%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP064^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.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 : Wed Feb 25 08:55:16 AM UTC 2026
% Result : Theorem 2.79s 1.90s
% Output : Refutation 2.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 26 unt; 0 typ; 1 def)
% Number of atoms : 143 ( 31 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 369 ( 8 ~; 10 |; 11 &; 317 @)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 70 ( 66 usr; 13 con; 0-4 aty)
% ( 12 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 41 ( 15 ^; 26 !; 0 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_6,type,
real: $tType ).
thf(func_def_0,type,
real: $tType ).
thf(func_def_1,type,
nat: $tType ).
thf(func_def_2,type,
type:
!>[X0: $tType] : $o ).
thf(func_def_3,type,
one:
!>[X0: $tType] : $o ).
thf(func_def_4,type,
zero:
!>[X0: $tType] : $o ).
thf(func_def_5,type,
minus:
!>[X0: $tType] : $o ).
thf(func_def_6,type,
ord:
!>[X0: $tType] : $o ).
thf(func_def_7,type,
order:
!>[X0: $tType] : $o ).
thf(func_def_8,type,
group_add:
!>[X0: $tType] : $o ).
thf(func_def_9,type,
monoid_add:
!>[X0: $tType] : $o ).
thf(func_def_10,type,
linorder:
!>[X0: $tType] : $o ).
thf(func_def_11,type,
preorder:
!>[X0: $tType] : $o ).
thf(func_def_12,type,
idom_abs_sgn:
!>[X0: $tType] : $o ).
thf(func_def_13,type,
zero_neq_one:
!>[X0: $tType] : $o ).
thf(func_def_14,type,
ab_group_add:
!>[X0: $tType] : $o ).
thf(func_def_15,type,
semigroup_add:
!>[X0: $tType] : $o ).
thf(func_def_16,type,
linordered_idom:
!>[X0: $tType] : $o ).
thf(func_def_17,type,
comm_monoid_add:
!>[X0: $tType] : $o ).
thf(func_def_18,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
thf(func_def_19,type,
comm_monoid_diff:
!>[X0: $tType] : $o ).
thf(func_def_20,type,
linordered_semidom:
!>[X0: $tType] : $o ).
thf(func_def_21,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
thf(func_def_22,type,
ordered_ab_group_add:
!>[X0: $tType] : $o ).
thf(func_def_23,type,
cancel1352612707id_add:
!>[X0: $tType] : $o ).
thf(func_def_24,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
thf(func_def_25,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
thf(func_def_26,type,
ordere216010020id_add:
!>[X0: $tType] : $o ).
thf(func_def_27,type,
ordere142940540dd_abs:
!>[X0: $tType] : $o ).
thf(func_def_28,type,
ordere779506340up_add:
!>[X0: $tType] : $o ).
thf(func_def_29,type,
linord1659791738miring:
!>[X0: $tType] : $o ).
thf(func_def_30,type,
canoni770627133id_add:
!>[X0: $tType] : $o ).
thf(func_def_31,type,
ordere236663937imp_le:
!>[X0: $tType] : $o ).
thf(func_def_32,type,
ordere623563068d_diff:
!>[X0: $tType] : $o ).
thf(func_def_33,type,
ordere516151231imp_le:
!>[X0: $tType] : $o ).
thf(func_def_34,type,
genClo1160817912lle_IC: nat > nat > real > real ).
thf(func_def_35,type,
genClo721845095Lambda: real ).
thf(func_def_36,type,
genClo1278781456e_beta: real ).
thf(func_def_37,type,
genClo1400225944_theta: nat > nat > nat > real ).
thf(func_def_38,type,
genClo1015804716orrect: nat > real > $o ).
thf(func_def_39,type,
genClo293725281kRead1: ( nat > real ) > real > ( nat > $o ) > $o ).
thf(func_def_40,type,
genClo293725282kRead2: ( nat > real ) > ( nat > real ) > real > ( nat > $o ) > $o ).
thf(func_def_41,type,
genClo208577157axsync: nat > real > $o ).
thf(func_def_42,type,
genClo1650508560e_rmax: real ).
thf(func_def_43,type,
genClo1651033342e_rmin: real ).
thf(func_def_44,type,
genClo1163638703lle_te: nat > nat > real ).
thf(func_def_45,type,
abs_abs:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_46,type,
minus_minus:
!>[X0: $tType] : ( X0 > X0 > X0 ) ).
thf(func_def_47,type,
one_one:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
plus_plus:
!>[X0: $tType] : ( X0 > X0 > X0 ) ).
thf(func_def_49,type,
zero_zero:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
if:
!>[X0: $tType] : ( $o > X0 > X0 > X0 ) ).
thf(func_def_51,type,
ord_less_eq:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_52,type,
ord_max:
!>[X0: $tType] : ( X0 > X0 > X0 ) ).
thf(func_def_53,type,
delta_S: real ).
thf(func_def_54,type,
i: nat ).
thf(func_def_55,type,
l: nat ).
thf(func_def_56,type,
m: nat ).
thf(func_def_57,type,
p: nat ).
thf(func_def_75,type,
sK1:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_76,type,
sK2:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_77,type,
sK3:
!>[X0: $tType] : ( X0 > X0 > X0 ) ).
thf(func_def_78,type,
sK4:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_79,type,
sK5:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_80,type,
sK6:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_81,type,
sK7:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_82,type,
sK8:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).
thf(func_def_83,type,
ph9:
!>[X0: $tType] : X0 ).
thf(f3267,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f3022,f3266]) ).
thf(f3266,plain,
spl0_6,
inference(avatar_split_clause,[status(thm)],[f3261,f2988]) ).
thf(f2988,definition,
( spl0_6
<=> ( ( genClo1015804716orrect @ m @ ( genClo1163638703lle_te @ p @ ( plus_plus @ nat @ i @ one_one @ nat ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f3261,plain,
( ( genClo1015804716orrect @ m @ ( genClo1163638703lle_te @ p @ ( plus_plus @ nat @ i @ one_one @ nat ) ) )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f3253]) ).
thf(f3253,plain,
( ( $true = $false )
| ( ( genClo1015804716orrect @ m @ ( genClo1163638703lle_te @ p @ ( plus_plus @ nat @ i @ one_one @ nat ) ) )
= $false ) ),
inference(superposition,[status(thm)],[f1053,f2492]) ).
thf(f2492,plain,
! [X0: real] :
( ( ( ord_less_eq @ real @ ( ord_max @ real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) @ X0 )
= $false )
| ( $false
= ( genClo1015804716orrect @ m @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f2471]) ).
thf(f2471,plain,
! [X0: real] :
( ( $false
= ( genClo1015804716orrect @ m @ X0 ) )
| ( $true = $false )
| ( ( ord_less_eq @ real @ ( ord_max @ real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) @ X0 )
= $false ) ),
inference(superposition,[status(thm)],[f2119,f1983]) ).
thf(f1983,plain,
( ( genClo1015804716orrect @ m @ ( ord_max @ real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f1118]) ).
thf(f1118,plain,
( $true
= ( ~ ( genClo1015804716orrect @ m @ ( ord_max @ real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f791]) ).
thf(f791,plain,
( $true
= ( ~ ( genClo1015804716orrect @ m @ ( ord_max @ real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f790]) ).
thf(f790,plain,
~ ( genClo1015804716orrect @ m @ ( ord_max @ real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) ),
inference(rectify,[status(thm)],[f320]) ).
thf(f320,negated_conjecture,
~ ( genClo1015804716orrect @ m @ ( ord_max @ real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) ),
inference(negated_conjecture,[status(cth)],[f319]) ).
thf(f319,conjecture,
genClo1015804716orrect @ m @ ( ord_max @ real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ),
file('/export/starexec/sandbox2/tmp/tmp.Kaf6658Iwd/DTF2THF_740.p',conj_0) ).
thf(f2119,plain,
! [X2: real,X3: nat,X1: real] :
( ( ( genClo1015804716orrect @ X3 @ X1 )
= $false )
| ( ( ord_less_eq @ real @ X2 @ X1 )
= $false )
| ( ( genClo1015804716orrect @ X3 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f2118]) ).
thf(f2118,plain,
! [X2: real,X3: nat,X1: real] :
( ( ( genClo1015804716orrect @ X3 @ X2 )
= $true )
| ( ( ( ord_less_eq @ real @ X2 @ X1 )
& ( genClo1015804716orrect @ X3 @ X1 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f2117]) ).
thf(f2117,plain,
! [X2: real,X3: nat,X1: real] :
( ( ( ( ord_less_eq @ real @ X2 @ X1 )
& ( genClo1015804716orrect @ X3 @ X1 ) )
=> ( genClo1015804716orrect @ X3 @ X2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2116]) ).
thf(f2116,plain,
! [X2: real,X3: nat,X1: real] :
( ( ^ [Y0: nat] :
( ( ( ord_less_eq @ real @ X2 @ X1 )
& ( genClo1015804716orrect @ Y0 @ X1 ) )
=> ( genClo1015804716orrect @ Y0 @ X2 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f2115]) ).
thf(f2115,plain,
! [X2: real,X1: real] :
( ( !! @ nat
@ ^ [Y0: nat] :
( ( ( ord_less_eq @ real @ X2 @ X1 )
& ( genClo1015804716orrect @ Y0 @ X1 ) )
=> ( genClo1015804716orrect @ Y0 @ X2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2114]) ).
thf(f2114,plain,
! [X2: real,X1: real] :
( ( ^ [Y0: real] :
( !! @ nat
@ ^ [Y1: nat] :
( ( ( ord_less_eq @ real @ Y0 @ X1 )
& ( genClo1015804716orrect @ Y1 @ X1 ) )
=> ( genClo1015804716orrect @ Y1 @ Y0 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f2113]) ).
thf(f2113,plain,
! [X1: real] :
( ( !! @ real
@ ^ [Y0: real] :
( !! @ nat
@ ^ [Y1: nat] :
( ( ( ord_less_eq @ real @ Y0 @ X1 )
& ( genClo1015804716orrect @ Y1 @ X1 ) )
=> ( genClo1015804716orrect @ Y1 @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2112]) ).
thf(f2112,plain,
! [X1: real] :
( ( ^ [Y0: real] :
( !! @ real
@ ^ [Y1: real] :
( !! @ nat
@ ^ [Y2: nat] :
( ( ( ord_less_eq @ real @ Y1 @ Y0 )
& ( genClo1015804716orrect @ Y2 @ Y0 ) )
=> ( genClo1015804716orrect @ Y2 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f1063]) ).
thf(f1063,plain,
( ( !! @ real
@ ^ [Y0: real] :
( !! @ real
@ ^ [Y1: real] :
( !! @ nat
@ ^ [Y2: nat] :
( ( ( ord_less_eq @ real @ Y1 @ Y0 )
& ( genClo1015804716orrect @ Y2 @ Y0 ) )
=> ( genClo1015804716orrect @ Y2 @ Y1 ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f495]) ).
thf(f495,plain,
( ( !! @ real
@ ^ [Y0: real] :
( !! @ real
@ ^ [Y1: real] :
( !! @ nat
@ ^ [Y2: nat] :
( ( ( ord_less_eq @ real @ Y1 @ Y0 )
& ( genClo1015804716orrect @ Y2 @ Y0 ) )
=> ( genClo1015804716orrect @ Y2 @ Y1 ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f494]) ).
thf(f494,plain,
! [X0: nat,X1: real,X2: real] :
( ( ( genClo1015804716orrect @ X0 @ X2 )
& ( ord_less_eq @ real @ X1 @ X2 ) )
=> ( genClo1015804716orrect @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: nat,X2: real,X3: real] :
( ( ( genClo1015804716orrect @ X1 @ X3 )
& ( ord_less_eq @ real @ X2 @ X3 ) )
=> ( genClo1015804716orrect @ X1 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.Kaf6658Iwd/DTF2THF_740.p',fact_0_correct__closed) ).
thf(f1053,plain,
( ( ord_less_eq @ real @ ( ord_max @ real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) @ ( genClo1163638703lle_te @ p @ ( plus_plus @ nat @ i @ one_one @ nat ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f703]) ).
thf(f703,plain,
( ( ord_less_eq @ real @ ( ord_max @ real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) @ ( genClo1163638703lle_te @ p @ ( plus_plus @ nat @ i @ one_one @ nat ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f702]) ).
thf(f702,plain,
ord_less_eq @ real @ ( ord_max @ real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) @ ( genClo1163638703lle_te @ p @ ( plus_plus @ nat @ i @ one_one @ nat ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
ord_less_eq @ real @ ( ord_max @ real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) @ ( genClo1163638703lle_te @ p @ ( plus_plus @ nat @ i @ one_one @ nat ) ),
file('/export/starexec/sandbox2/tmp/tmp.Kaf6658Iwd/DTF2THF_740.p',fact_3_tml__le__tp) ).
thf(f3022,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[status(thm)],[f3021]) ).
thf(f3021,plain,
( $false
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f3015]) ).
thf(f3015,plain,
( ( $true = $false )
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f1131,f2990]) ).
thf(f2990,plain,
( ( ( genClo1015804716orrect @ m @ ( genClo1163638703lle_te @ p @ ( plus_plus @ nat @ i @ one_one @ nat ) ) )
= $false )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f2988]) ).
thf(f1131,plain,
( ( genClo1015804716orrect @ m @ ( genClo1163638703lle_te @ p @ ( plus_plus @ nat @ i @ one_one @ nat ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f621]) ).
thf(f621,plain,
( ( genClo1015804716orrect @ m @ ( genClo1163638703lle_te @ p @ ( plus_plus @ nat @ i @ one_one @ nat ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f620]) ).
thf(f620,plain,
genClo1015804716orrect @ m @ ( genClo1163638703lle_te @ p @ ( plus_plus @ nat @ i @ one_one @ nat ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
genClo1015804716orrect @ m @ ( genClo1163638703lle_te @ p @ ( plus_plus @ nat @ i @ one_one @ nat ) ),
file('/export/starexec/sandbox2/tmp/tmp.Kaf6658Iwd/DTF2THF_740.p',fact_1_corr__m) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP064^2 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n006.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 08:25:15 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.26/0.46 ---- Original DTF file ---
% 0.26/0.46 thf(spec,logic,$$dhol).
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 % File : ITP064^2 : TPTP v9.2.1. Released v7.5.0.
% 0.26/0.46 % Domain : Interactive Theorem Proving
% 0.26/0.46 % Problem : Sledgehammer GenClock problem prob_727__3251548_1
% 0.26/0.46 % Version : Especial.
% 0.26/0.46 % English :
% 0.26/0.46
% 0.26/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.26/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.26/0.46 % Source : [Des21]
% 0.26/0.46 % Names : GenClock/prob_727__3251548_1 [Des21]
% 0.26/0.46
% 0.26/0.46 % Status : Theorem
% 0.26/0.46 % Rating : 0.33 v9.1.0, 0.00 v7.5.0
% 0.26/0.46 % Syntax : Number of formulae : 377 ( 89 unt; 58 typ; 0 def)
% 0.26/0.46 % Number of atoms : 845 ( 252 equ; 0 cnn)
% 0.26/0.46 % Maximal formula atoms : 13 ( 2 avg)
% 0.26/0.46 % Number of connectives : 3289 ( 16 ~; 4 |; 27 &;2871 @)
% 0.26/0.46 % ( 0 <=>; 371 =>; 0 <=; 0 <~>)
% 0.26/0.46 % Maximal formula depth : 17 ( 7 avg)
% 0.26/0.46 % Number of types : 3 ( 2 usr)
% 0.26/0.46 % Number of type conns : 72 ( 72 >; 0 *; 0 +; 0 <<)
% 0.26/0.46 % Number of symbols : 59 ( 56 usr; 11 con; 0-4 aty)
% 0.26/0.46 % Number of variables : 880 ( 51 ^; 785 !; 4 ?; 880 :)
% 0.26/0.46 % ( 40 !>; 0 ?*; 0 @-; 0 @+)
% 0.26/0.46 % SPC : TH1_THM_EQU_NAR
% 0.26/0.46
% 0.26/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 16:16:43.808
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 % Could-be-implicit typings (2)
% 0.26/0.46 thf(ty_t_Real_Oreal,type,
% 0.26/0.46 real: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_t_Nat_Onat,type,
% 0.26/0.46 nat: $tType ).
% 0.26/0.46
% 0.26/0.46 % Explicit typings (56)
% 0.26/0.46 thf(sy_cl_HOL_Otype,type,
% 0.26/0.46 type:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Groups_Oone,type,
% 0.26/0.46 one:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Groups_Ozero,type,
% 0.26/0.46 zero:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Groups_Ominus,type,
% 0.26/0.46 minus:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Orderings_Oord,type,
% 0.26/0.46 ord:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Orderings_Oorder,type,
% 0.26/0.46 order:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Groups_Ogroup__add,type,
% 0.26/0.46 group_add:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Groups_Omonoid__add,type,
% 0.26/0.46 monoid_add:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Orderings_Olinorder,type,
% 0.26/0.46 linorder:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Orderings_Opreorder,type,
% 0.26/0.46 preorder:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Rings_Oidom__abs__sgn,type,
% 0.26/0.46 idom_abs_sgn:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Rings_Ozero__neq__one,type,
% 0.26/0.46 zero_neq_one:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Groups_Oab__group__add,type,
% 0.26/0.46 ab_group_add:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Groups_Osemigroup__add,type,
% 0.26/0.46 semigroup_add:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Rings_Olinordered__idom,type,
% 0.26/0.46 linordered_idom:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 0.26/0.46 comm_monoid_add:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 0.26/0.46 ab_semigroup_add:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Groups_Ocomm__monoid__diff,type,
% 0.26/0.46 comm_monoid_diff:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Rings_Olinordered__semidom,type,
% 0.26/0.46 linordered_semidom:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 0.26/0.46 cancel_semigroup_add:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.26/0.46 ordered_ab_group_add:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 0.26/0.46 cancel1352612707id_add:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 0.26/0.46 cancel146912293up_add:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 0.26/0.46 linord219039673up_add:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Groups_Oordered__comm__monoid__add,type,
% 0.26/0.46 ordere216010020id_add:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Groups_Oordered__ab__group__add__abs,type,
% 0.26/0.46 ordere142940540dd_abs:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 0.26/0.46 ordere779506340up_add:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 0.26/0.46 linord1659791738miring:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.26/0.46 canoni770627133id_add:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 0.26/0.46 ordere236663937imp_le:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Groups_Oordered__cancel__comm__monoid__diff,type,
% 0.26/0.46 ordere623563068d_diff:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le,type,
% 0.26/0.46 ordere516151231imp_le:
% 0.26/0.46 !>[A: $tType] : $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_GenClock__Mirabelle__pukziqipvs_OIC,type,
% 0.26/0.46 genClo1160817912lle_IC: nat > nat > real > real ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_GenClock__Mirabelle__pukziqipvs_O_092_060Lambda_062,type,
% 0.26/0.46 genClo721845095Lambda: real ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_GenClock__Mirabelle__pukziqipvs_O_092_060beta_062,type,
% 0.26/0.46 genClo1278781456e_beta: real ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_GenClock__Mirabelle__pukziqipvs_O_092_060theta_062,type,
% 0.26/0.46 genClo1400225944_theta: nat > nat > nat > real ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_GenClock__Mirabelle__pukziqipvs_Ocorrect,type,
% 0.26/0.46 genClo1015804716orrect: nat > real > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_GenClock__Mirabelle__pukziqipvs_OokRead1,type,
% 0.26/0.46 genClo293725281kRead1: ( nat > real ) > real > ( nat > $o ) > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_GenClock__Mirabelle__pukziqipvs_OokRead2,type,
% 0.26/0.46 genClo293725282kRead2: ( nat > real ) > ( nat > real ) > real > ( nat > $o ) > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_GenClock__Mirabelle__pukziqipvs_Ookmaxsync,type,
% 0.26/0.46 genClo208577157axsync: nat > real > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_GenClock__Mirabelle__pukziqipvs_Ormax,type,
% 0.26/0.46 genClo1650508560e_rmax: real ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_GenClock__Mirabelle__pukziqipvs_Ormin,type,
% 0.26/0.46 genClo1651033342e_rmin: real ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_GenClock__Mirabelle__pukziqipvs_Ote,type,
% 0.26/0.46 genClo1163638703lle_te: nat > nat > real ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Groups_Oabs__class_Oabs,type,
% 0.26/0.46 abs_abs:
% 0.26/0.46 !>[A: $tType] : ( A > A ) ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.26/0.46 minus_minus:
% 0.26/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.26/0.46 one_one:
% 0.26/0.46 !>[A: $tType] : A ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 0.26/0.46 plus_plus:
% 0.26/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.26/0.46 zero_zero:
% 0.26/0.46 !>[A: $tType] : A ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_If,type,
% 0.26/0.46 if:
% 0.26/0.46 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.26/0.46 ord_less_eq:
% 0.26/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Orderings_Oord__class_Omax,type,
% 0.26/0.46 ord_max:
% 0.26/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.26/0.46
% 0.26/0.46 thf(sy_v__092_060delta_062S,type,
% 0.26/0.46 delta_S: real ).
% 0.26/0.46
% 0.26/0.46 thf(sy_v_i,type,
% 0.26/0.46 i: nat ).
% 0.26/0.46
% 0.26/0.46 thf(sy_v_l,type,
% 0.26/0.46 l: nat ).
% 0.26/0.46
% 0.26/0.46 thf(sy_v_m,type,
% 0.26/0.46 m: nat ).
% 0.26/0.46
% 0.26/0.46 thf(sy_v_p,type,
% 0.26/0.46 p: nat ).
% 0.26/0.46
% 0.26/0.46 % Relevant facts (254)
% 0.26/0.46 thf(fact_0_correct__closed,axiom,
% 0.26/0.46 ! [P: nat,S: real,T: real] :
% 0.26/0.46 ( ( ( ord_less_eq @ real @ S @ T )
% 0.26/0.46 & ( genClo1015804716orrect @ P @ T ) )
% 0.26/0.46 => ( genClo1015804716orrect @ P @ S ) ) ).
