptp.fun_re2478310338295953701at_nat (tptp.produc1319942482725812455at_nat) Bool)
% 5.91/6.25 (declare-fun tptp.gcd_Gcd_int (tptp.set_int) tptp.int)
% 5.91/6.25 (declare-fun tptp.gcd_Gcd_nat (tptp.set_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.bezw (tptp.nat tptp.nat) tptp.product_prod_int_int)
% 5.91/6.25 (declare-fun tptp.bezw_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 5.91/6.25 (declare-fun tptp.gcd_gcd_int (tptp.int tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.gcd_gcd_nat (tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.gcd_nat_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 5.91/6.25 (declare-fun tptp.semiri4256215615220890538in_int (tptp.set_int) tptp.int)
% 5.91/6.25 (declare-fun tptp.semiri4258706085729940814in_nat (tptp.set_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.abs_abs_Code_integer (tptp.code_integer) tptp.code_integer)
% 5.91/6.25 (declare-fun tptp.abs_abs_complex (tptp.complex) tptp.complex)
% 5.91/6.25 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.abs_abs_rat (tptp.rat) tptp.rat)
% 5.91/6.25 (declare-fun tptp.abs_abs_real (tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.comm_monoid_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.minus_8641456556474268591_rat_o ((-> (-> tptp.nat tptp.rat) Bool) (-> (-> tptp.nat tptp.rat) Bool) (-> tptp.nat tptp.rat)) Bool)
% 5.91/6.25 (declare-fun tptp.minus_minus_o_o ((-> Bool Bool) (-> Bool Bool) Bool) Bool)
% 5.91/6.25 (declare-fun tptp.minus_minus_int_o ((-> tptp.int Bool) (-> tptp.int Bool) tptp.int) Bool)
% 5.91/6.25 (declare-fun tptp.minus_minus_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.minus_7664381017404958329_rat_o ((-> tptp.set_nat_rat Bool) (-> tptp.set_nat_rat Bool) tptp.set_nat_rat) Bool)
% 5.91/6.25 (declare-fun tptp.minus_6910147592129066416_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool) tptp.set_nat) Bool)
% 5.91/6.25 (declare-fun tptp.minus_8373710615458151222nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.91/6.25 (declare-fun tptp.minus_minus_complex (tptp.complex tptp.complex) tptp.complex)
% 5.91/6.25 (declare-fun tptp.minus_3235023915231533773d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 5.91/6.25 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.minus_minus_rat (tptp.rat tptp.rat) tptp.rat)
% 5.91/6.25 (declare-fun tptp.minus_minus_real (tptp.real tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.minus_1741603841019369558at_rat (tptp.set_nat_rat tptp.set_nat_rat) tptp.set_nat_rat)
% 5.91/6.25 (declare-fun tptp.minus_minus_set_o (tptp.set_o tptp.set_o) tptp.set_o)
% 5.91/6.25 (declare-fun tptp.minus_811609699411566653omplex (tptp.set_complex tptp.set_complex) tptp.set_complex)
% 5.91/6.25 (declare-fun tptp.minus_925952699566721837d_enat (tptp.set_Extended_enat tptp.set_Extended_enat) tptp.set_Extended_enat)
% 5.91/6.25 (declare-fun tptp.minus_minus_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 5.91/6.25 (declare-fun tptp.minus_7954133019191499631st_nat (tptp.set_list_nat tptp.set_list_nat) tptp.set_list_nat)
% 5.91/6.25 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.minus_1356011639430497352at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 5.91/6.25 (declare-fun tptp.minus_minus_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 5.91/6.25 (declare-fun tptp.minus_1626877696091177228at_rat (tptp.set_set_nat_rat tptp.set_set_nat_rat) tptp.set_set_nat_rat)
% 5.91/6.25 (declare-fun tptp.minus_2163939370556025621et_nat (tptp.set_set_nat tptp.set_set_nat) tptp.set_set_nat)
% 5.91/6.25 (declare-fun tptp.minus_5127226145743854075T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 5.91/6.25 (declare-fun tptp.monoid_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.one_one_Code_integer () tptp.code_integer)
% 5.91/6.25 (declare-fun tptp.one_one_complex () tptp.complex)
% 5.91/6.25 (declare-fun tptp.one_on7984719198319812577d_enat () tptp.extended_enat)
% 5.91/6.25 (declare-fun tptp.one_one_int () tptp.int)
% 5.91/6.25 (declare-fun tptp.one_one_nat () tptp.nat)
% 5.91/6.25 (declare-fun tptp.one_one_rat () tptp.rat)
% 5.91/6.25 (declare-fun tptp.one_one_real () tptp.real)
% 5.91/6.25 (declare-fun tptp.plus_p5714425477246183910nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.91/6.25 (declare-fun tptp.plus_plus_complex (tptp.complex tptp.complex) tptp.complex)
% 5.91/6.25 (declare-fun tptp.plus_p3455044024723400733d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 5.91/6.25 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 5.91/6.25 (declare-fun tptp.plus_plus_rat (tptp.rat tptp.rat) tptp.rat)
% 5.91/6.25 (declare-fun tptp.plus_plus_real (tptp.real tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.plus_plus_literal (tptp.literal tptp.literal) tptp.literal)
% 5.91/6.25 (declare-fun tptp.sgn_sgn_complex (tptp.complex) tptp.complex)
% 5.91/6.25 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.sgn_sgn_rat (tptp.rat) tptp.rat)
% 5.91/6.25 (declare-fun tptp.sgn_sgn_real (tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.times_3573771949741848930nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.91/6.25 (declare-fun tptp.times_times_complex (tptp.complex tptp.complex) tptp.complex)
% 5.91/6.25 (declare-fun tptp.times_7803423173614009249d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 5.91/6.25 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.times_times_num (tptp.num tptp.num) tptp.num)
% 5.91/6.25 (declare-fun tptp.times_times_rat (tptp.rat tptp.rat) tptp.rat)
% 5.91/6.25 (declare-fun tptp.times_times_real (tptp.real tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.uminus8974390361584276543_rat_o ((-> (-> tptp.nat tptp.rat) Bool) (-> tptp.nat tptp.rat)) Bool)
% 5.91/6.25 (declare-fun tptp.uminus_uminus_o_o ((-> Bool Bool) Bool) Bool)
% 5.91/6.25 (declare-fun tptp.uminus_uminus_int_o ((-> tptp.int Bool) tptp.int) Bool)
% 5.91/6.25 (declare-fun tptp.uminus_uminus_nat_o ((-> tptp.nat Bool) tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.uminus6216118484121566985_rat_o ((-> tptp.set_nat_rat Bool) tptp.set_nat_rat) Bool)
% 5.91/6.25 (declare-fun tptp.uminus6401447641752708672_nat_o ((-> tptp.set_nat Bool) tptp.set_nat) Bool)
% 5.91/6.25 (declare-fun tptp.uminus1351360451143612070nteger (tptp.code_integer) tptp.code_integer)
% 5.91/6.25 (declare-fun tptp.uminus1482373934393186551omplex (tptp.complex) tptp.complex)
% 5.91/6.25 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.uminus_uminus_rat (tptp.rat) tptp.rat)
% 5.91/6.25 (declare-fun tptp.uminus_uminus_real (tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.uminus6988975074191911878at_rat (tptp.set_nat_rat) tptp.set_nat_rat)
% 5.91/6.25 (declare-fun tptp.uminus_uminus_set_o (tptp.set_o) tptp.set_o)
% 5.91/6.25 (declare-fun tptp.uminus1532241313380277803et_int (tptp.set_int) tptp.set_int)
% 5.91/6.25 (declare-fun tptp.uminus5710092332889474511et_nat (tptp.set_nat) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.uminus6524753893492686040at_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 5.91/6.25 (declare-fun tptp.uminus612125837232591019t_real (tptp.set_real) tptp.set_real)
% 5.91/6.25 (declare-fun tptp.uminus3098529973357106300at_rat (tptp.set_set_nat_rat) tptp.set_set_nat_rat)
% 5.91/6.25 (declare-fun tptp.uminus613421341184616069et_nat (tptp.set_set_nat) tptp.set_set_nat)
% 5.91/6.25 (declare-fun tptp.zero_z3403309356797280102nteger () tptp.code_integer)
% 5.91/6.25 (declare-fun tptp.zero_zero_complex () tptp.complex)
% 5.91/6.25 (declare-fun tptp.zero_z5237406670263579293d_enat () tptp.extended_enat)
% 5.91/6.25 (declare-fun tptp.zero_zero_int () tptp.int)
% 5.91/6.25 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 5.91/6.25 (declare-fun tptp.zero_zero_rat () tptp.rat)
% 5.91/6.25 (declare-fun tptp.zero_zero_real () tptp.real)
% 5.91/6.25 (declare-fun tptp.zero_zero_literal () tptp.literal)
% 5.91/6.25 (declare-fun tptp.groups5328290441151304332omplex ((-> Bool tptp.complex) tptp.set_o) tptp.complex)
% 5.91/6.25 (declare-fun tptp.groups8505340233167759370_o_int ((-> Bool tptp.int) tptp.set_o) tptp.int)
% 5.91/6.25 (declare-fun tptp.groups8507830703676809646_o_nat ((-> Bool tptp.nat) tptp.set_o) tptp.nat)
% 5.91/6.25 (declare-fun tptp.groups7872700643590313910_o_rat ((-> Bool tptp.rat) tptp.set_o) tptp.rat)
% 5.91/6.25 (declare-fun tptp.groups8691415230153176458o_real ((-> Bool tptp.real) tptp.set_o) tptp.real)
% 5.91/6.25 (declare-fun tptp.groups7754918857620584856omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 5.91/6.25 (declare-fun tptp.groups5690904116761175830ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 5.91/6.25 (declare-fun tptp.groups5693394587270226106ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 5.91/6.25 (declare-fun tptp.groups5058264527183730370ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 5.91/6.25 (declare-fun tptp.groups5808333547571424918x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 5.91/6.25 (declare-fun tptp.groups6818542070133387226omplex ((-> tptp.extended_enat tptp.complex) tptp.set_Extended_enat) tptp.complex)
% 5.91/6.25 (declare-fun tptp.groups2027974829824023292at_nat ((-> tptp.extended_enat tptp.nat) tptp.set_Extended_enat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.groups1392844769737527556at_rat ((-> tptp.extended_enat tptp.rat) tptp.set_Extended_enat) tptp.rat)
% 5.91/6.25 (declare-fun tptp.groups4148127829035722712t_real ((-> tptp.extended_enat tptp.real) tptp.set_Extended_enat) tptp.real)
% 5.91/6.25 (declare-fun tptp.groups3049146728041665814omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 5.91/6.25 (declare-fun tptp.groups4538972089207619220nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 5.91/6.25 (declare-fun tptp.groups4541462559716669496nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 5.91/6.25 (declare-fun tptp.groups3906332499630173760nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 5.91/6.25 (declare-fun tptp.groups8778361861064173332t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 5.91/6.25 (declare-fun tptp.groups2073611262835488442omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 5.91/6.25 (declare-fun tptp.groups3539618377306564664at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 5.91/6.25 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.groups2906978787729119204at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 5.91/6.25 (declare-fun tptp.groups6591440286371151544t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 5.91/6.25 (declare-fun tptp.groups977919841031483927at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.groups4567486121110086003t_real ((-> tptp.product_prod_nat_nat tptp.real) tptp.set_Pr1261947904930325089at_nat) tptp.real)
% 5.91/6.25 (declare-fun tptp.groups1932886352136224148al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 5.91/6.25 (declare-fun tptp.groups1935376822645274424al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 5.91/6.25 (declare-fun tptp.groups1300246762558778688al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 5.91/6.25 (declare-fun tptp.groups8097168146408367636l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 5.91/6.25 (declare-fun tptp.groups6246630355582004071omplex ((-> tptp.set_nat_rat tptp.complex) tptp.set_set_nat_rat) tptp.complex)
% 5.91/6.25 (declare-fun tptp.groups4357547368389691109t_real ((-> tptp.set_nat_rat tptp.real) tptp.set_set_nat_rat) tptp.real)
% 5.91/6.25 (declare-fun tptp.groups8255218700646806128omplex ((-> tptp.set_nat tptp.complex) tptp.set_set_nat) tptp.complex)
% 5.91/6.25 (declare-fun tptp.groups5107569545109728110t_real ((-> tptp.set_nat tptp.real) tptp.set_set_nat) tptp.real)
% 5.91/6.25 (declare-fun tptp.groups4859619685533338977omplex ((-> Bool tptp.complex) tptp.set_o) tptp.complex)
% 5.91/6.25 (declare-fun tptp.groups3502327434004483295_o_int ((-> Bool tptp.int) tptp.set_o) tptp.int)
% 5.91/6.25 (declare-fun tptp.groups3504817904513533571_o_nat ((-> Bool tptp.nat) tptp.set_o) tptp.nat)
% 5.91/6.25 (declare-fun tptp.groups2869687844427037835_o_rat ((-> Bool tptp.rat) tptp.set_o) tptp.rat)
% 5.91/6.25 (declare-fun tptp.groups234877984723959775o_real ((-> Bool tptp.real) tptp.set_o) tptp.real)
% 5.91/6.25 (declare-fun tptp.groups3708469109370488835omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 5.91/6.25 (declare-fun tptp.groups858564598930262913ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 5.91/6.25 (declare-fun tptp.groups861055069439313189ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 5.91/6.25 (declare-fun tptp.groups225925009352817453ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 5.91/6.25 (declare-fun tptp.groups766887009212190081x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 5.91/6.25 (declare-fun tptp.groups4622424608036095791omplex ((-> tptp.extended_enat tptp.complex) tptp.set_Extended_enat) tptp.complex)
% 5.91/6.25 (declare-fun tptp.groups2878480467620962989at_int ((-> tptp.extended_enat tptp.int) tptp.set_Extended_enat) tptp.int)
% 5.91/6.25 (declare-fun tptp.groups2880970938130013265at_nat ((-> tptp.extended_enat tptp.nat) tptp.set_Extended_enat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.groups2245840878043517529at_rat ((-> tptp.extended_enat tptp.rat) tptp.set_Extended_enat) tptp.rat)
% 5.91/6.25 (declare-fun tptp.groups97031904164794029t_real ((-> tptp.extended_enat tptp.real) tptp.set_Extended_enat) tptp.real)
% 5.91/6.25 (declare-fun tptp.groups7440179247065528705omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 5.91/6.25 (declare-fun tptp.groups1705073143266064639nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 5.91/6.25 (declare-fun tptp.groups1707563613775114915nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 5.91/6.25 (declare-fun tptp.groups1072433553688619179nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 5.91/6.25 (declare-fun tptp.groups2316167850115554303t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 5.91/6.25 (declare-fun tptp.groups6464643781859351333omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 5.91/6.25 (declare-fun tptp.groups705719431365010083at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 5.91/6.25 (declare-fun tptp.groups708209901874060359at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.groups73079841787564623at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 5.91/6.25 (declare-fun tptp.groups129246275422532515t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 5.91/6.25 (declare-fun tptp.groups4077766827762148844at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.groups6036352826371341000t_real ((-> tptp.product_prod_nat_nat tptp.real) tptp.set_Pr1261947904930325089at_nat) tptp.real)
% 5.91/6.25 (declare-fun tptp.groups713298508707869441omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 5.91/6.25 (declare-fun tptp.groups4694064378042380927al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 5.91/6.25 (declare-fun tptp.groups4696554848551431203al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 5.91/6.25 (declare-fun tptp.groups4061424788464935467al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 5.91/6.25 (declare-fun tptp.groups1681761925125756287l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 5.91/6.25 (declare-fun tptp.groups4561878855575611511st_nat (tptp.list_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.the_int ((-> tptp.int Bool)) tptp.int)
% 5.91/6.25 (declare-fun tptp.the_real ((-> tptp.real Bool)) tptp.real)
% 5.91/6.25 (declare-fun tptp.if_nat_rat (Bool (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) tptp.nat) tptp.rat)
% 5.91/6.25 (declare-fun tptp.if_Code_integer (Bool tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.91/6.25 (declare-fun tptp.if_complex (Bool tptp.complex tptp.complex) tptp.complex)
% 5.91/6.25 (declare-fun tptp.if_Extended_enat (Bool tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 5.91/6.25 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.if_list_int (Bool tptp.list_int tptp.list_int) tptp.list_int)
% 5.91/6.25 (declare-fun tptp.if_list_nat (Bool tptp.list_nat tptp.list_nat) tptp.list_nat)
% 5.91/6.25 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.if_num (Bool tptp.num tptp.num) tptp.num)
% 5.91/6.25 (declare-fun tptp.if_option_nat (Bool tptp.option_nat tptp.option_nat) tptp.option_nat)
% 5.91/6.25 (declare-fun tptp.if_option_num (Bool tptp.option_num tptp.option_num) tptp.option_num)
% 5.91/6.25 (declare-fun tptp.if_Pro6119634080678213985nteger (Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.91/6.25 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 5.91/6.25 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 5.91/6.25 (declare-fun tptp.if_rat (Bool tptp.rat tptp.rat) tptp.rat)
% 5.91/6.25 (declare-fun tptp.if_real (Bool tptp.real tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.if_set_int (Bool tptp.set_int tptp.set_int) tptp.set_int)
% 5.91/6.25 (declare-fun tptp.if_VEBT_VEBT (Bool tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 5.91/6.25 (declare-fun tptp.infini7641415182203889163d_enat (tptp.set_Extended_enat tptp.nat) tptp.extended_enat)
% 5.91/6.25 (declare-fun tptp.infini8530281810654367211te_nat (tptp.set_nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.abs_Integ (tptp.product_prod_nat_nat) tptp.int)
% 5.91/6.25 (declare-fun tptp.rep_Integ (tptp.int) tptp.product_prod_nat_nat)
% 5.91/6.25 (declare-fun tptp.int_ge_less_than (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 5.91/6.25 (declare-fun tptp.int_ge_less_than2 (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 5.91/6.25 (declare-fun tptp.intrel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 5.91/6.25 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 5.91/6.25 (declare-fun tptp.pcr_int (tptp.product_prod_nat_nat tptp.int) Bool)
% 5.91/6.25 (declare-fun tptp.power_int_real (tptp.real tptp.int) tptp.real)
% 5.91/6.25 (declare-fun tptp.ring_1_Ints_complex () tptp.set_complex)
% 5.91/6.25 (declare-fun tptp.ring_1_Ints_int () tptp.set_int)
% 5.91/6.25 (declare-fun tptp.ring_1_Ints_rat () tptp.set_rat)
% 5.91/6.25 (declare-fun tptp.ring_1_Ints_real () tptp.set_real)
% 5.91/6.25 (declare-fun tptp.ring_18347121197199848620nteger (tptp.int) tptp.code_integer)
% 5.91/6.25 (declare-fun tptp.ring_17405671764205052669omplex (tptp.int) tptp.complex)
% 5.91/6.25 (declare-fun tptp.ring_1_of_int_int (tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.ring_1_of_int_rat (tptp.int) tptp.rat)
% 5.91/6.25 (declare-fun tptp.ring_1_of_int_real (tptp.int) tptp.real)
% 5.91/6.25 (declare-fun tptp.inf_inf_nat (tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.inf_in2572325071724192079at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 5.91/6.25 (declare-fun tptp.semila9081495762789891438tr_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.semila1623282765462674594er_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 5.91/6.25 (declare-fun tptp.sup_sup_nat (tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.sup_sup_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.sup_su718114333110466843at_nat (tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr8693737435421807431at_nat)
% 5.91/6.25 (declare-fun tptp.sup_su5525570899277871387at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4329608150637261639at_nat)
% 5.91/6.25 (declare-fun tptp.lattic921264341876707157d_enat (tptp.set_Extended_enat) tptp.extended_enat)
% 5.91/6.25 (declare-fun tptp.lattic8265883725875713057ax_nat (tptp.set_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.lattic8556559851467007577_o_num ((-> Bool tptp.num) tptp.set_o) Bool)
% 5.91/6.25 (declare-fun tptp.lattic2140725968369957399_o_rat ((-> Bool tptp.rat) tptp.set_o) Bool)
% 5.91/6.25 (declare-fun tptp.lattic8697145971487455083o_real ((-> Bool tptp.real) tptp.set_o) Bool)
% 5.91/6.25 (declare-fun tptp.lattic1922116423962787043ex_num ((-> tptp.complex tptp.num) tptp.set_complex) tptp.complex)
% 5.91/6.25 (declare-fun tptp.lattic4729654577720512673ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.complex)
% 5.91/6.25 (declare-fun tptp.lattic8794016678065449205x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.complex)
% 5.91/6.25 (declare-fun tptp.lattic402713867396545063at_num ((-> tptp.extended_enat tptp.num) tptp.set_Extended_enat) tptp.extended_enat)
% 5.91/6.25 (declare-fun tptp.lattic3210252021154270693at_rat ((-> tptp.extended_enat tptp.rat) tptp.set_Extended_enat) tptp.extended_enat)
% 5.91/6.25 (declare-fun tptp.lattic1189837152898106425t_real ((-> tptp.extended_enat tptp.real) tptp.set_Extended_enat) tptp.extended_enat)
% 5.91/6.25 (declare-fun tptp.lattic7811156612396918303nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.int)
% 5.91/6.25 (declare-fun tptp.lattic2675449441010098035t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.int)
% 5.91/6.25 (declare-fun tptp.lattic6811802900495863747at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.lattic488527866317076247t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.lattic1613168225601753569al_num ((-> tptp.real tptp.num) tptp.set_real) tptp.real)
% 5.91/6.25 (declare-fun tptp.lattic4420706379359479199al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.real)
% 5.91/6.25 (declare-fun tptp.lattic8440615504127631091l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 5.91/6.25 (declare-fun tptp.quotie3684837364556693515t_real ((-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> (-> tptp.nat tptp.rat) tptp.real) (-> tptp.real tptp.nat tptp.rat) (-> (-> tptp.nat tptp.rat) tptp.real Bool)) Bool)
% 5.91/6.25 (declare-fun tptp.bfun_nat_real ((-> tptp.nat tptp.real) tptp.filter_nat) Bool)
% 5.91/6.25 (declare-fun tptp.at_infinity_real () tptp.filter_real)
% 5.91/6.25 (declare-fun tptp.append_int (tptp.list_int tptp.list_int) tptp.list_int)
% 5.91/6.25 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 5.91/6.25 (declare-fun tptp.concat_nat (tptp.list_list_nat) tptp.list_nat)
% 5.91/6.25 (declare-fun tptp.concat_VEBT_VEBT (tptp.list_list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 5.91/6.25 (declare-fun tptp.count_list_o (tptp.list_o Bool) tptp.nat)
% 5.91/6.25 (declare-fun tptp.count_list_int (tptp.list_int tptp.int) tptp.nat)
% 5.91/6.25 (declare-fun tptp.count_list_nat (tptp.list_nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.count_6735058137522573441at_rat (tptp.list_set_nat_rat tptp.set_nat_rat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.count_list_set_nat (tptp.list_set_nat tptp.set_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.count_list_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.vEBT_VEBT) tptp.nat)
% 5.91/6.25 (declare-fun tptp.distinct_complex (tptp.list_complex) Bool)
% 5.91/6.25 (declare-fun tptp.distin4523846830085650399d_enat (tptp.list_Extended_enat) Bool)
% 5.91/6.25 (declare-fun tptp.distinct_int (tptp.list_int) Bool)
% 5.91/6.25 (declare-fun tptp.distinct_list_nat (tptp.list_list_nat) Bool)
% 5.91/6.25 (declare-fun tptp.distinct_nat (tptp.list_nat) Bool)
% 5.91/6.25 (declare-fun tptp.distin6923225563576452346at_nat (tptp.list_P6011104703257516679at_nat) Bool)
% 5.91/6.25 (declare-fun tptp.distinct_set_nat (tptp.list_set_nat) Bool)
% 5.91/6.25 (declare-fun tptp.distinct_VEBT_VEBT (tptp.list_VEBT_VEBT) Bool)
% 5.91/6.25 (declare-fun tptp.enumerate_int (tptp.nat tptp.list_int) tptp.list_P3521021558325789923at_int)
% 5.91/6.25 (declare-fun tptp.enumerate_nat (tptp.nat tptp.list_nat) tptp.list_P6011104703257516679at_nat)
% 5.91/6.25 (declare-fun tptp.enumerate_VEBT_VEBT (tptp.nat tptp.list_VEBT_VEBT) tptp.list_P5647936690300460905T_VEBT)
% 5.91/6.25 (declare-fun tptp.find_int ((-> tptp.int Bool) tptp.list_int) tptp.option_int)
% 5.91/6.25 (declare-fun tptp.find_nat ((-> tptp.nat Bool) tptp.list_nat) tptp.option_nat)
% 5.91/6.25 (declare-fun tptp.find_num ((-> tptp.num Bool) tptp.list_num) tptp.option_num)
% 5.91/6.25 (declare-fun tptp.find_P8199882355184865565at_nat ((-> tptp.product_prod_nat_nat Bool) tptp.list_P6011104703257516679at_nat) tptp.option4927543243414619207at_nat)
% 5.91/6.25 (declare-fun tptp.find_VEBT_VEBT ((-> tptp.vEBT_VEBT Bool) tptp.list_VEBT_VEBT) tptp.option_VEBT_VEBT)
% 5.91/6.25 (declare-fun tptp.fold_nat_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.list_nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.last_nat (tptp.list_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.linord2614967742042102400et_nat (tptp.set_nat) tptp.list_nat)
% 5.91/6.25 (declare-fun tptp.cons_o (Bool tptp.list_o) tptp.list_o)
% 5.91/6.25 (declare-fun tptp.cons_int (tptp.int tptp.list_int) tptp.list_int)
% 5.91/6.25 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 5.91/6.25 (declare-fun tptp.cons_set_nat_rat (tptp.set_nat_rat tptp.list_set_nat_rat) tptp.list_set_nat_rat)
% 5.91/6.25 (declare-fun tptp.cons_set_nat (tptp.set_nat tptp.list_set_nat) tptp.list_set_nat)
% 5.91/6.25 (declare-fun tptp.cons_VEBT_VEBT (tptp.vEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 5.91/6.25 (declare-fun tptp.nil_int () tptp.list_int)
% 5.91/6.25 (declare-fun tptp.nil_nat () tptp.list_nat)
% 5.91/6.25 (declare-fun tptp.hd_nat (tptp.list_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.map_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 5.91/6.25 (declare-fun tptp.map_VE8901447254227204932T_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 5.91/6.25 (declare-fun tptp.set_o2 (tptp.list_o) tptp.set_o)
% 5.91/6.25 (declare-fun tptp.set_complex2 (tptp.list_complex) tptp.set_complex)
% 5.91/6.25 (declare-fun tptp.set_Extended_enat2 (tptp.list_Extended_enat) tptp.set_Extended_enat)
% 5.91/6.25 (declare-fun tptp.set_int2 (tptp.list_int) tptp.set_int)
% 5.91/6.25 (declare-fun tptp.set_list_nat2 (tptp.list_list_nat) tptp.set_list_nat)
% 5.91/6.25 (declare-fun tptp.set_list_VEBT_VEBT2 (tptp.list_list_VEBT_VEBT) tptp.set_list_VEBT_VEBT)
% 5.91/6.25 (declare-fun tptp.set_nat2 (tptp.list_nat) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.set_Pr5648618587558075414at_nat (tptp.list_P6011104703257516679at_nat) tptp.set_Pr1261947904930325089at_nat)
% 5.91/6.25 (declare-fun tptp.set_real2 (tptp.list_real) tptp.set_real)
% 5.91/6.25 (declare-fun tptp.set_set_nat_rat2 (tptp.list_set_nat_rat) tptp.set_set_nat_rat)
% 5.91/6.25 (declare-fun tptp.set_set_nat2 (tptp.list_set_nat) tptp.set_set_nat)
% 5.91/6.25 (declare-fun tptp.set_VEBT_VEBT2 (tptp.list_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 5.91/6.25 (declare-fun tptp.size_list_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.nat) tptp.list_VEBT_VEBT) tptp.nat)
% 5.91/6.25 (declare-fun tptp.list_update_o (tptp.list_o tptp.nat Bool) tptp.list_o)
% 5.91/6.25 (declare-fun tptp.list_update_int (tptp.list_int tptp.nat tptp.int) tptp.list_int)
% 5.91/6.25 (declare-fun tptp.list_update_nat (tptp.list_nat tptp.nat tptp.nat) tptp.list_nat)
% 5.91/6.25 (declare-fun tptp.list_u6180841689913720943at_nat (tptp.list_P6011104703257516679at_nat tptp.nat tptp.product_prod_nat_nat) tptp.list_P6011104703257516679at_nat)
% 5.91/6.25 (declare-fun tptp.list_update_real (tptp.list_real tptp.nat tptp.real) tptp.list_real)
% 5.91/6.25 (declare-fun tptp.list_u886106648575569423at_rat (tptp.list_set_nat_rat tptp.nat tptp.set_nat_rat) tptp.list_set_nat_rat)
% 5.91/6.25 (declare-fun tptp.list_update_set_nat (tptp.list_set_nat tptp.nat tptp.set_nat) tptp.list_set_nat)
% 5.91/6.25 (declare-fun tptp.list_u1324408373059187874T_VEBT (tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 5.91/6.25 (declare-fun tptp.nth_o (tptp.list_o tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 5.91/6.25 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.nth_num (tptp.list_num tptp.nat) tptp.num)
% 5.91/6.25 (declare-fun tptp.nth_Pr4439495888332055232nt_int (tptp.list_P5707943133018811711nt_int tptp.nat) tptp.product_prod_int_int)
% 5.91/6.25 (declare-fun tptp.nth_Pr8617346907841251940nt_nat (tptp.list_P8198026277950538467nt_nat tptp.nat) tptp.product_prod_int_nat)
% 5.91/6.25 (declare-fun tptp.nth_Pr3474266648193625910T_VEBT (tptp.list_P7524865323317820941T_VEBT tptp.nat) tptp.produc1531783533982839933T_VEBT)
% 5.91/6.25 (declare-fun tptp.nth_Pr3440142176431000676at_int (tptp.list_P3521021558325789923at_int tptp.nat) tptp.product_prod_nat_int)
% 5.91/6.25 (declare-fun tptp.nth_Pr7617993195940197384at_nat (tptp.list_P6011104703257516679at_nat tptp.nat) tptp.product_prod_nat_nat)
% 5.91/6.25 (declare-fun tptp.nth_Pr744662078594809490T_VEBT (tptp.list_P5647936690300460905T_VEBT tptp.nat) tptp.produc8025551001238799321T_VEBT)
% 5.91/6.25 (declare-fun tptp.nth_Pr6744343527793145070at_nat (tptp.list_P8469869581646625389at_nat tptp.nat) tptp.produc859450856879609959at_nat)
% 5.91/6.25 (declare-fun tptp.nth_Pr6837108013167703752BT_int (tptp.list_P4547456442757143711BT_int tptp.nat) tptp.produc4894624898956917775BT_int)
% 5.91/6.25 (declare-fun tptp.nth_Pr1791586995822124652BT_nat (tptp.list_P7037539587688870467BT_nat tptp.nat) tptp.produc9072475918466114483BT_nat)
% 5.91/6.25 (declare-fun tptp.nth_Pr4953567300277697838T_VEBT (tptp.list_P7413028617227757229T_VEBT tptp.nat) tptp.produc8243902056947475879T_VEBT)
% 5.91/6.25 (declare-fun tptp.nth_set_nat_rat (tptp.list_set_nat_rat tptp.nat) tptp.set_nat_rat)
% 5.91/6.25 (declare-fun tptp.nth_set_nat (tptp.list_set_nat tptp.nat) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.nth_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 5.91/6.25 (declare-fun tptp.product_int_int (tptp.list_int tptp.list_int) tptp.list_P5707943133018811711nt_int)
% 5.91/6.25 (declare-fun tptp.product_int_nat (tptp.list_int tptp.list_nat) tptp.list_P8198026277950538467nt_nat)
% 5.91/6.25 (declare-fun tptp.produc662631939642741121T_VEBT (tptp.list_int tptp.list_VEBT_VEBT) tptp.list_P7524865323317820941T_VEBT)
% 5.91/6.25 (declare-fun tptp.product_nat_int (tptp.list_nat tptp.list_int) tptp.list_P3521021558325789923at_int)
% 5.91/6.25 (declare-fun tptp.product_nat_nat (tptp.list_nat tptp.list_nat) tptp.list_P6011104703257516679at_nat)
% 5.91/6.25 (declare-fun tptp.produc7156399406898700509T_VEBT (tptp.list_nat tptp.list_VEBT_VEBT) tptp.list_P5647936690300460905T_VEBT)
% 5.91/6.25 (declare-fun tptp.produc3544356994491977349at_nat (tptp.list_P6011104703257516679at_nat tptp.list_P6011104703257516679at_nat) tptp.list_P8469869581646625389at_nat)
% 5.91/6.25 (declare-fun tptp.produc7292646706713671643BT_int (tptp.list_VEBT_VEBT tptp.list_int) tptp.list_P4547456442757143711BT_int)
% 5.91/6.25 (declare-fun tptp.produc7295137177222721919BT_nat (tptp.list_VEBT_VEBT tptp.list_nat) tptp.list_P7037539587688870467BT_nat)
% 5.91/6.25 (declare-fun tptp.produc4743750530478302277T_VEBT (tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_P7413028617227757229T_VEBT)
% 5.91/6.25 (declare-fun tptp.removeAll_o (Bool tptp.list_o) tptp.list_o)
% 5.91/6.25 (declare-fun tptp.removeAll_int (tptp.int tptp.list_int) tptp.list_int)
% 5.91/6.25 (declare-fun tptp.removeAll_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 5.91/6.25 (declare-fun tptp.remove3673390508374433037at_nat (tptp.product_prod_nat_nat tptp.list_P6011104703257516679at_nat) tptp.list_P6011104703257516679at_nat)
% 5.91/6.25 (declare-fun tptp.removeAll_real (tptp.real tptp.list_real) tptp.list_real)
% 5.91/6.25 (declare-fun tptp.remove939820145577552881at_rat (tptp.set_nat_rat tptp.list_set_nat_rat) tptp.list_set_nat_rat)
% 5.91/6.25 (declare-fun tptp.removeAll_set_nat (tptp.set_nat tptp.list_set_nat) tptp.list_set_nat)
% 5.91/6.25 (declare-fun tptp.removeAll_VEBT_VEBT (tptp.vEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 5.91/6.25 (declare-fun tptp.replicate_VEBT_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 5.91/6.25 (declare-fun tptp.rotate1_int (tptp.list_int) tptp.list_int)
% 5.91/6.25 (declare-fun tptp.rotate1_nat (tptp.list_nat) tptp.list_nat)
% 5.91/6.25 (declare-fun tptp.rotate1_VEBT_VEBT (tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 5.91/6.25 (declare-fun tptp.sorted_wrt_int ((-> tptp.int tptp.int Bool) tptp.list_int) Bool)
% 5.91/6.25 (declare-fun tptp.sorted_wrt_nat ((-> tptp.nat tptp.nat Bool) tptp.list_nat) Bool)
% 5.91/6.25 (declare-fun tptp.take_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 5.91/6.25 (declare-fun tptp.take_VEBT_VEBT (tptp.nat tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 5.91/6.25 (declare-fun tptp.upt (tptp.nat tptp.nat) tptp.list_nat)
% 5.91/6.25 (declare-fun tptp.upto (tptp.int tptp.int) tptp.list_int)
% 5.91/6.25 (declare-fun tptp.upto_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 5.91/6.25 (declare-fun tptp.zip_int_int (tptp.list_int tptp.list_int) tptp.list_P5707943133018811711nt_int)
% 5.91/6.25 (declare-fun tptp.zip_int_nat (tptp.list_int tptp.list_nat) tptp.list_P8198026277950538467nt_nat)
% 5.91/6.25 (declare-fun tptp.zip_int_VEBT_VEBT (tptp.list_int tptp.list_VEBT_VEBT) tptp.list_P7524865323317820941T_VEBT)
% 5.91/6.25 (declare-fun tptp.zip_nat_int (tptp.list_nat tptp.list_int) tptp.list_P3521021558325789923at_int)
% 5.91/6.25 (declare-fun tptp.zip_nat_nat (tptp.list_nat tptp.list_nat) tptp.list_P6011104703257516679at_nat)
% 5.91/6.25 (declare-fun tptp.zip_nat_VEBT_VEBT (tptp.list_nat tptp.list_VEBT_VEBT) tptp.list_P5647936690300460905T_VEBT)
% 5.91/6.25 (declare-fun tptp.zip_Pr4664179122662387191at_nat (tptp.list_P6011104703257516679at_nat tptp.list_P6011104703257516679at_nat) tptp.list_P8469869581646625389at_nat)
% 5.91/6.25 (declare-fun tptp.zip_VEBT_VEBT_int (tptp.list_VEBT_VEBT tptp.list_int) tptp.list_P4547456442757143711BT_int)
% 5.91/6.25 (declare-fun tptp.zip_VEBT_VEBT_nat (tptp.list_VEBT_VEBT tptp.list_nat) tptp.list_P7037539587688870467BT_nat)
% 5.91/6.25 (declare-fun tptp.zip_VE537291747668921783T_VEBT (tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_P7413028617227757229T_VEBT)
% 5.91/6.25 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.compow_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.case_nat_o (Bool (-> tptp.nat Bool) tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.case_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.pred (tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.semiri4939895301339042750nteger (tptp.nat) tptp.code_integer)
% 5.91/6.25 (declare-fun tptp.semiri8010041392384452111omplex (tptp.nat) tptp.complex)
% 5.91/6.25 (declare-fun tptp.semiri4216267220026989637d_enat (tptp.nat) tptp.extended_enat)
% 5.91/6.25 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 5.91/6.25 (declare-fun tptp.semiri1316708129612266289at_nat (tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.semiri681578069525770553at_rat (tptp.nat) tptp.rat)
% 5.91/6.25 (declare-fun tptp.semiri5074537144036343181t_real (tptp.nat) tptp.real)
% 5.91/6.25 (declare-fun tptp.size_size_list_o (tptp.list_o) tptp.nat)
% 5.91/6.25 (declare-fun tptp.size_s3451745648224563538omplex (tptp.list_complex) tptp.nat)
% 5.91/6.25 (declare-fun tptp.size_s3941691890525107288d_enat (tptp.list_Extended_enat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.size_size_list_int (tptp.list_int) tptp.nat)
% 5.91/6.25 (declare-fun tptp.size_s3023201423986296836st_nat (tptp.list_list_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.size_s8217280938318005548T_VEBT (tptp.list_list_VEBT_VEBT) tptp.nat)
% 5.91/6.25 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.size_size_list_num (tptp.list_num) tptp.nat)
% 5.91/6.25 (declare-fun tptp.size_s5460976970255530739at_nat (tptp.list_P6011104703257516679at_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.size_s3959913991096427681at_rat (tptp.list_set_nat_rat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.size_s3254054031482475050et_nat (tptp.list_set_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.size_s6755466524823107622T_VEBT (tptp.list_VEBT_VEBT) tptp.nat)
% 5.91/6.25 (declare-fun tptp.size_size_num (tptp.num) tptp.nat)
% 5.91/6.25 (declare-fun tptp.size_size_option_nat (tptp.option_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.size_size_option_num (tptp.option_num) tptp.nat)
% 5.91/6.25 (declare-fun tptp.size_s170228958280169651at_nat (tptp.option4927543243414619207at_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.size_size_char (tptp.char) tptp.nat)
% 5.91/6.25 (declare-fun tptp.size_size_VEBT_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 5.91/6.25 (declare-fun tptp.nat_list_decode (tptp.nat) tptp.list_nat)
% 5.91/6.25 (declare-fun tptp.nat_list_decode_rel (tptp.nat tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.nat_list_encode (tptp.list_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.nat_list_encode_rel (tptp.list_nat tptp.list_nat) Bool)
% 5.91/6.25 (declare-fun tptp.nat_prod_decode (tptp.nat) tptp.product_prod_nat_nat)
% 5.91/6.25 (declare-fun tptp.nat_prod_decode_aux (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 5.91/6.25 (declare-fun tptp.nat_pr5047031295181774490ux_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 5.91/6.25 (declare-fun tptp.nat_prod_encode (tptp.product_prod_nat_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.nat_set_decode (tptp.nat) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.nat_set_encode (tptp.set_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.root (tptp.nat tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.sqrt (tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.bitM (tptp.num) tptp.num)
% 5.91/6.25 (declare-fun tptp.inc (tptp.num) tptp.num)
% 5.91/6.25 (declare-fun tptp.nat_of_num (tptp.num) tptp.nat)
% 5.91/6.25 (declare-fun tptp.neg_nu8804712462038260780nteger (tptp.code_integer) tptp.code_integer)
% 5.91/6.25 (declare-fun tptp.neg_nu7009210354673126013omplex (tptp.complex) tptp.complex)
% 5.91/6.25 (declare-fun tptp.neg_numeral_dbl_int (tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.neg_numeral_dbl_rat (tptp.rat) tptp.rat)
% 5.91/6.25 (declare-fun tptp.neg_numeral_dbl_real (tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.neg_nu7757733837767384882nteger (tptp.code_integer) tptp.code_integer)
% 5.91/6.25 (declare-fun tptp.neg_nu6511756317524482435omplex (tptp.complex) tptp.complex)
% 5.91/6.25 (declare-fun tptp.neg_nu3811975205180677377ec_int (tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.neg_nu3179335615603231917ec_rat (tptp.rat) tptp.rat)
% 5.91/6.25 (declare-fun tptp.neg_nu6075765906172075777c_real (tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.neg_nu5831290666863070958nteger (tptp.code_integer) tptp.code_integer)
% 5.91/6.25 (declare-fun tptp.neg_nu8557863876264182079omplex (tptp.complex) tptp.complex)
% 5.91/6.25 (declare-fun tptp.neg_nu5851722552734809277nc_int (tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.neg_nu5219082963157363817nc_rat (tptp.rat) tptp.rat)
% 5.91/6.25 (declare-fun tptp.neg_nu8295874005876285629c_real (tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 5.91/6.25 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 5.91/6.25 (declare-fun tptp.one () tptp.num)
% 5.91/6.25 (declare-fun tptp.size_num (tptp.num) tptp.nat)
% 5.91/6.25 (declare-fun tptp.num_of_nat (tptp.nat) tptp.num)
% 5.91/6.25 (declare-fun tptp.numera6620942414471956472nteger (tptp.num) tptp.code_integer)
% 5.91/6.25 (declare-fun tptp.numera6690914467698888265omplex (tptp.num) tptp.complex)
% 5.91/6.25 (declare-fun tptp.numera1916890842035813515d_enat (tptp.num) tptp.extended_enat)
% 5.91/6.25 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 5.91/6.25 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 5.91/6.25 (declare-fun tptp.numeral_numeral_rat (tptp.num) tptp.rat)
% 5.91/6.25 (declare-fun tptp.numeral_numeral_real (tptp.num) tptp.real)
% 5.91/6.25 (declare-fun tptp.pow (tptp.num tptp.num) tptp.num)
% 5.91/6.25 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 5.91/6.25 (declare-fun tptp.sqr (tptp.num) tptp.num)
% 5.91/6.25 (declare-fun tptp.none_nat () tptp.option_nat)
% 5.91/6.25 (declare-fun tptp.none_num () tptp.option_num)
% 5.91/6.25 (declare-fun tptp.none_P5556105721700978146at_nat () tptp.option4927543243414619207at_nat)
% 5.91/6.25 (declare-fun tptp.some_int (tptp.int) tptp.option_int)
% 5.91/6.25 (declare-fun tptp.some_nat (tptp.nat) tptp.option_nat)
% 5.91/6.25 (declare-fun tptp.some_num (tptp.num) tptp.option_num)
% 5.91/6.25 (declare-fun tptp.some_P7363390416028606310at_nat (tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat)
% 5.91/6.25 (declare-fun tptp.some_VEBT_VEBT (tptp.vEBT_VEBT) tptp.option_VEBT_VEBT)
% 5.91/6.25 (declare-fun tptp.case_o184042715313410164at_nat (Bool (-> tptp.product_prod_nat_nat Bool) tptp.option4927543243414619207at_nat) Bool)
% 5.91/6.25 (declare-fun tptp.size_option_nat ((-> tptp.nat tptp.nat) tptp.option_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.size_option_num ((-> tptp.num tptp.nat) tptp.option_num) tptp.nat)
% 5.91/6.25 (declare-fun tptp.size_o8335143837870341156at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.option4927543243414619207at_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.the_nat (tptp.option_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.order_underS_nat (tptp.set_Pr1261947904930325089at_nat tptp.nat) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.order_2888998067076097458on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 5.91/6.25 (declare-fun tptp.bot_bot_nat_rat_o ((-> tptp.nat tptp.rat)) Bool)
% 5.91/6.25 (declare-fun tptp.bot_bot_o_o (Bool) Bool)
% 5.91/6.25 (declare-fun tptp.bot_bot_int_int_o (tptp.int tptp.int) Bool)
% 5.91/6.25 (declare-fun tptp.bot_bot_int_o (tptp.int) Bool)
% 5.91/6.25 (declare-fun tptp.bot_bot_nat_nat_o (tptp.nat tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.bot_bot_nat_o (tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.bot_bo4898103413517107610_nat_o (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 5.91/6.25 (declare-fun tptp.bot_bot_real_o (tptp.real) Bool)
% 5.91/6.25 (declare-fun tptp.bot_bo3445895781125589758_rat_o (tptp.set_nat_rat) Bool)
% 5.91/6.25 (declare-fun tptp.bot_bot_set_nat_o (tptp.set_nat) Bool)
% 5.91/6.25 (declare-fun tptp.bot_bo394778441745866138_nat_o (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 5.91/6.25 (declare-fun tptp.bot_bo3364206721330744218_nat_o (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) Bool)
% 5.91/6.25 (declare-fun tptp.bot_bo4199563552545308370d_enat () tptp.extended_enat)
% 5.91/6.25 (declare-fun tptp.bot_bot_filter_nat () tptp.filter_nat)
% 5.91/6.25 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 5.91/6.25 (declare-fun tptp.bot_bot_set_nat_rat () tptp.set_nat_rat)
% 5.91/6.25 (declare-fun tptp.bot_bot_set_o () tptp.set_o)
% 5.91/6.25 (declare-fun tptp.bot_bot_set_complex () tptp.set_complex)
% 5.91/6.25 (declare-fun tptp.bot_bo7653980558646680370d_enat () tptp.set_Extended_enat)
% 5.91/6.25 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 5.91/6.25 (declare-fun tptp.bot_bot_set_list_nat () tptp.set_list_nat)
% 5.91/6.25 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.bot_bot_set_num () tptp.set_num)
% 5.91/6.25 (declare-fun tptp.bot_bo1796632182523588997nt_int () tptp.set_Pr958786334691620121nt_int)
% 5.91/6.25 (declare-fun tptp.bot_bo2099793752762293965at_nat () tptp.set_Pr1261947904930325089at_nat)
% 5.91/6.25 (declare-fun tptp.bot_bo5327735625951526323at_nat () tptp.set_Pr8693737435421807431at_nat)
% 5.91/6.25 (declare-fun tptp.bot_bo228742789529271731at_nat () tptp.set_Pr4329608150637261639at_nat)
% 5.91/6.25 (declare-fun tptp.bot_bo4948859079157340979at_nat () tptp.set_Pr7459493094073627847at_nat)
% 5.91/6.25 (declare-fun tptp.bot_bot_set_rat () tptp.set_rat)
% 5.91/6.25 (declare-fun tptp.bot_bot_set_real () tptp.set_real)
% 5.91/6.25 (declare-fun tptp.bot_bo6797373522285170759at_rat () tptp.set_set_nat_rat)
% 5.91/6.25 (declare-fun tptp.bot_bot_set_set_int () tptp.set_set_int)
% 5.91/6.25 (declare-fun tptp.bot_bot_set_set_nat () tptp.set_set_nat)
% 5.91/6.25 (declare-fun tptp.bot_bo8194388402131092736T_VEBT () tptp.set_VEBT_VEBT)
% 5.91/6.25 (declare-fun tptp.ord_Le1955565732374568822d_enat ((-> tptp.extended_enat Bool)) tptp.extended_enat)
% 5.91/6.25 (declare-fun tptp.ord_Least_nat ((-> tptp.nat Bool)) tptp.nat)
% 5.91/6.25 (declare-fun tptp.ord_Least_real ((-> tptp.real Bool)) tptp.real)
% 5.91/6.25 (declare-fun tptp.ord_less_o_o ((-> Bool Bool) (-> Bool Bool)) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le6823063569548456766_rat_o ((-> tptp.set_nat_rat Bool) (-> tptp.set_nat_rat Bool)) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_set_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool)) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_o (Bool Bool) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le6747313008572928689nteger (tptp.code_integer tptp.code_integer) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le72135733267957522d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_num (tptp.num tptp.num) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_rat (tptp.rat tptp.rat) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_set_o (tptp.set_o tptp.set_o) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_set_complex (tptp.set_complex tptp.set_complex) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le2529575680413868914d_enat (tptp.set_Extended_enat tptp.set_Extended_enat) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le1190675801316882794st_nat (tptp.set_list_nat tptp.set_list_nat) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_set_num (tptp.set_num tptp.set_num) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le7866589430770878221at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_set_real (tptp.set_real tptp.set_real) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le1311537459589289991at_rat (tptp.set_set_nat_rat tptp.set_set_nat_rat) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_set_set_int (tptp.set_set_int tptp.set_set_int) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_set_set_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_eq_o_o ((-> Bool Bool) (-> Bool Bool)) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le6741204236512500942_int_o ((-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool)) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_eq_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le6558929396352911974_nat_o ((-> tptp.list_nat tptp.list_nat Bool) (-> tptp.list_nat tptp.list_nat Bool)) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le1520216061033275535_nat_o ((-> tptp.list_nat Bool) (-> tptp.list_nat Bool)) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le2646555220125990790_nat_o ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_eq_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 5.91/6.25 (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)
% 5.91/6.25 (declare-fun tptp.ord_le8369615600986905444_int_o ((-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool)) Bool)
% 5.91/6.25 (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)
% 5.91/6.25 (declare-fun tptp.ord_le704812498762024988_nat_o ((-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool)) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le1077754993875142464_nat_o ((-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool) (-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool)) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le7812727212727832188_nat_o ((-> tptp.produc9072475918466114483BT_nat Bool) (-> tptp.produc9072475918466114483BT_nat Bool)) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le4100815579384348210_rat_o ((-> tptp.set_nat_rat Bool) (-> tptp.set_nat_rat Bool)) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le3964352015994296041_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool)) Bool)
% 5.91/6.25 (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)
% 5.91/6.25 (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)
% 5.91/6.25 (declare-fun tptp.ord_less_eq_o (Bool Bool) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le3102999989581377725nteger (tptp.code_integer tptp.code_integer) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le2932123472753598470d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le2510731241096832064er_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le4104064031414453916r_real (tptp.filter_real tptp.filter_real) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_eq_num (tptp.num tptp.num) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_eq_rat (tptp.rat tptp.rat) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le2679597024174929757at_rat (tptp.set_nat_rat tptp.set_nat_rat) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_eq_set_o (tptp.set_o tptp.set_o) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le211207098394363844omplex (tptp.set_complex tptp.set_complex) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le7203529160286727270d_enat (tptp.set_Extended_enat tptp.set_Extended_enat) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le6045566169113846134st_nat (tptp.set_list_nat tptp.set_list_nat) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_eq_set_num (tptp.set_num tptp.set_num) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le2843351958646193337nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le3146513528884898305at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le3000389064537975527at_nat (tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le1268244103169919719at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le5997549366648089703at_nat (tptp.set_Pr7459493094073627847at_nat tptp.set_Pr7459493094073627847at_nat) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_eq_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 5.91/6.25 (declare-fun tptp.ord_less_eq_set_real (tptp.set_real tptp.set_real) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le4375437777232675859at_rat (tptp.set_set_nat_rat tptp.set_set_nat_rat) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le4403425263959731960et_int (tptp.set_set_int tptp.set_set_int) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le6893508408891458716et_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 5.91/6.25 (declare-fun tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 5.91/6.25 (declare-fun tptp.ord_max_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.91/6.25 (declare-fun tptp.ord_ma741700101516333627d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 5.91/6.25 (declare-fun tptp.ord_max_int (tptp.int tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.ord_max_num (tptp.num tptp.num) tptp.num)
% 5.91/6.25 (declare-fun tptp.ord_max_rat (tptp.rat tptp.rat) tptp.rat)
% 5.91/6.25 (declare-fun tptp.ord_max_real (tptp.real tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.ord_max_set_o (tptp.set_o tptp.set_o) tptp.set_o)
% 5.91/6.25 (declare-fun tptp.ord_max_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 5.91/6.25 (declare-fun tptp.ord_max_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.ord_max_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 5.91/6.25 (declare-fun tptp.ord_min_nat (tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.order_Greatest_nat ((-> tptp.nat Bool)) tptp.nat)
% 5.91/6.25 (declare-fun tptp.order_9091379641038594480t_real ((-> tptp.nat tptp.real)) Bool)
% 5.91/6.25 (declare-fun tptp.order_mono_nat_nat ((-> tptp.nat tptp.nat)) Bool)
% 5.91/6.25 (declare-fun tptp.order_mono_nat_real ((-> tptp.nat tptp.real)) Bool)
% 5.91/6.25 (declare-fun tptp.order_5726023648592871131at_nat ((-> tptp.nat tptp.nat)) Bool)
% 5.91/6.25 (declare-fun tptp.ordering_top_nat ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.top_top_set_o () tptp.set_o)
% 5.91/6.25 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.top_to1996260823553986621t_unit () tptp.set_Product_unit)
% 5.91/6.25 (declare-fun tptp.top_top_set_real () tptp.set_real)
% 5.91/6.25 (declare-fun tptp.top_top_set_char () tptp.set_char)
% 5.91/6.25 (declare-fun tptp.power_8256067586552552935nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 5.91/6.25 (declare-fun tptp.power_power_complex (tptp.complex tptp.nat) tptp.complex)
% 5.91/6.25 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 5.91/6.25 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.power_power_rat (tptp.rat tptp.nat) tptp.rat)
% 5.91/6.25 (declare-fun tptp.power_power_real (tptp.real tptp.nat) tptp.real)
% 5.91/6.25 (declare-fun tptp.produc3209952032786966637at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc7248412053542808358at_nat) tptp.produc4471711990508489141at_nat)
% 5.91/6.25 (declare-fun tptp.produc1086072967326762835nteger (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 5.91/6.25 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 5.91/6.25 (declare-fun tptp.product_Pair_int_nat (tptp.int tptp.nat) tptp.product_prod_int_nat)
% 5.91/6.25 (declare-fun tptp.produc3329399203697025711T_VEBT (tptp.int tptp.vEBT_VEBT) tptp.produc1531783533982839933T_VEBT)
% 5.91/6.25 (declare-fun tptp.product_Pair_nat_int (tptp.nat tptp.int) tptp.product_prod_nat_int)
% 5.91/6.25 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 5.91/6.25 (declare-fun tptp.produc487386426758144856at_nat (tptp.nat tptp.product_prod_nat_nat) tptp.produc7248412053542808358at_nat)
% 5.91/6.25 (declare-fun tptp.produc599794634098209291T_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.produc8025551001238799321T_VEBT)
% 5.91/6.25 (declare-fun tptp.produc6161850002892822231at_nat (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.produc859450856879609959at_nat)
% 5.91/6.25 (declare-fun tptp.produc2922128104949294807at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.produc3843707927480180839at_nat)
% 5.91/6.25 (declare-fun tptp.produc9060074326276436823at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) tptp.produc1319942482725812455at_nat)
% 5.91/6.25 (declare-fun tptp.produc581526299967858633d_enat (tptp.vEBT_VEBT tptp.extended_enat) tptp.produc7272778201969148633d_enat)
% 5.91/6.25 (declare-fun tptp.produc736041933913180425BT_int (tptp.vEBT_VEBT tptp.int) tptp.produc4894624898956917775BT_int)
% 5.91/6.25 (declare-fun tptp.produc738532404422230701BT_nat (tptp.vEBT_VEBT tptp.nat) tptp.produc9072475918466114483BT_nat)
% 5.91/6.25 (declare-fun tptp.produc537772716801021591T_VEBT (tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.produc8243902056947475879T_VEBT)
% 5.91/6.25 (declare-fun tptp.produc457027306803732586at_nat (tptp.set_nat (-> tptp.nat tptp.set_nat)) tptp.set_Pr1261947904930325089at_nat)
% 5.91/6.25 (declare-fun tptp.produc1555791787009142072er_nat ((-> tptp.code_integer tptp.code_integer tptp.nat) tptp.produc8923325533196201883nteger) tptp.nat)
% 5.91/6.25 (declare-fun tptp.produc7336495610019696514er_num ((-> tptp.code_integer tptp.code_integer tptp.num) tptp.produc8923325533196201883nteger) tptp.num)
% 5.91/6.25 (declare-fun tptp.produc6916734918728496179nteger ((-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.91/6.25 (declare-fun tptp.produc4947309494688390418_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 5.91/6.25 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 5.91/6.25 (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)
% 5.91/6.25 (declare-fun tptp.produc6081775807080527818_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 5.91/6.25 (declare-fun tptp.produc2761476792215241774st_nat ((-> tptp.nat tptp.nat tptp.list_nat) tptp.product_prod_nat_nat) tptp.list_nat)
% 5.91/6.25 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 5.91/6.25 (declare-fun tptp.product_fst_int_int (tptp.product_prod_int_int) tptp.int)
% 5.91/6.25 (declare-fun tptp.product_fst_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.product_snd_int_int (tptp.product_prod_int_int) tptp.int)
% 5.91/6.25 (declare-fun tptp.product_snd_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.product_Abs_unit (Bool) tptp.product_unit)
% 5.91/6.25 (declare-fun tptp.product_Rep_unit (tptp.product_unit) Bool)
% 5.91/6.25 (declare-fun tptp.quot_a3129823074075660125t_real ((-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> tptp.set_nat_rat tptp.real) (-> tptp.nat tptp.rat)) tptp.real)
% 5.91/6.25 (declare-fun tptp.quot_r1730120044975580712at_rat ((-> tptp.real tptp.set_nat_rat) tptp.real tptp.nat) tptp.rat)
% 5.91/6.25 (declare-fun tptp.fract (tptp.int tptp.int) tptp.rat)
% 5.91/6.25 (declare-fun tptp.field_5140801741446780682s_real () tptp.set_real)
% 5.91/6.25 (declare-fun tptp.field_7254667332652039916t_real (tptp.rat) tptp.real)
% 5.91/6.25 (declare-fun tptp.quotient_of (tptp.rat) tptp.product_prod_int_int)
% 5.91/6.25 (declare-fun tptp.real2 ((-> tptp.nat tptp.rat)) tptp.real)
% 5.91/6.25 (declare-fun tptp.cauchy ((-> tptp.nat tptp.rat)) Bool)
% 5.91/6.25 (declare-fun tptp.cr_real ((-> tptp.nat tptp.rat) tptp.real) Bool)
% 5.91/6.25 (declare-fun tptp.pcr_real ((-> tptp.nat tptp.rat) tptp.real) Bool)
% 5.91/6.25 (declare-fun tptp.positive (tptp.real) Bool)
% 5.91/6.25 (declare-fun tptp.abs_real (tptp.set_nat_rat) tptp.real)
% 5.91/6.25 (declare-fun tptp.rep_real (tptp.real) tptp.set_nat_rat)
% 5.91/6.25 (declare-fun tptp.realrel ((-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat)) Bool)
% 5.91/6.25 (declare-fun tptp.rep_real2 (tptp.real tptp.nat) tptp.rat)
% 5.91/6.25 (declare-fun tptp.vanishes ((-> tptp.nat tptp.rat)) Bool)
% 5.91/6.25 (declare-fun tptp.real_V7139242839884736329omplex ((-> tptp.complex tptp.complex)) Bool)
% 5.91/6.25 (declare-fun tptp.real_V1022390504157884413omplex (tptp.complex) tptp.real)
% 5.91/6.25 (declare-fun tptp.real_V7735802525324610683m_real (tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.real_V4546457046886955230omplex (tptp.real) tptp.complex)
% 5.91/6.25 (declare-fun tptp.real_V1803761363581548252l_real (tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.domainp_nat_rat_real ((-> (-> tptp.nat tptp.rat) tptp.real Bool) (-> tptp.nat tptp.rat)) Bool)
% 5.91/6.25 (declare-fun tptp.field_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.id_Pro2258643101195443293at_nat () tptp.set_Pr8693737435421807431at_nat)
% 5.91/6.25 (declare-fun tptp.relcom2856161143838007533t_real ((-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> (-> tptp.nat tptp.rat) tptp.real Bool) (-> tptp.nat tptp.rat) tptp.real) Bool)
% 5.91/6.25 (declare-fun tptp.total_3592101749530773125at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr8693737435421807431at_nat) Bool)
% 5.91/6.25 (declare-fun tptp.trans_4347625901269045472at_nat (tptp.set_Pr8693737435421807431at_nat) Bool)
% 5.91/6.25 (declare-fun tptp.transp_nat_rat ((-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool)) Bool)
% 5.91/6.25 (declare-fun tptp.algebr934650988132801477me_nat (tptp.nat tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.divide6298287555418463151nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.91/6.25 (declare-fun tptp.divide1717551699836669952omplex (tptp.complex tptp.complex) tptp.complex)
% 5.91/6.25 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.divide_divide_rat (tptp.rat tptp.rat) tptp.rat)
% 5.91/6.25 (declare-fun tptp.divide_divide_real (tptp.real tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 5.91/6.25 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.modulo364778990260209775nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.91/6.25 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 5.91/6.25 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 5.91/6.25 (declare-fun tptp.suminf_complex ((-> tptp.nat tptp.complex)) tptp.complex)
% 5.91/6.25 (declare-fun tptp.suminf_int ((-> tptp.nat tptp.int)) tptp.int)
% 5.91/6.25 (declare-fun tptp.suminf_nat ((-> tptp.nat tptp.nat)) tptp.nat)
% 5.91/6.25 (declare-fun tptp.suminf_real ((-> tptp.nat tptp.real)) tptp.real)
% 5.91/6.25 (declare-fun tptp.summable_complex ((-> tptp.nat tptp.complex)) Bool)
% 5.91/6.25 (declare-fun tptp.summable_int ((-> tptp.nat tptp.int)) Bool)
% 5.91/6.25 (declare-fun tptp.summable_nat ((-> tptp.nat tptp.nat)) Bool)
% 5.91/6.25 (declare-fun tptp.summable_real ((-> tptp.nat tptp.real)) Bool)
% 5.91/6.25 (declare-fun tptp.sums_real ((-> tptp.nat tptp.real) tptp.real) Bool)
% 5.91/6.25 (declare-fun tptp.collect_nat_rat ((-> (-> tptp.nat tptp.rat) Bool)) tptp.set_nat_rat)
% 5.91/6.25 (declare-fun tptp.collect_o ((-> Bool Bool)) tptp.set_o)
% 5.91/6.25 (declare-fun tptp.collect_complex ((-> tptp.complex Bool)) tptp.set_complex)
% 5.91/6.25 (declare-fun tptp.collec4429806609662206161d_enat ((-> tptp.extended_enat Bool)) tptp.set_Extended_enat)
% 5.91/6.25 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 5.91/6.25 (declare-fun tptp.collect_list_complex ((-> tptp.list_complex Bool)) tptp.set_list_complex)
% 5.91/6.25 (declare-fun tptp.collec8433460942617342167d_enat ((-> tptp.list_Extended_enat Bool)) tptp.set_li5464603477888414924d_enat)
% 5.91/6.25 (declare-fun tptp.collect_list_int ((-> tptp.list_int Bool)) tptp.set_list_int)
% 5.91/6.25 (declare-fun tptp.collec5989764272469232197st_nat ((-> tptp.list_list_nat Bool)) tptp.set_list_list_nat)
% 5.91/6.25 (declare-fun tptp.collect_list_nat ((-> tptp.list_nat Bool)) tptp.set_list_nat)
% 5.91/6.25 (declare-fun tptp.collec3343600615725829874at_nat ((-> tptp.list_P6011104703257516679at_nat Bool)) tptp.set_li5450038453877631591at_nat)
% 5.91/6.25 (declare-fun tptp.collect_list_set_nat ((-> tptp.list_set_nat Bool)) tptp.set_list_set_nat)
% 5.91/6.25 (declare-fun tptp.collec5608196760682091941T_VEBT ((-> tptp.list_VEBT_VEBT Bool)) tptp.set_list_VEBT_VEBT)
% 5.91/6.25 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.collec213857154873943460nt_int ((-> tptp.product_prod_int_int Bool)) tptp.set_Pr958786334691620121nt_int)
% 5.91/6.25 (declare-fun tptp.collec3392354462482085612at_nat ((-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1261947904930325089at_nat)
% 5.91/6.25 (declare-fun tptp.collect_rat ((-> tptp.rat Bool)) tptp.set_rat)
% 5.91/6.25 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real)
% 5.91/6.25 (declare-fun tptp.collect_set_nat_rat ((-> tptp.set_nat_rat Bool)) tptp.set_set_nat_rat)
% 5.91/6.25 (declare-fun tptp.collect_set_complex ((-> tptp.set_complex Bool)) tptp.set_set_complex)
% 5.91/6.25 (declare-fun tptp.collec2260605976452661553d_enat ((-> tptp.set_Extended_enat Bool)) tptp.set_se7270636423289371942d_enat)
% 5.91/6.25 (declare-fun tptp.collect_set_int ((-> tptp.set_int Bool)) tptp.set_set_int)
% 5.91/6.25 (declare-fun tptp.collect_set_list_nat ((-> tptp.set_list_nat Bool)) tptp.set_set_list_nat)
% 5.91/6.25 (declare-fun tptp.collect_set_nat ((-> tptp.set_nat Bool)) tptp.set_set_nat)
% 5.91/6.25 (declare-fun tptp.collec5514110066124741708at_nat ((-> tptp.set_Pr1261947904930325089at_nat Bool)) tptp.set_se7855581050983116737at_nat)
% 5.91/6.25 (declare-fun tptp.collect_set_set_nat ((-> tptp.set_set_nat Bool)) tptp.set_set_set_nat)
% 5.91/6.25 (declare-fun tptp.pow_nat (tptp.set_nat) tptp.set_set_nat)
% 5.91/6.25 (declare-fun tptp.image_80655429650038917d_enat ((-> tptp.extended_enat tptp.extended_enat) tptp.set_Extended_enat) tptp.set_Extended_enat)
% 5.91/6.25 (declare-fun tptp.image_int_int ((-> tptp.int tptp.int) tptp.set_int) tptp.set_int)
% 5.91/6.25 (declare-fun tptp.image_int_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.image_nat_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.set_int)
% 5.91/6.25 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.image_nat_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.set_real)
% 5.91/6.25 (declare-fun tptp.image_nat_set_nat ((-> tptp.nat tptp.set_nat) tptp.set_nat) tptp.set_set_nat)
% 5.91/6.25 (declare-fun tptp.image_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) tptp.set_char)
% 5.91/6.25 (declare-fun tptp.image_real_real ((-> tptp.real tptp.real) tptp.set_real) tptp.set_real)
% 5.91/6.25 (declare-fun tptp.image_char_nat ((-> tptp.char tptp.nat) tptp.set_char) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.insert_nat_rat ((-> tptp.nat tptp.rat) tptp.set_nat_rat) tptp.set_nat_rat)
% 5.91/6.25 (declare-fun tptp.insert_o (Bool tptp.set_o) tptp.set_o)
% 5.91/6.25 (declare-fun tptp.insert_complex (tptp.complex tptp.set_complex) tptp.set_complex)
% 5.91/6.25 (declare-fun tptp.insert_Extended_enat (tptp.extended_enat tptp.set_Extended_enat) tptp.set_Extended_enat)
% 5.91/6.25 (declare-fun tptp.insert_int (tptp.int tptp.set_int) tptp.set_int)
% 5.91/6.25 (declare-fun tptp.insert_list_nat (tptp.list_nat tptp.set_list_nat) tptp.set_list_nat)
% 5.91/6.25 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.insert_num (tptp.num tptp.set_num) tptp.set_num)
% 5.91/6.25 (declare-fun tptp.insert8211810215607154385at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 5.91/6.25 (declare-fun tptp.insert9069300056098147895at_nat (tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4329608150637261639at_nat)
% 5.91/6.25 (declare-fun tptp.insert_rat (tptp.rat tptp.set_rat) tptp.set_rat)
% 5.91/6.25 (declare-fun tptp.insert_real (tptp.real tptp.set_real) tptp.set_real)
% 5.91/6.25 (declare-fun tptp.insert_set_nat_rat (tptp.set_nat_rat tptp.set_set_nat_rat) tptp.set_set_nat_rat)
% 5.91/6.25 (declare-fun tptp.insert_set_nat (tptp.set_nat tptp.set_set_nat) tptp.set_set_nat)
% 5.91/6.25 (declare-fun tptp.insert_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 5.91/6.25 (declare-fun tptp.is_empty_o (tptp.set_o) Bool)
% 5.91/6.25 (declare-fun tptp.is_empty_int (tptp.set_int) Bool)
% 5.91/6.25 (declare-fun tptp.is_empty_nat (tptp.set_nat) Bool)
% 5.91/6.25 (declare-fun tptp.is_empty_real (tptp.set_real) Bool)
% 5.91/6.25 (declare-fun tptp.is_singleton_o (tptp.set_o) Bool)
% 5.91/6.25 (declare-fun tptp.is_singleton_complex (tptp.set_complex) Bool)
% 5.91/6.25 (declare-fun tptp.is_singleton_int (tptp.set_int) Bool)
% 5.91/6.25 (declare-fun tptp.is_sin2641923865335537900st_nat (tptp.set_list_nat) Bool)
% 5.91/6.25 (declare-fun tptp.is_singleton_nat (tptp.set_nat) Bool)
% 5.91/6.25 (declare-fun tptp.is_sin2850979758926227957at_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 5.91/6.25 (declare-fun tptp.is_singleton_real (tptp.set_real) Bool)
% 5.91/6.25 (declare-fun tptp.is_sin2571591796506819849at_rat (tptp.set_set_nat_rat) Bool)
% 5.91/6.25 (declare-fun tptp.is_singleton_set_nat (tptp.set_set_nat) Bool)
% 5.91/6.25 (declare-fun tptp.remove_o (Bool tptp.set_o) tptp.set_o)
% 5.91/6.25 (declare-fun tptp.remove_int (tptp.int tptp.set_int) tptp.set_int)
% 5.91/6.25 (declare-fun tptp.remove_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.remove6466555014256735590at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 5.91/6.25 (declare-fun tptp.remove_real (tptp.real tptp.set_real) tptp.set_real)
% 5.91/6.25 (declare-fun tptp.remove_set_nat_rat (tptp.set_nat_rat tptp.set_set_nat_rat) tptp.set_set_nat_rat)
% 5.91/6.25 (declare-fun tptp.remove_set_nat (tptp.set_nat tptp.set_set_nat) tptp.set_set_nat)
% 5.91/6.25 (declare-fun tptp.the_elem_o (tptp.set_o) Bool)
% 5.91/6.25 (declare-fun tptp.the_elem_int (tptp.set_int) tptp.int)
% 5.91/6.25 (declare-fun tptp.the_elem_nat (tptp.set_nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.the_el2281957884133575798at_nat (tptp.set_Pr1261947904930325089at_nat) tptp.product_prod_nat_nat)
% 5.91/6.25 (declare-fun tptp.the_elem_real (tptp.set_real) tptp.real)
% 5.91/6.25 (declare-fun tptp.vimage_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.set_fo1517530859248394432omplex ((-> tptp.nat tptp.complex tptp.complex) tptp.nat tptp.nat tptp.complex) tptp.complex)
% 5.91/6.25 (declare-fun tptp.set_fo2581907887559384638at_int ((-> tptp.nat tptp.int tptp.int) tptp.nat tptp.nat tptp.int) tptp.int)
% 5.91/6.25 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.set_fo1949268297981939178at_rat ((-> tptp.nat tptp.rat tptp.rat) tptp.nat tptp.nat tptp.rat) tptp.rat)
% 5.91/6.25 (declare-fun tptp.set_fo3111899725591712190t_real ((-> tptp.nat tptp.real tptp.real) tptp.nat tptp.nat tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.set_or8904488021354931149Most_o (Bool Bool) tptp.set_o)
% 5.91/6.25 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 5.91/6.25 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.set_or7049704709247886629st_num (tptp.num tptp.num) tptp.set_num)
% 5.91/6.25 (declare-fun tptp.set_or633870826150836451st_rat (tptp.rat tptp.rat) tptp.set_rat)
% 5.91/6.25 (declare-fun tptp.set_or1222579329274155063t_real (tptp.real tptp.real) tptp.set_real)
% 5.91/6.25 (declare-fun tptp.set_or5795412311047298440at_rat (tptp.set_nat_rat tptp.set_nat_rat) tptp.set_set_nat_rat)
% 5.91/6.25 (declare-fun tptp.set_or370866239135849197et_int (tptp.set_int tptp.set_int) tptp.set_set_int)
% 5.91/6.25 (declare-fun tptp.set_or4548717258645045905et_nat (tptp.set_nat tptp.set_nat) tptp.set_set_nat)
% 5.91/6.25 (declare-fun tptp.set_or4662586982721622107an_int (tptp.int tptp.int) tptp.set_int)
% 5.91/6.25 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.set_ord_atLeast_nat (tptp.nat) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.set_ord_atLeast_real (tptp.real) tptp.set_real)
% 5.91/6.25 (declare-fun tptp.set_ord_atMost_int (tptp.int) tptp.set_int)
% 5.91/6.25 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.set_or6656581121297822940st_int (tptp.int tptp.int) tptp.set_int)
% 5.91/6.25 (declare-fun tptp.set_or6659071591806873216st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.set_or5832277885323065728an_int (tptp.int tptp.int) tptp.set_int)
% 5.91/6.25 (declare-fun tptp.set_or5834768355832116004an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.set_or1633881224788618240n_real (tptp.real tptp.real) tptp.set_real)
% 5.91/6.25 (declare-fun tptp.set_or1210151606488870762an_nat (tptp.nat) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.set_ord_lessThan_int (tptp.int) tptp.set_int)
% 5.91/6.25 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.abort_real (tptp.literal (-> tptp.product_unit tptp.real)) tptp.real)
% 5.91/6.25 (declare-fun tptp.literal2 (Bool Bool Bool Bool Bool Bool Bool tptp.literal) tptp.literal)
% 5.91/6.25 (declare-fun tptp.char2 (Bool Bool Bool Bool Bool Bool Bool Bool) tptp.char)
% 5.91/6.25 (declare-fun tptp.size_char (tptp.char) tptp.nat)
% 5.91/6.25 (declare-fun tptp.comm_s629917340098488124ar_nat (tptp.char) tptp.nat)
% 5.91/6.25 (declare-fun tptp.unique3096191561947761185of_nat (tptp.nat) tptp.char)
% 5.91/6.25 (declare-fun tptp.topolo4422821103128117721l_real (tptp.filter_real (-> tptp.real tptp.real)) Bool)
% 5.91/6.25 (declare-fun tptp.topolo5044208981011980120l_real (tptp.set_real (-> tptp.real tptp.real)) Bool)
% 5.91/6.25 (declare-fun tptp.topolo6980174941875973593q_real ((-> tptp.nat tptp.real)) Bool)
% 5.91/6.25 (declare-fun tptp.topolo2177554685111907308n_real (tptp.real tptp.set_real) tptp.filter_real)
% 5.91/6.25 (declare-fun tptp.topolo7531315842566124627t_real ((-> tptp.nat tptp.real)) Bool)
% 5.91/6.25 (declare-fun tptp.topolo2815343760600316023s_real (tptp.real) tptp.filter_real)
% 5.91/6.25 (declare-fun tptp.topolo6517432010174082258omplex ((-> tptp.nat tptp.complex)) Bool)
% 5.91/6.25 (declare-fun tptp.topolo4055970368930404560y_real ((-> tptp.nat tptp.real)) Bool)
% 5.91/6.25 (declare-fun tptp.arccos (tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.arcosh_real (tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.arcsin (tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.arctan (tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.arsinh_real (tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.artanh_real (tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.cos_real (tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.cos_coeff (tptp.nat) tptp.real)
% 5.91/6.25 (declare-fun tptp.cosh_real (tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.exp_complex (tptp.complex) tptp.complex)
% 5.91/6.25 (declare-fun tptp.exp_real (tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.ln_ln_real (tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.log (tptp.real tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.pi () tptp.real)
% 5.91/6.25 (declare-fun tptp.powr_real (tptp.real tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.powr_real2 (tptp.real tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.sin_real (tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.sin_coeff (tptp.nat) tptp.real)
% 5.91/6.25 (declare-fun tptp.sinh_complex (tptp.complex) tptp.complex)
% 5.91/6.25 (declare-fun tptp.sinh_real (tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.tan_real (tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.tanh_real (tptp.real) tptp.real)
% 5.91/6.25 (declare-fun tptp.left_t2768085380646472630at_rat ((-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool)) Bool)
% 5.91/6.25 (declare-fun tptp.transi2905341329935302413cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 5.91/6.25 (declare-fun tptp.transi6264000038957366511cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 5.91/6.25 (declare-fun tptp.type_d6188575255521822967unit_o ((-> tptp.product_unit Bool) (-> Bool tptp.product_unit) tptp.set_o) Bool)
% 5.91/6.25 (declare-fun tptp.type_d8072115097938612567at_rat ((-> tptp.real tptp.set_nat_rat) (-> tptp.set_nat_rat tptp.real) tptp.set_set_nat_rat) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_Leaf (Bool Bool) tptp.vEBT_VEBT)
% 5.91/6.25 (declare-fun tptp.vEBT_Node (tptp.option4927543243414619207at_nat tptp.nat tptp.list_VEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 5.91/6.25 (declare-fun tptp.vEBT_size_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 5.91/6.25 (declare-fun tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_VEBT tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_VEBT_elim_dead (tptp.vEBT_VEBT tptp.extended_enat) tptp.vEBT_VEBT)
% 5.91/6.25 (declare-fun tptp.vEBT_V312737461966249ad_rel (tptp.produc7272778201969148633d_enat tptp.produc7272778201969148633d_enat) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_VEBT_high (tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.vEBT_V5917875025757280293ildren (tptp.nat tptp.list_VEBT_VEBT tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_VEBT_low (tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.vEBT_VEBT_membermima (tptp.vEBT_VEBT tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_V4351362008482014158ma_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_V5719532721284313246member (tptp.vEBT_VEBT tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_V5765760719290551771er_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_VEBT_valid (tptp.vEBT_VEBT tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_VEBT_valid_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_invar_vebt (tptp.vEBT_VEBT tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.vEBT_vebt_buildup (tptp.nat) tptp.vEBT_VEBT)
% 5.91/6.25 (declare-fun tptp.vEBT_v4011308405150292612up_rel (tptp.nat tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_vebt_delete (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 5.91/6.25 (declare-fun tptp.vEBT_vebt_delete_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_vebt_insert (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 5.91/6.25 (declare-fun tptp.vEBT_vebt_insert_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_VEBT_bit_concat (tptp.nat tptp.nat tptp.nat) tptp.nat)
% 5.91/6.25 (declare-fun tptp.vEBT_VEBT_minNull (tptp.vEBT_VEBT) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_V6963167321098673237ll_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_VEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 5.91/6.25 (declare-fun tptp.vEBT_vebt_member (tptp.vEBT_VEBT tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_vebt_member_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_VEBT_add (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 5.91/6.25 (declare-fun tptp.vEBT_VEBT_greater (tptp.option_nat tptp.option_nat) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_VEBT_less (tptp.option_nat tptp.option_nat) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_VEBT_lesseq (tptp.option_nat tptp.option_nat) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_VEBT_max_in_set (tptp.set_nat tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_VEBT_min_in_set (tptp.set_nat tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_VEBT_mul (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 5.91/6.25 (declare-fun tptp.vEBT_V4262088993061758097ft_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.option_nat tptp.option_nat) tptp.option_nat)
% 5.91/6.25 (declare-fun tptp.vEBT_VEBT_power (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 5.91/6.25 (declare-fun tptp.vEBT_vebt_maxt (tptp.vEBT_VEBT) tptp.option_nat)
% 5.91/6.25 (declare-fun tptp.vEBT_vebt_maxt_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_vebt_mint (tptp.vEBT_VEBT) tptp.option_nat)
% 5.91/6.25 (declare-fun tptp.vEBT_vebt_mint_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_is_pred_in_set (tptp.set_nat tptp.nat tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_vebt_pred (tptp.vEBT_VEBT tptp.nat) tptp.option_nat)
% 5.91/6.25 (declare-fun tptp.vEBT_vebt_pred_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_is_succ_in_set (tptp.set_nat tptp.nat tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.vEBT_vebt_succ (tptp.vEBT_VEBT tptp.nat) tptp.option_nat)
% 5.91/6.25 (declare-fun tptp.vEBT_vebt_succ_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 5.91/6.25 (declare-fun tptp.accp_list_nat ((-> tptp.list_nat tptp.list_nat Bool) tptp.list_nat) Bool)
% 5.91/6.25 (declare-fun tptp.accp_nat ((-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 5.91/6.25 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 5.91/6.25 (declare-fun tptp.accp_P4275260045618599050at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 5.91/6.25 (declare-fun tptp.accp_P6183159247885693666d_enat ((-> tptp.produc7272778201969148633d_enat tptp.produc7272778201969148633d_enat Bool) tptp.produc7272778201969148633d_enat) Bool)
% 5.91/6.25 (declare-fun tptp.accp_P2887432264394892906BT_nat ((-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool) tptp.produc9072475918466114483BT_nat) Bool)
% 5.91/6.25 (declare-fun tptp.accp_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT Bool) tptp.vEBT_VEBT) Bool)
% 5.91/6.25 (declare-fun tptp.less_than () tptp.set_Pr1261947904930325089at_nat)
% 5.91/6.25 (declare-fun tptp.lex_prod_nat_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr8693737435421807431at_nat)
% 5.91/6.25 (declare-fun tptp.max_ex8135407076693332796at_nat (tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr4329608150637261639at_nat)
% 5.91/6.25 (declare-fun tptp.min_ex6901939911449802026at_nat (tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr4329608150637261639at_nat)
% 5.91/6.25 (declare-fun tptp.pred_nat () tptp.set_Pr1261947904930325089at_nat)
% 5.91/6.25 (declare-fun tptp.wf_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 5.91/6.25 (declare-fun tptp.wf_Pro7803398752247294826at_nat (tptp.set_Pr8693737435421807431at_nat) Bool)
% 5.91/6.25 (declare-fun tptp.fChoice_real ((-> tptp.real Bool)) tptp.real)
% 5.91/6.25 (declare-fun tptp.member_nat_rat ((-> tptp.nat tptp.rat) tptp.set_nat_rat) Bool)
% 5.91/6.25 (declare-fun tptp.member_o (Bool tptp.set_o) Bool)
% 5.91/6.25 (declare-fun tptp.member_complex (tptp.complex tptp.set_complex) Bool)
% 5.91/6.25 (declare-fun tptp.member_Extended_enat (tptp.extended_enat tptp.set_Extended_enat) Bool)
% 5.91/6.25 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 5.91/6.25 (declare-fun tptp.member_list_nat (tptp.list_nat tptp.set_list_nat) Bool)
% 5.91/6.25 (declare-fun tptp.member2936631157270082147T_VEBT (tptp.list_VEBT_VEBT tptp.set_list_VEBT_VEBT) Bool)
% 5.91/6.25 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 5.91/6.25 (declare-fun tptp.member_num (tptp.num tptp.set_num) Bool)
% 5.91/6.25 (declare-fun tptp.member5262025264175285858nt_int (tptp.product_prod_int_int tptp.set_Pr958786334691620121nt_int) Bool)
% 5.91/6.25 (declare-fun tptp.member8440522571783428010at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 5.91/6.25 (declare-fun tptp.member8206827879206165904at_nat (tptp.produc859450856879609959at_nat tptp.set_Pr8693737435421807431at_nat) Bool)
% 5.91/6.25 (declare-fun tptp.member8757157785044589968at_nat (tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat) Bool)
% 5.91/6.25 (declare-fun tptp.member1466754251312161552at_nat (tptp.produc1319942482725812455at_nat tptp.set_Pr7459493094073627847at_nat) Bool)
% 5.91/6.25 (declare-fun tptp.member_rat (tptp.rat tptp.set_rat) Bool)
% 5.91/6.25 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool)
% 5.91/6.25 (declare-fun tptp.member_set_nat_rat (tptp.set_nat_rat tptp.set_set_nat_rat) Bool)
% 5.91/6.25 (declare-fun tptp.member_set_int (tptp.set_int tptp.set_set_int) Bool)
% 5.91/6.25 (declare-fun tptp.member_set_nat (tptp.set_nat tptp.set_set_nat) Bool)
% 5.91/6.25 (declare-fun tptp.member_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 5.91/6.25 (declare-fun tptp.n () tptp.nat)
% 5.91/6.25 (declare-fun tptp.t () tptp.vEBT_VEBT)
% 5.91/6.25 (declare-fun tptp.x () tptp.nat)
% 5.91/6.25 (assert (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))
% 5.91/6.25 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) D) (@ (@ tptp.vEBT_VEBT_valid T) D))))
% 5.91/6.25 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid T) D) (@ (@ tptp.vEBT_invar_vebt T) D))))
% 5.91/6.25 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_delete T) X)) Y) (and (not (= X Y)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) Y))))))
% 5.91/6.25 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 5.91/6.25 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 5.91/6.25 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary)) N) (= Deg N))))
% 5.91/6.25 (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)))))
% 5.91/6.25 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.member_nat X) (@ tptp.vEBT_set_vebt T))))))
% 5.91/6.25 (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)))))
% 5.91/6.25 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 5.91/6.25 (assert (forall ((A Bool) (B Bool)) (not (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat))))
% 5.91/6.25 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_vebt_member T) X)))))
% 5.91/6.25 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_vebt_member T) X)))))
% 5.91/6.25 (assert (forall ((Xs tptp.set_nat) (A tptp.nat)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_pred_in_set Xs) A) X_1))) (=> (@ tptp.finite_finite_nat Xs) (not (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) Xs) (@ (@ tptp.ord_less_nat X2) A))))))))
% 5.91/6.25 (assert (forall ((Xs tptp.set_nat) (A tptp.nat)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_succ_in_set Xs) A) X_1))) (=> (@ tptp.finite_finite_nat Xs) (not (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) Xs) (@ (@ tptp.ord_less_nat A) X2))))))))
% 5.91/6.25 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N)) N))))
% 5.91/6.25 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 5.91/6.25 (assert (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 5.91/6.25 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 5.91/6.25 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 5.91/6.25 (assert (forall ((A Bool) (B Bool)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat) (@ (@ tptp.vEBT_Leaf false) B))))
% 5.91/6.25 (assert (forall ((Z tptp.nat) (X tptp.nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat Z) X) (=> (@ (@ tptp.vEBT_VEBT_min_in_set A2) Z) (=> (@ tptp.finite_finite_nat A2) (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_pred_in_set A2) X) X_1)))))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Z tptp.nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat X) Z) (=> (@ (@ tptp.vEBT_VEBT_max_in_set A2) Z) (=> (@ tptp.finite_finite_nat B2) (=> (= A2 B2) (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_succ_in_set A2) X) X_1))))))))
% 5.91/6.25 (assert (forall ((X21 Bool) (X22 Bool) (Y21 Bool) (Y22 Bool)) (= (= (@ (@ tptp.vEBT_Leaf X21) X22) (@ (@ tptp.vEBT_Leaf Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 5.91/6.25 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (Y11 tptp.option4927543243414619207at_nat) (Y12 tptp.nat) (Y13 tptp.list_VEBT_VEBT) (Y14 tptp.vEBT_VEBT)) (= (= (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14) (@ (@ (@ (@ tptp.vEBT_Node Y11) Y12) Y13) Y14)) (and (= X11 Y11) (= X12 Y12) (= X13 Y13) (= X14 Y14)))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (=> (forall ((B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B3) A3) (@ P B3))) (@ P A3)))) (@ P A2)))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((A3 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (=> (forall ((B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B3) A3) (@ P B3))) (@ P A3)))) (@ P A2)))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((A3 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (forall ((B3 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex B3) A3) (@ P B3))) (@ P A3)))) (@ P A2)))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat A2) (=> (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (forall ((B3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat B3) A3) (@ P B3))) (@ P A3)))) (@ P A2)))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((A3 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (forall ((B3 tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le2529575680413868914d_enat B3) A3) (@ P B3))) (@ P A3)))) (@ P A2)))))
% 5.91/6.25 (assert (= (@ tptp.vEBT_vebt_buildup tptp.zero_zero_nat) (@ (@ tptp.vEBT_Leaf false) false)))
% 5.91/6.25 (assert (forall ((X tptp.literal)) (= (= tptp.zero_zero_literal X) (= X tptp.zero_zero_literal))))
% 5.91/6.25 (assert (forall ((X tptp.real)) (= (= tptp.zero_zero_real X) (= X tptp.zero_zero_real))))
% 5.91/6.25 (assert (forall ((X tptp.rat)) (= (= tptp.zero_zero_rat X) (= X tptp.zero_zero_rat))))
% 5.91/6.25 (assert (forall ((X tptp.nat)) (= (= tptp.zero_zero_nat X) (= X tptp.zero_zero_nat))))
% 5.91/6.25 (assert (forall ((X tptp.int)) (= (= tptp.zero_zero_int X) (= X tptp.zero_zero_int))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 5.91/6.25 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (not (@ P N2)) (exists ((M tptp.nat)) (and (@ (@ tptp.ord_less_nat M) N2) (not (@ P M)))))) (@ P N))))
% 5.91/6.25 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ P M))) (@ P N2))) (@ P N))))
% 5.91/6.25 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 5.91/6.25 (assert (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))))
% 5.91/6.25 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M2) (not (= M2 N)))))
% 5.91/6.25 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 5.91/6.25 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (not (= M2 N)) (or (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_nat N) M2)))))
% 5.91/6.25 (assert (forall ((A Bool) (P (-> Bool Bool))) (= (@ (@ tptp.member_o A) (@ tptp.collect_o P)) (@ P A))))
% 5.91/6.25 (assert (forall ((A tptp.set_nat) (P (-> tptp.set_nat Bool))) (= (@ (@ tptp.member_set_nat A) (@ tptp.collect_set_nat P)) (@ P A))))
% 5.91/6.25 (assert (forall ((A tptp.set_nat_rat) (P (-> tptp.set_nat_rat Bool))) (= (@ (@ tptp.member_set_nat_rat A) (@ tptp.collect_set_nat_rat P)) (@ P A))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))))
% 5.91/6.25 (assert (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A) (@ tptp.collect_int P)) (@ P A))))
% 5.91/6.25 (assert (forall ((A (-> tptp.nat tptp.rat)) (P (-> (-> tptp.nat tptp.rat) Bool))) (= (@ (@ tptp.member_nat_rat A) (@ tptp.collect_nat_rat P)) (@ P A))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_o)) (= (@ tptp.collect_o (lambda ((X3 Bool)) (@ (@ tptp.member_o X3) A2))) A2)))
% 5.91/6.25 (assert (forall ((A2 tptp.set_set_nat)) (= (@ tptp.collect_set_nat (lambda ((X3 tptp.set_nat)) (@ (@ tptp.member_set_nat X3) A2))) A2)))
% 5.91/6.25 (assert (forall ((A2 tptp.set_set_nat_rat)) (= (@ tptp.collect_set_nat_rat (lambda ((X3 tptp.set_nat_rat)) (@ (@ tptp.member_set_nat_rat X3) A2))) A2)))
% 5.91/6.25 (assert (forall ((A2 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) A2))) A2)))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X3 tptp.int)) (@ (@ tptp.member_int X3) A2))) A2)))
% 5.91/6.25 (assert (forall ((A2 tptp.set_nat_rat)) (= (@ tptp.collect_nat_rat (lambda ((X3 (-> tptp.nat tptp.rat))) (@ (@ tptp.member_nat_rat X3) A2))) A2)))
% 5.91/6.25 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (forall ((X4 tptp.set_nat)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_set_nat P) (@ tptp.collect_set_nat Q)))))
% 5.91/6.25 (assert (forall ((P (-> tptp.set_nat_rat Bool)) (Q (-> tptp.set_nat_rat Bool))) (=> (forall ((X4 tptp.set_nat_rat)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_set_nat_rat P) (@ tptp.collect_set_nat_rat Q)))))
% 5.91/6.25 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X4 tptp.nat)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_nat P) (@ tptp.collect_nat Q)))))
% 5.91/6.25 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_int P) (@ tptp.collect_int Q)))))
% 5.91/6.25 (assert (forall ((P (-> (-> tptp.nat tptp.rat) Bool)) (Q (-> (-> tptp.nat tptp.rat) Bool))) (=> (forall ((X4 (-> tptp.nat tptp.rat))) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_nat_rat P) (@ tptp.collect_nat_rat Q)))))
% 5.91/6.25 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= N tptp.zero_zero_nat)))))
% 5.91/6.25 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (not (= N tptp.zero_zero_nat)))))
% 5.91/6.25 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 5.91/6.25 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 5.91/6.25 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (@ P N2)) (exists ((M tptp.nat)) (and (@ (@ tptp.ord_less_nat M) N2) (not (@ P M))))))) (@ P N)))))
% 5.91/6.25 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (not (= N tptp.zero_zero_nat)))))
% 5.91/6.25 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 5.91/6.25 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 5.91/6.25 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 5.91/6.25 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 5.91/6.25 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 5.91/6.25 (assert (forall ((Y tptp.vEBT_VEBT)) (=> (forall ((X112 tptp.option4927543243414619207at_nat) (X122 tptp.nat) (X132 tptp.list_VEBT_VEBT) (X142 tptp.vEBT_VEBT)) (not (= Y (@ (@ (@ (@ tptp.vEBT_Node X112) X122) X132) X142)))) (not (forall ((X212 Bool) (X222 Bool)) (not (= Y (@ (@ tptp.vEBT_Leaf X212) X222))))))))
% 5.91/6.25 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (X21 Bool) (X22 Bool)) (not (= (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14) (@ (@ tptp.vEBT_Leaf X21) X22)))))
% 5.91/6.25 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Y) (and (@ (@ tptp.vEBT_vebt_member T) Y) (@ (@ tptp.ord_less_nat X) Y) (forall ((Z2 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z2) (@ (@ tptp.ord_less_nat X) Z2)) (@ (@ tptp.ord_less_eq_nat Y) Z2)))))))
% 5.91/6.25 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Y) (and (@ (@ tptp.vEBT_vebt_member T) Y) (@ (@ tptp.ord_less_nat Y) X) (forall ((Z2 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z2) (@ (@ tptp.ord_less_nat Z2) X)) (@ (@ tptp.ord_less_eq_nat Z2) Y)))))))
% 5.91/6.25 (assert (forall ((N tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N)) X))))
% 5.91/6.25 (assert (forall ((N tptp.nat)) (= (@ tptp.vEBT_VEBT_set_vebt (@ tptp.vEBT_vebt_buildup N)) tptp.bot_bot_set_nat)))
% 5.91/6.25 (assert (forall ((N tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N)) X))))
% 5.91/6.25 (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))))))
% 5.91/6.25 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A5 Bool) (B5 Bool)) (= T (@ (@ tptp.vEBT_Leaf A5) B5))))))
% 5.91/6.25 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= N tptp.one_one_nat) (exists ((A5 Bool) (B5 Bool)) (= T (@ (@ tptp.vEBT_Leaf A5) B5)))))))
% 5.91/6.25 (assert (= tptp.finite_finite_nat (lambda ((N3 tptp.set_nat)) (exists ((M3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N3) (@ (@ tptp.ord_less_nat X3) M3)))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S2)) (forall ((M3 tptp.nat)) (exists ((N4 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N4) (@ (@ tptp.member_nat N4) S2)))))))
% 5.91/6.25 (assert (forall ((N5 tptp.set_nat) (N tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) N5) (@ (@ tptp.ord_less_nat X4) N))) (@ tptp.finite_finite_nat N5))))
% 5.91/6.25 (assert (forall ((K tptp.nat) (S2 tptp.set_nat)) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) M4) (exists ((N6 tptp.nat)) (and (@ (@ tptp.ord_less_nat M4) N6) (@ (@ tptp.member_nat N6) S2))))) (not (@ tptp.finite_finite_nat S2)))))
% 5.91/6.25 (assert (= tptp.vEBT_VEBT_max_in_set (lambda ((Xs2 tptp.set_nat) (X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) Xs2) (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) Xs2) (@ (@ tptp.ord_less_eq_nat Y2) X3)))))))
% 5.91/6.25 (assert (= tptp.vEBT_VEBT_min_in_set (lambda ((Xs2 tptp.set_nat) (X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) Xs2) (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) Xs2) (@ (@ tptp.ord_less_eq_nat X3) Y2)))))))
% 5.91/6.25 (assert (= tptp.vEBT_V8194947554948674370ptions (lambda ((T2 tptp.vEBT_VEBT) (X3 tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T2) X3) (@ (@ tptp.vEBT_VEBT_membermima T2) X3)))))
% 5.91/6.25 (assert (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N) (=> (@ (@ tptp.vEBT_vebt_member Tree) X) (or (@ (@ tptp.vEBT_V5719532721284313246member Tree) X) (@ (@ tptp.vEBT_VEBT_membermima Tree) X))))))
% 5.91/6.25 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 5.91/6.25 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)))
% 5.91/6.25 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 5.91/6.25 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) tptp.one_one_nat) (= N tptp.zero_zero_nat))))
% 5.91/6.25 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (exists ((X4 tptp.nat)) (and (@ P X4) (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) X4)))))))))
% 5.91/6.25 (assert (forall ((X tptp.complex)) (= (= tptp.one_one_complex X) (= X tptp.one_one_complex))))
% 5.91/6.25 (assert (forall ((X tptp.real)) (= (= tptp.one_one_real X) (= X tptp.one_one_real))))
% 5.91/6.25 (assert (forall ((X tptp.rat)) (= (= tptp.one_one_rat X) (= X tptp.one_one_rat))))
% 5.91/6.25 (assert (forall ((X tptp.nat)) (= (= tptp.one_one_nat X) (= X tptp.one_one_nat))))
% 5.91/6.25 (assert (forall ((X tptp.int)) (= (= tptp.one_one_int X) (= X tptp.one_one_int))))
% 5.91/6.25 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat N) M2))))
% 5.91/6.25 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= M2 N)))))
% 5.91/6.25 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (= M2 N) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 5.91/6.25 (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))))))
% 5.91/6.25 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 5.91/6.25 (assert (forall ((P (-> tptp.nat Bool)) (X tptp.nat) (M5 tptp.nat)) (=> (@ P X) (=> (forall ((X4 tptp.nat)) (=> (@ P X4) (@ (@ tptp.ord_less_eq_nat X4) M5))) (not (forall ((M4 tptp.nat)) (=> (@ P M4) (not (forall ((X2 tptp.nat)) (=> (@ P X2) (@ (@ tptp.ord_less_eq_nat X2) M4)))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (forall ((Xa tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Xa) A2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Xa) X4) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_real)) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real Xa) X4) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_o)) (=> (@ tptp.finite_finite_o A2) (=> (not (= A2 tptp.bot_bot_set_o)) (exists ((X4 Bool)) (and (@ (@ tptp.member_o X4) A2) (forall ((Xa Bool)) (=> (@ (@ tptp.member_o Xa) A2) (=> (@ (@ tptp.ord_less_eq_o Xa) X4) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_set_int)) (=> (@ tptp.finite6197958912794628473et_int A2) (=> (not (= A2 tptp.bot_bot_set_set_int)) (exists ((X4 tptp.set_int)) (and (@ (@ tptp.member_set_int X4) A2) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_int Xa) X4) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A2) (=> (not (= A2 tptp.bot_bot_set_rat)) (exists ((X4 tptp.rat)) (and (@ (@ tptp.member_rat X4) A2) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A2) (=> (@ (@ tptp.ord_less_eq_rat Xa) X4) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_num)) (=> (@ tptp.finite_finite_num A2) (=> (not (= A2 tptp.bot_bot_set_num)) (exists ((X4 tptp.num)) (and (@ (@ tptp.member_num X4) A2) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num Xa) X4) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat Xa) X4) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int Xa) X4) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (forall ((Xa tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Xa) A2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X4) Xa) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_real)) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A2) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real X4) Xa) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_o)) (=> (@ tptp.finite_finite_o A2) (=> (not (= A2 tptp.bot_bot_set_o)) (exists ((X4 Bool)) (and (@ (@ tptp.member_o X4) A2) (forall ((Xa Bool)) (=> (@ (@ tptp.member_o Xa) A2) (=> (@ (@ tptp.ord_less_eq_o X4) Xa) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_set_int)) (=> (@ tptp.finite6197958912794628473et_int A2) (=> (not (= A2 tptp.bot_bot_set_set_int)) (exists ((X4 tptp.set_int)) (and (@ (@ tptp.member_set_int X4) A2) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_int X4) Xa) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A2) (=> (not (= A2 tptp.bot_bot_set_rat)) (exists ((X4 tptp.rat)) (and (@ (@ tptp.member_rat X4) A2) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A2) (=> (@ (@ tptp.ord_less_eq_rat X4) Xa) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_num)) (=> (@ tptp.finite_finite_num A2) (=> (not (= A2 tptp.bot_bot_set_num)) (exists ((X4 tptp.num)) (and (@ (@ tptp.member_num X4) A2) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num X4) Xa) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat X4) Xa) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int X4) Xa) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_set_nat) (R (-> tptp.set_nat tptp.set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (forall ((X4 tptp.set_nat)) (not (@ (@ R X4) X4))) (=> (forall ((X4 tptp.set_nat) (Y3 tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ R X4))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z3) (@ _let_1 Z3))))) (=> (forall ((X4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X4) A2) (exists ((Y4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat Y4) A2) (@ (@ R X4) Y4))))) (= A2 tptp.bot_bot_set_set_nat)))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_set_nat_rat) (R (-> tptp.set_nat_rat tptp.set_nat_rat Bool))) (=> (@ tptp.finite6430367030675640852at_rat A2) (=> (forall ((X4 tptp.set_nat_rat)) (not (@ (@ R X4) X4))) (=> (forall ((X4 tptp.set_nat_rat) (Y3 tptp.set_nat_rat) (Z3 tptp.set_nat_rat)) (let ((_let_1 (@ R X4))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z3) (@ _let_1 Z3))))) (=> (forall ((X4 tptp.set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat X4) A2) (exists ((Y4 tptp.set_nat_rat)) (and (@ (@ tptp.member_set_nat_rat Y4) A2) (@ (@ R X4) Y4))))) (= A2 tptp.bot_bo6797373522285170759at_rat)))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_complex) (R (-> tptp.complex tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X4 tptp.complex)) (not (@ (@ R X4) X4))) (=> (forall ((X4 tptp.complex) (Y3 tptp.complex) (Z3 tptp.complex)) (let ((_let_1 (@ R X4))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z3) (@ _let_1 Z3))))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A2) (exists ((Y4 tptp.complex)) (and (@ (@ tptp.member_complex Y4) A2) (@ (@ R X4) Y4))))) (= A2 tptp.bot_bot_set_complex)))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (R (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat A2) (=> (forall ((X4 tptp.product_prod_nat_nat)) (not (@ (@ R X4) X4))) (=> (forall ((X4 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat) (Z3 tptp.product_prod_nat_nat)) (let ((_let_1 (@ R X4))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z3) (@ _let_1 Z3))))) (=> (forall ((X4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X4) A2) (exists ((Y4 tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat Y4) A2) (@ (@ R X4) Y4))))) (= A2 tptp.bot_bo2099793752762293965at_nat)))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_Extended_enat) (R (-> tptp.extended_enat tptp.extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((X4 tptp.extended_enat)) (not (@ (@ R X4) X4))) (=> (forall ((X4 tptp.extended_enat) (Y3 tptp.extended_enat) (Z3 tptp.extended_enat)) (let ((_let_1 (@ R X4))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z3) (@ _let_1 Z3))))) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) A2) (exists ((Y4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Y4) A2) (@ (@ R X4) Y4))))) (= A2 tptp.bot_bo7653980558646680370d_enat)))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_real) (R (-> tptp.real tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X4 tptp.real)) (not (@ (@ R X4) X4))) (=> (forall ((X4 tptp.real) (Y3 tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ R X4))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z3) (@ _let_1 Z3))))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (exists ((Y4 tptp.real)) (and (@ (@ tptp.member_real Y4) A2) (@ (@ R X4) Y4))))) (= A2 tptp.bot_bot_set_real)))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_o) (R (-> Bool Bool Bool))) (=> (@ tptp.finite_finite_o A2) (=> (forall ((X4 Bool)) (not (@ (@ R X4) X4))) (=> (forall ((X4 Bool) (Y3 Bool) (Z3 Bool)) (let ((_let_1 (@ R X4))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z3) (@ _let_1 Z3))))) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A2) (exists ((Y4 Bool)) (and (@ (@ tptp.member_o Y4) A2) (@ (@ R X4) Y4))))) (= A2 tptp.bot_bot_set_o)))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X4 tptp.nat)) (not (@ (@ R X4) X4))) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ R X4))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z3) (@ _let_1 Z3))))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (exists ((Y4 tptp.nat)) (and (@ (@ tptp.member_nat Y4) A2) (@ (@ R X4) Y4))))) (= A2 tptp.bot_bot_set_nat)))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int) (R (-> tptp.int tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X4 tptp.int)) (not (@ (@ R X4) X4))) (=> (forall ((X4 tptp.int) (Y3 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ R X4))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z3) (@ _let_1 Z3))))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (exists ((Y4 tptp.int)) (and (@ (@ tptp.member_int Y4) A2) (@ (@ R X4) Y4))))) (= A2 tptp.bot_bot_set_int)))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S2)) (forall ((M3 tptp.nat)) (exists ((N4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M3) N4) (@ (@ tptp.member_nat N4) S2)))))))
% 5.91/6.25 (assert (= tptp.finite_finite_nat (lambda ((N3 tptp.set_nat)) (exists ((M3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N3) (@ (@ tptp.ord_less_eq_nat X3) M3)))))))
% 5.91/6.25 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X)))
% 5.91/6.25 (assert (forall ((A2 tptp.set_o) (A Bool)) (=> (@ tptp.finite_finite_o A2) (=> (@ (@ tptp.member_o A) A2) (exists ((X4 Bool)) (and (@ (@ tptp.member_o X4) A2) (@ (@ tptp.ord_less_eq_o A) X4) (forall ((Xa Bool)) (=> (@ (@ tptp.member_o Xa) A2) (=> (@ (@ tptp.ord_less_eq_o X4) Xa) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ (@ tptp.member_set_nat A) A2) (exists ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) A2) (@ (@ tptp.ord_less_eq_set_nat A) X4) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat X4) Xa) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_set_nat_rat) (A tptp.set_nat_rat)) (=> (@ tptp.finite6430367030675640852at_rat A2) (=> (@ (@ tptp.member_set_nat_rat A) A2) (exists ((X4 tptp.set_nat_rat)) (and (@ (@ tptp.member_set_nat_rat X4) A2) (@ (@ tptp.ord_le2679597024174929757at_rat A) X4) (forall ((Xa tptp.set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat Xa) A2) (=> (@ (@ tptp.ord_le2679597024174929757at_rat X4) Xa) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat A) A2) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ tptp.ord_le2932123472753598470d_enat A) X4) (forall ((Xa tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Xa) A2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X4) Xa) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_set_int) (A tptp.set_int)) (=> (@ tptp.finite6197958912794628473et_int A2) (=> (@ (@ tptp.member_set_int A) A2) (exists ((X4 tptp.set_int)) (and (@ (@ tptp.member_set_int X4) A2) (@ (@ tptp.ord_less_eq_set_int A) X4) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_int X4) Xa) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_rat) (A tptp.rat)) (=> (@ tptp.finite_finite_rat A2) (=> (@ (@ tptp.member_rat A) A2) (exists ((X4 tptp.rat)) (and (@ (@ tptp.member_rat X4) A2) (@ (@ tptp.ord_less_eq_rat A) X4) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A2) (=> (@ (@ tptp.ord_less_eq_rat X4) Xa) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_num) (A tptp.num)) (=> (@ tptp.finite_finite_num A2) (=> (@ (@ tptp.member_num A) A2) (exists ((X4 tptp.num)) (and (@ (@ tptp.member_num X4) A2) (@ (@ tptp.ord_less_eq_num A) X4) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num X4) Xa) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_nat A) X4) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat X4) Xa) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_int A) X4) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int X4) Xa) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_o) (A Bool)) (=> (@ tptp.finite_finite_o A2) (=> (@ (@ tptp.member_o A) A2) (exists ((X4 Bool)) (and (@ (@ tptp.member_o X4) A2) (@ (@ tptp.ord_less_eq_o X4) A) (forall ((Xa Bool)) (=> (@ (@ tptp.member_o Xa) A2) (=> (@ (@ tptp.ord_less_eq_o Xa) X4) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ (@ tptp.member_set_nat A) A2) (exists ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) A2) (@ (@ tptp.ord_less_eq_set_nat X4) A) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat Xa) X4) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_set_nat_rat) (A tptp.set_nat_rat)) (=> (@ tptp.finite6430367030675640852at_rat A2) (=> (@ (@ tptp.member_set_nat_rat A) A2) (exists ((X4 tptp.set_nat_rat)) (and (@ (@ tptp.member_set_nat_rat X4) A2) (@ (@ tptp.ord_le2679597024174929757at_rat X4) A) (forall ((Xa tptp.set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat Xa) A2) (=> (@ (@ tptp.ord_le2679597024174929757at_rat Xa) X4) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat A) A2) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ tptp.ord_le2932123472753598470d_enat X4) A) (forall ((Xa tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Xa) A2) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Xa) X4) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_set_int) (A tptp.set_int)) (=> (@ tptp.finite6197958912794628473et_int A2) (=> (@ (@ tptp.member_set_int A) A2) (exists ((X4 tptp.set_int)) (and (@ (@ tptp.member_set_int X4) A2) (@ (@ tptp.ord_less_eq_set_int X4) A) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_int Xa) X4) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_rat) (A tptp.rat)) (=> (@ tptp.finite_finite_rat A2) (=> (@ (@ tptp.member_rat A) A2) (exists ((X4 tptp.rat)) (and (@ (@ tptp.member_rat X4) A2) (@ (@ tptp.ord_less_eq_rat X4) A) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A2) (=> (@ (@ tptp.ord_less_eq_rat Xa) X4) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_num) (A tptp.num)) (=> (@ tptp.finite_finite_num A2) (=> (@ (@ tptp.member_num A) A2) (exists ((X4 tptp.num)) (and (@ (@ tptp.member_num X4) A2) (@ (@ tptp.ord_less_eq_num X4) A) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num Xa) X4) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_nat X4) A) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat Xa) X4) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_int X4) A) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int Xa) X4) (= X4 Xa))))))))))
% 5.91/6.25 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 5.91/6.25 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 5.91/6.25 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 5.91/6.25 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 5.91/6.25 (assert (= tptp.ord_less_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M3) N4) (not (= M3 N4))))))
% 5.91/6.25 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 5.91/6.25 (assert (= tptp.ord_less_eq_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (or (@ (@ tptp.ord_less_nat M3) N4) (= M3 N4)))))
% 5.91/6.25 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M2) N) (= M2 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 5.91/6.25 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (not (= M2 N)) (@ (@ tptp.ord_less_nat M2) N)))))
% 5.91/6.25 (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))))))
% 5.91/6.25 (assert (@ tptp.finite3207457112153483333omplex tptp.bot_bot_set_complex))
% 5.91/6.25 (assert (@ tptp.finite6177210948735845034at_nat tptp.bot_bo2099793752762293965at_nat))
% 5.91/6.25 (assert (@ tptp.finite4001608067531595151d_enat tptp.bot_bo7653980558646680370d_enat))
% 5.91/6.25 (assert (@ tptp.finite_finite_real tptp.bot_bot_set_real))
% 5.91/6.25 (assert (@ tptp.finite_finite_o tptp.bot_bot_set_o))
% 5.91/6.25 (assert (@ tptp.finite_finite_nat tptp.bot_bot_set_nat))
% 5.91/6.25 (assert (@ tptp.finite_finite_int tptp.bot_bot_set_int))
% 5.91/6.25 (assert (forall ((S2 tptp.set_complex)) (=> (not (@ tptp.finite3207457112153483333omplex S2)) (not (= S2 tptp.bot_bot_set_complex)))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_Pr1261947904930325089at_nat)) (=> (not (@ tptp.finite6177210948735845034at_nat S2)) (not (= S2 tptp.bot_bo2099793752762293965at_nat)))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_Extended_enat)) (=> (not (@ tptp.finite4001608067531595151d_enat S2)) (not (= S2 tptp.bot_bo7653980558646680370d_enat)))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_real)) (=> (not (@ tptp.finite_finite_real S2)) (not (= S2 tptp.bot_bot_set_real)))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_o)) (=> (not (@ tptp.finite_finite_o S2)) (not (= S2 tptp.bot_bot_set_o)))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S2)) (not (= S2 tptp.bot_bot_set_nat)))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_int)) (=> (not (@ tptp.finite_finite_int S2)) (not (= S2 tptp.bot_bot_set_int)))))
% 5.91/6.25 (assert (forall ((A Bool) (B Bool) (X tptp.nat)) (let ((_let_1 (= X tptp.one_one_nat))) (let ((_let_2 (= X tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.vEBT_Leaf A) B)) X) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))
% 5.91/6.25 (assert (forall ((Uu Bool) (Uv Bool) (Uw tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.vEBT_Leaf Uu) Uv)) Uw))))
% 5.91/6.25 (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)))))))
% 5.91/6.25 (assert (forall ((Uu Bool) (Uv Bool) (D tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ tptp.vEBT_Leaf Uu) Uv)) D) (= D tptp.one_one_nat))))
% 5.91/6.25 (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))))
% 5.91/6.25 (assert (forall ((A Bool) (B Bool) (X tptp.nat)) (let ((_let_1 (= X tptp.one_one_nat))) (let ((_let_2 (= X tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_Leaf A) B)) X) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))
% 5.91/6.25 (assert (= tptp.vEBT_is_pred_in_set (lambda ((Xs2 tptp.set_nat) (X3 tptp.nat) (Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) Xs2) (@ (@ tptp.ord_less_nat Y2) X3) (forall ((Z2 tptp.nat)) (=> (@ (@ tptp.member_nat Z2) Xs2) (=> (@ (@ tptp.ord_less_nat Z2) X3) (@ (@ tptp.ord_less_eq_nat Z2) Y2))))))))
% 5.91/6.25 (assert (= tptp.vEBT_is_succ_in_set (lambda ((Xs2 tptp.set_nat) (X3 tptp.nat) (Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) Xs2) (@ (@ tptp.ord_less_nat X3) Y2) (forall ((Z2 tptp.nat)) (=> (@ (@ tptp.member_nat Z2) Xs2) (=> (@ (@ tptp.ord_less_nat X3) Z2) (@ (@ tptp.ord_less_eq_nat Y2) Z2))))))))
% 5.91/6.25 (assert (forall ((X5 tptp.set_Extended_enat)) (=> (not (= X5 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) X5) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) X5) (@ (@ tptp.ord_le72135733267957522d_enat X4) Xa))))) (not (@ tptp.finite4001608067531595151d_enat X5))))))
% 5.91/6.25 (assert (forall ((X5 tptp.set_o)) (=> (not (= X5 tptp.bot_bot_set_o)) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) X5) (exists ((Xa Bool)) (and (@ (@ tptp.member_o Xa) X5) (@ (@ tptp.ord_less_o X4) Xa))))) (not (@ tptp.finite_finite_o X5))))))
% 5.91/6.25 (assert (forall ((X5 tptp.set_real)) (=> (not (= X5 tptp.bot_bot_set_real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) X5) (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) X5) (@ (@ tptp.ord_less_real X4) Xa))))) (not (@ tptp.finite_finite_real X5))))))
% 5.91/6.25 (assert (forall ((X5 tptp.set_rat)) (=> (not (= X5 tptp.bot_bot_set_rat)) (=> (forall ((X4 tptp.rat)) (=> (@ (@ tptp.member_rat X4) X5) (exists ((Xa tptp.rat)) (and (@ (@ tptp.member_rat Xa) X5) (@ (@ tptp.ord_less_rat X4) Xa))))) (not (@ tptp.finite_finite_rat X5))))))
% 5.91/6.25 (assert (forall ((X5 tptp.set_num)) (=> (not (= X5 tptp.bot_bot_set_num)) (=> (forall ((X4 tptp.num)) (=> (@ (@ tptp.member_num X4) X5) (exists ((Xa tptp.num)) (and (@ (@ tptp.member_num Xa) X5) (@ (@ tptp.ord_less_num X4) Xa))))) (not (@ tptp.finite_finite_num X5))))))
% 5.91/6.25 (assert (forall ((X5 tptp.set_nat)) (=> (not (= X5 tptp.bot_bot_set_nat)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) X5) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) X5) (@ (@ tptp.ord_less_nat X4) Xa))))) (not (@ tptp.finite_finite_nat X5))))))
% 5.91/6.25 (assert (forall ((X5 tptp.set_int)) (=> (not (= X5 tptp.bot_bot_set_int)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) X5) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) X5) (@ (@ tptp.ord_less_int X4) Xa))))) (not (@ tptp.finite_finite_int X5))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (not (= S2 tptp.bot_bo7653980558646680370d_enat)) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) S2) (not (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) S2) (@ (@ tptp.ord_le72135733267957522d_enat Xa) X4))))))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_o)) (=> (@ tptp.finite_finite_o S2) (=> (not (= S2 tptp.bot_bot_set_o)) (exists ((X4 Bool)) (and (@ (@ tptp.member_o X4) S2) (not (exists ((Xa Bool)) (and (@ (@ tptp.member_o Xa) S2) (@ (@ tptp.ord_less_o Xa) X4))))))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_real)) (=> (@ tptp.finite_finite_real S2) (=> (not (= S2 tptp.bot_bot_set_real)) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) S2) (not (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) S2) (@ (@ tptp.ord_less_real Xa) X4))))))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_rat)) (=> (@ tptp.finite_finite_rat S2) (=> (not (= S2 tptp.bot_bot_set_rat)) (exists ((X4 tptp.rat)) (and (@ (@ tptp.member_rat X4) S2) (not (exists ((Xa tptp.rat)) (and (@ (@ tptp.member_rat Xa) S2) (@ (@ tptp.ord_less_rat Xa) X4))))))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_num)) (=> (@ tptp.finite_finite_num S2) (=> (not (= S2 tptp.bot_bot_set_num)) (exists ((X4 tptp.num)) (and (@ (@ tptp.member_num X4) S2) (not (exists ((Xa tptp.num)) (and (@ (@ tptp.member_num Xa) S2) (@ (@ tptp.ord_less_num Xa) X4))))))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S2) (=> (not (= S2 tptp.bot_bot_set_nat)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) S2) (not (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) S2) (@ (@ tptp.ord_less_nat Xa) X4))))))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_int)) (=> (@ tptp.finite_finite_int S2) (=> (not (= S2 tptp.bot_bot_set_int)) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) S2) (not (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) S2) (@ (@ tptp.ord_less_int Xa) X4))))))))))
% 5.91/6.25 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 5.91/6.25 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 5.91/6.25 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 5.91/6.25 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 5.91/6.25 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 5.91/6.25 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 5.91/6.25 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 5.91/6.25 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 5.91/6.25 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real)))
% 5.91/6.25 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 5.91/6.25 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 5.91/6.25 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 5.91/6.25 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 5.91/6.25 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 5.91/6.25 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 5.91/6.25 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 5.91/6.25 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 5.91/6.25 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 5.91/6.25 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 5.91/6.25 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 5.91/6.25 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.zero_zero_real)))
% 5.91/6.25 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 5.91/6.25 (assert (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 5.91/6.25 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)))
% 5.91/6.25 (assert (forall ((C tptp.set_nat)) (not (@ (@ tptp.member_set_nat C) tptp.bot_bot_set_set_nat))))
% 5.91/6.25 (assert (forall ((C tptp.set_nat_rat)) (not (@ (@ tptp.member_set_nat_rat C) tptp.bot_bo6797373522285170759at_rat))))
% 5.91/6.25 (assert (forall ((C tptp.real)) (not (@ (@ tptp.member_real C) tptp.bot_bot_set_real))))
% 5.91/6.25 (assert (forall ((C Bool)) (not (@ (@ tptp.member_o C) tptp.bot_bot_set_o))))
% 5.91/6.25 (assert (forall ((C tptp.nat)) (not (@ (@ tptp.member_nat C) tptp.bot_bot_set_nat))))
% 5.91/6.25 (assert (forall ((C tptp.int)) (not (@ (@ tptp.member_int C) tptp.bot_bot_set_int))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A2)))
% 5.91/6.25 (assert (forall ((A2 tptp.set_o)) (@ (@ tptp.ord_less_eq_set_o tptp.bot_bot_set_o) A2)))
% 5.91/6.25 (assert (forall ((A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A2)))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A2)))
% 5.91/6.25 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A2) tptp.bot_bot_set_real) (= A2 tptp.bot_bot_set_real))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o A2) tptp.bot_bot_set_o) (= A2 tptp.bot_bot_set_o))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) tptp.bot_bot_set_nat) (= A2 tptp.bot_bot_set_nat))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) tptp.bot_bot_set_int) (= A2 tptp.bot_bot_set_int))))
% 5.91/6.25 (assert (forall ((P (-> tptp.set_nat Bool))) (= (= tptp.bot_bot_set_set_nat (@ tptp.collect_set_nat P)) (forall ((X3 tptp.set_nat)) (not (@ P X3))))))
% 5.91/6.25 (assert (forall ((P (-> tptp.set_nat_rat Bool))) (= (= tptp.bot_bo6797373522285170759at_rat (@ tptp.collect_set_nat_rat P)) (forall ((X3 tptp.set_nat_rat)) (not (@ P X3))))))
% 5.91/6.25 (assert (forall ((P (-> (-> tptp.nat tptp.rat) Bool))) (= (= tptp.bot_bot_set_nat_rat (@ tptp.collect_nat_rat P)) (forall ((X3 (-> tptp.nat tptp.rat))) (not (@ P X3))))))
% 5.91/6.25 (assert (forall ((P (-> tptp.real Bool))) (= (= tptp.bot_bot_set_real (@ tptp.collect_real P)) (forall ((X3 tptp.real)) (not (@ P X3))))))
% 5.91/6.25 (assert (forall ((P (-> Bool Bool))) (= (= tptp.bot_bot_set_o (@ tptp.collect_o P)) (forall ((X3 Bool)) (not (@ P X3))))))
% 5.91/6.25 (assert (forall ((P (-> tptp.nat Bool))) (= (= tptp.bot_bot_set_nat (@ tptp.collect_nat P)) (forall ((X3 tptp.nat)) (not (@ P X3))))))
% 5.91/6.25 (assert (forall ((P (-> tptp.int Bool))) (= (= tptp.bot_bot_set_int (@ tptp.collect_int P)) (forall ((X3 tptp.int)) (not (@ P X3))))))
% 5.91/6.25 (assert (forall ((P (-> tptp.set_nat Bool))) (= (= (@ tptp.collect_set_nat P) tptp.bot_bot_set_set_nat) (forall ((X3 tptp.set_nat)) (not (@ P X3))))))
% 5.91/6.25 (assert (forall ((P (-> tptp.set_nat_rat Bool))) (= (= (@ tptp.collect_set_nat_rat P) tptp.bot_bo6797373522285170759at_rat) (forall ((X3 tptp.set_nat_rat)) (not (@ P X3))))))
% 5.91/6.25 (assert (forall ((P (-> (-> tptp.nat tptp.rat) Bool))) (= (= (@ tptp.collect_nat_rat P) tptp.bot_bot_set_nat_rat) (forall ((X3 (-> tptp.nat tptp.rat))) (not (@ P X3))))))
% 5.91/6.25 (assert (forall ((P (-> tptp.real Bool))) (= (= (@ tptp.collect_real P) tptp.bot_bot_set_real) (forall ((X3 tptp.real)) (not (@ P X3))))))
% 5.91/6.25 (assert (forall ((P (-> Bool Bool))) (= (= (@ tptp.collect_o P) tptp.bot_bot_set_o) (forall ((X3 Bool)) (not (@ P X3))))))
% 5.91/6.25 (assert (forall ((P (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P) tptp.bot_bot_set_nat) (forall ((X3 tptp.nat)) (not (@ P X3))))))
% 5.91/6.25 (assert (forall ((P (-> tptp.int Bool))) (= (= (@ tptp.collect_int P) tptp.bot_bot_set_int) (forall ((X3 tptp.int)) (not (@ P X3))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_set_nat)) (= (forall ((X3 tptp.set_nat)) (not (@ (@ tptp.member_set_nat X3) A2))) (= A2 tptp.bot_bot_set_set_nat))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_set_nat_rat)) (= (forall ((X3 tptp.set_nat_rat)) (not (@ (@ tptp.member_set_nat_rat X3) A2))) (= A2 tptp.bot_bo6797373522285170759at_rat))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_real)) (= (forall ((X3 tptp.real)) (not (@ (@ tptp.member_real X3) A2))) (= A2 tptp.bot_bot_set_real))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_o)) (= (forall ((X3 Bool)) (not (@ (@ tptp.member_o X3) A2))) (= A2 tptp.bot_bot_set_o))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_nat)) (= (forall ((X3 tptp.nat)) (not (@ (@ tptp.member_nat X3) A2))) (= A2 tptp.bot_bot_set_nat))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int)) (= (forall ((X3 tptp.int)) (not (@ (@ tptp.member_int X3) A2))) (= A2 tptp.bot_bot_set_int))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (not (= A2 B2)) (@ (@ tptp.ord_less_set_int A2) B2)))))
% 5.91/6.25 (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)))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int) (C2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (@ (@ tptp.ord_less_set_int B2) C2) (@ (@ tptp.ord_less_set_int A2) C2)))))
% 5.91/6.25 (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))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_int B2) C2) (@ _let_1 C2))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B2) (@ (@ tptp.ord_less_eq_set_int A2) B2))))
% 5.91/6.25 (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))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B2) (not (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (@ (@ tptp.ord_less_eq_set_int B2) A2))))))
% 5.91/6.25 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (@ tptp.finite_finite_nat A2)))))
% 5.91/6.25 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (@ tptp.finite3207457112153483333omplex A2)))))
% 5.91/6.25 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B2) (@ tptp.finite6177210948735845034at_nat A2)))))
% 5.91/6.25 (assert (forall ((B2 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B2) (@ tptp.finite4001608067531595151d_enat A2)))))
% 5.91/6.25 (assert (forall ((B2 tptp.set_int) (A2 tptp.set_int)) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (@ tptp.finite_finite_int A2)))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_nat) (T3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat S2) T3) (=> (not (@ tptp.finite_finite_nat S2)) (not (@ tptp.finite_finite_nat T3))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_complex) (T3 tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (not (@ tptp.finite3207457112153483333omplex S2)) (not (@ tptp.finite3207457112153483333omplex T3))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_Pr1261947904930325089at_nat) (T3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat S2) T3) (=> (not (@ tptp.finite6177210948735845034at_nat S2)) (not (@ tptp.finite6177210948735845034at_nat T3))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_Extended_enat) (T3 tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (not (@ tptp.finite4001608067531595151d_enat S2)) (not (@ tptp.finite4001608067531595151d_enat T3))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_int) (T3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int S2) T3) (=> (not (@ tptp.finite_finite_int S2)) (not (@ tptp.finite_finite_int T3))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (@ tptp.finite_finite_nat B2) (@ tptp.finite_finite_nat A2)))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_complex) (B2 tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (@ tptp.finite3207457112153483333omplex B2) (@ tptp.finite3207457112153483333omplex A2)))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B2) (=> (@ tptp.finite6177210948735845034at_nat B2) (@ tptp.finite6177210948735845034at_nat A2)))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B2) (=> (@ tptp.finite4001608067531595151d_enat B2) (@ tptp.finite4001608067531595151d_enat A2)))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (@ tptp.finite_finite_int B2) (@ tptp.finite_finite_int A2)))))
% 5.91/6.25 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_real Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_rat Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_set_nat)) (= (exists ((X3 tptp.set_nat)) (@ (@ tptp.member_set_nat X3) A2)) (not (= A2 tptp.bot_bot_set_set_nat)))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_set_nat_rat)) (= (exists ((X3 tptp.set_nat_rat)) (@ (@ tptp.member_set_nat_rat X3) A2)) (not (= A2 tptp.bot_bo6797373522285170759at_rat)))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_real)) (= (exists ((X3 tptp.real)) (@ (@ tptp.member_real X3) A2)) (not (= A2 tptp.bot_bot_set_real)))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_o)) (= (exists ((X3 Bool)) (@ (@ tptp.member_o X3) A2)) (not (= A2 tptp.bot_bot_set_o)))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_nat)) (= (exists ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) A2)) (not (= A2 tptp.bot_bot_set_nat)))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int)) (= (exists ((X3 tptp.int)) (@ (@ tptp.member_int X3) A2)) (not (= A2 tptp.bot_bot_set_int)))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_set_nat)) (=> (forall ((Y3 tptp.set_nat)) (not (@ (@ tptp.member_set_nat Y3) A2))) (= A2 tptp.bot_bot_set_set_nat))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_set_nat_rat)) (=> (forall ((Y3 tptp.set_nat_rat)) (not (@ (@ tptp.member_set_nat_rat Y3) A2))) (= A2 tptp.bot_bo6797373522285170759at_rat))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_real)) (=> (forall ((Y3 tptp.real)) (not (@ (@ tptp.member_real Y3) A2))) (= A2 tptp.bot_bot_set_real))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_o)) (=> (forall ((Y3 Bool)) (not (@ (@ tptp.member_o Y3) A2))) (= A2 tptp.bot_bot_set_o))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_nat)) (=> (forall ((Y3 tptp.nat)) (not (@ (@ tptp.member_nat Y3) A2))) (= A2 tptp.bot_bot_set_nat))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int)) (=> (forall ((Y3 tptp.int)) (not (@ (@ tptp.member_int Y3) A2))) (= A2 tptp.bot_bot_set_int))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_set_nat) (A tptp.set_nat)) (=> (= A2 tptp.bot_bot_set_set_nat) (not (@ (@ tptp.member_set_nat A) A2)))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_set_nat_rat) (A tptp.set_nat_rat)) (=> (= A2 tptp.bot_bo6797373522285170759at_rat) (not (@ (@ tptp.member_set_nat_rat A) A2)))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_real) (A tptp.real)) (=> (= A2 tptp.bot_bot_set_real) (not (@ (@ tptp.member_real A) A2)))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_o) (A Bool)) (=> (= A2 tptp.bot_bot_set_o) (not (@ (@ tptp.member_o A) A2)))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (= A2 tptp.bot_bot_set_nat) (not (@ (@ tptp.member_nat A) A2)))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int) (A tptp.int)) (=> (= A2 tptp.bot_bot_set_int) (not (@ (@ tptp.member_int A) A2)))))
% 5.91/6.25 (assert (forall ((A tptp.set_nat)) (not (@ (@ tptp.member_set_nat A) tptp.bot_bot_set_set_nat))))
% 5.91/6.25 (assert (forall ((A tptp.set_nat_rat)) (not (@ (@ tptp.member_set_nat_rat A) tptp.bot_bo6797373522285170759at_rat))))
% 5.91/6.25 (assert (forall ((A tptp.real)) (not (@ (@ tptp.member_real A) tptp.bot_bot_set_real))))
% 5.91/6.25 (assert (forall ((A Bool)) (not (@ (@ tptp.member_o A) tptp.bot_bot_set_o))))
% 5.91/6.25 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.member_nat A) tptp.bot_bot_set_nat))))
% 5.91/6.25 (assert (forall ((A tptp.int)) (not (@ (@ tptp.member_int A) tptp.bot_bot_set_int))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_o) (B2 tptp.set_o) (C Bool)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ (@ tptp.ord_less_set_o A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 5.91/6.25 (assert (forall ((A2 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 A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_set_nat_rat) (B2 tptp.set_set_nat_rat) (C tptp.set_nat_rat)) (let ((_let_1 (@ tptp.member_set_nat_rat C))) (=> (@ (@ tptp.ord_le1311537459589289991at_rat A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_set_nat A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_set_int A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 5.91/6.25 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.91/6.25 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 5.91/6.25 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 5.91/6.25 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 5.91/6.25 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.zero_zero_real)))
% 5.91/6.25 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 5.91/6.25 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 5.91/6.25 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 5.91/6.25 (assert (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.one_one_real))
% 5.91/6.25 (assert (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.one_one_rat))
% 5.91/6.25 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 5.91/6.25 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 5.91/6.25 (assert (not (= tptp.zero_zero_complex tptp.one_one_complex)))
% 5.91/6.25 (assert (not (= tptp.zero_zero_real tptp.one_one_real)))
% 5.91/6.25 (assert (not (= tptp.zero_zero_rat tptp.one_one_rat)))
% 5.91/6.25 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 5.91/6.25 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 5.91/6.25 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.one_one_real)))
% 5.91/6.25 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.one_one_rat)))
% 5.91/6.25 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 5.91/6.25 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 5.91/6.25 (assert (forall ((A2 tptp.set_real)) (not (@ (@ tptp.ord_less_set_real A2) tptp.bot_bot_set_real))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_o)) (not (@ (@ tptp.ord_less_set_o A2) tptp.bot_bot_set_o))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A2) tptp.bot_bot_set_nat))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A2) tptp.bot_bot_set_int))))
% 5.91/6.25 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) A)))
% 5.91/6.25 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 5.91/6.25 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 5.91/6.25 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 5.91/6.25 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 5.91/6.25 (assert (forall ((X tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X) X)))
% 5.91/6.25 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) X)))
% 5.91/6.25 (assert (forall ((X tptp.num)) (@ (@ tptp.ord_less_eq_num X) X)))
% 5.91/6.25 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) X)))
% 5.91/6.25 (assert (forall ((X tptp.int)) (@ (@ tptp.ord_less_eq_int X) X)))
% 5.91/6.25 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (not (= S2 tptp.bot_bot_set_complex)) (not (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) S2) (@ (@ tptp.ord_less_real (@ F X2)) (@ F (@ (@ tptp.lattic8794016678065449205x_real F) S2))))))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (not (= S2 tptp.bot_bo7653980558646680370d_enat)) (not (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X2) S2) (@ (@ tptp.ord_less_real (@ F X2)) (@ F (@ (@ tptp.lattic1189837152898106425t_real F) S2))))))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real S2) (=> (not (= S2 tptp.bot_bot_set_real)) (not (exists ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) S2) (@ (@ tptp.ord_less_real (@ F X2)) (@ F (@ (@ tptp.lattic8440615504127631091l_real F) S2))))))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_o) (F (-> Bool tptp.real))) (=> (@ tptp.finite_finite_o S2) (=> (not (= S2 tptp.bot_bot_set_o)) (not (exists ((X2 Bool)) (and (@ (@ tptp.member_o X2) S2) (@ (@ tptp.ord_less_real (@ F X2)) (@ F (@ (@ tptp.lattic8697145971487455083o_real F) S2))))))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat S2) (=> (not (= S2 tptp.bot_bot_set_nat)) (not (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) S2) (@ (@ tptp.ord_less_real (@ F X2)) (@ F (@ (@ tptp.lattic488527866317076247t_real F) S2))))))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S2) (=> (not (= S2 tptp.bot_bot_set_int)) (not (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) S2) (@ (@ tptp.ord_less_real (@ F X2)) (@ F (@ (@ tptp.lattic2675449441010098035t_real F) S2))))))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (not (= S2 tptp.bot_bot_set_complex)) (not (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) S2) (@ (@ tptp.ord_less_rat (@ F X2)) (@ F (@ (@ tptp.lattic4729654577720512673ex_rat F) S2))))))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (not (= S2 tptp.bot_bo7653980558646680370d_enat)) (not (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X2) S2) (@ (@ tptp.ord_less_rat (@ F X2)) (@ F (@ (@ tptp.lattic3210252021154270693at_rat F) S2))))))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real S2) (=> (not (= S2 tptp.bot_bot_set_real)) (not (exists ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) S2) (@ (@ tptp.ord_less_rat (@ F X2)) (@ F (@ (@ tptp.lattic4420706379359479199al_rat F) S2))))))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_o) (F (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o S2) (=> (not (= S2 tptp.bot_bot_set_o)) (not (exists ((X2 Bool)) (and (@ (@ tptp.member_o X2) S2) (@ (@ tptp.ord_less_rat (@ F X2)) (@ F (@ (@ tptp.lattic2140725968369957399_o_rat F) S2))))))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_complex) (Y tptp.complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (not (= S2 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.member_complex Y) S2) (@ (@ tptp.ord_less_eq_rat (@ F (@ (@ tptp.lattic4729654577720512673ex_rat F) S2))) (@ F Y)))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_Extended_enat) (Y tptp.extended_enat) (F (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (not (= S2 tptp.bot_bo7653980558646680370d_enat)) (=> (@ (@ tptp.member_Extended_enat Y) S2) (@ (@ tptp.ord_less_eq_rat (@ F (@ (@ tptp.lattic3210252021154270693at_rat F) S2))) (@ F Y)))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_real) (Y tptp.real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real S2) (=> (not (= S2 tptp.bot_bot_set_real)) (=> (@ (@ tptp.member_real Y) S2) (@ (@ tptp.ord_less_eq_rat (@ F (@ (@ tptp.lattic4420706379359479199al_rat F) S2))) (@ F Y)))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_o) (Y Bool) (F (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o S2) (=> (not (= S2 tptp.bot_bot_set_o)) (=> (@ (@ tptp.member_o Y) S2) (@ (@ tptp.ord_less_eq_rat (@ F (@ (@ tptp.lattic2140725968369957399_o_rat F) S2))) (@ F Y)))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_nat) (Y tptp.nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S2) (=> (not (= S2 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.member_nat Y) S2) (@ (@ tptp.ord_less_eq_rat (@ F (@ (@ tptp.lattic6811802900495863747at_rat F) S2))) (@ F Y)))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_int) (Y tptp.int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S2) (=> (not (= S2 tptp.bot_bot_set_int)) (=> (@ (@ tptp.member_int Y) S2) (@ (@ tptp.ord_less_eq_rat (@ F (@ (@ tptp.lattic7811156612396918303nt_rat F) S2))) (@ F Y)))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_complex) (Y tptp.complex) (F (-> tptp.complex tptp.num))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (not (= S2 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.member_complex Y) S2) (@ (@ tptp.ord_less_eq_num (@ F (@ (@ tptp.lattic1922116423962787043ex_num F) S2))) (@ F Y)))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_Extended_enat) (Y tptp.extended_enat) (F (-> tptp.extended_enat tptp.num))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (not (= S2 tptp.bot_bo7653980558646680370d_enat)) (=> (@ (@ tptp.member_Extended_enat Y) S2) (@ (@ tptp.ord_less_eq_num (@ F (@ (@ tptp.lattic402713867396545063at_num F) S2))) (@ F Y)))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_real) (Y tptp.real) (F (-> tptp.real tptp.num))) (=> (@ tptp.finite_finite_real S2) (=> (not (= S2 tptp.bot_bot_set_real)) (=> (@ (@ tptp.member_real Y) S2) (@ (@ tptp.ord_less_eq_num (@ F (@ (@ tptp.lattic1613168225601753569al_num F) S2))) (@ F Y)))))))
% 5.91/6.25 (assert (forall ((S2 tptp.set_o) (Y Bool) (F (-> Bool tptp.num))) (=> (@ tptp.finite_finite_o S2) (=> (not (= S2 tptp.bot_bot_set_o)) (=> (@ (@ tptp.member_o Y) S2) (@ (@ tptp.ord_less_eq_num (@ F (@ (@ tptp.lattic8556559851467007577_o_num F) S2))) (@ F Y)))))))
% 5.91/6.25 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool)) (M2 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 M2)))))
% 5.91/6.25 (assert (forall ((A tptp.set_real)) (= (not (= A tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_set_real tptp.bot_bot_set_real) A))))
% 5.91/6.25 (assert (forall ((A tptp.set_o)) (= (not (= A tptp.bot_bot_set_o)) (@ (@ tptp.ord_less_set_o tptp.bot_bot_set_o) A))))
% 5.91/6.25 (assert (forall ((A tptp.set_nat)) (= (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_set_nat tptp.bot_bot_set_nat) A))))
% 5.91/6.25 (assert (forall ((A tptp.set_int)) (= (not (= A tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_set_int tptp.bot_bot_set_int) A))))
% 5.91/6.25 (assert (forall ((A tptp.nat)) (= (not (= A tptp.bot_bot_nat)) (@ (@ tptp.ord_less_nat tptp.bot_bot_nat) A))))
% 5.91/6.25 (assert (forall ((A tptp.set_real)) (not (@ (@ tptp.ord_less_set_real A) tptp.bot_bot_set_real))))
% 5.91/6.25 (assert (forall ((A tptp.set_o)) (not (@ (@ tptp.ord_less_set_o A) tptp.bot_bot_set_o))))
% 5.91/6.25 (assert (forall ((A tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A) tptp.bot_bot_set_nat))))
% 5.91/6.25 (assert (forall ((A tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A) tptp.bot_bot_set_int))))
% 5.91/6.25 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.bot_bot_nat))))
% 5.91/6.25 (assert (forall ((A tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))))
% 5.91/6.25 (assert (forall ((A tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A) tptp.bot_bot_set_o) (= A tptp.bot_bot_set_o))))
% 5.91/6.25 (assert (forall ((A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 5.91/6.25 (assert (forall ((A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 5.91/6.25 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 5.91/6.25 (assert (forall ((A tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))))
% 5.91/6.25 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o A) tptp.bot_bot_set_o) (= A tptp.bot_bot_set_o))))
% 5.91/6.25 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 5.91/6.25 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 5.91/6.25 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 5.91/6.25 (assert (forall ((A tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A)))
% 5.91/6.25 (assert (forall ((A tptp.set_o)) (@ (@ tptp.ord_less_eq_set_o tptp.bot_bot_set_o) A)))
% 5.91/6.25 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A)))
% 5.91/6.25 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A)))
% 5.91/6.25 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A)))
% 5.91/6.25 (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)))))))))
% 5.91/6.25 (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)))))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_o) (B2 tptp.set_o)) (=> (forall ((X4 Bool)) (let ((_let_1 (@ tptp.member_o X4))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_less_eq_set_o A2) B2))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_set_nat) (B2 tptp.set_set_nat)) (=> (forall ((X4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X4))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_le6893508408891458716et_nat A2) B2))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_set_nat_rat) (B2 tptp.set_set_nat_rat)) (=> (forall ((X4 tptp.set_nat_rat)) (let ((_let_1 (@ tptp.member_set_nat_rat X4))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_le4375437777232675859at_rat A2) B2))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X4))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_less_eq_set_nat A2) B2))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (=> (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.member_int X4))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_less_eq_set_int A2) B2))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (@ (@ tptp.ord_less_eq_set_int B2) A2) (= A2 B2)))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_o) (B2 tptp.set_o) (X Bool)) (let ((_let_1 (@ tptp.member_o X))) (=> (@ (@ tptp.ord_less_eq_set_o A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_set_nat) (B2 tptp.set_set_nat) (X tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X))) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_set_nat_rat) (B2 tptp.set_set_nat_rat) (X tptp.set_nat_rat)) (let ((_let_1 (@ tptp.member_set_nat_rat X))) (=> (@ (@ tptp.ord_le4375437777232675859at_rat A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int) (X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_o) (B2 tptp.set_o) (C Bool)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ (@ tptp.ord_less_eq_set_o A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 5.91/6.25 (assert (forall ((A2 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 A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_set_nat_rat) (B2 tptp.set_set_nat_rat) (C tptp.set_nat_rat)) (let ((_let_1 (@ tptp.member_set_nat_rat C))) (=> (@ (@ tptp.ord_le4375437777232675859at_rat A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (=> (= A2 B2) (not (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (not (@ (@ tptp.ord_less_eq_set_int B2) A2)))))))
% 5.91/6.25 (assert (= tptp.ord_less_eq_set_o (lambda ((A6 tptp.set_o) (B6 tptp.set_o)) (forall ((X3 Bool)) (let ((_let_1 (@ tptp.member_o X3))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 5.91/6.25 (assert (= tptp.ord_le6893508408891458716et_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (forall ((X3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X3))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 5.91/6.25 (assert (= tptp.ord_le4375437777232675859at_rat (lambda ((A6 tptp.set_set_nat_rat) (B6 tptp.set_set_nat_rat)) (forall ((X3 tptp.set_nat_rat)) (let ((_let_1 (@ tptp.member_set_nat_rat X3))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 5.91/6.25 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 5.91/6.25 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (=> (= A2 B2) (@ (@ tptp.ord_less_eq_set_int A2) B2))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (=> (= A2 B2) (@ (@ tptp.ord_less_eq_set_int B2) A2))))
% 5.91/6.25 (assert (= tptp.ord_less_eq_set_o (lambda ((A6 tptp.set_o) (B6 tptp.set_o)) (forall ((T2 Bool)) (let ((_let_1 (@ tptp.member_o T2))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 5.91/6.25 (assert (= tptp.ord_le6893508408891458716et_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (forall ((T2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat T2))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 5.91/6.25 (assert (= tptp.ord_le4375437777232675859at_rat (lambda ((A6 tptp.set_set_nat_rat) (B6 tptp.set_set_nat_rat)) (forall ((T2 tptp.set_nat_rat)) (let ((_let_1 (@ tptp.member_set_nat_rat T2))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 5.91/6.25 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (forall ((T2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat T2))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 5.91/6.25 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (forall ((T2 tptp.int)) (let ((_let_1 (@ tptp.member_int T2))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A2) A2)))
% 5.91/6.25 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (forall ((X4 tptp.set_nat)) (=> (@ P X4) (@ Q X4))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat P)) (@ tptp.collect_set_nat Q)))))
% 5.91/6.25 (assert (forall ((P (-> tptp.set_nat_rat Bool)) (Q (-> tptp.set_nat_rat Bool))) (=> (forall ((X4 tptp.set_nat_rat)) (=> (@ P X4) (@ Q X4))) (@ (@ tptp.ord_le4375437777232675859at_rat (@ tptp.collect_set_nat_rat P)) (@ tptp.collect_set_nat_rat Q)))))
% 5.91/6.25 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X4 tptp.nat)) (=> (@ P X4) (@ Q X4))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)))))
% 5.91/6.25 (assert (forall ((P (-> (-> tptp.nat tptp.rat) Bool)) (Q (-> (-> tptp.nat tptp.rat) Bool))) (=> (forall ((X4 (-> tptp.nat tptp.rat))) (=> (@ P X4) (@ Q X4))) (@ (@ tptp.ord_le2679597024174929757at_rat (@ tptp.collect_nat_rat P)) (@ tptp.collect_nat_rat Q)))))
% 5.91/6.25 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int)) (=> (@ P X4) (@ Q X4))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)))))
% 5.91/6.25 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_int B2) C2) (@ _let_1 C2))))))
% 5.91/6.25 (assert (= (lambda ((Y5 tptp.set_int) (Z4 tptp.set_int)) (= Y5 Z4)) (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)))))
% 5.91/6.25 (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 ((X3 tptp.set_nat)) (=> (@ P X3) (@ Q X3))))))
% 5.91/6.25 (assert (forall ((P (-> tptp.set_nat_rat Bool)) (Q (-> tptp.set_nat_rat Bool))) (= (@ (@ tptp.ord_le4375437777232675859at_rat (@ tptp.collect_set_nat_rat P)) (@ tptp.collect_set_nat_rat Q)) (forall ((X3 tptp.set_nat_rat)) (=> (@ P X3) (@ Q X3))))))
% 5.91/6.25 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)) (forall ((X3 tptp.nat)) (=> (@ P X3) (@ Q X3))))))
% 5.91/6.25 (assert (forall ((P (-> (-> tptp.nat tptp.rat) Bool)) (Q (-> (-> tptp.nat tptp.rat) Bool))) (= (@ (@ tptp.ord_le2679597024174929757at_rat (@ tptp.collect_nat_rat P)) (@ tptp.collect_nat_rat Q)) (forall ((X3 (-> tptp.nat tptp.rat))) (=> (@ P X3) (@ Q X3))))))
% 5.91/6.25 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)) (forall ((X3 tptp.int)) (=> (@ P X3) (@ Q X3))))))
% 5.91/6.25 (assert (= tptp.bot_bot_set_set_nat (@ tptp.collect_set_nat tptp.bot_bot_set_nat_o)))
% 5.91/6.25 (assert (= tptp.bot_bo6797373522285170759at_rat (@ tptp.collect_set_nat_rat tptp.bot_bo3445895781125589758_rat_o)))
% 5.91/6.25 (assert (= tptp.bot_bot_set_nat_rat (@ tptp.collect_nat_rat tptp.bot_bot_nat_rat_o)))
% 5.91/6.25 (assert (= tptp.bot_bot_set_real (@ tptp.collect_real tptp.bot_bot_real_o)))
% 5.91/6.25 (assert (= tptp.bot_bot_set_o (@ tptp.collect_o tptp.bot_bot_o_o)))
% 5.91/6.25 (assert (= tptp.bot_bot_set_nat (@ tptp.collect_nat tptp.bot_bot_nat_o)))
% 5.91/6.25 (assert (= tptp.bot_bot_set_int (@ tptp.collect_int tptp.bot_bot_int_o)))
% 5.91/6.25 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_eq_rat B) A) (not (= B A))))))
% 5.91/6.25 (assert (forall ((A tptp.num) (B tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ (@ tptp.ord_less_eq_num B) A) (not (= B A))))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ (@ tptp.ord_less_eq_nat B) A) (not (= B A))))))
% 5.91/6.25 (assert (forall ((A tptp.int) (B tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ (@ tptp.ord_less_eq_int B) A) (not (= B A))))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_rat Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_rat Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 5.91/6.25 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_num Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_num Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 5.91/6.25 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_int Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_int Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 5.91/6.25 (assert (= (lambda ((Y5 tptp.set_int) (Z4 tptp.set_int)) (= Y5 Z4)) (lambda ((X3 tptp.set_int) (Y2 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X3) Y2) (@ (@ tptp.ord_less_eq_set_int Y2) X3)))))
% 5.91/6.25 (assert (= (lambda ((Y5 tptp.rat) (Z4 tptp.rat)) (= Y5 Z4)) (lambda ((X3 tptp.rat) (Y2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X3) Y2) (@ (@ tptp.ord_less_eq_rat Y2) X3)))))
% 5.91/6.25 (assert (= (lambda ((Y5 tptp.num) (Z4 tptp.num)) (= Y5 Z4)) (lambda ((X3 tptp.num) (Y2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X3) Y2) (@ (@ tptp.ord_less_eq_num Y2) X3)))))
% 5.91/6.25 (assert (= (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)) (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat Y2) X3)))))
% 5.91/6.25 (assert (= (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4)) (lambda ((X3 tptp.int) (Y2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_int Y2) X3)))))
% 5.91/6.25 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_set_int B) C) (@ (@ tptp.ord_less_eq_set_int A) C)))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ (@ tptp.ord_less_eq_rat A) C)))))
% 5.91/6.25 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_num B) C) (@ (@ tptp.ord_less_eq_num A) C)))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_eq_nat A) C)))))
% 5.91/6.25 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ (@ tptp.ord_less_eq_int A) C)))))
% 5.91/6.25 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.91/6.25 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.91/6.25 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.91/6.25 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) X) (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (=> (@ (@ tptp.ord_less_eq_num Y) X) (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= X Y)))))
% 5.91/6.25 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_int B) C) (@ _let_1 C))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ _let_1 C))))))
% 5.91/6.25 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_num B) C) (@ _let_1 C))))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))))
% 5.91/6.25 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ _let_1 C))))))
% 5.91/6.25 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) Z) (@ _let_1 Z))))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z) (@ _let_1 Z))))))
% 5.91/6.25 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z) (@ _let_1 Z))))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))))
% 5.91/6.25 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))))
% 5.91/6.25 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B tptp.rat)) (=> (forall ((A5 tptp.rat) (B5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.rat) (B5 tptp.rat)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B)))))
% 5.91/6.25 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B)))))
% 5.91/6.25 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B)))))
% 5.91/6.25 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B)))))
% 5.91/6.25 (assert (= (lambda ((Y5 tptp.set_int) (Z4 tptp.set_int)) (= Y5 Z4)) (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)))))
% 5.91/6.25 (assert (= (lambda ((Y5 tptp.rat) (Z4 tptp.rat)) (= Y5 Z4)) (lambda ((A4 tptp.rat) (B4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B4) A4) (@ (@ tptp.ord_less_eq_rat A4) B4)))))
% 5.91/6.25 (assert (= (lambda ((Y5 tptp.num) (Z4 tptp.num)) (= Y5 Z4)) (lambda ((A4 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B4) A4) (@ (@ tptp.ord_less_eq_num A4) B4)))))
% 5.91/6.25 (assert (= (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)) (lambda ((A4 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B4) A4) (@ (@ tptp.ord_less_eq_nat A4) B4)))))
% 5.91/6.25 (assert (= (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4)) (lambda ((A4 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B4) A4) (@ (@ tptp.ord_less_eq_int A4) B4)))))
% 5.91/6.25 (assert (forall ((B tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (= A B)))))
% 5.91/6.25 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= A B)))))
% 5.91/6.25 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num A) B) (= A B)))))
% 5.91/6.25 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))))
% 5.91/6.25 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int A) B) (= A B)))))
% 5.91/6.25 (assert (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C))) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.91/6.25 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.91/6.25 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.91/6.25 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.91/6.25 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.91/6.25 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (= A B)))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A B)))))
% 5.91/6.25 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A B)))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A B)))))
% 5.91/6.25 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A B)))))
% 5.91/6.25 (assert (= (lambda ((Y5 tptp.set_int) (Z4 tptp.set_int)) (= Y5 Z4)) (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)))))
% 5.91/6.25 (assert (= (lambda ((Y5 tptp.rat) (Z4 tptp.rat)) (= Y5 Z4)) (lambda ((A4 tptp.rat) (B4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A4) B4) (@ (@ tptp.ord_less_eq_rat B4) A4)))))
% 5.91/6.25 (assert (= (lambda ((Y5 tptp.num) (Z4 tptp.num)) (= Y5 Z4)) (lambda ((A4 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A4) B4) (@ (@ tptp.ord_less_eq_num B4) A4)))))
% 5.91/6.25 (assert (= (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)) (lambda ((A4 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A4) B4) (@ (@ tptp.ord_less_eq_nat B4) A4)))))
% 5.91/6.25 (assert (= (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4)) (lambda ((A4 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B4) (@ (@ tptp.ord_less_eq_int B4) A4)))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.25 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.25 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.25 (assert (forall ((A tptp.num) (F (-> tptp.nat tptp.num)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.25 (assert (forall ((A tptp.num) (F (-> tptp.int tptp.num)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (= X Y) (@ (@ tptp.ord_less_eq_set_int X) Y))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 5.91/6.25 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (= X Y) (@ (@ tptp.ord_less_eq_num X) Y))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 5.91/6.25 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (= X Y) (@ (@ tptp.ord_less_eq_int X) Y))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 5.91/6.25 (assert (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X) Y) (@ (@ tptp.ord_less_eq_num Y) X))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 5.91/6.25 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_eq_int Y) X))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 5.91/6.25 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 5.91/6.25 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 5.91/6.25 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 5.91/6.25 (assert (forall ((A tptp.int) (F (-> tptp.num tptp.int)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 5.91/6.25 (assert (forall ((A tptp.num) (F (-> tptp.nat tptp.num)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat X) Y)) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 5.91/6.25 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 5.91/6.25 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 5.91/6.25 (assert (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X) (= (@ (@ tptp.ord_less_eq_set_int X) Y) (= X Y)))))
% 5.91/6.25 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= (@ (@ tptp.ord_less_eq_rat X) Y) (= X Y)))))
% 5.91/6.25 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (= (@ (@ tptp.ord_less_eq_num X) Y) (= X Y)))))
% 5.91/6.25 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))))
% 5.91/6.25 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.ord_less_eq_int X) Y) (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X))))
% 5.91/6.25 (assert (forall ((X tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X))))
% 5.91/6.25 (assert (forall ((X tptp.int)) (exists ((Y3 tptp.int)) (@ (@ tptp.ord_less_int Y3) X))))
% 5.91/6.25 (assert (forall ((X tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X) X_1))))
% 5.91/6.25 (assert (forall ((X tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X) X_1))))
% 5.91/6.25 (assert (forall ((X tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X) X_1))))
% 5.91/6.25 (assert (forall ((X tptp.int)) (exists ((X_1 tptp.int)) (@ (@ tptp.ord_less_int X) X_1))))
% 5.91/6.25 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (exists ((Z3 tptp.real)) (and (@ (@ tptp.ord_less_real X) Z3) (@ (@ tptp.ord_less_real Z3) Y))))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (exists ((Z3 tptp.rat)) (and (@ (@ tptp.ord_less_rat X) Z3) (@ (@ tptp.ord_less_rat Z3) Y))))))
% 5.91/6.25 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= X Y)))))
% 5.91/6.25 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 5.91/6.25 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 5.91/6.25 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 5.91/6.25 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (= A B) (=> (@ (@ tptp.ord_less_real B) C) (@ (@ tptp.ord_less_real A) C)))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (= A B) (=> (@ (@ tptp.ord_less_rat B) C) (@ (@ tptp.ord_less_rat A) C)))))
% 5.91/6.25 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (= A B) (=> (@ (@ tptp.ord_less_num B) C) (@ (@ tptp.ord_less_num A) C)))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))))
% 5.91/6.25 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_int B) C) (@ (@ tptp.ord_less_int A) C)))))
% 5.91/6.25 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.91/6.25 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.91/6.25 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.91/6.25 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y4) X4) (@ P Y4))) (@ P X4))) (@ P A))))
% 5.91/6.25 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.ord_less_real Y) X)) (= (not (@ (@ tptp.ord_less_real X) Y)) (= X Y)))))
% 5.91/6.25 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat Y) X)) (= (not (@ (@ tptp.ord_less_rat X) Y)) (= X Y)))))
% 5.91/6.25 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_num Y) X)) (= (not (@ (@ tptp.ord_less_num X) Y)) (= X Y)))))
% 5.91/6.25 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y) X)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))))
% 5.91/6.25 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y) X)) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_real Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_rat Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_num Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 5.91/6.25 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real A) B)))))
% 5.91/6.25 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat A) B)))))
% 5.91/6.25 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num A) B)))))
% 5.91/6.25 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))))
% 5.91/6.25 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int A) B)))))
% 5.91/6.25 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 5.91/6.25 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 5.91/6.25 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 5.91/6.25 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 5.91/6.25 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 5.91/6.25 (assert (= (lambda ((P2 (-> tptp.nat Bool))) (exists ((X6 tptp.nat)) (@ P2 X6))) (lambda ((P3 (-> tptp.nat Bool))) (exists ((N4 tptp.nat)) (and (@ P3 N4) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N4) (not (@ P3 M3)))))))))
% 5.91/6.25 (assert (forall ((P (-> tptp.real tptp.real Bool)) (A tptp.real) (B tptp.real)) (=> (forall ((A5 tptp.real) (B5 tptp.real)) (=> (@ (@ tptp.ord_less_real A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.real)) (@ (@ P A5) A5)) (=> (forall ((A5 tptp.real) (B5 tptp.real)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B))))))
% 5.91/6.25 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B tptp.rat)) (=> (forall ((A5 tptp.rat) (B5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.rat)) (@ (@ P A5) A5)) (=> (forall ((A5 tptp.rat) (B5 tptp.rat)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B))))))
% 5.91/6.25 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (@ (@ tptp.ord_less_num A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.num)) (@ (@ P A5) A5)) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B))))))
% 5.91/6.25 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.nat)) (@ (@ P A5) A5)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B))))))
% 5.91/6.25 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (@ (@ tptp.ord_less_int A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.int)) (@ (@ P A5) A5)) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B))))))
% 5.91/6.25 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_real B) C) (@ _let_1 C))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_rat B) C) (@ _let_1 C))))))
% 5.91/6.25 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_num B) C) (@ _let_1 C))))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat B) C) (@ _let_1 C))))))
% 5.91/6.25 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_int B) C) (@ _let_1 C))))))
% 5.91/6.25 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X) Y)) (or (@ (@ tptp.ord_less_real Y) X) (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X) Y)) (or (@ (@ tptp.ord_less_rat Y) X) (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y)) (or (@ (@ tptp.ord_less_num Y) X) (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (or (@ (@ tptp.ord_less_nat Y) X) (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (or (@ (@ tptp.ord_less_int Y) X) (= X Y)))))
% 5.91/6.25 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.91/6.25 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.91/6.25 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ (@ tptp.ord_less_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.91/6.25 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.91/6.25 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.91/6.25 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (= A B)))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (= A B)))))
% 5.91/6.25 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (= A B)))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (= A B)))))
% 5.91/6.25 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (= A B)))))
% 5.91/6.25 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (= A B)))))
% 5.91/6.25 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (= A B)))))
% 5.91/6.25 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (= A B)))))
% 5.91/6.25 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (= A B)))))
% 5.91/6.25 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (= A B)))))
% 5.91/6.25 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_real Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_rat Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_num Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (@ (@ tptp.ord_less_real Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (@ (@ tptp.ord_less_rat Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_rat X) Y) (@ (@ tptp.ord_less_rat Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_num X) Y) (@ (@ tptp.ord_less_num Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_nat Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_int X) Y) (@ (@ tptp.ord_less_int Y) X)))))
% 5.91/6.25 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 5.91/6.25 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 5.91/6.25 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 5.91/6.25 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_real Y) Z) (@ _let_1 Z))))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_rat Y) Z) (@ _let_1 Z))))))
% 5.91/6.25 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_num Y) Z) (@ _let_1 Z))))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ _let_1 Z))))))
% 5.91/6.25 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ _let_1 Z))))))
% 5.91/6.25 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 5.91/6.25 (assert (forall ((A tptp.num) (F (-> tptp.real tptp.num)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (F (-> tptp.real tptp.nat)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 5.91/6.25 (assert (forall ((A tptp.int) (F (-> tptp.real tptp.int)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 5.91/6.25 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 5.91/6.25 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 5.91/6.25 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 5.91/6.25 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_real X) X))))
% 5.91/6.25 (assert (forall ((X tptp.rat)) (not (@ (@ tptp.ord_less_rat X) X))))
% 5.91/6.25 (assert (forall ((X tptp.num)) (not (@ (@ tptp.ord_less_num X) X))))
% 5.91/6.25 (assert (forall ((X tptp.nat)) (not (@ (@ tptp.ord_less_nat X) X))))
% 5.91/6.25 (assert (forall ((X tptp.int)) (not (@ (@ tptp.ord_less_int X) X))))
% 5.91/6.25 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.25 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.25 (assert (forall ((A tptp.real) (F (-> tptp.num tptp.real)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.25 (assert (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.25 (assert (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.25 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 5.91/6.25 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (@ (@ tptp.ord_less_real Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (@ (@ tptp.ord_less_rat Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.real) (Y tptp.real) (P Bool)) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_real Y) X) P))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat) (P Bool)) (=> (@ (@ tptp.ord_less_rat X) Y) (=> (@ (@ tptp.ord_less_rat Y) X) P))))
% 5.91/6.25 (assert (forall ((X tptp.num) (Y tptp.num) (P Bool)) (=> (@ (@ tptp.ord_less_num X) Y) (=> (@ (@ tptp.ord_less_num Y) X) P))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Y tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) X) P))))
% 5.91/6.25 (assert (forall ((X tptp.int) (Y tptp.int) (P Bool)) (=> (@ (@ tptp.ord_less_int X) Y) (=> (@ (@ tptp.ord_less_int Y) X) P))))
% 5.91/6.25 (assert (forall ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X) Y) (= X Y) (@ (@ tptp.ord_less_real Y) X))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_rat X) Y) (= X Y) (@ (@ tptp.ord_less_rat Y) X))))
% 5.91/6.25 (assert (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_num X) Y) (= X Y) (@ (@ tptp.ord_less_num Y) X))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y) (@ (@ tptp.ord_less_nat Y) X))))
% 5.91/6.25 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X) Y) (= X Y) (@ (@ tptp.ord_less_int Y) X))))
% 5.91/6.25 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (= Y X)))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (= Y X)))))
% 5.91/6.25 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= Y X)))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= Y X)))))
% 5.91/6.25 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= Y X)))))
% 5.91/6.25 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (@ (@ tptp.ord_less_real Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (@ (@ tptp.ord_less_rat Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 5.91/6.25 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 5.91/6.25 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X) (not (@ (@ tptp.ord_less_real X) Y)))))
% 5.91/6.25 (assert (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X) (not (@ (@ tptp.ord_less_set_int X) Y)))))
% 5.91/6.25 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (not (@ (@ tptp.ord_less_rat X) Y)))))
% 5.91/6.25 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (not (@ (@ tptp.ord_less_num X) Y)))))
% 5.91/6.25 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (not (@ (@ tptp.ord_less_nat X) Y)))))
% 5.91/6.25 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (not (@ (@ tptp.ord_less_int X) Y)))))
% 5.91/6.25 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_eq_real Y) X))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 5.91/6.25 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 5.91/6.25 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 5.91/6.25 (assert (forall ((A tptp.real) (B tptp.real)) (= (not (@ (@ tptp.ord_less_real A) B)) (or (not (@ (@ tptp.ord_less_eq_real A) B)) (= A B)))))
% 5.91/6.25 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (not (@ (@ tptp.ord_less_set_int A) B)) (or (not (@ (@ tptp.ord_less_eq_set_int A) B)) (= A B)))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ (@ tptp.ord_less_rat A) B)) (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (= A B)))))
% 5.91/6.25 (assert (forall ((A tptp.num) (B tptp.num)) (= (not (@ (@ tptp.ord_less_num A) B)) (or (not (@ (@ tptp.ord_less_eq_num A) B)) (= A B)))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (not (@ (@ tptp.ord_less_nat A) B)) (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (= A B)))))
% 5.91/6.25 (assert (forall ((A tptp.int) (B tptp.int)) (= (not (@ (@ tptp.ord_less_int A) B)) (or (not (@ (@ tptp.ord_less_eq_int A) B)) (= A B)))))
% 5.91/6.25 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (= (@ (@ tptp.ord_less_eq_real X) Y) (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (not (@ (@ tptp.ord_less_set_int X) Y)) (= (@ (@ tptp.ord_less_eq_set_int X) Y) (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (= (@ (@ tptp.ord_less_eq_rat X) Y) (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (= (@ (@ tptp.ord_less_eq_num X) Y) (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (= (@ (@ tptp.ord_less_eq_int X) Y) (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (= (not (@ (@ tptp.ord_less_real X) Y)) (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (= (not (@ (@ tptp.ord_less_set_int X) Y)) (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (= (not (@ (@ tptp.ord_less_rat X) Y)) (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (= (not (@ (@ tptp.ord_less_num X) Y)) (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))))
% 5.91/6.25 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))))
% 5.91/6.25 (assert (forall ((Z tptp.real) (Y tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X4) (@ (@ tptp.ord_less_eq_real Y) X4))) (@ (@ tptp.ord_less_eq_real Y) Z))))
% 5.91/6.25 (assert (forall ((Z tptp.rat) (Y tptp.rat)) (=> (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X4) (@ (@ tptp.ord_less_eq_rat Y) X4))) (@ (@ tptp.ord_less_eq_rat Y) Z))))
% 5.91/6.25 (assert (forall ((Y tptp.real) (Z tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_eq_real X4) Z))) (@ (@ tptp.ord_less_eq_real Y) Z))))
% 5.91/6.25 (assert (forall ((Y tptp.rat) (Z tptp.rat)) (=> (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (@ (@ tptp.ord_less_eq_rat X4) Z))) (@ (@ tptp.ord_less_eq_rat Y) Z))))
% 5.91/6.25 (assert (= tptp.ord_less_real (lambda ((X3 tptp.real) (Y2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X3) Y2) (not (@ (@ tptp.ord_less_eq_real Y2) X3))))))
% 5.91/6.25 (assert (= tptp.ord_less_set_int (lambda ((X3 tptp.set_int) (Y2 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X3) Y2) (not (@ (@ tptp.ord_less_eq_set_int Y2) X3))))))
% 5.91/6.25 (assert (= tptp.ord_less_rat (lambda ((X3 tptp.rat) (Y2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X3) Y2) (not (@ (@ tptp.ord_less_eq_rat Y2) X3))))))
% 5.91/6.25 (assert (= tptp.ord_less_num (lambda ((X3 tptp.num) (Y2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X3) Y2) (not (@ (@ tptp.ord_less_eq_num Y2) X3))))))
% 5.91/6.25 (assert (= tptp.ord_less_nat (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y2) (not (@ (@ tptp.ord_less_eq_nat Y2) X3))))))
% 5.91/6.25 (assert (= tptp.ord_less_int (lambda ((X3 tptp.int) (Y2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X3) Y2) (not (@ (@ tptp.ord_less_eq_int Y2) X3))))))
% 5.91/6.25 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real Y) X)) (@ (@ tptp.ord_less_real X) Y))))
% 5.91/6.25 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat Y) X)) (@ (@ tptp.ord_less_rat X) Y))))
% 5.91/6.25 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num Y) X)) (@ (@ tptp.ord_less_num X) Y))))
% 5.91/6.25 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y) X)) (@ (@ tptp.ord_less_nat X) Y))))
% 5.91/6.25 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y) X)) (@ (@ tptp.ord_less_int X) Y))))
% 5.91/6.25 (assert (= tptp.ord_less_eq_real (lambda ((A4 tptp.real) (B4 tptp.real)) (or (@ (@ tptp.ord_less_real A4) B4) (= A4 B4)))))
% 5.91/6.25 (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)))))
% 5.91/6.25 (assert (= tptp.ord_less_eq_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (or (@ (@ tptp.ord_less_rat A4) B4) (= A4 B4)))))
% 5.91/6.25 (assert (= tptp.ord_less_eq_num (lambda ((A4 tptp.num) (B4 tptp.num)) (or (@ (@ tptp.ord_less_num A4) B4) (= A4 B4)))))
% 5.91/6.25 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (or (@ (@ tptp.ord_less_nat A4) B4) (= A4 B4)))))
% 5.91/6.25 (assert (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B4 tptp.int)) (or (@ (@ tptp.ord_less_int A4) B4) (= A4 B4)))))
% 5.91/6.25 (assert (= tptp.ord_less_real (lambda ((A4 tptp.real) (B4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A4) B4) (not (= A4 B4))))))
% 5.91/6.25 (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))))))
% 5.91/6.25 (assert (= tptp.ord_less_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A4) B4) (not (= A4 B4))))))
% 5.91/6.25 (assert (= tptp.ord_less_num (lambda ((A4 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A4) B4) (not (= A4 B4))))))
% 5.91/6.25 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A4) B4) (not (= A4 B4))))))
% 5.91/6.25 (assert (= tptp.ord_less_int (lambda ((A4 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B4) (not (= A4 B4))))))
% 5.91/6.25 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real B) C) (@ (@ tptp.ord_less_real A) C)))))
% 5.91/6.25 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (@ (@ tptp.ord_less_set_int B) C) (@ (@ tptp.ord_less_set_int A) C)))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat B) C) (@ (@ tptp.ord_less_rat A) C)))))
% 5.91/6.25 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_num B) C) (@ (@ tptp.ord_less_num A) C)))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))))
% 5.91/6.25 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int B) C) (@ (@ tptp.ord_less_int A) C)))))
% 5.91/6.25 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_real B) C) (@ _let_1 C))))))
% 5.91/6.25 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_int B) C) (@ _let_1 C))))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ _let_1 C))))))
% 5.91/6.25 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_num B) C) (@ _let_1 C))))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))))
% 5.91/6.25 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ _let_1 C))))))
% 5.91/6.25 (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))))))
% 5.91/6.25 (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))))))
% 5.91/6.25 (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))))))
% 5.91/6.25 (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))))))
% 5.91/6.25 (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))))))
% 5.91/6.25 (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))))))
% 5.91/6.25 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X) (=> (forall ((W tptp.real)) (=> (@ (@ tptp.ord_less_real Z) W) (=> (@ (@ tptp.ord_less_real W) X) (@ (@ tptp.ord_less_eq_real Y) W)))) (@ (@ tptp.ord_less_eq_real Y) Z)))))
% 5.91/6.25 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X) (=> (forall ((W tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) W) (=> (@ (@ tptp.ord_less_rat W) X) (@ (@ tptp.ord_less_eq_rat Y) W)))) (@ (@ tptp.ord_less_eq_rat Y) Z)))))
% 5.91/6.25 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (=> (forall ((W tptp.real)) (=> (@ (@ tptp.ord_less_real X) W) (=> (@ (@ tptp.ord_less_real W) Y) (@ (@ tptp.ord_less_eq_real W) Z)))) (@ (@ tptp.ord_less_eq_real Y) Z)))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (=> (forall ((W tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) W) (=> (@ (@ tptp.ord_less_rat W) Y) (@ (@ tptp.ord_less_eq_rat W) Z)))) (@ (@ tptp.ord_less_eq_rat Y) Z)))))
% 5.91/6.25 (assert (= tptp.ord_less_eq_real (lambda ((B4 tptp.real) (A4 tptp.real)) (or (@ (@ tptp.ord_less_real B4) A4) (= A4 B4)))))
% 5.91/6.25 (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)))))
% 5.91/6.25 (assert (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A4 tptp.rat)) (or (@ (@ tptp.ord_less_rat B4) A4) (= A4 B4)))))
% 5.91/6.25 (assert (= tptp.ord_less_eq_num (lambda ((B4 tptp.num) (A4 tptp.num)) (or (@ (@ tptp.ord_less_num B4) A4) (= A4 B4)))))
% 5.91/6.25 (assert (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (or (@ (@ tptp.ord_less_nat B4) A4) (= A4 B4)))))
% 5.91/6.25 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A4 tptp.int)) (or (@ (@ tptp.ord_less_int B4) A4) (= A4 B4)))))
% 5.91/6.25 (assert (= tptp.ord_less_real (lambda ((B4 tptp.real) (A4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B4) A4) (not (= A4 B4))))))
% 5.91/6.25 (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))))))
% 5.91/6.25 (assert (= tptp.ord_less_rat (lambda ((B4 tptp.rat) (A4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B4) A4) (not (= A4 B4))))))
% 5.91/6.25 (assert (= tptp.ord_less_num (lambda ((B4 tptp.num) (A4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B4) A4) (not (= A4 B4))))))
% 5.91/6.25 (assert (= tptp.ord_less_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B4) A4) (not (= A4 B4))))))
% 5.91/6.25 (assert (= tptp.ord_less_int (lambda ((B4 tptp.int) (A4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B4) A4) (not (= A4 B4))))))
% 5.91/6.25 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.91/6.25 (assert (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int C))) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.91/6.25 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.91/6.25 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.91/6.25 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.91/6.25 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.91/6.25 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_eq_real C) B) (@ (@ tptp.ord_less_real C) A)))))
% 5.91/6.25 (assert (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B) A) (=> (@ (@ tptp.ord_less_eq_set_int C) B) (@ (@ tptp.ord_less_set_int C) A)))))
% 5.91/6.25 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) B) (@ (@ tptp.ord_less_rat C) A)))))
% 5.91/6.25 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (=> (@ (@ tptp.ord_less_eq_num C) B) (@ (@ tptp.ord_less_num C) A)))))
% 5.91/6.25 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C) B) (@ (@ tptp.ord_less_nat C) A)))))
% 5.91/6.25 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) B) (@ (@ tptp.ord_less_int C) A)))))
% 5.91/6.25 (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))))))
% 5.91/6.25 (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))))))
% 5.91/6.25 (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))))))
% 5.91/6.25 (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))))))
% 5.91/6.25 (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))))))
% 5.91/6.25 (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))))))
% 5.91/6.25 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_eq_real A) B))))
% 5.91/6.25 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A) B) (@ (@ tptp.ord_less_eq_set_int A) B))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_eq_rat A) B))))
% 5.91/6.25 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (@ (@ tptp.ord_less_eq_num A) B))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_eq_nat A) B))))
% 5.91/6.25 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_eq_int A) B))))
% 5.91/6.25 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_eq_real B) A))))
% 5.91/6.25 (assert (forall ((B tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B) A) (@ (@ tptp.ord_less_eq_set_int B) A))))
% 5.91/6.25 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_eq_rat B) A))))
% 5.91/6.25 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (@ (@ tptp.ord_less_eq_num B) A))))
% 5.91/6.25 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (@ (@ tptp.ord_less_eq_nat B) A))))
% 5.91/6.25 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_eq_int B) A))))
% 5.91/6.25 (assert (= tptp.ord_less_eq_real (lambda ((X3 tptp.real) (Y2 tptp.real)) (or (@ (@ tptp.ord_less_real X3) Y2) (= X3 Y2)))))
% 5.91/6.25 (assert (= tptp.ord_less_eq_set_int (lambda ((X3 tptp.set_int) (Y2 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int X3) Y2) (= X3 Y2)))))
% 5.91/6.25 (assert (= tptp.ord_less_eq_rat (lambda ((X3 tptp.rat) (Y2 tptp.rat)) (or (@ (@ tptp.ord_less_rat X3) Y2) (= X3 Y2)))))
% 5.91/6.25 (assert (= tptp.ord_less_eq_num (lambda ((X3 tptp.num) (Y2 tptp.num)) (or (@ (@ tptp.ord_less_num X3) Y2) (= X3 Y2)))))
% 5.91/6.25 (assert (= tptp.ord_less_eq_nat (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (or (@ (@ tptp.ord_less_nat X3) Y2) (= X3 Y2)))))
% 5.91/6.25 (assert (= tptp.ord_less_eq_int (lambda ((X3 tptp.int) (Y2 tptp.int)) (or (@ (@ tptp.ord_less_int X3) Y2) (= X3 Y2)))))
% 5.91/6.25 (assert (= tptp.ord_less_real (lambda ((X3 tptp.real) (Y2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X3) Y2) (not (= X3 Y2))))))