% 0.26/0.46
% 0.26/0.46 % correct_closed
% 0.26/0.46 thf(fact_1_corr__m,axiom,
% 0.26/0.46 genClo1015804716orrect @ m @ ( genClo1163638703lle_te @ p @ ( plus_plus @ nat @ i @ ( one_one @ nat ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % corr_m
% 0.26/0.46 thf(fact_2_corr__p,axiom,
% 0.26/0.46 genClo1015804716orrect @ p @ ( genClo1163638703lle_te @ p @ ( plus_plus @ nat @ i @ ( one_one @ nat ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % corr_p
% 0.26/0.46 thf(fact_3_tml__le__tp,axiom,
% 0.26/0.46 ord_less_eq @ real @ ( ord_max @ real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) @ ( genClo1163638703lle_te @ p @ ( plus_plus @ nat @ i @ ( one_one @ nat ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % tml_le_tp
% 0.26/0.46 thf(fact_4_corr__l,axiom,
% 0.26/0.46 genClo1015804716orrect @ l @ ( genClo1163638703lle_te @ p @ ( plus_plus @ nat @ i @ ( one_one @ nat ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % corr_l
% 0.26/0.46 thf(fact_5_corr__l__tml,axiom,
% 0.26/0.46 genClo1015804716orrect @ l @ ( ord_max @ real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) ).
% 0.26/0.46
% 0.26/0.46 % corr_l_tml
% 0.26/0.46 thf(fact_6_tmi__le__tp,axiom,
% 0.26/0.46 ord_less_eq @ real @ ( genClo1163638703lle_te @ m @ i ) @ ( genClo1163638703lle_te @ p @ ( plus_plus @ nat @ i @ ( one_one @ nat ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % tmi_le_tp
% 0.26/0.46 thf(fact_7_tli__le__tp,axiom,
% 0.26/0.46 ord_less_eq @ real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ p @ ( plus_plus @ nat @ i @ ( one_one @ nat ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % tli_le_tp
% 0.26/0.46 thf(fact_8_max_Oidem,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linorder @ A )
% 0.26/0.46 => ! [A2: A] :
% 0.26/0.46 ( ( ord_max @ A @ A2 @ A2 )
% 0.26/0.46 = A2 ) ) ).
% 0.26/0.46
% 0.26/0.46 % max.idem
% 0.26/0.46 thf(fact_9_max_Oleft__idem,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linorder @ A )
% 0.26/0.46 => ! [A2: A,B: A] :
% 0.26/0.46 ( ( ord_max @ A @ A2 @ ( ord_max @ A @ A2 @ B ) )
% 0.26/0.46 = ( ord_max @ A @ A2 @ B ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % max.left_idem
% 0.26/0.46 thf(fact_10_max_Oright__idem,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linorder @ A )
% 0.26/0.46 => ! [A2: A,B: A] :
% 0.26/0.46 ( ( ord_max @ A @ ( ord_max @ A @ A2 @ B ) @ B )
% 0.26/0.46 = ( ord_max @ A @ A2 @ B ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % max.right_idem
% 0.26/0.46 thf(fact_11_IC__bound,axiom,
% 0.26/0.46 ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ ( genClo1160817912lle_IC @ l @ i @ ( ord_max @ real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) ) @ ( genClo1160817912lle_IC @ m @ i @ ( ord_max @ real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) ) ) ) @ delta_S ).
% 0.26/0.46
% 0.26/0.46 % IC_bound
% 0.26/0.46 thf(fact_12_max_Oassoc,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linorder @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A] :
% 0.26/0.46 ( ( ord_max @ A @ ( ord_max @ A @ A2 @ B ) @ C )
% 0.26/0.46 = ( ord_max @ A @ A2 @ ( ord_max @ A @ B @ C ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % max.assoc
% 0.26/0.46 thf(fact_13_max_Ocommute,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linorder @ A )
% 0.26/0.46 => ( ( ord_max @ A )
% 0.26/0.46 = ( ^ [A3: A,B2: A] : ( ord_max @ A @ B2 @ A3 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % max.commute
% 0.26/0.46 thf(fact_14_max_Oleft__commute,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linorder @ A )
% 0.26/0.46 => ! [B: A,A2: A,C: A] :
% 0.26/0.46 ( ( ord_max @ A @ B @ ( ord_max @ A @ A2 @ C ) )
% 0.26/0.46 = ( ord_max @ A @ A2 @ ( ord_max @ A @ B @ C ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % max.left_commute
% 0.26/0.46 thf(fact_15_rte,axiom,
% 0.26/0.46 ! [P2: nat,I: nat] :
% 0.26/0.46 ( ( genClo1015804716orrect @ P2 @ ( genClo1163638703lle_te @ P2 @ ( plus_plus @ nat @ I @ ( one_one @ nat ) ) ) )
% 0.26/0.46 => ( ord_less_eq @ real @ ( genClo1163638703lle_te @ P2 @ I ) @ ( genClo1163638703lle_te @ P2 @ ( plus_plus @ nat @ I @ ( one_one @ nat ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % rte
% 0.26/0.46 thf(fact_16_max_Obounded__iff,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linorder @ A )
% 0.26/0.46 => ! [B: A,C: A,A2: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ ( ord_max @ A @ B @ C ) @ A2 )
% 0.26/0.46 = ( ( ord_less_eq @ A @ B @ A2 )
% 0.26/0.46 & ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % max.bounded_iff
% 0.26/0.46 thf(fact_17_max__absorb1,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( order @ A )
% 0.26/0.46 => ! [Y: A,X: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ Y @ X )
% 0.26/0.46 => ( ( ord_max @ A @ X @ Y )
% 0.26/0.46 = X ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % max_absorb1
% 0.26/0.46 thf(fact_18_order__refl,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( preorder @ A )
% 0.26/0.46 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.26/0.46
% 0.26/0.46 % order_refl
% 0.26/0.46 thf(fact_19_minus__apply,axiom,
% 0.26/0.46 ! [B3: $tType,A: $tType] :
% 0.26/0.46 ( ( minus @ B3 )
% 0.26/0.46 => ( ( minus_minus @ ( A > B3 ) )
% 0.26/0.46 = ( ^ [A4: A > B3,B4: A > B3,X2: A] : ( minus_minus @ B3 @ ( A4 @ X2 ) @ ( B4 @ X2 ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % minus_apply
% 0.26/0.46 thf(fact_20_le__funD,axiom,
% 0.26/0.46 ! [B3: $tType,A: $tType] :
% 0.26/0.46 ( ( ord @ B3 )
% 0.26/0.46 => ! [F: A > B3,G: A > B3,X: A] :
% 0.26/0.46 ( ( ord_less_eq @ ( A > B3 ) @ F @ G )
% 0.26/0.46 => ( ord_less_eq @ B3 @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % le_funD
% 0.26/0.46 thf(fact_21_le__funE,axiom,
% 0.26/0.46 ! [B3: $tType,A: $tType] :
% 0.26/0.46 ( ( ord @ B3 )
% 0.26/0.46 => ! [F: A > B3,G: A > B3,X: A] :
% 0.26/0.46 ( ( ord_less_eq @ ( A > B3 ) @ F @ G )
% 0.26/0.46 => ( ord_less_eq @ B3 @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % le_funE
% 0.26/0.46 thf(fact_22_le__funI,axiom,
% 0.26/0.46 ! [B3: $tType,A: $tType] :
% 0.26/0.46 ( ( ord @ B3 )
% 0.26/0.46 => ! [F: A > B3,G: A > B3] :
% 0.26/0.46 ( ! [X3: A] : ( ord_less_eq @ B3 @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.26/0.46 => ( ord_less_eq @ ( A > B3 ) @ F @ G ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % le_funI
% 0.26/0.46 thf(fact_23_le__fun__def,axiom,
% 0.26/0.46 ! [B3: $tType,A: $tType] :
% 0.26/0.46 ( ( ord @ B3 )
% 0.26/0.46 => ( ( ord_less_eq @ ( A > B3 ) )
% 0.26/0.46 = ( ^ [F2: A > B3,G2: A > B3] :
% 0.26/0.46 ! [X2: A] : ( ord_less_eq @ B3 @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % le_fun_def
% 0.26/0.46 thf(fact_24_fun__diff__def,axiom,
% 0.26/0.46 ! [B3: $tType,A: $tType] :
% 0.26/0.46 ( ( minus @ B3 )
% 0.26/0.46 => ( ( minus_minus @ ( A > B3 ) )
% 0.26/0.46 = ( ^ [A4: A > B3,B4: A > B3,X2: A] : ( minus_minus @ B3 @ ( A4 @ X2 ) @ ( B4 @ X2 ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % fun_diff_def
% 0.26/0.46 thf(fact_25_order__subst1,axiom,
% 0.26/0.46 ! [A: $tType,B3: $tType] :
% 0.26/0.46 ( ( ( order @ B3 )
% 0.26/0.46 & ( order @ A ) )
% 0.26/0.46 => ! [A2: A,F: B3 > A,B: B3,C: B3] :
% 0.26/0.46 ( ( ord_less_eq @ A @ A2 @ ( F @ B ) )
% 0.26/0.46 => ( ( ord_less_eq @ B3 @ B @ C )
% 0.26/0.46 => ( ! [X3: B3,Y2: B3] :
% 0.26/0.46 ( ( ord_less_eq @ B3 @ X3 @ Y2 )
% 0.26/0.46 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.26/0.46 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % order_subst1
% 0.26/0.46 thf(fact_26_order__subst2,axiom,
% 0.26/0.46 ! [A: $tType,C2: $tType] :
% 0.26/0.46 ( ( ( order @ C2 )
% 0.26/0.46 & ( order @ A ) )
% 0.26/0.46 => ! [A2: A,B: A,F: A > C2,C: C2] :
% 0.26/0.46 ( ( ord_less_eq @ A @ A2 @ B )
% 0.26/0.46 => ( ( ord_less_eq @ C2 @ ( F @ B ) @ C )
% 0.26/0.46 => ( ! [X3: A,Y2: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.26/0.46 => ( ord_less_eq @ C2 @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.26/0.46 => ( ord_less_eq @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % order_subst2
% 0.26/0.46 thf(fact_27_ord__eq__le__subst,axiom,
% 0.26/0.46 ! [A: $tType,B3: $tType] :
% 0.26/0.46 ( ( ( ord @ B3 )
% 0.26/0.46 & ( ord @ A ) )
% 0.26/0.46 => ! [A2: A,F: B3 > A,B: B3,C: B3] :
% 0.26/0.46 ( ( A2
% 0.26/0.46 = ( F @ B ) )
% 0.26/0.46 => ( ( ord_less_eq @ B3 @ B @ C )
% 0.26/0.46 => ( ! [X3: B3,Y2: B3] :
% 0.26/0.46 ( ( ord_less_eq @ B3 @ X3 @ Y2 )
% 0.26/0.46 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.26/0.46 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ord_eq_le_subst
% 0.26/0.46 thf(fact_28_ord__le__eq__subst,axiom,
% 0.26/0.46 ! [A: $tType,B3: $tType] :
% 0.26/0.46 ( ( ( ord @ B3 )
% 0.26/0.46 & ( ord @ A ) )
% 0.26/0.46 => ! [A2: A,B: A,F: A > B3,C: B3] :
% 0.26/0.46 ( ( ord_less_eq @ A @ A2 @ B )
% 0.26/0.46 => ( ( ( F @ B )
% 0.26/0.46 = C )
% 0.26/0.46 => ( ! [X3: A,Y2: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.26/0.46 => ( ord_less_eq @ B3 @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.26/0.46 => ( ord_less_eq @ B3 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ord_le_eq_subst
% 0.26/0.46 thf(fact_29_eq__iff,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( order @ A )
% 0.26/0.46 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 0.26/0.46 = ( ^ [X2: A,Y4: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ X2 @ Y4 )
% 0.26/0.46 & ( ord_less_eq @ A @ Y4 @ X2 ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % eq_iff
% 0.26/0.46 thf(fact_30_antisym,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( order @ A )
% 0.26/0.46 => ! [X: A,Y: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ X @ Y )
% 0.26/0.46 => ( ( ord_less_eq @ A @ Y @ X )
% 0.26/0.46 => ( X = Y ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % antisym
% 0.26/0.46 thf(fact_31_linear,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linorder @ A )
% 0.26/0.46 => ! [X: A,Y: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ X @ Y )
% 0.26/0.46 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % linear
% 0.26/0.46 thf(fact_32_eq__refl,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( preorder @ A )
% 0.26/0.46 => ! [X: A,Y: A] :
% 0.26/0.46 ( ( X = Y )
% 0.26/0.46 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % eq_refl
% 0.26/0.46 thf(fact_33_le__cases,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linorder @ A )
% 0.26/0.46 => ! [X: A,Y: A] :
% 0.26/0.46 ( ~ ( ord_less_eq @ A @ X @ Y )
% 0.26/0.46 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % le_cases
% 0.26/0.46 thf(fact_34_order_Otrans,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( order @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ A2 @ B )
% 0.26/0.46 => ( ( ord_less_eq @ A @ B @ C )
% 0.26/0.46 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % order.trans
% 0.26/0.46 thf(fact_35_le__cases3,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linorder @ A )
% 0.26/0.46 => ! [X: A,Y: A,Z2: A] :
% 0.26/0.46 ( ( ( ord_less_eq @ A @ X @ Y )
% 0.26/0.46 => ~ ( ord_less_eq @ A @ Y @ Z2 ) )
% 0.26/0.46 => ( ( ( ord_less_eq @ A @ Y @ X )
% 0.26/0.46 => ~ ( ord_less_eq @ A @ X @ Z2 ) )
% 0.26/0.46 => ( ( ( ord_less_eq @ A @ X @ Z2 )
% 0.26/0.46 => ~ ( ord_less_eq @ A @ Z2 @ Y ) )
% 0.26/0.46 => ( ( ( ord_less_eq @ A @ Z2 @ Y )
% 0.26/0.46 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 0.26/0.46 => ( ( ( ord_less_eq @ A @ Y @ Z2 )
% 0.26/0.46 => ~ ( ord_less_eq @ A @ Z2 @ X ) )
% 0.26/0.46 => ~ ( ( ord_less_eq @ A @ Z2 @ X )
% 0.26/0.46 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % le_cases3
% 0.26/0.46 thf(fact_36_antisym__conv,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( order @ A )
% 0.26/0.46 => ! [Y: A,X: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ Y @ X )
% 0.26/0.46 => ( ( ord_less_eq @ A @ X @ Y )
% 0.26/0.46 = ( X = Y ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % antisym_conv
% 0.26/0.46 thf(fact_37_order__class_Oorder_Oeq__iff,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( order @ A )
% 0.26/0.46 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 0.26/0.46 = ( ^ [A3: A,B2: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.26/0.46 & ( ord_less_eq @ A @ B2 @ A3 ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % order_class.order.eq_iff
% 0.26/0.46 thf(fact_38_ord__eq__le__trans,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ord @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A] :
% 0.26/0.46 ( ( A2 = B )
% 0.26/0.46 => ( ( ord_less_eq @ A @ B @ C )
% 0.26/0.46 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ord_eq_le_trans
% 0.26/0.46 thf(fact_39_ord__le__eq__trans,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ord @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ A2 @ B )
% 0.26/0.46 => ( ( B = C )
% 0.26/0.46 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ord_le_eq_trans
% 0.26/0.46 thf(fact_40_order__class_Oorder_Oantisym,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( order @ A )
% 0.26/0.46 => ! [A2: A,B: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ A2 @ B )
% 0.26/0.46 => ( ( ord_less_eq @ A @ B @ A2 )
% 0.26/0.46 => ( A2 = B ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % order_class.order.antisym
% 0.26/0.46 thf(fact_41_order__trans,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( preorder @ A )
% 0.26/0.46 => ! [X: A,Y: A,Z2: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ X @ Y )
% 0.26/0.46 => ( ( ord_less_eq @ A @ Y @ Z2 )
% 0.26/0.46 => ( ord_less_eq @ A @ X @ Z2 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % order_trans
% 0.26/0.46 thf(fact_42_dual__order_Orefl,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( order @ A )
% 0.26/0.46 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.26/0.46
% 0.26/0.46 % dual_order.refl
% 0.26/0.46 thf(fact_43_linorder__wlog,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linorder @ A )
% 0.26/0.46 => ! [P3: A > A > $o,A2: A,B: A] :
% 0.26/0.46 ( ! [A5: A,B5: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ A5 @ B5 )
% 0.26/0.46 => ( P3 @ A5 @ B5 ) )
% 0.26/0.46 => ( ! [A5: A,B5: A] :
% 0.26/0.46 ( ( P3 @ B5 @ A5 )
% 0.26/0.46 => ( P3 @ A5 @ B5 ) )
% 0.26/0.46 => ( P3 @ A2 @ B ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % linorder_wlog
% 0.26/0.46 thf(fact_44_dual__order_Otrans,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( order @ A )
% 0.26/0.46 => ! [B: A,A2: A,C: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ B @ A2 )
% 0.26/0.46 => ( ( ord_less_eq @ A @ C @ B )
% 0.26/0.46 => ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % dual_order.trans
% 0.26/0.46 thf(fact_45_ext,axiom,
% 0.26/0.46 ! [B3: $tType,A: $tType,F: A > B3,G: A > B3] :
% 0.26/0.46 ( ! [X3: A] :
% 0.26/0.46 ( ( F @ X3 )
% 0.26/0.46 = ( G @ X3 ) )
% 0.26/0.46 => ( F = G ) ) ).
% 0.26/0.46
% 0.26/0.46 % ext
% 0.26/0.46 thf(fact_46_dual__order_Oeq__iff,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( order @ A )
% 0.26/0.46 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 0.26/0.46 = ( ^ [A3: A,B2: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ B2 @ A3 )
% 0.26/0.46 & ( ord_less_eq @ A @ A3 @ B2 ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % dual_order.eq_iff
% 0.26/0.46 thf(fact_47_dual__order_Oantisym,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( order @ A )
% 0.26/0.46 => ! [B: A,A2: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ B @ A2 )
% 0.26/0.46 => ( ( ord_less_eq @ A @ A2 @ B )
% 0.26/0.46 => ( A2 = B ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % dual_order.antisym
% 0.26/0.46 thf(fact_48_max_OcoboundedI2,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linorder @ A )
% 0.26/0.46 => ! [C: A,B: A,A2: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ C @ B )
% 0.26/0.46 => ( ord_less_eq @ A @ C @ ( ord_max @ A @ A2 @ B ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % max.coboundedI2
% 0.26/0.46 thf(fact_49_max_OcoboundedI1,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linorder @ A )
% 0.26/0.46 => ! [C: A,A2: A,B: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ C @ A2 )
% 0.26/0.46 => ( ord_less_eq @ A @ C @ ( ord_max @ A @ A2 @ B ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % max.coboundedI1
% 0.26/0.46 thf(fact_50_max_Oabsorb__iff2,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linorder @ A )
% 0.26/0.46 => ( ( ord_less_eq @ A )
% 0.26/0.46 = ( ^ [A3: A,B2: A] :
% 0.26/0.46 ( ( ord_max @ A @ A3 @ B2 )
% 0.26/0.46 = B2 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % max.absorb_iff2
% 0.26/0.46 thf(fact_51_max_Oabsorb__iff1,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linorder @ A )
% 0.26/0.46 => ( ( ord_less_eq @ A )
% 0.26/0.46 = ( ^ [B2: A,A3: A] :
% 0.26/0.46 ( ( ord_max @ A @ A3 @ B2 )
% 0.26/0.46 = A3 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % max.absorb_iff1
% 0.26/0.46 thf(fact_52_le__max__iff__disj,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linorder @ A )
% 0.26/0.46 => ! [Z2: A,X: A,Y: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ Z2 @ ( ord_max @ A @ X @ Y ) )
% 0.26/0.46 = ( ( ord_less_eq @ A @ Z2 @ X )
% 0.26/0.46 | ( ord_less_eq @ A @ Z2 @ Y ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % le_max_iff_disj
% 0.26/0.46 thf(fact_53_max_Ocobounded2,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linorder @ A )
% 0.26/0.46 => ! [B: A,A2: A] : ( ord_less_eq @ A @ B @ ( ord_max @ A @ A2 @ B ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % max.cobounded2
% 0.26/0.46 thf(fact_54_max_Ocobounded1,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linorder @ A )
% 0.26/0.46 => ! [A2: A,B: A] : ( ord_less_eq @ A @ A2 @ ( ord_max @ A @ A2 @ B ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % max.cobounded1
% 0.26/0.46 thf(fact_55_max_Oorder__iff,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linorder @ A )
% 0.26/0.46 => ( ( ord_less_eq @ A )
% 0.26/0.46 = ( ^ [B2: A,A3: A] :
% 0.26/0.46 ( A3
% 0.26/0.46 = ( ord_max @ A @ A3 @ B2 ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % max.order_iff
% 0.26/0.46 thf(fact_56_max_OboundedI,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linorder @ A )
% 0.26/0.46 => ! [B: A,A2: A,C: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ B @ A2 )
% 0.26/0.46 => ( ( ord_less_eq @ A @ C @ A2 )
% 0.26/0.46 => ( ord_less_eq @ A @ ( ord_max @ A @ B @ C ) @ A2 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % max.boundedI
% 0.26/0.46 thf(fact_57_max_OboundedE,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linorder @ A )
% 0.26/0.46 => ! [B: A,C: A,A2: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ ( ord_max @ A @ B @ C ) @ A2 )
% 0.26/0.46 => ~ ( ( ord_less_eq @ A @ B @ A2 )
% 0.26/0.46 => ~ ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % max.boundedE
% 0.26/0.46 thf(fact_58_max_Oabsorb2,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linorder @ A )
% 0.26/0.46 => ! [A2: A,B: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ A2 @ B )
% 0.26/0.46 => ( ( ord_max @ A @ A2 @ B )
% 0.26/0.46 = B ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % max.absorb2
% 0.26/0.46 thf(fact_59_max_Oabsorb1,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linorder @ A )
% 0.26/0.46 => ! [B: A,A2: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ B @ A2 )
% 0.26/0.46 => ( ( ord_max @ A @ A2 @ B )
% 0.26/0.46 = A2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % max.absorb1
% 0.26/0.46 thf(fact_60_max_OorderI,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linorder @ A )
% 0.26/0.46 => ! [A2: A,B: A] :
% 0.26/0.46 ( ( A2
% 0.26/0.46 = ( ord_max @ A @ A2 @ B ) )
% 0.26/0.46 => ( ord_less_eq @ A @ B @ A2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % max.orderI
% 0.26/0.46 thf(fact_61_max_OorderE,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linorder @ A )
% 0.26/0.46 => ! [B: A,A2: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ B @ A2 )
% 0.26/0.46 => ( A2
% 0.26/0.46 = ( ord_max @ A @ A2 @ B ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % max.orderE
% 0.26/0.46 thf(fact_62_max_Omono,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linorder @ A )
% 0.26/0.46 => ! [C: A,A2: A,D: A,B: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ C @ A2 )
% 0.26/0.46 => ( ( ord_less_eq @ A @ D @ B )
% 0.26/0.46 => ( ord_less_eq @ A @ ( ord_max @ A @ C @ D ) @ ( ord_max @ A @ A2 @ B ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % max.mono
% 0.26/0.46 thf(fact_63_max__def,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ord @ A )
% 0.26/0.46 => ( ( ord_max @ A )
% 0.26/0.46 = ( ^ [A3: A,B2: A] : ( if @ A @ ( ord_less_eq @ A @ A3 @ B2 ) @ B2 @ A3 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % max_def
% 0.26/0.46 thf(fact_64_max__absorb2,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ord @ A )
% 0.26/0.46 => ! [X: A,Y: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ X @ Y )
% 0.26/0.46 => ( ( ord_max @ A @ X @ Y )
% 0.26/0.46 = Y ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % max_absorb2
% 0.26/0.46 thf(fact_65_okmaxsync__def,axiom,
% 0.26/0.46 ( genClo208577157axsync
% 0.26/0.46 = ( ^ [I2: nat,X2: real] :
% 0.26/0.46 ! [P4: nat,Q: nat] :
% 0.26/0.46 ( ( ( genClo1015804716orrect @ P4 @ ( ord_max @ real @ ( genClo1163638703lle_te @ P4 @ I2 ) @ ( genClo1163638703lle_te @ Q @ I2 ) ) )
% 0.26/0.46 & ( genClo1015804716orrect @ Q @ ( ord_max @ real @ ( genClo1163638703lle_te @ P4 @ I2 ) @ ( genClo1163638703lle_te @ Q @ I2 ) ) ) )
% 0.26/0.46 => ( ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ ( genClo1160817912lle_IC @ P4 @ I2 @ ( ord_max @ real @ ( genClo1163638703lle_te @ P4 @ I2 ) @ ( genClo1163638703lle_te @ Q @ I2 ) ) ) @ ( genClo1160817912lle_IC @ Q @ I2 @ ( ord_max @ real @ ( genClo1163638703lle_te @ P4 @ I2 ) @ ( genClo1163638703lle_te @ Q @ I2 ) ) ) ) ) @ X2 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % okmaxsync_def
% 0.26/0.46 thf(fact_66_le__add__diff__inverse,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linordered_semidom @ A )
% 0.26/0.46 => ! [B: A,A2: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ B @ A2 )
% 0.26/0.46 => ( ( plus_plus @ A @ B @ ( minus_minus @ A @ A2 @ B ) )
% 0.26/0.46 = A2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % le_add_diff_inverse
% 0.26/0.46 thf(fact_67_le__add__diff__inverse2,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linordered_semidom @ A )
% 0.26/0.46 => ! [B: A,A2: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ B @ A2 )
% 0.26/0.46 => ( ( plus_plus @ A @ ( minus_minus @ A @ A2 @ B ) @ B )
% 0.26/0.46 = A2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % le_add_diff_inverse2
% 0.26/0.46 thf(fact_68_abs__1,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( idom_abs_sgn @ A )
% 0.26/0.46 => ( ( abs_abs @ A @ ( one_one @ A ) )
% 0.26/0.46 = ( one_one @ A ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % abs_1
% 0.26/0.46 thf(fact_69_abs__add__abs,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere142940540dd_abs @ A )
% 0.26/0.46 => ! [A2: A,B: A] :
% 0.26/0.46 ( ( abs_abs @ A @ ( plus_plus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) )
% 0.26/0.46 = ( plus_plus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % abs_add_abs
% 0.26/0.46 thf(fact_70_add__diff__cancel,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( group_add @ A )
% 0.26/0.46 => ! [A2: A,B: A] :
% 0.26/0.46 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ B )
% 0.26/0.46 = A2 ) ) ).
% 0.26/0.46
% 0.26/0.46 % add_diff_cancel
% 0.26/0.46 thf(fact_71_diff__add__cancel,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( group_add @ A )
% 0.26/0.46 => ! [A2: A,B: A] :
% 0.26/0.46 ( ( plus_plus @ A @ ( minus_minus @ A @ A2 @ B ) @ B )
% 0.26/0.46 = A2 ) ) ).
% 0.26/0.46
% 0.26/0.46 % diff_add_cancel
% 0.26/0.46 thf(fact_72_add__diff__cancel__left,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( cancel146912293up_add @ A )
% 0.26/0.46 => ! [C: A,A2: A,B: A] :
% 0.26/0.46 ( ( minus_minus @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 0.26/0.46 = ( minus_minus @ A @ A2 @ B ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % add_diff_cancel_left
% 0.26/0.46 thf(fact_73_add__diff__cancel__left_H,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( cancel146912293up_add @ A )
% 0.26/0.46 => ! [A2: A,B: A] :
% 0.26/0.46 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ A2 )
% 0.26/0.46 = B ) ) ).
% 0.26/0.46
% 0.26/0.46 % add_diff_cancel_left'
% 0.26/0.46 thf(fact_74_add__diff__cancel__right,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( cancel146912293up_add @ A )
% 0.26/0.46 => ! [A2: A,C: A,B: A] :
% 0.26/0.46 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 0.26/0.46 = ( minus_minus @ A @ A2 @ B ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % add_diff_cancel_right
% 0.26/0.46 thf(fact_75_add__right__cancel,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( cancel_semigroup_add @ A )
% 0.26/0.46 => ! [B: A,A2: A,C: A] :
% 0.26/0.46 ( ( ( plus_plus @ A @ B @ A2 )
% 0.26/0.46 = ( plus_plus @ A @ C @ A2 ) )
% 0.26/0.46 = ( B = C ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % add_right_cancel
% 0.26/0.46 thf(fact_76_add__left__cancel,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( cancel_semigroup_add @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A] :
% 0.26/0.46 ( ( ( plus_plus @ A @ A2 @ B )
% 0.26/0.46 = ( plus_plus @ A @ A2 @ C ) )
% 0.26/0.46 = ( B = C ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % add_left_cancel
% 0.26/0.46 thf(fact_77_abs__idempotent,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere142940540dd_abs @ A )
% 0.26/0.46 => ! [A2: A] :
% 0.26/0.46 ( ( abs_abs @ A @ ( abs_abs @ A @ A2 ) )
% 0.26/0.46 = ( abs_abs @ A @ A2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % abs_idempotent
% 0.26/0.46 thf(fact_78_abs__abs,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( idom_abs_sgn @ A )
% 0.26/0.46 => ! [A2: A] :
% 0.26/0.46 ( ( abs_abs @ A @ ( abs_abs @ A @ A2 ) )
% 0.26/0.46 = ( abs_abs @ A @ A2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % abs_abs
% 0.26/0.46 thf(fact_79_add__le__cancel__right,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere236663937imp_le @ A )
% 0.26/0.46 => ! [A2: A,C: A,B: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 0.26/0.46 = ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % add_le_cancel_right
% 0.26/0.46 thf(fact_80_add__le__cancel__left,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere236663937imp_le @ A )
% 0.26/0.46 => ! [C: A,A2: A,B: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 0.26/0.46 = ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % add_le_cancel_left
% 0.26/0.46 thf(fact_81_add__diff__cancel__right_H,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( cancel146912293up_add @ A )
% 0.26/0.46 => ! [A2: A,B: A] :
% 0.26/0.46 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ B )
% 0.26/0.46 = A2 ) ) ).
% 0.26/0.46
% 0.26/0.46 % add_diff_cancel_right'
% 0.26/0.46 thf(fact_82_add__right__imp__eq,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( cancel_semigroup_add @ A )
% 0.26/0.46 => ! [B: A,A2: A,C: A] :
% 0.26/0.46 ( ( ( plus_plus @ A @ B @ A2 )
% 0.26/0.46 = ( plus_plus @ A @ C @ A2 ) )
% 0.26/0.46 => ( B = C ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % add_right_imp_eq
% 0.26/0.46 thf(fact_83_add__left__imp__eq,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( cancel_semigroup_add @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A] :
% 0.26/0.46 ( ( ( plus_plus @ A @ A2 @ B )
% 0.26/0.46 = ( plus_plus @ A @ A2 @ C ) )
% 0.26/0.46 => ( B = C ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % add_left_imp_eq
% 0.26/0.46 thf(fact_84_add_Oleft__commute,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ab_semigroup_add @ A )
% 0.26/0.46 => ! [B: A,A2: A,C: A] :
% 0.26/0.46 ( ( plus_plus @ A @ B @ ( plus_plus @ A @ A2 @ C ) )
% 0.26/0.46 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % add.left_commute
% 0.26/0.46 thf(fact_85_add_Ocommute,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ab_semigroup_add @ A )
% 0.26/0.46 => ( ( plus_plus @ A )
% 0.26/0.46 = ( ^ [A3: A,B2: A] : ( plus_plus @ A @ B2 @ A3 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % add.commute
% 0.26/0.46 thf(fact_86_add_Oright__cancel,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( group_add @ A )
% 0.26/0.46 => ! [B: A,A2: A,C: A] :
% 0.26/0.46 ( ( ( plus_plus @ A @ B @ A2 )
% 0.26/0.46 = ( plus_plus @ A @ C @ A2 ) )
% 0.26/0.46 = ( B = C ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % add.right_cancel
% 0.26/0.46 thf(fact_87_add_Oleft__cancel,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( group_add @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A] :
% 0.26/0.46 ( ( ( plus_plus @ A @ A2 @ B )
% 0.26/0.46 = ( plus_plus @ A @ A2 @ C ) )
% 0.26/0.46 = ( B = C ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % add.left_cancel
% 0.26/0.46 thf(fact_88_add_Oassoc,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( semigroup_add @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A] :
% 0.26/0.46 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.26/0.46 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % add.assoc
% 0.26/0.46 thf(fact_89_group__cancel_Oadd2,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( comm_monoid_add @ A )
% 0.26/0.46 => ! [B6: A,K: A,B: A,A2: A] :
% 0.26/0.46 ( ( B6
% 0.26/0.46 = ( plus_plus @ A @ K @ B ) )
% 0.26/0.46 => ( ( plus_plus @ A @ A2 @ B6 )
% 0.26/0.46 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % group_cancel.add2
% 0.26/0.46 thf(fact_90_group__cancel_Oadd1,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( comm_monoid_add @ A )
% 0.26/0.46 => ! [A6: A,K: A,A2: A,B: A] :
% 0.26/0.46 ( ( A6
% 0.26/0.46 = ( plus_plus @ A @ K @ A2 ) )
% 0.26/0.46 => ( ( plus_plus @ A @ A6 @ B )
% 0.26/0.46 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % group_cancel.add1
% 0.26/0.46 thf(fact_91_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere779506340up_add @ A )
% 0.26/0.46 => ! [I: A,J: A,K: A,L: A] :
% 0.26/0.46 ( ( ( I = J )
% 0.26/0.46 & ( K = L ) )
% 0.26/0.46 => ( ( plus_plus @ A @ I @ K )
% 0.26/0.46 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % add_mono_thms_linordered_semiring(4)
% 0.26/0.46 thf(fact_92_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ab_semigroup_add @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A] :
% 0.26/0.46 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.26/0.46 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ab_semigroup_add_class.add_ac(1)
% 0.26/0.46 thf(fact_93_one__reorient,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( one @ A )
% 0.26/0.46 => ! [X: A] :
% 0.26/0.46 ( ( ( one_one @ A )
% 0.26/0.46 = X )
% 0.26/0.46 = ( X
% 0.26/0.46 = ( one_one @ A ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % one_reorient
% 0.26/0.46 thf(fact_94_diff__right__commute,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( cancel146912293up_add @ A )
% 0.26/0.46 => ! [A2: A,C: A,B: A] :
% 0.26/0.46 ( ( minus_minus @ A @ ( minus_minus @ A @ A2 @ C ) @ B )
% 0.26/0.46 = ( minus_minus @ A @ ( minus_minus @ A @ A2 @ B ) @ C ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % diff_right_commute
% 0.26/0.46 thf(fact_95_diff__eq__diff__eq,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( group_add @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A,D: A] :
% 0.26/0.46 ( ( ( minus_minus @ A @ A2 @ B )
% 0.26/0.46 = ( minus_minus @ A @ C @ D ) )
% 0.26/0.46 => ( ( A2 = B )
% 0.26/0.46 = ( C = D ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % diff_eq_diff_eq
% 0.26/0.46 thf(fact_96_add__le__imp__le__right,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere236663937imp_le @ A )
% 0.26/0.46 => ! [A2: A,C: A,B: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 0.26/0.46 => ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % add_le_imp_le_right
% 0.26/0.46 thf(fact_97_add__le__imp__le__left,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere236663937imp_le @ A )
% 0.26/0.46 => ! [C: A,A2: A,B: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 0.26/0.46 => ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % add_le_imp_le_left
% 0.26/0.46 thf(fact_98_le__iff__add,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( canoni770627133id_add @ A )
% 0.26/0.46 => ( ( ord_less_eq @ A )
% 0.26/0.46 = ( ^ [A3: A,B2: A] :
% 0.26/0.46 ? [C3: A] :
% 0.26/0.46 ( B2
% 0.26/0.46 = ( plus_plus @ A @ A3 @ C3 ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % le_iff_add
% 0.26/0.46 thf(fact_99_add__right__mono,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere779506340up_add @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ A2 @ B )
% 0.26/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % add_right_mono
% 0.26/0.46 thf(fact_100_less__eqE,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( canoni770627133id_add @ A )
% 0.26/0.46 => ! [A2: A,B: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ A2 @ B )
% 0.26/0.46 => ~ ! [C4: A] :
% 0.26/0.46 ( B
% 0.26/0.46 != ( plus_plus @ A @ A2 @ C4 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % less_eqE
% 0.26/0.46 thf(fact_101_add__left__mono,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere779506340up_add @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ A2 @ B )
% 0.26/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % add_left_mono
% 0.26/0.46 thf(fact_102_add__mono,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere779506340up_add @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A,D: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ A2 @ B )
% 0.26/0.46 => ( ( ord_less_eq @ A @ C @ D )
% 0.26/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ D ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % add_mono
% 0.26/0.46 thf(fact_103_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere779506340up_add @ A )
% 0.26/0.46 => ! [I: A,J: A,K: A,L: A] :
% 0.26/0.46 ( ( ( ord_less_eq @ A @ I @ J )
% 0.26/0.46 & ( ord_less_eq @ A @ K @ L ) )
% 0.26/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % add_mono_thms_linordered_semiring(1)
% 0.26/0.46 thf(fact_104_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere779506340up_add @ A )
% 0.26/0.46 => ! [I: A,J: A,K: A,L: A] :
% 0.26/0.46 ( ( ( I = J )
% 0.26/0.46 & ( ord_less_eq @ A @ K @ L ) )
% 0.26/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % add_mono_thms_linordered_semiring(2)
% 0.26/0.46 thf(fact_105_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere779506340up_add @ A )
% 0.26/0.46 => ! [I: A,J: A,K: A,L: A] :
% 0.26/0.46 ( ( ( ord_less_eq @ A @ I @ J )
% 0.26/0.46 & ( K = L ) )
% 0.26/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % add_mono_thms_linordered_semiring(3)
% 0.26/0.46 thf(fact_106_diff__eq__diff__less__eq,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordered_ab_group_add @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A,D: A] :
% 0.26/0.46 ( ( ( minus_minus @ A @ A2 @ B )
% 0.26/0.46 = ( minus_minus @ A @ C @ D ) )
% 0.26/0.46 => ( ( ord_less_eq @ A @ A2 @ B )
% 0.26/0.46 = ( ord_less_eq @ A @ C @ D ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % diff_eq_diff_less_eq
% 0.26/0.46 thf(fact_107_diff__right__mono,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordered_ab_group_add @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ A2 @ B )
% 0.26/0.46 => ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B @ C ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % diff_right_mono
% 0.26/0.46 thf(fact_108_diff__left__mono,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordered_ab_group_add @ A )
% 0.26/0.46 => ! [B: A,A2: A,C: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ B @ A2 )
% 0.26/0.46 => ( ord_less_eq @ A @ ( minus_minus @ A @ C @ A2 ) @ ( minus_minus @ A @ C @ B ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % diff_left_mono