% 5.91/6.25 (assert (= tptp.ord_less_set_int (lambda ((X3 tptp.set_int) (Y2 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X3) Y2) (not (= X3 Y2))))))
% 5.91/6.25 (assert (= tptp.ord_less_rat (lambda ((X3 tptp.rat) (Y2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X3) Y2) (not (= X3 Y2))))))
% 5.91/6.25 (assert (= tptp.ord_less_num (lambda ((X3 tptp.num) (Y2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X3) Y2) (not (= X3 Y2))))))
% 5.91/6.25 (assert (= tptp.ord_less_nat (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y2) (not (= X3 Y2))))))
% 5.91/6.25 (assert (= tptp.ord_less_int (lambda ((X3 tptp.int) (Y2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X3) Y2) (not (= X3 Y2))))))
% 5.91/6.25 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real X) Y)) (@ (@ tptp.ord_less_real Y) X))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat X) Y)) (@ (@ tptp.ord_less_rat Y) X))))
% 5.91/6.25 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num X) Y)) (@ (@ tptp.ord_less_num Y) X))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X))))
% 5.91/6.25 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X) Y)) (@ (@ tptp.ord_less_int Y) X))))
% 5.91/6.25 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_eq_real Y) X))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 5.91/6.25 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 5.91/6.25 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 5.91/6.25 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_eq_real X) Y))))
% 5.91/6.25 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int X) Y) (@ (@ tptp.ord_less_eq_set_int X) Y))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 5.91/6.25 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (@ (@ tptp.ord_less_eq_num X) Y))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 5.91/6.25 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (@ (@ tptp.ord_less_eq_int X) Y))))
% 5.91/6.25 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_real A) B)))))
% 5.91/6.25 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_set_int A) B)))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_rat A) B)))))
% 5.91/6.25 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_num A) B)))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_nat A) B)))))
% 5.91/6.25 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_int A) B)))))
% 5.91/6.25 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_real A) B)))))
% 5.91/6.25 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (@ (@ tptp.ord_less_set_int A) B)))))
% 5.91/6.25 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_rat A) B)))))
% 5.91/6.25 (assert (forall ((A tptp.num) (B tptp.num)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_num A) B) (@ (@ tptp.ord_less_num A) B)))))
% 5.91/6.25 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_nat A) B)))))
% 5.91/6.25 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_int A) B)))))
% 5.91/6.25 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_real Y) Z) (@ (@ tptp.ord_less_real X) Z)))))
% 5.91/6.25 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (=> (@ (@ tptp.ord_less_set_int Y) Z) (@ (@ tptp.ord_less_set_int X) Z)))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ (@ tptp.ord_less_rat Y) Z) (@ (@ tptp.ord_less_rat X) Z)))))
% 5.91/6.25 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (=> (@ (@ tptp.ord_less_num Y) Z) (@ (@ tptp.ord_less_num X) Z)))))
% 5.91/6.25 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ (@ tptp.ord_less_nat X) Z)))))
% 5.91/6.25 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int X) Z)))))
% 5.91/6.25 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) Z) (@ _let_1 Z))))))
% 5.91/6.25 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) Z) (@ _let_1 Z))))))
% 5.91/6.25 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z) (@ _let_1 Z))))))
% 5.91/6.26 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z) (@ _let_1 Z))))))
% 5.91/6.26 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))))
% 5.91/6.26 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (F (-> tptp.num tptp.real)) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 5.91/6.26 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 5.91/6.26 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 5.91/6.26 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 5.91/6.26 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 5.91/6.26 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.26 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (F (-> tptp.num tptp.real)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.26 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (F (-> tptp.num tptp.int)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 5.91/6.26 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 5.91/6.26 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 5.91/6.26 (assert (forall ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_real Y) X))))
% 5.91/6.26 (assert (forall ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_rat Y) X))))
% 5.91/6.26 (assert (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X) Y) (@ (@ tptp.ord_less_num Y) X))))
% 5.91/6.26 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_nat Y) X))))
% 5.91/6.26 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_int Y) X))))
% 5.91/6.26 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (or (@ (@ tptp.ord_less_real X) Y) (= X Y)))))
% 5.91/6.26 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (or (@ (@ tptp.ord_less_set_int X) Y) (= X Y)))))
% 5.91/6.26 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (or (@ (@ tptp.ord_less_rat X) Y) (= X Y)))))
% 5.91/6.26 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (or (@ (@ tptp.ord_less_num X) Y) (= X Y)))))
% 5.91/6.26 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y)))))
% 5.91/6.26 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (or (@ (@ tptp.ord_less_int X) Y) (= X Y)))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_set_nat)) (=> (forall ((X4 tptp.set_nat)) (not (@ (@ tptp.member_set_nat X4) A2))) (@ (@ tptp.ord_le6893508408891458716et_nat A2) tptp.bot_bot_set_set_nat))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_set_nat_rat)) (=> (forall ((X4 tptp.set_nat_rat)) (not (@ (@ tptp.member_set_nat_rat X4) A2))) (@ (@ tptp.ord_le4375437777232675859at_rat A2) tptp.bot_bo6797373522285170759at_rat))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_real)) (=> (forall ((X4 tptp.real)) (not (@ (@ tptp.member_real X4) A2))) (@ (@ tptp.ord_less_eq_set_real A2) tptp.bot_bot_set_real))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_o)) (=> (forall ((X4 Bool)) (not (@ (@ tptp.member_o X4) A2))) (@ (@ tptp.ord_less_eq_set_o A2) tptp.bot_bot_set_o))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_nat)) (=> (forall ((X4 tptp.nat)) (not (@ (@ tptp.member_nat X4) A2))) (@ (@ tptp.ord_less_eq_set_nat A2) tptp.bot_bot_set_nat))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_int)) (=> (forall ((X4 tptp.int)) (not (@ (@ tptp.member_int X4) A2))) (@ (@ tptp.ord_less_eq_set_int A2) tptp.bot_bot_set_int))))
% 5.91/6.26 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z3) (not (@ (@ tptp.ord_less_eq_real T) X2)))))))
% 5.91/6.26 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Z3) (not (@ (@ tptp.ord_less_eq_rat T) X2)))))))
% 5.91/6.26 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Z3) (not (@ (@ tptp.ord_less_eq_num T) X2)))))))
% 5.91/6.26 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z3) (not (@ (@ tptp.ord_less_eq_nat T) X2)))))))
% 5.91/6.26 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z3) (not (@ (@ tptp.ord_less_eq_int T) X2)))))))
% 5.91/6.26 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z3) (@ (@ tptp.ord_less_eq_real X2) T))))))
% 5.91/6.26 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Z3) (@ (@ tptp.ord_less_eq_rat X2) T))))))
% 5.91/6.26 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Z3) (@ (@ tptp.ord_less_eq_num X2) T))))))
% 5.91/6.26 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z3) (@ (@ tptp.ord_less_eq_nat X2) T))))))
% 5.91/6.26 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z3) (@ (@ tptp.ord_less_eq_int X2) T))))))
% 5.91/6.26 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X2) (@ (@ tptp.ord_less_eq_real T) X2))))))
% 5.91/6.26 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X2) (@ (@ tptp.ord_less_eq_rat T) X2))))))
% 5.91/6.26 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X2) (@ (@ tptp.ord_less_eq_num T) X2))))))
% 5.91/6.26 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X2) (@ (@ tptp.ord_less_eq_nat T) X2))))))
% 5.91/6.26 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X2) (@ (@ tptp.ord_less_eq_int T) X2))))))
% 5.91/6.26 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X2) (not (@ (@ tptp.ord_less_eq_real X2) T)))))))
% 5.91/6.26 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X2) (not (@ (@ tptp.ord_less_eq_rat X2) T)))))))
% 5.91/6.26 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X2) (not (@ (@ tptp.ord_less_eq_num X2) T)))))))
% 5.91/6.26 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X2) (not (@ (@ tptp.ord_less_eq_nat X2) T)))))))
% 5.91/6.26 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X2) (not (@ (@ tptp.ord_less_eq_int X2) T)))))))
% 5.91/6.26 (assert (forall ((B7 tptp.real) (A7 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B7) A7)) (@ (@ tptp.ord_less_real A7) B7))))
% 5.91/6.26 (assert (forall ((B7 tptp.rat) (A7 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat B7) A7)) (@ (@ tptp.ord_less_rat A7) B7))))
% 5.91/6.26 (assert (forall ((B7 tptp.num) (A7 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B7) A7)) (@ (@ tptp.ord_less_num A7) B7))))
% 5.91/6.26 (assert (forall ((B7 tptp.nat) (A7 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B7) A7)) (@ (@ tptp.ord_less_nat A7) B7))))
% 5.91/6.26 (assert (forall ((B7 tptp.int) (A7 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B7) A7)) (@ (@ tptp.ord_less_int A7) B7))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (P (-> tptp.real Bool))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ P A) (=> (not (@ P B)) (exists ((C3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A) C3) (@ (@ tptp.ord_less_eq_real C3) B) (forall ((X2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X2) (@ (@ tptp.ord_less_real X2) C3)) (@ P X2))) (forall ((D3 tptp.real)) (=> (forall ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X4) (@ (@ tptp.ord_less_real X4) D3)) (@ P X4))) (@ (@ tptp.ord_less_eq_real D3) C3))))))))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ P A) (=> (not (@ P B)) (exists ((C3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A) C3) (@ (@ tptp.ord_less_eq_nat C3) B) (forall ((X2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A) X2) (@ (@ tptp.ord_less_nat X2) C3)) (@ P X2))) (forall ((D3 tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A) X4) (@ (@ tptp.ord_less_nat X4) D3)) (@ P X4))) (@ (@ tptp.ord_less_eq_nat D3) C3))))))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ P A) (=> (not (@ P B)) (exists ((C3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) C3) (@ (@ tptp.ord_less_eq_int C3) B) (forall ((X2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int A) X2) (@ (@ tptp.ord_less_int X2) C3)) (@ P X2))) (forall ((D3 tptp.int)) (=> (forall ((X4 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int A) X4) (@ (@ tptp.ord_less_int X4) D3)) (@ P X4))) (@ (@ tptp.ord_less_eq_int D3) C3))))))))))
% 5.91/6.26 (assert (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) (@ tptp.suc (@ tptp.suc N))) (exists ((Info2 tptp.option4927543243414619207at_nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (= Tree (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc (@ tptp.suc N))) TreeList2) S3))))))
% 5.91/6.26 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.zero_zero_complex) tptp.one_one_complex))
% 5.91/6.26 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.zero_zero_real) tptp.one_one_real))
% 5.91/6.26 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 5.91/6.26 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int))
% 5.91/6.26 (assert (forall ((X21 Bool) (X22 Bool)) (= (@ tptp.vEBT_size_VEBT (@ (@ tptp.vEBT_Leaf X21) X22)) tptp.zero_zero_nat)))
% 5.91/6.26 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (@ tptp.vEBT_VEBT_minNull T) (not (@ (@ tptp.vEBT_vebt_member T) X)))))
% 5.91/6.26 (assert (forall ((T tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull T)) (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_1)))))
% 5.91/6.26 (assert (forall ((X23 tptp.nat) (Y23 tptp.nat)) (= (= (@ tptp.suc X23) (@ tptp.suc Y23)) (= X23 Y23))))
% 5.91/6.26 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M2) N))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N)))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.suc M2)) (@ (@ tptp.ord_less_eq_nat N) M2))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y)) (= X Y))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M4 tptp.nat)) (= N (@ tptp.suc M4))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M2)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M2)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat)) (not (= (@ tptp.suc M2) tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N2 tptp.nat)) (=> (@ P (@ tptp.suc N2)) (@ P N2))) (@ P tptp.zero_zero_nat)))))
% 5.91/6.26 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (=> (forall ((X4 tptp.nat)) (@ (@ P X4) tptp.zero_zero_nat)) (=> (forall ((Y3 tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y3))) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ P X4) Y3) (@ (@ P (@ tptp.suc X4)) (@ tptp.suc Y3)))) (@ (@ P M2) N))))))
% 5.91/6.26 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N2 tptp.nat)) (=> (@ P N2) (@ P (@ tptp.suc N2)))) (@ P N)))))
% 5.91/6.26 (assert (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (=> (not (= X (@ tptp.suc tptp.zero_zero_nat))) (not (forall ((Va tptp.nat)) (not (= X (@ tptp.suc (@ tptp.suc Va))))))))))
% 5.91/6.26 (assert (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y (@ tptp.suc Nat3))))))))
% 5.91/6.26 (assert (forall ((Nat tptp.nat) (X23 tptp.nat)) (=> (= Nat (@ tptp.suc X23)) (not (= Nat tptp.zero_zero_nat)))))
% 5.91/6.26 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 5.91/6.26 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((X23 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X23)))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M2)) (= (@ _let_1 (@ tptp.suc M2)) (= N M2))))))
% 5.91/6.26 (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))))))
% 5.91/6.26 (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))))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M2) N))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M2)) (=> (@ _let_1 (@ tptp.suc M2)) (= M2 N))))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) M2) (exists ((M6 tptp.nat)) (and (= M2 (@ tptp.suc M6)) (@ (@ tptp.ord_less_nat N) M6))))))
% 5.91/6.26 (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)))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M2) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M2)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (= (@ _let_1 (@ tptp.suc N)) (or (@ _let_1 N) (= M2 N))))))
% 5.91/6.26 (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)))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (=> (@ _let_1 (@ tptp.suc N)) (=> (not (@ _let_1 N)) (= M2 N))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (=> (@ (@ tptp.ord_less_nat M2) N) (=> (not (= _let_1 N)) (@ (@ tptp.ord_less_nat _let_1) N))))))
% 5.91/6.26 (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)))))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_nat M2) N))))
% 5.91/6.26 (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))))))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M2))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N)) (= M2 _let_1)))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M2))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 5.91/6.26 (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))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M2))) (= (@ _let_2 _let_1) (or (@ _let_2 N) (= M2 _let_1)))))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M2) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M2))))
% 5.91/6.26 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ P M))) (@ P N2))) (@ P N))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (@ P M2) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (=> (@ P N2) (@ P (@ tptp.suc N2))))) (@ P N))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (forall ((X4 tptp.nat)) (@ (@ R X4) X4)) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ R X4))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z3) (@ _let_1 Z3))))) (=> (forall ((N2 tptp.nat)) (@ (@ R N2) (@ tptp.suc N2))) (@ (@ R M2) N)))))))
% 5.91/6.26 (assert (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf false) false)))
% 5.91/6.26 (assert (forall ((Uv Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf true) Uv)))))
% 5.91/6.26 (assert (forall ((Uu Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf Uu) true)))))
% 5.91/6.26 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_real (@ F N)) (@ F M2)) (@ (@ tptp.ord_less_nat N) M2)))))
% 5.91/6.26 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_rat (@ F N)) (@ F M2)) (@ (@ tptp.ord_less_nat N) M2)))))
% 5.91/6.26 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_num (@ F N)) (@ F M2)) (@ (@ tptp.ord_less_nat N) M2)))))
% 5.91/6.26 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_nat (@ F N)) (@ F M2)) (@ (@ tptp.ord_less_nat N) M2)))))
% 5.91/6.26 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_int (@ F N)) (@ F M2)) (@ (@ tptp.ord_less_nat N) M2)))))
% 5.91/6.26 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N7) (@ (@ tptp.ord_less_real (@ F N)) (@ F N7))))))
% 5.91/6.26 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N7) (@ (@ tptp.ord_less_rat (@ F N)) (@ F N7))))))
% 5.91/6.26 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N7) (@ (@ tptp.ord_less_num (@ F N)) (@ F N7))))))
% 5.91/6.26 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N7) (@ (@ tptp.ord_less_nat (@ F N)) (@ F N7))))))
% 5.91/6.26 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N7) (@ (@ tptp.ord_less_int (@ F N)) (@ F N7))))))
% 5.91/6.26 (assert (forall ((F (-> tptp.nat tptp.set_int)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (@ (@ tptp.ord_less_eq_set_int (@ F N)) (@ F N7))))))
% 5.91/6.26 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (@ (@ tptp.ord_less_eq_rat (@ F N)) (@ F N7))))))
% 5.91/6.26 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (@ (@ tptp.ord_less_eq_num (@ F N)) (@ F N7))))))
% 5.91/6.26 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (@ (@ tptp.ord_less_eq_nat (@ F N)) (@ F N7))))))
% 5.91/6.26 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (@ (@ tptp.ord_less_eq_int (@ F N)) (@ F N7))))))
% 5.91/6.26 (assert (forall ((F (-> tptp.nat tptp.set_int)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (@ (@ tptp.ord_less_eq_set_int (@ F N7)) (@ F N))))))
% 5.91/6.26 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (@ (@ tptp.ord_less_eq_rat (@ F N7)) (@ F N))))))
% 5.91/6.26 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (@ (@ tptp.ord_less_eq_num (@ F N7)) (@ F N))))))
% 5.91/6.26 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (@ (@ tptp.ord_less_eq_nat (@ F N7)) (@ F N))))))
% 5.91/6.26 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N7 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N7) (@ (@ tptp.ord_less_eq_int (@ F N7)) (@ F N))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M2) (@ tptp.suc N)) (or (= M2 tptp.zero_zero_nat) (exists ((J3 tptp.nat)) (and (= M2 (@ tptp.suc J3)) (@ (@ tptp.ord_less_nat J3) N)))))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M4 tptp.nat)) (= N (@ tptp.suc M4))))))
% 5.91/6.26 (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))))))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M3 tptp.nat)) (= N (@ tptp.suc M3))))))
% 5.91/6.26 (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))))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_nat M2) N))))
% 5.91/6.26 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P I) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N2) (=> (@ (@ tptp.ord_less_nat N2) J) (=> (@ P N2) (@ P (@ tptp.suc N2)))))) (@ P J))))))
% 5.91/6.26 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P J) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N2) (=> (@ (@ tptp.ord_less_nat N2) J) (=> (@ P (@ tptp.suc N2)) (@ P N2))))) (@ P I))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_nat M2) N))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc M2)) (= N M2)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M2) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 5.91/6.26 (assert (= tptp.ord_less_nat (lambda ((N4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N4)) __flatten_var_0))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_nat M2) (@ tptp.suc N)))))
% 5.91/6.26 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 5.91/6.26 (assert (forall ((A Bool) (B Bool) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A) B))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) (@ tptp.suc (@ tptp.suc N))) _let_1))))
% 5.91/6.26 (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))))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (or (= A B) (not (@ (@ tptp.ord_less_eq_rat A) B)) (not (@ (@ tptp.ord_less_eq_rat B) A)))))
% 5.91/6.26 (assert (forall ((A tptp.num) (B tptp.num)) (or (= A B) (not (@ (@ tptp.ord_less_eq_num A) B)) (not (@ (@ tptp.ord_less_eq_num B) A)))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (or (= A B) (not (@ (@ tptp.ord_less_eq_nat A) B)) (not (@ (@ tptp.ord_less_eq_nat B) A)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (or (= A B) (not (@ (@ tptp.ord_less_eq_int A) B)) (not (@ (@ tptp.ord_less_eq_int B) A)))))
% 5.91/6.26 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) A)))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 5.91/6.26 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 5.91/6.26 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 5.91/6.26 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 5.91/6.26 (assert (forall ((A tptp.real)) (exists ((B5 tptp.real)) (or (@ (@ tptp.ord_less_real A) B5) (@ (@ tptp.ord_less_real B5) A)))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 5.91/6.26 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 5.91/6.26 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 5.91/6.26 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 5.91/6.26 (assert (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q2 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X4) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X2) (= (and (@ P X2) (@ Q X2)) (and (@ P4 X2) (@ Q2 X2))))))))))
% 5.91/6.26 (assert (forall ((P (-> tptp.rat Bool)) (P4 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q2 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X4) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X2) (= (and (@ P X2) (@ Q X2)) (and (@ P4 X2) (@ Q2 X2))))))))))
% 5.91/6.26 (assert (forall ((P (-> tptp.num Bool)) (P4 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q2 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X4) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X2) (= (and (@ P X2) (@ Q X2)) (and (@ P4 X2) (@ Q2 X2))))))))))
% 5.91/6.26 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X4) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X2) (= (and (@ P X2) (@ Q X2)) (and (@ P4 X2) (@ Q2 X2))))))))))
% 5.91/6.26 (assert (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X2) (= (and (@ P X2) (@ Q X2)) (and (@ P4 X2) (@ Q2 X2))))))))))
% 5.91/6.26 (assert (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q2 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X4) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X2) (= (or (@ P X2) (@ Q X2)) (or (@ P4 X2) (@ Q2 X2))))))))))
% 5.91/6.26 (assert (forall ((P (-> tptp.rat Bool)) (P4 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q2 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X4) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X2) (= (or (@ P X2) (@ Q X2)) (or (@ P4 X2) (@ Q2 X2))))))))))
% 5.91/6.26 (assert (forall ((P (-> tptp.num Bool)) (P4 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q2 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X4) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X2) (= (or (@ P X2) (@ Q X2)) (or (@ P4 X2) (@ Q2 X2))))))))))
% 5.91/6.26 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X4) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X2) (= (or (@ P X2) (@ Q X2)) (or (@ P4 X2) (@ Q2 X2))))))))))
% 5.91/6.26 (assert (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X2) (= (or (@ P X2) (@ Q X2)) (or (@ P4 X2) (@ Q2 X2))))))))))
% 5.91/6.26 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X2) (not (= X2 T)))))))
% 5.91/6.26 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X2) (not (= X2 T)))))))
% 5.91/6.26 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X2) (not (= X2 T)))))))
% 5.91/6.26 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X2) (not (= X2 T)))))))
% 5.91/6.26 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X2) (not (= X2 T)))))))
% 5.91/6.26 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X2) (not (= X2 T)))))))
% 5.91/6.26 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X2) (not (= X2 T)))))))
% 5.91/6.26 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X2) (not (= X2 T)))))))
% 5.91/6.26 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X2) (not (= X2 T)))))))
% 5.91/6.26 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X2) (not (= X2 T)))))))
% 5.91/6.26 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X2) (not (@ (@ tptp.ord_less_real X2) T)))))))
% 5.91/6.26 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X2) (not (@ (@ tptp.ord_less_rat X2) T)))))))
% 5.91/6.26 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X2) (not (@ (@ tptp.ord_less_num X2) T)))))))
% 5.91/6.26 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X2) (not (@ (@ tptp.ord_less_nat X2) T)))))))
% 5.91/6.26 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X2) (not (@ (@ tptp.ord_less_int X2) T)))))))
% 5.91/6.26 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X2) (@ (@ tptp.ord_less_real T) X2))))))
% 5.91/6.26 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X2) (@ (@ tptp.ord_less_rat T) X2))))))
% 5.91/6.26 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X2) (@ (@ tptp.ord_less_num T) X2))))))
% 5.91/6.26 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X2) (@ (@ tptp.ord_less_nat T) X2))))))
% 5.91/6.26 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X2) (@ (@ tptp.ord_less_int T) X2))))))
% 5.91/6.26 (assert (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q2 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z5) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z5) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z3) (= (and (@ P X2) (@ Q X2)) (and (@ P4 X2) (@ Q2 X2))))))))))
% 5.91/6.26 (assert (forall ((P (-> tptp.rat Bool)) (P4 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q2 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z5) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z5) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Z3) (= (and (@ P X2) (@ Q X2)) (and (@ P4 X2) (@ Q2 X2))))))))))
% 5.91/6.26 (assert (forall ((P (-> tptp.num Bool)) (P4 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q2 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z5) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z5) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Z3) (= (and (@ P X2) (@ Q X2)) (and (@ P4 X2) (@ Q2 X2))))))))))
% 5.91/6.26 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z5) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z5) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z3) (= (and (@ P X2) (@ Q X2)) (and (@ P4 X2) (@ Q2 X2))))))))))
% 5.91/6.26 (assert (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z3) (= (and (@ P X2) (@ Q X2)) (and (@ P4 X2) (@ Q2 X2))))))))))
% 5.91/6.26 (assert (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q2 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z5) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z5) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z3) (= (or (@ P X2) (@ Q X2)) (or (@ P4 X2) (@ Q2 X2))))))))))
% 5.91/6.26 (assert (forall ((P (-> tptp.rat Bool)) (P4 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q2 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z5) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z5) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Z3) (= (or (@ P X2) (@ Q X2)) (or (@ P4 X2) (@ Q2 X2))))))))))
% 5.91/6.26 (assert (forall ((P (-> tptp.num Bool)) (P4 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q2 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z5) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z5) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Z3) (= (or (@ P X2) (@ Q X2)) (or (@ P4 X2) (@ Q2 X2))))))))))
% 5.91/6.26 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z5) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z5) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z3) (= (or (@ P X2) (@ Q X2)) (or (@ P4 X2) (@ Q2 X2))))))))))
% 5.91/6.26 (assert (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z3) (= (or (@ P X2) (@ Q X2)) (or (@ P4 X2) (@ Q2 X2))))))))))
% 5.91/6.26 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z3) (not (= X2 T)))))))
% 5.91/6.26 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Z3) (not (= X2 T)))))))
% 5.91/6.26 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Z3) (not (= X2 T)))))))
% 5.91/6.26 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z3) (not (= X2 T)))))))
% 5.91/6.26 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z3) (not (= X2 T)))))))
% 5.91/6.26 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z3) (not (= X2 T)))))))
% 5.91/6.26 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Z3) (not (= X2 T)))))))
% 5.91/6.26 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Z3) (not (= X2 T)))))))
% 5.91/6.26 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z3) (not (= X2 T)))))))
% 5.91/6.26 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z3) (not (= X2 T)))))))
% 5.91/6.26 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 5.91/6.26 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X2))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 5.91/6.26 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X2))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 5.91/6.26 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X2))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 5.91/6.26 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X2))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 5.91/6.26 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z3) (not (@ (@ tptp.ord_less_real T) X2)))))))
% 5.91/6.26 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Z3) (not (@ (@ tptp.ord_less_rat T) X2)))))))
% 5.91/6.26 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Z3) (not (@ (@ tptp.ord_less_num T) X2)))))))
% 5.91/6.26 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z3) (not (@ (@ tptp.ord_less_nat T) X2)))))))
% 5.91/6.26 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z3) (not (@ (@ tptp.ord_less_int T) X2)))))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ P tptp.one_one_nat) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ P N2) (@ P (@ tptp.suc N2))))) (@ P N))))))
% 5.91/6.26 (assert (forall ((A Bool) (B Bool)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A))) (= (@ (@ tptp.vEBT_vebt_delete (@ _let_1 B)) (@ tptp.suc tptp.zero_zero_nat)) (@ _let_1 false)))))
% 5.91/6.26 (assert (= (@ tptp.vEBT_vebt_buildup (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.vEBT_Leaf false) false)))
% 5.91/6.26 (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))))
% 5.91/6.26 (assert (forall ((P (-> tptp.set_nat_rat Bool))) (= (= (@ tptp.collect_set_nat_rat P) tptp.bot_bo6797373522285170759at_rat) (= P tptp.bot_bo3445895781125589758_rat_o))))
% 5.91/6.26 (assert (forall ((P (-> (-> tptp.nat tptp.rat) Bool))) (= (= (@ tptp.collect_nat_rat P) tptp.bot_bot_set_nat_rat) (= P tptp.bot_bot_nat_rat_o))))
% 5.91/6.26 (assert (forall ((P (-> tptp.real Bool))) (= (= (@ tptp.collect_real P) tptp.bot_bot_set_real) (= P tptp.bot_bot_real_o))))
% 5.91/6.26 (assert (forall ((P (-> Bool Bool))) (= (= (@ tptp.collect_o P) tptp.bot_bot_set_o) (= P tptp.bot_bot_o_o))))
% 5.91/6.26 (assert (forall ((P (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P) tptp.bot_bot_set_nat) (= P tptp.bot_bot_nat_o))))
% 5.91/6.26 (assert (forall ((P (-> tptp.int Bool))) (= (= (@ tptp.collect_int P) tptp.bot_bot_set_int) (= P tptp.bot_bot_int_o))))
% 5.91/6.26 (assert (= tptp.bot_bot_set_nat_o (lambda ((X3 tptp.set_nat)) (@ (@ tptp.member_set_nat X3) tptp.bot_bot_set_set_nat))))
% 5.91/6.26 (assert (= tptp.bot_bo3445895781125589758_rat_o (lambda ((X3 tptp.set_nat_rat)) (@ (@ tptp.member_set_nat_rat X3) tptp.bot_bo6797373522285170759at_rat))))
% 5.91/6.26 (assert (= tptp.bot_bot_real_o (lambda ((X3 tptp.real)) (@ (@ tptp.member_real X3) tptp.bot_bot_set_real))))
% 5.91/6.26 (assert (= tptp.bot_bot_o_o (lambda ((X3 Bool)) (@ (@ tptp.member_o X3) tptp.bot_bot_set_o))))
% 5.91/6.26 (assert (= tptp.bot_bot_nat_o (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) tptp.bot_bot_set_nat))))
% 5.91/6.26 (assert (= tptp.bot_bot_int_o (lambda ((X3 tptp.int)) (@ (@ tptp.member_int X3) tptp.bot_bot_set_int))))
% 5.91/6.26 (assert (forall ((P (-> tptp.nat Bool))) (=> (not (@ P tptp.zero_zero_nat)) (=> (exists ((X_12 tptp.nat)) (@ P X_12)) (exists ((N2 tptp.nat)) (and (not (@ P N2)) (@ P (@ tptp.suc N2))))))))
% 5.91/6.26 (assert (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (not (forall ((N2 tptp.nat)) (not (= X (@ tptp.suc N2))))))))
% 5.91/6.26 (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))))
% 5.91/6.26 (assert (= tptp.is_empty_real (lambda ((A6 tptp.set_real)) (= A6 tptp.bot_bot_set_real))))
% 5.91/6.26 (assert (= tptp.is_empty_o (lambda ((A6 tptp.set_o)) (= A6 tptp.bot_bot_set_o))))
% 5.91/6.26 (assert (= tptp.is_empty_nat (lambda ((A6 tptp.set_nat)) (= A6 tptp.bot_bot_set_nat))))
% 5.91/6.26 (assert (= tptp.is_empty_int (lambda ((A6 tptp.set_int)) (= A6 tptp.bot_bot_set_int))))
% 5.91/6.26 (assert (= (@ tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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))))
% 5.91/6.26 (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))))
% 5.91/6.26 (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))))
% 5.91/6.26 (assert (forall ((X21 Bool) (X22 Bool)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ tptp.vEBT_Leaf X21) X22)) tptp.zero_zero_nat)))
% 5.91/6.26 (assert (forall ((S2 tptp.set_Extended_enat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.infini7641415182203889163d_enat S2))) (=> (not (@ tptp.finite4001608067531595151d_enat S2)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N))))))
% 5.91/6.26 (assert (forall ((S2 tptp.set_nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.infini8530281810654367211te_nat S2))) (=> (not (@ tptp.finite_finite_nat S2)) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M2) (@ tptp.semiri1314217659103216013at_int N)) (= M2 N))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M2) (@ tptp.semiri5074537144036343181t_real N)) (= M2 N))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M2) (@ tptp.semiri681578069525770553at_rat N)) (= M2 N))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 5.91/6.26 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 5.91/6.26 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) tptp.zero_zero_nat) A)))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 5.91/6.26 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) A) tptp.zero_zero_nat)))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) N)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M2) N)) K))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M2) N))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 5.91/6.26 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat M2) M2) tptp.zero_zero_nat)))
% 5.91/6.26 (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)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.ord_less_eq_real B) A))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.ord_less_real B) A))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.ord_less_rat B) A))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.ord_less_int B) A))))
% 5.91/6.26 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) tptp.one_one_complex) tptp.zero_zero_complex))
% 5.91/6.26 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) tptp.one_one_real) tptp.zero_zero_real))
% 5.91/6.26 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) tptp.one_one_rat) tptp.zero_zero_rat))
% 5.91/6.26 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) tptp.one_one_int) tptp.zero_zero_int))
% 5.91/6.26 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 5.91/6.26 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 5.91/6.26 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real))
% 5.91/6.26 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N)) (= tptp.zero_zero_nat N))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N)) (= tptp.zero_zero_nat N))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_real (@ tptp.semiri5074537144036343181t_real N)) (= tptp.zero_zero_nat N))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_rat (@ tptp.semiri681578069525770553at_rat N)) (= tptp.zero_zero_nat N))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M2) tptp.zero_zero_nat) (= M2 tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M2) tptp.zero_zero_int) (= M2 tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M2) tptp.zero_zero_real) (= M2 tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M2) tptp.zero_zero_rat) (= M2 tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_nat M2) N))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat M2) N))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat M2) N))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat M2) N))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) M2)) (@ (@ tptp.ord_less_nat M2) N))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.minus_minus_nat M2) N) tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M2) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex N) tptp.one_one_complex) (= N tptp.one_one_nat))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N) tptp.one_one_nat) (= N tptp.one_one_nat))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N) tptp.one_one_int) (= N tptp.one_one_nat))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real N) tptp.one_one_real) (= N tptp.one_one_nat))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat N) tptp.one_one_rat) (= N tptp.one_one_nat))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_complex (@ tptp.semiri8010041392384452111omplex N)) (= N tptp.one_one_nat))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N)) (= N tptp.one_one_nat))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N)) (= N tptp.one_one_nat))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_real (@ tptp.semiri5074537144036343181t_real N)) (= N tptp.one_one_nat))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_rat (@ tptp.semiri681578069525770553at_rat N)) (= N tptp.one_one_nat))))
% 5.91/6.26 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.one_one_nat) tptp.one_one_complex))
% 5.91/6.26 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat))
% 5.91/6.26 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 5.91/6.26 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real))
% 5.91/6.26 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) tptp.one_one_nat) N)))
% 5.91/6.26 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M2)) tptp.zero_zero_real) (= M2 tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M2)) tptp.zero_zero_rat) (= M2 tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M2)) tptp.zero_zero_nat) (= M2 tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M2)) tptp.zero_zero_int) (= M2 tptp.zero_zero_nat))))
% 5.91/6.26 (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))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.minus_minus_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N))))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N))))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N))))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N))))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.minus_minus_real (@ _let_1 C)) B) (@ (@ tptp.minus_minus_real (@ _let_1 B)) C)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 C)) B) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C)))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 C)) B) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 C)) B) (@ (@ tptp.minus_minus_int (@ _let_1 B)) C)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D)) (= (= A B) (= C D)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D)) (= (= A B) (= C D)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D)) (= (= A B) (= C D)))))
% 5.91/6.26 (assert (forall ((X tptp.real)) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real N2)))))
% 5.91/6.26 (assert (forall ((X tptp.rat)) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.semiri681578069525770553at_rat N2)))))
% 5.91/6.26 (assert (forall ((X tptp.real)) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real N2)))))
% 5.91/6.26 (assert (forall ((X tptp.rat)) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat X) (@ tptp.semiri681578069525770553at_rat N2)))))
% 5.91/6.26 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (=> (not (= (@ tptp.size_size_VEBT_VEBT X) (@ tptp.size_size_VEBT_VEBT Y))) (not (= X Y)))))
% 5.91/6.26 (assert (forall ((X tptp.list_VEBT_VEBT) (Y tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT X) (@ tptp.size_s6755466524823107622T_VEBT Y))) (not (= X Y)))))
% 5.91/6.26 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (= (@ tptp.size_size_num X) (@ tptp.size_size_num Y))) (not (= X Y)))))
% 5.91/6.26 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X) (@ tptp.size_size_list_nat Y))) (not (= X Y)))))
% 5.91/6.26 (assert (forall ((X tptp.char) (Y tptp.char)) (=> (not (= (@ tptp.size_size_char X) (@ tptp.size_size_char Y))) (not (= X Y)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D)) (= (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real C) D)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D)) (= (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat C) D)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D)) (= (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int C) D)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) C)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) C)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) C)))))
% 5.91/6.26 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))
% 5.91/6.26 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))
% 5.91/6.26 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (D tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real D) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) D))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (D tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat D) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) D))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int D) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) D))))))
% 5.91/6.26 (assert (= (lambda ((Y5 tptp.real) (Z4 tptp.real)) (= Y5 Z4)) (lambda ((A4 tptp.real) (B4 tptp.real)) (= (@ (@ tptp.minus_minus_real A4) B4) tptp.zero_zero_real))))
% 5.91/6.26 (assert (= (lambda ((Y5 tptp.rat) (Z4 tptp.rat)) (= Y5 Z4)) (lambda ((A4 tptp.rat) (B4 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A4) B4) tptp.zero_zero_rat))))
% 5.91/6.26 (assert (= (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4)) (lambda ((A4 tptp.int) (B4 tptp.int)) (= (@ (@ tptp.minus_minus_int A4) B4) tptp.zero_zero_int))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (D tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real D) C) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) D))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (D tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat D) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) D))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int D) C) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) D))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D)) (= (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real C) D)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D)) (= (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat C) D)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D)) (= (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int C) D)))))
% 5.91/6.26 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real C))) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))
% 5.91/6.26 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))
% 5.91/6.26 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) C)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) C)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) C)))))
% 5.91/6.26 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 5.91/6.26 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (I tptp.nat)) (=> (@ P K) (=> (forall ((N2 tptp.nat)) (=> (@ P (@ tptp.suc N2)) (@ P N2))) (@ P (@ (@ tptp.minus_minus_nat K) I))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat M2) tptp.zero_zero_nat) M2)))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M2) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N) M2) tptp.zero_zero_nat) (= M2 N)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M2))) (=> (@ _let_2 N) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 M2))))))))
% 5.91/6.26 (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))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M2))))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (let ((_let_2 (@ tptp.minus_minus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ _let_1 C) (= (@ (@ tptp.ord_less_eq_nat (@ _let_2 A)) (@ _let_2 B)) (@ _let_1 A))))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M2) N)) M2)))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M2) L)) (@ (@ tptp.minus_minus_nat N) L)))))
% 5.91/6.26 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M2))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M2) (=> (@ _let_2 N) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N) K)) (@ _let_1 N))))))))
% 5.91/6.26 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M2) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_eq_nat M2) N)))))))
% 5.91/6.26 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (= (= (@ (@ tptp.minus_minus_nat M2) K) (@ (@ tptp.minus_minus_nat N) K)) (= M2 N)))))))
% 5.91/6.26 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 5.91/6.26 (assert (forall ((S2 tptp.set_Extended_enat) (N tptp.nat)) (=> (not (@ tptp.finite4001608067531595151d_enat S2)) (@ (@ tptp.member_Extended_enat (@ (@ tptp.infini7641415182203889163d_enat S2) N)) S2))))
% 5.91/6.26 (assert (forall ((S2 tptp.set_nat) (N tptp.nat)) (=> (not (@ tptp.finite_finite_nat S2)) (@ (@ tptp.member_nat (@ (@ tptp.infini8530281810654367211te_nat S2) N)) S2))))
% 5.91/6.26 (assert (forall ((S2 tptp.set_nat) (S tptp.nat)) (=> (not (@ tptp.finite_finite_nat S2)) (=> (@ (@ tptp.member_nat S) S2) (exists ((N2 tptp.nat)) (= (@ (@ tptp.infini8530281810654367211te_nat S2) N2) S))))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M2)) tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) tptp.zero_zero_int))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M2)) tptp.zero_zero_real))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M2)) tptp.zero_zero_rat))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N)) tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) tptp.zero_zero_int))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)) tptp.zero_zero_real))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N)) tptp.zero_zero_rat))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_nat M2) N))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat M2) N))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat M2) N))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat M2) N))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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))))
% 5.91/6.26 (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))))
% 5.91/6.26 (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))))
% 5.91/6.26 (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))))
% 5.91/6.26 (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))))
% 5.91/6.26 (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))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M2) N)) (@ tptp.suc M2))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M2))) (=> (@ (@ tptp.ord_less_nat N) M2) (= (@ tptp.suc (@ _let_1 (@ tptp.suc N))) (@ _let_1 N))))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ _let_1 M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M2) N)) M2))))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) N) (@ tptp.suc (@ (@ tptp.minus_minus_nat M2) N))))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat A) C)) (@ (@ tptp.minus_minus_nat B) C))))))
% 5.91/6.26 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M2) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_nat M2) N)))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N)))))
% 5.91/6.26 (assert (forall ((S2 tptp.set_nat) (N tptp.nat)) (=> (not (@ tptp.finite_finite_nat S2)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.infini8530281810654367211te_nat S2) N)))))
% 5.91/6.26 (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))))
% 5.91/6.26 (assert (forall ((S2 tptp.set_Extended_enat) (N tptp.nat)) (let ((_let_1 (@ tptp.infini7641415182203889163d_enat S2))) (=> (not (@ tptp.finite4001608067531595151d_enat S2)) (@ (@ tptp.ord_le72135733267957522d_enat (@ _let_1 N)) (@ _let_1 (@ tptp.suc N)))))))
% 5.91/6.26 (assert (forall ((S2 tptp.set_nat) (N tptp.nat)) (let ((_let_1 (@ tptp.infini8530281810654367211te_nat S2))) (=> (not (@ tptp.finite_finite_nat S2)) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 (@ tptp.suc N)))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat) (S2 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.infini7641415182203889163d_enat S2))) (=> (@ (@ tptp.ord_less_nat M2) N) (=> (not (@ tptp.finite4001608067531595151d_enat S2)) (@ (@ tptp.ord_le72135733267957522d_enat (@ _let_1 M2)) (@ _let_1 N)))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat) (S2 tptp.set_nat)) (let ((_let_1 (@ tptp.infini8530281810654367211te_nat S2))) (=> (@ (@ tptp.ord_less_nat M2) N) (=> (not (@ tptp.finite_finite_nat S2)) (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)))))))
% 5.91/6.26 (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))))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) N) (@ (@ tptp.minus_minus_nat M2) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 5.91/6.26 (assert (= (@ tptp.arsinh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.91/6.26 (assert (= (@ tptp.artanh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.91/6.26 (assert (forall ((X tptp.set_real) (Y tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real X) Y) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real X) Y))))
% 5.91/6.26 (assert (forall ((X tptp.set_o) (Y tptp.set_o)) (= (= (@ (@ tptp.minus_minus_set_o X) Y) tptp.bot_bot_set_o) (@ (@ tptp.ord_less_eq_set_o X) Y))))
% 5.91/6.26 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat X) Y) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X) Y))))
% 5.91/6.26 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int X) Y) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X) Y))))
% 5.91/6.26 (assert (= (@ tptp.ln_ln_real tptp.one_one_real) tptp.zero_zero_real))
% 5.91/6.26 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (not (forall ((N2 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N2)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))))))
% 5.91/6.26 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= K (@ tptp.semiri1314217659103216013at_int N2)))))))
% 5.91/6.26 (assert (= (@ tptp.nat_set_encode tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 5.91/6.26 (assert (forall ((X tptp.real)) (= (= (@ tptp.archim2898591450579166408c_real X) X) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 5.91/6.26 (assert (forall ((X tptp.rat)) (= (= (@ tptp.archimedean_frac_rat X) X) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (@ (@ tptp.ord_less_rat X) tptp.one_one_rat)))))
% 5.91/6.26 (assert (forall ((X5 tptp.set_Extended_enat) (Y6 tptp.set_Extended_enat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.finite121521170596916366d_enat X5)) (= (@ (@ tptp.infini7641415182203889163d_enat X5) I2) (@ (@ tptp.infini7641415182203889163d_enat Y6) I2)))) (=> (@ tptp.finite4001608067531595151d_enat X5) (=> (@ tptp.finite4001608067531595151d_enat Y6) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite121521170596916366d_enat X5)) (@ tptp.finite121521170596916366d_enat Y6)) (@ (@ tptp.ord_le7203529160286727270d_enat X5) Y6)))))))
% 5.91/6.26 (assert (forall ((X5 tptp.set_nat) (Y6 tptp.set_nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.finite_card_nat X5)) (= (@ (@ tptp.infini8530281810654367211te_nat X5) I2) (@ (@ tptp.infini8530281810654367211te_nat Y6) I2)))) (=> (@ tptp.finite_finite_nat X5) (=> (@ tptp.finite_finite_nat Y6) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat X5)) (@ tptp.finite_card_nat Y6)) (@ (@ tptp.ord_less_eq_set_nat X5) Y6)))))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real M2))) (@ _let_1 (@ tptp.semiri5074537144036343181t_real N))))))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 (@ tptp.semiri681578069525770553at_rat M2))) (@ _let_1 (@ tptp.semiri681578069525770553at_rat N))))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real A2) A2) tptp.bot_bot_set_real)))
% 5.91/6.26 (assert (forall ((A2 tptp.set_o)) (= (@ (@ tptp.minus_minus_set_o A2) A2) tptp.bot_bot_set_o)))
% 5.91/6.26 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A2) A2) tptp.bot_bot_set_int)))
% 5.91/6.26 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A2) A2) tptp.bot_bot_set_nat)))
% 5.91/6.26 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real tptp.bot_bot_set_real) A2) tptp.bot_bot_set_real)))
% 5.91/6.26 (assert (forall ((A2 tptp.set_o)) (= (@ (@ tptp.minus_minus_set_o tptp.bot_bot_set_o) A2) tptp.bot_bot_set_o)))
% 5.91/6.26 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int tptp.bot_bot_set_int) A2) tptp.bot_bot_set_int)))
% 5.91/6.26 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat tptp.bot_bot_set_nat) A2) tptp.bot_bot_set_nat)))
% 5.91/6.26 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real A2) tptp.bot_bot_set_real) A2)))
% 5.91/6.26 (assert (forall ((A2 tptp.set_o)) (= (@ (@ tptp.minus_minus_set_o A2) tptp.bot_bot_set_o) A2)))
% 5.91/6.26 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A2) tptp.bot_bot_set_int) A2)))
% 5.91/6.26 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A2) tptp.bot_bot_set_nat) A2)))
% 5.91/6.26 (assert (forall ((B2 tptp.set_int) (A2 tptp.set_int)) (=> (@ tptp.finite_finite_int B2) (= (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_set_int A2) B2)) (@ tptp.finite_finite_int A2)))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B2) (= (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex A2) B2)) (@ tptp.finite3207457112153483333omplex A2)))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B2) (= (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) B2)) (@ tptp.finite6177210948735845034at_nat A2)))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat B2) (= (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.minus_925952699566721837d_enat A2) B2)) (@ tptp.finite4001608067531595151d_enat A2)))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B2) (= (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat A2) B2)) (@ tptp.finite_finite_nat A2)))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_set_int A2) B2)))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_complex) (B2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex A2) B2)))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A2) (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) B2)))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.minus_925952699566721837d_enat A2) B2)))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat A2) B2)))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 5.91/6.26 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 5.91/6.26 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 5.91/6.26 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.one_one_complex) A)))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.one_one_rat) A)))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 5.91/6.26 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.one_one_real) A)))
% 5.91/6.26 (assert (forall ((A2 tptp.set_real) (B2 tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real A2) B2) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real A2) B2))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_o) (B2 tptp.set_o)) (= (= (@ (@ tptp.minus_minus_set_o A2) B2) tptp.bot_bot_set_o) (@ (@ tptp.ord_less_eq_set_o A2) B2))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat A2) B2) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat A2) B2))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int A2) B2) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int A2) B2))))
% 5.91/6.26 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 5.91/6.26 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int A) A) tptp.one_one_int))))
% 5.91/6.26 (assert (forall ((A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat A) A) tptp.one_one_nat))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 5.91/6.26 (assert (= (@ tptp.finite_card_complex tptp.bot_bot_set_complex) tptp.zero_zero_nat))
% 5.91/6.26 (assert (= (@ tptp.finite_card_list_nat tptp.bot_bot_set_list_nat) tptp.zero_zero_nat))
% 5.91/6.26 (assert (= (@ tptp.finite_card_set_nat tptp.bot_bot_set_set_nat) tptp.zero_zero_nat))
% 5.91/6.26 (assert (= (@ tptp.finite_card_real tptp.bot_bot_set_real) tptp.zero_zero_nat))
% 5.91/6.26 (assert (= (@ tptp.finite_card_o tptp.bot_bot_set_o) tptp.zero_zero_nat))
% 5.91/6.26 (assert (= (@ tptp.finite_card_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 5.91/6.26 (assert (= (@ tptp.finite_card_int tptp.bot_bot_set_int) tptp.zero_zero_nat))
% 5.91/6.26 (assert (forall ((A2 tptp.set_list_nat)) (=> (not (@ tptp.finite8100373058378681591st_nat A2)) (= (@ tptp.finite_card_list_nat A2) tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_set_nat)) (=> (not (@ tptp.finite1152437895449049373et_nat A2)) (= (@ tptp.finite_card_set_nat A2) tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ tptp.finite_card_nat A2) tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_int)) (=> (not (@ tptp.finite_finite_int A2)) (= (@ tptp.finite_card_int A2) tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_complex)) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ tptp.finite_card_complex A2) tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (=> (not (@ tptp.finite6177210948735845034at_nat A2)) (= (@ tptp.finite711546835091564841at_nat A2) tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_Extended_enat)) (=> (not (@ tptp.finite4001608067531595151d_enat A2)) (= (@ tptp.finite121521170596916366d_enat A2) tptp.zero_zero_nat))))
% 5.91/6.26 (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))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A2) (= (= (@ tptp.finite_card_list_nat A2) tptp.zero_zero_nat) (= A2 tptp.bot_bot_set_list_nat)))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (= (= (@ tptp.finite_card_set_nat A2) tptp.zero_zero_nat) (= A2 tptp.bot_bot_set_set_nat)))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ tptp.finite_card_complex A2) tptp.zero_zero_nat) (= A2 tptp.bot_bot_set_complex)))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A2) (= (= (@ tptp.finite711546835091564841at_nat A2) tptp.zero_zero_nat) (= A2 tptp.bot_bo2099793752762293965at_nat)))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (= (@ tptp.finite121521170596916366d_enat A2) tptp.zero_zero_nat) (= A2 tptp.bot_bo7653980558646680370d_enat)))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_real)) (=> (@ tptp.finite_finite_real A2) (= (= (@ tptp.finite_card_real A2) tptp.zero_zero_nat) (= A2 tptp.bot_bot_set_real)))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_o)) (=> (@ tptp.finite_finite_o A2) (= (= (@ tptp.finite_card_o A2) tptp.zero_zero_nat) (= A2 tptp.bot_bot_set_o)))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (= (= (@ tptp.finite_card_nat A2) tptp.zero_zero_nat) (= A2 tptp.bot_bot_set_nat)))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (= (= (@ tptp.finite_card_int A2) tptp.zero_zero_nat) (= A2 tptp.bot_bot_set_int)))))
% 5.91/6.26 (assert (forall ((S2 tptp.set_Extended_enat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (let ((_let_2 (@ tptp.infini7641415182203889163d_enat S2))) (let ((_let_3 (@ tptp.finite121521170596916366d_enat S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (@ _let_1 _let_3) (=> (@ (@ tptp.ord_less_nat N) _let_3) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ _let_2 M2)) (@ _let_2 N)) (@ _let_1 N))))))))))
% 5.91/6.26 (assert (forall ((S2 tptp.set_nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (let ((_let_2 (@ tptp.infini8530281810654367211te_nat S2))) (let ((_let_3 (@ tptp.finite_card_nat S2))) (=> (@ tptp.finite_finite_nat S2) (=> (@ _let_1 _let_3) (=> (@ (@ tptp.ord_less_nat N) _let_3) (= (@ (@ tptp.ord_less_nat (@ _let_2 M2)) (@ _let_2 N)) (@ _let_1 N))))))))))
% 5.91/6.26 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (not (forall ((N2 tptp.nat)) (not (= K (@ tptp.semiri1314217659103216013at_int N2))))))))
% 5.91/6.26 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (exists ((N2 tptp.nat)) (= K (@ tptp.semiri1314217659103216013at_int N2))))))
% 5.91/6.26 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 5.91/6.26 (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))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (X tptp.int)) (or (@ (@ tptp.ord_less_eq_int A) X) (= A X) (@ (@ tptp.ord_less_eq_int X) A))))
% 5.91/6.26 (assert (forall ((X 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))) (=> (= X X7) (=> (=> _let_2 (= P P4)) (= (and (@ _let_1 X) P) (and _let_2 P4))))))))
% 5.91/6.26 (assert (forall ((X 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))) (=> (= X X7) (=> (=> _let_2 (= P P4)) (= (=> (@ _let_1 X) P) (=> _let_2 P4))))))))
% 5.91/6.26 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 5.91/6.26 (assert (forall ((A2 tptp.set_list_nat) (B2 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A2) (=> (@ tptp.finite8100373058378681591st_nat B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_list_nat A2)) (@ tptp.finite_card_list_nat B2)) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A2) B2))) (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat B2) A2))))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_set_nat) (B2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ tptp.finite1152437895449049373et_nat B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_set_nat A2)) (@ tptp.finite_card_set_nat B2)) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A2) B2))) (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat B2) A2))))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_int A2)) (@ tptp.finite_card_int B2)) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A2) B2))) (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int B2) A2))))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_complex) (B2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_complex A2)) (@ tptp.finite_card_complex B2)) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A2) B2))) (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex B2) A2))))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A2) (=> (@ tptp.finite6177210948735845034at_nat B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite711546835091564841at_nat A2)) (@ tptp.finite711546835091564841at_nat B2)) (@ (@ tptp.ord_less_nat (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) B2))) (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat B2) A2))))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite121521170596916366d_enat A2)) (@ tptp.finite121521170596916366d_enat B2)) (@ (@ tptp.ord_less_nat (@ tptp.finite121521170596916366d_enat (@ (@ tptp.minus_925952699566721837d_enat A2) B2))) (@ tptp.finite121521170596916366d_enat (@ (@ tptp.minus_925952699566721837d_enat B2) A2))))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_nat A2)) (@ tptp.finite_card_nat B2)) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A2) B2))) (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat B2) A2))))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_list_nat) (B2 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A2) (=> (@ tptp.finite8100373058378681591st_nat B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat A2)) (@ tptp.finite_card_list_nat B2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A2) B2))) (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat B2) A2))))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_set_nat) (B2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ tptp.finite1152437895449049373et_nat B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat A2)) (@ tptp.finite_card_set_nat B2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A2) B2))) (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat B2) A2))))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A2)) (@ tptp.finite_card_int B2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A2) B2))) (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int B2) A2))))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_complex) (B2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A2)) (@ tptp.finite_card_complex B2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A2) B2))) (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex B2) A2))))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A2) (=> (@ tptp.finite6177210948735845034at_nat B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat A2)) (@ tptp.finite711546835091564841at_nat B2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) B2))) (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat B2) A2))))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite121521170596916366d_enat A2)) (@ tptp.finite121521170596916366d_enat B2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite121521170596916366d_enat (@ (@ tptp.minus_925952699566721837d_enat A2) B2))) (@ tptp.finite121521170596916366d_enat (@ (@ tptp.minus_925952699566721837d_enat B2) A2))))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A2)) (@ tptp.finite_card_nat B2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A2) B2))) (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat B2) A2))))))))
% 5.91/6.26 (assert (forall ((T3 tptp.set_int) (S2 tptp.set_int)) (=> (@ tptp.finite_finite_int T3) (=> (not (@ tptp.finite_finite_int S2)) (not (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_set_int S2) T3)))))))
% 5.91/6.26 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (not (@ tptp.finite3207457112153483333omplex S2)) (not (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex S2) T3)))))))
% 5.91/6.26 (assert (forall ((T3 tptp.set_Pr1261947904930325089at_nat) (S2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat T3) (=> (not (@ tptp.finite6177210948735845034at_nat S2)) (not (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.minus_1356011639430497352at_nat S2) T3)))))))
% 5.91/6.26 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (not (@ tptp.finite4001608067531595151d_enat S2)) (not (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.minus_925952699566721837d_enat S2) T3)))))))
% 5.91/6.26 (assert (forall ((T3 tptp.set_nat) (S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat T3) (=> (not (@ tptp.finite_finite_nat S2)) (not (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat S2) T3)))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (C2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C2) (= (@ (@ tptp.minus_minus_set_nat B2) (@ (@ tptp.minus_minus_set_nat C2) A2)) A2)))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int) (C2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (@ (@ tptp.ord_less_eq_set_int B2) C2) (= (@ (@ tptp.minus_minus_set_int B2) (@ (@ tptp.minus_minus_set_int C2) A2)) A2)))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B2)) A2)))
% 5.91/6.26 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) B2)) A2)))
% 5.91/6.26 (assert (forall ((A2 tptp.set_nat) (C2 tptp.set_nat) (D4 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C2) (=> (@ (@ tptp.ord_less_eq_set_nat D4) B2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B2)) (@ (@ tptp.minus_minus_set_nat C2) D4))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_int) (C2 tptp.set_int) (D4 tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) C2) (=> (@ (@ tptp.ord_less_eq_set_int D4) B2) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) B2)) (@ (@ tptp.minus_minus_set_int C2) D4))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_o) (B2 tptp.set_o)) (=> (@ (@ tptp.ord_less_set_o A2) B2) (exists ((B5 Bool)) (@ (@ tptp.member_o B5) (@ (@ tptp.minus_minus_set_o B2) A2))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_set_nat) (B2 tptp.set_set_nat)) (=> (@ (@ tptp.ord_less_set_set_nat A2) B2) (exists ((B5 tptp.set_nat)) (@ (@ tptp.member_set_nat B5) (@ (@ tptp.minus_2163939370556025621et_nat B2) A2))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_set_nat_rat) (B2 tptp.set_set_nat_rat)) (=> (@ (@ tptp.ord_le1311537459589289991at_rat A2) B2) (exists ((B5 tptp.set_nat_rat)) (@ (@ tptp.member_set_nat_rat B5) (@ (@ tptp.minus_1626877696091177228at_rat B2) A2))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B2) (exists ((B5 tptp.int)) (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int B2) A2))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B2) (exists ((B5 tptp.nat)) (@ (@ tptp.member_nat B5) (@ (@ tptp.minus_minus_set_nat B2) A2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_list_nat) (A2 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B2) (=> (@ (@ tptp.ord_le6045566169113846134st_nat B2) A2) (= (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A2) B2)) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_list_nat A2)) (@ tptp.finite_card_list_nat B2)))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_set_nat) (A2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B2) (=> (@ (@ tptp.ord_le6893508408891458716et_nat B2) A2) (= (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A2) B2)) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_set_nat A2)) (@ tptp.finite_card_set_nat B2)))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A2) (= (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A2) B2)) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_complex A2)) (@ tptp.finite_card_complex B2)))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B2) A2) (= (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) B2)) (@ (@ tptp.minus_minus_nat (@ tptp.finite711546835091564841at_nat A2)) (@ tptp.finite711546835091564841at_nat B2)))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B2) A2) (= (@ tptp.finite121521170596916366d_enat (@ (@ tptp.minus_925952699566721837d_enat A2) B2)) (@ (@ tptp.minus_minus_nat (@ tptp.finite121521170596916366d_enat A2)) (@ tptp.finite121521170596916366d_enat B2)))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (= (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A2) B2)) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_nat A2)) (@ tptp.finite_card_nat B2)))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_int) (A2 tptp.set_int)) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int B2) A2) (= (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A2) B2)) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_int A2)) (@ tptp.finite_card_int B2)))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_list_nat) (A2 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_list_nat A2)) (@ tptp.finite_card_list_nat B2))) (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A2) B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_set_nat) (A2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_set_nat A2)) (@ tptp.finite_card_set_nat B2))) (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A2) B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_int) (A2 tptp.set_int)) (=> (@ tptp.finite_finite_int B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_int A2)) (@ tptp.finite_card_int B2))) (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A2) B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_complex A2)) (@ tptp.finite_card_complex B2))) (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A2) B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite711546835091564841at_nat A2)) (@ tptp.finite711546835091564841at_nat B2))) (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite121521170596916366d_enat A2)) (@ tptp.finite121521170596916366d_enat B2))) (@ tptp.finite121521170596916366d_enat (@ (@ tptp.minus_925952699566721837d_enat A2) B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_nat A2)) (@ tptp.finite_card_nat B2))) (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A2) B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_list_nat) (A2 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B2) (=> (@ (@ tptp.ord_le6045566169113846134st_nat A2) B2) (=> (= (@ tptp.finite_card_list_nat A2) (@ tptp.finite_card_list_nat B2)) (= A2 B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_set_nat) (A2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B2) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A2) B2) (=> (= (@ tptp.finite_card_set_nat A2) (@ tptp.finite_card_set_nat B2)) (= A2 B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (= (@ tptp.finite_card_nat A2) (@ tptp.finite_card_nat B2)) (= A2 B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (= (@ tptp.finite_card_complex A2) (@ tptp.finite_card_complex B2)) (= A2 B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B2) (=> (= (@ tptp.finite711546835091564841at_nat A2) (@ tptp.finite711546835091564841at_nat B2)) (= A2 B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B2) (=> (= (@ tptp.finite121521170596916366d_enat A2) (@ tptp.finite121521170596916366d_enat B2)) (= A2 B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_int) (A2 tptp.set_int)) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (= (@ tptp.finite_card_int A2) (@ tptp.finite_card_int B2)) (= A2 B2))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_list_nat) (N tptp.nat)) (=> (not (@ tptp.finite8100373058378681591st_nat A2)) (exists ((B8 tptp.set_list_nat)) (and (@ tptp.finite8100373058378681591st_nat B8) (= (@ tptp.finite_card_list_nat B8) N) (@ (@ tptp.ord_le6045566169113846134st_nat B8) A2))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_set_nat) (N tptp.nat)) (=> (not (@ tptp.finite1152437895449049373et_nat A2)) (exists ((B8 tptp.set_set_nat)) (and (@ tptp.finite1152437895449049373et_nat B8) (= (@ tptp.finite_card_set_nat B8) N) (@ (@ tptp.ord_le6893508408891458716et_nat B8) A2))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_nat) (N tptp.nat)) (=> (not (@ tptp.finite_finite_nat A2)) (exists ((B8 tptp.set_nat)) (and (@ tptp.finite_finite_nat B8) (= (@ tptp.finite_card_nat B8) N) (@ (@ tptp.ord_less_eq_set_nat B8) A2))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_complex) (N tptp.nat)) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (exists ((B8 tptp.set_complex)) (and (@ tptp.finite3207457112153483333omplex B8) (= (@ tptp.finite_card_complex B8) N) (@ (@ tptp.ord_le211207098394363844omplex B8) A2))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (N tptp.nat)) (=> (not (@ tptp.finite6177210948735845034at_nat A2)) (exists ((B8 tptp.set_Pr1261947904930325089at_nat)) (and (@ tptp.finite6177210948735845034at_nat B8) (= (@ tptp.finite711546835091564841at_nat B8) N) (@ (@ tptp.ord_le3146513528884898305at_nat B8) A2))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_Extended_enat) (N tptp.nat)) (=> (not (@ tptp.finite4001608067531595151d_enat A2)) (exists ((B8 tptp.set_Extended_enat)) (and (@ tptp.finite4001608067531595151d_enat B8) (= (@ tptp.finite121521170596916366d_enat B8) N) (@ (@ tptp.ord_le7203529160286727270d_enat B8) A2))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_int) (N tptp.nat)) (=> (not (@ tptp.finite_finite_int A2)) (exists ((B8 tptp.set_int)) (and (@ tptp.finite_finite_int B8) (= (@ tptp.finite_card_int B8) N) (@ (@ tptp.ord_less_eq_set_int B8) A2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_o) (A2 tptp.set_o) (R2 (-> Bool Bool Bool))) (=> (@ tptp.finite_finite_o B2) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) A2) (exists ((B9 Bool)) (and (@ (@ tptp.member_o B9) B2) (@ (@ R2 A5) B9))))) (=> (forall ((A1 Bool) (A22 Bool) (B5 Bool)) (=> (@ (@ tptp.member_o A1) A2) (=> (@ (@ tptp.member_o A22) A2) (=> (@ (@ tptp.member_o B5) B2) (=> (@ (@ R2 A1) B5) (=> (@ (@ R2 A22) B5) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o A2)) (@ tptp.finite_card_o B2)))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_o) (A2 tptp.set_complex) (R2 (-> tptp.complex Bool Bool))) (=> (@ tptp.finite_finite_o B2) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A2) (exists ((B9 Bool)) (and (@ (@ tptp.member_o B9) B2) (@ (@ R2 A5) B9))))) (=> (forall ((A1 tptp.complex) (A22 tptp.complex) (B5 Bool)) (=> (@ (@ tptp.member_complex A1) A2) (=> (@ (@ tptp.member_complex A22) A2) (=> (@ (@ tptp.member_o B5) B2) (=> (@ (@ R2 A1) B5) (=> (@ (@ R2 A22) B5) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A2)) (@ tptp.finite_card_o B2)))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_o) (A2 tptp.set_nat) (R2 (-> tptp.nat Bool Bool))) (=> (@ tptp.finite_finite_o B2) (=> (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (exists ((B9 Bool)) (and (@ (@ tptp.member_o B9) B2) (@ (@ R2 A5) B9))))) (=> (forall ((A1 tptp.nat) (A22 tptp.nat) (B5 Bool)) (=> (@ (@ tptp.member_nat A1) A2) (=> (@ (@ tptp.member_nat A22) A2) (=> (@ (@ tptp.member_o B5) B2) (=> (@ (@ R2 A1) B5) (=> (@ (@ R2 A22) B5) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A2)) (@ tptp.finite_card_o B2)))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_o) (A2 tptp.set_int) (R2 (-> tptp.int Bool Bool))) (=> (@ tptp.finite_finite_o B2) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A2) (exists ((B9 Bool)) (and (@ (@ tptp.member_o B9) B2) (@ (@ R2 A5) B9))))) (=> (forall ((A1 tptp.int) (A22 tptp.int) (B5 Bool)) (=> (@ (@ tptp.member_int A1) A2) (=> (@ (@ tptp.member_int A22) A2) (=> (@ (@ tptp.member_o B5) B2) (=> (@ (@ R2 A1) B5) (=> (@ (@ R2 A22) B5) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A2)) (@ tptp.finite_card_o B2)))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_o) (R2 (-> Bool tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B2) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) A2) (exists ((B9 tptp.nat)) (and (@ (@ tptp.member_nat B9) B2) (@ (@ R2 A5) B9))))) (=> (forall ((A1 Bool) (A22 Bool) (B5 tptp.nat)) (=> (@ (@ tptp.member_o A1) A2) (=> (@ (@ tptp.member_o A22) A2) (=> (@ (@ tptp.member_nat B5) B2) (=> (@ (@ R2 A1) B5) (=> (@ (@ R2 A22) B5) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o A2)) (@ tptp.finite_card_nat B2)))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_complex) (R2 (-> tptp.complex tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B2) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A2) (exists ((B9 tptp.nat)) (and (@ (@ tptp.member_nat B9) B2) (@ (@ R2 A5) B9))))) (=> (forall ((A1 tptp.complex) (A22 tptp.complex) (B5 tptp.nat)) (=> (@ (@ tptp.member_complex A1) A2) (=> (@ (@ tptp.member_complex A22) A2) (=> (@ (@ tptp.member_nat B5) B2) (=> (@ (@ R2 A1) B5) (=> (@ (@ R2 A22) B5) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A2)) (@ tptp.finite_card_nat B2)))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (R2 (-> tptp.nat tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B2) (=> (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (exists ((B9 tptp.nat)) (and (@ (@ tptp.member_nat B9) B2) (@ (@ R2 A5) B9))))) (=> (forall ((A1 tptp.nat) (A22 tptp.nat) (B5 tptp.nat)) (=> (@ (@ tptp.member_nat A1) A2) (=> (@ (@ tptp.member_nat A22) A2) (=> (@ (@ tptp.member_nat B5) B2) (=> (@ (@ R2 A1) B5) (=> (@ (@ R2 A22) B5) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A2)) (@ tptp.finite_card_nat B2)))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_int) (R2 (-> tptp.int tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B2) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A2) (exists ((B9 tptp.nat)) (and (@ (@ tptp.member_nat B9) B2) (@ (@ R2 A5) B9))))) (=> (forall ((A1 tptp.int) (A22 tptp.int) (B5 tptp.nat)) (=> (@ (@ tptp.member_int A1) A2) (=> (@ (@ tptp.member_int A22) A2) (=> (@ (@ tptp.member_nat B5) B2) (=> (@ (@ R2 A1) B5) (=> (@ (@ R2 A22) B5) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A2)) (@ tptp.finite_card_nat B2)))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_int) (A2 tptp.set_o) (R2 (-> Bool tptp.int Bool))) (=> (@ tptp.finite_finite_int B2) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) A2) (exists ((B9 tptp.int)) (and (@ (@ tptp.member_int B9) B2) (@ (@ R2 A5) B9))))) (=> (forall ((A1 Bool) (A22 Bool) (B5 tptp.int)) (=> (@ (@ tptp.member_o A1) A2) (=> (@ (@ tptp.member_o A22) A2) (=> (@ (@ tptp.member_int B5) B2) (=> (@ (@ R2 A1) B5) (=> (@ (@ R2 A22) B5) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o A2)) (@ tptp.finite_card_int B2)))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_int) (A2 tptp.set_complex) (R2 (-> tptp.complex tptp.int Bool))) (=> (@ tptp.finite_finite_int B2) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A2) (exists ((B9 tptp.int)) (and (@ (@ tptp.member_int B9) B2) (@ (@ R2 A5) B9))))) (=> (forall ((A1 tptp.complex) (A22 tptp.complex) (B5 tptp.int)) (=> (@ (@ tptp.member_complex A1) A2) (=> (@ (@ tptp.member_complex A22) A2) (=> (@ (@ tptp.member_int B5) B2) (=> (@ (@ R2 A1) B5) (=> (@ (@ R2 A22) B5) (= A1 A22))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A2)) (@ tptp.finite_card_int B2)))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ tptp.finite_finite_nat B2) (= (= (@ tptp.nat_set_encode A2) (@ tptp.nat_set_encode B2)) (= A2 B2))))))
% 5.91/6.26 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.archim2898591450579166408c_real X))))
% 5.91/6.26 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.archimedean_frac_rat X))))
% 5.91/6.26 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.archim2898591450579166408c_real X)) tptp.one_one_real)))
% 5.91/6.26 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_rat (@ tptp.archimedean_frac_rat X)) tptp.one_one_rat)))
% 5.91/6.26 (assert (forall ((A2 tptp.set_list_nat)) (= (= (@ tptp.finite_card_list_nat A2) tptp.zero_zero_nat) (or (= A2 tptp.bot_bot_set_list_nat) (not (@ tptp.finite8100373058378681591st_nat A2))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_set_nat)) (= (= (@ tptp.finite_card_set_nat A2) tptp.zero_zero_nat) (or (= A2 tptp.bot_bot_set_set_nat) (not (@ tptp.finite1152437895449049373et_nat A2))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_complex)) (= (= (@ tptp.finite_card_complex A2) tptp.zero_zero_nat) (or (= A2 tptp.bot_bot_set_complex) (not (@ tptp.finite3207457112153483333omplex A2))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ tptp.finite711546835091564841at_nat A2) tptp.zero_zero_nat) (or (= A2 tptp.bot_bo2099793752762293965at_nat) (not (@ tptp.finite6177210948735845034at_nat A2))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_Extended_enat)) (= (= (@ tptp.finite121521170596916366d_enat A2) tptp.zero_zero_nat) (or (= A2 tptp.bot_bo7653980558646680370d_enat) (not (@ tptp.finite4001608067531595151d_enat A2))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_real)) (= (= (@ tptp.finite_card_real A2) tptp.zero_zero_nat) (or (= A2 tptp.bot_bot_set_real) (not (@ tptp.finite_finite_real A2))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_o)) (= (= (@ tptp.finite_card_o A2) tptp.zero_zero_nat) (or (= A2 tptp.bot_bot_set_o) (not (@ tptp.finite_finite_o A2))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_nat)) (= (= (@ tptp.finite_card_nat A2) tptp.zero_zero_nat) (or (= A2 tptp.bot_bot_set_nat) (not (@ tptp.finite_finite_nat A2))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_int)) (= (= (@ tptp.finite_card_int A2) tptp.zero_zero_nat) (or (= A2 tptp.bot_bot_set_int) (not (@ tptp.finite_finite_int A2))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_list_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_list_nat A2)) (@ tptp.finite8100373058378681591st_nat A2))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_set_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_set_nat A2)) (@ tptp.finite1152437895449049373et_nat A2))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat A2)) (@ tptp.finite_finite_nat A2))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_int A2)) (@ tptp.finite_finite_int A2))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_complex A2)) (@ tptp.finite3207457112153483333omplex A2))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite711546835091564841at_nat A2)) (@ tptp.finite6177210948735845034at_nat A2))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite121521170596916366d_enat A2)) (@ tptp.finite4001608067531595151d_enat A2))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (S2 tptp.set_list_nat)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_list_nat S2)) (not (forall ((T4 tptp.set_list_nat)) (=> (@ (@ tptp.ord_le6045566169113846134st_nat T4) S2) (=> (= (@ tptp.finite_card_list_nat T4) N) (not (@ tptp.finite8100373058378681591st_nat T4)))))))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (S2 tptp.set_set_nat)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_set_nat S2)) (not (forall ((T4 tptp.set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat T4) S2) (=> (= (@ tptp.finite_card_set_nat T4) N) (not (@ tptp.finite1152437895449049373et_nat T4)))))))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (S2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_nat S2)) (not (forall ((T4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat T4) S2) (=> (= (@ tptp.finite_card_nat T4) N) (not (@ tptp.finite_finite_nat T4)))))))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (S2 tptp.set_complex)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_complex S2)) (not (forall ((T4 tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex T4) S2) (=> (= (@ tptp.finite_card_complex T4) N) (not (@ tptp.finite3207457112153483333omplex T4)))))))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (S2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite711546835091564841at_nat S2)) (not (forall ((T4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat T4) S2) (=> (= (@ tptp.finite711546835091564841at_nat T4) N) (not (@ tptp.finite6177210948735845034at_nat T4)))))))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (S2 tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite121521170596916366d_enat S2)) (not (forall ((T4 tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le7203529160286727270d_enat T4) S2) (=> (= (@ tptp.finite121521170596916366d_enat T4) N) (not (@ tptp.finite4001608067531595151d_enat T4)))))))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (S2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite_card_int S2)) (not (forall ((T4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int T4) S2) (=> (= (@ tptp.finite_card_int T4) N) (not (@ tptp.finite_finite_int T4)))))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_list_nat) (A2 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B2) (=> (@ (@ tptp.ord_le6045566169113846134st_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat B2)) (@ tptp.finite_card_list_nat A2)) (= A2 B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_set_nat) (A2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B2) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat B2)) (@ tptp.finite_card_set_nat A2)) (= A2 B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat B2)) (@ tptp.finite_card_nat A2)) (= A2 B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex B2)) (@ tptp.finite_card_complex A2)) (= A2 B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat B2)) (@ tptp.finite711546835091564841at_nat A2)) (= A2 B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite121521170596916366d_enat B2)) (@ tptp.finite121521170596916366d_enat A2)) (= A2 B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_int) (A2 tptp.set_int)) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int B2)) (@ tptp.finite_card_int A2)) (= A2 B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_list_nat) (A2 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B2) (=> (@ (@ tptp.ord_le6045566169113846134st_nat A2) B2) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat A2)) (@ tptp.finite_card_list_nat B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_set_nat) (A2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B2) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A2) B2) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat A2)) (@ tptp.finite_card_set_nat B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A2)) (@ tptp.finite_card_nat B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A2)) (@ tptp.finite_card_complex B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B2) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat A2)) (@ tptp.finite711546835091564841at_nat B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B2) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite121521170596916366d_enat A2)) (@ tptp.finite121521170596916366d_enat B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_int) (A2 tptp.set_int)) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A2)) (@ tptp.finite_card_int B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_list_nat) (A2 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B2) (=> (@ (@ tptp.ord_le1190675801316882794st_nat A2) B2) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_list_nat A2)) (@ tptp.finite_card_list_nat B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_set_nat) (A2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B2) (=> (@ (@ tptp.ord_less_set_set_nat A2) B2) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_set_nat A2)) (@ tptp.finite_card_set_nat B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_set_nat A2) B2) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_nat A2)) (@ tptp.finite_card_nat B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_int) (A2 tptp.set_int)) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_set_int A2) B2) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_int A2)) (@ tptp.finite_card_int B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_less_set_complex A2) B2) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_complex A2)) (@ tptp.finite_card_complex B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B2) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A2) B2) (@ (@ tptp.ord_less_nat (@ tptp.finite711546835091564841at_nat A2)) (@ tptp.finite711546835091564841at_nat B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (@ (@ tptp.ord_le2529575680413868914d_enat A2) B2) (@ (@ tptp.ord_less_nat (@ tptp.finite121521170596916366d_enat A2)) (@ tptp.finite121521170596916366d_enat B2))))))
% 5.91/6.26 (assert (forall ((S2 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat S2) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.finite_card_nat S2)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.infini8530281810654367211te_nat S2) N))))))
% 5.91/6.26 (assert (forall ((P (-> tptp.int Bool)) (X tptp.nat) (Y tptp.nat)) (= (@ P (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X) Y))) (and (=> (@ (@ tptp.ord_less_eq_nat Y) X) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y)))) (=> (@ (@ tptp.ord_less_nat X) Y) (@ P tptp.zero_zero_int))))))
% 5.91/6.26 (assert (forall ((S2 tptp.set_Extended_enat) (N tptp.nat)) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.finite121521170596916366d_enat S2)) (@ (@ tptp.member_Extended_enat (@ (@ tptp.infini7641415182203889163d_enat S2) N)) S2)))))
% 5.91/6.26 (assert (forall ((S2 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat S2) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.finite_card_nat S2)) (@ (@ tptp.member_nat (@ (@ tptp.infini8530281810654367211te_nat S2) N)) S2)))))
% 5.91/6.26 (assert (forall ((S2 tptp.set_Extended_enat) (S tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (@ (@ tptp.member_Extended_enat S) S2) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat N2) (@ tptp.finite121521170596916366d_enat S2)) (= (@ (@ tptp.infini7641415182203889163d_enat S2) N2) S)))))))
% 5.91/6.26 (assert (forall ((S2 tptp.set_nat) (S tptp.nat)) (=> (@ tptp.finite_finite_nat S2) (=> (@ (@ tptp.member_nat S) S2) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat N2) (@ tptp.finite_card_nat S2)) (= (@ (@ tptp.infini8530281810654367211te_nat S2) N2) S)))))))
% 5.91/6.26 (assert (forall ((X5 tptp.set_Extended_enat) (Y6 tptp.set_Extended_enat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.finite121521170596916366d_enat X5)) (= (@ (@ tptp.infini7641415182203889163d_enat X5) I2) (@ (@ tptp.infini7641415182203889163d_enat Y6) I2)))) (=> (@ tptp.finite4001608067531595151d_enat X5) (=> (@ tptp.finite4001608067531595151d_enat Y6) (=> (= (@ tptp.finite121521170596916366d_enat X5) (@ tptp.finite121521170596916366d_enat Y6)) (= X5 Y6)))))))
% 5.91/6.26 (assert (forall ((X5 tptp.set_nat) (Y6 tptp.set_nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.finite_card_nat X5)) (= (@ (@ tptp.infini8530281810654367211te_nat X5) I2) (@ (@ tptp.infini8530281810654367211te_nat Y6) I2)))) (=> (@ tptp.finite_finite_nat X5) (=> (@ tptp.finite_finite_nat Y6) (=> (= (@ tptp.finite_card_nat X5) (@ tptp.finite_card_nat Y6)) (= X5 Y6)))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ tptp.nat_set_encode A2) tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_list_nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_list_nat A2)) (and (not (= A2 tptp.bot_bot_set_list_nat)) (@ tptp.finite8100373058378681591st_nat A2)))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_set_nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_set_nat A2)) (and (not (= A2 tptp.bot_bot_set_set_nat)) (@ tptp.finite1152437895449049373et_nat A2)))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_complex)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_complex A2)) (and (not (= A2 tptp.bot_bot_set_complex)) (@ tptp.finite3207457112153483333omplex A2)))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite711546835091564841at_nat A2)) (and (not (= A2 tptp.bot_bo2099793752762293965at_nat)) (@ tptp.finite6177210948735845034at_nat A2)))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_Extended_enat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite121521170596916366d_enat A2)) (and (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (@ tptp.finite4001608067531595151d_enat A2)))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_real A2)) (and (not (= A2 tptp.bot_bot_set_real)) (@ tptp.finite_finite_real A2)))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_o)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_o A2)) (and (not (= A2 tptp.bot_bot_set_o)) (@ tptp.finite_finite_o A2)))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat A2)) (and (not (= A2 tptp.bot_bot_set_nat)) (@ tptp.finite_finite_nat A2)))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_int A2)) (and (not (= A2 tptp.bot_bot_set_int)) (@ tptp.finite_finite_int A2)))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A2) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat A2)) (@ tptp.suc tptp.zero_zero_nat)) (forall ((X3 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X3) A2) (forall ((Y2 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat Y2) A2) (= X3 Y2)))))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat A2)) (@ tptp.suc tptp.zero_zero_nat)) (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) A2) (forall ((Y2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Y2) A2) (= X3 Y2)))))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A2)) (@ tptp.suc tptp.zero_zero_nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) A2) (= X3 Y2)))))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A2)) (@ tptp.suc tptp.zero_zero_nat)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member_int Y2) A2) (= X3 Y2)))))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A2)) (@ tptp.suc tptp.zero_zero_nat)) (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (forall ((Y2 tptp.complex)) (=> (@ (@ tptp.member_complex Y2) A2) (= X3 Y2)))))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A2) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat A2)) (@ tptp.suc tptp.zero_zero_nat)) (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) A2) (forall ((Y2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y2) A2) (= X3 Y2)))))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.finite121521170596916366d_enat A2)) (@ tptp.suc tptp.zero_zero_nat)) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X3) A2) (forall ((Y2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Y2) A2) (= X3 Y2)))))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_list_nat) (A2 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B2) (=> (@ (@ tptp.ord_le6045566169113846134st_nat A2) B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_list_nat A2)) (@ tptp.finite_card_list_nat B2)) (@ (@ tptp.ord_le1190675801316882794st_nat A2) B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_set_nat) (A2 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B2) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A2) B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_set_nat A2)) (@ tptp.finite_card_set_nat B2)) (@ (@ tptp.ord_less_set_set_nat A2) B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_nat A2)) (@ tptp.finite_card_nat B2)) (@ (@ tptp.ord_less_set_nat A2) B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_complex A2)) (@ tptp.finite_card_complex B2)) (@ (@ tptp.ord_less_set_complex A2) B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite711546835091564841at_nat A2)) (@ tptp.finite711546835091564841at_nat B2)) (@ (@ tptp.ord_le7866589430770878221at_nat A2) B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite121521170596916366d_enat A2)) (@ tptp.finite121521170596916366d_enat B2)) (@ (@ tptp.ord_le2529575680413868914d_enat A2) B2))))))
% 5.91/6.26 (assert (forall ((B2 tptp.set_int) (A2 tptp.set_int)) (=> (@ tptp.finite_finite_int B2) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_int A2)) (@ tptp.finite_card_int B2)) (@ (@ tptp.ord_less_set_int A2) B2))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat) (S2 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.infini7641415182203889163d_enat S2))) (=> (@ (@ tptp.ord_less_nat M2) N) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.finite121521170596916366d_enat S2)) (@ (@ tptp.ord_le72135733267957522d_enat (@ _let_1 M2)) (@ _let_1 N))))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat) (S2 tptp.set_nat)) (let ((_let_1 (@ tptp.infini8530281810654367211te_nat S2))) (=> (@ (@ tptp.ord_less_nat M2) N) (=> (@ tptp.finite_finite_nat S2) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.finite_card_nat S2)) (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N))))))))
% 5.91/6.26 (assert (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (not (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))) E2)))))))
% 5.91/6.26 (assert (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (not (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N2)))) E2)))))))
% 5.91/6.26 (assert (forall ((S2 tptp.set_Extended_enat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.infini7641415182203889163d_enat S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (@ (@ tptp.ord_less_nat _let_1) (@ tptp.finite121521170596916366d_enat S2)) (@ (@ tptp.ord_le72135733267957522d_enat (@ _let_2 N)) (@ _let_2 _let_1))))))))
% 5.91/6.26 (assert (forall ((S2 tptp.set_nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.infini8530281810654367211te_nat S2))) (=> (@ tptp.finite_finite_nat S2) (=> (@ (@ tptp.ord_less_nat _let_1) (@ tptp.finite_card_nat S2)) (@ (@ tptp.ord_less_nat (@ _let_2 N)) (@ _let_2 _let_1))))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_eq_real A) B)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_eq_real B) A)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_eq_rat B) A)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real B) A)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat B) A)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real A) B)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (@ _let_1 A)))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (@ _let_1 A)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_rat A) B)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_real A) B)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_rat B) A)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_real B) A)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_rat B) A)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ (@ tptp.ord_less_real B) A)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ _let_1 B))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ _let_1 B))))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A2) B2))) (= (@ (@ tptp.minus_minus_set_nat _let_1) B2) _let_1))))
% 5.91/6.26 (assert (forall ((C Bool) (A2 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_o A2) B2)) (and (@ _let_1 A2) (not (@ _let_1 B2)))))))
% 5.91/6.26 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (= (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B2)) (and (@ _let_1 A2) (not (@ _let_1 B2)))))))
% 5.91/6.26 (assert (forall ((C tptp.set_nat_rat) (A2 tptp.set_set_nat_rat) (B2 tptp.set_set_nat_rat)) (let ((_let_1 (@ tptp.member_set_nat_rat C))) (= (@ _let_1 (@ (@ tptp.minus_1626877696091177228at_rat A2) B2)) (and (@ _let_1 A2) (not (@ _let_1 B2)))))))
% 5.91/6.26 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B2)) (and (@ _let_1 A2) (not (@ _let_1 B2)))))))
% 5.91/6.26 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B2)) (and (@ _let_1 A2) (not (@ _let_1 B2)))))))
% 5.91/6.26 (assert (forall ((C Bool) (A2 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B2)) (@ _let_1 (@ (@ tptp.minus_minus_set_o A2) B2)))))))
% 5.91/6.26 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B2)) (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B2)))))))
% 5.91/6.26 (assert (forall ((C tptp.set_nat_rat) (A2 tptp.set_set_nat_rat) (B2 tptp.set_set_nat_rat)) (let ((_let_1 (@ tptp.member_set_nat_rat C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B2)) (@ _let_1 (@ (@ tptp.minus_1626877696091177228at_rat A2) B2)))))))
% 5.91/6.26 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B2)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B2)))))))
% 5.91/6.26 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B2)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B2)))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 5.91/6.26 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (= A B))))))
% 5.91/6.26 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_real) (= A B))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) C) (@ (@ tptp.divide_divide_rat B) C)) (or (= C tptp.zero_zero_rat) (= A B)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B) C)) (or (= C tptp.zero_zero_real) (= A B)))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 5.91/6.26 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (and (not (= B tptp.zero_zero_complex)) (= A B)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.one_one_rat) (and (not (= B tptp.zero_zero_rat)) (= A B)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.one_one_real) (and (not (= B tptp.zero_zero_real)) (= A B)))))
% 5.91/6.26 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= tptp.one_one_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) (and (not (= B tptp.zero_zero_complex)) (= A B)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= tptp.one_one_rat (@ (@ tptp.divide_divide_rat A) B)) (and (not (= B tptp.zero_zero_rat)) (= A B)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (= (= tptp.one_one_real (@ (@ tptp.divide_divide_real A) B)) (and (not (= B tptp.zero_zero_real)) (= A B)))))
% 5.91/6.26 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 5.91/6.26 (assert (forall ((A tptp.complex)) (let ((_let_1 (@ (@ tptp.divide1717551699836669952omplex A) A))) (let ((_let_2 (= A tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 tptp.zero_zero_complex)) (=> (not _let_2) (= _let_1 tptp.one_one_complex)))))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ (@ tptp.divide_divide_rat A) A))) (let ((_let_2 (= A tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 tptp.one_one_rat)))))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real A) A))) (let ((_let_2 (= A tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 5.91/6.26 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat B) A) tptp.one_one_rat) (and (not (= A tptp.zero_zero_rat)) (= A B)))))
% 5.91/6.26 (assert (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.divide_divide_real B) A) tptp.one_one_real) (and (not (= A tptp.zero_zero_real)) (= A B)))))
% 5.91/6.26 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= tptp.one_one_rat (@ (@ tptp.divide_divide_rat B) A)) (and (not (= A tptp.zero_zero_rat)) (= A B)))))
% 5.91/6.26 (assert (forall ((B tptp.real) (A tptp.real)) (= (= tptp.one_one_real (@ (@ tptp.divide_divide_real B) A)) (and (not (= A tptp.zero_zero_real)) (= A B)))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.divide_divide_real tptp.one_one_real) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (= A tptp.zero_zero_rat))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (= A tptp.zero_zero_real))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (@ _let_1 A)))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (@ _let_1 A)))))
% 5.91/6.26 (assert (forall ((C Bool) (A2 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_o A2) B2)) (not (@ _let_1 B2))))))
% 5.91/6.26 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B2)) (not (@ _let_1 B2))))))
% 5.91/6.26 (assert (forall ((C tptp.set_nat_rat) (A2 tptp.set_set_nat_rat) (B2 tptp.set_set_nat_rat)) (let ((_let_1 (@ tptp.member_set_nat_rat C))) (=> (@ _let_1 (@ (@ tptp.minus_1626877696091177228at_rat A2) B2)) (not (@ _let_1 B2))))))
% 5.91/6.26 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B2)) (not (@ _let_1 B2))))))
% 5.91/6.26 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B2)) (not (@ _let_1 B2))))))
% 5.91/6.26 (assert (forall ((C Bool) (A2 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_o A2) B2)) (@ _let_1 A2)))))
% 5.91/6.26 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B2)) (@ _let_1 A2)))))
% 5.91/6.26 (assert (forall ((C tptp.set_nat_rat) (A2 tptp.set_set_nat_rat) (B2 tptp.set_set_nat_rat)) (let ((_let_1 (@ tptp.member_set_nat_rat C))) (=> (@ _let_1 (@ (@ tptp.minus_1626877696091177228at_rat A2) B2)) (@ _let_1 A2)))))
% 5.91/6.26 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B2)) (@ _let_1 A2)))))
% 5.91/6.26 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B2)) (@ _let_1 A2)))))
% 5.91/6.26 (assert (forall ((C Bool) (A2 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_o A2) B2)) (not (=> (@ _let_1 A2) (@ _let_1 B2)))))))
% 5.91/6.26 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B2)) (not (=> (@ _let_1 A2) (@ _let_1 B2)))))))
% 5.91/6.26 (assert (forall ((C tptp.set_nat_rat) (A2 tptp.set_set_nat_rat) (B2 tptp.set_set_nat_rat)) (let ((_let_1 (@ tptp.member_set_nat_rat C))) (=> (@ _let_1 (@ (@ tptp.minus_1626877696091177228at_rat A2) B2)) (not (=> (@ _let_1 A2) (@ _let_1 B2)))))))
% 5.91/6.26 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B2)) (not (=> (@ _let_1 A2) (@ _let_1 B2)))))))
% 5.91/6.26 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B2)) (not (=> (@ _let_1 A2) (@ _let_1 B2)))))))
% 5.91/6.26 (assert (forall ((X2 tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X2))))
% 5.91/6.26 (assert (forall ((X2 tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X2))))
% 5.91/6.26 (assert (forall ((X2 tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X2) X_1))))
% 5.91/6.26 (assert (forall ((X2 tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X2) X_1))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)))))))
% 5.91/6.26 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))))
% 5.91/6.26 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X) Y)))))))
% 5.91/6.26 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 5.91/6.26 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 5.91/6.26 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 5.91/6.26 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 5.91/6.26 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))))
% 5.91/6.26 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X) Y))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.divide_divide_real A) C))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.divide_divide_rat A) C))))))
% 5.91/6.26 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X) Y))))))
% 5.91/6.26 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))))
% 5.91/6.26 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 5.91/6.26 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 5.91/6.26 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 5.91/6.26 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 5.91/6.26 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X) Y)))))))
% 5.91/6.26 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)) (not (= C tptp.zero_zero_rat))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)) (not (= C tptp.zero_zero_real))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C))))))
% 5.91/6.26 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))))
% 5.91/6.26 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C))))))
% 5.91/6.26 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (= A B)))))
% 5.91/6.26 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.one_one_rat) (= A B)))))
% 5.91/6.26 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.one_one_real) (= A B)))))
% 5.91/6.26 (assert (forall ((Y tptp.real) (X tptp.real) (W2 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W2) (=> (@ (@ tptp.ord_less_eq_real W2) Z) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Z)) (@ (@ tptp.divide_divide_real Y) W2))))))))
% 5.91/6.26 (assert (forall ((Y tptp.rat) (X tptp.rat) (W2 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W2) (=> (@ (@ tptp.ord_less_eq_rat W2) Z) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Z)) (@ (@ tptp.divide_divide_rat Y) W2))))))))
% 5.91/6.26 (assert (forall ((X tptp.real) (Y tptp.real) (W2 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W2) (=> (@ (@ tptp.ord_less_eq_real W2) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Z)) (@ (@ tptp.divide_divide_real Y) W2))))))))
% 5.91/6.26 (assert (forall ((X tptp.rat) (Y tptp.rat) (W2 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_rat X) Y) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W2) (=> (@ (@ tptp.ord_less_eq_rat W2) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Z)) (@ (@ tptp.divide_divide_rat Y) W2))))))))
% 5.91/6.26 (assert (forall ((X tptp.real) (Y tptp.real) (W2 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ _let_1 W2) (=> (@ (@ tptp.ord_less_real W2) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Z)) (@ (@ tptp.divide_divide_real Y) W2)))))))))
% 5.91/6.26 (assert (forall ((X tptp.rat) (Y tptp.rat) (W2 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ _let_1 W2) (=> (@ (@ tptp.ord_less_rat W2) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Z)) (@ (@ tptp.divide_divide_rat Y) W2)))))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 5.91/6.26 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 5.91/6.26 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 5.91/6.26 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))))
% 5.91/6.26 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X) Y)))))))
% 5.91/6.26 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))))
% 5.91/6.26 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X) Y))))))
% 5.91/6.26 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 5.91/6.26 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 5.91/6.26 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat B) A)) (and (@ _let_1 tptp.zero_zero_rat) (@ _let_1 B)) (= A tptp.zero_zero_rat))))))
% 5.91/6.26 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real B) A)) (and (@ _let_1 tptp.zero_zero_real) (@ _let_1 B)) (= A tptp.zero_zero_real))))))
% 5.91/6.26 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ _let_1 B)) (and (@ _let_1 tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 5.91/6.26 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ _let_1 B)) (and (@ _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)))))))
% 5.91/6.26 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real B) A)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) B)) (= A tptp.zero_zero_real)))))
% 5.91/6.26 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat B) A)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) B)) (= A tptp.zero_zero_rat)))))
% 5.91/6.26 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real A) B)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A))))))
% 5.91/6.26 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ (@ tptp.divide_divide_nat M2) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M2) N)) N)))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (= (@ (@ tptp.divide_divide_nat M2) N) tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat M2) (@ tptp.suc tptp.zero_zero_nat)) M2)))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 5.91/6.26 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 5.91/6.26 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 5.91/6.26 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 5.91/6.26 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (@ (@ tptp.ord_less_nat M2) N)) (= (@ (@ tptp.divide_divide_nat M2) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M2) N)) N)))))))
% 5.91/6.26 (assert (= tptp.divide_divide_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M3) N4) (= N4 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M3) N4)) N4))))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X))))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X)))) tptp.one_one_real)))
% 5.91/6.26 (assert (forall ((N tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M2) N)) M2)))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M2) K)) (@ (@ tptp.divide_divide_nat N) K)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.divide_divide_nat M2) N) tptp.zero_zero_nat) (or (@ (@ tptp.ord_less_nat M2) N) (= N tptp.zero_zero_nat)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M2) N)) (@ (@ tptp.divide_divide_nat (@ tptp.suc M2)) N))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.divide_divide_nat M2) N)) (and (@ (@ tptp.ord_less_eq_nat N) M2) (@ _let_1 N))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M2)))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (= (= (@ (@ tptp.divide_divide_nat M2) N) M2) (= N tptp.one_one_nat)))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M2) N)) M2)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (A7 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A7) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int A7) B))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B7 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B7) (=> (@ (@ tptp.ord_less_eq_int B7) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B)) (@ _let_1 B7))))))))
% 5.91/6.26 (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))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (A7 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A7) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A7) B)) (@ (@ tptp.divide_divide_int A) B))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B7 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B7) (=> (@ (@ tptp.ord_less_eq_int B7) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B7)) (@ _let_1 B))))))))
% 5.91/6.26 (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)))))))
% 5.91/6.26 (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)))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int)))))
% 5.91/6.26 (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))))))
% 5.91/6.26 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)))))
% 5.91/6.26 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ _let_1 (@ (@ tptp.divide_divide_int A) B)) (@ _let_1 A))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ _let_1 (@ (@ tptp.divide_divide_int A) B)) (and (@ (@ tptp.ord_less_eq_int B) A) (@ _let_1 B)))))))
% 5.91/6.26 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (@ _let_1 (@ (@ tptp.divide_divide_nat A) B)))))))
% 5.91/6.26 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) A) (@ _let_1 (@ (@ tptp.divide_divide_int A) B)))))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.power_power_int K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ tptp.divide_divide_int (@ _let_1 M2)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 5.91/6.26 (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))))))))
% 5.91/6.26 (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))))))
% 5.91/6.26 (assert (forall ((X tptp.real) (A tptp.real)) (= (= (@ tptp.archim2898591450579166408c_real X) A) (and (@ (@ tptp.member_real (@ (@ tptp.minus_minus_real X) A)) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real A) tptp.one_one_real)))))
% 5.91/6.26 (assert (forall ((X tptp.rat) (A tptp.rat)) (= (= (@ tptp.archimedean_frac_rat X) A) (and (@ (@ tptp.member_rat (@ (@ tptp.minus_minus_rat X) A)) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (Y tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat Y)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat (@ (@ tptp.insert8211810215607154385at_nat X) Y))) N)))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (Y tptp.set_real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real Y)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real (@ (@ tptp.insert_real X) Y))) N)))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (Y tptp.set_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o Y)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o (@ (@ tptp.insert_o X) Y))) N)))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (Y tptp.set_complex) (X tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex Y)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex (@ (@ tptp.insert_complex X) Y))) N)))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (Y tptp.set_list_nat) (X tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat Y)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat (@ (@ tptp.insert_list_nat X) Y))) N)))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (Y tptp.set_set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat Y)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat (@ (@ tptp.insert_set_nat X) Y))) N)))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (Y tptp.set_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat Y)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X) Y))) N)))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (Y tptp.set_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int Y)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.insert_int X) Y))) N)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat M2) 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 M2) N) (=> (@ (@ tptp.ord_less_eq_int (@ F M2)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M2) I2) (@ (@ tptp.ord_less_eq_nat I2) N) (= (@ F I2) K)))))))))
% 5.91/6.26 (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))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (= (@ tptp.nat_set_decode (@ tptp.nat_set_encode A2)) A2))))
% 5.91/6.26 (assert (forall ((S2 tptp.set_nat) (N tptp.nat)) (let ((_let_1 (@ tptp.infini8530281810654367211te_nat S2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.infini8530281810654367211te_nat (@ (@ tptp.minus_minus_set_nat S2) (@ (@ tptp.insert_nat (@ _let_1 tptp.zero_zero_nat)) tptp.bot_bot_set_nat))) N)))))
% 5.91/6.26 (assert (forall ((P (-> tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (= (@ P (@ (@ tptp.divide_divide_nat M2) N)) (or (and (= N tptp.zero_zero_nat) (@ P tptp.zero_zero_nat)) (exists ((Q3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q3)) M2) (@ (@ tptp.ord_less_nat M2) (@ _let_1 (@ tptp.suc Q3))) (@ P Q3))))))))
% 5.91/6.26 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C))))
% 5.91/6.26 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C) A)) (= B C))))
% 5.91/6.26 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C) A)) (= B C))))
% 5.91/6.26 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C) A)) (= B C))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.91/6.26 (assert (forall ((X tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X))) (let ((_let_2 (@ _let_1 A2))) (= (@ _let_1 _let_2) _let_2)))))
% 5.91/6.26 (assert (forall ((X tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ _let_1 A2))) (= (@ _let_1 _let_2) _let_2)))))
% 5.91/6.26 (assert (forall ((X Bool) (A2 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o X))) (let ((_let_2 (@ _let_1 A2))) (= (@ _let_1 _let_2) _let_2)))))
% 5.91/6.26 (assert (forall ((X tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ _let_1 A2))) (= (@ _let_1 _let_2) _let_2)))))
% 5.91/6.26 (assert (forall ((X tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ _let_1 A2))) (= (@ _let_1 _let_2) _let_2)))))
% 5.91/6.26 (assert (forall ((A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A))) (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat B) A2)) (or (= A B) (@ _let_1 A2))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real A))) (= (@ _let_1 (@ (@ tptp.insert_real B) A2)) (or (= A B) (@ _let_1 A2))))))
% 5.91/6.26 (assert (forall ((A Bool) (B Bool) (A2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o A))) (= (@ _let_1 (@ (@ tptp.insert_o B) A2)) (or (= A B) (@ _let_1 A2))))))
% 5.91/6.26 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat A))) (= (@ _let_1 (@ (@ tptp.insert_set_nat B) A2)) (or (= A B) (@ _let_1 A2))))))
% 5.91/6.26 (assert (forall ((A tptp.set_nat_rat) (B tptp.set_nat_rat) (A2 tptp.set_set_nat_rat)) (let ((_let_1 (@ tptp.member_set_nat_rat A))) (= (@ _let_1 (@ (@ tptp.insert_set_nat_rat B) A2)) (or (= A B) (@ _let_1 A2))))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A))) (= (@ _let_1 (@ (@ tptp.insert_nat B) A2)) (or (= A B) (@ _let_1 A2))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A))) (= (@ _let_1 (@ (@ tptp.insert_int B) A2)) (or (= A B) (@ _let_1 A2))))))
% 5.91/6.26 (assert (forall ((A tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (B tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A))) (=> (=> (not (@ _let_1 B2)) (= A B)) (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat B) B2))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B2 tptp.set_real) (B tptp.real)) (let ((_let_1 (@ tptp.member_real A))) (=> (=> (not (@ _let_1 B2)) (= A B)) (@ _let_1 (@ (@ tptp.insert_real B) B2))))))
% 5.91/6.26 (assert (forall ((A Bool) (B2 tptp.set_o) (B Bool)) (let ((_let_1 (@ tptp.member_o A))) (=> (=> (not (@ _let_1 B2)) (= A B)) (@ _let_1 (@ (@ tptp.insert_o B) B2))))))
% 5.91/6.26 (assert (forall ((A tptp.set_nat) (B2 tptp.set_set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat A))) (=> (=> (not (@ _let_1 B2)) (= A B)) (@ _let_1 (@ (@ tptp.insert_set_nat B) B2))))))
% 5.91/6.26 (assert (forall ((A tptp.set_nat_rat) (B2 tptp.set_set_nat_rat) (B tptp.set_nat_rat)) (let ((_let_1 (@ tptp.member_set_nat_rat A))) (=> (=> (not (@ _let_1 B2)) (= A B)) (@ _let_1 (@ (@ tptp.insert_set_nat_rat B) B2))))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B2 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ tptp.member_nat A))) (=> (=> (not (@ _let_1 B2)) (= A B)) (@ _let_1 (@ (@ tptp.insert_nat B) B2))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B2 tptp.set_int) (B tptp.int)) (let ((_let_1 (@ tptp.member_int A))) (=> (=> (not (@ _let_1 B2)) (= A B)) (@ _let_1 (@ (@ tptp.insert_int B) B2))))))
% 5.91/6.26 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 5.91/6.26 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 5.91/6.26 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 5.91/6.26 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))))
% 5.91/6.26 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_real) (= A B))))))
% 5.91/6.26 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (= A B))))))
% 5.91/6.26 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_nat) (= A B))))))
% 5.91/6.26 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_int) (= A B))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) C) (@ (@ tptp.times_times_real B) C)) (or (= C tptp.zero_zero_real) (= A B)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) C) (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (= A B)))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B) C)) (or (= C tptp.zero_zero_nat) (= A B)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) C) (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (= A B)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_eq_real A) B))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 5.91/6.26 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_eq_int A) B))))
% 5.91/6.26 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B)))))
% 5.91/6.26 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 5.91/6.26 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 5.91/6.26 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B)))))
% 5.91/6.26 (assert (forall ((A tptp.literal)) (= (@ (@ tptp.plus_plus_literal A) tptp.zero_zero_literal) A)))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 5.91/6.26 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.plus_plus_rat A) A)) (= A tptp.zero_zero_rat))))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))))
% 5.91/6.26 (assert (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) A) (= B tptp.zero_zero_real))))
% 5.91/6.26 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) A) (= B tptp.zero_zero_rat))))
% 5.91/6.26 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((B tptp.int) (A tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) A) (= B tptp.zero_zero_int))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) A) (= B tptp.zero_zero_real))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) A) (= B tptp.zero_zero_rat))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) A) (= B tptp.zero_zero_int))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real B) A)) (= B tptp.zero_zero_real))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat B) A)) (= B tptp.zero_zero_rat))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B) A)) (= B tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int B) A)) (= B tptp.zero_zero_int))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real A) B)) (= B tptp.zero_zero_real))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat A) B)) (= B tptp.zero_zero_rat))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B)) (= B tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int A) B)) (= B tptp.zero_zero_int))))
% 5.91/6.26 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 5.91/6.26 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X) Y)) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 5.91/6.26 (assert (forall ((A tptp.literal)) (= (@ (@ tptp.plus_plus_literal tptp.zero_zero_literal) A) A)))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 5.91/6.26 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 5.91/6.26 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B)))))
% 5.91/6.26 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B)))))
% 5.91/6.26 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))))
% 5.91/6.26 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_real A) B))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_rat A) B))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_nat A) B))))
% 5.91/6.26 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_int A) B))))
% 5.91/6.26 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 5.91/6.26 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 5.91/6.26 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 5.91/6.26 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) B) A)))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 5.91/6.26 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.minus_minus_real A) B))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.minus_minus_rat A) B))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.minus_minus_nat A) B))))
% 5.91/6.26 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.minus_minus_int A) B))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) A) B)))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) A) B)))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) A) B)))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) A) B)))
% 5.91/6.26 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.minus_minus_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_real A) B)))))
% 5.91/6.26 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_rat A) B)))))
% 5.91/6.26 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_nat A) B)))))
% 5.91/6.26 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.minus_minus_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_int A) B)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A)))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A)))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A)))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.abs_abs_real A)) (= A tptp.zero_zero_real))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.abs_abs_rat A)) (= A tptp.zero_zero_rat))))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.abs_abs_int A)) (= A tptp.zero_zero_int))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 5.91/6.26 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.91/6.26 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 5.91/6.26 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 5.91/6.26 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.91/6.26 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 5.91/6.26 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.plus_plus_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N)))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ (@ tptp.times_times_real A) A)))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) (@ (@ tptp.times_times_rat A) A)))))
% 5.91/6.26 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ (@ tptp.times_times_int A) A)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 5.91/6.26 (assert (= (@ tptp.abs_abs_complex tptp.one_one_complex) tptp.one_one_complex))
% 5.91/6.26 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 5.91/6.26 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 5.91/6.26 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 5.91/6.26 (assert (forall ((A tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat A) (@ (@ tptp.insert8211810215607154385at_nat A) tptp.bot_bo2099793752762293965at_nat))))
% 5.91/6.26 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.member_set_nat A) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))))
% 5.91/6.26 (assert (forall ((A tptp.set_nat_rat)) (@ (@ tptp.member_set_nat_rat A) (@ (@ tptp.insert_set_nat_rat A) tptp.bot_bo6797373522285170759at_rat))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (@ (@ tptp.member_real A) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))
% 5.91/6.26 (assert (forall ((A Bool)) (@ (@ tptp.member_o A) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o))))
% 5.91/6.26 (assert (forall ((A tptp.nat)) (@ (@ tptp.member_nat A) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))
% 5.91/6.26 (assert (forall ((A tptp.int)) (@ (@ tptp.member_int A) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))
% 5.91/6.26 (assert (forall ((A tptp.real) (A2 tptp.set_real)) (= (@ tptp.finite_finite_real (@ (@ tptp.insert_real A) A2)) (@ tptp.finite_finite_real A2))))
% 5.91/6.26 (assert (forall ((A Bool) (A2 tptp.set_o)) (= (@ tptp.finite_finite_o (@ (@ tptp.insert_o A) A2)) (@ tptp.finite_finite_o A2))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (A2 tptp.set_nat)) (= (@ tptp.finite_finite_nat (@ (@ tptp.insert_nat A) A2)) (@ tptp.finite_finite_nat A2))))
% 5.91/6.26 (assert (forall ((A tptp.int) (A2 tptp.set_int)) (= (@ tptp.finite_finite_int (@ (@ tptp.insert_int A) A2)) (@ tptp.finite_finite_int A2))))
% 5.91/6.26 (assert (forall ((A tptp.complex) (A2 tptp.set_complex)) (= (@ tptp.finite3207457112153483333omplex (@ (@ tptp.insert_complex A) A2)) (@ tptp.finite3207457112153483333omplex A2))))
% 5.91/6.26 (assert (forall ((A tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.insert8211810215607154385at_nat A) A2)) (@ tptp.finite6177210948735845034at_nat A2))))
% 5.91/6.26 (assert (forall ((A tptp.extended_enat) (A2 tptp.set_Extended_enat)) (= (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.insert_Extended_enat A) A2)) (@ tptp.finite4001608067531595151d_enat A2))))
% 5.91/6.26 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y)) (@ (@ tptp.ord_less_eq_real X) Y)))))))
% 5.91/6.26 (assert (forall ((X tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.insert8211810215607154385at_nat X) A2)) B2) (and (@ (@ tptp.member8440522571783428010at_nat X) B2) (@ (@ tptp.ord_le3146513528884898305at_nat A2) B2)))))
% 5.91/6.26 (assert (forall ((X tptp.real) (A2 tptp.set_real) (B2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.insert_real X) A2)) B2) (and (@ (@ tptp.member_real X) B2) (@ (@ tptp.ord_less_eq_set_real A2) B2)))))
% 5.91/6.26 (assert (forall ((X Bool) (A2 tptp.set_o) (B2 tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.insert_o X) A2)) B2) (and (@ (@ tptp.member_o X) B2) (@ (@ tptp.ord_less_eq_set_o A2) B2)))))
% 5.91/6.26 (assert (forall ((X tptp.set_nat) (A2 tptp.set_set_nat) (B2 tptp.set_set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.insert_set_nat X) A2)) B2) (and (@ (@ tptp.member_set_nat X) B2) (@ (@ tptp.ord_le6893508408891458716et_nat A2) B2)))))
% 5.91/6.26 (assert (forall ((X tptp.set_nat_rat) (A2 tptp.set_set_nat_rat) (B2 tptp.set_set_nat_rat)) (= (@ (@ tptp.ord_le4375437777232675859at_rat (@ (@ tptp.insert_set_nat_rat X) A2)) B2) (and (@ (@ tptp.member_set_nat_rat X) B2) (@ (@ tptp.ord_le4375437777232675859at_rat A2) B2)))))
% 5.91/6.26 (assert (forall ((X tptp.nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat X) A2)) B2) (and (@ (@ tptp.member_nat X) B2) (@ (@ tptp.ord_less_eq_set_nat A2) B2)))))
% 5.91/6.26 (assert (forall ((X tptp.int) (A2 tptp.set_int) (B2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.insert_int X) A2)) B2) (and (@ (@ tptp.member_int X) B2) (@ (@ tptp.ord_less_eq_set_int A2) B2)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M2) N) tptp.zero_zero_nat) (or (= M2 tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.times_times_nat M2) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 5.91/6.26 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M2) (@ _let_1 N)) (or (= M2 N) (= K tptp.zero_zero_nat))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (K tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M2) K) (@ (@ tptp.times_times_nat N) K)) (or (= M2 N) (= K tptp.zero_zero_nat)))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 5.91/6.26 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 5.91/6.26 (assert (forall ((X tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X) B2) (= (@ (@ tptp.minus_1356011639430497352at_nat (@ (@ tptp.insert8211810215607154385at_nat X) A2)) B2) (@ (@ tptp.minus_1356011639430497352at_nat A2) B2)))))
% 5.91/6.26 (assert (forall ((X tptp.real) (B2 tptp.set_real) (A2 tptp.set_real)) (=> (@ (@ tptp.member_real X) B2) (= (@ (@ tptp.minus_minus_set_real (@ (@ tptp.insert_real X) A2)) B2) (@ (@ tptp.minus_minus_set_real A2) B2)))))
% 5.91/6.26 (assert (forall ((X Bool) (B2 tptp.set_o) (A2 tptp.set_o)) (=> (@ (@ tptp.member_o X) B2) (= (@ (@ tptp.minus_minus_set_o (@ (@ tptp.insert_o X) A2)) B2) (@ (@ tptp.minus_minus_set_o A2) B2)))))
% 5.91/6.26 (assert (forall ((X tptp.set_nat) (B2 tptp.set_set_nat) (A2 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat X) B2) (= (@ (@ tptp.minus_2163939370556025621et_nat (@ (@ tptp.insert_set_nat X) A2)) B2) (@ (@ tptp.minus_2163939370556025621et_nat A2) B2)))))
% 5.91/6.26 (assert (forall ((X tptp.set_nat_rat) (B2 tptp.set_set_nat_rat) (A2 tptp.set_set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat X) B2) (= (@ (@ tptp.minus_1626877696091177228at_rat (@ (@ tptp.insert_set_nat_rat X) A2)) B2) (@ (@ tptp.minus_1626877696091177228at_rat A2) B2)))))
% 5.91/6.26 (assert (forall ((X tptp.int) (B2 tptp.set_int) (A2 tptp.set_int)) (=> (@ (@ tptp.member_int X) B2) (= (@ (@ tptp.minus_minus_set_int (@ (@ tptp.insert_int X) A2)) B2) (@ (@ tptp.minus_minus_set_int A2) B2)))))
% 5.91/6.26 (assert (forall ((X tptp.nat) (B2 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.member_nat X) B2) (= (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.insert_nat X) A2)) B2) (@ (@ tptp.minus_minus_set_nat A2) B2)))))
% 5.91/6.26 (assert (forall ((X tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A2))) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X) B2)) (@ _let_1 B2))))))
% 5.91/6.26 (assert (forall ((X tptp.real) (A2 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real A2))) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) B2)) (@ _let_1 B2))))))
% 5.91/6.26 (assert (forall ((X Bool) (A2 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.minus_minus_set_o A2))) (=> (not (@ (@ tptp.member_o X) A2)) (= (@ _let_1 (@ (@ tptp.insert_o X) B2)) (@ _let_1 B2))))))
% 5.91/6.26 (assert (forall ((X tptp.set_nat) (A2 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.minus_2163939370556025621et_nat A2))) (=> (not (@ (@ tptp.member_set_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_set_nat X) B2)) (@ _let_1 B2))))))
% 5.91/6.26 (assert (forall ((X tptp.set_nat_rat) (A2 tptp.set_set_nat_rat) (B2 tptp.set_set_nat_rat)) (let ((_let_1 (@ tptp.minus_1626877696091177228at_rat A2))) (=> (not (@ (@ tptp.member_set_nat_rat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_set_nat_rat X) B2)) (@ _let_1 B2))))))
% 5.91/6.26 (assert (forall ((X tptp.int) (A2 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int A2))) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) B2)) (@ _let_1 B2))))))
% 5.91/6.26 (assert (forall ((X tptp.nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A2))) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X) B2)) (@ _let_1 B2))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M2) N) tptp.one_one_nat) (and (= M2 tptp.one_one_nat) (= N tptp.one_one_nat)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M2) N)) (and (= M2 tptp.one_one_nat) (= N tptp.one_one_nat)))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) A)) (@ _let_1 A)))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A) A)) (@ _let_1 A)))))
% 5.91/6.26 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) A)) (@ _let_1 A)))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real B) A)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat B) A)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.plus_plus_nat B) A)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int B) A)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) B) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) B) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 5.91/6.26 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real B) A)) B) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 5.91/6.26 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat B) A)) B) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 5.91/6.26 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 5.91/6.26 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real B) A)) B) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 5.91/6.26 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat B) A)) B) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 5.91/6.26 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) B) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) B) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real B) A)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat B) A)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat B) A)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int B) A)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) A)) (@ _let_1 A)))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A) A)) (@ _let_1 A)))))
% 5.91/6.26 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) A)) (@ _let_1 A)))))
% 5.91/6.26 (assert (forall ((C tptp.complex) (B tptp.complex)) (= (= C (@ (@ tptp.times_times_complex C) B)) (or (= C tptp.zero_zero_complex) (= B tptp.one_one_complex)))))
% 5.91/6.26 (assert (forall ((C tptp.real) (B tptp.real)) (= (= C (@ (@ tptp.times_times_real C) B)) (or (= C tptp.zero_zero_real) (= B tptp.one_one_real)))))
% 5.91/6.26 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (= C (@ (@ tptp.times_times_rat C) B)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))))
% 5.91/6.26 (assert (forall ((C tptp.int) (B tptp.int)) (= (= C (@ (@ tptp.times_times_int C) B)) (or (= C tptp.zero_zero_int) (= B tptp.one_one_int)))))
% 5.91/6.26 (assert (forall ((C tptp.complex) (A tptp.complex)) (= (= (@ (@ tptp.times_times_complex C) A) C) (or (= C tptp.zero_zero_complex) (= A tptp.one_one_complex)))))
% 5.91/6.26 (assert (forall ((C tptp.real) (A tptp.real)) (= (= (@ (@ tptp.times_times_real C) A) C) (or (= C tptp.zero_zero_real) (= A tptp.one_one_real)))))
% 5.91/6.26 (assert (forall ((C tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.times_times_rat C) A) C) (or (= C tptp.zero_zero_rat) (= A tptp.one_one_rat)))))
% 5.91/6.26 (assert (forall ((C tptp.int) (A tptp.int)) (= (= (@ (@ tptp.times_times_int C) A) C) (or (= C tptp.zero_zero_int) (= A tptp.one_one_int)))))
% 5.91/6.26 (assert (forall ((C tptp.complex) (B tptp.complex)) (= (= C (@ (@ tptp.times_times_complex B) C)) (or (= C tptp.zero_zero_complex) (= B tptp.one_one_complex)))))
% 5.91/6.26 (assert (forall ((C tptp.real) (B tptp.real)) (= (= C (@ (@ tptp.times_times_real B) C)) (or (= C tptp.zero_zero_real) (= B tptp.one_one_real)))))
% 5.91/6.26 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (= C (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))))
% 5.91/6.26 (assert (forall ((C tptp.int) (B tptp.int)) (= (= C (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (= B tptp.one_one_int)))))
% 5.91/6.26 (assert (forall ((A tptp.complex) (C tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) C) C) (or (= C tptp.zero_zero_complex) (= A tptp.one_one_complex)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.times_times_real A) C) C) (or (= C tptp.zero_zero_real) (= A tptp.one_one_real)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) C) C) (or (= C tptp.zero_zero_rat) (= A tptp.one_one_rat)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.times_times_int A) C) C) (or (= C tptp.zero_zero_int) (= A tptp.one_one_int)))))
% 5.91/6.26 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (let ((_let_2 (@ (@ tptp.divide_divide_rat (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_rat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat A) B)))))))))
% 5.91/6.26 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (let ((_let_2 (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_real))) (and (=> _let_3 (= _let_2 tptp.zero_zero_real)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real A) B)))))))))
% 5.91/6.26 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_rat A) B))))))
% 5.91/6.26 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_real A) B))))))
% 5.91/6.26 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat C) A)) (@ (@ tptp.times_times_rat B) C)) (@ (@ tptp.divide_divide_rat A) B)))))
% 5.91/6.26 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real C) A)) (@ (@ tptp.times_times_real B) C)) (@ (@ tptp.divide_divide_real A) B)))))
% 5.91/6.26 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (@ (@ tptp.divide_divide_rat A) B)))))
% 5.91/6.26 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (@ (@ tptp.divide_divide_real A) B)))))
% 5.91/6.26 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat C) B)) (@ (@ tptp.divide_divide_rat A) B)))))
% 5.91/6.26 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real C) B)) (@ (@ tptp.divide_divide_real A) B)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) B)) A) B))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) B)) A) B))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) B)) A) B))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) B)) A) B))))
% 5.91/6.26 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) B)) B) A))))
% 5.91/6.26 (assert (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) B)) B) A))))
% 5.91/6.26 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) B)) B) A))))
% 5.91/6.26 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) B)) B) A))))
% 5.91/6.26 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_int A) B))))))
% 5.91/6.26 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_nat A) B))))))
% 5.91/6.26 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int A) B)))))
% 5.91/6.26 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat A) B)))))
% 5.91/6.26 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int A) B)))))))))
% 5.91/6.26 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat A) B)))))))))
% 5.91/6.26 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A))))
% 5.91/6.26 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A))))
% 5.91/6.26 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat A) B)) B) A))))
% 5.91/6.26 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A))))
% 5.91/6.26 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (= (@ (@ tptp.plus_plus_real B) (@ (@ tptp.minus_minus_real A) B)) A))))
% 5.91/6.26 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.minus_minus_rat A) B)) A))))
% 5.91/6.26 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.minus_minus_nat A) B)) A))))
% 5.91/6.26 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.plus_plus_int B) (@ (@ tptp.minus_minus_int A) B)) A))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) A) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 5.91/6.26 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.abs_abs_real A)) (not (= A tptp.zero_zero_real)))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A)) (not (= A tptp.zero_zero_rat)))))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A)) (not (= A tptp.zero_zero_int)))))
% 5.91/6.26 (assert (forall ((A tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat B) tptp.bot_bo2099793752762293965at_nat))) (= (= (@ (@ tptp.insert8211810215607154385at_nat A) A2) _let_1) (and (= A B) (@ (@ tptp.ord_le3146513528884898305at_nat A2) _let_1))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (A2 tptp.set_real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real B) tptp.bot_bot_set_real))) (= (= (@ (@ tptp.insert_real A) A2) _let_1) (and (= A B) (@ (@ tptp.ord_less_eq_set_real A2) _let_1))))))
% 5.91/6.26 (assert (forall ((A Bool) (A2 tptp.set_o) (B Bool)) (let ((_let_1 (@ (@ tptp.insert_o B) tptp.bot_bot_set_o))) (= (= (@ (@ tptp.insert_o A) A2) _let_1) (and (= A B) (@ (@ tptp.ord_less_eq_set_o A2) _let_1))))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (A2 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (= (= (@ (@ tptp.insert_nat A) A2) _let_1) (and (= A B) (@ (@ tptp.ord_less_eq_set_nat A2) _let_1))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (A2 tptp.set_int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (= (= (@ (@ tptp.insert_int A) A2) _let_1) (and (= A B) (@ (@ tptp.ord_less_eq_set_int A2) _let_1))))))
% 5.91/6.26 (assert (forall ((B tptp.product_prod_nat_nat) (A tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat B) tptp.bot_bo2099793752762293965at_nat))) (= (= _let_1 (@ (@ tptp.insert8211810215607154385at_nat A) A2)) (and (= A B) (@ (@ tptp.ord_le3146513528884898305at_nat A2) _let_1))))))
% 5.91/6.26 (assert (forall ((B tptp.real) (A tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ (@ tptp.insert_real B) tptp.bot_bot_set_real))) (= (= _let_1 (@ (@ tptp.insert_real A) A2)) (and (= A B) (@ (@ tptp.ord_less_eq_set_real A2) _let_1))))))
% 5.91/6.26 (assert (forall ((B Bool) (A Bool) (A2 tptp.set_o)) (let ((_let_1 (@ (@ tptp.insert_o B) tptp.bot_bot_set_o))) (= (= _let_1 (@ (@ tptp.insert_o A) A2)) (and (= A B) (@ (@ tptp.ord_less_eq_set_o A2) _let_1))))))
% 5.91/6.26 (assert (forall ((B tptp.nat) (A tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (= (= _let_1 (@ (@ tptp.insert_nat A) A2)) (and (= A B) (@ (@ tptp.ord_less_eq_set_nat A2) _let_1))))))
% 5.91/6.26 (assert (forall ((B tptp.int) (A tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (= (= _let_1 (@ (@ tptp.insert_int A) A2)) (and (= A B) (@ (@ tptp.ord_less_eq_set_int A2) _let_1))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.times_times_nat M2) N)) (and (= M2 _let_1) (= N _let_1))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.times_times_nat M2) N) _let_1) (and (= M2 _let_1) (= N _let_1))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.times_times_nat M2) N)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat M2) N)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.times_times_nat M2) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri5074537144036343181t_real N)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.times_times_nat M2) N)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri681578069525770553at_rat N)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M2) K)) (@ (@ tptp.times_times_nat N) K)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M2) N)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M2) N)) (and (@ _let_1 M2) (@ _let_1 N))))))
% 5.91/6.26 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))))
% 5.91/6.26 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real)))))
% 5.91/6.26 (assert (forall ((A tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A))) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) (@ _let_1 A2)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))) (@ _let_1 A2)))))
% 5.91/6.26 (assert (forall ((A Bool) (A2 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_o A2) (@ _let_1 tptp.bot_bot_set_o))) (@ _let_1 A2)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))) (@ _let_1 A2)))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ _let_1 tptp.bot_bot_set_nat))) (@ _let_1 A2)))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_real) (A tptp.real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real A2))) (= (@ tptp.finite_finite_real (@ _let_1 (@ (@ tptp.insert_real A) B2))) (@ tptp.finite_finite_real (@ _let_1 B2))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_o) (A Bool) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.minus_minus_set_o A2))) (= (@ tptp.finite_finite_o (@ _let_1 (@ (@ tptp.insert_o A) B2))) (@ tptp.finite_finite_o (@ _let_1 B2))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_int) (A tptp.int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int A2))) (= (@ tptp.finite_finite_int (@ _let_1 (@ (@ tptp.insert_int A) B2))) (@ tptp.finite_finite_int (@ _let_1 B2))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_complex) (A tptp.complex) (B2 tptp.set_complex)) (let ((_let_1 (@ tptp.minus_811609699411566653omplex A2))) (= (@ tptp.finite3207457112153483333omplex (@ _let_1 (@ (@ tptp.insert_complex A) B2))) (@ tptp.finite3207457112153483333omplex (@ _let_1 B2))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (A tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A2))) (= (@ tptp.finite6177210948735845034at_nat (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat A) B2))) (@ tptp.finite6177210948735845034at_nat (@ _let_1 B2))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat) (B2 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.minus_925952699566721837d_enat A2))) (= (@ tptp.finite4001608067531595151d_enat (@ _let_1 (@ (@ tptp.insert_Extended_enat A) B2))) (@ tptp.finite4001608067531595151d_enat (@ _let_1 B2))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_nat) (A tptp.nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A2))) (= (@ tptp.finite_finite_nat (@ _let_1 (@ (@ tptp.insert_nat A) B2))) (@ tptp.finite_finite_nat (@ _let_1 B2))))))
% 5.91/6.26 (assert (forall ((X tptp.real)) (= (= (@ tptp.archim2898591450579166408c_real X) tptp.zero_zero_real) (@ (@ tptp.member_real X) tptp.ring_1_Ints_real))))
% 5.91/6.26 (assert (forall ((X tptp.rat)) (= (= (@ tptp.archimedean_frac_rat X) tptp.zero_zero_rat) (@ (@ tptp.member_rat X) tptp.ring_1_Ints_rat))))
% 5.91/6.26 (assert (= (@ tptp.nat_set_decode tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 5.91/6.26 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) B))) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 5.91/6.26 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C) B))) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 5.91/6.26 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B) C))) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 5.91/6.26 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B) C))) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 5.91/6.26 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) B)) A)) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 5.91/6.26 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) B)) A)) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 5.91/6.26 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) C)) A)) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 5.91/6.26 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) C)) A)) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 5.91/6.26 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) B)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) B)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) B)))))
% 5.91/6.26 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex B) (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) A)))))
% 5.91/6.26 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat B) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)))))
% 5.91/6.26 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real B) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) A)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) (@ tptp.abs_abs_real B))) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.abs_abs_rat B))) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.abs_abs_real B))) (or (@ _let_1 A) (= B tptp.zero_zero_real))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.abs_abs_rat B))) (or (@ _let_1 A) (= B tptp.zero_zero_rat))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc M2)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.semiri8010041392384452111omplex M2)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M2)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M2)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M2)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M2)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M2)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real M2)))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc M2)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat M2)))))
% 5.91/6.26 (assert (forall ((M2 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 M2) N)) (and (@ _let_1 M2) (@ _let_1 N))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_real) (X tptp.real)) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ tptp.finite_card_real (@ (@ tptp.insert_real X) A2)) (@ tptp.suc (@ tptp.finite_card_real A2)))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A2) (=> (not (@ (@ tptp.member_o X) A2)) (= (@ tptp.finite_card_o (@ (@ tptp.insert_o X) A2)) (@ tptp.suc (@ tptp.finite_card_o A2)))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_set_nat_rat) (X tptp.set_nat_rat)) (=> (@ tptp.finite6430367030675640852at_rat A2) (=> (not (@ (@ tptp.member_set_nat_rat X) A2)) (= (@ tptp.finite8736671560171388117at_rat (@ (@ tptp.insert_set_nat_rat X) A2)) (@ tptp.suc (@ tptp.finite8736671560171388117at_rat A2)))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_list_nat) (X tptp.list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A2) (=> (not (@ (@ tptp.member_list_nat X) A2)) (= (@ tptp.finite_card_list_nat (@ (@ tptp.insert_list_nat X) A2)) (@ tptp.suc (@ tptp.finite_card_list_nat A2)))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_set_nat) (X tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (not (@ (@ tptp.member_set_nat X) A2)) (= (@ tptp.finite_card_set_nat (@ (@ tptp.insert_set_nat X) A2)) (@ tptp.suc (@ tptp.finite_card_set_nat A2)))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X) A2)) (@ tptp.suc (@ tptp.finite_card_nat A2)))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ tptp.finite_card_int (@ (@ tptp.insert_int X) A2)) (@ tptp.suc (@ tptp.finite_card_int A2)))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_complex) (X tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ tptp.finite_card_complex (@ (@ tptp.insert_complex X) A2)) (@ tptp.suc (@ tptp.finite_card_complex A2)))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (=> (@ tptp.finite6177210948735845034at_nat A2) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) A2)) (= (@ tptp.finite711546835091564841at_nat (@ (@ tptp.insert8211810215607154385at_nat X) A2)) (@ tptp.suc (@ tptp.finite711546835091564841at_nat A2)))))))
% 5.91/6.26 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (@ (@ tptp.member_Extended_enat X) A2)) (= (@ tptp.finite121521170596916366d_enat (@ (@ tptp.insert_Extended_enat X) A2)) (@ tptp.suc (@ tptp.finite121521170596916366d_enat A2)))))))
% 5.91/6.26 (assert (forall ((M2 tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M2) K)) (@ (@ tptp.times_times_nat N) K)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M2) N)))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat M2) N)) N) M2))))
% 5.91/6.26 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) M2)) N) M2))))
% 5.91/6.26 (assert (= (@ tptp.nat2 tptp.one_one_int) (@ tptp.suc tptp.zero_zero_nat)))
% 5.91/6.26 (assert (forall ((I tptp.int)) (= (= (@ tptp.nat2 I) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int I) tptp.zero_zero_int))))
% 5.91/6.26 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 Z) tptp.zero_zero_nat))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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))))
% 5.91/6.26 (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)))))))
% 5.91/6.26 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.archim2898591450579166408c_real X)) (not (@ (@ tptp.member_real X) tptp.ring_1_Ints_real)))))
% 5.91/6.26 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.archimedean_frac_rat X)) (not (@ (@ tptp.member_rat X) tptp.ring_1_Ints_rat)))))
% 5.91/6.26 (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))))
% 5.91/6.26 (assert (forall ((A tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A2))) (let ((_let_2 (@ tptp.member8440522571783428010at_nat A))) (=> (@ _let_2 A2) (=> (not (@ _let_2 B2)) (= (@ tptp.finite711546835091564841at_nat (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat A) B2))) (@ (@ tptp.minus_minus_nat (@ tptp.finite711546835091564841at_nat (@ _let_1 B2))) tptp.one_one_nat))))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (A2 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real A2))) (let ((_let_2 (@ tptp.member_real A))) (=> (@ _let_2 A2) (=> (not (@ _let_2 B2)) (= (@ tptp.finite_card_real (@ _let_1 (@ (@ tptp.insert_real A) B2))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_real (@ _let_1 B2))) tptp.one_one_nat))))))))
% 5.91/6.26 (assert (forall ((A Bool) (A2 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.minus_minus_set_o A2))) (let ((_let_2 (@ tptp.member_o A))) (=> (@ _let_2 A2) (=> (not (@ _let_2 B2)) (= (@ tptp.finite_card_o (@ _let_1 (@ (@ tptp.insert_o A) B2))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_o (@ _let_1 B2))) tptp.one_one_nat))))))))
% 5.91/6.26 (assert (forall ((A tptp.set_nat_rat) (A2 tptp.set_set_nat_rat) (B2 tptp.set_set_nat_rat)) (let ((_let_1 (@ tptp.minus_1626877696091177228at_rat A2))) (let ((_let_2 (@ tptp.member_set_nat_rat A))) (=> (@ _let_2 A2) (=> (not (@ _let_2 B2)) (= (@ tptp.finite8736671560171388117at_rat (@ _let_1 (@ (@ tptp.insert_set_nat_rat A) B2))) (@ (@ tptp.minus_minus_nat (@ tptp.finite8736671560171388117at_rat (@ _let_1 B2))) tptp.one_one_nat))))))))
% 5.91/6.26 (assert (forall ((A tptp.complex) (A2 tptp.set_complex) (B2 tptp.set_complex)) (let ((_let_1 (@ tptp.minus_811609699411566653omplex A2))) (let ((_let_2 (@ tptp.member_complex A))) (=> (@ _let_2 A2) (=> (not (@ _let_2 B2)) (= (@ tptp.finite_card_complex (@ _let_1 (@ (@ tptp.insert_complex A) B2))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_complex (@ _let_1 B2))) tptp.one_one_nat))))))))
% 5.91/6.26 (assert (forall ((A tptp.list_nat) (A2 tptp.set_list_nat) (B2 tptp.set_list_nat)) (let ((_let_1 (@ tptp.minus_7954133019191499631st_nat A2))) (let ((_let_2 (@ tptp.member_list_nat A))) (=> (@ _let_2 A2) (=> (not (@ _let_2 B2)) (= (@ tptp.finite_card_list_nat (@ _let_1 (@ (@ tptp.insert_list_nat A) B2))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_list_nat (@ _let_1 B2))) tptp.one_one_nat))))))))
% 5.91/6.26 (assert (forall ((A tptp.set_nat) (A2 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.minus_2163939370556025621et_nat A2))) (let ((_let_2 (@ tptp.member_set_nat A))) (=> (@ _let_2 A2) (=> (not (@ _let_2 B2)) (= (@ tptp.finite_card_set_nat (@ _let_1 (@ (@ tptp.insert_set_nat A) B2))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_set_nat (@ _let_1 B2))) tptp.one_one_nat))))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (A2 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int A2))) (let ((_let_2 (@ tptp.member_int A))) (=> (@ _let_2 A2) (=> (not (@ _let_2 B2)) (= (@ tptp.finite_card_int (@ _let_1 (@ (@ tptp.insert_int A) B2))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_int (@ _let_1 B2))) tptp.one_one_nat))))))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A2))) (let ((_let_2 (@ tptp.member_nat A))) (=> (@ _let_2 A2) (=> (not (@ _let_2 B2)) (= (@ tptp.finite_card_nat (@ _let_1 (@ (@ tptp.insert_nat A) B2))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_nat (@ _let_1 B2))) tptp.one_one_nat))))))))
% 5.91/6.26 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) Y)) Y)))))))
% 5.91/6.26 (assert (forall ((X tptp.real) (Y tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (= (@ (@ tptp.minus_minus_real (@ _let_1 Y)) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_real Y) B))) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) A)) B))))))
% 5.91/6.26 (assert (forall ((X tptp.rat) (Y tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 Y)) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_rat Y) B))) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) A)) B))))))
% 5.91/6.26 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (= (@ (@ tptp.minus_minus_int (@ _let_1 Y)) (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_int Y) B))) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) A)) B))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E2)) C) D))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E2)) C) D))))
% 5.91/6.26 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E2)) C) D))))
% 5.91/6.26 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (= C (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E2)) D)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (= C (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E2)) D)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (= C (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E2)) D)))))
% 5.91/6.26 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_real X) Y)))))
% 5.91/6.26 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ (@ tptp.minus_minus_rat X) Y)))))
% 5.91/6.26 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) Y)) (@ (@ tptp.minus_minus_int X) Y)))))
% 5.91/6.26 (assert (= tptp.ord_less_eq_real (lambda ((X3 tptp.real) (Y2 tptp.real)) (or (@ (@ tptp.ord_less_real X3) Y2) (= X3 Y2)))))
% 5.91/6.26 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) X))))
% 5.91/6.26 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)))))
% 5.91/6.26 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real A) B))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.plus_plus_rat A) B))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int A) B))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))
% 5.91/6.26 (assert (forall ((S2 tptp.set_real)) (=> (exists ((X2 tptp.real)) (@ (@ tptp.member_real X2) S2)) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S2) (@ (@ tptp.ord_less_eq_real X4) Z5)))) (exists ((Y3 tptp.real)) (and (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) S2) (@ (@ tptp.ord_less_eq_real X2) Y3))) (forall ((Z5 tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S2) (@ (@ tptp.ord_less_eq_real X4) Z5))) (@ (@ tptp.ord_less_eq_real Y3) Z5)))))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real B))) (let ((_let_2 (@ tptp.abs_abs_real A))) (=> (@ (@ tptp.ord_less_real _let_2) C) (=> (@ (@ tptp.ord_less_real _let_1) D) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real _let_2) _let_1)) (@ (@ tptp.times_times_real C) D))))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat B))) (let ((_let_2 (@ tptp.abs_abs_rat A))) (=> (@ (@ tptp.ord_less_rat _let_2) C) (=> (@ (@ tptp.ord_less_rat _let_1) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat _let_2) _let_1)) (@ (@ tptp.times_times_rat C) D))))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int B))) (let ((_let_2 (@ tptp.abs_abs_int A))) (=> (@ (@ tptp.ord_less_int _let_2) C) (=> (@ (@ tptp.ord_less_int _let_1) D) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.times_times_int C) D))))))))
% 5.91/6.26 (assert (forall ((A tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat A) A2) (exists ((B8 tptp.set_Pr1261947904930325089at_nat)) (and (= A2 (@ (@ tptp.insert8211810215607154385at_nat A) B8)) (not (@ (@ tptp.member8440522571783428010at_nat A) B8)))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.member_real A) A2) (exists ((B8 tptp.set_real)) (and (= A2 (@ (@ tptp.insert_real A) B8)) (not (@ (@ tptp.member_real A) B8)))))))
% 5.91/6.26 (assert (forall ((A Bool) (A2 tptp.set_o)) (=> (@ (@ tptp.member_o A) A2) (exists ((B8 tptp.set_o)) (and (= A2 (@ (@ tptp.insert_o A) B8)) (not (@ (@ tptp.member_o A) B8)))))))
% 5.91/6.26 (assert (forall ((A tptp.set_nat) (A2 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat A) A2) (exists ((B8 tptp.set_set_nat)) (and (= A2 (@ (@ tptp.insert_set_nat A) B8)) (not (@ (@ tptp.member_set_nat A) B8)))))))
% 5.91/6.26 (assert (forall ((A tptp.set_nat_rat) (A2 tptp.set_set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat A) A2) (exists ((B8 tptp.set_set_nat_rat)) (and (= A2 (@ (@ tptp.insert_set_nat_rat A) B8)) (not (@ (@ tptp.member_set_nat_rat A) B8)))))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.member_nat A) A2) (exists ((B8 tptp.set_nat)) (and (= A2 (@ (@ tptp.insert_nat A) B8)) (not (@ (@ tptp.member_nat A) B8)))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.member_int A) A2) (exists ((B8 tptp.set_int)) (and (= A2 (@ (@ tptp.insert_int A) B8)) (not (@ (@ tptp.member_int A) B8)))))))
% 5.91/6.26 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X))) (let ((_let_2 (@ tptp.insert8211810215607154385at_nat Y))) (= (@ _let_1 (@ _let_2 A2)) (@ _let_2 (@ _let_1 A2)))))))
% 5.91/6.26 (assert (forall ((X tptp.real) (Y tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.insert_real Y))) (= (@ _let_1 (@ _let_2 A2)) (@ _let_2 (@ _let_1 A2)))))))
% 5.91/6.26 (assert (forall ((X Bool) (Y Bool) (A2 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o X))) (let ((_let_2 (@ tptp.insert_o Y))) (= (@ _let_1 (@ _let_2 A2)) (@ _let_2 (@ _let_1 A2)))))))
% 5.91/6.26 (assert (forall ((X tptp.nat) (Y tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ tptp.insert_nat Y))) (= (@ _let_1 (@ _let_2 A2)) (@ _let_2 (@ _let_1 A2)))))))
% 5.91/6.26 (assert (forall ((X tptp.int) (Y tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.insert_int Y))) (= (@ _let_1 (@ _let_2 A2)) (@ _let_2 (@ _let_1 A2)))))))
% 5.91/6.26 (assert (forall ((A tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (= A B))) (=> (not (@ (@ tptp.member8440522571783428010at_nat A) A2)) (=> (not (@ (@ tptp.member8440522571783428010at_nat B) B2)) (= (= (@ (@ tptp.insert8211810215607154385at_nat A) A2) (@ (@ tptp.insert8211810215607154385at_nat B) B2)) (and (=> _let_1 (= A2 B2)) (=> (not _let_1) (exists ((C4 tptp.set_Pr1261947904930325089at_nat)) (and (= A2 (@ (@ tptp.insert8211810215607154385at_nat B) C4)) (not (@ (@ tptp.member8440522571783428010at_nat B) C4)) (= B2 (@ (@ tptp.insert8211810215607154385at_nat A) C4)) (not (@ (@ tptp.member8440522571783428010at_nat A) C4))))))))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (A2 tptp.set_real) (B tptp.real) (B2 tptp.set_real)) (let ((_let_1 (= A B))) (=> (not (@ (@ tptp.member_real A) A2)) (=> (not (@ (@ tptp.member_real B) B2)) (= (= (@ (@ tptp.insert_real A) A2) (@ (@ tptp.insert_real B) B2)) (and (=> _let_1 (= A2 B2)) (=> (not _let_1) (exists ((C4 tptp.set_real)) (and (= A2 (@ (@ tptp.insert_real B) C4)) (not (@ (@ tptp.member_real B) C4)) (= B2 (@ (@ tptp.insert_real A) C4)) (not (@ (@ tptp.member_real A) C4))))))))))))
% 5.91/6.26 (assert (forall ((A Bool) (A2 tptp.set_o) (B Bool) (B2 tptp.set_o)) (=> (not (@ (@ tptp.member_o A) A2)) (=> (not (@ (@ tptp.member_o B) B2)) (= (= (@ (@ tptp.insert_o A) A2) (@ (@ tptp.insert_o B) B2)) (and (=> (= A B) (= A2 B2)) (=> (= A (not B)) (exists ((C4 tptp.set_o)) (and (= A2 (@ (@ tptp.insert_o B) C4)) (not (@ (@ tptp.member_o B) C4)) (= B2 (@ (@ tptp.insert_o A) C4)) (not (@ (@ tptp.member_o A) C4)))))))))))
% 5.91/6.26 (assert (forall ((A tptp.set_nat) (A2 tptp.set_set_nat) (B tptp.set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (= A B))) (=> (not (@ (@ tptp.member_set_nat A) A2)) (=> (not (@ (@ tptp.member_set_nat B) B2)) (= (= (@ (@ tptp.insert_set_nat A) A2) (@ (@ tptp.insert_set_nat B) B2)) (and (=> _let_1 (= A2 B2)) (=> (not _let_1) (exists ((C4 tptp.set_set_nat)) (and (= A2 (@ (@ tptp.insert_set_nat B) C4)) (not (@ (@ tptp.member_set_nat B) C4)) (= B2 (@ (@ tptp.insert_set_nat A) C4)) (not (@ (@ tptp.member_set_nat A) C4))))))))))))
% 5.91/6.26 (assert (forall ((A tptp.set_nat_rat) (A2 tptp.set_set_nat_rat) (B tptp.set_nat_rat) (B2 tptp.set_set_nat_rat)) (let ((_let_1 (= A B))) (=> (not (@ (@ tptp.member_set_nat_rat A) A2)) (=> (not (@ (@ tptp.member_set_nat_rat B) B2)) (= (= (@ (@ tptp.insert_set_nat_rat A) A2) (@ (@ tptp.insert_set_nat_rat B) B2)) (and (=> _let_1 (= A2 B2)) (=> (not _let_1) (exists ((C4 tptp.set_set_nat_rat)) (and (= A2 (@ (@ tptp.insert_set_nat_rat B) C4)) (not (@ (@ tptp.member_set_nat_rat B) C4)) (= B2 (@ (@ tptp.insert_set_nat_rat A) C4)) (not (@ (@ tptp.member_set_nat_rat A) C4))))))))))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (A2 tptp.set_nat) (B tptp.nat) (B2 tptp.set_nat)) (let ((_let_1 (= A B))) (=> (not (@ (@ tptp.member_nat A) A2)) (=> (not (@ (@ tptp.member_nat B) B2)) (= (= (@ (@ tptp.insert_nat A) A2) (@ (@ tptp.insert_nat B) B2)) (and (=> _let_1 (= A2 B2)) (=> (not _let_1) (exists ((C4 tptp.set_nat)) (and (= A2 (@ (@ tptp.insert_nat B) C4)) (not (@ (@ tptp.member_nat B) C4)) (= B2 (@ (@ tptp.insert_nat A) C4)) (not (@ (@ tptp.member_nat A) C4))))))))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (A2 tptp.set_int) (B tptp.int) (B2 tptp.set_int)) (let ((_let_1 (= A B))) (=> (not (@ (@ tptp.member_int A) A2)) (=> (not (@ (@ tptp.member_int B) B2)) (= (= (@ (@ tptp.insert_int A) A2) (@ (@ tptp.insert_int B) B2)) (and (=> _let_1 (= A2 B2)) (=> (not _let_1) (exists ((C4 tptp.set_int)) (and (= A2 (@ (@ tptp.insert_int B) C4)) (not (@ (@ tptp.member_int B) C4)) (= B2 (@ (@ tptp.insert_int A) C4)) (not (@ (@ tptp.member_int A) C4))))))))))))
% 5.91/6.26 (assert (forall ((A tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat A) A2) (= (@ (@ tptp.insert8211810215607154385at_nat A) A2) A2))))
% 5.91/6.26 (assert (forall ((A tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.member_real A) A2) (= (@ (@ tptp.insert_real A) A2) A2))))
% 5.91/6.26 (assert (forall ((A Bool) (A2 tptp.set_o)) (=> (@ (@ tptp.member_o A) A2) (= (@ (@ tptp.insert_o A) A2) A2))))
% 5.91/6.26 (assert (forall ((A tptp.set_nat) (A2 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat A) A2) (= (@ (@ tptp.insert_set_nat A) A2) A2))))
% 5.91/6.26 (assert (forall ((A tptp.set_nat_rat) (A2 tptp.set_set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat A) A2) (= (@ (@ tptp.insert_set_nat_rat A) A2) A2))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.member_nat A) A2) (= (@ (@ tptp.insert_nat A) A2) A2))))
% 5.91/6.26 (assert (forall ((A tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.member_int A) A2) (= (@ (@ tptp.insert_int A) A2) A2))))
% 5.91/6.26 (assert (forall ((X tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X))) (let ((_let_2 (@ tptp.member8440522571783428010at_nat X))) (=> (not (@ _let_2 A2)) (=> (not (@ _let_2 B2)) (= (= (@ _let_1 A2) (@ _let_1 B2)) (= A2 B2))))))))
% 5.91/6.26 (assert (forall ((X tptp.real) (A2 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.member_real X))) (=> (not (@ _let_2 A2)) (=> (not (@ _let_2 B2)) (= (= (@ _let_1 A2) (@ _let_1 B2)) (= A2 B2))))))))
% 5.91/6.26 (assert (forall ((X Bool) (A2 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o X))) (let ((_let_2 (@ tptp.member_o X))) (=> (not (@ _let_2 A2)) (=> (not (@ _let_2 B2)) (= (= (@ _let_1 A2) (@ _let_1 B2)) (= A2 B2))))))))
% 5.91/6.26 (assert (forall ((X tptp.set_nat) (A2 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.insert_set_nat X))) (let ((_let_2 (@ tptp.member_set_nat X))) (=> (not (@ _let_2 A2)) (=> (not (@ _let_2 B2)) (= (= (@ _let_1 A2) (@ _let_1 B2)) (= A2 B2))))))))
% 5.91/6.26 (assert (forall ((X tptp.set_nat_rat) (A2 tptp.set_set_nat_rat) (B2 tptp.set_set_nat_rat)) (let ((_let_1 (@ tptp.insert_set_nat_rat X))) (let ((_let_2 (@ tptp.member_set_nat_rat X))) (=> (not (@ _let_2 A2)) (=> (not (@ _let_2 B2)) (= (= (@ _let_1 A2) (@ _let_1 B2)) (= A2 B2))))))))
% 5.91/6.26 (assert (forall ((X tptp.nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ tptp.member_nat X))) (=> (not (@ _let_2 A2)) (=> (not (@ _let_2 B2)) (= (= (@ _let_1 A2) (@ _let_1 B2)) (= A2 B2))))))))
% 5.91/6.26 (assert (forall ((X tptp.int) (A2 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.member_int X))) (=> (not (@ _let_2 A2)) (=> (not (@ _let_2 B2)) (= (= (@ _let_1 A2) (@ _let_1 B2)) (= A2 B2))))))))
% 5.91/6.26 (assert (forall ((X tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X) A2) (not (forall ((B8 tptp.set_Pr1261947904930325089at_nat)) (=> (= A2 (@ (@ tptp.insert8211810215607154385at_nat X) B8)) (@ (@ tptp.member8440522571783428010at_nat X) B8)))))))
% 5.91/6.26 (assert (forall ((X tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.member_real X) A2) (not (forall ((B8 tptp.set_real)) (=> (= A2 (@ (@ tptp.insert_real X) B8)) (@ (@ tptp.member_real X) B8)))))))
% 5.91/6.26 (assert (forall ((X Bool) (A2 tptp.set_o)) (=> (@ (@ tptp.member_o X) A2) (not (forall ((B8 tptp.set_o)) (=> (= A2 (@ (@ tptp.insert_o X) B8)) (@ (@ tptp.member_o X) B8)))))))
% 5.91/6.26 (assert (forall ((X tptp.set_nat) (A2 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat X) A2) (not (forall ((B8 tptp.set_set_nat)) (=> (= A2 (@ (@ tptp.insert_set_nat X) B8)) (@ (@ tptp.member_set_nat X) B8)))))))
% 5.91/6.26 (assert (forall ((X tptp.set_nat_rat) (A2 tptp.set_set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat X) A2) (not (forall ((B8 tptp.set_set_nat_rat)) (=> (= A2 (@ (@ tptp.insert_set_nat_rat X) B8)) (@ (@ tptp.member_set_nat_rat X) B8)))))))
% 5.91/6.26 (assert (forall ((X tptp.nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.member_nat X) A2) (not (forall ((B8 tptp.set_nat)) (=> (= A2 (@ (@ tptp.insert_nat X) B8)) (@ (@ tptp.member_nat X) B8)))))))
% 5.91/6.26 (assert (forall ((X tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.member_int X) A2) (not (forall ((B8 tptp.set_int)) (=> (= A2 (@ (@ tptp.insert_int X) B8)) (@ (@ tptp.member_int X) B8)))))))
% 5.91/6.26 (assert (forall ((A tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (B tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat B) B2))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B2 tptp.set_real) (B tptp.real)) (let ((_let_1 (@ tptp.member_real A))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert_real B) B2))))))
% 5.91/6.26 (assert (forall ((A Bool) (B2 tptp.set_o) (B Bool)) (let ((_let_1 (@ tptp.member_o A))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert_o B) B2))))))
% 5.91/6.26 (assert (forall ((A tptp.set_nat) (B2 tptp.set_set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat A))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert_set_nat B) B2))))))
% 5.91/6.26 (assert (forall ((A tptp.set_nat_rat) (B2 tptp.set_set_nat_rat) (B tptp.set_nat_rat)) (let ((_let_1 (@ tptp.member_set_nat_rat A))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert_set_nat_rat B) B2))))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B2 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ tptp.member_nat A))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert_nat B) B2))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B2 tptp.set_int) (B tptp.int)) (let ((_let_1 (@ tptp.member_int A))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert_int B) B2))))))
% 5.91/6.26 (assert (forall ((A tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.member8440522571783428010at_nat A) (@ (@ tptp.insert8211810215607154385at_nat A) B2))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B2 tptp.set_real)) (@ (@ tptp.member_real A) (@ (@ tptp.insert_real A) B2))))
% 5.91/6.26 (assert (forall ((A Bool) (B2 tptp.set_o)) (@ (@ tptp.member_o A) (@ (@ tptp.insert_o A) B2))))
% 5.91/6.26 (assert (forall ((A tptp.set_nat) (B2 tptp.set_set_nat)) (@ (@ tptp.member_set_nat A) (@ (@ tptp.insert_set_nat A) B2))))
% 5.91/6.26 (assert (forall ((A tptp.set_nat_rat) (B2 tptp.set_set_nat_rat)) (@ (@ tptp.member_set_nat_rat A) (@ (@ tptp.insert_set_nat_rat A) B2))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B2 tptp.set_nat)) (@ (@ tptp.member_nat A) (@ (@ tptp.insert_nat A) B2))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B2 tptp.set_int)) (@ (@ tptp.member_int A) (@ (@ tptp.insert_int A) B2))))
% 5.91/6.26 (assert (forall ((A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A))) (=> (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat B) A2)) (=> (not (= A B)) (@ _let_1 A2))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real A))) (=> (@ _let_1 (@ (@ tptp.insert_real B) A2)) (=> (not (= A B)) (@ _let_1 A2))))))
% 5.91/6.26 (assert (forall ((A Bool) (B Bool) (A2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o A))) (=> (@ _let_1 (@ (@ tptp.insert_o B) A2)) (=> (= A (not B)) (@ _let_1 A2))))))
% 5.91/6.26 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat A))) (=> (@ _let_1 (@ (@ tptp.insert_set_nat B) A2)) (=> (not (= A B)) (@ _let_1 A2))))))
% 5.91/6.26 (assert (forall ((A tptp.set_nat_rat) (B tptp.set_nat_rat) (A2 tptp.set_set_nat_rat)) (let ((_let_1 (@ tptp.member_set_nat_rat A))) (=> (@ _let_1 (@ (@ tptp.insert_set_nat_rat B) A2)) (=> (not (= A B)) (@ _let_1 A2))))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A))) (=> (@ _let_1 (@ (@ tptp.insert_nat B) A2)) (=> (not (= A B)) (@ _let_1 A2))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A))) (=> (@ _let_1 (@ (@ tptp.insert_int B) A2)) (=> (not (= A B)) (@ _let_1 A2))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (E2 tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) E2)) C))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (E2 tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) E2)) C))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (E2 tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) E2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) E2)) C)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) E2)) C))))
% 5.91/6.26 (assert (forall ((A tptp.int) (E2 tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) E2)) C))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 5.91/6.26 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C))))
% 5.91/6.26 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C) A)) (= B C))))
% 5.91/6.26 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C) A)) (= B C))))