% 0.26/0.46 thf(fact_109_diff__mono,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordered_ab_group_add @ A )
% 0.26/0.46 => ! [A2: A,B: A,D: A,C: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ A2 @ B )
% 0.26/0.46 => ( ( ord_less_eq @ A @ D @ C )
% 0.26/0.46 => ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B @ D ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % diff_mono
% 0.26/0.46 thf(fact_110_add__implies__diff,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( cancel1352612707id_add @ A )
% 0.26/0.46 => ! [C: A,B: A,A2: A] :
% 0.26/0.46 ( ( ( plus_plus @ A @ C @ B )
% 0.26/0.46 = A2 )
% 0.26/0.46 => ( C
% 0.26/0.46 = ( minus_minus @ A @ A2 @ B ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % add_implies_diff
% 0.26/0.46 thf(fact_111_diff__diff__add,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( cancel146912293up_add @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A] :
% 0.26/0.46 ( ( minus_minus @ A @ ( minus_minus @ A @ A2 @ B ) @ C )
% 0.26/0.46 = ( minus_minus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % diff_diff_add
% 0.26/0.46 thf(fact_112_diff__add__eq__diff__diff__swap,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( group_add @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A] :
% 0.26/0.46 ( ( minus_minus @ A @ A2 @ ( plus_plus @ A @ B @ C ) )
% 0.26/0.46 = ( minus_minus @ A @ ( minus_minus @ A @ A2 @ C ) @ B ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % diff_add_eq_diff_diff_swap
% 0.26/0.46 thf(fact_113_diff__add__eq,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ab_group_add @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A] :
% 0.26/0.46 ( ( plus_plus @ A @ ( minus_minus @ A @ A2 @ B ) @ C )
% 0.26/0.46 = ( minus_minus @ A @ ( plus_plus @ A @ A2 @ C ) @ B ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % diff_add_eq
% 0.26/0.46 thf(fact_114_diff__diff__eq2,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( group_add @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A] :
% 0.26/0.46 ( ( minus_minus @ A @ A2 @ ( minus_minus @ A @ B @ C ) )
% 0.26/0.46 = ( minus_minus @ A @ ( plus_plus @ A @ A2 @ C ) @ B ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % diff_diff_eq2
% 0.26/0.46 thf(fact_115_add__diff__eq,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( group_add @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A] :
% 0.26/0.46 ( ( plus_plus @ A @ A2 @ ( minus_minus @ A @ B @ C ) )
% 0.26/0.46 = ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ C ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % add_diff_eq
% 0.26/0.46 thf(fact_116_eq__diff__eq,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( group_add @ A )
% 0.26/0.46 => ! [A2: A,C: A,B: A] :
% 0.26/0.46 ( ( A2
% 0.26/0.46 = ( minus_minus @ A @ C @ B ) )
% 0.26/0.46 = ( ( plus_plus @ A @ A2 @ B )
% 0.26/0.46 = C ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % eq_diff_eq
% 0.26/0.46 thf(fact_117_diff__eq__eq,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( group_add @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A] :
% 0.26/0.46 ( ( ( minus_minus @ A @ A2 @ B )
% 0.26/0.46 = C )
% 0.26/0.46 = ( A2
% 0.26/0.46 = ( plus_plus @ A @ C @ B ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % diff_eq_eq
% 0.26/0.46 thf(fact_118_group__cancel_Osub1,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ab_group_add @ A )
% 0.26/0.46 => ! [A6: A,K: A,A2: A,B: A] :
% 0.26/0.46 ( ( A6
% 0.26/0.46 = ( plus_plus @ A @ K @ A2 ) )
% 0.26/0.46 => ( ( minus_minus @ A @ A6 @ B )
% 0.26/0.46 = ( plus_plus @ A @ K @ ( minus_minus @ A @ A2 @ B ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % group_cancel.sub1
% 0.26/0.46 thf(fact_119_abs__ge__self,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere142940540dd_abs @ A )
% 0.26/0.46 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ ( abs_abs @ A @ A2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % abs_ge_self
% 0.26/0.46 thf(fact_120_abs__le__D1,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere142940540dd_abs @ A )
% 0.26/0.46 => ! [A2: A,B: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ ( abs_abs @ A @ A2 ) @ B )
% 0.26/0.46 => ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % abs_le_D1
% 0.26/0.46 thf(fact_121_abs__one,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linordered_idom @ A )
% 0.26/0.46 => ( ( abs_abs @ A @ ( one_one @ A ) )
% 0.26/0.46 = ( one_one @ A ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % abs_one
% 0.26/0.46 thf(fact_122_abs__minus__commute,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere142940540dd_abs @ A )
% 0.26/0.46 => ! [A2: A,B: A] :
% 0.26/0.46 ( ( abs_abs @ A @ ( minus_minus @ A @ A2 @ B ) )
% 0.26/0.46 = ( abs_abs @ A @ ( minus_minus @ A @ B @ A2 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % abs_minus_commute
% 0.26/0.46 thf(fact_123_max__add__distrib__left,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere236663937imp_le @ A )
% 0.26/0.46 => ! [X: A,Y: A,Z2: A] :
% 0.26/0.46 ( ( plus_plus @ A @ ( ord_max @ A @ X @ Y ) @ Z2 )
% 0.26/0.46 = ( ord_max @ A @ ( plus_plus @ A @ X @ Z2 ) @ ( plus_plus @ A @ Y @ Z2 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % max_add_distrib_left
% 0.26/0.46 thf(fact_124_max__add__distrib__right,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere236663937imp_le @ A )
% 0.26/0.46 => ! [X: A,Y: A,Z2: A] :
% 0.26/0.46 ( ( plus_plus @ A @ X @ ( ord_max @ A @ Y @ Z2 ) )
% 0.26/0.46 = ( ord_max @ A @ ( plus_plus @ A @ X @ Y ) @ ( plus_plus @ A @ X @ Z2 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % max_add_distrib_right
% 0.26/0.46 thf(fact_125_max__diff__distrib__left,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordered_ab_group_add @ A )
% 0.26/0.46 => ! [X: A,Y: A,Z2: A] :
% 0.26/0.46 ( ( minus_minus @ A @ ( ord_max @ A @ X @ Y ) @ Z2 )
% 0.26/0.46 = ( ord_max @ A @ ( minus_minus @ A @ X @ Z2 ) @ ( minus_minus @ A @ Y @ Z2 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % max_diff_distrib_left
% 0.26/0.46 thf(fact_126_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere623563068d_diff @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ A2 @ B )
% 0.26/0.46 => ( ( ord_less_eq @ A @ A2 @ B )
% 0.26/0.46 => ( ( ( minus_minus @ A @ B @ A2 )
% 0.26/0.46 = C )
% 0.26/0.46 = ( B
% 0.26/0.46 = ( plus_plus @ A @ C @ A2 ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 0.26/0.46 thf(fact_127_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere623563068d_diff @ A )
% 0.26/0.46 => ! [A2: A,B: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ A2 @ B )
% 0.26/0.46 => ( ( plus_plus @ A @ A2 @ ( minus_minus @ A @ B @ A2 ) )
% 0.26/0.46 = B ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 0.26/0.46 thf(fact_128_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere623563068d_diff @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ A2 @ B )
% 0.26/0.46 => ( ( minus_minus @ A @ C @ ( minus_minus @ A @ B @ A2 ) )
% 0.26/0.46 = ( minus_minus @ A @ ( plus_plus @ A @ C @ A2 ) @ B ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 0.26/0.46 thf(fact_129_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere623563068d_diff @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ A2 @ B )
% 0.26/0.46 => ( ( minus_minus @ A @ ( plus_plus @ A @ B @ C ) @ A2 )
% 0.26/0.46 = ( plus_plus @ A @ ( minus_minus @ A @ B @ A2 ) @ C ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 0.26/0.46 thf(fact_130_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere623563068d_diff @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ A2 @ B )
% 0.26/0.46 => ( ( plus_plus @ A @ ( minus_minus @ A @ B @ A2 ) @ C )
% 0.26/0.46 = ( minus_minus @ A @ ( plus_plus @ A @ B @ C ) @ A2 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 0.26/0.46 thf(fact_131_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere623563068d_diff @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ A2 @ B )
% 0.26/0.46 => ( ( minus_minus @ A @ ( plus_plus @ A @ C @ B ) @ A2 )
% 0.26/0.46 = ( plus_plus @ A @ C @ ( minus_minus @ A @ B @ A2 ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 0.26/0.46 thf(fact_132_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere623563068d_diff @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ A2 @ B )
% 0.26/0.46 => ( ( plus_plus @ A @ C @ ( minus_minus @ A @ B @ A2 ) )
% 0.26/0.46 = ( minus_minus @ A @ ( plus_plus @ A @ C @ B ) @ A2 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 0.26/0.46 thf(fact_133_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere623563068d_diff @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ A2 @ B )
% 0.26/0.46 => ( ( ord_less_eq @ A @ C @ ( minus_minus @ A @ B @ A2 ) )
% 0.26/0.46 = ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ B ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 0.26/0.46 thf(fact_134_le__add__diff,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere623563068d_diff @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ A2 @ B )
% 0.26/0.46 => ( ord_less_eq @ A @ C @ ( minus_minus @ A @ ( plus_plus @ A @ B @ C ) @ A2 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % le_add_diff
% 0.26/0.46 thf(fact_135_add__le__add__imp__diff__le,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linordered_semidom @ A )
% 0.26/0.46 => ! [I: A,K: A,N: A,J: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ N )
% 0.26/0.46 => ( ( ord_less_eq @ A @ N @ ( plus_plus @ A @ J @ K ) )
% 0.26/0.46 => ( ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ N )
% 0.26/0.46 => ( ( ord_less_eq @ A @ N @ ( plus_plus @ A @ J @ K ) )
% 0.26/0.46 => ( ord_less_eq @ A @ ( minus_minus @ A @ N @ K ) @ J ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % add_le_add_imp_diff_le
% 0.26/0.46 thf(fact_136_diff__add,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere623563068d_diff @ A )
% 0.26/0.46 => ! [A2: A,B: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ A2 @ B )
% 0.26/0.46 => ( ( plus_plus @ A @ ( minus_minus @ A @ B @ A2 ) @ A2 )
% 0.26/0.46 = B ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % diff_add
% 0.26/0.46 thf(fact_137_add__le__imp__le__diff,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linordered_semidom @ A )
% 0.26/0.46 => ! [I: A,K: A,N: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ N )
% 0.26/0.46 => ( ord_less_eq @ A @ I @ ( minus_minus @ A @ N @ K ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % add_le_imp_le_diff
% 0.26/0.46 thf(fact_138_le__diff__eq,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordered_ab_group_add @ A )
% 0.26/0.46 => ! [A2: A,C: A,B: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ A2 @ ( minus_minus @ A @ C @ B ) )
% 0.26/0.46 = ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B ) @ C ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % le_diff_eq
% 0.26/0.46 thf(fact_139_diff__le__eq,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordered_ab_group_add @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ B ) @ C )
% 0.26/0.46 = ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ C @ B ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % diff_le_eq
% 0.26/0.46 thf(fact_140_abs__triangle__ineq,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere142940540dd_abs @ A )
% 0.26/0.46 => ! [A2: A,B: A] : ( ord_less_eq @ A @ ( abs_abs @ A @ ( plus_plus @ A @ A2 @ B ) ) @ ( plus_plus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % abs_triangle_ineq
% 0.26/0.46 thf(fact_141_abs__triangle__ineq2__sym,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere142940540dd_abs @ A )
% 0.26/0.46 => ! [A2: A,B: A] : ( ord_less_eq @ A @ ( minus_minus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) @ ( abs_abs @ A @ ( minus_minus @ A @ B @ A2 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % abs_triangle_ineq2_sym
% 0.26/0.46 thf(fact_142_abs__triangle__ineq3,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere142940540dd_abs @ A )
% 0.26/0.46 => ! [A2: A,B: A] : ( ord_less_eq @ A @ ( abs_abs @ A @ ( minus_minus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) ) @ ( abs_abs @ A @ ( minus_minus @ A @ A2 @ B ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % abs_triangle_ineq3
% 0.26/0.46 thf(fact_143_abs__triangle__ineq2,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere142940540dd_abs @ A )
% 0.26/0.46 => ! [A2: A,B: A] : ( ord_less_eq @ A @ ( minus_minus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) @ ( abs_abs @ A @ ( minus_minus @ A @ A2 @ B ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % abs_triangle_ineq2
% 0.26/0.46 thf(fact_144_abs__diff__triangle__ineq,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere142940540dd_abs @ A )
% 0.26/0.46 => ! [A2: A,B: A,C: A,D: A] : ( ord_less_eq @ A @ ( abs_abs @ A @ ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ ( plus_plus @ A @ C @ D ) ) ) @ ( plus_plus @ A @ ( abs_abs @ A @ ( minus_minus @ A @ A2 @ C ) ) @ ( abs_abs @ A @ ( minus_minus @ A @ B @ D ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % abs_diff_triangle_ineq
% 0.26/0.46 thf(fact_145_abs__triangle__ineq4,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( ordere142940540dd_abs @ A )
% 0.26/0.46 => ! [A2: A,B: A] : ( ord_less_eq @ A @ ( abs_abs @ A @ ( minus_minus @ A @ A2 @ B ) ) @ ( plus_plus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % abs_triangle_ineq4
% 0.26/0.46 thf(fact_146_abs__diff__le__iff,axiom,
% 0.26/0.46 ! [A: $tType] :
% 0.26/0.46 ( ( linordered_idom @ A )
% 0.26/0.46 => ! [X: A,A2: A,R: A] :
% 0.26/0.46 ( ( ord_less_eq @ A @ ( abs_abs @ A @ ( minus_minus @ A @ X @ A2 ) ) @ R )
% 0.26/0.46 = ( ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ R ) @ X )
% 0.26/0.46 & ( ord_less_eq @ A @ X @ ( plus_plus @ A @ A2 @ R ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % abs_diff_le_iff
% 0.26/0.46 thf(fact_147_rts1,axiom,
% 0.26/0.46 ! [P: nat,T: real,I3: nat] :
% 0.26/0.46 ( ( ( genClo1015804716orrect @ P @ T )
% 0.26/0.46 & ( ord_less_eq @ real @ ( genClo1163638703lle_te @ P @ ( plus_plus @ nat @ I3 @ ( one_one @ nat ) ) ) @ T ) )
% 0.26/0.46 => ( ord_less_eq @ real @ genClo1651033342e_rmin @ ( minus_minus @ real @ T @ ( genClo1163638703lle_te @ P @ I3 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % rts1
% 0.26/0.46 thf(fact_148_rts1d,axiom,
% 0.26/0.46 ! [P2: nat,I: nat] :
% 0.26/0.46 ( ( genClo1015804716orrect @ P2 @ ( genClo1163638703lle_te @ P2 @ ( plus_plus @ nat @ I @ ( one_one @ nat ) ) ) )
% 0.26/0.46 => ( ord_less_eq @ real @ genClo1651033342e_rmin @ ( minus_minus @ real @ ( genClo1163638703lle_te @ P2 @ ( plus_plus @ nat @ I @ ( one_one @ nat ) ) ) @ ( genClo1163638703lle_te @ P2 @ I ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % rts1d
% 0.26/0.46 thf(fact_149_rts0,axiom,
% 0.26/0.46 ! [P: nat,T: real,I3: nat] :
% 0.26/0.46 ( ( ( genClo1015804716orrect @ P @ T )
% 0.26/0.46 & ( ord_less_eq @ real @ T @ ( genClo1163638703lle_te @ P @ ( plus_plus @ nat @ I3 @ ( one_one @ nat ) ) ) ) )
% 0.26/0.46 => ( ord_less_eq @ real @ ( minus_minus @ real @ T @ ( genClo1163638703lle_te @ P @ I3 ) ) @ genClo1650508560e_rmax ) ) ).
% 0.26/0.46
% 0.26/0.46 % rts0
% 0.26/0.46 thf(fact_150_rts0d,axiom,
% 0.26/0.46 ! [P2: nat,I: nat] :
% 0.26/0.46 ( ( genClo1015804716orrect @ P2 @ ( genClo1163638703lle_te @ P2 @ ( plus_plus @ nat @ I @ ( one_one @ nat ) ) ) )
% 0.26/0.46 => ( ord_less_eq @ real @ ( minus_minus @ real @ ( genClo1163638703lle_te @ P2 @ ( plus_plus @ nat @ I @ ( one_one @ nat ) ) ) @ ( genClo1163638703lle_te @ P2 @ I ) ) @ genClo1650508560e_rmax ) ) ).
% 0.26/0.46
% 0.26/0.46 % rts0d
% 0.26/0.46 thf(fact_151_okRead2__def,axiom,
% 0.26/0.46 ( genClo293725282kRead2
% 0.26/0.46 = ( ^ [F2: nat > real,G2: nat > real,X2: real,Ppred: nat > $o] :
% 0.26/0.46 ! [P4: nat] :
% 0.26/0.46 ( ( Ppred @ P4 )
% 0.26/0.46 => ( ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ ( F2 @ P4 ) @ ( G2 @ P4 ) ) ) @ X2 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % okRead2_def
% 0.26/0.46 thf(fact_152_sin__bound__lemma,axiom,
% 0.26/0.46 ! [X: real,Y: real,U: real,V: real] :
% 0.26/0.46 ( ( X = Y )
% 0.26/0.46 => ( ( ord_less_eq @ real @ ( abs_abs @ real @ U ) @ V )
% 0.26/0.46 => ( ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ ( plus_plus @ real @ X @ U ) @ Y ) ) @ V ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % sin_bound_lemma
% 0.26/0.46 thf(fact_153_eq__diff__eq_H,axiom,
% 0.26/0.46 ! [X: real,Y: real,Z2: real] :
% 0.26/0.46 ( ( X
% 0.26/0.46 = ( minus_minus @ real @ Y @ Z2 ) )
% 0.26/0.46 = ( Y
% 0.26/0.46 = ( plus_plus @ real @ X @ Z2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % eq_diff_eq'
% 0.26/0.46 thf(fact_154_beta__bound2,axiom,
% 0.26/0.46 ! [P2: nat,I: nat,Q2: nat] :
% 0.26/0.46 ( ( genClo1015804716orrect @ P2 @ ( genClo1163638703lle_te @ P2 @ ( plus_plus @ nat @ I @ ( one_one @ nat ) ) ) )
% 0.26/0.46 => ( ( genClo1015804716orrect @ Q2 @ ( genClo1163638703lle_te @ Q2 @ I ) )
% 0.26/0.46 => ( ord_less_eq @ real @ ( minus_minus @ real @ ( genClo1163638703lle_te @ P2 @ ( plus_plus @ nat @ I @ ( one_one @ nat ) ) ) @ ( genClo1163638703lle_te @ Q2 @ I ) ) @ ( plus_plus @ real @ genClo1650508560e_rmax @ genClo1278781456e_beta ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % beta_bound2
% 0.26/0.46 thf(fact_155_rts2b,axiom,
% 0.26/0.46 ! [P: nat,Q3: nat,I3: nat] :
% 0.26/0.46 ( ( ( genClo1015804716orrect @ P @ ( genClo1163638703lle_te @ P @ I3 ) )
% 0.26/0.46 & ( genClo1015804716orrect @ Q3 @ ( genClo1163638703lle_te @ Q3 @ I3 ) ) )
% 0.26/0.46 => ( ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ ( genClo1163638703lle_te @ P @ I3 ) @ ( genClo1163638703lle_te @ Q3 @ I3 ) ) ) @ genClo1278781456e_beta ) ) ).
% 0.26/0.46
% 0.26/0.46 % rts2b
% 0.26/0.46 thf(fact_156_nat__add__left__cancel__le,axiom,
% 0.26/0.46 ! [K: nat,M: nat,N: nat] :
% 0.26/0.46 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 0.26/0.46 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.26/0.46
% 0.26/0.46 % nat_add_left_cancel_le
% 0.26/0.46 thf(fact_157_diff__diff__cancel,axiom,
% 0.26/0.46 ! [I: nat,N: nat] :
% 0.26/0.46 ( ( ord_less_eq @ nat @ I @ N )
% 0.26/0.46 => ( ( minus_minus @ nat @ N @ ( minus_minus @ nat @ N @ I ) )
% 0.26/0.46 = I ) ) ).
% 0.26/0.46
% 0.26/0.46 % diff_diff_cancel
% 0.26/0.46 thf(fact_158_diff__diff__left,axiom,
% 0.26/0.46 ! [I: nat,J: nat,K: nat] :
% 0.26/0.46 ( ( minus_minus @ nat @ ( minus_minus @ nat @ I @ J ) @ K )
% 0.26/0.46 = ( minus_minus @ nat @ I @ ( plus_plus @ nat @ J @ K ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % diff_diff_left
% 0.26/0.46 thf(fact_159_Nat_Odiff__diff__right,axiom,
% 0.26/0.46 ! [K: nat,J: nat,I: nat] :
% 0.26/0.46 ( ( ord_less_eq @ nat @ K @ J )
% 0.26/0.46 => ( ( minus_minus @ nat @ I @ ( minus_minus @ nat @ J @ K ) )
% 0.26/0.46 = ( minus_minus @ nat @ ( plus_plus @ nat @ I @ K ) @ J ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Nat.diff_diff_right
% 0.26/0.46 thf(fact_160_Nat_Oadd__diff__assoc2,axiom,
% 0.26/0.46 ! [K: nat,J: nat,I: nat] :
% 0.26/0.46 ( ( ord_less_eq @ nat @ K @ J )
% 0.26/0.46 => ( ( plus_plus @ nat @ ( minus_minus @ nat @ J @ K ) @ I )
% 0.26/0.46 = ( minus_minus @ nat @ ( plus_plus @ nat @ J @ I ) @ K ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Nat.add_diff_assoc2
% 0.26/0.46 thf(fact_161_Nat_Oadd__diff__assoc,axiom,
% 0.26/0.46 ! [K: nat,J: nat,I: nat] :
% 0.26/0.46 ( ( ord_less_eq @ nat @ K @ J )
% 0.26/0.46 => ( ( plus_plus @ nat @ I @ ( minus_minus @ nat @ J @ K ) )
% 0.26/0.46 = ( minus_minus @ nat @ ( plus_plus @ nat @ I @ J ) @ K ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Nat.add_diff_assoc
% 0.26/0.46 thf(fact_162_Nat_Oex__has__greatest__nat,axiom,
% 0.26/0.46 ! [P3: nat > $o,K: nat,B: nat] :
% 0.26/0.46 ( ( P3 @ K )
% 0.26/0.46 => ( ! [Y2: nat] :
% 0.26/0.46 ( ( P3 @ Y2 )
% 0.26/0.46 => ( ord_less_eq @ nat @ Y2 @ B ) )
% 0.26/0.46 => ? [X3: nat] :
% 0.26/0.46 ( ( P3 @ X3 )
% 0.26/0.46 & ! [Y5: nat] :
% 0.26/0.46 ( ( P3 @ Y5 )
% 0.26/0.46 => ( ord_less_eq @ nat @ Y5 @ X3 ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Nat.ex_has_greatest_nat
% 0.26/0.46 thf(fact_163_nat__le__linear,axiom,
% 0.26/0.46 ! [M: nat,N: nat] :
% 0.26/0.46 ( ( ord_less_eq @ nat @ M @ N )
% 0.26/0.46 | ( ord_less_eq @ nat @ N @ M ) ) ).
% 0.26/0.46
% 0.26/0.46 % nat_le_linear
% 0.26/0.46 thf(fact_164_diff__le__mono2,axiom,
% 0.26/0.46 ! [M: nat,N: nat,L: nat] :
% 0.26/0.46 ( ( ord_less_eq @ nat @ M @ N )
% 0.26/0.46 => ( ord_less_eq @ nat @ ( minus_minus @ nat @ L @ N ) @ ( minus_minus @ nat @ L @ M ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % diff_le_mono2
% 0.26/0.46 thf(fact_165_le__diff__iff_H,axiom,
% 0.26/0.46 ! [A2: nat,C: nat,B: nat] :
% 0.26/0.46 ( ( ord_less_eq @ nat @ A2 @ C )
% 0.26/0.46 => ( ( ord_less_eq @ nat @ B @ C )
% 0.26/0.46 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ C @ A2 ) @ ( minus_minus @ nat @ C @ B ) )
% 0.26/0.46 = ( ord_less_eq @ nat @ B @ A2 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % le_diff_iff'
% 0.26/0.46 thf(fact_166_diff__le__self,axiom,
% 0.26/0.46 ! [M: nat,N: nat] : ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ N ) @ M ) ).
% 0.26/0.46
% 0.26/0.46 % diff_le_self
% 0.26/0.46 thf(fact_167_diff__le__mono,axiom,
% 0.26/0.46 ! [M: nat,N: nat,L: nat] :
% 0.26/0.46 ( ( ord_less_eq @ nat @ M @ N )
% 0.26/0.46 => ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ L ) @ ( minus_minus @ nat @ N @ L ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % diff_le_mono
% 0.26/0.46 thf(fact_168_Nat_Odiff__diff__eq,axiom,
% 0.26/0.46 ! [K: nat,M: nat,N: nat] :
% 0.26/0.46 ( ( ord_less_eq @ nat @ K @ M )
% 0.26/0.46 => ( ( ord_less_eq @ nat @ K @ N )
% 0.26/0.46 => ( ( minus_minus @ nat @ ( minus_minus @ nat @ M @ K ) @ ( minus_minus @ nat @ N @ K ) )
% 0.26/0.46 = ( minus_minus @ nat @ M @ N ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Nat.diff_diff_eq
% 0.26/0.46 thf(fact_169_le__diff__iff,axiom,
% 0.26/0.46 ! [K: nat,M: nat,N: nat] :
% 0.26/0.46 ( ( ord_less_eq @ nat @ K @ M )
% 0.26/0.46 => ( ( ord_less_eq @ nat @ K @ N )
% 0.26/0.46 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ K ) @ ( minus_minus @ nat @ N @ K ) )
% 0.26/0.46 = ( ord_less_eq @ nat @ M @ N ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % le_diff_iff
% 0.26/0.46 thf(fact_170_eq__diff__iff,axiom,
% 0.26/0.46 ! [K: nat,M: nat,N: nat] :
% 0.26/0.46 ( ( ord_less_eq @ nat @ K @ M )
% 0.26/0.46 => ( ( ord_less_eq @ nat @ K @ N )
% 0.26/0.46 => ( ( ( minus_minus @ nat @ M @ K )
% 0.26/0.46 = ( minus_minus @ nat @ N @ K ) )
% 0.26/0.46 = ( M = N ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % eq_diff_iff
% 0.26/0.46 thf(fact_171_le__antisym,axiom,
% 0.26/0.46 ! [M: nat,N: nat] :
% 0.26/0.46 ( ( ord_less_eq @ nat @ M @ N )
% 0.26/0.46 => ( ( ord_less_eq @ nat @ N @ M )
% 0.26/0.46 => ( M = N ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % le_antisym
% 0.26/0.46 thf(fact_172_eq__imp__le,axiom,
% 0.26/0.46 ! [M: nat,N: nat] :
% 0.26/0.46 ( ( M = N )
% 0.26/0.46 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.26/0.46
% 0.26/0.46 % eq_imp_le
% 0.26/0.46 thf(fact_173_le__trans,axiom,
% 0.26/0.46 ! [I: nat,J: nat,K: nat] :
% 0.26/0.46 ( ( ord_less_eq @ nat @ I @ J )
% 0.26/0.46 => ( ( ord_less_eq @ nat @ J @ K )
% 0.26/0.46 => ( ord_less_eq @ nat @ I @ K ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % le_trans
% 0.26/0.46 thf(fact_174_le__refl,axiom,
% 0.26/0.46 ! [N: nat] : ( ord_less_eq @ nat @ N @ N ) ).
% 0.26/0.46
% 0.26/0.46 % le_refl
% 0.26/0.46 thf(fact_175_Nat_Ole__imp__diff__is__add,axiom,
% 0.26/0.46 ! [I: nat,J: nat,K: nat] :
% 0.26/0.46 ( ( ord_less_eq @ nat @ I @ J )
% 0.26/0.46 => ( ( ( minus_minus @ nat @ J @ I )
% 0.26/0.46 = K )
% 0.26/0.46 = ( J
% 0.26/0.46 = ( plus_plus @ nat @ K @ I ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Nat.le_imp_diff_is_add
% 0.26/0.46 thf(fact_176_nat__minus__add__max,axiom,
% 0.26/0.46 ! [N: nat,M: nat] :
% 0.26/0.46 ( ( plus_plus @ nat @ ( minus_minus @ nat @ N @ M ) @ M )
% 0.26/0.46 = ( ord_max @ nat @ N @ M ) ) ).
% 0.26/0.46
% 0.26/0.46 % nat_minus_add_max
% 0.26/0.46 thf(fact_177_diff__add__inverse2,axiom,
% 0.26/0.46 ! [M: nat,N: nat] :
% 0.26/0.46 ( ( minus_minus @ nat @ ( plus_plus @ nat @ M @ N ) @ N )
% 0.26/0.46 = M ) ).
% 0.26/0.46
% 0.26/0.46 % diff_add_inverse2
% 0.26/0.46 thf(fact_178_diff__add__inverse,axiom,
% 0.26/0.46 ! [N: nat,M: nat] :
% 0.26/0.46 ( ( minus_minus @ nat @ ( plus_plus @ nat @ N @ M ) @ N )
% 0.26/0.46 = M ) ).
% 0.26/0.46
% 0.26/0.46 % diff_add_inverse
% 0.26/0.46 thf(fact_179_Nat_Odiff__add__assoc2,axiom,
% 0.26/0.46 ! [K: nat,J: nat,I: nat] :
% 0.26/0.46 ( ( ord_less_eq @ nat @ K @ J )
% 0.26/0.46 => ( ( minus_minus @ nat @ ( plus_plus @ nat @ J @ I ) @ K )
% 0.26/0.46 = ( plus_plus @ nat @ ( minus_minus @ nat @ J @ K ) @ I ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Nat.diff_add_assoc2
% 0.26/0.46 thf(fact_180_Nat_Odiff__add__assoc,axiom,
% 0.26/0.46 ! [K: nat,J: nat,I: nat] :
% 0.26/0.46 ( ( ord_less_eq @ nat @ K @ J )
% 0.26/0.46 => ( ( minus_minus @ nat @ ( plus_plus @ nat @ I @ J ) @ K )
% 0.26/0.46 = ( plus_plus @ nat @ I @ ( minus_minus @ nat @ J @ K ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Nat.diff_add_assoc
% 0.26/0.46 thf(fact_181_Nat_Ole__diff__conv2,axiom,
% 0.26/0.46 ! [K: nat,J: nat,I: nat] :
% 0.26/0.46 ( ( ord_less_eq @ nat @ K @ J )
% 0.26/0.46 => ( ( ord_less_eq @ nat @ I @ ( minus_minus @ nat @ J @ K ) )
% 0.26/0.46 = ( ord_less_eq @ nat @ ( plus_plus @ nat @ I @ K ) @ J ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Nat.le_diff_conv2
% 0.26/0.46 thf(fact_182_le__diff__conv,axiom,
% 0.26/0.46 ! [J: nat,K: nat,I: nat] :
% 0.26/0.47 ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ J @ K ) @ I )
% 0.26/0.47 = ( ord_less_eq @ nat @ J @ ( plus_plus @ nat @ I @ K ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % le_diff_conv
% 0.26/0.47 thf(fact_183_diff__cancel2,axiom,
% 0.26/0.47 ! [M: nat,K: nat,N: nat] :
% 0.26/0.47 ( ( minus_minus @ nat @ ( plus_plus @ nat @ M @ K ) @ ( plus_plus @ nat @ N @ K ) )
% 0.26/0.47 = ( minus_minus @ nat @ M @ N ) ) ).
% 0.26/0.47
% 0.26/0.47 % diff_cancel2
% 0.26/0.47 thf(fact_184_Nat_Odiff__cancel,axiom,
% 0.26/0.47 ! [K: nat,M: nat,N: nat] :
% 0.26/0.47 ( ( minus_minus @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 0.26/0.47 = ( minus_minus @ nat @ M @ N ) ) ).
% 0.26/0.47
% 0.26/0.47 % Nat.diff_cancel
% 0.26/0.47 thf(fact_185_nat__add__max__right,axiom,
% 0.26/0.47 ! [M: nat,N: nat,Q2: nat] :
% 0.26/0.47 ( ( plus_plus @ nat @ M @ ( ord_max @ nat @ N @ Q2 ) )
% 0.26/0.47 = ( ord_max @ nat @ ( plus_plus @ nat @ M @ N ) @ ( plus_plus @ nat @ M @ Q2 ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % nat_add_max_right
% 0.26/0.47 thf(fact_186_nat__add__max__left,axiom,
% 0.26/0.47 ! [M: nat,N: nat,Q2: nat] :
% 0.26/0.47 ( ( plus_plus @ nat @ ( ord_max @ nat @ M @ N ) @ Q2 )
% 0.26/0.47 = ( ord_max @ nat @ ( plus_plus @ nat @ M @ Q2 ) @ ( plus_plus @ nat @ N @ Q2 ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % nat_add_max_left
% 0.26/0.47 thf(fact_187_nat__le__iff__add,axiom,
% 0.26/0.47 ( ( ord_less_eq @ nat )
% 0.26/0.47 = ( ^ [M2: nat,N2: nat] :
% 0.26/0.47 ? [K2: nat] :
% 0.26/0.47 ( N2
% 0.26/0.47 = ( plus_plus @ nat @ M2 @ K2 ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % nat_le_iff_add
% 0.26/0.47 thf(fact_188_trans__le__add2,axiom,
% 0.26/0.47 ! [I: nat,J: nat,M: nat] :
% 0.26/0.47 ( ( ord_less_eq @ nat @ I @ J )
% 0.26/0.47 => ( ord_less_eq @ nat @ I @ ( plus_plus @ nat @ M @ J ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % trans_le_add2
% 0.26/0.47 thf(fact_189_trans__le__add1,axiom,
% 0.26/0.47 ! [I: nat,J: nat,M: nat] :
% 0.26/0.47 ( ( ord_less_eq @ nat @ I @ J )
% 0.26/0.47 => ( ord_less_eq @ nat @ I @ ( plus_plus @ nat @ J @ M ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % trans_le_add1
% 0.26/0.47 thf(fact_190_add__le__mono1,axiom,
% 0.26/0.47 ! [I: nat,J: nat,K: nat] :
% 0.26/0.47 ( ( ord_less_eq @ nat @ I @ J )
% 0.26/0.47 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ K ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % add_le_mono1
% 0.26/0.47 thf(fact_191_add__le__mono,axiom,
% 0.26/0.47 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.26/0.47 ( ( ord_less_eq @ nat @ I @ J )
% 0.26/0.47 => ( ( ord_less_eq @ nat @ K @ L )
% 0.26/0.47 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ L ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % add_le_mono
% 0.26/0.47 thf(fact_192_le__Suc__ex,axiom,
% 0.26/0.47 ! [K: nat,L: nat] :
% 0.26/0.47 ( ( ord_less_eq @ nat @ K @ L )
% 0.26/0.47 => ? [N3: nat] :
% 0.26/0.47 ( L
% 0.26/0.47 = ( plus_plus @ nat @ K @ N3 ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % le_Suc_ex
% 0.26/0.47 thf(fact_193_add__leD2,axiom,
% 0.26/0.47 ! [M: nat,K: nat,N: nat] :
% 0.26/0.47 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K ) @ N )
% 0.26/0.47 => ( ord_less_eq @ nat @ K @ N ) ) ).
% 0.26/0.47
% 0.26/0.47 % add_leD2
% 0.26/0.47 thf(fact_194_add__leD1,axiom,
% 0.26/0.47 ! [M: nat,K: nat,N: nat] :
% 0.26/0.47 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K ) @ N )
% 0.26/0.47 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.26/0.47
% 0.26/0.47 % add_leD1
% 0.26/0.47 thf(fact_195_le__add2,axiom,
% 0.26/0.47 ! [N: nat,M: nat] : ( ord_less_eq @ nat @ N @ ( plus_plus @ nat @ M @ N ) ) ).
% 0.26/0.47
% 0.26/0.47 % le_add2
% 0.26/0.47 thf(fact_196_le__add1,axiom,
% 0.26/0.47 ! [N: nat,M: nat] : ( ord_less_eq @ nat @ N @ ( plus_plus @ nat @ N @ M ) ) ).
% 0.26/0.47
% 0.26/0.47 % le_add1
% 0.26/0.47 thf(fact_197_add__leE,axiom,
% 0.26/0.47 ! [M: nat,K: nat,N: nat] :
% 0.26/0.47 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K ) @ N )
% 0.26/0.47 => ~ ( ( ord_less_eq @ nat @ M @ N )
% 0.26/0.47 => ~ ( ord_less_eq @ nat @ K @ N ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % add_leE
% 0.26/0.47 thf(fact_198_nonoverlap,axiom,
% 0.26/0.47 ord_less_eq @ real @ genClo1278781456e_beta @ genClo1651033342e_rmin ).
% 0.26/0.47
% 0.26/0.47 % nonoverlap
% 0.26/0.47 thf(fact_199_rts2a,axiom,
% 0.26/0.47 ! [P: nat,Q3: nat,T: real,I3: nat] :
% 0.26/0.47 ( ( ( genClo1015804716orrect @ P @ T )
% 0.26/0.47 & ( genClo1015804716orrect @ Q3 @ T )
% 0.26/0.47 & ( ord_less_eq @ real @ ( plus_plus @ real @ ( genClo1163638703lle_te @ Q3 @ I3 ) @ genClo1278781456e_beta ) @ T ) )
% 0.26/0.47 => ( ord_less_eq @ real @ ( genClo1163638703lle_te @ P @ I3 ) @ T ) ) ).
% 0.26/0.47
% 0.26/0.47 % rts2a
% 0.26/0.47 thf(fact_200_readerror,axiom,
% 0.26/0.47 ! [P: nat,Q3: nat,I3: nat] :
% 0.26/0.47 ( ( ( genClo1015804716orrect @ P @ ( genClo1163638703lle_te @ P @ ( plus_plus @ nat @ I3 @ ( one_one @ nat ) ) ) )
% 0.26/0.47 & ( genClo1015804716orrect @ Q3 @ ( genClo1163638703lle_te @ P @ ( plus_plus @ nat @ I3 @ ( one_one @ nat ) ) ) ) )
% 0.26/0.47 => ( ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ ( genClo1400225944_theta @ P @ ( plus_plus @ nat @ I3 @ ( one_one @ nat ) ) @ Q3 ) @ ( genClo1160817912lle_IC @ Q3 @ I3 @ ( genClo1163638703lle_te @ P @ ( plus_plus @ nat @ I3 @ ( one_one @ nat ) ) ) ) ) ) @ genClo721845095Lambda ) ) ).
% 0.26/0.47
% 0.26/0.47 % readerror
% 0.26/0.47 thf(fact_201_okRead1__def,axiom,
% 0.26/0.47 ( genClo293725281kRead1
% 0.26/0.47 = ( ^ [F2: nat > real,X2: real,Ppred: nat > $o] :
% 0.26/0.47 ! [L2: nat,M2: nat] :
% 0.26/0.47 ( ( ( Ppred @ L2 )
% 0.26/0.47 & ( Ppred @ M2 ) )
% 0.26/0.47 => ( ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ ( F2 @ L2 ) @ ( F2 @ M2 ) ) ) @ X2 ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % okRead1_def
% 0.26/0.47 thf(fact_202_beta__bound1,axiom,
% 0.26/0.47 ! [P2: nat,I: nat,Q2: nat] :
% 0.26/0.47 ( ( genClo1015804716orrect @ P2 @ ( genClo1163638703lle_te @ P2 @ ( plus_plus @ nat @ I @ ( one_one @ nat ) ) ) )
% 0.26/0.47 => ( ( genClo1015804716orrect @ Q2 @ ( genClo1163638703lle_te @ P2 @ ( plus_plus @ nat @ I @ ( one_one @ nat ) ) ) )
% 0.26/0.47 => ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( minus_minus @ real @ ( genClo1163638703lle_te @ P2 @ ( plus_plus @ nat @ I @ ( one_one @ nat ) ) ) @ ( genClo1163638703lle_te @ Q2 @ I ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % beta_bound1
% 0.26/0.47 thf(fact_203_le__zero__eq,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( canoni770627133id_add @ A )
% 0.26/0.47 => ! [N: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 0.26/0.47 = ( N
% 0.26/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % le_zero_eq
% 0.26/0.47 thf(fact_204_zero__eq__add__iff__both__eq__0,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( canoni770627133id_add @ A )
% 0.26/0.47 => ! [X: A,Y: A] :
% 0.26/0.47 ( ( ( zero_zero @ A )
% 0.26/0.47 = ( plus_plus @ A @ X @ Y ) )
% 0.26/0.47 = ( ( X
% 0.26/0.47 = ( zero_zero @ A ) )
% 0.26/0.47 & ( Y
% 0.26/0.47 = ( zero_zero @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % zero_eq_add_iff_both_eq_0
% 0.26/0.47 thf(fact_205_add__eq__0__iff__both__eq__0,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( canoni770627133id_add @ A )
% 0.26/0.47 => ! [X: A,Y: A] :
% 0.26/0.47 ( ( ( plus_plus @ A @ X @ Y )
% 0.26/0.47 = ( zero_zero @ A ) )
% 0.26/0.47 = ( ( X
% 0.26/0.47 = ( zero_zero @ A ) )
% 0.26/0.47 & ( Y
% 0.26/0.47 = ( zero_zero @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % add_eq_0_iff_both_eq_0
% 0.26/0.47 thf(fact_206_add__cancel__right__right,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( cancel1352612707id_add @ A )
% 0.26/0.47 => ! [A2: A,B: A] :
% 0.26/0.47 ( ( A2
% 0.26/0.47 = ( plus_plus @ A @ A2 @ B ) )
% 0.26/0.47 = ( B
% 0.26/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % add_cancel_right_right
% 0.26/0.47 thf(fact_207_add__cancel__right__left,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( cancel1352612707id_add @ A )
% 0.26/0.47 => ! [A2: A,B: A] :
% 0.26/0.47 ( ( A2
% 0.26/0.47 = ( plus_plus @ A @ B @ A2 ) )
% 0.26/0.47 = ( B
% 0.26/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % add_cancel_right_left
% 0.26/0.47 thf(fact_208_add__cancel__left__right,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( cancel1352612707id_add @ A )
% 0.26/0.47 => ! [A2: A,B: A] :
% 0.26/0.47 ( ( ( plus_plus @ A @ A2 @ B )
% 0.26/0.47 = A2 )
% 0.26/0.47 = ( B
% 0.26/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % add_cancel_left_right
% 0.26/0.47 thf(fact_209_add__cancel__left__left,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( cancel1352612707id_add @ A )
% 0.26/0.47 => ! [B: A,A2: A] :
% 0.26/0.47 ( ( ( plus_plus @ A @ B @ A2 )
% 0.26/0.47 = A2 )
% 0.26/0.47 = ( B
% 0.26/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % add_cancel_left_left
% 0.26/0.47 thf(fact_210_double__zero__sym,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( linord219039673up_add @ A )
% 0.26/0.47 => ! [A2: A] :
% 0.26/0.47 ( ( ( zero_zero @ A )
% 0.26/0.47 = ( plus_plus @ A @ A2 @ A2 ) )
% 0.26/0.47 = ( A2
% 0.26/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % double_zero_sym
% 0.26/0.47 thf(fact_211_double__zero,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( linord219039673up_add @ A )
% 0.26/0.47 => ! [A2: A] :
% 0.26/0.47 ( ( ( plus_plus @ A @ A2 @ A2 )
% 0.26/0.47 = ( zero_zero @ A ) )
% 0.26/0.47 = ( A2
% 0.26/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % double_zero
% 0.26/0.47 thf(fact_212_add_Oright__neutral,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( monoid_add @ A )
% 0.26/0.47 => ! [A2: A] :
% 0.26/0.47 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 0.26/0.47 = A2 ) ) ).
% 0.26/0.47
% 0.26/0.47 % add.right_neutral
% 0.26/0.47 thf(fact_213_add_Oleft__neutral,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( monoid_add @ A )
% 0.26/0.47 => ! [A2: A] :
% 0.26/0.47 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.26/0.47 = A2 ) ) ).
% 0.26/0.47
% 0.26/0.47 % add.left_neutral
% 0.26/0.47 thf(fact_214_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( cancel1352612707id_add @ A )
% 0.26/0.47 => ! [A2: A] :
% 0.26/0.47 ( ( minus_minus @ A @ A2 @ A2 )
% 0.26/0.47 = ( zero_zero @ A ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % cancel_comm_monoid_add_class.diff_cancel
% 0.26/0.47 thf(fact_215_diff__zero,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( cancel1352612707id_add @ A )
% 0.26/0.47 => ! [A2: A] :
% 0.26/0.47 ( ( minus_minus @ A @ A2 @ ( zero_zero @ A ) )
% 0.26/0.47 = A2 ) ) ).
% 0.26/0.47
% 0.26/0.47 % diff_zero
% 0.26/0.47 thf(fact_216_zero__diff,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( comm_monoid_diff @ A )
% 0.26/0.47 => ! [A2: A] :
% 0.26/0.47 ( ( minus_minus @ A @ ( zero_zero @ A ) @ A2 )
% 0.26/0.47 = ( zero_zero @ A ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % zero_diff
% 0.26/0.47 thf(fact_217_diff__0__right,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( group_add @ A )
% 0.26/0.47 => ! [A2: A] :
% 0.26/0.47 ( ( minus_minus @ A @ A2 @ ( zero_zero @ A ) )
% 0.26/0.47 = A2 ) ) ).