% 5.91/6.26 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C) A)) (= B C))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.91/6.26 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.91/6.26 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B))) (let ((_let_2 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.91/6.26 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.91/6.26 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.91/6.26 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real B))) (let ((_let_2 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.91/6.26 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat B))) (let ((_let_2 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.91/6.26 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat B))) (let ((_let_2 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.91/6.26 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int B))) (let ((_let_2 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.91/6.26 (assert (= tptp.times_times_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.times_times_real B4) A4))))
% 5.91/6.26 (assert (= tptp.times_times_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.times_times_rat B4) A4))))
% 5.91/6.26 (assert (= tptp.times_times_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.times_times_nat B4) A4))))
% 5.91/6.26 (assert (= tptp.times_times_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.times_times_int B4) A4))))
% 5.91/6.26 (assert (= tptp.plus_plus_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.plus_plus_real B4) A4))))
% 5.91/6.26 (assert (= tptp.plus_plus_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.plus_plus_rat B4) A4))))
% 5.91/6.26 (assert (= tptp.plus_plus_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.plus_plus_nat B4) A4))))
% 5.91/6.26 (assert (= tptp.plus_plus_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int B4) A4))))
% 5.91/6.26 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C))))
% 5.91/6.26 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C) A)) (= B C))))
% 5.91/6.26 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C) A)) (= B C))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 5.91/6.26 (assert (forall ((B2 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (let ((_let_2 (@ tptp.plus_plus_real K))) (=> (= B2 (@ _let_2 B)) (= (@ _let_1 B2) (@ _let_2 (@ _let_1 B))))))))
% 5.91/6.26 (assert (forall ((B2 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (let ((_let_2 (@ tptp.plus_plus_rat K))) (=> (= B2 (@ _let_2 B)) (= (@ _let_1 B2) (@ _let_2 (@ _let_1 B))))))))
% 5.91/6.26 (assert (forall ((B2 tptp.nat) (K tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (=> (= B2 (@ _let_2 B)) (= (@ _let_1 B2) (@ _let_2 (@ _let_1 B))))))))
% 5.91/6.26 (assert (forall ((B2 tptp.int) (K tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (let ((_let_2 (@ tptp.plus_plus_int K))) (=> (= B2 (@ _let_2 B)) (= (@ _let_1 B2) (@ _let_2 (@ _let_1 B))))))))
% 5.91/6.26 (assert (forall ((A2 tptp.real) (K tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_real A2) B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 5.91/6.26 (assert (forall ((A2 tptp.rat) (K tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_rat A2) B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 5.91/6.26 (assert (forall ((A2 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_nat A2) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 5.91/6.26 (assert (forall ((A2 tptp.int) (K tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_int A2) B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real)))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat)))))
% 5.91/6.26 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int)))))
% 5.91/6.26 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)))))
% 5.91/6.26 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real Y)) X) (@ tptp.abs_abs_real (@ (@ tptp.times_times_real Y) X))))))
% 5.91/6.26 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat Y)) X) (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat Y) X))))))
% 5.91/6.26 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int Y)) X) (@ tptp.abs_abs_int (@ (@ tptp.times_times_int Y) X))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (or (@ _let_1 B) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real))) (= (@ tptp.abs_abs_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (or (@ _let_1 B) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat))) (= (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (or (@ _let_1 B) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int))) (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) C))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) D))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat C) D)))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) C))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) D))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int C) D)))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) C))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) D))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))
% 5.91/6.26 (assert (forall ((X tptp.real) (A tptp.real) (R2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) A))) R2) (and (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) R2)) X) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real A) R2))))))
% 5.91/6.26 (assert (forall ((X tptp.rat) (A tptp.rat) (R2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X) A))) R2) (and (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) R2)) X) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.plus_plus_rat A) R2))))))
% 5.91/6.26 (assert (forall ((X tptp.int) (A tptp.int) (R2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) A))) R2) (and (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) R2)) X) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.plus_plus_int A) R2))))))
% 5.91/6.26 (assert (forall ((X tptp.real) (A tptp.real) (R2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) A))) R2) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) R2)) X) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real A) R2))))))
% 5.91/6.26 (assert (forall ((X tptp.rat) (A tptp.rat) (R2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X) A))) R2) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) R2)) X) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat A) R2))))))
% 5.91/6.26 (assert (forall ((X tptp.int) (A tptp.int) (R2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) A))) R2) (and (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) R2)) X) (@ (@ tptp.ord_less_int X) (@ (@ tptp.plus_plus_int A) R2))))))
% 5.91/6.26 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)))))
% 5.91/6.26 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y)))))
% 5.91/6.26 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)))))
% 5.91/6.26 (assert (forall ((X tptp.real) (Y tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real))))
% 5.91/6.26 (assert (forall ((X tptp.rat) (Y tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat))))
% 5.91/6.26 (assert (forall ((X tptp.int) (Y tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int))))
% 5.91/6.26 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E2)) C)) D))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E2)) C)) D))))
% 5.91/6.26 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E2)) C)) D))))
% 5.91/6.26 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E2)) D)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E2)) D)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E2)) D)))))
% 5.91/6.26 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 5.91/6.26 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 5.91/6.26 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.divide_divide_rat B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) Z)) B)) Z))))))))
% 5.91/6.26 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real A) (@ (@ tptp.divide_divide_real B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) Z)) B)) Z))))))))
% 5.91/6.26 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W2) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W2) Y))) (@ (@ tptp.times_times_rat Y) Z)))))))
% 5.91/6.26 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W2) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W2) Y))) (@ (@ tptp.times_times_real Y) Z)))))))
% 5.91/6.26 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Y)) Z) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Z) Y))) Y)))))
% 5.91/6.26 (assert (forall ((Y tptp.real) (X tptp.real) (Z tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y)) Z) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z) Y))) Y)))))
% 5.91/6.26 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Z) Y))) Y)))))
% 5.91/6.26 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z) Y))) Y)))))
% 5.91/6.26 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.divide_divide_rat Y) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) Z)) Y)) Z)))))
% 5.91/6.26 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real Y) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) Z)) Y)) Z)))))
% 5.91/6.26 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Z)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 5.91/6.26 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Z)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E2)) C)) D))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E2)) C)) D))))
% 5.91/6.26 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E2)) C)) D))))
% 5.91/6.26 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (@ (@ tptp.ord_less_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E2)) D)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (@ (@ tptp.ord_less_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E2)) D)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (@ (@ tptp.ord_less_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E2)) D)))))
% 5.91/6.26 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) X)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X) tptp.one_one_complex)))))
% 5.91/6.26 (assert (forall ((X tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) X)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)))))
% 5.91/6.26 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) X)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)))))
% 5.91/6.26 (assert (forall ((X tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X) tptp.one_one_int)))))
% 5.91/6.26 (assert (forall ((A tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (not (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex tptp.one_one_complex) A)) A) tptp.zero_zero_complex)))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (not (= (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) A)) A) tptp.zero_zero_real)))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (not (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat tptp.one_one_rat) A)) A) tptp.zero_zero_rat)))))
% 5.91/6.26 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) A) tptp.zero_zero_int)))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) (@ tptp.abs_abs_real A))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ tptp.abs_abs_rat A))))
% 5.91/6.26 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ tptp.abs_abs_int A))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B) (@ (@ tptp.ord_less_eq_real A) B))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (@ (@ tptp.ord_less_eq_rat A) B))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B) (@ (@ tptp.ord_less_eq_int A) B))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 5.91/6.26 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 5.91/6.26 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 5.91/6.26 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) A)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) A)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_eq_real A) B))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 5.91/6.26 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_eq_int A) B))))
% 5.91/6.26 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B)))))
% 5.91/6.26 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 5.91/6.26 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 5.91/6.26 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B)))))
% 5.91/6.26 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (exists ((C5 tptp.nat)) (= B4 (@ (@ tptp.plus_plus_nat A4) C5))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (not (forall ((C3 tptp.nat)) (not (= B (@ (@ tptp.plus_plus_nat A) C3))))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B))))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 5.91/6.26 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 5.91/6.26 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 5.91/6.26 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 5.91/6.26 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 5.91/6.26 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 5.91/6.26 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (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)))))
% 5.91/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 5.91/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 5.91/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 5.91/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)))))
% 5.98/6.26 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B)))))
% 5.98/6.26 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B)))))
% 5.98/6.26 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))))
% 5.98/6.26 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B)))))
% 5.98/6.26 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_real A) B))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_rat A) B))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_nat A) B))))
% 5.98/6.26 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_int A) B))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real)) (and (not (= A tptp.zero_zero_real)) (not (= B tptp.zero_zero_real))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat)) (and (not (= A tptp.zero_zero_rat)) (not (= B tptp.zero_zero_rat))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat)) (and (not (= A tptp.zero_zero_nat)) (not (= B tptp.zero_zero_nat))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int)) (and (not (= A tptp.zero_zero_int)) (not (= B tptp.zero_zero_int))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (not (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (not (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= B tptp.zero_zero_nat)) (not (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= B tptp.zero_zero_int)) (not (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int))))))
% 5.98/6.26 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 5.98/6.26 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 5.98/6.26 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 5.98/6.26 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 5.98/6.26 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (@ (@ tptp.times_times_real A) C) (@ (@ tptp.times_times_real B) C)) (= A B)))))
% 5.98/6.26 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ (@ tptp.times_times_rat A) C) (@ (@ tptp.times_times_rat B) C)) (= A B)))))
% 5.98/6.26 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B) C)) (= A B)))))
% 5.98/6.26 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (= (@ (@ tptp.times_times_int A) C) (@ (@ tptp.times_times_int B) C)) (= A B)))))
% 5.98/6.26 (assert (forall ((S2 tptp.set_int)) (= (not (@ tptp.finite_finite_int S2)) (forall ((M3 tptp.int)) (exists ((N4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int M3) (@ tptp.abs_abs_int N4)) (@ (@ tptp.member_int N4) S2)))))))
% 5.98/6.26 (assert (forall ((B tptp.product_prod_nat_nat) (A tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat B) (@ (@ tptp.insert8211810215607154385at_nat A) tptp.bot_bo2099793752762293965at_nat)) (= B A))))
% 5.98/6.26 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.member_set_nat B) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat)) (= B A))))
% 5.98/6.26 (assert (forall ((B tptp.set_nat_rat) (A tptp.set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat B) (@ (@ tptp.insert_set_nat_rat A) tptp.bot_bo6797373522285170759at_rat)) (= B A))))
% 5.98/6.26 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.member_real B) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real)) (= B A))))
% 5.98/6.26 (assert (forall ((B Bool) (A Bool)) (=> (@ (@ tptp.member_o B) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o)) (= B A))))
% 5.98/6.26 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.member_nat B) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat)) (= B A))))
% 5.98/6.26 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.member_int B) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int)) (= B A))))
% 5.98/6.26 (assert (forall ((B tptp.product_prod_nat_nat) (A tptp.product_prod_nat_nat)) (= (@ (@ tptp.member8440522571783428010at_nat B) (@ (@ tptp.insert8211810215607154385at_nat A) tptp.bot_bo2099793752762293965at_nat)) (= B A))))
% 5.98/6.26 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (= (@ (@ tptp.member_set_nat B) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat)) (= B A))))
% 5.98/6.26 (assert (forall ((B tptp.set_nat_rat) (A tptp.set_nat_rat)) (= (@ (@ tptp.member_set_nat_rat B) (@ (@ tptp.insert_set_nat_rat A) tptp.bot_bo6797373522285170759at_rat)) (= B A))))
% 5.98/6.26 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.member_real B) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real)) (= B A))))
% 5.98/6.26 (assert (forall ((B Bool) (A Bool)) (= (@ (@ tptp.member_o B) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o)) (= B A))))
% 5.98/6.26 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.member_nat B) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat)) (= B A))))
% 5.98/6.26 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.member_int B) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int)) (= B A))))
% 5.98/6.26 (assert (forall ((A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat) (C tptp.product_prod_nat_nat) (D tptp.product_prod_nat_nat)) (= (= (@ (@ tptp.insert8211810215607154385at_nat A) (@ (@ tptp.insert8211810215607154385at_nat B) tptp.bot_bo2099793752762293965at_nat)) (@ (@ tptp.insert8211810215607154385at_nat C) (@ (@ tptp.insert8211810215607154385at_nat D) tptp.bot_bo2099793752762293965at_nat))) (or (and (= A C) (= B D)) (and (= A D) (= B C))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (= (= (@ (@ tptp.insert_real A) (@ (@ tptp.insert_real B) tptp.bot_bot_set_real)) (@ (@ tptp.insert_real C) (@ (@ tptp.insert_real D) tptp.bot_bot_set_real))) (or (and (= A C) (= B D)) (and (= A D) (= B C))))))
% 5.98/6.26 (assert (forall ((A Bool) (B Bool) (C Bool) (D Bool)) (= (= (@ (@ tptp.insert_o A) (@ (@ tptp.insert_o B) tptp.bot_bot_set_o)) (@ (@ tptp.insert_o C) (@ (@ tptp.insert_o D) tptp.bot_bot_set_o))) (or (and (= A C) (= B D)) (and (= A D) (= B C))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (= (= (@ (@ tptp.insert_nat A) (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat)) (@ (@ tptp.insert_nat C) (@ (@ tptp.insert_nat D) tptp.bot_bot_set_nat))) (or (and (= A C) (= B D)) (and (= A D) (= B C))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (= (= (@ (@ tptp.insert_int A) (@ (@ tptp.insert_int B) tptp.bot_bot_set_int)) (@ (@ tptp.insert_int C) (@ (@ tptp.insert_int D) tptp.bot_bot_set_int))) (or (and (= A C) (= B D)) (and (= A D) (= B C))))))
% 5.98/6.26 (assert (forall ((A tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (not (= (@ (@ tptp.insert8211810215607154385at_nat A) A2) tptp.bot_bo2099793752762293965at_nat))))
% 5.98/6.26 (assert (forall ((A tptp.real) (A2 tptp.set_real)) (not (= (@ (@ tptp.insert_real A) A2) tptp.bot_bot_set_real))))
% 5.98/6.26 (assert (forall ((A Bool) (A2 tptp.set_o)) (not (= (@ (@ tptp.insert_o A) A2) tptp.bot_bot_set_o))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (A2 tptp.set_nat)) (not (= (@ (@ tptp.insert_nat A) A2) tptp.bot_bot_set_nat))))
% 5.98/6.26 (assert (forall ((A tptp.int) (A2 tptp.set_int)) (not (= (@ (@ tptp.insert_int A) A2) tptp.bot_bot_set_int))))
% 5.98/6.26 (assert (forall ((A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat)) (=> (= (@ (@ tptp.insert8211810215607154385at_nat A) tptp.bot_bo2099793752762293965at_nat) (@ (@ tptp.insert8211810215607154385at_nat B) tptp.bot_bo2099793752762293965at_nat)) (= A B))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.insert_real A) tptp.bot_bot_set_real) (@ (@ tptp.insert_real B) tptp.bot_bot_set_real)) (= A B))))
% 5.98/6.26 (assert (forall ((A Bool) (B Bool)) (=> (= (@ (@ tptp.insert_o A) tptp.bot_bot_set_o) (@ (@ tptp.insert_o B) tptp.bot_bot_set_o)) (= A B))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat) (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat)) (= A B))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.insert_int A) tptp.bot_bot_set_int) (@ (@ tptp.insert_int B) tptp.bot_bot_set_int)) (= A B))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A2) (@ tptp.finite_finite_real (@ (@ tptp.insert_real A) A2)))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_o) (A Bool)) (=> (@ tptp.finite_finite_o A2) (@ tptp.finite_finite_o (@ (@ tptp.insert_o A) A2)))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite_finite_nat (@ (@ tptp.insert_nat A) A2)))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite_finite_int (@ (@ tptp.insert_int A) A2)))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_complex) (A tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite3207457112153483333omplex (@ (@ tptp.insert_complex A) A2)))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (A tptp.product_prod_nat_nat)) (=> (@ tptp.finite6177210948735845034at_nat A2) (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.insert8211810215607154385at_nat A) A2)))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_Extended_enat) (A tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.insert_Extended_enat A) A2)))))
% 5.98/6.26 (assert (forall ((S2 tptp.set_int)) (= (not (@ tptp.finite_finite_int S2)) (forall ((M3 tptp.int)) (exists ((N4 tptp.int)) (and (@ (@ tptp.ord_less_int M3) (@ tptp.abs_abs_int N4)) (@ (@ tptp.member_int N4) S2)))))))
% 5.98/6.26 (assert (forall ((C2 tptp.set_Pr1261947904930325089at_nat) (D4 tptp.set_Pr1261947904930325089at_nat) (A tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat C2) D4) (@ (@ tptp.ord_le3146513528884898305at_nat (@ _let_1 C2)) (@ _let_1 D4))))))
% 5.98/6.26 (assert (forall ((C2 tptp.set_real) (D4 tptp.set_real) (A tptp.real)) (let ((_let_1 (@ tptp.insert_real A))) (=> (@ (@ tptp.ord_less_eq_set_real C2) D4) (@ (@ tptp.ord_less_eq_set_real (@ _let_1 C2)) (@ _let_1 D4))))))
% 5.98/6.26 (assert (forall ((C2 tptp.set_o) (D4 tptp.set_o) (A Bool)) (let ((_let_1 (@ tptp.insert_o A))) (=> (@ (@ tptp.ord_less_eq_set_o C2) D4) (@ (@ tptp.ord_less_eq_set_o (@ _let_1 C2)) (@ _let_1 D4))))))
% 5.98/6.26 (assert (forall ((C2 tptp.set_nat) (D4 tptp.set_nat) (A tptp.nat)) (let ((_let_1 (@ tptp.insert_nat A))) (=> (@ (@ tptp.ord_less_eq_set_nat C2) D4) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 C2)) (@ _let_1 D4))))))
% 5.98/6.26 (assert (forall ((C2 tptp.set_int) (D4 tptp.set_int) (A tptp.int)) (let ((_let_1 (@ tptp.insert_int A))) (=> (@ (@ tptp.ord_less_eq_set_int C2) D4) (@ (@ tptp.ord_less_eq_set_int (@ _let_1 C2)) (@ _let_1 D4))))))
% 5.98/6.26 (assert (forall ((X tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A2))) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X) B2)) (@ _let_1 B2))))))
% 5.98/6.26 (assert (forall ((X tptp.real) (A2 tptp.set_real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A2))) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) B2)) (@ _let_1 B2))))))
% 5.98/6.26 (assert (forall ((X Bool) (A2 tptp.set_o) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.ord_less_eq_set_o A2))) (=> (not (@ (@ tptp.member_o X) A2)) (= (@ _let_1 (@ (@ tptp.insert_o X) B2)) (@ _let_1 B2))))))
% 5.98/6.26 (assert (forall ((X tptp.set_nat) (A2 tptp.set_set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.ord_le6893508408891458716et_nat A2))) (=> (not (@ (@ tptp.member_set_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_set_nat X) B2)) (@ _let_1 B2))))))
% 5.98/6.26 (assert (forall ((X tptp.set_nat_rat) (A2 tptp.set_set_nat_rat) (B2 tptp.set_set_nat_rat)) (let ((_let_1 (@ tptp.ord_le4375437777232675859at_rat A2))) (=> (not (@ (@ tptp.member_set_nat_rat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_set_nat_rat X) B2)) (@ _let_1 B2))))))
% 5.98/6.26 (assert (forall ((X tptp.nat) (A2 tptp.set_nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X) B2)) (@ _let_1 B2))))))
% 5.98/6.26 (assert (forall ((X tptp.int) (A2 tptp.set_int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) B2)) (@ _let_1 B2))))))
% 5.98/6.26 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (A tptp.product_prod_nat_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat B2) (@ (@ tptp.insert8211810215607154385at_nat A) B2))))
% 5.98/6.26 (assert (forall ((B2 tptp.set_real) (A tptp.real)) (@ (@ tptp.ord_less_eq_set_real B2) (@ (@ tptp.insert_real A) B2))))
% 5.98/6.26 (assert (forall ((B2 tptp.set_o) (A Bool)) (@ (@ tptp.ord_less_eq_set_o B2) (@ (@ tptp.insert_o A) B2))))
% 5.98/6.26 (assert (forall ((B2 tptp.set_nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat B2) (@ (@ tptp.insert_nat A) B2))))
% 5.98/6.26 (assert (forall ((B2 tptp.set_int) (A tptp.int)) (@ (@ tptp.ord_less_eq_set_int B2) (@ (@ tptp.insert_int A) B2))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (B tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat B) B2))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_real) (B2 tptp.set_real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert_real B) B2))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_o) (B2 tptp.set_o) (B Bool)) (let ((_let_1 (@ tptp.ord_less_eq_set_o A2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert_o B) B2))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert_nat B) B2))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.insert_int B) B2))))))
% 5.98/6.26 (assert (forall ((X tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (X5 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X) A2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat X5) A2) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.insert8211810215607154385at_nat X) X5)) A2)))))
% 5.98/6.26 (assert (forall ((X tptp.real) (A2 tptp.set_real) (X5 tptp.set_real)) (=> (@ (@ tptp.member_real X) A2) (=> (@ (@ tptp.ord_less_eq_set_real X5) A2) (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.insert_real X) X5)) A2)))))
% 5.98/6.26 (assert (forall ((X Bool) (A2 tptp.set_o) (X5 tptp.set_o)) (=> (@ (@ tptp.member_o X) A2) (=> (@ (@ tptp.ord_less_eq_set_o X5) A2) (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.insert_o X) X5)) A2)))))
% 5.98/6.26 (assert (forall ((X tptp.set_nat) (A2 tptp.set_set_nat) (X5 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat X) A2) (=> (@ (@ tptp.ord_le6893508408891458716et_nat X5) A2) (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.insert_set_nat X) X5)) A2)))))
% 5.98/6.26 (assert (forall ((X tptp.set_nat_rat) (A2 tptp.set_set_nat_rat) (X5 tptp.set_set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat X) A2) (=> (@ (@ tptp.ord_le4375437777232675859at_rat X5) A2) (@ (@ tptp.ord_le4375437777232675859at_rat (@ (@ tptp.insert_set_nat_rat X) X5)) A2)))))
% 5.98/6.26 (assert (forall ((X tptp.nat) (A2 tptp.set_nat) (X5 tptp.set_nat)) (=> (@ (@ tptp.member_nat X) A2) (=> (@ (@ tptp.ord_less_eq_set_nat X5) A2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat X) X5)) A2)))))
% 5.98/6.26 (assert (forall ((X tptp.int) (A2 tptp.set_int) (X5 tptp.set_int)) (=> (@ (@ tptp.member_int X) A2) (=> (@ (@ tptp.ord_less_eq_set_int X5) A2) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.insert_int X) X5)) A2)))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.minus_minus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 5.98/6.26 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (= (@ (@ tptp.plus_plus_real C) B) A) (= C (@ (@ tptp.minus_minus_real A) B)))))
% 5.98/6.26 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat C) B) A) (= C (@ (@ tptp.minus_minus_rat A) B)))))
% 5.98/6.26 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat C) B) A) (= C (@ (@ tptp.minus_minus_nat A) B)))))
% 5.98/6.26 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (= (@ (@ tptp.plus_plus_int C) B) A) (= C (@ (@ tptp.minus_minus_int A) B)))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 C)) B)))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 C)) B)))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 C)) B)))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) B))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) B))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) B))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) B))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) B))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) B))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) C)))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C)))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) C)))))
% 5.98/6.26 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.minus_minus_real C) B)) (= (@ (@ tptp.plus_plus_real A) B) C))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.minus_minus_rat C) B)) (= (@ (@ tptp.plus_plus_rat A) B) C))))
% 5.98/6.26 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.minus_minus_int C) B)) (= (@ (@ tptp.plus_plus_int A) B) C))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (= (@ (@ tptp.minus_minus_real A) B) C) (= A (@ (@ tptp.plus_plus_real C) B)))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.minus_minus_rat A) B) C) (= A (@ (@ tptp.plus_plus_rat C) B)))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (= (@ (@ tptp.minus_minus_int A) B) C) (= A (@ (@ tptp.plus_plus_int C) B)))))
% 5.98/6.26 (assert (forall ((A2 tptp.real) (K tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_real A2) B) (@ _let_1 (@ (@ tptp.minus_minus_real A) B)))))))
% 5.98/6.26 (assert (forall ((A2 tptp.rat) (K tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_rat A2) B) (@ _let_1 (@ (@ tptp.minus_minus_rat A) B)))))))
% 5.98/6.26 (assert (forall ((A2 tptp.int) (K tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_int A2) B) (@ _let_1 (@ (@ tptp.minus_minus_int A) B)))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D)) (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real C) D)))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat C) D)))))
% 5.98/6.26 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D)) (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int C) D)))))
% 5.98/6.26 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 5.98/6.26 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 5.98/6.26 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 5.98/6.26 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 5.98/6.26 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 5.98/6.26 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 5.98/6.26 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 5.98/6.26 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 5.98/6.26 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 5.98/6.26 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B) C)) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.26 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) C)) A) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real B) A)) (@ (@ tptp.times_times_real C) A)))))
% 5.98/6.26 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) C)) A) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat B) A)) (@ (@ tptp.times_times_rat C) A)))))
% 5.98/6.26 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat B) C)) A) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.times_times_nat C) A)))))
% 5.98/6.26 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) C)) A) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.times_times_int C) A)))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 5.98/6.26 (assert (@ (@ tptp.member_real tptp.zero_zero_real) tptp.ring_1_Ints_real))
% 5.98/6.26 (assert (@ (@ tptp.member_rat tptp.zero_zero_rat) tptp.ring_1_Ints_rat))
% 5.98/6.26 (assert (@ (@ tptp.member_int tptp.zero_zero_int) tptp.ring_1_Ints_int))
% 5.98/6.26 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N)))))
% 5.98/6.26 (assert (forall ((X tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.minus_1356011639430497352at_nat A2) B2))) (let ((_let_2 (@ tptp.insert8211810215607154385at_nat X))) (let ((_let_3 (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_2 A2)) B2))) (let ((_let_4 (@ (@ tptp.member8440522571783428010at_nat X) B2))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 5.98/6.26 (assert (forall ((X tptp.real) (B2 tptp.set_real) (A2 tptp.set_real)) (let ((_let_1 (@ (@ tptp.minus_minus_set_real A2) B2))) (let ((_let_2 (@ tptp.insert_real X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_real (@ _let_2 A2)) B2))) (let ((_let_4 (@ (@ tptp.member_real X) B2))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 5.98/6.26 (assert (forall ((X Bool) (B2 tptp.set_o) (A2 tptp.set_o)) (let ((_let_1 (@ (@ tptp.minus_minus_set_o A2) B2))) (let ((_let_2 (@ tptp.insert_o X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_o (@ _let_2 A2)) B2))) (let ((_let_4 (@ (@ tptp.member_o X) B2))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 5.98/6.26 (assert (forall ((X tptp.set_nat) (B2 tptp.set_set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B2))) (let ((_let_2 (@ tptp.insert_set_nat X))) (let ((_let_3 (@ (@ tptp.minus_2163939370556025621et_nat (@ _let_2 A2)) B2))) (let ((_let_4 (@ (@ tptp.member_set_nat X) B2))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 5.98/6.26 (assert (forall ((X tptp.set_nat_rat) (B2 tptp.set_set_nat_rat) (A2 tptp.set_set_nat_rat)) (let ((_let_1 (@ (@ tptp.minus_1626877696091177228at_rat A2) B2))) (let ((_let_2 (@ tptp.insert_set_nat_rat X))) (let ((_let_3 (@ (@ tptp.minus_1626877696091177228at_rat (@ _let_2 A2)) B2))) (let ((_let_4 (@ (@ tptp.member_set_nat_rat X) B2))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 5.98/6.26 (assert (forall ((X tptp.int) (B2 tptp.set_int) (A2 tptp.set_int)) (let ((_let_1 (@ (@ tptp.minus_minus_set_int A2) B2))) (let ((_let_2 (@ tptp.insert_int X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_int (@ _let_2 A2)) B2))) (let ((_let_4 (@ (@ tptp.member_int X) B2))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 5.98/6.26 (assert (forall ((X tptp.nat) (B2 tptp.set_nat) (A2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A2) B2))) (let ((_let_2 (@ tptp.insert_nat X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_nat (@ _let_2 A2)) B2))) (let ((_let_4 (@ (@ tptp.member_nat X) B2))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 5.98/6.26 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 5.98/6.26 (assert (@ (@ tptp.member_complex tptp.one_one_complex) tptp.ring_1_Ints_complex))
% 5.98/6.26 (assert (@ (@ tptp.member_real tptp.one_one_real) tptp.ring_1_Ints_real))
% 5.98/6.26 (assert (@ (@ tptp.member_rat tptp.one_one_rat) tptp.ring_1_Ints_rat))
% 5.98/6.26 (assert (@ (@ tptp.member_int tptp.one_one_int) tptp.ring_1_Ints_int))
% 5.98/6.26 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat X))) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ (@ tptp.times_times_nat Y) _let_1)))))
% 5.98/6.26 (assert (forall ((X tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int X))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))))
% 5.98/6.26 (assert (forall ((X tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real X))) (= (@ (@ tptp.times_times_real _let_1) Y) (@ (@ tptp.times_times_real Y) _let_1)))))
% 5.98/6.26 (assert (forall ((X tptp.nat) (Y tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat X))) (= (@ (@ tptp.times_times_rat _let_1) Y) (@ (@ tptp.times_times_rat Y) _let_1)))))
% 5.98/6.26 (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))))))
% 5.98/6.26 (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)))))
% 5.98/6.26 (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))))))
% 5.98/6.26 (assert (forall ((M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.times_times_nat M2) M2))))
% 5.98/6.26 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M2))) (@ (@ tptp.ord_less_eq_nat M2) (@ _let_1 (@ _let_1 M2))))))
% 5.98/6.26 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.minus_minus_nat (@ _let_1 M2)) (@ _let_1 N))))))
% 5.98/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M2) N)) K) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat M2) K)) (@ (@ tptp.times_times_nat N) K)))))
% 5.98/6.26 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat N) tptp.one_one_nat) N)))
% 5.98/6.26 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N) N)))
% 5.98/6.26 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.abs_abs_real X)))))
% 5.98/6.26 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.abs_abs_rat X)))))
% 5.98/6.26 (assert (forall ((X tptp.int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.abs_abs_int X)))))
% 5.98/6.26 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) tptp.ring_1_Ints_real) (=> (not (= X tptp.zero_zero_real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.abs_abs_real X))))))
% 5.98/6.26 (assert (forall ((X tptp.rat)) (=> (@ (@ tptp.member_rat X) tptp.ring_1_Ints_rat) (=> (not (= X tptp.zero_zero_rat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.abs_abs_rat X))))))
% 5.98/6.26 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) tptp.ring_1_Ints_int) (=> (not (= X tptp.zero_zero_int)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.abs_abs_int X))))))
% 5.98/6.26 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) tptp.ring_1_Ints_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= X tptp.zero_zero_real)))))
% 5.98/6.26 (assert (forall ((X tptp.rat)) (=> (@ (@ tptp.member_rat X) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X)) tptp.one_one_rat) (= X tptp.zero_zero_rat)))))
% 5.98/6.26 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) tptp.ring_1_Ints_int) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X)) tptp.one_one_int) (= X tptp.zero_zero_int)))))
% 5.98/6.26 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.member_real X) tptp.ring_1_Ints_real) (=> (@ (@ tptp.member_real Y) tptp.ring_1_Ints_real) (= (= X Y) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y))) tptp.one_one_real))))))
% 5.98/6.26 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.member_rat X) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.member_rat Y) tptp.ring_1_Ints_rat) (= (= X Y) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X) Y))) tptp.one_one_rat))))))
% 5.98/6.26 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.member_int X) tptp.ring_1_Ints_int) (=> (@ (@ tptp.member_int Y) tptp.ring_1_Ints_int) (= (= X Y) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) Y))) tptp.one_one_int))))))
% 5.98/6.26 (assert (forall ((X tptp.real) (A tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real X) A) (=> (@ (@ tptp.ord_less_eq_real Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X)) (@ (@ tptp.times_times_real V) Y))) A)))))))))
% 5.98/6.26 (assert (forall ((X tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat X) A) (=> (@ (@ tptp.ord_less_eq_rat Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X)) (@ (@ tptp.times_times_rat V) Y))) A)))))))))
% 5.98/6.26 (assert (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int X) A) (=> (@ (@ tptp.ord_less_eq_int Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V) Y))) A)))))))))
% 5.98/6.26 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) A)) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))))
% 5.98/6.26 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat tptp.one_one_rat) A)) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat)))))
% 5.98/6.26 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 5.98/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.nat_set_decode M2)) (@ tptp.nat_set_decode N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 5.98/6.26 (assert (forall ((X tptp.real) (A tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real X) A) (=> (@ (@ tptp.ord_less_real Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X)) (@ (@ tptp.times_times_real V) Y))) A)))))))))
% 5.98/6.26 (assert (forall ((X tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat X) A) (=> (@ (@ tptp.ord_less_rat Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X)) (@ (@ tptp.times_times_rat V) Y))) A)))))))))
% 5.98/6.26 (assert (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X) A) (=> (@ (@ tptp.ord_less_int Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V) Y))) A)))))))))
% 5.98/6.26 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.abs_abs_real A))))
% 5.98/6.26 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A))))
% 5.98/6.26 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A))))
% 5.98/6.26 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 5.98/6.26 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 5.98/6.26 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 5.98/6.26 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real))))
% 5.98/6.26 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat))))
% 5.98/6.26 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int))))
% 5.98/6.26 (assert (forall ((U tptp.real) (V tptp.real) (R2 tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real U) V) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R2) (=> (@ (@ tptp.ord_less_eq_real R2) S) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real R2) (@ (@ tptp.minus_minus_real V) U))) S))) V))))))
% 5.98/6.26 (assert (forall ((U tptp.rat) (V tptp.rat) (R2 tptp.rat) (S tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat U) V) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R2) (=> (@ (@ tptp.ord_less_eq_rat R2) S) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat R2) (@ (@ tptp.minus_minus_rat V) U))) S))) V))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat A) B))) (and (=> _let_2 (= _let_1 (@ (@ tptp.minus_minus_nat B) A))) (=> (not _let_2) (= _let_1 (@ (@ tptp.minus_minus_nat A) B))))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) A)))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) A)))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B)))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B)))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)))))
% 5.98/6.26 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))))))
% 5.98/6.26 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))))))
% 5.98/6.26 (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))))))
% 5.98/6.26 (assert (= tptp.zero_zero_nat (@ tptp.nat2 tptp.zero_zero_int)))
% 5.98/6.26 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y)))))
% 5.98/6.26 (assert (forall ((N tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.nat_set_decode N))))
% 5.98/6.26 (assert (= (lambda ((P2 (-> tptp.nat Bool))) (exists ((X6 tptp.nat)) (@ P2 X6))) (lambda ((P3 (-> tptp.nat Bool))) (exists ((X3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X3) (@ P3 (@ tptp.nat2 X3)))))))
% 5.98/6.26 (assert (= (lambda ((P2 (-> tptp.nat Bool))) (forall ((X6 tptp.nat)) (@ P2 X6))) (lambda ((P3 (-> tptp.nat Bool))) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X3) (@ P3 (@ tptp.nat2 X3)))))))
% 5.98/6.26 (assert (forall ((Z tptp.int) (Z6 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z6) (= (= (@ tptp.nat2 Z) (@ tptp.nat2 Z6)) (= Z Z6)))))))
% 5.98/6.26 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (= (@ (@ tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))))
% 5.98/6.26 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (= (= (@ (@ tptp.plus_plus_rat X) Y) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))))
% 5.98/6.26 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))))
% 5.98/6.26 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))))
% 5.98/6.26 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))))
% 5.98/6.26 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_rat X) Y) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))))
% 5.98/6.26 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat))))))))
% 5.98/6.26 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 5.98/6.26 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 5.98/6.26 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 5.98/6.26 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 5.98/6.26 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 5.98/6.26 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) B)))))
% 5.98/6.26 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) B)))))
% 5.98/6.26 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) B)))))
% 5.98/6.26 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) B)))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real C) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) B)))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat C) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) B)))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat C) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) B)))))
% 5.98/6.26 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int C) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) B)))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 5.98/6.26 (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)))))
% 5.98/6.26 (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)))))
% 5.98/6.26 (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)))))
% 5.98/6.26 (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)))))
% 5.98/6.26 (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)))))
% 5.98/6.26 (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)))))
% 5.98/6.26 (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)))))
% 5.98/6.26 (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)))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (forall ((C3 tptp.nat)) (=> (= B (@ (@ tptp.plus_plus_nat A) C3)) (= C3 tptp.zero_zero_nat)))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 5.98/6.26 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X) Y)) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real)))))
% 5.98/6.26 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat X) Y)) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat)))))
% 5.98/6.26 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X) Y)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Y) tptp.zero_zero_int)))))
% 5.98/6.26 (assert (= tptp.one_one_nat (@ tptp.nat2 tptp.one_one_int)))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D)))))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D)))))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D)))))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D)))))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))))))
% 5.98/6.26 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) A))))
% 5.98/6.26 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) A))))
% 5.98/6.26 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) A))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real))) (@ _let_1 (@ (@ tptp.times_times_real A) B))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat))) (@ _let_1 (@ (@ tptp.times_times_rat A) B))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int))) (@ _let_1 (@ (@ tptp.times_times_int A) B))))))
% 5.98/6.26 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 5.98/6.26 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 5.98/6.26 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat)) (and (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_real A) B)))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat A) B)))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat A) B)))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int A) B)))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real B) A)) tptp.zero_zero_real)))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat B) A)) tptp.zero_zero_rat)))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat B) A)) tptp.zero_zero_nat)))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int B) A)) tptp.zero_zero_int)))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat A) B))) (=> _let_1 (=> _let_1 (= (= (@ (@ tptp.minus_minus_nat B) A) C) (= B (@ (@ tptp.plus_plus_nat C) A))))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.minus_minus_nat B) A)) B))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat C) (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat C) A)) B)))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) C)))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A)))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A) (@ _let_1 (@ (@ tptp.minus_minus_nat B) A)))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat C) A)) B)))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A)))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) A) B))))
% 5.98/6.26 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.minus_minus_real C) B)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) C))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.minus_minus_rat C) B)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) C))))
% 5.98/6.26 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.minus_minus_int C) B)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real C) B)))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat C) B)))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int C) B)))))
% 5.98/6.26 (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)))))))))
% 5.98/6.26 (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)))))))))
% 5.98/6.26 (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)))))))))
% 5.98/6.26 (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)))))))))
% 5.98/6.26 (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)))))
% 5.98/6.26 (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)))))
% 5.98/6.26 (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)))))
% 5.98/6.26 (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)))))
% 5.98/6.26 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) tptp.one_one_real))))
% 5.98/6.26 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))))
% 5.98/6.26 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat))))
% 5.98/6.26 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) tptp.one_one_int))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) (@ (@ tptp.plus_plus_real B) tptp.one_one_real)))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat B) tptp.one_one_rat)))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat B) tptp.one_one_nat)))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) (@ (@ tptp.plus_plus_int B) tptp.one_one_int)))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B))))))
% 5.98/6.26 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) A)) tptp.zero_zero_real))))
% 5.98/6.26 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) A)) tptp.zero_zero_rat))))
% 5.98/6.26 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) A)) tptp.zero_zero_int))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_real A) B)))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat A) B)))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat A) B)))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int A) B)))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real B) A)) tptp.zero_zero_real)))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat B) A)) tptp.zero_zero_rat)))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat B) A)) tptp.zero_zero_nat)))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int B) A)) tptp.zero_zero_int)))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.zero_zero_int)))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.26 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.26 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.26 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.26 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.26 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real B) A))))))
% 5.98/6.26 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat B) A))))))
% 5.98/6.26 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int B) A))))))
% 5.98/6.26 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B))))))
% 5.98/6.26 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B))))))
% 5.98/6.26 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B))))))
% 5.98/6.26 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (and (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)))))))
% 5.98/6.26 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 5.98/6.26 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A)))))))
% 5.98/6.26 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 5.98/6.26 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 5.98/6.26 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (and (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.minus_minus_real C) B)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) C))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.minus_minus_rat C) B)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) C))))
% 5.98/6.26 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int C) B)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real C) B)))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat C) B)))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int C) B)))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (@ (@ tptp.ord_less_real A) B)) (= (@ (@ tptp.plus_plus_real B) (@ (@ tptp.minus_minus_real A) B)) A))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat A) B)) (= (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.minus_minus_rat A) B)) A))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat A) B)) (= (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.minus_minus_nat A) B)) A))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (@ (@ tptp.ord_less_int A) B)) (= (@ (@ tptp.plus_plus_int B) (@ (@ tptp.minus_minus_int A) B)) A))))
% 5.98/6.26 (assert (forall ((P (-> tptp.set_set_nat Bool)) (A2 tptp.set_set_nat)) (=> (forall ((A3 tptp.set_set_nat)) (=> (not (@ tptp.finite1152437895449049373et_nat A3)) (@ P A3))) (=> (@ P tptp.bot_bot_set_set_nat) (=> (forall ((X4 tptp.set_nat) (F3 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat F3) (=> (not (@ (@ tptp.member_set_nat X4) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_set_nat X4) F3)))))) (@ P A2))))))
% 5.98/6.26 (assert (forall ((P (-> tptp.set_set_nat_rat Bool)) (A2 tptp.set_set_nat_rat)) (=> (forall ((A3 tptp.set_set_nat_rat)) (=> (not (@ tptp.finite6430367030675640852at_rat A3)) (@ P A3))) (=> (@ P tptp.bot_bo6797373522285170759at_rat) (=> (forall ((X4 tptp.set_nat_rat) (F3 tptp.set_set_nat_rat)) (=> (@ tptp.finite6430367030675640852at_rat F3) (=> (not (@ (@ tptp.member_set_nat_rat X4) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_set_nat_rat X4) F3)))))) (@ P A2))))))
% 5.98/6.26 (assert (forall ((P (-> tptp.set_complex Bool)) (A2 tptp.set_complex)) (=> (forall ((A3 tptp.set_complex)) (=> (not (@ tptp.finite3207457112153483333omplex A3)) (@ P A3))) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X4 tptp.complex) (F3 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex F3) (=> (not (@ (@ tptp.member_complex X4) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_complex X4) F3)))))) (@ P A2))))))
% 5.98/6.26 (assert (forall ((P (-> tptp.set_Pr1261947904930325089at_nat Bool)) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (=> (not (@ tptp.finite6177210948735845034at_nat A3)) (@ P A3))) (=> (@ P tptp.bot_bo2099793752762293965at_nat) (=> (forall ((X4 tptp.product_prod_nat_nat) (F3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat F3) (=> (not (@ (@ tptp.member8440522571783428010at_nat X4) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert8211810215607154385at_nat X4) F3)))))) (@ P A2))))))
% 5.98/6.26 (assert (forall ((P (-> tptp.set_Extended_enat Bool)) (A2 tptp.set_Extended_enat)) (=> (forall ((A3 tptp.set_Extended_enat)) (=> (not (@ tptp.finite4001608067531595151d_enat A3)) (@ P A3))) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((X4 tptp.extended_enat) (F3 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat F3) (=> (not (@ (@ tptp.member_Extended_enat X4) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_Extended_enat X4) F3)))))) (@ P A2))))))
% 5.98/6.26 (assert (forall ((P (-> tptp.set_real Bool)) (A2 tptp.set_real)) (=> (forall ((A3 tptp.set_real)) (=> (not (@ tptp.finite_finite_real A3)) (@ P A3))) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X4 tptp.real) (F3 tptp.set_real)) (=> (@ tptp.finite_finite_real F3) (=> (not (@ (@ tptp.member_real X4) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_real X4) F3)))))) (@ P A2))))))
% 5.98/6.26 (assert (forall ((P (-> tptp.set_o Bool)) (A2 tptp.set_o)) (=> (forall ((A3 tptp.set_o)) (=> (not (@ tptp.finite_finite_o A3)) (@ P A3))) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((X4 Bool) (F3 tptp.set_o)) (=> (@ tptp.finite_finite_o F3) (=> (not (@ (@ tptp.member_o X4) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_o X4) F3)))))) (@ P A2))))))
% 5.98/6.26 (assert (forall ((P (-> tptp.set_nat Bool)) (A2 tptp.set_nat)) (=> (forall ((A3 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A3)) (@ P A3))) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X4 tptp.nat) (F3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat F3) (=> (not (@ (@ tptp.member_nat X4) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_nat X4) F3)))))) (@ P A2))))))
% 5.98/6.26 (assert (forall ((P (-> tptp.set_int Bool)) (A2 tptp.set_int)) (=> (forall ((A3 tptp.set_int)) (=> (not (@ tptp.finite_finite_int A3)) (@ P A3))) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X4 tptp.int) (F3 tptp.set_int)) (=> (@ tptp.finite_finite_int F3) (=> (not (@ (@ tptp.member_int X4) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_int X4) F3)))))) (@ P A2))))))
% 5.98/6.26 (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 ((X4 tptp.set_nat)) (@ P (@ (@ tptp.insert_set_nat X4) tptp.bot_bot_set_set_nat))) (=> (forall ((X4 tptp.set_nat) (F3 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat F3) (=> (not (= F3 tptp.bot_bot_set_set_nat)) (=> (not (@ (@ tptp.member_set_nat X4) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_set_nat X4) F3))))))) (@ P F2)))))))
% 5.98/6.26 (assert (forall ((F2 tptp.set_set_nat_rat) (P (-> tptp.set_set_nat_rat Bool))) (=> (@ tptp.finite6430367030675640852at_rat F2) (=> (not (= F2 tptp.bot_bo6797373522285170759at_rat)) (=> (forall ((X4 tptp.set_nat_rat)) (@ P (@ (@ tptp.insert_set_nat_rat X4) tptp.bot_bo6797373522285170759at_rat))) (=> (forall ((X4 tptp.set_nat_rat) (F3 tptp.set_set_nat_rat)) (=> (@ tptp.finite6430367030675640852at_rat F3) (=> (not (= F3 tptp.bot_bo6797373522285170759at_rat)) (=> (not (@ (@ tptp.member_set_nat_rat X4) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_set_nat_rat X4) F3))))))) (@ P F2)))))))
% 5.98/6.26 (assert (forall ((F2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex F2) (=> (not (= F2 tptp.bot_bot_set_complex)) (=> (forall ((X4 tptp.complex)) (@ P (@ (@ tptp.insert_complex X4) tptp.bot_bot_set_complex))) (=> (forall ((X4 tptp.complex) (F3 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex F3) (=> (not (= F3 tptp.bot_bot_set_complex)) (=> (not (@ (@ tptp.member_complex X4) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_complex X4) F3))))))) (@ P F2)))))))
% 5.98/6.26 (assert (forall ((F2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat F2) (=> (not (= F2 tptp.bot_bo2099793752762293965at_nat)) (=> (forall ((X4 tptp.product_prod_nat_nat)) (@ P (@ (@ tptp.insert8211810215607154385at_nat X4) tptp.bot_bo2099793752762293965at_nat))) (=> (forall ((X4 tptp.product_prod_nat_nat) (F3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat F3) (=> (not (= F3 tptp.bot_bo2099793752762293965at_nat)) (=> (not (@ (@ tptp.member8440522571783428010at_nat X4) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert8211810215607154385at_nat X4) F3))))))) (@ P F2)))))))
% 5.98/6.26 (assert (forall ((F2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat F2) (=> (not (= F2 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((X4 tptp.extended_enat)) (@ P (@ (@ tptp.insert_Extended_enat X4) tptp.bot_bo7653980558646680370d_enat))) (=> (forall ((X4 tptp.extended_enat) (F3 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat F3) (=> (not (= F3 tptp.bot_bo7653980558646680370d_enat)) (=> (not (@ (@ tptp.member_Extended_enat X4) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_Extended_enat X4) F3))))))) (@ P F2)))))))
% 5.98/6.26 (assert (forall ((F2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real F2) (=> (not (= F2 tptp.bot_bot_set_real)) (=> (forall ((X4 tptp.real)) (@ P (@ (@ tptp.insert_real X4) tptp.bot_bot_set_real))) (=> (forall ((X4 tptp.real) (F3 tptp.set_real)) (=> (@ tptp.finite_finite_real F3) (=> (not (= F3 tptp.bot_bot_set_real)) (=> (not (@ (@ tptp.member_real X4) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_real X4) F3))))))) (@ P F2)))))))
% 5.98/6.26 (assert (forall ((F2 tptp.set_o) (P (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o F2) (=> (not (= F2 tptp.bot_bot_set_o)) (=> (forall ((X4 Bool)) (@ P (@ (@ tptp.insert_o X4) tptp.bot_bot_set_o))) (=> (forall ((X4 Bool) (F3 tptp.set_o)) (=> (@ tptp.finite_finite_o F3) (=> (not (= F3 tptp.bot_bot_set_o)) (=> (not (@ (@ tptp.member_o X4) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_o X4) F3))))))) (@ P F2)))))))
% 5.98/6.26 (assert (forall ((F2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F2) (=> (not (= F2 tptp.bot_bot_set_nat)) (=> (forall ((X4 tptp.nat)) (@ P (@ (@ tptp.insert_nat X4) tptp.bot_bot_set_nat))) (=> (forall ((X4 tptp.nat) (F3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat F3) (=> (not (= F3 tptp.bot_bot_set_nat)) (=> (not (@ (@ tptp.member_nat X4) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_nat X4) F3))))))) (@ P F2)))))))
% 5.98/6.26 (assert (forall ((F2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F2) (=> (not (= F2 tptp.bot_bot_set_int)) (=> (forall ((X4 tptp.int)) (@ P (@ (@ tptp.insert_int X4) tptp.bot_bot_set_int))) (=> (forall ((X4 tptp.int) (F3 tptp.set_int)) (=> (@ tptp.finite_finite_int F3) (=> (not (= F3 tptp.bot_bot_set_int)) (=> (not (@ (@ tptp.member_int X4) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_int X4) F3))))))) (@ P F2)))))))
% 5.98/6.26 (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 ((X4 tptp.set_nat) (F3 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat F3) (=> (not (@ (@ tptp.member_set_nat X4) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_set_nat X4) F3)))))) (@ P F2))))))
% 5.98/6.26 (assert (forall ((F2 tptp.set_set_nat_rat) (P (-> tptp.set_set_nat_rat Bool))) (=> (@ tptp.finite6430367030675640852at_rat F2) (=> (@ P tptp.bot_bo6797373522285170759at_rat) (=> (forall ((X4 tptp.set_nat_rat) (F3 tptp.set_set_nat_rat)) (=> (@ tptp.finite6430367030675640852at_rat F3) (=> (not (@ (@ tptp.member_set_nat_rat X4) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_set_nat_rat X4) F3)))))) (@ P F2))))))
% 5.98/6.26 (assert (forall ((F2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex F2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X4 tptp.complex) (F3 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex F3) (=> (not (@ (@ tptp.member_complex X4) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_complex X4) F3)))))) (@ P F2))))))
% 5.98/6.26 (assert (forall ((F2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat F2) (=> (@ P tptp.bot_bo2099793752762293965at_nat) (=> (forall ((X4 tptp.product_prod_nat_nat) (F3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat F3) (=> (not (@ (@ tptp.member8440522571783428010at_nat X4) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert8211810215607154385at_nat X4) F3)))))) (@ P F2))))))
% 5.98/6.26 (assert (forall ((F2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat F2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((X4 tptp.extended_enat) (F3 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat F3) (=> (not (@ (@ tptp.member_Extended_enat X4) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_Extended_enat X4) F3)))))) (@ P F2))))))
% 5.98/6.26 (assert (forall ((F2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real F2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X4 tptp.real) (F3 tptp.set_real)) (=> (@ tptp.finite_finite_real F3) (=> (not (@ (@ tptp.member_real X4) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_real X4) F3)))))) (@ P F2))))))
% 5.98/6.26 (assert (forall ((F2 tptp.set_o) (P (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o F2) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((X4 Bool) (F3 tptp.set_o)) (=> (@ tptp.finite_finite_o F3) (=> (not (@ (@ tptp.member_o X4) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_o X4) F3)))))) (@ P F2))))))
% 5.98/6.26 (assert (forall ((F2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X4 tptp.nat) (F3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat F3) (=> (not (@ (@ tptp.member_nat X4) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_nat X4) F3)))))) (@ P F2))))))
% 5.98/6.26 (assert (forall ((F2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X4 tptp.int) (F3 tptp.set_int)) (=> (@ tptp.finite_finite_int F3) (=> (not (@ (@ tptp.member_int X4) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_int X4) F3)))))) (@ P F2))))))
% 5.98/6.26 (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)))))))
% 5.98/6.26 (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)))))))
% 5.98/6.26 (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)))))))
% 5.98/6.26 (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)))))))
% 5.98/6.26 (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)))))))
% 5.98/6.26 (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)))))))
% 5.98/6.26 (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)))))))
% 5.98/6.26 (assert (forall ((A tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A) (=> (not (= A tptp.bot_bot_set_complex)) (not (forall ((A3 tptp.set_complex)) (=> (exists ((A5 tptp.complex)) (= A (@ (@ tptp.insert_complex A5) A3))) (not (@ tptp.finite3207457112153483333omplex A3)))))))))
% 5.98/6.26 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A) (=> (not (= A tptp.bot_bo2099793752762293965at_nat)) (not (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (=> (exists ((A5 tptp.product_prod_nat_nat)) (= A (@ (@ tptp.insert8211810215607154385at_nat A5) A3))) (not (@ tptp.finite6177210948735845034at_nat A3)))))))))
% 5.98/6.26 (assert (forall ((A tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A) (=> (not (= A tptp.bot_bo7653980558646680370d_enat)) (not (forall ((A3 tptp.set_Extended_enat)) (=> (exists ((A5 tptp.extended_enat)) (= A (@ (@ tptp.insert_Extended_enat A5) A3))) (not (@ tptp.finite4001608067531595151d_enat A3)))))))))
% 5.98/6.26 (assert (forall ((A tptp.set_real)) (=> (@ tptp.finite_finite_real A) (=> (not (= A tptp.bot_bot_set_real)) (not (forall ((A3 tptp.set_real)) (=> (exists ((A5 tptp.real)) (= A (@ (@ tptp.insert_real A5) A3))) (not (@ tptp.finite_finite_real A3)))))))))
% 5.98/6.26 (assert (forall ((A tptp.set_o)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (not (forall ((A3 tptp.set_o)) (=> (exists ((A5 Bool)) (= A (@ (@ tptp.insert_o A5) A3))) (not (@ tptp.finite_finite_o A3)))))))))
% 5.98/6.26 (assert (forall ((A tptp.set_nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (not (forall ((A3 tptp.set_nat)) (=> (exists ((A5 tptp.nat)) (= A (@ (@ tptp.insert_nat A5) A3))) (not (@ tptp.finite_finite_nat A3)))))))))
% 5.98/6.26 (assert (forall ((A tptp.set_int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (not (forall ((A3 tptp.set_int)) (=> (exists ((A5 tptp.int)) (= A (@ (@ tptp.insert_int A5) A3))) (not (@ tptp.finite_finite_int A3)))))))))
% 5.98/6.26 (assert (forall ((X5 tptp.set_Pr1261947904930325089at_nat) (A tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat A) tptp.bot_bo2099793752762293965at_nat))) (= (@ (@ tptp.ord_le3146513528884898305at_nat X5) _let_1) (or (= X5 tptp.bot_bo2099793752762293965at_nat) (= X5 _let_1))))))
% 5.98/6.26 (assert (forall ((X5 tptp.set_real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))) (= (@ (@ tptp.ord_less_eq_set_real X5) _let_1) (or (= X5 tptp.bot_bot_set_real) (= X5 _let_1))))))
% 5.98/6.26 (assert (forall ((X5 tptp.set_o) (A Bool)) (let ((_let_1 (@ (@ tptp.insert_o A) tptp.bot_bot_set_o))) (= (@ (@ tptp.ord_less_eq_set_o X5) _let_1) (or (= X5 tptp.bot_bot_set_o) (= X5 _let_1))))))
% 5.98/6.26 (assert (forall ((X5 tptp.set_nat) (A tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (= (@ (@ tptp.ord_less_eq_set_nat X5) _let_1) (or (= X5 tptp.bot_bot_set_nat) (= X5 _let_1))))))
% 5.98/6.26 (assert (forall ((X5 tptp.set_int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))) (= (@ (@ tptp.ord_less_eq_set_int X5) _let_1) (or (= X5 tptp.bot_bot_set_int) (= X5 _let_1))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) _let_1) (or (= A2 tptp.bot_bo2099793752762293965at_nat) (= A2 _let_1))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_real) (X tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))) (=> (@ (@ tptp.ord_less_eq_set_real A2) _let_1) (or (= A2 tptp.bot_bot_set_real) (= A2 _let_1))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_o) (X Bool)) (let ((_let_1 (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))) (=> (@ (@ tptp.ord_less_eq_set_o A2) _let_1) (or (= A2 tptp.bot_bot_set_o) (= A2 _let_1))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) _let_1) (or (= A2 tptp.bot_bot_set_nat) (= A2 _let_1))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_int) (X tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))) (=> (@ (@ tptp.ord_less_eq_set_int A2) _let_1) (or (= A2 tptp.bot_bot_set_int) (= A2 _let_1))))))
% 5.98/6.26 (assert (forall ((M2 tptp.real) (N tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_real M2) N)))))))
% 5.98/6.26 (assert (forall ((M2 tptp.rat) (N tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_rat M2) N)))))))
% 5.98/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_nat M2) N)))))))
% 5.98/6.26 (assert (forall ((M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_int M2) N)))))))
% 5.98/6.26 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat X) Y) (@ (@ tptp.divide_divide_rat W2) Z)) (= (@ (@ tptp.times_times_rat X) Z) (@ (@ tptp.times_times_rat W2) Y)))))))
% 5.98/6.26 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real X) Y) (@ (@ tptp.divide_divide_real W2) Z)) (= (@ (@ tptp.times_times_real X) Z) (@ (@ tptp.times_times_real W2) Y)))))))
% 5.98/6.26 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 5.98/6.26 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_real A) C))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A) C) B)) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A) C) B)) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 5.98/6.26 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= B (@ (@ tptp.times_times_rat A) C)) (= (@ (@ tptp.divide_divide_rat B) C) A)))))
% 5.98/6.26 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= B (@ (@ tptp.times_times_real A) C)) (= (@ (@ tptp.divide_divide_real B) C) A)))))
% 5.98/6.26 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= (@ (@ tptp.times_times_rat A) C) B) (= A (@ (@ tptp.divide_divide_rat B) C))))))
% 5.98/6.26 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= (@ (@ tptp.times_times_real A) C) B) (= A (@ (@ tptp.divide_divide_real B) C))))))
% 5.98/6.26 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat B) C) A) (= B (@ (@ tptp.times_times_rat A) C))))))
% 5.98/6.26 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real B) C) A) (= B (@ (@ tptp.times_times_real A) C))))))
% 5.98/6.26 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= A (@ (@ tptp.divide_divide_rat B) C)) (= (@ (@ tptp.times_times_rat A) C) B)))))
% 5.98/6.26 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= A (@ (@ tptp.divide_divide_real B) C)) (= (@ (@ tptp.times_times_real A) C) B)))))
% 5.98/6.26 (assert (forall ((X tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X))) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) A2)) (= (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_1 A2)) (@ _let_1 tptp.bot_bo2099793752762293965at_nat)) A2)))))
% 5.98/6.26 (assert (forall ((X tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.insert_set_nat X))) (=> (not (@ (@ tptp.member_set_nat X) A2)) (= (@ (@ tptp.minus_2163939370556025621et_nat (@ _let_1 A2)) (@ _let_1 tptp.bot_bot_set_set_nat)) A2)))))
% 5.98/6.26 (assert (forall ((X tptp.set_nat_rat) (A2 tptp.set_set_nat_rat)) (let ((_let_1 (@ tptp.insert_set_nat_rat X))) (=> (not (@ (@ tptp.member_set_nat_rat X) A2)) (= (@ (@ tptp.minus_1626877696091177228at_rat (@ _let_1 A2)) (@ _let_1 tptp.bot_bo6797373522285170759at_rat)) A2)))))
% 5.98/6.26 (assert (forall ((X tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X))) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ (@ tptp.minus_minus_set_real (@ _let_1 A2)) (@ _let_1 tptp.bot_bot_set_real)) A2)))))
% 5.98/6.26 (assert (forall ((X Bool) (A2 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o X))) (=> (not (@ (@ tptp.member_o X) A2)) (= (@ (@ tptp.minus_minus_set_o (@ _let_1 A2)) (@ _let_1 tptp.bot_bot_set_o)) A2)))))
% 5.98/6.26 (assert (forall ((X tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ (@ tptp.minus_minus_set_int (@ _let_1 A2)) (@ _let_1 tptp.bot_bot_set_int)) A2)))))
% 5.98/6.26 (assert (forall ((X tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ (@ tptp.minus_minus_set_nat (@ _let_1 A2)) (@ _let_1 tptp.bot_bot_set_nat)) A2)))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (A tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A))) (let ((_let_2 (@ tptp.minus_1356011639430497352at_nat A2))) (= (@ _let_2 (@ _let_1 B2)) (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_2 (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) B2))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_real) (A tptp.real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real A))) (let ((_let_2 (@ tptp.minus_minus_set_real A2))) (= (@ _let_2 (@ _let_1 B2)) (@ (@ tptp.minus_minus_set_real (@ _let_2 (@ _let_1 tptp.bot_bot_set_real))) B2))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_o) (A Bool) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A))) (let ((_let_2 (@ tptp.minus_minus_set_o A2))) (= (@ _let_2 (@ _let_1 B2)) (@ (@ tptp.minus_minus_set_o (@ _let_2 (@ _let_1 tptp.bot_bot_set_o))) B2))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_int) (A tptp.int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (let ((_let_2 (@ tptp.minus_minus_set_int A2))) (= (@ _let_2 (@ _let_1 B2)) (@ (@ tptp.minus_minus_set_int (@ _let_2 (@ _let_1 tptp.bot_bot_set_int))) B2))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_nat) (A tptp.nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (let ((_let_2 (@ tptp.minus_minus_set_nat A2))) (= (@ _let_2 (@ _let_1 B2)) (@ (@ tptp.minus_minus_set_nat (@ _let_2 (@ _let_1 tptp.bot_bot_set_nat))) B2))))))
% 5.98/6.26 (assert (forall ((A tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A))) (=> (@ (@ tptp.member8440522571783428010at_nat A) A2) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) A2)))))
% 5.98/6.26 (assert (forall ((A tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.insert_set_nat A))) (=> (@ (@ tptp.member_set_nat A) A2) (= (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) (@ _let_1 tptp.bot_bot_set_set_nat))) A2)))))
% 5.98/6.26 (assert (forall ((A tptp.set_nat_rat) (A2 tptp.set_set_nat_rat)) (let ((_let_1 (@ tptp.insert_set_nat_rat A))) (=> (@ (@ tptp.member_set_nat_rat A) A2) (= (@ _let_1 (@ (@ tptp.minus_1626877696091177228at_rat A2) (@ _let_1 tptp.bot_bo6797373522285170759at_rat))) A2)))))
% 5.98/6.26 (assert (forall ((A tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real A))) (=> (@ (@ tptp.member_real A) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))) A2)))))
% 5.98/6.26 (assert (forall ((A Bool) (A2 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A))) (=> (@ (@ tptp.member_o A) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_o A2) (@ _let_1 tptp.bot_bot_set_o))) A2)))))
% 5.98/6.26 (assert (forall ((A tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (=> (@ (@ tptp.member_int A) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))) A2)))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (=> (@ (@ tptp.member_nat A) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ _let_1 tptp.bot_bot_set_nat))) A2)))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (A tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A))) (let ((_let_2 (@ tptp.minus_1356011639430497352at_nat A2))) (= (@ _let_2 (@ _let_1 B2)) (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_2 B2)) (@ _let_1 tptp.bot_bo2099793752762293965at_nat)))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_real) (A tptp.real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real A))) (let ((_let_2 (@ tptp.minus_minus_set_real A2))) (= (@ _let_2 (@ _let_1 B2)) (@ (@ tptp.minus_minus_set_real (@ _let_2 B2)) (@ _let_1 tptp.bot_bot_set_real)))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_o) (A Bool) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A))) (let ((_let_2 (@ tptp.minus_minus_set_o A2))) (= (@ _let_2 (@ _let_1 B2)) (@ (@ tptp.minus_minus_set_o (@ _let_2 B2)) (@ _let_1 tptp.bot_bot_set_o)))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_int) (A tptp.int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (let ((_let_2 (@ tptp.minus_minus_set_int A2))) (= (@ _let_2 (@ _let_1 B2)) (@ (@ tptp.minus_minus_set_int (@ _let_2 B2)) (@ _let_1 tptp.bot_bot_set_int)))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_nat) (A tptp.nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (let ((_let_2 (@ tptp.minus_minus_set_nat A2))) (= (@ _let_2 (@ _let_1 B2)) (@ (@ tptp.minus_minus_set_nat (@ _let_2 B2)) (@ _let_1 tptp.bot_bot_set_nat)))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat) (X 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 A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X) C2))) (and (@ _let_2 (@ _let_1 C2)) (not (@ (@ tptp.member8440522571783428010at_nat X) A2))))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_real) (B2 tptp.set_real) (X tptp.real) (C2 tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real B2))) (let ((_let_2 (@ tptp.ord_less_eq_set_real A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_real X) C2))) (and (@ _let_2 (@ _let_1 C2)) (not (@ (@ tptp.member_real X) A2))))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_o) (B2 tptp.set_o) (X Bool) (C2 tptp.set_o)) (let ((_let_1 (@ tptp.minus_minus_set_o B2))) (let ((_let_2 (@ tptp.ord_less_eq_set_o A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_o X) C2))) (and (@ _let_2 (@ _let_1 C2)) (not (@ (@ tptp.member_o X) A2))))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_set_nat) (B2 tptp.set_set_nat) (X tptp.set_nat) (C2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.minus_2163939370556025621et_nat B2))) (let ((_let_2 (@ tptp.ord_le6893508408891458716et_nat A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_set_nat X) C2))) (and (@ _let_2 (@ _let_1 C2)) (not (@ (@ tptp.member_set_nat X) A2))))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_set_nat_rat) (B2 tptp.set_set_nat_rat) (X tptp.set_nat_rat) (C2 tptp.set_set_nat_rat)) (let ((_let_1 (@ tptp.minus_1626877696091177228at_rat B2))) (let ((_let_2 (@ tptp.ord_le4375437777232675859at_rat A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_set_nat_rat X) C2))) (and (@ _let_2 (@ _let_1 C2)) (not (@ (@ tptp.member_set_nat_rat X) A2))))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (X tptp.nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat B2))) (let ((_let_2 (@ tptp.ord_less_eq_set_nat A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_nat X) C2))) (and (@ _let_2 (@ _let_1 C2)) (not (@ (@ tptp.member_nat X) A2))))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int) (X tptp.int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int B2))) (let ((_let_2 (@ tptp.ord_less_eq_set_int A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_int X) C2))) (and (@ _let_2 (@ _let_1 C2)) (not (@ (@ tptp.member_int X) A2))))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat A2)) (@ tptp.finite711546835091564841at_nat (@ (@ tptp.insert8211810215607154385at_nat X) A2)))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_real) (X tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real A2)) (@ tptp.finite_card_real (@ (@ tptp.insert_real X) A2)))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_o) (X Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o A2)) (@ tptp.finite_card_o (@ (@ tptp.insert_o X) A2)))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_complex) (X tptp.complex)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A2)) (@ tptp.finite_card_complex (@ (@ tptp.insert_complex X) A2)))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_list_nat) (X tptp.list_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat A2)) (@ tptp.finite_card_list_nat (@ (@ tptp.insert_list_nat X) A2)))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_set_nat) (X tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat A2)) (@ tptp.finite_card_set_nat (@ (@ tptp.insert_set_nat X) A2)))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A2)) (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X) A2)))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_int) (X tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A2)) (@ tptp.finite_card_int (@ (@ tptp.insert_int X) A2)))))
% 5.98/6.26 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N)))))
% 5.98/6.26 (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))))))
% 5.98/6.26 (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)))))))
% 5.98/6.26 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N)))))
% 5.98/6.26 (assert (forall ((M2 tptp.nat) (I tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.times_times_nat I) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M2) N)) I))))
% 5.98/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (= M2 (@ (@ tptp.times_times_nat M2) N)) (or (= N tptp.one_one_nat) (= M2 tptp.zero_zero_nat)))))
% 5.98/6.26 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M2) N)) N)) M2)))
% 5.98/6.26 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.divide_divide_nat M2) N))) M2)))
% 5.98/6.26 (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))))))
% 5.98/6.26 (assert (= tptp.ord_less_eq_int (lambda ((W3 tptp.int) (Z2 tptp.int)) (exists ((N4 tptp.nat)) (= Z2 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int N4)))))))
% 5.98/6.26 (assert (forall ((X tptp.real)) (= (@ tptp.archim2898591450579166408c_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) (@ tptp.archim2898591450579166408c_real X))))
% 5.98/6.26 (assert (forall ((X tptp.rat)) (= (@ tptp.archimedean_frac_rat (@ (@ tptp.plus_plus_rat X) tptp.one_one_rat)) (@ tptp.archimedean_frac_rat X))))
% 5.98/6.26 (assert (= tptp.neg_nu8557863876264182079omplex (lambda ((X3 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex X3) X3)) tptp.one_one_complex))))
% 5.98/6.26 (assert (= tptp.neg_nu8295874005876285629c_real (lambda ((X3 tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real X3) X3)) tptp.one_one_real))))
% 5.98/6.26 (assert (= tptp.neg_nu5219082963157363817nc_rat (lambda ((X3 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat X3) X3)) tptp.one_one_rat))))
% 5.98/6.26 (assert (= tptp.neg_nu5851722552734809277nc_int (lambda ((X3 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X3) X3)) tptp.one_one_int))))
% 5.98/6.26 (assert (forall ((X tptp.real)) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) E))) (= X tptp.zero_zero_real))))
% 5.98/6.26 (assert (forall ((X tptp.rat)) (=> (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) E))) (= X tptp.zero_zero_rat))))
% 5.98/6.26 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (= (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat X)) Y) (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat X) Y))))))
% 5.98/6.26 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (= (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real X)) Y) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X) Y))))))
% 5.98/6.26 (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)))))
% 5.98/6.26 (assert (forall ((M2 tptp.nat) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat M2) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M2)) Z))))
% 5.98/6.26 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real Y) E)))) (@ (@ tptp.ord_less_eq_real X) Y))))
% 5.98/6.26 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.plus_plus_rat Y) E)))) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B) C) (@ (@ tptp.ord_less_real B) (@ (@ tptp.plus_plus_real A) C))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.plus_plus_rat A) C))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_nat B) (@ (@ tptp.plus_plus_nat A) C))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ (@ tptp.ord_less_int B) (@ (@ tptp.plus_plus_int A) C))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 5.98/6.26 (assert (forall ((X tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X)) N) (@ (@ tptp.ord_less_eq_int X) (@ tptp.semiri1314217659103216013at_int N)))))
% 5.98/6.26 (assert (forall ((M2 tptp.nat) (Z tptp.int)) (= (= (@ tptp.semiri1314217659103216013at_int M2) Z) (and (= M2 (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z)))))
% 5.98/6.26 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)) Z))))
% 5.98/6.26 (assert (forall ((S2 tptp.set_complex) (P (-> tptp.set_complex Bool)) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X4 tptp.complex) (S4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (forall ((Y4 tptp.complex)) (=> (@ (@ tptp.member_complex Y4) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y4)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_complex X4) S4)))))) (@ P S2))))))
% 5.98/6.26 (assert (forall ((S2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool)) (F (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((X4 tptp.extended_enat) (S4 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S4) (=> (forall ((Y4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Y4) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y4)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_Extended_enat X4) S4)))))) (@ P S2))))))
% 5.98/6.26 (assert (forall ((S2 tptp.set_real) (P (-> tptp.set_real Bool)) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real S2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X4 tptp.real) (S4 tptp.set_real)) (=> (@ tptp.finite_finite_real S4) (=> (forall ((Y4 tptp.real)) (=> (@ (@ tptp.member_real Y4) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y4)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_real X4) S4)))))) (@ P S2))))))
% 5.98/6.26 (assert (forall ((S2 tptp.set_o) (P (-> tptp.set_o Bool)) (F (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o S2) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((X4 Bool) (S4 tptp.set_o)) (=> (@ tptp.finite_finite_o S4) (=> (forall ((Y4 Bool)) (=> (@ (@ tptp.member_o Y4) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y4)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_o X4) S4)))))) (@ P S2))))))
% 5.98/6.26 (assert (forall ((S2 tptp.set_nat) (P (-> tptp.set_nat Bool)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X4 tptp.nat) (S4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S4) (=> (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member_nat Y4) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y4)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_nat X4) S4)))))) (@ P S2))))))
% 5.98/6.26 (assert (forall ((S2 tptp.set_int) (P (-> tptp.set_int Bool)) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X4 tptp.int) (S4 tptp.set_int)) (=> (@ tptp.finite_finite_int S4) (=> (forall ((Y4 tptp.int)) (=> (@ (@ tptp.member_int Y4) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y4)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_int X4) S4)))))) (@ P S2))))))
% 5.98/6.26 (assert (forall ((S2 tptp.set_complex) (P (-> tptp.set_complex Bool)) (F (-> tptp.complex tptp.num))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X4 tptp.complex) (S4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (forall ((Y4 tptp.complex)) (=> (@ (@ tptp.member_complex Y4) S4) (@ (@ tptp.ord_less_eq_num (@ F Y4)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_complex X4) S4)))))) (@ P S2))))))
% 5.98/6.26 (assert (forall ((S2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool)) (F (-> tptp.extended_enat tptp.num))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((X4 tptp.extended_enat) (S4 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S4) (=> (forall ((Y4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Y4) S4) (@ (@ tptp.ord_less_eq_num (@ F Y4)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_Extended_enat X4) S4)))))) (@ P S2))))))
% 5.98/6.26 (assert (forall ((S2 tptp.set_real) (P (-> tptp.set_real Bool)) (F (-> tptp.real tptp.num))) (=> (@ tptp.finite_finite_real S2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X4 tptp.real) (S4 tptp.set_real)) (=> (@ tptp.finite_finite_real S4) (=> (forall ((Y4 tptp.real)) (=> (@ (@ tptp.member_real Y4) S4) (@ (@ tptp.ord_less_eq_num (@ F Y4)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_real X4) S4)))))) (@ P S2))))))
% 5.98/6.26 (assert (forall ((S2 tptp.set_o) (P (-> tptp.set_o Bool)) (F (-> Bool tptp.num))) (=> (@ tptp.finite_finite_o S2) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((X4 Bool) (S4 tptp.set_o)) (=> (@ tptp.finite_finite_o S4) (=> (forall ((Y4 Bool)) (=> (@ (@ tptp.member_o Y4) S4) (@ (@ tptp.ord_less_eq_num (@ F Y4)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_o X4) S4)))))) (@ P S2))))))
% 5.98/6.26 (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))))
% 5.98/6.26 (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))))
% 5.98/6.26 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))
% 5.98/6.26 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))
% 5.98/6.26 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 5.98/6.26 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 5.98/6.26 (assert (forall ((A2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((B5 tptp.extended_enat) (A3 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X2) A3) (@ (@ tptp.ord_le72135733267957522d_enat X2) B5))) (=> (@ P A3) (@ P (@ (@ tptp.insert_Extended_enat B5) A3)))))) (@ P A2))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_o) (P (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o A2) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((B5 Bool) (A3 tptp.set_o)) (=> (@ tptp.finite_finite_o A3) (=> (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A3) (@ (@ tptp.ord_less_o X2) B5))) (=> (@ P A3) (@ P (@ (@ tptp.insert_o B5) A3)))))) (@ P A2))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((B5 tptp.real) (A3 tptp.set_real)) (=> (@ tptp.finite_finite_real A3) (=> (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) A3) (@ (@ tptp.ord_less_real X2) B5))) (=> (@ P A3) (@ P (@ (@ tptp.insert_real B5) A3)))))) (@ P A2))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_rat) (P (-> tptp.set_rat Bool))) (=> (@ tptp.finite_finite_rat A2) (=> (@ P tptp.bot_bot_set_rat) (=> (forall ((B5 tptp.rat) (A3 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A3) (=> (forall ((X2 tptp.rat)) (=> (@ (@ tptp.member_rat X2) A3) (@ (@ tptp.ord_less_rat X2) B5))) (=> (@ P A3) (@ P (@ (@ tptp.insert_rat B5) A3)))))) (@ P A2))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_num) (P (-> tptp.set_num Bool))) (=> (@ tptp.finite_finite_num A2) (=> (@ P tptp.bot_bot_set_num) (=> (forall ((B5 tptp.num) (A3 tptp.set_num)) (=> (@ tptp.finite_finite_num A3) (=> (forall ((X2 tptp.num)) (=> (@ (@ tptp.member_num X2) A3) (@ (@ tptp.ord_less_num X2) B5))) (=> (@ P A3) (@ P (@ (@ tptp.insert_num B5) A3)))))) (@ P A2))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B5 tptp.nat) (A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (=> (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A3) (@ (@ tptp.ord_less_nat X2) B5))) (=> (@ P A3) (@ P (@ (@ tptp.insert_nat B5) A3)))))) (@ P A2))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B5 tptp.int) (A3 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (=> (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A3) (@ (@ tptp.ord_less_int X2) B5))) (=> (@ P A3) (@ P (@ (@ tptp.insert_int B5) A3)))))) (@ P A2))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((B5 tptp.extended_enat) (A3 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X2) A3) (@ (@ tptp.ord_le72135733267957522d_enat B5) X2))) (=> (@ P A3) (@ P (@ (@ tptp.insert_Extended_enat B5) A3)))))) (@ P A2))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_o) (P (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o A2) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((B5 Bool) (A3 tptp.set_o)) (=> (@ tptp.finite_finite_o A3) (=> (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A3) (@ (@ tptp.ord_less_o B5) X2))) (=> (@ P A3) (@ P (@ (@ tptp.insert_o B5) A3)))))) (@ P A2))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((B5 tptp.real) (A3 tptp.set_real)) (=> (@ tptp.finite_finite_real A3) (=> (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) A3) (@ (@ tptp.ord_less_real B5) X2))) (=> (@ P A3) (@ P (@ (@ tptp.insert_real B5) A3)))))) (@ P A2))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_rat) (P (-> tptp.set_rat Bool))) (=> (@ tptp.finite_finite_rat A2) (=> (@ P tptp.bot_bot_set_rat) (=> (forall ((B5 tptp.rat) (A3 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A3) (=> (forall ((X2 tptp.rat)) (=> (@ (@ tptp.member_rat X2) A3) (@ (@ tptp.ord_less_rat B5) X2))) (=> (@ P A3) (@ P (@ (@ tptp.insert_rat B5) A3)))))) (@ P A2))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_num) (P (-> tptp.set_num Bool))) (=> (@ tptp.finite_finite_num A2) (=> (@ P tptp.bot_bot_set_num) (=> (forall ((B5 tptp.num) (A3 tptp.set_num)) (=> (@ tptp.finite_finite_num A3) (=> (forall ((X2 tptp.num)) (=> (@ (@ tptp.member_num X2) A3) (@ (@ tptp.ord_less_num B5) X2))) (=> (@ P A3) (@ P (@ (@ tptp.insert_num B5) A3)))))) (@ P A2))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B5 tptp.nat) (A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (=> (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A3) (@ (@ tptp.ord_less_nat B5) X2))) (=> (@ P A3) (@ P (@ (@ tptp.insert_nat B5) A3)))))) (@ P A2))))))
% 5.98/6.26 (assert (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B5 tptp.int) (A3 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (=> (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A3) (@ (@ tptp.ord_less_int B5) X2))) (=> (@ P A3) (@ P (@ (@ tptp.insert_int B5) A3)))))) (@ P A2))))))
% 5.98/6.26 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A)))))))
% 5.98/6.26 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A)))))))
% 5.98/6.26 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) A)))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) A))))))
% 5.98/6.26 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B))))))
% 5.98/6.26 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B))))))
% 5.98/6.26 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A) B))))))
% 5.98/6.26 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B))))))
% 5.98/6.26 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D))))))))
% 5.98/6.26 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))))))
% 5.98/6.26 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D))))))))
% 5.98/6.26 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D))))))))
% 5.98/6.26 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)))))))
% 5.98/6.26 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 5.98/6.26 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A)))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A) B)))))
% 5.98/6.27 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D)))))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D)))))))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A))))))
% 5.98/6.27 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real B) A))))))
% 5.98/6.27 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 5.98/6.27 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int B) A))))))
% 5.98/6.27 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))))
% 5.98/6.27 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 5.98/6.27 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B))))))
% 5.98/6.27 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B))))))
% 5.98/6.27 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 5.98/6.27 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A) B))))))
% 5.98/6.27 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 5.98/6.27 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D))))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D))))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D))))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D))))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D))))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D))))))))
% 5.98/6.27 (assert (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))))
% 5.98/6.27 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))))
% 5.98/6.27 (assert (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))))
% 5.98/6.27 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat))) B))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real))) B))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Y) X)) X)))))))
% 5.98/6.27 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Y) X)) X)))))))
% 5.98/6.27 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y) X)) X)))))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Y)) X)))))))
% 5.98/6.27 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X) Y)) X)))))))
% 5.98/6.27 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Y)) X)))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_eq_real B) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.one_one_real))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.one_one_rat))))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.one_one_nat))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.one_one_int))))))
% 5.98/6.27 (assert (forall ((C tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) A)))))
% 5.98/6.27 (assert (forall ((C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) A)))))
% 5.98/6.27 (assert (forall ((C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) A)))))
% 5.98/6.27 (assert (forall ((C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) A)))))
% 5.98/6.27 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))))
% 5.98/6.27 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 5.98/6.27 (assert (forall ((F2 tptp.set_set_nat) (A2 tptp.set_set_nat) (P (-> tptp.set_set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat F2) (=> (@ (@ tptp.ord_le6893508408891458716et_nat F2) A2) (=> (@ P tptp.bot_bot_set_set_nat) (=> (forall ((A5 tptp.set_nat) (F3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat A5))) (=> (@ tptp.finite1152437895449049373et_nat F3) (=> (@ _let_1 A2) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_set_nat A5) F3)))))))) (@ P F2)))))))
% 5.98/6.27 (assert (forall ((F2 tptp.set_set_nat_rat) (A2 tptp.set_set_nat_rat) (P (-> tptp.set_set_nat_rat Bool))) (=> (@ tptp.finite6430367030675640852at_rat F2) (=> (@ (@ tptp.ord_le4375437777232675859at_rat F2) A2) (=> (@ P tptp.bot_bo6797373522285170759at_rat) (=> (forall ((A5 tptp.set_nat_rat) (F3 tptp.set_set_nat_rat)) (let ((_let_1 (@ tptp.member_set_nat_rat A5))) (=> (@ tptp.finite6430367030675640852at_rat F3) (=> (@ _let_1 A2) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_set_nat_rat A5) F3)))))))) (@ P F2)))))))
% 5.98/6.27 (assert (forall ((F2 tptp.set_complex) (A2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex F2) (=> (@ (@ tptp.ord_le211207098394363844omplex F2) A2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((A5 tptp.complex) (F3 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex A5))) (=> (@ tptp.finite3207457112153483333omplex F3) (=> (@ _let_1 A2) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_complex A5) F3)))))))) (@ P F2)))))))
% 5.98/6.27 (assert (forall ((F2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat F2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat F2) A2) (=> (@ P tptp.bot_bo2099793752762293965at_nat) (=> (forall ((A5 tptp.product_prod_nat_nat) (F3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A5))) (=> (@ tptp.finite6177210948735845034at_nat F3) (=> (@ _let_1 A2) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert8211810215607154385at_nat A5) F3)))))))) (@ P F2)))))))
% 5.98/6.27 (assert (forall ((F2 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat F2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat F2) A2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((A5 tptp.extended_enat) (F3 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat A5))) (=> (@ tptp.finite4001608067531595151d_enat F3) (=> (@ _let_1 A2) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_Extended_enat A5) F3)))))))) (@ P F2)))))))
% 5.98/6.27 (assert (forall ((F2 tptp.set_real) (A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real F2) (=> (@ (@ tptp.ord_less_eq_set_real F2) A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((A5 tptp.real) (F3 tptp.set_real)) (let ((_let_1 (@ tptp.member_real A5))) (=> (@ tptp.finite_finite_real F3) (=> (@ _let_1 A2) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_real A5) F3)))))))) (@ P F2)))))))
% 5.98/6.27 (assert (forall ((F2 tptp.set_o) (A2 tptp.set_o) (P (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o F2) (=> (@ (@ tptp.ord_less_eq_set_o F2) A2) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((A5 Bool) (F3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o A5))) (=> (@ tptp.finite_finite_o F3) (=> (@ _let_1 A2) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_o A5) F3)))))))) (@ P F2)))))))
% 5.98/6.27 (assert (forall ((F2 tptp.set_nat) (A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F2) (=> (@ (@ tptp.ord_less_eq_set_nat F2) A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A5 tptp.nat) (F3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A5))) (=> (@ tptp.finite_finite_nat F3) (=> (@ _let_1 A2) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_nat A5) F3)))))))) (@ P F2)))))))
% 5.98/6.27 (assert (forall ((F2 tptp.set_int) (A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F2) (=> (@ (@ tptp.ord_less_eq_set_int F2) A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((A5 tptp.int) (F3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A5))) (=> (@ tptp.finite_finite_int F3) (=> (@ _let_1 A2) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_int A5) F3)))))))) (@ P F2)))))))
% 5.98/6.27 (assert (forall ((F2 tptp.set_set_nat) (A2 tptp.set_set_nat) (P (-> tptp.set_set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat F2) (=> (@ (@ tptp.ord_le6893508408891458716et_nat F2) A2) (=> (@ P tptp.bot_bot_set_set_nat) (=> (forall ((A5 tptp.set_nat) (F3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat A5))) (=> (@ tptp.finite1152437895449049373et_nat F3) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_le6893508408891458716et_nat F3) A2) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_set_nat A5) F3))))))))) (@ P F2)))))))
% 5.98/6.27 (assert (forall ((F2 tptp.set_set_nat_rat) (A2 tptp.set_set_nat_rat) (P (-> tptp.set_set_nat_rat Bool))) (=> (@ tptp.finite6430367030675640852at_rat F2) (=> (@ (@ tptp.ord_le4375437777232675859at_rat F2) A2) (=> (@ P tptp.bot_bo6797373522285170759at_rat) (=> (forall ((A5 tptp.set_nat_rat) (F3 tptp.set_set_nat_rat)) (let ((_let_1 (@ tptp.member_set_nat_rat A5))) (=> (@ tptp.finite6430367030675640852at_rat F3) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_le4375437777232675859at_rat F3) A2) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_set_nat_rat A5) F3))))))))) (@ P F2)))))))
% 5.98/6.27 (assert (forall ((F2 tptp.set_complex) (A2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex F2) (=> (@ (@ tptp.ord_le211207098394363844omplex F2) A2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((A5 tptp.complex) (F3 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex A5))) (=> (@ tptp.finite3207457112153483333omplex F3) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_le211207098394363844omplex F3) A2) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_complex A5) F3))))))))) (@ P F2)))))))
% 5.98/6.27 (assert (forall ((F2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat F2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat F2) A2) (=> (@ P tptp.bot_bo2099793752762293965at_nat) (=> (forall ((A5 tptp.product_prod_nat_nat) (F3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A5))) (=> (@ tptp.finite6177210948735845034at_nat F3) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat F3) A2) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert8211810215607154385at_nat A5) F3))))))))) (@ P F2)))))))
% 5.98/6.27 (assert (forall ((F2 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat F2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat F2) A2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((A5 tptp.extended_enat) (F3 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat A5))) (=> (@ tptp.finite4001608067531595151d_enat F3) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat F3) A2) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_Extended_enat A5) F3))))))))) (@ P F2)))))))
% 5.98/6.27 (assert (forall ((F2 tptp.set_real) (A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real F2) (=> (@ (@ tptp.ord_less_eq_set_real F2) A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((A5 tptp.real) (F3 tptp.set_real)) (let ((_let_1 (@ tptp.member_real A5))) (=> (@ tptp.finite_finite_real F3) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_set_real F3) A2) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_real A5) F3))))))))) (@ P F2)))))))
% 5.98/6.27 (assert (forall ((F2 tptp.set_o) (A2 tptp.set_o) (P (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o F2) (=> (@ (@ tptp.ord_less_eq_set_o F2) A2) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((A5 Bool) (F3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o A5))) (=> (@ tptp.finite_finite_o F3) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_set_o F3) A2) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_o A5) F3))))))))) (@ P F2)))))))
% 5.98/6.27 (assert (forall ((F2 tptp.set_nat) (A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F2) (=> (@ (@ tptp.ord_less_eq_set_nat F2) A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A5 tptp.nat) (F3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A5))) (=> (@ tptp.finite_finite_nat F3) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_set_nat F3) A2) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_nat A5) F3))))))))) (@ P F2)))))))
% 5.98/6.27 (assert (forall ((F2 tptp.set_int) (A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F2) (=> (@ (@ tptp.ord_less_eq_set_int F2) A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((A5 tptp.int) (F3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A5))) (=> (@ tptp.finite_finite_int F3) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_set_int F3) A2) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_int A5) F3))))))))) (@ P F2)))))))
% 5.98/6.27 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ _let_1 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> _let_4 (@ (@ tptp.ord_less_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_3) B)) (=> (not _let_2) (@ _let_1 A))))))))))))
% 5.98/6.27 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ _let_1 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) A) (and (=> _let_4 (@ (@ tptp.ord_less_real B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_3) B)) (=> (not _let_2) (@ _let_1 A))))))))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_rat _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_real _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_real B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real))))))))))))
% 5.98/6.27 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 5.98/6.27 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) B)))))
% 5.98/6.27 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 5.98/6.27 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) C))))))
% 5.98/6.27 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 5.98/6.27 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) C))))))
% 5.98/6.27 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 5.98/6.27 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) B)))))
% 5.98/6.27 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat X) (@ (@ tptp.times_times_rat Z) Y)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) Z)))))
% 5.98/6.27 (assert (forall ((Y tptp.real) (X tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real Z) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) Z)))))
% 5.98/6.27 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat Z) Y)) X) (@ (@ tptp.ord_less_rat Z) (@ (@ tptp.divide_divide_rat X) Y))))))
% 5.98/6.27 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real Z) Y)) X) (@ (@ tptp.ord_less_real Z) (@ (@ tptp.divide_divide_real X) Y))))))
% 5.98/6.27 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ _let_2 C) (=> (@ _let_2 (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))))
% 5.98/6.27 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ _let_2 C) (=> (@ _let_2 (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))))
% 5.98/6.27 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.divide_divide_rat B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) Z)) B)) Z))))))))
% 5.98/6.27 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real A) (@ (@ tptp.divide_divide_real B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) Z)) B)) Z))))))))
% 5.98/6.27 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W2) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W2) Y))) (@ (@ tptp.times_times_rat Y) Z)))))))
% 5.98/6.27 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W2) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W2) Y))) (@ (@ tptp.times_times_real Y) Z)))))))
% 5.98/6.27 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.divide_divide_rat Y) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) Y)) Z)))))
% 5.98/6.27 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real Y) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) Y)) Z)))))
% 5.98/6.27 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X) Z)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 5.98/6.27 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Z)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X))))))
% 5.98/6.27 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat Y) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N2)) X))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_real) (X tptp.real)) (let ((_let_1 (@ tptp.finite_card_real A2))) (let ((_let_2 (@ tptp.finite_card_real (@ (@ tptp.insert_real X) A2)))) (let ((_let_3 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_o) (X Bool)) (let ((_let_1 (@ tptp.finite_card_o A2))) (let ((_let_2 (@ tptp.finite_card_o (@ (@ tptp.insert_o X) A2)))) (let ((_let_3 (@ (@ tptp.member_o X) A2))) (=> (@ tptp.finite_finite_o A2) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat_rat) (X tptp.set_nat_rat)) (let ((_let_1 (@ tptp.finite8736671560171388117at_rat A2))) (let ((_let_2 (@ tptp.finite8736671560171388117at_rat (@ (@ tptp.insert_set_nat_rat X) A2)))) (let ((_let_3 (@ (@ tptp.member_set_nat_rat X) A2))) (=> (@ tptp.finite6430367030675640852at_rat A2) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_list_nat) (X tptp.list_nat)) (let ((_let_1 (@ tptp.finite_card_list_nat A2))) (let ((_let_2 (@ tptp.finite_card_list_nat (@ (@ tptp.insert_list_nat X) A2)))) (let ((_let_3 (@ (@ tptp.member_list_nat X) A2))) (=> (@ tptp.finite8100373058378681591st_nat A2) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat) (X tptp.set_nat)) (let ((_let_1 (@ tptp.finite_card_set_nat A2))) (let ((_let_2 (@ tptp.finite_card_set_nat (@ (@ tptp.insert_set_nat X) A2)))) (let ((_let_3 (@ (@ tptp.member_set_nat X) A2))) (=> (@ tptp.finite1152437895449049373et_nat A2) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.finite_card_nat A2))) (let ((_let_2 (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X) A2)))) (let ((_let_3 (@ (@ tptp.member_nat X) A2))) (=> (@ tptp.finite_finite_nat A2) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_int) (X tptp.int)) (let ((_let_1 (@ tptp.finite_card_int A2))) (let ((_let_2 (@ tptp.finite_card_int (@ (@ tptp.insert_int X) A2)))) (let ((_let_3 (@ (@ tptp.member_int X) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_complex) (X tptp.complex)) (let ((_let_1 (@ tptp.finite_card_complex A2))) (let ((_let_2 (@ tptp.finite_card_complex (@ (@ tptp.insert_complex X) A2)))) (let ((_let_3 (@ (@ tptp.member_complex X) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.finite711546835091564841at_nat A2))) (let ((_let_2 (@ tptp.finite711546835091564841at_nat (@ (@ tptp.insert8211810215607154385at_nat X) A2)))) (let ((_let_3 (@ (@ tptp.member8440522571783428010at_nat X) A2))) (=> (@ tptp.finite6177210948735845034at_nat A2) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.finite121521170596916366d_enat A2))) (let ((_let_2 (@ tptp.finite121521170596916366d_enat (@ (@ tptp.insert_Extended_enat X) A2)))) (let ((_let_3 (@ (@ tptp.member_Extended_enat X) A2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_real) (K tptp.nat)) (= (= (@ tptp.finite_card_real A2) (@ tptp.suc K)) (exists ((B4 tptp.real) (B6 tptp.set_real)) (and (= A2 (@ (@ tptp.insert_real B4) B6)) (not (@ (@ tptp.member_real B4) B6)) (= (@ tptp.finite_card_real B6) K) (@ tptp.finite_finite_real B6))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_o) (K tptp.nat)) (= (= (@ tptp.finite_card_o A2) (@ tptp.suc K)) (exists ((B4 Bool) (B6 tptp.set_o)) (and (= A2 (@ (@ tptp.insert_o B4) B6)) (not (@ (@ tptp.member_o B4) B6)) (= (@ tptp.finite_card_o B6) K) (@ tptp.finite_finite_o B6))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat_rat) (K tptp.nat)) (= (= (@ tptp.finite8736671560171388117at_rat A2) (@ tptp.suc K)) (exists ((B4 tptp.set_nat_rat) (B6 tptp.set_set_nat_rat)) (and (= A2 (@ (@ tptp.insert_set_nat_rat B4) B6)) (not (@ (@ tptp.member_set_nat_rat B4) B6)) (= (@ tptp.finite8736671560171388117at_rat B6) K) (@ tptp.finite6430367030675640852at_rat B6))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_list_nat) (K tptp.nat)) (= (= (@ tptp.finite_card_list_nat A2) (@ tptp.suc K)) (exists ((B4 tptp.list_nat) (B6 tptp.set_list_nat)) (and (= A2 (@ (@ tptp.insert_list_nat B4) B6)) (not (@ (@ tptp.member_list_nat B4) B6)) (= (@ tptp.finite_card_list_nat B6) K) (@ tptp.finite8100373058378681591st_nat B6))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat) (K tptp.nat)) (= (= (@ tptp.finite_card_set_nat A2) (@ tptp.suc K)) (exists ((B4 tptp.set_nat) (B6 tptp.set_set_nat)) (and (= A2 (@ (@ tptp.insert_set_nat B4) B6)) (not (@ (@ tptp.member_set_nat B4) B6)) (= (@ tptp.finite_card_set_nat B6) K) (@ tptp.finite1152437895449049373et_nat B6))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_nat) (K tptp.nat)) (= (= (@ tptp.finite_card_nat A2) (@ tptp.suc K)) (exists ((B4 tptp.nat) (B6 tptp.set_nat)) (and (= A2 (@ (@ tptp.insert_nat B4) B6)) (not (@ (@ tptp.member_nat B4) B6)) (= (@ tptp.finite_card_nat B6) K) (@ tptp.finite_finite_nat B6))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_int) (K tptp.nat)) (= (= (@ tptp.finite_card_int A2) (@ tptp.suc K)) (exists ((B4 tptp.int) (B6 tptp.set_int)) (and (= A2 (@ (@ tptp.insert_int B4) B6)) (not (@ (@ tptp.member_int B4) B6)) (= (@ tptp.finite_card_int B6) K) (@ tptp.finite_finite_int B6))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_complex) (K tptp.nat)) (= (= (@ tptp.finite_card_complex A2) (@ tptp.suc K)) (exists ((B4 tptp.complex) (B6 tptp.set_complex)) (and (= A2 (@ (@ tptp.insert_complex B4) B6)) (not (@ (@ tptp.member_complex B4) B6)) (= (@ tptp.finite_card_complex B6) K) (@ tptp.finite3207457112153483333omplex B6))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (K tptp.nat)) (= (= (@ tptp.finite711546835091564841at_nat A2) (@ tptp.suc K)) (exists ((B4 tptp.product_prod_nat_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (and (= A2 (@ (@ tptp.insert8211810215607154385at_nat B4) B6)) (not (@ (@ tptp.member8440522571783428010at_nat B4) B6)) (= (@ tptp.finite711546835091564841at_nat B6) K) (@ tptp.finite6177210948735845034at_nat B6))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Extended_enat) (K tptp.nat)) (= (= (@ tptp.finite121521170596916366d_enat A2) (@ tptp.suc K)) (exists ((B4 tptp.extended_enat) (B6 tptp.set_Extended_enat)) (and (= A2 (@ (@ tptp.insert_Extended_enat B4) B6)) (not (@ (@ tptp.member_Extended_enat B4) B6)) (= (@ tptp.finite121521170596916366d_enat B6) K) (@ tptp.finite4001608067531595151d_enat B6))))))
% 5.98/6.27 (assert (forall ((S2 tptp.set_complex) (A tptp.complex)) (=> (not (@ tptp.finite3207457112153483333omplex S2)) (not (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex S2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex)))))))
% 5.98/6.27 (assert (forall ((S2 tptp.set_Pr1261947904930325089at_nat) (A tptp.product_prod_nat_nat)) (=> (not (@ tptp.finite6177210948735845034at_nat S2)) (not (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.minus_1356011639430497352at_nat S2) (@ (@ tptp.insert8211810215607154385at_nat A) tptp.bot_bo2099793752762293965at_nat)))))))
% 5.98/6.27 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat)) (=> (not (@ tptp.finite4001608067531595151d_enat S2)) (not (@ tptp.finite4001608067531595151d_enat (@ (@ tptp.minus_925952699566721837d_enat S2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat)))))))
% 5.98/6.27 (assert (forall ((S2 tptp.set_real) (A tptp.real)) (=> (not (@ tptp.finite_finite_real S2)) (not (@ tptp.finite_finite_real (@ (@ tptp.minus_minus_set_real S2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real)))))))
% 5.98/6.27 (assert (forall ((S2 tptp.set_o) (A Bool)) (=> (not (@ tptp.finite_finite_o S2)) (not (@ tptp.finite_finite_o (@ (@ tptp.minus_minus_set_o S2) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o)))))))
% 5.98/6.27 (assert (forall ((S2 tptp.set_int) (A tptp.int)) (=> (not (@ tptp.finite_finite_int S2)) (not (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_set_int S2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int)))))))
% 5.98/6.27 (assert (forall ((S2 tptp.set_nat) (A tptp.nat)) (=> (not (@ tptp.finite_finite_nat S2)) (not (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat S2) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat)))))))
% 5.98/6.27 (assert (forall ((X5 (-> tptp.set_complex Bool)) (A2 tptp.set_complex)) (=> (@ X5 A2) (=> (forall ((A3 tptp.set_complex)) (=> (@ X5 A3) (exists ((X2 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_811609699411566653omplex A3) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex)))) (and (@ (@ tptp.member_complex X2) A3) (or (@ X5 _let_1) (not (@ tptp.finite3207457112153483333omplex _let_1)))))))) (not (@ tptp.finite3207457112153483333omplex A2))))))
% 5.98/6.27 (assert (forall ((X5 (-> tptp.set_Pr1261947904930325089at_nat Bool)) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ X5 A2) (=> (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ X5 A3) (exists ((X2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.minus_1356011639430497352at_nat A3) (@ (@ tptp.insert8211810215607154385at_nat X2) tptp.bot_bo2099793752762293965at_nat)))) (and (@ (@ tptp.member8440522571783428010at_nat X2) A3) (or (@ X5 _let_1) (not (@ tptp.finite6177210948735845034at_nat _let_1)))))))) (not (@ tptp.finite6177210948735845034at_nat A2))))))
% 5.98/6.27 (assert (forall ((X5 (-> tptp.set_Extended_enat Bool)) (A2 tptp.set_Extended_enat)) (=> (@ X5 A2) (=> (forall ((A3 tptp.set_Extended_enat)) (=> (@ X5 A3) (exists ((X2 tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) (@ (@ tptp.insert_Extended_enat X2) tptp.bot_bo7653980558646680370d_enat)))) (and (@ (@ tptp.member_Extended_enat X2) A3) (or (@ X5 _let_1) (not (@ tptp.finite4001608067531595151d_enat _let_1)))))))) (not (@ tptp.finite4001608067531595151d_enat A2))))))
% 5.98/6.27 (assert (forall ((X5 (-> tptp.set_real Bool)) (A2 tptp.set_real)) (=> (@ X5 A2) (=> (forall ((A3 tptp.set_real)) (=> (@ X5 A3) (exists ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_set_real A3) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real)))) (and (@ (@ tptp.member_real X2) A3) (or (@ X5 _let_1) (not (@ tptp.finite_finite_real _let_1)))))))) (not (@ tptp.finite_finite_real A2))))))
% 5.98/6.27 (assert (forall ((X5 (-> tptp.set_o Bool)) (A2 tptp.set_o)) (=> (@ X5 A2) (=> (forall ((A3 tptp.set_o)) (=> (@ X5 A3) (exists ((X2 Bool)) (let ((_let_1 (@ (@ tptp.minus_minus_set_o A3) (@ (@ tptp.insert_o X2) tptp.bot_bot_set_o)))) (and (@ (@ tptp.member_o X2) A3) (or (@ X5 _let_1) (not (@ tptp.finite_finite_o _let_1)))))))) (not (@ tptp.finite_finite_o A2))))))
% 5.98/6.27 (assert (forall ((X5 (-> tptp.set_int Bool)) (A2 tptp.set_int)) (=> (@ X5 A2) (=> (forall ((A3 tptp.set_int)) (=> (@ X5 A3) (exists ((X2 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_set_int A3) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int)))) (and (@ (@ tptp.member_int X2) A3) (or (@ X5 _let_1) (not (@ tptp.finite_finite_int _let_1)))))))) (not (@ tptp.finite_finite_int A2))))))
% 5.98/6.27 (assert (forall ((X5 (-> tptp.set_nat Bool)) (A2 tptp.set_nat)) (=> (@ X5 A2) (=> (forall ((A3 tptp.set_nat)) (=> (@ X5 A3) (exists ((X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A3) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat)))) (and (@ (@ tptp.member_nat X2) A3) (or (@ X5 _let_1) (not (@ tptp.finite_finite_nat _let_1)))))))) (not (@ tptp.finite_finite_nat A2))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat) (P (-> tptp.set_set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ P A2) (=> (forall ((A5 tptp.set_nat) (A3 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A3) (=> (@ (@ tptp.member_set_nat A5) A3) (=> (@ P A3) (@ P (@ (@ tptp.minus_2163939370556025621et_nat A3) (@ (@ tptp.insert_set_nat A5) tptp.bot_bot_set_set_nat))))))) (@ P tptp.bot_bot_set_set_nat))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat_rat) (P (-> tptp.set_set_nat_rat Bool))) (=> (@ tptp.finite6430367030675640852at_rat A2) (=> (@ P A2) (=> (forall ((A5 tptp.set_nat_rat) (A3 tptp.set_set_nat_rat)) (=> (@ tptp.finite6430367030675640852at_rat A3) (=> (@ (@ tptp.member_set_nat_rat A5) A3) (=> (@ P A3) (@ P (@ (@ tptp.minus_1626877696091177228at_rat A3) (@ (@ tptp.insert_set_nat_rat A5) tptp.bot_bo6797373522285170759at_rat))))))) (@ P tptp.bot_bo6797373522285170759at_rat))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ P A2) (=> (forall ((A5 tptp.complex) (A3 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (@ (@ tptp.member_complex A5) A3) (=> (@ P A3) (@ P (@ (@ tptp.minus_811609699411566653omplex A3) (@ (@ tptp.insert_complex A5) tptp.bot_bot_set_complex))))))) (@ P tptp.bot_bot_set_complex))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat A2) (=> (@ P A2) (=> (forall ((A5 tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (@ (@ tptp.member8440522571783428010at_nat A5) A3) (=> (@ P A3) (@ P (@ (@ tptp.minus_1356011639430497352at_nat A3) (@ (@ tptp.insert8211810215607154385at_nat A5) tptp.bot_bo2099793752762293965at_nat))))))) (@ P tptp.bot_bo2099793752762293965at_nat))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ P A2) (=> (forall ((A5 tptp.extended_enat) (A3 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (@ (@ tptp.member_Extended_enat A5) A3) (=> (@ P A3) (@ P (@ (@ tptp.minus_925952699566721837d_enat A3) (@ (@ tptp.insert_Extended_enat A5) tptp.bot_bo7653980558646680370d_enat))))))) (@ P tptp.bot_bo7653980558646680370d_enat))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ P A2) (=> (forall ((A5 tptp.real) (A3 tptp.set_real)) (=> (@ tptp.finite_finite_real A3) (=> (@ (@ tptp.member_real A5) A3) (=> (@ P A3) (@ P (@ (@ tptp.minus_minus_set_real A3) (@ (@ tptp.insert_real A5) tptp.bot_bot_set_real))))))) (@ P tptp.bot_bot_set_real))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_o) (P (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o A2) (=> (@ P A2) (=> (forall ((A5 Bool) (A3 tptp.set_o)) (=> (@ tptp.finite_finite_o A3) (=> (@ (@ tptp.member_o A5) A3) (=> (@ P A3) (@ P (@ (@ tptp.minus_minus_set_o A3) (@ (@ tptp.insert_o A5) tptp.bot_bot_set_o))))))) (@ P tptp.bot_bot_set_o))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ P A2) (=> (forall ((A5 tptp.int) (A3 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (=> (@ (@ tptp.member_int A5) A3) (=> (@ P A3) (@ P (@ (@ tptp.minus_minus_set_int A3) (@ (@ tptp.insert_int A5) tptp.bot_bot_set_int))))))) (@ P tptp.bot_bot_set_int))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ P A2) (=> (forall ((A5 tptp.nat) (A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (=> (@ (@ tptp.member_nat A5) A3) (=> (@ P A3) (@ P (@ (@ tptp.minus_minus_set_nat A3) (@ (@ tptp.insert_nat A5) tptp.bot_bot_set_nat))))))) (@ P tptp.bot_bot_set_nat))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) B2) (@ (@ tptp.ord_le3146513528884898305at_nat A2) (@ _let_1 B2))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_real) (X tptp.real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X))) (=> (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))) B2) (@ (@ tptp.ord_less_eq_set_real A2) (@ _let_1 B2))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_o) (X Bool) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o X))) (=> (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.minus_minus_set_o A2) (@ _let_1 tptp.bot_bot_set_o))) B2) (@ (@ tptp.ord_less_eq_set_o A2) (@ _let_1 B2))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_1 tptp.bot_bot_set_nat))) B2) (@ (@ tptp.ord_less_eq_set_nat A2) (@ _let_1 B2))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_int) (X tptp.int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))) B2) (@ (@ tptp.ord_less_eq_set_int A2) (@ _let_1 B2))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A2))) (let ((_let_2 (@ (@ tptp.member8440522571783428010at_nat X) A2))) (let ((_let_3 (@ tptp.insert8211810215607154385at_nat X))) (= (@ _let_1 (@ _let_3 B2)) (and (=> _let_2 (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ _let_3 tptp.bot_bo2099793752762293965at_nat))) B2)) (=> (not _let_2) (@ _let_1 B2)))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat) (X tptp.set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.ord_le6893508408891458716et_nat A2))) (let ((_let_2 (@ (@ tptp.member_set_nat X) A2))) (let ((_let_3 (@ tptp.insert_set_nat X))) (= (@ _let_1 (@ _let_3 B2)) (and (=> _let_2 (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.minus_2163939370556025621et_nat A2) (@ _let_3 tptp.bot_bot_set_set_nat))) B2)) (=> (not _let_2) (@ _let_1 B2)))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat_rat) (X tptp.set_nat_rat) (B2 tptp.set_set_nat_rat)) (let ((_let_1 (@ tptp.ord_le4375437777232675859at_rat A2))) (let ((_let_2 (@ (@ tptp.member_set_nat_rat X) A2))) (let ((_let_3 (@ tptp.insert_set_nat_rat X))) (= (@ _let_1 (@ _let_3 B2)) (and (=> _let_2 (@ (@ tptp.ord_le4375437777232675859at_rat (@ (@ tptp.minus_1626877696091177228at_rat A2) (@ _let_3 tptp.bot_bo6797373522285170759at_rat))) B2)) (=> (not _let_2) (@ _let_1 B2)))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_real) (X tptp.real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A2))) (let ((_let_2 (@ (@ tptp.member_real X) A2))) (let ((_let_3 (@ tptp.insert_real X))) (= (@ _let_1 (@ _let_3 B2)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_3 tptp.bot_bot_set_real))) B2)) (=> (not _let_2) (@ _let_1 B2)))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_o) (X Bool) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.ord_less_eq_set_o A2))) (let ((_let_2 (@ (@ tptp.member_o X) A2))) (let ((_let_3 (@ tptp.insert_o X))) (= (@ _let_1 (@ _let_3 B2)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.minus_minus_set_o A2) (@ _let_3 tptp.bot_bot_set_o))) B2)) (=> (not _let_2) (@ _let_1 B2)))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (let ((_let_2 (@ (@ tptp.member_nat X) A2))) (let ((_let_3 (@ tptp.insert_nat X))) (= (@ _let_1 (@ _let_3 B2)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_3 tptp.bot_bot_set_nat))) B2)) (=> (not _let_2) (@ _let_1 B2)))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_int) (X tptp.int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (let ((_let_2 (@ (@ tptp.member_int X) A2))) (let ((_let_3 (@ tptp.insert_int X))) (= (@ _let_1 (@ _let_3 B2)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_3 tptp.bot_bot_set_int))) B2)) (=> (not _let_2) (@ _let_1 B2)))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (=> (= (@ tptp.finite711546835091564841at_nat A2) tptp.one_one_nat) (not (forall ((X4 tptp.product_prod_nat_nat)) (not (= A2 (@ (@ tptp.insert8211810215607154385at_nat X4) tptp.bot_bo2099793752762293965at_nat))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_complex)) (=> (= (@ tptp.finite_card_complex A2) tptp.one_one_nat) (not (forall ((X4 tptp.complex)) (not (= A2 (@ (@ tptp.insert_complex X4) tptp.bot_bot_set_complex))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_list_nat)) (=> (= (@ tptp.finite_card_list_nat A2) tptp.one_one_nat) (not (forall ((X4 tptp.list_nat)) (not (= A2 (@ (@ tptp.insert_list_nat X4) tptp.bot_bot_set_list_nat))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat)) (=> (= (@ tptp.finite_card_set_nat A2) tptp.one_one_nat) (not (forall ((X4 tptp.set_nat)) (not (= A2 (@ (@ tptp.insert_set_nat X4) tptp.bot_bot_set_set_nat))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_real)) (=> (= (@ tptp.finite_card_real A2) tptp.one_one_nat) (not (forall ((X4 tptp.real)) (not (= A2 (@ (@ tptp.insert_real X4) tptp.bot_bot_set_real))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_o)) (=> (= (@ tptp.finite_card_o A2) tptp.one_one_nat) (not (forall ((X4 Bool)) (not (= A2 (@ (@ tptp.insert_o X4) tptp.bot_bot_set_o))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_nat)) (=> (= (@ tptp.finite_card_nat A2) tptp.one_one_nat) (not (forall ((X4 tptp.nat)) (not (= A2 (@ (@ tptp.insert_nat X4) tptp.bot_bot_set_nat))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_int)) (=> (= (@ tptp.finite_card_int A2) tptp.one_one_nat) (not (forall ((X4 tptp.int)) (not (= A2 (@ (@ tptp.insert_int X4) tptp.bot_bot_set_int))))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N) (=> (@ _let_1 M2) (@ _let_1 (@ (@ tptp.times_times_nat M2) N)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M2) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat M2) N))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M2) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat N) M2))))))
% 5.98/6.27 (assert (forall ((Q4 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q4) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M2) Q4)) N) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.times_times_nat N) Q4))))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (assert (forall ((W2 tptp.int) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W2))) (= (= (@ tptp.nat2 W2) M2) (and (=> _let_1 (= W2 (@ tptp.semiri1314217659103216013at_int M2))) (=> (not _let_1) (= M2 tptp.zero_zero_nat)))))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (W2 tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W2))) (= (= M2 (@ tptp.nat2 W2)) (and (=> _let_1 (= W2 (@ tptp.semiri1314217659103216013at_int M2))) (=> (not _let_1) (= M2 tptp.zero_zero_nat)))))))
% 5.98/6.27 (assert (forall ((P (-> tptp.nat Bool)) (I tptp.int)) (= (@ P (@ tptp.nat2 I)) (and (forall ((N4 tptp.nat)) (=> (= I (@ tptp.semiri1314217659103216013at_int N4)) (@ P N4))) (=> (@ (@ tptp.ord_less_int I) tptp.zero_zero_int) (@ P tptp.zero_zero_nat))))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))))
% 5.98/6.27 (assert (forall ((Z6 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z6) (=> (@ (@ tptp.ord_less_eq_int Z6) Z) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int Z) Z6)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z6)))))))
% 5.98/6.27 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X) Y)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))
% 5.98/6.27 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X) Y)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z3) (=> (@ (@ tptp.ord_less_real Z3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z3) X)) Y)))) (@ (@ tptp.ord_less_eq_real X) Y))))
% 5.98/6.27 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (forall ((Z3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z3) (=> (@ (@ tptp.ord_less_rat Z3) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z3) X)) Y)))) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 5.98/6.27 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.times_times_real C) B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.one_one_real))))))
% 5.98/6.27 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat C) B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))))
% 5.98/6.27 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int C) B)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int))))))
% 5.98/6.27 (assert (forall ((C tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real C) A)) C) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A))))))
% 5.98/6.27 (assert (forall ((C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat C) A)) C) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A))))))
% 5.98/6.27 (assert (forall ((C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int C) A)) C) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A))))))
% 5.98/6.27 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.one_one_real))))))
% 5.98/6.27 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))))
% 5.98/6.27 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) C) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) C) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) C) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A))))))
% 5.98/6.27 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real C) (@ (@ tptp.times_times_real C) B)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.one_one_real))))))
% 5.98/6.27 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat C) B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))))
% 5.98/6.27 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int C) B)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.one_one_int))))))
% 5.98/6.27 (assert (forall ((C tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real C) A)) C) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) A))))))
% 5.98/6.27 (assert (forall ((C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat C) A)) C) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A))))))
% 5.98/6.27 (assert (forall ((C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int C) A)) C) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A))))))
% 5.98/6.27 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real C) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.one_one_real))))))
% 5.98/6.27 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))))
% 5.98/6.27 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.one_one_int))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) C) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) A))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) C) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) C) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A))))))
% 5.98/6.27 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.times_times_real A) C))) (let ((_let_3 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) A) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_real _let_2) B)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A)))))))))))
% 5.98/6.27 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.times_times_rat A) C))) (let ((_let_3 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_2) B)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))))))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real))))))))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))))
% 5.98/6.27 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))))
% 5.98/6.27 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 5.98/6.27 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) B)))))
% 5.98/6.27 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 5.98/6.27 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) C))))))
% 5.98/6.27 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 5.98/6.27 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) C))))))
% 5.98/6.27 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 5.98/6.27 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) B)))))
% 5.98/6.27 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 5.98/6.27 (assert (forall ((Y tptp.real) (X tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.times_times_real Z) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) Z)))))
% 5.98/6.27 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.times_times_rat Z) Y)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) Z)))))
% 5.98/6.27 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z) Y)) X) (@ (@ tptp.ord_less_eq_real Z) (@ (@ tptp.divide_divide_real X) Y))))))
% 5.98/6.27 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z) Y)) X) (@ (@ tptp.ord_less_eq_rat Z) (@ (@ tptp.divide_divide_rat X) Y))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 5.98/6.27 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W2) Z)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W2) Y))) (@ (@ tptp.times_times_real Y) Z))) tptp.zero_zero_real))))))
% 5.98/6.27 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W2) Z)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W2) Y))) (@ (@ tptp.times_times_rat Y) Z))) tptp.zero_zero_rat))))))
% 5.98/6.27 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W2) Z)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W2) Y))) (@ (@ tptp.times_times_rat Y) Z))) tptp.zero_zero_rat))))))
% 5.98/6.27 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W2) Z)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W2) Y))) (@ (@ tptp.times_times_real Y) Z))) tptp.zero_zero_real))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (K tptp.nat)) (= (= (@ tptp.finite711546835091564841at_nat A2) (@ tptp.suc K)) (exists ((B4 tptp.product_prod_nat_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (and (= A2 (@ (@ 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)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat_rat) (K tptp.nat)) (= (= (@ tptp.finite8736671560171388117at_rat A2) (@ tptp.suc K)) (exists ((B4 tptp.set_nat_rat) (B6 tptp.set_set_nat_rat)) (and (= A2 (@ (@ tptp.insert_set_nat_rat B4) B6)) (not (@ (@ tptp.member_set_nat_rat B4) B6)) (= (@ tptp.finite8736671560171388117at_rat B6) K) (=> (= K tptp.zero_zero_nat) (= B6 tptp.bot_bo6797373522285170759at_rat)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_complex) (K tptp.nat)) (= (= (@ tptp.finite_card_complex A2) (@ tptp.suc K)) (exists ((B4 tptp.complex) (B6 tptp.set_complex)) (and (= A2 (@ (@ 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)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_list_nat) (K tptp.nat)) (= (= (@ tptp.finite_card_list_nat A2) (@ tptp.suc K)) (exists ((B4 tptp.list_nat) (B6 tptp.set_list_nat)) (and (= A2 (@ (@ 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)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat) (K tptp.nat)) (= (= (@ tptp.finite_card_set_nat A2) (@ tptp.suc K)) (exists ((B4 tptp.set_nat) (B6 tptp.set_set_nat)) (and (= A2 (@ (@ 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)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_real) (K tptp.nat)) (= (= (@ tptp.finite_card_real A2) (@ tptp.suc K)) (exists ((B4 tptp.real) (B6 tptp.set_real)) (and (= A2 (@ (@ 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)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_o) (K tptp.nat)) (= (= (@ tptp.finite_card_o A2) (@ tptp.suc K)) (exists ((B4 Bool) (B6 tptp.set_o)) (and (= A2 (@ (@ 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)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_nat) (K tptp.nat)) (= (= (@ tptp.finite_card_nat A2) (@ tptp.suc K)) (exists ((B4 tptp.nat) (B6 tptp.set_nat)) (and (= A2 (@ (@ 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)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_int) (K tptp.nat)) (= (= (@ tptp.finite_card_int A2) (@ tptp.suc K)) (exists ((B4 tptp.int) (B6 tptp.set_int)) (and (= A2 (@ (@ 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)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (K tptp.nat)) (=> (= (@ tptp.finite711546835091564841at_nat A2) (@ tptp.suc K)) (exists ((B5 tptp.product_prod_nat_nat) (B8 tptp.set_Pr1261947904930325089at_nat)) (and (= A2 (@ (@ tptp.insert8211810215607154385at_nat B5) B8)) (not (@ (@ tptp.member8440522571783428010at_nat B5) B8)) (= (@ tptp.finite711546835091564841at_nat B8) K) (=> (= K tptp.zero_zero_nat) (= B8 tptp.bot_bo2099793752762293965at_nat)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat_rat) (K tptp.nat)) (=> (= (@ tptp.finite8736671560171388117at_rat A2) (@ tptp.suc K)) (exists ((B5 tptp.set_nat_rat) (B8 tptp.set_set_nat_rat)) (and (= A2 (@ (@ tptp.insert_set_nat_rat B5) B8)) (not (@ (@ tptp.member_set_nat_rat B5) B8)) (= (@ tptp.finite8736671560171388117at_rat B8) K) (=> (= K tptp.zero_zero_nat) (= B8 tptp.bot_bo6797373522285170759at_rat)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_complex) (K tptp.nat)) (=> (= (@ tptp.finite_card_complex A2) (@ tptp.suc K)) (exists ((B5 tptp.complex) (B8 tptp.set_complex)) (and (= A2 (@ (@ tptp.insert_complex B5) B8)) (not (@ (@ tptp.member_complex B5) B8)) (= (@ tptp.finite_card_complex B8) K) (=> (= K tptp.zero_zero_nat) (= B8 tptp.bot_bot_set_complex)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_list_nat) (K tptp.nat)) (=> (= (@ tptp.finite_card_list_nat A2) (@ tptp.suc K)) (exists ((B5 tptp.list_nat) (B8 tptp.set_list_nat)) (and (= A2 (@ (@ tptp.insert_list_nat B5) B8)) (not (@ (@ tptp.member_list_nat B5) B8)) (= (@ tptp.finite_card_list_nat B8) K) (=> (= K tptp.zero_zero_nat) (= B8 tptp.bot_bot_set_list_nat)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat) (K tptp.nat)) (=> (= (@ tptp.finite_card_set_nat A2) (@ tptp.suc K)) (exists ((B5 tptp.set_nat) (B8 tptp.set_set_nat)) (and (= A2 (@ (@ tptp.insert_set_nat B5) B8)) (not (@ (@ tptp.member_set_nat B5) B8)) (= (@ tptp.finite_card_set_nat B8) K) (=> (= K tptp.zero_zero_nat) (= B8 tptp.bot_bot_set_set_nat)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_real) (K tptp.nat)) (=> (= (@ tptp.finite_card_real A2) (@ tptp.suc K)) (exists ((B5 tptp.real) (B8 tptp.set_real)) (and (= A2 (@ (@ tptp.insert_real B5) B8)) (not (@ (@ tptp.member_real B5) B8)) (= (@ tptp.finite_card_real B8) K) (=> (= K tptp.zero_zero_nat) (= B8 tptp.bot_bot_set_real)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_o) (K tptp.nat)) (=> (= (@ tptp.finite_card_o A2) (@ tptp.suc K)) (exists ((B5 Bool) (B8 tptp.set_o)) (and (= A2 (@ (@ tptp.insert_o B5) B8)) (not (@ (@ tptp.member_o B5) B8)) (= (@ tptp.finite_card_o B8) K) (=> (= K tptp.zero_zero_nat) (= B8 tptp.bot_bot_set_o)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_nat) (K tptp.nat)) (=> (= (@ tptp.finite_card_nat A2) (@ tptp.suc K)) (exists ((B5 tptp.nat) (B8 tptp.set_nat)) (and (= A2 (@ (@ tptp.insert_nat B5) B8)) (not (@ (@ tptp.member_nat B5) B8)) (= (@ tptp.finite_card_nat B8) K) (=> (= K tptp.zero_zero_nat) (= B8 tptp.bot_bot_set_nat)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_int) (K tptp.nat)) (=> (= (@ tptp.finite_card_int A2) (@ tptp.suc K)) (exists ((B5 tptp.int) (B8 tptp.set_int)) (and (= A2 (@ (@ tptp.insert_int B5) B8)) (not (@ (@ tptp.member_int B5) B8)) (= (@ tptp.finite_card_int B8) K) (=> (= K tptp.zero_zero_nat) (= B8 tptp.bot_bot_set_int)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ tptp.finite711546835091564841at_nat A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X3 tptp.product_prod_nat_nat)) (= A2 (@ (@ tptp.insert8211810215607154385at_nat X3) tptp.bot_bo2099793752762293965at_nat))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_complex)) (= (= (@ tptp.finite_card_complex A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X3 tptp.complex)) (= A2 (@ (@ tptp.insert_complex X3) tptp.bot_bot_set_complex))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_list_nat)) (= (= (@ tptp.finite_card_list_nat A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X3 tptp.list_nat)) (= A2 (@ (@ tptp.insert_list_nat X3) tptp.bot_bot_set_list_nat))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat)) (= (= (@ tptp.finite_card_set_nat A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X3 tptp.set_nat)) (= A2 (@ (@ tptp.insert_set_nat X3) tptp.bot_bot_set_set_nat))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_real)) (= (= (@ tptp.finite_card_real A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X3 tptp.real)) (= A2 (@ (@ tptp.insert_real X3) tptp.bot_bot_set_real))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_o)) (= (= (@ tptp.finite_card_o A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X3 Bool)) (= A2 (@ (@ tptp.insert_o X3) tptp.bot_bot_set_o))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_nat)) (= (= (@ tptp.finite_card_nat A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X3 tptp.nat)) (= A2 (@ (@ tptp.insert_nat X3) tptp.bot_bot_set_nat))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_int)) (= (= (@ tptp.finite_card_int A2) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X3 tptp.int)) (= A2 (@ (@ tptp.insert_int X3) tptp.bot_bot_set_int))))))
% 5.98/6.27 (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 ((A3 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A3) (=> (not (= A3 tptp.bot_bot_set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A3) B2) (=> (forall ((X2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X2) A3) (@ P (@ (@ tptp.minus_2163939370556025621et_nat A3) (@ (@ tptp.insert_set_nat X2) tptp.bot_bot_set_set_nat))))) (@ P A3)))))) _let_1))))))
% 5.98/6.27 (assert (forall ((P (-> tptp.set_set_nat_rat Bool)) (B2 tptp.set_set_nat_rat)) (let ((_let_1 (@ P B2))) (=> (@ P tptp.bot_bo6797373522285170759at_rat) (=> (=> (not (@ tptp.finite6430367030675640852at_rat B2)) _let_1) (=> (forall ((A3 tptp.set_set_nat_rat)) (=> (@ tptp.finite6430367030675640852at_rat A3) (=> (not (= A3 tptp.bot_bo6797373522285170759at_rat)) (=> (@ (@ tptp.ord_le4375437777232675859at_rat A3) B2) (=> (forall ((X2 tptp.set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat X2) A3) (@ P (@ (@ tptp.minus_1626877696091177228at_rat A3) (@ (@ tptp.insert_set_nat_rat X2) tptp.bot_bo6797373522285170759at_rat))))) (@ P A3)))))) _let_1))))))
% 5.98/6.27 (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 ((A3 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (not (= A3 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A3) B2) (=> (forall ((X2 tptp.complex)) (=> (@ (@ tptp.member_complex X2) A3) (@ P (@ (@ tptp.minus_811609699411566653omplex A3) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))) (@ P A3)))))) _let_1))))))
% 5.98/6.27 (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 ((A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (not (= A3 tptp.bot_bo2099793752762293965at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A3) B2) (=> (forall ((X2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X2) A3) (@ P (@ (@ tptp.minus_1356011639430497352at_nat A3) (@ (@ tptp.insert8211810215607154385at_nat X2) tptp.bot_bo2099793752762293965at_nat))))) (@ P A3)))))) _let_1))))))
% 5.98/6.27 (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 ((A3 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (not (= A3 tptp.bot_bo7653980558646680370d_enat)) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A3) B2) (=> (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X2) A3) (@ P (@ (@ tptp.minus_925952699566721837d_enat A3) (@ (@ tptp.insert_Extended_enat X2) tptp.bot_bo7653980558646680370d_enat))))) (@ P A3)))))) _let_1))))))
% 5.98/6.27 (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 ((A3 tptp.set_real)) (=> (@ tptp.finite_finite_real A3) (=> (not (= A3 tptp.bot_bot_set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A3) B2) (=> (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) A3) (@ P (@ (@ tptp.minus_minus_set_real A3) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))))) (@ P A3)))))) _let_1))))))
% 5.98/6.27 (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 ((A3 tptp.set_o)) (=> (@ tptp.finite_finite_o A3) (=> (not (= A3 tptp.bot_bot_set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A3) B2) (=> (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A3) (@ P (@ (@ tptp.minus_minus_set_o A3) (@ (@ tptp.insert_o X2) tptp.bot_bot_set_o))))) (@ P A3)))))) _let_1))))))
% 5.98/6.27 (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 ((A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (=> (not (= A3 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B2) (=> (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A3) (@ P (@ (@ tptp.minus_minus_set_nat A3) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))))) (@ P A3)))))) _let_1))))))
% 5.98/6.27 (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 ((A3 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (=> (not (= A3 tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) B2) (=> (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A3) (@ P (@ (@ tptp.minus_minus_set_int A3) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))))) (@ P A3)))))) _let_1))))))
% 5.98/6.27 (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 ((A3 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A3) (=> (not (= A3 tptp.bot_bot_set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A3) B2) (=> (forall ((X2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X2) A3) (@ P (@ (@ tptp.minus_2163939370556025621et_nat A3) (@ (@ tptp.insert_set_nat X2) tptp.bot_bot_set_set_nat))))) (@ P A3)))))) (@ P B2))))))
% 5.98/6.27 (assert (forall ((B2 tptp.set_set_nat_rat) (P (-> tptp.set_set_nat_rat Bool))) (=> (@ tptp.finite6430367030675640852at_rat B2) (=> (@ P tptp.bot_bo6797373522285170759at_rat) (=> (forall ((A3 tptp.set_set_nat_rat)) (=> (@ tptp.finite6430367030675640852at_rat A3) (=> (not (= A3 tptp.bot_bo6797373522285170759at_rat)) (=> (@ (@ tptp.ord_le4375437777232675859at_rat A3) B2) (=> (forall ((X2 tptp.set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat X2) A3) (@ P (@ (@ tptp.minus_1626877696091177228at_rat A3) (@ (@ tptp.insert_set_nat_rat X2) tptp.bot_bo6797373522285170759at_rat))))) (@ P A3)))))) (@ P B2))))))
% 5.98/6.27 (assert (forall ((B2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((A3 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A3) (=> (not (= A3 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A3) B2) (=> (forall ((X2 tptp.complex)) (=> (@ (@ tptp.member_complex X2) A3) (@ P (@ (@ tptp.minus_811609699411566653omplex A3) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))) (@ P A3)))))) (@ P B2))))))
% 5.98/6.27 (assert (forall ((B2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat B2) (=> (@ P tptp.bot_bo2099793752762293965at_nat) (=> (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (not (= A3 tptp.bot_bo2099793752762293965at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A3) B2) (=> (forall ((X2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X2) A3) (@ P (@ (@ tptp.minus_1356011639430497352at_nat A3) (@ (@ tptp.insert8211810215607154385at_nat X2) tptp.bot_bo2099793752762293965at_nat))))) (@ P A3)))))) (@ P B2))))))
% 5.98/6.27 (assert (forall ((B2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((A3 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (not (= A3 tptp.bot_bo7653980558646680370d_enat)) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A3) B2) (=> (forall ((X2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X2) A3) (@ P (@ (@ tptp.minus_925952699566721837d_enat A3) (@ (@ tptp.insert_Extended_enat X2) tptp.bot_bo7653980558646680370d_enat))))) (@ P A3)))))) (@ P B2))))))
% 5.98/6.27 (assert (forall ((B2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real B2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((A3 tptp.set_real)) (=> (@ tptp.finite_finite_real A3) (=> (not (= A3 tptp.bot_bot_set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A3) B2) (=> (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) A3) (@ P (@ (@ tptp.minus_minus_set_real A3) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))))) (@ P A3)))))) (@ P B2))))))
% 5.98/6.27 (assert (forall ((B2 tptp.set_o) (P (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o B2) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((A3 tptp.set_o)) (=> (@ tptp.finite_finite_o A3) (=> (not (= A3 tptp.bot_bot_set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A3) B2) (=> (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A3) (@ P (@ (@ tptp.minus_minus_set_o A3) (@ (@ tptp.insert_o X2) tptp.bot_bot_set_o))))) (@ P A3)))))) (@ P B2))))))
% 5.98/6.27 (assert (forall ((B2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat B2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (=> (not (= A3 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B2) (=> (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A3) (@ P (@ (@ tptp.minus_minus_set_nat A3) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))))) (@ P A3)))))) (@ P B2))))))
% 5.98/6.27 (assert (forall ((B2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int B2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((A3 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (=> (not (= A3 tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) B2) (=> (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A3) (@ P (@ (@ tptp.minus_minus_set_int A3) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))))) (@ P A3)))))) (@ P B2))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (A2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite_card_real A2)) (exists ((A4 tptp.real) (B6 tptp.set_real)) (and (= A2 (@ (@ 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))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (A2 tptp.set_o)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite_card_o A2)) (exists ((A4 Bool) (B6 tptp.set_o)) (and (= A2 (@ (@ 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))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (A2 tptp.set_set_nat_rat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite8736671560171388117at_rat A2)) (exists ((A4 tptp.set_nat_rat) (B6 tptp.set_set_nat_rat)) (and (= A2 (@ (@ tptp.insert_set_nat_rat A4) B6)) (not (@ (@ tptp.member_set_nat_rat A4) B6)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.finite8736671560171388117at_rat B6)) (@ tptp.finite6430367030675640852at_rat B6))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (A2 tptp.set_list_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite_card_list_nat A2)) (exists ((A4 tptp.list_nat) (B6 tptp.set_list_nat)) (and (= A2 (@ (@ 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))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (A2 tptp.set_set_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite_card_set_nat A2)) (exists ((A4 tptp.set_nat) (B6 tptp.set_set_nat)) (and (= A2 (@ (@ 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))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite_card_nat A2)) (exists ((A4 tptp.nat) (B6 tptp.set_nat)) (and (= A2 (@ (@ 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))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite_card_int A2)) (exists ((A4 tptp.int) (B6 tptp.set_int)) (and (= A2 (@ (@ 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))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (A2 tptp.set_complex)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite_card_complex A2)) (exists ((A4 tptp.complex) (B6 tptp.set_complex)) (and (= A2 (@ (@ 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))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite711546835091564841at_nat A2)) (exists ((A4 tptp.product_prod_nat_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (and (= A2 (@ (@ 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))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (A2 tptp.set_Extended_enat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.finite121521170596916366d_enat A2)) (exists ((A4 tptp.extended_enat) (B6 tptp.set_Extended_enat)) (and (= A2 (@ (@ 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))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat)))) (@ tptp.finite711546835091564841at_nat A2))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_complex) (X tptp.complex)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex)))) (@ tptp.finite_card_complex A2))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_list_nat) (X tptp.list_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A2) (@ (@ tptp.insert_list_nat X) tptp.bot_bot_set_list_nat)))) (@ tptp.finite_card_list_nat A2))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat) (X tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A2) (@ (@ tptp.insert_set_nat X) tptp.bot_bot_set_set_nat)))) (@ tptp.finite_card_set_nat A2))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_real) (X tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_real (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real)))) (@ tptp.finite_card_real A2))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_o) (X Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o (@ (@ tptp.minus_minus_set_o A2) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)))) (@ tptp.finite_card_o A2))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_int) (X tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))) (@ tptp.finite_card_int A2))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))) (@ tptp.finite_card_nat A2))))
% 5.98/6.27 (assert (forall ((S2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((T4 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex T4) S2) (=> (@ P T4) (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) (@ (@ tptp.minus_811609699411566653omplex S2) T4)) (@ P (@ (@ tptp.insert_complex X2) T4))))))) (@ P S2))))))
% 5.98/6.27 (assert (forall ((S2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat S2) (=> (@ P tptp.bot_bo2099793752762293965at_nat) (=> (forall ((T4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat T4) S2) (=> (@ P T4) (exists ((X2 tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat X2) (@ (@ tptp.minus_1356011639430497352at_nat S2) T4)) (@ P (@ (@ tptp.insert8211810215607154385at_nat X2) T4))))))) (@ P S2))))))
% 5.98/6.27 (assert (forall ((S2 tptp.set_Extended_enat) (P (-> tptp.set_Extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (@ P tptp.bot_bo7653980558646680370d_enat) (=> (forall ((T4 tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le2529575680413868914d_enat T4) S2) (=> (@ P T4) (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X2) (@ (@ tptp.minus_925952699566721837d_enat S2) T4)) (@ P (@ (@ tptp.insert_Extended_enat X2) T4))))))) (@ P S2))))))
% 5.98/6.27 (assert (forall ((S2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real S2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((T4 tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real T4) S2) (=> (@ P T4) (exists ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) (@ (@ tptp.minus_minus_set_real S2) T4)) (@ P (@ (@ tptp.insert_real X2) T4))))))) (@ P S2))))))
% 5.98/6.27 (assert (forall ((S2 tptp.set_o) (P (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o S2) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((T4 tptp.set_o)) (=> (@ (@ tptp.ord_less_set_o T4) S2) (=> (@ P T4) (exists ((X2 Bool)) (and (@ (@ tptp.member_o X2) (@ (@ tptp.minus_minus_set_o S2) T4)) (@ P (@ (@ tptp.insert_o X2) T4))))))) (@ P S2))))))
% 5.98/6.27 (assert (forall ((S2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int S2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((T4 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int T4) S2) (=> (@ P T4) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.minus_minus_set_int S2) T4)) (@ P (@ (@ tptp.insert_int X2) T4))))))) (@ P S2))))))
% 5.98/6.27 (assert (forall ((S2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat S2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((T4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat T4) S2) (=> (@ P T4) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.minus_minus_set_nat S2) T4)) (@ P (@ (@ tptp.insert_nat X2) T4))))))) (@ P S2))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert8211810215607154385at_nat X))) (let ((_let_4 (@ _let_1 B2))) (let ((_let_5 (@ tptp.ord_le7866589430770878221at_nat A2))) (= (@ _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 A2) (@ _let_3 tptp.bot_bo2099793752762293965at_nat))) B2)) (=> (not _let_2) (@ (@ tptp.ord_le3146513528884898305at_nat A2) B2)))))))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat) (X tptp.set_nat) (B2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_set_nat X))) (let ((_let_4 (@ _let_1 B2))) (let ((_let_5 (@ tptp.ord_less_set_set_nat A2))) (= (@ _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 A2) (@ _let_3 tptp.bot_bot_set_set_nat))) B2)) (=> (not _let_2) (@ (@ tptp.ord_le6893508408891458716et_nat A2) B2)))))))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat_rat) (X tptp.set_nat_rat) (B2 tptp.set_set_nat_rat)) (let ((_let_1 (@ tptp.member_set_nat_rat X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_set_nat_rat X))) (let ((_let_4 (@ _let_1 B2))) (let ((_let_5 (@ tptp.ord_le1311537459589289991at_rat A2))) (= (@ _let_5 (@ _let_3 B2)) (and (=> _let_4 (@ _let_5 B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le1311537459589289991at_rat (@ (@ tptp.minus_1626877696091177228at_rat A2) (@ _let_3 tptp.bot_bo6797373522285170759at_rat))) B2)) (=> (not _let_2) (@ (@ tptp.ord_le4375437777232675859at_rat A2) B2)))))))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_real) (X tptp.real) (B2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_real X))) (let ((_let_4 (@ _let_1 B2))) (let ((_let_5 (@ tptp.ord_less_set_real A2))) (= (@ _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 A2) (@ _let_3 tptp.bot_bot_set_real))) B2)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_real A2) B2)))))))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_o) (X Bool) (B2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_o X))) (let ((_let_4 (@ _let_1 B2))) (let ((_let_5 (@ tptp.ord_less_set_o A2))) (= (@ _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 A2) (@ _let_3 tptp.bot_bot_set_o))) B2)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_o A2) B2)))))))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (B2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_nat X))) (let ((_let_4 (@ _let_1 B2))) (let ((_let_5 (@ tptp.ord_less_set_nat A2))) (= (@ _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 A2) (@ _let_3 tptp.bot_bot_set_nat))) B2)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_nat A2) B2)))))))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_int) (X tptp.int) (B2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_int X))) (let ((_let_4 (@ _let_1 B2))) (let ((_let_5 (@ tptp.ord_less_set_int A2))) (= (@ _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 A2) (@ _let_3 tptp.bot_bot_set_int))) B2)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_int A2) B2)))))))))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (Q4 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q4)) M2) (=> (@ (@ tptp.ord_less_nat M2) (@ _let_1 (@ tptp.suc Q4))) (= (@ (@ tptp.divide_divide_nat M2) N) Q4))))))
% 5.98/6.27 (assert (forall ((Q4 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q4) (= (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.divide_divide_nat N) Q4)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M2) Q4)) N)))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.archim2898591450579166408c_real X)) (@ tptp.archim2898591450579166408c_real Y)))) (let ((_let_2 (@ tptp.archim2898591450579166408c_real (@ (@ tptp.plus_plus_real X) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_real _let_1) tptp.one_one_real))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)))))))))
% 5.98/6.27 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.archimedean_frac_rat X)) (@ tptp.archimedean_frac_rat Y)))) (let ((_let_2 (@ tptp.archimedean_frac_rat (@ (@ tptp.plus_plus_rat X) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_rat _let_1) tptp.one_one_rat))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)))))))))
% 5.98/6.27 (assert (forall ((W2 tptp.int) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W2) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W2)) M2) (@ (@ tptp.ord_less_int W2) (@ tptp.semiri1314217659103216013at_int M2))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 M2)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M2))) (=> (not (= A tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2))))))))))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M2)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M2))) (=> (not (= A tptp.zero_zero_nat)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2))))))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat_rat) (X tptp.set_nat_rat)) (=> (@ tptp.finite6430367030675640852at_rat A2) (=> (@ (@ tptp.member_set_nat_rat X) A2) (= (@ tptp.finite8736671560171388117at_rat A2) (@ tptp.suc (@ tptp.finite8736671560171388117at_rat (@ (@ tptp.minus_1626877696091177228at_rat A2) (@ (@ tptp.insert_set_nat_rat X) tptp.bot_bo6797373522285170759at_rat)))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_list_nat) (X tptp.list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A2) (=> (@ (@ tptp.member_list_nat X) A2) (= (@ tptp.finite_card_list_nat A2) (@ tptp.suc (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A2) (@ (@ tptp.insert_list_nat X) tptp.bot_bot_set_list_nat)))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat) (X tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ (@ tptp.member_set_nat X) A2) (= (@ tptp.finite_card_set_nat A2) (@ tptp.suc (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A2) (@ (@ tptp.insert_set_nat X) tptp.bot_bot_set_set_nat)))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_complex) (X tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ tptp.finite_card_complex A2) (@ tptp.suc (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex)))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (=> (@ tptp.finite6177210948735845034at_nat A2) (=> (@ (@ tptp.member8440522571783428010at_nat X) A2) (= (@ tptp.finite711546835091564841at_nat A2) (@ tptp.suc (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat)))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat X) A2) (= (@ tptp.finite121521170596916366d_enat A2) (@ tptp.suc (@ tptp.finite121521170596916366d_enat (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat)))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_real) (X tptp.real)) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ tptp.finite_card_real A2) (@ tptp.suc (@ tptp.finite_card_real (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real)))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A2) (=> (@ (@ tptp.member_o X) A2) (= (@ tptp.finite_card_o A2) (@ tptp.suc (@ tptp.finite_card_o (@ (@ tptp.minus_minus_set_o A2) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int X) A2) (= (@ tptp.finite_card_int A2) (@ tptp.suc (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat X) A2) (= (@ tptp.finite_card_nat A2) (@ tptp.suc (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_list_nat) (X tptp.list_nat)) (let ((_let_1 (@ tptp.insert_list_nat X))) (=> (@ tptp.finite8100373058378681591st_nat A2) (= (@ tptp.finite_card_list_nat (@ _let_1 A2)) (@ tptp.suc (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A2) (@ _let_1 tptp.bot_bot_set_list_nat)))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat) (X tptp.set_nat)) (let ((_let_1 (@ tptp.insert_set_nat X))) (=> (@ tptp.finite1152437895449049373et_nat A2) (= (@ tptp.finite_card_set_nat (@ _let_1 A2)) (@ tptp.suc (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A2) (@ _let_1 tptp.bot_bot_set_set_nat)))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_complex) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ tptp.finite_card_complex (@ _let_1 A2)) (@ tptp.suc (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex)))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X))) (=> (@ tptp.finite6177210948735845034at_nat A2) (= (@ tptp.finite711546835091564841at_nat (@ _let_1 A2)) (@ tptp.suc (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ _let_1 tptp.bot_bo2099793752762293965at_nat)))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ tptp.finite121521170596916366d_enat (@ _let_1 A2)) (@ tptp.suc (@ tptp.finite121521170596916366d_enat (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_1 tptp.bot_bo7653980558646680370d_enat)))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_real) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (=> (@ tptp.finite_finite_real A2) (= (@ tptp.finite_card_real (@ _let_1 A2)) (@ tptp.suc (@ tptp.finite_card_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real)))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_o) (X Bool)) (let ((_let_1 (@ tptp.insert_o X))) (=> (@ tptp.finite_finite_o A2) (= (@ tptp.finite_card_o (@ _let_1 A2)) (@ tptp.suc (@ tptp.finite_card_o (@ (@ tptp.minus_minus_set_o A2) (@ _let_1 tptp.bot_bot_set_o)))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_int) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (=> (@ tptp.finite_finite_int A2) (= (@ tptp.finite_card_int (@ _let_1 A2)) (@ tptp.suc (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int)))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.insert_nat X))) (=> (@ tptp.finite_finite_nat A2) (= (@ tptp.finite_card_nat (@ _let_1 A2)) (@ tptp.suc (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_1 tptp.bot_bot_set_nat)))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat_rat) (X tptp.set_nat_rat)) (=> (@ tptp.finite6430367030675640852at_rat A2) (=> (@ (@ tptp.member_set_nat_rat X) A2) (= (@ tptp.suc (@ tptp.finite8736671560171388117at_rat (@ (@ tptp.minus_1626877696091177228at_rat A2) (@ (@ tptp.insert_set_nat_rat X) tptp.bot_bo6797373522285170759at_rat)))) (@ tptp.finite8736671560171388117at_rat A2))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_list_nat) (X tptp.list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A2) (=> (@ (@ tptp.member_list_nat X) A2) (= (@ tptp.suc (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A2) (@ (@ tptp.insert_list_nat X) tptp.bot_bot_set_list_nat)))) (@ tptp.finite_card_list_nat A2))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat) (X tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ (@ tptp.member_set_nat X) A2) (= (@ tptp.suc (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A2) (@ (@ tptp.insert_set_nat X) tptp.bot_bot_set_set_nat)))) (@ tptp.finite_card_set_nat A2))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_complex) (X tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ tptp.suc (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex)))) (@ tptp.finite_card_complex A2))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (=> (@ tptp.finite6177210948735845034at_nat A2) (=> (@ (@ tptp.member8440522571783428010at_nat X) A2) (= (@ tptp.suc (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat)))) (@ tptp.finite711546835091564841at_nat A2))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat X) A2) (= (@ tptp.suc (@ tptp.finite121521170596916366d_enat (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat)))) (@ tptp.finite121521170596916366d_enat A2))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_real) (X tptp.real)) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ tptp.suc (@ tptp.finite_card_real (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real)))) (@ tptp.finite_card_real A2))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A2) (=> (@ (@ tptp.member_o X) A2) (= (@ tptp.suc (@ tptp.finite_card_o (@ (@ tptp.minus_minus_set_o A2) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)))) (@ tptp.finite_card_o A2))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int X) A2) (= (@ tptp.suc (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))) (@ tptp.finite_card_int A2))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat X) A2) (= (@ tptp.suc (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))) (@ tptp.finite_card_nat A2))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat_rat) (X tptp.set_nat_rat)) (= (@ (@ tptp.ord_less_nat (@ tptp.finite8736671560171388117at_rat (@ (@ tptp.minus_1626877696091177228at_rat A2) (@ (@ tptp.insert_set_nat_rat X) tptp.bot_bo6797373522285170759at_rat)))) (@ tptp.finite8736671560171388117at_rat A2)) (and (@ tptp.finite6430367030675640852at_rat A2) (@ (@ tptp.member_set_nat_rat X) A2)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_list_nat) (X tptp.list_nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A2) (@ (@ tptp.insert_list_nat X) tptp.bot_bot_set_list_nat)))) (@ tptp.finite_card_list_nat A2)) (and (@ tptp.finite8100373058378681591st_nat A2) (@ (@ tptp.member_list_nat X) A2)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat) (X tptp.set_nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A2) (@ (@ tptp.insert_set_nat X) tptp.bot_bot_set_set_nat)))) (@ tptp.finite_card_set_nat A2)) (and (@ tptp.finite1152437895449049373et_nat A2) (@ (@ tptp.member_set_nat X) A2)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_complex) (X tptp.complex)) (= (@ (@ tptp.ord_less_nat (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex)))) (@ tptp.finite_card_complex A2)) (and (@ tptp.finite3207457112153483333omplex A2) (@ (@ tptp.member_complex X) A2)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat)))) (@ tptp.finite711546835091564841at_nat A2)) (and (@ tptp.finite6177210948735845034at_nat A2) (@ (@ tptp.member8440522571783428010at_nat X) A2)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat)) (= (@ (@ tptp.ord_less_nat (@ tptp.finite121521170596916366d_enat (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat)))) (@ tptp.finite121521170596916366d_enat A2)) (and (@ tptp.finite4001608067531595151d_enat A2) (@ (@ tptp.member_Extended_enat X) A2)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_real) (X tptp.real)) (= (@ (@ tptp.ord_less_nat (@ tptp.finite_card_real (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real)))) (@ tptp.finite_card_real A2)) (and (@ tptp.finite_finite_real A2) (@ (@ tptp.member_real X) A2)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_o) (X Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.finite_card_o (@ (@ tptp.minus_minus_set_o A2) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)))) (@ tptp.finite_card_o A2)) (and (@ tptp.finite_finite_o A2) (@ (@ tptp.member_o X) A2)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_int) (X tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))) (@ tptp.finite_card_int A2)) (and (@ tptp.finite_finite_int A2) (@ (@ tptp.member_int X) A2)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))) (@ tptp.finite_card_nat A2)) (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat X) A2)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat_rat) (X tptp.set_nat_rat) (Y tptp.set_nat_rat)) (=> (@ tptp.finite6430367030675640852at_rat A2) (=> (@ (@ tptp.member_set_nat_rat X) A2) (=> (@ (@ tptp.member_set_nat_rat Y) A2) (@ (@ tptp.ord_less_nat (@ tptp.finite8736671560171388117at_rat (@ (@ tptp.minus_1626877696091177228at_rat (@ (@ tptp.minus_1626877696091177228at_rat A2) (@ (@ tptp.insert_set_nat_rat X) tptp.bot_bo6797373522285170759at_rat))) (@ (@ tptp.insert_set_nat_rat Y) tptp.bot_bo6797373522285170759at_rat)))) (@ tptp.finite8736671560171388117at_rat A2)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_list_nat) (X tptp.list_nat) (Y tptp.list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A2) (=> (@ (@ tptp.member_list_nat X) A2) (=> (@ (@ tptp.member_list_nat Y) A2) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat (@ (@ tptp.minus_7954133019191499631st_nat A2) (@ (@ tptp.insert_list_nat X) tptp.bot_bot_set_list_nat))) (@ (@ tptp.insert_list_nat Y) tptp.bot_bot_set_list_nat)))) (@ tptp.finite_card_list_nat A2)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat) (X tptp.set_nat) (Y tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ (@ tptp.member_set_nat X) A2) (=> (@ (@ tptp.member_set_nat Y) A2) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat (@ (@ tptp.minus_2163939370556025621et_nat A2) (@ (@ tptp.insert_set_nat X) tptp.bot_bot_set_set_nat))) (@ (@ tptp.insert_set_nat Y) tptp.bot_bot_set_set_nat)))) (@ tptp.finite_card_set_nat A2)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (Y tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (=> (@ (@ tptp.member_complex Y) A2) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))) (@ (@ tptp.insert_complex Y) tptp.bot_bot_set_complex)))) (@ tptp.finite_card_complex A2)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (=> (@ tptp.finite6177210948735845034at_nat A2) (=> (@ (@ tptp.member8440522571783428010at_nat X) A2) (=> (@ (@ tptp.member8440522571783428010at_nat Y) A2) (@ (@ tptp.ord_less_nat (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat))) (@ (@ tptp.insert8211810215607154385at_nat Y) tptp.bot_bo2099793752762293965at_nat)))) (@ tptp.finite711546835091564841at_nat A2)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat X) A2) (=> (@ (@ tptp.member_Extended_enat Y) A2) (@ (@ tptp.ord_less_nat (@ tptp.finite121521170596916366d_enat (@ (@ tptp.minus_925952699566721837d_enat (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat))) (@ (@ tptp.insert_Extended_enat Y) tptp.bot_bo7653980558646680370d_enat)))) (@ tptp.finite121521170596916366d_enat A2)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_real) (X tptp.real) (Y tptp.real)) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (=> (@ (@ tptp.member_real Y) A2) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_real (@ (@ tptp.minus_minus_set_real (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))) (@ (@ tptp.insert_real Y) tptp.bot_bot_set_real)))) (@ tptp.finite_card_real A2)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_o) (X Bool) (Y Bool)) (=> (@ tptp.finite_finite_o A2) (=> (@ (@ tptp.member_o X) A2) (=> (@ (@ tptp.member_o Y) A2) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_o (@ (@ tptp.minus_minus_set_o (@ (@ tptp.minus_minus_set_o A2) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))) (@ (@ tptp.insert_o Y) tptp.bot_bot_set_o)))) (@ tptp.finite_card_o A2)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_int) (X tptp.int) (Y tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int X) A2) (=> (@ (@ tptp.member_int Y) A2) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))) (@ (@ tptp.insert_int Y) tptp.bot_bot_set_int)))) (@ tptp.finite_card_int A2)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (Y tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat X) A2) (=> (@ (@ tptp.member_nat Y) A2) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) (@ (@ tptp.insert_nat Y) tptp.bot_bot_set_nat)))) (@ tptp.finite_card_nat A2)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat_rat) (X tptp.set_nat_rat)) (=> (@ tptp.finite6430367030675640852at_rat A2) (=> (@ (@ tptp.member_set_nat_rat X) A2) (@ (@ tptp.ord_less_nat (@ tptp.finite8736671560171388117at_rat (@ (@ tptp.minus_1626877696091177228at_rat A2) (@ (@ tptp.insert_set_nat_rat X) tptp.bot_bo6797373522285170759at_rat)))) (@ tptp.finite8736671560171388117at_rat A2))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_list_nat) (X tptp.list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A2) (=> (@ (@ tptp.member_list_nat X) A2) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A2) (@ (@ tptp.insert_list_nat X) tptp.bot_bot_set_list_nat)))) (@ tptp.finite_card_list_nat A2))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat) (X tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ (@ tptp.member_set_nat X) A2) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A2) (@ (@ tptp.insert_set_nat X) tptp.bot_bot_set_set_nat)))) (@ tptp.finite_card_set_nat A2))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_complex) (X tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex)))) (@ tptp.finite_card_complex A2))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (=> (@ tptp.finite6177210948735845034at_nat A2) (=> (@ (@ tptp.member8440522571783428010at_nat X) A2) (@ (@ tptp.ord_less_nat (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat)))) (@ tptp.finite711546835091564841at_nat A2))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat X) A2) (@ (@ tptp.ord_less_nat (@ tptp.finite121521170596916366d_enat (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat)))) (@ tptp.finite121521170596916366d_enat A2))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_real) (X tptp.real)) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_real (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real)))) (@ tptp.finite_card_real A2))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A2) (=> (@ (@ tptp.member_o X) A2) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_o (@ (@ tptp.minus_minus_set_o A2) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)))) (@ tptp.finite_card_o A2))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int X) A2) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))) (@ tptp.finite_card_int A2))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat X) A2) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))) (@ tptp.finite_card_nat A2))))))