% 0.26/0.47
% 0.26/0.47 % diff_0_right
% 0.26/0.47 thf(fact_218_diff__self,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( group_add @ A )
% 0.26/0.47 => ! [A2: A] :
% 0.26/0.47 ( ( minus_minus @ A @ A2 @ A2 )
% 0.26/0.47 = ( zero_zero @ A ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % diff_self
% 0.26/0.47 thf(fact_219_abs__zero,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordere142940540dd_abs @ A )
% 0.26/0.47 => ( ( abs_abs @ A @ ( zero_zero @ A ) )
% 0.26/0.47 = ( zero_zero @ A ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % abs_zero
% 0.26/0.47 thf(fact_220_abs__eq__0,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordere142940540dd_abs @ A )
% 0.26/0.47 => ! [A2: A] :
% 0.26/0.47 ( ( ( abs_abs @ A @ A2 )
% 0.26/0.47 = ( zero_zero @ A ) )
% 0.26/0.47 = ( A2
% 0.26/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % abs_eq_0
% 0.26/0.47 thf(fact_221_abs__0__eq,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordere142940540dd_abs @ A )
% 0.26/0.47 => ! [A2: A] :
% 0.26/0.47 ( ( ( zero_zero @ A )
% 0.26/0.47 = ( abs_abs @ A @ A2 ) )
% 0.26/0.47 = ( A2
% 0.26/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % abs_0_eq
% 0.26/0.47 thf(fact_222_abs__0,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( idom_abs_sgn @ A )
% 0.26/0.47 => ( ( abs_abs @ A @ ( zero_zero @ A ) )
% 0.26/0.47 = ( zero_zero @ A ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % abs_0
% 0.26/0.47 thf(fact_223_add__le__same__cancel1,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordere516151231imp_le @ A )
% 0.26/0.47 => ! [B: A,A2: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ B @ A2 ) @ B )
% 0.26/0.47 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % add_le_same_cancel1
% 0.26/0.47 thf(fact_224_add__le__same__cancel2,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordere516151231imp_le @ A )
% 0.26/0.47 => ! [A2: A,B: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B ) @ B )
% 0.26/0.47 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % add_le_same_cancel2
% 0.26/0.47 thf(fact_225_le__add__same__cancel1,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordere516151231imp_le @ A )
% 0.26/0.47 => ! [A2: A,B: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ A2 @ B ) )
% 0.26/0.47 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % le_add_same_cancel1
% 0.26/0.47 thf(fact_226_le__add__same__cancel2,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordere516151231imp_le @ A )
% 0.26/0.47 => ! [A2: A,B: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ B @ A2 ) )
% 0.26/0.47 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % le_add_same_cancel2
% 0.26/0.47 thf(fact_227_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( linord219039673up_add @ A )
% 0.26/0.47 => ! [A2: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ A2 ) @ ( zero_zero @ A ) )
% 0.26/0.47 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % double_add_le_zero_iff_single_add_le_zero
% 0.26/0.47 thf(fact_228_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( linord219039673up_add @ A )
% 0.26/0.47 => ! [A2: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ A2 ) )
% 0.26/0.47 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % zero_le_double_add_iff_zero_le_single_add
% 0.26/0.47 thf(fact_229_diff__ge__0__iff__ge,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordered_ab_group_add @ A )
% 0.26/0.47 => ! [A2: A,B: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( minus_minus @ A @ A2 @ B ) )
% 0.26/0.47 = ( ord_less_eq @ A @ B @ A2 ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % diff_ge_0_iff_ge
% 0.26/0.47 thf(fact_230_diff__add__zero,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( comm_monoid_diff @ A )
% 0.26/0.47 => ! [A2: A,B: A] :
% 0.26/0.47 ( ( minus_minus @ A @ A2 @ ( plus_plus @ A @ A2 @ B ) )
% 0.26/0.47 = ( zero_zero @ A ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % diff_add_zero
% 0.26/0.47 thf(fact_231_abs__of__nonneg,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordere142940540dd_abs @ A )
% 0.26/0.47 => ! [A2: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.26/0.47 => ( ( abs_abs @ A @ A2 )
% 0.26/0.47 = A2 ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % abs_of_nonneg
% 0.26/0.47 thf(fact_232_abs__le__self__iff,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordere142940540dd_abs @ A )
% 0.26/0.47 => ! [A2: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ ( abs_abs @ A @ A2 ) @ A2 )
% 0.26/0.47 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % abs_le_self_iff
% 0.26/0.47 thf(fact_233_abs__le__zero__iff,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordere142940540dd_abs @ A )
% 0.26/0.47 => ! [A2: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ ( abs_abs @ A @ A2 ) @ ( zero_zero @ A ) )
% 0.26/0.47 = ( A2
% 0.26/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % abs_le_zero_iff
% 0.26/0.47 thf(fact_234_zero__le,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( canoni770627133id_add @ A )
% 0.26/0.47 => ! [X: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X ) ) ).
% 0.26/0.47
% 0.26/0.47 % zero_le
% 0.26/0.47 thf(fact_235_diff__commute,axiom,
% 0.26/0.47 ! [I: nat,J: nat,K: nat] :
% 0.26/0.47 ( ( minus_minus @ nat @ ( minus_minus @ nat @ I @ J ) @ K )
% 0.26/0.47 = ( minus_minus @ nat @ ( minus_minus @ nat @ I @ K ) @ J ) ) ).
% 0.26/0.47
% 0.26/0.47 % diff_commute
% 0.26/0.47 thf(fact_236_zero__reorient,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( zero @ A )
% 0.26/0.47 => ! [X: A] :
% 0.26/0.47 ( ( ( zero_zero @ A )
% 0.26/0.47 = X )
% 0.26/0.47 = ( X
% 0.26/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % zero_reorient
% 0.26/0.47 thf(fact_237_abs__eq__0__iff,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( idom_abs_sgn @ A )
% 0.26/0.47 => ! [A2: A] :
% 0.26/0.47 ( ( ( abs_abs @ A @ A2 )
% 0.26/0.47 = ( zero_zero @ A ) )
% 0.26/0.47 = ( A2
% 0.26/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % abs_eq_0_iff
% 0.26/0.47 thf(fact_238_eq__iff__diff__eq__0,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( group_add @ A )
% 0.26/0.47 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 0.26/0.47 = ( ^ [A3: A,B2: A] :
% 0.26/0.47 ( ( minus_minus @ A @ A3 @ B2 )
% 0.26/0.47 = ( zero_zero @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % eq_iff_diff_eq_0
% 0.26/0.47 thf(fact_239_zero__neq__one,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( zero_neq_one @ A )
% 0.26/0.47 => ( ( zero_zero @ A )
% 0.26/0.47 != ( one_one @ A ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % zero_neq_one
% 0.26/0.47 thf(fact_240_add_Ogroup__left__neutral,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( group_add @ A )
% 0.26/0.47 => ! [A2: A] :
% 0.26/0.47 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.26/0.47 = A2 ) ) ).
% 0.26/0.47
% 0.26/0.47 % add.group_left_neutral
% 0.26/0.47 thf(fact_241_add_Ocomm__neutral,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( comm_monoid_add @ A )
% 0.26/0.47 => ! [A2: A] :
% 0.26/0.47 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 0.26/0.47 = A2 ) ) ).
% 0.26/0.47
% 0.26/0.47 % add.comm_neutral
% 0.26/0.47 thf(fact_242_comm__monoid__add__class_Oadd__0,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( comm_monoid_add @ A )
% 0.26/0.47 => ! [A2: A] :
% 0.26/0.47 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.26/0.47 = A2 ) ) ).
% 0.26/0.47
% 0.26/0.47 % comm_monoid_add_class.add_0
% 0.26/0.47 thf(fact_243_add__decreasing,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordere216010020id_add @ A )
% 0.26/0.47 => ! [A2: A,C: A,B: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.26/0.47 => ( ( ord_less_eq @ A @ C @ B )
% 0.26/0.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ B ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % add_decreasing
% 0.26/0.47 thf(fact_244_add__increasing,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordere216010020id_add @ A )
% 0.26/0.47 => ! [A2: A,B: A,C: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.26/0.47 => ( ( ord_less_eq @ A @ B @ C )
% 0.26/0.47 => ( ord_less_eq @ A @ B @ ( plus_plus @ A @ A2 @ C ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % add_increasing
% 0.26/0.47 thf(fact_245_add__decreasing2,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordere216010020id_add @ A )
% 0.26/0.47 => ! [C: A,A2: A,B: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ C @ ( zero_zero @ A ) )
% 0.26/0.47 => ( ( ord_less_eq @ A @ A2 @ B )
% 0.26/0.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ B ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % add_decreasing2
% 0.26/0.47 thf(fact_246_add__increasing2,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordere216010020id_add @ A )
% 0.26/0.47 => ! [C: A,B: A,A2: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 0.26/0.47 => ( ( ord_less_eq @ A @ B @ A2 )
% 0.26/0.47 => ( ord_less_eq @ A @ B @ ( plus_plus @ A @ A2 @ C ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % add_increasing2
% 0.26/0.47 thf(fact_247_add__nonneg__nonneg,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordere216010020id_add @ A )
% 0.26/0.47 => ! [A2: A,B: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.26/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B )
% 0.26/0.47 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ B ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % add_nonneg_nonneg
% 0.26/0.47 thf(fact_248_add__nonpos__nonpos,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordere216010020id_add @ A )
% 0.26/0.47 => ! [A2: A,B: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.26/0.47 => ( ( ord_less_eq @ A @ B @ ( zero_zero @ A ) )
% 0.26/0.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % add_nonpos_nonpos
% 0.26/0.47 thf(fact_249_add__nonneg__eq__0__iff,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordere216010020id_add @ A )
% 0.26/0.47 => ! [X: A,Y: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X )
% 0.26/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ Y )
% 0.26/0.47 => ( ( ( plus_plus @ A @ X @ Y )
% 0.26/0.47 = ( zero_zero @ A ) )
% 0.26/0.47 = ( ( X
% 0.26/0.47 = ( zero_zero @ A ) )
% 0.26/0.47 & ( Y
% 0.26/0.47 = ( zero_zero @ A ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % add_nonneg_eq_0_iff
% 0.26/0.47 thf(fact_250_add__nonpos__eq__0__iff,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordere216010020id_add @ A )
% 0.26/0.47 => ! [X: A,Y: A] :
% 0.26/0.47 ( ( ord_less_eq @ A @ X @ ( zero_zero @ A ) )
% 0.26/0.47 => ( ( ord_less_eq @ A @ Y @ ( zero_zero @ A ) )
% 0.26/0.47 => ( ( ( plus_plus @ A @ X @ Y )
% 0.26/0.47 = ( zero_zero @ A ) )
% 0.26/0.47 = ( ( X
% 0.26/0.47 = ( zero_zero @ A ) )
% 0.26/0.47 & ( Y
% 0.26/0.47 = ( zero_zero @ A ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % add_nonpos_eq_0_iff
% 0.26/0.47 thf(fact_251_zero__le__one,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( linord1659791738miring @ A )
% 0.26/0.47 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % zero_le_one
% 0.26/0.47 thf(fact_252_not__one__le__zero,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( linord1659791738miring @ A )
% 0.26/0.47 => ~ ( ord_less_eq @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % not_one_le_zero
% 0.26/0.47 thf(fact_253_le__iff__diff__le__0,axiom,
% 0.26/0.47 ! [A: $tType] :
% 0.26/0.47 ( ( ordered_ab_group_add @ A )
% 0.26/0.47 => ( ( ord_less_eq @ A )
% 0.26/0.47 = ( ^ [A3: A,B2: A] : ( ord_less_eq @ A @ ( minus_minus @ A @ A3 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 % le_iff_diff_le_0
% 0.26/0.47
% 0.26/0.47 % Type constructors (61)
% 0.26/0.47 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.26/0.47 ! [A7: $tType,A8: $tType] :
% 0.26/0.47 ( ( preorder @ A8 )
% 0.26/0.47 => ( preorder @ ( A7 > A8 ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.26/0.47 ! [A7: $tType,A8: $tType] :
% 0.26/0.47 ( ( order @ A8 )
% 0.26/0.47 => ( order @ ( A7 > A8 ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_fun___Orderings_Oord,axiom,
% 0.26/0.47 ! [A7: $tType,A8: $tType] :
% 0.26/0.47 ( ( ord @ A8 )
% 0.26/0.47 => ( ord @ ( A7 > A8 ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_fun___Groups_Ominus,axiom,
% 0.26/0.47 ! [A7: $tType,A8: $tType] :
% 0.26/0.47 ( ( minus @ A8 )
% 0.26/0.47 => ( minus @ ( A7 > A8 ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le,axiom,
% 0.26/0.47 ordere516151231imp_le @ nat ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Nat_Onat___Groups_Oordered__cancel__comm__monoid__diff,axiom,
% 0.26/0.47 ordere623563068d_diff @ nat ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 0.26/0.47 ordere236663937imp_le @ nat ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.26/0.47 canoni770627133id_add @ nat ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring,axiom,
% 0.26/0.47 linord1659791738miring @ nat ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
% 0.26/0.47 ordere779506340up_add @ nat ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Nat_Onat___Groups_Oordered__comm__monoid__add,axiom,
% 0.26/0.47 ordere216010020id_add @ nat ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
% 0.26/0.47 cancel146912293up_add @ nat ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add,axiom,
% 0.26/0.47 cancel1352612707id_add @ nat ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
% 0.26/0.47 cancel_semigroup_add @ nat ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Nat_Onat___Rings_Olinordered__semidom,axiom,
% 0.26/0.47 linordered_semidom @ nat ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__diff,axiom,
% 0.26/0.47 comm_monoid_diff @ nat ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add,axiom,
% 0.26/0.47 ab_semigroup_add @ nat ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
% 0.26/0.47 comm_monoid_add @ nat ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Nat_Onat___Groups_Osemigroup__add,axiom,
% 0.26/0.47 semigroup_add @ nat ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Nat_Onat___Rings_Ozero__neq__one,axiom,
% 0.26/0.47 zero_neq_one @ nat ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 0.26/0.47 preorder @ nat ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.26/0.47 linorder @ nat ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Nat_Onat___Groups_Omonoid__add,axiom,
% 0.26/0.47 monoid_add @ nat ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 0.26/0.47 order @ nat ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 0.26/0.47 ord @ nat ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Nat_Onat___Groups_Ominus_4,axiom,
% 0.26/0.47 minus @ nat ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 0.26/0.47 zero @ nat ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 0.26/0.47 one @ nat ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_HOL_Obool___Orderings_Opreorder_5,axiom,
% 0.26/0.47 preorder @ $o ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_HOL_Obool___Orderings_Olinorder_6,axiom,
% 0.26/0.47 linorder @ $o ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_HOL_Obool___Orderings_Oorder_7,axiom,
% 0.26/0.47 order @ $o ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_HOL_Obool___Orderings_Oord_8,axiom,
% 0.26/0.47 ord @ $o ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_HOL_Obool___Groups_Ominus_9,axiom,
% 0.26/0.47 minus @ $o ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__monoid__add__imp__le_10,axiom,
% 0.26/0.47 ordere516151231imp_le @ real ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le_11,axiom,
% 0.26/0.47 ordere236663937imp_le @ real ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_12,axiom,
% 0.26/0.47 linord1659791738miring @ real ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add_13,axiom,
% 0.26/0.47 ordere779506340up_add @ real ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Groups_Oordered__ab__group__add__abs,axiom,
% 0.26/0.47 ordere142940540dd_abs @ real ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Groups_Oordered__comm__monoid__add_14,axiom,
% 0.26/0.47 ordere216010020id_add @ real ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Groups_Olinordered__ab__group__add,axiom,
% 0.26/0.47 linord219039673up_add @ real ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Groups_Ocancel__ab__semigroup__add_15,axiom,
% 0.26/0.47 cancel146912293up_add @ real ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add_16,axiom,
% 0.26/0.47 cancel1352612707id_add @ real ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Groups_Oordered__ab__group__add,axiom,
% 0.26/0.47 ordered_ab_group_add @ real ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Groups_Ocancel__semigroup__add_17,axiom,
% 0.26/0.47 cancel_semigroup_add @ real ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Rings_Olinordered__semidom_18,axiom,
% 0.26/0.47 linordered_semidom @ real ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Groups_Oab__semigroup__add_19,axiom,
% 0.26/0.47 ab_semigroup_add @ real ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Groups_Ocomm__monoid__add_20,axiom,
% 0.26/0.47 comm_monoid_add @ real ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Rings_Olinordered__idom,axiom,
% 0.26/0.47 linordered_idom @ real ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Groups_Osemigroup__add_21,axiom,
% 0.26/0.47 semigroup_add @ real ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Groups_Oab__group__add,axiom,
% 0.26/0.47 ab_group_add @ real ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Rings_Ozero__neq__one_22,axiom,
% 0.26/0.47 zero_neq_one @ real ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Rings_Oidom__abs__sgn,axiom,
% 0.26/0.47 idom_abs_sgn @ real ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Orderings_Opreorder_23,axiom,
% 0.26/0.47 preorder @ real ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Orderings_Olinorder_24,axiom,
% 0.26/0.47 linorder @ real ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Groups_Omonoid__add_25,axiom,
% 0.26/0.47 monoid_add @ real ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Groups_Ogroup__add,axiom,
% 0.26/0.47 group_add @ real ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Orderings_Oorder_26,axiom,
% 0.26/0.47 order @ real ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Orderings_Oord_27,axiom,
% 0.26/0.47 ord @ real ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Groups_Ominus_28,axiom,
% 0.26/0.47 minus @ real ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Groups_Ozero_29,axiom,
% 0.26/0.47 zero @ real ).
% 0.26/0.47
% 0.26/0.47 thf(tcon_Real_Oreal___Groups_Oone_30,axiom,
% 0.26/0.47 one @ real ).
% 0.26/0.47
% 0.26/0.47 % Helper facts (3)
% 0.26/0.47 thf(help_If_3_1_T,axiom,
% 0.26/0.47 ! [P3: $o] :
% 0.26/0.47 ( ( P3 = $true )
% 0.26/0.47 | ( P3 = $false ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(help_If_2_1_T,axiom,
% 0.26/0.47 ! [A: $tType,X: A,Y: A] :
% 0.26/0.47 ( ( if @ A @ $false @ X @ Y )
% 0.26/0.47 = Y ) ).
% 0.26/0.47
% 0.26/0.47 thf(help_If_1_1_T,axiom,
% 0.26/0.47 ! [A: $tType,X: A,Y: A] :
% 0.26/0.47 ( ( if @ A @ $true @ X @ Y )
% 0.26/0.47 = X ) ).
% 0.26/0.47
% 0.26/0.47 % Conjectures (1)
% 0.26/0.47 thf(conj_0,conjecture,
% 0.26/0.47 genClo1015804716orrect @ m @ ( ord_max @ real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) ).
% 0.26/0.47
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 ------------------------
% 2.71/1.43 ---- Embedded in THF ---
% 2.71/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.71/1.43 %%% Generated on Tue Feb 24 08:25:16 EST 2026
% 2.71/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 2.71/1.43 %%% Logic specification used:
% 2.71/1.43 %%% thf(spec, logic, $$dhol).
% 2.71/1.43
% 2.71/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Kaf6658Iwd/DTF2DTF740.p
% See solution above
% 2.71/1.43 ------------------------
% 2.71/1.46 ---- Cleaned THF ---
% 2.71/1.46 thf(ty_t_Real_Oreal,type,
% 2.71/1.46 real: $tType ).
% 2.71/1.46
% 2.71/1.46 thf(ty_t_Nat_Onat,type,
% 2.71/1.46 nat: $tType ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_HOL_Otype,type,
% 2.71/1.46 type:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Groups_Oone,type,
% 2.71/1.46 one:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Groups_Ozero,type,
% 2.71/1.46 zero:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Groups_Ominus,type,
% 2.71/1.46 minus:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Orderings_Oord,type,
% 2.71/1.46 ord:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Orderings_Oorder,type,
% 2.71/1.46 order:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Groups_Ogroup__add,type,
% 2.71/1.46 group_add:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Groups_Omonoid__add,type,
% 2.71/1.46 monoid_add:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Orderings_Olinorder,type,
% 2.71/1.46 linorder:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Orderings_Opreorder,type,
% 2.71/1.46 preorder:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Rings_Oidom__abs__sgn,type,
% 2.71/1.46 idom_abs_sgn:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Rings_Ozero__neq__one,type,
% 2.71/1.46 zero_neq_one:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Groups_Oab__group__add,type,
% 2.71/1.46 ab_group_add:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Groups_Osemigroup__add,type,
% 2.71/1.46 semigroup_add:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Rings_Olinordered__idom,type,
% 2.71/1.46 linordered_idom:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 2.71/1.46 comm_monoid_add:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 2.71/1.46 ab_semigroup_add:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Groups_Ocomm__monoid__diff,type,
% 2.71/1.46 comm_monoid_diff:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Rings_Olinordered__semidom,type,
% 2.71/1.46 linordered_semidom:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 2.71/1.46 cancel_semigroup_add:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 2.71/1.46 ordered_ab_group_add:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 2.71/1.46 cancel1352612707id_add:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 2.71/1.46 cancel146912293up_add:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 2.71/1.46 linord219039673up_add:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Groups_Oordered__comm__monoid__add,type,
% 2.71/1.46 ordere216010020id_add:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Groups_Oordered__ab__group__add__abs,type,
% 2.71/1.46 ordere142940540dd_abs:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 2.71/1.46 ordere779506340up_add:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 2.71/1.46 linord1659791738miring:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 2.71/1.46 canoni770627133id_add:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 2.71/1.46 ordere236663937imp_le:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Groups_Oordered__cancel__comm__monoid__diff,type,
% 2.71/1.46 ordere623563068d_diff:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le,type,
% 2.71/1.46 ordere516151231imp_le:
% 2.71/1.46 !>[A: $tType] : $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_c_GenClock__Mirabelle__pukziqipvs_OIC,type,
% 2.71/1.46 genClo1160817912lle_IC: nat > nat > real > real ).
% 2.71/1.46
% 2.71/1.46 thf(sy_c_GenClock__Mirabelle__pukziqipvs_O_092_060Lambda_062,type,
% 2.71/1.46 genClo721845095Lambda: real ).
% 2.71/1.46
% 2.71/1.46 thf(sy_c_GenClock__Mirabelle__pukziqipvs_O_092_060beta_062,type,
% 2.71/1.46 genClo1278781456e_beta: real ).
% 2.71/1.46
% 2.71/1.46 thf(sy_c_GenClock__Mirabelle__pukziqipvs_O_092_060theta_062,type,
% 2.71/1.46 genClo1400225944_theta: nat > nat > nat > real ).
% 2.71/1.46
% 2.71/1.46 thf(sy_c_GenClock__Mirabelle__pukziqipvs_Ocorrect,type,
% 2.71/1.46 genClo1015804716orrect: nat > real > $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_c_GenClock__Mirabelle__pukziqipvs_OokRead1,type,
% 2.71/1.46 genClo293725281kRead1: ( nat > real ) > real > ( nat > $o ) > $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_c_GenClock__Mirabelle__pukziqipvs_OokRead2,type,
% 2.71/1.46 genClo293725282kRead2: ( nat > real ) > ( nat > real ) > real > ( nat > $o ) > $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_c_GenClock__Mirabelle__pukziqipvs_Ookmaxsync,type,
% 2.71/1.46 genClo208577157axsync: nat > real > $o ).
% 2.71/1.46
% 2.71/1.46 thf(sy_c_GenClock__Mirabelle__pukziqipvs_Ormax,type,
% 2.71/1.46 genClo1650508560e_rmax: real ).