% 5.98/6.27 (assert (forall ((X tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.finite711546835091564841at_nat A2))) (let ((_let_2 (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat))))) (let ((_let_3 (@ (@ tptp.member8440522571783428010at_nat X) A2))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 5.98/6.27 (assert (forall ((X tptp.set_nat_rat) (A2 tptp.set_set_nat_rat)) (let ((_let_1 (@ tptp.finite8736671560171388117at_rat A2))) (let ((_let_2 (@ tptp.finite8736671560171388117at_rat (@ (@ tptp.minus_1626877696091177228at_rat A2) (@ (@ tptp.insert_set_nat_rat X) tptp.bot_bo6797373522285170759at_rat))))) (let ((_let_3 (@ (@ tptp.member_set_nat_rat X) A2))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 5.98/6.27 (assert (forall ((X tptp.complex) (A2 tptp.set_complex)) (let ((_let_1 (@ tptp.finite_card_complex A2))) (let ((_let_2 (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))) (let ((_let_3 (@ (@ tptp.member_complex X) A2))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 5.98/6.27 (assert (forall ((X tptp.list_nat) (A2 tptp.set_list_nat)) (let ((_let_1 (@ tptp.finite_card_list_nat A2))) (let ((_let_2 (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A2) (@ (@ tptp.insert_list_nat X) tptp.bot_bot_set_list_nat))))) (let ((_let_3 (@ (@ tptp.member_list_nat X) A2))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 5.98/6.27 (assert (forall ((X tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.finite_card_set_nat A2))) (let ((_let_2 (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A2) (@ (@ tptp.insert_set_nat X) tptp.bot_bot_set_set_nat))))) (let ((_let_3 (@ (@ tptp.member_set_nat X) A2))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 5.98/6.27 (assert (forall ((X tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.finite_card_real A2))) (let ((_let_2 (@ tptp.finite_card_real (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))) (let ((_let_3 (@ (@ tptp.member_real X) A2))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 5.98/6.27 (assert (forall ((X Bool) (A2 tptp.set_o)) (let ((_let_1 (@ tptp.finite_card_o A2))) (let ((_let_2 (@ tptp.finite_card_o (@ (@ tptp.minus_minus_set_o A2) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))))) (let ((_let_3 (@ (@ tptp.member_o X) A2))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 5.98/6.27 (assert (forall ((X tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.finite_card_int A2))) (let ((_let_2 (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))) (let ((_let_3 (@ (@ tptp.member_int X) A2))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.finite_card_nat A2))) (let ((_let_2 (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))) (let ((_let_3 (@ (@ tptp.member_nat X) A2))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 5.98/6.27 (assert (forall ((X tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X) A2) (= (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A2) (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat))) (@ (@ tptp.minus_minus_nat (@ tptp.finite711546835091564841at_nat A2)) tptp.one_one_nat)))))
% 5.98/6.27 (assert (forall ((X tptp.set_nat_rat) (A2 tptp.set_set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat X) A2) (= (@ tptp.finite8736671560171388117at_rat (@ (@ tptp.minus_1626877696091177228at_rat A2) (@ (@ tptp.insert_set_nat_rat X) tptp.bot_bo6797373522285170759at_rat))) (@ (@ tptp.minus_minus_nat (@ tptp.finite8736671560171388117at_rat A2)) tptp.one_one_nat)))))
% 5.98/6.27 (assert (forall ((X tptp.complex) (A2 tptp.set_complex)) (=> (@ (@ tptp.member_complex X) A2) (= (@ tptp.finite_card_complex (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_complex A2)) tptp.one_one_nat)))))
% 5.98/6.27 (assert (forall ((X tptp.list_nat) (A2 tptp.set_list_nat)) (=> (@ (@ tptp.member_list_nat X) A2) (= (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A2) (@ (@ tptp.insert_list_nat X) tptp.bot_bot_set_list_nat))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_list_nat A2)) tptp.one_one_nat)))))
% 5.98/6.27 (assert (forall ((X tptp.set_nat) (A2 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat X) A2) (= (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A2) (@ (@ tptp.insert_set_nat X) tptp.bot_bot_set_set_nat))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_set_nat A2)) tptp.one_one_nat)))))
% 5.98/6.27 (assert (forall ((X tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.member_real X) A2) (= (@ tptp.finite_card_real (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_real A2)) tptp.one_one_nat)))))
% 5.98/6.27 (assert (forall ((X Bool) (A2 tptp.set_o)) (=> (@ (@ tptp.member_o X) A2) (= (@ tptp.finite_card_o (@ (@ tptp.minus_minus_set_o A2) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_o A2)) tptp.one_one_nat)))))
% 5.98/6.27 (assert (forall ((X tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.member_int X) A2) (= (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_int A2)) tptp.one_one_nat)))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.member_nat X) A2) (= (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_nat A2)) tptp.one_one_nat)))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat X)) N)) (or (@ _let_1 X) (= N tptp.zero_zero_nat))))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int X)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N tptp.zero_zero_nat)))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real X)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N tptp.zero_zero_nat)))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat X)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N tptp.zero_zero_nat)))))
% 5.98/6.27 (assert (forall ((B tptp.real) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_real B) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))))
% 5.98/6.27 (assert (forall ((B tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_rat B) tptp.one_one_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))))
% 5.98/6.27 (assert (forall ((B tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))))
% 5.98/6.27 (assert (forall ((B tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N)) (or (not (= A tptp.zero_zero_real)) (= N tptp.zero_zero_nat)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N)) (or (not (= A tptp.zero_zero_rat)) (= N tptp.zero_zero_nat)))))
% 5.98/6.27 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N)) (or (not (= A tptp.zero_zero_int)) (= N tptp.zero_zero_nat)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)) (@ (@ tptp.ord_less_eq_real A) B))))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)) (@ (@ tptp.ord_less_eq_rat A) B))))))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (@ (@ tptp.ord_less_eq_nat A) B))))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (@ (@ tptp.ord_less_eq_int A) B))))))))
% 5.98/6.27 (assert (forall ((B tptp.real) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 5.98/6.27 (assert (forall ((B tptp.rat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 5.98/6.27 (assert (forall ((B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 5.98/6.27 (assert (forall ((B tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 5.98/6.27 (assert (forall ((B tptp.real) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_real B) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))))
% 5.98/6.27 (assert (forall ((B tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_rat B) tptp.one_one_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))))
% 5.98/6.27 (assert (forall ((B tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))))
% 5.98/6.27 (assert (forall ((B tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_int (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W2)))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W2)))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W2)))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W2)))))
% 5.98/6.27 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W2)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W2)) X))))
% 5.98/6.27 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W2)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W2)) X))))
% 5.98/6.27 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W2)) (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W2)) X))))
% 5.98/6.27 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W2)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W2)) X))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W2)))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W2)))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W2)))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W2)))))
% 5.98/6.27 (assert (forall ((X tptp.nat)) (=> (forall ((N2 tptp.nat)) (not (= X (@ (@ tptp.plus_plus_nat N2) N2)))) (not (forall ((N2 tptp.nat)) (not (= X (@ (@ tptp.plus_plus_nat N2) (@ tptp.suc N2)))))))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.one_one_rat) N) tptp.one_one_rat)))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N) tptp.one_one_int)))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N) tptp.one_one_nat)))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.one_one_real) N) tptp.one_one_real)))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.one_one_complex) N) tptp.one_one_complex)))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M2))) (= (@ _let_1 (@ tptp.suc N)) (@ tptp.suc (@ _let_1 N))))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat M2) tptp.zero_zero_nat) M2)))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M2) N) tptp.zero_zero_nat) (and (= M2 tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N)))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N)))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.one_one_nat) A)))
% 5.98/6.27 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.one_one_nat) A)))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.one_one_nat) A)))
% 5.98/6.27 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.one_one_nat) A)))
% 5.98/6.27 (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))))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))
% 5.98/6.27 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))
% 5.98/6.27 (assert (forall ((X tptp.int) (Y tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.suc N)) tptp.zero_zero_rat)))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.suc N)) tptp.zero_zero_int)))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.suc N)) tptp.zero_zero_nat)))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.suc N)) tptp.zero_zero_real)))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.suc N)) tptp.zero_zero_complex)))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 5.98/6.27 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 5.98/6.27 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (or (@ _let_1 M2) (@ _let_1 N))))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M2) N))))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.power_power_nat X) M2) _let_1) (or (= M2 tptp.zero_zero_nat) (= X _let_1))))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N) _let_1))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat M2) (@ _let_1 N))))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X) N)) (or (@ _let_1 X) (= N tptp.zero_zero_nat))))))
% 5.98/6.27 (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))))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M2)) (@ _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 M2) N)))))))))
% 5.98/6.27 (assert (forall ((B tptp.real) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 5.98/6.27 (assert (forall ((B tptp.rat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 5.98/6.27 (assert (forall ((B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_nat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 5.98/6.27 (assert (forall ((B tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_rat A) N) tptp.zero_zero_rat) (and (= A tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 5.98/6.27 (assert (forall ((A tptp.int) (N tptp.nat)) (= (= (@ (@ tptp.power_power_int A) N) tptp.zero_zero_int) (and (= A tptp.zero_zero_int) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_nat A) N) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (N tptp.nat)) (= (= (@ (@ tptp.power_power_real A) N) tptp.zero_zero_real) (and (= A tptp.zero_zero_real) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (= (@ (@ tptp.power_power_complex A) N) tptp.zero_zero_complex) (and (= A tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 5.98/6.27 (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))))))
% 5.98/6.27 (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))))))
% 5.98/6.27 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W2)) (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W2)) X))))
% 5.98/6.27 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W2)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W2)) X))))
% 5.98/6.27 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W2)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W2)) X))))
% 5.98/6.27 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W2)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W2)) X))))
% 5.98/6.27 (assert (forall ((A2 tptp.nat) (K tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A2 (@ _let_1 A)) (= (@ tptp.suc A2) (@ _let_1 (@ tptp.suc A)))))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M2)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) N)))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M2)) N) (@ (@ tptp.plus_plus_nat M2) (@ tptp.suc N)))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M2) N) M2) (= N tptp.zero_zero_nat))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N) N)))
% 5.98/6.27 (assert (forall ((K tptp.nat) (L tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L) (=> (= (@ (@ tptp.plus_plus_nat M2) L) (@ (@ tptp.plus_plus_nat K) N)) (@ (@ tptp.ord_less_nat M2) N)))))
% 5.98/6.27 (assert (forall ((I tptp.nat) (J tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M2) J))))))
% 5.98/6.27 (assert (forall ((I tptp.nat) (J tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M2))))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (assert (forall ((J tptp.nat) (I tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I)) I))))
% 5.98/6.27 (assert (forall ((I tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) I))))
% 5.98/6.27 (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))))))
% 5.98/6.27 (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))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.power_power_real X) N2))))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M2) K)) N) (not (=> (@ (@ tptp.ord_less_eq_nat M2) N) (not (@ (@ tptp.ord_less_eq_nat K) N)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M2))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M2) N))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M2) K)) N) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M2) K)) N) (@ (@ tptp.ord_less_eq_nat K) N))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) L) (exists ((N2 tptp.nat)) (= L (@ (@ tptp.plus_plus_nat K) N2))))))
% 5.98/6.27 (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))))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (assert (forall ((I tptp.nat) (J tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M2))))))
% 5.98/6.27 (assert (forall ((I tptp.nat) (J tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M2) J))))))
% 5.98/6.27 (assert (= tptp.ord_less_eq_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (exists ((K3 tptp.nat)) (= N4 (@ (@ tptp.plus_plus_nat M3) K3))))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.minus_minus_nat M2) N)))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) K)) (@ (@ tptp.plus_plus_nat N) K)) (@ (@ tptp.minus_minus_nat M2) N))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M2)) N) M2)))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N)) N) M2)))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat M2) N)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat M2) K)) (@ (@ tptp.times_times_nat N) K)))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.plus_plus_nat (@ _let_1 M2)) (@ _let_1 N))))))
% 5.98/6.27 (assert (forall ((I tptp.nat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N))))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (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))))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M2) N) _let_1) (or (and (= M2 _let_1) (= N tptp.zero_zero_nat)) (and (= M2 tptp.zero_zero_nat) (= N _let_1)))))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (or (and (= M2 _let_1) (= N tptp.zero_zero_nat)) (and (= M2 tptp.zero_zero_nat) (= N _let_1)))))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (not (forall ((Q5 tptp.nat)) (not (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) Q5)))))))))
% 5.98/6.27 (assert (forall ((I tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) M2)))))
% 5.98/6.27 (assert (forall ((I tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) I)))))
% 5.98/6.27 (assert (= tptp.ord_less_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (exists ((K3 tptp.nat)) (= N4 (@ tptp.suc (@ (@ tptp.plus_plus_nat M3) K3)))))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (exists ((K2 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) K2)))))))
% 5.98/6.27 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) N2)) Y))))))
% 5.98/6.27 (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))))))
% 5.98/6.27 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M2 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)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.minus_minus_nat M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 5.98/6.27 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M2 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)) M2)) (@ (@ 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)) M2)) N)))))
% 5.98/6.27 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M2 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)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 5.98/6.27 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M2 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)) M2)) (@ (@ 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)) M2)) N)))))
% 5.98/6.27 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (= M2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 5.98/6.27 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M2) (@ (@ 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)) M2) N)))))
% 5.98/6.27 (assert (forall ((F (-> tptp.nat tptp.nat)) (M2 tptp.nat) (K tptp.nat)) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M4) N2) (@ (@ tptp.ord_less_nat (@ F M4)) (@ F N2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M2)) K)) (@ F (@ (@ tptp.plus_plus_nat M2) K))))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.suc M2)) N) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat M2) N)))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.plus_plus_nat N) M2)) tptp.zero_zero_nat)))
% 5.98/6.27 (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))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M2) N)) (= (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat M2) N)) M2))))
% 5.98/6.27 (assert (= tptp.suc (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_nat N4) tptp.one_one_nat))))
% 5.98/6.27 (assert (= (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.suc))
% 5.98/6.27 (assert (= tptp.suc (@ tptp.plus_plus_nat tptp.one_one_nat)))
% 5.98/6.27 (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)))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (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)))))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (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))))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (forall ((Y4 tptp.real)) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real Y4) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X)))))))
% 5.98/6.27 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M2 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)) M2)) (@ (@ 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)) M2)) N)))))
% 5.98/6.27 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M2 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)) M2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))))
% 5.98/6.27 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B)) (not (or (and (@ (@ tptp.ord_less_nat A) B) (not (@ P tptp.zero_zero_nat))) (exists ((D5 tptp.nat)) (and (= A (@ (@ tptp.plus_plus_nat B) D5)) (not (@ P D5)))))))))
% 5.98/6.27 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B)) (and (=> (@ (@ tptp.ord_less_nat A) B) (@ P tptp.zero_zero_nat)) (forall ((D5 tptp.nat)) (=> (= A (@ (@ tptp.plus_plus_nat B) D5)) (@ P D5)))))))
% 5.98/6.27 (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))))))
% 5.98/6.27 (assert (= tptp.ord_less_eq_nat (lambda ((N4 tptp.nat) (M3 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M3)) tptp.one_one_real)))))
% 5.98/6.27 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 5.98/6.27 (assert (= tptp.plus_plus_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) N4) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)) N4))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat N) (@ (@ tptp.divide_divide_nat M2) N)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M2) N)) N))))))
% 5.98/6.27 (assert (forall ((P (-> tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.divide_divide_nat M2) 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) (=> (= M2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I4)) J3)) (@ P I4))))))))))
% 5.98/6.27 (assert (= tptp.ord_less_nat (lambda ((N4 tptp.nat) (M3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N4)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real M3)))))
% 5.98/6.27 (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)))))))
% 5.98/6.27 (assert (= tptp.times_times_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N4) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)) N4))))))
% 5.98/6.27 (assert (forall ((B7 tptp.int) (Q6 tptp.int) (R3 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) Q6)) R3)) (=> (@ (@ tptp.ord_less_int R3) B7) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B7) (@ _let_1 Q6)))))))
% 5.98/6.27 (assert (forall ((B tptp.int) (Q4 tptp.int) (R2 tptp.int) (B7 tptp.int) (Q6 tptp.int) (R3 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) Q6)) R3))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q4)) R2) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R3) B7) (=> (@ _let_1 R2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B7) (=> (@ (@ tptp.ord_less_eq_int B7) B) (@ (@ tptp.ord_less_eq_int Q4) Q6)))))))))))
% 5.98/6.27 (assert (forall ((B tptp.int) (Q4 tptp.int) (R2 tptp.int) (B7 tptp.int) (Q6 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B7) Q6)) R3))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q4)) R2) _let_1) (=> (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int R2) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B7) (=> (@ (@ tptp.ord_less_eq_int B7) B) (@ (@ tptp.ord_less_eq_int Q6) Q4))))))))))
% 5.98/6.27 (assert (forall ((B tptp.int) (Q6 tptp.int) (R3 tptp.int) (Q4 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_1 Q6)) R3)) (@ (@ tptp.plus_plus_int (@ _let_1 Q4)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R3) (=> (@ (@ tptp.ord_less_int R3) B) (=> (@ (@ tptp.ord_less_int R2) B) (@ (@ tptp.ord_less_eq_int Q6) Q4))))))))
% 5.98/6.27 (assert (forall ((B tptp.int) (Q6 tptp.int) (R3 tptp.int) (Q4 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_2 Q6)) R3)) (@ (@ tptp.plus_plus_int (@ _let_2 Q4)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ _let_1 R2) (=> (@ _let_1 R3) (@ (@ tptp.ord_less_eq_int Q4) Q6)))))))))
% 5.98/6.27 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X4 tptp.int)) (=> (@ P X4) (@ P (@ (@ tptp.plus_plus_int X4) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X2 tptp.int)) (=> (@ P X2) (@ P (@ (@ tptp.plus_plus_int X2) (@ (@ tptp.times_times_int K) D))))))))))
% 5.98/6.27 (assert (forall ((Z tptp.int) (Z6 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z6)) (@ (@ tptp.times_times_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z6))))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X4 tptp.int)) (=> (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X2 tptp.int)) (=> (@ P X2) (@ P (@ (@ tptp.minus_minus_int X2) (@ (@ tptp.times_times_int K) D))))))))))
% 5.98/6.27 (assert (forall ((Z tptp.int) (Z6 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z6) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int Z) Z6)) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z6))))))))
% 5.98/6.27 (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))))))
% 5.98/6.27 (assert (forall ((X tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 C) (=> (forall ((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)) X)) C))) (= X tptp.zero_zero_real)))))))
% 5.98/6.27 (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))))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int) (Q4 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q4)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R2) (= (@ (@ tptp.divide_divide_int A) B) Q4))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int) (Q4 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q4)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (=> (@ (@ tptp.ord_less_int R2) B) (= (@ (@ tptp.divide_divide_int A) B) Q4))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (not (= A tptp.zero_zero_rat)) (not (= (@ (@ tptp.power_power_rat A) N) tptp.zero_zero_rat)))))
% 5.98/6.27 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (not (= A tptp.zero_zero_int)) (not (= (@ (@ tptp.power_power_int A) N) tptp.zero_zero_int)))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (not (= (@ (@ tptp.power_power_nat A) N) tptp.zero_zero_nat)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (not (= A tptp.zero_zero_real)) (not (= (@ (@ tptp.power_power_real A) N) tptp.zero_zero_real)))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (N tptp.nat)) (=> (not (= A tptp.zero_zero_complex)) (not (= (@ (@ tptp.power_power_complex A) N) tptp.zero_zero_complex)))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M2) (@ _let_1 N)) (or (= K tptp.zero_zero_nat) (= M2 N))))))
% 5.98/6.27 (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))))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N))))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))))
% 5.98/6.27 (assert (forall ((X tptp.complex) (Y tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_complex X) Y) tptp.one_one_complex) (= (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_complex Y) N)) tptp.one_one_complex))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_real X) Y) tptp.one_one_real) (= (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real Y) N)) tptp.one_one_real))))
% 5.98/6.27 (assert (forall ((X tptp.rat) (Y tptp.rat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_rat X) Y) tptp.one_one_rat) (= (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X) N)) (@ (@ tptp.power_power_rat Y) N)) tptp.one_one_rat))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_nat X) Y) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X) N)) (@ (@ tptp.power_power_nat Y) N)) tptp.one_one_nat))))
% 5.98/6.27 (assert (forall ((X tptp.int) (Y tptp.int) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_int X) Y) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) N)) (@ (@ tptp.power_power_int Y) N)) tptp.one_one_int))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (= (@ (@ tptp.power_power_rat (@ _let_1 A)) N) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex tptp.one_one_complex))) (= (@ (@ tptp.power_power_complex (@ _let_1 A)) N) (@ _let_1 (@ (@ tptp.power_power_complex A) N))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (= (@ (@ tptp.power_power_real (@ _let_1 A)) N) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 5.98/6.27 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 5.98/6.27 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 5.98/6.27 (assert (forall ((K tptp.nat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N))))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))
% 5.98/6.27 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))
% 5.98/6.27 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_real A) B)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_rat A) B)))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat A) B)))))
% 5.98/6.27 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int A) B)))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) (or (not (= X tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real))))))
% 5.98/6.27 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y))) (or (not (= X tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat))))))
% 5.98/6.27 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) tptp.one_one_real)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) tptp.one_one_rat)))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) tptp.one_one_nat)))))
% 5.98/6.27 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) tptp.one_one_int)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_eq_real A) B))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) _let_1)) (@ (@ tptp.power_power_rat B) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) _let_1)) (@ (@ tptp.power_power_nat B) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat A) B))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) _let_1)) (@ (@ tptp.power_power_int B) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int A) B))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_real A) _let_2) (@ (@ tptp.power_power_real B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_rat A) _let_2) (@ (@ tptp.power_power_rat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_nat A) _let_2) (@ (@ tptp.power_power_nat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_int A) _let_2) (@ (@ tptp.power_power_int B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.times_times_real A) _let_1))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat _let_1) (@ (@ tptp.times_times_rat A) _let_1))))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat _let_1) (@ (@ tptp.times_times_nat A) _let_1))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int _let_1) (@ (@ tptp.times_times_int A) _let_1))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_real A) (@ (@ tptp.power_power_real A) N)))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_rat A) (@ (@ tptp.power_power_rat A) N)))))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_nat A) (@ (@ tptp.power_power_nat A) N)))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int A) N)))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) (@ tptp.suc N)))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) (@ tptp.suc N)))))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) (@ tptp.suc N)))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc N)))))))
% 5.98/6.27 (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)))))))
% 5.98/6.27 (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)))))))
% 5.98/6.27 (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)))))))
% 5.98/6.27 (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)))))))
% 5.98/6.27 (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)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real (@ _let_1 N)) (@ _let_1 N5)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat (@ _let_1 N)) (@ _let_1 N5)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 N5)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int (@ _let_1 N)) (@ _let_1 N5)))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_rat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N))))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_int (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N))))
% 5.98/6.27 (assert (forall ((A tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 N)) (@ _let_1 N5)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N)) (@ _let_1 N5)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 N5)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) (@ _let_1 N5)))))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.divide_divide_nat M2) N))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) _let_1))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) _let_1))))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) _let_1)) _let_1))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) _let_1)) _let_1))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) (@ tptp.suc N))) A)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc N))) A)))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N))) A)))))
% 5.98/6.27 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) (@ tptp.suc N))) A)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.suc N))) tptp.one_one_real)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc N))) tptp.one_one_rat)))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N))) tptp.one_one_nat)))))
% 5.98/6.27 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc N))) tptp.one_one_int)))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N5)) (@ _let_1 N))))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ _let_1 N5)) (@ _let_1 N))))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N5)) (@ _let_1 N))))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N5)) (@ _let_1 N))))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 N5)) (@ _let_1 N))))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N5)) (@ _let_1 N))))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N5)) (@ _let_1 N))))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 N5)) (@ _let_1 N))))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real A) N) (@ (@ tptp.power_power_real B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat A) N) (@ (@ tptp.power_power_rat B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (@ (@ tptp.power_power_nat A) N) (@ (@ tptp.power_power_nat B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (@ (@ tptp.power_power_int A) N) (@ (@ tptp.power_power_int B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_real A) N) (@ (@ tptp.power_power_real B) N)) (= A B))))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_rat A) N) (@ (@ tptp.power_power_rat B) N)) (= A B))))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_nat A) N) (@ (@ tptp.power_power_nat B) N)) (= A B))))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_int A) N) (@ (@ tptp.power_power_int B) N)) (= A B))))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.power_power_real A) N))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.power_power_rat A) N))))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.power_power_nat A) N))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int A) N))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_real A) N)))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_rat A) N)))))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_nat A) N)))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_int A) N)))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.divide_divide_rat (@ _let_1 M2)) (@ _let_1 N))))))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 M2)) (@ _let_1 N))))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.divide_divide_int (@ _let_1 M2)) (@ _let_1 N))))))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.divide_divide_nat (@ _let_1 M2)) (@ _let_1 N))))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (@ (@ tptp.divide_divide_real (@ _let_1 M2)) (@ _let_1 N))))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)))))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)))))))
% 5.98/6.27 (assert (= tptp.power_power_complex (lambda ((P5 tptp.complex) (M3 tptp.nat)) (@ (@ (@ tptp.if_complex (= M3 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex P5) (@ (@ tptp.power_power_complex P5) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 5.98/6.27 (assert (= tptp.power_power_real (lambda ((P5 tptp.real) (M3 tptp.nat)) (@ (@ (@ tptp.if_real (= M3 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real P5) (@ (@ tptp.power_power_real P5) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 5.98/6.27 (assert (= tptp.power_power_rat (lambda ((P5 tptp.rat) (M3 tptp.nat)) (@ (@ (@ tptp.if_rat (= M3 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat P5) (@ (@ tptp.power_power_rat P5) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 5.98/6.27 (assert (= tptp.power_power_nat (lambda ((P5 tptp.nat) (M3 tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P5) (@ (@ tptp.power_power_nat P5) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 5.98/6.27 (assert (= tptp.power_power_int (lambda ((P5 tptp.int) (M3 tptp.nat)) (@ (@ (@ tptp.if_int (= M3 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P5) (@ (@ tptp.power_power_int P5) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 5.98/6.27 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X)) tptp.one_one_real)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) N)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (X tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (exists ((D6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D6) (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y4))) D6) (and (@ (@ tptp.ord_less_eq_real A) Y4) (@ (@ tptp.ord_less_eq_real Y4) B))))))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real) (P (-> tptp.real tptp.real Bool))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((A5 tptp.real) (B5 tptp.real) (C3 tptp.real)) (let ((_let_1 (@ P A5))) (=> (@ _let_1 B5) (=> (@ (@ P B5) C3) (=> (@ (@ tptp.ord_less_eq_real A5) B5) (=> (@ (@ tptp.ord_less_eq_real B5) C3) (@ _let_1 C3))))))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((A5 tptp.real) (B5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A5) X4) (@ (@ tptp.ord_less_eq_real X4) B5) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real B5) A5)) D3)) (@ (@ P A5) B5)))))))) (@ (@ P A) B))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.power_power_real X4) N) A) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (= (@ (@ tptp.power_power_real Y4) N) A)) (= Y4 X4)))))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R4) (= (@ (@ tptp.power_power_real R4) N) A)))))))
% 5.98/6.27 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.times_times_real Z))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 5.98/6.27 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat Z))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_rat X) Y))))))
% 5.98/6.27 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_int X) Y))))))
% 5.98/6.27 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_eq_real X) Y)))))
% 5.98/6.27 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_eq_rat X) Y)))))
% 5.98/6.27 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_eq_int X) Y)))))
% 5.98/6.27 (assert (forall ((R2 tptp.real) (A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (=> (not (= R2 tptp.zero_zero_real)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_real A) (@ _let_1 C)) (@ (@ tptp.plus_plus_real B) (@ _let_1 D)))))))))
% 5.98/6.27 (assert (forall ((R2 tptp.rat) (A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat R2))) (=> (not (= R2 tptp.zero_zero_rat)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_rat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_rat B) (@ _let_1 D)))))))))
% 5.98/6.27 (assert (forall ((R2 tptp.nat) (A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R2))) (=> (not (= R2 tptp.zero_zero_nat)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_nat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_nat B) (@ _let_1 D)))))))))
% 5.98/6.27 (assert (forall ((R2 tptp.int) (A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int R2))) (=> (not (= R2 tptp.zero_zero_int)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_int A) (@ _let_1 C)) (@ (@ tptp.plus_plus_int B) (@ _let_1 D)))))))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (assert (forall ((M5 tptp.set_list_VEBT_VEBT)) (=> (@ tptp.finite3004134309566078307T_VEBT M5) (exists ((N2 tptp.nat)) (forall ((X2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member2936631157270082147T_VEBT X2) M5) (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT X2)) N2)))))))
% 5.98/6.27 (assert (forall ((M5 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat M5) (exists ((N2 tptp.nat)) (forall ((X2 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X2) M5) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat X2)) N2)))))))
% 5.98/6.27 (assert (forall ((B tptp.real) (A tptp.real)) (= (= B (@ (@ tptp.plus_plus_real B) A)) (= A tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= B (@ (@ tptp.plus_plus_rat B) A)) (= A tptp.zero_zero_rat))))
% 5.98/6.27 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= B (@ (@ tptp.plus_plus_nat B) A)) (= A tptp.zero_zero_nat))))
% 5.98/6.27 (assert (forall ((B tptp.int) (A tptp.int)) (= (= B (@ (@ tptp.plus_plus_int B) A)) (= A tptp.zero_zero_int))))
% 5.98/6.27 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_real X) Y)))))
% 5.98/6.27 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_rat X) Y)))))
% 5.98/6.27 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_int X) Y)))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (=> (= X Y) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real U)) V) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X) U)) Y))) V)))))
% 5.98/6.27 (assert (forall ((X tptp.product_prod_nat_nat)) (= (@ tptp.the_el2281957884133575798at_nat (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat)) X)))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ tptp.the_elem_real (@ (@ tptp.insert_real X) tptp.bot_bot_set_real)) X)))
% 5.98/6.27 (assert (forall ((X Bool)) (= (@ tptp.the_elem_o (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)) X)))
% 5.98/6.27 (assert (forall ((X tptp.nat)) (= (@ tptp.the_elem_nat (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)) X)))
% 5.98/6.27 (assert (forall ((X tptp.int)) (= (@ tptp.the_elem_int (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)) X)))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.plus_plus_real (@ tptp.arctan X)) (@ tptp.arctan Y)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real X) Y)))))))))
% 5.98/6.27 (assert (forall ((X tptp.product_prod_nat_nat)) (@ tptp.is_sin2850979758926227957at_nat (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (@ tptp.is_singleton_real (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))
% 5.98/6.27 (assert (forall ((X Bool)) (@ tptp.is_singleton_o (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))))
% 5.98/6.27 (assert (forall ((X tptp.nat)) (@ tptp.is_singleton_nat (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))
% 5.98/6.27 (assert (forall ((X tptp.int)) (@ tptp.is_singleton_int (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))
% 5.98/6.27 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (= (@ (@ P A5) B5) (@ (@ P B5) A5))) (=> (forall ((A5 tptp.nat)) (@ (@ P A5) tptp.zero_zero_nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (let ((_let_1 (@ P A5))) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.plus_plus_nat A5) B5))))) (@ (@ P A) B))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ tptp.ln_ln_real (@ (@ tptp.root N) B)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.semiri5074537144036343181t_real N)))))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M2))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (A tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_complex A) K) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_real A) K) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real A) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_rat A) K) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 5.98/6.27 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_real tptp.zero_zero_real) (@ tptp.suc K)) tptp.zero_zero_real)))
% 5.98/6.27 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_rat tptp.zero_zero_rat) (@ tptp.suc K)) tptp.zero_zero_rat)))
% 5.98/6.27 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_nat tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 5.98/6.27 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_int tptp.zero_zero_int) (@ tptp.suc K)) tptp.zero_zero_int)))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.root (@ tptp.suc tptp.zero_zero_nat)) X) X)))
% 5.98/6.27 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.gbinomial_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (@ (@ tptp.gbinomial_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.gbinomial_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 5.98/6.27 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gbinomial_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (@ (@ tptp.gbinomial_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ _let_1 X) (@ _let_1 Y)) (= X Y))))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.root tptp.zero_zero_nat) X) tptp.zero_zero_real)))
% 5.98/6.27 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X)) (@ _let_1 X)))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_real X) Y))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X) tptp.one_one_real) (= X tptp.one_one_real)))))
% 5.98/6.27 (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))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real)))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y)) (@ _let_1 Y))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real)))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y)) (@ _let_1 Y))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y)) (@ _let_1 Y))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real)))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y)) (@ _let_1 Y))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.log A) X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.log A) X)) (@ (@ tptp.ord_less_eq_real A) X))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) A))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y)))))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X)) N) X)))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) (@ tptp.arctan Y)))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) (@ tptp.arctan Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 5.98/6.27 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.root N) X))))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_complex A))) (= (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex)) _let_1) (@ (@ tptp.plus_plus_complex (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_real A))) (= (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) _let_1) (@ (@ tptp.plus_plus_real (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (= (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) _let_1) (@ (@ tptp.plus_plus_rat (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 5.98/6.27 (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)))))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat N)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 5.98/6.27 (assert (= tptp.is_sin2850979758926227957at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat)) (= A6 (@ (@ tptp.insert8211810215607154385at_nat (@ tptp.the_el2281957884133575798at_nat A6)) tptp.bot_bo2099793752762293965at_nat)))))
% 5.98/6.27 (assert (= tptp.is_singleton_real (lambda ((A6 tptp.set_real)) (= A6 (@ (@ tptp.insert_real (@ tptp.the_elem_real A6)) tptp.bot_bot_set_real)))))
% 5.98/6.27 (assert (= tptp.is_singleton_o (lambda ((A6 tptp.set_o)) (= A6 (@ (@ tptp.insert_o (@ tptp.the_elem_o A6)) tptp.bot_bot_set_o)))))
% 5.98/6.27 (assert (= tptp.is_singleton_nat (lambda ((A6 tptp.set_nat)) (= A6 (@ (@ tptp.insert_nat (@ tptp.the_elem_nat A6)) tptp.bot_bot_set_nat)))))
% 5.98/6.27 (assert (= tptp.is_singleton_int (lambda ((A6 tptp.set_int)) (= A6 (@ (@ tptp.insert_int (@ tptp.the_elem_int A6)) tptp.bot_bot_set_int)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat)) (=> (not (= A2 tptp.bot_bot_set_set_nat)) (=> (forall ((X4 tptp.set_nat) (Y3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X4) A2) (=> (@ (@ tptp.member_set_nat Y3) A2) (= X4 Y3)))) (@ tptp.is_singleton_set_nat A2)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat_rat)) (=> (not (= A2 tptp.bot_bo6797373522285170759at_rat)) (=> (forall ((X4 tptp.set_nat_rat) (Y3 tptp.set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat X4) A2) (=> (@ (@ tptp.member_set_nat_rat Y3) A2) (= X4 Y3)))) (@ tptp.is_sin2571591796506819849at_rat A2)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_real)) (=> (not (= A2 tptp.bot_bot_set_real)) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (=> (@ (@ tptp.member_real Y3) A2) (= X4 Y3)))) (@ tptp.is_singleton_real A2)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_o)) (=> (not (= A2 tptp.bot_bot_set_o)) (=> (forall ((X4 Bool) (Y3 Bool)) (=> (@ (@ tptp.member_o X4) A2) (=> (@ (@ tptp.member_o Y3) A2) (= X4 Y3)))) (@ tptp.is_singleton_o A2)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_nat)) (=> (not (= A2 tptp.bot_bot_set_nat)) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (=> (@ (@ tptp.member_nat Y3) A2) (= X4 Y3)))) (@ tptp.is_singleton_nat A2)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_int)) (=> (not (= A2 tptp.bot_bot_set_int)) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (=> (@ (@ tptp.member_int Y3) A2) (= X4 Y3)))) (@ tptp.is_singleton_int A2)))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ _let_1 (@ (@ tptp.root N) A)) (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (B tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ (@ tptp.log (@ (@ tptp.root N) B)) X) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) X)))))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_complex A) _let_2) (@ (@ tptp.plus_plus_complex (@ _let_1 _let_2)) (@ _let_1 K)))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_real A) _let_2) (@ (@ tptp.plus_plus_real (@ _let_1 _let_2)) (@ _let_1 K)))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_rat A) _let_2) (@ (@ tptp.plus_plus_rat (@ _let_1 _let_2)) (@ _let_1 K)))))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.gbinomial_complex A) K)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.gbinomial_complex (@ _let_1 tptp.one_one_complex)) K))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.gbinomial_real A) K)) (@ (@ tptp.times_times_real A) (@ (@ tptp.gbinomial_real (@ _let_1 tptp.one_one_real)) K))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.gbinomial_rat A) K)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.gbinomial_rat (@ _let_1 tptp.one_one_rat)) K))))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real K))) (=> (@ (@ tptp.ord_less_eq_real _let_1) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real A) _let_1)) K)) (@ (@ tptp.gbinomial_real A) K))))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat K))) (=> (@ (@ tptp.ord_less_eq_rat _let_1) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat A) _let_1)) K)) (@ (@ tptp.gbinomial_rat A) K))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.power_power_real X) K)) (@ (@ tptp.power_power_real (@ _let_1 X)) K))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real (@ _let_1 X)))))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_2)) (@ (@ tptp.gbinomial_complex _let_1) _let_2)) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.gbinomial_complex A) K)))))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_2)) (@ (@ tptp.gbinomial_real _let_1) _let_2)) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.gbinomial_real A) K)))))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_2)) (@ (@ tptp.gbinomial_rat _let_1) _let_2)) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.gbinomial_rat A) K)))))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ (@ tptp.gbinomial_complex A) _let_1)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)) K))))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ (@ tptp.gbinomial_real A) _let_1)) (@ (@ tptp.times_times_real A) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)) K))))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ (@ tptp.gbinomial_rat A) _let_1)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) K))))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (M2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.gbinomial_real A))) (=> (@ (@ tptp.ord_less_eq_nat K) M2) (= (@ (@ tptp.times_times_real (@ _let_1 M2)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real M2)) K)) (@ (@ tptp.times_times_real (@ _let_1 K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.minus_minus_nat M2) K))))))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (M2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat A))) (=> (@ (@ tptp.ord_less_eq_nat K) M2) (= (@ (@ tptp.times_times_rat (@ _let_1 M2)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat M2)) K)) (@ (@ tptp.times_times_rat (@ _let_1 K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.minus_minus_nat M2) K))))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.root N) X)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (N5 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real (@ (@ tptp.root N5) X)) (@ (@ tptp.root N) X)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (Y tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.abs_abs_real (@ (@ tptp.root N) (@ (@ tptp.power_power_real Y) N))) (@ tptp.abs_abs_real Y)))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex))) (= (@ (@ tptp.gbinomial_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex A) K)) (@ (@ tptp.divide1717551699836669952omplex _let_2) (@ tptp.semiri8010041392384452111omplex _let_1))))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (= (@ (@ tptp.gbinomial_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real A) K)) (@ (@ tptp.divide_divide_real _let_2) (@ tptp.semiri5074537144036343181t_real _let_1))))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (= (@ (@ tptp.gbinomial_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K)) (@ (@ tptp.divide_divide_rat _let_2) (@ tptp.semiri681578069525770553at_rat _let_1))))))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex))) (= (@ (@ tptp.gbinomial_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex _let_2) (@ tptp.semiri8010041392384452111omplex _let_1))) (@ (@ tptp.gbinomial_complex A) K)))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (= (@ (@ tptp.gbinomial_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real _let_2) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.gbinomial_real A) K)))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (= (@ (@ tptp.gbinomial_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat _let_2) (@ tptp.semiri681578069525770553at_rat _let_1))) (@ (@ tptp.gbinomial_rat A) K)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.root N) X))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (N5 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X)) (@ (@ tptp.root N5) X))))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (N5 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N5) X)) (@ (@ tptp.root N) X)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X)) N) X)))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (= (@ (@ tptp.power_power_real Y) N) X) (= (@ (@ tptp.root N) X) Y))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.root N) (@ (@ tptp.power_power_real X) N)) X)))))
% 5.98/6.27 (assert (forall ((B tptp.real) (N tptp.nat) (M2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real B) N)) M2) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) M2))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.is_sin2850979758926227957at_nat A2) (not (forall ((X4 tptp.product_prod_nat_nat)) (not (= A2 (@ (@ tptp.insert8211810215607154385at_nat X4) tptp.bot_bo2099793752762293965at_nat))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_real)) (=> (@ tptp.is_singleton_real A2) (not (forall ((X4 tptp.real)) (not (= A2 (@ (@ tptp.insert_real X4) tptp.bot_bot_set_real))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_o)) (=> (@ tptp.is_singleton_o A2) (not (forall ((X4 Bool)) (not (= A2 (@ (@ tptp.insert_o X4) tptp.bot_bot_set_o))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.is_singleton_nat A2) (not (forall ((X4 tptp.nat)) (not (= A2 (@ (@ tptp.insert_nat X4) tptp.bot_bot_set_nat))))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.is_singleton_int A2) (not (forall ((X4 tptp.int)) (not (= A2 (@ (@ tptp.insert_int X4) tptp.bot_bot_set_int))))))))
% 5.98/6.27 (assert (= tptp.is_sin2850979758926227957at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat)) (exists ((X3 tptp.product_prod_nat_nat)) (= A6 (@ (@ tptp.insert8211810215607154385at_nat X3) tptp.bot_bo2099793752762293965at_nat))))))
% 5.98/6.27 (assert (= tptp.is_singleton_real (lambda ((A6 tptp.set_real)) (exists ((X3 tptp.real)) (= A6 (@ (@ tptp.insert_real X3) tptp.bot_bot_set_real))))))
% 5.98/6.27 (assert (= tptp.is_singleton_o (lambda ((A6 tptp.set_o)) (exists ((X3 Bool)) (= A6 (@ (@ tptp.insert_o X3) tptp.bot_bot_set_o))))))
% 5.98/6.27 (assert (= tptp.is_singleton_nat (lambda ((A6 tptp.set_nat)) (exists ((X3 tptp.nat)) (= A6 (@ (@ tptp.insert_nat X3) tptp.bot_bot_set_nat))))))
% 5.98/6.27 (assert (= tptp.is_singleton_int (lambda ((A6 tptp.set_int)) (exists ((X3 tptp.int)) (= A6 (@ (@ tptp.insert_int X3) tptp.bot_bot_set_int))))))
% 5.98/6.27 (assert (= tptp.is_singleton_complex (lambda ((A6 tptp.set_complex)) (= (@ tptp.finite_card_complex A6) tptp.one_one_nat))))
% 5.98/6.27 (assert (= tptp.is_sin2641923865335537900st_nat (lambda ((A6 tptp.set_list_nat)) (= (@ tptp.finite_card_list_nat A6) tptp.one_one_nat))))
% 5.98/6.27 (assert (= tptp.is_singleton_set_nat (lambda ((A6 tptp.set_set_nat)) (= (@ tptp.finite_card_set_nat A6) tptp.one_one_nat))))
% 5.98/6.27 (assert (= tptp.is_singleton_nat (lambda ((A6 tptp.set_nat)) (= (@ tptp.finite_card_nat A6) tptp.one_one_nat))))
% 5.98/6.27 (assert (= tptp.is_singleton_int (lambda ((A6 tptp.set_int)) (= (@ tptp.finite_card_int A6) tptp.one_one_nat))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_complex A) K) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_real A) K) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_rat A) K) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (N5 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X)) (@ (@ tptp.root N5) X))))))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M2))) (=> (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.root N) X) (@ (@ tptp.powr_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N))))))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (K tptp.nat)) (= (@ (@ tptp.gbinomial_complex (@ tptp.uminus1482373934393186551omplex A)) K) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (K tptp.nat)) (= (@ (@ tptp.gbinomial_real (@ tptp.uminus_uminus_real A)) K) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (K tptp.nat)) (= (@ (@ tptp.gbinomial_rat (@ tptp.uminus_uminus_rat A)) K) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K)))))
% 5.98/6.27 (assert (forall ((P (-> tptp.real Bool)) (N tptp.nat) (X tptp.real)) (= (@ P (@ (@ tptp.root N) X)) (and (=> (= N tptp.zero_zero_nat) (@ P tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (forall ((Y2 tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y2)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y2)) N)) X) (@ P Y2))))))))
% 5.98/6.27 (assert (= tptp.vEBT_VEBT_power (@ tptp.vEBT_V4262088993061758097ft_nat tptp.power_power_nat)))
% 5.98/6.27 (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))))))
% 5.98/6.27 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X))) (@ (@ tptp.power_power_real (@ _let_1 X)) N))))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X))) (@ tptp.uminus_uminus_real X))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_nat)) (= (= (@ tptp.gcd_Gcd_nat A2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_set_nat A2) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_int)) (= (= (@ tptp.gcd_Gcd_int A2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_set_int A2) (@ (@ tptp.insert_int tptp.zero_zero_int) tptp.bot_bot_set_int)))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B)) (= A B))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)) (= A B))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) (@ tptp.uminus_uminus_rat B)) (= A B))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) (@ tptp.uminus1482373934393186551omplex B)) (= A B))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int A)) A)))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real A)) A)))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat A)) A)))
% 5.98/6.27 (assert (forall ((A tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.uminus1482373934393186551omplex A)) A)))
% 5.98/6.27 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B2) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int B2)) (@ tptp.uminus1532241313380277803et_int A2)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int A2)) (@ tptp.uminus1532241313380277803et_int B2)) (@ (@ tptp.ord_less_eq_set_int B2) A2))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (= (@ tptp.sgn_sgn_real _let_1) _let_1))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int A))) (= (@ tptp.sgn_sgn_int _let_1) _let_1))))
% 5.98/6.27 (assert (forall ((A tptp.complex)) (let ((_let_1 (@ tptp.sgn_sgn_complex A))) (= (@ tptp.sgn_sgn_complex _let_1) _let_1))))
% 5.98/6.27 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_eq_real A) B))))
% 5.98/6.27 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 5.98/6.27 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_eq_int A) B))))
% 5.98/6.27 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int X)) (@ tptp.uminus1532241313380277803et_int Y)) (@ (@ tptp.ord_less_eq_set_int Y) X))))
% 5.98/6.27 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 5.98/6.27 (assert (= (@ tptp.uminus_uminus_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.27 (assert (= (@ tptp.uminus_uminus_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 5.98/6.27 (assert (= (@ tptp.uminus1482373934393186551omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.uminus_uminus_int A)) (= tptp.zero_zero_int A))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.uminus_uminus_real A)) (= tptp.zero_zero_real A))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat A)) (= tptp.zero_zero_rat A))))
% 5.98/6.27 (assert (forall ((A tptp.complex)) (= (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex A)) (= tptp.zero_zero_complex A))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 5.98/6.27 (assert (forall ((A tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (= A (@ tptp.uminus_uminus_int A)) (= A tptp.zero_zero_int))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (= A (@ tptp.uminus_uminus_real A)) (= A tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat A)) (= A tptp.zero_zero_rat))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) A) (= A tptp.zero_zero_int))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) A) (= A tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) A) (= A tptp.zero_zero_rat))))
% 5.98/6.27 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_int A) B))))
% 5.98/6.27 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_real A) B))))
% 5.98/6.27 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_rat A) B))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ _let_1 B))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real (@ _let_1 B))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat (@ _let_1 B))))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex (@ _let_1 B))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.times_times_int A) B))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) B))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) B))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.times_times_complex A) B))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) B) (@ tptp.uminus_uminus_int (@ (@ tptp.times_times_int A) B)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) B) (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real A) B)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) B) (@ tptp.uminus_uminus_rat (@ (@ tptp.times_times_rat A) B)))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex A) B)))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ (@ tptp.plus_plus_int A) B)) B)))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.plus_plus_real A) B)) B)))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.plus_plus_rat A) B)) B)))
% 5.98/6.27 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.plus_plus_complex A) B)) B)))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B)) B)))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B)) B)))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B)) B)))
% 5.98/6.27 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B)) B)))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int B) A))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real B) A))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat B) A))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B)) (@ (@ tptp.minus_minus_complex B) A))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 5.98/6.27 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.abs_abs_complex A))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 5.98/6.27 (assert (= (@ tptp.sgn_sgn_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 5.98/6.27 (assert (= (@ tptp.sgn_sgn_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.27 (assert (= (@ tptp.sgn_sgn_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 5.98/6.27 (assert (= (@ tptp.sgn_sgn_int tptp.zero_zero_int) tptp.zero_zero_int))
% 5.98/6.27 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.powr_real tptp.zero_zero_real) Z) tptp.zero_zero_real)))
% 5.98/6.27 (assert (forall ((W2 tptp.real) (Z tptp.real)) (= (= (@ (@ tptp.powr_real W2) Z) tptp.zero_zero_real) (= W2 tptp.zero_zero_real))))
% 5.98/6.27 (assert (= (@ tptp.sgn_sgn_rat tptp.one_one_rat) tptp.one_one_rat))
% 5.98/6.27 (assert (= (@ tptp.sgn_sgn_real tptp.one_one_real) tptp.one_one_real))
% 5.98/6.27 (assert (= (@ tptp.sgn_sgn_int tptp.one_one_int) tptp.one_one_int))
% 5.98/6.27 (assert (= (@ tptp.sgn_sgn_complex tptp.one_one_complex) tptp.one_one_complex))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (@ tptp.sgn_sgn_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int (@ tptp.sgn_sgn_int A)))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (@ tptp.sgn_sgn_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real (@ tptp.sgn_sgn_real A)))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat (@ tptp.sgn_sgn_rat A)))))
% 5.98/6.27 (assert (forall ((A tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex (@ tptp.sgn_sgn_complex A)))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (@ (@ tptp.powr_real tptp.one_one_real) A) tptp.one_one_real)))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ _let_1 tptp.zero_zero_real)))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat A)) (@ _let_1 tptp.zero_zero_rat)))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 tptp.zero_zero_int)))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 tptp.zero_zero_int)))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ _let_1 tptp.zero_zero_real)))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat A)) (@ _let_1 tptp.zero_zero_rat)))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 5.98/6.27 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int)))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real)))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)))
% 5.98/6.27 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ tptp.uminus1482373934393186551omplex A)) tptp.zero_zero_complex)))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) A) (@ tptp.uminus_uminus_int A))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) A) (@ tptp.uminus_uminus_real A))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) A) (@ tptp.uminus_uminus_rat A))))
% 5.98/6.27 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) A) (@ tptp.uminus1482373934393186551omplex A))))
% 5.98/6.27 (assert (forall ((B tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) B) (@ tptp.uminus_uminus_int B))))
% 5.98/6.27 (assert (forall ((B tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) B) (@ tptp.uminus_uminus_real B))))
% 5.98/6.27 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) B) (@ tptp.uminus_uminus_rat B))))
% 5.98/6.27 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) B) (@ tptp.uminus1482373934393186551omplex B))))
% 5.98/6.27 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int Z))))
% 5.98/6.27 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real Z))))
% 5.98/6.27 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat Z))))
% 5.98/6.27 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex Z))))
% 5.98/6.27 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int tptp.one_one_int)) Z) (@ tptp.uminus_uminus_int Z))))
% 5.98/6.27 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Z) (@ tptp.uminus_uminus_real Z))))
% 5.98/6.27 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) Z) (@ tptp.uminus_uminus_rat Z))))
% 5.98/6.27 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Z) (@ tptp.uminus1482373934393186551omplex Z))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.minus_minus_int B) A))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.minus_minus_real B) A))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.minus_minus_rat B) A))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.minus_minus_complex B) A))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.plus_plus_int A) B))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.plus_plus_real A) B))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.plus_plus_rat A) B))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.plus_plus_complex A) B))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.divide_divide_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real X))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.divide_divide_rat X) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat X))))
% 5.98/6.27 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex X))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int A))))
% 5.98/6.27 (assert (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 5.98/6.27 (assert (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 5.98/6.27 (assert (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sgn_sgn_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.sgn_sgn_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.sgn_sgn_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sgn_sgn_real A)) (@ _let_1 A)))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ tptp.sgn_sgn_rat A)) (@ _let_1 A)))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.sgn_sgn_int A)) (@ _let_1 A)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat A2) (@ tptp.uminus6524753893492686040at_nat (@ (@ tptp.insert8211810215607154385at_nat B) tptp.bot_bo2099793752762293965at_nat))) (not (@ (@ tptp.member8440522571783428010at_nat B) A2)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat) (B tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat A2) (@ tptp.uminus613421341184616069et_nat (@ (@ tptp.insert_set_nat B) tptp.bot_bot_set_set_nat))) (not (@ (@ tptp.member_set_nat B) A2)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_set_nat_rat) (B tptp.set_nat_rat)) (= (@ (@ tptp.ord_le4375437777232675859at_rat A2) (@ tptp.uminus3098529973357106300at_rat (@ (@ tptp.insert_set_nat_rat B) tptp.bot_bo6797373522285170759at_rat))) (not (@ (@ tptp.member_set_nat_rat B) A2)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real A2) (@ tptp.uminus612125837232591019t_real (@ (@ tptp.insert_real B) tptp.bot_bot_set_real))) (not (@ (@ tptp.member_real B) A2)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_o) (B Bool)) (= (@ (@ tptp.ord_less_eq_set_o A2) (@ tptp.uminus_uminus_set_o (@ (@ tptp.insert_o B) tptp.bot_bot_set_o))) (not (@ (@ tptp.member_o B) A2)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (not (@ (@ tptp.member_nat B) A2)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int A2) (@ tptp.uminus1532241313380277803et_int (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (not (@ (@ tptp.member_int B) A2)))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.powr_real X) tptp.zero_zero_real))) (let ((_let_2 (= X tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (= (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1314217659103216013at_int M2)) (and (= N tptp.zero_zero_nat) (= M2 tptp.zero_zero_nat)))))
% 5.98/6.27 (assert (forall ((X tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real X) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (= X A))))
% 5.98/6.27 (assert (forall ((A tptp.real) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real A) X)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 5.98/6.27 (assert (= (@ tptp.gcd_Gcd_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 5.98/6.27 (assert (= (@ tptp.gcd_Gcd_int tptp.bot_bot_set_int) tptp.zero_zero_int))
% 5.98/6.27 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) (@ tptp.semiri1314217659103216013at_int M2))))
% 5.98/6.27 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.neg_nu5851722552734809277nc_int _let_1) _let_1)))
% 5.98/6.27 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ tptp.neg_nu8295874005876285629c_real _let_1) _let_1)))
% 5.98/6.27 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ tptp.neg_nu5219082963157363817nc_rat _let_1) _let_1)))
% 5.98/6.27 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ tptp.neg_nu8557863876264182079omplex _let_1) _let_1)))
% 5.98/6.27 (assert (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) tptp.zero_zero_int))
% 5.98/6.27 (assert (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) tptp.zero_zero_real))
% 5.98/6.27 (assert (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) tptp.zero_zero_rat))
% 5.98/6.27 (assert (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) tptp.zero_zero_complex))
% 5.98/6.27 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 5.98/6.27 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 5.98/6.27 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 5.98/6.27 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.zero_zero_complex))
% 5.98/6.27 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.minus_minus_int _let_1) _let_1) tptp.zero_zero_int)))
% 5.98/6.27 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.minus_minus_real _let_1) _let_1) tptp.zero_zero_real)))
% 5.98/6.27 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.minus_minus_rat _let_1) _let_1) tptp.zero_zero_rat)))
% 5.98/6.27 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.minus_minus_complex _let_1) _let_1) tptp.zero_zero_complex)))
% 5.98/6.27 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N))) (= (@ (@ tptp.times_times_int _let_1) _let_1) tptp.one_one_int))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N))) (= (@ (@ tptp.times_times_real _let_1) _let_1) tptp.one_one_real))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) tptp.one_one_rat))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N))) (= (@ (@ tptp.times_times_complex _let_1) _let_1) tptp.one_one_complex))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.sgn_sgn_real A) tptp.one_one_real))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.sgn_sgn_rat A) tptp.one_one_rat))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.sgn_sgn_int A) tptp.one_one_int))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ tptp.sgn_sgn_real A)) tptp.one_one_real))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.abs_abs_rat (@ tptp.sgn_sgn_rat A)) tptp.one_one_rat))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A)) tptp.one_one_int))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) tptp.one_one_real) X))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.powr_real X) tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 5.98/6.27 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) tptp.zero_zero_nat)))
% 5.98/6.27 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.sgn_sgn_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.sgn_sgn_real A) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.sgn_sgn_rat A) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ tptp.uminus_uminus_int B) A))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ tptp.uminus_uminus_real B) A))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ tptp.uminus_uminus_rat B) A))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ tptp.uminus1482373934393186551omplex B) A))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= B (@ tptp.uminus_uminus_int A)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= B (@ tptp.uminus_uminus_real A)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= B (@ tptp.uminus_uminus_rat A)))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 5.98/6.27 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.sgn_sgn_int _let_1) _let_1)))
% 5.98/6.27 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ tptp.sgn_sgn_real _let_1) _let_1)))
% 5.98/6.27 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ tptp.sgn_sgn_rat _let_1) _let_1)))
% 5.98/6.27 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ tptp.sgn_sgn_complex _let_1) _let_1)))
% 5.98/6.27 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int B))) (let ((_let_2 (@ tptp.sgn_sgn_int A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_int)) (=> (not (= _let_1 tptp.zero_zero_int)) (= _let_2 (@ tptp.uminus_uminus_int _let_1)))))))))
% 5.98/6.27 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real B))) (let ((_let_2 (@ tptp.sgn_sgn_real A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))))
% 5.98/6.27 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat B))) (let ((_let_2 (@ tptp.sgn_sgn_rat A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_rat)) (=> (not (= _let_1 tptp.zero_zero_rat)) (= _let_2 (@ tptp.uminus_uminus_rat _let_1)))))))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 5.98/6.27 (assert (forall ((A tptp.complex)) (= (= (@ tptp.sgn_sgn_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.times_times_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.sgn_sgn_complex B)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.sgn_sgn_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ tptp.sgn_sgn_real B)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.sgn_sgn_rat B)))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.sgn_sgn_int (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.sgn_sgn_int B)))))
% 5.98/6.27 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (=> (= (@ tptp.sgn_sgn_real B) _let_1) (= (@ tptp.sgn_sgn_real (@ (@ tptp.plus_plus_real A) B)) _let_1)))))
% 5.98/6.27 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (=> (= (@ tptp.sgn_sgn_rat B) _let_1) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.plus_plus_rat A) B)) _let_1)))))
% 5.98/6.27 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int A))) (=> (= (@ tptp.sgn_sgn_int B) _let_1) (= (@ tptp.sgn_sgn_int (@ (@ tptp.plus_plus_int A) B)) _let_1)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) A))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) A))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) A))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.ord_less_eq_real B) (@ tptp.uminus_uminus_real A)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.ord_less_eq_rat B) (@ tptp.uminus_uminus_rat A)))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.ord_less_eq_int B) (@ tptp.uminus_uminus_int A)))))
% 5.98/6.27 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int Y)) (@ tptp.uminus1532241313380277803et_int X)))))
% 5.98/6.27 (assert (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) (@ tptp.uminus1532241313380277803et_int X)) (@ (@ tptp.ord_less_eq_set_int X) (@ tptp.uminus1532241313380277803et_int Y)))))
% 5.98/6.27 (assert (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int Y)) X) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int X)) Y))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.ord_less_int B) (@ tptp.uminus_uminus_int A)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.ord_less_real B) (@ tptp.uminus_uminus_real A)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.ord_less_rat B) (@ tptp.uminus_uminus_rat A)))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) A))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) A))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) A))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.times_times_int A) (@ tptp.uminus_uminus_int B)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.times_times_real A) (@ tptp.uminus_uminus_real B)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.times_times_rat A) (@ tptp.uminus_uminus_rat B)))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.times_times_complex A) (@ tptp.uminus1482373934393186551omplex B)))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) A) (@ (@ tptp.times_times_int B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_int B))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) A) (@ (@ tptp.times_times_real B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_real B))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) A) (@ (@ tptp.times_times_rat B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_rat B))))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) A) (@ (@ tptp.times_times_complex B) B)) (or (= A B) (= A (@ tptp.uminus1482373934393186551omplex B))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex A)))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex A)))))
% 5.98/6.27 (assert (forall ((A2 tptp.int) (K tptp.int) (A tptp.int)) (=> (= A2 (@ (@ tptp.plus_plus_int K) A)) (= (@ tptp.uminus_uminus_int A2) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ tptp.uminus_uminus_int A))))))
% 5.98/6.27 (assert (forall ((A2 tptp.real) (K tptp.real) (A tptp.real)) (=> (= A2 (@ (@ tptp.plus_plus_real K) A)) (= (@ tptp.uminus_uminus_real A2) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ tptp.uminus_uminus_real A))))))
% 5.98/6.27 (assert (forall ((A2 tptp.rat) (K tptp.rat) (A tptp.rat)) (=> (= A2 (@ (@ tptp.plus_plus_rat K) A)) (= (@ tptp.uminus_uminus_rat A2) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ tptp.uminus_uminus_rat A))))))
% 5.98/6.27 (assert (forall ((A2 tptp.complex) (K tptp.complex) (A tptp.complex)) (=> (= A2 (@ (@ tptp.plus_plus_complex K) A)) (= (@ tptp.uminus1482373934393186551omplex A2) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ tptp.uminus1482373934393186551omplex A))))))
% 5.98/6.27 (assert (not (= tptp.one_one_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 5.98/6.27 (assert (not (= tptp.one_one_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 5.98/6.27 (assert (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 5.98/6.27 (assert (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 5.98/6.27 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int B)) A) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A)) B))))
% 5.98/6.27 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real B)) A) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) B))))
% 5.98/6.27 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat B)) A) (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) B))))
% 5.98/6.27 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex B)) A) (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B)))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B)))))
% 5.98/6.27 (assert (forall ((X tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_1 A))))))
% 5.98/6.27 (assert (forall ((X tptp.int) (Y tptp.int)) (= (= (@ tptp.abs_abs_int X) (@ tptp.abs_abs_int Y)) (or (= X Y) (= X (@ tptp.uminus_uminus_int Y))))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ tptp.abs_abs_real X) (@ tptp.abs_abs_real Y)) (or (= X Y) (= X (@ tptp.uminus_uminus_real Y))))))
% 5.98/6.27 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (= (@ tptp.abs_abs_rat X) (@ tptp.abs_abs_rat Y)) (or (= X Y) (= X (@ tptp.uminus_uminus_rat Y))))))
% 5.98/6.27 (assert (forall ((N5 tptp.set_nat)) (=> (@ (@ tptp.member_nat tptp.one_one_nat) N5) (= (@ tptp.gcd_Gcd_nat N5) tptp.one_one_nat))))
% 5.98/6.27 (assert (= tptp.sgn_sgn_int (lambda ((X3 tptp.int)) (@ (@ (@ tptp.if_int (= X3 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) X3)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 5.98/6.27 (assert (= tptp.sgn_sgn_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.if_real (= X3 tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 5.98/6.27 (assert (= tptp.sgn_sgn_rat (lambda ((X3 tptp.rat)) (@ (@ (@ tptp.if_rat (= X3 tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X3)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 5.98/6.27 (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))))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_nat)) (=> (@ (@ tptp.member_nat tptp.one_one_nat) A2) (= (@ tptp.gcd_Gcd_nat A2) tptp.one_one_nat))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_int)) (=> (@ (@ tptp.member_int tptp.one_one_int) A2) (= (@ tptp.gcd_Gcd_int A2) tptp.one_one_int))))
% 5.98/6.27 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A))))))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.powr_real X) Y))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X)) (@ tptp.abs_abs_real X)) X)))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat X)) (@ tptp.abs_abs_rat X)) X)))
% 5.98/6.27 (assert (forall ((X tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int X)) (@ tptp.abs_abs_int X)) X)))
% 5.98/6.27 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.abs_abs_complex A)) A)))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ tptp.abs_abs_real A)) A)))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.abs_abs_rat A)) A)))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.abs_abs_int A)) A)))
% 5.98/6.27 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.abs_abs_complex A)) (@ tptp.sgn_sgn_complex A)) A)))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.sgn_sgn_real A)) A)))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.sgn_sgn_rat A)) A)))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.sgn_sgn_int A)) A)))
% 5.98/6.27 (assert (= tptp.abs_abs_real (lambda ((K3 tptp.real)) (@ (@ tptp.times_times_real K3) (@ tptp.sgn_sgn_real K3)))))
% 5.98/6.27 (assert (= tptp.abs_abs_rat (lambda ((K3 tptp.rat)) (@ (@ tptp.times_times_rat K3) (@ tptp.sgn_sgn_rat K3)))))
% 5.98/6.27 (assert (= tptp.abs_abs_int (lambda ((K3 tptp.int)) (@ (@ tptp.times_times_int K3) (@ tptp.sgn_sgn_int K3)))))
% 5.98/6.27 (assert (forall ((B tptp.real) (A tptp.real)) (=> (= (@ tptp.sgn_sgn_real B) (@ tptp.sgn_sgn_real A)) (= (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))))))
% 5.98/6.27 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (= (@ tptp.sgn_sgn_rat B) (@ tptp.sgn_sgn_rat A)) (= (@ tptp.abs_abs_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))))))
% 5.98/6.27 (assert (forall ((B tptp.int) (A tptp.int)) (=> (= (@ tptp.sgn_sgn_int B) (@ tptp.sgn_sgn_int A)) (= (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B))))))
% 5.98/6.27 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 5.98/6.27 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 5.98/6.27 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 5.98/6.27 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 5.98/6.27 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 5.98/6.27 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= B (@ tptp.uminus_uminus_int A)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= B (@ tptp.uminus_uminus_real A)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= B (@ tptp.uminus_uminus_rat A)))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 5.98/6.27 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A) B))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= (@ tptp.uminus_uminus_real A) B))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= (@ tptp.uminus_uminus_rat A) B))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= (@ tptp.uminus1482373934393186551omplex A) B))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 5.98/6.27 (assert (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 5.98/6.27 (assert (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 5.98/6.27 (assert (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 5.98/6.27 (assert (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 5.98/6.27 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 5.98/6.27 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 5.98/6.27 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 5.98/6.27 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 5.98/6.27 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 5.98/6.27 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 5.98/6.27 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.uminus_uminus_real (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_real B)))))))
% 5.98/6.27 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (=> (not (= B tptp.zero_zero_rat)) (= (@ tptp.uminus_uminus_rat (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_rat B)))))))
% 5.98/6.27 (assert (forall ((B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (=> (not (= B tptp.zero_zero_complex)) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B)))))))
% 5.98/6.27 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.divide_divide_real A) B)))))
% 5.98/6.27 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.divide_divide_rat A) B)))))
% 5.98/6.27 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 5.98/6.27 (assert (forall ((X tptp.int)) (= (= (@ (@ tptp.times_times_int X) X) tptp.one_one_int) (or (= X tptp.one_one_int) (= X (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.times_times_real X) X) tptp.one_one_real) (or (= X tptp.one_one_real) (= X (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (= (@ (@ tptp.times_times_rat X) X) tptp.one_one_rat) (or (= X tptp.one_one_rat) (= X (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 5.98/6.27 (assert (forall ((X tptp.complex)) (= (= (@ (@ tptp.times_times_complex X) X) tptp.one_one_complex) (or (= X tptp.one_one_complex) (= X (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))))
% 5.98/6.27 (assert (forall ((B2 tptp.int) (K tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (=> (= B2 (@ (@ tptp.plus_plus_int K) B)) (= (@ _let_1 B2) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ _let_1 B)))))))
% 5.98/6.27 (assert (forall ((B2 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (=> (= B2 (@ (@ tptp.plus_plus_real K) B)) (= (@ _let_1 B2) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ _let_1 B)))))))
% 5.98/6.27 (assert (forall ((B2 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (=> (= B2 (@ (@ tptp.plus_plus_rat K) B)) (= (@ _let_1 B2) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ _let_1 B)))))))
% 5.98/6.27 (assert (forall ((B2 tptp.complex) (K tptp.complex) (B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (=> (= B2 (@ (@ tptp.plus_plus_complex K) B)) (= (@ _let_1 B2) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ _let_1 B)))))))
% 5.98/6.27 (assert (= tptp.minus_minus_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int A4) (@ tptp.uminus_uminus_int B4)))))
% 5.98/6.27 (assert (= tptp.minus_minus_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.plus_plus_real A4) (@ tptp.uminus_uminus_real B4)))))
% 5.98/6.27 (assert (= tptp.minus_minus_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.plus_plus_rat A4) (@ tptp.uminus_uminus_rat B4)))))
% 5.98/6.27 (assert (= tptp.minus_minus_complex (lambda ((A4 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.plus_plus_complex A4) (@ tptp.uminus1482373934393186551omplex B4)))))
% 5.98/6.27 (assert (= tptp.minus_minus_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int A4) (@ tptp.uminus_uminus_int B4)))))
% 5.98/6.27 (assert (= tptp.minus_minus_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.plus_plus_real A4) (@ tptp.uminus_uminus_real B4)))))
% 5.98/6.27 (assert (= tptp.minus_minus_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.plus_plus_rat A4) (@ tptp.uminus_uminus_rat B4)))))
% 5.98/6.27 (assert (= tptp.minus_minus_complex (lambda ((A4 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.plus_plus_complex A4) (@ tptp.uminus1482373934393186551omplex B4)))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B) (and (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (and (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B)))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B) (and (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B)))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B)))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) B) (and (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) B)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) B) (and (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) B) (and (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) B)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A2) (@ tptp.uminus612125837232591019t_real A2)) (= A2 tptp.bot_bot_set_real))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o A2) (@ tptp.uminus_uminus_set_o A2)) (= A2 tptp.bot_bot_set_o))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) (@ tptp.uminus5710092332889474511et_nat A2)) (= A2 tptp.bot_bot_set_nat))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) (@ tptp.uminus1532241313380277803et_int A2)) (= A2 tptp.bot_bot_set_int))))
% 5.98/6.27 (assert (forall ((U tptp.real) (X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real U) U))) (@ (@ tptp.times_times_real X) X))))
% 5.98/6.27 (assert (= tptp.minus_minus_real (lambda ((X3 tptp.real) (Y2 tptp.real)) (@ (@ tptp.plus_plus_real X3) (@ tptp.uminus_uminus_real Y2)))))
% 5.98/6.27 (assert (forall ((K4 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.gcd_Gcd_int K4))))
% 5.98/6.27 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real Y) A)) (@ (@ tptp.powr_real X) A)))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A)))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) tptp.one_one_real)))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) B))))))))
% 5.98/6.27 (assert (forall ((X tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ _let_1 (@ (@ tptp.powr_real X) A)))))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.powr_real (@ (@ tptp.divide_divide_real X) Y)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A))))))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.powr_real (@ (@ tptp.times_times_real X) Y)) A) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A))))))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.sgn_sgn_real (@ (@ tptp.root N) X)) (@ tptp.sgn_sgn_real X)))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real (@ tptp.sgn_sgn_real A)))) (let ((_let_2 (= A tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat (@ tptp.sgn_sgn_rat A)))) (let ((_let_2 (= A tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 tptp.one_one_rat)))))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A)))) (let ((_let_2 (= A tptp.zero_zero_int))) (and (=> _let_2 (= _let_1 tptp.zero_zero_int)) (=> (not _let_2) (= _let_1 tptp.one_one_int)))))))
% 5.98/6.27 (assert (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 5.98/6.27 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 5.98/6.27 (assert (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 5.98/6.27 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 5.98/6.27 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 5.98/6.27 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 5.98/6.27 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 5.98/6.27 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 5.98/6.27 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 5.98/6.27 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 5.98/6.27 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 5.98/6.27 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= A (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A) C) (@ tptp.uminus_uminus_real B))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A) C) (@ tptp.uminus_uminus_rat B))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A) C) (@ tptp.uminus1482373934393186551omplex B))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 5.98/6.27 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_real B) (@ (@ tptp.times_times_real A) C))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 5.98/6.27 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_rat B) (@ (@ tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 5.98/6.27 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus1482373934393186551omplex B) (@ (@ tptp.times_times_complex A) C))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 5.98/6.27 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B)) C) (= (@ tptp.uminus_uminus_real A) (@ (@ tptp.times_times_real C) B))))))
% 5.98/6.27 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B)) C) (= (@ tptp.uminus_uminus_rat A) (@ (@ tptp.times_times_rat C) B))))))
% 5.98/6.27 (assert (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) C) (= (@ tptp.uminus1482373934393186551omplex A) (@ (@ tptp.times_times_complex C) B))))))
% 5.98/6.27 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= C (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B))) (= (@ (@ tptp.times_times_real C) B) (@ tptp.uminus_uminus_real A))))))
% 5.98/6.27 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= C (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B))) (= (@ (@ tptp.times_times_rat C) B) (@ tptp.uminus_uminus_rat A))))))
% 5.98/6.27 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= C (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B))) (= (@ (@ tptp.times_times_complex C) B) (@ tptp.uminus1482373934393186551omplex A))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B) (@ tptp.uminus_uminus_real tptp.one_one_real)) (and (not (= B tptp.zero_zero_real)) (= A (@ tptp.uminus_uminus_real B))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (and (not (= B tptp.zero_zero_rat)) (= A (@ tptp.uminus_uminus_rat B))))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (not (= B tptp.zero_zero_complex)) (= A (@ tptp.uminus1482373934393186551omplex B))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)) (@ (@ tptp.power_power_int A) N)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ (@ tptp.power_power_real A) N)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)) (@ (@ tptp.power_power_rat A) N)))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)) (@ (@ tptp.power_power_complex A) N)))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.abs_abs_real A))) tptp.zero_zero_real)))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.abs_abs_rat A))) tptp.zero_zero_rat)))
% 5.98/6.27 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.abs_abs_int A))) tptp.zero_zero_int)))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.abs_abs_real A) B) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (or (= A B) (= A (@ tptp.uminus_uminus_real B)))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.abs_abs_rat A) B) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (or (= A B) (= A (@ tptp.uminus_uminus_rat B)))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.abs_abs_int A) B) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (or (= A B) (= A (@ tptp.uminus_uminus_int B)))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.abs_abs_real B)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (or (= B A) (= B (@ tptp.uminus_uminus_real A)))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.abs_abs_rat B)) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (or (= B A) (= B (@ tptp.uminus_uminus_rat A)))))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.abs_abs_int B)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (or (= B A) (= B (@ tptp.uminus_uminus_int A)))))))
% 5.98/6.27 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (assert (forall ((X tptp.product_prod_nat_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X))) (= (@ tptp.uminus6524753893492686040at_nat (@ _let_1 A2)) (@ (@ tptp.minus_1356011639430497352at_nat (@ tptp.uminus6524753893492686040at_nat A2)) (@ _let_1 tptp.bot_bo2099793752762293965at_nat))))))
% 5.98/6.27 (assert (forall ((X tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X))) (= (@ tptp.uminus612125837232591019t_real (@ _let_1 A2)) (@ (@ tptp.minus_minus_set_real (@ tptp.uminus612125837232591019t_real A2)) (@ _let_1 tptp.bot_bot_set_real))))))
% 5.98/6.27 (assert (forall ((X Bool) (A2 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o X))) (= (@ tptp.uminus_uminus_set_o (@ _let_1 A2)) (@ (@ tptp.minus_minus_set_o (@ tptp.uminus_uminus_set_o A2)) (@ _let_1 tptp.bot_bot_set_o))))))
% 5.98/6.27 (assert (forall ((X tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (= (@ tptp.uminus1532241313380277803et_int (@ _let_1 A2)) (@ (@ tptp.minus_minus_set_int (@ tptp.uminus1532241313380277803et_int A2)) (@ _let_1 tptp.bot_bot_set_int))))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (= (@ tptp.uminus5710092332889474511et_nat (@ _let_1 A2)) (@ (@ tptp.minus_minus_set_nat (@ tptp.uminus5710092332889474511et_nat A2)) (@ _let_1 tptp.bot_bot_set_nat))))))
% 5.98/6.27 (assert (forall ((M2 tptp.int)) (=> (forall ((N2 tptp.nat)) (not (= M2 (@ tptp.semiri1314217659103216013at_int N2)))) (not (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (not (= M2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))))))))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X) Y)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) (@ tptp.uminus_uminus_real X)))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real X)) Y))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real X) Y)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real Y) (@ tptp.uminus_uminus_real X)))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X)) Y))))
% 5.98/6.27 (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))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M2))) (and (= N tptp.zero_zero_nat) (= M2 tptp.zero_zero_nat)))))
% 5.98/6.27 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (not (forall ((N2 tptp.nat)) (not (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2)))))))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) tptp.zero_zero_int)))
% 5.98/6.27 (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)))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ tptp.uminus_uminus_real B))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real)))))))))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))))
% 5.98/6.27 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ tptp.uminus_uminus_real B))) (let ((_let_4 (@ (@ tptp.times_times_real A) C))) (let ((_let_5 (@ _let_1 C))) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 A)))))))))))))
% 5.98/6.27 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ tptp.uminus_uminus_rat B))) (let ((_let_4 (@ (@ tptp.times_times_rat A) C))) (let ((_let_5 (@ _let_1 C))) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 A)))))))))))))
% 5.98/6.27 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 5.98/6.27 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 5.98/6.27 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 5.98/6.27 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 5.98/6.27 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 5.98/6.27 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 5.98/6.27 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 5.98/6.27 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 5.98/6.27 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 5.98/6.27 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X) Z))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 5.98/6.27 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 5.98/6.27 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 5.98/6.27 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 5.98/6.27 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 5.98/6.27 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 5.98/6.27 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X) Z))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 5.98/6.27 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 5.98/6.27 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_real B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real A) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 5.98/6.27 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 5.98/6.27 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (@ tptp.uminus1482373934393186551omplex B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 5.98/6.27 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_real B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 5.98/6.27 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 5.98/6.27 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (@ tptp.uminus1482373934393186551omplex B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 5.98/6.27 (assert (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (=> (forall ((N2 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N2)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (not (forall ((N2 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))))))
% 5.98/6.27 (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)))))))
% 5.98/6.27 (assert (forall ((A2 tptp.int) (B2 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) 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 A2) N))))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.times_times_real X) (@ _let_1 Y)) (@ _let_1 (@ (@ tptp.plus_plus_real tptp.one_one_real) Y)))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (N tptp.nat) (X tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N)) X) (=> (= X (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real B)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real B)) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))
% 5.98/6.27 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.log B) X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y)) X))))))
% 5.98/6.27 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X)) Y) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.powr_real B) Y)))))))
% 5.98/6.27 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.powr_real B) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X)) Y))))))
% 5.98/6.27 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y)) X) (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.log B) X)))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ tptp.uminus_uminus_real B))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real)))))))))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))))
% 5.98/6.27 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_2 (@ tptp.uminus_uminus_real B))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real _let_2) _let_3)) (=> (not _let_4) (and (=> _let_1 (@ (@ tptp.ord_less_eq_real _let_3) _let_2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))))))))))
% 5.98/6.27 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.uminus_uminus_rat B))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_2) _let_3)) (=> (not _let_4) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_3) _let_2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))))))))))
% 5.98/6.27 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 5.98/6.27 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 5.98/6.27 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 5.98/6.27 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 5.98/6.27 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 5.98/6.27 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 5.98/6.27 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 5.98/6.27 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 5.98/6.27 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (not (forall ((N2 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))))))
% 5.98/6.27 (assert (forall ((Z tptp.int) (Z6 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z6)) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.uminus_uminus_int Z))) (@ tptp.nat2 (@ tptp.uminus_uminus_int Z6)))))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.archim2898591450579166408c_real (@ tptp.uminus_uminus_real X)))) (let ((_let_2 (@ (@ tptp.member_real X) 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 X)))))))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (let ((_let_1 (@ tptp.archimedean_frac_rat (@ tptp.uminus_uminus_rat X)))) (let ((_let_2 (@ (@ tptp.member_rat X) 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 X)))))))))
% 5.98/6.27 (assert (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X) A)) A))))))
% 5.98/6.27 (assert (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real (@ tptp.ln_ln_real X)) A)) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real A) A)) X))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ (@ tptp.root N) X))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real _let_1)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real _let_1)) N)) X)))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (Y tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.root N) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N))) Y))))
% 5.98/6.27 (assert (= tptp.gbinomial_complex (lambda ((A4 tptp.complex) (K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K3)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex K3)) A4)) tptp.one_one_complex)) K3)))))
% 5.98/6.27 (assert (= tptp.gbinomial_real (lambda ((A4 tptp.real) (K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real K3)) A4)) tptp.one_one_real)) K3)))))
% 5.98/6.27 (assert (= tptp.gbinomial_rat (lambda ((A4 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K3)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat K3)) A4)) tptp.one_one_rat)) K3)))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (= (@ (@ tptp.times_times_complex (@ _let_1 K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) tptp.one_one_complex)) K)) (@ (@ tptp.times_times_complex (@ _let_1 N)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) N))))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)))) (= (@ (@ tptp.times_times_real (@ _let_1 K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) tptp.one_one_real)) K)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) N))))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (= (@ (@ tptp.times_times_rat (@ _let_1 K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) tptp.one_one_rat)) K)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) N))))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sgn_sgn_real X)) (@ _let_1 X)))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sgn_sgn_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 5.98/6.27 (assert (= tptp.vEBT_VEBT_mul (@ tptp.vEBT_V4262088993061758097ft_nat tptp.times_times_nat)))
% 5.98/6.27 (assert (= tptp.vEBT_VEBT_add (@ tptp.vEBT_V4262088993061758097ft_nat tptp.plus_plus_nat)))
% 5.98/6.27 (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)))))))
% 5.98/6.27 (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)))))))
% 5.98/6.27 (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)))))))
% 5.98/6.27 (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)))))))
% 5.98/6.27 (assert (= (@ tptp.sgn_sgn_real tptp.one_one_real) tptp.one_one_real))
% 5.98/6.27 (assert (= (@ tptp.sgn_sgn_complex tptp.one_one_complex) tptp.one_one_complex))
% 5.98/6.27 (assert (= (@ tptp.sgn_sgn_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 5.98/6.27 (assert (= (@ tptp.sgn_sgn_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.27 (assert (forall ((X tptp.real) (B tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log B) X)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) X) (@ (@ tptp.ord_less_eq_real X) (@ _let_1 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))))
% 5.98/6.27 (assert (forall ((C Bool) (A2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (= (@ _let_1 (@ tptp.uminus_uminus_set_o A2)) (not (@ _let_1 A2))))))
% 5.98/6.27 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (= (@ _let_1 (@ tptp.uminus613421341184616069et_nat A2)) (not (@ _let_1 A2))))))
% 5.98/6.27 (assert (forall ((C tptp.set_nat_rat) (A2 tptp.set_set_nat_rat)) (let ((_let_1 (@ tptp.member_set_nat_rat C))) (= (@ _let_1 (@ tptp.uminus3098529973357106300at_rat A2)) (not (@ _let_1 A2))))))
% 5.98/6.27 (assert (forall ((C tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ tptp.uminus5710092332889474511et_nat A2)) (not (@ _let_1 A2))))))
% 5.98/6.27 (assert (forall ((C tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ tptp.uminus1532241313380277803et_int A2)) (not (@ _let_1 A2))))))
% 5.98/6.27 (assert (forall ((C Bool) (A2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (not (@ _let_1 A2)) (@ _let_1 (@ tptp.uminus_uminus_set_o A2))))))
% 5.98/6.27 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (not (@ _let_1 A2)) (@ _let_1 (@ tptp.uminus613421341184616069et_nat A2))))))
% 5.98/6.27 (assert (forall ((C tptp.set_nat_rat) (A2 tptp.set_set_nat_rat)) (let ((_let_1 (@ tptp.member_set_nat_rat C))) (=> (not (@ _let_1 A2)) (@ _let_1 (@ tptp.uminus3098529973357106300at_rat A2))))))
% 5.98/6.27 (assert (forall ((C tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (not (@ _let_1 A2)) (@ _let_1 (@ tptp.uminus5710092332889474511et_nat A2))))))
% 5.98/6.27 (assert (forall ((C tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (not (@ _let_1 A2)) (@ _let_1 (@ tptp.uminus1532241313380277803et_int A2))))))
% 5.98/6.27 (assert (= (@ tptp.archim2889992004027027881ng_rat tptp.zero_zero_rat) tptp.zero_zero_int))
% 5.98/6.27 (assert (= (@ tptp.archim7802044766580827645g_real tptp.zero_zero_real) tptp.zero_zero_int))
% 5.98/6.27 (assert (= (@ tptp.archim2889992004027027881ng_rat tptp.one_one_rat) tptp.one_one_int))
% 5.98/6.27 (assert (= (@ tptp.archim7802044766580827645g_real tptp.one_one_real) tptp.one_one_int))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X) tptp.one_one_rat))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real tptp.one_one_real) X))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X) tptp.one_one_rat)) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int))))
% 5.98/6.27 (assert (forall ((X tptp.real) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X))) A) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real A)))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X))))
% 5.98/6.27 (assert (forall ((C Bool) (A2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ tptp.uminus_uminus_set_o A2)) (not (@ _let_1 A2))))))
% 5.98/6.27 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ tptp.uminus613421341184616069et_nat A2)) (not (@ _let_1 A2))))))
% 5.98/6.27 (assert (forall ((C tptp.set_nat_rat) (A2 tptp.set_set_nat_rat)) (let ((_let_1 (@ tptp.member_set_nat_rat C))) (=> (@ _let_1 (@ tptp.uminus3098529973357106300at_rat A2)) (not (@ _let_1 A2))))))
% 5.98/6.27 (assert (forall ((C tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ tptp.uminus5710092332889474511et_nat A2)) (not (@ _let_1 A2))))))
% 5.98/6.27 (assert (forall ((C tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ tptp.uminus1532241313380277803et_int A2)) (not (@ _let_1 A2))))))
% 5.98/6.27 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real Y)) (@ tptp.archim7802044766580827645g_real X)))))
% 5.98/6.27 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat Y)) (@ tptp.archim2889992004027027881ng_rat X)))))
% 5.98/6.27 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.archim2889992004027027881ng_rat Y)) (@ (@ tptp.ord_less_rat X) Y))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.archim7802044766580827645g_real Y)) (@ (@ tptp.ord_less_real X) Y))))
% 5.98/6.27 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_eq_real R2) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real R2))))))
% 5.98/6.27 (assert (forall ((R2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat R2) (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.archim2889992004027027881ng_rat R2))))))
% 5.98/6.27 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X) Y))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.archim2889992004027027881ng_rat Y)))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.archim7802044766580827645g_real Y)))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B))) (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B))))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B))) (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B))))))))
% 5.98/6.27 (assert (forall ((X tptp.complex)) (= (= (@ tptp.sgn_sgn_complex X) tptp.zero_zero_complex) (= X tptp.zero_zero_complex))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (= (@ tptp.sgn_sgn_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((X tptp.real) (I tptp.int)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.powr_real X) (@ tptp.ring_1_of_int_real I)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 I)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int I)))))))))))))
% 5.98/6.27 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 5.98/6.27 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 5.98/6.27 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 5.98/6.27 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 5.98/6.27 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) _let_1))) N)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X))))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) _let_1))) N)) (@ tptp.exp_real X)))))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.power_power_nat X) Y) Z) (= (@ (@ tptp.vEBT_VEBT_power (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ tptp.some_nat Z)))))
% 5.98/6.27 (assert (forall ((B tptp.complex) (K tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex B)) K) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex B) (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K)))))
% 5.98/6.27 (assert (forall ((B tptp.int) (K tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int B)) K) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) K)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int B) (@ tptp.semiri1314217659103216013at_int K))) tptp.one_one_int)) K)))))
% 5.98/6.27 (assert (forall ((B tptp.real) (K tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real B)) K) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real B) (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K)))))
% 5.98/6.27 (assert (forall ((B tptp.rat) (K tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat B)) K) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat B) (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K)))))
% 5.98/6.27 (assert (forall ((B tptp.complex) (K tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex B) (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex B)) K)))))
% 5.98/6.27 (assert (forall ((B tptp.int) (K tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int B) (@ tptp.semiri1314217659103216013at_int K))) tptp.one_one_int)) K) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) K)) (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int B)) K)))))
% 5.98/6.27 (assert (forall ((B tptp.real) (K tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real B) (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K)) (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real B)) K)))))
% 5.98/6.27 (assert (forall ((B tptp.rat) (K tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat B) (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat B)) K)))))
% 5.98/6.27 (assert (forall ((N tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_real _let_1) X) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim7802044766580827645g_real X) (@ (@ tptp.plus_plus_int N) tptp.one_one_int)))))))
% 5.98/6.27 (assert (forall ((N tptp.int) (X tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat N))) (=> (@ (@ tptp.ord_less_rat _let_1) X) (=> (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (= (@ tptp.archim2889992004027027881ng_rat X) (@ (@ tptp.plus_plus_int N) tptp.one_one_int)))))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y) Z) (= (@ (@ tptp.vEBT_VEBT_add (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ tptp.some_nat Z)))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.times_times_nat X) Y) Z) (= (@ (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ tptp.some_nat Z)))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (= (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X)) X) (exists ((N4 tptp.int)) (= X (@ tptp.ring_1_of_int_rat N4))))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (= (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X)) X) (exists ((N4 tptp.int)) (= X (@ tptp.ring_1_of_int_real N4))))))
% 5.98/6.27 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.one_one_complex) tptp.one_one_complex))
% 5.98/6.27 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.one_one_real) tptp.one_one_real))
% 5.98/6.27 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.one_one_rat) tptp.one_one_rat))
% 5.98/6.27 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int))
% 5.98/6.27 (assert (= (@ tptp.ring_1_of_int_int tptp.zero_zero_int) tptp.zero_zero_int))
% 5.98/6.27 (assert (= (@ tptp.ring_1_of_int_real tptp.zero_zero_int) tptp.zero_zero_real))
% 5.98/6.27 (assert (= (@ tptp.ring_1_of_int_rat tptp.zero_zero_int) tptp.zero_zero_rat))
% 5.98/6.27 (assert (forall ((Z tptp.int)) (= (= tptp.zero_zero_int (@ tptp.ring_1_of_int_int Z)) (= Z tptp.zero_zero_int))))
% 5.98/6.27 (assert (forall ((Z tptp.int)) (= (= tptp.zero_zero_real (@ tptp.ring_1_of_int_real Z)) (= Z tptp.zero_zero_int))))
% 5.98/6.27 (assert (forall ((Z tptp.int)) (= (= tptp.zero_zero_rat (@ tptp.ring_1_of_int_rat Z)) (= Z tptp.zero_zero_int))))
% 5.98/6.27 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z) tptp.zero_zero_int) (= Z tptp.zero_zero_int))))
% 5.98/6.27 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z) tptp.zero_zero_real) (= Z tptp.zero_zero_int))))
% 5.98/6.27 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_rat Z) tptp.zero_zero_rat) (= Z tptp.zero_zero_int))))
% 5.98/6.27 (assert (= (@ tptp.exp_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 5.98/6.27 (assert (= (@ tptp.exp_real tptp.zero_zero_real) tptp.one_one_real))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (assert (= (@ tptp.ring_17405671764205052669omplex tptp.one_one_int) tptp.one_one_complex))
% 5.98/6.27 (assert (= (@ tptp.ring_1_of_int_int tptp.one_one_int) tptp.one_one_int))
% 5.98/6.27 (assert (= (@ tptp.ring_1_of_int_real tptp.one_one_int) tptp.one_one_real))
% 5.98/6.27 (assert (= (@ tptp.ring_1_of_int_rat tptp.one_one_int) tptp.one_one_rat))
% 5.98/6.27 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_17405671764205052669omplex Z) tptp.one_one_complex) (= Z tptp.one_one_int))))
% 5.98/6.27 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z) tptp.one_one_int) (= Z tptp.one_one_int))))
% 5.98/6.27 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z) tptp.one_one_real) (= Z tptp.one_one_int))))
% 5.98/6.27 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_rat Z) tptp.one_one_rat) (= Z tptp.one_one_int))))
% 5.98/6.27 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 5.98/6.27 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 5.98/6.27 (assert (forall ((A tptp.int)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 5.98/6.27 (assert (forall ((Z tptp.int)) (= (@ tptp.archim2898591450579166408c_real (@ tptp.ring_1_of_int_real Z)) tptp.zero_zero_real)))
% 5.98/6.27 (assert (forall ((Z tptp.int)) (= (@ tptp.archimedean_frac_rat (@ tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat)))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.exp_real X)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 5.98/6.27 (assert (= tptp.ord_less_eq_nat (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.vEBT_VEBT_lesseq (@ tptp.some_nat X3)) (@ tptp.some_nat Y2)))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (assert (forall ((B tptp.int) (W2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W2)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W2)) X))))
% 5.98/6.27 (assert (forall ((B tptp.int) (W2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W2)) (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W2)) X))))
% 5.98/6.27 (assert (forall ((B tptp.int) (W2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W2)) (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W2)) X))))
% 5.98/6.27 (assert (forall ((X tptp.int) (B tptp.int) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W2)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B) W2)))))
% 5.98/6.27 (assert (forall ((X tptp.int) (B tptp.int) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W2)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B) W2)))))
% 5.98/6.27 (assert (forall ((X tptp.int) (B tptp.int) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W2)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B) W2)))))
% 5.98/6.27 (assert (forall ((B tptp.int) (W2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W2)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W2)) X))))
% 5.98/6.27 (assert (forall ((B tptp.int) (W2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W2)) (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W2)) X))))
% 5.98/6.27 (assert (forall ((B tptp.int) (W2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W2)) (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W2)) X))))
% 5.98/6.27 (assert (forall ((X tptp.int) (B tptp.int) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W2)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B) W2)))))
% 5.98/6.27 (assert (forall ((X tptp.int) (B tptp.int) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W2)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B) W2)))))
% 5.98/6.27 (assert (forall ((X tptp.int) (B tptp.int) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W2)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B) W2)))))
% 5.98/6.27 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)) (@ tptp.ring_1_of_int_int Z)))))
% 5.98/6.27 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 Z)) (@ tptp.ring_1_of_int_real Z)))))
% 5.98/6.27 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 Z)) (@ tptp.ring_1_of_int_rat Z)))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real Z3)))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.ring_1_of_int_rat Z3)))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real Z3)))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat Z3)))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z3)) X))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z3)) X))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (not (= (@ tptp.exp_real X) tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.exp_real X))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X)))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X)))))
% 5.98/6.27 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s7457072308508201937r_real X) N))))))
% 5.98/6.27 (assert (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4028243227959126397er_rat X) N))))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4663373288045622133er_nat X) N))))))
% 5.98/6.27 (assert (forall ((X tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4660882817536571857er_int X) N))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (= (@ _let_1 N) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 M2) tptp.zero_zero_real))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (= (@ _let_1 N) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 M2) tptp.zero_zero_rat))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (not (= (@ _let_1 M2) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (not (= (@ _let_1 N) tptp.zero_zero_real)))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (not (= (@ _let_1 M2) tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (not (= (@ _let_1 N) tptp.zero_zero_rat)))))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ tptp.exp_real X))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X))) tptp.one_one_real)))
% 5.98/6.27 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X))) tptp.one_one_complex)))
% 5.98/6.27 (assert (forall ((X tptp.real) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) A))))
% 5.98/6.27 (assert (forall ((X tptp.rat) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat X) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) A))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) Z) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real Z)))))
% 5.98/6.27 (assert (forall ((X tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) Z) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.ring_1_of_int_rat Z)))))
% 5.98/6.27 (assert (forall ((Z tptp.int) (X tptp.rat)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) X))))
% 5.98/6.27 (assert (forall ((Z tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) X))))
% 5.98/6.27 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.comm_s7457072308508201937r_real X) N)))))
% 5.98/6.27 (assert (forall ((X tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.comm_s4028243227959126397er_rat X) N)))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.comm_s4663373288045622133er_nat X) N)))))
% 5.98/6.27 (assert (forall ((X tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.comm_s4660882817536571857er_int X) N)))))
% 5.98/6.27 (assert (forall ((N tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X)))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s2602460028002588243omplex tptp.zero_zero_complex) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s7457072308508201937r_real tptp.zero_zero_real) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4028243227959126397er_rat tptp.zero_zero_rat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4663373288045622133er_nat tptp.zero_zero_nat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4660882817536571857er_int tptp.zero_zero_int) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ tptp.exp_real X)))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (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))))))
% 5.98/6.27 (assert (forall ((N tptp.int) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))))
% 5.98/6.27 (assert (forall ((N tptp.int) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X)))))
% 5.98/6.27 (assert (forall ((N tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) X)))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (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))))))
% 5.98/6.27 (assert (forall ((N tptp.int) (X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_real tptp.one_one_real) X)))))
% 5.98/6.27 (assert (forall ((N tptp.int) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X)))))
% 5.98/6.27 (assert (forall ((N tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) X)))))
% 5.98/6.27 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) Y) (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.minus_minus_real Y) tptp.one_one_real)) (= (@ tptp.exp_real X4) Y))))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real Y) (@ tptp.ln_ln_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real Y)) X)))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (exists ((Z3 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z3)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z3) tptp.one_one_int)))))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (exists ((Z3 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z3)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z3) tptp.one_one_int)))))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (exists ((X4 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X4)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int X4) tptp.one_one_int))) (forall ((Y4 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Y4)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Y4) tptp.one_one_int)))) (= Y4 X4)))))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (exists ((X4 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X4)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int X4) tptp.one_one_int))) (forall ((Y4 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Y4)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Y4) tptp.one_one_int)))) (= Y4 X4)))))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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)))
% 5.98/6.27 (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)))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real Y)) Y)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X)) X))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int X)) (@ _let_1 X)))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) X))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) X))))
% 5.98/6.27 (assert (= tptp.ord_less_eq_int (lambda ((N4 tptp.int) (M3 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real N4)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real M3)) tptp.one_one_real)))))
% 5.98/6.27 (assert (= tptp.ord_less_int (lambda ((N4 tptp.int) (M3 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real N4)) tptp.one_one_real)) (@ tptp.ring_1_of_int_real M3)))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat A)) (@ tptp.ring_1_of_int_rat B))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B)))))
% 5.98/6.27 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real A)) (@ tptp.ring_1_of_int_real B))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B)))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) (@ tptp.suc N)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex)) N)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.times_times_real A) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) N)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) N)))))
% 5.98/6.27 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.times_times_nat A) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) N)))))
% 5.98/6.27 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.times_times_int A) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) N)))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) K) tptp.zero_zero_complex))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) K) tptp.zero_zero_int))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) K) tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) K) tptp.zero_zero_rat))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) K) tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat N) K))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) K) tptp.zero_zero_int) (@ (@ tptp.ord_less_nat N) K))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) K) tptp.zero_zero_real) (@ (@ tptp.ord_less_nat N) K))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) K) tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat N) K))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex A) N) tptp.zero_zero_complex) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (= A (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K3))))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (N tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real A) N) tptp.zero_zero_real) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (= A (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K3))))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat A) N) tptp.zero_zero_rat) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (= A (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K3))))))))
% 5.98/6.27 (assert (= tptp.powr_real (lambda ((X3 tptp.real) (A4 tptp.real)) (@ (@ (@ tptp.if_real (= X3 tptp.zero_zero_real)) tptp.zero_zero_real) (@ tptp.exp_real (@ (@ tptp.times_times_real A4) (@ tptp.ln_ln_real X3)))))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) K) tptp.zero_zero_complex)))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) K) tptp.zero_zero_int)))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) K) tptp.zero_zero_real)))))
% 5.98/6.27 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) K) tptp.zero_zero_rat)))))
% 5.98/6.27 (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)))))))
% 5.98/6.27 (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)))))))
% 5.98/6.27 (assert (forall ((X tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim7802044766580827645g_real X) A) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real X) _let_1))))))
% 5.98/6.27 (assert (forall ((X tptp.rat) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat A))) (= (= (@ tptp.archim2889992004027027881ng_rat X) A) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X) (@ (@ tptp.ord_less_eq_rat X) _let_1))))))
% 5.98/6.27 (assert (forall ((Z tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (= (@ tptp.archim7802044766580827645g_real X) Z))))))
% 5.98/6.27 (assert (forall ((Z tptp.int) (X tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat Z))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X) (=> (@ (@ tptp.ord_less_eq_rat X) _let_1) (= (@ tptp.archim2889992004027027881ng_rat X) Z))))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X)))) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real X) _let_1)))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X)))) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X) (@ (@ tptp.ord_less_eq_rat X) _let_1)))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) Z) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)))))
% 5.98/6.27 (assert (forall ((X tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) Z) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)))))
% 5.98/6.27 (assert (forall ((Z tptp.int) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X))))
% 5.98/6.27 (assert (forall ((Z tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_complex (@ tptp.exp_complex (@ (@ tptp.divide1717551699836669952omplex X) (@ tptp.semiri8010041392384452111omplex N)))) N) (@ tptp.exp_complex X)))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_real (@ tptp.exp_real (@ (@ tptp.divide_divide_real X) (@ tptp.semiri5074537144036343181t_real N)))) N) (@ tptp.exp_real X)))))
% 5.98/6.27 (assert (forall ((N tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X))))))
% 5.98/6.27 (assert (forall ((N tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X)))) tptp.one_one_real)))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 N) (@ (@ tptp.times_times_nat (@ _let_1 M2)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat M2))) (@ (@ tptp.minus_minus_nat N) M2))))))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Z tptp.int)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 N) (@ (@ tptp.times_times_int (@ _let_1 M2)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int M2))) (@ (@ tptp.minus_minus_nat N) M2))))))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Z tptp.real)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 N) (@ (@ tptp.times_times_real (@ _let_1 M2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real M2))) (@ (@ tptp.minus_minus_nat N) M2))))))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Z tptp.rat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 N) (@ (@ tptp.times_times_rat (@ _let_1 M2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat M2))) (@ (@ tptp.minus_minus_nat N) M2))))))))
% 5.98/6.27 (assert (forall ((Q4 tptp.real) (P6 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q4) (@ (@ tptp.ord_less_eq_real P6) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real P6) Q4)))) Q4)))))
% 5.98/6.27 (assert (forall ((Q4 tptp.rat) (P6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q4) (@ (@ tptp.ord_less_eq_rat P6) (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat P6) Q4)))) Q4)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B)))) (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B))))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B)))) (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B))))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B)))) (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B))))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B)))) (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B))))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B)))) (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B))))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B)))) (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B))))))))
% 5.98/6.27 (assert (= tptp.neg_nu6511756317524482435omplex (lambda ((X3 tptp.complex)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex X3) X3)) tptp.one_one_complex))))
% 5.98/6.27 (assert (= tptp.neg_nu6075765906172075777c_real (lambda ((X3 tptp.real)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X3) X3)) tptp.one_one_real))))
% 5.98/6.27 (assert (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X3 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X3) X3)) tptp.one_one_rat))))
% 5.98/6.27 (assert (= tptp.neg_nu3811975205180677377ec_int (lambda ((X3 tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X3) X3)) tptp.one_one_int))))
% 5.98/6.27 (assert (forall ((R2 tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex R2))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex R2) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.comm_s2602460028002588243omplex _let_1) K)) (@ (@ tptp.times_times_complex R2) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) K))))))
% 5.98/6.27 (assert (forall ((R2 tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int R2))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int R2) (@ tptp.semiri1314217659103216013at_int K))) (@ (@ tptp.comm_s4660882817536571857er_int _let_1) K)) (@ (@ tptp.times_times_int R2) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) K))))))
% 5.98/6.27 (assert (forall ((R2 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real R2))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real R2) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.comm_s7457072308508201937r_real _let_1) K)) (@ (@ tptp.times_times_real R2) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) K))))))
% 5.98/6.27 (assert (forall ((R2 tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat R2))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat R2) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.comm_s4028243227959126397er_rat _let_1) K)) (@ (@ tptp.times_times_rat R2) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) K))))))
% 5.98/6.27 (assert (forall ((Q4 tptp.rat) (P6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q4) (@ (@ 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) Q4)))) tptp.one_one_rat)) Q4)) P6))))
% 5.98/6.27 (assert (forall ((Q4 tptp.real) (P6 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q4) (@ (@ 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) Q4)))) tptp.one_one_real)) Q4)) P6))))
% 5.98/6.27 (assert (= tptp.ord_less_nat (lambda ((Y2 tptp.nat) (X3 tptp.nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat X3)) (@ tptp.some_nat Y2)))))
% 5.98/6.27 (assert (= tptp.ord_less_nat (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat X3)) (@ tptp.some_nat Y2)))))
% 5.98/6.27 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_succ T) X) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_set_vebt T)) X) Sx)))))
% 5.98/6.27 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_pred T) X) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_set_vebt T)) X) Sx)))))
% 5.98/6.27 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_succ T) X) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Sx)))))
% 5.98/6.27 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Px tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_pred T) X) (@ tptp.some_nat Px)) (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Px)))))
% 5.98/6.27 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_VEBT_max_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X))))))
% 5.98/6.27 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Maxi tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat Maxi)) (=> (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.ord_less_eq_nat X) Maxi))))))
% 5.98/6.27 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X)) (@ (@ tptp.vEBT_VEBT_max_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X)))))
% 5.98/6.27 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat X)) (@ (@ tptp.vEBT_VEBT_min_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X)))))
% 5.98/6.27 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_VEBT_min_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat X))))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Mini tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat Mini)) (=> (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.ord_less_eq_nat Mini) X))))))
% 5.98/6.27 (assert (forall ((X23 tptp.nat)) (= (@ tptp.size_size_option_nat (@ tptp.some_nat X23)) (@ tptp.suc tptp.zero_zero_nat))))
% 5.98/6.27 (assert (forall ((X23 tptp.product_prod_nat_nat)) (= (@ tptp.size_s170228958280169651at_nat (@ tptp.some_P7363390416028606310at_nat X23)) (@ tptp.suc tptp.zero_zero_nat))))
% 5.98/6.27 (assert (forall ((X23 tptp.num)) (= (@ tptp.size_size_option_num (@ tptp.some_num X23)) (@ tptp.suc tptp.zero_zero_nat))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (assert (forall ((X tptp.real) (N tptp.int)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.powr_real X) (@ tptp.ring_1_of_int_real N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) N))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 N)))) (=> (not _let_3) (= _let_2 (@ tptp.inverse_inverse_real (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int N)))))))))))))
% 5.98/6.27 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull T) (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat))))
% 5.98/6.27 (assert (forall ((T tptp.vEBT_VEBT)) (=> (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat) (@ tptp.vEBT_VEBT_minNull T))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (assert (= (@ tptp.inverse_inverse_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.27 (assert (= (@ tptp.inverse_inverse_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (= (@ tptp.inverse_inverse_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 5.98/6.27 (assert (forall ((X tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex X) tptp.one_one_complex) (= X tptp.one_one_complex))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (= (@ tptp.inverse_inverse_real X) tptp.one_one_real) (= X tptp.one_one_real))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (= (@ tptp.inverse_inverse_rat X) tptp.one_one_rat) (= X tptp.one_one_rat))))
% 5.98/6.27 (assert (= (@ tptp.invers8013647133539491842omplex tptp.one_one_complex) tptp.one_one_complex))
% 5.98/6.27 (assert (= (@ tptp.inverse_inverse_real tptp.one_one_real) tptp.one_one_real))
% 5.98/6.27 (assert (= (@ tptp.inverse_inverse_rat tptp.one_one_rat) tptp.one_one_rat))
% 5.98/6.27 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.inverse_inverse_real A)) (@ _let_1 A)))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ tptp.inverse_inverse_rat A)) (@ _let_1 A)))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (@ (@ tptp.ord_less_real B) A)))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (@ (@ tptp.ord_less_rat B) A)))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (@ _let_1 A)))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ _let_1 tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (@ _let_1 A)))))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.inverse_inverse_real A)) (@ _let_1 A)))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ tptp.inverse_inverse_rat A)) (@ _let_1 A)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (@ (@ tptp.ord_less_eq_real B) A)))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (@ (@ tptp.ord_less_eq_rat B) A)))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (@ (@ tptp.ord_less_eq_real B) A))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 5.98/6.27 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) A) tptp.one_one_complex))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real A)) A) tptp.one_one_real))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat A)) A) tptp.one_one_rat))))
% 5.98/6.27 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.invers8013647133539491842omplex A)) tptp.one_one_complex))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.times_times_real A) (@ tptp.inverse_inverse_real A)) tptp.one_one_real))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.times_times_rat A) (@ tptp.inverse_inverse_rat A)) tptp.one_one_rat))))
% 5.98/6.27 (assert (= (@ tptp.inverse_inverse_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.27 (assert (= (@ tptp.inverse_inverse_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 5.98/6.27 (assert (forall ((A tptp.real)) (=> (= (@ tptp.inverse_inverse_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (=> (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ tptp.inverse_inverse_real A) (@ tptp.inverse_inverse_real B)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= A B))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ tptp.inverse_inverse_rat A) (@ tptp.inverse_inverse_rat B)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= A B))))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real (@ tptp.inverse_inverse_real A)) A))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.inverse_inverse_rat A)) A))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (not (= (@ tptp.inverse_inverse_real A) tptp.zero_zero_real)))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (not (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat)))))
% 5.98/6.27 (assert (= (@ tptp.size_size_option_nat tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 5.98/6.27 (assert (= (@ tptp.size_s170228958280169651at_nat tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 5.98/6.27 (assert (= (@ tptp.size_size_option_num tptp.none_num) (@ tptp.suc tptp.zero_zero_nat)))
% 5.98/6.27 (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)))
% 5.98/6.27 (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)))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real B) A)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat B) A)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real B)) (@ tptp.inverse_inverse_real A))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (=> (@ _let_1 tptp.zero_zero_real) (@ _let_1 A))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (=> (@ _let_1 tptp.zero_zero_rat) (@ _let_1 A))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real B)) (@ tptp.inverse_inverse_real A))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A))))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) tptp.zero_zero_real) (=> (not (= A tptp.zero_zero_real)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) tptp.zero_zero_rat) (=> (not (= A tptp.zero_zero_rat)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat)))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ tptp.inverse_inverse_real A)) (=> (not (= A tptp.zero_zero_real)) (@ _let_1 A))))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ tptp.inverse_inverse_rat A)) (=> (not (= A tptp.zero_zero_rat)) (@ _let_1 A))))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) tptp.zero_zero_rat))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ tptp.inverse_inverse_real A))))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ tptp.inverse_inverse_rat A))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real B)) (@ tptp.inverse_inverse_real A)))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A)))))))
% 5.98/6.27 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex (@ tptp.invers8013647133539491842omplex A))))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real A))))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat (@ tptp.inverse_inverse_rat A))))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.times_times_complex A) B) tptp.one_one_complex) (= (@ tptp.invers8013647133539491842omplex A) B))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real A) B) tptp.one_one_real) (= (@ tptp.inverse_inverse_real A) B))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.times_times_rat A) B) tptp.one_one_rat) (= (@ tptp.inverse_inverse_rat A) B))))
% 5.98/6.27 (assert (= tptp.invers8013647133539491842omplex (@ tptp.divide1717551699836669952omplex tptp.one_one_complex)))
% 5.98/6.27 (assert (= tptp.inverse_inverse_real (@ tptp.divide_divide_real tptp.one_one_real)))
% 5.98/6.27 (assert (= tptp.inverse_inverse_rat (@ tptp.divide_divide_rat tptp.one_one_rat)))
% 5.98/6.27 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real (@ tptp.abs_abs_real A))))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.abs_abs_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat (@ tptp.abs_abs_rat A))))))
% 5.98/6.27 (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)))
% 5.98/6.27 (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)))
% 5.98/6.27 (assert (= tptp.divide_divide_real (lambda ((X3 tptp.real) (Y2 tptp.real)) (@ (@ tptp.times_times_real X3) (@ tptp.inverse_inverse_real Y2)))))
% 5.98/6.27 (assert (forall ((Uz tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz)) Va2) Vb) Vc)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real B) A)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat B) A)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real B)) (@ tptp.inverse_inverse_real A))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A)))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real B)) (@ tptp.inverse_inverse_real A))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A))))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real X)) tptp.one_one_real) (or (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat X)) tptp.one_one_rat) (or (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X)))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.inverse_inverse_real A))))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat A))))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.inverse_inverse_real X)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat X)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (@ (@ tptp.ord_less_rat X) tptp.one_one_rat)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real B))) (let ((_let_2 (@ tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) _let_2)) _let_1))))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) _let_2)) _let_1))))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real B))) (let ((_let_2 (@ tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.plus_plus_real A) B))) _let_1))))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat _let_2) (@ (@ tptp.plus_plus_rat A) B))) _let_1))))))))
% 5.98/6.27 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) A) tptp.one_one_complex))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real A)) A) tptp.one_one_real))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat A)) A) tptp.one_one_rat))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real B))) (let ((_let_2 (@ tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.minus_minus_real B) A))) _let_1))))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat _let_2) (@ (@ tptp.minus_minus_rat B) A))) _let_1))))))))
% 5.98/6.27 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex A) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) A)))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real A) (@ (@ tptp.divide_divide_real tptp.one_one_real) A)))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat A) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)))))
% 5.98/6.27 (assert (forall ((Y tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ (@ tptp.powr_real (@ tptp.inverse_inverse_real Y)) A) (@ tptp.inverse_inverse_real (@ (@ tptp.powr_real Y) A))))))
% 5.98/6.27 (assert (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz)) X))))
% 5.98/6.27 (assert (forall ((X tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X)) (=> (forall ((Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf true) Uv2)))) (=> (forall ((Uu2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu2) true)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))))))))))
% 5.98/6.27 (assert (forall ((Uv Bool) (Uw Bool) (N tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ tptp.vEBT_Leaf Uv) Uw)) (@ tptp.suc N)) tptp.none_nat)))
% 5.98/6.27 (assert (forall ((Uu Bool) (Uv Bool)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf Uu) Uv)) tptp.zero_zero_nat) tptp.none_nat)))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real A) B))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real B) A)) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) B)))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.times_times_rat A) B))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat B) A)) (=> (@ (@ tptp.ord_less_eq_rat _let_1) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) B)))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real A) B))) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real B) A)) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) B)))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.times_times_rat A) B))) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat B) A)) (=> (@ (@ tptp.ord_less_eq_rat _let_1) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) B)))))))
% 5.98/6.27 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.inverse_inverse_real A))))))
% 5.98/6.27 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat A))))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real X)) tptp.one_one_real) (or (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) X)))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat X)) tptp.one_one_rat) (or (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X)))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.inverse_inverse_real X)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real)))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat X)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (@ (@ tptp.ord_less_eq_rat X) tptp.one_one_rat)))))
% 5.98/6.27 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex B))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex _let_2) _let_1) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_2) (@ (@ tptp.minus_minus_complex A) B))) _let_1)))))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real B))) (let ((_let_2 (@ tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real _let_2) _let_1) (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.minus_minus_real A) B))) _let_1)))))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat _let_2) _let_1) (@ tptp.uminus_uminus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat _let_2) (@ (@ tptp.minus_minus_rat A) B))) _let_1)))))))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))) X)))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N2)))) X)))))
% 5.98/6.27 (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 ((N2 tptp.nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ P E2))))))
% 5.98/6.27 (assert (forall ((E2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N4)))) (and (not (= N4 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) E2)))))))
% 5.98/6.27 (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 ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N2))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ P E2))))))
% 5.98/6.27 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N2))) X))))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat (@ tptp.semiri681578069525770553at_rat N2))) X))))))
% 5.98/6.27 (assert (forall ((X tptp.complex) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (=> (not (= X tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2)) (@ (@ tptp.times_times_complex (@ _let_1 N)) (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex X)) M2))))))))
% 5.98/6.27 (assert (forall ((X tptp.real) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (=> (not (= X tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real X)) M2))))))))
% 5.98/6.27 (assert (forall ((X tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (=> (not (= X tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.power_power_rat (@ tptp.inverse_inverse_rat X)) M2))))))))
% 5.98/6.27 (assert (forall ((A Bool) (Uw Bool)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf A) Uw)) (@ tptp.suc tptp.zero_zero_nat)))) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))
% 5.98/6.27 (assert (forall ((B Bool) (Uu Bool)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_succ (@ (@ tptp.vEBT_Leaf Uu) B)) tptp.zero_zero_nat))) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (= _let_1 tptp.none_nat))))))
% 5.98/6.27 (assert (forall ((B Bool) (A Bool) (Va2 tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc (@ tptp.suc Va2))))) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))))
% 5.98/6.27 (assert (forall ((B Bool) (A Bool)) (let ((_let_1 (@ tptp.vEBT_vebt_maxt (@ (@ tptp.vEBT_Leaf A) B)))) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))))
% 5.98/6.27 (assert (forall ((A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_vebt_mint (@ (@ tptp.vEBT_Leaf A) B)))) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (= _let_1 tptp.none_nat))))))))
% 5.98/6.27 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (=> (@ (@ tptp.ord_less_eq_nat Ma) X) (= (@ (@ tptp.vEBT_vebt_succ _let_1) X) tptp.none_nat))))))
% 5.98/6.27 (assert (forall ((X (-> tptp.nat tptp.nat)) (X23 tptp.nat)) (= (@ (@ tptp.size_option_nat X) (@ tptp.some_nat X23)) (@ (@ tptp.plus_plus_nat (@ X X23)) (@ tptp.suc tptp.zero_zero_nat)))))
% 5.98/6.27 (assert (forall ((X (-> tptp.product_prod_nat_nat tptp.nat)) (X23 tptp.product_prod_nat_nat)) (= (@ (@ tptp.size_o8335143837870341156at_nat X) (@ tptp.some_P7363390416028606310at_nat X23)) (@ (@ tptp.plus_plus_nat (@ X X23)) (@ tptp.suc tptp.zero_zero_nat)))))
% 5.98/6.27 (assert (forall ((X (-> tptp.num tptp.nat)) (X23 tptp.num)) (= (@ (@ tptp.size_option_num X) (@ tptp.some_num X23)) (@ (@ tptp.plus_plus_nat (@ X X23)) (@ tptp.suc tptp.zero_zero_nat)))))
% 5.98/6.27 (assert (forall ((X tptp.real) (B tptp.real) (K tptp.int)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log B) X)) K) (and (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.ring_1_of_int_real K))) X) (@ (@ tptp.ord_less_real X) (@ _let_1 (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))))))))
% 5.98/6.27 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X8 (-> tptp.nat tptp.real))) (forall ((J3 tptp.nat)) (exists ((M8 tptp.nat)) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M3) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N4) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X8 M3)) (@ X8 N4)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3)))))))))))))
% 5.98/6.27 (assert (forall ((X (-> tptp.nat tptp.nat))) (= (@ (@ tptp.size_option_nat X) tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 5.98/6.27 (assert (forall ((X (-> tptp.product_prod_nat_nat tptp.nat))) (= (@ (@ tptp.size_o8335143837870341156at_nat X) tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 5.98/6.27 (assert (forall ((X (-> tptp.num tptp.nat))) (= (@ (@ tptp.size_option_num X) tptp.none_num) (@ tptp.suc tptp.zero_zero_nat))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (= (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X)) X) (exists ((N4 tptp.int)) (= X (@ tptp.ring_1_of_int_real N4))))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (= (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X)) X) (exists ((N4 tptp.int)) (= X (@ tptp.ring_1_of_int_rat N4))))))
% 5.98/6.27 (assert (= (@ tptp.archim6058952711729229775r_real tptp.zero_zero_real) tptp.zero_zero_int))
% 5.98/6.27 (assert (= (@ tptp.archim3151403230148437115or_rat tptp.zero_zero_rat) tptp.zero_zero_int))
% 5.98/6.27 (assert (= (@ tptp.archim6058952711729229775r_real tptp.one_one_real) tptp.one_one_int))
% 5.98/6.27 (assert (= (@ tptp.archim3151403230148437115or_rat tptp.one_one_rat) tptp.one_one_int))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X) tptp.one_one_real))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_rat X) tptp.one_one_rat))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_real X) tptp.one_one_real))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) tptp.one_one_int) (@ (@ tptp.ord_less_rat X) tptp.one_one_rat))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X)) tptp.one_one_int))))
% 5.98/6.27 (assert (forall ((X tptp.vEBT_VEBT)) (=> (forall ((A5 Bool) (B5 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf A5) B5)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2)))))))))
% 5.98/6.27 (assert (forall ((R2 tptp.set_Pr8693737435421807431at_nat) (S tptp.set_Pr8693737435421807431at_nat)) (=> (forall ((X4 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X4) Y3)))) (=> (@ _let_1 R2) (@ _let_1 S)))) (@ (@ tptp.ord_le3000389064537975527at_nat R2) S))))
% 5.98/6.27 (assert (forall ((R2 tptp.set_Pr7459493094073627847at_nat) (S tptp.set_Pr7459493094073627847at_nat)) (=> (forall ((X4 tptp.set_Pr4329608150637261639at_nat) (Y3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member1466754251312161552at_nat (@ (@ tptp.produc9060074326276436823at_nat X4) Y3)))) (=> (@ _let_1 R2) (@ _let_1 S)))) (@ (@ tptp.ord_le5997549366648089703at_nat R2) S))))
% 5.98/6.27 (assert (forall ((R2 tptp.set_Pr4329608150637261639at_nat) (S tptp.set_Pr4329608150637261639at_nat)) (=> (forall ((X4 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X4) Y3)))) (=> (@ _let_1 R2) (@ _let_1 S)))) (@ (@ tptp.ord_le1268244103169919719at_nat R2) S))))
% 5.98/6.27 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y3)))) (=> (@ _let_1 R2) (@ _let_1 S)))) (@ (@ tptp.ord_le3146513528884898305at_nat R2) S))))
% 5.98/6.27 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (S tptp.set_Pr958786334691620121nt_int)) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X4) Y3)))) (=> (@ _let_1 R2) (@ _let_1 S)))) (@ (@ tptp.ord_le2843351958646193337nt_int R2) S))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y)))))
% 5.98/6.27 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim3151403230148437115or_rat Y)))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X))) X)))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X))) X)))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y)) (@ (@ tptp.ord_less_real X) Y))))
% 5.98/6.27 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim3151403230148437115or_rat Y)) (@ (@ tptp.ord_less_rat X) Y))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim7802044766580827645g_real X))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim2889992004027027881ng_rat X))))
% 5.98/6.27 (assert (forall ((X tptp.vEBT_VEBT)) (=> (not (= X (@ (@ tptp.vEBT_Leaf false) false))) (=> (forall ((Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf true) Uv2)))) (=> (forall ((Uu2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu2) true)))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2)))))))))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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)))
% 5.98/6.27 (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)))
% 5.98/6.27 (assert (forall ((Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Uu tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) Uu) _let_1))))
% 5.98/6.27 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) X))))
% 5.98/6.27 (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))))
% 5.98/6.27 (assert (forall ((Z tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) X))))
% 5.98/6.27 (assert (forall ((Z tptp.int) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) X))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) Z) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real Z)))))
% 5.98/6.27 (assert (forall ((X tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) Z) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat Z)))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) Y)))))
% 5.98/6.27 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim3151403230148437115or_rat Y))) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X) Y)))))
% 5.98/6.27 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X))) (=> (= X (@ tptp.ring_1_of_int_real _let_1)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_int _let_1) N))))))
% 5.98/6.27 (assert (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X))) (=> (= X (@ tptp.ring_1_of_int_rat _let_1)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.power_power_rat X) N)) (@ (@ tptp.power_power_int _let_1) N))))))
% 5.98/6.27 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X) Y) (=> (forall ((A5 Bool) (B5 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (not (and (=> A5 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (and (=> B5 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (= Y tptp.none_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (not (= Y tptp.none_nat))) (not (forall ((Mi2 tptp.nat)) (=> (exists ((Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (not (= Y (@ tptp.some_nat Mi2)))))))))))
% 5.98/6.27 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X) Y) (=> (forall ((A5 Bool) (B5 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (not (and (=> B5 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (and (=> A5 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y tptp.none_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (not (= Y tptp.none_nat))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (not (= Y (@ tptp.some_nat Ma2)))))))))))
% 5.98/6.27 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (TrLst tptp.list_VEBT_VEBT) (Smry tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) TrLst) Smry))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) _let_1))))
% 5.98/6.27 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT) (X tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) Va2) Vb)) X) (or (= X Mi) (= X Ma)))))
% 5.98/6.27 (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))))
% 5.98/6.27 (assert (forall ((X tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull X) (=> (not (= X (@ (@ tptp.vEBT_Leaf false) false))) (not (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2)))))))))
% 5.98/6.27 (assert (forall ((X tptp.vEBT_VEBT) (Y Bool)) (let ((_let_1 (not Y))) (=> (= (@ tptp.vEBT_VEBT_minNull X) Y) (=> (=> (= X (@ (@ tptp.vEBT_Leaf false) false)) _let_1) (=> (=> (exists ((Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf true) Uv2))) Y) (=> (=> (exists ((Uu2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) true))) Y) (=> (=> (exists ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) _let_1) (not (=> (exists ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))) Y))))))))))
% 5.98/6.27 (assert (forall ((Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (Va2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux) Uy) Uz)) Va2) tptp.none_nat)))
% 5.98/6.27 (assert (forall ((Uy tptp.nat) (Uz tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT) (Vb tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy) Uz) Va2)) Vb) tptp.none_nat)))
% 5.98/6.27 (assert (forall ((R2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R2) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real R2)))) R2))))
% 5.98/6.27 (assert (forall ((R2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R2) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat R2)))) R2))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X)) tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X) tptp.one_one_rat)))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A))) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real B)))) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat A))) (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat B)))) (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) tptp.zero_zero_nat))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) N)))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) A) (@ (@ tptp.ord_less_eq_nat X) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A))))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.archim6058952711729229775r_real X))) tptp.one_one_int)))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.archim3151403230148437115or_rat X))) tptp.one_one_int)))
% 5.98/6.27 (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))))
% 5.98/6.27 (assert (forall ((N tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_real _let_1) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X) N))))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Tr tptp.list_VEBT_VEBT) (Sm tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) (@ tptp.suc tptp.zero_zero_nat)) Tr) Sm))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) _let_1))))
% 5.98/6.27 (assert (forall ((Z tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X) Z))))))
% 5.98/6.27 (assert (forall ((Z tptp.int) (X tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat Z))) (=> (@ (@ tptp.ord_less_eq_rat _let_1) X) (=> (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (= (@ tptp.archim3151403230148437115or_rat X) Z))))))
% 5.98/6.27 (assert (forall ((X tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim6058952711729229775r_real X) A) (and (@ (@ tptp.ord_less_eq_real _let_1) X) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 5.98/6.27 (assert (forall ((X tptp.rat) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat A))) (= (= (@ tptp.archim3151403230148437115or_rat X) A) (and (@ (@ tptp.ord_less_eq_rat _let_1) X) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))))
% 5.98/6.27 (assert (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim6058952711729229775r_real T)) (forall ((I4 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I4))) (=> (and (@ (@ tptp.ord_less_eq_real _let_1) T) (@ (@ tptp.ord_less_real T) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))) (@ P I4)))))))
% 5.98/6.27 (assert (forall ((P (-> tptp.int Bool)) (T tptp.rat)) (= (@ P (@ tptp.archim3151403230148437115or_rat T)) (forall ((I4 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I4))) (=> (and (@ (@ tptp.ord_less_eq_rat _let_1) T) (@ (@ tptp.ord_less_rat T) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))) (@ P I4)))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B))) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))))
% 5.98/6.27 (assert (forall ((Z tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X))))
% 5.98/6.27 (assert (forall ((Z tptp.int) (X tptp.rat)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) Z) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)))))
% 5.98/6.27 (assert (forall ((X tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) Z) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real _let_1)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))
% 5.98/6.27 (assert (forall ((X tptp.rat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X))) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat _let_1)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) N)))))
% 5.98/6.27 (assert (forall ((N tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X) N))))))
% 5.98/6.27 (assert (forall ((B tptp.int) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real A) (@ tptp.ring_1_of_int_real B))) (@ (@ tptp.divide_divide_int (@ tptp.archim6058952711729229775r_real A)) B)))))
% 5.98/6.27 (assert (forall ((Q4 tptp.real) (P6 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real P6) Q4)))) Q4)) P6))))
% 5.98/6.27 (assert (forall ((Q4 tptp.rat) (P6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q4) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat P6) Q4)))) Q4)) P6))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B)))) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B)))) (@ tptp.ring_1_of_int_rat (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))))
% 5.98/6.27 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B)))) (@ tptp.ring_1_of_int_int (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B)))) (@ tptp.ring_1_of_int_real (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B)))) (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))))
% 5.98/6.27 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B)))) (@ tptp.ring_1_of_int_int (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y)))) (let ((_let_2 (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.archim2898591450579166408c_real X)) (@ tptp.archim2898591450579166408c_real Y))) tptp.one_one_real))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))))
% 5.98/6.27 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim3151403230148437115or_rat Y)))) (let ((_let_2 (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ tptp.archimedean_frac_rat X)) (@ tptp.archimedean_frac_rat Y))) tptp.one_one_rat))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))))
% 5.98/6.27 (assert (forall ((Q4 tptp.real) (P6 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q4) (@ (@ tptp.ord_less_real P6) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real P6) Q4)))) tptp.one_one_real)) Q4)))))
% 5.98/6.27 (assert (forall ((Q4 tptp.rat) (P6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q4) (@ (@ tptp.ord_less_rat P6) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat P6) Q4)))) tptp.one_one_rat)) Q4)))))
% 5.98/6.27 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg) (=> (= Mi Ma) (and (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X_12))))) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))))))))
% 5.98/6.27 (assert (forall ((Q4 tptp.nat) (R2 tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q4) R2)) (= R2 tptp.zero_zero_nat))))
% 5.98/6.27 (assert (forall ((Q4 tptp.int) (R2 tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q4) R2)) (= R2 tptp.zero_zero_int))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.suc X))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat Xa2) X))) (=> (= (@ (@ tptp.nat_prod_decode_aux X) Xa2) Y) (and (=> _let_2 (= Y (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X) Xa2)))) (=> (not _let_2) (= Y (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat Xa2) _let_1))))))))))
% 5.98/6.27 (assert (= tptp.nat_prod_decode_aux (lambda ((K3 tptp.nat) (M3 tptp.nat)) (let ((_let_1 (@ tptp.suc K3))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat M3) K3)) (@ (@ tptp.product_Pair_nat_nat M3) (@ (@ tptp.minus_minus_nat K3) M3))) (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat M3) _let_1)))))))
% 5.98/6.27 (assert (= tptp.gbinomial_complex (lambda ((A4 tptp.complex) (K3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A4) (@ tptp.semiri8010041392384452111omplex K3))) tptp.one_one_complex)) K3)) (@ tptp.semiri5044797733671781792omplex K3)))))
% 5.98/6.27 (assert (= tptp.gbinomial_rat (lambda ((A4 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A4) (@ tptp.semiri681578069525770553at_rat K3))) tptp.one_one_rat)) K3)) (@ tptp.semiri773545260158071498ct_rat K3)))))
% 5.98/6.27 (assert (= tptp.gbinomial_real (lambda ((A4 tptp.real) (K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A4) (@ tptp.semiri5074537144036343181t_real K3))) tptp.one_one_real)) K3)) (@ tptp.semiri2265585572941072030t_real K3)))))
% 5.98/6.27 (assert (= tptp.gbinomial_rat (lambda ((A4 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K3)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat A4)) K3))) (@ tptp.semiri773545260158071498ct_rat K3)))))
% 5.98/6.27 (assert (= tptp.gbinomial_complex (lambda ((A4 tptp.complex) (K3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K3)) (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex A4)) K3))) (@ tptp.semiri5044797733671781792omplex K3)))))
% 5.98/6.27 (assert (= tptp.gbinomial_real (lambda ((A4 tptp.real) (K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real A4)) K3))) (@ tptp.semiri2265585572941072030t_real K3)))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (= (@ tptp.sinh_real X) tptp.zero_zero_real) (@ (@ tptp.member_real (@ tptp.exp_real X)) (@ (@ tptp.insert_real tptp.one_one_real) (@ (@ tptp.insert_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.bot_bot_set_real))))))
% 5.98/6.27 (assert (forall ((X tptp.complex)) (= (= (@ tptp.sinh_complex X) tptp.zero_zero_complex) (@ (@ tptp.member_complex (@ tptp.exp_complex X)) (@ (@ tptp.insert_complex tptp.one_one_complex) (@ (@ tptp.insert_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.bot_bot_set_complex))))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X)) (@ tptp.sinh_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X)) (@ _let_1 X)))))
% 5.98/6.27 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_VEBT_VEBT)) (@ tptp.finite5795047828879050333T_VEBT (@ tptp.set_VEBT_VEBT2 Xs))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_nat)) (@ tptp.finite_finite_nat (@ tptp.set_nat2 Xs))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_int)) (@ tptp.finite_finite_int (@ tptp.set_int2 Xs))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_complex)) (@ tptp.finite3207457112153483333omplex (@ tptp.set_complex2 Xs))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat)) (@ tptp.finite6177210948735845034at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_Extended_enat)) (@ tptp.finite4001608067531595151d_enat (@ tptp.set_Extended_enat2 Xs))))
% 5.98/6.27 (assert (= (@ tptp.sinh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.27 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.zero_zero_nat) tptp.one_one_complex))
% 5.98/6.27 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.zero_zero_nat) tptp.one_one_rat))
% 5.98/6.27 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.zero_zero_nat) tptp.one_one_int))
% 5.98/6.27 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 5.98/6.27 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.zero_zero_nat) tptp.one_one_real))
% 5.98/6.27 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.one_one_nat) tptp.one_one_complex))
% 5.98/6.27 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.one_one_nat) tptp.one_one_rat))
% 5.98/6.27 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.one_one_nat) tptp.one_one_int))
% 5.98/6.27 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.one_one_nat) tptp.one_one_nat))
% 5.98/6.27 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.one_one_nat) tptp.one_one_real))
% 5.98/6.27 (assert (= (@ tptp.semiri5044797733671781792omplex (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_complex))
% 5.98/6.27 (assert (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_rat))
% 5.98/6.27 (assert (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 5.98/6.27 (assert (= (@ tptp.semiri1408675320244567234ct_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 5.98/6.27 (assert (= (@ tptp.semiri2265585572941072030t_real (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_real))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.semiri1408675320244567234ct_nat N))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri773545260158071498ct_rat N) tptp.zero_zero_rat))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1406184849735516958ct_int N) tptp.zero_zero_int))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1408675320244567234ct_nat N) tptp.zero_zero_nat))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri2265585572941072030t_real N) tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 Xs3) A2)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.set_nat2 Xs3) A2)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (exists ((Xs3 tptp.list_int)) (= (@ tptp.set_int2 Xs3) A2)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (exists ((Xs3 tptp.list_complex)) (= (@ tptp.set_complex2 Xs3) A2)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A2) (exists ((Xs3 tptp.list_P6011104703257516679at_nat)) (= (@ tptp.set_Pr5648618587558075414at_nat Xs3) A2)))))
% 5.98/6.27 (assert (forall ((A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (exists ((Xs3 tptp.list_Extended_enat)) (= (@ tptp.set_Extended_enat2 Xs3) A2)))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_o) (B2 tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) B2) (forall ((X3 Bool)) (let ((_let_1 (@ tptp.member_o X3))) (=> (@ _let_1 (@ tptp.set_o2 Xs)) (@ _let_1 B2)))))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_set_nat) (B2 tptp.set_set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 Xs)) B2) (forall ((X3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X3))) (=> (@ _let_1 (@ tptp.set_set_nat2 Xs)) (@ _let_1 B2)))))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_set_nat_rat) (B2 tptp.set_set_nat_rat)) (= (@ (@ tptp.ord_le4375437777232675859at_rat (@ tptp.set_set_nat_rat2 Xs)) B2) (forall ((X3 tptp.set_nat_rat)) (let ((_let_1 (@ tptp.member_set_nat_rat X3))) (=> (@ _let_1 (@ tptp.set_set_nat_rat2 Xs)) (@ _let_1 B2)))))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_VEBT_VEBT) (B2 tptp.set_VEBT_VEBT)) (= (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) B2) (forall ((X3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X3))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBT2 Xs)) (@ _let_1 B2)))))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_nat) (B2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) B2) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (=> (@ _let_1 (@ tptp.set_nat2 Xs)) (@ _let_1 B2)))))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_int) (B2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) B2) (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (=> (@ _let_1 (@ tptp.set_int2 Xs)) (@ _let_1 B2)))))))
% 5.98/6.27 (assert (forall ((X tptp.produc4471711990508489141at_nat)) (not (forall ((F4 (-> tptp.nat tptp.nat tptp.nat)) (A5 tptp.nat) (B5 tptp.nat) (Acc tptp.nat)) (not (= X (@ (@ tptp.produc3209952032786966637at_nat F4) (@ (@ tptp.produc487386426758144856at_nat A5) (@ (@ tptp.product_Pair_nat_nat B5) Acc)))))))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat N)) tptp.zero_zero_rat))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int N)) tptp.zero_zero_int))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat N)) tptp.zero_zero_nat))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real N)) tptp.zero_zero_real))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.semiri2265585572941072030t_real N))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat M2)) (@ tptp.semiri773545260158071498ct_rat N)))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int M2)) (@ tptp.semiri1406184849735516958ct_int N)))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real M2)) (@ tptp.semiri2265585572941072030t_real N)))))
% 5.98/6.27 (assert (= tptp.semiri5044797733671781792omplex (@ tptp.comm_s2602460028002588243omplex tptp.one_one_complex)))
% 5.98/6.27 (assert (= tptp.semiri773545260158071498ct_rat (@ tptp.comm_s4028243227959126397er_rat tptp.one_one_rat)))
% 5.98/6.27 (assert (= tptp.semiri1406184849735516958ct_int (@ tptp.comm_s4660882817536571857er_int tptp.one_one_int)))
% 5.98/6.27 (assert (= tptp.semiri1408675320244567234ct_nat (@ tptp.comm_s4663373288045622133er_nat tptp.one_one_nat)))
% 5.98/6.27 (assert (= tptp.semiri2265585572941072030t_real (@ tptp.comm_s7457072308508201937r_real tptp.one_one_real)))
% 5.98/6.27 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (D6 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) D6)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Deg3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) Deg3))))))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat M2)) (@ tptp.semiri773545260158071498ct_rat N))))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int M2)) (@ tptp.semiri1406184849735516958ct_int N))))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real M2)) (@ tptp.semiri2265585572941072030t_real N))))))
% 5.98/6.27 (assert (forall ((X Bool) (Xs tptp.list_o)) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs)))))
% 5.98/6.27 (assert (forall ((X tptp.set_nat) (Xs tptp.list_set_nat)) (=> (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3254054031482475050et_nat Xs)))))
% 5.98/6.27 (assert (forall ((X tptp.set_nat_rat) (Xs tptp.list_set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat X) (@ tptp.set_set_nat_rat2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3959913991096427681at_rat Xs)))))
% 5.98/6.27 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs)))))
% 5.98/6.27 (assert (forall ((X tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs)))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs)))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_complex)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex (@ tptp.set_complex2 Xs))) (@ tptp.size_s3451745648224563538omplex Xs))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (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))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat N) N)))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat N) N)))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat N) N)))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat N) N)))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (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 M2) N)))))))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool) (X4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) X4)))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (Ux2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)) Ux2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList2) S3)) X4)))))))))
% 5.98/6.27 (assert (= tptp.semiri5044797733671781792omplex (lambda ((M3 tptp.nat)) (@ (@ (@ tptp.if_complex (= M3 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M3)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 5.98/6.27 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((M3 tptp.nat)) (@ (@ (@ tptp.if_int (= M3 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M3)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 5.98/6.27 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((M3 tptp.nat)) (@ (@ (@ tptp.if_rat (= M3 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M3)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 5.98/6.27 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((M3 tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M3)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 5.98/6.27 (assert (= tptp.semiri2265585572941072030t_real (lambda ((M3 tptp.nat)) (@ (@ (@ tptp.if_real (= M3 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M3)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri1406184849735516958ct_int N) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri773545260158071498ct_rat N) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri1408675320244567234ct_nat N) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri2265585572941072030t_real N) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) N) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)) (@ tptp.semiri5044797733671781792omplex N)))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)) (@ tptp.semiri1406184849735516958ct_int N)))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)) (@ tptp.semiri773545260158071498ct_rat N)))))
% 5.98/6.27 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) N) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ tptp.semiri2265585572941072030t_real N)))))
% 5.98/6.27 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) tptp.zero_zero_nat)))) (=> (forall ((A5 Bool) (B5 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) (@ tptp.suc tptp.zero_zero_nat))))) (=> (forall ((A5 Bool) (B5 Bool) (N2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) (@ tptp.suc (@ tptp.suc N2)))))) (=> (forall ((Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Uu2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2)) Uu2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (TrLst2 tptp.list_VEBT_VEBT) (Smry2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) TrLst2) Smry2)) X4)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Tr2 tptp.list_VEBT_VEBT) (Sm2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (@ (@ 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)) X4)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList2) Summary2)) X4)))))))))))))
% 5.98/6.27 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (Uw2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) Uw2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT) (Uz2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)) Uz2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2)) X4)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList2) Vc2)) X4)))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList2) Vd2)) X4)))))))))))
% 5.98/6.27 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) tptp.zero_zero_nat)))) (=> (forall ((A5 Bool) (Uw2 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) Uw2)) (@ tptp.suc tptp.zero_zero_nat))))) (=> (forall ((A5 Bool) (B5 Bool) (Va tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) (@ tptp.suc (@ tptp.suc Va)))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT) (Vb2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va3)) Vb2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT) (Vf2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve2)) Vf2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT) (Vj2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2)) Vj2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList2) Summary2)) X4)))))))))))))
% 5.98/6.27 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (B5 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) B5)) tptp.zero_zero_nat)))) (=> (forall ((Uv2 Bool) (Uw2 Bool) (N2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) (@ tptp.suc N2))))) (=> (forall ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (Va3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2)) Va3)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (Ve2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2)) Ve2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT) (Vi2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2)) Vi2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList2) Summary2)) X4))))))))))))
% 5.98/6.27 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool) (X4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) X4)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)) X4)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)) X4)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)) X4)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList2) Summary2)) X4)))))))))))
% 5.98/6.27 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool) (X4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) X4)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts) S3)) X4)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts) S3)) X4)))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList2) Summary2)) X4)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList2) Summary2)) X4)))))))))))
% 5.98/6.27 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X) Y) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) X) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X _let_1) (=> (and (=> B5 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (and (=> A5 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y tptp.none_nat))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X _let_1) (=> (= Y (@ tptp.some_nat Ma2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))))))))))
% 5.98/6.27 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X) Y) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) X) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X _let_1) (=> (and (=> A5 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (and (=> B5 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (= Y tptp.none_nat))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X _let_1) (=> (= Y (@ tptp.some_nat Mi2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))))))))))
% 5.98/6.27 (assert (forall ((K tptp.int) (L tptp.int) (Q4 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 Q4) R2)) (and (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int L) Q4)) 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) (= Q4 tptp.zero_zero_int)))))))))))
% 5.98/6.27 (assert (forall ((X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (= (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.remove3673390508374433037at_nat X) Xs)) (@ (@ tptp.minus_1356011639430497352at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat)))))
% 5.98/6.27 (assert (forall ((X tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.removeAll_VEBT_VEBT X) Xs)) (@ (@ tptp.minus_5127226145743854075T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT)))))
% 5.98/6.27 (assert (forall ((X tptp.real) (Xs tptp.list_real)) (= (@ tptp.set_real2 (@ (@ tptp.removeAll_real X) Xs)) (@ (@ tptp.minus_minus_set_real (@ tptp.set_real2 Xs)) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real)))))
% 5.98/6.27 (assert (forall ((X Bool) (Xs tptp.list_o)) (= (@ tptp.set_o2 (@ (@ tptp.removeAll_o X) Xs)) (@ (@ tptp.minus_minus_set_o (@ tptp.set_o2 Xs)) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)))))
% 5.98/6.27 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (= (@ tptp.set_int2 (@ (@ tptp.removeAll_int X) Xs)) (@ (@ tptp.minus_minus_set_int (@ tptp.set_int2 Xs)) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.set_nat2 (@ (@ tptp.removeAll_nat X) Xs)) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_nat2 Xs)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_o) (P (-> Bool Bool)) (N tptp.nat)) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) (@ tptp.set_o2 Xs)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) N))))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_set_nat) (P (-> tptp.set_nat Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X4) (@ tptp.set_set_nat2 Xs)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3254054031482475050et_nat Xs)) (@ P (@ (@ tptp.nth_set_nat Xs) N))))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_set_nat_rat) (P (-> tptp.set_nat_rat Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat X4) (@ tptp.set_set_nat_rat2 Xs)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3959913991096427681at_rat Xs)) (@ P (@ (@ tptp.nth_set_nat_rat Xs) N))))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) N))))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) N))))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) N))))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (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)))))))))
% 5.98/6.27 (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)))))))))
% 5.98/6.27 (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)))))))))
% 5.98/6.27 (assert (= (lambda ((Y5 tptp.list_int) (Z4 tptp.list_int)) (= Y5 Z4)) (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))))))))
% 5.98/6.27 (assert (= (lambda ((Y5 tptp.list_VEBT_VEBT) (Z4 tptp.list_VEBT_VEBT)) (= Y5 Z4)) (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))))))))
% 5.98/6.27 (assert (= (lambda ((Y5 tptp.list_nat) (Z4 tptp.list_nat)) (= Y5 Z4)) (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))))))))
% 5.98/6.27 (assert (forall ((X tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.removeAll_VEBT_VEBT X) Xs))) (@ tptp.size_s6755466524823107622T_VEBT Xs))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat (@ (@ tptp.removeAll_nat X) Xs))) (@ tptp.size_size_list_nat Xs))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (Xs tptp.list_set_nat_rat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3959913991096427681at_rat Xs)) (@ (@ tptp.member_set_nat_rat (@ (@ tptp.nth_set_nat_rat Xs) N)) (@ tptp.set_set_nat_rat2 Xs)))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (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)))))
% 5.98/6.27 (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 ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs)) (@ P X4))) (@ P (@ (@ tptp.nth_int Xs) N))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X4))) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) N))))))
% 5.98/6.27 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs)) (@ P X4))) (@ P (@ (@ tptp.nth_nat Xs) N))))))
% 5.98/6.27 (assert (forall ((X Bool) (Xs tptp.list_o)) (= (@ (@ tptp.member_o X) (@ 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) X))))))
% 5.98/6.27 (assert (forall ((X tptp.set_nat) (Xs tptp.list_set_nat)) (= (@ (@ tptp.member_set_nat X) (@ 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) X))))))
% 5.98/6.27 (assert (forall ((X tptp.set_nat_rat) (Xs tptp.list_set_nat_rat)) (= (@ (@ tptp.member_set_nat_rat X) (@ tptp.set_set_nat_rat2 Xs)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s3959913991096427681at_rat Xs)) (= (@ (@ tptp.nth_set_nat_rat Xs) I4) X))))))
% 5.98/6.27 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (= (@ (@ tptp.member_int X) (@ 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) X))))))
% 5.98/6.27 (assert (forall ((X tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X) (@ 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) X))))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.member_nat X) (@ 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) X))))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_o) (P (-> Bool Bool)) (X 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 X) (@ tptp.set_o2 Xs)) (@ P X)))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_set_nat) (P (-> tptp.set_nat Bool)) (X tptp.set_nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s3254054031482475050et_nat Xs)) (@ P (@ (@ tptp.nth_set_nat Xs) I2)))) (=> (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs)) (@ P X)))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_set_nat_rat) (P (-> tptp.set_nat_rat Bool)) (X tptp.set_nat_rat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s3959913991096427681at_rat Xs)) (@ P (@ (@ tptp.nth_set_nat_rat Xs) I2)))) (=> (@ (@ tptp.member_set_nat_rat X) (@ tptp.set_set_nat_rat2 Xs)) (@ P X)))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool)) (X 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 X) (@ tptp.set_int2 Xs)) (@ P X)))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (X tptp.vEBT_VEBT)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) I2)))) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X)))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool)) (X 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 X) (@ tptp.set_nat2 Xs)) (@ P X)))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool))) (= (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs)) (@ P X3))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) I4)))))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X3))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) I4)))))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool))) (= (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs)) (@ P X3))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) I4)))))))
% 5.98/6.27 (assert (forall ((X Bool) (Xs tptp.list_o)) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs)) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o (@ (@ tptp.removeAll_o X) Xs))) (@ tptp.size_size_list_o Xs)))))
% 5.98/6.27 (assert (forall ((X tptp.set_nat) (Xs tptp.list_set_nat)) (=> (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs)) (@ (@ tptp.ord_less_nat (@ tptp.size_s3254054031482475050et_nat (@ (@ tptp.removeAll_set_nat X) Xs))) (@ tptp.size_s3254054031482475050et_nat Xs)))))
% 5.98/6.27 (assert (forall ((X tptp.set_nat_rat) (Xs tptp.list_set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat X) (@ tptp.set_set_nat_rat2 Xs)) (@ (@ tptp.ord_less_nat (@ tptp.size_s3959913991096427681at_rat (@ (@ tptp.remove939820145577552881at_rat X) Xs))) (@ tptp.size_s3959913991096427681at_rat Xs)))))
% 5.98/6.27 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int (@ (@ tptp.removeAll_int X) Xs))) (@ tptp.size_size_list_int Xs)))))
% 5.98/6.27 (assert (forall ((X tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs)) (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.removeAll_VEBT_VEBT X) Xs))) (@ tptp.size_s6755466524823107622T_VEBT Xs)))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat (@ (@ tptp.removeAll_nat X) Xs))) (@ tptp.size_size_list_nat Xs)))))
% 5.98/6.27 (assert (forall ((X tptp.vEBT_VEBT) (Y Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_2 (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel))) (=> (= (@ tptp.vEBT_VEBT_minNull X) Y) (=> (@ _let_2 X) (=> (=> (= X _let_1) (=> Y (not (@ _let_2 _let_1)))) (=> (forall ((Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uu2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) true))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) (=> (= X _let_1) (=> Y (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))))))
% 5.98/6.27 (assert (forall ((X tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_2 (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel))) (=> (@ tptp.vEBT_VEBT_minNull X) (=> (@ _let_2 X) (=> (=> (= X _let_1) (not (@ _let_2 _let_1))) (not (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))
% 5.98/6.27 (assert (forall ((X tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X)) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) X) (=> (forall ((Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv2))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))) (=> (forall ((Uu2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) true))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (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))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))))))))))
% 5.98/6.27 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.bezw X) tptp.zero_zero_nat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (Xs tptp.list_int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_Pr3440142176431000676at_int (@ (@ tptp.enumerate_int N) Xs)) M2) (@ (@ tptp.product_Pair_nat_int (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.nth_int Xs) M2))))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_Pr744662078594809490T_VEBT (@ (@ tptp.enumerate_VEBT_VEBT N) Xs)) M2) (@ (@ tptp.produc599794634098209291T_VEBT (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.nth_VEBT_VEBT Xs) M2))))))
% 5.98/6.27 (assert (forall ((M2 tptp.nat) (Xs tptp.list_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat (@ (@ tptp.enumerate_nat N) Xs)) M2) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat N) M2)) (@ (@ tptp.nth_nat Xs) M2))))))
% 5.98/6.27 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V)))) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X) X))) _let_1) TreeList) Summary)))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_list_VEBT_VEBT) (N tptp.nat)) (=> (forall ((X4 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member2936631157270082147T_VEBT X4) (@ tptp.set_list_VEBT_VEBT2 Xs)) (= (@ tptp.size_s6755466524823107622T_VEBT X4) N))) (= (@ tptp.size_s6755466524823107622T_VEBT (@ tptp.concat_VEBT_VEBT Xs)) (@ (@ tptp.times_times_nat (@ tptp.size_s8217280938318005548T_VEBT Xs)) N)))))
% 5.98/6.27 (assert (forall ((Xs tptp.list_list_nat) (N tptp.nat)) (=> (forall ((X4 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X4) (@ tptp.set_list_nat2 Xs)) (= (@ tptp.size_size_list_nat X4) N))) (= (@ tptp.size_size_list_nat (@ tptp.concat_nat Xs)) (@ (@ tptp.times_times_nat (@ tptp.size_s3023201423986296836st_nat Xs)) N)))))
% 5.98/6.27 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts2) S))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))
% 5.98/6.27 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ (@ tptp.vEBT_vebt_insert _let_2) X))) (let ((_let_4 (= X tptp.one_one_nat))) (let ((_let_5 (= X tptp.zero_zero_nat))) (and (=> _let_5 (= _let_3 (@ (@ tptp.vEBT_Leaf true) B))) (=> (not _let_5) (and (=> _let_4 (= _let_3 (@ _let_1 true))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 5.98/6.27 (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))))))))
% 5.98/6.27 (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))))))))
% 5.98/6.27 (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))))))))
% 5.98/6.27 (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))))))))
% 5.98/6.27 (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))))))))
% 5.98/6.27 (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))))))))
% 5.98/6.27 (assert (forall ((I tptp.nat) (Xs tptp.list_nat) (Ys2 tptp.list_int)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_nat Xs)) (=> (@ _let_1 (@ tptp.size_size_list_int Ys2)) (= (@ (@ tptp.nth_Pr3440142176431000676at_int (@ (@ tptp.zip_nat_int Xs) Ys2)) I) (@ (@ tptp.product_Pair_nat_int (@ (@ tptp.nth_nat Xs) I)) (@ (@ tptp.nth_int Ys2) I))))))))
% 5.98/6.27 (assert (forall ((I tptp.nat) (Xs tptp.list_nat) (Ys2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_nat Xs)) (=> (@ _let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys2)) (= (@ (@ tptp.nth_Pr744662078594809490T_VEBT (@ (@ tptp.zip_nat_VEBT_VEBT Xs) Ys2)) I) (@ (@ tptp.produc599794634098209291T_VEBT (@ (@ tptp.nth_nat Xs) I)) (@ (@ tptp.nth_VEBT_VEBT Ys2) I))))))))
% 5.98/6.27 (assert (forall ((I tptp.nat) (Xs tptp.list_nat) (Ys2 tptp.list_nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_size_list_nat Xs)) (=> (@ _let_1 (@ tptp.size_size_list_nat Ys2)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat (@ (@ tptp.zip_nat_nat Xs) Ys2)) I) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.nth_nat Xs) I)) (@ (@ tptp.nth_nat Ys2) I))))))))
% 5.98/6.27 (assert (forall ((I tptp.nat) (Xs tptp.list_P6011104703257516679at_nat) (Ys2 tptp.list_P6011104703257516679at_nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 (@ tptp.size_s5460976970255530739at_nat Xs)) (=> (@ _let_1 (@ tptp.size_s5460976970255530739at_nat Ys2)) (= (@ (@ tptp.nth_Pr6744343527793145070at_nat (@ (@ tptp.zip_Pr4664179122662387191at_nat Xs) Ys2)) I) (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) I)) (@ (@ tptp.nth_Pr7617993195940197384at_nat Ys2) I))))))))
% 5.98/6.27 (assert (forall ((P (-> tptp.int Bool)) (Xs tptp.list_int) (X tptp.int)) (= (= (@ (@ tptp.find_int P) Xs) (@ tptp.some_int X)) (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) (= X _let_1) (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) I4) (not (@ P (@ (@ tptp.nth_int Xs) J3)))))))))))
% 5.98/6.27 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Xs tptp.list_P6011104703257516679at_nat) (X tptp.product_prod_nat_nat)) (= (= (@ (@ tptp.find_P8199882355184865565at_nat P) Xs) (@ tptp.some_P7363390416028606310at_nat X)) (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) (= X _let_1) (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) I4) (not (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) J3)))))))))))
% 5.98/6.27 (assert (forall ((P (-> tptp.num Bool)) (Xs tptp.list_num) (X tptp.num)) (= (= (@ (@ tptp.find_num P) Xs) (@ tptp.some_num X)) (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) (= X _let_1) (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) I4) (not (@ P (@ (@ tptp.nth_num Xs) J3)))))))))))
% 5.98/6.27 (assert (forall ((P (-> tptp.vEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (= (= (@ (@ tptp.find_VEBT_VEBT P) Xs) (@ tptp.some_VEBT_VEBT X)) (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) (= X _let_1) (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) I4) (not (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) J3)))))))))))
% 5.98/6.27 (assert (forall ((P (-> tptp.nat Bool)) (Xs tptp.list_nat) (X tptp.nat)) (= (= (@ (@ tptp.find_nat P) Xs) (@ tptp.some_nat X)) (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) (= X _let_1) (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) I4) (not (@ P (@ (@ tptp.nth_nat Xs) J3)))))))))))
% 5.98/6.27 (assert (forall ((X tptp.int) (P (-> tptp.int Bool)) (Xs tptp.list_int)) (= (= (@ tptp.some_int X) (@ (@ 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) (= X _let_1) (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) I4) (not (@ P (@ (@ tptp.nth_int Xs) J3)))))))))))
% 5.98/6.27 (assert (forall ((X tptp.product_prod_nat_nat) (P (-> tptp.product_prod_nat_nat Bool)) (Xs tptp.list_P6011104703257516679at_nat)) (= (= (@ tptp.some_P7363390416028606310at_nat X) (@ (@ 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) (= X _let_1) (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) I4) (not (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) J3)))))))))))
% 5.98/6.27 (assert (forall ((X tptp.num) (P (-> tptp.num Bool)) (Xs tptp.list_num)) (= (= (@ tptp.some_num X) (@ (@ 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) (= X _let_1) (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) I4) (not (@ P (@ (@ tptp.nth_num Xs) J3)))))))))))
% 5.98/6.27 (assert (forall ((X tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT)) (= (= (@ tptp.some_VEBT_VEBT X) (@ (@ 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) (= X _let_1) (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) I4) (not (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) J3)))))))))))
% 5.98/6.27 (assert (forall ((X tptp.nat) (P (-> tptp.nat Bool)) (Xs tptp.list_nat)) (= (= (@ tptp.some_nat X) (@ (@ 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) (= X _let_1) (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) I4) (not (@ P (@ (@ tptp.nth_nat Xs) J3)))))))))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (X 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 X) Xs)) N) (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (X tptp.int) (Xs tptp.list_int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs)) N) (@ (@ tptp.nth_int Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs)) N) (@ (@ tptp.nth_nat Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 5.98/6.28 (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))))
% 5.98/6.28 (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))))
% 5.98/6.28 (assert (= tptp.remove6466555014256735590at_nat (lambda ((X3 tptp.product_prod_nat_nat) (A6 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.minus_1356011639430497352at_nat A6) (@ (@ tptp.insert8211810215607154385at_nat X3) tptp.bot_bo2099793752762293965at_nat)))))
% 5.98/6.28 (assert (= tptp.remove_real (lambda ((X3 tptp.real) (A6 tptp.set_real)) (@ (@ tptp.minus_minus_set_real A6) (@ (@ tptp.insert_real X3) tptp.bot_bot_set_real)))))
% 5.98/6.28 (assert (= tptp.remove_o (lambda ((X3 Bool) (A6 tptp.set_o)) (@ (@ tptp.minus_minus_set_o A6) (@ (@ tptp.insert_o X3) tptp.bot_bot_set_o)))))
% 5.98/6.28 (assert (= tptp.remove_int (lambda ((X3 tptp.int) (A6 tptp.set_int)) (@ (@ tptp.minus_minus_set_int A6) (@ (@ tptp.insert_int X3) tptp.bot_bot_set_int)))))
% 5.98/6.28 (assert (= tptp.remove_nat (lambda ((X3 tptp.nat) (A6 tptp.set_nat)) (@ (@ tptp.minus_minus_set_nat A6) (@ (@ tptp.insert_nat X3) tptp.bot_bot_set_nat)))))
% 5.98/6.28 (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)))))))
% 5.98/6.28 (assert (forall ((X Bool) (Y Bool) (A2 tptp.set_o)) (let ((_let_1 (@ tptp.member_o X))) (= (@ _let_1 (@ (@ tptp.remove_o Y) A2)) (and (@ _let_1 A2) (not (= X Y)))))))
% 5.98/6.28 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat X))) (= (@ _let_1 (@ (@ tptp.remove_set_nat Y) A2)) (and (@ _let_1 A2) (not (= X Y)))))))
% 5.98/6.28 (assert (forall ((X tptp.set_nat_rat) (Y tptp.set_nat_rat) (A2 tptp.set_set_nat_rat)) (let ((_let_1 (@ tptp.member_set_nat_rat X))) (= (@ _let_1 (@ (@ tptp.remove_set_nat_rat Y) A2)) (and (@ _let_1 A2) (not (= X Y)))))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Y tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat X))) (= (@ _let_1 (@ (@ tptp.remove_nat Y) A2)) (and (@ _let_1 A2) (not (= X Y)))))))
% 5.98/6.28 (assert (forall ((X tptp.int) (Y tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int X))) (= (@ _let_1 (@ (@ tptp.remove_int Y) A2)) (and (@ _let_1 A2) (not (= X Y)))))))
% 5.98/6.28 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 5.98/6.28 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 5.98/6.28 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) A) tptp.zero_zero_int)))
% 5.98/6.28 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) A) tptp.zero_zero_nat)))
% 5.98/6.28 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.zero_zero_int) A)))
% 5.98/6.28 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.zero_zero_nat) A)))
% 5.98/6.28 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 5.98/6.28 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 5.98/6.28 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int B) A)) B) tptp.zero_zero_int)))
% 5.98/6.28 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat B) A)) B) tptp.zero_zero_nat)))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) B) tptp.zero_zero_int)))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) B) tptp.zero_zero_nat)))
% 5.98/6.28 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 5.98/6.28 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 5.98/6.28 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 5.98/6.28 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT X) Xs)) tptp.zero_zero_nat) X)))
% 5.98/6.28 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs)) tptp.zero_zero_nat) X)))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs)) tptp.zero_zero_nat) X)))
% 5.98/6.28 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int)))
% 5.98/6.28 (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)))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat A) B)) A))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int A) B)) A))))
% 5.98/6.28 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A) B)) B))))
% 5.98/6.28 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A) B)) B))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B) A) (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B) A) (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat))))
% 5.98/6.28 (assert (forall ((M2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) M2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int M2) K)) M2))))
% 5.98/6.28 (assert (forall ((Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.cons_VEBT_VEBT X) Xs)))))
% 5.98/6.28 (assert (forall ((Xs tptp.list_nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) (@ tptp.set_nat2 (@ (@ tptp.cons_nat X) Xs)))))
% 5.98/6.28 (assert (forall ((Xs tptp.list_int) (X tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) (@ tptp.set_int2 (@ (@ tptp.cons_int X) Xs)))))
% 5.98/6.28 (assert (forall ((Xs tptp.list_int) (Ys2 tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) (@ tptp.size_size_list_int Ys2)) (not (= Xs (@ (@ tptp.cons_int X) Ys2))))))
% 5.98/6.28 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys2)) (not (= Xs (@ (@ tptp.cons_VEBT_VEBT X) Ys2))))))
% 5.98/6.28 (assert (forall ((Xs tptp.list_nat) (Ys2 tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_nat Ys2)) (not (= Xs (@ (@ tptp.cons_nat X) Ys2))))))
% 5.98/6.28 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 5.98/6.28 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int A) B)))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.modulo_modulo_nat A) B) A)))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.modulo_modulo_int A) B) A)))))
% 5.98/6.28 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B))) C) (@ (@ tptp.plus_plus_int A) C))))
% 5.98/6.28 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B))) C) (@ (@ tptp.plus_plus_nat A) C))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B))) C) (@ (@ tptp.plus_plus_int A) C))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B))) C) (@ (@ tptp.plus_plus_nat A) C))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B)))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat)) (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B)) A)))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B)) A)))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) A)))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) A)))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) A)))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) A)))
% 5.98/6.28 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B)) A)))
% 5.98/6.28 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B)) A)))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B)))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B)))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1406184849735516958ct_int M2)) tptp.zero_zero_int))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat M2)) tptp.zero_zero_nat))))
% 5.98/6.28 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (let ((_let_2 (@ tptp.ord_less_int B))) (=> (@ _let_2 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int) (@ _let_2 _let_1)))))))
% 5.98/6.28 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_int _let_1) B))))))
% 5.98/6.28 (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))))))
% 5.98/6.28 (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))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (Xs tptp.list_int)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.size_size_list_int Xs)) (exists ((X3 tptp.int) (Ys3 tptp.list_int)) (and (= Xs (@ (@ tptp.cons_int X3) Ys3)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_int Ys3)))))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (exists ((X3 tptp.vEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (and (= Xs (@ (@ tptp.cons_VEBT_VEBT X3) Ys3)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_s6755466524823107622T_VEBT Ys3)))))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.size_size_list_nat Xs)) (exists ((X3 tptp.nat) (Ys3 tptp.list_nat)) (and (= Xs (@ (@ tptp.cons_nat X3) Ys3)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_nat Ys3)))))))
% 5.98/6.28 (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))))))
% 5.98/6.28 (assert (forall ((X21 tptp.int) (X22 tptp.list_int)) (= (@ tptp.size_size_list_int (@ (@ tptp.cons_int X21) X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_int X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 5.98/6.28 (assert (forall ((X21 tptp.vEBT_VEBT) (X22 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.cons_VEBT_VEBT X21) X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_s6755466524823107622T_VEBT X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 5.98/6.28 (assert (forall ((X21 tptp.nat) (X22 tptp.list_nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.cons_nat X21) X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_nat X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 5.98/6.28 (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))))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (X tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT X) Xs)) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (X tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs)) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_int Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs)) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))))
% 5.98/6.28 (assert (forall ((X tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real D))) (= (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real X)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int X) D))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.modulo_modulo_int X) D))) _let_1))))))
% 5.98/6.28 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) B)) C))) (@ _let_1 B))))))))
% 5.98/6.28 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) B)) C))) (@ _let_1 B))))))))
% 5.98/6.28 (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))))))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int) (Q4 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q4)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R2) (= (@ (@ tptp.modulo_modulo_int A) B) R2))))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int) (Q4 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q4)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (=> (@ (@ tptp.ord_less_int R2) B) (= (@ (@ tptp.modulo_modulo_int A) B) R2))))))
% 5.98/6.28 (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))))))
% 5.98/6.28 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) B)) C))) (@ _let_1 B))))))))
% 5.98/6.28 (assert (forall ((X Bool) (Xs tptp.list_o) (N tptp.nat)) (=> (not (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_o Xs)) (= (= (@ (@ tptp.nth_o (@ (@ tptp.cons_o X) Xs)) N) X) (= N tptp.zero_zero_nat))))))
% 5.98/6.28 (assert (forall ((X tptp.set_nat) (Xs tptp.list_set_nat) (N tptp.nat)) (=> (not (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_s3254054031482475050et_nat Xs)) (= (= (@ (@ tptp.nth_set_nat (@ (@ tptp.cons_set_nat X) Xs)) N) X) (= N tptp.zero_zero_nat))))))
% 5.98/6.28 (assert (forall ((X tptp.set_nat_rat) (Xs tptp.list_set_nat_rat) (N tptp.nat)) (=> (not (@ (@ tptp.member_set_nat_rat X) (@ tptp.set_set_nat_rat2 Xs))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_s3959913991096427681at_rat Xs)) (= (= (@ (@ tptp.nth_set_nat_rat (@ (@ tptp.cons_set_nat_rat X) Xs)) N) X) (= N tptp.zero_zero_nat))))))
% 5.98/6.28 (assert (forall ((X tptp.int) (Xs tptp.list_int) (N tptp.nat)) (=> (not (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_int Xs)) (= (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs)) N) X) (= N tptp.zero_zero_nat))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT) (N tptp.nat)) (=> (not (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT X) Xs)) N) X) (= N tptp.zero_zero_nat))))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (N tptp.nat)) (=> (not (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_nat Xs)) (= (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs)) N) X) (= N tptp.zero_zero_nat))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT) (N tptp.nat)) (=> (not (= X Y)) (= (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT X) Xs)) N) Y) (and (= (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) Y) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 5.98/6.28 (assert (forall ((X tptp.int) (Y tptp.int) (Xs tptp.list_int) (N tptp.nat)) (=> (not (= X Y)) (= (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs)) N) Y) (and (= (@ (@ tptp.nth_int Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) Y) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Y tptp.nat) (Xs tptp.list_nat) (N tptp.nat)) (=> (not (= X Y)) (= (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs)) N) Y) (and (= (@ (@ tptp.nth_nat Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) Y) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 5.98/6.28 (assert (forall ((A2 tptp.int) (B2 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A2) N)) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int B2) N) tptp.zero_zero_int)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.divide_divide_int B2) N))))))
% 5.98/6.28 (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)))))))
% 5.98/6.28 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A2) N)) (@ (@ (@ tptp.if_nat (= (@ (@ tptp.modulo_modulo_nat B2) N) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B2) N))))))
% 5.98/6.28 (assert (forall ((Z tptp.real) (W2 tptp.real) (M2 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) M2)) (@ (@ tptp.power_power_real W2) M2)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Z) W2))))))))
% 5.98/6.28 (assert (forall ((Z tptp.complex) (W2 tptp.complex) (M2 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) M2)) (@ (@ tptp.power_power_complex W2) M2)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Z) W2))))))))
% 5.98/6.28 (assert (forall ((W2 tptp.num) (B 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 B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 5.98/6.28 (assert (forall ((W2 tptp.num) (B 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 B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 5.98/6.28 (assert (forall ((B 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 B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1))))))))))))
% 5.98/6.28 (assert (forall ((B 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 B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat)) (= (= (@ tptp.semiri4258706085729940814in_nat A2) tptp.zero_zero_nat) (and (@ (@ tptp.ord_less_eq_set_nat A2) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)) (@ tptp.finite_finite_nat A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int)) (= (= (@ tptp.semiri4256215615220890538in_int A2) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_set_int A2) (@ (@ tptp.insert_int tptp.zero_zero_int) tptp.bot_bot_set_int)) (@ tptp.finite_finite_int A2)))))
% 5.98/6.28 (assert (forall ((X tptp.int) (Y tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ (@ tptp.count_list_int Xs) Y))) (let ((_let_2 (@ (@ tptp.count_list_int (@ (@ tptp.cons_int X) Xs)) Y))) (let ((_let_3 (= X Y))) (and (=> _let_3 (= _let_2 (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Y tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ (@ tptp.count_list_nat Xs) Y))) (let ((_let_2 (@ (@ tptp.count_list_nat (@ (@ tptp.cons_nat X) Xs)) Y))) (let ((_let_3 (= X Y))) (and (=> _let_3 (= _let_2 (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 5.98/6.28 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X2 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 ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X2 (@ (@ tptp.minus_minus_int Xb) Xa3))))))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.plus_plus_int X2) D4)))))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_real M2) (@ tptp.numeral_numeral_real N)) (= M2 N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_nat M2) (@ tptp.numeral_numeral_nat N)) (= M2 N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_int M2) (@ tptp.numeral_numeral_int N)) (= M2 N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.numera1916890842035813515d_enat M2) (@ tptp.numera1916890842035813515d_enat N)) (= M2 N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.numera6620942414471956472nteger M2) (@ tptp.numera6620942414471956472nteger N)) (= M2 N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M2)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_eq_num M2) N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_eq_num M2) N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.numera6620942414471956472nteger N)) (@ (@ tptp.ord_less_eq_num M2) N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_eq_num M2) N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_eq_num M2) N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_eq_num M2) N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_num M2) N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M2)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_num M2) N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_num M2) N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_num M2) N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_num M2) N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.numera6620942414471956472nteger N)) (@ (@ tptp.ord_less_num M2) N))))
% 5.98/6.28 (assert (forall ((V tptp.num) (W2 tptp.num) (Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W2)) Z)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W2))) Z))))
% 5.98/6.28 (assert (forall ((V tptp.num) (W2 tptp.num) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W2)) Z)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W2))) Z))))
% 5.98/6.28 (assert (forall ((V tptp.num) (W2 tptp.num) (Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat W2)) Z)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num V) W2))) Z))))
% 5.98/6.28 (assert (forall ((V tptp.num) (W2 tptp.num) (Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W2)) Z)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W2))) Z))))
% 5.98/6.28 (assert (forall ((V tptp.num) (W2 tptp.num) (Z tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat V)) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat W2)) Z)) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.times_times_num V) W2))) Z))))
% 5.98/6.28 (assert (forall ((V tptp.num) (W2 tptp.num) (Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger W2)) Z)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W2))) Z))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M2) N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M2)) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M2) N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M2) N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M2) N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.numera1916890842035813515d_enat N)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.times_times_num M2) N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M2) N)))))
% 5.98/6.28 (assert (forall ((V tptp.num) (W2 tptp.num) (Z tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat W2)) Z)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V) W2))) Z))))
% 5.98/6.28 (assert (forall ((V tptp.num) (W2 tptp.num) (Z tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real W2)) Z)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W2))) Z))))
% 5.98/6.28 (assert (forall ((V tptp.num) (W2 tptp.num) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat W2)) Z)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) W2))) Z))))
% 5.98/6.28 (assert (forall ((V tptp.num) (W2 tptp.num) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int W2)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W2))) Z))))
% 5.98/6.28 (assert (forall ((V tptp.num) (W2 tptp.num) (Z tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat V)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat W2)) Z)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num V) W2))) Z))))
% 5.98/6.28 (assert (forall ((V tptp.num) (W2 tptp.num) (Z tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.numera6620942414471956472nteger V)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.numera6620942414471956472nteger W2)) Z)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num V) W2))) Z))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M2) N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real M2)) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M2) N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M2) N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M2) N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.numera1916890842035813515d_enat N)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num M2) N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M2) N)))))
% 5.98/6.28 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_rat)))
% 5.98/6.28 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_int)))
% 5.98/6.28 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_nat)))
% 5.98/6.28 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_real)))
% 5.98/6.28 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_complex)))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= M2 N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (= M2 N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (= M2 N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (= M2 N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= M2 N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ tptp.semiri4216267220026989637d_enat (@ tptp.numeral_numeral_nat N)) (@ tptp.numera1916890842035813515d_enat N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.numeral_numeral_nat N)) (@ tptp.numera6620942414471956472nteger N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_real N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_rat N))))
% 5.98/6.28 (assert (forall ((L tptp.set_int) (H tptp.set_int) (L2 tptp.set_int) (H2 tptp.set_int)) (= (= (@ (@ tptp.set_or370866239135849197et_int L) H) (@ (@ tptp.set_or370866239135849197et_int L2) H2)) (or (and (= L L2) (= H H2)) (and (not (@ (@ tptp.ord_less_eq_set_int L) H)) (not (@ (@ tptp.ord_less_eq_set_int L2) H2)))))))
% 5.98/6.28 (assert (forall ((L tptp.rat) (H tptp.rat) (L2 tptp.rat) (H2 tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat L) H) (@ (@ tptp.set_or633870826150836451st_rat L2) H2)) (or (and (= L L2) (= H H2)) (and (not (@ (@ tptp.ord_less_eq_rat L) H)) (not (@ (@ tptp.ord_less_eq_rat L2) H2)))))))
% 5.98/6.28 (assert (forall ((L tptp.num) (H tptp.num) (L2 tptp.num) (H2 tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num L) H) (@ (@ tptp.set_or7049704709247886629st_num L2) H2)) (or (and (= L L2) (= H H2)) (and (not (@ (@ tptp.ord_less_eq_num L) H)) (not (@ (@ tptp.ord_less_eq_num L2) H2)))))))
% 5.98/6.28 (assert (forall ((L tptp.int) (H tptp.int) (L2 tptp.int) (H2 tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int L) H) (@ (@ tptp.set_or1266510415728281911st_int L2) H2)) (or (and (= L L2) (= H H2)) (and (not (@ (@ tptp.ord_less_eq_int L) H)) (not (@ (@ tptp.ord_less_eq_int L2) H2)))))))
% 5.98/6.28 (assert (forall ((L tptp.nat) (H tptp.nat) (L2 tptp.nat) (H2 tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat L) H) (@ (@ tptp.set_or1269000886237332187st_nat L2) H2)) (or (and (= L L2) (= H H2)) (and (not (@ (@ tptp.ord_less_eq_nat L) H)) (not (@ (@ tptp.ord_less_eq_nat L2) H2)))))))
% 5.98/6.28 (assert (forall ((L tptp.real) (H tptp.real) (L2 tptp.real) (H2 tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real L) H) (@ (@ tptp.set_or1222579329274155063t_real L2) H2)) (or (and (= L L2) (= H H2)) (and (not (@ (@ tptp.ord_less_eq_real L) H)) (not (@ (@ tptp.ord_less_eq_real L2) H2)))))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (assert (forall ((I tptp.set_nat_rat) (L tptp.set_nat_rat) (U tptp.set_nat_rat)) (= (@ (@ tptp.member_set_nat_rat I) (@ (@ tptp.set_or5795412311047298440at_rat L) U)) (and (@ (@ tptp.ord_le2679597024174929757at_rat L) I) (@ (@ tptp.ord_le2679597024174929757at_rat I) U)))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (= (@ (@ tptp.modulo_modulo_nat M2) N) M2))))
% 5.98/6.28 (assert (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or1266510415728281911st_int L) U))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ (@ tptp.ord_less_eq_num N) M2))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.ord_less_eq_num N) M2))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ (@ tptp.ord_less_eq_num N) M2))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ tptp.ord_less_eq_num N) M2))))
% 5.98/6.28 (assert (forall ((A tptp.rat) (B tptp.rat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) _let_1) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) _let_1)) (@ (@ tptp.times_times_rat B) _let_1))))))
% 5.98/6.28 (assert (forall ((A tptp.real) (B tptp.real) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real B) _let_1))))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) _let_1)) (@ (@ tptp.times_times_nat B) _let_1))))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V))) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B) _let_1))))))
% 5.98/6.28 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (V tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat V))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B)) _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat A) _let_1)) (@ (@ tptp.times_7803423173614009249d_enat B) _let_1))))))
% 5.98/6.28 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (V tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger V))) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) _let_1) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger B) _let_1))))))
% 5.98/6.28 (assert (forall ((V tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.28 (assert (forall ((V tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.28 (assert (forall ((V tptp.num) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.28 (assert (forall ((V tptp.num) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.28 (assert (forall ((V tptp.num) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat V)))) (= (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat B) C)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.28 (assert (forall ((V tptp.num) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V)))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ (@ tptp.ord_less_num N) M2))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ tptp.ord_less_num N) M2))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.ord_less_num N) M2))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ (@ tptp.ord_less_num N) M2))))
% 5.98/6.28 (assert (forall ((V tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.28 (assert (forall ((V tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.28 (assert (forall ((V tptp.num) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.28 (assert (forall ((V tptp.num) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V)))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.28 (assert (forall ((A tptp.rat) (B tptp.rat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) _let_1) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) _let_1)) (@ (@ tptp.times_times_rat B) _let_1))))))
% 5.98/6.28 (assert (forall ((A tptp.real) (B tptp.real) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real B) _let_1))))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B) _let_1))))))
% 5.98/6.28 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (V tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger V))) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) _let_1) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger B) _let_1))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M2) N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M2) N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M2) N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M2) N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M2))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M2) N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M2) N))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M2) N))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M2) N))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M2) N))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M2))) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M2) N))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M2) N))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M2) N))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M2) N))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M2) N))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M2) N))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M2))) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger _let_2)) (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_2) _let_1)))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int _let_2) _let_1)))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (let ((_let_2 (@ tptp.numeral_numeral_real M2))) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real _let_2)) (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real _let_2) _let_1)))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (let ((_let_2 (@ tptp.numeral_numeral_rat M2))) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat _let_2)) (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat _let_2) _let_1)))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex M2))) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex _let_2)) (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M2) N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M2) N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M2) N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M2) N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M2) N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M2) N))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M2) N))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M2) N))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M2) N))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M2))) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M2) N))))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger _let_1)) _let_1))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int _let_1)) _let_1))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat _let_1)) _let_1))))
% 5.98/6.28 (assert (forall ((A Bool) (B Bool)) (= (= (@ (@ tptp.set_or8904488021354931149Most_o A) B) tptp.bot_bot_set_o) (not (@ (@ tptp.ord_less_eq_o A) B)))))
% 5.98/6.28 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (= (@ (@ tptp.set_or370866239135849197et_int A) B) tptp.bot_bot_set_set_int) (not (@ (@ tptp.ord_less_eq_set_int A) B)))))
% 5.98/6.28 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat A) B) tptp.bot_bot_set_rat) (not (@ (@ tptp.ord_less_eq_rat A) B)))))
% 5.98/6.28 (assert (forall ((A tptp.num) (B tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num A) B) tptp.bot_bot_set_num) (not (@ (@ tptp.ord_less_eq_num A) B)))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int A) B) tptp.bot_bot_set_int) (not (@ (@ tptp.ord_less_eq_int A) B)))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) tptp.bot_bot_set_nat) (not (@ (@ tptp.ord_less_eq_nat A) B)))))
% 5.98/6.28 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real A) B) tptp.bot_bot_set_real) (not (@ (@ tptp.ord_less_eq_real A) B)))))
% 5.98/6.28 (assert (forall ((A Bool) (B Bool)) (= (= tptp.bot_bot_set_o (@ (@ tptp.set_or8904488021354931149Most_o A) B)) (not (@ (@ tptp.ord_less_eq_o A) B)))))
% 5.98/6.28 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (= tptp.bot_bot_set_set_int (@ (@ tptp.set_or370866239135849197et_int A) B)) (not (@ (@ tptp.ord_less_eq_set_int A) B)))))
% 5.98/6.28 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= tptp.bot_bot_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (not (@ (@ tptp.ord_less_eq_rat A) B)))))
% 5.98/6.28 (assert (forall ((A tptp.num) (B tptp.num)) (= (= tptp.bot_bot_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (not (@ (@ tptp.ord_less_eq_num A) B)))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (not (@ (@ tptp.ord_less_eq_int A) B)))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (not (@ (@ tptp.ord_less_eq_nat A) B)))))
% 5.98/6.28 (assert (forall ((A tptp.real) (B tptp.real)) (= (= tptp.bot_bot_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (not (@ (@ tptp.ord_less_eq_real A) B)))))
% 5.98/6.28 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int) (D tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ (@ tptp.set_or370866239135849197et_int A) B)) (@ (@ tptp.set_or370866239135849197et_int C) D)) (or (not (@ (@ tptp.ord_less_eq_set_int A) B)) (and (@ (@ tptp.ord_less_eq_set_int C) A) (@ (@ tptp.ord_less_eq_set_int B) D))))))
% 5.98/6.28 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C) D)) (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_eq_rat C) A) (@ (@ tptp.ord_less_eq_rat B) D))))))
% 5.98/6.28 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or7049704709247886629st_num C) D)) (or (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ (@ tptp.ord_less_eq_num C) A) (@ (@ tptp.ord_less_eq_num B) D))))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int C) D)) (or (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ (@ tptp.ord_less_eq_int C) A) (@ (@ tptp.ord_less_eq_int B) D))))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1269000886237332187st_nat C) D)) (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat B) D))))))
% 5.98/6.28 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C) D)) (or (not (@ (@ tptp.ord_less_eq_real A) B)) (and (@ (@ tptp.ord_less_eq_real C) A) (@ (@ tptp.ord_less_eq_real B) D))))))
% 5.98/6.28 (assert (forall ((B Bool) (A Bool)) (=> (@ (@ tptp.ord_less_o B) A) (= (@ (@ tptp.set_or8904488021354931149Most_o A) B) tptp.bot_bot_set_o))))
% 5.98/6.28 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.set_or633870826150836451st_rat A) B) tptp.bot_bot_set_rat))))
% 5.98/6.28 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (= (@ (@ tptp.set_or7049704709247886629st_num A) B) tptp.bot_bot_set_num))))
% 5.98/6.28 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.set_or1266510415728281911st_int A) B) tptp.bot_bot_set_int))))
% 5.98/6.28 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) tptp.bot_bot_set_nat))))
% 5.98/6.28 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (= (@ (@ tptp.set_or1222579329274155063t_real A) B) tptp.bot_bot_set_real))))
% 5.98/6.28 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ tptp.finite_finite_rat (@ (@ tptp.set_or633870826150836451st_rat A) B))) (@ (@ tptp.ord_less_rat A) B))))
% 5.98/6.28 (assert (forall ((A tptp.real) (B tptp.real)) (= (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A) B))) (@ (@ tptp.ord_less_real A) B))))
% 5.98/6.28 (assert (= (@ tptp.real_V7735802525324610683m_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.28 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.zero_zero_complex) tptp.zero_zero_real))
% 5.98/6.28 (assert (forall ((X tptp.real)) (= (= (@ tptp.real_V7735802525324610683m_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 5.98/6.28 (assert (forall ((X tptp.complex)) (= (= (@ tptp.real_V1022390504157884413omplex X) tptp.zero_zero_real) (= X tptp.zero_zero_complex))))
% 5.98/6.28 (assert (= (@ tptp.real_V7735802525324610683m_real tptp.one_one_real) tptp.one_one_real))
% 5.98/6.28 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.one_one_complex) tptp.one_one_real))
% 5.98/6.28 (assert (forall ((A Bool)) (= (@ (@ tptp.set_or8904488021354931149Most_o A) A) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o))))
% 5.98/6.28 (assert (forall ((A tptp.int)) (= (@ (@ tptp.set_or1266510415728281911st_int A) A) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))
% 5.98/6.28 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat A) A) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))
% 5.98/6.28 (assert (forall ((A tptp.real)) (= (@ (@ tptp.set_or1222579329274155063t_real A) A) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))
% 5.98/6.28 (assert (forall ((A Bool) (B Bool) (C Bool)) (= (= (@ (@ tptp.set_or8904488021354931149Most_o A) B) (@ (@ tptp.insert_o C) tptp.bot_bot_set_o)) (and (= A B) (= B C)))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int A) B) (@ (@ tptp.insert_int C) tptp.bot_bot_set_int)) (and (= A B) (= B C)))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) (@ (@ tptp.insert_nat C) tptp.bot_bot_set_nat)) (and (= A B) (= B C)))))
% 5.98/6.28 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real A) B) (@ (@ tptp.insert_real C) tptp.bot_bot_set_real)) (and (= A B) (= B C)))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M2) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 5.98/6.28 (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))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (assert (forall ((N tptp.num) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) (@ tptp.semiri5074537144036343181t_real M2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) M2))))
% 5.98/6.28 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.zero_zero_nat)))
% 5.98/6.28 (assert (= (@ tptp.semiri4258706085729940814in_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 5.98/6.28 (assert (= (@ tptp.semiri4256215615220890538in_int tptp.bot_bot_set_int) tptp.zero_zero_int))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ tptp.semiri4258706085729940814in_nat A2) tptp.one_one_nat))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int)) (=> (not (@ tptp.finite_finite_int A2)) (= (@ tptp.semiri4256215615220890538in_int A2) tptp.one_one_int))))
% 5.98/6.28 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int A)) (@ tptp.numeral_numeral_int B)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (= (@ tptp.semiri4258706085729940814in_nat A2) (@ tptp.gcd_Gcd_nat A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (= (@ tptp.semiri4256215615220890538in_int A2) (@ tptp.gcd_Gcd_int A2)))))
% 5.98/6.28 (assert (forall ((X Bool) (Xs tptp.list_o)) (=> (not (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs))) (= (@ (@ tptp.count_list_o Xs) X) tptp.zero_zero_nat))))
% 5.98/6.28 (assert (forall ((X tptp.set_nat) (Xs tptp.list_set_nat)) (=> (not (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs))) (= (@ (@ tptp.count_list_set_nat Xs) X) tptp.zero_zero_nat))))
% 5.98/6.28 (assert (forall ((X tptp.set_nat_rat) (Xs tptp.list_set_nat_rat)) (=> (not (@ (@ tptp.member_set_nat_rat X) (@ tptp.set_set_nat_rat2 Xs))) (= (@ (@ tptp.count_6735058137522573441at_rat Xs) X) tptp.zero_zero_nat))))
% 5.98/6.28 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (=> (not (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs))) (= (@ (@ tptp.count_list_int Xs) X) tptp.zero_zero_nat))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (=> (not (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs))) (= (@ (@ tptp.count_list_VEBT_VEBT Xs) X) tptp.zero_zero_nat))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (=> (not (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs))) (= (@ (@ tptp.count_list_nat Xs) X) tptp.zero_zero_nat))))
% 5.98/6.28 (assert (forall ((B tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 5.98/6.28 (assert (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 5.98/6.28 (assert (forall ((A tptp.real) (B tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 5.98/6.28 (assert (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 5.98/6.28 (assert (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 5.98/6.28 (assert (forall ((A tptp.real) (B tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 5.98/6.28 (assert (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 5.98/6.28 (assert (forall ((B tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 5.98/6.28 (assert (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 5.98/6.28 (assert (forall ((A tptp.real) (B tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 5.98/6.28 (assert (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 5.98/6.28 (assert (forall ((B tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 5.98/6.28 (assert (forall ((W2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W2))) (= (@ tptp.invers8013647133539491842omplex _let_1) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_1)))))
% 5.98/6.28 (assert (forall ((W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W2))) (= (@ tptp.inverse_inverse_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)))))
% 5.98/6.28 (assert (forall ((W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (= (@ tptp.inverse_inverse_rat _let_1) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_1)))))
% 5.98/6.28 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V7735802525324610683m_real X)) (not (= X tptp.zero_zero_real)))))
% 5.98/6.28 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X)) (not (= X tptp.zero_zero_complex)))))
% 5.98/6.28 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X)) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 5.98/6.28 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) tptp.zero_zero_real) (= X tptp.zero_zero_complex))))
% 5.98/6.28 (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))))
% 5.98/6.28 (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))))
% 5.98/6.28 (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))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (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))))
% 5.98/6.28 (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))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (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))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real V)) X))))
% 5.98/6.28 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat V)) X))))
% 5.98/6.28 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real V)))))
% 5.98/6.28 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_rat X) (@ tptp.numeral_numeral_rat V)))))
% 5.98/6.28 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.numeral_numeral_real V)))))
% 5.98/6.28 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.numeral_numeral_rat V)))))
% 5.98/6.28 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat V)) X))))
% 5.98/6.28 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real V)) X))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT X) Xs)) _let_1) (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))))
% 5.98/6.28 (assert (forall ((X tptp.int) (Xs tptp.list_int) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs)) _let_1) (@ (@ tptp.nth_int Xs) (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs)) _let_1) (@ (@ tptp.nth_nat Xs) (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))))
% 5.98/6.28 (assert (forall ((K tptp.num) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (=> (not (= _let_1 tptp.one_one_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) _let_1) tptp.one_one_nat)))))
% 5.98/6.28 (assert (forall ((X tptp.real) (N tptp.num)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat N))))))
% 5.98/6.28 (assert (forall ((X tptp.num) (N tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))))
% 5.98/6.28 (assert (forall ((X tptp.num) (N tptp.nat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))))
% 5.98/6.28 (assert (forall ((X tptp.num) (N tptp.nat)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))))
% 5.98/6.28 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int A))) (@ tptp.numeral_numeral_int B))))))
% 5.98/6.28 (assert (forall ((B tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 5.98/6.28 (assert (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 5.98/6.28 (assert (forall ((A tptp.real) (B tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 5.98/6.28 (assert (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 5.98/6.28 (assert (forall ((A tptp.real) (B 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))) (= (= A (@ (@ tptp.divide_divide_real B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 5.98/6.28 (assert (forall ((A tptp.rat) (B 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))) (= (= A (@ (@ tptp.divide_divide_rat B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 5.98/6.28 (assert (forall ((A tptp.complex) (B tptp.complex) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 5.98/6.28 (assert (forall ((B tptp.real) (W2 tptp.num) (A 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 B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 5.98/6.28 (assert (forall ((B tptp.rat) (W2 tptp.num) (A 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 B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 5.98/6.28 (assert (forall ((B tptp.complex) (W2 tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 5.98/6.28 (assert (forall ((A tptp.real) (B tptp.real) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 5.98/6.28 (assert (forall ((A tptp.rat) (B tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 5.98/6.28 (assert (forall ((B tptp.real) (W2 tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 5.98/6.28 (assert (forall ((B tptp.rat) (W2 tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 5.98/6.28 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K))) (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu5831290666863070958nteger _let_1))))))
% 5.98/6.28 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_nu5851722552734809277nc_int _let_1))))))
% 5.98/6.28 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real K))) (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_nu8295874005876285629c_real _let_1))))))
% 5.98/6.28 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat K))) (= (@ tptp.neg_nu3179335615603231917ec_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_nu5219082963157363817nc_rat _let_1))))))
% 5.98/6.28 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K))) (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu8557863876264182079omplex _let_1))))))
% 5.98/6.28 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K))) (= (@ tptp.neg_nu5831290666863070958nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu7757733837767384882nteger _let_1))))))
% 5.98/6.28 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_nu3811975205180677377ec_int _let_1))))))
% 5.98/6.28 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real K))) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_nu6075765906172075777c_real _let_1))))))
% 5.98/6.28 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat K))) (= (@ tptp.neg_nu5219082963157363817nc_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_nu3179335615603231917ec_rat _let_1))))))
% 5.98/6.28 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K))) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu6511756317524482435omplex _let_1))))))
% 5.98/6.28 (assert (forall ((W2 tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W2)))) (= (@ tptp.invers8013647133539491842omplex _let_1) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_1)))))
% 5.98/6.28 (assert (forall ((W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W2)))) (= (@ tptp.inverse_inverse_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)))))
% 5.98/6.28 (assert (forall ((W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (= (@ tptp.inverse_inverse_rat _let_1) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_1)))))
% 5.98/6.28 (assert (forall ((V tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat V)) tptp.one_one_nat) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int V)) tptp.one_one_int)))))
% 5.98/6.28 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 5.98/6.28 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 5.98/6.28 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 5.98/6.28 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (assert (forall ((B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real B))) (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int B)))))
% 5.98/6.28 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B)))) (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int A))) (@ tptp.numeral_numeral_int B)))))
% 5.98/6.28 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B)))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int A)) (@ tptp.numeral_numeral_int B))))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N))) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X)) _let_1) (@ (@ tptp.ord_less_nat X) _let_1)))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I)) N)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 5.98/6.28 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X)) (@ _let_1 X)))))
% 5.98/6.28 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I)) N)) (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 5.98/6.28 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 5.98/6.28 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 5.98/6.28 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 5.98/6.28 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I)) N)) (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 5.98/6.28 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 5.98/6.28 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 5.98/6.28 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X)) (@ _let_1 X)))))
% 5.98/6.28 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I)) N)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X)) _let_1) (@ (@ tptp.ord_less_eq_nat X) _let_1)))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 5.98/6.28 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X))))
% 5.98/6.28 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X))))
% 5.98/6.28 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))))
% 5.98/6.28 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)))))
% 5.98/6.28 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))))
% 5.98/6.28 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)))))
% 5.98/6.28 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X))))
% 5.98/6.28 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X))))
% 5.98/6.28 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X))))
% 5.98/6.28 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) X))))
% 5.98/6.28 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))))
% 5.98/6.28 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_rat X) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))))))
% 5.98/6.28 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))))
% 5.98/6.28 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))))))
% 5.98/6.28 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 5.98/6.28 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 5.98/6.28 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 5.98/6.28 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 5.98/6.28 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 5.98/6.28 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X)) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 5.98/6.28 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 5.98/6.28 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 5.98/6.28 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X))))
% 5.98/6.28 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) X))))
% 5.98/6.28 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 5.98/6.28 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 5.98/6.28 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 5.98/6.28 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 5.98/6.28 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 5.98/6.28 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 5.98/6.28 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 5.98/6.28 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X)) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 5.98/6.28 (assert (forall ((B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real B)))) (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int B)))))
% 5.98/6.28 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X))))
% 5.98/6.28 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X))))
% 5.98/6.28 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))))
% 5.98/6.28 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)))))
% 5.98/6.28 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))))
% 5.98/6.28 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)))))
% 5.98/6.28 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X))))
% 5.98/6.28 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X))))
% 5.98/6.28 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 5.98/6.28 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 5.98/6.28 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 5.98/6.28 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 5.98/6.28 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)) A))))
% 5.98/6.28 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)) A))))
% 5.98/6.28 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)) A))))
% 5.98/6.28 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 5.98/6.28 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 5.98/6.28 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 5.98/6.28 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 5.98/6.28 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 5.98/6.28 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)) A))))
% 5.98/6.28 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 5.98/6.28 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)) A))))
% 5.98/6.28 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)) A))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M2) N)) M2)))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.numeral_numeral_rat N)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.numeral_numeral_real N)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_nat (@ tptp.numeral_numeral_nat N)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.numeral_numeral_int N)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (= tptp.zero_z5237406670263579293d_enat (@ tptp.numera1916890842035813515d_enat N)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (@ tptp.numera6620942414471956472nteger N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger M2) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_int M2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_real M2) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_rat M2) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex M2) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.numera6620942414471956472nteger N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2)) (@ tptp.numeral_numeral_real N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.numeral_numeral_rat N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M2)) (@ tptp.numera6690914467698888265omplex N)))))
% 5.98/6.28 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ tptp.finite_finite_rat (@ (@ tptp.set_or633870826150836451st_rat A) B))))))
% 5.98/6.28 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A) B))))))
% 5.98/6.28 (assert (forall ((A Bool) (B Bool)) (=> (= A B) (= (@ (@ tptp.set_or8904488021354931149Most_o A) B) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o)))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A B) (= (@ (@ tptp.set_or1266510415728281911st_int A) B) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int)))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A B) (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat)))))
% 5.98/6.28 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= A B) (= (@ (@ tptp.set_or1222579329274155063t_real A) B) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real)))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M2) N)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M2)) N))) (let ((_let_3 (= _let_1 N))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat) (P6 tptp.nat) (M2 tptp.nat)) (=> (@ P N) (=> (@ (@ tptp.ord_less_nat N) P6) (=> (@ (@ tptp.ord_less_nat M2) P6) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) P6) (=> (@ P N2) (@ P (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N2)) P6))))) (@ P M2)))))))
% 5.98/6.28 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat M2) N)) N))))
% 5.98/6.28 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (=> (forall ((M4 tptp.nat)) (@ (@ P M4) tptp.zero_zero_nat)) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ P N2) (@ (@ tptp.modulo_modulo_nat M4) N2)) (@ (@ P M4) N2)))) (@ (@ P M2) N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M2) (@ tptp.suc N))) N)))
% 5.98/6.28 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.numera1916890842035813515d_enat N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat N)) tptp.zero_z5237406670263579293d_enat))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger N)) tptp.zero_z3403309356797280102nteger))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.numera1916890842035813515d_enat N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat N)) tptp.zero_z5237406670263579293d_enat))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger N)) tptp.zero_z3403309356797280102nteger))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (D tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M2) D) tptp.zero_zero_nat) (exists ((Q5 tptp.nat)) (= M2 (@ (@ tptp.times_times_nat D) Q5))))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N))))
% 5.98/6.28 (assert (= tptp.modulo_modulo_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M3) N4)) M3) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M3) N4)) N4)))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M2) N)) (= (@ (@ tptp.modulo_modulo_nat M2) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M2) N)) N)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat N)) tptp.one_on7984719198319812577d_enat))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger N)) tptp.one_one_Code_integer))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.numera6620942414471956472nteger N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.numeral_numeral_real N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.numeral_numeral_rat N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.numeral_numeral_int N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ (@ tptp.modulo_modulo_nat M2) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M2) N)) N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.numera6620942414471956472nteger N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.numeral_numeral_int N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.numeral_numeral_real N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.numeral_numeral_rat N))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex X))) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat)))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (= tptp.one_one_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (= tptp.one_one_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_real N) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_rat N) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex N) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))))
% 5.98/6.28 (assert (forall ((A tptp.set_int) (B 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 A) B)) (@ (@ tptp.set_or370866239135849197et_int C) D)) (and (or (not (@ (@ tptp.ord_less_eq_set_int A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_set_int B) D) (or (@ (@ tptp.ord_less_set_int C) A) (@ (@ tptp.ord_less_set_int B) D)))) (@ _let_1 D))))))
% 5.98/6.28 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (= (@ (@ tptp.ord_less_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C) D)) (and (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) D) (or (@ (@ tptp.ord_less_rat C) A) (@ (@ tptp.ord_less_rat B) D)))) (@ _let_1 D))))))
% 5.98/6.28 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (= (@ (@ tptp.ord_less_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or7049704709247886629st_num C) D)) (and (or (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_num B) D) (or (@ (@ tptp.ord_less_num C) A) (@ (@ tptp.ord_less_num B) D)))) (@ _let_1 D))))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (= (@ (@ tptp.ord_less_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int C) D)) (and (or (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) D) (or (@ (@ tptp.ord_less_int C) A) (@ (@ tptp.ord_less_int B) D)))) (@ _let_1 D))))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (= (@ (@ tptp.ord_less_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1269000886237332187st_nat C) D)) (and (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_nat B) D) (or (@ (@ tptp.ord_less_nat C) A) (@ (@ tptp.ord_less_nat B) D)))) (@ _let_1 D))))))
% 5.98/6.28 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C))) (= (@ (@ tptp.ord_less_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C) D)) (and (or (not (@ (@ tptp.ord_less_eq_real A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) D) (or (@ (@ tptp.ord_less_real C) A) (@ (@ tptp.ord_less_real B) D)))) (@ _let_1 D))))))
% 5.98/6.28 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B))))))
% 5.98/6.28 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B))))))
% 5.98/6.28 (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))))))
% 5.98/6.28 (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))))))
% 5.98/6.28 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y))) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y)))))
% 5.98/6.28 (assert (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M2) N)) N))))
% 5.98/6.28 (assert (forall ((M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.set_or1266510415728281911st_int M2))) (let ((_let_2 (@ (@ tptp.plus_plus_int tptp.one_one_int) N))) (=> (@ (@ tptp.ord_less_eq_int M2) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_int _let_2) (@ _let_1 N))))))))
% 5.98/6.28 (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))))))
% 5.98/6.28 (assert (forall ((X tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X) N))) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X)) N))))
% 5.98/6.28 (assert (forall ((X tptp.complex) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X) N))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X)) N))))
% 5.98/6.28 (assert (forall ((A tptp.real) (R2 tptp.real) (B tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real A)) R2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B)) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B))) (@ (@ tptp.plus_plus_real R2) S))))))
% 5.98/6.28 (assert (forall ((A tptp.complex) (R2 tptp.real) (B tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex A)) R2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B)) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B))) (@ (@ tptp.plus_plus_real R2) S))))))
% 5.98/6.28 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y)))))
% 5.98/6.28 (assert (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)))))
% 5.98/6.28 (assert (forall ((X tptp.real) (Y tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) E2))))
% 5.98/6.28 (assert (forall ((X tptp.complex) (Y tptp.complex) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) E2))))
% 5.98/6.28 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B))) C) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real A)) C)))))
% 5.98/6.28 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B))) C) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex A)) C)))))
% 5.98/6.28 (assert (forall ((X tptp.real) (Y tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X) Y))) E2))))
% 5.98/6.28 (assert (forall ((X tptp.complex) (Y tptp.complex) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X) Y))) E2))))
% 5.98/6.28 (assert (forall ((X tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Y) Z))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 5.98/6.28 (assert (forall ((X tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y) Z))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 5.98/6.28 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B)))))
% 5.98/6.28 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B)))))
% 5.98/6.28 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real Y)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X) Y))))))
% 5.98/6.28 (assert (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Y)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X) Y))))))
% 5.98/6.28 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ (@ tptp.modulo_modulo_nat A2) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B2) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A2) N)) (@ (@ tptp.divide_divide_nat B2) N))))))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 5.98/6.28 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 5.98/6.28 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 5.98/6.28 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 5.98/6.28 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 5.98/6.28 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 5.98/6.28 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 5.98/6.28 (assert (forall ((W2 tptp.num) (B 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 B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 5.98/6.28 (assert (forall ((W2 tptp.num) (B 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 B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 5.98/6.28 (assert (forall ((B 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 B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 5.98/6.28 (assert (forall ((B 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 B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 5.98/6.28 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B)))))
% 5.98/6.28 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B)))))
% 5.98/6.28 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B)))))
% 5.98/6.28 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) tptp.one_one_Code_integer)))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) tptp.one_one_real)))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) tptp.one_one_rat)))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) tptp.one_one_int)))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M2))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M2))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M2))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M2))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (Q4 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M2) Q4) (@ (@ tptp.modulo_modulo_nat N) Q4)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (not (forall ((S3 tptp.nat)) (not (= M2 (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat Q4) S3))))))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (Q4 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M2) Q4) (@ (@ tptp.modulo_modulo_nat N) Q4)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (not (forall ((S3 tptp.nat)) (not (= N (@ (@ tptp.plus_plus_nat M2) (@ (@ tptp.times_times_nat Q4) S3))))))))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (N tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat X) N) (@ (@ tptp.modulo_modulo_nat Y) N)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (exists ((Q5 tptp.nat)) (= X (@ (@ tptp.plus_plus_nat Y) (@ (@ tptp.times_times_nat N) Q5))))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) tptp.one_one_Code_integer)))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) tptp.one_one_int)))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) tptp.one_one_real)))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) tptp.one_one_rat)))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M2))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M2))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M2))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M2))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M2)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))))))
% 5.98/6.28 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real (@ tptp.real_V7735802525324610683m_real A))))))
% 5.98/6.28 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.invers8013647133539491842omplex A)) (@ tptp.inverse_inverse_real (@ tptp.real_V1022390504157884413omplex A))))))
% 5.98/6.28 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real X))) (@ tptp.exp_real (@ tptp.real_V7735802525324610683m_real X)))))
% 5.98/6.28 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex X))) (@ tptp.exp_real (@ tptp.real_V1022390504157884413omplex X)))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) C))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real B) D))))))
% 5.98/6.28 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) C))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex B) D))))))
% 5.98/6.28 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real (@ tptp.sgn_sgn_real X)))) (let ((_let_2 (= X tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 5.98/6.28 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex (@ tptp.sgn_sgn_complex X)))) (let ((_let_2 (= X tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.nat Bool)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.modulo_modulo_nat M2) N)) (and (=> _let_1 (@ P M2)) (=> (not _let_1) (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I4)) J3)) (@ P J3))))))))))
% 5.98/6.28 (assert (forall ((B 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 B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 5.98/6.28 (assert (forall ((B 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 B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 5.98/6.28 (assert (forall ((W2 tptp.num) (B 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 B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 5.98/6.28 (assert (forall ((W2 tptp.num) (B 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 B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 5.98/6.28 (assert (forall ((W2 tptp.num) (B 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 B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 5.98/6.28 (assert (forall ((W2 tptp.num) (B 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 B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 5.98/6.28 (assert (forall ((W2 tptp.num) (B 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 B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 5.98/6.28 (assert (forall ((B 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 B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 5.98/6.28 (assert (forall ((B 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 B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 5.98/6.28 (assert (forall ((B 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 B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 5.98/6.28 (assert (forall ((Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.count_list_VEBT_VEBT Xs) X)) (@ tptp.size_s6755466524823107622T_VEBT Xs))))
% 5.98/6.28 (assert (forall ((Xs tptp.list_nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.count_list_nat Xs) X)) (@ tptp.size_size_list_nat Xs))))
% 5.98/6.28 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B)))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B)))))
% 5.98/6.28 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B)))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B)))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real D))) (= (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real X)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat X) D))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat X) D))) _let_1))))))
% 5.98/6.28 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int X) Y)) (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))))
% 5.98/6.28 (assert (forall ((B 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 B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1))))))))))))
% 5.98/6.28 (assert (forall ((B 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 B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))))
% 5.98/6.28 (assert (forall ((W2 tptp.num) (B 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 B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 5.98/6.28 (assert (forall ((W2 tptp.num) (B 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 B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M2) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat M2) N))) M2) tptp.one_one_nat))))
% 5.98/6.28 (assert (forall ((W2 tptp.num) (B 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 B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 5.98/6.28 (assert (forall ((W2 tptp.num) (B 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 B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 5.98/6.28 (assert (forall ((B 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 B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 5.98/6.28 (assert (forall ((B 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 B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 5.98/6.28 (assert (forall ((R2 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real R2) (@ tptp.real_V7735802525324610683m_real X)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.inverse_inverse_real X))) (@ tptp.inverse_inverse_real R2))))))
% 5.98/6.28 (assert (forall ((R2 tptp.real) (X tptp.complex)) (=> (@ (@ tptp.ord_less_eq_real R2) (@ tptp.real_V1022390504157884413omplex X)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.invers8013647133539491842omplex X))) (@ tptp.inverse_inverse_real R2))))))
% 5.98/6.28 (assert (forall ((X5 (-> tptp.nat tptp.complex)) (E2 tptp.real)) (=> (@ tptp.topolo6517432010174082258omplex X5) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((M9 tptp.nat)) (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) M) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) N6) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ X5 M)) (@ X5 N6)))) E2))))))))))
% 5.98/6.28 (assert (forall ((X5 (-> tptp.nat tptp.real)) (E2 tptp.real)) (=> (@ tptp.topolo4055970368930404560y_real X5) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((M9 tptp.nat)) (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) M) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) N6) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ X5 M)) (@ X5 N6)))) E2))))))))))
% 5.98/6.28 (assert (forall ((X5 (-> tptp.nat tptp.complex))) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M10 tptp.nat)) (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M10) M4) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M10) N2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ X5 M4)) (@ X5 N2)))) E)))))))) (@ tptp.topolo6517432010174082258omplex X5))))
% 5.98/6.28 (assert (forall ((X5 (-> tptp.nat tptp.real))) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M10 tptp.nat)) (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M10) M4) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M10) N2) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ X5 M4)) (@ X5 N2)))) E)))))))) (@ tptp.topolo4055970368930404560y_real X5))))
% 5.98/6.28 (assert (= tptp.topolo6517432010174082258omplex (lambda ((X8 (-> tptp.nat tptp.complex))) (forall ((E3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E3) (exists ((M8 tptp.nat)) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M3) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N4) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ X8 M3)) (@ X8 N4)))) E3)))))))))))
% 5.98/6.28 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X8 (-> tptp.nat tptp.real))) (forall ((E3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E3) (exists ((M8 tptp.nat)) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M3) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N4) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ X8 M3)) (@ X8 N4)))) E3)))))))))))
% 5.98/6.28 (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)))))))
% 5.98/6.28 (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)))))))
% 5.98/6.28 (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)))))))
% 5.98/6.28 (assert (forall ((D4 tptp.int) (B2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X2 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B2) (not (= X2 (@ (@ tptp.plus_plus_int Xb) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X2) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int X2) D4)) T)))))))
% 5.98/6.28 (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 ((X2 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 ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B2) (not (= X2 (@ (@ tptp.plus_plus_int Xb) Xa3))))))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.minus_minus_int X2) D4))))))))))
% 5.98/6.28 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A2) (forall ((X2 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X2 (@ (@ tptp.minus_minus_int Xb) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X2) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int X2) D4)) T))))))))
% 5.98/6.28 (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))))))))
% 5.98/6.28 (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))))))))
% 5.98/6.28 (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))))))))
% 5.98/6.28 (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))))))))
% 5.98/6.28 (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))))))))
% 5.98/6.28 (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))))))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (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_nat Xs)) _let_1)) (= (@ (@ tptp.nth_Pr3440142176431000676at_int (@ (@ tptp.product_nat_int Xs) Ys2)) N) (@ (@ tptp.product_Pair_nat_int (@ (@ tptp.nth_nat Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (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_nat Xs)) _let_1)) (= (@ (@ tptp.nth_Pr744662078594809490T_VEBT (@ (@ tptp.produc7156399406898700509T_VEBT Xs) Ys2)) N) (@ (@ tptp.produc599794634098209291T_VEBT (@ (@ tptp.nth_nat Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (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_nat Xs)) _let_1)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat (@ (@ tptp.product_nat_nat Xs) Ys2)) N) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.nth_nat Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (Xs tptp.list_P6011104703257516679at_nat) (Ys2 tptp.list_P6011104703257516679at_nat)) (let ((_let_1 (@ tptp.size_s5460976970255530739at_nat Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s5460976970255530739at_nat Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6744343527793145070at_nat (@ (@ tptp.produc3544356994491977349at_nat Xs) Ys2)) N) (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_Pr7617993195940197384at_nat Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N)))))
% 5.98/6.28 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) N) (=> (not (= Mi Ma)) (and (@ (@ tptp.ord_less_nat Mi) Ma) (exists ((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))))))))))))
% 5.98/6.28 (assert (forall ((H 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) H))) (=> (not (= H 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))) H)) (@ _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 H)))))))))))))
% 5.98/6.28 (assert (forall ((H 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) H))) (=> (not (= H 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))) H)) (@ (@ 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 H))))))))))))
% 5.98/6.28 (assert (= tptp.real_V7139242839884736329omplex (lambda ((F5 (-> tptp.complex tptp.complex))) (exists ((K5 tptp.real)) (forall ((X3 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F5 X3))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X3)) K5)))))))
% 5.98/6.28 (assert (forall ((F (-> tptp.complex tptp.complex))) (=> (exists ((K6 tptp.real)) (forall ((X4 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X4))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X4)) K6)))) (@ tptp.real_V7139242839884736329omplex F))))
% 5.98/6.28 (assert (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or1269000886237332187st_nat L) U))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))) (@ _let_1 A)) (@ _let_1 B)))))
% 5.98/6.28 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ _let_1 (@ (@ tptp.minus_minus_nat A) B)) (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.28 (assert (forall ((Tree tptp.vEBT_VEBT) (X tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member Tree) X) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 5.98/6.28 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N)))))
% 5.98/6.28 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.some_nat M2) (@ tptp.vEBT_vebt_mint T)) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary))) (=> (or (= X Mi) (= X Ma)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))))
% 5.98/6.28 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ (@ tptp.vEBT_vebt_succ T) X) (@ tptp.some_nat Y)) (@ (@ tptp.ord_less_nat Y) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 5.98/6.28 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ (@ tptp.vEBT_vebt_pred T) X) (@ tptp.some_nat Y)) (@ (@ tptp.ord_less_nat Y) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 5.98/6.28 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X) _let_1) (=> (@ (@ tptp.ord_less_nat Y) _let_1) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) Y)) X))))))))
% 5.98/6.28 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) X)) X)))))
% 5.98/6.28 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X) _let_1) (=> (@ (@ tptp.ord_less_nat Y) _let_1) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_vebt_insert T) X)) Y) (or (@ (@ tptp.vEBT_vebt_member T) Y) (= X Y)))))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M2)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_eq_num M2) N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_num tptp.one) N)))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary))) (=> (or (@ (@ tptp.ord_less_nat X) Mi) (@ (@ tptp.ord_less_nat Ma) X)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) _let_1))))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (and (= X Mi) (= X Ma)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary))))))
% 5.98/6.28 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) N) (and (@ (@ tptp.ord_less_eq_nat Mi) Ma) (@ (@ tptp.ord_less_nat Ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg))))))
% 5.98/6.28 (assert (forall ((Deg tptp.nat) (Ma tptp.nat) (X tptp.nat) (Mi tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (=> (@ (@ tptp.ord_less_nat Ma) X) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (@ tptp.some_nat Ma))))))
% 5.98/6.28 (assert (forall ((Deg tptp.nat) (X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (=> (@ (@ tptp.ord_less_nat X) Mi) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (@ tptp.some_nat Mi))))))
% 5.98/6.28 (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))))))
% 5.98/6.28 (assert (= tptp.vEBT_VEBT_bit_concat (lambda ((H3 tptp.nat) (L3 tptp.nat) (D5 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) D5))) L3))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (= tptp.one_one_complex (@ tptp.numera6690914467698888265omplex N)) (= tptp.one N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (= tptp.one_one_rat (@ tptp.numeral_numeral_rat N)) (= tptp.one N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (= tptp.one_one_real (@ tptp.numeral_numeral_real N)) (= tptp.one N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (= tptp.one_one_nat (@ tptp.numeral_numeral_nat N)) (= tptp.one N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (= tptp.one_one_int (@ tptp.numeral_numeral_int N)) (= tptp.one N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (= tptp.one_on7984719198319812577d_enat (@ tptp.numera1916890842035813515d_enat N)) (= tptp.one N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (= tptp.one_one_Code_integer (@ tptp.numera6620942414471956472nteger N)) (= tptp.one N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex N) tptp.one_one_complex) (= N tptp.one))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_rat N) tptp.one_one_rat) (= N tptp.one))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_real N) tptp.one_one_real) (= N tptp.one))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_nat N) tptp.one_one_nat) (= N tptp.one))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_int N) tptp.one_one_int) (= N tptp.one))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (= (@ tptp.numera1916890842035813515d_enat N) tptp.one_on7984719198319812577d_enat) (= N tptp.one))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (= (@ tptp.numera6620942414471956472nteger N) tptp.one_one_Code_integer) (= N tptp.one))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 tptp.one)) N) (@ tptp.bit0 N))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M2)) tptp.one))))
% 5.98/6.28 (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))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= N tptp.one))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int tptp.one_one_int)) (= N tptp.one))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real tptp.one_one_real)) (= N tptp.one))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (= N tptp.one))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (= N tptp.one))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= N tptp.one))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (= N tptp.one))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (= N tptp.one))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (= N tptp.one))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= N tptp.one))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (= (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2)))) (not (= M2 tptp.one)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2)))) (not (= M2 tptp.one)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2)))) (not (= M2 tptp.one)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2)))) (not (= M2 tptp.one)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (not (= M2 tptp.one)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (not (= M2 tptp.one)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) (@ tptp.uminus_uminus_real tptp.one_one_real)) (not (= M2 tptp.one)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (not (= M2 tptp.one)))))
% 5.98/6.28 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 5.98/6.28 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 5.98/6.28 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 5.98/6.28 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 5.98/6.28 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 5.98/6.28 (assert (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))))
% 5.98/6.28 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 5.98/6.28 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 5.98/6.28 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 5.98/6.28 (assert (forall ((A tptp.nat)) (= (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 5.98/6.28 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 5.98/6.28 (assert (forall ((A tptp.complex)) (= (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 5.98/6.28 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 5.98/6.28 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 5.98/6.28 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 5.98/6.28 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 5.98/6.28 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 5.98/6.28 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 5.98/6.28 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N)))))
% 5.98/6.28 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ tptp.suc (@ tptp.suc N)))))
% 5.98/6.28 (assert (= (@ tptp.suc tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex N)) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat N)) tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.numera6620942414471956472nteger N)) tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat N)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 5.98/6.28 (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))))
% 5.98/6.28 (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))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger N)) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 5.98/6.28 (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))))
% 5.98/6.28 (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))))
% 5.98/6.28 (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))))
% 5.98/6.28 (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))))
% 5.98/6.28 (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))))
% 5.98/6.28 (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))))
% 5.98/6.28 (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))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 5.98/6.28 (assert (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 5.98/6.28 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 5.98/6.28 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 5.98/6.28 (assert (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 5.98/6.28 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 5.98/6.28 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 5.98/6.28 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 5.98/6.28 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 5.98/6.28 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 5.98/6.28 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_real X) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (= X Y))))))))
% 5.98/6.28 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_rat X) _let_1) (@ (@ tptp.power_power_rat Y) _let_1)) (= X Y))))))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_nat X) _let_1) (@ (@ tptp.power_power_nat Y) _let_1)) (= X Y))))))))
% 5.98/6.28 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_int X) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (= X Y))))))))
% 5.98/6.28 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A tptp.zero_zero_real)))))
% 5.98/6.28 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A tptp.zero_zero_rat)))))
% 5.98/6.28 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A tptp.zero_zero_int)))))
% 5.98/6.28 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 5.98/6.28 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.plus_plus_int _let_1) _let_1) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 5.98/6.28 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.plus_plus_real _let_1) _let_1) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 5.98/6.28 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.plus_plus_rat _let_1) _let_1) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 5.98/6.28 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.plus_plus_complex _let_1) _let_1) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 5.98/6.28 (assert (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 5.98/6.28 (assert (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))
% 5.98/6.28 (assert (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 5.98/6.28 (assert (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))
% 5.98/6.28 (assert (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 5.98/6.28 (assert (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 5.98/6.28 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 5.98/6.28 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 5.98/6.28 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 5.98/6.28 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 5.98/6.28 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.divide6298287555418463151nteger _let_1) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)))
% 5.98/6.28 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.divide_divide_int _let_1) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)))
% 5.98/6.28 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))
% 5.98/6.28 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))
% 5.98/6.28 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))
% 5.98/6.28 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_z3403309356797280102nteger)) (= _let_1 tptp.one_one_Code_integer)))))
% 5.98/6.28 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_zero_int)) (= _let_1 tptp.one_one_int)))))
% 5.98/6.28 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_zero_nat)) (= _let_1 tptp.one_one_nat)))))
% 5.98/6.28 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_Code_integer)) (= _let_1 tptp.zero_z3403309356797280102nteger)))))
% 5.98/6.28 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_int)) (= _let_1 tptp.zero_zero_int)))))
% 5.98/6.28 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_nat)) (= _let_1 tptp.zero_zero_nat)))))
% 5.98/6.28 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 5.98/6.28 (assert (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 5.98/6.28 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 5.98/6.28 (assert (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 5.98/6.28 (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)))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M2) tptp.one))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M2) tptp.one))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M2))) tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M2) tptp.one))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M2) tptp.one))))))
% 5.98/6.28 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M2))) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M2) tptp.one))))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat M2) M2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat)))
% 5.98/6.28 (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)))))
% 5.98/6.28 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int)))
% 5.98/6.28 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_real)))
% 5.98/6.28 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_rat)))
% 5.98/6.28 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_complex)))
% 5.98/6.28 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X))))
% 5.98/6.28 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) X))))
% 5.98/6.28 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 5.98/6.28 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) tptp.one_one_int) (@ (@ tptp.ord_less_rat X) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat M2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (= _let_1 tptp.one_one_nat)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat N) A2)) (= (@ tptp.nat_set_encode (@ (@ tptp.insert_nat N) A2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.nat_set_encode A2)))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_complex)) (= (= (@ tptp.finite_card_complex S2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) S2) (exists ((Y2 tptp.complex)) (and (@ (@ tptp.member_complex Y2) S2) (not (= X3 Y2)) (forall ((Z2 tptp.complex)) (=> (@ (@ tptp.member_complex Z2) S2) (or (= Z2 X3) (= Z2 Y2)))))))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_list_nat)) (= (= (@ tptp.finite_card_list_nat S2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X3 tptp.list_nat)) (and (@ (@ tptp.member_list_nat X3) S2) (exists ((Y2 tptp.list_nat)) (and (@ (@ tptp.member_list_nat Y2) S2) (not (= X3 Y2)) (forall ((Z2 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat Z2) S2) (or (= Z2 X3) (= Z2 Y2)))))))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_set_nat)) (= (= (@ tptp.finite_card_set_nat S2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) S2) (exists ((Y2 tptp.set_nat)) (and (@ (@ tptp.member_set_nat Y2) S2) (not (= X3 Y2)) (forall ((Z2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Z2) S2) (or (= Z2 X3) (= Z2 Y2)))))))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_nat)) (= (= (@ tptp.finite_card_nat S2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) S2) (exists ((Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) S2) (not (= X3 Y2)) (forall ((Z2 tptp.nat)) (=> (@ (@ tptp.member_nat Z2) S2) (or (= Z2 X3) (= Z2 Y2)))))))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_int)) (= (= (@ tptp.finite_card_int S2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) S2) (exists ((Y2 tptp.int)) (and (@ (@ tptp.member_int Y2) S2) (not (= X3 Y2)) (forall ((Z2 tptp.int)) (=> (@ (@ tptp.member_int Z2) S2) (or (= Z2 X3) (= Z2 Y2)))))))))))
% 5.98/6.28 (assert (forall ((Z tptp.extended_enat) (Y tptp.extended_enat) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat X))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Z) Y) (= (@ _let_1 (@ (@ tptp.minus_3235023915231533773d_enat Y) Z)) (@ (@ tptp.minus_3235023915231533773d_enat (@ _let_1 Y)) Z))))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (= (@ (@ tptp.ord_less_eq_num X) tptp.one) (= X tptp.one))))
% 5.98/6.28 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat N) tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat))))
% 5.98/6.28 (assert (forall ((N tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) N)))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) N) (@ (@ tptp.plus_plus_num N) tptp.one))))
% 5.98/6.28 (assert (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat))
% 5.98/6.28 (assert (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 5.98/6.28 (assert (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 5.98/6.28 (assert (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real))
% 5.98/6.28 (assert (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex))
% 5.98/6.28 (assert (= (@ (@ tptp.power_power_rat tptp.one_one_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat))
% 5.98/6.28 (assert (= (@ (@ tptp.power_power_int tptp.one_one_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 5.98/6.28 (assert (= (@ (@ tptp.power_power_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 5.98/6.28 (assert (= (@ (@ tptp.power_power_real tptp.one_one_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real))
% 5.98/6.28 (assert (= (@ (@ tptp.power_power_complex tptp.one_one_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex))
% 5.98/6.28 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 5.98/6.28 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 5.98/6.28 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 5.98/6.28 (assert (forall ((M2 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 M2) _let_1)) (@ (@ tptp.power_power_nat N) _let_1)) (@ (@ tptp.ord_less_eq_nat M2) N)))))
% 5.98/6.28 (assert (forall ((K tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.power_power_nat K) M2)))))
% 5.98/6.28 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 5.98/6.28 (assert (= (@ tptp.size_size_num tptp.one) tptp.zero_zero_nat))
% 5.98/6.28 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 5.98/6.28 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 5.98/6.28 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 5.98/6.28 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 5.98/6.28 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_real X) _let_2) (@ (@ tptp.power_power_real Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 5.98/6.28 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_rat X) _let_2) (@ (@ tptp.power_power_rat Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_nat X) _let_2) (@ (@ tptp.power_power_nat Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 5.98/6.28 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_int X) _let_2) (@ (@ tptp.power_power_int Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 5.98/6.28 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 5.98/6.28 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat X) Y))))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 5.98/6.28 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int X) Y))))))
% 5.98/6.28 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))))
% 5.98/6.28 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_rat))))
% 5.98/6.28 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_int))))
% 5.98/6.28 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_rat Z) Z))))
% 5.98/6.28 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_real Z) Z))))
% 5.98/6.28 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_nat Z) Z))))
% 5.98/6.28 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_int Z) Z))))
% 5.98/6.28 (assert (forall ((Z tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_p3455044024723400733d_enat Z) Z))))
% 5.98/6.28 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_p5714425477246183910nteger Z) Z))))
% 5.98/6.28 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_rat Z) Z))))
% 5.98/6.28 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real Z) Z))))
% 5.98/6.28 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat Z) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z) Z))))
% 5.98/6.28 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z) Z))))
% 5.98/6.28 (assert (forall ((Z tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat Z) (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_p3455044024723400733d_enat Z) Z))))
% 5.98/6.28 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_p5714425477246183910nteger Z) Z))))
% 5.98/6.28 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) A)) B)))))
% 5.98/6.28 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) A)) B)))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) B)))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) B)))))
% 5.98/6.28 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) A)) B)))))
% 5.98/6.28 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) B)))))
% 5.98/6.28 (assert (forall ((X tptp.rat)) (let ((_let_1 (@ (@ tptp.divide_divide_rat X) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_rat _let_1) _let_1) X))))
% 5.98/6.28 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_real _let_1) _let_1) X))))
% 5.98/6.28 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int) (or (= A tptp.one_one_int) (= A (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 5.98/6.28 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (or (= A tptp.one_one_real) (= A (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 5.98/6.28 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat) (or (= A tptp.one_one_rat) (= A (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 5.98/6.28 (assert (forall ((A tptp.complex)) (= (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex) (or (= A tptp.one_one_complex) (= A (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))))
% 5.98/6.28 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))))
% 5.98/6.28 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) (@ tptp.abs_abs_rat Y)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))))))
% 5.98/6.28 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) (@ tptp.abs_abs_int Y)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))))
% 5.98/6.28 (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))))))
% 5.98/6.28 (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))))))
% 5.98/6.28 (assert (forall ((X tptp.rat)) (= (= (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat) (= (@ tptp.abs_abs_rat X) tptp.one_one_rat))))
% 5.98/6.28 (assert (forall ((X tptp.int)) (= (= (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int) (= (@ tptp.abs_abs_int X) tptp.one_one_int))))
% 5.98/6.28 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.abs_abs_real X) tptp.one_one_real))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ tptp.finite711546835091564841at_nat S2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X3 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (and (= S2 (@ (@ tptp.insert8211810215607154385at_nat X3) (@ (@ tptp.insert8211810215607154385at_nat Y2) tptp.bot_bo2099793752762293965at_nat))) (not (= X3 Y2)))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_complex)) (= (= (@ tptp.finite_card_complex S2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X3 tptp.complex) (Y2 tptp.complex)) (and (= S2 (@ (@ tptp.insert_complex X3) (@ (@ tptp.insert_complex Y2) tptp.bot_bot_set_complex))) (not (= X3 Y2)))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_list_nat)) (= (= (@ tptp.finite_card_list_nat S2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X3 tptp.list_nat) (Y2 tptp.list_nat)) (and (= S2 (@ (@ tptp.insert_list_nat X3) (@ (@ tptp.insert_list_nat Y2) tptp.bot_bot_set_list_nat))) (not (= X3 Y2)))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_set_nat)) (= (= (@ tptp.finite_card_set_nat S2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X3 tptp.set_nat) (Y2 tptp.set_nat)) (and (= S2 (@ (@ tptp.insert_set_nat X3) (@ (@ tptp.insert_set_nat Y2) tptp.bot_bot_set_set_nat))) (not (= X3 Y2)))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_real)) (= (= (@ tptp.finite_card_real S2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X3 tptp.real) (Y2 tptp.real)) (and (= S2 (@ (@ tptp.insert_real X3) (@ (@ tptp.insert_real Y2) tptp.bot_bot_set_real))) (not (= X3 Y2)))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_o)) (= (= (@ tptp.finite_card_o S2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X3 Bool) (Y2 Bool)) (and (= S2 (@ (@ tptp.insert_o X3) (@ (@ tptp.insert_o Y2) tptp.bot_bot_set_o))) (not (= X3 Y2)))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_nat)) (= (= (@ tptp.finite_card_nat S2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X3 tptp.nat) (Y2 tptp.nat)) (and (= S2 (@ (@ tptp.insert_nat X3) (@ (@ tptp.insert_nat Y2) tptp.bot_bot_set_nat))) (not (= X3 Y2)))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_int)) (= (= (@ tptp.finite_card_int S2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (exists ((X3 tptp.int) (Y2 tptp.int)) (and (= S2 (@ (@ tptp.insert_int X3) (@ (@ tptp.insert_int Y2) tptp.bot_bot_set_int))) (not (= X3 Y2)))))))
% 5.98/6.28 (assert (= (@ tptp.nat2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 5.98/6.28 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (@ P tptp.one_one_nat) (=> (forall ((N2 tptp.nat)) (=> (@ P N2) (@ P (@ (@ tptp.plus_plus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ P N))))))
% 5.98/6.28 (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))))))
% 5.98/6.28 (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))))
% 5.98/6.28 (assert (forall ((K tptp.nat) (M2 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 M2) N)) (@ (@ tptp.minus_minus_nat (@ _let_1 M2)) (@ _let_1 N)))))))
% 5.98/6.28 (assert (forall ((U tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real U) _let_1))) (@ (@ tptp.power_power_real X) _let_1)))))
% 5.98/6.28 (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))))
% 5.98/6.28 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real X) Y))))))
% 5.98/6.28 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_rat X) Y))))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_nat X) Y))))))
% 5.98/6.28 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_int X) Y))))))
% 5.98/6.28 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 5.98/6.28 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 5.98/6.28 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ _let_1 A)))))
% 5.98/6.28 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 A)))))
% 5.98/6.28 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))))
% 5.98/6.28 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))))))
% 5.98/6.28 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))))
% 5.98/6.28 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))
% 5.98/6.28 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))
% 5.98/6.28 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))
% 5.98/6.28 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real)))))
% 5.98/6.28 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat)))))
% 5.98/6.28 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int)))))
% 5.98/6.28 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (or (not (= X tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real)))))))
% 5.98/6.28 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) (or (not (= X tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat)))))))
% 5.98/6.28 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int)))))))
% 5.98/6.28 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 5.98/6.28 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 5.98/6.28 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))
% 5.98/6.28 (assert (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat)))))
% 5.98/6.28 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X) (=> (@ (@ tptp.ord_less_eq_int X) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int)))))
% 5.98/6.28 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger N)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N))))
% 5.98/6.28 (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))))
% 5.98/6.28 (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))))
% 5.98/6.28 (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))))
% 5.98/6.28 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) Y))))))
% 5.98/6.28 (assert (forall ((Y tptp.rat) (X tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) Y))))))
% 5.98/6.28 (assert (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) Y))))))
% 5.98/6.28 (assert (forall ((M2 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 M2) N)) tptp.zero_zero_nat)) (not (= (@ _let_1 M2) tptp.zero_zero_nat))))))
% 5.98/6.28 (assert (forall ((M2 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 M2) N)) tptp.zero_zero_int)) (not (= (@ _let_1 M2) tptp.zero_zero_int))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) tptp.zero_z3403309356797280102nteger)) (not (= (@ _let_1 M2) tptp.zero_z3403309356797280102nteger))))))
% 5.98/6.28 (assert (forall ((M2 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 M2) N)) tptp.zero_zero_nat)) (not (= (@ _let_1 N) tptp.zero_zero_nat))))))
% 5.98/6.28 (assert (forall ((M2 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 M2) N)) tptp.zero_zero_int)) (not (= (@ _let_1 N) tptp.zero_zero_int))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) tptp.zero_z3403309356797280102nteger)) (not (= (@ _let_1 N) tptp.zero_z3403309356797280102nteger))))))
% 5.98/6.28 (assert (forall ((A tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 5.98/6.28 (assert (forall ((A tptp.rat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 5.98/6.28 (assert (forall ((A tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (M2 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) M2)) tptp.zero_zero_nat))))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (M2 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) M2)) tptp.zero_zero_int))))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (M2 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) M2)) tptp.zero_z3403309356797280102nteger))))))
% 5.98/6.28 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real))))
% 5.98/6.28 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) tptp.one_one_rat))))
% 5.98/6.28 (assert (forall ((X tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) tptp.one_one_int))))
% 5.98/6.28 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real))))
% 5.98/6.28 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X)) tptp.one_one_rat))))
% 5.98/6.28 (assert (forall ((X tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X)) tptp.one_one_int))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N) (@ P M3))) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X3))))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M3) N) (@ P M3))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X3))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N2 tptp.nat)) (=> (@ P N2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ P (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (=> (forall ((N2 tptp.nat)) (=> (@ P N2) (@ P (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (@ P N))))))
% 5.98/6.28 (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)))))))
% 5.98/6.28 (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))))))))
% 5.98/6.28 (assert (forall ((X tptp.real)) (=> (= (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.real_V7735802525324610683m_real X) tptp.one_one_real))))
% 5.98/6.28 (assert (forall ((X tptp.complex)) (=> (= (@ (@ tptp.power_power_complex X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex) (= (@ tptp.real_V1022390504157884413omplex X) tptp.one_one_real))))
% 5.98/6.28 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ (@ tptp.times_times_real A) C))) (@ (@ tptp.times_times_real B) D))) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A) _let_2)) (@ (@ tptp.power_power_real D) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real B) _let_2)) (@ (@ tptp.power_power_real C) _let_2))))))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat N))) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 N)) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) _let_1)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N)) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)))))
% 5.98/6.28 (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)))
% 5.98/6.28 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real X))) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real _let_1) (@ tptp.inverse_inverse_real _let_1))))))
% 5.98/6.28 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 5.98/6.28 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 5.98/6.28 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat tptp.one)) A)))
% 5.98/6.28 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int tptp.one)) A)))
% 5.98/6.28 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat A) (@ tptp.numera1916890842035813515d_enat tptp.one)) A)))
% 5.98/6.28 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.numera6620942414471956472nteger tptp.one)) A)))
% 5.98/6.28 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat tptp.one)) A) A)))
% 5.98/6.28 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real tptp.one)) A) A)))
% 5.98/6.28 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat tptp.one)) A) A)))
% 5.98/6.28 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int tptp.one)) A) A)))
% 5.98/6.28 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat tptp.one)) A) A)))
% 5.98/6.28 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger tptp.one)) A) A)))
% 5.98/6.28 (assert (= (@ tptp.numera6690914467698888265omplex tptp.one) tptp.one_one_complex))
% 5.98/6.28 (assert (= (@ tptp.numeral_numeral_rat tptp.one) tptp.one_one_rat))
% 5.98/6.28 (assert (= (@ tptp.numeral_numeral_real tptp.one) tptp.one_one_real))
% 5.98/6.28 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 5.98/6.28 (assert (= (@ tptp.numeral_numeral_int tptp.one) tptp.one_one_int))
% 5.98/6.28 (assert (= (@ tptp.numera1916890842035813515d_enat tptp.one) tptp.one_on7984719198319812577d_enat))
% 5.98/6.28 (assert (= (@ tptp.numera6620942414471956472nteger tptp.one) tptp.one_one_Code_integer))
% 5.98/6.28 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 5.98/6.28 (assert (= (@ tptp.numeral_numeral_nat tptp.one) (@ tptp.suc tptp.zero_zero_nat)))
% 5.98/6.28 (assert (forall ((V tptp.num) (N tptp.nat)) (= (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) N)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) tptp.one))) N))))
% 5.98/6.28 (assert (let ((_let_1 (@ tptp.numeral_numeral_real tptp.one))) (= (@ tptp.inverse_inverse_real _let_1) _let_1)))
% 5.98/6.28 (assert (let ((_let_1 (@ tptp.numeral_numeral_rat tptp.one))) (= (@ tptp.inverse_inverse_rat _let_1) _let_1)))
% 5.98/6.28 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))))))
% 5.98/6.28 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X)) Y)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2)))))))
% 5.98/6.28 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_2) B) (= _let_2 (@ _let_1 B))))))))
% 5.98/6.28 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int _let_2) B) (= _let_2 (@ _let_1 B))))))))
% 5.98/6.28 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat _let_2) B) (= _let_2 (@ _let_1 B))))))))
% 5.98/6.28 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) tptp.zero_z3403309356797280102nteger)))))
% 5.98/6.28 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.modulo_modulo_int A) _let_1)) tptp.zero_zero_int)))))
% 5.98/6.28 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (= (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.modulo_modulo_nat A) _let_1)) tptp.zero_zero_nat)))))
% 5.98/6.28 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.power_power_real A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))))
% 5.98/6.28 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.power_power_rat A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))))
% 5.98/6.28 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))))
% 5.98/6.28 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_real))))
% 5.98/6.28 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_rat))))
% 5.98/6.28 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_int))))
% 5.98/6.28 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.power_power_int _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 5.98/6.28 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.power_power_real _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 5.98/6.28 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.power_power_rat _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 5.98/6.28 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.power_power_complex _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 5.98/6.28 (assert (forall ((B tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ _let_1 B) (=> (@ _let_1 K) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_nat (@ _let_1 N2)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)))))))))))
% 5.98/6.28 (assert (forall ((B tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) K) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))))))))
% 5.98/6.28 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real X) (@ tptp.inverse_inverse_real X))))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) M2) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M2)))))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (M2 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)) M2) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M2)))))))
% 5.98/6.28 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))))
% 5.98/6.28 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))))
% 5.98/6.28 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2)))) _let_2)))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2)))) _let_2)))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2)))) _let_2)))))))
% 5.98/6.28 (assert (forall ((N tptp.num) (Q4 tptp.num)) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q4))) tptp.zero_z3403309356797280102nteger) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger Q4)) tptp.zero_z3403309356797280102nteger))))
% 5.98/6.28 (assert (forall ((N tptp.num) (Q4 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q4))) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int Q4)) tptp.zero_zero_int))))
% 5.98/6.28 (assert (forall ((N tptp.num) (Q4 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q4))) tptp.zero_zero_nat) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat Q4)) tptp.zero_zero_nat))))
% 5.98/6.28 (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)))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.set_or1269000886237332187st_nat M2) N) (@ (@ tptp.insert_nat M2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N))))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.insert_nat M2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N)) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))))
% 5.98/6.28 (assert (forall ((X23 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit0 X23)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X23)) (@ tptp.suc tptp.zero_zero_nat)))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ (@ tptp.ord_less_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M2))) (@ tptp.semiri5074537144036343181t_real N)))))))
% 5.98/6.28 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B) tptp.one_one_int)) A))))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.divide_divide_int B) A))))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.plus_plus_int tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ (@ tptp.modulo_modulo_int (@ _let_2 (@ _let_1 B))) (@ _let_1 A)) (@ _let_2 (@ _let_1 (@ (@ tptp.modulo_modulo_int B) A)))))))))
% 5.98/6.28 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 5.98/6.28 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) B) (@ tptp.uminus1351360451143612070nteger B))))
% 5.98/6.28 (assert (forall ((B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one))) B) (@ tptp.uminus_uminus_int B))))
% 5.98/6.28 (assert (forall ((B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one))) B) (@ tptp.uminus_uminus_real B))))
% 5.98/6.28 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one))) B) (@ tptp.uminus_uminus_rat B))))
% 5.98/6.28 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) B) (@ tptp.uminus1482373934393186551omplex B))))
% 5.98/6.28 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) (@ tptp.uminus1351360451143612070nteger B))))
% 5.98/6.28 (assert (forall ((B tptp.int)) (= (@ (@ tptp.times_times_int B) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one))) (@ tptp.uminus_uminus_int B))))
% 5.98/6.28 (assert (forall ((B tptp.real)) (= (@ (@ tptp.times_times_real B) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one))) (@ tptp.uminus_uminus_real B))))
% 5.98/6.28 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.times_times_rat B) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one))) (@ tptp.uminus_uminus_rat B))))
% 5.98/6.28 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) (@ tptp.uminus1482373934393186551omplex B))))
% 5.98/6.28 (assert (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 5.98/6.28 (assert (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one)) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 5.98/6.28 (assert (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 5.98/6.28 (assert (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 5.98/6.28 (assert (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 5.98/6.28 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real X))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger tptp.one)) tptp.zero_z3403309356797280102nteger)))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)))
% 5.98/6.28 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)))
% 5.98/6.28 (assert (forall ((U tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real U) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_real X) Y)) (=> (@ _let_2 X) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ tptp.numeral_numeral_real _let_1))))))))))
% 5.98/6.28 (assert (forall ((U tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat U) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_rat X) Y)) (=> (@ _let_2 X) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ tptp.numeral_numeral_rat _let_1))))))))))
% 5.98/6.28 (assert (forall ((M2 tptp.code_integer) (X tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger X))) (let ((_let_2 (@ _let_1 M2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) M2)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) M2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_p5714425477246183910nteger _let_2) M2))))))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat X))) (let ((_let_2 (@ _let_1 M2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_nat _let_2) M2))))))))))
% 5.98/6.28 (assert (forall ((M2 tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int X))) (let ((_let_2 (@ _let_1 M2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) M2)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_int _let_2) M2))))))))))
% 5.98/6.28 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) _let_2) (= (@ (@ tptp.minus_8373710615458151222nteger _let_2) B) (@ _let_1 B)))))))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) _let_2) (= (@ (@ tptp.minus_minus_nat _let_2) B) (@ _let_1 B)))))))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) _let_2) (= (@ (@ tptp.minus_minus_int _let_2) B) (@ _let_1 B)))))))))
% 5.98/6.28 (assert (forall ((N5 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N5) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ tptp.finite_finite_nat N5))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M2))) (@ tptp.semiri5074537144036343181t_real N)))))))
% 5.98/6.28 (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))))))))
% 5.98/6.28 (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))))))))
% 5.98/6.28 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_1) X))))))))
% 5.98/6.28 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))) (@ tptp.numeral_numeral_real _let_1)))) (@ tptp.exp_real X))))))
% 5.98/6.28 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)))))))
% 5.98/6.28 (assert (= tptp.artanh_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X3)) (@ (@ tptp.minus_minus_real tptp.one_one_real) X3)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.minus_minus_int (@ _let_1 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int B) tptp.one_one_int)) A))) tptp.one_one_int))))))
% 5.98/6.28 (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))))))))
% 5.98/6.28 (assert (forall ((B tptp.int) (A tptp.int) (Q4 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 Q4))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ _let_3 R2)) (@ (@ (@ tptp.eucl_rel_int (@ _let_2 (@ _let_1 A))) (@ _let_1 B)) (@ _let_3 (@ _let_2 (@ _let_1 R2)))))))))))
% 5.98/6.28 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M2 tptp.nat) (Deg tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (=> (= M2 N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M2)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_1))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary)) Deg))))))))))
% 5.98/6.28 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N))) (= (@ tptp.semiri5044797733671781792omplex _let_3) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex _let_2) _let_3)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2)) N))) (@ tptp.semiri5044797733671781792omplex N))))))))
% 5.98/6.28 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N))) (= (@ tptp.semiri773545260158071498ct_rat _let_3) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat _let_2) _let_3)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2)) N))) (@ tptp.semiri773545260158071498ct_rat N))))))))
% 5.98/6.28 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N))) (= (@ tptp.semiri2265585572941072030t_real _let_3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real _let_2) _let_3)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) N))) (@ tptp.semiri2265585572941072030t_real N))))))))
% 5.98/6.28 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 5.98/6.28 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M2 tptp.nat) (Deg tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (=> (= M2 (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M2)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_1))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary)) Deg))))))))))
% 5.98/6.28 (assert (forall ((B tptp.int) (A tptp.int) (Q4 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 Q4))) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (=> (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) B) (@ _let_2 R2)) (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 A))) (@ _let_1 B)) (@ _let_2 (@ (@ tptp.minus_minus_int (@ _let_1 R2)) tptp.one_one_int)))))))))
% 5.98/6.28 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) (@ (@ tptp.modulo364778990260209775nteger A) _let_3)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_Code_integer) (@ _let_1 B))))))))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.modulo_modulo_nat A) _let_3)) (= (@ (@ tptp.plus_plus_nat (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_nat) (@ _let_1 B))))))))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.modulo_modulo_int A) _let_3)) (= (@ (@ tptp.plus_plus_int (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_int) (@ _let_1 B))))))))))
% 5.98/6.28 (assert (forall ((Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.times_times_complex _let_2) Z)) _let_4) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s2602460028002588243omplex Z) N))) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2))) N)))))))))
% 5.98/6.28 (assert (forall ((Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.times_times_real _let_2) Z)) _let_4) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s7457072308508201937r_real Z) N))) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) N)))))))))
% 5.98/6.28 (assert (forall ((Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.times_times_rat _let_2) Z)) _let_4) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s4028243227959126397er_rat Z) N))) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2))) N)))))))))
% 5.98/6.28 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))))) (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X)))))))))
% 5.98/6.28 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 5.98/6.28 (assert (forall ((B tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) K) (=> (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N))))))))
% 5.98/6.28 (assert (forall ((B tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N)) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))))))))
% 5.98/6.28 (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))))))))
% 5.98/6.28 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 5.98/6.28 (assert (forall ((B tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 N)) K) (=> (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))))))
% 5.98/6.28 (assert (forall ((B tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_nat (@ _let_1 N)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))))))))
% 5.98/6.28 (assert (forall ((L tptp.num) (R2 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ (@ tptp.unique5026877609467782581ep_nat L) (@ (@ tptp.product_Pair_nat_nat Q4) 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))))))))))
% 5.98/6.28 (assert (forall ((L tptp.num) (R2 tptp.int) (Q4 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ (@ tptp.unique5024387138958732305ep_int L) (@ (@ tptp.product_Pair_int_int Q4) 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))))))))))
% 5.98/6.28 (assert (forall ((L tptp.num) (R2 tptp.code_integer) (Q4 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ (@ tptp.unique4921790084139445826nteger L) (@ (@ tptp.produc1086072967326762835nteger Q4) 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))))))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.real tptp.real Bool)) (X tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ P X4) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_real X)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (X tptp.rat)) (=> (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X4) (@ (@ P X4) (@ (@ tptp.power_power_rat X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_rat X)) (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.int tptp.int Bool)) (X tptp.int)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (@ (@ P X4) (@ (@ tptp.power_power_int X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_int X)) (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 5.98/6.28 (assert (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X) Ma) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (@ (@ tptp.vEBT_VEBT_high X) (@ (@ tptp.divide_divide_nat Deg) _let_1))) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) tptp.none_nat)))))))
% 5.98/6.28 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat Mi) X) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (@ (@ tptp.vEBT_VEBT_high X) (@ (@ tptp.divide_divide_nat Deg) _let_1))) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) tptp.none_nat)))))))
% 5.98/6.28 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2793503036327961859nteger tptp.zero_zero_nat) A) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1)))))))
% 5.98/6.28 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7879613467334960850it_int tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1)))))))
% 5.98/6.28 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7882103937844011126it_nat tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1)))))))
% 5.98/6.28 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se8260200283734997820nteger tptp.zero_zero_nat) A) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))
% 5.98/6.28 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4205575877204974255it_nat tptp.zero_zero_nat) A) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))))))
% 5.98/6.28 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4203085406695923979it_int tptp.zero_zero_nat) A) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))))
% 5.98/6.28 (assert (= tptp.vEBT_VEBT_high (lambda ((X3 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.divide_divide_nat X3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))
% 5.98/6.28 (assert (forall ((Ma tptp.nat) (N tptp.nat) (M2 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) M2))) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high Ma) N)) (@ _let_1 M2))))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (N tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X) _let_1) (= (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X)) N) Y)))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (assert (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat))
% 5.98/6.28 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se4203085406695923979it_int N) K)) K)))
% 5.98/6.28 (assert (forall ((K tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se7879613467334960850it_int N) K))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M2))) (=> (@ _let_2 N) (=> (@ _let_2 M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high X) N)) (@ _let_1 M2)))))))))
% 5.98/6.28 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 5.98/6.28 (assert (forall ((B tptp.complex) (A tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex B) A))) (@ tptp.real_V1022390504157884413omplex B))) (@ tptp.real_V1022390504157884413omplex A))))
% 5.98/6.28 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (Va2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Va2) _let_1))) (let ((_let_3 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) N) (=> (= N (@ tptp.suc (@ tptp.suc Va2))) (=> (not (@ (@ tptp.ord_less_nat Ma) Mi)) (=> (not (= Ma Mi)) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_3) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.power_power_nat _let_1) _let_2)))) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))))) (@ tptp.suc _let_2))) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))))))))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high X) _let_1))) (=> (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low X) _let_1)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X))))))))
% 5.98/6.28 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (and (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (or (= X Mi) (= X Ma) (and (@ (@ tptp.ord_less_nat X) Ma) (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2)))))))))))
% 5.98/6.28 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (or (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X) _let_1))) (@ (@ tptp.vEBT_VEBT_low X) _let_1)) (= X Mi) (= X Ma)))))))
% 5.98/6.28 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg) (=> (not (= Mi Ma)) (= (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt Summary)) (@ (@ tptp.vEBT_VEBT_high Ma) (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 5.98/6.28 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_2) Deg)) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (@ (@ tptp.vEBT_VEBT_low X) _let_3)) (@ (@ tptp.vEBT_V8194947554948674370ptions _let_1) X)))))))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (D tptp.nat)) (= (@ (@ (@ tptp.vEBT_VEBT_bit_concat (@ (@ tptp.vEBT_VEBT_high X) D)) (@ (@ tptp.vEBT_VEBT_low X) D)) D) X)))
% 5.98/6.28 (assert (= tptp.vEBT_VEBT_low (lambda ((X3 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.modulo_modulo_nat X3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (N tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X) _let_1) (= (@ (@ tptp.vEBT_VEBT_low (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X)) N) X)))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M2))) (=> (@ _let_2 N) (=> (@ _let_2 M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low X) N)) (@ _let_1 N)))))))))
% 5.98/6.28 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M2 tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M2)) (=> (= M2 N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M2)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (= (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I2)))) (=> (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) (@ (@ tptp.vEBT_VEBT_low X4) N))) (and (@ (@ tptp.ord_less_nat Mi) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg)))))))))))))))
% 5.98/6.28 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M2 tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M2)) (=> (= M2 (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M2)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (= (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I2)))) (=> (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) (@ (@ tptp.vEBT_VEBT_low X4) N))) (and (@ (@ tptp.ord_less_nat Mi) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg)))))))))))))))
% 5.98/6.28 (assert (forall ((A12 tptp.vEBT_VEBT) (A23 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt A12) A23) (=> (=> (exists ((A5 Bool) (B5 Bool)) (= A12 (@ (@ tptp.vEBT_Leaf A5) B5))) (not (= A23 (@ tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2)) (=> (= A23 Deg2) (=> (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X2) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (=> (= M4 N2) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N2) M4)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_12))) (not (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X_12))))))))))))))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2)) (=> (= A23 Deg2) (=> (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X2) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (=> (= M4 (@ tptp.suc N2)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N2) M4)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_12))) (not (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X_12))))))))))))))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 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))))) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList2) Summary2)) (=> (= A23 Deg2) (=> (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X2) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M4)) (=> (= M4 N2) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N2) 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 TreeList2) I3)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3)))) (=> (=> _let_1 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) 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) N2) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low Ma2) N2))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N2) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low X2) N2))) (and (@ (@ tptp.ord_less_nat Mi2) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma2))))))))))))))))))))))) (not (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 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))))) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList2) Summary2)) (=> (= A23 Deg2) (=> (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X2) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M4)) (=> (= M4 (@ tptp.suc N2)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N2) 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 TreeList2) I3)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3)))) (=> (=> _let_1 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) 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) N2) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low Ma2) N2))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N2) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low X2) N2))) (and (@ (@ tptp.ord_less_nat Mi2) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma2)))))))))))))))))))))))))))))))
% 5.98/6.28 (assert (= tptp.vEBT_invar_vebt (lambda ((A13 tptp.vEBT_VEBT) (A24 tptp.nat)) (or (and (exists ((A4 Bool) (B4 Bool)) (= A13 (@ (@ tptp.vEBT_Leaf A4) B4))) (= A24 (@ tptp.suc tptp.zero_zero_nat))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (and (= A13 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A24) TreeList3) Summary3)) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (@ (@ tptp.vEBT_invar_vebt Summary3) N4) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) (= A24 (@ (@ tptp.plus_plus_nat N4) N4)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X8))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc N4))) (and (= A13 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A24) TreeList3) Summary3)) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_1) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (= A24 (@ (@ tptp.plus_plus_nat N4) _let_1)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X8))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8)))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (and (= A13 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A24) TreeList3) Summary3)) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (@ (@ tptp.vEBT_invar_vebt Summary3) N4) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 N4)) (= A24 (@ (@ tptp.plus_plus_nat N4) N4)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) (= (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I4)))) (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A24)) (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N4) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low Ma3) N4))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N4) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low X3) N4))) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.suc N4))) (and (= A13 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A24) TreeList3) Summary3)) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 _let_3)) (= A24 (@ (@ tptp.plus_plus_nat N4) _let_3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N4))) (= (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I4)))) (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A24)) (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N4))) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N4) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low Ma3) N4))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N4) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low X3) N4))) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))))))))
% 5.98/6.28 (assert (= tptp.vEBT_V5917875025757280293ildren (lambda ((N4 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) (@ (@ tptp.vEBT_VEBT_high X3) N4))) (@ (@ tptp.vEBT_VEBT_low X3) N4)))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (L tptp.nat) (Newnode tptp.vEBT_VEBT) (Newlist tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.power_power_nat _let_1) _let_2))) (let ((_let_4 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xn) _let_2))) (let ((_let_6 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (= _let_5 H) (=> (= Xn (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_6) _let_3)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_4 _let_6))))) (=> (= (@ (@ tptp.vEBT_VEBT_low Xn) _let_2) L) (=> (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_4 H)) L)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) H) Newnode)) (=> (not (@ tptp.vEBT_VEBT_minNull Newnode)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xn) (@ (@ (@ tptp.if_nat (= Xn Ma)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H) _let_3)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) H))))) Ma)))) Deg) Newlist) Summary))))))))))))))))))))
% 5.98/6.28 (assert (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H tptp.nat) (L tptp.nat) (Newnode tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (Newlist tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ tptp.product_Pair_nat_nat Mi))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (=> (and (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (= _let_4 H) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_2) L) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList) H)) L)) (=> (not (@ tptp.vEBT_VEBT_minNull Newnode)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) H) Newnode)) (=> (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_3 Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_3 (@ (@ (@ tptp.if_nat (= X Ma)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H) (@ (@ tptp.power_power_nat _let_1) _let_2))) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) H))))) Ma)))) Deg) Newlist) Summary)))))))))))))))))
% 5.98/6.28 (assert (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_pred Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_mint _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X) Ma) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_pred _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_maxt (@ _let_5 (@ tptp.the_nat _let_4)))))))))))))))))))))
% 5.98/6.28 (assert (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (Mi tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_pred Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_mint _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X) Ma) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_pred _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_maxt (@ _let_5 (@ tptp.the_nat _let_4))))))) tptp.none_nat)))))))))))))))
% 5.98/6.28 (assert (= tptp.vEBT_VEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_vebt_member T2)))))
% 5.98/6.28 (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 ((X3 tptp.set_nat)) (and (@ P X3) (@ Q X3))))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.set_nat_rat Bool)) (Q (-> tptp.set_nat_rat Bool))) (=> (or (@ tptp.finite6430367030675640852at_rat (@ tptp.collect_set_nat_rat P)) (@ tptp.finite6430367030675640852at_rat (@ tptp.collect_set_nat_rat Q))) (@ tptp.finite6430367030675640852at_rat (@ tptp.collect_set_nat_rat (lambda ((X3 tptp.set_nat_rat)) (and (@ P X3) (@ Q X3))))))))
% 5.98/6.28 (assert (forall ((P (-> (-> tptp.nat tptp.rat) Bool)) (Q (-> (-> tptp.nat tptp.rat) Bool))) (=> (or (@ tptp.finite7830837933032798814at_rat (@ tptp.collect_nat_rat P)) (@ tptp.finite7830837933032798814at_rat (@ tptp.collect_nat_rat Q))) (@ tptp.finite7830837933032798814at_rat (@ tptp.collect_nat_rat (lambda ((X3 (-> tptp.nat tptp.rat))) (and (@ P X3) (@ Q X3))))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (or (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (and (@ P X3) (@ Q X3))))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (or (@ tptp.finite_finite_int (@ tptp.collect_int P)) (@ tptp.finite_finite_int (@ tptp.collect_int Q))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (@ P X3) (@ Q X3))))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (=> (or (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex P)) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex Q))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (and (@ P X3) (@ Q X3))))))))
% 5.98/6.28 (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 ((X3 tptp.product_prod_nat_nat)) (and (@ P X3) (@ Q X3))))))))
% 5.98/6.28 (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 ((X3 tptp.extended_enat)) (and (@ P X3) (@ Q X3))))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (= (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((X3 tptp.set_nat)) (or (@ P X3) (@ Q X3))))) (and (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat P)) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat Q))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.set_nat_rat Bool)) (Q (-> tptp.set_nat_rat Bool))) (= (@ tptp.finite6430367030675640852at_rat (@ tptp.collect_set_nat_rat (lambda ((X3 tptp.set_nat_rat)) (or (@ P X3) (@ Q X3))))) (and (@ tptp.finite6430367030675640852at_rat (@ tptp.collect_set_nat_rat P)) (@ tptp.finite6430367030675640852at_rat (@ tptp.collect_set_nat_rat Q))))))