% 2.71/1.46
% 2.71/1.46 thf(sy_c_GenClock__Mirabelle__pukziqipvs_Ormin,type,
% 2.71/1.46 genClo1651033342e_rmin: real ).
% 2.71/1.46
% 2.71/1.46 thf(sy_c_GenClock__Mirabelle__pukziqipvs_Ote,type,
% 2.71/1.46 genClo1163638703lle_te: nat > nat > real ).
% 2.71/1.46
% 2.71/1.46 thf(sy_c_Groups_Oabs__class_Oabs,type,
% 2.71/1.46 abs_abs:
% 2.71/1.46 !>[A: $tType] : ( A > A ) ).
% 2.71/1.46
% 2.71/1.46 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 2.71/1.46 minus_minus:
% 2.71/1.46 !>[A: $tType] : ( A > A > A ) ).
% 2.71/1.46
% 2.71/1.46 thf(sy_c_Groups_Oone__class_Oone,type,
% 2.71/1.46 one_one:
% 2.71/1.46 !>[A: $tType] : A ).
% 2.71/1.46
% 2.71/1.46 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 2.71/1.46 plus_plus:
% 2.71/1.46 !>[A: $tType] : ( A > A > A ) ).
% 2.71/1.46
% 2.71/1.46 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 2.71/1.46 zero_zero:
% 2.71/1.46 !>[A: $tType] : A ).
% 2.71/1.46
% 2.71/1.46 thf(sy_c_If,type,
% 2.71/1.46 if:
% 2.71/1.46 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.71/1.46
% 2.71/1.46 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.71/1.46 ord_less_eq:
% 2.71/1.46 !>[A: $tType] : ( A > A > $o ) ).
% 2.71/1.46
% 2.71/1.46 thf(sy_c_Orderings_Oord__class_Omax,type,
% 2.71/1.46 ord_max:
% 2.71/1.46 !>[A: $tType] : ( A > A > A ) ).
% 2.71/1.46
% 2.71/1.46 thf(sy_v__092_060delta_062S,type,
% 2.71/1.46 delta_S: real ).
% 2.71/1.46
% 2.71/1.46 thf(sy_v_i,type,
% 2.71/1.46 i: nat ).
% 2.71/1.46
% 2.71/1.46 thf(sy_v_l,type,
% 2.71/1.46 l: nat ).
% 2.71/1.46
% 2.71/1.46 thf(sy_v_m,type,
% 2.71/1.46 m: nat ).
% 2.71/1.46
% 2.71/1.46 thf(sy_v_p,type,
% 2.71/1.46 p: nat ).
% 2.71/1.46
% 2.71/1.46 thf(fact_0_correct__closed,axiom,
% 2.71/1.46 ! [P: nat,S: real,T: real] :
% 2.71/1.46 ( ( ( ord_less_eq @ real @ S @ T )
% 2.71/1.46 & ( genClo1015804716orrect @ P @ T ) )
% 2.71/1.46 => ( genClo1015804716orrect @ P @ S ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_1_corr__m,axiom,
% 2.71/1.46 genClo1015804716orrect @ m @ ( genClo1163638703lle_te @ p @ ( plus_plus @ nat @ i @ ( one_one @ nat ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_2_corr__p,axiom,
% 2.71/1.46 genClo1015804716orrect @ p @ ( genClo1163638703lle_te @ p @ ( plus_plus @ nat @ i @ ( one_one @ nat ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_3_tml__le__tp,axiom,
% 2.71/1.46 ord_less_eq @ real @ ( ord_max @ real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) @ ( genClo1163638703lle_te @ p @ ( plus_plus @ nat @ i @ ( one_one @ nat ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_4_corr__l,axiom,
% 2.71/1.46 genClo1015804716orrect @ l @ ( genClo1163638703lle_te @ p @ ( plus_plus @ nat @ i @ ( one_one @ nat ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_5_corr__l__tml,axiom,
% 2.71/1.46 genClo1015804716orrect @ l @ ( ord_max @ real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_6_tmi__le__tp,axiom,
% 2.71/1.46 ord_less_eq @ real @ ( genClo1163638703lle_te @ m @ i ) @ ( genClo1163638703lle_te @ p @ ( plus_plus @ nat @ i @ ( one_one @ nat ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_7_tli__le__tp,axiom,
% 2.71/1.46 ord_less_eq @ real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ p @ ( plus_plus @ nat @ i @ ( one_one @ nat ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_8_max_Oidem,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linorder @ A )
% 2.71/1.46 => ! [A2: A] :
% 2.71/1.46 ( ( ord_max @ A @ A2 @ A2 )
% 2.71/1.46 = A2 ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_9_max_Oleft__idem,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linorder @ A )
% 2.71/1.46 => ! [A2: A,B: A] :
% 2.71/1.46 ( ( ord_max @ A @ A2 @ ( ord_max @ A @ A2 @ B ) )
% 2.71/1.46 = ( ord_max @ A @ A2 @ B ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_10_max_Oright__idem,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linorder @ A )
% 2.71/1.46 => ! [A2: A,B: A] :
% 2.71/1.46 ( ( ord_max @ A @ ( ord_max @ A @ A2 @ B ) @ B )
% 2.71/1.46 = ( ord_max @ A @ A2 @ B ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_11_IC__bound,axiom,
% 2.71/1.46 ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ ( genClo1160817912lle_IC @ l @ i @ ( ord_max @ real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) ) @ ( genClo1160817912lle_IC @ m @ i @ ( ord_max @ real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) ) ) ) @ delta_S ).
% 2.71/1.46
% 2.71/1.46 thf(fact_12_max_Oassoc,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linorder @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A] :
% 2.71/1.46 ( ( ord_max @ A @ ( ord_max @ A @ A2 @ B ) @ C )
% 2.71/1.46 = ( ord_max @ A @ A2 @ ( ord_max @ A @ B @ C ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_13_max_Ocommute,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linorder @ A )
% 2.71/1.46 => ( ( ord_max @ A )
% 2.71/1.46 = ( ^ [A3: A,B2: A] : ( ord_max @ A @ B2 @ A3 ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_14_max_Oleft__commute,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linorder @ A )
% 2.71/1.46 => ! [B: A,A2: A,C: A] :
% 2.71/1.46 ( ( ord_max @ A @ B @ ( ord_max @ A @ A2 @ C ) )
% 2.71/1.46 = ( ord_max @ A @ A2 @ ( ord_max @ A @ B @ C ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_15_rte,axiom,
% 2.71/1.46 ! [P2: nat,I: nat] :
% 2.71/1.46 ( ( genClo1015804716orrect @ P2 @ ( genClo1163638703lle_te @ P2 @ ( plus_plus @ nat @ I @ ( one_one @ nat ) ) ) )
% 2.71/1.46 => ( ord_less_eq @ real @ ( genClo1163638703lle_te @ P2 @ I ) @ ( genClo1163638703lle_te @ P2 @ ( plus_plus @ nat @ I @ ( one_one @ nat ) ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_16_max_Obounded__iff,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linorder @ A )
% 2.71/1.46 => ! [B: A,C: A,A2: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ ( ord_max @ A @ B @ C ) @ A2 )
% 2.71/1.46 = ( ( ord_less_eq @ A @ B @ A2 )
% 2.71/1.46 & ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_17_max__absorb1,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( order @ A )
% 2.71/1.46 => ! [Y: A,X: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ Y @ X )
% 2.71/1.46 => ( ( ord_max @ A @ X @ Y )
% 2.71/1.46 = X ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_18_order__refl,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( preorder @ A )
% 2.71/1.46 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_19_minus__apply,axiom,
% 2.71/1.46 ! [B3: $tType,A: $tType] :
% 2.71/1.46 ( ( minus @ B3 )
% 2.71/1.46 => ( ( minus_minus @ ( A > B3 ) )
% 2.71/1.46 = ( ^ [A4: A > B3,B4: A > B3,X2: A] : ( minus_minus @ B3 @ ( A4 @ X2 ) @ ( B4 @ X2 ) ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_20_le__funD,axiom,
% 2.71/1.46 ! [B3: $tType,A: $tType] :
% 2.71/1.46 ( ( ord @ B3 )
% 2.71/1.46 => ! [F: A > B3,G: A > B3,X: A] :
% 2.71/1.46 ( ( ord_less_eq @ ( A > B3 ) @ F @ G )
% 2.71/1.46 => ( ord_less_eq @ B3 @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_21_le__funE,axiom,
% 2.71/1.46 ! [B3: $tType,A: $tType] :
% 2.71/1.46 ( ( ord @ B3 )
% 2.71/1.46 => ! [F: A > B3,G: A > B3,X: A] :
% 2.71/1.46 ( ( ord_less_eq @ ( A > B3 ) @ F @ G )
% 2.71/1.46 => ( ord_less_eq @ B3 @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_22_le__funI,axiom,
% 2.71/1.46 ! [B3: $tType,A: $tType] :
% 2.71/1.46 ( ( ord @ B3 )
% 2.71/1.46 => ! [F: A > B3,G: A > B3] :
% 2.71/1.46 ( ! [X3: A] : ( ord_less_eq @ B3 @ ( F @ X3 ) @ ( G @ X3 ) )
% 2.71/1.46 => ( ord_less_eq @ ( A > B3 ) @ F @ G ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_23_le__fun__def,axiom,
% 2.71/1.46 ! [B3: $tType,A: $tType] :
% 2.71/1.46 ( ( ord @ B3 )
% 2.71/1.46 => ( ( ord_less_eq @ ( A > B3 ) )
% 2.71/1.46 = ( ^ [F2: A > B3,G2: A > B3] :
% 2.71/1.46 ! [X2: A] : ( ord_less_eq @ B3 @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_24_fun__diff__def,axiom,
% 2.71/1.46 ! [B3: $tType,A: $tType] :
% 2.71/1.46 ( ( minus @ B3 )
% 2.71/1.46 => ( ( minus_minus @ ( A > B3 ) )
% 2.71/1.46 = ( ^ [A4: A > B3,B4: A > B3,X2: A] : ( minus_minus @ B3 @ ( A4 @ X2 ) @ ( B4 @ X2 ) ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_25_order__subst1,axiom,
% 2.71/1.46 ! [A: $tType,B3: $tType] :
% 2.71/1.46 ( ( ( order @ B3 )
% 2.71/1.46 & ( order @ A ) )
% 2.71/1.46 => ! [A2: A,F: B3 > A,B: B3,C: B3] :
% 2.71/1.46 ( ( ord_less_eq @ A @ A2 @ ( F @ B ) )
% 2.71/1.46 => ( ( ord_less_eq @ B3 @ B @ C )
% 2.71/1.46 => ( ! [X3: B3,Y2: B3] :
% 2.71/1.46 ( ( ord_less_eq @ B3 @ X3 @ Y2 )
% 2.71/1.46 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 2.71/1.46 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_26_order__subst2,axiom,
% 2.71/1.46 ! [A: $tType,C2: $tType] :
% 2.71/1.46 ( ( ( order @ C2 )
% 2.71/1.46 & ( order @ A ) )
% 2.71/1.46 => ! [A2: A,B: A,F: A > C2,C: C2] :
% 2.71/1.46 ( ( ord_less_eq @ A @ A2 @ B )
% 2.71/1.46 => ( ( ord_less_eq @ C2 @ ( F @ B ) @ C )
% 2.71/1.46 => ( ! [X3: A,Y2: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 2.71/1.46 => ( ord_less_eq @ C2 @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 2.71/1.46 => ( ord_less_eq @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_27_ord__eq__le__subst,axiom,
% 2.71/1.46 ! [A: $tType,B3: $tType] :
% 2.71/1.46 ( ( ( ord @ B3 )
% 2.71/1.46 & ( ord @ A ) )
% 2.71/1.46 => ! [A2: A,F: B3 > A,B: B3,C: B3] :
% 2.71/1.46 ( ( A2
% 2.71/1.46 = ( F @ B ) )
% 2.71/1.46 => ( ( ord_less_eq @ B3 @ B @ C )
% 2.71/1.46 => ( ! [X3: B3,Y2: B3] :
% 2.71/1.46 ( ( ord_less_eq @ B3 @ X3 @ Y2 )
% 2.71/1.46 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 2.71/1.46 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_28_ord__le__eq__subst,axiom,
% 2.71/1.46 ! [A: $tType,B3: $tType] :
% 2.71/1.46 ( ( ( ord @ B3 )
% 2.71/1.46 & ( ord @ A ) )
% 2.71/1.46 => ! [A2: A,B: A,F: A > B3,C: B3] :
% 2.71/1.46 ( ( ord_less_eq @ A @ A2 @ B )
% 2.71/1.46 => ( ( ( F @ B )
% 2.71/1.46 = C )
% 2.71/1.46 => ( ! [X3: A,Y2: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 2.71/1.46 => ( ord_less_eq @ B3 @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 2.71/1.46 => ( ord_less_eq @ B3 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_29_eq__iff,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( order @ A )
% 2.71/1.46 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 2.71/1.46 = ( ^ [X2: A,Y4: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ X2 @ Y4 )
% 2.71/1.46 & ( ord_less_eq @ A @ Y4 @ X2 ) ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_30_antisym,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( order @ A )
% 2.71/1.46 => ! [X: A,Y: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ X @ Y )
% 2.71/1.46 => ( ( ord_less_eq @ A @ Y @ X )
% 2.71/1.46 => ( X = Y ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_31_linear,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linorder @ A )
% 2.71/1.46 => ! [X: A,Y: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ X @ Y )
% 2.71/1.46 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_32_eq__refl,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( preorder @ A )
% 2.71/1.46 => ! [X: A,Y: A] :
% 2.71/1.46 ( ( X = Y )
% 2.71/1.46 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_33_le__cases,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linorder @ A )
% 2.71/1.46 => ! [X: A,Y: A] :
% 2.71/1.46 ( ~ ( ord_less_eq @ A @ X @ Y )
% 2.71/1.46 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_34_order_Otrans,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( order @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ A2 @ B )
% 2.71/1.46 => ( ( ord_less_eq @ A @ B @ C )
% 2.71/1.46 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_35_le__cases3,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linorder @ A )
% 2.71/1.46 => ! [X: A,Y: A,Z2: A] :
% 2.71/1.46 ( ( ( ord_less_eq @ A @ X @ Y )
% 2.71/1.46 => ~ ( ord_less_eq @ A @ Y @ Z2 ) )
% 2.71/1.46 => ( ( ( ord_less_eq @ A @ Y @ X )
% 2.71/1.46 => ~ ( ord_less_eq @ A @ X @ Z2 ) )
% 2.71/1.46 => ( ( ( ord_less_eq @ A @ X @ Z2 )
% 2.71/1.46 => ~ ( ord_less_eq @ A @ Z2 @ Y ) )
% 2.71/1.46 => ( ( ( ord_less_eq @ A @ Z2 @ Y )
% 2.71/1.46 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 2.71/1.46 => ( ( ( ord_less_eq @ A @ Y @ Z2 )
% 2.71/1.46 => ~ ( ord_less_eq @ A @ Z2 @ X ) )
% 2.71/1.46 => ~ ( ( ord_less_eq @ A @ Z2 @ X )
% 2.71/1.46 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_36_antisym__conv,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( order @ A )
% 2.71/1.46 => ! [Y: A,X: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ Y @ X )
% 2.71/1.46 => ( ( ord_less_eq @ A @ X @ Y )
% 2.71/1.46 = ( X = Y ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_37_order__class_Oorder_Oeq__iff,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( order @ A )
% 2.71/1.46 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 2.71/1.46 = ( ^ [A3: A,B2: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ A3 @ B2 )
% 2.71/1.46 & ( ord_less_eq @ A @ B2 @ A3 ) ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_38_ord__eq__le__trans,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ord @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A] :
% 2.71/1.46 ( ( A2 = B )
% 2.71/1.46 => ( ( ord_less_eq @ A @ B @ C )
% 2.71/1.46 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_39_ord__le__eq__trans,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ord @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ A2 @ B )
% 2.71/1.46 => ( ( B = C )
% 2.71/1.46 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_40_order__class_Oorder_Oantisym,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( order @ A )
% 2.71/1.46 => ! [A2: A,B: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ A2 @ B )
% 2.71/1.46 => ( ( ord_less_eq @ A @ B @ A2 )
% 2.71/1.46 => ( A2 = B ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_41_order__trans,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( preorder @ A )
% 2.71/1.46 => ! [X: A,Y: A,Z2: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ X @ Y )
% 2.71/1.46 => ( ( ord_less_eq @ A @ Y @ Z2 )
% 2.71/1.46 => ( ord_less_eq @ A @ X @ Z2 ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_42_dual__order_Orefl,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( order @ A )
% 2.71/1.46 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_43_linorder__wlog,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linorder @ A )
% 2.71/1.46 => ! [P3: A > A > $o,A2: A,B: A] :
% 2.71/1.46 ( ! [A5: A,B5: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ A5 @ B5 )
% 2.71/1.46 => ( P3 @ A5 @ B5 ) )
% 2.71/1.46 => ( ! [A5: A,B5: A] :
% 2.71/1.46 ( ( P3 @ B5 @ A5 )
% 2.71/1.46 => ( P3 @ A5 @ B5 ) )
% 2.71/1.46 => ( P3 @ A2 @ B ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_44_dual__order_Otrans,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( order @ A )
% 2.71/1.46 => ! [B: A,A2: A,C: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ B @ A2 )
% 2.71/1.46 => ( ( ord_less_eq @ A @ C @ B )
% 2.71/1.46 => ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_45_ext,axiom,
% 2.71/1.46 ! [B3: $tType,A: $tType,F: A > B3,G: A > B3] :
% 2.71/1.46 ( ! [X3: A] :
% 2.71/1.46 ( ( F @ X3 )
% 2.71/1.46 = ( G @ X3 ) )
% 2.71/1.46 => ( F = G ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_46_dual__order_Oeq__iff,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( order @ A )
% 2.71/1.46 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 2.71/1.46 = ( ^ [A3: A,B2: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ B2 @ A3 )
% 2.71/1.46 & ( ord_less_eq @ A @ A3 @ B2 ) ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_47_dual__order_Oantisym,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( order @ A )
% 2.71/1.46 => ! [B: A,A2: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ B @ A2 )
% 2.71/1.46 => ( ( ord_less_eq @ A @ A2 @ B )
% 2.71/1.46 => ( A2 = B ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_48_max_OcoboundedI2,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linorder @ A )
% 2.71/1.46 => ! [C: A,B: A,A2: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ C @ B )
% 2.71/1.46 => ( ord_less_eq @ A @ C @ ( ord_max @ A @ A2 @ B ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_49_max_OcoboundedI1,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linorder @ A )
% 2.71/1.46 => ! [C: A,A2: A,B: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ C @ A2 )
% 2.71/1.46 => ( ord_less_eq @ A @ C @ ( ord_max @ A @ A2 @ B ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_50_max_Oabsorb__iff2,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linorder @ A )
% 2.71/1.46 => ( ( ord_less_eq @ A )
% 2.71/1.46 = ( ^ [A3: A,B2: A] :
% 2.71/1.46 ( ( ord_max @ A @ A3 @ B2 )
% 2.71/1.46 = B2 ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_51_max_Oabsorb__iff1,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linorder @ A )
% 2.71/1.46 => ( ( ord_less_eq @ A )
% 2.71/1.46 = ( ^ [B2: A,A3: A] :
% 2.71/1.46 ( ( ord_max @ A @ A3 @ B2 )
% 2.71/1.46 = A3 ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_52_le__max__iff__disj,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linorder @ A )
% 2.71/1.46 => ! [Z2: A,X: A,Y: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ Z2 @ ( ord_max @ A @ X @ Y ) )
% 2.71/1.46 = ( ( ord_less_eq @ A @ Z2 @ X )
% 2.71/1.46 | ( ord_less_eq @ A @ Z2 @ Y ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_53_max_Ocobounded2,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linorder @ A )
% 2.71/1.46 => ! [B: A,A2: A] : ( ord_less_eq @ A @ B @ ( ord_max @ A @ A2 @ B ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_54_max_Ocobounded1,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linorder @ A )
% 2.71/1.46 => ! [A2: A,B: A] : ( ord_less_eq @ A @ A2 @ ( ord_max @ A @ A2 @ B ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_55_max_Oorder__iff,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linorder @ A )
% 2.71/1.46 => ( ( ord_less_eq @ A )
% 2.71/1.46 = ( ^ [B2: A,A3: A] :
% 2.71/1.46 ( A3
% 2.71/1.46 = ( ord_max @ A @ A3 @ B2 ) ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_56_max_OboundedI,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linorder @ A )
% 2.71/1.46 => ! [B: A,A2: A,C: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ B @ A2 )
% 2.71/1.46 => ( ( ord_less_eq @ A @ C @ A2 )
% 2.71/1.46 => ( ord_less_eq @ A @ ( ord_max @ A @ B @ C ) @ A2 ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_57_max_OboundedE,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linorder @ A )
% 2.71/1.46 => ! [B: A,C: A,A2: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ ( ord_max @ A @ B @ C ) @ A2 )
% 2.71/1.46 => ~ ( ( ord_less_eq @ A @ B @ A2 )
% 2.71/1.46 => ~ ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_58_max_Oabsorb2,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linorder @ A )
% 2.71/1.46 => ! [A2: A,B: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ A2 @ B )
% 2.71/1.46 => ( ( ord_max @ A @ A2 @ B )
% 2.71/1.46 = B ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_59_max_Oabsorb1,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linorder @ A )
% 2.71/1.46 => ! [B: A,A2: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ B @ A2 )
% 2.71/1.46 => ( ( ord_max @ A @ A2 @ B )
% 2.71/1.46 = A2 ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_60_max_OorderI,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linorder @ A )
% 2.71/1.46 => ! [A2: A,B: A] :
% 2.71/1.46 ( ( A2
% 2.71/1.46 = ( ord_max @ A @ A2 @ B ) )
% 2.71/1.46 => ( ord_less_eq @ A @ B @ A2 ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_61_max_OorderE,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linorder @ A )
% 2.71/1.46 => ! [B: A,A2: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ B @ A2 )
% 2.71/1.46 => ( A2
% 2.71/1.46 = ( ord_max @ A @ A2 @ B ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_62_max_Omono,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linorder @ A )
% 2.71/1.46 => ! [C: A,A2: A,D: A,B: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ C @ A2 )
% 2.71/1.46 => ( ( ord_less_eq @ A @ D @ B )
% 2.71/1.46 => ( ord_less_eq @ A @ ( ord_max @ A @ C @ D ) @ ( ord_max @ A @ A2 @ B ) ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_63_max__def,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ord @ A )
% 2.71/1.46 => ( ( ord_max @ A )
% 2.71/1.46 = ( ^ [A3: A,B2: A] : ( if @ A @ ( ord_less_eq @ A @ A3 @ B2 ) @ B2 @ A3 ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_64_max__absorb2,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ord @ A )
% 2.71/1.46 => ! [X: A,Y: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ X @ Y )
% 2.71/1.46 => ( ( ord_max @ A @ X @ Y )
% 2.71/1.46 = Y ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_65_okmaxsync__def,axiom,
% 2.71/1.46 ( genClo208577157axsync
% 2.71/1.46 = ( ^ [I2: nat,X2: real] :
% 2.71/1.46 ! [P4: nat,Q: nat] :
% 2.71/1.46 ( ( ( genClo1015804716orrect @ P4 @ ( ord_max @ real @ ( genClo1163638703lle_te @ P4 @ I2 ) @ ( genClo1163638703lle_te @ Q @ I2 ) ) )
% 2.71/1.46 & ( genClo1015804716orrect @ Q @ ( ord_max @ real @ ( genClo1163638703lle_te @ P4 @ I2 ) @ ( genClo1163638703lle_te @ Q @ I2 ) ) ) )