% 5.98/6.28 (assert (forall ((P (-> (-> tptp.nat tptp.rat) Bool)) (Q (-> (-> tptp.nat tptp.rat) Bool))) (= (@ tptp.finite7830837933032798814at_rat (@ tptp.collect_nat_rat (lambda ((X3 (-> tptp.nat tptp.rat))) (or (@ P X3) (@ Q X3))))) (and (@ tptp.finite7830837933032798814at_rat (@ tptp.collect_nat_rat P)) (@ tptp.finite7830837933032798814at_rat (@ tptp.collect_nat_rat Q))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (or (@ P X3) (@ Q X3))))) (and (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X3 tptp.int)) (or (@ P X3) (@ Q X3))))) (and (@ tptp.finite_finite_int (@ tptp.collect_int P)) (@ tptp.finite_finite_int (@ tptp.collect_int Q))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (= (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (or (@ P X3) (@ Q X3))))) (and (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex P)) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex Q))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (= (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat (lambda ((X3 tptp.product_prod_nat_nat)) (or (@ P X3) (@ Q X3))))) (and (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat P)) (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat Q))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.extended_enat Bool)) (Q (-> tptp.extended_enat Bool))) (= (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((X3 tptp.extended_enat)) (or (@ P X3) (@ Q X3))))) (and (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat P)) (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat Q))))))
% 5.98/6.28 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_pred T) X) tptp.none_nat) (= (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.vEBT_vebt_member T) Y2) (@ (@ tptp.ord_less_nat Y2) X)))) tptp.bot_bot_set_nat)))))
% 5.98/6.28 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_succ T) X) tptp.none_nat) (= (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.vEBT_vebt_member T) Y2) (@ (@ tptp.ord_less_nat X) Y2)))) tptp.bot_bot_set_nat)))))
% 5.98/6.28 (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)))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat_rat)) (=> (@ tptp.finite7830837933032798814at_rat A2) (@ tptp.finite6430367030675640852at_rat (@ tptp.collect_set_nat_rat (lambda ((B6 tptp.set_nat_rat)) (@ (@ tptp.ord_le2679597024174929757at_rat B6) A2)))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((B6 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B6) A2)))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite6551019134538273531omplex (@ tptp.collect_set_complex (lambda ((B6 tptp.set_complex)) (@ (@ tptp.ord_le211207098394363844omplex B6) A2)))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A2) (@ tptp.finite9047747110432174090at_nat (@ tptp.collec5514110066124741708at_nat (lambda ((B6 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat B6) A2)))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (@ tptp.finite5468666774076196335d_enat (@ tptp.collec2260605976452661553d_enat (lambda ((B6 tptp.set_Extended_enat)) (@ (@ tptp.ord_le7203529160286727270d_enat B6) A2)))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite6197958912794628473et_int (@ tptp.collect_set_int (lambda ((B6 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int B6) A2)))))))
% 5.98/6.28 (assert (forall ((A tptp.product_prod_nat_nat)) (= (@ tptp.collec3392354462482085612at_nat (lambda ((X3 tptp.product_prod_nat_nat)) (= X3 A))) (@ (@ tptp.insert8211810215607154385at_nat A) tptp.bot_bo2099793752762293965at_nat))))
% 5.98/6.28 (assert (forall ((A tptp.set_nat)) (= (@ tptp.collect_set_nat (lambda ((X3 tptp.set_nat)) (= X3 A))) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))))
% 5.98/6.28 (assert (forall ((A tptp.set_nat_rat)) (= (@ tptp.collect_set_nat_rat (lambda ((X3 tptp.set_nat_rat)) (= X3 A))) (@ (@ tptp.insert_set_nat_rat A) tptp.bot_bo6797373522285170759at_rat))))
% 5.98/6.28 (assert (forall ((A (-> tptp.nat tptp.rat))) (= (@ tptp.collect_nat_rat (lambda ((X3 (-> tptp.nat tptp.rat))) (= X3 A))) (@ (@ tptp.insert_nat_rat A) tptp.bot_bot_set_nat_rat))))
% 5.98/6.28 (assert (forall ((A tptp.real)) (= (@ tptp.collect_real (lambda ((X3 tptp.real)) (= X3 A))) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))
% 5.98/6.28 (assert (forall ((A Bool)) (= (@ tptp.collect_o (lambda ((X3 Bool)) (= X3 A))) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o))))
% 5.98/6.28 (assert (forall ((A tptp.nat)) (= (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (= X3 A))) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))
% 5.98/6.28 (assert (forall ((A tptp.int)) (= (@ tptp.collect_int (lambda ((X3 tptp.int)) (= X3 A))) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))
% 5.98/6.28 (assert (forall ((A tptp.product_prod_nat_nat)) (= (@ tptp.collec3392354462482085612at_nat (@ (lambda ((Y5 tptp.product_prod_nat_nat) (Z4 tptp.product_prod_nat_nat)) (= Y5 Z4)) A)) (@ (@ tptp.insert8211810215607154385at_nat A) tptp.bot_bo2099793752762293965at_nat))))
% 5.98/6.28 (assert (forall ((A tptp.set_nat)) (= (@ tptp.collect_set_nat (@ (lambda ((Y5 tptp.set_nat) (Z4 tptp.set_nat)) (= Y5 Z4)) A)) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))))
% 5.98/6.28 (assert (forall ((A tptp.set_nat_rat)) (= (@ tptp.collect_set_nat_rat (@ (lambda ((Y5 tptp.set_nat_rat) (Z4 tptp.set_nat_rat)) (= Y5 Z4)) A)) (@ (@ tptp.insert_set_nat_rat A) tptp.bot_bo6797373522285170759at_rat))))
% 5.98/6.28 (assert (forall ((A (-> tptp.nat tptp.rat))) (= (@ tptp.collect_nat_rat (@ (lambda ((Y5 (-> tptp.nat tptp.rat)) (Z4 (-> tptp.nat tptp.rat))) (= Y5 Z4)) A)) (@ (@ tptp.insert_nat_rat A) tptp.bot_bot_set_nat_rat))))
% 5.98/6.28 (assert (forall ((A tptp.real)) (= (@ tptp.collect_real (@ (lambda ((Y5 tptp.real) (Z4 tptp.real)) (= Y5 Z4)) A)) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))
% 5.98/6.28 (assert (forall ((A Bool)) (= (@ tptp.collect_o (@ (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4)) A)) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o))))
% 5.98/6.28 (assert (forall ((A tptp.nat)) (= (@ tptp.collect_nat (@ (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)) A)) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))
% 5.98/6.28 (assert (forall ((A tptp.int)) (= (@ tptp.collect_int (@ (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4)) A)) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))
% 5.98/6.28 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.ord_less_nat N4) K))))))
% 5.98/6.28 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N4) K))))))
% 5.98/6.28 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_nat I4) N)))) N)))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I4) (@ (@ tptp.ord_less_eq_int I4) B)))))))
% 5.98/6.28 (assert (forall ((Xs tptp.list_VEBT_VEBT) (I tptp.nat) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) I) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X) Xs))))
% 5.98/6.28 (assert (forall ((Xs tptp.list_nat) (I tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) I) (= (@ (@ (@ tptp.list_update_nat Xs) I) X) Xs))))
% 5.98/6.28 (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))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.ord_less_int A) I4) (@ (@ tptp.ord_less_eq_int I4) B)))))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I4) (@ (@ tptp.ord_less_int I4) B)))))))
% 5.98/6.28 (assert (forall ((I tptp.nat) (Xs tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs) I) X)) I) X))))
% 5.98/6.28 (assert (forall ((I tptp.nat) (Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X)) I) X))))
% 5.98/6.28 (assert (forall ((I tptp.nat) (Xs tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I) X)) I) X))))
% 5.98/6.28 (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))))))))
% 5.98/6.28 (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))))))))
% 5.98/6.28 (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))))))))
% 5.98/6.28 (assert (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H tptp.nat) (L tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList) H)) L))) (let ((_let_2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) H) _let_1))) (let ((_let_3 (@ tptp.nth_VEBT_VEBT _let_2))) (let ((_let_4 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_5 (@ (@ tptp.divide_divide_nat Deg) _let_4))) (let ((_let_6 (@ (@ tptp.power_power_nat _let_4) _let_5))) (let ((_let_7 (@ tptp.if_nat (= X Ma)))) (let ((_let_8 (@ tptp.product_Pair_nat_nat Mi))) (let ((_let_9 (@ (@ tptp.vEBT_vebt_delete Summary) H))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ tptp.the_nat _let_10))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high X) _let_5))) (=> (and (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_4) Deg) (=> (= _let_12 H) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_5) L) (=> (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_8 Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_1)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_8 (@ (@ _let_7 (@ (@ (@ tptp.if_nat (= _let_10 tptp.none_nat)) 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 H) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_3 H))))) Ma)))) Deg) _let_2) Summary)))))))))))))))))))))))
% 5.98/6.28 (assert (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H tptp.nat) (L tptp.nat) (Newnode tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (Sn tptp.vEBT_VEBT) (Summary tptp.vEBT_VEBT) (Newlist tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.vEBT_vebt_maxt Sn))) (let ((_let_2 (@ tptp.the_nat _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat Deg) _let_3))) (let ((_let_5 (@ tptp.product_Pair_nat_nat Mi))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high X) _let_4))) (=> (and (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_3) Deg) (=> (= _let_6 H) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_4) L) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList) H)) L)) (=> (@ tptp.vEBT_VEBT_minNull Newnode) (=> (= Sn (@ (@ tptp.vEBT_vebt_delete Summary) H)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) H) Newnode)) (=> (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ (@ tptp.if_nat (= X Ma)) (@ (@ (@ tptp.if_nat (= _let_1 tptp.none_nat)) 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))))))))))))))))))))
% 5.98/6.28 (assert (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H tptp.nat) (L tptp.nat) (Newnode tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (Newlist tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Newlist))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_5 (@ tptp.if_nat (= X Ma)))) (let ((_let_6 (@ tptp.product_Pair_nat_nat Mi))) (let ((_let_7 (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 Ma))) Deg) TreeList) Summary)) X))) (let ((_let_8 (@ tptp.vEBT_VEBT_minNull Newnode))) (let ((_let_9 (@ (@ tptp.vEBT_vebt_delete Summary) H))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ tptp.the_nat _let_10))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (=> (and (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (=> (= _let_12 H) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_3) L) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList) H)) L)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) H) Newnode)) (=> (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (and (=> _let_8 (= _let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 (@ (@ _let_5 (@ (@ (@ tptp.if_nat (= _let_10 tptp.none_nat)) Mi) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) _let_11)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_1 _let_11)))))) Ma)))) Deg) Newlist) _let_9))) (=> (not _let_8) (= _let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 (@ (@ _let_5 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H) _let_4)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_1 H))))) Ma)))) Deg) Newlist) Summary))))))))))))))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_7 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_5 _let_4)))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_high _let_7) _let_3))) (let ((_let_9 (@ (@ tptp.vEBT_vebt_delete (@ _let_5 _let_8)) (@ (@ tptp.vEBT_VEBT_low _let_7) _let_3)))) (let ((_let_10 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_8) _let_9))) (let ((_let_11 (@ tptp.nth_VEBT_VEBT _let_10))) (let ((_let_12 (@ tptp.if_nat (= _let_7 Ma)))) (let ((_let_13 (@ tptp.product_Pair_nat_nat _let_7))) (let ((_let_14 (@ (@ tptp.vEBT_vebt_delete Summary) _let_8))) (let ((_let_15 (@ tptp.vEBT_vebt_maxt _let_14))) (let ((_let_16 (@ tptp.the_nat _let_15))) (=> (and (= X Mi) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_8) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_9)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_13 (@ (@ _let_12 (@ (@ (@ tptp.if_nat (= _let_15 tptp.none_nat)) _let_7) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_6) _let_16)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_11 _let_16)))))) Ma)))) Deg) _let_10) _let_14)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_13 (@ (@ _let_12 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_8) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_11 _let_8))))) Ma)))) Deg) _let_10) Summary))) _let_1)))))))))))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (L tptp.nat) (Newnode tptp.vEBT_VEBT) (Newlist tptp.list_VEBT_VEBT) (Sn tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.vEBT_vebt_maxt Sn))) (let ((_let_2 (@ tptp.the_nat _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat Deg) _let_3))) (let ((_let_5 (@ (@ tptp.power_power_nat _let_3) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_high Xn) _let_4))) (let ((_let_8 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_3) Deg) (=> (= _let_7 H) (=> (= Xn (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_8) _let_5)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_6 _let_8))))) (=> (= (@ (@ tptp.vEBT_VEBT_low Xn) _let_4) L) (=> (@ (@ tptp.ord_less_nat _let_7) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_6 H)) L)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) H) Newnode)) (=> (@ tptp.vEBT_VEBT_minNull Newnode) (=> (= Sn (@ (@ tptp.vEBT_vebt_delete Summary) H)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat 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)))))))))))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (L tptp.nat) (Newnode tptp.vEBT_VEBT) (Newlist tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Newlist))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_5 (@ tptp.if_nat (= Xn Ma)))) (let ((_let_6 (@ tptp.product_Pair_nat_nat Xn))) (let ((_let_7 (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X))) (let ((_let_8 (@ tptp.vEBT_VEBT_minNull Newnode))) (let ((_let_9 (@ (@ tptp.vEBT_vebt_delete Summary) H))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ tptp.the_nat _let_10))) (let ((_let_12 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_13 (@ (@ tptp.vEBT_VEBT_high Xn) _let_3))) (let ((_let_14 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (=> (= _let_13 H) (=> (= Xn (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_14) _let_4)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_12 _let_14))))) (=> (= (@ (@ tptp.vEBT_VEBT_low Xn) _let_3) L) (=> (@ (@ tptp.ord_less_nat _let_13) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_12 H)) L)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) H) 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 H) _let_4)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_1 H))))) Ma)))) Deg) Newlist) Summary)))))))))))))))))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (L tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_2 (@ (@ tptp.vEBT_vebt_delete (@ _let_1 H)) L))) (let ((_let_3 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) H) _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) H))) (let ((_let_11 (@ tptp.vEBT_vebt_maxt _let_10))) (let ((_let_12 (@ tptp.the_nat _let_11))) (let ((_let_13 (@ (@ tptp.vEBT_VEBT_high Xn) _let_6))) (let ((_let_14 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_5) Deg) (=> (= _let_13 H) (=> (= Xn (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_14) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_1 _let_14))))) (=> (= (@ (@ tptp.vEBT_VEBT_low Xn) _let_6) L) (=> (@ (@ tptp.ord_less_nat _let_13) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_2)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_9 (@ (@ _let_8 (@ (@ (@ tptp.if_nat (= _let_11 tptp.none_nat)) Xn) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_12)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_4 _let_12)))))) Ma)))) Deg) _let_3) _let_10)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_9 (@ (@ _let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_4 H))))) Ma)))) Deg) _let_3) Summary))))))))))))))))))))))))))
% 5.98/6.28 (assert (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_7 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_5 _let_4)))))) (let ((_let_8 (= X Mi))) (let ((_let_9 (@ tptp.if_nat _let_8))) (let ((_let_10 (@ (@ _let_9 _let_7) X))) (let ((_let_11 (@ (@ tptp.vEBT_VEBT_high _let_10) _let_3))) (let ((_let_12 (@ (@ tptp.vEBT_vebt_delete (@ _let_5 _let_11)) (@ (@ tptp.vEBT_VEBT_low _let_10) _let_3)))) (let ((_let_13 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_11) _let_12))) (let ((_let_14 (@ tptp.nth_VEBT_VEBT _let_13))) (let ((_let_15 (@ tptp.if_nat (and (=> _let_8 (= _let_7 Ma)) (=> (not _let_8) (= X Ma)))))) (let ((_let_16 (@ (@ _let_9 _let_10) 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) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_11) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_12)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_17 (@ (@ _let_15 (@ (@ (@ tptp.if_nat (= _let_19 tptp.none_nat)) _let_16) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_6) _let_20)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_14 _let_20)))))) Ma)))) Deg) _let_13) _let_18)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_17 (@ (@ _let_15 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_11) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_14 _let_11))))) Ma)))) Deg) _let_13) Summary))) _let_1)))))))))))))))))))))))))))
% 5.98/6.28 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_succ Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_maxt _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat Mi) X) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_succ _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_mint (@ _let_5 (@ tptp.the_nat _let_4)))))))))))))))))))))
% 5.98/6.28 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_succ Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_maxt _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat Mi) X) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_succ _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_mint (@ _let_5 (@ tptp.the_nat _let_4))))))) tptp.none_nat)))))))))))))))
% 5.98/6.28 (assert (= tptp.bot_bo4898103413517107610_nat_o (lambda ((X3 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X3) Y2)) tptp.bot_bo5327735625951526323at_nat))))
% 5.98/6.28 (assert (= tptp.bot_bo3364206721330744218_nat_o (lambda ((X3 tptp.set_Pr4329608150637261639at_nat) (Y2 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.member1466754251312161552at_nat (@ (@ tptp.produc9060074326276436823at_nat X3) Y2)) tptp.bot_bo4948859079157340979at_nat))))
% 5.98/6.28 (assert (= tptp.bot_bo394778441745866138_nat_o (lambda ((X3 tptp.set_Pr1261947904930325089at_nat) (Y2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X3) Y2)) tptp.bot_bo228742789529271731at_nat))))
% 5.98/6.28 (assert (= tptp.bot_bot_nat_nat_o (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y2)) tptp.bot_bo2099793752762293965at_nat))))
% 5.98/6.28 (assert (= tptp.bot_bot_int_int_o (lambda ((X3 tptp.int) (Y2 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Y2)) tptp.bot_bo1796632182523588997nt_int))))
% 5.98/6.28 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (A tptp.product_prod_nat_nat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collec3392354462482085612at_nat (lambda ((X3 tptp.product_prod_nat_nat)) (and (= X3 A) (@ P X3)))) (@ (@ tptp.insert8211810215607154385at_nat A) tptp.bot_bo2099793752762293965at_nat))) (=> (not _let_1) (= (@ tptp.collec3392354462482085612at_nat (lambda ((X3 tptp.product_prod_nat_nat)) (and (= X3 A) (@ P X3)))) tptp.bot_bo2099793752762293965at_nat))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.set_nat Bool)) (A tptp.set_nat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_set_nat (lambda ((X3 tptp.set_nat)) (and (= X3 A) (@ P X3)))) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))) (=> (not _let_1) (= (@ tptp.collect_set_nat (lambda ((X3 tptp.set_nat)) (and (= X3 A) (@ P X3)))) tptp.bot_bot_set_set_nat))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.set_nat_rat Bool)) (A tptp.set_nat_rat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_set_nat_rat (lambda ((X3 tptp.set_nat_rat)) (and (= X3 A) (@ P X3)))) (@ (@ tptp.insert_set_nat_rat A) tptp.bot_bo6797373522285170759at_rat))) (=> (not _let_1) (= (@ tptp.collect_set_nat_rat (lambda ((X3 tptp.set_nat_rat)) (and (= X3 A) (@ P X3)))) tptp.bot_bo6797373522285170759at_rat))))))
% 5.98/6.28 (assert (forall ((P (-> (-> tptp.nat tptp.rat) Bool)) (A (-> tptp.nat tptp.rat))) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_nat_rat (lambda ((X3 (-> tptp.nat tptp.rat))) (and (= X3 A) (@ P X3)))) (@ (@ tptp.insert_nat_rat A) tptp.bot_bot_set_nat_rat))) (=> (not _let_1) (= (@ tptp.collect_nat_rat (lambda ((X3 (-> tptp.nat tptp.rat))) (and (= X3 A) (@ P X3)))) tptp.bot_bot_set_nat_rat))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.real Bool)) (A tptp.real)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_real (lambda ((X3 tptp.real)) (and (= X3 A) (@ P X3)))) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))) (=> (not _let_1) (= (@ tptp.collect_real (lambda ((X3 tptp.real)) (and (= X3 A) (@ P X3)))) tptp.bot_bot_set_real))))))
% 5.98/6.28 (assert (forall ((P (-> Bool Bool)) (A Bool)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_o (lambda ((X3 Bool)) (and (= X3 A) (@ P X3)))) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o))) (=> (not _let_1) (= (@ tptp.collect_o (lambda ((X3 Bool)) (and (= X3 A) (@ P X3)))) tptp.bot_bot_set_o))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (and (= X3 A) (@ P X3)))) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (=> (not _let_1) (= (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (and (= X3 A) (@ P X3)))) tptp.bot_bot_set_nat))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.int Bool)) (A tptp.int)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (= X3 A) (@ P X3)))) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))) (=> (not _let_1) (= (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (= X3 A) (@ P X3)))) tptp.bot_bot_set_int))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (A tptp.product_prod_nat_nat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collec3392354462482085612at_nat (lambda ((X3 tptp.product_prod_nat_nat)) (and (= A X3) (@ P X3)))) (@ (@ tptp.insert8211810215607154385at_nat A) tptp.bot_bo2099793752762293965at_nat))) (=> (not _let_1) (= (@ tptp.collec3392354462482085612at_nat (lambda ((X3 tptp.product_prod_nat_nat)) (and (= A X3) (@ P X3)))) tptp.bot_bo2099793752762293965at_nat))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.set_nat Bool)) (A tptp.set_nat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_set_nat (lambda ((X3 tptp.set_nat)) (and (= A X3) (@ P X3)))) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))) (=> (not _let_1) (= (@ tptp.collect_set_nat (lambda ((X3 tptp.set_nat)) (and (= A X3) (@ P X3)))) tptp.bot_bot_set_set_nat))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.set_nat_rat Bool)) (A tptp.set_nat_rat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_set_nat_rat (lambda ((X3 tptp.set_nat_rat)) (and (= A X3) (@ P X3)))) (@ (@ tptp.insert_set_nat_rat A) tptp.bot_bo6797373522285170759at_rat))) (=> (not _let_1) (= (@ tptp.collect_set_nat_rat (lambda ((X3 tptp.set_nat_rat)) (and (= A X3) (@ P X3)))) tptp.bot_bo6797373522285170759at_rat))))))
% 5.98/6.28 (assert (forall ((P (-> (-> tptp.nat tptp.rat) Bool)) (A (-> tptp.nat tptp.rat))) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_nat_rat (lambda ((X3 (-> tptp.nat tptp.rat))) (and (= A X3) (@ P X3)))) (@ (@ tptp.insert_nat_rat A) tptp.bot_bot_set_nat_rat))) (=> (not _let_1) (= (@ tptp.collect_nat_rat (lambda ((X3 (-> tptp.nat tptp.rat))) (and (= A X3) (@ P X3)))) tptp.bot_bot_set_nat_rat))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.real Bool)) (A tptp.real)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_real (lambda ((X3 tptp.real)) (and (= A X3) (@ P X3)))) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))) (=> (not _let_1) (= (@ tptp.collect_real (lambda ((X3 tptp.real)) (and (= A X3) (@ P X3)))) tptp.bot_bot_set_real))))))
% 5.98/6.28 (assert (forall ((P (-> Bool Bool)) (A Bool)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_o (lambda ((X3 Bool)) (and (= A X3) (@ P X3)))) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o))) (=> (not _let_1) (= (@ tptp.collect_o (lambda ((X3 Bool)) (and (= A X3) (@ P X3)))) tptp.bot_bot_set_o))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (and (= A X3) (@ P X3)))) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (=> (not _let_1) (= (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (and (= A X3) (@ P X3)))) tptp.bot_bot_set_nat))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.int Bool)) (A tptp.int)) (let ((_let_1 (@ P A))) (and (=> _let_1 (= (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (= A X3) (@ P X3)))) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))) (=> (not _let_1) (= (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (= A X3) (@ P X3)))) tptp.bot_bot_set_int))))))
% 5.98/6.28 (assert (= tptp.bot_bot_set_set_nat (@ tptp.collect_set_nat (lambda ((X3 tptp.set_nat)) false))))
% 5.98/6.28 (assert (= tptp.bot_bo6797373522285170759at_rat (@ tptp.collect_set_nat_rat (lambda ((X3 tptp.set_nat_rat)) false))))
% 5.98/6.28 (assert (= tptp.bot_bot_set_nat_rat (@ tptp.collect_nat_rat (lambda ((X3 (-> tptp.nat tptp.rat))) false))))
% 5.98/6.28 (assert (= tptp.bot_bot_set_real (@ tptp.collect_real (lambda ((X3 tptp.real)) false))))
% 5.98/6.28 (assert (= tptp.bot_bot_set_o (@ tptp.collect_o (lambda ((X3 Bool)) false))))
% 5.98/6.28 (assert (= tptp.bot_bot_set_nat (@ tptp.collect_nat (lambda ((X3 tptp.nat)) false))))
% 5.98/6.28 (assert (= tptp.bot_bot_set_int (@ tptp.collect_int (lambda ((X3 tptp.int)) false))))
% 5.98/6.28 (assert (= (lambda ((X3 tptp.complex)) X3) (@ tptp.times_times_complex tptp.one_one_complex)))
% 5.98/6.28 (assert (= (lambda ((X3 tptp.real)) X3) (@ tptp.times_times_real tptp.one_one_real)))
% 5.98/6.28 (assert (= (lambda ((X3 tptp.rat)) X3) (@ tptp.times_times_rat tptp.one_one_rat)))
% 5.98/6.28 (assert (= (lambda ((X3 tptp.nat)) X3) (@ tptp.times_times_nat tptp.one_one_nat)))
% 5.98/6.28 (assert (= (lambda ((X3 tptp.int)) X3) (@ tptp.times_times_int tptp.one_one_int)))
% 5.98/6.28 (assert (forall ((R tptp.set_o) (S2 tptp.set_o)) (= (@ (@ tptp.ord_less_eq_o_o (lambda ((X3 Bool)) (@ (@ tptp.member_o X3) R))) (lambda ((X3 Bool)) (@ (@ tptp.member_o X3) S2))) (@ (@ tptp.ord_less_eq_set_o R) S2))))
% 5.98/6.28 (assert (forall ((R tptp.set_set_nat) (S2 tptp.set_set_nat)) (= (@ (@ tptp.ord_le3964352015994296041_nat_o (lambda ((X3 tptp.set_nat)) (@ (@ tptp.member_set_nat X3) R))) (lambda ((X3 tptp.set_nat)) (@ (@ tptp.member_set_nat X3) S2))) (@ (@ tptp.ord_le6893508408891458716et_nat R) S2))))
% 5.98/6.28 (assert (forall ((R tptp.set_set_nat_rat) (S2 tptp.set_set_nat_rat)) (= (@ (@ tptp.ord_le4100815579384348210_rat_o (lambda ((X3 tptp.set_nat_rat)) (@ (@ tptp.member_set_nat_rat X3) R))) (lambda ((X3 tptp.set_nat_rat)) (@ (@ tptp.member_set_nat_rat X3) S2))) (@ (@ tptp.ord_le4375437777232675859at_rat R) S2))))
% 5.98/6.28 (assert (forall ((R tptp.set_nat) (S2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_nat_o (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) R))) (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) S2))) (@ (@ tptp.ord_less_eq_set_nat R) S2))))
% 5.98/6.28 (assert (forall ((R tptp.set_int) (S2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_int_o (lambda ((X3 tptp.int)) (@ (@ tptp.member_int X3) R))) (lambda ((X3 tptp.int)) (@ (@ tptp.member_int X3) S2))) (@ (@ tptp.ord_less_eq_set_int R) S2))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_o) (P (-> Bool Bool))) (@ (@ tptp.ord_less_eq_set_o (@ tptp.collect_o (lambda ((X3 Bool)) (and (@ (@ tptp.member_o X3) A2) (@ P X3))))) A2)))
% 5.98/6.28 (assert (forall ((A2 tptp.set_set_nat) (P (-> tptp.set_nat Bool))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat (lambda ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A2) (@ P X3))))) A2)))
% 5.98/6.28 (assert (forall ((A2 tptp.set_set_nat_rat) (P (-> tptp.set_nat_rat Bool))) (@ (@ tptp.ord_le4375437777232675859at_rat (@ tptp.collect_set_nat_rat (lambda ((X3 tptp.set_nat_rat)) (and (@ (@ tptp.member_set_nat_rat X3) A2) (@ P X3))))) A2)))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (@ P X3))))) A2)))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat_rat) (P (-> (-> tptp.nat tptp.rat) Bool))) (@ (@ tptp.ord_le2679597024174929757at_rat (@ tptp.collect_nat_rat (lambda ((X3 (-> tptp.nat tptp.rat))) (and (@ (@ tptp.member_nat_rat X3) A2) (@ P X3))))) A2)))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (P (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (@ P X3))))) A2)))
% 5.98/6.28 (assert (= tptp.ord_less_eq_set_o (lambda ((A6 tptp.set_o) (B6 tptp.set_o)) (@ (@ tptp.ord_less_eq_o_o (lambda ((X3 Bool)) (@ (@ tptp.member_o X3) A6))) (lambda ((X3 Bool)) (@ (@ tptp.member_o X3) B6))))))
% 5.98/6.28 (assert (= tptp.ord_le6893508408891458716et_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (@ (@ tptp.ord_le3964352015994296041_nat_o (lambda ((X3 tptp.set_nat)) (@ (@ tptp.member_set_nat X3) A6))) (lambda ((X3 tptp.set_nat)) (@ (@ tptp.member_set_nat X3) B6))))))
% 5.98/6.28 (assert (= tptp.ord_le4375437777232675859at_rat (lambda ((A6 tptp.set_set_nat_rat) (B6 tptp.set_set_nat_rat)) (@ (@ tptp.ord_le4100815579384348210_rat_o (lambda ((X3 tptp.set_nat_rat)) (@ (@ tptp.member_set_nat_rat X3) A6))) (lambda ((X3 tptp.set_nat_rat)) (@ (@ tptp.member_set_nat_rat X3) B6))))))
% 5.98/6.28 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat_o (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) A6))) (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) B6))))))
% 5.98/6.28 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ (@ tptp.ord_less_eq_int_o (lambda ((X3 tptp.int)) (@ (@ tptp.member_int X3) A6))) (lambda ((X3 tptp.int)) (@ (@ tptp.member_int X3) B6))))))
% 5.98/6.28 (assert (forall ((X5 tptp.set_o) (P (-> Bool Bool))) (@ (@ tptp.ord_less_eq_set_o (@ tptp.collect_o (lambda ((X3 Bool)) (and (@ (@ tptp.member_o X3) X5) (@ P X3))))) X5)))
% 5.98/6.28 (assert (forall ((X5 tptp.set_set_nat) (P (-> tptp.set_nat Bool))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat (lambda ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) X5) (@ P X3))))) X5)))
% 5.98/6.28 (assert (forall ((X5 tptp.set_set_nat_rat) (P (-> tptp.set_nat_rat Bool))) (@ (@ tptp.ord_le4375437777232675859at_rat (@ tptp.collect_set_nat_rat (lambda ((X3 tptp.set_nat_rat)) (and (@ (@ tptp.member_set_nat_rat X3) X5) (@ P X3))))) X5)))
% 5.98/6.28 (assert (forall ((X5 tptp.set_nat) (P (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) X5) (@ P X3))))) X5)))
% 5.98/6.28 (assert (forall ((X5 tptp.set_nat_rat) (P (-> (-> tptp.nat tptp.rat) Bool))) (@ (@ tptp.ord_le2679597024174929757at_rat (@ tptp.collect_nat_rat (lambda ((X3 (-> tptp.nat tptp.rat))) (and (@ (@ tptp.member_nat_rat X3) X5) (@ P X3))))) X5)))
% 5.98/6.28 (assert (forall ((X5 tptp.set_int) (P (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) X5) (@ P X3))))) X5)))
% 5.98/6.28 (assert (forall ((X Bool) (Z7 tptp.set_o) (X5 tptp.set_o) (P (-> Bool Bool))) (=> (@ (@ tptp.member_o X) Z7) (=> (@ (@ tptp.ord_less_eq_set_o Z7) (@ tptp.collect_o (lambda ((X3 Bool)) (and (@ (@ tptp.member_o X3) X5) (@ P X3))))) (@ P X)))))
% 5.98/6.28 (assert (forall ((X tptp.set_nat) (Z7 tptp.set_set_nat) (X5 tptp.set_set_nat) (P (-> tptp.set_nat Bool))) (=> (@ (@ tptp.member_set_nat X) Z7) (=> (@ (@ tptp.ord_le6893508408891458716et_nat Z7) (@ tptp.collect_set_nat (lambda ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) X5) (@ P X3))))) (@ P X)))))
% 5.98/6.28 (assert (forall ((X tptp.set_nat_rat) (Z7 tptp.set_set_nat_rat) (X5 tptp.set_set_nat_rat) (P (-> tptp.set_nat_rat Bool))) (=> (@ (@ tptp.member_set_nat_rat X) Z7) (=> (@ (@ tptp.ord_le4375437777232675859at_rat Z7) (@ tptp.collect_set_nat_rat (lambda ((X3 tptp.set_nat_rat)) (and (@ (@ tptp.member_set_nat_rat X3) X5) (@ P X3))))) (@ P X)))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Z7 tptp.set_nat) (X5 tptp.set_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X) Z7) (=> (@ (@ tptp.ord_less_eq_set_nat Z7) (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) X5) (@ P X3))))) (@ P X)))))
% 5.98/6.28 (assert (forall ((X (-> tptp.nat tptp.rat)) (Z7 tptp.set_nat_rat) (X5 tptp.set_nat_rat) (P (-> (-> tptp.nat tptp.rat) Bool))) (=> (@ (@ tptp.member_nat_rat X) Z7) (=> (@ (@ tptp.ord_le2679597024174929757at_rat Z7) (@ tptp.collect_nat_rat (lambda ((X3 (-> tptp.nat tptp.rat))) (and (@ (@ tptp.member_nat_rat X3) X5) (@ P X3))))) (@ P X)))))
% 5.98/6.28 (assert (forall ((X tptp.int) (Z7 tptp.set_int) (X5 tptp.set_int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.member_int X) Z7) (=> (@ (@ tptp.ord_less_eq_set_int Z7) (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) X5) (@ P X3))))) (@ P X)))))
% 5.98/6.28 (assert (= tptp.ord_less_set_o (lambda ((A6 tptp.set_o) (B6 tptp.set_o)) (@ (@ tptp.ord_less_o_o (lambda ((X3 Bool)) (@ (@ tptp.member_o X3) A6))) (lambda ((X3 Bool)) (@ (@ tptp.member_o X3) B6))))))
% 5.98/6.28 (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 ((X3 tptp.set_nat)) (@ (@ tptp.member_set_nat X3) A6))) (lambda ((X3 tptp.set_nat)) (@ (@ tptp.member_set_nat X3) B6))))))
% 5.98/6.28 (assert (= tptp.ord_le1311537459589289991at_rat (lambda ((A6 tptp.set_set_nat_rat) (B6 tptp.set_set_nat_rat)) (@ (@ tptp.ord_le6823063569548456766_rat_o (lambda ((X3 tptp.set_nat_rat)) (@ (@ tptp.member_set_nat_rat X3) A6))) (lambda ((X3 tptp.set_nat_rat)) (@ (@ tptp.member_set_nat_rat X3) B6))))))
% 5.98/6.28 (assert (= tptp.ord_less_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ (@ tptp.ord_less_nat_o (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) A6))) (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) B6))))))
% 5.98/6.28 (assert (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ (@ tptp.ord_less_int_o (lambda ((X3 tptp.int)) (@ (@ tptp.member_int X3) A6))) (lambda ((X3 tptp.int)) (@ (@ tptp.member_int X3) B6))))))
% 5.98/6.28 (assert (= tptp.insert8211810215607154385at_nat (lambda ((A4 tptp.product_prod_nat_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ tptp.collec3392354462482085612at_nat (lambda ((X3 tptp.product_prod_nat_nat)) (or (= X3 A4) (@ (@ tptp.member8440522571783428010at_nat X3) B6)))))))
% 5.98/6.28 (assert (= tptp.insert_real (lambda ((A4 tptp.real) (B6 tptp.set_real)) (@ tptp.collect_real (lambda ((X3 tptp.real)) (or (= X3 A4) (@ (@ tptp.member_real X3) B6)))))))
% 5.98/6.28 (assert (= tptp.insert_o (lambda ((A4 Bool) (B6 tptp.set_o)) (@ tptp.collect_o (lambda ((X3 Bool)) (or (= X3 A4) (@ (@ tptp.member_o X3) B6)))))))
% 5.98/6.28 (assert (= tptp.insert_set_nat (lambda ((A4 tptp.set_nat) (B6 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X3 tptp.set_nat)) (or (= X3 A4) (@ (@ tptp.member_set_nat X3) B6)))))))
% 5.98/6.28 (assert (= tptp.insert_set_nat_rat (lambda ((A4 tptp.set_nat_rat) (B6 tptp.set_set_nat_rat)) (@ tptp.collect_set_nat_rat (lambda ((X3 tptp.set_nat_rat)) (or (= X3 A4) (@ (@ tptp.member_set_nat_rat X3) B6)))))))
% 5.98/6.28 (assert (= tptp.insert_nat (lambda ((A4 tptp.nat) (B6 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (or (= X3 A4) (@ (@ tptp.member_nat X3) B6)))))))
% 5.98/6.28 (assert (= tptp.insert_int (lambda ((A4 tptp.int) (B6 tptp.set_int)) (@ tptp.collect_int (lambda ((X3 tptp.int)) (or (= X3 A4) (@ (@ tptp.member_int X3) B6)))))))
% 5.98/6.28 (assert (= tptp.insert_nat_rat (lambda ((A4 (-> tptp.nat tptp.rat)) (B6 tptp.set_nat_rat)) (@ tptp.collect_nat_rat (lambda ((X3 (-> tptp.nat tptp.rat))) (or (= X3 A4) (@ (@ tptp.member_nat_rat X3) B6)))))))
% 5.98/6.28 (assert (forall ((A tptp.product_prod_nat_nat) (P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.insert8211810215607154385at_nat A) (@ tptp.collec3392354462482085612at_nat P)) (@ tptp.collec3392354462482085612at_nat (lambda ((U2 tptp.product_prod_nat_nat)) (=> (not (= U2 A)) (@ P U2)))))))
% 5.98/6.28 (assert (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.insert_real A) (@ tptp.collect_real P)) (@ tptp.collect_real (lambda ((U2 tptp.real)) (=> (not (= U2 A)) (@ P U2)))))))
% 5.98/6.28 (assert (forall ((A Bool) (P (-> Bool Bool))) (= (@ (@ tptp.insert_o A) (@ tptp.collect_o P)) (@ tptp.collect_o (lambda ((U2 Bool)) (=> (not (= U2 A)) (@ P U2)))))))
% 5.98/6.28 (assert (forall ((A tptp.set_nat) (P (-> tptp.set_nat Bool))) (= (@ (@ tptp.insert_set_nat A) (@ tptp.collect_set_nat P)) (@ tptp.collect_set_nat (lambda ((U2 tptp.set_nat)) (=> (not (= U2 A)) (@ P U2)))))))
% 5.98/6.28 (assert (forall ((A tptp.set_nat_rat) (P (-> tptp.set_nat_rat Bool))) (= (@ (@ tptp.insert_set_nat_rat A) (@ tptp.collect_set_nat_rat P)) (@ tptp.collect_set_nat_rat (lambda ((U2 tptp.set_nat_rat)) (=> (not (= U2 A)) (@ P U2)))))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.insert_nat A) (@ tptp.collect_nat P)) (@ tptp.collect_nat (lambda ((U2 tptp.nat)) (=> (not (= U2 A)) (@ P U2)))))))
% 5.98/6.28 (assert (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.insert_int A) (@ tptp.collect_int P)) (@ tptp.collect_int (lambda ((U2 tptp.int)) (=> (not (= U2 A)) (@ P U2)))))))
% 5.98/6.28 (assert (forall ((A (-> tptp.nat tptp.rat)) (P (-> (-> tptp.nat tptp.rat) Bool))) (= (@ (@ tptp.insert_nat_rat A) (@ tptp.collect_nat_rat P)) (@ tptp.collect_nat_rat (lambda ((U2 (-> tptp.nat tptp.rat))) (=> (not (= U2 A)) (@ P U2)))))))
% 5.98/6.28 (assert (forall ((R tptp.set_Pr8693737435421807431at_nat) (S2 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.ord_le5604493270027003598_nat_o (lambda ((X3 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X3) Y2)) R))) (lambda ((X3 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X3) Y2)) S2))) (@ (@ tptp.ord_le3000389064537975527at_nat R) S2))))
% 5.98/6.28 (assert (forall ((R tptp.set_Pr7459493094073627847at_nat) (S2 tptp.set_Pr7459493094073627847at_nat)) (= (@ (@ tptp.ord_le3072208448688395470_nat_o (lambda ((X3 tptp.set_Pr4329608150637261639at_nat) (Y2 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.member1466754251312161552at_nat (@ (@ tptp.produc9060074326276436823at_nat X3) Y2)) R))) (lambda ((X3 tptp.set_Pr4329608150637261639at_nat) (Y2 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.member1466754251312161552at_nat (@ (@ tptp.produc9060074326276436823at_nat X3) Y2)) S2))) (@ (@ tptp.ord_le5997549366648089703at_nat R) S2))))
% 5.98/6.28 (assert (forall ((R tptp.set_Pr4329608150637261639at_nat) (S2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le3935385432712749774_nat_o (lambda ((X3 tptp.set_Pr1261947904930325089at_nat) (Y2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X3) Y2)) R))) (lambda ((X3 tptp.set_Pr1261947904930325089at_nat) (Y2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X3) Y2)) S2))) (@ (@ tptp.ord_le1268244103169919719at_nat R) S2))))
% 5.98/6.28 (assert (forall ((R tptp.set_Pr1261947904930325089at_nat) (S2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le2646555220125990790_nat_o (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y2)) R))) (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y2)) S2))) (@ (@ tptp.ord_le3146513528884898305at_nat R) S2))))
% 5.98/6.28 (assert (forall ((R tptp.set_Pr958786334691620121nt_int) (S2 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.ord_le6741204236512500942_int_o (lambda ((X3 tptp.int) (Y2 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Y2)) R))) (lambda ((X3 tptp.int) (Y2 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Y2)) S2))) (@ (@ tptp.ord_le2843351958646193337nt_int R) S2))))
% 5.98/6.28 (assert (= tptp.uminus_uminus_set_o (lambda ((A6 tptp.set_o)) (@ tptp.collect_o (@ tptp.uminus_uminus_o_o (lambda ((X3 Bool)) (@ (@ tptp.member_o X3) A6)))))))
% 5.98/6.28 (assert (= tptp.uminus613421341184616069et_nat (lambda ((A6 tptp.set_set_nat)) (@ tptp.collect_set_nat (@ tptp.uminus6401447641752708672_nat_o (lambda ((X3 tptp.set_nat)) (@ (@ tptp.member_set_nat X3) A6)))))))
% 5.98/6.28 (assert (= tptp.uminus3098529973357106300at_rat (lambda ((A6 tptp.set_set_nat_rat)) (@ tptp.collect_set_nat_rat (@ tptp.uminus6216118484121566985_rat_o (lambda ((X3 tptp.set_nat_rat)) (@ (@ tptp.member_set_nat_rat X3) A6)))))))
% 5.98/6.28 (assert (= tptp.uminus5710092332889474511et_nat (lambda ((A6 tptp.set_nat)) (@ tptp.collect_nat (@ tptp.uminus_uminus_nat_o (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) A6)))))))
% 5.98/6.28 (assert (= tptp.uminus1532241313380277803et_int (lambda ((A6 tptp.set_int)) (@ tptp.collect_int (@ tptp.uminus_uminus_int_o (lambda ((X3 tptp.int)) (@ (@ tptp.member_int X3) A6)))))))
% 5.98/6.28 (assert (= tptp.uminus6988975074191911878at_rat (lambda ((A6 tptp.set_nat_rat)) (@ tptp.collect_nat_rat (@ tptp.uminus8974390361584276543_rat_o (lambda ((X3 (-> tptp.nat tptp.rat))) (@ (@ tptp.member_nat_rat X3) A6)))))))
% 5.98/6.28 (assert (forall ((P (-> tptp.set_nat Bool))) (= (@ tptp.collect_set_nat (lambda ((X3 tptp.set_nat)) (not (@ P X3)))) (@ tptp.uminus613421341184616069et_nat (@ tptp.collect_set_nat P)))))
% 5.98/6.28 (assert (forall ((P (-> tptp.set_nat_rat Bool))) (= (@ tptp.collect_set_nat_rat (lambda ((X3 tptp.set_nat_rat)) (not (@ P X3)))) (@ tptp.uminus3098529973357106300at_rat (@ tptp.collect_set_nat_rat P)))))
% 5.98/6.28 (assert (forall ((P (-> tptp.nat Bool))) (= (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (not (@ P X3)))) (@ tptp.uminus5710092332889474511et_nat (@ tptp.collect_nat P)))))
% 5.98/6.28 (assert (forall ((P (-> tptp.int Bool))) (= (@ tptp.collect_int (lambda ((X3 tptp.int)) (not (@ P X3)))) (@ tptp.uminus1532241313380277803et_int (@ tptp.collect_int P)))))
% 5.98/6.28 (assert (forall ((P (-> (-> tptp.nat tptp.rat) Bool))) (= (@ tptp.collect_nat_rat (lambda ((X3 (-> tptp.nat tptp.rat))) (not (@ P X3)))) (@ tptp.uminus6988975074191911878at_rat (@ tptp.collect_nat_rat P)))))
% 5.98/6.28 (assert (= tptp.uminus_uminus_set_o (lambda ((A6 tptp.set_o)) (@ tptp.collect_o (lambda ((X3 Bool)) (not (@ (@ tptp.member_o X3) A6)))))))
% 5.98/6.28 (assert (= tptp.uminus613421341184616069et_nat (lambda ((A6 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X3 tptp.set_nat)) (not (@ (@ tptp.member_set_nat X3) A6)))))))
% 5.98/6.28 (assert (= tptp.uminus3098529973357106300at_rat (lambda ((A6 tptp.set_set_nat_rat)) (@ tptp.collect_set_nat_rat (lambda ((X3 tptp.set_nat_rat)) (not (@ (@ tptp.member_set_nat_rat X3) A6)))))))
% 5.98/6.28 (assert (= tptp.uminus5710092332889474511et_nat (lambda ((A6 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (not (@ (@ tptp.member_nat X3) A6)))))))
% 5.98/6.28 (assert (= tptp.uminus1532241313380277803et_int (lambda ((A6 tptp.set_int)) (@ tptp.collect_int (lambda ((X3 tptp.int)) (not (@ (@ tptp.member_int X3) A6)))))))
% 5.98/6.28 (assert (= tptp.uminus6988975074191911878at_rat (lambda ((A6 tptp.set_nat_rat)) (@ tptp.collect_nat_rat (lambda ((X3 (-> tptp.nat tptp.rat))) (not (@ (@ tptp.member_nat_rat X3) A6)))))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (assert (forall ((P (-> tptp.set_nat_rat Bool))) (=> (not (@ tptp.finite6430367030675640852at_rat (@ tptp.collect_set_nat_rat P))) (exists ((X_1 tptp.set_nat_rat)) (@ P X_1)))))
% 5.98/6.28 (assert (forall ((P (-> (-> tptp.nat tptp.rat) Bool))) (=> (not (@ tptp.finite7830837933032798814at_rat (@ tptp.collect_nat_rat P))) (exists ((X_1 (-> tptp.nat tptp.rat))) (@ P X_1)))))
% 5.98/6.28 (assert (forall ((P (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat (@ tptp.collect_nat P))) (exists ((X_1 tptp.nat)) (@ P X_1)))))
% 5.98/6.28 (assert (forall ((P (-> tptp.int Bool))) (=> (not (@ tptp.finite_finite_int (@ tptp.collect_int P))) (exists ((X_1 tptp.int)) (@ P X_1)))))
% 5.98/6.28 (assert (forall ((P (-> tptp.complex Bool))) (=> (not (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex P))) (exists ((X_1 tptp.complex)) (@ P X_1)))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (assert (forall ((P (-> tptp.extended_enat Bool))) (=> (not (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat P))) (exists ((X_1 tptp.extended_enat)) (@ P X_1)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_o) (B2 tptp.set_nat) (R (-> Bool tptp.nat Bool))) (=> (not (@ tptp.finite_finite_o A2)) (=> (@ tptp.finite_finite_nat B2) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) B2) (@ (@ R X4) Xa))))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) B2) (not (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((A4 Bool)) (and (@ (@ tptp.member_o A4) A2) (@ (@ R A4) X4)))))))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_o) (B2 tptp.set_int) (R (-> Bool tptp.int Bool))) (=> (not (@ tptp.finite_finite_o A2)) (=> (@ tptp.finite_finite_int B2) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) B2) (@ (@ R X4) Xa))))) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) B2) (not (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((A4 Bool)) (and (@ (@ tptp.member_o A4) A2) (@ (@ R A4) X4)))))))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_o) (B2 tptp.set_complex) (R (-> Bool tptp.complex Bool))) (=> (not (@ tptp.finite_finite_o A2)) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) B2) (@ (@ R X4) Xa))))) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) B2) (not (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((A4 Bool)) (and (@ (@ tptp.member_o A4) A2) (@ (@ R A4) X4)))))))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_o) (B2 tptp.set_Extended_enat) (R (-> Bool tptp.extended_enat Bool))) (=> (not (@ tptp.finite_finite_o A2)) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A2) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) B2) (@ (@ R X4) Xa))))) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) B2) (not (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((A4 Bool)) (and (@ (@ tptp.member_o A4) A2) (@ (@ R A4) X4)))))))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_nat) (R (-> tptp.nat tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A2)) (=> (@ tptp.finite_finite_nat B2) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) B2) (@ (@ R X4) Xa))))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) B2) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A4 tptp.nat)) (and (@ (@ tptp.member_nat A4) A2) (@ (@ R A4) X4)))))))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_int) (R (-> tptp.nat tptp.int Bool))) (=> (not (@ tptp.finite_finite_nat A2)) (=> (@ tptp.finite_finite_int B2) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) B2) (@ (@ R X4) Xa))))) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) B2) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A4 tptp.nat)) (and (@ (@ tptp.member_nat A4) A2) (@ (@ R A4) X4)))))))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_complex) (R (-> tptp.nat tptp.complex Bool))) (=> (not (@ tptp.finite_finite_nat A2)) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) B2) (@ (@ R X4) Xa))))) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) B2) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A4 tptp.nat)) (and (@ (@ tptp.member_nat A4) A2) (@ (@ R A4) X4)))))))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_Extended_enat) (R (-> tptp.nat tptp.extended_enat Bool))) (=> (not (@ tptp.finite_finite_nat A2)) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) B2) (@ (@ R X4) Xa))))) (exists ((X4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X4) B2) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A4 tptp.nat)) (and (@ (@ tptp.member_nat A4) A2) (@ (@ R A4) X4)))))))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_nat) (R (-> tptp.int tptp.nat Bool))) (=> (not (@ tptp.finite_finite_int A2)) (=> (@ tptp.finite_finite_nat B2) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) B2) (@ (@ R X4) Xa))))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) B2) (not (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((A4 tptp.int)) (and (@ (@ tptp.member_int A4) A2) (@ (@ R A4) X4)))))))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_int) (R (-> tptp.int tptp.int Bool))) (=> (not (@ tptp.finite_finite_int A2)) (=> (@ tptp.finite_finite_int B2) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) B2) (@ (@ R X4) Xa))))) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) B2) (not (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((A4 tptp.int)) (and (@ (@ tptp.member_int A4) A2) (@ (@ R A4) X4)))))))))))))
% 5.98/6.28 (assert (forall ((F (-> tptp.nat tptp.nat)) (U tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ F N2))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N4)) U)))))))
% 5.98/6.28 (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)))))))
% 5.98/6.28 (assert (= tptp.minus_minus_set_o (lambda ((A6 tptp.set_o) (B6 tptp.set_o)) (@ tptp.collect_o (@ (@ tptp.minus_minus_o_o (lambda ((X3 Bool)) (@ (@ tptp.member_o X3) A6))) (lambda ((X3 Bool)) (@ (@ tptp.member_o X3) B6)))))))
% 5.98/6.28 (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 ((X3 tptp.set_nat)) (@ (@ tptp.member_set_nat X3) A6))) (lambda ((X3 tptp.set_nat)) (@ (@ tptp.member_set_nat X3) B6)))))))
% 5.98/6.28 (assert (= tptp.minus_1626877696091177228at_rat (lambda ((A6 tptp.set_set_nat_rat) (B6 tptp.set_set_nat_rat)) (@ tptp.collect_set_nat_rat (@ (@ tptp.minus_7664381017404958329_rat_o (lambda ((X3 tptp.set_nat_rat)) (@ (@ tptp.member_set_nat_rat X3) A6))) (lambda ((X3 tptp.set_nat_rat)) (@ (@ tptp.member_set_nat_rat X3) B6)))))))
% 5.98/6.28 (assert (= tptp.minus_minus_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ tptp.collect_int (@ (@ tptp.minus_minus_int_o (lambda ((X3 tptp.int)) (@ (@ tptp.member_int X3) A6))) (lambda ((X3 tptp.int)) (@ (@ tptp.member_int X3) B6)))))))
% 5.98/6.28 (assert (= tptp.minus_1741603841019369558at_rat (lambda ((A6 tptp.set_nat_rat) (B6 tptp.set_nat_rat)) (@ tptp.collect_nat_rat (@ (@ tptp.minus_8641456556474268591_rat_o (lambda ((X3 (-> tptp.nat tptp.rat))) (@ (@ tptp.member_nat_rat X3) A6))) (lambda ((X3 (-> tptp.nat tptp.rat))) (@ (@ tptp.member_nat_rat X3) B6)))))))
% 5.98/6.28 (assert (= tptp.minus_minus_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ tptp.collect_nat (@ (@ tptp.minus_minus_nat_o (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) A6))) (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) B6)))))))
% 5.98/6.28 (assert (= tptp.minus_minus_set_o (lambda ((A6 tptp.set_o) (B6 tptp.set_o)) (@ tptp.collect_o (lambda ((X3 Bool)) (let ((_let_1 (@ tptp.member_o X3))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 5.98/6.28 (assert (= tptp.minus_2163939370556025621et_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X3))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 5.98/6.28 (assert (= tptp.minus_1626877696091177228at_rat (lambda ((A6 tptp.set_set_nat_rat) (B6 tptp.set_set_nat_rat)) (@ tptp.collect_set_nat_rat (lambda ((X3 tptp.set_nat_rat)) (let ((_let_1 (@ tptp.member_set_nat_rat X3))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 5.98/6.28 (assert (= tptp.minus_minus_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ tptp.collect_int (lambda ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 5.98/6.28 (assert (= tptp.minus_1741603841019369558at_rat (lambda ((A6 tptp.set_nat_rat) (B6 tptp.set_nat_rat)) (@ tptp.collect_nat_rat (lambda ((X3 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.member_nat_rat X3))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 5.98/6.28 (assert (= tptp.minus_minus_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 5.98/6.28 (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))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (assert (= (lambda ((H3 tptp.real)) tptp.zero_zero_real) (@ tptp.times_times_real tptp.zero_zero_real)))
% 5.98/6.28 (assert (= (lambda ((H3 tptp.rat)) tptp.zero_zero_rat) (@ tptp.times_times_rat tptp.zero_zero_rat)))
% 5.98/6.28 (assert (= (lambda ((H3 tptp.nat)) tptp.zero_zero_nat) (@ tptp.times_times_nat tptp.zero_zero_nat)))
% 5.98/6.28 (assert (= (lambda ((H3 tptp.int)) tptp.zero_zero_int) (@ tptp.times_times_int tptp.zero_zero_int)))
% 5.98/6.28 (assert (= tptp.vEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T2)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat N))) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 N)) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) _let_1)))))
% 5.98/6.28 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N)) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)))))
% 5.98/6.28 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ tptp.finite_finite_rat (@ tptp.collect_rat (lambda ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat A) X3) (@ (@ tptp.ord_less_eq_rat X3) B)))))))
% 5.98/6.28 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4)))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (assert (forall ((A 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)) A)))))))
% 5.98/6.28 (assert (forall ((A 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)) A)))))))
% 5.98/6.28 (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))))))))))
% 5.98/6.28 (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))))))))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (assert (forall ((X tptp.int) (Xs tptp.list_int) (Y tptp.int)) (= (@ (@ (@ tptp.list_update_int (@ (@ tptp.cons_int X) Xs)) tptp.zero_zero_nat) Y) (@ (@ tptp.cons_int Y) Xs))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (Y tptp.nat)) (= (@ (@ (@ tptp.list_update_nat (@ (@ tptp.cons_nat X) Xs)) tptp.zero_zero_nat) Y) (@ (@ tptp.cons_nat Y) Xs))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ tptp.cons_VEBT_VEBT X) Xs)) tptp.zero_zero_nat) Y) (@ (@ tptp.cons_VEBT_VEBT Y) Xs))))
% 5.98/6.28 (assert (forall ((Xs tptp.list_o) (A2 tptp.set_o) (X Bool) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A2) (=> (@ (@ tptp.member_o X) A2) (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs) I) X))) A2)))))
% 5.98/6.28 (assert (forall ((Xs tptp.list_set_nat) (A2 tptp.set_set_nat) (X tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 Xs)) A2) (=> (@ (@ tptp.member_set_nat X) A2) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 (@ (@ (@ tptp.list_update_set_nat Xs) I) X))) A2)))))
% 5.98/6.28 (assert (forall ((Xs tptp.list_set_nat_rat) (A2 tptp.set_set_nat_rat) (X tptp.set_nat_rat) (I tptp.nat)) (=> (@ (@ tptp.ord_le4375437777232675859at_rat (@ tptp.set_set_nat_rat2 Xs)) A2) (=> (@ (@ tptp.member_set_nat_rat X) A2) (@ (@ tptp.ord_le4375437777232675859at_rat (@ tptp.set_set_nat_rat2 (@ (@ (@ tptp.list_u886106648575569423at_rat Xs) I) X))) A2)))))
% 5.98/6.28 (assert (forall ((Xs tptp.list_nat) (A2 tptp.set_nat) (X tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A2) (=> (@ (@ tptp.member_nat X) A2) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) I) X))) A2)))))
% 5.98/6.28 (assert (forall ((Xs tptp.list_VEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (I tptp.nat)) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A2) (=> (@ (@ tptp.member_VEBT_VEBT X) A2) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X))) A2)))))
% 5.98/6.28 (assert (forall ((Xs tptp.list_int) (A2 tptp.set_int) (X tptp.int) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A2) (=> (@ (@ tptp.member_int X) A2) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) I) X))) A2)))))
% 5.98/6.28 (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)))))))
% 5.98/6.28 (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)))))))
% 5.98/6.28 (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))))
% 5.98/6.28 (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))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs2 tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) A2) (= (@ tptp.size_s3451745648224563538omplex Xs2) N))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (N tptp.nat)) (=> (@ tptp.finite6177210948735845034at_nat A2) (@ tptp.finite500796754983035824at_nat (@ tptp.collec3343600615725829874at_nat (lambda ((Xs2 tptp.list_P6011104703257516679at_nat)) (and (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs2)) A2) (= (@ tptp.size_s5460976970255530739at_nat Xs2) N))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_Extended_enat) (N tptp.nat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (@ tptp.finite1862508098717546133d_enat (@ tptp.collec8433460942617342167d_enat (lambda ((Xs2 tptp.list_Extended_enat)) (and (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.set_Extended_enat2 Xs2)) A2) (= (@ tptp.size_s3941691890525107288d_enat Xs2) N))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs2 tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) A2) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) N))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs2 tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) A2) (= (@ tptp.size_size_list_nat Xs2) N))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs2 tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) A2) (= (@ tptp.size_size_list_int Xs2) N))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_list_nat) (N tptp.nat)) (=> (@ tptp.finite8100373058378681591st_nat A2) (= (@ tptp.finite7325466520557071688st_nat (@ tptp.collec5989764272469232197st_nat (lambda ((Xs2 tptp.list_list_nat)) (and (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.set_list_nat2 Xs2)) A2) (= (@ tptp.size_s3023201423986296836st_nat Xs2) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite_card_list_nat A2)) N)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_set_nat) (N tptp.nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (= (@ tptp.finite5631907774883551598et_nat (@ tptp.collect_list_set_nat (lambda ((Xs2 tptp.list_set_nat)) (and (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 Xs2)) A2) (= (@ tptp.size_s3254054031482475050et_nat Xs2) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite_card_set_nat A2)) N)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ tptp.finite5120063068150530198omplex (@ tptp.collect_list_complex (lambda ((Xs2 tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) A2) (= (@ tptp.size_s3451745648224563538omplex Xs2) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite_card_complex A2)) N)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (N tptp.nat)) (=> (@ tptp.finite6177210948735845034at_nat A2) (= (@ tptp.finite249151656366948015at_nat (@ tptp.collec3343600615725829874at_nat (lambda ((Xs2 tptp.list_P6011104703257516679at_nat)) (and (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs2)) A2) (= (@ tptp.size_s5460976970255530739at_nat Xs2) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite711546835091564841at_nat A2)) N)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_Extended_enat) (N tptp.nat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ tptp.finite7441382602597825044d_enat (@ tptp.collec8433460942617342167d_enat (lambda ((Xs2 tptp.list_Extended_enat)) (and (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.set_Extended_enat2 Xs2)) A2) (= (@ tptp.size_s3941691890525107288d_enat Xs2) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite121521170596916366d_enat A2)) N)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (= (@ tptp.finite5915292604075114978T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs2 tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) A2) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite7802652506058667612T_VEBT A2)) N)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (= (@ 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)) A2) (= (@ tptp.size_size_list_nat Xs2) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite_card_nat A2)) N)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A2) (= (@ 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)) A2) (= (@ tptp.size_size_list_int Xs2) N))))) (@ (@ tptp.power_power_nat (@ tptp.finite_card_int A2)) N)))))
% 5.98/6.28 (assert (forall ((Z6 tptp.int) (Z tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int Z) Z6))) (let ((_let_2 (@ tptp.nat2 Z))) (let ((_let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ tptp.nat2 Z6)))) (let ((_let_4 (@ (@ tptp.ord_less_int Z6) tptp.zero_zero_int))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int)) tptp.zero_zero_nat) (@ tptp.nat2 _let_1)))))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs2 tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3451745648224563538omplex Xs2)) N))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (N tptp.nat)) (=> (@ tptp.finite6177210948735845034at_nat A2) (@ tptp.finite500796754983035824at_nat (@ tptp.collec3343600615725829874at_nat (lambda ((Xs2 tptp.list_P6011104703257516679at_nat)) (and (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs2)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s5460976970255530739at_nat Xs2)) N))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_Extended_enat) (N tptp.nat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (@ tptp.finite1862508098717546133d_enat (@ tptp.collec8433460942617342167d_enat (lambda ((Xs2 tptp.list_Extended_enat)) (and (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.set_Extended_enat2 Xs2)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3941691890525107288d_enat Xs2)) N))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs2 tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) N))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs2 tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs2)) N))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs2 tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs2)) N))))))))
% 5.98/6.28 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat) (I tptp.nat) (X tptp.product_prod_nat_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs) I) X))) (@ (@ tptp.insert8211810215607154385at_nat X) (@ tptp.set_Pr5648618587558075414at_nat Xs)))))
% 5.98/6.28 (assert (forall ((Xs tptp.list_real) (I tptp.nat) (X tptp.real)) (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs) I) X))) (@ (@ tptp.insert_real X) (@ tptp.set_real2 Xs)))))
% 5.98/6.28 (assert (forall ((Xs tptp.list_o) (I tptp.nat) (X Bool)) (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs) I) X))) (@ (@ tptp.insert_o X) (@ tptp.set_o2 Xs)))))
% 5.98/6.28 (assert (forall ((Xs tptp.list_nat) (I tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) I) X))) (@ (@ tptp.insert_nat X) (@ tptp.set_nat2 Xs)))))
% 5.98/6.28 (assert (forall ((Xs tptp.list_VEBT_VEBT) (I tptp.nat) (X tptp.vEBT_VEBT)) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X))) (@ (@ tptp.insert_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs)))))
% 5.98/6.28 (assert (forall ((Xs tptp.list_int) (I tptp.nat) (X tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) I) X))) (@ (@ tptp.insert_int X) (@ tptp.set_int2 Xs)))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (@ (@ tptp.member_o X) (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs) N) X))))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (Xs tptp.list_set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3254054031482475050et_nat Xs)) (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 (@ (@ (@ tptp.list_update_set_nat Xs) N) X))))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (Xs tptp.list_set_nat_rat) (X tptp.set_nat_rat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3959913991096427681at_rat Xs)) (@ (@ tptp.member_set_nat_rat X) (@ tptp.set_set_nat_rat2 (@ (@ (@ tptp.list_u886106648575569423at_rat Xs) N) X))))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (Xs tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) N) X))))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) N) X))))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) N) X))))))
% 5.98/6.28 (assert (forall ((I tptp.nat) (Xs tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (= (= (@ (@ (@ tptp.list_update_int Xs) I) X) Xs) (= (@ (@ tptp.nth_int Xs) I) X)))))
% 5.98/6.28 (assert (forall ((I tptp.nat) (Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X) Xs) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I) X)))))
% 5.98/6.28 (assert (forall ((I tptp.nat) (Xs tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (= (= (@ (@ (@ tptp.list_update_nat Xs) I) X) Xs) (= (@ (@ tptp.nth_nat Xs) I) X)))))
% 5.98/6.28 (assert (forall ((I tptp.nat) (Xs tptp.list_int) (J tptp.nat) (X tptp.int)) (let ((_let_1 (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs) I) X)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_int Xs) J)))))))))
% 5.98/6.28 (assert (forall ((I tptp.nat) (Xs tptp.list_VEBT_VEBT) (J tptp.nat) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) X)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_VEBT_VEBT Xs) J)))))))))
% 5.98/6.28 (assert (forall ((I tptp.nat) (Xs tptp.list_nat) (J tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I) X)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs) J)))))))))
% 5.98/6.28 (assert (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList) S)) X) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))
% 5.98/6.28 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Vd)) X) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))
% 5.98/6.28 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma) X)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat X) Mi)))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary)) X) (=> (not (= X Mi)) (=> (not (= X Ma)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))))))))))
% 5.98/6.28 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Vc)) X) (or (= X Mi) (= X Ma) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4)))))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) Y) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (= Y (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) Y) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList2) S3))) (= Y (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList2) S3))) (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList2) S3))) (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_7 (@ (@ tptp.power_power_nat _let_3) _let_4))) (let ((_let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_6 _let_5)))))) (let ((_let_9 (= X Mi))) (let ((_let_10 (@ tptp.if_nat _let_9))) (let ((_let_11 (@ (@ _let_10 _let_8) X))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high _let_11) _let_4))) (let ((_let_13 (@ (@ tptp.vEBT_vebt_delete (@ _let_6 _let_12)) (@ (@ tptp.vEBT_VEBT_low _let_11) _let_4)))) (let ((_let_14 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_12) _let_13))) (let ((_let_15 (@ tptp.nth_VEBT_VEBT _let_14))) (let ((_let_16 (= X Ma))) (let ((_let_17 (@ tptp.if_nat (and (=> _let_9 (= _let_8 Ma)) (=> (not _let_9) _let_16))))) (let ((_let_18 (@ (@ _let_10 _let_11) 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) X))) (let ((_let_24 (and _let_9 _let_16))) (let ((_let_25 (or (@ (@ tptp.ord_less_nat X) Mi) (@ (@ tptp.ord_less_nat Ma) X)))) (and (=> _let_25 (= _let_23 _let_2)) (=> (not _let_25) (and (=> _let_24 (= _let_23 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Summary))) (=> (not _let_24) (= _let_23 (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_13)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ (@ tptp.if_nat (= _let_21 tptp.none_nat)) _let_18) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_22)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_22)))))) Ma)))) _let_1) _let_14) _let_20)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_12) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_12))))) Ma)))) _let_1) _let_14) Summary))) _let_2)))))))))))))))))))))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList2) Vc2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList2) Vd2))) (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X) Xa2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList2) Summary2))) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (or (= Xa2 Mi2) (= Xa2 Ma2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList2) Vc2))) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList2) Vd2))) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) Y) (=> (=> (exists ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) Y) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (= Y (not (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList2) Vc2))) (= Y (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList2) Vd2))) (= Y (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_delete X) Xa2) Y) (=> (forall ((A5 Bool) (B5 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (=> (= Xa2 tptp.zero_zero_nat) (not (= Y (@ (@ tptp.vEBT_Leaf false) B5)))))) (=> (forall ((A5 Bool)) (=> (exists ((B5 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= Xa2 (@ tptp.suc tptp.zero_zero_nat)) (not (= Y (@ (@ tptp.vEBT_Leaf A5) false)))))) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X _let_1) (=> (exists ((N2 tptp.nat)) (= Xa2 (@ tptp.suc (@ tptp.suc N2)))) (not (= Y _let_1)))))) (=> (forall ((Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((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))) (=> (= X _let_1) (not (= Y _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))) (=> (= X _let_1) (not (= Y _let_1))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary2)))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ (@ tptp.power_power_nat _let_3) _let_4))) (let ((_let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_6 _let_5)))))) (let ((_let_9 (= 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 TreeList2) _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)))) (=> (= X _let_2) (not (and (=> _let_24 (= Y _let_2)) (=> (not _let_24) (and (=> _let_23 (= Y (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary2))) (=> (not _let_23) (= Y (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_13)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ (@ tptp.if_nat (= _let_21 tptp.none_nat)) _let_18) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_22)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_22)))))) Ma2)))) _let_1) _let_14) _let_20)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_12) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_12))))) Ma2)))) _let_1) _let_14) Summary2))) _let_2)))))))))))))))))))))))))))))))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa2) Y) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (= Y (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) Y) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) Y) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) Y) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList2) Summary2))) (= Y (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList2) Summary2))) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_succ Summary) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low X) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_2) TreeList) Summary)) X))) (let ((_let_12 (@ (@ tptp.ord_less_nat X) Mi))) (and (=> _let_12 (= _let_11 (@ tptp.some_nat Mi))) (=> (not _let_12) (= _let_11 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_succ _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_mint (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))))
% 5.98/6.28 (assert (forall ((Ma tptp.nat) (X tptp.nat) (Mi tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_pred Summary) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low X) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_mint _let_9))) (let ((_let_11 (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_2) TreeList) Summary)) X))) (let ((_let_12 (@ (@ tptp.ord_less_nat Ma) X))) (and (=> _let_12 (= _let_11 (@ tptp.some_nat Ma))) (=> (not _let_12) (= _let_11 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_pred _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_maxt (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_pred X) Xa2) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= Xa2 tptp.zero_zero_nat) _let_1)) (=> (forall ((A5 Bool)) (=> (exists ((Uw2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) Uw2))) (=> (= Xa2 (@ tptp.suc tptp.zero_zero_nat)) (not (and (=> A5 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y tptp.none_nat))))))) (=> (forall ((A5 Bool) (B5 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (=> (exists ((Va tptp.nat)) (= Xa2 (@ tptp.suc (@ tptp.suc Va)))) (not (and (=> B5 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (and (=> A5 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y tptp.none_nat))))))))) (=> (=> (exists ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va3))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_pred Summary2) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_mint _let_9))) (let ((_let_11 (@ (@ tptp.ord_less_nat Ma2) Xa2))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList2) Summary2)) (not (and (=> _let_11 (= Y (@ tptp.some_nat Ma2))) (=> (not _let_11) (= Y (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_pred _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat 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)))))))))))))))))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_succ X) Xa2) Y) (=> (forall ((Uu2 Bool) (B5 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf Uu2) B5)) (=> (= Xa2 tptp.zero_zero_nat) (not (and (=> B5 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (= Y tptp.none_nat))))))) (=> (=> (exists ((Uv2 Bool) (Uw2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uv2) Uw2))) (=> (exists ((N2 tptp.nat)) (= Xa2 (@ tptp.suc N2))) _let_1)) (=> (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_succ Summary2) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ (@ tptp.ord_less_nat Xa2) Mi2))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList2) Summary2)) (not (and (=> _let_11 (= Y (@ tptp.some_nat Mi2))) (=> (not _let_11) (= Y (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT 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))))))))))))))))))))))))))))
% 5.98/6.28 (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))))))))))
% 5.98/6.28 (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)))))))))
% 5.98/6.28 (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))))))))))
% 5.98/6.28 (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))))))))))
% 5.98/6.28 (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))))))))))
% 5.98/6.28 (assert (forall ((Mi tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Mi) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_nat X) Mi) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X) (@ (@ tptp.ord_max_nat Mi) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low Mi) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary)))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))) (let ((_let_5 (@ tptp.product_Pair_nat_nat Mi))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_nat Mi) X) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ tptp.ord_max_nat X) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low X) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X) Xa2) Y) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A5))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_2) (not (and (=> _let_4 (= Y (@ (@ tptp.vEBT_Leaf true) B5))) (=> (not _let_4) (and (=> _let_3 (= Y (@ _let_1 true))) (=> (not _let_3) (= Y _let_2)))))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts) S3))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts) S3))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V2)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary2)) (not (= Y (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList2) Summary2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6))) (=> (= X _let_2) (not (= Y (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa2) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2))))))))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_succ X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) B5))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (and (=> B5 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (= Y tptp.none_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((Uv2 Bool) (Uw2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (=> (= Xa2 _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) _let_1))))))))) (=> (forall ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.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 TreeList2))) (let ((_let_8 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_3) _let_4))))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_4))) (let ((_let_10 (@ _let_7 _let_5))) (let ((_let_11 (@ tptp.vEBT_vebt_maxt _let_10))) (let ((_let_12 (@ (@ tptp.ord_less_nat Xa2) Mi2))) (=> (= X _let_2) (=> (and (=> _let_12 (= Y (@ tptp.some_nat Mi2))) (=> (not _let_12) (= Y (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_9)) _let_11))) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 (@ tptp.some_nat _let_5))) (@ (@ tptp.vEBT_vebt_succ _let_10) _let_9))) (@ (@ (@ tptp.if_option_nat (= _let_6 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 _let_6)) (@ tptp.vEBT_vebt_mint (@ _let_7 (@ tptp.the_nat _let_6))))))) tptp.none_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_pred X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((A5 Bool) (Uw2 Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A5) Uw2))) (=> (= X _let_2) (=> (= Xa2 _let_1) (=> (and (=> A5 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y tptp.none_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1))))))))) (=> (forall ((A5 Bool) (B5 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (=> (= Xa2 _let_1) (=> (and (=> B5 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (and (=> A5 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y tptp.none_nat))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) _let_1))))))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va3))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.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 TreeList2))) (let ((_let_8 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_3) _let_4))))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_4))) (let ((_let_10 (@ _let_7 _let_5))) (let ((_let_11 (@ tptp.vEBT_vebt_mint _let_10))) (let ((_let_12 (@ (@ tptp.ord_less_nat Ma2) Xa2))) (=> (= X _let_2) (=> (and (=> _let_12 (= Y (@ tptp.some_nat Ma2))) (=> (not _let_12) (= Y (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_9)) _let_11))) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 (@ tptp.some_nat _let_5))) (@ (@ tptp.vEBT_vebt_pred _let_10) _let_9))) (@ (@ (@ tptp.if_option_nat (= _let_6 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi2) 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)))))))))))))))))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.set_real)) (= (@ (@ tptp.ord_max_set_real X) tptp.bot_bot_set_real) X)))
% 5.98/6.28 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.ord_max_set_o X) tptp.bot_bot_set_o) X)))
% 5.98/6.28 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat X) tptp.bot_bot_set_nat) X)))
% 5.98/6.28 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_max_set_int X) tptp.bot_bot_set_int) X)))
% 5.98/6.28 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.ord_max_nat X) tptp.bot_bot_nat) X)))
% 5.98/6.28 (assert (forall ((X tptp.set_real)) (= (@ (@ tptp.ord_max_set_real tptp.bot_bot_set_real) X) X)))
% 5.98/6.28 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.ord_max_set_o tptp.bot_bot_set_o) X) X)))
% 5.98/6.28 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat tptp.bot_bot_set_nat) X) X)))
% 5.98/6.28 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_max_set_int tptp.bot_bot_set_int) X) X)))
% 5.98/6.28 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.bot_bot_nat) X) X)))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_max_nat M2) N)))))
% 5.98/6.28 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat N) tptp.zero_zero_nat) N)))
% 5.98/6.28 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N) N)))
% 5.98/6.28 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) tptp.zero_zero_nat) A)))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.ord_max_nat A) B)) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 5.98/6.28 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) A) A)))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.ord_max_nat A) B) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 5.98/6.28 (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)))))))))
% 5.98/6.28 (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)))))))))
% 5.98/6.28 (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)))))))))
% 5.98/6.28 (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)))))))))
% 5.98/6.28 (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)))))))))
% 5.98/6.28 (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)))))))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) _let_1) _let_1))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) _let_1) _let_1))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) _let_1) _let_1))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) _let_1) _let_1))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) _let_1) _let_1))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer tptp.zero_z3403309356797280102nteger) _let_1) _let_1))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.ord_max_rat _let_1) tptp.zero_zero_rat) _let_1))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real _let_1) tptp.zero_zero_real) _let_1))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.zero_zero_nat) _let_1))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int _let_1) tptp.zero_zero_int) _let_1))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.zero_z5237406670263579293d_enat) _let_1))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer _let_1) tptp.zero_z3403309356797280102nteger) _let_1))))
% 5.98/6.28 (assert (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) tptp.one_one_real) tptp.one_one_real))
% 5.98/6.28 (assert (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) tptp.one_one_rat) tptp.one_one_rat))
% 5.98/6.28 (assert (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) tptp.one_one_int) tptp.one_one_int))
% 5.98/6.28 (assert (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) tptp.one_one_nat) tptp.one_one_nat))
% 5.98/6.28 (assert (= (@ (@ tptp.ord_max_real tptp.one_one_real) tptp.zero_zero_real) tptp.one_one_real))
% 5.98/6.28 (assert (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) tptp.zero_zero_rat) tptp.one_one_rat))
% 5.98/6.28 (assert (= (@ (@ tptp.ord_max_int tptp.one_one_int) tptp.zero_zero_int) tptp.one_one_int))
% 5.98/6.28 (assert (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) tptp.zero_zero_nat) tptp.one_one_nat))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) _let_1) _let_1))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real tptp.one_one_real) _let_1) _let_1))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) _let_1) _let_1))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int tptp.one_one_int) _let_1) _let_1))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) _let_1) _let_1))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer tptp.one_one_Code_integer) _let_1) _let_1))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.ord_max_rat _let_1) tptp.one_one_rat) _let_1))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real _let_1) tptp.one_one_real) _let_1))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.one_one_nat) _let_1))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int _let_1) tptp.one_one_int) _let_1))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.one_on7984719198319812577d_enat) _let_1))))
% 5.98/6.28 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer _let_1) tptp.one_one_Code_integer) _let_1))))
% 5.98/6.28 (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)))))))))
% 5.98/6.28 (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)))))))))
% 5.98/6.28 (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)))))))))
% 5.98/6.28 (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)))))))))
% 5.98/6.28 (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)))))))))
% 5.98/6.28 (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)))))))))
% 5.98/6.28 (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)))))))))
% 5.98/6.28 (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)))))))))
% 5.98/6.28 (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)))))))))
% 5.98/6.28 (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)))))))))
% 5.98/6.28 (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)))))))))
% 5.98/6.28 (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)))))))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ tptp.semiri1316708129612266289at_nat Y)))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y)))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_real (@ tptp.semiri5074537144036343181t_real X)) (@ tptp.semiri5074537144036343181t_real Y)))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_rat (@ tptp.semiri681578069525770553at_rat X)) (@ tptp.semiri681578069525770553at_rat Y)))))
% 5.98/6.28 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (= (@ (@ tptp.ord_max_set_int X) Y) Y))))
% 5.98/6.28 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (= (@ (@ tptp.ord_max_rat X) Y) Y))))
% 5.98/6.28 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (= (@ (@ tptp.ord_max_num X) Y) Y))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.ord_max_nat X) Y) Y))))
% 5.98/6.28 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (@ (@ tptp.ord_max_int X) Y) Y))))
% 5.98/6.28 (assert (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X) (= (@ (@ tptp.ord_max_set_int X) Y) X))))
% 5.98/6.28 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= (@ (@ tptp.ord_max_rat X) Y) X))))
% 5.98/6.28 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (= (@ (@ tptp.ord_max_num X) Y) X))))
% 5.98/6.28 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_max_nat X) Y) X))))
% 5.98/6.28 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.ord_max_int X) Y) X))))
% 5.98/6.28 (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))))
% 5.98/6.28 (assert (= tptp.ord_max_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A4) B4)) B4) A4))))
% 5.98/6.28 (assert (= tptp.ord_max_num (lambda ((A4 tptp.num) (B4 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A4) B4)) B4) A4))))
% 5.98/6.28 (assert (= tptp.ord_max_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A4) B4)) B4) A4))))
% 5.98/6.28 (assert (= tptp.ord_max_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A4) B4)) B4) A4))))
% 5.98/6.28 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.ord_max_real X) Y)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.plus_plus_real X) Z)) (@ (@ tptp.plus_plus_real Y) Z)))))
% 5.98/6.28 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.ord_max_rat X) Y)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.plus_plus_rat X) Z)) (@ (@ tptp.plus_plus_rat Y) Z)))))
% 5.98/6.28 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int X) Y)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.plus_plus_int X) Z)) (@ (@ tptp.plus_plus_int Y) Z)))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat X) Y)) Z) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat X) Z)) (@ (@ tptp.plus_plus_nat Y) Z)))))
% 5.98/6.28 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real X))) (= (@ _let_1 (@ (@ tptp.ord_max_real Y) Z)) (@ (@ tptp.ord_max_real (@ _let_1 Y)) (@ _let_1 Z))))))
% 5.98/6.28 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat X))) (= (@ _let_1 (@ (@ tptp.ord_max_rat Y) Z)) (@ (@ tptp.ord_max_rat (@ _let_1 Y)) (@ _let_1 Z))))))
% 5.98/6.28 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (= (@ _let_1 (@ (@ tptp.ord_max_int Y) Z)) (@ (@ tptp.ord_max_int (@ _let_1 Y)) (@ _let_1 Z))))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X))) (= (@ _let_1 (@ (@ tptp.ord_max_nat Y) Z)) (@ (@ tptp.ord_max_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 5.98/6.28 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.ord_max_real X) Y)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.minus_minus_real X) Z)) (@ (@ tptp.minus_minus_real Y) Z)))))
% 5.98/6.28 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.ord_max_rat X) Y)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.minus_minus_rat X) Z)) (@ (@ tptp.minus_minus_rat Y) Z)))))
% 5.98/6.28 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.ord_max_int X) Y)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.minus_minus_int X) Z)) (@ (@ tptp.minus_minus_int Y) Z)))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M2))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N) Q4)) (@ (@ tptp.ord_max_nat (@ _let_1 N)) (@ _let_1 Q4))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Q4 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat M2) N)) Q4) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat M2) Q4)) (@ (@ tptp.plus_plus_nat N) Q4)))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Q4 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_max_nat M2) N)) Q4) (@ (@ tptp.ord_max_nat (@ (@ tptp.times_times_nat M2) Q4)) (@ (@ tptp.times_times_nat N) Q4)))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M2))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N) Q4)) (@ (@ tptp.ord_max_nat (@ _let_1 N)) (@ _let_1 Q4))))))
% 5.98/6.28 (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))))
% 5.98/6.28 (assert (= tptp.ord_max_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A4) B4)) B4) A4))))
% 5.98/6.28 (assert (= tptp.ord_max_num (lambda ((A4 tptp.num) (B4 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A4) B4)) B4) A4))))
% 5.98/6.28 (assert (= tptp.ord_max_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A4) B4)) B4) A4))))
% 5.98/6.28 (assert (= tptp.ord_max_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A4) B4)) B4) A4))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat N) M2)) M2) (@ (@ tptp.ord_max_nat N) M2))))
% 5.98/6.28 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat X) Mi)))) (let ((_let_5 (@ (@ _let_4 Mi) X))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_6))) (= (@ (@ tptp.vEBT_vebt_insert _let_2) X) (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (not (or (= X Mi) (= X Ma))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 X) Mi)) (@ (@ tptp.ord_max_nat _let_5) Ma)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_6)) Summary))) _let_2)))))))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_delete X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (= Y (@ (@ tptp.vEBT_Leaf false) B5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.vEBT_Leaf A5))) (let ((_let_3 (@ _let_2 B5))) (=> (= X _let_3) (=> (= Xa2 _let_1) (=> (= Y (@ _let_2 false)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) _let_1)))))))))) (=> (forall ((A5 Bool) (B5 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc N2)))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= Xa2 _let_1) (=> (= Y _let_2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1)))))))))) (=> (forall ((Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) 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))) (=> (= X _let_1) (=> (= Y _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))) (=> (= X _let_1) (=> (= Y _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) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary2)))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ (@ tptp.power_power_nat _let_3) _let_4))) (let ((_let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_6 _let_5)))))) (let ((_let_9 (= 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 TreeList2) _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)))) (=> (= X _let_2) (=> (and (=> _let_24 (= Y _let_2)) (=> (not _let_24) (and (=> _let_23 (= Y (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary2))) (=> (not _let_23) (= Y (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_13)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ (@ tptp.if_nat (= _let_21 tptp.none_nat)) _let_18) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_22)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_22)))))) Ma2)))) _let_1) _let_14) _let_20)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_12) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_12))))) Ma2)))) _let_1) _let_14) Summary2))) _let_2)))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))))))))))))))))))))))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A5))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_2) (=> (and (=> _let_4 (= Y (@ (@ tptp.vEBT_Leaf true) B5))) (=> (not _let_4) (and (=> _let_3 (= Y (@ _let_1 true))) (=> (not _let_3) (= Y _let_2))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts) S3))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts) S3))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary2))) (=> (= X _let_2) (=> (= Y (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList2) Summary2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6))) (=> (= X _let_2) (=> (= Y (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa2) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y (and (=> _let_3 A5) (=> (not _let_3) (and (=> _let_2 B5) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_7 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (= X _let_2) (=> (= Y (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_7 (=> _let_7 (and _let_6 (=> _let_6 (and (=> _let_5 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (=> (= X _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa2)) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList2) S3))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList2) S3))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (=> (= X _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa2)) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y (and (=> _let_3 A5) (=> (not _let_3) (and (=> _let_2 B5) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList2) S3))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (= X _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (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))) (=> (= X _let_1) (=> (= Y (or (= Xa2 Mi2) (= Xa2 Ma2))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Vc2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (= X _let_2) (=> (= Y (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (= X _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (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))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Vc2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))
% 5.98/6.28 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (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))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Vc2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))))))))))
% 5.98/6.28 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (= (@ (@ tptp.ord_max_real A) B) A))))
% 5.98/6.28 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 5.98/6.28 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 5.98/6.28 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 5.98/6.28 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 5.98/6.28 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (= (@ (@ tptp.ord_max_real A) B) B))))
% 5.98/6.28 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 5.98/6.28 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 5.98/6.28 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real X) Y)) Z) (and (@ (@ tptp.ord_less_real X) Z) (@ (@ tptp.ord_less_real Y) Z)))))
% 5.98/6.28 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat X) Y)) Z) (and (@ (@ tptp.ord_less_rat X) Z) (@ (@ tptp.ord_less_rat Y) Z)))))
% 5.98/6.28 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (= (@ (@ tptp.ord_less_num (@ (@ tptp.ord_max_num X) Y)) Z) (and (@ (@ tptp.ord_less_num X) Z) (@ (@ tptp.ord_less_num Y) Z)))))
% 5.98/6.28 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat X) Y)) Z) (and (@ (@ tptp.ord_less_nat X) Z) (@ (@ tptp.ord_less_nat Y) Z)))))
% 5.98/6.28 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int X) Y)) Z) (and (@ (@ tptp.ord_less_int X) Z) (@ (@ tptp.ord_less_int Y) Z)))))
% 5.98/6.28 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 5.98/6.28 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 5.98/6.28 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 5.98/6.28 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 5.98/6.28 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 5.98/6.28 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 5.98/6.28 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A) (and (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat C) A)))))
% 5.98/6.28 (assert (forall ((B tptp.num) (C tptp.num) (A tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C)) A) (and (@ (@ tptp.ord_less_eq_num B) A) (@ (@ tptp.ord_less_eq_num C) A)))))
% 5.98/6.28 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C)) A) (and (@ (@ tptp.ord_less_eq_nat B) A) (@ (@ tptp.ord_less_eq_nat C) A)))))
% 5.98/6.28 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C)) A) (and (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int C) A)))))
% 5.98/6.28 (assert (forall ((C tptp.rat) (A tptp.rat) (D tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) A) (=> (@ (@ tptp.ord_less_eq_rat D) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat C) D)) (@ (@ tptp.ord_max_rat A) B))))))
% 5.98/6.28 (assert (forall ((C tptp.num) (A tptp.num) (D tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num C) A) (=> (@ (@ tptp.ord_less_eq_num D) B) (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num C) D)) (@ (@ tptp.ord_max_num A) B))))))
% 5.98/6.28 (assert (forall ((C tptp.nat) (A tptp.nat) (D tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) A) (=> (@ (@ tptp.ord_less_eq_nat D) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat C) D)) (@ (@ tptp.ord_max_nat A) B))))))
% 5.98/6.28 (assert (forall ((C tptp.int) (A tptp.int) (D tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) A) (=> (@ (@ tptp.ord_less_eq_int D) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int C) D)) (@ (@ tptp.ord_max_int A) B))))))
% 5.98/6.28 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A (@ (@ tptp.ord_max_rat A) B)))))
% 5.98/6.28 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A (@ (@ tptp.ord_max_num A) B)))))
% 5.98/6.28 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A (@ (@ tptp.ord_max_nat A) B)))))
% 5.98/6.28 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A (@ (@ tptp.ord_max_int A) B)))))
% 5.98/6.28 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (@ (@ tptp.ord_max_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))))
% 5.98/6.28 (assert (forall ((A tptp.num) (B tptp.num)) (=> (= A (@ (@ tptp.ord_max_num A) B)) (@ (@ tptp.ord_less_eq_num B) A))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.ord_max_nat A) B)) (@ (@ tptp.ord_less_eq_nat B) A))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A (@ (@ tptp.ord_max_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))))
% 5.98/6.28 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_rat B) A) (not (@ (@ tptp.ord_less_eq_rat C) A)))))))
% 5.98/6.28 (assert (forall ((B tptp.num) (C tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_num B) A) (not (@ (@ tptp.ord_less_eq_num C) A)))))))
% 5.98/6.28 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_nat B) A) (not (@ (@ tptp.ord_less_eq_nat C) A)))))))
% 5.98/6.28 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_int B) A) (not (@ (@ tptp.ord_less_eq_int C) A)))))))
% 5.98/6.28 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A)))))
% 5.98/6.28 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num C) A) (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C)) A)))))
% 5.98/6.28 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C)) A)))))
% 5.98/6.28 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C)) A)))))
% 5.98/6.28 (assert (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A4 tptp.rat)) (= A4 (@ (@ tptp.ord_max_rat A4) B4)))))
% 5.98/6.28 (assert (= tptp.ord_less_eq_num (lambda ((B4 tptp.num) (A4 tptp.num)) (= A4 (@ (@ tptp.ord_max_num A4) B4)))))
% 5.98/6.28 (assert (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (= A4 (@ (@ tptp.ord_max_nat A4) B4)))))
% 5.98/6.28 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A4 tptp.int)) (= A4 (@ (@ tptp.ord_max_int A4) B4)))))
% 5.98/6.28 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.ord_max_rat A) B))))
% 5.98/6.28 (assert (forall ((A tptp.num) (B tptp.num)) (@ (@ tptp.ord_less_eq_num A) (@ (@ tptp.ord_max_num A) B))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.ord_max_nat A) B))))
% 5.98/6.28 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.ord_max_int A) B))))
% 5.98/6.28 (assert (forall ((B tptp.rat) (A tptp.rat)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.ord_max_rat A) B))))
% 5.98/6.28 (assert (forall ((B tptp.num) (A tptp.num)) (@ (@ tptp.ord_less_eq_num B) (@ (@ tptp.ord_max_num A) B))))
% 5.98/6.28 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.ord_max_nat A) B))))
% 5.98/6.28 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.ord_max_int A) B))))
% 5.98/6.28 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 5.98/6.28 (assert (forall ((Z tptp.num) (X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 5.98/6.28 (assert (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 5.98/6.28 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 5.98/6.28 (assert (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A4 tptp.rat)) (= (@ (@ tptp.ord_max_rat A4) B4) A4))))
% 5.98/6.28 (assert (= tptp.ord_less_eq_num (lambda ((B4 tptp.num) (A4 tptp.num)) (= (@ (@ tptp.ord_max_num A4) B4) A4))))
% 5.98/6.28 (assert (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (= (@ (@ tptp.ord_max_nat A4) B4) A4))))
% 5.98/6.28 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A4 tptp.int)) (= (@ (@ tptp.ord_max_int A4) B4) A4))))
% 5.98/6.28 (assert (= tptp.ord_less_eq_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (= (@ (@ tptp.ord_max_rat A4) B4) B4))))
% 5.98/6.28 (assert (= tptp.ord_less_eq_num (lambda ((A4 tptp.num) (B4 tptp.num)) (= (@ (@ tptp.ord_max_num A4) B4) B4))))
% 5.98/6.28 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (= (@ (@ tptp.ord_max_nat A4) B4) B4))))
% 5.98/6.28 (assert (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B4 tptp.int)) (= (@ (@ tptp.ord_max_int A4) B4) B4))))
% 5.98/6.28 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 5.98/6.28 (assert (forall ((C tptp.num) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 5.98/6.28 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 5.98/6.28 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 5.98/6.28 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 5.98/6.28 (assert (forall ((C tptp.num) (B tptp.num) (A tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 5.98/6.28 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 5.98/6.28 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 5.98/6.28 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Z))) (= (@ _let_1 (@ (@ tptp.ord_max_real X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 5.98/6.28 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 5.98/6.28 (assert (forall ((Z tptp.num) (X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.ord_less_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 5.98/6.28 (assert (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 5.98/6.28 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 5.98/6.28 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real B) C)) A) (not (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real C) A)))))))
% 5.98/6.28 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat B) C)) A) (not (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat C) A)))))))
% 5.98/6.28 (assert (forall ((B tptp.num) (C tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num (@ (@ tptp.ord_max_num B) C)) A) (not (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num C) A)))))))
% 5.98/6.28 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat C) A)))))))
% 5.98/6.28 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int B) C)) A) (not (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int C) A)))))))
% 5.98/6.28 (assert (= tptp.ord_less_real (lambda ((B4 tptp.real) (A4 tptp.real)) (and (= A4 (@ (@ tptp.ord_max_real A4) B4)) (not (= A4 B4))))))
% 5.98/6.28 (assert (= tptp.ord_less_rat (lambda ((B4 tptp.rat) (A4 tptp.rat)) (and (= A4 (@ (@ tptp.ord_max_rat A4) B4)) (not (= A4 B4))))))
% 5.98/6.28 (assert (= tptp.ord_less_num (lambda ((B4 tptp.num) (A4 tptp.num)) (and (= A4 (@ (@ tptp.ord_max_num A4) B4)) (not (= A4 B4))))))
% 5.98/6.28 (assert (= tptp.ord_less_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (and (= A4 (@ (@ tptp.ord_max_nat A4) B4)) (not (= A4 B4))))))
% 5.98/6.28 (assert (= tptp.ord_less_int (lambda ((B4 tptp.int) (A4 tptp.int)) (and (= A4 (@ (@ tptp.ord_max_int A4) B4)) (not (= A4 B4))))))
% 5.98/6.28 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_real A) B))))))
% 5.98/6.28 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 5.98/6.28 (assert (forall ((C tptp.num) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 5.98/6.28 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 5.98/6.28 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 5.98/6.28 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_real A) B))))))
% 5.98/6.28 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 5.98/6.28 (assert (forall ((C tptp.num) (B tptp.num) (A tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 5.98/6.28 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 5.98/6.28 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 5.98/6.28 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))))))
% 5.98/6.28 (assert (= tptp.gbinomial_complex (lambda ((A4 tptp.complex) (K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.divide1717551699836669952omplex (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((L3 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A4) (@ tptp.semiri8010041392384452111omplex L3))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_complex)) (@ tptp.semiri5044797733671781792omplex K3))))))
% 5.98/6.28 (assert (= tptp.gbinomial_rat (lambda ((A4 tptp.rat) (K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.divide_divide_rat (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((L3 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A4) (@ tptp.semiri681578069525770553at_rat L3))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_rat)) (@ tptp.semiri773545260158071498ct_rat K3))))))
% 5.98/6.28 (assert (= tptp.gbinomial_real (lambda ((A4 tptp.real) (K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.divide_divide_real (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((L3 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A4) (@ tptp.semiri5074537144036343181t_real L3))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_real)) (@ tptp.semiri2265585572941072030t_real K3))))))
% 5.98/6.28 (assert (forall ((Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.comm_s2602460028002588243omplex Z) _let_2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex _let_1)))) _let_2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex K3)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))))
% 5.98/6.28 (assert (forall ((Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_real (@ (@ tptp.comm_s7457072308508201937r_real Z) _let_2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1)))) _let_2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real K3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))))
% 5.98/6.28 (assert (forall ((Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.comm_s4028243227959126397er_rat Z) _let_2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat _let_1)))) _let_2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat K3)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))))
% 5.98/6.28 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.ln_ln_real X) (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N4)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N4) tptp.one_one_nat))))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ tptp.suc N4))))))))))
% 5.98/6.28 (assert (= tptp.bit_ri6519982836138164636nteger (lambda ((N4 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 (= N4 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 N4) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A4) _let_1))))))))))
% 5.98/6.28 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N4 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 (= N4 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 N4) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A4) _let_1))))))))))
% 5.98/6.28 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ tptp.arctan X) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))))))))
% 5.98/6.28 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int N) tptp.zero_zero_int) tptp.zero_zero_int)))
% 5.98/6.28 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)))
% 5.98/6.28 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_ri631733984087533419it_int N) _let_1) _let_1))))
% 5.98/6.28 (assert (forall ((K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat K)) tptp.one_one_int) tptp.one_one_int)))
% 5.98/6.28 (assert (forall ((F (-> tptp.nat tptp.complex))) (= (@ tptp.suminf_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N4)))) (@ F tptp.zero_zero_nat))))
% 5.98/6.28 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F N4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N4)))) (@ F tptp.zero_zero_nat))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups6464643781859351333omplex G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.one_one_complex)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_complex (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups129246275422532515t_real G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.one_one_real)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_real (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups73079841787564623at_rat G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.one_one_rat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_rat (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups708209901874060359at_nat G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.one_one_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_nat (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups705719431365010083at_int G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.one_one_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_int (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))))
% 5.98/6.28 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_ri6519982836138164636nteger tptp.zero_zero_nat) A) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))
% 5.98/6.28 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_ri631733984087533419it_int tptp.zero_zero_nat) A) (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 5.98/6.28 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups6464643781859351333omplex F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ F A4)) __flatten_var_0))) A) B) tptp.one_one_complex))))
% 5.98/6.28 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ F A4)) __flatten_var_0))) A) B) tptp.one_one_real))))
% 5.98/6.28 (assert (forall ((F (-> tptp.nat tptp.rat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ F A4)) __flatten_var_0))) A) B) tptp.one_one_rat))))
% 5.98/6.28 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ F A4)) __flatten_var_0))) A) B) tptp.one_one_nat))))
% 5.98/6.28 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ F A4)) __flatten_var_0))) A) B) tptp.one_one_int))))
% 5.98/6.28 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) (@ tptp.suc N))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G2 (@ tptp.suc I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))))
% 5.98/6.28 (assert (forall ((G2 (-> tptp.nat tptp.int)) (M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) (@ tptp.suc N))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G2 (@ tptp.suc I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))))
% 5.98/6.28 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (M2 tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M2) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G2 (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))))
% 5.98/6.28 (assert (forall ((G2 (-> tptp.nat tptp.int)) (M2 tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M2) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G2 (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))))
% 5.98/6.28 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M2))) (= (@ (@ tptp.groups708209901874060359at_nat G2) _let_1) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G2 (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N)) I4)))) _let_1)))))
% 5.98/6.28 (assert (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M2))) (= (@ (@ tptp.groups705719431365010083at_int G2) _let_1) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G2 (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N)) I4)))) _let_1)))))
% 5.98/6.28 (assert (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups129246275422532515t_real G2))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_real (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))
% 5.98/6.28 (assert (forall ((G2 (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups73079841787564623at_rat G2))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_rat (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))
% 5.98/6.28 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups708209901874060359at_nat G2))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_nat (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))
% 5.98/6.28 (assert (forall ((G2 (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups705719431365010083at_int G2))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_int (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.times_times_real (@ G2 M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.times_times_rat (@ G2 M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.times_times_nat (@ G2 M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.times_times_int (@ G2 M2)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) N))))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G2))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_real (@ G2 _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G2))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_rat (@ G2 _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G2))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_nat (@ G2 _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G2))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_int (@ G2 _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups129246275422532515t_real G2) _let_1)) (@ G2 (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ G2 M2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ G2 (@ tptp.suc I4)))) _let_1)))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_rat (@ (@ tptp.groups73079841787564623at_rat G2) _let_1)) (@ G2 (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ G2 M2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ G2 (@ tptp.suc I4)))) _let_1)))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G2) _let_1)) (@ G2 (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ G2 M2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G2 (@ tptp.suc I4)))) _let_1)))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M2) N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G2) _let_1)) (@ G2 (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ G2 M2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G2 (@ tptp.suc I4)))) _let_1)))))))
% 5.98/6.28 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((N4 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N4))))))
% 5.98/6.28 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((N4 tptp.nat)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.groups708209901874060359at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N4))))))
% 5.98/6.28 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((N4 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N4))))))
% 5.98/6.28 (assert (= tptp.semiri2265585572941072030t_real (lambda ((N4 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.groups708209901874060359at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N4))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.real)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups129246275422532515t_real G2))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_real (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.rat)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups73079841787564623at_rat G2))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_rat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.nat)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups708209901874060359at_nat G2))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_nat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 5.98/6.28 (assert (forall ((M2 tptp.nat) (N tptp.nat) (G2 (-> tptp.nat tptp.int)) (P6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P6))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups705719431365010083at_int G2))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_int (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 5.98/6.28 (assert (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.nat) (Xb2 tptp.nat) (Xc tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.set_fo2584398358068434914at_nat X))) (let ((_let_2 (@ (@ tptp.ord_less_nat Xb2) Xa2))) (=> (= (@ (@ (@ _let_1 Xa2) Xb2) Xc) Y) (and (=> _let_2 (= Y Xc)) (=> (not _let_2) (= Y (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat Xa2) tptp.one_one_nat)) Xb2) (@ (@ X Xa2) Xc))))))))))
% 5.98/6.28 (assert (= tptp.set_fo2584398358068434914at_nat (lambda ((F5 (-> tptp.nat tptp.nat tptp.nat)) (A4 tptp.nat) (B4 tptp.nat) (Acc2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat B4) A4)) Acc2) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat F5) (@ (@ tptp.plus_plus_nat A4) tptp.one_one_nat)) B4) (@ (@ F5 A4) Acc2))))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ tptp.semiri1408675320244567234ct_nat M2) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N)) M2)))))))
% 5.98/6.28 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (@ tptp.power_power_real X))))))
% 5.98/6.28 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 5.98/6.28 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 5.98/6.28 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 5.98/6.28 (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)))))
% 5.98/6.28 (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))))
% 5.98/6.28 (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))))
% 5.98/6.28 (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))))
% 5.98/6.28 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A4 tptp.real) (N4 tptp.nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_real A4) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N4) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N4)))))
% 5.98/6.28 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A4 tptp.rat) (N4 tptp.nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_rat A4) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N4) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N4)))))
% 5.98/6.28 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A4 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A4) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N4) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N4)))))
% 5.98/6.28 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A4 tptp.int) (N4 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A4) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N4) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N4)))))
% 5.98/6.28 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M2))))))
% 5.98/6.28 (assert (forall ((G2 (-> tptp.nat tptp.real)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups129246275422532515t_real G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_real (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))))
% 5.98/6.28 (assert (forall ((G2 (-> tptp.nat tptp.rat)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups73079841787564623at_rat G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_rat (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))))
% 5.98/6.28 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups708209901874060359at_nat G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_nat (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))))
% 5.98/6.28 (assert (forall ((G2 (-> tptp.nat tptp.int)) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups705719431365010083at_int G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M2)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_int (@ G2 _let_1)) (@ G2 (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N))))))
% 5.98/6.28 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 5.98/6.28 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 5.98/6.28 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 5.98/6.28 (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))))))))
% 5.98/6.28 (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))))))
% 5.98/6.28 (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))))))
% 5.98/6.28 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_rat A) _let_1) (@ (@ tptp.divide_divide_rat (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri773545260158071498ct_rat _let_1))))))
% 5.98/6.28 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_real A) _let_1) (@ (@ tptp.divide_divide_real (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_real A) (@ tptp.semiri5074537144036343181t_real I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri2265585572941072030t_real _let_1))))))
% 5.98/6.28 (assert (forall ((A tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_nat A) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat A) (@ tptp.semiri1316708129612266289at_nat I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri1408675320244567234ct_nat _let_1))))))
% 5.98/6.28 (assert (forall ((A tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_int A) _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_int A) (@ tptp.semiri1314217659103216013at_int I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri1406184849735516958ct_int _let_1))))))
% 5.98/6.28 (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))))))
% 5.98/6.28 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((N4 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4) tptp.one_one_nat)))))
% 5.98/6.28 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((N4 tptp.nat)) (@ tptp.semiri681578069525770553at_rat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4) tptp.one_one_nat)))))
% 5.98/6.28 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((N4 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4) tptp.one_one_nat)))))
% 5.98/6.28 (assert (= tptp.semiri2265585572941072030t_real (lambda ((N4 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4) tptp.one_one_nat)))))
% 5.98/6.28 (assert (= tptp.comm_s2602460028002588243omplex (lambda ((A4 tptp.complex) (N4 tptp.nat)) (@ (@ (@ tptp.if_complex (= N4 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((O tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A4) (@ tptp.semiri8010041392384452111omplex O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_complex)))))
% 5.98/6.28 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A4 tptp.int) (N4 tptp.nat)) (@ (@ (@ tptp.if_int (= N4 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((O tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A4) (@ tptp.semiri1314217659103216013at_int O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_int)))))
% 5.98/6.28 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A4 tptp.real) (N4 tptp.nat)) (@ (@ (@ tptp.if_real (= N4 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((O tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A4) (@ tptp.semiri5074537144036343181t_real O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_real)))))
% 5.98/6.28 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A4 tptp.rat) (N4 tptp.nat)) (@ (@ (@ tptp.if_rat (= N4 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((O tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A4) (@ tptp.semiri681578069525770553at_rat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_rat)))))
% 5.98/6.28 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A4 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((O tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A4) (@ tptp.semiri1316708129612266289at_nat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_nat)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G2))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 A2))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_o) (X Bool) (G2 (-> Bool tptp.real))) (let ((_let_1 (@ tptp.groups234877984723959775o_real G2))) (=> (@ tptp.finite_finite_o A2) (=> (not (@ (@ tptp.member_o X) A2)) (= (@ _let_1 (@ (@ tptp.insert_o X) A2)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 A2))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G2))) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X) A2)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 A2))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G2))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) A2)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 A2))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G2))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 A2))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G2 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real G2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (@ (@ tptp.member_Extended_enat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_Extended_enat X) A2)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 A2))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat G2))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_1 A2))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_o) (X Bool) (G2 (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups2869687844427037835_o_rat G2))) (=> (@ tptp.finite_finite_o A2) (=> (not (@ (@ tptp.member_o X) A2)) (= (@ _let_1 (@ (@ tptp.insert_o X) A2)) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_1 A2))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G2))) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X) A2)) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_1 A2))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G2))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) A2)) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_1 A2))))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_o) (A Bool) (B (-> Bool tptp.complex))) (let ((_let_1 (@ (@ tptp.member_o A) S2))) (=> (@ tptp.finite_finite_o S2) (and (=> _let_1 (= (@ (@ tptp.groups4859619685533338977omplex (lambda ((K3 Bool)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.one_one_complex))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups4859619685533338977omplex (lambda ((K3 Bool)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S2))) (=> (@ tptp.finite_finite_nat S2) (and (=> _let_1 (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.one_one_complex))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.one_one_complex))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.complex))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.one_one_complex))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_1 (= (@ (@ tptp.groups4622424608036095791omplex (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.one_one_complex))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups4622424608036095791omplex (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_o) (A Bool) (B (-> Bool tptp.real))) (let ((_let_1 (@ (@ tptp.member_o A) S2))) (=> (@ tptp.finite_finite_o S2) (and (=> _let_1 (= (@ (@ tptp.groups234877984723959775o_real (lambda ((K3 Bool)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups234877984723959775o_real (lambda ((K3 Bool)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S2) tptp.one_one_real)))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.member_nat A) S2))) (=> (@ tptp.finite_finite_nat S2) (and (=> _let_1 (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S2) tptp.one_one_real)))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S2) tptp.one_one_real)))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S2) tptp.one_one_real)))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_1 (= (@ (@ tptp.groups97031904164794029t_real (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups97031904164794029t_real (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S2) tptp.one_one_real)))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_o) (A Bool) (B (-> Bool tptp.complex))) (let ((_let_1 (@ (@ tptp.member_o A) S2))) (=> (@ tptp.finite_finite_o S2) (and (=> _let_1 (= (@ (@ tptp.groups4859619685533338977omplex (lambda ((K3 Bool)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.one_one_complex))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups4859619685533338977omplex (lambda ((K3 Bool)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S2))) (=> (@ tptp.finite_finite_nat S2) (and (=> _let_1 (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.one_one_complex))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.one_one_complex))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.complex))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.one_one_complex))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_1 (= (@ (@ tptp.groups4622424608036095791omplex (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.one_one_complex))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups4622424608036095791omplex (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.one_one_complex))) S2) tptp.one_one_complex)))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_o) (A Bool) (B (-> Bool tptp.real))) (let ((_let_1 (@ (@ tptp.member_o A) S2))) (=> (@ tptp.finite_finite_o S2) (and (=> _let_1 (= (@ (@ tptp.groups234877984723959775o_real (lambda ((K3 Bool)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups234877984723959775o_real (lambda ((K3 Bool)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S2) tptp.one_one_real)))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.member_nat A) S2))) (=> (@ tptp.finite_finite_nat S2) (and (=> _let_1 (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S2) tptp.one_one_real)))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S2) tptp.one_one_real)))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S2) tptp.one_one_real)))))))
% 5.98/6.28 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_1 (= (@ (@ tptp.groups97031904164794029t_real (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups97031904164794029t_real (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S2) tptp.one_one_real)))))))
% 5.98/6.28 (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))))))
% 5.98/6.28 (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))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (G2 (-> tptp.nat tptp.complex))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups6464643781859351333omplex G2) A2) tptp.one_one_complex))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (G2 (-> tptp.int tptp.complex))) (=> (not (@ tptp.finite_finite_int A2)) (= (@ (@ tptp.groups7440179247065528705omplex G2) A2) tptp.one_one_complex))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_complex) (G2 (-> tptp.complex tptp.complex))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups3708469109370488835omplex G2) A2) tptp.one_one_complex))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.complex))) (=> (not (@ tptp.finite4001608067531595151d_enat A2)) (= (@ (@ tptp.groups4622424608036095791omplex G2) A2) tptp.one_one_complex))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (G2 (-> tptp.nat tptp.real))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups129246275422532515t_real G2) A2) tptp.one_one_real))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (G2 (-> tptp.int tptp.real))) (=> (not (@ tptp.finite_finite_int A2)) (= (@ (@ tptp.groups2316167850115554303t_real G2) A2) tptp.one_one_real))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_complex) (G2 (-> tptp.complex tptp.real))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups766887009212190081x_real G2) A2) tptp.one_one_real))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.real))) (=> (not (@ tptp.finite4001608067531595151d_enat A2)) (= (@ (@ tptp.groups97031904164794029t_real G2) A2) tptp.one_one_real))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (G2 (-> tptp.nat tptp.rat))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups73079841787564623at_rat G2) A2) tptp.one_one_rat))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (G2 (-> tptp.int tptp.rat))) (=> (not (@ tptp.finite_finite_int A2)) (= (@ (@ tptp.groups1072433553688619179nt_rat G2) A2) tptp.one_one_rat))))
% 5.98/6.28 (assert (forall ((G2 (-> tptp.real tptp.complex))) (= (@ (@ tptp.groups713298508707869441omplex G2) tptp.bot_bot_set_real) tptp.one_one_complex)))
% 5.98/6.28 (assert (forall ((G2 (-> tptp.real tptp.real))) (= (@ (@ tptp.groups1681761925125756287l_real G2) tptp.bot_bot_set_real) tptp.one_one_real)))
% 5.98/6.28 (assert (forall ((G2 (-> tptp.real tptp.rat))) (= (@ (@ tptp.groups4061424788464935467al_rat G2) tptp.bot_bot_set_real) tptp.one_one_rat)))
% 5.98/6.28 (assert (forall ((G2 (-> tptp.real tptp.nat))) (= (@ (@ tptp.groups4696554848551431203al_nat G2) tptp.bot_bot_set_real) tptp.one_one_nat)))
% 5.98/6.28 (assert (forall ((G2 (-> tptp.real tptp.int))) (= (@ (@ tptp.groups4694064378042380927al_int G2) tptp.bot_bot_set_real) tptp.one_one_int)))
% 5.98/6.28 (assert (forall ((G2 (-> Bool tptp.complex))) (= (@ (@ tptp.groups4859619685533338977omplex G2) tptp.bot_bot_set_o) tptp.one_one_complex)))
% 5.98/6.28 (assert (forall ((G2 (-> Bool tptp.real))) (= (@ (@ tptp.groups234877984723959775o_real G2) tptp.bot_bot_set_o) tptp.one_one_real)))
% 5.98/6.28 (assert (forall ((G2 (-> Bool tptp.rat))) (= (@ (@ tptp.groups2869687844427037835_o_rat G2) tptp.bot_bot_set_o) tptp.one_one_rat)))
% 5.98/6.28 (assert (forall ((G2 (-> Bool tptp.nat))) (= (@ (@ tptp.groups3504817904513533571_o_nat G2) tptp.bot_bot_set_o) tptp.one_one_nat)))
% 5.98/6.28 (assert (forall ((G2 (-> Bool tptp.int))) (= (@ (@ tptp.groups3502327434004483295_o_int G2) tptp.bot_bot_set_o) tptp.one_one_int)))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((Uu3 tptp.nat)) tptp.one_one_nat)) A2) tptp.one_one_nat)))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((Uu3 tptp.nat)) tptp.one_one_int)) A2) tptp.one_one_int)))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Uu3 tptp.int)) tptp.one_one_int)) A2) tptp.one_one_int)))
% 5.98/6.28 (assert (= (@ tptp.suminf_real (lambda ((N4 tptp.nat)) tptp.zero_zero_real)) tptp.zero_zero_real))
% 5.98/6.28 (assert (= (@ tptp.suminf_nat (lambda ((N4 tptp.nat)) tptp.zero_zero_nat)) tptp.zero_zero_nat))
% 5.98/6.28 (assert (= (@ tptp.suminf_int (lambda ((N4 tptp.nat)) tptp.zero_zero_int)) tptp.zero_zero_int))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups129246275422532515t_real F) A2) tptp.zero_zero_real) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (= (@ F X3) tptp.zero_zero_real)))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (= (= (@ (@ tptp.groups2316167850115554303t_real F) A2) tptp.zero_zero_real) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (= (@ F X3) tptp.zero_zero_real)))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups766887009212190081x_real F) A2) tptp.zero_zero_real) (exists ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A2) (= (@ F X3) tptp.zero_zero_real)))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (= (@ (@ tptp.groups97031904164794029t_real F) A2) tptp.zero_zero_real) (exists ((X3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X3) A2) (= (@ F X3) tptp.zero_zero_real)))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups73079841787564623at_rat F) A2) tptp.zero_zero_rat) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (= (@ F X3) tptp.zero_zero_rat)))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A2) (= (= (@ (@ tptp.groups1072433553688619179nt_rat F) A2) tptp.zero_zero_rat) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (= (@ F X3) tptp.zero_zero_rat)))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups225925009352817453ex_rat F) A2) tptp.zero_zero_rat) (exists ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A2) (= (@ F X3) tptp.zero_zero_rat)))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (= (@ (@ tptp.groups2245840878043517529at_rat F) A2) tptp.zero_zero_rat) (exists ((X3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X3) A2) (= (@ F X3) tptp.zero_zero_rat)))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (= (@ (@ tptp.groups1707563613775114915nt_nat F) A2) tptp.zero_zero_nat) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (= (@ F X3) tptp.zero_zero_nat)))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups861055069439313189ex_nat F) A2) tptp.zero_zero_nat) (exists ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A2) (= (@ F X3) tptp.zero_zero_nat)))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (= (@ (@ tptp.groups1707563613775114915nt_nat F) A2) tptp.one_one_nat) (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (= (@ F X3) tptp.one_one_nat)))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups861055069439313189ex_nat F) A2) tptp.one_one_nat) (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (= (@ F X3) tptp.one_one_nat)))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.nat))) (=> (@ tptp.finite6177210948735845034at_nat A2) (= (= (@ (@ tptp.groups4077766827762148844at_nat F) A2) tptp.one_one_nat) (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) A2) (= (@ F X3) tptp.one_one_nat)))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (= (@ (@ tptp.groups2880970938130013265at_nat F) A2) tptp.one_one_nat) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X3) A2) (= (@ F X3) tptp.one_one_nat)))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups708209901874060359at_nat F) A2) tptp.one_one_nat) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (= (@ F X3) tptp.one_one_nat)))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X3))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X3))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.nat))) (=> (@ tptp.finite6177210948735845034at_nat A2) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups4077766827762148844at_nat F) A2)) (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X3))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups2880970938130013265at_nat F) A2)) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X3) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X3))))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A2)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X3))))))))
% 5.98/6.28 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I) J)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X3 tptp.int)) X3)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int J))))))
% 5.98/6.28 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) J))) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I) _let_1)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X3 tptp.int)) X3)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int _let_1)))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (G2 (-> tptp.nat tptp.nat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (= (@ G2 X4) tptp.one_one_nat))) (= (@ (@ tptp.groups708209901874060359at_nat G2) A2) tptp.one_one_nat))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (G2 (-> tptp.nat tptp.int))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (= (@ G2 X4) tptp.one_one_int))) (= (@ (@ tptp.groups705719431365010083at_int G2) A2) tptp.one_one_int))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (G2 (-> tptp.int tptp.int))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (= (@ G2 X4) tptp.one_one_int))) (= (@ (@ tptp.groups1705073143266064639nt_int G2) A2) tptp.one_one_int))))
% 5.98/6.28 (assert (forall ((G2 (-> Bool tptp.complex)) (A2 tptp.set_o)) (=> (not (= (@ (@ tptp.groups4859619685533338977omplex G2) A2) tptp.one_one_complex)) (not (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) A2) (= (@ G2 A5) tptp.one_one_complex)))))))
% 5.98/6.28 (assert (forall ((G2 (-> tptp.nat tptp.complex)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups6464643781859351333omplex G2) A2) tptp.one_one_complex)) (not (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (= (@ G2 A5) tptp.one_one_complex)))))))
% 5.98/6.28 (assert (forall ((G2 (-> tptp.int tptp.complex)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups7440179247065528705omplex G2) A2) tptp.one_one_complex)) (not (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A2) (= (@ G2 A5) tptp.one_one_complex)))))))
% 5.98/6.28 (assert (forall ((G2 (-> Bool tptp.real)) (A2 tptp.set_o)) (=> (not (= (@ (@ tptp.groups234877984723959775o_real G2) A2) tptp.one_one_real)) (not (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) A2) (= (@ G2 A5) tptp.one_one_real)))))))
% 5.98/6.28 (assert (forall ((G2 (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups129246275422532515t_real G2) A2) tptp.one_one_real)) (not (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (= (@ G2 A5) tptp.one_one_real)))))))
% 5.98/6.28 (assert (forall ((G2 (-> tptp.int tptp.real)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups2316167850115554303t_real G2) A2) tptp.one_one_real)) (not (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A2) (= (@ G2 A5) tptp.one_one_real)))))))
% 5.98/6.28 (assert (forall ((G2 (-> Bool tptp.rat)) (A2 tptp.set_o)) (=> (not (= (@ (@ tptp.groups2869687844427037835_o_rat G2) A2) tptp.one_one_rat)) (not (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) A2) (= (@ G2 A5) tptp.one_one_rat)))))))
% 5.98/6.28 (assert (forall ((G2 (-> tptp.nat tptp.rat)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups73079841787564623at_rat G2) A2) tptp.one_one_rat)) (not (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (= (@ G2 A5) tptp.one_one_rat)))))))
% 5.98/6.28 (assert (forall ((G2 (-> tptp.int tptp.rat)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups1072433553688619179nt_rat G2) A2) tptp.one_one_rat)) (not (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A2) (= (@ G2 A5) tptp.one_one_rat)))))))
% 5.98/6.28 (assert (forall ((G2 (-> Bool tptp.nat)) (A2 tptp.set_o)) (=> (not (= (@ (@ tptp.groups3504817904513533571_o_nat G2) A2) tptp.one_one_nat)) (not (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) A2) (= (@ G2 A5) tptp.one_one_nat)))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_o) (B2 tptp.set_nat) (G2 (-> Bool tptp.nat tptp.nat)) (R (-> Bool tptp.nat Bool))) (=> (@ tptp.finite_finite_o A2) (=> (@ tptp.finite_finite_nat B2) (= (@ (@ tptp.groups3504817904513533571_o_nat (lambda ((X3 Bool)) (@ (@ tptp.groups708209901874060359at_nat (@ G2 X3)) (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) B2) (@ (@ R X3) Y2))))))) A2) (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y2 tptp.nat)) (@ (@ tptp.groups3504817904513533571_o_nat (lambda ((X3 Bool)) (@ (@ G2 X3) Y2))) (@ tptp.collect_o (lambda ((X3 Bool)) (and (@ (@ tptp.member_o X3) A2) (@ (@ R X3) Y2))))))) B2))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_nat) (G2 (-> tptp.int tptp.nat tptp.nat)) (R (-> tptp.int tptp.nat Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ tptp.finite_finite_nat B2) (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((X3 tptp.int)) (@ (@ tptp.groups708209901874060359at_nat (@ G2 X3)) (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) B2) (@ (@ R X3) Y2))))))) A2) (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y2 tptp.nat)) (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((X3 tptp.int)) (@ (@ G2 X3) Y2))) (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (@ (@ R X3) Y2))))))) B2))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_complex) (B2 tptp.set_nat) (G2 (-> tptp.complex tptp.nat tptp.nat)) (R (-> tptp.complex tptp.nat Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ tptp.finite_finite_nat B2) (= (@ (@ tptp.groups861055069439313189ex_nat (lambda ((X3 tptp.complex)) (@ (@ tptp.groups708209901874060359at_nat (@ G2 X3)) (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) B2) (@ (@ R X3) Y2))))))) A2) (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y2 tptp.nat)) (@ (@ tptp.groups861055069439313189ex_nat (lambda ((X3 tptp.complex)) (@ (@ G2 X3) Y2))) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A2) (@ (@ R X3) Y2))))))) B2))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_Extended_enat) (B2 tptp.set_nat) (G2 (-> tptp.extended_enat tptp.nat tptp.nat)) (R (-> tptp.extended_enat tptp.nat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ tptp.finite_finite_nat B2) (= (@ (@ tptp.groups2880970938130013265at_nat (lambda ((X3 tptp.extended_enat)) (@ (@ tptp.groups708209901874060359at_nat (@ G2 X3)) (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) B2) (@ (@ R X3) Y2))))))) A2) (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y2 tptp.nat)) (@ (@ tptp.groups2880970938130013265at_nat (lambda ((X3 tptp.extended_enat)) (@ (@ G2 X3) Y2))) (@ tptp.collec4429806609662206161d_enat (lambda ((X3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X3) A2) (@ (@ R X3) Y2))))))) B2))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_o) (B2 tptp.set_nat) (G2 (-> Bool tptp.nat tptp.int)) (R (-> Bool tptp.nat Bool))) (=> (@ tptp.finite_finite_o A2) (=> (@ tptp.finite_finite_nat B2) (= (@ (@ tptp.groups3502327434004483295_o_int (lambda ((X3 Bool)) (@ (@ tptp.groups705719431365010083at_int (@ G2 X3)) (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) B2) (@ (@ R X3) Y2))))))) A2) (@ (@ tptp.groups705719431365010083at_int (lambda ((Y2 tptp.nat)) (@ (@ tptp.groups3502327434004483295_o_int (lambda ((X3 Bool)) (@ (@ G2 X3) Y2))) (@ tptp.collect_o (lambda ((X3 Bool)) (and (@ (@ tptp.member_o X3) A2) (@ (@ R X3) Y2))))))) B2))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_complex) (B2 tptp.set_nat) (G2 (-> tptp.complex tptp.nat tptp.int)) (R (-> tptp.complex tptp.nat Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ tptp.finite_finite_nat B2) (= (@ (@ tptp.groups858564598930262913ex_int (lambda ((X3 tptp.complex)) (@ (@ tptp.groups705719431365010083at_int (@ G2 X3)) (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) B2) (@ (@ R X3) Y2))))))) A2) (@ (@ tptp.groups705719431365010083at_int (lambda ((Y2 tptp.nat)) (@ (@ tptp.groups858564598930262913ex_int (lambda ((X3 tptp.complex)) (@ (@ G2 X3) Y2))) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A2) (@ (@ R X3) Y2))))))) B2))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_Extended_enat) (B2 tptp.set_nat) (G2 (-> tptp.extended_enat tptp.nat tptp.int)) (R (-> tptp.extended_enat tptp.nat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ tptp.finite_finite_nat B2) (= (@ (@ tptp.groups2878480467620962989at_int (lambda ((X3 tptp.extended_enat)) (@ (@ tptp.groups705719431365010083at_int (@ G2 X3)) (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) B2) (@ (@ R X3) Y2))))))) A2) (@ (@ tptp.groups705719431365010083at_int (lambda ((Y2 tptp.nat)) (@ (@ tptp.groups2878480467620962989at_int (lambda ((X3 tptp.extended_enat)) (@ (@ G2 X3) Y2))) (@ tptp.collec4429806609662206161d_enat (lambda ((X3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X3) A2) (@ (@ R X3) Y2))))))) B2))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_o) (B2 tptp.set_int) (G2 (-> Bool tptp.int tptp.int)) (R (-> Bool tptp.int Bool))) (=> (@ tptp.finite_finite_o A2) (=> (@ tptp.finite_finite_int B2) (= (@ (@ tptp.groups3502327434004483295_o_int (lambda ((X3 Bool)) (@ (@ tptp.groups1705073143266064639nt_int (@ G2 X3)) (@ tptp.collect_int (lambda ((Y2 tptp.int)) (and (@ (@ tptp.member_int Y2) B2) (@ (@ R X3) Y2))))))) A2) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Y2 tptp.int)) (@ (@ tptp.groups3502327434004483295_o_int (lambda ((X3 Bool)) (@ (@ G2 X3) Y2))) (@ tptp.collect_o (lambda ((X3 Bool)) (and (@ (@ tptp.member_o X3) A2) (@ (@ R X3) Y2))))))) B2))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_complex) (B2 tptp.set_int) (G2 (-> tptp.complex tptp.int tptp.int)) (R (-> tptp.complex tptp.int Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ tptp.finite_finite_int B2) (= (@ (@ tptp.groups858564598930262913ex_int (lambda ((X3 tptp.complex)) (@ (@ tptp.groups1705073143266064639nt_int (@ G2 X3)) (@ tptp.collect_int (lambda ((Y2 tptp.int)) (and (@ (@ tptp.member_int Y2) B2) (@ (@ R X3) Y2))))))) A2) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Y2 tptp.int)) (@ (@ tptp.groups858564598930262913ex_int (lambda ((X3 tptp.complex)) (@ (@ G2 X3) Y2))) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A2) (@ (@ R X3) Y2))))))) B2))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_Extended_enat) (B2 tptp.set_int) (G2 (-> tptp.extended_enat tptp.int tptp.int)) (R (-> tptp.extended_enat tptp.int Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ tptp.finite_finite_int B2) (= (@ (@ tptp.groups2878480467620962989at_int (lambda ((X3 tptp.extended_enat)) (@ (@ tptp.groups1705073143266064639nt_int (@ G2 X3)) (@ tptp.collect_int (lambda ((Y2 tptp.int)) (and (@ (@ tptp.member_int Y2) B2) (@ (@ R X3) Y2))))))) A2) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Y2 tptp.int)) (@ (@ tptp.groups2878480467620962989at_int (lambda ((X3 tptp.extended_enat)) (@ (@ G2 X3) Y2))) (@ tptp.collec4429806609662206161d_enat (lambda ((X3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X3) A2) (@ (@ R X3) Y2))))))) B2))))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X4)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F) A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X4)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F) A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.real)) (G2 (-> Bool tptp.real))) (=> (forall ((I2 Bool)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_o I2) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G2 I2)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups234877984723959775o_real F) A2)) (@ (@ tptp.groups234877984723959775o_real G2) A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.real))) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_nat I2) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G2 I2)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups129246275422532515t_real F) A2)) (@ (@ tptp.groups129246275422532515t_real G2) A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G2 (-> tptp.int tptp.real))) (=> (forall ((I2 tptp.int)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_int I2) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G2 I2)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2316167850115554303t_real F) A2)) (@ (@ tptp.groups2316167850115554303t_real G2) A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.rat)) (G2 (-> Bool tptp.rat))) (=> (forall ((I2 Bool)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_o I2) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G2 I2)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2869687844427037835_o_rat F) A2)) (@ (@ tptp.groups2869687844427037835_o_rat G2) A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G2 (-> tptp.nat tptp.rat))) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_nat I2) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G2 I2)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups73079841787564623at_rat F) A2)) (@ (@ tptp.groups73079841787564623at_rat G2) A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat)) (G2 (-> tptp.int tptp.rat))) (=> (forall ((I2 tptp.int)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_int I2) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G2 I2)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A2)) (@ (@ tptp.groups1072433553688619179nt_rat G2) A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.nat)) (G2 (-> Bool tptp.nat))) (=> (forall ((I2 Bool)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_o I2) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G2 I2)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3504817904513533571_o_nat F) A2)) (@ (@ tptp.groups3504817904513533571_o_nat G2) A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G2 (-> tptp.int tptp.nat))) (=> (forall ((I2 tptp.int)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_int I2) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G2 I2)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (@ (@ tptp.groups1707563613775114915nt_nat G2) A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.int)) (G2 (-> Bool tptp.int))) (=> (forall ((I2 Bool)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_o I2) A2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_eq_int _let_1) (@ G2 I2)))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3502327434004483295_o_int F) A2)) (@ (@ tptp.groups3502327434004483295_o_int G2) A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G2 (-> tptp.nat tptp.nat))) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_nat I2) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G2 I2)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups708209901874060359at_nat G2) A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X4)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F X4)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F) A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F X4)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F) A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.real))) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups234877984723959775o_real F) A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups129246275422532515t_real F) A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups2316167850115554303t_real F) A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.rat))) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups2869687844427037835_o_rat F) A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups73079841787564623at_rat F) A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups1072433553688619179nt_rat F) A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.nat))) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A2) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X4)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups3504817904513533571_o_nat F) A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X4)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups1707563613775114915nt_nat F) A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.int))) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A2) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F X4)))) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ (@ tptp.groups3502327434004483295_o_int F) A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X4)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups708209901874060359at_nat F) A2)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A2) (=> (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (= (@ F X2) tptp.zero_zero_real))) (= (@ (@ tptp.groups129246275422532515t_real F) A2) tptp.zero_zero_real)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (= (@ F X2) tptp.zero_zero_real))) (= (@ (@ tptp.groups2316167850115554303t_real F) A2) tptp.zero_zero_real)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.zero_zero_real))) (= (@ (@ tptp.groups766887009212190081x_real F) A2) tptp.zero_zero_real)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X2) A2) (= (@ F X2) tptp.zero_zero_real))) (= (@ (@ tptp.groups97031904164794029t_real F) A2) tptp.zero_zero_real)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A2) (=> (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (= (@ F X2) tptp.zero_zero_rat))) (= (@ (@ tptp.groups73079841787564623at_rat F) A2) tptp.zero_zero_rat)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A2) (=> (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (= (@ F X2) tptp.zero_zero_rat))) (= (@ (@ tptp.groups1072433553688619179nt_rat F) A2) tptp.zero_zero_rat)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.zero_zero_rat))) (= (@ (@ tptp.groups225925009352817453ex_rat F) A2) tptp.zero_zero_rat)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X2) A2) (= (@ F X2) tptp.zero_zero_rat))) (= (@ (@ tptp.groups2245840878043517529at_rat F) A2) tptp.zero_zero_rat)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (= (@ F X2) tptp.zero_zero_nat))) (= (@ (@ tptp.groups1707563613775114915nt_nat F) A2) tptp.zero_zero_nat)))))
% 5.98/6.28 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.zero_zero_nat))) (= (@ (@ tptp.groups861055069439313189ex_nat F) A2) tptp.zero_zero_nat)))))
% 5.98/6.28 (assert (forall ((I5 tptp.set_o) (X (-> Bool tptp.real)) (Y (-> Bool tptp.real))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ X I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ Y 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 (@ X I4)) (@ Y I4)) tptp.zero_zero_real))))))))))
% 5.98/6.28 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.real)) (Y (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y 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 (@ X I4)) (@ Y I4)) tptp.zero_zero_real))))))))))
% 5.98/6.28 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.real)) (Y (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ X I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y 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 (@ X I4)) (@ Y I4)) tptp.zero_zero_real))))))))))
% 5.98/6.28 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.real)) (Y (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ X I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ Y 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 (@ X I4)) (@ Y I4)) tptp.zero_zero_real))))))))))
% 5.98/6.28 (assert (forall ((I5 tptp.set_Extended_enat) (X (-> tptp.extended_enat tptp.real)) (Y (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ X I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ Y 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 (@ X I4)) (@ Y I4)) tptp.zero_zero_real))))))))))
% 5.98/6.28 (assert (forall ((I5 tptp.set_o) (X (-> Bool tptp.rat)) (Y (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ X I4) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ Y 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 (@ X I4)) (@ Y I4)) tptp.zero_zero_rat))))))))))
% 5.98/6.28 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.rat)) (Y (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X I4) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y 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 (@ X I4)) (@ Y I4)) tptp.zero_zero_rat))))))))))
% 5.98/6.28 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.rat)) (Y (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ X I4) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y 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 (@ X I4)) (@ Y I4)) tptp.zero_zero_rat))))))))))
% 5.98/6.28 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.rat)) (Y (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ X I4) tptp.zero_zero_rat)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ Y I4) tptp.zero_zero_rat)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X I4)) (@ Y I4)) tptp.zero_zero_rat))))))))))
% 5.98/6.28 (assert (forall ((I5 tptp.set_Extended_enat) (X (-> tptp.extended_enat tptp.rat)) (Y (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ X I4) tptp.zero_zero_rat)))))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ Y I4) tptp.zero_zero_rat)))))) (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X I4)) (@ Y I4)) tptp.zero_zero_rat))))))))))
% 5.98/6.28 (assert (forall ((I5 tptp.set_o) (X (-> Bool tptp.complex)) (Y (-> Bool tptp.complex))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ X I4) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ Y 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 (@ X I4)) (@ Y I4)) tptp.one_one_complex))))))))))
% 5.98/6.28 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.complex)) (Y (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X I4) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y 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 (@ X I4)) (@ Y I4)) tptp.one_one_complex))))))))))
% 5.98/6.28 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.complex)) (Y (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ X I4) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y 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 (@ X I4)) (@ Y I4)) tptp.one_one_complex))))))))))
% 5.98/6.28 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.complex)) (Y (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ X I4) tptp.one_one_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ Y 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 (@ X I4)) (@ Y I4)) tptp.one_one_complex))))))))))
% 5.98/6.29 (assert (forall ((I5 tptp.set_Extended_enat) (X (-> tptp.extended_enat tptp.complex)) (Y (-> tptp.extended_enat tptp.complex))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ X I4) tptp.one_one_complex)))))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ Y 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 (@ X I4)) (@ Y I4)) tptp.one_one_complex))))))))))
% 5.98/6.29 (assert (forall ((I5 tptp.set_o) (X (-> Bool tptp.real)) (Y (-> Bool tptp.real))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ X I4) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ Y 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 (@ X I4)) (@ Y I4)) tptp.one_one_real))))))))))
% 5.98/6.29 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.real)) (Y (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X I4) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y 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 (@ X I4)) (@ Y I4)) tptp.one_one_real))))))))))
% 5.98/6.29 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.real)) (Y (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ X I4) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y 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 (@ X I4)) (@ Y I4)) tptp.one_one_real))))))))))
% 5.98/6.29 (assert (forall ((I5 tptp.set_complex) (X (-> tptp.complex tptp.real)) (Y (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ X I4) tptp.one_one_real)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ Y I4) tptp.one_one_real)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ (@ tptp.times_times_real (@ X I4)) (@ Y I4)) tptp.one_one_real))))))))))
% 5.98/6.29 (assert (forall ((I5 tptp.set_Extended_enat) (X (-> tptp.extended_enat tptp.real)) (Y (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ X I4) tptp.one_one_real)))))) (=> (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ Y I4) tptp.one_one_real)))))) (@ tptp.finite4001608067531595151d_enat (@ tptp.collec4429806609662206161d_enat (lambda ((I4 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat I4) I5) (not (= (@ (@ tptp.times_times_real (@ X I4)) (@ Y I4)) tptp.one_one_real))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (G2 (-> Bool tptp.complex)) (P (-> Bool Bool))) (=> (@ tptp.finite_finite_o A2) (= (@ (@ tptp.groups4859619685533338977omplex G2) (@ tptp.collect_o (lambda ((X3 Bool)) (and (@ (@ tptp.member_o X3) A2) (@ P X3))))) (@ (@ tptp.groups4859619685533338977omplex (lambda ((X3 Bool)) (@ (@ (@ tptp.if_complex (@ P X3)) (@ G2 X3)) tptp.one_one_complex))) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (G2 (-> tptp.nat tptp.complex)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.groups6464643781859351333omplex G2) (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (@ P X3))))) (@ (@ tptp.groups6464643781859351333omplex (lambda ((X3 tptp.nat)) (@ (@ (@ tptp.if_complex (@ P X3)) (@ G2 X3)) tptp.one_one_complex))) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (G2 (-> tptp.int tptp.complex)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups7440179247065528705omplex G2) (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (@ P X3))))) (@ (@ tptp.groups7440179247065528705omplex (lambda ((X3 tptp.int)) (@ (@ (@ tptp.if_complex (@ P X3)) (@ G2 X3)) tptp.one_one_complex))) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (G2 (-> tptp.complex tptp.complex)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups3708469109370488835omplex G2) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A2) (@ P X3))))) (@ (@ tptp.groups3708469109370488835omplex (lambda ((X3 tptp.complex)) (@ (@ (@ tptp.if_complex (@ P X3)) (@ G2 X3)) tptp.one_one_complex))) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.complex)) (P (-> tptp.extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ (@ tptp.groups4622424608036095791omplex G2) (@ tptp.collec4429806609662206161d_enat (lambda ((X3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X3) A2) (@ P X3))))) (@ (@ tptp.groups4622424608036095791omplex (lambda ((X3 tptp.extended_enat)) (@ (@ (@ tptp.if_complex (@ P X3)) (@ G2 X3)) tptp.one_one_complex))) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (G2 (-> Bool tptp.real)) (P (-> Bool Bool))) (=> (@ tptp.finite_finite_o A2) (= (@ (@ tptp.groups234877984723959775o_real G2) (@ tptp.collect_o (lambda ((X3 Bool)) (and (@ (@ tptp.member_o X3) A2) (@ P X3))))) (@ (@ tptp.groups234877984723959775o_real (lambda ((X3 Bool)) (@ (@ (@ tptp.if_real (@ P X3)) (@ G2 X3)) tptp.one_one_real))) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (G2 (-> tptp.nat tptp.real)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.groups129246275422532515t_real G2) (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (@ P X3))))) (@ (@ tptp.groups129246275422532515t_real (lambda ((X3 tptp.nat)) (@ (@ (@ tptp.if_real (@ P X3)) (@ G2 X3)) tptp.one_one_real))) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (G2 (-> tptp.int tptp.real)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups2316167850115554303t_real G2) (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (@ P X3))))) (@ (@ tptp.groups2316167850115554303t_real (lambda ((X3 tptp.int)) (@ (@ (@ tptp.if_real (@ P X3)) (@ G2 X3)) tptp.one_one_real))) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (G2 (-> tptp.complex tptp.real)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups766887009212190081x_real G2) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A2) (@ P X3))))) (@ (@ tptp.groups766887009212190081x_real (lambda ((X3 tptp.complex)) (@ (@ (@ tptp.if_real (@ P X3)) (@ G2 X3)) tptp.one_one_real))) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.real)) (P (-> tptp.extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ (@ tptp.groups97031904164794029t_real G2) (@ tptp.collec4429806609662206161d_enat (lambda ((X3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X3) A2) (@ P X3))))) (@ (@ tptp.groups97031904164794029t_real (lambda ((X3 tptp.extended_enat)) (@ (@ (@ tptp.if_real (@ P X3)) (@ G2 X3)) tptp.one_one_real))) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.real))) (=> (forall ((X4 Bool)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_o X4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups234877984723959775o_real F) A2)) tptp.one_one_real))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (forall ((X4 tptp.nat)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_nat X4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups129246275422532515t_real F) A2)) tptp.one_one_real))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X4 tptp.int)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_int X4) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.one_one_real))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2316167850115554303t_real F) A2)) tptp.one_one_real))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.rat))) (=> (forall ((X4 Bool)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_o X4) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2869687844427037835_o_rat F) A2)) tptp.one_one_rat))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X4 tptp.nat)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_nat X4) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups73079841787564623at_rat F) A2)) tptp.one_one_rat))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X4 tptp.int)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_int X4) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A2)) tptp.one_one_rat))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.nat))) (=> (forall ((X4 Bool)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_o X4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3504817904513533571_o_nat F) A2)) tptp.one_one_nat))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X4 tptp.int)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_int X4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) tptp.one_one_nat))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.int))) (=> (forall ((X4 Bool)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_o X4) A2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_eq_int _let_1) tptp.one_one_int))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3502327434004483295_o_int F) A2)) tptp.one_one_int))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X4 tptp.nat)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_nat X4) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) tptp.one_one_nat))))
% 5.98/6.29 (assert (forall ((R (-> tptp.complex tptp.complex Bool)) (S2 tptp.set_nat) (H (-> tptp.nat tptp.complex)) (G2 (-> tptp.nat tptp.complex))) (=> (@ (@ R tptp.one_one_complex) tptp.one_one_complex) (=> (forall ((X1 tptp.complex) (Y1 tptp.complex) (X24 tptp.complex) (Y24 tptp.complex)) (=> (and (@ (@ R X1) X24) (@ (@ R Y1) Y24)) (@ (@ R (@ (@ tptp.times_times_complex X1) Y1)) (@ (@ tptp.times_times_complex X24) Y24)))) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S2) (@ (@ R (@ H X4)) (@ G2 X4)))) (@ (@ R (@ (@ tptp.groups6464643781859351333omplex H) S2)) (@ (@ tptp.groups6464643781859351333omplex G2) S2))))))))
% 5.98/6.29 (assert (forall ((R (-> tptp.complex tptp.complex Bool)) (S2 tptp.set_int) (H (-> tptp.int tptp.complex)) (G2 (-> tptp.int tptp.complex))) (=> (@ (@ R tptp.one_one_complex) tptp.one_one_complex) (=> (forall ((X1 tptp.complex) (Y1 tptp.complex) (X24 tptp.complex) (Y24 tptp.complex)) (=> (and (@ (@ R X1) X24) (@ (@ R Y1) Y24)) (@ (@ R (@ (@ tptp.times_times_complex X1) Y1)) (@ (@ tptp.times_times_complex X24) Y24)))) (=> (@ tptp.finite_finite_int S2) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S2) (@ (@ R (@ H X4)) (@ G2 X4)))) (@ (@ R (@ (@ tptp.groups7440179247065528705omplex H) S2)) (@ (@ tptp.groups7440179247065528705omplex G2) S2))))))))
% 5.98/6.29 (assert (forall ((R (-> tptp.complex tptp.complex Bool)) (S2 tptp.set_complex) (H (-> tptp.complex tptp.complex)) (G2 (-> tptp.complex tptp.complex))) (=> (@ (@ R tptp.one_one_complex) tptp.one_one_complex) (=> (forall ((X1 tptp.complex) (Y1 tptp.complex) (X24 tptp.complex) (Y24 tptp.complex)) (=> (and (@ (@ R X1) X24) (@ (@ R Y1) Y24)) (@ (@ R (@ (@ tptp.times_times_complex X1) Y1)) (@ (@ tptp.times_times_complex X24) Y24)))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S2) (@ (@ R (@ H X4)) (@ G2 X4)))) (@ (@ R (@ (@ tptp.groups3708469109370488835omplex H) S2)) (@ (@ tptp.groups3708469109370488835omplex G2) S2))))))))
% 5.98/6.29 (assert (forall ((R (-> tptp.complex tptp.complex Bool)) (S2 tptp.set_Extended_enat) (H (-> tptp.extended_enat tptp.complex)) (G2 (-> tptp.extended_enat tptp.complex))) (=> (@ (@ R tptp.one_one_complex) tptp.one_one_complex) (=> (forall ((X1 tptp.complex) (Y1 tptp.complex) (X24 tptp.complex) (Y24 tptp.complex)) (=> (and (@ (@ R X1) X24) (@ (@ R Y1) Y24)) (@ (@ R (@ (@ tptp.times_times_complex X1) Y1)) (@ (@ tptp.times_times_complex X24) Y24)))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) S2) (@ (@ R (@ H X4)) (@ G2 X4)))) (@ (@ R (@ (@ tptp.groups4622424608036095791omplex H) S2)) (@ (@ tptp.groups4622424608036095791omplex G2) S2))))))))
% 5.98/6.29 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S2 tptp.set_nat) (H (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.real))) (=> (@ (@ R tptp.one_one_real) tptp.one_one_real) (=> (forall ((X1 tptp.real) (Y1 tptp.real) (X24 tptp.real) (Y24 tptp.real)) (=> (and (@ (@ R X1) X24) (@ (@ R Y1) Y24)) (@ (@ R (@ (@ tptp.times_times_real X1) Y1)) (@ (@ tptp.times_times_real X24) Y24)))) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S2) (@ (@ R (@ H X4)) (@ G2 X4)))) (@ (@ R (@ (@ tptp.groups129246275422532515t_real H) S2)) (@ (@ tptp.groups129246275422532515t_real G2) S2))))))))
% 5.98/6.29 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S2 tptp.set_int) (H (-> tptp.int tptp.real)) (G2 (-> tptp.int tptp.real))) (=> (@ (@ R tptp.one_one_real) tptp.one_one_real) (=> (forall ((X1 tptp.real) (Y1 tptp.real) (X24 tptp.real) (Y24 tptp.real)) (=> (and (@ (@ R X1) X24) (@ (@ R Y1) Y24)) (@ (@ R (@ (@ tptp.times_times_real X1) Y1)) (@ (@ tptp.times_times_real X24) Y24)))) (=> (@ tptp.finite_finite_int S2) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S2) (@ (@ R (@ H X4)) (@ G2 X4)))) (@ (@ R (@ (@ tptp.groups2316167850115554303t_real H) S2)) (@ (@ tptp.groups2316167850115554303t_real G2) S2))))))))
% 5.98/6.29 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S2 tptp.set_complex) (H (-> tptp.complex tptp.real)) (G2 (-> tptp.complex tptp.real))) (=> (@ (@ R tptp.one_one_real) tptp.one_one_real) (=> (forall ((X1 tptp.real) (Y1 tptp.real) (X24 tptp.real) (Y24 tptp.real)) (=> (and (@ (@ R X1) X24) (@ (@ R Y1) Y24)) (@ (@ R (@ (@ tptp.times_times_real X1) Y1)) (@ (@ tptp.times_times_real X24) Y24)))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S2) (@ (@ R (@ H X4)) (@ G2 X4)))) (@ (@ R (@ (@ tptp.groups766887009212190081x_real H) S2)) (@ (@ tptp.groups766887009212190081x_real G2) S2))))))))
% 5.98/6.29 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S2 tptp.set_Extended_enat) (H (-> tptp.extended_enat tptp.real)) (G2 (-> tptp.extended_enat tptp.real))) (=> (@ (@ R tptp.one_one_real) tptp.one_one_real) (=> (forall ((X1 tptp.real) (Y1 tptp.real) (X24 tptp.real) (Y24 tptp.real)) (=> (and (@ (@ R X1) X24) (@ (@ R Y1) Y24)) (@ (@ R (@ (@ tptp.times_times_real X1) Y1)) (@ (@ tptp.times_times_real X24) Y24)))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) S2) (@ (@ R (@ H X4)) (@ G2 X4)))) (@ (@ R (@ (@ tptp.groups97031904164794029t_real H) S2)) (@ (@ tptp.groups97031904164794029t_real G2) S2))))))))
% 5.98/6.29 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S2 tptp.set_nat) (H (-> tptp.nat tptp.rat)) (G2 (-> tptp.nat tptp.rat))) (=> (@ (@ R tptp.one_one_rat) tptp.one_one_rat) (=> (forall ((X1 tptp.rat) (Y1 tptp.rat) (X24 tptp.rat) (Y24 tptp.rat)) (=> (and (@ (@ R X1) X24) (@ (@ R Y1) Y24)) (@ (@ R (@ (@ tptp.times_times_rat X1) Y1)) (@ (@ tptp.times_times_rat X24) Y24)))) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S2) (@ (@ R (@ H X4)) (@ G2 X4)))) (@ (@ R (@ (@ tptp.groups73079841787564623at_rat H) S2)) (@ (@ tptp.groups73079841787564623at_rat G2) S2))))))))
% 5.98/6.29 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S2 tptp.set_int) (H (-> tptp.int tptp.rat)) (G2 (-> tptp.int tptp.rat))) (=> (@ (@ R tptp.one_one_rat) tptp.one_one_rat) (=> (forall ((X1 tptp.rat) (Y1 tptp.rat) (X24 tptp.rat) (Y24 tptp.rat)) (=> (and (@ (@ R X1) X24) (@ (@ R Y1) Y24)) (@ (@ R (@ (@ tptp.times_times_rat X1) Y1)) (@ (@ tptp.times_times_rat X24) Y24)))) (=> (@ tptp.finite_finite_int S2) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S2) (@ (@ R (@ H X4)) (@ G2 X4)))) (@ (@ R (@ (@ tptp.groups1072433553688619179nt_rat H) S2)) (@ (@ tptp.groups1072433553688619179nt_rat G2) S2))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A2)))) (let ((_let_4 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G2 X)) _let_2)))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (X Bool) (G2 (-> Bool tptp.real))) (let ((_let_1 (@ tptp.groups234877984723959775o_real G2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_o X) A2)))) (let ((_let_4 (@ (@ tptp.member_o X) A2))) (=> (@ tptp.finite_finite_o A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G2 X)) _let_2)))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X) A2)))) (let ((_let_4 (@ (@ tptp.member_nat X) A2))) (=> (@ tptp.finite_finite_nat A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G2 X)) _let_2)))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A2)))) (let ((_let_4 (@ (@ tptp.member_int X) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G2 X)) _let_2)))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X) A2)))) (let ((_let_4 (@ (@ tptp.member_complex X) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G2 X)) _let_2)))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G2 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real G2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Extended_enat X) A2)))) (let ((_let_4 (@ (@ tptp.member_Extended_enat X) A2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G2 X)) _let_2)))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat G2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A2)))) (let ((_let_4 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G2 X)) _let_2)))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (X Bool) (G2 (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups2869687844427037835_o_rat G2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_o X) A2)))) (let ((_let_4 (@ (@ tptp.member_o X) A2))) (=> (@ tptp.finite_finite_o A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G2 X)) _let_2)))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X) A2)))) (let ((_let_4 (@ (@ tptp.member_nat X) A2))) (=> (@ tptp.finite_finite_nat A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G2 X)) _let_2)))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A2)))) (let ((_let_4 (@ (@ tptp.member_int X) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G2 X)) _let_2)))))))))))
% 5.98/6.29 (assert (forall ((S5 tptp.set_o) (T5 tptp.set_o) (S2 tptp.set_o) (I (-> Bool Bool)) (J (-> Bool Bool)) (T3 tptp.set_o) (G2 (-> Bool tptp.complex)) (H (-> Bool tptp.complex))) (=> (@ tptp.finite_finite_o S5) (=> (@ tptp.finite_finite_o T5) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) (@ (@ tptp.minus_minus_set_o S2) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) (@ (@ tptp.minus_minus_set_o S2) S5)) (@ (@ tptp.member_o (@ J A5)) (@ (@ tptp.minus_minus_set_o T3) T5)))) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) (@ (@ tptp.minus_minus_set_o T3) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) (@ (@ tptp.minus_minus_set_o T3) T5)) (@ (@ tptp.member_o (@ I B5)) (@ (@ tptp.minus_minus_set_o S2) S5)))) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) S5) (= (@ G2 A5) tptp.one_one_complex))) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) T5) (= (@ H B5) tptp.one_one_complex))) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) S2) (= (@ H (@ J A5)) (@ G2 A5)))) (= (@ (@ tptp.groups4859619685533338977omplex G2) S2) (@ (@ tptp.groups4859619685533338977omplex H) T3)))))))))))))
% 5.98/6.29 (assert (forall ((S5 tptp.set_o) (T5 tptp.set_int) (S2 tptp.set_o) (I (-> tptp.int Bool)) (J (-> Bool tptp.int)) (T3 tptp.set_int) (G2 (-> Bool tptp.complex)) (H (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_o S5) (=> (@ tptp.finite_finite_int T5) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) (@ (@ tptp.minus_minus_set_o S2) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) (@ (@ tptp.minus_minus_set_o S2) S5)) (@ (@ tptp.member_int (@ J A5)) (@ (@ tptp.minus_minus_set_int T3) T5)))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T5)) (@ (@ tptp.member_o (@ I B5)) (@ (@ tptp.minus_minus_set_o S2) S5)))) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) S5) (= (@ G2 A5) tptp.one_one_complex))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) T5) (= (@ H B5) tptp.one_one_complex))) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) S2) (= (@ H (@ J A5)) (@ G2 A5)))) (= (@ (@ tptp.groups4859619685533338977omplex G2) S2) (@ (@ tptp.groups7440179247065528705omplex H) T3)))))))))))))
% 5.98/6.29 (assert (forall ((S5 tptp.set_o) (T5 tptp.set_complex) (S2 tptp.set_o) (I (-> tptp.complex Bool)) (J (-> Bool tptp.complex)) (T3 tptp.set_complex) (G2 (-> Bool tptp.complex)) (H (-> tptp.complex tptp.complex))) (=> (@ tptp.finite_finite_o S5) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) (@ (@ tptp.minus_minus_set_o S2) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) (@ (@ tptp.minus_minus_set_o S2) S5)) (@ (@ tptp.member_complex (@ J A5)) (@ (@ tptp.minus_811609699411566653omplex T3) T5)))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (@ (@ tptp.member_o (@ I B5)) (@ (@ tptp.minus_minus_set_o S2) S5)))) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) S5) (= (@ G2 A5) tptp.one_one_complex))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) T5) (= (@ H B5) tptp.one_one_complex))) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) S2) (= (@ H (@ J A5)) (@ G2 A5)))) (= (@ (@ tptp.groups4859619685533338977omplex G2) S2) (@ (@ tptp.groups3708469109370488835omplex H) T3)))))))))))))
% 5.98/6.29 (assert (forall ((S5 tptp.set_o) (T5 tptp.set_Extended_enat) (S2 tptp.set_o) (I (-> tptp.extended_enat Bool)) (J (-> Bool tptp.extended_enat)) (T3 tptp.set_Extended_enat) (G2 (-> Bool tptp.complex)) (H (-> tptp.extended_enat tptp.complex))) (=> (@ tptp.finite_finite_o S5) (=> (@ tptp.finite4001608067531595151d_enat T5) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) (@ (@ tptp.minus_minus_set_o S2) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) (@ (@ tptp.minus_minus_set_o S2) S5)) (@ (@ tptp.member_Extended_enat (@ J A5)) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)))) (=> (forall ((B5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B5) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B5) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)) (@ (@ tptp.member_o (@ I B5)) (@ (@ tptp.minus_minus_set_o S2) S5)))) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) S5) (= (@ G2 A5) tptp.one_one_complex))) (=> (forall ((B5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B5) T5) (= (@ H B5) tptp.one_one_complex))) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) S2) (= (@ H (@ J A5)) (@ G2 A5)))) (= (@ (@ tptp.groups4859619685533338977omplex G2) S2) (@ (@ tptp.groups4622424608036095791omplex H) T3)))))))))))))
% 5.98/6.29 (assert (forall ((S5 tptp.set_int) (T5 tptp.set_o) (S2 tptp.set_int) (I (-> Bool tptp.int)) (J (-> tptp.int Bool)) (T3 tptp.set_o) (G2 (-> tptp.int tptp.complex)) (H (-> Bool tptp.complex))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite_finite_o T5) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S5)) (@ (@ tptp.member_o (@ J A5)) (@ (@ tptp.minus_minus_set_o T3) T5)))) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) (@ (@ tptp.minus_minus_set_o T3) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) (@ (@ tptp.minus_minus_set_o T3) T5)) (@ (@ tptp.member_int (@ I B5)) (@ (@ tptp.minus_minus_set_int S2) S5)))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S5) (= (@ G2 A5) tptp.one_one_complex))) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) T5) (= (@ H B5) tptp.one_one_complex))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S2) (= (@ H (@ J A5)) (@ G2 A5)))) (= (@ (@ tptp.groups7440179247065528705omplex G2) S2) (@ (@ tptp.groups4859619685533338977omplex H) T3)))))))))))))
% 5.98/6.29 (assert (forall ((S5 tptp.set_int) (T5 tptp.set_int) (S2 tptp.set_int) (I (-> tptp.int tptp.int)) (J (-> tptp.int tptp.int)) (T3 tptp.set_int) (G2 (-> tptp.int tptp.complex)) (H (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite_finite_int T5) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S5)) (@ (@ tptp.member_int (@ J A5)) (@ (@ tptp.minus_minus_set_int T3) T5)))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T5)) (@ (@ tptp.member_int (@ I B5)) (@ (@ tptp.minus_minus_set_int S2) S5)))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S5) (= (@ G2 A5) tptp.one_one_complex))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) T5) (= (@ H B5) tptp.one_one_complex))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S2) (= (@ H (@ J A5)) (@ G2 A5)))) (= (@ (@ tptp.groups7440179247065528705omplex G2) S2) (@ (@ tptp.groups7440179247065528705omplex H) T3)))))))))))))
% 5.98/6.29 (assert (forall ((S5 tptp.set_int) (T5 tptp.set_complex) (S2 tptp.set_int) (I (-> tptp.complex tptp.int)) (J (-> tptp.int tptp.complex)) (T3 tptp.set_complex) (G2 (-> tptp.int tptp.complex)) (H (-> tptp.complex tptp.complex))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S5)) (@ (@ tptp.member_complex (@ J A5)) (@ (@ tptp.minus_811609699411566653omplex T3) T5)))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (@ (@ tptp.member_int (@ I B5)) (@ (@ tptp.minus_minus_set_int S2) S5)))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S5) (= (@ G2 A5) tptp.one_one_complex))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) T5) (= (@ H B5) tptp.one_one_complex))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S2) (= (@ H (@ J A5)) (@ G2 A5)))) (= (@ (@ tptp.groups7440179247065528705omplex G2) S2) (@ (@ tptp.groups3708469109370488835omplex H) T3)))))))))))))
% 5.98/6.29 (assert (forall ((S5 tptp.set_int) (T5 tptp.set_Extended_enat) (S2 tptp.set_int) (I (-> tptp.extended_enat tptp.int)) (J (-> tptp.int tptp.extended_enat)) (T3 tptp.set_Extended_enat) (G2 (-> tptp.int tptp.complex)) (H (-> tptp.extended_enat tptp.complex))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite4001608067531595151d_enat T5) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S5)) (@ (@ tptp.member_Extended_enat (@ J A5)) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)))) (=> (forall ((B5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B5) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B5) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)) (@ (@ tptp.member_int (@ I B5)) (@ (@ tptp.minus_minus_set_int S2) S5)))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S5) (= (@ G2 A5) tptp.one_one_complex))) (=> (forall ((B5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B5) T5) (= (@ H B5) tptp.one_one_complex))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S2) (= (@ H (@ J A5)) (@ G2 A5)))) (= (@ (@ tptp.groups7440179247065528705omplex G2) S2) (@ (@ tptp.groups4622424608036095791omplex H) T3)))))))))))))
% 5.98/6.29 (assert (forall ((S5 tptp.set_complex) (T5 tptp.set_o) (S2 tptp.set_complex) (I (-> Bool tptp.complex)) (J (-> tptp.complex Bool)) (T3 tptp.set_o) (G2 (-> tptp.complex tptp.complex)) (H (-> Bool tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite_finite_o T5) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (@ (@ tptp.member_o (@ J A5)) (@ (@ tptp.minus_minus_set_o T3) T5)))) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) (@ (@ tptp.minus_minus_set_o T3) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) (@ (@ tptp.minus_minus_set_o T3) T5)) (@ (@ tptp.member_complex (@ I B5)) (@ (@ tptp.minus_811609699411566653omplex S2) S5)))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) S5) (= (@ G2 A5) tptp.one_one_complex))) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) T5) (= (@ H B5) tptp.one_one_complex))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) S2) (= (@ H (@ J A5)) (@ G2 A5)))) (= (@ (@ tptp.groups3708469109370488835omplex G2) S2) (@ (@ tptp.groups4859619685533338977omplex H) T3)))))))))))))
% 5.98/6.29 (assert (forall ((S5 tptp.set_complex) (T5 tptp.set_int) (S2 tptp.set_complex) (I (-> tptp.int tptp.complex)) (J (-> tptp.complex tptp.int)) (T3 tptp.set_int) (G2 (-> tptp.complex tptp.complex)) (H (-> tptp.int tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite_finite_int T5) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (@ (@ tptp.member_int (@ J A5)) (@ (@ tptp.minus_minus_set_int T3) T5)))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T5)) (@ (@ tptp.member_complex (@ I B5)) (@ (@ tptp.minus_811609699411566653omplex S2) S5)))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) S5) (= (@ G2 A5) tptp.one_one_complex))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) T5) (= (@ H B5) tptp.one_one_complex))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) S2) (= (@ H (@ J A5)) (@ G2 A5)))) (= (@ (@ tptp.groups3708469109370488835omplex G2) S2) (@ (@ tptp.groups7440179247065528705omplex H) T3)))))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (G2 (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups7440179247065528705omplex G2))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X3 tptp.int)) (= (@ G2 X3) tptp.one_one_complex))))) (@ _let_1 A2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (G2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G2))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (= (@ G2 X3) tptp.one_one_complex))))) (@ _let_1 A2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ tptp.groups4622424608036095791omplex G2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ tptp.collec4429806609662206161d_enat (lambda ((X3 tptp.extended_enat)) (= (@ G2 X3) tptp.one_one_complex))))) (@ _let_1 A2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G2))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X3 tptp.int)) (= (@ G2 X3) tptp.one_one_real))))) (@ _let_1 A2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G2))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (= (@ G2 X3) tptp.one_one_real))))) (@ _let_1 A2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real G2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ tptp.collec4429806609662206161d_enat (lambda ((X3 tptp.extended_enat)) (= (@ G2 X3) tptp.one_one_real))))) (@ _let_1 A2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G2))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X3 tptp.int)) (= (@ G2 X3) tptp.one_one_rat))))) (@ _let_1 A2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (= (@ G2 X3) tptp.one_one_rat))))) (@ _let_1 A2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups2245840878043517529at_rat G2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ tptp.collec4429806609662206161d_enat (lambda ((X3 tptp.extended_enat)) (= (@ G2 X3) tptp.one_one_rat))))) (@ _let_1 A2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (G2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G2))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X3 tptp.int)) (= (@ G2 X3) tptp.one_one_nat))))) (@ _let_1 A2))))))
% 5.98/6.29 (assert (forall ((I5 tptp.set_o) (I Bool) (F (-> Bool tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_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.one_one_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups234877984723959775o_real F) I5)))))))))
% 5.98/6.29 (assert (forall ((I5 tptp.set_nat) (I tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_nat I5) (=> (@ (@ tptp.member_nat I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups129246275422532515t_real F) I5)))))))))
% 5.98/6.29 (assert (forall ((I5 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_int 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.one_one_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups2316167850115554303t_real F) I5)))))))))
% 5.98/6.29 (assert (forall ((I5 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_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.one_one_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups766887009212190081x_real F) I5)))))))))
% 5.98/6.29 (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.one_one_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.one_one_real) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups97031904164794029t_real F) I5)))))))))
% 5.98/6.29 (assert (forall ((I5 tptp.set_o) (I Bool) (F (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_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.one_one_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups2869687844427037835_o_rat F) I5)))))))))
% 5.98/6.29 (assert (forall ((I5 tptp.set_nat) (I tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite_finite_nat 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.one_one_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups73079841787564623at_rat F) I5)))))))))
% 5.98/6.29 (assert (forall ((I5 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite_finite_int 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.one_one_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups1072433553688619179nt_rat F) I5)))))))))
% 5.98/6.29 (assert (forall ((I5 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_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.one_one_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups225925009352817453ex_rat F) I5)))))))))
% 5.98/6.29 (assert (forall ((I5 tptp.set_Extended_enat) (I tptp.extended_enat) (F (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ 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_rat tptp.one_one_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups2245840878043517529at_rat F) I5)))))))))
% 5.98/6.29 (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.one_one_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups766887009212190081x_real F) I5)))))))
% 5.98/6.29 (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.one_one_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups97031904164794029t_real F) I5)))))))
% 5.98/6.29 (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.one_one_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups1681761925125756287l_real F) I5)))))))
% 5.98/6.29 (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.one_one_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups234877984723959775o_real F) I5)))))))
% 5.98/6.29 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat I5) (=> (not (= I5 tptp.bot_bot_set_nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups129246275422532515t_real F) I5)))))))
% 5.98/6.29 (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.one_one_real) (@ F I2)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups2316167850115554303t_real F) I5)))))))
% 5.98/6.29 (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.one_one_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups225925009352817453ex_rat F) I5)))))))
% 5.98/6.29 (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.one_one_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups2245840878043517529at_rat F) I5)))))))
% 5.98/6.29 (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.one_one_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups4061424788464935467al_rat F) I5)))))))
% 5.98/6.29 (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.one_one_rat) (@ F I2)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups2869687844427037835_o_rat F) I5)))))))
% 5.98/6.29 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G2))) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B2))) (@ _let_1 B2))))))))
% 5.98/6.29 (assert (forall ((B2 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real G2))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B2) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B2))) (@ _let_1 B2))))))))
% 5.98/6.29 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G2))) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B2))) (@ _let_1 B2))))))))
% 5.98/6.29 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G2))) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B2))) (@ _let_1 B2))))))))
% 5.98/6.29 (assert (forall ((B2 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups2245840878043517529at_rat G2))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B2) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B2))) (@ _let_1 B2))))))))
% 5.98/6.29 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G2))) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B2))) (@ _let_1 B2))))))))
% 5.98/6.29 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (G2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G2))) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B2))) (@ _let_1 B2))))))))
% 5.98/6.29 (assert (forall ((B2 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2880970938130013265at_nat G2))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B2) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B2))) (@ _let_1 B2))))))))
% 5.98/6.29 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (G2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G2))) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B2))) (@ _let_1 B2))))))))
% 5.98/6.29 (assert (forall ((B2 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2878480467620962989at_int G2))) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B2) A2) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) B2))) (@ _let_1 B2))))))))
% 5.98/6.29 (assert (forall ((C2 tptp.set_o) (A2 tptp.set_o) (B2 tptp.set_o) (G2 (-> Bool tptp.complex)) (H (-> Bool tptp.complex))) (let ((_let_1 (@ tptp.groups4859619685533338977omplex H))) (let ((_let_2 (@ tptp.groups4859619685533338977omplex G2))) (=> (@ tptp.finite_finite_o C2) (=> (@ (@ tptp.ord_less_eq_set_o A2) C2) (=> (@ (@ tptp.ord_less_eq_set_o B2) C2) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) (@ (@ tptp.minus_minus_set_o C2) A2)) (= (@ G2 A5) tptp.one_one_complex))) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) (@ (@ tptp.minus_minus_set_o C2) B2)) (= (@ H B5) tptp.one_one_complex))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 5.98/6.29 (assert (forall ((C2 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G2 (-> tptp.complex tptp.complex)) (H (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex H))) (let ((_let_2 (@ tptp.groups3708469109370488835omplex G2))) (=> (@ tptp.finite3207457112153483333omplex C2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C2) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C2) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex C2) A2)) (= (@ G2 A5) tptp.one_one_complex))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex C2) B2)) (= (@ H B5) tptp.one_one_complex))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 5.98/6.29 (assert (forall ((C2 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.complex)) (H (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ tptp.groups4622424608036095791omplex H))) (let ((_let_2 (@ tptp.groups4622424608036095791omplex G2))) (=> (@ tptp.finite4001608067531595151d_enat C2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B2) C2) (=> (forall ((A5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A5) (@ (@ tptp.minus_925952699566721837d_enat C2) A2)) (= (@ G2 A5) tptp.one_one_complex))) (=> (forall ((B5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B5) (@ (@ tptp.minus_925952699566721837d_enat C2) B2)) (= (@ H B5) tptp.one_one_complex))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 5.98/6.29 (assert (forall ((C2 tptp.set_o) (A2 tptp.set_o) (B2 tptp.set_o) (G2 (-> Bool tptp.real)) (H (-> Bool tptp.real))) (let ((_let_1 (@ tptp.groups234877984723959775o_real H))) (let ((_let_2 (@ tptp.groups234877984723959775o_real G2))) (=> (@ tptp.finite_finite_o C2) (=> (@ (@ tptp.ord_less_eq_set_o A2) C2) (=> (@ (@ tptp.ord_less_eq_set_o B2) C2) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) (@ (@ tptp.minus_minus_set_o C2) A2)) (= (@ G2 A5) tptp.one_one_real))) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) (@ (@ tptp.minus_minus_set_o C2) B2)) (= (@ H B5) tptp.one_one_real))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 5.98/6.29 (assert (forall ((C2 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G2 (-> tptp.complex tptp.real)) (H (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real H))) (let ((_let_2 (@ tptp.groups766887009212190081x_real G2))) (=> (@ tptp.finite3207457112153483333omplex C2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C2) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C2) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex C2) A2)) (= (@ G2 A5) tptp.one_one_real))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex C2) B2)) (= (@ H B5) tptp.one_one_real))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 5.98/6.29 (assert (forall ((C2 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.real)) (H (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real H))) (let ((_let_2 (@ tptp.groups97031904164794029t_real G2))) (=> (@ tptp.finite4001608067531595151d_enat C2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B2) C2) (=> (forall ((A5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A5) (@ (@ tptp.minus_925952699566721837d_enat C2) A2)) (= (@ G2 A5) tptp.one_one_real))) (=> (forall ((B5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B5) (@ (@ tptp.minus_925952699566721837d_enat C2) B2)) (= (@ H B5) tptp.one_one_real))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 5.98/6.29 (assert (forall ((C2 tptp.set_o) (A2 tptp.set_o) (B2 tptp.set_o) (G2 (-> Bool tptp.rat)) (H (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups2869687844427037835_o_rat H))) (let ((_let_2 (@ tptp.groups2869687844427037835_o_rat G2))) (=> (@ tptp.finite_finite_o C2) (=> (@ (@ tptp.ord_less_eq_set_o A2) C2) (=> (@ (@ tptp.ord_less_eq_set_o B2) C2) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) (@ (@ tptp.minus_minus_set_o C2) A2)) (= (@ G2 A5) tptp.one_one_rat))) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) (@ (@ tptp.minus_minus_set_o C2) B2)) (= (@ H B5) tptp.one_one_rat))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 5.98/6.29 (assert (forall ((C2 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G2 (-> tptp.complex tptp.rat)) (H (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat H))) (let ((_let_2 (@ tptp.groups225925009352817453ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex C2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C2) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C2) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex C2) A2)) (= (@ G2 A5) tptp.one_one_rat))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex C2) B2)) (= (@ H B5) tptp.one_one_rat))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 5.98/6.29 (assert (forall ((C2 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.rat)) (H (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups2245840878043517529at_rat H))) (let ((_let_2 (@ tptp.groups2245840878043517529at_rat G2))) (=> (@ tptp.finite4001608067531595151d_enat C2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B2) C2) (=> (forall ((A5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A5) (@ (@ tptp.minus_925952699566721837d_enat C2) A2)) (= (@ G2 A5) tptp.one_one_rat))) (=> (forall ((B5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B5) (@ (@ tptp.minus_925952699566721837d_enat C2) B2)) (= (@ H B5) tptp.one_one_rat))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 5.98/6.29 (assert (forall ((C2 tptp.set_o) (A2 tptp.set_o) (B2 tptp.set_o) (G2 (-> Bool tptp.nat)) (H (-> Bool tptp.nat))) (let ((_let_1 (@ tptp.groups3504817904513533571_o_nat H))) (let ((_let_2 (@ tptp.groups3504817904513533571_o_nat G2))) (=> (@ tptp.finite_finite_o C2) (=> (@ (@ tptp.ord_less_eq_set_o A2) C2) (=> (@ (@ tptp.ord_less_eq_set_o B2) C2) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) (@ (@ tptp.minus_minus_set_o C2) A2)) (= (@ G2 A5) tptp.one_one_nat))) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) (@ (@ tptp.minus_minus_set_o C2) B2)) (= (@ H B5) tptp.one_one_nat))) (= (= (@ _let_2 A2) (@ _let_1 B2)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 5.98/6.29 (assert (forall ((C2 tptp.set_o) (A2 tptp.set_o) (B2 tptp.set_o) (G2 (-> Bool tptp.complex)) (H (-> Bool tptp.complex))) (let ((_let_1 (@ tptp.groups4859619685533338977omplex H))) (let ((_let_2 (@ tptp.groups4859619685533338977omplex G2))) (=> (@ tptp.finite_finite_o C2) (=> (@ (@ tptp.ord_less_eq_set_o A2) C2) (=> (@ (@ tptp.ord_less_eq_set_o B2) C2) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) (@ (@ tptp.minus_minus_set_o C2) A2)) (= (@ G2 A5) tptp.one_one_complex))) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) (@ (@ tptp.minus_minus_set_o C2) B2)) (= (@ H B5) tptp.one_one_complex))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 5.98/6.29 (assert (forall ((C2 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G2 (-> tptp.complex tptp.complex)) (H (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex H))) (let ((_let_2 (@ tptp.groups3708469109370488835omplex G2))) (=> (@ tptp.finite3207457112153483333omplex C2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C2) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C2) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex C2) A2)) (= (@ G2 A5) tptp.one_one_complex))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex C2) B2)) (= (@ H B5) tptp.one_one_complex))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 5.98/6.29 (assert (forall ((C2 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.complex)) (H (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ tptp.groups4622424608036095791omplex H))) (let ((_let_2 (@ tptp.groups4622424608036095791omplex G2))) (=> (@ tptp.finite4001608067531595151d_enat C2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B2) C2) (=> (forall ((A5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A5) (@ (@ tptp.minus_925952699566721837d_enat C2) A2)) (= (@ G2 A5) tptp.one_one_complex))) (=> (forall ((B5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B5) (@ (@ tptp.minus_925952699566721837d_enat C2) B2)) (= (@ H B5) tptp.one_one_complex))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 5.98/6.29 (assert (forall ((C2 tptp.set_o) (A2 tptp.set_o) (B2 tptp.set_o) (G2 (-> Bool tptp.real)) (H (-> Bool tptp.real))) (let ((_let_1 (@ tptp.groups234877984723959775o_real H))) (let ((_let_2 (@ tptp.groups234877984723959775o_real G2))) (=> (@ tptp.finite_finite_o C2) (=> (@ (@ tptp.ord_less_eq_set_o A2) C2) (=> (@ (@ tptp.ord_less_eq_set_o B2) C2) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) (@ (@ tptp.minus_minus_set_o C2) A2)) (= (@ G2 A5) tptp.one_one_real))) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) (@ (@ tptp.minus_minus_set_o C2) B2)) (= (@ H B5) tptp.one_one_real))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 5.98/6.29 (assert (forall ((C2 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G2 (-> tptp.complex tptp.real)) (H (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real H))) (let ((_let_2 (@ tptp.groups766887009212190081x_real G2))) (=> (@ tptp.finite3207457112153483333omplex C2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C2) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C2) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex C2) A2)) (= (@ G2 A5) tptp.one_one_real))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex C2) B2)) (= (@ H B5) tptp.one_one_real))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 5.98/6.29 (assert (forall ((C2 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.real)) (H (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real H))) (let ((_let_2 (@ tptp.groups97031904164794029t_real G2))) (=> (@ tptp.finite4001608067531595151d_enat C2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B2) C2) (=> (forall ((A5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A5) (@ (@ tptp.minus_925952699566721837d_enat C2) A2)) (= (@ G2 A5) tptp.one_one_real))) (=> (forall ((B5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B5) (@ (@ tptp.minus_925952699566721837d_enat C2) B2)) (= (@ H B5) tptp.one_one_real))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 5.98/6.29 (assert (forall ((C2 tptp.set_o) (A2 tptp.set_o) (B2 tptp.set_o) (G2 (-> Bool tptp.rat)) (H (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups2869687844427037835_o_rat H))) (let ((_let_2 (@ tptp.groups2869687844427037835_o_rat G2))) (=> (@ tptp.finite_finite_o C2) (=> (@ (@ tptp.ord_less_eq_set_o A2) C2) (=> (@ (@ tptp.ord_less_eq_set_o B2) C2) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) (@ (@ tptp.minus_minus_set_o C2) A2)) (= (@ G2 A5) tptp.one_one_rat))) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) (@ (@ tptp.minus_minus_set_o C2) B2)) (= (@ H B5) tptp.one_one_rat))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 5.98/6.29 (assert (forall ((C2 tptp.set_complex) (A2 tptp.set_complex) (B2 tptp.set_complex) (G2 (-> tptp.complex tptp.rat)) (H (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat H))) (let ((_let_2 (@ tptp.groups225925009352817453ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex C2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C2) (=> (@ (@ tptp.ord_le211207098394363844omplex B2) C2) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex C2) A2)) (= (@ G2 A5) tptp.one_one_rat))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex C2) B2)) (= (@ H B5) tptp.one_one_rat))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 5.98/6.29 (assert (forall ((C2 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (B2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.rat)) (H (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups2245840878043517529at_rat H))) (let ((_let_2 (@ tptp.groups2245840878043517529at_rat G2))) (=> (@ tptp.finite4001608067531595151d_enat C2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) C2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat B2) C2) (=> (forall ((A5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A5) (@ (@ tptp.minus_925952699566721837d_enat C2) A2)) (= (@ G2 A5) tptp.one_one_rat))) (=> (forall ((B5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B5) (@ (@ tptp.minus_925952699566721837d_enat C2) B2)) (= (@ H B5) tptp.one_one_rat))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 5.98/6.29 (assert (forall ((C2 tptp.set_o) (A2 tptp.set_o) (B2 tptp.set_o) (G2 (-> Bool tptp.nat)) (H (-> Bool tptp.nat))) (let ((_let_1 (@ tptp.groups3504817904513533571_o_nat H))) (let ((_let_2 (@ tptp.groups3504817904513533571_o_nat G2))) (=> (@ tptp.finite_finite_o C2) (=> (@ (@ tptp.ord_less_eq_set_o A2) C2) (=> (@ (@ tptp.ord_less_eq_set_o B2) C2) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) (@ (@ tptp.minus_minus_set_o C2) A2)) (= (@ G2 A5) tptp.one_one_nat))) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) (@ (@ tptp.minus_minus_set_o C2) B2)) (= (@ H B5) tptp.one_one_nat))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A2) (@ _let_1 B2))))))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G2))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G2 X4) tptp.one_one_complex))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ tptp.groups4622424608036095791omplex G2))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G2 X4) tptp.one_one_complex))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G2))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G2 X4) tptp.one_one_real))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real G2))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G2 X4) tptp.one_one_real))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G2 X4) tptp.one_one_rat))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups2245840878043517529at_rat G2))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G2 X4) tptp.one_one_rat))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G2))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G2 X4) tptp.one_one_nat))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2880970938130013265at_nat G2))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G2 X4) tptp.one_one_nat))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G2))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G2 X4) tptp.one_one_int))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2878480467620962989at_int G2))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G2 X4) tptp.one_one_int))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G2 (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G2))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G2 X4) tptp.one_one_complex))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.complex))) (let ((_let_1 (@ tptp.groups4622424608036095791omplex G2))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G2 X4) tptp.one_one_complex))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G2))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G2 X4) tptp.one_one_real))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real G2))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G2 X4) tptp.one_one_real))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G2 X4) tptp.one_one_rat))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups2245840878043517529at_rat G2))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G2 X4) tptp.one_one_rat))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G2))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G2 X4) tptp.one_one_nat))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2880970938130013265at_nat G2))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G2 X4) tptp.one_one_nat))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G2))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G2 X4) tptp.one_one_int))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.int))) (let ((_let_1 (@ tptp.groups2878480467620962989at_int G2))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G2 X4) tptp.one_one_int))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_o) (S2 tptp.set_o) (H (-> Bool tptp.complex)) (G2 (-> Bool tptp.complex))) (=> (@ tptp.finite_finite_o T3) (=> (@ (@ tptp.ord_less_eq_set_o S2) T3) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) (@ (@ tptp.minus_minus_set_o T3) S2)) (= (@ H X4) tptp.one_one_complex))) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) S2) (= (@ G2 X4) (@ H X4)))) (= (@ (@ tptp.groups4859619685533338977omplex G2) S2) (@ (@ tptp.groups4859619685533338977omplex H) T3))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (H (-> tptp.complex tptp.complex)) (G2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ H X4) tptp.one_one_complex))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S2) (= (@ G2 X4) (@ H X4)))) (= (@ (@ tptp.groups3708469109370488835omplex G2) S2) (@ (@ tptp.groups3708469109370488835omplex H) T3))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (H (-> tptp.extended_enat tptp.complex)) (G2 (-> tptp.extended_enat tptp.complex))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ H X4) tptp.one_one_complex))) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) S2) (= (@ G2 X4) (@ H X4)))) (= (@ (@ tptp.groups4622424608036095791omplex G2) S2) (@ (@ tptp.groups4622424608036095791omplex H) T3))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_o) (S2 tptp.set_o) (H (-> Bool tptp.real)) (G2 (-> Bool tptp.real))) (=> (@ tptp.finite_finite_o T3) (=> (@ (@ tptp.ord_less_eq_set_o S2) T3) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) (@ (@ tptp.minus_minus_set_o T3) S2)) (= (@ H X4) tptp.one_one_real))) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) S2) (= (@ G2 X4) (@ H X4)))) (= (@ (@ tptp.groups234877984723959775o_real G2) S2) (@ (@ tptp.groups234877984723959775o_real H) T3))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (H (-> tptp.complex tptp.real)) (G2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ H X4) tptp.one_one_real))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S2) (= (@ G2 X4) (@ H X4)))) (= (@ (@ tptp.groups766887009212190081x_real G2) S2) (@ (@ tptp.groups766887009212190081x_real H) T3))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (H (-> tptp.extended_enat tptp.real)) (G2 (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ H X4) tptp.one_one_real))) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) S2) (= (@ G2 X4) (@ H X4)))) (= (@ (@ tptp.groups97031904164794029t_real G2) S2) (@ (@ tptp.groups97031904164794029t_real H) T3))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_o) (S2 tptp.set_o) (H (-> Bool tptp.rat)) (G2 (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o T3) (=> (@ (@ tptp.ord_less_eq_set_o S2) T3) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) (@ (@ tptp.minus_minus_set_o T3) S2)) (= (@ H X4) tptp.one_one_rat))) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) S2) (= (@ G2 X4) (@ H X4)))) (= (@ (@ tptp.groups2869687844427037835_o_rat G2) S2) (@ (@ tptp.groups2869687844427037835_o_rat H) T3))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (H (-> tptp.complex tptp.rat)) (G2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ H X4) tptp.one_one_rat))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S2) (= (@ G2 X4) (@ H X4)))) (= (@ (@ tptp.groups225925009352817453ex_rat G2) S2) (@ (@ tptp.groups225925009352817453ex_rat H) T3))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (H (-> tptp.extended_enat tptp.rat)) (G2 (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ H X4) tptp.one_one_rat))) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) S2) (= (@ G2 X4) (@ H X4)))) (= (@ (@ tptp.groups2245840878043517529at_rat G2) S2) (@ (@ tptp.groups2245840878043517529at_rat H) T3))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_o) (S2 tptp.set_o) (H (-> Bool tptp.nat)) (G2 (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o T3) (=> (@ (@ tptp.ord_less_eq_set_o S2) T3) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) (@ (@ tptp.minus_minus_set_o T3) S2)) (= (@ H X4) tptp.one_one_nat))) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) S2) (= (@ G2 X4) (@ H X4)))) (= (@ (@ tptp.groups3504817904513533571_o_nat G2) S2) (@ (@ tptp.groups3504817904513533571_o_nat H) T3))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_o) (S2 tptp.set_o) (G2 (-> Bool tptp.complex)) (H (-> Bool tptp.complex))) (=> (@ tptp.finite_finite_o T3) (=> (@ (@ tptp.ord_less_eq_set_o S2) T3) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) (@ (@ tptp.minus_minus_set_o T3) S2)) (= (@ G2 X4) tptp.one_one_complex))) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) S2) (= (@ G2 X4) (@ H X4)))) (= (@ (@ tptp.groups4859619685533338977omplex G2) T3) (@ (@ tptp.groups4859619685533338977omplex H) S2))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G2 (-> tptp.complex tptp.complex)) (H (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G2 X4) tptp.one_one_complex))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S2) (= (@ G2 X4) (@ H X4)))) (= (@ (@ tptp.groups3708469109370488835omplex G2) T3) (@ (@ tptp.groups3708469109370488835omplex H) S2))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.complex)) (H (-> tptp.extended_enat tptp.complex))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G2 X4) tptp.one_one_complex))) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) S2) (= (@ G2 X4) (@ H X4)))) (= (@ (@ tptp.groups4622424608036095791omplex G2) T3) (@ (@ tptp.groups4622424608036095791omplex H) S2))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_o) (S2 tptp.set_o) (G2 (-> Bool tptp.real)) (H (-> Bool tptp.real))) (=> (@ tptp.finite_finite_o T3) (=> (@ (@ tptp.ord_less_eq_set_o S2) T3) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) (@ (@ tptp.minus_minus_set_o T3) S2)) (= (@ G2 X4) tptp.one_one_real))) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) S2) (= (@ G2 X4) (@ H X4)))) (= (@ (@ tptp.groups234877984723959775o_real G2) T3) (@ (@ tptp.groups234877984723959775o_real H) S2))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G2 (-> tptp.complex tptp.real)) (H (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G2 X4) tptp.one_one_real))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S2) (= (@ G2 X4) (@ H X4)))) (= (@ (@ tptp.groups766887009212190081x_real G2) T3) (@ (@ tptp.groups766887009212190081x_real H) S2))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.real)) (H (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G2 X4) tptp.one_one_real))) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) S2) (= (@ G2 X4) (@ H X4)))) (= (@ (@ tptp.groups97031904164794029t_real G2) T3) (@ (@ tptp.groups97031904164794029t_real H) S2))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_o) (S2 tptp.set_o) (G2 (-> Bool tptp.rat)) (H (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o T3) (=> (@ (@ tptp.ord_less_eq_set_o S2) T3) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) (@ (@ tptp.minus_minus_set_o T3) S2)) (= (@ G2 X4) tptp.one_one_rat))) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) S2) (= (@ G2 X4) (@ H X4)))) (= (@ (@ tptp.groups2869687844427037835_o_rat G2) T3) (@ (@ tptp.groups2869687844427037835_o_rat H) S2))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G2 (-> tptp.complex tptp.rat)) (H (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G2 X4) tptp.one_one_rat))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S2) (= (@ G2 X4) (@ H X4)))) (= (@ (@ tptp.groups225925009352817453ex_rat G2) T3) (@ (@ tptp.groups225925009352817453ex_rat H) S2))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_Extended_enat) (S2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.rat)) (H (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat T3) (=> (@ (@ tptp.ord_le7203529160286727270d_enat S2) T3) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ (@ tptp.minus_925952699566721837d_enat T3) S2)) (= (@ G2 X4) tptp.one_one_rat))) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) S2) (= (@ G2 X4) (@ H X4)))) (= (@ (@ tptp.groups2245840878043517529at_rat G2) T3) (@ (@ tptp.groups2245840878043517529at_rat H) S2))))))))
% 5.98/6.29 (assert (forall ((T3 tptp.set_o) (S2 tptp.set_o) (G2 (-> Bool tptp.nat)) (H (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o T3) (=> (@ (@ tptp.ord_less_eq_set_o S2) T3) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) (@ (@ tptp.minus_minus_set_o T3) S2)) (= (@ G2 X4) tptp.one_one_nat))) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) S2) (= (@ G2 X4) (@ H X4)))) (= (@ (@ tptp.groups3504817904513533571_o_nat G2) T3) (@ (@ tptp.groups3504817904513533571_o_nat H) S2))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((I2 tptp.complex)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_complex I2) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G2 I2)))))) (=> (not (= A2 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups766887009212190081x_real F) A2)) (@ (@ tptp.groups766887009212190081x_real G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (G2 (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((I2 tptp.extended_enat)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_Extended_enat I2) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G2 I2)))))) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups97031904164794029t_real F) A2)) (@ (@ tptp.groups97031904164794029t_real G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((I2 tptp.real)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_real I2) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G2 I2)))))) (=> (not (= A2 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups1681761925125756287l_real F) A2)) (@ (@ tptp.groups1681761925125756287l_real G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.real)) (G2 (-> Bool tptp.real))) (=> (@ tptp.finite_finite_o A2) (=> (forall ((I2 Bool)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_o I2) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G2 I2)))))) (=> (not (= A2 tptp.bot_bot_set_o)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups234877984723959775o_real F) A2)) (@ (@ tptp.groups234877984723959775o_real G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_nat I2) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G2 I2)))))) (=> (not (= A2 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups129246275422532515t_real F) A2)) (@ (@ tptp.groups129246275422532515t_real G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((I2 tptp.int)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_int I2) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G2 I2)))))) (=> (not (= A2 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups2316167850115554303t_real F) A2)) (@ (@ tptp.groups2316167850115554303t_real G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((I2 tptp.complex)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_complex I2) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G2 I2)))))) (=> (not (= A2 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups225925009352817453ex_rat F) A2)) (@ (@ tptp.groups225925009352817453ex_rat G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat)) (G2 (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((I2 tptp.extended_enat)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_Extended_enat I2) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G2 I2)))))) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2245840878043517529at_rat F) A2)) (@ (@ tptp.groups2245840878043517529at_rat G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat)) (G2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((I2 tptp.real)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_real I2) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G2 I2)))))) (=> (not (= A2 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups4061424788464935467al_rat F) A2)) (@ (@ tptp.groups4061424788464935467al_rat G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.rat)) (G2 (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o A2) (=> (forall ((I2 Bool)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_o I2) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G2 I2)))))) (=> (not (= A2 tptp.bot_bot_set_o)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2869687844427037835_o_rat F) A2)) (@ (@ tptp.groups2869687844427037835_o_rat G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (G2 (-> tptp.complex tptp.real)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups766887009212190081x_real G2))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.real)) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X))) (let ((_let_2 (@ tptp.groups97031904164794029t_real G2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_real) (G2 (-> tptp.real tptp.real)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups1681761925125756287l_real G2))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (G2 (-> Bool tptp.real)) (X Bool)) (let ((_let_1 (@ tptp.insert_o X))) (let ((_let_2 (@ tptp.groups234877984723959775o_real G2))) (=> (@ tptp.finite_finite_o A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_minus_set_o A2) (@ _let_1 tptp.bot_bot_set_o))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (G2 (-> tptp.int tptp.real)) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.groups2316167850115554303t_real G2))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (G2 (-> tptp.nat tptp.real)) (X tptp.nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G2))) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_minus_set_nat A2) (@ _let_1 tptp.bot_bot_set_nat))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (G2 (-> tptp.complex tptp.rat)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups225925009352817453ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.rat)) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.insert_Extended_enat X))) (let ((_let_2 (@ tptp.groups2245840878043517529at_rat G2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ _let_1 tptp.bot_bo7653980558646680370d_enat))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_real) (G2 (-> tptp.real tptp.rat)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups4061424788464935467al_rat G2))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (G2 (-> Bool tptp.rat)) (X Bool)) (let ((_let_1 (@ tptp.insert_o X))) (let ((_let_2 (@ tptp.groups2869687844427037835_o_rat G2))) (=> (@ tptp.finite_finite_o A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_2 (@ (@ tptp.minus_minus_set_o A2) (@ _let_1 tptp.bot_bot_set_o))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G2))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G2 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real G2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G2))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (X Bool) (G2 (-> Bool tptp.real))) (let ((_let_1 (@ tptp.groups234877984723959775o_real G2))) (=> (@ tptp.finite_finite_o A2) (=> (@ (@ tptp.member_o X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_minus_set_o A2) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G2))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G2))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G2 (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups2245840878043517529at_rat G2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.member_Extended_enat X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat X) tptp.bot_bo7653980558646680370d_enat))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat G2))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (X Bool) (G2 (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups2869687844427037835_o_rat G2))) (=> (@ tptp.finite_finite_o A2) (=> (@ (@ tptp.member_o X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_rat (@ G2 X)) (@ _let_1 (@ (@ tptp.minus_minus_set_o A2) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))))))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real)) (C (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.groups766887009212190081x_real C) (@ (@ tptp.minus_811609699411566653omplex S2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_2 (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S2) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S2) _let_1))))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B (-> tptp.extended_enat tptp.real)) (C (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ (@ tptp.groups97031904164794029t_real C) (@ (@ tptp.minus_925952699566721837d_enat S2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_2 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_2 (= (@ (@ tptp.groups97031904164794029t_real (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S2) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups97031904164794029t_real (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S2) _let_1))))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real)) (C (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.groups1681761925125756287l_real C) (@ (@ tptp.minus_minus_set_real S2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_2 (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S2) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S2) _let_1))))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_o) (A Bool) (B (-> Bool tptp.real)) (C (-> Bool tptp.real))) (let ((_let_1 (@ (@ tptp.groups234877984723959775o_real C) (@ (@ tptp.minus_minus_set_o S2) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o))))) (let ((_let_2 (@ (@ tptp.member_o A) S2))) (=> (@ tptp.finite_finite_o S2) (and (=> _let_2 (= (@ (@ tptp.groups234877984723959775o_real (lambda ((K3 Bool)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S2) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups234877984723959775o_real (lambda ((K3 Bool)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S2) _let_1))))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real)) (C (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.groups2316167850115554303t_real C) (@ (@ tptp.minus_minus_set_int S2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_2 (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S2) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S2) _let_1))))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.real)) (C (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.groups129246275422532515t_real C) (@ (@ tptp.minus_minus_set_nat S2) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_2 (@ (@ tptp.member_nat A) S2))) (=> (@ tptp.finite_finite_nat S2) (and (=> _let_2 (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S2) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S2) _let_1))))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.rat)) (C (-> tptp.complex tptp.rat))) (let ((_let_1 (@ (@ tptp.groups225925009352817453ex_rat C) (@ (@ tptp.minus_811609699411566653omplex S2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_2 (= (@ (@ tptp.groups225925009352817453ex_rat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C K3)))) S2) (@ (@ tptp.times_times_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups225925009352817453ex_rat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C K3)))) S2) _let_1))))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B (-> tptp.extended_enat tptp.rat)) (C (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ (@ tptp.groups2245840878043517529at_rat C) (@ (@ tptp.minus_925952699566721837d_enat S2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_2 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_2 (= (@ (@ tptp.groups2245840878043517529at_rat (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C K3)))) S2) (@ (@ tptp.times_times_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2245840878043517529at_rat (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C K3)))) S2) _let_1))))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.rat)) (C (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.groups4061424788464935467al_rat C) (@ (@ tptp.minus_minus_set_real S2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_2 (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C K3)))) S2) (@ (@ tptp.times_times_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C K3)))) S2) _let_1))))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_o) (A Bool) (B (-> Bool tptp.rat)) (C (-> Bool tptp.rat))) (let ((_let_1 (@ (@ tptp.groups2869687844427037835_o_rat C) (@ (@ tptp.minus_minus_set_o S2) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o))))) (let ((_let_2 (@ (@ tptp.member_o A) S2))) (=> (@ tptp.finite_finite_o S2) (and (=> _let_2 (= (@ (@ tptp.groups2869687844427037835_o_rat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C K3)))) S2) (@ (@ tptp.times_times_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2869687844427037835_o_rat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C K3)))) S2) _let_1))))))))
% 5.98/6.29 (assert (forall ((B2 tptp.set_o) (A2 tptp.set_o) (F (-> Bool tptp.real))) (let ((_let_1 (@ tptp.groups234877984723959775o_real F))) (=> (@ tptp.finite_finite_o B2) (=> (@ (@ tptp.ord_less_eq_set_o A2) B2) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) (@ (@ tptp.minus_minus_set_o B2) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B5)))) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A5)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2)))))))))
% 5.98/6.29 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex B2) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B5)))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A5)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2)))))))))
% 5.98/6.29 (assert (forall ((B2 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups97031904164794029t_real F))) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B2) (=> (forall ((B5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B5) (@ (@ tptp.minus_925952699566721837d_enat B2) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B5)))) (=> (forall ((A5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A5)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2)))))))))
% 5.98/6.29 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real F))) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (forall ((B5 tptp.nat)) (=> (@ (@ tptp.member_nat B5) (@ (@ tptp.minus_minus_set_nat B2) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B5)))) (=> (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A5)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B2)))))))))
% 5.98/6.29 (assert (forall ((B2 tptp.set_o) (A2 tptp.set_o) (F (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups2869687844427037835_o_rat F))) (=> (@ tptp.finite_finite_o B2) (=> (@ (@ tptp.ord_less_eq_set_o A2) B2) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) (@ (@ tptp.minus_minus_set_o B2) A2)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B5)))) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A5)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)))))))))
% 5.98/6.29 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex B2) A2)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B5)))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A5)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)))))))))
% 5.98/6.29 (assert (forall ((B2 tptp.set_Extended_enat) (A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups2245840878043517529at_rat F))) (=> (@ tptp.finite4001608067531595151d_enat B2) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A2) B2) (=> (forall ((B5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B5) (@ (@ tptp.minus_925952699566721837d_enat B2) A2)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B5)))) (=> (forall ((A5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A5) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A5)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)))))))))
% 5.98/6.29 (assert (forall ((B2 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat F))) (=> (@ tptp.finite_finite_nat B2) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B2) (=> (forall ((B5 tptp.nat)) (=> (@ (@ tptp.member_nat B5) (@ (@ tptp.minus_minus_set_nat B2) A2)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B5)))) (=> (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A5)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B2)))))))))
% 5.98/6.29 (assert (forall ((B2 tptp.set_o) (A2 tptp.set_o) (F (-> Bool tptp.int))) (let ((_let_1 (@ tptp.groups3502327434004483295_o_int F))) (=> (@ tptp.finite_finite_o B2) (=> (@ (@ tptp.ord_less_eq_set_o A2) B2) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) (@ (@ tptp.minus_minus_set_o B2) A2)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F B5)))) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F A5)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)))))))))
% 5.98/6.29 (assert (forall ((B2 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int F))) (=> (@ tptp.finite3207457112153483333omplex B2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B2) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex B2) A2)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F B5)))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F A5)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B2)))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.real)) (N tptp.real) (K tptp.nat)) (=> (forall ((I2 Bool)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_o I2) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o A2)) K) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups234877984723959775o_real F) A2)) (@ (@ tptp.power_power_real N) K)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (N tptp.real) (K tptp.nat)) (=> (forall ((I2 tptp.complex)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_complex I2) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A2)) K) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups766887009212190081x_real F) A2)) (@ (@ tptp.power_power_real N) K)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (N tptp.real) (K tptp.nat)) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_nat I2) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A2)) K) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups129246275422532515t_real F) A2)) (@ (@ tptp.power_power_real N) K)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (N tptp.real) (K tptp.nat)) (=> (forall ((I2 tptp.int)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_int I2) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A2)) K) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2316167850115554303t_real F) A2)) (@ (@ tptp.power_power_real N) K)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.rat)) (N tptp.rat) (K tptp.nat)) (=> (forall ((I2 Bool)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_o I2) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o A2)) K) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) N) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2869687844427037835_o_rat F) A2)) (@ (@ tptp.power_power_rat N) K)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (N tptp.rat) (K tptp.nat)) (=> (forall ((I2 tptp.complex)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_complex I2) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A2)) K) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) N) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups225925009352817453ex_rat F) A2)) (@ (@ tptp.power_power_rat N) K)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (N tptp.rat) (K tptp.nat)) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_nat I2) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A2)) K) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) N) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups73079841787564623at_rat F) A2)) (@ (@ tptp.power_power_rat N) K)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat)) (N tptp.rat) (K tptp.nat)) (=> (forall ((I2 tptp.int)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_int I2) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A2)) K) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) N) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A2)) (@ (@ tptp.power_power_rat N) K)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.nat)) (N tptp.nat) (K tptp.nat)) (=> (forall ((I2 Bool)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_o I2) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o A2)) K) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3504817904513533571_o_nat F) A2)) (@ (@ tptp.power_power_nat N) K)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (N tptp.nat) (K tptp.nat)) (=> (forall ((I2 tptp.complex)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_complex I2) A2) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) N))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_complex A2)) K) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (@ (@ tptp.power_power_nat N) K)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (A tptp.complex)) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= _let_5 tptp.zero_zero_rat)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_rat _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat)) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.groups2245840878043517529at_rat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_4 (@ (@ tptp.member_Extended_enat A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (= _let_5 tptp.zero_zero_rat)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_rat _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat)) (A tptp.real)) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_real A2) (=> (not (= _let_5 tptp.zero_zero_rat)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_rat _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.rat)) (A Bool)) (let ((_let_1 (@ tptp.groups2869687844427037835_o_rat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_o A2) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o))))) (let ((_let_4 (@ (@ tptp.member_o A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_o A2) (=> (not (= _let_5 tptp.zero_zero_rat)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_rat _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat)) (A tptp.int)) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_int A2) (=> (not (= _let_5 tptp.zero_zero_rat)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_rat _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (A tptp.nat)) (let ((_let_1 (@ tptp.groups73079841787564623at_rat F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_nat A2) (=> (not (= _let_5 tptp.zero_zero_rat)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_rat _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int)) (A tptp.complex)) (let ((_let_1 (@ tptp.groups858564598930262913ex_int F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= _let_5 tptp.zero_zero_int)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_int _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.int)) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.groups2878480467620962989at_int F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ (@ tptp.insert_Extended_enat A) tptp.bot_bo7653980558646680370d_enat))))) (let ((_let_4 (@ (@ tptp.member_Extended_enat A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (= _let_5 tptp.zero_zero_int)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_int _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.int)) (A tptp.real)) (let ((_let_1 (@ tptp.groups4694064378042380927al_int F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_real A2) (=> (not (= _let_5 tptp.zero_zero_int)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_int _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.int)) (A Bool)) (let ((_let_1 (@ tptp.groups3502327434004483295_o_int F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_o A2) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o))))) (let ((_let_4 (@ (@ tptp.member_o A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_o A2) (=> (not (= _let_5 tptp.zero_zero_int)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_int _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_o) (A Bool) (B (-> Bool tptp.complex)) (C tptp.complex)) (let ((_let_1 (@ tptp.finite_card_o S2))) (let ((_let_2 (@ tptp.power_power_complex C))) (let ((_let_3 (@ (@ tptp.member_o A) S2))) (=> (@ tptp.finite_finite_o S2) (and (=> _let_3 (= (@ (@ tptp.groups4859619685533338977omplex (lambda ((K3 Bool)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) C))) S2) (@ (@ tptp.times_times_complex (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups4859619685533338977omplex (lambda ((K3 Bool)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) C))) S2) (@ _let_2 _let_1))))))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex)) (C tptp.complex)) (let ((_let_1 (@ tptp.finite_card_nat S2))) (let ((_let_2 (@ tptp.power_power_complex C))) (let ((_let_3 (@ (@ tptp.member_nat A) S2))) (=> (@ tptp.finite_finite_nat S2) (and (=> _let_3 (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) C))) S2) (@ (@ tptp.times_times_complex (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) C))) S2) (@ _let_2 _let_1))))))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex)) (C tptp.complex)) (let ((_let_1 (@ tptp.finite_card_int S2))) (let ((_let_2 (@ tptp.power_power_complex C))) (let ((_let_3 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_3 (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) C))) S2) (@ (@ tptp.times_times_complex (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) C))) S2) (@ _let_2 _let_1))))))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.complex)) (C tptp.complex)) (let ((_let_1 (@ tptp.finite_card_complex S2))) (let ((_let_2 (@ tptp.power_power_complex C))) (let ((_let_3 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_3 (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) C))) S2) (@ (@ tptp.times_times_complex (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) C))) S2) (@ _let_2 _let_1))))))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B (-> tptp.extended_enat tptp.complex)) (C tptp.complex)) (let ((_let_1 (@ tptp.finite121521170596916366d_enat S2))) (let ((_let_2 (@ tptp.power_power_complex C))) (let ((_let_3 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_3 (= (@ (@ tptp.groups4622424608036095791omplex (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) C))) S2) (@ (@ tptp.times_times_complex (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups4622424608036095791omplex (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) C))) S2) (@ _let_2 _let_1))))))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_o) (A Bool) (B (-> Bool tptp.real)) (C tptp.real)) (let ((_let_1 (@ tptp.finite_card_o S2))) (let ((_let_2 (@ tptp.power_power_real C))) (let ((_let_3 (@ (@ tptp.member_o A) S2))) (=> (@ tptp.finite_finite_o S2) (and (=> _let_3 (= (@ (@ tptp.groups234877984723959775o_real (lambda ((K3 Bool)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) C))) S2) (@ (@ tptp.times_times_real (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups234877984723959775o_real (lambda ((K3 Bool)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) C))) S2) (@ _let_2 _let_1))))))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.real)) (C tptp.real)) (let ((_let_1 (@ tptp.finite_card_nat S2))) (let ((_let_2 (@ tptp.power_power_real C))) (let ((_let_3 (@ (@ tptp.member_nat A) S2))) (=> (@ tptp.finite_finite_nat S2) (and (=> _let_3 (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) C))) S2) (@ (@ tptp.times_times_real (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) C))) S2) (@ _let_2 _let_1))))))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real)) (C tptp.real)) (let ((_let_1 (@ tptp.finite_card_int S2))) (let ((_let_2 (@ tptp.power_power_real C))) (let ((_let_3 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_3 (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) C))) S2) (@ (@ tptp.times_times_real (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) C))) S2) (@ _let_2 _let_1))))))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real)) (C tptp.real)) (let ((_let_1 (@ tptp.finite_card_complex S2))) (let ((_let_2 (@ tptp.power_power_real C))) (let ((_let_3 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_3 (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) C))) S2) (@ (@ tptp.times_times_real (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) C))) S2) (@ _let_2 _let_1))))))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B (-> tptp.extended_enat tptp.real)) (C tptp.real)) (let ((_let_1 (@ tptp.finite121521170596916366d_enat S2))) (let ((_let_2 (@ tptp.power_power_real C))) (let ((_let_3 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_3 (= (@ (@ tptp.groups97031904164794029t_real (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) C))) S2) (@ (@ tptp.times_times_real (@ B A)) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))) (=> (not _let_3) (= (@ (@ tptp.groups97031904164794029t_real (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) C))) S2) (@ _let_2 _let_1))))))))))
% 5.98/6.29 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat)))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ring_1_of_int_real Y))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_real _let_2) (@ (@ tptp.plus_plus_real X) _let_1)) (= (@ tptp.archim8280529875227126926d_real X) Y)))))))
% 5.98/6.29 (assert (forall ((X tptp.rat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ring_1_of_int_rat Y))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_rat _let_2) (@ (@ tptp.plus_plus_rat X) _let_1)) (= (@ tptp.archim7778729529865785530nd_rat X) Y)))))))
% 5.98/6.29 (assert (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 5.98/6.29 (assert (= (@ tptp.neg_numeral_dbl_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))
% 5.98/6.29 (assert (= (@ tptp.neg_numeral_dbl_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 5.98/6.29 (assert (= (@ tptp.neg_numeral_dbl_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))
% 5.98/6.29 (assert (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ tptp.summable_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1)))))))))
% 5.98/6.29 (assert (= tptp.archim8280529875227126926d_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.archim2898591450579166408c_real X3))) (@ tptp.archim7802044766580827645g_real X3)) (@ tptp.archim6058952711729229775r_real X3)))))
% 5.98/6.29 (assert (= tptp.archim7778729529865785530nd_rat (lambda ((X3 tptp.rat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.archimedean_frac_rat X3))) (@ tptp.archim2889992004027027881ng_rat X3)) (@ tptp.archim3151403230148437115or_rat X3)))))
% 5.98/6.29 (assert (forall ((X tptp.rat) (N tptp.int)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X) (@ tptp.ring_1_of_int_rat N)))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim7778729529865785530nd_rat X) N))))
% 5.98/6.29 (assert (forall ((X tptp.real) (N tptp.int)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) (@ tptp.ring_1_of_int_real N)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim8280529875227126926d_real X) N))))
% 5.98/6.29 (assert (= (@ tptp.neg_numeral_dbl_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.29 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 5.98/6.29 (assert (= (@ tptp.neg_numeral_dbl_int tptp.zero_zero_int) tptp.zero_zero_int))
% 5.98/6.29 (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)))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (@ tptp.summable_real (lambda ((N4 tptp.nat)) tptp.zero_zero_real)))
% 5.98/6.29 (assert (@ tptp.summable_nat (lambda ((N4 tptp.nat)) tptp.zero_zero_nat)))
% 5.98/6.29 (assert (@ tptp.summable_int (lambda ((N4 tptp.nat)) tptp.zero_zero_int)))
% 5.98/6.29 (assert (= (@ tptp.archim8280529875227126926d_real tptp.zero_zero_real) tptp.zero_zero_int))
% 5.98/6.29 (assert (= (@ tptp.archim7778729529865785530nd_rat tptp.zero_zero_rat) tptp.zero_zero_int))
% 5.98/6.29 (assert (= (@ tptp.archim8280529875227126926d_real tptp.one_one_real) tptp.one_one_int))
% 5.98/6.29 (assert (= (@ tptp.archim7778729529865785530nd_rat tptp.one_one_rat) tptp.one_one_int))
% 5.98/6.29 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N4)))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))))
% 5.98/6.29 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit0 K)))))
% 5.98/6.29 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))
% 5.98/6.29 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 K)))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (= (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N4)) C))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))))
% 5.98/6.29 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K))) (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu8804712462038260780nteger _let_1))))))
% 5.98/6.29 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.neg_numeral_dbl_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_numeral_dbl_int _let_1))))))
% 5.98/6.29 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real K))) (= (@ tptp.neg_numeral_dbl_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_numeral_dbl_real _let_1))))))
% 5.98/6.29 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat K))) (= (@ tptp.neg_numeral_dbl_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_numeral_dbl_rat _let_1))))))
% 5.98/6.29 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K))) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu7009210354673126013omplex _let_1))))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A2) (@ tptp.summable_real (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_nat R5) A2)) (@ F R5)) tptp.zero_zero_real))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (@ tptp.summable_nat (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.member_nat R5) A2)) (@ F R5)) tptp.zero_zero_nat))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A2) (@ tptp.summable_int (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.member_nat R5) A2)) (@ F R5)) tptp.zero_zero_int))))))
% 5.98/6.29 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 5.98/6.29 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 5.98/6.29 (assert (= (@ tptp.neg_numeral_dbl_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 5.98/6.29 (assert (= (@ tptp.neg_numeral_dbl_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 5.98/6.29 (assert (= (@ tptp.neg_nu8804712462038260780nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N2))) (@ G2 N2))))) (=> (@ tptp.summable_real G2) (@ tptp.summable_real F)))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.complex)) (G2 (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N2))) (@ G2 N2))))) (=> (@ tptp.summable_real G2) (@ tptp.summable_complex F)))))
% 5.98/6.29 (assert (forall ((G2 (-> tptp.nat tptp.real)) (N5 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real G2) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N2))) (@ G2 N2)))) (@ tptp.summable_real F)))))
% 5.98/6.29 (assert (forall ((G2 (-> tptp.nat tptp.real)) (N5 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real G2) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N2))) (@ G2 N2)))) (@ tptp.summable_complex F)))))
% 5.98/6.29 (assert (forall ((C tptp.real)) (= (@ tptp.summable_real (lambda ((Uu3 tptp.nat)) C)) (= C tptp.zero_zero_real))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.real))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N2)) (@ G2 N2))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G2) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) (@ tptp.suminf_real G2)))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.nat)) (G2 (-> tptp.nat tptp.nat))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N2)) (@ G2 N2))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G2) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) (@ tptp.suminf_nat G2)))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.int)) (G2 (-> tptp.nat tptp.int))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N2)) (@ G2 N2))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G2) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) (@ tptp.suminf_int G2)))))))
% 5.98/6.29 (assert (forall ((N5 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat N5) (=> (forall ((N2 tptp.nat)) (=> (not (@ (@ tptp.member_nat N2) N5)) (= (@ F N2) tptp.zero_zero_real))) (@ tptp.summable_real F)))))
% 5.98/6.29 (assert (forall ((N5 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat N5) (=> (forall ((N2 tptp.nat)) (=> (not (@ (@ tptp.member_nat N2) N5)) (= (@ F N2) tptp.zero_zero_nat))) (@ tptp.summable_nat F)))))
% 5.98/6.29 (assert (forall ((N5 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat N5) (=> (forall ((N2 tptp.nat)) (=> (not (@ (@ tptp.member_nat N2) N5)) (= (@ F N2) tptp.zero_zero_int))) (@ tptp.summable_int F)))))
% 5.98/6.29 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N4)))) (=> (not (= C tptp.zero_zero_real)) (@ tptp.summable_real F)))))
% 5.98/6.29 (assert (@ tptp.summable_int (@ tptp.power_power_int tptp.zero_zero_int)))
% 5.98/6.29 (assert (@ tptp.summable_real (@ tptp.power_power_real tptp.zero_zero_real)))
% 5.98/6.29 (assert (@ tptp.summable_complex (@ tptp.power_power_complex tptp.zero_zero_complex)))
% 5.98/6.29 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.pi))
% 5.98/6.29 (assert (= tptp.neg_numeral_dbl_real (lambda ((X3 tptp.real)) (@ (@ tptp.plus_plus_real X3) X3))))
% 5.98/6.29 (assert (= tptp.neg_numeral_dbl_rat (lambda ((X3 tptp.rat)) (@ (@ tptp.plus_plus_rat X3) X3))))
% 5.98/6.29 (assert (= tptp.neg_numeral_dbl_int (lambda ((X3 tptp.int)) (@ (@ tptp.plus_plus_int X3) X3))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N2))) (= (= (@ tptp.suminf_real F) tptp.zero_zero_real) (forall ((N4 tptp.nat)) (= (@ F N4) tptp.zero_zero_real)))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N2))) (= (= (@ tptp.suminf_nat F) tptp.zero_zero_nat) (forall ((N4 tptp.nat)) (= (@ F N4) tptp.zero_zero_nat)))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N2))) (= (= (@ tptp.suminf_int F) tptp.zero_zero_int) (forall ((N4 tptp.nat)) (= (@ F N4) tptp.zero_zero_int)))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N2))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.suminf_real F))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N2))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N2))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.suminf_int F))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F N2))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.suminf_real F))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F N2))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F N2))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.suminf_int F))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N4))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F N4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N4))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.int))) (@ tptp.summable_int (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_int (@ F N4)) (@ (@ tptp.power_power_int tptp.zero_zero_int) N4))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N4))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F N4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N4))))))
% 5.98/6.29 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7778729529865785530nd_rat X)) (@ tptp.archim7778729529865785530nd_rat Y)))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.complex)) (G2 (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N2))) (@ G2 N2))))) (=> (@ tptp.summable_real G2) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N4))))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ F N2))) (@ G2 N2))))) (=> (@ tptp.summable_real G2) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ tptp.abs_abs_real (@ F N4))))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim8280529875227126926d_real X))))
% 5.98/6.29 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim7778729529865785530nd_rat X))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim8280529875227126926d_real X)) (@ tptp.archim7802044766580827645g_real X))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ tptp.abs_abs_real (@ F N4)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ tptp.abs_abs_real (@ F N4))))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N2))) (= (@ (@ 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))))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N2))) (= (@ (@ 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))))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N2))) (= (@ (@ 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))))))))
% 5.98/6.29 (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 ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N2))) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ tptp.suminf_real F))))))))
% 5.98/6.29 (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 ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N2))) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ tptp.suminf_nat F))))))))
% 5.98/6.29 (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 ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N2))) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ tptp.suminf_int F))))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ F (@ tptp.suc N4)))) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ F tptp.zero_zero_nat))))))
% 5.98/6.29 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F N4)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F N4))))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N4)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex F))) (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N4))))))))
% 5.98/6.29 (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)))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N4)) (@ (@ tptp.power_power_complex Z) N4)))) (= (@ tptp.suminf_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N4)) (@ (@ tptp.power_power_complex Z) N4)))) (@ (@ tptp.plus_plus_complex (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N4))) (@ (@ tptp.power_power_complex Z) N4))))) Z))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F N4)) (@ (@ tptp.power_power_real Z) N4)))) (= (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F N4)) (@ (@ tptp.power_power_real Z) N4)))) (@ (@ tptp.plus_plus_real (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N4))) (@ (@ tptp.power_power_real Z) N4))))) Z))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N4)) (@ (@ tptp.power_power_complex Z) N4)))) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N4))) (@ (@ tptp.power_power_complex Z) N4))))) Z) (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N4)) (@ (@ tptp.power_power_complex Z) N4))))) (@ F tptp.zero_zero_nat))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F N4)) (@ (@ tptp.power_power_real Z) N4)))) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N4))) (@ (@ tptp.power_power_real Z) N4))))) Z) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F N4)) (@ (@ tptp.power_power_real Z) N4))))) (@ F tptp.zero_zero_nat))))))
% 5.98/6.29 (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 ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) N6) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N6)))))) R2))))))))
% 5.98/6.29 (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 ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) N6) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N6)))))) R2))))))))
% 5.98/6.29 (assert (forall ((Z tptp.real) (M2 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 M2)))))))
% 5.98/6.29 (assert (forall ((Z tptp.rat) (M2 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 M2)))))))
% 5.98/6.29 (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))))))))))
% 5.98/6.29 (assert (forall ((R2 tptp.real) (R0 tptp.real) (A (-> tptp.nat tptp.complex)) (M5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R2) (=> (@ (@ tptp.ord_less_real R2) R0) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex (@ A N2))) (@ (@ tptp.power_power_real R0) N2))) M5)) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex (@ A N4))) (@ (@ tptp.power_power_real R2) N4)))))))))
% 5.98/6.29 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 5.98/6.29 (assert (forall ((C tptp.real) (N5 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real C) tptp.one_one_real) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F (@ tptp.suc N2)))) (@ (@ tptp.times_times_real C) (@ tptp.real_V7735802525324610683m_real (@ F N2)))))) (@ tptp.summable_real F)))))
% 5.98/6.29 (assert (forall ((C tptp.real) (N5 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real C) tptp.one_one_real) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F (@ tptp.suc N2)))) (@ (@ tptp.times_times_real C) (@ tptp.real_V1022390504157884413omplex (@ F N2)))))) (@ tptp.summable_complex F)))))
% 5.98/6.29 (assert (= tptp.archim8280529875227126926d_real (lambda ((X3 tptp.real)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 5.98/6.29 (assert (= tptp.archim7778729529865785530nd_rat (lambda ((X3 tptp.rat)) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X3) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X))) (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 5.98/6.29 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X))) (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X)))))
% 5.98/6.29 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X)))))
% 5.98/6.29 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X)))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X)))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X))) X))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 5.98/6.29 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X))) X))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_list_nat) (K tptp.nat)) (let ((_let_1 (@ tptp.finite_card_list_nat A2))) (=> (@ tptp.finite8100373058378681591st_nat A2) (=> (@ (@ tptp.ord_less_eq_nat K) _let_1) (= (@ tptp.finite7325466520557071688st_nat (@ tptp.collec5989764272469232197st_nat (lambda ((Xs2 tptp.list_list_nat)) (and (= (@ tptp.size_s3023201423986296836st_nat Xs2) K) (@ tptp.distinct_list_nat Xs2) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.set_list_nat2 Xs2)) A2))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K)) tptp.one_one_nat)) _let_1))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_set_nat) (K tptp.nat)) (let ((_let_1 (@ tptp.finite_card_set_nat A2))) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ (@ tptp.ord_less_eq_nat K) _let_1) (= (@ tptp.finite5631907774883551598et_nat (@ tptp.collect_list_set_nat (lambda ((Xs2 tptp.list_set_nat)) (and (= (@ tptp.size_s3254054031482475050et_nat Xs2) K) (@ tptp.distinct_set_nat Xs2) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 Xs2)) A2))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K)) tptp.one_one_nat)) _let_1))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (K tptp.nat)) (let ((_let_1 (@ tptp.finite_card_complex A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.ord_less_eq_nat K) _let_1) (= (@ tptp.finite5120063068150530198omplex (@ tptp.collect_list_complex (lambda ((Xs2 tptp.list_complex)) (and (= (@ tptp.size_s3451745648224563538omplex Xs2) K) (@ tptp.distinct_complex Xs2) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) A2))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K)) tptp.one_one_nat)) _let_1))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (K tptp.nat)) (let ((_let_1 (@ tptp.finite711546835091564841at_nat A2))) (=> (@ tptp.finite6177210948735845034at_nat A2) (=> (@ (@ tptp.ord_less_eq_nat K) _let_1) (= (@ tptp.finite249151656366948015at_nat (@ tptp.collec3343600615725829874at_nat (lambda ((Xs2 tptp.list_P6011104703257516679at_nat)) (and (= (@ tptp.size_s5460976970255530739at_nat Xs2) K) (@ tptp.distin6923225563576452346at_nat Xs2) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs2)) A2))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K)) tptp.one_one_nat)) _let_1))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (K tptp.nat)) (let ((_let_1 (@ tptp.finite121521170596916366d_enat A2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ (@ tptp.ord_less_eq_nat K) _let_1) (= (@ tptp.finite7441382602597825044d_enat (@ tptp.collec8433460942617342167d_enat (lambda ((Xs2 tptp.list_Extended_enat)) (and (= (@ tptp.size_s3941691890525107288d_enat Xs2) K) (@ tptp.distin4523846830085650399d_enat Xs2) (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.set_Extended_enat2 Xs2)) A2))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K)) tptp.one_one_nat)) _let_1))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_VEBT_VEBT) (K tptp.nat)) (let ((_let_1 (@ tptp.finite7802652506058667612T_VEBT A2))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (@ (@ tptp.ord_less_eq_nat K) _let_1) (= (@ tptp.finite5915292604075114978T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs2 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) K) (@ tptp.distinct_VEBT_VEBT Xs2) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) A2))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K)) tptp.one_one_nat)) _let_1))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (K tptp.nat)) (let ((_let_1 (@ tptp.finite_card_nat A2))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.ord_less_eq_nat K) _let_1) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((Xs2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs2) K) (@ tptp.distinct_nat Xs2) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) A2))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K)) tptp.one_one_nat)) _let_1))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (K tptp.nat)) (let ((_let_1 (@ tptp.finite_card_int A2))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.ord_less_eq_nat K) _let_1) (= (@ tptp.finite_card_list_int (@ tptp.collect_list_int (lambda ((Xs2 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs2) K) (@ tptp.distinct_int Xs2) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) A2))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat _let_1) K)) tptp.one_one_nat)) _let_1))))))))
% 5.98/6.29 (assert (= tptp.arcosh_real (lambda ((X3 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.powr_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat _let_1))) tptp.one_one_real)) (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))))))))))
% 5.98/6.29 (assert (= tptp.binomial (lambda ((N4 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N4) K3))) (let ((_let_2 (@ tptp.ord_less_nat N4))) (@ (@ (@ tptp.if_nat (@ _let_2 K3)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K3))) (@ (@ tptp.binomial N4) _let_1)) (@ (@ tptp.divide_divide_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N4) tptp.one_one_nat)) (@ tptp.semiri1408675320244567234ct_nat K3)))))))))
% 5.98/6.29 (assert (forall ((R1 (-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool)) (R22 (-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool))) (=> (@ (@ tptp.ord_le1077754993875142464_nat_o R1) R22) (@ (@ tptp.ord_le7812727212727832188_nat_o (@ tptp.accp_P2887432264394892906BT_nat R22)) (@ tptp.accp_P2887432264394892906BT_nat R1)))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (M2 tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))) (let ((_let_3 (= X tptp.one_one_complex))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M2))) (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)) M2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X)))))))))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (M2 tptp.nat) (X tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X))) (let ((_let_2 (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))) (let ((_let_3 (= X tptp.one_one_rat))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M2))) (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)) M2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X)))))))))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (M2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))) (let ((_let_3 (= X tptp.one_one_real))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M2))) (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)) M2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 M2)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_real tptp.one_one_real) X)))))))))))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) N) tptp.one_one_nat)))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Uu3 tptp.nat)) tptp.zero_zero_nat)) A2) tptp.zero_zero_nat)))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((Uu3 tptp.complex)) tptp.zero_zero_complex)) A2) tptp.zero_zero_complex)))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Uu3 tptp.int)) tptp.zero_zero_int)) A2) tptp.zero_zero_int)))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((Uu3 tptp.nat)) tptp.zero_zero_real)) A2) tptp.zero_zero_real)))
% 5.98/6.29 (assert (forall ((G2 (-> tptp.real tptp.real))) (= (@ (@ tptp.groups8097168146408367636l_real G2) tptp.bot_bot_set_real) tptp.zero_zero_real)))
% 5.98/6.29 (assert (forall ((G2 (-> tptp.real tptp.rat))) (= (@ (@ tptp.groups1300246762558778688al_rat G2) tptp.bot_bot_set_real) tptp.zero_zero_rat)))
% 5.98/6.29 (assert (forall ((G2 (-> tptp.real tptp.nat))) (= (@ (@ tptp.groups1935376822645274424al_nat G2) tptp.bot_bot_set_real) tptp.zero_zero_nat)))
% 5.98/6.29 (assert (forall ((G2 (-> tptp.real tptp.int))) (= (@ (@ tptp.groups1932886352136224148al_int G2) tptp.bot_bot_set_real) tptp.zero_zero_int)))
% 5.98/6.29 (assert (forall ((G2 (-> Bool tptp.real))) (= (@ (@ tptp.groups8691415230153176458o_real G2) tptp.bot_bot_set_o) tptp.zero_zero_real)))
% 5.98/6.29 (assert (forall ((G2 (-> Bool tptp.rat))) (= (@ (@ tptp.groups7872700643590313910_o_rat G2) tptp.bot_bot_set_o) tptp.zero_zero_rat)))
% 5.98/6.29 (assert (forall ((G2 (-> Bool tptp.nat))) (= (@ (@ tptp.groups8507830703676809646_o_nat G2) tptp.bot_bot_set_o) tptp.zero_zero_nat)))
% 5.98/6.29 (assert (forall ((G2 (-> Bool tptp.int))) (= (@ (@ tptp.groups8505340233167759370_o_int G2) tptp.bot_bot_set_o) tptp.zero_zero_int)))
% 5.98/6.29 (assert (forall ((G2 (-> tptp.nat tptp.rat))) (= (@ (@ tptp.groups2906978787729119204at_rat G2) tptp.bot_bot_set_nat) tptp.zero_zero_rat)))
% 5.98/6.29 (assert (forall ((G2 (-> tptp.nat tptp.int))) (= (@ (@ tptp.groups3539618377306564664at_int G2) tptp.bot_bot_set_nat) tptp.zero_zero_int)))
% 5.98/6.29 (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 ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) F2) (= (@ F X3) tptp.zero_zero_nat)))))))
% 5.98/6.29 (assert (forall ((F2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex F2) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) F2) tptp.zero_zero_nat) (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) F2) (= (@ F X3) tptp.zero_zero_nat)))))))
% 5.98/6.29 (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 ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) F2) (= (@ F X3) tptp.zero_zero_nat)))))))
% 5.98/6.29 (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 ((X3 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X3) F2) (= (@ F X3) tptp.zero_zero_nat)))))))
% 5.98/6.29 (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 ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) F2) (= (@ F X3) tptp.zero_zero_nat)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (G2 (-> tptp.int tptp.real))) (=> (not (@ tptp.finite_finite_int A2)) (= (@ (@ tptp.groups8778361861064173332t_real G2) A2) tptp.zero_zero_real))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (G2 (-> tptp.complex tptp.real))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups5808333547571424918x_real G2) A2) tptp.zero_zero_real))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.real))) (=> (not (@ tptp.finite4001608067531595151d_enat A2)) (= (@ (@ tptp.groups4148127829035722712t_real G2) A2) tptp.zero_zero_real))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (G2 (-> tptp.nat tptp.rat))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups2906978787729119204at_rat G2) A2) tptp.zero_zero_rat))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (G2 (-> tptp.int tptp.rat))) (=> (not (@ tptp.finite_finite_int A2)) (= (@ (@ tptp.groups3906332499630173760nt_rat G2) A2) tptp.zero_zero_rat))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (G2 (-> tptp.complex tptp.rat))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups5058264527183730370ex_rat G2) A2) tptp.zero_zero_rat))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.rat))) (=> (not (@ tptp.finite4001608067531595151d_enat A2)) (= (@ (@ tptp.groups1392844769737527556at_rat G2) A2) tptp.zero_zero_rat))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (G2 (-> tptp.int tptp.nat))) (=> (not (@ tptp.finite_finite_int A2)) (= (@ (@ tptp.groups4541462559716669496nt_nat G2) A2) tptp.zero_zero_nat))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (G2 (-> tptp.complex tptp.nat))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups5693394587270226106ex_nat G2) A2) tptp.zero_zero_nat))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.nat))) (=> (not (@ tptp.finite4001608067531595151d_enat A2)) (= (@ (@ tptp.groups2027974829824023292at_nat G2) A2) tptp.zero_zero_nat))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (= (= (@ tptp.real_V1803761363581548252l_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (= (= (@ tptp.real_V4546457046886955230omplex X) tptp.zero_zero_complex) (= X tptp.zero_zero_real))))
% 5.98/6.29 (assert (= (@ tptp.real_V1803761363581548252l_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.29 (assert (= (@ tptp.real_V4546457046886955230omplex tptp.zero_zero_real) tptp.zero_zero_complex))
% 5.98/6.29 (assert (forall ((X tptp.real)) (= (= (@ tptp.real_V1803761363581548252l_real X) tptp.one_one_real) (= X tptp.one_one_real))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (= (= (@ tptp.real_V4546457046886955230omplex X) tptp.one_one_complex) (= X tptp.one_one_real))))
% 5.98/6.29 (assert (= (@ tptp.real_V1803761363581548252l_real tptp.one_one_real) tptp.one_one_real))
% 5.98/6.29 (assert (= (@ tptp.real_V4546457046886955230omplex tptp.one_one_real) tptp.one_one_complex))
% 5.98/6.29 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.binomial tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) (@ tptp.suc tptp.zero_zero_nat)) N)))
% 5.98/6.29 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N) K))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.zero_zero_nat) tptp.one_one_nat)))
% 5.98/6.29 (assert (forall ((S2 tptp.set_o) (A Bool) (B (-> Bool tptp.real))) (let ((_let_1 (@ (@ tptp.member_o A) S2))) (=> (@ tptp.finite_finite_o S2) (and (=> _let_1 (= (@ (@ tptp.groups8691415230153176458o_real (lambda ((K3 Bool)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.zero_zero_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8691415230153176458o_real (lambda ((K3 Bool)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.zero_zero_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.zero_zero_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_1 (= (@ (@ tptp.groups4148127829035722712t_real (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.zero_zero_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups4148127829035722712t_real (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_o) (A Bool) (B (-> Bool tptp.rat))) (let ((_let_1 (@ (@ tptp.member_o A) S2))) (=> (@ tptp.finite_finite_o S2) (and (=> _let_1 (= (@ (@ tptp.groups7872700643590313910_o_rat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7872700643590313910_o_rat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S2) tptp.zero_zero_rat)))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.member_nat A) S2))) (=> (@ tptp.finite_finite_nat S2) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S2) tptp.zero_zero_rat)))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.rat))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S2) tptp.zero_zero_rat)))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.rat))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S2) tptp.zero_zero_rat)))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_1 (= (@ (@ tptp.groups1392844769737527556at_rat (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1392844769737527556at_rat (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S2) tptp.zero_zero_rat)))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_o) (A Bool) (B (-> Bool tptp.nat))) (let ((_let_1 (@ (@ tptp.member_o A) S2))) (=> (@ tptp.finite_finite_o S2) (and (=> _let_1 (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) tptp.zero_zero_nat))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) tptp.zero_zero_nat))) S2) tptp.zero_zero_nat)))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_o) (A Bool) (B (-> Bool tptp.real))) (let ((_let_1 (@ (@ tptp.member_o A) S2))) (=> (@ tptp.finite_finite_o S2) (and (=> _let_1 (= (@ (@ tptp.groups8691415230153176458o_real (lambda ((K3 Bool)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.zero_zero_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8691415230153176458o_real (lambda ((K3 Bool)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.zero_zero_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.zero_zero_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_1 (= (@ (@ tptp.groups4148127829035722712t_real (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.zero_zero_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups4148127829035722712t_real (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_o) (A Bool) (B (-> Bool tptp.rat))) (let ((_let_1 (@ (@ tptp.member_o A) S2))) (=> (@ tptp.finite_finite_o S2) (and (=> _let_1 (= (@ (@ tptp.groups7872700643590313910_o_rat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7872700643590313910_o_rat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S2) tptp.zero_zero_rat)))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.member_nat A) S2))) (=> (@ tptp.finite_finite_nat S2) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S2) tptp.zero_zero_rat)))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.rat))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S2) tptp.zero_zero_rat)))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.rat))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S2) tptp.zero_zero_rat)))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_Extended_enat) (A tptp.extended_enat) (B (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ (@ tptp.member_Extended_enat A) S2))) (=> (@ tptp.finite4001608067531595151d_enat S2) (and (=> _let_1 (= (@ (@ tptp.groups1392844769737527556at_rat (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1392844769737527556at_rat (lambda ((K3 tptp.extended_enat)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S2) tptp.zero_zero_rat)))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_o) (A Bool) (B (-> Bool tptp.nat))) (let ((_let_1 (@ (@ tptp.member_o A) S2))) (=> (@ tptp.finite_finite_o S2) (and (=> _let_1 (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_nat (= A K3)) (@ B K3)) tptp.zero_zero_nat))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_nat (= A K3)) (@ B K3)) tptp.zero_zero_nat))) S2) tptp.zero_zero_nat)))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.groups4538972089207619220nt_int F) A2))) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ tptp.abs_abs_int (@ F I4)))) A2))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.groups6591440286371151544t_real F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ tptp.abs_abs_real (@ F I4)))) A2))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G2))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.plus_plus_real (@ G2 X)) (@ _let_1 A2))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (X Bool) (G2 (-> Bool tptp.real))) (let ((_let_1 (@ tptp.groups8691415230153176458o_real G2))) (=> (@ tptp.finite_finite_o A2) (=> (not (@ (@ tptp.member_o X) A2)) (= (@ _let_1 (@ (@ tptp.insert_o X) A2)) (@ (@ tptp.plus_plus_real (@ G2 X)) (@ _let_1 A2))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G2))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) A2)) (@ (@ tptp.plus_plus_real (@ G2 X)) (@ _let_1 A2))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G2))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.plus_plus_real (@ G2 X)) (@ _let_1 A2))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G2 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (@ (@ tptp.member_Extended_enat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_Extended_enat X) A2)) (@ (@ tptp.plus_plus_real (@ G2 X)) (@ _let_1 A2))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat G2))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.plus_plus_rat (@ G2 X)) (@ _let_1 A2))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (X Bool) (G2 (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups7872700643590313910_o_rat G2))) (=> (@ tptp.finite_finite_o A2) (=> (not (@ (@ tptp.member_o X) A2)) (= (@ _let_1 (@ (@ tptp.insert_o X) A2)) (@ (@ tptp.plus_plus_rat (@ G2 X)) (@ _let_1 A2))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G2))) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X) A2)) (@ (@ tptp.plus_plus_rat (@ G2 X)) (@ _let_1 A2))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G2))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) A2)) (@ (@ tptp.plus_plus_rat (@ G2 X)) (@ _let_1 A2))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.plus_plus_rat (@ G2 X)) (@ _let_1 A2))))))))
% 5.98/6.29 (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))))
% 5.98/6.29 (assert (forall ((F (-> tptp.int tptp.int)) (A2 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)))) A2))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 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)))) A2))))
% 5.98/6.29 (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.distinct_int (@ (@ (@ tptp.list_update_int (@ (@ (@ tptp.list_update_int Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.distinct_int Xs))))))))
% 5.98/6.29 (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.distinct_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.distinct_VEBT_VEBT Xs))))))))
% 5.98/6.29 (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.distinct_nat (@ (@ (@ tptp.list_update_nat (@ (@ (@ tptp.list_update_nat Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.distinct_nat Xs))))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups2906978787729119204at_rat G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.zero_zero_rat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_rat (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.zero_zero_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.zero_zero_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (M2 tptp.nat) (G2 (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M2))) (let ((_let_3 (@ tptp.groups6591440286371151544t_real G2))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M2))) (and (=> _let_5 (= _let_4 tptp.zero_zero_real)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N))) (@ G2 _let_1))))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I4)))) A2) (@ 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)))) A2) tptp.zero_zero_complex))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.rat))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4)))) A2) (@ 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)))) A2) tptp.zero_zero_rat))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I4)))) A2) (@ 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)))) A2) tptp.zero_zero_real))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs2 tptp.list_complex)) (and (= (@ tptp.size_s3451745648224563538omplex Xs2) N) (@ tptp.distinct_complex Xs2) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) A2))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (N tptp.nat)) (=> (@ tptp.finite6177210948735845034at_nat A2) (@ tptp.finite500796754983035824at_nat (@ tptp.collec3343600615725829874at_nat (lambda ((Xs2 tptp.list_P6011104703257516679at_nat)) (and (= (@ tptp.size_s5460976970255530739at_nat Xs2) N) (@ tptp.distin6923225563576452346at_nat Xs2) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs2)) A2))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (N tptp.nat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (@ tptp.finite1862508098717546133d_enat (@ tptp.collec8433460942617342167d_enat (lambda ((Xs2 tptp.list_Extended_enat)) (and (= (@ tptp.size_s3941691890525107288d_enat Xs2) N) (@ tptp.distin4523846830085650399d_enat Xs2) (@ (@ tptp.ord_le7203529160286727270d_enat (@ tptp.set_Extended_enat2 Xs2)) A2))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs2 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) N) (@ tptp.distinct_VEBT_VEBT Xs2) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) A2))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs2) N) (@ tptp.distinct_nat Xs2) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) A2))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs2 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs2) N) (@ tptp.distinct_int Xs2) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) A2))))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X)) tptp.one_one_real)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X)) tptp.one_one_complex)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.complex)) (D (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I4))) (@ D I4)))) A2) (@ (@ 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)))) A2) tptp.zero_zero_complex))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.rat)) (D (-> tptp.nat tptp.rat))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4))) (@ D I4)))) A2) (@ (@ 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)))) A2) tptp.zero_zero_rat))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.real)) (D (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I4))) (@ D I4)))) A2) (@ (@ 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)))) A2) tptp.zero_zero_real))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_o) (F (-> Bool tptp.complex)) (G2 (-> Bool tptp.real))) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X4))) (@ G2 X4)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups5328290441151304332omplex F) S2))) (@ (@ tptp.groups8691415230153176458o_real G2) S2)))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_set_nat) (F (-> tptp.set_nat tptp.complex)) (G2 (-> tptp.set_nat tptp.real))) (=> (forall ((X4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X4) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X4))) (@ G2 X4)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups8255218700646806128omplex F) S2))) (@ (@ tptp.groups5107569545109728110t_real G2) S2)))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_set_nat_rat) (F (-> tptp.set_nat_rat tptp.complex)) (G2 (-> tptp.set_nat_rat tptp.real))) (=> (forall ((X4 tptp.set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat X4) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X4))) (@ G2 X4)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups6246630355582004071omplex F) S2))) (@ (@ tptp.groups4357547368389691109t_real G2) S2)))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.complex)) (G2 (-> tptp.int tptp.real))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X4))) (@ G2 X4)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups3049146728041665814omplex F) S2))) (@ (@ tptp.groups8778361861064173332t_real G2) S2)))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.complex)) (G2 (-> tptp.nat tptp.real))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X4))) (@ G2 X4)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) S2))) (@ (@ tptp.groups6591440286371151544t_real G2) S2)))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.complex)) (G2 (-> tptp.complex tptp.real))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X4))) (@ G2 X4)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F) S2))) (@ (@ tptp.groups5808333547571424918x_real G2) S2)))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.real))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F X4))) (@ G2 X4)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) S2))) (@ (@ tptp.groups6591440286371151544t_real G2) S2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (G2 (-> tptp.nat tptp.nat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (= (@ G2 X4) tptp.zero_zero_nat))) (= (@ (@ tptp.groups3542108847815614940at_nat G2) A2) tptp.zero_zero_nat))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (G2 (-> tptp.complex tptp.complex))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A2) (= (@ G2 X4) tptp.zero_zero_complex))) (= (@ (@ tptp.groups7754918857620584856omplex G2) A2) tptp.zero_zero_complex))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (G2 (-> tptp.int tptp.int))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (= (@ G2 X4) tptp.zero_zero_int))) (= (@ (@ tptp.groups4538972089207619220nt_int G2) A2) tptp.zero_zero_int))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (G2 (-> tptp.nat tptp.real))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (= (@ G2 X4) tptp.zero_zero_real))) (= (@ (@ tptp.groups6591440286371151544t_real G2) A2) tptp.zero_zero_real))))
% 5.98/6.29 (assert (forall ((G2 (-> Bool tptp.real)) (A2 tptp.set_o)) (=> (not (= (@ (@ tptp.groups8691415230153176458o_real G2) A2) tptp.zero_zero_real)) (not (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) A2) (= (@ G2 A5) tptp.zero_zero_real)))))))
% 5.98/6.29 (assert (forall ((G2 (-> tptp.int tptp.real)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups8778361861064173332t_real G2) A2) tptp.zero_zero_real)) (not (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A2) (= (@ G2 A5) tptp.zero_zero_real)))))))
% 5.98/6.29 (assert (forall ((G2 (-> Bool tptp.rat)) (A2 tptp.set_o)) (=> (not (= (@ (@ tptp.groups7872700643590313910_o_rat G2) A2) tptp.zero_zero_rat)) (not (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) A2) (= (@ G2 A5) tptp.zero_zero_rat)))))))
% 5.98/6.29 (assert (forall ((G2 (-> tptp.nat tptp.rat)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups2906978787729119204at_rat G2) A2) tptp.zero_zero_rat)) (not (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (= (@ G2 A5) tptp.zero_zero_rat)))))))
% 5.98/6.29 (assert (forall ((G2 (-> tptp.int tptp.rat)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups3906332499630173760nt_rat G2) A2) tptp.zero_zero_rat)) (not (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A2) (= (@ G2 A5) tptp.zero_zero_rat)))))))
% 5.98/6.29 (assert (forall ((G2 (-> Bool tptp.nat)) (A2 tptp.set_o)) (=> (not (= (@ (@ tptp.groups8507830703676809646_o_nat G2) A2) tptp.zero_zero_nat)) (not (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) A2) (= (@ G2 A5) tptp.zero_zero_nat)))))))
% 5.98/6.29 (assert (forall ((G2 (-> tptp.int tptp.nat)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups4541462559716669496nt_nat G2) A2) tptp.zero_zero_nat)) (not (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A2) (= (@ G2 A5) tptp.zero_zero_nat)))))))
% 5.98/6.29 (assert (forall ((G2 (-> Bool tptp.int)) (A2 tptp.set_o)) (=> (not (= (@ (@ tptp.groups8505340233167759370_o_int G2) A2) tptp.zero_zero_int)) (not (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) A2) (= (@ G2 A5) tptp.zero_zero_int)))))))
% 5.98/6.29 (assert (forall ((G2 (-> tptp.nat tptp.int)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups3539618377306564664at_int G2) A2) tptp.zero_zero_int)) (not (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (= (@ G2 A5) tptp.zero_zero_int)))))))
% 5.98/6.29 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups3542108847815614940at_nat G2) A2) tptp.zero_zero_nat)) (not (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (= (@ G2 A5) tptp.zero_zero_nat)))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.complex)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F I4)))) A2))))
% 5.98/6.29 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F) A2))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((I4 tptp.complex)) (@ tptp.real_V1022390504157884413omplex (@ F I4)))) A2))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F I4)))) A2))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.one_one_nat) N)))
% 5.98/6.29 (assert (forall ((K4 tptp.set_o) (F (-> Bool tptp.rat)) (G2 (-> Bool tptp.rat))) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) K4) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G2 I2)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups7872700643590313910_o_rat F) K4)) (@ (@ tptp.groups7872700643590313910_o_rat G2) K4)))))
% 5.98/6.29 (assert (forall ((K4 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G2 (-> tptp.nat tptp.rat))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) K4) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G2 I2)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) K4)) (@ (@ tptp.groups2906978787729119204at_rat G2) K4)))))
% 5.98/6.29 (assert (forall ((K4 tptp.set_int) (F (-> tptp.int tptp.rat)) (G2 (-> tptp.int tptp.rat))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) K4) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G2 I2)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) K4)) (@ (@ tptp.groups3906332499630173760nt_rat G2) K4)))))
% 5.98/6.29 (assert (forall ((K4 tptp.set_o) (F (-> Bool tptp.nat)) (G2 (-> Bool tptp.nat))) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) K4) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G2 I2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups8507830703676809646_o_nat F) K4)) (@ (@ tptp.groups8507830703676809646_o_nat G2) K4)))))
% 5.98/6.29 (assert (forall ((K4 tptp.set_int) (F (-> tptp.int tptp.nat)) (G2 (-> tptp.int tptp.nat))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) K4) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G2 I2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) K4)) (@ (@ tptp.groups4541462559716669496nt_nat G2) K4)))))
% 5.98/6.29 (assert (forall ((K4 tptp.set_o) (F (-> Bool tptp.int)) (G2 (-> Bool tptp.int))) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) K4) (@ (@ tptp.ord_less_eq_int (@ F I2)) (@ G2 I2)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups8505340233167759370_o_int F) K4)) (@ (@ tptp.groups8505340233167759370_o_int G2) K4)))))
% 5.98/6.29 (assert (forall ((K4 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G2 (-> tptp.nat tptp.int))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) K4) (@ (@ tptp.ord_less_eq_int (@ F I2)) (@ G2 I2)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) K4)) (@ (@ tptp.groups3539618377306564664at_int G2) K4)))))
% 5.98/6.29 (assert (forall ((K4 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G2 (-> tptp.nat tptp.nat))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) K4) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G2 I2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) K4)) (@ (@ tptp.groups3542108847815614940at_nat G2) K4)))))
% 5.98/6.29 (assert (forall ((K4 tptp.set_int) (F (-> tptp.int tptp.int)) (G2 (-> tptp.int tptp.int))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) K4) (@ (@ tptp.ord_less_eq_int (@ F I2)) (@ G2 I2)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups4538972089207619220nt_int F) K4)) (@ (@ tptp.groups4538972089207619220nt_int G2) K4)))))
% 5.98/6.29 (assert (forall ((K4 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.real))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) K4) (@ (@ tptp.ord_less_eq_real (@ F I2)) (@ G2 I2)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) K4)) (@ (@ tptp.groups6591440286371151544t_real G2) K4)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (B2 tptp.set_nat) (G2 (-> Bool tptp.nat tptp.nat)) (R (-> Bool tptp.nat Bool))) (=> (@ tptp.finite_finite_o A2) (=> (@ tptp.finite_finite_nat B2) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((X3 Bool)) (@ (@ tptp.groups3542108847815614940at_nat (@ G2 X3)) (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) B2) (@ (@ R X3) Y2))))))) A2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y2 tptp.nat)) (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((X3 Bool)) (@ (@ G2 X3) Y2))) (@ tptp.collect_o (lambda ((X3 Bool)) (and (@ (@ tptp.member_o X3) A2) (@ (@ R X3) Y2))))))) B2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_nat) (G2 (-> tptp.int tptp.nat tptp.nat)) (R (-> tptp.int tptp.nat Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ tptp.finite_finite_nat B2) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X3 tptp.int)) (@ (@ tptp.groups3542108847815614940at_nat (@ G2 X3)) (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) B2) (@ (@ R X3) Y2))))))) A2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y2 tptp.nat)) (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X3 tptp.int)) (@ (@ G2 X3) Y2))) (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (@ (@ R X3) Y2))))))) B2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (B2 tptp.set_nat) (G2 (-> tptp.complex tptp.nat tptp.nat)) (R (-> tptp.complex tptp.nat Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ tptp.finite_finite_nat B2) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X3 tptp.complex)) (@ (@ tptp.groups3542108847815614940at_nat (@ G2 X3)) (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) B2) (@ (@ R X3) Y2))))))) A2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y2 tptp.nat)) (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X3 tptp.complex)) (@ (@ G2 X3) Y2))) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A2) (@ (@ R X3) Y2))))))) B2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (B2 tptp.set_nat) (G2 (-> tptp.extended_enat tptp.nat tptp.nat)) (R (-> tptp.extended_enat tptp.nat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ tptp.finite_finite_nat B2) (= (@ (@ tptp.groups2027974829824023292at_nat (lambda ((X3 tptp.extended_enat)) (@ (@ tptp.groups3542108847815614940at_nat (@ G2 X3)) (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) B2) (@ (@ R X3) Y2))))))) A2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y2 tptp.nat)) (@ (@ tptp.groups2027974829824023292at_nat (lambda ((X3 tptp.extended_enat)) (@ (@ G2 X3) Y2))) (@ tptp.collec4429806609662206161d_enat (lambda ((X3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X3) A2) (@ (@ R X3) Y2))))))) B2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (B2 tptp.set_complex) (G2 (-> Bool tptp.complex tptp.complex)) (R (-> Bool tptp.complex Bool))) (=> (@ tptp.finite_finite_o A2) (=> (@ tptp.finite3207457112153483333omplex B2) (= (@ (@ tptp.groups5328290441151304332omplex (lambda ((X3 Bool)) (@ (@ tptp.groups7754918857620584856omplex (@ G2 X3)) (@ tptp.collect_complex (lambda ((Y2 tptp.complex)) (and (@ (@ tptp.member_complex Y2) B2) (@ (@ R X3) Y2))))))) A2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((Y2 tptp.complex)) (@ (@ tptp.groups5328290441151304332omplex (lambda ((X3 Bool)) (@ (@ G2 X3) Y2))) (@ tptp.collect_o (lambda ((X3 Bool)) (and (@ (@ tptp.member_o X3) A2) (@ (@ R X3) Y2))))))) B2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_complex) (G2 (-> tptp.nat tptp.complex tptp.complex)) (R (-> tptp.nat tptp.complex Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ tptp.finite3207457112153483333omplex B2) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((X3 tptp.nat)) (@ (@ tptp.groups7754918857620584856omplex (@ G2 X3)) (@ tptp.collect_complex (lambda ((Y2 tptp.complex)) (and (@ (@ tptp.member_complex Y2) B2) (@ (@ R X3) Y2))))))) A2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((Y2 tptp.complex)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((X3 tptp.nat)) (@ (@ G2 X3) Y2))) (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (@ (@ R X3) Y2))))))) B2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (B2 tptp.set_complex) (G2 (-> tptp.int tptp.complex tptp.complex)) (R (-> tptp.int tptp.complex Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ tptp.finite3207457112153483333omplex B2) (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((X3 tptp.int)) (@ (@ tptp.groups7754918857620584856omplex (@ G2 X3)) (@ tptp.collect_complex (lambda ((Y2 tptp.complex)) (and (@ (@ tptp.member_complex Y2) B2) (@ (@ R X3) Y2))))))) A2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((Y2 tptp.complex)) (@ (@ tptp.groups3049146728041665814omplex (lambda ((X3 tptp.int)) (@ (@ G2 X3) Y2))) (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (@ (@ R X3) Y2))))))) B2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (B2 tptp.set_complex) (G2 (-> tptp.extended_enat tptp.complex tptp.complex)) (R (-> tptp.extended_enat tptp.complex Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (@ tptp.finite3207457112153483333omplex B2) (= (@ (@ tptp.groups6818542070133387226omplex (lambda ((X3 tptp.extended_enat)) (@ (@ tptp.groups7754918857620584856omplex (@ G2 X3)) (@ tptp.collect_complex (lambda ((Y2 tptp.complex)) (and (@ (@ tptp.member_complex Y2) B2) (@ (@ R X3) Y2))))))) A2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((Y2 tptp.complex)) (@ (@ tptp.groups6818542070133387226omplex (lambda ((X3 tptp.extended_enat)) (@ (@ G2 X3) Y2))) (@ tptp.collec4429806609662206161d_enat (lambda ((X3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X3) A2) (@ (@ R X3) Y2))))))) B2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (B2 tptp.set_int) (G2 (-> Bool tptp.int tptp.int)) (R (-> Bool tptp.int Bool))) (=> (@ tptp.finite_finite_o A2) (=> (@ tptp.finite_finite_int B2) (= (@ (@ tptp.groups8505340233167759370_o_int (lambda ((X3 Bool)) (@ (@ tptp.groups4538972089207619220nt_int (@ G2 X3)) (@ tptp.collect_int (lambda ((Y2 tptp.int)) (and (@ (@ tptp.member_int Y2) B2) (@ (@ R X3) Y2))))))) A2) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Y2 tptp.int)) (@ (@ tptp.groups8505340233167759370_o_int (lambda ((X3 Bool)) (@ (@ G2 X3) Y2))) (@ tptp.collect_o (lambda ((X3 Bool)) (and (@ (@ tptp.member_o X3) A2) (@ (@ R X3) Y2))))))) B2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (B2 tptp.set_int) (G2 (-> tptp.nat tptp.int tptp.int)) (R (-> tptp.nat tptp.int Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ tptp.finite_finite_int B2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((X3 tptp.nat)) (@ (@ tptp.groups4538972089207619220nt_int (@ G2 X3)) (@ tptp.collect_int (lambda ((Y2 tptp.int)) (and (@ (@ tptp.member_int Y2) B2) (@ (@ R X3) Y2))))))) A2) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Y2 tptp.int)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((X3 tptp.nat)) (@ (@ G2 X3) Y2))) (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (@ (@ R X3) Y2))))))) B2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.real))) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A2) (@ (@ tptp.ord_less_eq_real (@ F X4)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8691415230153176458o_real F) A2)) tptp.zero_zero_real))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_real (@ F X4)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) A2)) tptp.zero_zero_real))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.rat))) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A2) (@ (@ tptp.ord_less_eq_rat (@ F X4)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups7872700643590313910_o_rat F) A2)) tptp.zero_zero_rat))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_rat (@ F X4)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) A2)) tptp.zero_zero_rat))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_rat (@ F X4)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A2)) tptp.zero_zero_rat))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.nat))) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A2) (@ (@ tptp.ord_less_eq_nat (@ F X4)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups8507830703676809646_o_nat F) A2)) tptp.zero_zero_nat))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_nat (@ F X4)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) tptp.zero_zero_nat))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.int))) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A2) (@ (@ tptp.ord_less_eq_int (@ F X4)) tptp.zero_zero_int))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups8505340233167759370_o_int F) A2)) tptp.zero_zero_int))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_int (@ F X4)) tptp.zero_zero_int))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) A2)) tptp.zero_zero_int))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_nat (@ F X4)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) tptp.zero_zero_nat))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.real))) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8691415230153176458o_real F) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.rat))) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups7872700643590313910_o_rat F) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.nat))) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups8507830703676809646_o_nat F) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.int))) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X4)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups8505340233167759370_o_int F) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X4)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups3539618377306564664at_int F) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups3542108847815614940at_nat F) A2)))))
% 5.98/6.29 (assert (forall ((F (-> Bool tptp.rat)) (I5 tptp.set_o) (G2 (-> Bool tptp.rat)) (I Bool)) (=> (= (@ (@ tptp.groups7872700643590313910_o_rat F) I5) (@ (@ tptp.groups7872700643590313910_o_rat G2) I5)) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) I5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G2 I2)))) (=> (@ (@ tptp.member_o I) I5) (=> (@ tptp.finite_finite_o I5) (= (@ F I) (@ G2 I))))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.rat)) (I5 tptp.set_nat) (G2 (-> tptp.nat tptp.rat)) (I tptp.nat)) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) I5) (@ (@ tptp.groups2906978787729119204at_rat G2) I5)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G2 I2)))) (=> (@ (@ tptp.member_nat I) I5) (=> (@ tptp.finite_finite_nat I5) (= (@ F I) (@ G2 I))))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.int tptp.rat)) (I5 tptp.set_int) (G2 (-> tptp.int tptp.rat)) (I tptp.int)) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) I5) (@ (@ tptp.groups3906332499630173760nt_rat G2) I5)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G2 I2)))) (=> (@ (@ tptp.member_int I) I5) (=> (@ tptp.finite_finite_int I5) (= (@ F I) (@ G2 I))))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.complex tptp.rat)) (I5 tptp.set_complex) (G2 (-> tptp.complex tptp.rat)) (I tptp.complex)) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) I5) (@ (@ tptp.groups5058264527183730370ex_rat G2) I5)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G2 I2)))) (=> (@ (@ tptp.member_complex I) I5) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ F I) (@ G2 I))))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.extended_enat tptp.rat)) (I5 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.rat)) (I tptp.extended_enat)) (=> (= (@ (@ tptp.groups1392844769737527556at_rat F) I5) (@ (@ tptp.groups1392844769737527556at_rat G2) I5)) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) I5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G2 I2)))) (=> (@ (@ tptp.member_Extended_enat I) I5) (=> (@ tptp.finite4001608067531595151d_enat I5) (= (@ F I) (@ G2 I))))))))
% 5.98/6.29 (assert (forall ((F (-> Bool tptp.nat)) (I5 tptp.set_o) (G2 (-> Bool tptp.nat)) (I Bool)) (=> (= (@ (@ tptp.groups8507830703676809646_o_nat F) I5) (@ (@ tptp.groups8507830703676809646_o_nat G2) I5)) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) I5) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G2 I2)))) (=> (@ (@ tptp.member_o I) I5) (=> (@ tptp.finite_finite_o I5) (= (@ F I) (@ G2 I))))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.int tptp.nat)) (I5 tptp.set_int) (G2 (-> tptp.int tptp.nat)) (I tptp.int)) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) I5) (@ (@ tptp.groups4541462559716669496nt_nat G2) I5)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I5) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G2 I2)))) (=> (@ (@ tptp.member_int I) I5) (=> (@ tptp.finite_finite_int I5) (= (@ F I) (@ G2 I))))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.complex tptp.nat)) (I5 tptp.set_complex) (G2 (-> tptp.complex tptp.nat)) (I tptp.complex)) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) I5) (@ (@ tptp.groups5693394587270226106ex_nat G2) I5)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I5) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G2 I2)))) (=> (@ (@ tptp.member_complex I) I5) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ F I) (@ G2 I))))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.extended_enat tptp.nat)) (I5 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.nat)) (I tptp.extended_enat)) (=> (= (@ (@ tptp.groups2027974829824023292at_nat F) I5) (@ (@ tptp.groups2027974829824023292at_nat G2) I5)) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) I5) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G2 I2)))) (=> (@ (@ tptp.member_Extended_enat I) I5) (=> (@ tptp.finite4001608067531595151d_enat I5) (= (@ F I) (@ G2 I))))))))
% 5.98/6.29 (assert (forall ((F (-> Bool tptp.int)) (I5 tptp.set_o) (G2 (-> Bool tptp.int)) (I Bool)) (=> (= (@ (@ tptp.groups8505340233167759370_o_int F) I5) (@ (@ tptp.groups8505340233167759370_o_int G2) I5)) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) I5) (@ (@ tptp.ord_less_eq_int (@ F I2)) (@ G2 I2)))) (=> (@ (@ tptp.member_o I) I5) (=> (@ tptp.finite_finite_o I5) (= (@ F I) (@ G2 I))))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (exists ((Xs3 tptp.list_VEBT_VEBT)) (and (= (@ tptp.set_VEBT_VEBT2 Xs3) A2) (@ tptp.distinct_VEBT_VEBT Xs3))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (exists ((Xs3 tptp.list_nat)) (and (= (@ tptp.set_nat2 Xs3) A2) (@ tptp.distinct_nat Xs3))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (exists ((Xs3 tptp.list_int)) (and (= (@ tptp.set_int2 Xs3) A2) (@ tptp.distinct_int Xs3))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (exists ((Xs3 tptp.list_complex)) (and (= (@ tptp.set_complex2 Xs3) A2) (@ tptp.distinct_complex Xs3))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A2) (exists ((Xs3 tptp.list_P6011104703257516679at_nat)) (and (= (@ tptp.set_Pr5648618587558075414at_nat Xs3) A2) (@ tptp.distin6923225563576452346at_nat Xs3))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (exists ((Xs3 tptp.list_Extended_enat)) (and (= (@ tptp.set_Extended_enat2 Xs3) A2) (@ tptp.distin4523846830085650399d_enat Xs3))))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G2 (-> tptp.nat tptp.nat))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)) (=> (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.suc X4))) (=> (@ (@ tptp.member_nat _let_1) A2) (= (@ F _let_1) (@ G2 _let_1))))) (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ (@ tptp.groups3542108847815614940at_nat G2) A2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.real))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)) (=> (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.suc X4))) (=> (@ (@ tptp.member_nat _let_1) A2) (= (@ F _let_1) (@ G2 _let_1))))) (= (@ (@ tptp.groups6591440286371151544t_real F) A2) (@ (@ tptp.groups6591440286371151544t_real G2) A2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (G2 (-> Bool tptp.real)) (P (-> Bool Bool))) (=> (@ tptp.finite_finite_o A2) (= (@ (@ tptp.groups8691415230153176458o_real G2) (@ tptp.collect_o (lambda ((X3 Bool)) (and (@ (@ tptp.member_o X3) A2) (@ P X3))))) (@ (@ tptp.groups8691415230153176458o_real (lambda ((X3 Bool)) (@ (@ (@ tptp.if_real (@ P X3)) (@ G2 X3)) tptp.zero_zero_real))) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (G2 (-> tptp.int tptp.real)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups8778361861064173332t_real G2) (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (@ P X3))))) (@ (@ tptp.groups8778361861064173332t_real (lambda ((X3 tptp.int)) (@ (@ (@ tptp.if_real (@ P X3)) (@ G2 X3)) tptp.zero_zero_real))) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (G2 (-> tptp.complex tptp.real)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups5808333547571424918x_real G2) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A2) (@ P X3))))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((X3 tptp.complex)) (@ (@ (@ tptp.if_real (@ P X3)) (@ G2 X3)) tptp.zero_zero_real))) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.real)) (P (-> tptp.extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ (@ tptp.groups4148127829035722712t_real G2) (@ tptp.collec4429806609662206161d_enat (lambda ((X3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X3) A2) (@ P X3))))) (@ (@ tptp.groups4148127829035722712t_real (lambda ((X3 tptp.extended_enat)) (@ (@ (@ tptp.if_real (@ P X3)) (@ G2 X3)) tptp.zero_zero_real))) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (G2 (-> Bool tptp.rat)) (P (-> Bool Bool))) (=> (@ tptp.finite_finite_o A2) (= (@ (@ tptp.groups7872700643590313910_o_rat G2) (@ tptp.collect_o (lambda ((X3 Bool)) (and (@ (@ tptp.member_o X3) A2) (@ P X3))))) (@ (@ tptp.groups7872700643590313910_o_rat (lambda ((X3 Bool)) (@ (@ (@ tptp.if_rat (@ P X3)) (@ G2 X3)) tptp.zero_zero_rat))) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (G2 (-> tptp.nat tptp.rat)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.groups2906978787729119204at_rat G2) (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (@ P X3))))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((X3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ P X3)) (@ G2 X3)) tptp.zero_zero_rat))) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (G2 (-> tptp.int tptp.rat)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups3906332499630173760nt_rat G2) (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (@ P X3))))) (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X3 tptp.int)) (@ (@ (@ tptp.if_rat (@ P X3)) (@ G2 X3)) tptp.zero_zero_rat))) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (G2 (-> tptp.complex tptp.rat)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups5058264527183730370ex_rat G2) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A2) (@ P X3))))) (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((X3 tptp.complex)) (@ (@ (@ tptp.if_rat (@ P X3)) (@ G2 X3)) tptp.zero_zero_rat))) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.rat)) (P (-> tptp.extended_enat Bool))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ (@ tptp.groups1392844769737527556at_rat G2) (@ tptp.collec4429806609662206161d_enat (lambda ((X3 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X3) A2) (@ P X3))))) (@ (@ tptp.groups1392844769737527556at_rat (lambda ((X3 tptp.extended_enat)) (@ (@ (@ tptp.if_rat (@ P X3)) (@ G2 X3)) tptp.zero_zero_rat))) A2)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (G2 (-> Bool tptp.nat)) (P (-> Bool Bool))) (=> (@ tptp.finite_finite_o A2) (= (@ (@ tptp.groups8507830703676809646_o_nat G2) (@ tptp.collect_o (lambda ((X3 Bool)) (and (@ (@ tptp.member_o X3) A2) (@ P X3))))) (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((X3 Bool)) (@ (@ (@ tptp.if_nat (@ P X3)) (@ G2 X3)) tptp.zero_zero_nat))) A2)))))
% 5.98/6.29 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) (@ tptp.suc N))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G2 (@ tptp.suc I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))))
% 5.98/6.29 (assert (forall ((G2 (-> tptp.nat tptp.real)) (M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M2)) (@ tptp.suc N))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G2 (@ tptp.suc I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))))
% 5.98/6.29 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (M2 tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M2) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G2 (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))))
% 5.98/6.29 (assert (forall ((G2 (-> tptp.nat tptp.real)) (M2 tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G2) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M2) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G2 (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.real))) (=> (@ tptp.finite_finite_o A2) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (= (= (@ (@ tptp.groups8691415230153176458o_real F) A2) tptp.zero_zero_real) (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A2) (= (@ F X3) tptp.zero_zero_real))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (= (= (@ (@ tptp.groups8778361861064173332t_real F) A2) tptp.zero_zero_real) (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (= (@ F X3) tptp.zero_zero_real))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (= (= (@ (@ tptp.groups5808333547571424918x_real F) A2) tptp.zero_zero_real) (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (= (@ F X3) tptp.zero_zero_real))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (= (= (@ (@ tptp.groups4148127829035722712t_real F) A2) tptp.zero_zero_real) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X3) A2) (= (@ F X3) tptp.zero_zero_real))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o A2) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (= (= (@ (@ tptp.groups7872700643590313910_o_rat F) A2) tptp.zero_zero_rat) (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A2) (= (@ F X3) tptp.zero_zero_rat))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (= (= (@ (@ tptp.groups2906978787729119204at_rat F) A2) tptp.zero_zero_rat) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (= (@ F X3) tptp.zero_zero_rat))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (= (= (@ (@ tptp.groups3906332499630173760nt_rat F) A2) tptp.zero_zero_rat) (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (= (@ F X3) tptp.zero_zero_rat))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (= (= (@ (@ tptp.groups5058264527183730370ex_rat F) A2) tptp.zero_zero_rat) (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (= (@ F X3) tptp.zero_zero_rat))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (= (= (@ (@ tptp.groups1392844769737527556at_rat F) A2) tptp.zero_zero_rat) (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X3) A2) (= (@ F X3) tptp.zero_zero_rat))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o A2) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (= (= (@ (@ tptp.groups8507830703676809646_o_nat F) A2) tptp.zero_zero_nat) (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A2) (= (@ F X3) tptp.zero_zero_nat))))))))
% 5.98/6.29 (assert (forall ((S tptp.set_int) (T tptp.set_int) (G2 (-> tptp.int tptp.real)) (I (-> tptp.int tptp.int)) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite_finite_int T) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G2 X4)))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) S)) (@ (@ tptp.groups8778361861064173332t_real G2) T))))))))
% 5.98/6.29 (assert (forall ((S tptp.set_int) (T tptp.set_complex) (G2 (-> tptp.complex tptp.real)) (I (-> tptp.complex tptp.int)) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G2 X4)))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) S)) (@ (@ tptp.groups5808333547571424918x_real G2) T))))))))
% 5.98/6.29 (assert (forall ((S tptp.set_int) (T tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.real)) (I (-> tptp.extended_enat tptp.int)) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite4001608067531595151d_enat T) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G2 X4)))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) S)) (@ (@ tptp.groups4148127829035722712t_real G2) T))))))))
% 5.98/6.29 (assert (forall ((S tptp.set_complex) (T tptp.set_int) (G2 (-> tptp.int tptp.real)) (I (-> tptp.int tptp.complex)) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ tptp.finite_finite_int T) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G2 X4)))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) S)) (@ (@ tptp.groups8778361861064173332t_real G2) T))))))))
% 5.98/6.29 (assert (forall ((S tptp.set_complex) (T tptp.set_complex) (G2 (-> tptp.complex tptp.real)) (I (-> tptp.complex tptp.complex)) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G2 X4)))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) S)) (@ (@ tptp.groups5808333547571424918x_real G2) T))))))))
% 5.98/6.29 (assert (forall ((S tptp.set_complex) (T tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.real)) (I (-> tptp.extended_enat tptp.complex)) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ tptp.finite4001608067531595151d_enat T) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G2 X4)))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) S)) (@ (@ tptp.groups4148127829035722712t_real G2) T))))))))
% 5.98/6.29 (assert (forall ((S tptp.set_Extended_enat) (T tptp.set_int) (G2 (-> tptp.int tptp.real)) (I (-> tptp.int tptp.extended_enat)) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (@ tptp.finite_finite_int T) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G2 X4)))) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) S) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups4148127829035722712t_real F) S)) (@ (@ tptp.groups8778361861064173332t_real G2) T))))))))
% 5.98/6.29 (assert (forall ((S tptp.set_Extended_enat) (T tptp.set_complex) (G2 (-> tptp.complex tptp.real)) (I (-> tptp.complex tptp.extended_enat)) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G2 X4)))) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) S) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups4148127829035722712t_real F) S)) (@ (@ tptp.groups5808333547571424918x_real G2) T))))))))
% 5.98/6.29 (assert (forall ((S tptp.set_Extended_enat) (T tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.real)) (I (-> tptp.extended_enat tptp.extended_enat)) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (@ tptp.finite4001608067531595151d_enat T) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G2 X4)))) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) S) (exists ((Xa tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups4148127829035722712t_real F) S)) (@ (@ tptp.groups4148127829035722712t_real G2) T))))))))
% 5.98/6.29 (assert (forall ((S tptp.set_nat) (T tptp.set_nat) (G2 (-> tptp.nat tptp.rat)) (I (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G2 X4)))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ G2 Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) S)) (@ (@ tptp.groups2906978787729119204at_rat G2) T))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G2 X4)))) (=> (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ (@ tptp.ord_less_real (@ F X2)) (@ G2 X2)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8778361861064173332t_real F) A2)) (@ (@ tptp.groups8778361861064173332t_real G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G2 X4)))) (=> (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ (@ tptp.ord_less_real (@ F X2)) (@ G2 X2)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups5808333547571424918x_real F) A2)) (@ (@ tptp.groups5808333547571424918x_real G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (G2 (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G2 X4)))) (=> (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X2) A2) (@ (@ tptp.ord_less_real (@ F X2)) (@ G2 X2)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups4148127829035722712t_real F) A2)) (@ (@ tptp.groups4148127829035722712t_real G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ G2 X4)))) (=> (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ (@ tptp.ord_less_rat (@ F X2)) (@ G2 X2)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F) A2)) (@ (@ tptp.groups2906978787729119204at_rat G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat)) (G2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ G2 X4)))) (=> (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ (@ tptp.ord_less_rat (@ F X2)) (@ G2 X2)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A2)) (@ (@ tptp.groups3906332499630173760nt_rat G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ G2 X4)))) (=> (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ (@ tptp.ord_less_rat (@ F X2)) (@ G2 X2)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A2)) (@ (@ tptp.groups5058264527183730370ex_rat G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat)) (G2 (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ G2 X4)))) (=> (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X2) A2) (@ (@ tptp.ord_less_rat (@ F X2)) (@ G2 X2)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups1392844769737527556at_rat F) A2)) (@ (@ tptp.groups1392844769737527556at_rat G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ G2 X4)))) (=> (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ G2 X2)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_nat G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ G2 X4)))) (=> (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ G2 X2)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups5693394587270226106ex_nat G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.nat)) (G2 (-> tptp.extended_enat tptp.nat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ G2 X4)))) (=> (exists ((X2 tptp.extended_enat)) (and (@ (@ tptp.member_Extended_enat X2) A2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ G2 X2)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups2027974829824023292at_nat F) A2)) (@ (@ tptp.groups2027974829824023292at_nat G2) A2)))))))
% 5.98/6.29 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S2 tptp.set_int) (H (-> tptp.int tptp.real)) (G2 (-> tptp.int tptp.real))) (=> (@ (@ R tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X1 tptp.real) (Y1 tptp.real) (X24 tptp.real) (Y24 tptp.real)) (=> (and (@ (@ R X1) X24) (@ (@ R Y1) Y24)) (@ (@ R (@ (@ tptp.plus_plus_real X1) Y1)) (@ (@ tptp.plus_plus_real X24) Y24)))) (=> (@ tptp.finite_finite_int S2) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S2) (@ (@ R (@ H X4)) (@ G2 X4)))) (@ (@ R (@ (@ tptp.groups8778361861064173332t_real H) S2)) (@ (@ tptp.groups8778361861064173332t_real G2) S2))))))))
% 5.98/6.29 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S2 tptp.set_complex) (H (-> tptp.complex tptp.real)) (G2 (-> tptp.complex tptp.real))) (=> (@ (@ R tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X1 tptp.real) (Y1 tptp.real) (X24 tptp.real) (Y24 tptp.real)) (=> (and (@ (@ R X1) X24) (@ (@ R Y1) Y24)) (@ (@ R (@ (@ tptp.plus_plus_real X1) Y1)) (@ (@ tptp.plus_plus_real X24) Y24)))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S2) (@ (@ R (@ H X4)) (@ G2 X4)))) (@ (@ R (@ (@ tptp.groups5808333547571424918x_real H) S2)) (@ (@ tptp.groups5808333547571424918x_real G2) S2))))))))
% 5.98/6.29 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S2 tptp.set_Extended_enat) (H (-> tptp.extended_enat tptp.real)) (G2 (-> tptp.extended_enat tptp.real))) (=> (@ (@ R tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X1 tptp.real) (Y1 tptp.real) (X24 tptp.real) (Y24 tptp.real)) (=> (and (@ (@ R X1) X24) (@ (@ R Y1) Y24)) (@ (@ R (@ (@ tptp.plus_plus_real X1) Y1)) (@ (@ tptp.plus_plus_real X24) Y24)))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) S2) (@ (@ R (@ H X4)) (@ G2 X4)))) (@ (@ R (@ (@ tptp.groups4148127829035722712t_real H) S2)) (@ (@ tptp.groups4148127829035722712t_real G2) S2))))))))
% 5.98/6.29 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S2 tptp.set_nat) (H (-> tptp.nat tptp.rat)) (G2 (-> tptp.nat tptp.rat))) (=> (@ (@ R tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X1 tptp.rat) (Y1 tptp.rat) (X24 tptp.rat) (Y24 tptp.rat)) (=> (and (@ (@ R X1) X24) (@ (@ R Y1) Y24)) (@ (@ R (@ (@ tptp.plus_plus_rat X1) Y1)) (@ (@ tptp.plus_plus_rat X24) Y24)))) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S2) (@ (@ R (@ H X4)) (@ G2 X4)))) (@ (@ R (@ (@ tptp.groups2906978787729119204at_rat H) S2)) (@ (@ tptp.groups2906978787729119204at_rat G2) S2))))))))
% 5.98/6.29 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S2 tptp.set_int) (H (-> tptp.int tptp.rat)) (G2 (-> tptp.int tptp.rat))) (=> (@ (@ R tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X1 tptp.rat) (Y1 tptp.rat) (X24 tptp.rat) (Y24 tptp.rat)) (=> (and (@ (@ R X1) X24) (@ (@ R Y1) Y24)) (@ (@ R (@ (@ tptp.plus_plus_rat X1) Y1)) (@ (@ tptp.plus_plus_rat X24) Y24)))) (=> (@ tptp.finite_finite_int S2) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S2) (@ (@ R (@ H X4)) (@ G2 X4)))) (@ (@ R (@ (@ tptp.groups3906332499630173760nt_rat H) S2)) (@ (@ tptp.groups3906332499630173760nt_rat G2) S2))))))))
% 5.98/6.29 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S2 tptp.set_complex) (H (-> tptp.complex tptp.rat)) (G2 (-> tptp.complex tptp.rat))) (=> (@ (@ R tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X1 tptp.rat) (Y1 tptp.rat) (X24 tptp.rat) (Y24 tptp.rat)) (=> (and (@ (@ R X1) X24) (@ (@ R Y1) Y24)) (@ (@ R (@ (@ tptp.plus_plus_rat X1) Y1)) (@ (@ tptp.plus_plus_rat X24) Y24)))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S2) (@ (@ R (@ H X4)) (@ G2 X4)))) (@ (@ R (@ (@ tptp.groups5058264527183730370ex_rat H) S2)) (@ (@ tptp.groups5058264527183730370ex_rat G2) S2))))))))
% 5.98/6.29 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S2 tptp.set_Extended_enat) (H (-> tptp.extended_enat tptp.rat)) (G2 (-> tptp.extended_enat tptp.rat))) (=> (@ (@ R tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X1 tptp.rat) (Y1 tptp.rat) (X24 tptp.rat) (Y24 tptp.rat)) (=> (and (@ (@ R X1) X24) (@ (@ R Y1) Y24)) (@ (@ R (@ (@ tptp.plus_plus_rat X1) Y1)) (@ (@ tptp.plus_plus_rat X24) Y24)))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) S2) (@ (@ R (@ H X4)) (@ G2 X4)))) (@ (@ R (@ (@ tptp.groups1392844769737527556at_rat H) S2)) (@ (@ tptp.groups1392844769737527556at_rat G2) S2))))))))
% 5.98/6.29 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S2 tptp.set_int) (H (-> tptp.int tptp.nat)) (G2 (-> tptp.int tptp.nat))) (=> (@ (@ R tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X1 tptp.nat) (Y1 tptp.nat) (X24 tptp.nat) (Y24 tptp.nat)) (=> (and (@ (@ R X1) X24) (@ (@ R Y1) Y24)) (@ (@ R (@ (@ tptp.plus_plus_nat X1) Y1)) (@ (@ tptp.plus_plus_nat X24) Y24)))) (=> (@ tptp.finite_finite_int S2) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S2) (@ (@ R (@ H X4)) (@ G2 X4)))) (@ (@ R (@ (@ tptp.groups4541462559716669496nt_nat H) S2)) (@ (@ tptp.groups4541462559716669496nt_nat G2) S2))))))))
% 5.98/6.29 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S2 tptp.set_complex) (H (-> tptp.complex tptp.nat)) (G2 (-> tptp.complex tptp.nat))) (=> (@ (@ R tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X1 tptp.nat) (Y1 tptp.nat) (X24 tptp.nat) (Y24 tptp.nat)) (=> (and (@ (@ R X1) X24) (@ (@ R Y1) Y24)) (@ (@ R (@ (@ tptp.plus_plus_nat X1) Y1)) (@ (@ tptp.plus_plus_nat X24) Y24)))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S2) (@ (@ R (@ H X4)) (@ G2 X4)))) (@ (@ R (@ (@ tptp.groups5693394587270226106ex_nat H) S2)) (@ (@ tptp.groups5693394587270226106ex_nat G2) S2))))))))
% 5.98/6.29 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S2 tptp.set_Extended_enat) (H (-> tptp.extended_enat tptp.nat)) (G2 (-> tptp.extended_enat tptp.nat))) (=> (@ (@ R tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X1 tptp.nat) (Y1 tptp.nat) (X24 tptp.nat) (Y24 tptp.nat)) (=> (and (@ (@ R X1) X24) (@ (@ R Y1) Y24)) (@ (@ R (@ (@ tptp.plus_plus_nat X1) Y1)) (@ (@ tptp.plus_plus_nat X24) Y24)))) (=> (@ tptp.finite4001608067531595151d_enat S2) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) S2) (@ (@ R (@ H X4)) (@ G2 X4)))) (@ (@ R (@ (@ tptp.groups2027974829824023292at_nat H) S2)) (@ (@ tptp.groups2027974829824023292at_nat G2) S2))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= A2 tptp.bot_bot_set_complex)) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.ord_less_real (@ F X4)) (@ G2 X4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups5808333547571424918x_real F) A2)) (@ (@ tptp.groups5808333547571424918x_real G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (G2 (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ tptp.ord_less_real (@ F X4)) (@ G2 X4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups4148127829035722712t_real F) A2)) (@ (@ tptp.groups4148127829035722712t_real G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_real (@ F X4)) (@ G2 X4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8097168146408367636l_real F) A2)) (@ (@ tptp.groups8097168146408367636l_real G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.real)) (G2 (-> Bool tptp.real))) (=> (@ tptp.finite_finite_o A2) (=> (not (= A2 tptp.bot_bot_set_o)) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A2) (@ (@ tptp.ord_less_real (@ F X4)) (@ G2 X4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8691415230153176458o_real F) A2)) (@ (@ tptp.groups8691415230153176458o_real G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_real (@ F X4)) (@ G2 X4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8778361861064173332t_real F) A2)) (@ (@ tptp.groups8778361861064173332t_real G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= A2 tptp.bot_bot_set_complex)) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G2 X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A2)) (@ (@ tptp.groups5058264527183730370ex_rat G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat)) (G2 (-> tptp.extended_enat tptp.rat))) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (=> (forall ((X4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) A2) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G2 X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups1392844769737527556at_rat F) A2)) (@ (@ tptp.groups1392844769737527556at_rat G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat)) (G2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G2 X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups1300246762558778688al_rat F) A2)) (@ (@ tptp.groups1300246762558778688al_rat G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.rat)) (G2 (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o A2) (=> (not (= A2 tptp.bot_bot_set_o)) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A2) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G2 X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups7872700643590313910_o_rat F) A2)) (@ (@ tptp.groups7872700643590313910_o_rat G2) A2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G2 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G2 X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F) A2)) (@ (@ tptp.groups2906978787729119204at_rat G2) A2)))))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A2)))) (let ((_let_4 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G2 X)) _let_2)))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (X Bool) (G2 (-> Bool tptp.real))) (let ((_let_1 (@ tptp.groups8691415230153176458o_real G2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_o X) A2)))) (let ((_let_4 (@ (@ tptp.member_o X) A2))) (=> (@ tptp.finite_finite_o A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G2 X)) _let_2)))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A2)))) (let ((_let_4 (@ (@ tptp.member_int X) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G2 X)) _let_2)))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X) A2)))) (let ((_let_4 (@ (@ tptp.member_complex X) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G2 X)) _let_2)))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (X tptp.extended_enat) (G2 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Extended_enat X) A2)))) (let ((_let_4 (@ (@ tptp.member_Extended_enat X) A2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G2 X)) _let_2)))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat G2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A2)))) (let ((_let_4 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G2 X)) _let_2)))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (X Bool) (G2 (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups7872700643590313910_o_rat G2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_o X) A2)))) (let ((_let_4 (@ (@ tptp.member_o X) A2))) (=> (@ tptp.finite_finite_o A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G2 X)) _let_2)))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X) A2)))) (let ((_let_4 (@ (@ tptp.member_nat X) A2))) (=> (@ tptp.finite_finite_nat A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G2 X)) _let_2)))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A2)))) (let ((_let_4 (@ (@ tptp.member_int X) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G2 X)) _let_2)))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G2))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X) A2)))) (let ((_let_4 (@ (@ tptp.member_complex X) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G2 X)) _let_2)))))))))))
% 5.98/6.29 (assert (forall ((S5 tptp.set_o) (T5 tptp.set_o) (S2 tptp.set_o) (I (-> Bool Bool)) (J (-> Bool Bool)) (T3 tptp.set_o) (G2 (-> Bool tptp.real)) (H (-> Bool tptp.real))) (=> (@ tptp.finite_finite_o S5) (=> (@ tptp.finite_finite_o T5) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) (@ (@ tptp.minus_minus_set_o S2) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) (@ (@ tptp.minus_minus_set_o S2) S5)) (@ (@ tptp.member_o (@ J A5)) (@ (@ tptp.minus_minus_set_o T3) T5)))) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) (@ (@ tptp.minus_minus_set_o T3) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) (@ (@ tptp.minus_minus_set_o T3) T5)) (@ (@ tptp.member_o (@ I B5)) (@ (@ tptp.minus_minus_set_o S2) S5)))) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) S5) (= (@ G2 A5) tptp.zero_zero_real))) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) T5) (= (@ H B5) tptp.zero_zero_real))) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) S2) (= (@ H (@ J A5)) (@ G2 A5)))) (= (@ (@ tptp.groups8691415230153176458o_real G2) S2) (@ (@ tptp.groups8691415230153176458o_real H) T3)))))))))))))
% 5.98/6.29 (assert (forall ((S5 tptp.set_o) (T5 tptp.set_int) (S2 tptp.set_o) (I (-> tptp.int Bool)) (J (-> Bool tptp.int)) (T3 tptp.set_int) (G2 (-> Bool tptp.real)) (H (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_o S5) (=> (@ tptp.finite_finite_int T5) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) (@ (@ tptp.minus_minus_set_o S2) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) (@ (@ tptp.minus_minus_set_o S2) S5)) (@ (@ tptp.member_int (@ J A5)) (@ (@ tptp.minus_minus_set_int T3) T5)))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T5)) (@ (@ tptp.member_o (@ I B5)) (@ (@ tptp.minus_minus_set_o S2) S5)))) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) S5) (= (@ G2 A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) T5) (= (@ H B5) tptp.zero_zero_real))) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) S2) (= (@ H (@ J A5)) (@ G2 A5)))) (= (@ (@ tptp.groups8691415230153176458o_real G2) S2) (@ (@ tptp.groups8778361861064173332t_real H) T3)))))))))))))
% 5.98/6.29 (assert (forall ((S5 tptp.set_o) (T5 tptp.set_complex) (S2 tptp.set_o) (I (-> tptp.complex Bool)) (J (-> Bool tptp.complex)) (T3 tptp.set_complex) (G2 (-> Bool tptp.real)) (H (-> tptp.complex tptp.real))) (=> (@ tptp.finite_finite_o S5) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) (@ (@ tptp.minus_minus_set_o S2) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) (@ (@ tptp.minus_minus_set_o S2) S5)) (@ (@ tptp.member_complex (@ J A5)) (@ (@ tptp.minus_811609699411566653omplex T3) T5)))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (@ (@ tptp.member_o (@ I B5)) (@ (@ tptp.minus_minus_set_o S2) S5)))) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) S5) (= (@ G2 A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) T5) (= (@ H B5) tptp.zero_zero_real))) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) S2) (= (@ H (@ J A5)) (@ G2 A5)))) (= (@ (@ tptp.groups8691415230153176458o_real G2) S2) (@ (@ tptp.groups5808333547571424918x_real H) T3)))))))))))))
% 5.98/6.29 (assert (forall ((S5 tptp.set_o) (T5 tptp.set_Extended_enat) (S2 tptp.set_o) (I (-> tptp.extended_enat Bool)) (J (-> Bool tptp.extended_enat)) (T3 tptp.set_Extended_enat) (G2 (-> Bool tptp.real)) (H (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite_finite_o S5) (=> (@ tptp.finite4001608067531595151d_enat T5) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) (@ (@ tptp.minus_minus_set_o S2) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) (@ (@ tptp.minus_minus_set_o S2) S5)) (@ (@ tptp.member_Extended_enat (@ J A5)) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)))) (=> (forall ((B5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B5) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B5) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)) (@ (@ tptp.member_o (@ I B5)) (@ (@ tptp.minus_minus_set_o S2) S5)))) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) S5) (= (@ G2 A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B5) T5) (= (@ H B5) tptp.zero_zero_real))) (=> (forall ((A5 Bool)) (=> (@ (@ tptp.member_o A5) S2) (= (@ H (@ J A5)) (@ G2 A5)))) (= (@ (@ tptp.groups8691415230153176458o_real G2) S2) (@ (@ tptp.groups4148127829035722712t_real H) T3)))))))))))))
% 5.98/6.29 (assert (forall ((S5 tptp.set_int) (T5 tptp.set_o) (S2 tptp.set_int) (I (-> Bool tptp.int)) (J (-> tptp.int Bool)) (T3 tptp.set_o) (G2 (-> tptp.int tptp.real)) (H (-> Bool tptp.real))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite_finite_o T5) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S5)) (@ (@ tptp.member_o (@ J A5)) (@ (@ tptp.minus_minus_set_o T3) T5)))) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) (@ (@ tptp.minus_minus_set_o T3) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) (@ (@ tptp.minus_minus_set_o T3) T5)) (@ (@ tptp.member_int (@ I B5)) (@ (@ tptp.minus_minus_set_int S2) S5)))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S5) (= (@ G2 A5) tptp.zero_zero_real))) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) T5) (= (@ H B5) tptp.zero_zero_real))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S2) (= (@ H (@ J A5)) (@ G2 A5)))) (= (@ (@ tptp.groups8778361861064173332t_real G2) S2) (@ (@ tptp.groups8691415230153176458o_real H) T3)))))))))))))
% 5.98/6.29 (assert (forall ((S5 tptp.set_int) (T5 tptp.set_int) (S2 tptp.set_int) (I (-> tptp.int tptp.int)) (J (-> tptp.int tptp.int)) (T3 tptp.set_int) (G2 (-> tptp.int tptp.real)) (H (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite_finite_int T5) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S5)) (@ (@ tptp.member_int (@ J A5)) (@ (@ tptp.minus_minus_set_int T3) T5)))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T5)) (@ (@ tptp.member_int (@ I B5)) (@ (@ tptp.minus_minus_set_int S2) S5)))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S5) (= (@ G2 A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) T5) (= (@ H B5) tptp.zero_zero_real))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S2) (= (@ H (@ J A5)) (@ G2 A5)))) (= (@ (@ tptp.groups8778361861064173332t_real G2) S2) (@ (@ tptp.groups8778361861064173332t_real H) T3)))))))))))))
% 5.98/6.29 (assert (forall ((S5 tptp.set_int) (T5 tptp.set_complex) (S2 tptp.set_int) (I (-> tptp.complex tptp.int)) (J (-> tptp.int tptp.complex)) (T3 tptp.set_complex) (G2 (-> tptp.int tptp.real)) (H (-> tptp.complex tptp.real))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S5)) (@ (@ tptp.member_complex (@ J A5)) (@ (@ tptp.minus_811609699411566653omplex T3) T5)))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex T3) T5)) (@ (@ tptp.member_int (@ I B5)) (@ (@ tptp.minus_minus_set_int S2) S5)))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S5) (= (@ G2 A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) T5) (= (@ H B5) tptp.zero_zero_real))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S2) (= (@ H (@ J A5)) (@ G2 A5)))) (= (@ (@ tptp.groups8778361861064173332t_real G2) S2) (@ (@ tptp.groups5808333547571424918x_real H) T3)))))))))))))
% 5.98/6.29 (assert (forall ((S5 tptp.set_int) (T5 tptp.set_Extended_enat) (S2 tptp.set_int) (I (-> tptp.extended_enat tptp.int)) (J (-> tptp.int tptp.extended_enat)) (T3 tptp.set_Extended_enat) (G2 (-> tptp.int tptp.real)) (H (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite4001608067531595151d_enat T5) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S5)) (@ (@ tptp.member_Extended_enat (@ J A5)) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)))) (=> (forall ((B5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B5) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B5) (@ (@ tptp.minus_925952699566721837d_enat T3) T5)) (@ (@ tptp.member_int (@ I B5)) (@ (@ tptp.minus_minus_set_int S2) S5)))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S5) (= (@ G2 A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat B5) T5) (= (@ H B5) tptp.zero_zero_real))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S2) (= (@ H (@ J A5)) (@ G2 A5)))) (= (@ (@ tptp.groups8778361861064173332t_real G2) S2) (@ (@ tptp.groups4148127829035722712t_real H) T3)))))))))))))
% 5.98/6.29 (assert (forall ((S5 tptp.set_complex) (T5 tptp.set_o) (S2 tptp.set_complex) (I (-> Bool tptp.complex)) (J (-> tptp.complex Bool)) (T3 tptp.set_o) (G2 (-> tptp.complex tptp.real)) (H (-> Bool tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite_finite_o T5) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (@ (@ tptp.member_o (@ J A5)) (@ (@ tptp.minus_minus_set_o T3) T5)))) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) (@ (@ tptp.minus_minus_set_o T3) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) (@ (@ tptp.minus_minus_set_o T3) T5)) (@ (@ tptp.member_complex (@ I B5)) (@ (@ tptp.minus_811609699411566653omplex S2) S5)))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) S5) (= (@ G2 A5) tptp.zero_zero_real))) (=> (forall ((B5 Bool)) (=> (@ (@ tptp.member_o B5) T5) (= (@ H B5) tptp.zero_zero_real))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) S2) (= (@ H (@ J A5)) (@ G2 A5)))) (= (@ (@ tptp.groups5808333547571424918x_real G2) S2) (@ (@ tptp.groups8691415230153176458o_real H) T3)))))))))))))
% 5.98/6.29 (assert (forall ((S5 tptp.set_complex) (T5 tptp.set_int) (S2 tptp.set_complex) (I (-> tptp.int tptp.complex)) (J (-> tptp.complex tptp.int)) (T3 tptp.set_int) (G2 (-> tptp.complex tptp.real)) (H (-> tptp.int tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite_finite_int T5) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex S2) S5)) (@ (@ tptp.member_int (@ J A5)) (@ (@ tptp.minus_minus_set_int T3) T5)))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T5)) (@ (@ tptp.member_complex (@ I B5)) (@ (@ tptp.minus_811609699411566653omplex S2) S5)))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) S5) (= (@ G2 A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) T5) (= (@ H B5) tptp.zero_zero_real))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) S2) (= (@ H (@ J A5)) (@ G2 A5)))) (= (@ (@ tptp.groups5808333547571424918x_real G2) S2) (@ (@ tptp.groups8778361861064173332t_real H) T3)))))))))))))
% 5.98/6.29 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) M2) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.times_times_nat (@ _let_1 M2)) (@ (@ tptp.binomial M2) K)) (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.minus_minus_nat M2) K)))))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (= (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ _let_1 tptp.one_one_nat)) K))))))
% 5.98/6.29 (assert (= tptp.distinct_int (lambda ((Xs2 tptp.list_int)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs2)) (forall ((J3 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs2))) (=> (@ (@ tptp.ord_less_nat J3) (@ tptp.size_size_list_int Xs2)) (=> (not (= I4 J3)) (not (= (@ _let_1 I4) (@ _let_1 J3))))))))))))
% 5.98/6.29 (assert (= tptp.distinct_VEBT_VEBT (lambda ((Xs2 tptp.list_VEBT_VEBT)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (forall ((J3 tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Xs2))) (=> (@ (@ tptp.ord_less_nat J3) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (=> (not (= I4 J3)) (not (= (@ _let_1 I4) (@ _let_1 J3))))))))))))
% 5.98/6.29 (assert (= tptp.distinct_nat (lambda ((Xs2 tptp.list_nat)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs2)) (forall ((J3 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_nat J3) (@ tptp.size_size_list_nat Xs2)) (=> (not (= I4 J3)) (not (= (@ _let_1 I4) (@ _let_1 J3))))))))))))
% 5.98/6.29 (assert (forall ((Xs tptp.list_int) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (let ((_let_2 (@ tptp.size_size_list_int Xs))) (=> (@ tptp.distinct_int Xs) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (= (@ _let_1 I) (@ _let_1 J)) (= I J)))))))))
% 5.98/6.29 (assert (forall ((Xs tptp.list_VEBT_VEBT) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Xs))) (let ((_let_2 (@ tptp.size_s6755466524823107622T_VEBT Xs))) (=> (@ tptp.distinct_VEBT_VEBT Xs) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (= (@ _let_1 I) (@ _let_1 J)) (= I J)))))))))
% 5.98/6.29 (assert (forall ((Xs tptp.list_nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (let ((_let_2 (@ tptp.size_size_list_nat Xs))) (=> (@ tptp.distinct_nat Xs) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (= (@ _let_1 I) (@ _let_1 J)) (= I J)))))))))
% 5.98/6.29 (assert (forall ((S tptp.set_o) (F (-> Bool tptp.real)) (I Bool)) (=> (@ tptp.finite_finite_o S) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups8691415230153176458o_real F) S) tptp.zero_zero_real) (=> (@ (@ tptp.member_o I) S) (= (@ F I) tptp.zero_zero_real)))))))
% 5.98/6.29 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.real)) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F) S) tptp.zero_zero_real) (=> (@ (@ tptp.member_int I) S) (= (@ F I) tptp.zero_zero_real)))))))
% 5.98/6.29 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.real)) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F) S) tptp.zero_zero_real) (=> (@ (@ tptp.member_complex I) S) (= (@ F I) tptp.zero_zero_real)))))))
% 5.98/6.29 (assert (forall ((S tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (I tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups4148127829035722712t_real F) S) tptp.zero_zero_real) (=> (@ (@ tptp.member_Extended_enat I) S) (= (@ F I) tptp.zero_zero_real)))))))
% 5.98/6.29 (assert (forall ((S tptp.set_o) (F (-> Bool tptp.rat)) (I Bool)) (=> (@ tptp.finite_finite_o S) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups7872700643590313910_o_rat F) S) tptp.zero_zero_rat) (=> (@ (@ tptp.member_o I) S) (= (@ F I) tptp.zero_zero_rat)))))))
% 5.98/6.29 (assert (forall ((S tptp.set_nat) (F (-> tptp.nat tptp.rat)) (I tptp.nat)) (=> (@ tptp.finite_finite_nat S) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) S) tptp.zero_zero_rat) (=> (@ (@ tptp.member_nat I) S) (= (@ F I) tptp.zero_zero_rat)))))))
% 5.98/6.29 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.rat)) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) S) tptp.zero_zero_rat) (=> (@ (@ tptp.member_int I) S) (= (@ F I) tptp.zero_zero_rat)))))))
% 5.98/6.29 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.rat)) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) S) tptp.zero_zero_rat) (=> (@ (@ tptp.member_complex I) S) (= (@ F I) tptp.zero_zero_rat)))))))
% 5.98/6.29 (assert (forall ((S tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat)) (I tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups1392844769737527556at_rat F) S) tptp.zero_zero_rat) (=> (@ (@ tptp.member_Extended_enat I) S) (= (@ F I) tptp.zero_zero_rat)))))))
% 5.98/6.29 (assert (forall ((S tptp.set_o) (F (-> Bool tptp.nat)) (I Bool)) (=> (@ tptp.finite_finite_o S) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) S) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I2)))) (=> (= (@ (@ tptp.groups8507830703676809646_o_nat F) S) tptp.zero_zero_nat) (=> (@ (@ tptp.member_o I) S) (= (@ F I) tptp.zero_zero_nat)))))))
% 5.98/6.29 (assert (forall ((S tptp.set_o) (F (-> Bool tptp.real)) (B2 tptp.real) (I Bool)) (=> (@ tptp.finite_finite_o S) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups8691415230153176458o_real F) S) B2) (=> (@ (@ tptp.member_o I) S) (@ (@ tptp.ord_less_eq_real (@ F I)) B2)))))))
% 5.98/6.29 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.real)) (B2 tptp.real) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F) S) B2) (=> (@ (@ tptp.member_int I) S) (@ (@ tptp.ord_less_eq_real (@ F I)) B2)))))))
% 5.98/6.29 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.real)) (B2 tptp.real) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F) S) B2) (=> (@ (@ tptp.member_complex I) S) (@ (@ tptp.ord_less_eq_real (@ F I)) B2)))))))
% 5.98/6.29 (assert (forall ((S tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (B2 tptp.real) (I tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) S) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2)))) (=> (= (@ (@ tptp.groups4148127829035722712t_real F) S) B2) (=> (@ (@ tptp.member_Extended_enat I) S) (@ (@ tptp.ord_less_eq_real (@ F I)) B2)))))))
% 5.98/6.29 (assert (forall ((S tptp.set_o) (F (-> Bool tptp.rat)) (B2 tptp.rat) (I Bool)) (=> (@ tptp.finite_finite_o S) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups7872700643590313910_o_rat F) S) B2) (=> (@ (@ tptp.member_o I) S) (@ (@ tptp.ord_less_eq_rat (@ F I)) B2)))))))
% 5.98/6.29 (assert (forall ((S tptp.set_nat) (F (-> tptp.nat tptp.rat)) (B2 tptp.rat) (I tptp.nat)) (=> (@ tptp.finite_finite_nat S) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) S) B2) (=> (@ (@ tptp.member_nat I) S) (@ (@ tptp.ord_less_eq_rat (@ F I)) B2)))))))
% 5.98/6.29 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.rat)) (B2 tptp.rat) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) S) B2) (=> (@ (@ tptp.member_int I) S) (@ (@ tptp.ord_less_eq_rat (@ F I)) B2)))))))
% 5.98/6.29 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.rat)) (B2 tptp.rat) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) S) B2) (=> (@ (@ tptp.member_complex I) S) (@ (@ tptp.ord_less_eq_rat (@ F I)) B2)))))))
% 5.98/6.29 (assert (forall ((S tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat)) (B2 tptp.rat) (I tptp.extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat S) (=> (forall ((I2 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat I2) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I2)))) (=> (= (@ (@ tptp.groups1392844769737527556at_rat F) S) B2) (=> (@ (@ tptp.member_Extended_enat I) S) (@ (@ tptp.ord_less_eq_rat (@ F I)) B2)))))))
% 5.98/6.29 (assert (forall ((S tptp.set_o) (F (-> Bool tptp.nat)) (B2 tptp.nat) (I Bool)) (=> (@ tptp.finite_finite_o S) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) S) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I2)))) (=> (= (@ (@ tptp.groups8507830703676809646_o_nat F) S) B2) (=> (@ (@ tptp.member_o I) S) (@ (@ tptp.ord_less_eq_nat (@ F I)) B2)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat_rat) (K tptp.nat)) (=> (@ tptp.finite7830837933032798814at_rat A2) (= (@ tptp.finite8736671560171388117at_rat (@ tptp.collect_set_nat_rat (lambda ((B6 tptp.set_nat_rat)) (and (@ (@ tptp.ord_le2679597024174929757at_rat B6) A2) (= (@ tptp.finite_card_nat_rat B6) K))))) (@ (@ tptp.binomial (@ tptp.finite_card_nat_rat A2)) K)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_list_nat) (K tptp.nat)) (=> (@ tptp.finite8100373058378681591st_nat A2) (= (@ tptp.finite2364142230527598318st_nat (@ tptp.collect_set_list_nat (lambda ((B6 tptp.set_list_nat)) (and (@ (@ tptp.ord_le6045566169113846134st_nat B6) A2) (= (@ tptp.finite_card_list_nat B6) K))))) (@ (@ tptp.binomial (@ tptp.finite_card_list_nat A2)) K)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_set_nat) (K tptp.nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (= (@ tptp.finite1149291290879098388et_nat (@ tptp.collect_set_set_nat (lambda ((B6 tptp.set_set_nat)) (and (@ (@ tptp.ord_le6893508408891458716et_nat B6) A2) (= (@ tptp.finite_card_set_nat B6) K))))) (@ (@ tptp.binomial (@ tptp.finite_card_set_nat A2)) K)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (K tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (= (@ tptp.finite_card_set_nat (@ tptp.collect_set_nat (lambda ((B6 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B6) A2) (= (@ tptp.finite_card_nat B6) K))))) (@ (@ tptp.binomial (@ tptp.finite_card_nat A2)) K)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (K tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ tptp.finite903997441450111292omplex (@ tptp.collect_set_complex (lambda ((B6 tptp.set_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex B6) A2) (= (@ tptp.finite_card_complex B6) K))))) (@ (@ tptp.binomial (@ tptp.finite_card_complex A2)) K)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (K tptp.nat)) (=> (@ tptp.finite6177210948735845034at_nat A2) (= (@ tptp.finite4356350796350151305at_nat (@ tptp.collec5514110066124741708at_nat (lambda ((B6 tptp.set_Pr1261947904930325089at_nat)) (and (@ (@ tptp.ord_le3146513528884898305at_nat B6) A2) (= (@ tptp.finite711546835091564841at_nat B6) K))))) (@ (@ tptp.binomial (@ tptp.finite711546835091564841at_nat A2)) K)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (K tptp.nat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ tptp.finite3719263829065406702d_enat (@ tptp.collec2260605976452661553d_enat (lambda ((B6 tptp.set_Extended_enat)) (and (@ (@ tptp.ord_le7203529160286727270d_enat B6) A2) (= (@ tptp.finite121521170596916366d_enat B6) K))))) (@ (@ tptp.binomial (@ tptp.finite121521170596916366d_enat A2)) K)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (K tptp.nat)) (=> (@ tptp.finite_finite_int A2) (= (@ tptp.finite_card_set_int (@ tptp.collect_set_int (lambda ((B6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B6) A2) (= (@ tptp.finite_card_int B6) K))))) (@ (@ tptp.binomial (@ tptp.finite_card_int A2)) K)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (G2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G2))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X3 tptp.int)) (= (@ G2 X3) tptp.zero_zero_real))))) (@ _let_1 A2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (G2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G2))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (= (@ G2 X3) tptp.zero_zero_real))))) (@ _let_1 A2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.real))) (let ((_let_1 (@ tptp.groups4148127829035722712t_real G2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ tptp.collec4429806609662206161d_enat (lambda ((X3 tptp.extended_enat)) (= (@ G2 X3) tptp.zero_zero_real))))) (@ _let_1 A2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (G2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G2))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X3 tptp.int)) (= (@ G2 X3) tptp.zero_zero_rat))))) (@ _let_1 A2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (G2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G2))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (= (@ G2 X3) tptp.zero_zero_rat))))) (@ _let_1 A2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.groups1392844769737527556at_rat G2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ tptp.collec4429806609662206161d_enat (lambda ((X3 tptp.extended_enat)) (= (@ G2 X3) tptp.zero_zero_rat))))) (@ _let_1 A2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (G2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G2))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X3 tptp.int)) (= (@ G2 X3) tptp.zero_zero_nat))))) (@ _let_1 A2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (G2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G2))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (= (@ G2 X3) tptp.zero_zero_nat))))) (@ _let_1 A2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (G2 (-> tptp.extended_enat tptp.nat))) (let ((_let_1 (@ tptp.groups2027974829824023292at_nat G2))) (=> (@ tptp.finite4001608067531595151d_enat A2) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A2) (@ tptp.collec4429806609662206161d_enat (lambda ((X3 tptp.extended_enat)) (= (@ G2 X3) tptp.zero_zero_nat))))) (@ _let_1 A2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (G2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G2))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (= (@ G2 X3) tptp.zero_zero_int))))) (@ _let_1 A2))))))
% 5.98/6.29 (assert (forall ((X tptp.complex) (M2 tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_complex X) (@ (@ tptp.plus_plus_nat M2) I4)))) I5) (@ (@ tptp.times_times_complex (@ _let_1 M2)) (@ (@ tptp.groups2073611262835488442omplex _let_1) I5))))))
% 5.98/6.29 (assert (forall ((X tptp.rat) (M2 tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_rat X) (@ (@ tptp.plus_plus_nat M2) I4)))) I5) (@ (@ tptp.times_times_rat (@ _let_1 M2)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) I5))))))
% 5.98/6.29 (assert (forall ((X tptp.int) (M2 tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_int X) (@ (@ tptp.plus_plus_nat M2) I4)))) I5) (@ (@ tptp.times_times_int (@ _let_1 M2)) (@ (@ tptp.groups3539618377306564664at_int _let_1) I5))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (M2 tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_real X))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_real X) (@ (@ tptp.plus_plus_nat M2) I4)))) I5) (@ (@ tptp.times_times_real (@ _let_1 M2)) (@ (@ tptp.groups6591440286371151544t_real _let_1) I5))))))
% 5.98/6.29 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I5) (= (@ tptp.exp_real (@ (@ tptp.groups8778361861064173332t_real F) I5)) (@ (@ tptp.groups2316167850115554303t_real (lambda ((X3 tptp.int)) (@ tptp.exp_real (@ F X3)))) I5)))))
% 5.98/6.29 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ tptp.exp_real (@ (@ tptp.groups5808333547571424918x_real F) I5)) (@ (@ tptp.groups766887009212190081x_real (lambda ((X3 tptp.complex)) (@ tptp.exp_real (@ F X3)))) I5)))))
% 5.98/6.29 (assert (forall ((I5 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.real))) (=> (@ tptp.finite6177210948735845034at_nat I5) (= (@ tptp.exp_real (@ (@ tptp.groups4567486121110086003t_real F) I5)) (@ (@ tptp.groups6036352826371341000t_real (lambda ((X3 tptp.product_prod_nat_nat)) (@ tptp.exp_real (@ F X3)))) I5)))))
% 5.98/6.29 (assert (forall ((I5 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (@ tptp.finite4001608067531595151d_enat I5) (= (@ tptp.exp_real (@ (@ tptp.groups4148127829035722712t_real F) I5)) (@ (@ tptp.groups97031904164794029t_real (lambda ((X3 tptp.extended_enat)) (@ tptp.exp_real (@ F X3)))) I5)))))
% 5.98/6.29 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ tptp.exp_complex (@ (@ tptp.groups7754918857620584856omplex F) I5)) (@ (@ tptp.groups3708469109370488835omplex (lambda ((X3 tptp.complex)) (@ tptp.exp_complex (@ F X3)))) I5)))))
% 5.98/6.29 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat I5) (= (@ tptp.exp_real (@ (@ tptp.groups6591440286371151544t_real F) I5)) (@ (@ tptp.groups129246275422532515t_real (lambda ((X3 tptp.nat)) (@ tptp.exp_real (@ F X3)))) I5)))))
% 5.98/6.29 (assert (forall ((G2 (-> tptp.nat tptp.nat)) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M2))) (= (@ (@ tptp.groups3542108847815614940at_nat G2) _let_1) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G2 (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N)) I4)))) _let_1)))))
% 5.98/6.29 (assert (forall ((G2 (-> tptp.nat tptp.real)) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M2))) (= (@ (@ tptp.groups6591440286371151544t_real G2) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G2 (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M2) N)) I4)))) _let_1)))))
% 5.98/6.29 (assert (forall ((N5 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat N5) (=> (forall ((N2 tptp.nat)) (=> (not (@ (@ tptp.member_nat N2) N5)) (= (@ F N2) tptp.zero_zero_int))) (= (@ tptp.suminf_int F) (@ (@ tptp.groups3539618377306564664at_int F) N5))))))
% 5.98/6.29 (assert (forall ((N5 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat N5) (=> (forall ((N2 tptp.nat)) (=> (not (@ (@ tptp.member_nat N2) N5)) (= (@ F N2) tptp.zero_zero_nat))) (= (@ tptp.suminf_nat F) (@ (@ tptp.groups3542108847815614940at_nat F) N5))))))
% 5.98/6.29 (assert (forall ((N5 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat N5) (=> (forall ((N2 tptp.nat)) (=> (not (@ (@ tptp.member_nat N2) N5)) (= (@ F N2) tptp.zero_zero_real))) (= (@ tptp.suminf_real F) (@ (@ tptp.groups6591440286371151544t_real F) N5))))))
% 5.98/6.29 (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)))))))))
% 5.98/6.29 (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)))))))))
% 5.98/6.29 (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)))))))))
% 5.98/6.29 (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)))))))))
% 5.98/6.29 (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)))))))))
% 5.98/6.29 (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)))))))))
% 5.98/6.29 (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)))))))))
% 5.98/6.29 (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)))))))))
% 5.98/6.29 (assert (forall ((I5 tptp.set_Extended_enat) (I tptp.extended_enat) (F (-> tptp.extended_enat tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ 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_rat tptp.zero_zero_rat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups1392844769737527556at_rat F) I5)))))))))
% 5.98/6.29 (assert (forall ((I5 tptp.set_o) (I Bool) (F (-> Bool tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ 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_nat tptp.zero_zero_nat) (@ F I2)))) (@ _let_1 (@ (@ tptp.groups8507830703676809646_o_nat F) I5)))))))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real X))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real _let_1)) tptp.one_one_real))))))
% 5.98/6.29 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex _let_1)) tptp.one_one_complex))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.rat)) (K4 tptp.rat)) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) A2) (@ (@ tptp.ord_less_eq_rat (@ F I2)) K4))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups7872700643590313910_o_rat F) A2)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_o A2))) K4)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (K4 tptp.rat)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) A2) (@ (@ tptp.ord_less_eq_rat (@ F I2)) K4))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A2)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_complex A2))) K4)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (K4 tptp.rat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) A2) (@ (@ tptp.ord_less_eq_rat (@ F I2)) K4))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) A2)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_nat A2))) K4)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat)) (K4 tptp.rat)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) A2) (@ (@ tptp.ord_less_eq_rat (@ F I2)) K4))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A2)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_int A2))) K4)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.nat)) (K4 tptp.nat)) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) A2) (@ (@ tptp.ord_less_eq_nat (@ F I2)) K4))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups8507830703676809646_o_nat F) A2)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_o A2))) K4)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (K4 tptp.nat)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) A2) (@ (@ tptp.ord_less_eq_nat (@ F I2)) K4))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_complex A2))) K4)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (K4 tptp.nat)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) A2) (@ (@ tptp.ord_less_eq_nat (@ F I2)) K4))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_int A2))) K4)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_o) (F (-> Bool tptp.int)) (K4 tptp.int)) (=> (forall ((I2 Bool)) (=> (@ (@ tptp.member_o I2) A2) (@ (@ tptp.ord_less_eq_int (@ F I2)) K4))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups8505340233167759370_o_int F) A2)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ tptp.finite_card_o A2))) K4)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int)) (K4 tptp.int)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) A2) (@ (@ tptp.ord_less_eq_int (@ F I2)) K4))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups5690904116761175830ex_int F) A2)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ tptp.finite_card_complex A2))) K4)))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int)) (K4 tptp.int)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) A2) (@ (@ tptp.ord_less_eq_int (@ F I2)) K4))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) A2)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ tptp.finite_card_nat A2))) K4)))))
% 5.98/6.29 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N) _let_1)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) K))))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (forall ((K tptp.nat) (K7 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) K7) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K7)) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 K7)))))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (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))))))))
% 5.98/6.29 (assert (forall ((K tptp.nat) (K7 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) K7) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) K) (=> (@ (@ tptp.ord_less_eq_nat K7) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K7)) (@ _let_1 K))))))))
% 5.98/6.29 (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))))
% 5.98/6.29 (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)))))))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (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))))))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (assert (forall ((K tptp.nat) (K7 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) K7) (=> (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K)) (=> (@ (@ tptp.ord_less_eq_nat K7) N) (@ (@ tptp.ord_less_nat (@ _let_1 K7)) (@ _let_1 K))))))))
% 5.98/6.29 (assert (forall ((K tptp.nat) (K7 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) K7) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K7)) N) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 K7)))))))
% 5.98/6.29 (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))))))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.binomial N) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) _let_1)))))
% 5.98/6.29 (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 ((Q3 tptp.nat)) (@ (@ tptp.ord_less_nat Q3) N))))))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) (@ tptp.suc N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 5.98/6.29 (assert (forall ((A 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 A) (@ (@ 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) A)) (@ (@ tptp.times_times_nat N) D)))) _let_1)))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or1269000886237332187st_nat M2) 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 M2) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (assert (forall ((A0 tptp.int) (A12 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int A0) A12)) (=> (forall ((K2 tptp.int) (L4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K2) L4)) (=> (=> (not (and (@ (@ tptp.member_int K2) _let_2) (@ (@ tptp.member_int L4) _let_2))) (@ (@ P (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L4) _let_1))) (@ (@ P K2) L4)))))) (@ (@ P A0) A12)))))
% 5.98/6.29 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.nat_pr5047031295181774490ux_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa2)))) (let ((_let_2 (@ tptp.suc X))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat Xa2) X))) (=> (= (@ (@ tptp.nat_prod_decode_aux X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X) Xa2)))) (=> (not _let_3) (= Y (@ (@ tptp.nat_prod_decode_aux _let_2) (@ (@ tptp.minus_minus_nat Xa2) _let_2))))) (not _let_1))))))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X3 tptp.complex)) X3)) (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) C)))) tptp.zero_zero_complex))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X3 tptp.complex)) X3)) (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N) tptp.one_one_complex)))) tptp.zero_zero_complex))))
% 5.98/6.29 (assert (forall ((M2 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M2) N) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X3 tptp.int)) X3)) (@ (@ tptp.set_or1266510415728281911st_int M2) 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 M2) (@ (@ tptp.minus_minus_int M2) tptp.one_one_int)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 5.98/6.29 (assert (forall ((A0 tptp.int) (A12 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int A0) A12)) (=> (forall ((I2 tptp.int) (J2 tptp.int)) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I2) J2)) (=> (=> (@ (@ tptp.ord_less_eq_int I2) J2) (@ (@ P (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J2)) (@ (@ P I2) J2)))) (@ (@ P A0) A12)))))
% 5.98/6.29 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.set_ord_lessThan_nat K))))
% 5.98/6.29 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.set_ord_atMost_nat K))))
% 5.98/6.29 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_lessThan_nat U)) U)))
% 5.98/6.29 (assert (= (@ tptp.set_ord_lessThan_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 5.98/6.29 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_atMost_nat U)) (@ tptp.suc U))))
% 5.98/6.29 (assert (= (@ tptp.set_ord_atMost_nat tptp.zero_zero_nat) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 5.98/6.29 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ tptp.set_ord_atMost_nat K))))
% 5.98/6.29 (assert (= tptp.set_ord_atMost_nat (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat)))
% 5.98/6.29 (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))))))
% 5.98/6.29 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ (@ tptp.insert_nat K) (@ tptp.set_ord_lessThan_nat K)))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N) tptp.bot_bot_set_nat) (= N tptp.zero_zero_nat))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S2) (exists ((K2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S2) (@ tptp.set_ord_lessThan_nat K2))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N) J3)) N))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ _let_1 M2)) tptp.one_one_nat)) (@ _let_1 tptp.one_one_nat))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N) J3)) N))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat N) M2)) tptp.one_one_nat)) M2))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) K3)) (@ (@ tptp.minus_minus_nat M2) K3)))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.binomial (@ tptp.suc N)) M2)))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (A (-> tptp.nat tptp.nat)) (N tptp.nat) (B (-> tptp.nat tptp.nat)) (X tptp.nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) I2) (= (@ A I2) tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J2) (= (@ B J2) tptp.zero_zero_nat))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I4)) (@ (@ tptp.power_power_nat X) I4)))) (@ tptp.set_ord_atMost_nat M2))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ B J3)) (@ (@ tptp.power_power_nat X) 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 (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_nat X) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M2) N))))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X)) (= (@ tptp.exp_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) M3)) (@ tptp.semiri2265585572941072030t_real M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) M2))) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.power_power_nat _let_1) _let_2))))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat I4) (@ (@ tptp.binomial N) I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (not (= X tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T6 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T6))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X)) (= (@ tptp.exp_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) M3)) (@ tptp.semiri2265585572941072030t_real M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M2) tptp.one_one_nat) (= M2 tptp.one_one_nat))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M2) _let_1) (= M2 _let_1)))))
% 5.98/6.29 (assert (forall ((K tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K)))
% 5.98/6.29 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N)) (or (= K tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat M2) N))))))
% 5.98/6.29 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ tptp.nat_set_decode X)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X)))))
% 5.98/6.29 (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))))
% 5.98/6.29 (assert (forall ((M2 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 M2) N)) (or (@ (@ tptp.ord_less_nat M2) N) (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)))))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat N) _let_1)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M2) N) (=> (@ (@ tptp.dvd_dvd_nat N) M2) (= M2 N)))))
% 5.98/6.29 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 5.98/6.29 (assert (forall ((A tptp.nat)) (let ((_let_1 (not (= A tptp.zero_zero_nat)))) (= _let_1 (and (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat) _let_1)))))
% 5.98/6.29 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 5.98/6.29 (assert (forall ((A tptp.nat)) (not (and (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (not (= tptp.zero_zero_nat A))))))
% 5.98/6.29 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)))
% 5.98/6.29 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)))))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_nat M2) N) (not (@ (@ tptp.dvd_dvd_nat N) M2))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ (@ tptp.dvd_dvd_nat M2) N) (@ _let_1 M2))))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M2))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2)) (or (@ (@ tptp.ord_less_nat N) M2) (@ _let_1 N))))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ _let_1 N) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2)))))))
% 5.98/6.29 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (=> (@ _let_1 M2) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (@ _let_1 N)))))))
% 5.98/6.29 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)) (=> (@ _let_1 N) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (@ _let_1 M2)))))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.dvd_dvd_nat M2) N))))))
% 5.98/6.29 (assert (forall ((K tptp.nat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.dvd_dvd_nat M2) N))))))
% 5.98/6.29 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((D6 tptp.nat) (X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D6))) (and (@ _let_1 A) (@ _let_1 B) (= (@ (@ tptp.times_times_nat A) X4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) D6))))))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat M2) N)) (not (@ (@ tptp.dvd_dvd_nat N) M2)))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (M2 tptp.nat) (Q4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (= (@ (@ tptp.modulo_modulo_nat M2) Q4) (@ (@ tptp.modulo_modulo_nat N) Q4)) (@ (@ tptp.dvd_dvd_nat Q4) (@ (@ tptp.minus_minus_nat M2) N))))))
% 5.98/6.29 (assert (forall ((D tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat D) N) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) D)) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real D))))))
% 5.98/6.29 (assert (forall ((G2 (-> tptp.nat tptp.real)) (X tptp.real)) (=> (@ (@ tptp.sums_real G2) X) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N4)) tptp.zero_zero_real) (@ G2 (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) _let_1)))))) X))))
% 5.98/6.29 (assert (forall ((G2 (-> tptp.nat tptp.real)) (X tptp.real) (F (-> tptp.nat tptp.real)) (Y tptp.real)) (=> (@ (@ tptp.sums_real G2) X) (=> (@ (@ tptp.sums_real F) Y) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N4)) (@ F (@ (@ tptp.divide_divide_nat N4) _let_1))) (@ G2 (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) _let_1)))))) (@ (@ tptp.plus_plus_real X) Y))))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M2) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.dvd_dvd_nat M2) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((D5 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D5) M2)))))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M2) N)) M2) (= N tptp.one_one_nat)))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat N) M2)) M2) (= N tptp.one_one_nat)))))
% 5.98/6.29 (assert (forall ((Q4 tptp.nat) (N tptp.nat) (R2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat R2) M2))) (let ((_let_2 (@ tptp.dvd_dvd_nat M2))) (let ((_let_3 (@ tptp.ord_less_eq_nat Q4))) (=> (@ _let_3 N) (=> (@ _let_3 _let_1) (= (@ _let_2 (@ (@ tptp.minus_minus_nat N) Q4)) (@ _let_2 (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat _let_1) Q4)))))))))))
% 5.98/6.29 (assert (forall ((I tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 5.98/6.29 (assert (forall ((R2 tptp.nat) (N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat R2) N) (=> (@ (@ tptp.ord_less_eq_nat R2) M2) (=> (@ (@ tptp.dvd_dvd_nat N) (@ (@ tptp.minus_minus_nat M2) R2)) (= (@ (@ tptp.modulo_modulo_nat M2) N) R2))))))
% 5.98/6.29 (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))))
% 5.98/6.29 (assert (forall ((K tptp.nat) (M2 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 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.nat_set_encode A2)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A2))))))
% 5.98/6.29 (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))))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) (@ F I4)) (@ G2 I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) tptp.one_one_nat)))) _let_1))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X))) (@ (@ tptp.power_power_real (@ _let_1 X)) N))))))
% 5.98/6.29 (assert (= tptp.sin_coeff (lambda ((N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N4)) tptp.zero_zero_real) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N4) (@ tptp.suc tptp.zero_zero_nat))) _let_1))) (@ tptp.semiri2265585572941072030t_real N4)))))))
% 5.98/6.29 (assert (forall ((X tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y (@ (@ tptp.vEBT_Leaf false) false))))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y) (=> (=> (= X tptp.zero_zero_nat) _let_1) (=> (=> (= X (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (=> (= X _let_2) (not (and (=> _let_8 (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4)))))))))))))))))))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N4)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))) (@ tptp.sin_real X))))
% 5.98/6.29 (assert (= (@ tptp.sin_coeff tptp.zero_zero_nat) tptp.zero_zero_real))
% 5.98/6.29 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) X))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) tptp.one_one_real)))
% 5.98/6.29 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X))) (@ tptp.abs_abs_real X))))
% 5.98/6.29 (assert (forall ((M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (=> (@ (@ tptp.dvd_dvd_int M2) N) (=> (@ (@ tptp.dvd_dvd_int N) M2) (= M2 N))))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X)) (@ tptp.sin_real X)))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ _let_1 (@ tptp.sin_real X)))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.sin_real X))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X))) tptp.one_one_real)))
% 5.98/6.29 (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)))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (assert (forall ((D tptp.int) (N tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) N) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) D)) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real D))))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real X)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M3)) (@ (@ tptp.power_power_real X) M3)))) (@ tptp.set_ord_lessThan_nat N))))) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real X)) N)))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (assert (forall ((Z tptp.int) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.nat2 Z)) M2) (and (=> _let_1 (@ (@ tptp.dvd_dvd_int Z) (@ tptp.semiri1314217659103216013at_int M2))) (=> (not _let_1) (= M2 tptp.zero_zero_nat)))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_1) (=> (= (@ tptp.sin_real X) (@ tptp.sin_real Y)) (= X Y))))))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) (@ tptp.sin_real Y)) (@ _let_1 Y)))))))))))
% 5.98/6.29 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y)) (@ tptp.sin_real X))))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.pi) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) tptp.zero_zero_real)))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_1) (= (@ (@ tptp.ord_less_real (@ tptp.sin_real X)) (@ tptp.sin_real Y)) (@ (@ tptp.ord_less_real X) Y))))))))))
% 5.98/6.29 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.sin_real Y)) (@ tptp.sin_real X))))))))
% 5.98/6.29 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (exists ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X4) (@ (@ tptp.ord_less_eq_real X4) _let_1) (= (@ tptp.sin_real X4) Y) (forall ((Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y4) (@ (@ tptp.ord_less_eq_real Y4) _let_1) (= (@ tptp.sin_real Y4) Y)) (= Y4 X4)))))))))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X)) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M3)) (@ (@ tptp.power_power_real X) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T6) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) X) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M3)) (@ (@ tptp.power_power_real X) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T6) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_real T6) X) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M3)) (@ (@ tptp.power_power_real X) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T6) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 5.98/6.29 (assert (forall ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ tptp.vEBT_vebt_buildup _let_2))) (let ((_let_9 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (and (=> _let_9 (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_9) (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))))))))))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 5.98/6.29 (assert (forall ((X tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel))) (let ((_let_3 (= Y (@ (@ tptp.vEBT_Leaf false) false)))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y) (=> (@ _let_2 X) (=> (=> (= X tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) _let_2))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_2))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_2) _let_1))) (=> (= X _let_1) (=> (and (=> _let_8 (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))) (not (@ (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel) _let_1)))))))))))))))))))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (not (forall ((T6 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (=> (@ (@ tptp.ord_less_real T6) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (=> (= X (@ tptp.cos_real T6)) (not (= Y (@ tptp.sin_real T6))))))))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) tptp.one_one_real)))
% 5.98/6.29 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ tptp.arcosh_real (@ tptp.cosh_real X)) X))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cosh_real X))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_eq_real X) Y)))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y))) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y)) (@ _let_1 X)))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.cosh_real X))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X)) (@ tptp.cosh_real X))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.pi) (=> (= (@ tptp.cos_real X) (@ tptp.cos_real Y)) (= X Y)))))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (=> (@ _let_2 Y) (=> (@ _let_1 tptp.pi) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)) (@ _let_1 X))))))))))
% 5.98/6.29 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.cos_real X))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.cos_real X))) tptp.one_one_real)))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_real X) Y)))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_real Y) X))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.pi) (= (@ (@ tptp.ord_less_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)) (@ (@ tptp.ord_less_real Y) X)))))))))
% 5.98/6.29 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ (@ tptp.ord_less_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)))))))
% 5.98/6.29 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real Y)) (@ tptp.cos_real X)))))))
% 5.98/6.29 (assert (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X4) tptp.zero_zero_real) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_eq_real Y4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real Y4) tptp.zero_zero_real)) (= Y4 X4))))))
% 5.98/6.29 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 5.98/6.29 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y) (=> (@ (@ tptp.ord_less_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cos_real Y)) (@ tptp.cos_real X)))))))
% 5.98/6.29 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (= (@ tptp.cos_real X4) Y) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_eq_real Y4) tptp.pi) (= (@ tptp.cos_real Y4) Y)) (= Y4 X4)))))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (exists ((Y3 tptp.real)) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) Y3) (@ (@ tptp.ord_less_eq_real Y3) tptp.pi) (= (@ tptp.sin_real Y3) (@ tptp.sin_real X)) (= (@ tptp.cos_real Y3) (@ tptp.cos_real X))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y))))) tptp.one_one_real)))
% 5.98/6.29 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cos_real X)))))))
% 5.98/6.29 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) tptp.pi) (= X (@ tptp.cos_real T6)) (= Y (@ tptp.sin_real T6)))))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.cos_real X) tptp.zero_zero_real) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= X (@ tptp.cos_real T6)) (= Y (@ tptp.sin_real T6)))))))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (= X (@ tptp.cos_real T6)) (= Y (@ tptp.sin_real T6))))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_real T6) X) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M3)) (@ (@ tptp.power_power_real X) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T6) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real X) T6) (@ (@ tptp.ord_less_real T6) tptp.zero_zero_real) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M3)) (@ (@ tptp.power_power_real X) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T6) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X)) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M3)) (@ (@ tptp.power_power_real X) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T6) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))
% 5.98/6.29 (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)))))))))))
% 5.98/6.29 (assert (= (@ tptp.cos_coeff tptp.zero_zero_nat) tptp.one_one_real))
% 5.98/6.29 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X)))))))
% 5.98/6.29 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_real X4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.tan_real X4) Y))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_real Y) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X)) (@ tptp.tan_real Y))))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_real X) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_real Y) _let_1) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X)) (@ tptp.tan_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))))))
% 5.98/6.29 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arcsin Y))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_2)) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) _let_2) (= (@ tptp.sin_real _let_1) Y))))))))
% 5.98/6.29 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arcsin Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.sin_real _let_1) Y)))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ _let_1 tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) Y) (@ _let_1 (@ tptp.sin_real Y)))))))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y) (=> (@ _let_1 (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ _let_1 (@ tptp.arcsin X)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y)) X))))))))))
% 5.98/6.29 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arcsin Y)) Y)))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.arcsin (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.arcsin X)))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (= (@ tptp.arcsin X) (@ tptp.arcsin Y)) (= X Y))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)) (@ (@ tptp.ord_less_real X) Y))))))
% 5.98/6.29 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_eq_real _let_2) _let_1))))))))
% 5.98/6.29 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin Y)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 5.98/6.29 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.arcsin Y))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (= (@ tptp.arcsin (@ tptp.sin_real X)) X))))))
% 5.98/6.29 (assert (= tptp.arcsin (lambda ((Y2 tptp.real)) (@ tptp.the_real (lambda ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X3) (@ (@ tptp.ord_less_eq_real X3) _let_1) (= (@ tptp.sin_real X3) Y2))))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (= (@ tptp.arcosh_real X) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))))
% 5.98/6.29 (assert (forall ((X23 tptp.num)) (= (@ tptp.size_num (@ tptp.bit0 X23)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X23)) (@ tptp.suc tptp.zero_zero_nat)))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 5.98/6.29 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 5.98/6.29 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.power_power_real (@ tptp.sqrt X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M2)) M2)))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Q4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat M2) Q4)) (@ (@ tptp.bit_se2925701944663578781it_nat N) Q4)))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ tptp.sqrt X))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.sqrt X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X) (@ _let_1 (@ tptp.sqrt X))))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int M2) K)) (@ (@ tptp.bit_se2923211474154528505it_int N) K)))))
% 5.98/6.29 (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))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N) K))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sqrt X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.divide_divide_real X) _let_1) _let_1)))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt X)) (@ tptp.sqrt Y))))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (= (@ tptp.ln_ln_real X) (@ tptp.the_real (lambda ((X3 tptp.real)) false))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sqrt X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.divide_divide_real _let_1) X) (@ tptp.inverse_inverse_real _let_1))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) M2) M2) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) M2) M2))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt Y)))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) Y) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 5.98/6.29 (assert (= (@ tptp.size_num tptp.one) tptp.zero_zero_nat))
% 5.98/6.29 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M2)) M2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) M2))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) Y)))))))
% 5.98/6.29 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (= (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ tptp.sqrt X) Y)))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 5.98/6.29 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real Y) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 5.98/6.29 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real A) C)) _let_1)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real B) D)) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)))) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real C) _let_1)) (@ (@ tptp.power_power_real D) _let_1))))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y))))
% 5.98/6.29 (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))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) Y)))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))) (@ (@ tptp.plus_plus_real X) Y))))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 5.98/6.29 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real Y))))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X)) N) (@ (@ tptp.power_power_real X) (@ (@ tptp.divide_divide_nat N) _let_1))))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real) (Xa2 tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sqrt (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa2) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.times_times_real X) Y))) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt X)))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L3 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q3 tptp.nat) (R5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q3))) (let ((_let_2 (@ tptp.numeral_numeral_nat L3))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R5)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R5) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R5)))))) __flatten_var_0))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) tptp.one_one_real))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L3 tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q3 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q3))) (let ((_let_2 (@ tptp.numeral_numeral_int L3))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R5)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R5) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R5)))))) __flatten_var_0))))
% 5.98/6.29 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real X3) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X3) tptp.zero_zero_real))))))
% 5.98/6.29 (assert (= tptp.pi (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real X3) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X3) tptp.zero_zero_real)))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (U tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.divide_divide_real U) (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_real X) _let_4) (=> (@ (@ tptp.ord_less_real Y) _let_4) (=> (@ _let_3 X) (=> (@ _let_3 Y) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))) U)))))))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sin_real X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= _let_1 (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arcsin X)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 5.98/6.29 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos Y)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos X)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 5.98/6.29 (assert (= tptp.divmod_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N4 tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M3) N4))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M3)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ tptp.suc Q3)) __flatten_var_0))) (@ (@ tptp.divmod_nat (@ (@ tptp.minus_minus_nat M3) N4)) N4))))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y)) Y)))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) (@ tptp.arccos X)))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real)) (= (= (@ tptp.arccos X) (@ tptp.arccos Y)) (= X Y)))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arccos X)) (@ tptp.arccos Y)) (@ (@ tptp.ord_less_eq_real Y) X))))))
% 5.98/6.29 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.arccos Y))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arccos Y)) (@ tptp.arccos X)))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arccos X)) (@ tptp.arccos Y)) (@ (@ tptp.ord_less_real Y) X))))))
% 5.98/6.29 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) tptp.pi)))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (= (@ tptp.arccos (@ tptp.cos_real X)) X)))))
% 5.98/6.29 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y)) Y))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arccos Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi)))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) X) (= (@ tptp.arccos (@ tptp.cos_real X)) (@ tptp.uminus_uminus_real X))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X)))))))
% 5.98/6.29 (assert (= tptp.arccos (lambda ((Y2 tptp.real)) (@ tptp.the_real (lambda ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real X3) tptp.pi) (= (@ tptp.cos_real X3) Y2)))))))
% 5.98/6.29 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arccos Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.cos_real _let_1) Y)))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X))))))
% 5.98/6.29 (assert (= tptp.archim6058952711729229775r_real (lambda ((X3 tptp.real)) (@ tptp.the_int (lambda ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z2)) X3) (@ (@ tptp.ord_less_real X3) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))))))
% 5.98/6.29 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 5.98/6.29 (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))))))))
% 5.98/6.29 (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))))))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (forall ((L tptp.int) (K tptp.int) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat M2) 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 M2))) (@ (@ 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) M2)))))))))))))))))))
% 5.98/6.29 (assert (forall ((L tptp.int) (K tptp.int) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M2) 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 M2)))) (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) M2)))))) _let_1)))))))))))))))))
% 5.98/6.29 (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))))))))))))))))
% 5.98/6.29 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int X) Xa2)))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_2))) (let ((_let_4 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_3 X)) (not (@ _let_3 Xa2)))))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int X) _let_5) (@ (@ tptp.member_int Xa2) _let_5)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_6 (= Y (@ tptp.uminus_uminus_int _let_4))) (=> (not _let_6) (= Y (@ (@ tptp.plus_plus_int _let_4) (@ (@ tptp.times_times_int _let_2) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_2)) (@ (@ tptp.divide_divide_int Xa2) _let_2))))))) (not _let_1)))))))))))))
% 5.98/6.29 (assert (= tptp.archim3151403230148437115or_rat (lambda ((X3 tptp.rat)) (@ tptp.the_int (lambda ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z2)) X3) (@ (@ tptp.ord_less_rat X3) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))))))
% 5.98/6.29 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 X)) (not (@ _let_2 Xa2)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_5 (and (@ (@ tptp.member_int X) _let_4) (@ (@ tptp.member_int Xa2) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa2) Y) (and (=> _let_5 (= Y (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_1)) (@ (@ tptp.divide_divide_int Xa2) _let_1)))))))))))))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (assert (= tptp.ord_less_eq_rat (lambda ((X3 tptp.rat) (Y2 tptp.rat)) (or (@ (@ tptp.ord_less_rat X3) Y2) (= X3 Y2)))))
% 5.98/6.29 (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)))))))))))
% 5.98/6.29 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int X) Y))))))
% 5.98/6.29 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) X))))
% 5.98/6.29 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) Y))))
% 5.98/6.29 (assert (forall ((Y tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int Y) Ya)) Z)))))
% 5.98/6.29 (assert (forall ((Y tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) Z)))))
% 5.98/6.29 (assert (forall ((Y tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) Z)))))
% 5.98/6.29 (assert (forall ((Y tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int Y) Ya)) Z)))))
% 5.98/6.29 (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))))
% 5.98/6.29 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K3)) (not (@ _let_2 L3)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (@ (@ (@ tptp.if_int (and (@ (@ tptp.member_int K3) _let_4) (@ (@ tptp.member_int L3) _let_4))) (@ tptp.uminus_uminus_int _let_3)) (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L3) _let_1))))))))))))
% 5.98/6.29 (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))))))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M2)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_eq_num M2) N))))
% 5.98/6.29 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M2)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_eq_num M2) N))))
% 5.98/6.29 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M2)) tptp.one))))
% 5.98/6.29 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 5.98/6.29 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) tptp.zero_zero_nat)))
% 5.98/6.29 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M2)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_eq_num M2) N))))
% 5.98/6.29 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M2)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M2) N))))
% 5.98/6.29 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) tptp.one_one_nat)))
% 5.98/6.29 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)))
% 5.98/6.29 (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))))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 X)))))
% 5.98/6.29 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))))
% 5.98/6.29 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y)))))
% 5.98/6.29 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))))
% 5.98/6.29 (assert (forall ((Y tptp.num)) (=> (not (= Y tptp.one)) (=> (forall ((X24 tptp.num)) (not (= Y (@ tptp.bit0 X24)))) (not (forall ((X32 tptp.num)) (not (= Y (@ tptp.bit1 X32)))))))))
% 5.98/6.29 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))))))
% 5.98/6.29 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)) (@ tptp.suc (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat)))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (= (@ tptp.suc (@ tptp.suc (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))
% 5.98/6.29 (assert (forall ((X33 tptp.num)) (= (@ tptp.size_num (@ tptp.bit1 X33)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X33)) (@ tptp.suc tptp.zero_zero_nat)))))
% 5.98/6.29 (assert (forall ((X33 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit1 X33)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X33)) (@ tptp.suc tptp.zero_zero_nat)))))
% 5.98/6.29 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat M2) (@ 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))))))))
% 5.98/6.29 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M3 tptp.zero_zero_nat) (= N4 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat M3) _let_1)) (@ (@ tptp.modulo_modulo_nat N4) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1)))))))))
% 5.98/6.29 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) N4) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) M3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat M3) _let_1)) (@ (@ tptp.modulo_modulo_nat N4) _let_1))) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1))))))))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X)) (@ tptp.tanh_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X)) (@ _let_1 X)))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat))
% 5.98/6.29 (assert (forall ((N tptp.nat) (K tptp.num)) (= (= (@ tptp.suc N) (@ tptp.numeral_numeral_nat K)) (= N (@ tptp.pred_numeral K)))))
% 5.98/6.29 (assert (forall ((K tptp.num) (N tptp.nat)) (= (= (@ tptp.numeral_numeral_nat K) (@ tptp.suc N)) (= (@ tptp.pred_numeral K) N))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (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))))
% 5.98/6.29 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit1 K)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))))
% 5.98/6.29 (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))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.minus_minus_nat N) (@ tptp.pred_numeral K)))))
% 5.98/6.29 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ tptp.pred_numeral K)) N))))
% 5.98/6.29 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_max_nat (@ tptp.pred_numeral K)) N)))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) (@ tptp.pred_numeral K))))))
% 5.98/6.29 (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))))
% 5.98/6.29 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int X) Y)))))))
% 5.98/6.29 (assert (= tptp.numeral_numeral_nat (lambda ((K3 tptp.num)) (@ tptp.suc (@ tptp.pred_numeral K3)))))
% 5.98/6.29 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat N4) (@ (@ tptp.bit_se547839408752420682it_nat M3) tptp.one_one_nat)))))
% 5.98/6.29 (assert (= tptp.pred_numeral (lambda ((K3 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K3)) tptp.one_one_nat))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (assert (forall ((X tptp.int) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int X) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int X) Y)) _let_1)))))))
% 5.98/6.29 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) N4) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) M3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M3) _let_1)) (@ (@ tptp.modulo_modulo_nat N4) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1))))))))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or4665077453230672383an_nat M2) 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 M2) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 5.98/6.29 (assert (forall ((P (-> tptp.nat Bool))) (=> (@ P tptp.zero_zero_nat) (= (@ tptp.ord_Least_nat P) tptp.zero_zero_nat))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or4665077453230672383an_nat L) U))))
% 5.98/6.29 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or4665077453230672383an_nat L) U)) (@ (@ tptp.minus_minus_nat U) L))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M2) (@ tptp.suc M2)) (@ (@ tptp.insert_nat M2) tptp.bot_bot_set_nat))))
% 5.98/6.29 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) (@ tptp.suc tptp.zero_zero_nat)) _let_1))))
% 5.98/6.29 (assert (forall ((Y tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) _let_1) _let_1))))
% 5.98/6.29 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))))
% 5.98/6.29 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))))
% 5.98/6.29 (assert (= tptp.bit_se7882103937844011126it_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat N4) (@ (@ tptp.bit_se547839408752420682it_nat M3) tptp.one_one_nat)))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.bit_se2002935070580805687sk_nat N))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N) (@ P M3))) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X3))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N) (@ P M3))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X3))))))
% 5.98/6.29 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat L) (@ tptp.suc U)) (@ (@ tptp.set_or1269000886237332187st_nat L) U))))
% 5.98/6.29 (assert (= tptp.set_ord_lessThan_nat (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat)))
% 5.98/6.29 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M2) tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_se2000444600071755411sk_int N))))
% 5.98/6.29 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat) (Q (-> tptp.nat Bool)) (M2 tptp.nat)) (=> (@ P N) (=> (@ Q M2) (=> (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)))))))))
% 5.98/6.29 (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 ((M3 tptp.nat)) (@ P (@ tptp.suc M3))))))))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (forall ((N5 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N5) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.finite_finite_nat N5))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat K) (@ (@ tptp.plus_plus_nat K) (@ tptp.finite_card_nat A2))))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) _let_1) (= A2 _let_1)))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M2))) (let ((_let_2 (@ _let_1 (@ tptp.suc N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat M2) N))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_nat N) (@ _let_1 N)))) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_nat))))))))
% 5.98/6.29 (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))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 5.98/6.29 (assert (forall ((N5 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N5) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat N5)) N))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat S2)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) X3)) S2))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (K tptp.num)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M2))) (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 M2) _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)))))))))
% 5.98/6.29 (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))))
% 5.98/6.29 (assert (= tptp.bit_se2002935070580805687sk_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_nat))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int (@ tptp.bit_se2000444600071755411sk_int N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.nat)) (B (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N))) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) N) (@ (@ tptp.ord_less_eq_nat (@ A I2)) (@ A J2))))) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) N) (@ (@ tptp.ord_less_eq_nat (@ B J2)) (@ B I2))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I4)) (@ B I4)))) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat A) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat B) _let_1))))))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int L) U))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int X) Y)))))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (forall ((U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U))))
% 5.98/6.29 (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))))
% 5.98/6.29 (assert (forall ((U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U)) (@ tptp.nat2 U))))
% 5.98/6.29 (assert (forall ((X tptp.int) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int X) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int X) Y)) _let_1)))))))
% 5.98/6.29 (assert (= tptp.unique4921790084139445826nteger (lambda ((L3 tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q3 tptp.code_integer) (R5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q3))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L3))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R5)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R5) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R5)))))) __flatten_var_0))))
% 5.98/6.29 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 5.98/6.29 (assert (= tptp.zero_zero_nat tptp.zero_zero_nat))
% 5.98/6.29 (assert (= tptp.one_one_nat tptp.one_one_nat))
% 5.98/6.29 (assert (= tptp.binomial (lambda ((N4 tptp.nat) (K3 tptp.nat)) (@ tptp.finite_card_set_nat (@ tptp.collect_set_nat (lambda ((K5 tptp.set_nat)) (and (@ (@ tptp.member_set_nat K5) (@ tptp.pow_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N4))) (= (@ tptp.finite_card_nat K5) K3))))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S2) (exists ((R4 (-> tptp.nat tptp.nat))) (and (@ (@ tptp.strict1292158309912662752at_nat R4) (@ tptp.set_ord_lessThan_nat (@ tptp.finite_card_nat S2))) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N6) (@ tptp.finite_card_nat S2)) (@ (@ tptp.member_nat (@ R4 N6)) S2))))))))
% 5.98/6.29 (assert (forall ((Nat tptp.nat)) (= (= Nat tptp.zero_zero_nat) (@ (@ (@ tptp.case_nat_o true) (lambda ((Uu3 tptp.nat)) false)) Nat))))
% 5.98/6.29 (assert (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (@ (@ (@ tptp.case_nat_o false) (lambda ((Uu3 tptp.nat)) true)) Nat))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N) (@ (@ (@ tptp.case_nat_o false) (@ tptp.ord_less_eq_nat M2)) N))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat M2) _let_1) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M6 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat M6) N)))) M2)))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat _let_1) M2) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M6 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) M6)))) M2)))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((K3 tptp.nat)) K3)) (@ _let_1 N))))))
% 5.98/6.29 (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 ((L3 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_num_of_integer L3))) (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))))))))
% 5.98/6.29 (assert (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X25 tptp.nat)) X25))))
% 5.98/6.29 (assert (= (@ tptp.complete_Sup_Sup_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 5.98/6.29 (assert (forall ((K4 tptp.set_nat)) (=> (not (= K4 tptp.bot_bot_set_nat)) (@ (@ tptp.member_nat (@ tptp.complete_Inf_Inf_nat K4)) K4))))
% 5.98/6.29 (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 ((L3 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_nat_of_integer L3))) (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))))))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (forall ((K tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger K) tptp.zero_z3403309356797280102nteger) (= (@ tptp.code_nat_of_integer K) tptp.zero_zero_nat))))
% 5.98/6.29 (assert (= (@ tptp.code_nat_of_integer tptp.zero_z3403309356797280102nteger) tptp.zero_zero_nat))
% 5.98/6.29 (assert (= (@ tptp.code_nat_of_integer tptp.one_one_Code_integer) tptp.one_one_nat))
% 5.98/6.29 (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))))))
% 5.98/6.29 (assert (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or5832277885323065728an_int L) U))))
% 5.98/6.29 (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))))
% 5.98/6.29 (assert (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or5834768355832116004an_nat L) U))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.compow_nat_nat N) tptp.suc) (@ tptp.plus_plus_nat N))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) N) (= N tptp.zero_zero_nat))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.suc N)))))
% 5.98/6.29 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or5834768355832116004an_nat L) U))))
% 5.98/6.29 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat N)))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se545348938243370406it_int M2) K)) N) (and (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.bit_se1146084159140164899it_int K) (@ (@ tptp.minus_minus_nat N) M2))))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (Q4 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se547839408752420682it_nat M2) Q4)) N) (and (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.bit_se1148574629649215175it_nat Q4) (@ (@ tptp.minus_minus_nat N) M2))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (M2 tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_nat N) M2) (=> (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int M2) K))))))
% 5.98/6.29 (assert (forall ((K tptp.int)) (not (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 M) (@ _let_1 N2))))) (not (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (not (@ _let_1 N2)))))))))))
% 5.98/6.29 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int X) Xa2)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int X) Xa2))) (=> (= (@ (@ tptp.upto X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa2)))) (=> (not _let_2) (= Y tptp.nil_int))) (not _let_1)))))))))
% 5.98/6.29 (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))))))))
% 5.98/6.29 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.ord_max_nat) tptp.zero_zero_nat) (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y2) X3))) (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.ord_less_nat Y2) X3))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (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)))))))))
% 5.98/6.29 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (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)))))))))
% 5.98/6.29 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2)))) (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)))))))))
% 5.98/6.29 (assert (forall ((M2 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 M2)))) (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)))))))))
% 5.98/6.29 (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))))))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int X) Xa2))) (=> (= (@ (@ tptp.upto X) Xa2) Y) (and (=> _let_1 (= Y (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa2)))) (=> (not _let_1) (= Y tptp.nil_int)))))))
% 5.98/6.29 (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))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (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))))))))
% 5.98/6.29 (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)))))))))
% 5.98/6.29 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit0 K)) (@ tptp.numeral_numeral_nat (@ tptp.bitM K)))))
% 5.98/6.29 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bitM N))))))
% 5.98/6.29 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 5.98/6.29 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bitM N)) tptp.one) (@ tptp.bit0 N))))
% 5.98/6.29 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_int A) B))) (let ((_let_2 (@ (@ tptp.fract A) B))) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat _let_1)) _let_2) (@ (@ tptp.ord_less_rat _let_2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))))
% 5.98/6.29 (assert (forall ((C tptp.nat) (Y tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X) Y))) (let ((_let_2 (@ (@ tptp.ord_less_nat X) Y))) (let ((_let_3 (@ (@ tptp.ord_less_nat C) Y))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X) C)) (@ (@ tptp.minus_minus_nat Y) C)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((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))))))))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int B) D))) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) D)) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int C) B)) _let_1))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) A2)))))
% 5.98/6.29 (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))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (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))))))))
% 5.98/6.29 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_eq_int B) A)))))
% 5.98/6.29 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_int A) B)))))
% 5.98/6.29 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A)))))
% 5.98/6.29 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (assert (= tptp.comple4887499456419720421f_real (lambda ((X8 tptp.set_real)) (@ tptp.uminus_uminus_real (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_real_real tptp.uminus_uminus_real) X8))))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 5.98/6.29 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or4665077453230672383an_nat A) B)) (@ (@ tptp.set_or4662586982721622107an_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 5.98/6.29 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.image_int_int (lambda ((X3 tptp.int)) (@ (@ tptp.plus_plus_int X3) L))) (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int U) L))) (@ (@ tptp.set_or4662586982721622107an_int L) U))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real X5) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X5 I2))) (= (@ tptp.suminf_real X5) (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_nat_real (lambda ((I4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real X5) (@ tptp.set_ord_lessThan_nat I4)))) tptp.top_top_set_nat)))))))
% 5.98/6.29 (assert (not (@ tptp.finite_finite_nat tptp.top_top_set_nat)))
% 5.98/6.29 (assert (not (@ tptp.finite_finite_nat tptp.top_top_set_nat)))
% 5.98/6.29 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_lessThan_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 5.98/6.29 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atMost_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 5.98/6.29 (assert (forall ((S2 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S2)) (= (@ (@ tptp.image_nat_nat (@ tptp.infini8530281810654367211te_nat S2)) tptp.top_top_set_nat) S2))))
% 5.98/6.29 (assert (= tptp.top_top_set_nat (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.image_nat_nat (lambda ((M3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M3) N))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 5.98/6.29 (assert (= (@ tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit) tptp.one_one_nat))
% 5.98/6.29 (assert (forall ((A tptp.real)) (let ((_let_1 (@ (@ tptp.image_real_real (@ tptp.times_times_real A)) tptp.top_top_set_real))) (let ((_let_2 (= A tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ (@ tptp.insert_real tptp.zero_zero_real) tptp.bot_bot_set_real))) (=> (not _let_2) (= _let_1 tptp.top_top_set_real)))))))
% 5.98/6.29 (assert (= tptp.sup_sup_nat tptp.ord_max_nat))
% 5.98/6.29 (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))))))))
% 5.98/6.29 (assert (= tptp.root (lambda ((N4 tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.if_real (= N4 tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ (@ tptp.the_in5290026491893676941l_real tptp.top_top_set_real) (lambda ((Y2 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y2)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y2)) N4)))) X3)))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (X tptp.real) (D4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))))) (let ((_let_3 (= D4 _let_2))) (let ((_let_4 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= X tptp.zero_zero_real)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) _let_3)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (= D4 (@ tptp.uminus_uminus_real _let_2)))) (=> (=> (not _let_4) _let_3) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) D4) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X9 tptp.real)) (@ tptp.suminf_real (lambda ((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 X) (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 5.98/6.29 (assert (forall ((A tptp.real) (B tptp.real) (G2 (-> tptp.real tptp.real)) (G3 (-> tptp.real tptp.real))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G2) (@ G3 X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G3 X4)))) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ G2 A)) (@ G2 B)))))))
% 5.98/6.29 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4)))))) (@ (@ tptp.ord_less_eq_real (@ F A)) (@ F B))))))
% 5.98/6.29 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real Y4) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_eq_real (@ F B)) (@ F A))))))
% 5.98/6.29 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4)))))) (@ (@ tptp.ord_less_real (@ F A)) (@ F B))))))
% 5.98/6.29 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_real (@ F B)) (@ F A))))))
% 5.98/6.29 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F6 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F6 X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (exists ((Z3 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z3) (@ (@ tptp.ord_less_real Z3) B) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) (@ F6 Z3)))))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y3))) D) (@ (@ tptp.ord_less_eq_real (@ F X)) (@ F Y3)))) (= L tptp.zero_zero_real))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y3))) D) (@ (@ tptp.ord_less_eq_real (@ F Y3)) (@ F X)))) (= L tptp.zero_zero_real))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (X tptp.real) (S tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ (@ tptp.power_power_real X3) N))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.topolo2177554685111907308n_real X) S))))
% 5.98/6.29 (assert (forall ((G2 (-> tptp.real tptp.real)) (M2 tptp.real) (X tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G2) M2) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ (@ tptp.power_power_real (@ G2 X3)) N))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ G2 X)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) M2)) _let_1)))))
% 5.98/6.29 (assert (forall ((F (-> tptp.real tptp.nat tptp.real)) (F6 (-> tptp.real tptp.nat tptp.real)) (X0 tptp.real) (A tptp.real) (B tptp.real) (L5 (-> tptp.nat tptp.real))) (let ((_let_1 (@ F6 X0))) (=> (forall ((N2 tptp.nat)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ (@ F X3) N2))) (@ (@ F6 X0) N2)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (@ tptp.summable_real (@ F X4)))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (=> (@ tptp.summable_real _let_1) (=> (@ tptp.summable_real L5) (=> (forall ((N2 tptp.nat) (X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B))) (=> (@ (@ tptp.member_real X4) _let_1) (=> (@ (@ tptp.member_real Y3) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ F X4) N2)) (@ (@ F Y3) N2)))) (@ (@ tptp.times_times_real (@ L5 N2)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X4) Y3)))))))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ tptp.suminf_real (@ F X3)))) (@ tptp.suminf_real _let_1)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))))))
% 5.98/6.29 (assert (forall ((G2 (-> tptp.real tptp.real)) (M2 tptp.real) (X tptp.real) (R2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (let ((_let_2 (@ G2 X))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G2) M2) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ (@ tptp.powr_real (@ G2 X3)) R2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real R2) (@ (@ tptp.powr_real _let_2) (@ (@ tptp.minus_minus_real R2) (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat))))) M2)) _let_1)))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))
% 5.98/6.29 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X tptp.real) (N tptp.nat)) (=> (and (= (@ Diff tptp.zero_zero_nat) F) (forall ((M4 tptp.nat) (X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))
% 5.98/6.29 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X tptp.real) (N tptp.nat)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (not (= X tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))
% 5.98/6.29 (assert (forall ((H 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) H) (=> (@ (@ 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) H)) (@ (@ (@ 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) H) (= (@ F H) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real H) M3)))) (@ 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 H) N))))))))))))
% 5.98/6.29 (assert (forall ((H 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) H) (=> (= (@ 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) H)) (@ (@ (@ 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) H) (= (@ F H) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real H) M3)))) (@ 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 H) N)))))))))))
% 5.98/6.29 (assert (forall ((H tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real H) 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 H) 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 H) T6) (@ (@ tptp.ord_less_real T6) tptp.zero_zero_real) (= (@ F H) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real H) M3)))) (@ 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 H) N))))))))))))
% 5.98/6.29 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= X tptp.zero_zero_real)) (=> (forall ((M4 tptp.nat) (X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (exists ((T6 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T6))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))))))
% 5.98/6.29 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((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 X))) (@ (@ (@ 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 X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real A) T6) (@ (@ tptp.ord_less_eq_real T6) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_real A) C) (=> (@ (@ tptp.ord_less_eq_real C) B) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real A) T6) (@ (@ tptp.ord_less_real T6) C) (= (@ F A) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) C)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) N)))))))))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real A) T6) (@ (@ tptp.ord_less_eq_real T6) B)) (@ (@ (@ 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 A) C) (=> (@ (@ tptp.ord_less_real C) B) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real C) T6) (@ (@ tptp.ord_less_real T6) B) (= (@ F B) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) C)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) N)))))))))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real A) T6) (@ (@ tptp.ord_less_eq_real T6) B)) (@ (@ (@ 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) B) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) B) (=> (not (= X C)) (exists ((T6 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real T6))) (let ((_let_2 (@ tptp.ord_less_real X))) (let ((_let_3 (@ _let_2 C))) (and (=> _let_3 (and (@ _let_2 T6) (@ _let_1 C))) (=> (not _let_3) (and (@ (@ tptp.ord_less_real C) T6) (@ _let_1 X))) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) C)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) C)) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) C)) N))))))))))))))))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (H 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) H)) (@ (@ (@ 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 ((M tptp.nat) (T7 tptp.real)) (let ((_let_1 (@ tptp.suc M))) (let ((_let_2 (@ (@ tptp.minus_minus_nat N) _let_1))) (=> (and (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T7) (@ (@ tptp.ord_less_eq_real T7) H)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((U2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) M))) (@ (@ tptp.minus_minus_real (@ (@ Diff M) 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 M) 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 M)) 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))))))))))
% 5.98/6.29 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (=> (@ (@ tptp.ord_less_real (@ A tptp.zero_zero_nat)) tptp.zero_zero_real) (forall ((N6 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N6))) (@ (@ 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)) (@ A 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)) (@ A 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)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))))
% 5.98/6.29 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ A tptp.zero_zero_nat)) (forall ((N6 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N6))) (@ (@ 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)) (@ A 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)) (@ A 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)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))))))))
% 5.98/6.29 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N2))) (@ A N2))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))))) tptp.at_top_nat))))))
% 5.98/6.29 (assert (not (= tptp.at_top_nat tptp.bot_bot_filter_nat)))
% 5.98/6.29 (assert (forall ((C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ (@ tptp.filterlim_nat_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.times_times_nat X3) C))) tptp.at_top_nat) tptp.at_top_nat))))
% 5.98/6.29 (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))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.real)) (B2 tptp.real)) (=> (@ tptp.topolo6980174941875973593q_real X5) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ X5 I2))) B2)) (not (forall ((L6 tptp.real)) (not (@ (@ (@ tptp.filterlim_nat_real X5) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat))))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.real))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ G2 (@ tptp.suc N2))) (@ G2 N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N2)) (@ G2 N2))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N4)) (@ G2 N4)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N6)) L4)) (@ (@ (@ tptp.filterlim_nat_real F) _let_1) tptp.at_top_nat) (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ G2 N6))) (@ (@ (@ tptp.filterlim_nat_real G2) _let_1) tptp.at_top_nat))))))))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.real))) (=> (forall ((R4 tptp.real)) (exists ((N8 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N2) (@ (@ tptp.ord_less_real R4) (@ X5 N2)))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_real (@ X5 N4)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real)) (L tptp.real)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N2)) L)) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real L) (@ (@ tptp.plus_plus_real (@ F N6)) E))))) (@ (@ (@ tptp.filterlim_nat_real F) (@ tptp.topolo2815343760600316023s_real L)) tptp.at_top_nat))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real X)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 5.98/6.29 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N2))) (@ A N2))) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N4)) (@ A N4)))))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 5.98/6.29 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N2))) (@ A N2))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))))) tptp.at_top_nat))))))
% 5.98/6.29 (assert (forall ((A (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N2))) (@ A N2))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A 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)) (@ A I4))))))))))
% 5.98/6.29 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N2))) (@ A N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N2))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N6 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)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N6)))) L4)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))))) _let_1) tptp.at_top_nat) (forall ((N6 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)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N6)) tptp.one_one_nat))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_nat))))) _let_1) tptp.at_top_nat)))))))))
% 5.98/6.29 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))))) tptp.at_top_nat)))))
% 5.98/6.29 (assert (forall ((A (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N2))) (@ A N2))) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A 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)) (@ A 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)))))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.image_nat_real F) tptp.top_top_set_nat)) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.bfun_nat_real F) tptp.at_top_nat))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.bfun_nat_real (@ tptp.power_power_real X)) tptp.at_top_nat)))))
% 5.98/6.29 (assert (forall ((B tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) X4) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_top_real) (@ (@ tptp.ord_less_real Flim) (@ F B))))))
% 5.98/6.29 (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 ((X3 tptp.real)) (@ (@ tptp.power_power_real (@ F X3)) N))) tptp.at_top_real) F2))))))
% 5.98/6.29 (assert (@ (@ tptp.ord_le4104064031414453916r_real tptp.at_top_real) tptp.at_infinity_real))
% 5.98/6.29 (assert (@ (@ tptp.ord_le4104064031414453916r_real tptp.at_bot_real) tptp.at_infinity_real))
% 5.98/6.29 (assert (forall ((C tptp.nat) (P (-> tptp.nat Bool))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) X4) (@ P X4))) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 5.98/6.29 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (exists ((N3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) N4) (@ P N4)))))))
% 5.98/6.29 (assert (forall ((F2 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat F2) tptp.at_top_nat) (forall ((N3 tptp.nat)) (@ (@ tptp.eventually_nat (@ tptp.ord_less_eq_nat N3)) F2)))))
% 5.98/6.29 (assert (forall ((B tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_bot_real) (@ (@ tptp.ord_less_real Flim) (@ F B))))))
% 5.98/6.29 (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 ((X3 tptp.real)) (@ (@ tptp.power_power_real (@ F X3)) N))) tptp.at_bot_real) F2))))))
% 5.98/6.29 (assert (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or6659071591806873216st_nat L) U))))
% 5.98/6.29 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or6659071591806873216st_nat L) U)) (@ (@ tptp.minus_minus_nat U) L))))
% 5.98/6.29 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or6659071591806873216st_nat L) U))))
% 5.98/6.29 (assert (forall ((P (-> tptp.nat Bool)) (B tptp.nat)) (=> (exists ((X_12 tptp.nat)) (@ P X_12)) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 5.98/6.29 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ (@ tptp.ord_less_eq_nat K) (@ tptp.order_Greatest_nat P))))))
% 5.98/6.29 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 5.98/6.29 (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))))))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (assert (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or6656581121297822940st_int L) U))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (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))))
% 5.98/6.29 (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 ((M3 tptp.nat)) (@ tptp.collect_nat (lambda ((D5 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D5) M3))))) M5)))))))))
% 5.98/6.29 (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))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S2) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat S2)) (@ tptp.suc (@ tptp.lattic8265883725875713057ax_nat S2))))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (= tptp.divide_divide_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat K3) N4)) M3))))))))
% 5.98/6.29 (assert (= (@ tptp.set_or1210151606488870762an_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat)))
% 5.98/6.29 (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))))))
% 5.98/6.29 (assert (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat tptp.set_or1210151606488870762an_nat) tptp.top_top_set_nat)) tptp.bot_bot_set_nat))
% 5.98/6.29 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X) Xa2) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Y (not (= Xa2 tptp.one_one_nat)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) (= Y (not (and (= Deg2 Xa2) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X3) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X8))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) 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 TreeList2) I4)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X3) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))))) Mima)))))))))))))
% 5.98/6.29 (assert (= (@ tptp.set_ord_atLeast_nat tptp.zero_zero_nat) tptp.top_top_set_nat))
% 5.98/6.29 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ tptp.set_or1210151606488870762an_nat K))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.real)) (B2 tptp.real)) (=> (@ tptp.order_9091379641038594480t_real X5) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real B2) (@ X5 I2))) (@ (@ tptp.bfun_nat_real X5) tptp.at_top_nat)))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.real)) (B2 tptp.real)) (=> (@ tptp.order_9091379641038594480t_real X5) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real B2) (@ X5 I2))) (not (forall ((L6 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real X5) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat) (not (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real L6) (@ X5 I3)))))))))))
% 5.98/6.29 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atLeast_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (forall ((Mima2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Deg4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ (@ (@ tptp.vEBT_Node Mima2) Deg) TreeList) Summary)) Deg4) (and (= Deg Deg4) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_VEBT_valid X3) (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X8))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) 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 TreeList) I4)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I4))))) (=> _let_2 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList) Ma3) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat _let_1) Deg)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList) X3) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))))) Mima2)))))))
% 5.98/6.29 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X) Xa2)) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Xa2 tptp.one_one_nat)) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) (and (= Deg2 Xa2) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ 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 TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X8))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) 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 TreeList2) I4)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X3) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))))) Mima)))))))))))
% 5.98/6.29 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X) Xa2) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (not (= Xa2 tptp.one_one_nat))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) (not (and (= Deg2 Xa2) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X2) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X8))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) 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 TreeList2) I4)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X3) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))))) Mima))))))))))))
% 5.98/6.29 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (= Y (= Xa2 tptp.one_one_nat)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_2)))) (=> (= X _let_1) (=> (= Y (and (= Deg2 Xa2) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X3) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_2) _let_3)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X8))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) 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 TreeList2) I4)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X3) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))))) Mima))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))))))))))))
% 5.98/6.29 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (not (= Xa2 tptp.one_one_nat)))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (= Deg2 Xa2) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X2) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X8))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) 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 TreeList2) I4)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X3) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))))) Mima)))))))))))))))
% 5.98/6.29 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (= Xa2 tptp.one_one_nat))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (= Deg2 Xa2) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ 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 TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X8))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) 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 TreeList2) I4)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X3) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))))) Mima))))))))))))))
% 5.98/6.29 (assert (= tptp.comple1385675409528146559p_real (lambda ((X8 tptp.set_real)) (@ tptp.ord_Least_real (lambda ((Z2 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) X8) (@ (@ tptp.ord_less_eq_real X3) Z2))))))))
% 5.98/6.29 (assert (= tptp.complete_Sup_Sup_int (lambda ((X8 tptp.set_int)) (@ tptp.the_int (lambda ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) X8) (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member_int Y2) X8) (@ (@ tptp.ord_less_eq_int Y2) X3)))))))))
% 5.98/6.29 (assert (let ((_let_1 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (= _let_1 _let_1)))
% 5.98/6.29 (assert (@ tptp.order_mono_nat_nat tptp.suc))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.order_mono_nat_nat (@ tptp.times_times_nat N)))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.real)) (B2 tptp.real)) (=> (@ tptp.order_mono_nat_real X5) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X5 I2)) B2)) (@ (@ tptp.bfun_nat_real X5) tptp.at_top_nat)))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.real)) (B2 tptp.real)) (=> (@ tptp.order_mono_nat_real X5) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X5 I2)) B2)) (not (forall ((L6 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real X5) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat) (not (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X5 I3)) L6))))))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_int)) (= (not (@ tptp.finite_finite_int S2)) (not (@ tptp.finite_finite_nat (@ (@ tptp.image_int_nat (@ (@ tptp.comp_int_nat_int tptp.nat2) tptp.abs_abs_int)) S2))))))
% 5.98/6.29 (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 ((M3 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat K) M3)) M3))))))
% 5.98/6.29 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num tptp.zero_zero_nat) M2) tptp.none_num)))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.nat))) (=> (forall ((X4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4))) (=> (@ tptp.order_mono_nat_real F) (=> (@ tptp.order_5726023648592871131at_nat G2) (= (@ (@ tptp.bfun_nat_real (lambda ((X3 tptp.nat)) (@ F (@ G2 X3)))) tptp.at_top_nat) (@ (@ tptp.bfun_nat_real F) tptp.at_top_nat)))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat)) (=> (@ tptp.order_5726023648592871131at_nat F) (@ (@ tptp.ord_less_eq_nat N) (@ F N)))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S2)) (exists ((R4 (-> tptp.nat tptp.nat))) (and (@ tptp.order_5726023648592871131at_nat R4) (forall ((N6 tptp.nat)) (@ (@ tptp.member_nat (@ R4 N6)) S2)))))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S2)) (@ tptp.order_5726023648592871131at_nat (@ tptp.infini8530281810654367211te_nat S2)))))
% 5.98/6.29 (assert (= tptp.bit_take_bit_num (lambda ((N4 tptp.nat) (M3 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N4) (@ tptp.numeral_numeral_nat M3)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))
% 5.98/6.29 (assert (forall ((Q4 tptp.num)) (= (@ tptp.num_of_nat (@ tptp.numeral_numeral_nat Q4)) Q4)))
% 5.98/6.29 (assert (= (@ tptp.num_of_nat tptp.zero_zero_nat) tptp.one))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N)) N))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) tptp.one_one_nat) (= (@ tptp.num_of_nat N) tptp.one))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.plus_plus_num (@ tptp.num_of_nat M2)) (@ tptp.num_of_nat N))))))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.inj_on_real_real (lambda ((Y2 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y2)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y2)) N)))) tptp.top_top_set_real))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_min_nat M2) N)))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 5.98/6.29 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_min_nat N) (@ tptp.pred_numeral K))))))
% 5.98/6.29 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_min_nat (@ tptp.pred_numeral K)) N)))))
% 5.98/6.29 (assert (= tptp.inf_inf_nat tptp.ord_min_nat))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (I tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ (@ tptp.minus_minus_nat M2) I)) (@ (@ tptp.minus_minus_nat N) I)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.ord_min_nat M2) N)) I))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M2))) (= (@ _let_1 (@ (@ tptp.ord_min_nat N) Q4)) (@ (@ tptp.ord_min_nat (@ _let_1 N)) (@ _let_1 Q4))))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Q4 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_min_nat M2) N)) Q4) (@ (@ tptp.ord_min_nat (@ (@ tptp.times_times_nat M2) Q4)) (@ (@ tptp.times_times_nat N) Q4)))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N)) M2) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M6 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat N) M6)))) M2))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat M2) (@ tptp.suc N)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M6 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat M6) N)))) M2))))
% 5.98/6.29 (assert (forall ((N5 tptp.set_nat)) (@ (@ tptp.inj_on_nat_nat tptp.suc) N5)))
% 5.98/6.29 (assert (forall ((N5 tptp.set_nat) (K tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.member_nat N2) N5) (@ (@ tptp.ord_less_eq_nat K) N2))) (@ (@ tptp.inj_on_nat_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_nat N4) K))) N5))))
% 5.98/6.29 (assert (@ (@ tptp.inj_on_set_nat_nat tptp.nat_set_encode) (@ tptp.collect_set_nat tptp.finite_finite_nat)))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.inj_on_nat_nat G2) tptp.top_top_set_nat) (=> (forall ((X4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4))) (@ tptp.summable_real (@ (@ tptp.comp_nat_real_nat F) G2)))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.inj_on_nat_nat G2) tptp.top_top_set_nat) (=> (forall ((X4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4))) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real (@ (@ tptp.comp_nat_real_nat F) G2))) (@ tptp.suminf_real F)))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real)) (G2 (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.inj_on_nat_nat G2) tptp.top_top_set_nat) (=> (forall ((X4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4))) (=> (forall ((X4 tptp.nat)) (=> (not (@ (@ tptp.member_nat X4) (@ (@ tptp.image_nat_nat G2) tptp.top_top_set_nat))) (= (@ F X4) tptp.zero_zero_real))) (= (@ tptp.suminf_real (@ (@ tptp.comp_nat_real_nat F) G2)) (@ tptp.suminf_real F))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.topolo5044208981011980120l_real A2))) (=> (@ _let_1 F) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X4)))) (@ _let_1 (lambda ((X3 tptp.real)) (@ tptp.arcosh_real (@ F X3)))))))))
% 5.98/6.29 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (exists ((C3 tptp.real) (D6 tptp.real)) (and (= (@ (@ tptp.image_real_real F) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C3) D6)) (@ (@ tptp.ord_less_eq_real C3) D6)))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) (@ tptp.set_ord_atLeast_real tptp.one_one_real)) (@ (@ tptp.topolo5044208981011980120l_real A2) tptp.arcosh_real))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) (@ (@ tptp.topolo5044208981011980120l_real A2) tptp.artanh_real))))
% 5.98/6.29 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (X tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (=> (@ (@ tptp.ord_less_eq_real A) X) (=> (@ (@ tptp.ord_less_eq_real X) B) (= (@ F X) (@ F A)))))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (or (not (= X tptp.zero_zero_real)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) N)) (= (@ (@ tptp.powr_real X) (@ tptp.ring_1_of_int_real N)) (@ (@ tptp.power_int_real X) N))))))
% 5.98/6.29 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X4) (@ (@ tptp.ord_less_eq_real X4) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) F))) (exists ((L6 tptp.real) (M9 tptp.real)) (and (forall ((X2 tptp.real)) (let ((_let_1 (@ F X2))) (=> (and (@ (@ tptp.ord_less_eq_real A) X2) (@ (@ tptp.ord_less_eq_real X2) B)) (and (@ (@ tptp.ord_less_eq_real L6) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) M9))))) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real L6) Y4) (@ (@ tptp.ord_less_eq_real Y4) M9)) (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A) X4) (@ (@ tptp.ord_less_eq_real X4) B) (= (@ F X4) Y4)))))))))))
% 5.98/6.29 (assert (forall ((A tptp.real) (X tptp.real) (B tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (= (@ G2 (@ F Z3)) Z3)))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) F)))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X)) tptp.top_top_set_real)) G2)))))))
% 5.98/6.29 (assert (forall ((B tptp.real) (X tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real B) X) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.set_or1633881224788618240n_real B) X)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (=> (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) F) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X)))))))
% 5.98/6.29 (assert (forall ((D tptp.real) (X tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z3) X))) D) (= (@ G2 (@ F Z3)) Z3))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z3) X))) D) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) F))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X)) tptp.top_top_set_real)) G2))))))
% 5.98/6.29 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (G3 (-> tptp.real tptp.real)) (F6 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) F)))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) G2)))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z3) (=> (@ (@ tptp.ord_less_real Z3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real G2) (@ G3 Z3)) (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real))))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z3) (=> (@ (@ tptp.ord_less_real Z3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F6 Z3)) (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real))))) (exists ((C3 tptp.real)) (and (@ (@ tptp.ord_less_real A) C3) (@ (@ tptp.ord_less_real C3) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) (@ G3 C3)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G2 B)) (@ G2 A))) (@ F6 C3))))))))))))
% 5.98/6.29 (assert (= tptp.condit2214826472909112428ve_nat tptp.finite_finite_nat))
% 5.98/6.29 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X4) (@ (@ tptp.ord_less_eq_real X4) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) F))) (=> (forall ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X4) (@ (@ tptp.ord_less_real X4) B)) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))) (=> (forall ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X4) (@ (@ tptp.ord_less_eq_real X4) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) G2))) (=> (forall ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X4) (@ (@ tptp.ord_less_real X4) B)) (@ (@ tptp.differ6690327859849518006l_real G2) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))) (exists ((G_c tptp.real) (F_c tptp.real) (C3 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real C3) tptp.top_top_set_real))) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real G2) G_c) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) F_c) _let_1) (@ (@ tptp.ord_less_real A) C3) (@ (@ tptp.ord_less_real C3) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) G_c) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G2 B)) (@ G2 A))) F_c))))))))))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.inc K)) (@ tptp.numeral_numeral_nat K))))
% 5.98/6.29 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.plus_plus_num X))) (= (@ _let_1 (@ tptp.inc Y)) (@ tptp.inc (@ _let_1 Y))))))
% 5.98/6.29 (assert (forall ((P (-> tptp.num Bool)) (X tptp.num)) (=> (@ P tptp.one) (=> (forall ((X4 tptp.num)) (=> (@ P X4) (@ P (@ tptp.inc X4)))) (@ P X)))))
% 5.98/6.29 (assert (= (@ tptp.inc tptp.one) (@ tptp.bit0 tptp.one)))
% 5.98/6.29 (assert (forall ((X tptp.num)) (= (@ tptp.inc (@ tptp.bit0 X)) (@ tptp.bit1 X))))
% 5.98/6.29 (assert (forall ((X tptp.num)) (= (@ tptp.inc (@ tptp.bit1 X)) (@ tptp.bit0 (@ tptp.inc X)))))
% 5.98/6.29 (assert (forall ((X tptp.num)) (= (@ (@ tptp.plus_plus_num X) tptp.one) (@ tptp.inc X))))
% 5.98/6.29 (assert (forall ((N tptp.num)) (= (@ tptp.inc (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 5.98/6.29 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.inc N)) (@ tptp.bit1 N))))
% 5.98/6.29 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.times_times_num X))) (= (@ _let_1 (@ tptp.inc Y)) (@ (@ tptp.plus_plus_num (@ _let_1 Y)) X)))))
% 5.98/6.29 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I4 tptp.int) (N4 tptp.nat)) (and (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I4)) (@ tptp.semiri5074537144036343181t_real N4))) (not (= N4 tptp.zero_zero_nat))))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (= (@ (@ tptp.member_real (@ tptp.abs_abs_real X)) tptp.field_5140801741446780682s_real) (@ (@ tptp.member_real X) tptp.field_5140801741446780682s_real))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X4) X)))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X) X4) (@ (@ tptp.ord_less_real X4) Y))))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_eq_real X) X4)))))
% 5.98/6.29 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I4 tptp.int) (J3 tptp.int)) (and (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I4)) (@ tptp.ring_1_of_int_real J3))) (not (= J3 tptp.zero_zero_int))))))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (assert (forall ((Z tptp.complex) (X tptp.real)) (=> (= (@ tptp.sgn_sgn_complex Z) (@ tptp.cis X)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (= (@ tptp.arg Z) X))))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (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))))))))
% 5.98/6.29 (assert (forall ((M5 tptp.set_nat) (N5 tptp.set_nat)) (= (@ (@ (@ tptp.bij_betw_nat_nat tptp.suc) M5) N5) (= (@ (@ tptp.image_nat_nat tptp.suc) M5) N5))))
% 5.98/6.29 (assert (forall ((S2 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S2)) (@ (@ (@ tptp.bij_betw_nat_nat (@ tptp.infini8530281810654367211te_nat S2)) tptp.top_top_set_nat) S2))))
% 5.98/6.29 (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))))))))
% 5.98/6.29 (assert (= tptp.ord_less_eq_int (lambda ((X3 tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y2 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 Y2) V3)) (@ (@ tptp.plus_plus_nat U2) Z2)))) __flatten_var_0))) (@ tptp.rep_Integ X3)) (@ tptp.rep_Integ Xa4)))))
% 5.98/6.29 (assert (= tptp.ord_less_int (lambda ((X3 tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y2 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 Y2) V3)) (@ (@ tptp.plus_plus_nat U2) Z2)))) __flatten_var_0))) (@ tptp.rep_Integ X3)) (@ tptp.rep_Integ Xa4)))))
% 5.98/6.29 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X3 tptp.nat) (Y2 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 X3) V3)) (@ (@ tptp.plus_plus_nat U2) Y2)))) __flatten_var_0))) Xa2) X))))
% 5.98/6.29 (assert (= tptp.zero_zero_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))))
% 5.98/6.29 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N4 tptp.nat)) (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat N4) tptp.zero_zero_nat)))))
% 5.98/6.29 (assert (= tptp.one_one_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))))
% 5.98/6.29 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X3 tptp.nat) (Y2 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 X3) V3)) (@ (@ tptp.plus_plus_nat U2) Y2)))) __flatten_var_0))) Xa2) X))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M2) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L3) M2) (= (@ tptp.groups4561878855575611511st_nat L3) N5))))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L3) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)) (= (@ tptp.groups4561878855575611511st_nat L3) N5)))))) (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L3) M2) (= (@ (@ tptp.plus_plus_nat (@ tptp.groups4561878855575611511st_nat L3)) tptp.one_one_nat) N5))))))))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N5 tptp.nat)) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L3) M2) (= (@ tptp.groups4561878855575611511st_nat L3) N5))))) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N5) M2)) tptp.one_one_nat)) N5))))
% 5.98/6.29 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ tptp.hd_nat (@ (@ tptp.upt I) J)) I))))
% 5.98/6.29 (assert (forall ((J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.upt I) J) tptp.nil_nat))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (forall ((I tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) M2))) (let ((_let_2 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) N) (= (@ (@ tptp.take_nat M2) (@ _let_2 N)) (@ _let_2 _let_1)))))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M2))) (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)))))))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ tptp.groups4561878855575611511st_nat (@ (@ tptp.upt M2) N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or4665077453230672383an_nat M2) N))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat I4) N))) (@ (@ tptp.upt tptp.zero_zero_nat) M2)) (@ (@ tptp.upt N) (@ (@ tptp.plus_plus_nat M2) N)))))
% 5.98/6.29 (assert (= tptp.set_ord_lessThan_nat (lambda ((N4 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) N4)))))
% 5.98/6.29 (assert (forall ((I tptp.nat)) (= (@ (@ tptp.upt I) tptp.zero_zero_nat) tptp.nil_nat)))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) (@ (@ tptp.upt M2) N))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ (@ tptp.upt M2) N))))
% 5.98/6.29 (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))))))))
% 5.98/6.29 (assert (= tptp.set_ord_atMost_nat (lambda ((N4 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) (@ tptp.suc N4))))))
% 5.98/6.29 (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))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (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))))))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_nat N4) (@ tptp.suc tptp.zero_zero_nat)))) (@ (@ tptp.upt (@ tptp.suc M2)) (@ tptp.suc N))) (@ (@ tptp.upt M2) N))))
% 5.98/6.29 (assert (forall ((I tptp.nat) (J tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (= (= (@ (@ tptp.upt I) J) (@ (@ tptp.cons_nat X) Xs)) (and (@ (@ tptp.ord_less_nat I) J) (= I X) (= (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I) tptp.one_one_nat)) J) Xs)))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (assert (forall ((M2 tptp.int) (N tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) (@ (@ tptp.upto M2) N))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (= (@ tptp.field_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) N) (@ (@ tptp.ord_less_nat Y2) N) (@ (@ tptp.ord_less_eq_nat X3) Y2)))))) (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.ord_less_nat X3) N))))))
% 5.98/6.29 (assert (= tptp.bNF_Ca8459412986667044542atLess (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))
% 5.98/6.29 (assert (@ tptp.wf_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))
% 5.98/6.29 (assert (= tptp.ord_less_eq_rat (lambda ((P5 tptp.rat) (Q3 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 Q3)))) (@ tptp.quotient_of P5)))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt X)) (@ tptp.csqrt (@ tptp.real_V4546457046886955230omplex X))))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ tptp.sqr N)) N))))))
% 5.98/6.29 (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))))
% 5.98/6.29 (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))))
% 5.98/6.29 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit0 N)) (@ tptp.bit0 (@ tptp.bit0 (@ tptp.sqr N))))))
% 5.98/6.29 (assert (= (@ tptp.sqr tptp.one) tptp.one))
% 5.98/6.29 (assert (= tptp.sqr (lambda ((X3 tptp.num)) (@ (@ tptp.times_times_num X3) X3))))
% 5.98/6.29 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.pow X))) (= (@ _let_1 (@ tptp.bit1 Y)) (@ (@ tptp.times_times_num (@ tptp.sqr (@ _let_1 Y))) X)))))
% 5.98/6.29 (assert (forall ((X tptp.num)) (= (@ (@ tptp.pow X) tptp.one) X)))
% 5.98/6.29 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.pow X))) (= (@ _let_1 (@ tptp.bit0 Y)) (@ tptp.sqr (@ _let_1 Y))))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (= tptp.bezw (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y2) (@ (@ tptp.modulo_modulo_nat X3) Y2)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= Y2 tptp.zero_zero_nat)) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X3) Y2)))))))))))
% 5.98/6.29 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X) Xa2)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa2) Y) (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_3) (= Y (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa2))))))))))))))
% 5.98/6.29 (assert (forall ((Y tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y) (@ (@ tptp.modulo_modulo_nat X) Y)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Y) (= (@ (@ tptp.bezw X) Y) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Y)))))))))))
% 5.98/6.29 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa2)))) (let ((_let_2 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X) Xa2)))) (let ((_let_3 (@ tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_4 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= Y (@ (@ tptp.product_Pair_int_int _let_3) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_2)) (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa2)))))))) (not _let_1)))))))))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (forall ((F2 tptp.set_nat)) (= (@ tptp.finite_finite_nat (@ (@ tptp.vimage_nat_nat tptp.suc) F2)) (@ tptp.finite_finite_nat F2))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat tptp.suc))) (= (@ _let_1 (@ (@ tptp.insert_nat tptp.zero_zero_nat) A2)) (@ _let_1 A2)))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (@ tptp.bNF_We3818239936649020644el_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) N) (@ (@ tptp.ord_less_nat Y2) N) (@ (@ tptp.ord_less_eq_nat X3) Y2))))))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M2) N)) (@ tptp.transi2905341329935302413cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 5.98/6.29 (assert (forall ((M2 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)) M2)))) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.set_ord_atMost_nat M2)) (lambda ((R5 tptp.nat)) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat M2) R5)))))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M2) N)) (@ tptp.transi6264000038957366511cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_nat M2) N))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real)) (M5 tptp.nat)) (=> (@ (@ tptp.bfun_nat_real (lambda ((N4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N4) M5)))) tptp.at_top_nat) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) M4) (=> (@ (@ tptp.ord_less_eq_nat M4) N2) (@ (@ tptp.ord_less_eq_real (@ F M4)) (@ F N2))))) (@ tptp.topolo7531315842566124627t_real F)))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.real))) (=> (@ (@ tptp.bfun_nat_real X5) tptp.at_top_nat) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N2) (@ (@ tptp.ord_less_eq_real (@ X5 M4)) (@ X5 N2)))) (@ tptp.topolo7531315842566124627t_real X5)))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ tptp.topolo7531315842566124627t_real (@ tptp.power_power_real X))))))
% 5.98/6.29 (assert (forall ((F (-> tptp.nat tptp.real)) (M5 tptp.nat)) (=> (@ (@ tptp.bfun_nat_real (lambda ((N4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N4) M5)))) tptp.at_top_nat) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) M4) (=> (@ (@ tptp.ord_less_eq_nat M4) N2) (@ (@ tptp.ord_less_eq_real (@ F N2)) (@ F M4))))) (@ tptp.topolo7531315842566124627t_real F)))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bNF_Ca8665028551170535155natLeq) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.ord_less_nat X3) N)))) (lambda ((Uu3 tptp.nat)) (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.ord_less_nat X3) N)))))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) N) (@ (@ tptp.ord_less_nat Y2) N) (@ (@ tptp.ord_less_eq_nat X3) Y2))))))))
% 5.98/6.29 (assert (= tptp.bNF_Ca8665028551170535155natLeq (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_eq_nat))))
% 5.98/6.29 (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 ((X3 tptp.nat) (Y2 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) N) (@ (@ tptp.ord_less_nat Y2) N) (@ (@ tptp.ord_less_eq_nat X3) Y2))))))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N) (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.ord_less_nat X3) N))))))
% 5.98/6.29 (assert (forall ((A tptp.nat) (B tptp.nat) (S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat S) T) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S)) (@ (@ tptp.product_Pair_nat_nat B) T))) tptp.fun_pair_less)))))
% 5.98/6.29 (assert (@ tptp.trans_4347625901269045472at_nat tptp.fun_pair_less))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.total_3592101749530773125at_nat A2) tptp.fun_pair_less)))
% 5.98/6.29 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat X))) (= (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ _let_1 Y)) (@ _let_1 Z))) tptp.fun_pair_less) (@ (@ tptp.ord_less_nat Y) Z)))))
% 5.98/6.29 (assert (@ tptp.wf_Pro7803398752247294826at_nat tptp.fun_pair_less))
% 5.98/6.29 (assert (forall ((A tptp.nat) (B tptp.nat) (S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S)) (@ (@ tptp.product_Pair_nat_nat B) T))) tptp.fun_pair_less))))
% 5.98/6.29 (assert (@ (@ (@ tptp.ordering_top_nat tptp.dvd_dvd_nat) (lambda ((M3 tptp.nat) (N4 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat M3) N4) (not (= M3 N4))))) tptp.zero_zero_nat))
% 5.98/6.29 (assert (@ (@ (@ tptp.ordering_top_nat (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y2) X3))) (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.ord_less_nat Y2) X3))) tptp.zero_zero_nat))
% 5.98/6.29 (assert (forall ((A tptp.nat) (B tptp.nat) (S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat S) T) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S)) (@ (@ tptp.product_Pair_nat_nat B) T))) tptp.fun_pair_leq)))))
% 5.98/6.29 (assert (forall ((A tptp.nat) (B tptp.nat) (S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S)) (@ (@ tptp.product_Pair_nat_nat B) T))) tptp.fun_pair_leq))))
% 5.98/6.29 (assert (= tptp.fun_pair_leq (@ (@ tptp.sup_su718114333110466843at_nat tptp.fun_pair_less) tptp.id_Pro2258643101195443293at_nat)))
% 5.98/6.29 (assert (forall ((Y tptp.product_prod_nat_nat) (YS tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (XS tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y) YS) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) 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 X) XS)) YS)) tptp.fun_max_weak))))))
% 5.98/6.29 (assert (forall ((X tptp.product_prod_nat_nat) (XS tptp.set_Pr1261947904930325089at_nat) (Y tptp.product_prod_nat_nat) (YS tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.produc2922128104949294807at_nat XS))) (=> (@ (@ tptp.member8440522571783428010at_nat X) XS) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) tptp.fun_pair_leq) (=> (@ (@ tptp.member8757157785044589968at_nat (@ _let_1 YS)) tptp.fun_min_weak) (@ (@ tptp.member8757157785044589968at_nat (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat Y) YS))) tptp.fun_min_weak)))))))
% 5.98/6.29 (assert (forall ((X5 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X5) tptp.bot_bo2099793752762293965at_nat)) tptp.fun_min_weak)))
% 5.98/6.29 (assert (forall ((X5 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat X5) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat tptp.bot_bo2099793752762293965at_nat) X5)) tptp.fun_max_weak))))
% 5.98/6.29 (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))))
% 5.98/6.29 (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))))
% 5.98/6.29 (assert (forall ((Y tptp.product_prod_nat_nat) (Y6 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (X5 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y) Y6) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) tptp.fun_pair_less) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X5) Y6)) tptp.fun_max_strict) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ (@ tptp.insert8211810215607154385at_nat X) X5)) Y6)) tptp.fun_max_strict))))))
% 5.98/6.29 (assert (forall ((X tptp.product_prod_nat_nat) (XS tptp.set_Pr1261947904930325089at_nat) (Y tptp.product_prod_nat_nat) (YS tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.produc2922128104949294807at_nat XS))) (=> (@ (@ tptp.member8440522571783428010at_nat X) XS) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) tptp.fun_pair_less) (=> (@ (@ tptp.member8757157785044589968at_nat (@ _let_1 YS)) tptp.fun_min_strict) (@ (@ tptp.member8757157785044589968at_nat (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat Y) YS))) tptp.fun_min_strict)))))))
% 5.98/6.29 (assert (forall ((Y6 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat Y6) (=> (not (= Y6 tptp.bot_bo2099793752762293965at_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat tptp.bot_bo2099793752762293965at_nat) Y6)) tptp.fun_max_strict)))))
% 5.98/6.29 (assert (forall ((X5 tptp.set_Pr1261947904930325089at_nat)) (=> (not (= X5 tptp.bot_bo2099793752762293965at_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X5) tptp.bot_bo2099793752762293965at_nat)) tptp.fun_min_strict))))
% 5.98/6.29 (assert (= tptp.fun_min_strict (@ tptp.min_ex6901939911449802026at_nat tptp.fun_pair_less)))
% 5.98/6.29 (assert (= tptp.fun_max_strict (@ tptp.max_ex8135407076693332796at_nat tptp.fun_pair_less)))
% 5.98/6.29 (assert (@ tptp.fun_re2478310338295953701at_nat (@ (@ tptp.produc9060074326276436823at_nat tptp.fun_max_strict) tptp.fun_max_weak)))
% 5.98/6.29 (assert (@ tptp.fun_re2478310338295953701at_nat (@ (@ tptp.produc9060074326276436823at_nat tptp.fun_min_strict) tptp.fun_min_weak)))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (K tptp.int) (L tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.bit_concat_bit M2) K) L)) N) (or (and (@ (@ tptp.ord_less_nat N) M2) (@ (@ tptp.bit_se1146084159140164899it_int K) N)) (and (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.bit_se1146084159140164899it_int L) (@ (@ tptp.minus_minus_nat N) M2)))))))
% 5.98/6.29 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit tptp.zero_zero_nat) K) L) L)))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (= tptp.euclid3398187327856392827nt_nat (lambda ((N4 tptp.nat)) tptp.one_one_nat)))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((M3 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) M3))) true) __flatten_var_0))))
% 5.98/6.29 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((M3 tptp.extended_enat) (N4 tptp.extended_enat)) (@ (@ (@ tptp.extended_case_enat_o (lambda ((M1 tptp.nat)) (@ (@ (@ tptp.extended_case_enat_o (@ tptp.ord_less_nat M1)) true) N4))) false) M3))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (exists ((Q5 tptp.rat)) (let ((_let_1 (@ tptp.field_7254667332652039916t_real Q5))) (and (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real _let_1) Y)))))))
% 5.98/6.29 (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)))))))))))))))))))))))))))))))))))))))))
% 5.98/6.29 (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))))))))))))
% 5.98/6.29 (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)))))))))))))
% 5.98/6.29 (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))))))))))))
% 5.98/6.29 (assert (forall ((X15 Bool) (X23 Bool) (X33 Bool) (X42 Bool) (X52 Bool) (X62 Bool) (X72 Bool) (X82 Bool)) (= (@ tptp.size_size_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 X15) X23) X33) X42) X52) X62) X72) X82)) tptp.zero_zero_nat)))
% 5.98/6.29 (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))))))))))))
% 5.98/6.29 (assert (forall ((X15 Bool) (X23 Bool) (X33 Bool) (X42 Bool) (X52 Bool) (X62 Bool) (X72 Bool) (X82 Bool)) (= (@ tptp.size_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 X15) X23) X33) X42) X52) X62) X72) X82)) tptp.zero_zero_nat)))
% 5.98/6.29 (assert (@ (@ tptp.pcr_int (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat)) tptp.one_one_int))
% 5.98/6.29 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) tptp.field_5140801741446780682s_real) (not (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (=> (= (@ tptp.abs_abs_real X) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real M4)) (@ tptp.semiri5074537144036343181t_real N2))) (not (@ (@ tptp.algebr934650988132801477me_nat M4) N2)))))))))
% 5.98/6.29 (assert (forall ((A tptp.nat) (B tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat X))) (=> (@ (@ tptp.algebr934650988132801477me_nat A) B) (=> (@ _let_1 A) (=> (@ _let_1 B) (= X tptp.one_one_nat)))))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat (@ tptp.suc tptp.zero_zero_nat)) N)))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat N) (@ tptp.suc tptp.zero_zero_nat))))
% 5.98/6.29 (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))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (@ (@ tptp.pcr_int (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat)) tptp.zero_zero_int))
% 5.98/6.29 (assert (@ (@ (@ (@ tptp.bNF_re578469030762574527_nat_o (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (@ (@ tptp.bNF_re4705727531993890431at_o_o (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4)))) tptp.ord_less_nat) tptp.ord_less_nat))
% 5.98/6.29 (assert (@ (@ (@ (@ tptp.bNF_re3403563459893282935_int_o (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4))) (@ (@ tptp.bNF_re5089333283451836215nt_o_o (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4))) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4)))) tptp.ord_less_eq_int) tptp.ord_less_eq_int))
% 5.98/6.29 (assert (@ (@ (@ (@ tptp.bNF_re578469030762574527_nat_o (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (@ (@ tptp.bNF_re4705727531993890431at_o_o (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4)))) tptp.ord_less_eq_nat) tptp.ord_less_eq_nat))
% 5.98/6.29 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X3 tptp.nat) (Y2 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 X3) V3)) (@ (@ tptp.plus_plus_nat U2) Y2)))) __flatten_var_0)))) tptp.ord_less_int))
% 5.98/6.29 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X3 tptp.nat) (Y2 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 X3) V3)) (@ (@ tptp.plus_plus_nat U2) Y2)))) __flatten_var_0)))) tptp.ord_less_eq_int))
% 5.98/6.29 (assert (@ (@ (@ (@ tptp.bNF_re6830278522597306478at_int (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) tptp.pcr_int) (lambda ((N4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat N4) tptp.zero_zero_nat))) tptp.semiri1314217659103216013at_int))
% 5.98/6.29 (assert (@ (@ (@ (@ tptp.bNF_re728719798268516973at_o_o tptp.realrel) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4))) (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 ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R5) (@ X8 N4))))))))) (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 ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R5) (@ X8 N4))))))))))
% 5.98/6.29 (assert (@ (@ (@ (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel) (@ (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X3 tptp.nat) (Y2 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 X3) V3)) (@ (@ tptp.plus_plus_nat U2) Y2)))) __flatten_var_0)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X3 tptp.nat) (Y2 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 X3) V3)) (@ (@ tptp.plus_plus_nat U2) Y2)))) __flatten_var_0)))))
% 5.98/6.29 (assert (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))) (@ (@ tptp.intrel _let_1) _let_1)))
% 5.98/6.29 (assert (@ tptp.transp_nat_rat tptp.realrel))
% 5.98/6.29 (assert (@ (@ tptp.realrel (lambda ((N4 tptp.nat)) tptp.one_one_rat)) (lambda ((N4 tptp.nat)) tptp.one_one_rat)))
% 5.98/6.29 (assert (@ (@ tptp.realrel (lambda ((N4 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N4 tptp.nat)) tptp.zero_zero_rat)))
% 5.98/6.29 (assert (@ (@ (@ (@ tptp.bNF_re895249473297799549at_rat tptp.realrel) tptp.realrel) (lambda ((X8 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X8 N4)))) (lambda ((X8 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X8 N4)))))
% 5.98/6.29 (assert (@ (@ (@ (@ tptp.bNF_re1962705104956426057at_rat tptp.realrel) (@ (@ tptp.bNF_re895249473297799549at_rat tptp.realrel) tptp.realrel)) (lambda ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ X8 N4)) (@ Y7 N4)))) (lambda ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ X8 N4)) (@ Y7 N4)))))
% 5.98/6.29 (assert (@ (@ (@ (@ tptp.bNF_re1962705104956426057at_rat tptp.realrel) (@ (@ tptp.bNF_re895249473297799549at_rat tptp.realrel) tptp.realrel)) (lambda ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X8 N4)) (@ Y7 N4)))) (lambda ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X8 N4)) (@ Y7 N4)))))
% 5.98/6.29 (assert (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.intrel _let_1) _let_1)))
% 5.98/6.29 (assert (@ (@ (@ (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel) (@ (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X3 tptp.nat) (Y2 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 X3) V3)) (@ (@ tptp.plus_plus_nat U2) Y2)))) __flatten_var_0)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X3 tptp.nat) (Y2 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 X3) V3)) (@ (@ tptp.plus_plus_nat U2) Y2)))) __flatten_var_0)))))
% 5.98/6.29 (assert (@ (@ (@ (@ tptp.bNF_re895249473297799549at_rat tptp.realrel) tptp.realrel) (lambda ((X8 (-> tptp.nat tptp.rat)) (__flatten_var_0 tptp.nat)) (@ (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X8)) (lambda ((N4 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X8 N4)))) __flatten_var_0))) (lambda ((X8 (-> tptp.nat tptp.rat)) (__flatten_var_0 tptp.nat)) (@ (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X8)) (lambda ((N4 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X8 N4)))) __flatten_var_0))))
% 5.98/6.29 (assert (forall ((C tptp.rat)) (= (@ tptp.vanishes (lambda ((N4 tptp.nat)) C)) (= C tptp.zero_zero_rat))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat))) (=> (@ tptp.vanishes X5) (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X5 N4)))))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.vanishes X5) (=> (@ tptp.vanishes Y6) (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X5 N4)) (@ Y6 N4))))))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.vanishes X5) (=> (@ tptp.vanishes Y6) (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X5 N4)) (@ Y6 N4))))))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat)) (R2 tptp.rat)) (=> (@ tptp.vanishes X5) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R2) (exists ((K2 tptp.nat)) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N6) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X5 N6))) R2))))))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat))) (=> (forall ((R4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R4) (exists ((K8 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K8) N2) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X5 N2))) R4)))))) (@ tptp.vanishes X5))))
% 5.98/6.29 (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 ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X8 N4))) R5)))))))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (exists ((A8 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A8) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X5 N2))) A8)))) (=> (@ tptp.vanishes Y6) (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ X5 N4)) (@ Y6 N4))))))))
% 5.98/6.29 (assert (@ (@ (@ (@ tptp.bNF_re3023117138289059399t_real tptp.pcr_real) tptp.pcr_real) (lambda ((X8 (-> tptp.nat tptp.rat)) (__flatten_var_0 tptp.nat)) (@ (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X8)) (lambda ((N4 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X8 N4)))) __flatten_var_0))) tptp.inverse_inverse_real))
% 5.98/6.29 (assert (forall ((X (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel X) X) (= (@ tptp.inverse_inverse_real (@ tptp.real2 X)) (@ tptp.real2 (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X)) (lambda ((N4 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X N4)))))))))
% 5.98/6.29 (assert (forall ((P (-> tptp.real Bool)) (X tptp.real)) (=> (forall ((Y3 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel Y3) Y3) (@ P (@ tptp.real2 Y3)))) (@ P X))))
% 5.98/6.29 (assert (= tptp.zero_zero_real (@ tptp.real2 (lambda ((N4 tptp.nat)) tptp.zero_zero_rat))))
% 5.98/6.29 (assert (= tptp.semiri5074537144036343181t_real (lambda ((X3 tptp.nat)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ tptp.semiri681578069525770553at_rat X3))))))
% 5.98/6.29 (assert (= tptp.one_one_real (@ tptp.real2 (lambda ((N4 tptp.nat)) tptp.one_one_rat))))
% 5.98/6.29 (assert (= tptp.field_7254667332652039916t_real (lambda ((X3 tptp.rat)) (@ tptp.real2 (lambda ((N4 tptp.nat)) X3)))))
% 5.98/6.29 (assert (= tptp.ring_1_of_int_real (lambda ((X3 tptp.int)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ tptp.ring_1_of_int_rat X3))))))
% 5.98/6.29 (assert (@ (@ (@ (@ tptp.bNF_re4521903465945308077real_o tptp.pcr_real) (@ (@ tptp.bNF_re4297313714947099218al_o_o tptp.pcr_real) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4)))) tptp.realrel) (lambda ((Y5 tptp.real) (Z4 tptp.real)) (= Y5 Z4))))
% 5.98/6.29 (assert (@ (@ tptp.pcr_real (lambda ((N4 tptp.nat)) tptp.zero_zero_rat)) tptp.zero_zero_real))
% 5.98/6.29 (assert (@ (@ tptp.pcr_real (lambda ((N4 tptp.nat)) tptp.one_one_rat)) tptp.one_one_real))
% 5.98/6.29 (assert (@ (@ (@ (@ tptp.bNF_re3023117138289059399t_real tptp.pcr_real) tptp.pcr_real) (lambda ((X8 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X8 N4)))) tptp.uminus_uminus_real))
% 5.98/6.29 (assert (@ (@ (@ (@ tptp.bNF_re4695409256820837752l_real tptp.pcr_real) (@ (@ tptp.bNF_re3023117138289059399t_real tptp.pcr_real) tptp.pcr_real)) (lambda ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X8 N4)) (@ Y7 N4)))) tptp.plus_plus_real))
% 5.98/6.29 (assert (forall ((X (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel X) X) (= (@ tptp.uminus_uminus_real (@ tptp.real2 X)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X N4))))))))
% 5.98/6.29 (assert (@ (@ (@ (@ tptp.bNF_re4695409256820837752l_real tptp.pcr_real) (@ (@ tptp.bNF_re3023117138289059399t_real tptp.pcr_real) tptp.pcr_real)) (lambda ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ X8 N4)) (@ Y7 N4)))) tptp.times_times_real))
% 5.98/6.29 (assert (forall ((Xa2 (-> tptp.nat tptp.rat)) (X (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel Xa2) Xa2) (=> (@ (@ tptp.realrel X) X) (= (@ (@ tptp.plus_plus_real (@ tptp.real2 Xa2)) (@ tptp.real2 X)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ Xa2 N4)) (@ X N4)))))))))
% 5.98/6.29 (assert (forall ((Xa2 (-> tptp.nat tptp.rat)) (X (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel Xa2) Xa2) (=> (@ (@ tptp.realrel X) X) (= (@ (@ tptp.times_times_real (@ tptp.real2 Xa2)) (@ tptp.real2 X)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ Xa2 N4)) (@ X N4)))))))))
% 5.98/6.29 (assert (@ (@ (@ (@ tptp.bNF_re4297313714947099218al_o_o tptp.pcr_real) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4))) (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 ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R5) (@ X8 N4))))))))) tptp.positive))
% 5.98/6.29 (assert (forall ((X (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel X) X) (= (@ tptp.positive (@ tptp.real2 X)) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R5) (@ X N4)))))))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ tptp.positive X) (=> (@ tptp.positive Y) (@ tptp.positive (@ (@ tptp.times_times_real X) Y))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ tptp.positive X) (=> (@ tptp.positive Y) (@ tptp.positive (@ (@ tptp.plus_plus_real X) Y))))))
% 5.98/6.29 (assert (not (@ tptp.positive tptp.zero_zero_real)))
% 5.98/6.29 (assert (forall ((X tptp.real)) (=> (not (@ tptp.positive X)) (=> (not (= X tptp.zero_zero_real)) (@ tptp.positive (@ tptp.uminus_uminus_real X))))))
% 5.98/6.29 (assert (= tptp.ord_less_real (lambda ((X3 tptp.real) (Y2 tptp.real)) (@ tptp.positive (@ (@ tptp.minus_minus_real Y2) X3)))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X5) (=> (@ tptp.cauchy Y6) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real2 X5)) (@ tptp.real2 Y6)) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_eq_rat (@ X5 N4)) (@ (@ tptp.plus_plus_rat (@ Y6 N4)) R5))))))))))))
% 5.98/6.29 (assert (= tptp.positive (lambda ((X3 tptp.real)) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R5) (@ (@ tptp.rep_real2 X3) N4))))))))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X5) (=> (not (@ tptp.vanishes X5)) (@ tptp.cauchy (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X5 N4))))))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X5) (@ (@ tptp.realrel X5) X5))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X5) (=> (@ tptp.cauchy Y6) (@ tptp.cauchy (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X5 N4)) (@ Y6 N4))))))))
% 5.98/6.29 (assert (forall ((X tptp.rat)) (@ tptp.cauchy (lambda ((N4 tptp.nat)) X))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X5) (@ tptp.cauchy (lambda ((N4 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X5 N4)))))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X5) (=> (@ tptp.cauchy Y6) (@ tptp.cauchy (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ X5 N4)) (@ Y6 N4))))))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X5) (=> (@ tptp.cauchy Y6) (@ tptp.cauchy (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X5 N4)) (@ Y6 N4))))))))
% 5.98/6.29 (assert (forall ((P (-> tptp.real Bool)) (X tptp.real)) (=> (forall ((X10 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X10) (@ P (@ tptp.real2 X10)))) (@ P X))))
% 5.98/6.29 (assert (= tptp.pcr_real (lambda ((X3 (-> tptp.nat tptp.rat)) (Y2 tptp.real)) (and (@ tptp.cauchy X3) (= (@ tptp.real2 X3) Y2)))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X5) (exists ((B5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B5) (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X5 N6))) B5)))))))
% 5.98/6.29 (assert (forall ((Y6 (-> tptp.nat tptp.rat)) (X tptp.real)) (=> (@ tptp.cauchy Y6) (=> (@ (@ tptp.ord_less_real X) (@ tptp.real2 Y6)) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real X) (@ tptp.field_7254667332652039916t_real (@ Y6 N2))))))))
% 5.98/6.29 (assert (forall ((Y6 (-> tptp.nat tptp.rat)) (X tptp.real)) (=> (@ tptp.cauchy Y6) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.field_7254667332652039916t_real (@ Y6 N2)))) (@ (@ tptp.ord_less_eq_real X) (@ tptp.real2 Y6))))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat)) (Y tptp.real)) (=> (@ tptp.cauchy X5) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.field_7254667332652039916t_real (@ X5 N2))) Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.real2 X5)) Y)))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X5) (= (@ tptp.uminus_uminus_real (@ tptp.real2 X5)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X5 N4))))))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X5) (=> (@ tptp.cauchy Y6) (= (@ (@ tptp.plus_plus_real (@ tptp.real2 X5)) (@ tptp.real2 Y6)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X5 N4)) (@ Y6 N4)))))))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X5) (=> (@ tptp.cauchy Y6) (= (@ (@ tptp.times_times_real (@ tptp.real2 X5)) (@ tptp.real2 Y6)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ X5 N4)) (@ Y6 N4)))))))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X5) (=> (@ tptp.cauchy Y6) (= (@ (@ tptp.minus_minus_real (@ tptp.real2 X5)) (@ tptp.real2 Y6)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X5 N4)) (@ Y6 N4)))))))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X5) (=> (@ tptp.cauchy Y6) (=> (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X5 N4)) (@ Y6 N4)))) (@ (@ tptp.realrel X5) Y6))))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X5) (=> (@ tptp.cauchy Y6) (= (= (@ tptp.real2 X5) (@ tptp.real2 Y6)) (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X5 N4)) (@ Y6 N4)))))))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat)) (Y6 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X5) (=> (not (@ tptp.vanishes X5)) (=> (@ tptp.cauchy Y6) (=> (not (@ tptp.vanishes Y6)) (=> (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X5 N4)) (@ Y6 N4)))) (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ tptp.inverse_inverse_rat (@ X5 N4))) (@ tptp.inverse_inverse_rat (@ Y6 N4))))))))))))
% 5.98/6.29 (assert (= tptp.realrel (lambda ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (and (@ tptp.cauchy X8) (@ tptp.cauchy Y7) (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X8 N4)) (@ Y7 N4))))))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X5) (=> (not (@ tptp.vanishes X5)) (exists ((B5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B5) (exists ((K2 tptp.nat)) (or (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N6) (@ (@ tptp.ord_less_rat B5) (@ tptp.uminus_uminus_rat (@ X5 N6))))) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N6) (@ (@ tptp.ord_less_rat B5) (@ X5 N6))))))))))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X5) (= (@ tptp.positive (@ tptp.real2 X5)) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R5) (@ X5 N4)))))))))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X5) (=> (not (@ tptp.vanishes X5)) (exists ((B5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B5) (exists ((K2 tptp.nat)) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N6) (@ (@ tptp.ord_less_rat B5) (@ tptp.abs_abs_rat (@ X5 N6))))))))))))
% 5.98/6.29 (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 ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) M3) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X8 M3)) (@ X8 N4)))) R5)))))))))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat))) (=> (forall ((R4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R4) (exists ((K8 tptp.nat)) (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K8) M4) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K8) N2) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X5 M4)) (@ X5 N2)))) R4)))))))) (@ tptp.cauchy X5))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat)) (R2 tptp.rat)) (=> (@ tptp.cauchy X5) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R2) (exists ((K2 tptp.nat)) (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) M) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N6) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X5 M)) (@ X5 N6)))) R2))))))))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.real2 X5)))) (let ((_let_2 (@ tptp.vanishes X5))) (=> (@ tptp.cauchy X5) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X5 N4))))))))))))
% 5.98/6.29 (assert (forall ((X5 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X5) (= (not (@ tptp.positive (@ tptp.real2 X5))) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_eq_rat (@ X5 N4)) R5))))))))))
% 5.98/6.29 (assert (= tptp.inverse_inverse_real (@ (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real2) tptp.real2) (lambda ((X8 (-> tptp.nat tptp.rat)) (__flatten_var_0 tptp.nat)) (@ (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X8)) (lambda ((N4 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X8 N4)))) __flatten_var_0)))))
% 5.98/6.29 (assert (= tptp.cr_real (lambda ((X3 (-> tptp.nat tptp.rat)) (Y2 tptp.real)) (and (@ (@ tptp.realrel X3) X3) (= (@ tptp.real2 X3) Y2)))))
% 5.98/6.29 (assert (= tptp.pcr_real tptp.cr_real))
% 5.98/6.29 (assert (= tptp.uminus_uminus_real (@ (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real2) tptp.real2) (lambda ((X8 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X8 N4))))))
% 5.98/6.29 (assert (= tptp.times_times_real (@ (@ (@ tptp.map_fu1532550112467129777l_real tptp.rep_real2) (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real2) tptp.real2)) (lambda ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ X8 N4)) (@ Y7 N4))))))
% 5.98/6.29 (assert (= tptp.plus_plus_real (@ (@ (@ tptp.map_fu1532550112467129777l_real tptp.rep_real2) (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real2) tptp.real2)) (lambda ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X8 N4)) (@ Y7 N4))))))
% 5.98/6.29 (assert (forall ((M2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.extended_enat2 N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M2)) N))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.extended_enat2 M2)) (@ tptp.extended_enat2 N)) (@ (@ tptp.ord_less_nat M2) N))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.extended_enat2 M2)) (@ tptp.extended_enat2 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))
% 5.98/6.29 (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))))
% 5.98/6.29 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N) (@ tptp.extended_enat2 tptp.zero_zero_nat)) N)))
% 5.98/6.29 (assert (forall ((M2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M2)) (@ tptp.extended_enat2 N)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M2)) N))))
% 5.98/6.29 (assert (= tptp.one_on7984719198319812577d_enat (@ tptp.extended_enat2 tptp.one_one_nat)))
% 5.98/6.29 (assert (forall ((X tptp.nat)) (= (= (@ tptp.extended_enat2 X) tptp.one_on7984719198319812577d_enat) (= X tptp.one_one_nat))))
% 5.98/6.29 (assert (forall ((X tptp.nat)) (= (= tptp.one_on7984719198319812577d_enat (@ tptp.extended_enat2 X)) (= X tptp.one_one_nat))))
% 5.98/6.29 (assert (forall ((X tptp.nat)) (= (= tptp.zero_z5237406670263579293d_enat (@ tptp.extended_enat2 X)) (= X tptp.zero_zero_nat))))
% 5.98/6.29 (assert (forall ((X tptp.nat)) (= (= (@ tptp.extended_enat2 X) tptp.zero_z5237406670263579293d_enat) (= X tptp.zero_zero_nat))))
% 5.98/6.29 (assert (= tptp.zero_z5237406670263579293d_enat (@ tptp.extended_enat2 tptp.zero_zero_nat)))
% 5.98/6.29 (assert (forall ((N tptp.extended_enat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat N) (@ tptp.extended_enat2 M2)) (not (forall ((K2 tptp.nat)) (=> (= N (@ tptp.extended_enat2 K2)) (not (@ (@ tptp.ord_less_nat K2) M2))))))))
% 5.98/6.29 (assert (forall ((N tptp.extended_enat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat N) (@ tptp.extended_enat2 M2)) (exists ((K2 tptp.nat)) (= N (@ tptp.extended_enat2 K2))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat) (N tptp.nat)) (=> (forall ((Y3 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Y3) A2) (@ (@ tptp.ord_le2932123472753598470d_enat Y3) (@ tptp.extended_enat2 N)))) (@ tptp.finite4001608067531595151d_enat A2))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.extended_enat2 (@ tptp.suc M2))) N) (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.extended_enat2 M2)) N))))
% 5.98/6.29 (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 ((N3 tptp.nat)) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) M3) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) N4) (@ P (@ (@ tptp.product_Pair_nat_nat N4) M3))))))))))
% 5.98/6.29 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (N tptp.nat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat X) Y)) (@ tptp.extended_enat2 N)) (exists ((Y8 tptp.nat) (X9 tptp.nat)) (and (= X (@ tptp.extended_enat2 X9)) (= Y (@ tptp.extended_enat2 Y8)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X9) Y8)) N))))))
% 5.98/6.29 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) 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)))))
% 5.98/6.29 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (L tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat L) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg) _let_1))))) (let ((_let_3 (@ (@ tptp.vEBT_Node Info) Deg))) (= (@ (@ tptp.vEBT_VEBT_elim_dead (@ (@ _let_3 TreeList) Summary)) (@ tptp.extended_enat2 L)) (@ (@ _let_3 (@ (@ tptp.take_VEBT_VEBT _let_2) (@ (@ tptp.map_VE8901447254227204932T_VEBT (lambda ((T2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vEBT_VEBT_elim_dead T2) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg) _let_1))))))) TreeList))) (@ (@ tptp.vEBT_VEBT_elim_dead Summary) (@ tptp.extended_enat2 _let_2)))))))))
% 5.98/6.29 (assert (forall ((A Bool) (B Bool) (Uu tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A) B))) (= (@ (@ tptp.vEBT_VEBT_elim_dead _let_1) Uu) _let_1))))
% 5.98/6.29 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.extended_enat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_VEBT_elim_dead X) Xa2) Y) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_Node Info2) Deg2))) (=> (= X (@ (@ _let_1 TreeList2) Summary2)) (=> (= Xa2 tptp.extend5688581933313929465d_enat) (not (= Y (@ (@ _let_1 (@ (@ tptp.map_VE8901447254227204932T_VEBT (lambda ((T2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vEBT_VEBT_elim_dead T2) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg2) _let_1))))))) TreeList2)) (@ (@ tptp.vEBT_VEBT_elim_dead Summary2) tptp.extend5688581933313929465d_enat)))))))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2)) (forall ((L4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat L4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg2) _let_1))))) (=> (= Xa2 (@ tptp.extended_enat2 L4)) (not (= Y (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) (@ (@ tptp.take_VEBT_VEBT _let_2) (@ (@ tptp.map_VE8901447254227204932T_VEBT (lambda ((T2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vEBT_VEBT_elim_dead T2) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg2) _let_1))))))) TreeList2))) (@ (@ tptp.vEBT_VEBT_elim_dead Summary2) (@ tptp.extended_enat2 _let_2)))))))))))))))))
% 5.98/6.29 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_Node Info) Deg))) (= (@ (@ tptp.vEBT_VEBT_elim_dead (@ (@ _let_1 TreeList) Summary)) tptp.extend5688581933313929465d_enat) (@ (@ _let_1 (@ (@ tptp.map_VE8901447254227204932T_VEBT (lambda ((T2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vEBT_VEBT_elim_dead T2) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg) _let_1))))))) TreeList)) (@ (@ tptp.vEBT_VEBT_elim_dead Summary) tptp.extend5688581933313929465d_enat))))))
% 5.98/6.29 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (= (@ (@ tptp.vEBT_VEBT_elim_dead _let_1) tptp.extend5688581933313929465d_enat) _let_1)))))
% 5.98/6.29 (assert (forall ((Q4 tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat Q4) tptp.extend5688581933313929465d_enat)))
% 5.98/6.29 (assert (forall ((Q4 tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat tptp.extend5688581933313929465d_enat) Q4) (= Q4 tptp.extend5688581933313929465d_enat))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.extended_enat2 M2)) tptp.extend5688581933313929465d_enat))) (let ((_let_2 (= M2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_z5237406670263579293d_enat)) (=> (not _let_2) (= _let_1 tptp.extend5688581933313929465d_enat)))))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_le2932123472753598470d_enat tptp.extend5688581933313929465d_enat) (@ tptp.extended_enat2 N)))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat)) (not (@ (@ tptp.ord_le2932123472753598470d_enat tptp.extend5688581933313929465d_enat) (@ tptp.extended_enat2 M2)))))
% 5.98/6.29 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat A))) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ _let_1 B)) (@ _let_1 C)) (or (= A tptp.extend5688581933313929465d_enat) (@ (@ tptp.ord_le2932123472753598470d_enat B) C))))))
% 5.98/6.29 (assert (forall ((Q4 tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat Q4) tptp.extend5688581933313929465d_enat)))
% 5.98/6.29 (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)))))
% 5.98/6.29 (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 ((X3 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X3) A6)))))))
% 5.98/6.29 (assert (forall ((X tptp.produc7272778201969148633d_enat)) (=> (forall ((A5 Bool) (B5 Bool) (Uu2 tptp.extended_enat)) (not (= X (@ (@ tptp.produc581526299967858633d_enat (@ (@ tptp.vEBT_Leaf A5) B5)) Uu2)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (not (= X (@ (@ tptp.produc581526299967858633d_enat (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2)) tptp.extend5688581933313929465d_enat)))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (L4 tptp.nat)) (not (= X (@ (@ tptp.produc581526299967858633d_enat (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2)) (@ tptp.extended_enat2 L4))))))))))
% 5.98/6.29 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.extended_enat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_VEBT_elim_dead X) Xa2) Y) (=> (@ (@ tptp.accp_P6183159247885693666d_enat tptp.vEBT_V312737461966249ad_rel) (@ (@ tptp.produc581526299967858633d_enat X) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P6183159247885693666d_enat tptp.vEBT_V312737461966249ad_rel) (@ (@ tptp.produc581526299967858633d_enat _let_1) Xa2))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_Node Info2) Deg2))) (let ((_let_2 (@ (@ _let_1 TreeList2) Summary2))) (=> (= X _let_2) (=> (= Xa2 tptp.extend5688581933313929465d_enat) (=> (= Y (@ (@ _let_1 (@ (@ tptp.map_VE8901447254227204932T_VEBT (lambda ((T2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vEBT_VEBT_elim_dead T2) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg2) _let_1))))))) TreeList2)) (@ (@ tptp.vEBT_VEBT_elim_dead Summary2) tptp.extend5688581933313929465d_enat))) (not (@ (@ tptp.accp_P6183159247885693666d_enat tptp.vEBT_V312737461966249ad_rel) (@ (@ tptp.produc581526299967858633d_enat _let_2) tptp.extend5688581933313929465d_enat))))))))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2)) (forall ((L4 tptp.nat)) (let ((_let_1 (@ tptp.extended_enat2 L4))) (let ((_let_2 (@ (@ tptp.vEBT_Node Info2) Deg2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat L4) (@ (@ tptp.power_power_nat _let_3) (@ (@ tptp.divide_divide_nat Deg2) _let_3))))) (=> (= Xa2 _let_1) (=> (= Y (@ (@ _let_2 (@ (@ tptp.take_VEBT_VEBT _let_4) (@ (@ tptp.map_VE8901447254227204932T_VEBT (lambda ((T2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vEBT_VEBT_elim_dead T2) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg2) _let_1))))))) TreeList2))) (@ (@ tptp.vEBT_VEBT_elim_dead Summary2) (@ tptp.extended_enat2 _let_4)))) (not (@ (@ tptp.accp_P6183159247885693666d_enat tptp.vEBT_V312737461966249ad_rel) (@ (@ tptp.produc581526299967858633d_enat (@ (@ _let_2 TreeList2) Summary2)) _let_1)))))))))))))))))))
% 5.98/6.29 (assert (= tptp.times_7803423173614009249d_enat (lambda ((M3 tptp.extended_enat) (N4 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)) N4))) (@ (@ (@ tptp.if_Extended_enat (= N4 tptp.zero_z5237406670263579293d_enat)) tptp.zero_z5237406670263579293d_enat) tptp.extend5688581933313929465d_enat)) M3))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A2) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (= (@ tptp.extended_eSuc (@ tptp.lattic921264341876707157d_enat A2)) (@ tptp.lattic921264341876707157d_enat (@ (@ tptp.image_80655429650038917d_enat tptp.extended_eSuc) A2)))))))
% 5.98/6.29 (assert (forall ((N tptp.extended_enat) (M2 tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.extended_eSuc N)) (@ tptp.extended_eSuc M2)) (@ (@ tptp.ord_le2932123472753598470d_enat N) M2))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.extended_enat)) (let ((_let_1 (@ tptp.extended_enat2 M2))) (= (@ (@ tptp.ord_le72135733267957522d_enat _let_1) (@ tptp.extended_eSuc N)) (@ (@ tptp.ord_le2932123472753598470d_enat _let_1) N)))))
% 5.98/6.29 (assert (forall ((N tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat N) (@ tptp.extended_eSuc N))))
% 5.98/6.29 (assert (forall ((N tptp.extended_enat)) (not (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.extended_eSuc N)) tptp.zero_z5237406670263579293d_enat))))
% 5.98/6.29 (assert (forall ((M2 tptp.extended_enat) (N tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M2) N) (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.extended_eSuc M2)) N))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_Extended_enat)) (=> (not (= A2 tptp.bot_bo7653980558646680370d_enat)) (= (@ tptp.extended_eSuc (@ tptp.comple4398354569131411667d_enat A2)) (@ tptp.comple4398354569131411667d_enat (@ (@ tptp.image_80655429650038917d_enat tptp.extended_eSuc) A2))))))
% 5.98/6.29 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) tptp.less_than) (@ (@ tptp.ord_less_nat X) Y))))
% 5.98/6.29 (assert (= tptp.fun_pair_less (@ (@ tptp.lex_prod_nat_nat tptp.less_than) tptp.less_than)))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (@ (@ tptp.order_2888998067076097458on_nat (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.ord_less_nat X3) N)))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) N) (@ (@ tptp.ord_less_nat Y2) N) (@ (@ tptp.ord_less_eq_nat X3) Y2))))))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (@ (@ tptp.order_2888998067076097458on_nat (@ tptp.field_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) N) (@ (@ tptp.ord_less_nat Y2) N) (@ (@ tptp.ord_less_eq_nat X3) Y2))))))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (and (@ (@ tptp.ord_less_nat X3) N) (@ (@ tptp.ord_less_nat Y2) N) (@ (@ tptp.ord_less_eq_nat X3) Y2))))))))
% 5.98/6.29 (assert (= tptp.positive (@ (@ (@ tptp.map_fu1856342031159181835at_o_o tptp.rep_real2) 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 ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R5) (@ X8 N4)))))))))))
% 5.98/6.29 (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)))))))
% 5.98/6.29 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re (@ tptp.csqrt Z)))))
% 5.98/6.29 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X))) (@ tptp.real_V1022390504157884413omplex X))))
% 5.98/6.29 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.re X)) (@ tptp.real_V1022390504157884413omplex X))))
% 5.98/6.29 (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)))))
% 5.98/6.29 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.re X))) (=> (= (@ tptp.im X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= (@ tptp.csqrt X) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt _let_1))))))))
% 5.98/6.29 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X))) (@ tptp.real_V1022390504157884413omplex X))))
% 5.98/6.29 (assert (forall ((X tptp.complex) (Y tptp.complex)) (=> (= (@ tptp.re X) (@ tptp.re Y)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X))) (@ tptp.abs_abs_real (@ tptp.im Y)))))))
% 5.98/6.29 (assert (forall ((X tptp.complex) (Y tptp.complex)) (=> (= (@ tptp.im X) (@ tptp.im Y)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X))) (@ tptp.abs_abs_real (@ tptp.re Y)))))))
% 5.98/6.29 (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))))))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (assert (forall ((B tptp.complex)) (let ((_let_1 (@ tptp.re B))) (=> (or (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.im B)))) (= (@ tptp.csqrt (@ (@ tptp.power_power_complex B) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) B)))))
% 5.98/6.29 (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))))))
% 5.98/6.29 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.re X))) (=> (= (@ tptp.im X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (= (@ tptp.csqrt X) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt (@ tptp.abs_abs_real _let_1))))))))))
% 5.98/6.29 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.im X))) (=> (or (@ (@ tptp.ord_less_real _let_1) tptp.zero_zero_real) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re X)))) (= (@ tptp.csqrt (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.csqrt X)))))))
% 5.98/6.29 (assert (= tptp.top_top_set_o (@ (@ tptp.insert_o false) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o))))
% 5.98/6.29 (assert (forall ((Y Bool) (P (-> Bool Bool))) (=> (@ (@ tptp.member_o Y) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o)) (=> (forall ((X4 tptp.product_unit)) (@ P (@ tptp.product_Rep_unit X4))) (@ P Y)))))
% 5.98/6.29 (assert (forall ((X Bool) (Y Bool)) (let ((_let_1 (@ (@ tptp.insert_o true) tptp.bot_bot_set_o))) (=> (@ (@ tptp.member_o X) _let_1) (=> (@ (@ tptp.member_o Y) _let_1) (= (= (@ tptp.product_Abs_unit X) (@ tptp.product_Abs_unit Y)) (= X Y)))))))
% 5.98/6.29 (assert (forall ((Y Bool)) (=> (@ (@ tptp.member_o Y) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o)) (= (@ tptp.product_Rep_unit (@ tptp.product_Abs_unit Y)) Y))))
% 5.98/6.29 (assert (forall ((X tptp.product_unit)) (@ (@ tptp.member_o (@ tptp.product_Rep_unit X)) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o))))
% 5.98/6.29 (assert (forall ((X tptp.product_unit)) (not (forall ((Y3 Bool)) (=> (= X (@ tptp.product_Abs_unit Y3)) (not (@ (@ tptp.member_o Y3) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o))))))))
% 5.98/6.29 (assert (forall ((Y Bool)) (=> (@ (@ tptp.member_o Y) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o)) (not (forall ((X4 tptp.product_unit)) (= Y (not (@ tptp.product_Rep_unit X4))))))))
% 5.98/6.29 (assert (forall ((P (-> tptp.product_unit Bool)) (X tptp.product_unit)) (=> (forall ((Y3 Bool)) (=> (@ (@ tptp.member_o Y3) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o)) (@ P (@ tptp.product_Abs_unit Y3)))) (@ P X))))
% 5.98/6.29 (assert (@ (@ (@ tptp.type_d6188575255521822967unit_o tptp.product_Rep_unit) tptp.product_Abs_unit) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o)))
% 5.98/6.29 (assert (@ (@ (@ (@ tptp.quotie3684837364556693515t_real tptp.realrel) tptp.real2) tptp.rep_real2) tptp.cr_real))
% 5.98/6.29 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.gcd_gcd_nat A) B) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 5.98/6.29 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat tptp.zero_zero_nat) A) A)))
% 5.98/6.29 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.gcd_gcd_nat A) B)) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 5.98/6.29 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat A) tptp.zero_zero_nat) A)))
% 5.98/6.29 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat X) tptp.zero_zero_nat) X)))
% 5.98/6.29 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat tptp.zero_zero_nat) X) X)))
% 5.98/6.29 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat M2) tptp.one_one_nat) tptp.one_one_nat)))
% 5.98/6.29 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.gcd_gcd_nat M2) _let_1) _let_1))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.gcd_gcd_nat M2) N)) (or (not (= M2 tptp.zero_zero_nat)) (not (= N tptp.zero_zero_nat))))))
% 5.98/6.29 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (= (@ (@ tptp.gcd_gcd_nat X) Y) (@ (@ tptp.gcd_gcd_nat Y) (@ (@ tptp.modulo_modulo_nat X) Y))))))
% 5.98/6.29 (assert (= tptp.gcd_gcd_nat (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ (@ tptp.if_nat (= Y2 tptp.zero_zero_nat)) X3) (@ (@ tptp.gcd_gcd_nat Y2) (@ (@ tptp.modulo_modulo_nat X3) Y2))))))
% 5.98/6.29 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X) Xa2) Y) (and (=> _let_1 (= Y X)) (=> (not _let_1) (= Y (@ (@ tptp.gcd_gcd_nat Xa2) (@ (@ tptp.modulo_modulo_nat X) Xa2)))))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat M2) N)) N) (@ (@ tptp.gcd_gcd_nat M2) N)))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat N) M2)) N) (@ (@ tptp.gcd_gcd_nat M2) N)))))
% 5.98/6.29 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.gcd_gcd_nat A) B)) A))))
% 5.98/6.29 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.gcd_gcd_nat A) B)) B))))
% 5.98/6.29 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.gcd_gcd_int X) Y))))
% 5.98/6.29 (assert (forall ((D tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) D) (@ _let_1 A) (@ _let_1 B) (forall ((E3 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int E3))) (=> (and (@ _let_1 A) (@ _let_1 B)) (@ _let_1 D))))) (= D (@ (@ tptp.gcd_gcd_int A) B))))))
% 5.98/6.29 (assert (forall ((B tptp.nat) (A tptp.nat)) (exists ((X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.gcd_gcd_nat A) B))) (let ((_let_2 (@ tptp.times_times_nat A))) (let ((_let_3 (@ _let_2 Y3))) (let ((_let_4 (@ tptp.times_times_nat B))) (let ((_let_5 (@ _let_4 X4))) (let ((_let_6 (@ _let_4 Y3))) (let ((_let_7 (@ _let_2 X4))) (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)))))))))))))
% 5.98/6.29 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((X4 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.times_times_nat A) X4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) (@ (@ tptp.gcd_gcd_nat A) B)))))))
% 5.98/6.29 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.gcd_gcd_int A) B)) A))))
% 5.98/6.29 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.gcd_gcd_int A) B)) B))))
% 5.98/6.29 (assert (forall ((X tptp.int) (Y tptp.int) (P (-> tptp.int Bool))) (let ((_let_1 (@ tptp.gcd_gcd_int X))) (let ((_let_2 (@ P (@ _let_1 Y)))) (let ((_let_3 (@ tptp.uminus_uminus_int Y))) (let ((_let_4 (@ tptp.gcd_gcd_int (@ tptp.uminus_uminus_int X)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int))) (let ((_let_6 (@ (@ tptp.ord_less_eq_int X) tptp.zero_zero_int))) (let ((_let_7 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_8 (@ _let_7 Y))) (let ((_let_9 (@ _let_7 X))) (=> (=> _let_9 (=> _let_8 _let_2)) (=> (=> _let_9 (=> _let_5 (@ P (@ _let_1 _let_3)))) (=> (=> _let_6 (=> _let_8 (@ P (@ _let_4 Y)))) (=> (=> _let_6 (=> _let_5 (@ P (@ _let_4 _let_3)))) _let_2)))))))))))))))
% 5.98/6.29 (assert (forall ((A2 tptp.set_nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (=> (@ (@ tptp.member_nat B5) A2) (@ (@ tptp.member_nat (@ (@ tptp.gcd_gcd_nat A5) B5)) A2)))) (=> (not (= A2 tptp.bot_bot_set_nat)) (@ (@ tptp.member_nat (@ tptp.gcd_Gcd_nat A2)) A2)))))
% 5.98/6.29 (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))))
% 5.98/6.29 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.gcd_gcd_nat) tptp.zero_zero_nat) tptp.dvd_dvd_nat) (lambda ((M3 tptp.nat) (N4 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat M3) N4) (not (= M3 N4))))))
% 5.98/6.29 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.gcd_gcd_nat M2) N) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D5 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D5))) (and (@ _let_1 M2) (@ _let_1 N))))))))))
% 5.98/6.29 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.gcd_nat_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa2)))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y X)) (=> (not _let_2) (= Y (@ (@ tptp.gcd_gcd_nat Xa2) (@ (@ tptp.modulo_modulo_nat X) Xa2))))) (not _let_1)))))))))
% 5.98/6.29 (assert (@ (@ tptp.semila9081495762789891438tr_nat tptp.ord_max_nat) tptp.zero_zero_nat))
% 5.98/6.29 (assert (@ (@ tptp.semila9081495762789891438tr_nat tptp.gcd_gcd_nat) tptp.zero_zero_nat))
% 5.98/6.29 (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 ((X3 tptp.nat) (Y2 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 X3) V3)) (@ (@ tptp.plus_plus_nat U2) Y2)))) __flatten_var_0))))))
% 5.98/6.29 (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 ((X3 tptp.nat) (Y2 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 X3) V3)) (@ (@ tptp.plus_plus_nat U2) Y2)))) __flatten_var_0))))))
% 5.98/6.29 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.cofinite_nat) (exists ((M3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N4) (@ P N4)))))))
% 5.98/6.29 (assert (forall ((M2 tptp.nat)) (@ (@ tptp.eventually_nat (@ tptp.ord_less_eq_nat M2)) tptp.cofinite_nat)))
% 5.98/6.29 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.cofinite_nat) (exists ((M3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N4) (@ P N4)))))))
% 5.98/6.29 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat (lambda ((N4 tptp.nat)) (@ P (@ tptp.suc N4)))) tptp.cofinite_nat) (@ (@ tptp.eventually_nat P) tptp.cofinite_nat))))
% 5.98/6.29 (assert (forall ((P (-> tptp.nat Bool))) (=> (@ (@ tptp.eventually_nat P) tptp.cofinite_nat) (@ (@ tptp.eventually_nat (lambda ((N4 tptp.nat)) (@ P (@ tptp.suc N4)))) tptp.cofinite_nat))))
% 5.98/6.29 (assert (forall ((P (-> tptp.nat Bool))) (=> (@ (@ tptp.eventually_nat (lambda ((N4 tptp.nat)) (@ P (@ tptp.suc N4)))) tptp.cofinite_nat) (@ (@ tptp.eventually_nat P) tptp.cofinite_nat))))
% 5.98/6.29 (assert (@ (@ tptp.monoid_nat tptp.gcd_gcd_nat) tptp.zero_zero_nat))
% 5.98/6.29 (assert (@ (@ tptp.monoid_nat tptp.ord_max_nat) tptp.zero_zero_nat))
% 5.98/6.29 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.frequently_nat P) tptp.cofinite_nat) (forall ((M3 tptp.nat)) (exists ((N4 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N4) (@ P N4)))))))
% 5.98/6.29 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.frequently_nat P) tptp.cofinite_nat) (forall ((M3 tptp.nat)) (exists ((N4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M3) N4) (@ P N4)))))))
% 5.98/6.29 (assert (forall ((X tptp.list_nat) (Y tptp.nat)) (=> (= (@ tptp.nat_list_encode X) Y) (=> (=> (= X tptp.nil_nat) (not (= Y tptp.zero_zero_nat))) (not (forall ((X4 tptp.nat) (Xs3 tptp.list_nat)) (=> (= X (@ (@ tptp.cons_nat X4) Xs3)) (not (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X4) (@ tptp.nat_list_encode Xs3)))))))))))))
% 5.98/6.29 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B)))))
% 5.98/6.29 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B)))))
% 5.98/6.29 (assert (= (@ tptp.nat_list_encode tptp.nil_nat) tptp.zero_zero_nat))
% 5.98/6.29 (assert (forall ((X tptp.list_nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.accp_list_nat tptp.nat_list_encode_rel))) (=> (= (@ tptp.nat_list_encode X) Y) (=> (@ _let_1 X) (=> (=> (= X tptp.nil_nat) (=> (= Y tptp.zero_zero_nat) (not (@ _let_1 tptp.nil_nat)))) (not (forall ((X4 tptp.nat) (Xs3 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X4) Xs3))) (=> (= X _let_1) (=> (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X4) (@ tptp.nat_list_encode Xs3))))) (not (@ (@ tptp.accp_list_nat tptp.nat_list_encode_rel) _let_1)))))))))))))
% 5.98/6.29 (assert (= tptp.nat_prod_decode (@ tptp.nat_prod_decode_aux tptp.zero_zero_nat)))
% 5.98/6.29 (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 ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) _let_1) (=> (forall ((X2 tptp.nat) (Y4 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat X2) Y4) (@ tptp.nat_prod_decode N2)) (@ P Y4))) (@ P _let_1))))) (@ P A0)))))))
% 5.98/6.29 (assert (forall ((X tptp.nat) (Y tptp.list_nat)) (=> (= (@ tptp.nat_list_decode X) Y) (=> (=> (= X tptp.zero_zero_nat) (not (= Y tptp.nil_nat))) (not (forall ((N2 tptp.nat)) (=> (= X (@ tptp.suc N2)) (not (= Y (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.cons_nat X3) (@ tptp.nat_list_decode Y2)))) (@ tptp.nat_prod_decode N2)))))))))))
% 5.98/6.29 (assert (=> (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) tptp.zero_zero_nat) (= (@ tptp.nat_list_decode tptp.zero_zero_nat) tptp.nil_nat)))
% 5.98/6.29 (assert (= (@ tptp.nat_list_decode tptp.zero_zero_nat) tptp.nil_nat))
% 5.98/6.29 (assert (forall ((X tptp.nat) (Y tptp.list_nat)) (let ((_let_1 (@ tptp.accp_nat tptp.nat_list_decode_rel))) (=> (= (@ tptp.nat_list_decode X) Y) (=> (@ _let_1 X) (=> (=> (= X tptp.zero_zero_nat) (=> (= Y tptp.nil_nat) (not (@ _let_1 tptp.zero_zero_nat)))) (not (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (=> (= X _let_1) (=> (= Y (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.cons_nat X3) (@ tptp.nat_list_decode Y2)))) (@ tptp.nat_prod_decode N2))) (not (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) _let_1)))))))))))))
% 5.98/6.29 (assert (= (@ tptp.code_integer_of_nat tptp.one_one_nat) tptp.one_one_Code_integer))
% 5.98/6.29 (assert (@ (@ tptp.comm_monoid_nat tptp.gcd_gcd_nat) tptp.zero_zero_nat))
% 5.98/6.29 (assert (@ (@ tptp.comm_monoid_nat tptp.ord_max_nat) tptp.zero_zero_nat))
% 5.98/6.29 (assert (= (@ tptp.code_integer_of_nat tptp.zero_zero_nat) tptp.zero_z3403309356797280102nteger))
% 5.98/6.29 (assert (= tptp.times_times_num (lambda ((M3 tptp.num) (N4 tptp.num)) (@ tptp.num_of_nat (@ (@ tptp.times_times_nat (@ tptp.nat_of_num M3)) (@ tptp.nat_of_num N4))))))
% 5.98/6.29 (assert (forall ((X tptp.num)) (not (= (@ tptp.nat_of_num X) tptp.zero_zero_nat))))
% 5.98/6.29 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.nat_of_num N))) (= (@ tptp.nat_of_num (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 5.98/6.29 (assert (forall ((X tptp.num)) (= (@ tptp.nat_of_num (@ tptp.inc X)) (@ tptp.suc (@ tptp.nat_of_num X)))))
% 5.98/6.29 (assert (= (lambda ((Y5 tptp.num) (Z4 tptp.num)) (= Y5 Z4)) (lambda ((X3 tptp.num) (Y2 tptp.num)) (= (@ tptp.nat_of_num X3) (@ tptp.nat_of_num Y2)))))
% 5.98/6.29 (assert (= tptp.nat_of_num tptp.numeral_numeral_nat))
% 5.98/6.29 (assert (forall ((X tptp.num)) (= (@ tptp.num_of_nat (@ tptp.nat_of_num X)) X)))
% 5.98/6.29 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.nat_of_num X))) (= (@ tptp.nat_of_num (@ tptp.bit0 X)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 5.98/6.29 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ tptp.nat_of_num (@ (@ tptp.plus_plus_num X) Y)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_of_num X)) (@ tptp.nat_of_num Y)))))
% 5.98/6.29 (assert (= (@ tptp.nat_of_num tptp.one) tptp.one_one_nat))
% 5.98/6.29 (assert (= tptp.ord_less_eq_num (lambda ((M3 tptp.num) (N4 tptp.num)) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat_of_num M3)) (@ tptp.nat_of_num N4)))))
% 5.98/6.29 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ tptp.nat_of_num (@ (@ tptp.times_times_num X) Y)) (@ (@ tptp.times_times_nat (@ tptp.nat_of_num X)) (@ tptp.nat_of_num Y)))))
% 5.98/6.29 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.nat_of_num X))) (= (@ tptp.nat_of_num (@ tptp.sqr X)) (@ (@ tptp.times_times_nat _let_1) _let_1)))))
% 5.98/6.29 (assert (forall ((X tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat_of_num X))))
% 5.98/6.29 (assert (= tptp.ord_less_num (lambda ((M3 tptp.num) (N4 tptp.num)) (@ (@ tptp.ord_less_nat (@ tptp.nat_of_num M3)) (@ tptp.nat_of_num N4)))))
% 5.98/6.29 (assert (= (@ tptp.nat_of_num tptp.one) (@ tptp.suc tptp.zero_zero_nat)))
% 5.98/6.29 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.nat_of_num X))) (= (@ tptp.nat_of_num (@ tptp.bit1 X)) (@ tptp.suc (@ (@ tptp.plus_plus_nat _let_1) _let_1))))))
% 5.98/6.29 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.nat_of_num (@ tptp.num_of_nat N)) N))))
% 5.98/6.29 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.nat_of_num N))) (= (@ tptp.nat_of_num (@ tptp.bit1 N)) (@ tptp.suc (@ (@ tptp.plus_plus_nat _let_1) _let_1))))))
% 5.98/6.29 (assert (= tptp.plus_plus_num (lambda ((M3 tptp.num) (N4 tptp.num)) (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat (@ tptp.nat_of_num M3)) (@ tptp.nat_of_num N4))))))
% 5.98/6.29 (assert (= tptp.pcr_real (@ (@ tptp.relcom2856161143838007533t_real (@ (@ tptp.bNF_re4702136315717946289at_rat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (lambda ((Y5 tptp.rat) (Z4 tptp.rat)) (= Y5 Z4)))) tptp.cr_real)))
% 5.98/6.29 (assert (= (@ tptp.domainp_nat_rat_real tptp.pcr_real) (lambda ((X3 (-> tptp.nat tptp.rat))) (exists ((Y2 (-> tptp.nat tptp.rat))) (and (@ (@ (@ (@ tptp.bNF_re4702136315717946289at_rat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (lambda ((Y5 tptp.rat) (Z4 tptp.rat)) (= Y5 Z4))) X3) Y2) (@ (@ tptp.realrel Y2) Y2))))))
% 5.98/6.29 (assert (= (@ tptp.domainp_nat_rat_real tptp.pcr_real) tptp.cauchy))
% 5.98/6.29 (assert (= (@ tptp.domainp_nat_rat_real tptp.pcr_real) (lambda ((X3 (-> tptp.nat tptp.rat))) (@ (@ tptp.realrel X3) X3))))
% 5.98/6.29 (assert (forall ((P4 (-> (-> tptp.nat tptp.rat) Bool))) (=> (@ tptp.left_t2768085380646472630at_rat (@ (@ tptp.bNF_re4702136315717946289at_rat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (lambda ((Y5 tptp.rat) (Z4 tptp.rat)) (= Y5 Z4)))) (=> (@ (@ (@ (@ tptp.bNF_re728719798268516973at_o_o (@ (@ tptp.bNF_re4702136315717946289at_rat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (lambda ((Y5 tptp.rat) (Z4 tptp.rat)) (= Y5 Z4)))) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4))) P4) (lambda ((X3 (-> tptp.nat tptp.rat))) (@ (@ tptp.realrel X3) X3))) (= (@ tptp.domainp_nat_rat_real tptp.pcr_real) P4)))))
% 5.98/6.29 (assert (forall ((X tptp.real)) (@ (@ tptp.member_set_nat_rat (@ tptp.rep_real X)) (@ tptp.collect_set_nat_rat (lambda ((C5 tptp.set_nat_rat)) (exists ((X3 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.realrel X3))) (and (@ _let_1 X3) (= C5 (@ tptp.collect_nat_rat _let_1))))))))))
% 5.98/6.29 (assert (forall ((Y tptp.set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat Y) (@ tptp.collect_set_nat_rat (lambda ((C5 tptp.set_nat_rat)) (exists ((X3 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.realrel X3))) (and (@ _let_1 X3) (= C5 (@ tptp.collect_nat_rat _let_1)))))))) (not (forall ((X4 tptp.real)) (not (= Y (@ tptp.rep_real X4))))))))
% 5.98/6.29 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ tptp.rep_real X) (@ tptp.rep_real Y)) (= X Y))))
% 5.98/6.29 (assert (forall ((Y tptp.set_nat_rat) (P (-> tptp.set_nat_rat Bool))) (=> (@ (@ tptp.member_set_nat_rat Y) (@ tptp.collect_set_nat_rat (lambda ((C5 tptp.set_nat_rat)) (exists ((X3 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.realrel X3))) (and (@ _let_1 X3) (= C5 (@ tptp.collect_nat_rat _let_1)))))))) (=> (forall ((X4 tptp.real)) (@ P (@ tptp.rep_real X4))) (@ P Y)))))
% 5.98/6.29 (assert (forall ((Y tptp.set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat Y) (@ tptp.collect_set_nat_rat (lambda ((C5 tptp.set_nat_rat)) (exists ((X3 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.realrel X3))) (and (@ _let_1 X3) (= C5 (@ tptp.collect_nat_rat _let_1)))))))) (= (@ tptp.rep_real (@ tptp.abs_real Y)) Y))))
% 5.98/6.29 (assert (= tptp.rep_real2 (@ tptp.quot_r1730120044975580712at_rat tptp.rep_real)))
% 5.98/6.29 (assert (forall ((X tptp.real)) (= (@ tptp.abs_real (@ tptp.rep_real X)) X)))
% 5.98/6.29 (assert (forall ((X tptp.real)) (not (forall ((Y3 tptp.set_nat_rat)) (=> (= X (@ tptp.abs_real Y3)) (not (@ (@ tptp.member_set_nat_rat Y3) (@ tptp.collect_set_nat_rat (lambda ((C5 tptp.set_nat_rat)) (exists ((X3 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.realrel X3))) (and (@ _let_1 X3) (= C5 (@ tptp.collect_nat_rat _let_1))))))))))))))
% 5.98/6.29 (assert (forall ((P (-> tptp.real Bool)) (X tptp.real)) (=> (forall ((Y3 tptp.set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat Y3) (@ tptp.collect_set_nat_rat (lambda ((C5 tptp.set_nat_rat)) (exists ((X3 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.realrel X3))) (and (@ _let_1 X3) (= C5 (@ tptp.collect_nat_rat _let_1)))))))) (@ P (@ tptp.abs_real Y3)))) (@ P X))))
% 5.98/6.29 (assert (forall ((X tptp.set_nat_rat) (Y tptp.set_nat_rat)) (=> (@ (@ tptp.member_set_nat_rat X) (@ tptp.collect_set_nat_rat (lambda ((C5 tptp.set_nat_rat)) (exists ((X3 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.realrel X3))) (and (@ _let_1 X3) (= C5 (@ tptp.collect_nat_rat _let_1)))))))) (=> (@ (@ tptp.member_set_nat_rat Y) (@ tptp.collect_set_nat_rat (lambda ((C5 tptp.set_nat_rat)) (exists ((X3 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.realrel X3))) (and (@ _let_1 X3) (= C5 (@ tptp.collect_nat_rat _let_1)))))))) (= (= (@ tptp.abs_real X) (@ tptp.abs_real Y)) (= X Y))))))
% 5.98/6.29 (assert (= tptp.real2 (@ (@ tptp.quot_a3129823074075660125t_real tptp.realrel) tptp.abs_real)))
% 5.98/6.29 (assert (@ (@ (@ tptp.type_d8072115097938612567at_rat tptp.rep_real) tptp.abs_real) (@ tptp.collect_set_nat_rat (lambda ((C5 tptp.set_nat_rat)) (exists ((X3 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.realrel X3))) (and (@ _let_1 X3) (= C5 (@ tptp.collect_nat_rat _let_1)))))))))
% 5.98/6.29 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int false) X) Y) Y)))
% 5.98/6.29 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int true) X) Y) X)))
% 5.98/6.29 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X) Y) Y)))
% 5.98/6.29 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X) Y) X)))
% 5.98/6.29 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num false) X) Y) Y)))
% 5.98/6.29 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num true) X) Y) X)))
% 5.98/6.29 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat false) X) Y) Y)))
% 5.98/6.29 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat true) X) Y) X)))
% 46.57/47.03 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real false) X) Y) Y)))
% 46.57/47.03 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real true) X) Y) X)))
% 46.57/47.03 (assert (forall ((P (-> tptp.real Bool))) (= (@ P (@ tptp.fChoice_real P)) (exists ((X8 tptp.real)) (@ P X8)))))
% 46.57/47.03 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex false) X) Y) Y)))
% 46.57/47.03 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex true) X) Y) X)))
% 46.57/47.03 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat false) X) Y) Y)))
% 46.57/47.03 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat true) X) Y) X)))
% 46.57/47.03 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X) Y) Y)))
% 46.57/47.03 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X) Y) X)))
% 46.57/47.03 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int false) X) Y) Y)))
% 46.57/47.03 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int true) X) Y) X)))
% 46.57/47.03 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT false) X) Y) Y)))
% 46.57/47.03 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT true) X) Y) X)))
% 46.57/47.03 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X) Y) Y)))
% 46.57/47.03 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X) Y) X)))
% 46.57/47.03 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat false) X) Y) Y)))
% 46.57/47.03 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat true) X) Y) X)))
% 46.57/47.03 (assert (forall ((X (-> tptp.nat tptp.rat)) (Y (-> tptp.nat tptp.rat))) (= (@ (@ (@ tptp.if_nat_rat false) X) Y) Y)))
% 46.57/47.03 (assert (forall ((X (-> tptp.nat tptp.rat)) (Y (-> tptp.nat tptp.rat))) (= (@ (@ (@ tptp.if_nat_rat true) X) Y) X)))
% 46.57/47.03 (assert (forall ((X tptp.option_nat) (Y tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat false) X) Y) Y)))
% 46.57/47.03 (assert (forall ((X tptp.option_nat) (Y tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat true) X) Y) X)))
% 46.57/47.03 (assert (forall ((X tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num false) X) Y) Y)))
% 46.57/47.03 (assert (forall ((X tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num true) X) Y) X)))
% 46.57/47.03 (assert (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X) Y) Y)))
% 46.57/47.03 (assert (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X) Y) X)))
% 46.57/47.03 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X) Y) Y)))
% 46.57/47.03 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat true) X) Y) X)))
% 46.57/47.03 (assert (forall ((P Bool)) (or (= P true) (= P false))))
% 46.57/47.03 (assert (forall ((X tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger false) X) Y) Y)))
% 46.57/47.03 (assert (forall ((X tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger true) X) Y) X)))
% 46.57/47.03 (assert (@ (@ tptp.vEBT_invar_vebt tptp.t) tptp.n))
% 46.57/47.03 (assert (not (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_vebt_delete tptp.t) tptp.x)) tptp.n)))
% 46.57/47.03 (set-info :filename cvc5---1.0.5_24675)
% 46.57/47.03 (check-sat-assuming ( true ))
% 46.57/47.03 ------- get file name : TPTP file name is ITP261^3
% 46.57/47.03 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_24675.smt2...
% 46.57/47.03 --- Run --ho-elim --full-saturate-quant at 10...
% 46.57/47.03 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 46.57/47.03 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 46.57/47.03 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 46.57/47.03 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 46.57/47.03 --- /export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 24867 Alarm clock ( read result; case "$result" in
% 299.83/300.14 unsat)
% 299.83/300.14 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.83/300.14 ;;
% 299.83/300.14 sat)
% 299.83/300.14 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.83/300.14 ;;
% 299.83/300.14 esac; exit 1 )
% 299.83/300.14 Alarm clock
% 299.83/300.14 % cvc5---1.0.5 exiting
% 299.83/300.15 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------