% 2.71/1.46 => ( ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ ( genClo1160817912lle_IC @ P4 @ I2 @ ( ord_max @ real @ ( genClo1163638703lle_te @ P4 @ I2 ) @ ( genClo1163638703lle_te @ Q @ I2 ) ) ) @ ( genClo1160817912lle_IC @ Q @ I2 @ ( ord_max @ real @ ( genClo1163638703lle_te @ P4 @ I2 ) @ ( genClo1163638703lle_te @ Q @ I2 ) ) ) ) ) @ X2 ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_66_le__add__diff__inverse,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linordered_semidom @ A )
% 2.71/1.46 => ! [B: A,A2: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ B @ A2 )
% 2.71/1.46 => ( ( plus_plus @ A @ B @ ( minus_minus @ A @ A2 @ B ) )
% 2.71/1.46 = A2 ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_67_le__add__diff__inverse2,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linordered_semidom @ A )
% 2.71/1.46 => ! [B: A,A2: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ B @ A2 )
% 2.71/1.46 => ( ( plus_plus @ A @ ( minus_minus @ A @ A2 @ B ) @ B )
% 2.71/1.46 = A2 ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_68_abs__1,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( idom_abs_sgn @ A )
% 2.71/1.46 => ( ( abs_abs @ A @ ( one_one @ A ) )
% 2.71/1.46 = ( one_one @ A ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_69_abs__add__abs,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordere142940540dd_abs @ A )
% 2.71/1.46 => ! [A2: A,B: A] :
% 2.71/1.46 ( ( abs_abs @ A @ ( plus_plus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) )
% 2.71/1.46 = ( plus_plus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_70_add__diff__cancel,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( group_add @ A )
% 2.71/1.46 => ! [A2: A,B: A] :
% 2.71/1.46 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ B )
% 2.71/1.46 = A2 ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_71_diff__add__cancel,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( group_add @ A )
% 2.71/1.46 => ! [A2: A,B: A] :
% 2.71/1.46 ( ( plus_plus @ A @ ( minus_minus @ A @ A2 @ B ) @ B )
% 2.71/1.46 = A2 ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_72_add__diff__cancel__left,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( cancel146912293up_add @ A )
% 2.71/1.46 => ! [C: A,A2: A,B: A] :
% 2.71/1.46 ( ( minus_minus @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 2.71/1.46 = ( minus_minus @ A @ A2 @ B ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_73_add__diff__cancel__left_H,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( cancel146912293up_add @ A )
% 2.71/1.46 => ! [A2: A,B: A] :
% 2.71/1.46 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ A2 )
% 2.71/1.46 = B ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_74_add__diff__cancel__right,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( cancel146912293up_add @ A )
% 2.71/1.46 => ! [A2: A,C: A,B: A] :
% 2.71/1.46 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 2.71/1.46 = ( minus_minus @ A @ A2 @ B ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_75_add__right__cancel,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( cancel_semigroup_add @ A )
% 2.71/1.46 => ! [B: A,A2: A,C: A] :
% 2.71/1.46 ( ( ( plus_plus @ A @ B @ A2 )
% 2.71/1.46 = ( plus_plus @ A @ C @ A2 ) )
% 2.71/1.46 = ( B = C ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_76_add__left__cancel,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( cancel_semigroup_add @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A] :
% 2.71/1.46 ( ( ( plus_plus @ A @ A2 @ B )
% 2.71/1.46 = ( plus_plus @ A @ A2 @ C ) )
% 2.71/1.46 = ( B = C ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_77_abs__idempotent,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordere142940540dd_abs @ A )
% 2.71/1.46 => ! [A2: A] :
% 2.71/1.46 ( ( abs_abs @ A @ ( abs_abs @ A @ A2 ) )
% 2.71/1.46 = ( abs_abs @ A @ A2 ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_78_abs__abs,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( idom_abs_sgn @ A )
% 2.71/1.46 => ! [A2: A] :
% 2.71/1.46 ( ( abs_abs @ A @ ( abs_abs @ A @ A2 ) )
% 2.71/1.46 = ( abs_abs @ A @ A2 ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_79_add__le__cancel__right,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordere236663937imp_le @ A )
% 2.71/1.46 => ! [A2: A,C: A,B: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 2.71/1.46 = ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_80_add__le__cancel__left,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordere236663937imp_le @ A )
% 2.71/1.46 => ! [C: A,A2: A,B: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 2.71/1.46 = ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_81_add__diff__cancel__right_H,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( cancel146912293up_add @ A )
% 2.71/1.46 => ! [A2: A,B: A] :
% 2.71/1.46 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ B )
% 2.71/1.46 = A2 ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_82_add__right__imp__eq,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( cancel_semigroup_add @ A )
% 2.71/1.46 => ! [B: A,A2: A,C: A] :
% 2.71/1.46 ( ( ( plus_plus @ A @ B @ A2 )
% 2.71/1.46 = ( plus_plus @ A @ C @ A2 ) )
% 2.71/1.46 => ( B = C ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_83_add__left__imp__eq,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( cancel_semigroup_add @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A] :
% 2.71/1.46 ( ( ( plus_plus @ A @ A2 @ B )
% 2.71/1.46 = ( plus_plus @ A @ A2 @ C ) )
% 2.71/1.46 => ( B = C ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_84_add_Oleft__commute,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ab_semigroup_add @ A )
% 2.71/1.46 => ! [B: A,A2: A,C: A] :
% 2.71/1.46 ( ( plus_plus @ A @ B @ ( plus_plus @ A @ A2 @ C ) )
% 2.71/1.46 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_85_add_Ocommute,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ab_semigroup_add @ A )
% 2.71/1.46 => ( ( plus_plus @ A )
% 2.71/1.46 = ( ^ [A3: A,B2: A] : ( plus_plus @ A @ B2 @ A3 ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_86_add_Oright__cancel,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( group_add @ A )
% 2.71/1.46 => ! [B: A,A2: A,C: A] :
% 2.71/1.46 ( ( ( plus_plus @ A @ B @ A2 )
% 2.71/1.46 = ( plus_plus @ A @ C @ A2 ) )
% 2.71/1.46 = ( B = C ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_87_add_Oleft__cancel,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( group_add @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A] :
% 2.71/1.46 ( ( ( plus_plus @ A @ A2 @ B )
% 2.71/1.46 = ( plus_plus @ A @ A2 @ C ) )
% 2.71/1.46 = ( B = C ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_88_add_Oassoc,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( semigroup_add @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A] :
% 2.71/1.46 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 2.71/1.46 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_89_group__cancel_Oadd2,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( comm_monoid_add @ A )
% 2.71/1.46 => ! [B6: A,K: A,B: A,A2: A] :
% 2.71/1.46 ( ( B6
% 2.71/1.46 = ( plus_plus @ A @ K @ B ) )
% 2.71/1.46 => ( ( plus_plus @ A @ A2 @ B6 )
% 2.71/1.46 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B ) ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_90_group__cancel_Oadd1,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( comm_monoid_add @ A )
% 2.71/1.46 => ! [A6: A,K: A,A2: A,B: A] :
% 2.71/1.46 ( ( A6
% 2.71/1.46 = ( plus_plus @ A @ K @ A2 ) )
% 2.71/1.46 => ( ( plus_plus @ A @ A6 @ B )
% 2.71/1.46 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B ) ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_91_add__mono__thms__linordered__semiring_I4_J,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordere779506340up_add @ A )
% 2.71/1.46 => ! [I: A,J: A,K: A,L: A] :
% 2.71/1.46 ( ( ( I = J )
% 2.71/1.46 & ( K = L ) )
% 2.71/1.46 => ( ( plus_plus @ A @ I @ K )
% 2.71/1.46 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_92_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ab_semigroup_add @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A] :
% 2.71/1.46 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 2.71/1.46 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_93_one__reorient,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( one @ A )
% 2.71/1.46 => ! [X: A] :
% 2.71/1.46 ( ( ( one_one @ A )
% 2.71/1.46 = X )
% 2.71/1.46 = ( X
% 2.71/1.46 = ( one_one @ A ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_94_diff__right__commute,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( cancel146912293up_add @ A )
% 2.71/1.46 => ! [A2: A,C: A,B: A] :
% 2.71/1.46 ( ( minus_minus @ A @ ( minus_minus @ A @ A2 @ C ) @ B )
% 2.71/1.46 = ( minus_minus @ A @ ( minus_minus @ A @ A2 @ B ) @ C ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_95_diff__eq__diff__eq,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( group_add @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A,D: A] :
% 2.71/1.46 ( ( ( minus_minus @ A @ A2 @ B )
% 2.71/1.46 = ( minus_minus @ A @ C @ D ) )
% 2.71/1.46 => ( ( A2 = B )
% 2.71/1.46 = ( C = D ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_96_add__le__imp__le__right,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordere236663937imp_le @ A )
% 2.71/1.46 => ! [A2: A,C: A,B: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 2.71/1.46 => ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_97_add__le__imp__le__left,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordere236663937imp_le @ A )
% 2.71/1.46 => ! [C: A,A2: A,B: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 2.71/1.46 => ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_98_le__iff__add,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( canoni770627133id_add @ A )
% 2.71/1.46 => ( ( ord_less_eq @ A )
% 2.71/1.46 = ( ^ [A3: A,B2: A] :
% 2.71/1.46 ? [C3: A] :
% 2.71/1.46 ( B2
% 2.71/1.46 = ( plus_plus @ A @ A3 @ C3 ) ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_99_add__right__mono,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordere779506340up_add @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ A2 @ B )
% 2.71/1.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_100_less__eqE,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( canoni770627133id_add @ A )
% 2.71/1.46 => ! [A2: A,B: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ A2 @ B )
% 2.71/1.46 => ~ ! [C4: A] :
% 2.71/1.46 ( B
% 2.71/1.46 != ( plus_plus @ A @ A2 @ C4 ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_101_add__left__mono,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordere779506340up_add @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ A2 @ B )
% 2.71/1.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_102_add__mono,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordere779506340up_add @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A,D: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ A2 @ B )
% 2.71/1.46 => ( ( ord_less_eq @ A @ C @ D )
% 2.71/1.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ D ) ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_103_add__mono__thms__linordered__semiring_I1_J,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordere779506340up_add @ A )
% 2.71/1.46 => ! [I: A,J: A,K: A,L: A] :
% 2.71/1.46 ( ( ( ord_less_eq @ A @ I @ J )
% 2.71/1.46 & ( ord_less_eq @ A @ K @ L ) )
% 2.71/1.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_104_add__mono__thms__linordered__semiring_I2_J,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordere779506340up_add @ A )
% 2.71/1.46 => ! [I: A,J: A,K: A,L: A] :
% 2.71/1.46 ( ( ( I = J )
% 2.71/1.46 & ( ord_less_eq @ A @ K @ L ) )
% 2.71/1.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_105_add__mono__thms__linordered__semiring_I3_J,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordere779506340up_add @ A )
% 2.71/1.46 => ! [I: A,J: A,K: A,L: A] :
% 2.71/1.46 ( ( ( ord_less_eq @ A @ I @ J )
% 2.71/1.46 & ( K = L ) )
% 2.71/1.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_106_diff__eq__diff__less__eq,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordered_ab_group_add @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A,D: A] :
% 2.71/1.46 ( ( ( minus_minus @ A @ A2 @ B )
% 2.71/1.46 = ( minus_minus @ A @ C @ D ) )
% 2.71/1.46 => ( ( ord_less_eq @ A @ A2 @ B )
% 2.71/1.46 = ( ord_less_eq @ A @ C @ D ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_107_diff__right__mono,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordered_ab_group_add @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ A2 @ B )
% 2.71/1.46 => ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B @ C ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_108_diff__left__mono,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordered_ab_group_add @ A )
% 2.71/1.46 => ! [B: A,A2: A,C: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ B @ A2 )
% 2.71/1.46 => ( ord_less_eq @ A @ ( minus_minus @ A @ C @ A2 ) @ ( minus_minus @ A @ C @ B ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_109_diff__mono,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordered_ab_group_add @ A )
% 2.71/1.46 => ! [A2: A,B: A,D: A,C: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ A2 @ B )
% 2.71/1.46 => ( ( ord_less_eq @ A @ D @ C )
% 2.71/1.46 => ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B @ D ) ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_110_add__implies__diff,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( cancel1352612707id_add @ A )
% 2.71/1.46 => ! [C: A,B: A,A2: A] :
% 2.71/1.46 ( ( ( plus_plus @ A @ C @ B )
% 2.71/1.46 = A2 )
% 2.71/1.46 => ( C
% 2.71/1.46 = ( minus_minus @ A @ A2 @ B ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_111_diff__diff__add,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( cancel146912293up_add @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A] :
% 2.71/1.46 ( ( minus_minus @ A @ ( minus_minus @ A @ A2 @ B ) @ C )
% 2.71/1.46 = ( minus_minus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_112_diff__add__eq__diff__diff__swap,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( group_add @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A] :
% 2.71/1.46 ( ( minus_minus @ A @ A2 @ ( plus_plus @ A @ B @ C ) )
% 2.71/1.46 = ( minus_minus @ A @ ( minus_minus @ A @ A2 @ C ) @ B ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_113_diff__add__eq,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ab_group_add @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A] :
% 2.71/1.46 ( ( plus_plus @ A @ ( minus_minus @ A @ A2 @ B ) @ C )
% 2.71/1.46 = ( minus_minus @ A @ ( plus_plus @ A @ A2 @ C ) @ B ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_114_diff__diff__eq2,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( group_add @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A] :
% 2.71/1.46 ( ( minus_minus @ A @ A2 @ ( minus_minus @ A @ B @ C ) )
% 2.71/1.46 = ( minus_minus @ A @ ( plus_plus @ A @ A2 @ C ) @ B ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_115_add__diff__eq,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( group_add @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A] :
% 2.71/1.46 ( ( plus_plus @ A @ A2 @ ( minus_minus @ A @ B @ C ) )
% 2.71/1.46 = ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ C ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_116_eq__diff__eq,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( group_add @ A )
% 2.71/1.46 => ! [A2: A,C: A,B: A] :
% 2.71/1.46 ( ( A2
% 2.71/1.46 = ( minus_minus @ A @ C @ B ) )
% 2.71/1.46 = ( ( plus_plus @ A @ A2 @ B )
% 2.71/1.46 = C ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_117_diff__eq__eq,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( group_add @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A] :
% 2.71/1.46 ( ( ( minus_minus @ A @ A2 @ B )
% 2.71/1.46 = C )
% 2.71/1.46 = ( A2
% 2.71/1.46 = ( plus_plus @ A @ C @ B ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_118_group__cancel_Osub1,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ab_group_add @ A )
% 2.71/1.46 => ! [A6: A,K: A,A2: A,B: A] :
% 2.71/1.46 ( ( A6
% 2.71/1.46 = ( plus_plus @ A @ K @ A2 ) )
% 2.71/1.46 => ( ( minus_minus @ A @ A6 @ B )
% 2.71/1.46 = ( plus_plus @ A @ K @ ( minus_minus @ A @ A2 @ B ) ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_119_abs__ge__self,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordere142940540dd_abs @ A )
% 2.71/1.46 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ ( abs_abs @ A @ A2 ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_120_abs__le__D1,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordere142940540dd_abs @ A )
% 2.71/1.46 => ! [A2: A,B: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ ( abs_abs @ A @ A2 ) @ B )
% 2.71/1.46 => ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_121_abs__one,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( linordered_idom @ A )
% 2.71/1.46 => ( ( abs_abs @ A @ ( one_one @ A ) )
% 2.71/1.46 = ( one_one @ A ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_122_abs__minus__commute,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordere142940540dd_abs @ A )
% 2.71/1.46 => ! [A2: A,B: A] :
% 2.71/1.46 ( ( abs_abs @ A @ ( minus_minus @ A @ A2 @ B ) )
% 2.71/1.46 = ( abs_abs @ A @ ( minus_minus @ A @ B @ A2 ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_123_max__add__distrib__left,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordere236663937imp_le @ A )
% 2.71/1.46 => ! [X: A,Y: A,Z2: A] :
% 2.71/1.46 ( ( plus_plus @ A @ ( ord_max @ A @ X @ Y ) @ Z2 )
% 2.71/1.46 = ( ord_max @ A @ ( plus_plus @ A @ X @ Z2 ) @ ( plus_plus @ A @ Y @ Z2 ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_124_max__add__distrib__right,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordere236663937imp_le @ A )
% 2.71/1.46 => ! [X: A,Y: A,Z2: A] :
% 2.71/1.46 ( ( plus_plus @ A @ X @ ( ord_max @ A @ Y @ Z2 ) )
% 2.71/1.46 = ( ord_max @ A @ ( plus_plus @ A @ X @ Y ) @ ( plus_plus @ A @ X @ Z2 ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_125_max__diff__distrib__left,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordered_ab_group_add @ A )
% 2.71/1.46 => ! [X: A,Y: A,Z2: A] :
% 2.71/1.46 ( ( minus_minus @ A @ ( ord_max @ A @ X @ Y ) @ Z2 )
% 2.71/1.46 = ( ord_max @ A @ ( minus_minus @ A @ X @ Z2 ) @ ( minus_minus @ A @ Y @ Z2 ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_126_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordere623563068d_diff @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ A2 @ B )
% 2.71/1.46 => ( ( ord_less_eq @ A @ A2 @ B )
% 2.71/1.46 => ( ( ( minus_minus @ A @ B @ A2 )
% 2.71/1.46 = C )
% 2.71/1.46 = ( B
% 2.71/1.46 = ( plus_plus @ A @ C @ A2 ) ) ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_127_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordere623563068d_diff @ A )
% 2.71/1.46 => ! [A2: A,B: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ A2 @ B )
% 2.71/1.46 => ( ( plus_plus @ A @ A2 @ ( minus_minus @ A @ B @ A2 ) )
% 2.71/1.46 = B ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_128_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordere623563068d_diff @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ A2 @ B )
% 2.71/1.46 => ( ( minus_minus @ A @ C @ ( minus_minus @ A @ B @ A2 ) )
% 2.71/1.46 = ( minus_minus @ A @ ( plus_plus @ A @ C @ A2 ) @ B ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_129_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordere623563068d_diff @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ A2 @ B )
% 2.71/1.46 => ( ( minus_minus @ A @ ( plus_plus @ A @ B @ C ) @ A2 )
% 2.71/1.46 = ( plus_plus @ A @ ( minus_minus @ A @ B @ A2 ) @ C ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_130_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordere623563068d_diff @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ A2 @ B )
% 2.71/1.46 => ( ( plus_plus @ A @ ( minus_minus @ A @ B @ A2 ) @ C )
% 2.71/1.46 = ( minus_minus @ A @ ( plus_plus @ A @ B @ C ) @ A2 ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_131_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordere623563068d_diff @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ A2 @ B )
% 2.71/1.46 => ( ( minus_minus @ A @ ( plus_plus @ A @ C @ B ) @ A2 )
% 2.71/1.46 = ( plus_plus @ A @ C @ ( minus_minus @ A @ B @ A2 ) ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_132_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordere623563068d_diff @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ A2 @ B )
% 2.71/1.46 => ( ( plus_plus @ A @ C @ ( minus_minus @ A @ B @ A2 ) )
% 2.71/1.46 = ( minus_minus @ A @ ( plus_plus @ A @ C @ B ) @ A2 ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_133_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordere623563068d_diff @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ A2 @ B )
% 2.71/1.46 => ( ( ord_less_eq @ A @ C @ ( minus_minus @ A @ B @ A2 ) )
% 2.71/1.46 = ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ B ) ) ) ) ).
% 2.71/1.46
% 2.71/1.46 thf(fact_134_le__add__diff,axiom,
% 2.71/1.46 ! [A: $tType] :
% 2.71/1.46 ( ( ordere623563068d_diff @ A )
% 2.71/1.46 => ! [A2: A,B: A,C: A] :
% 2.71/1.46 ( ( ord_less_eq @ A @ A2 @ B )
% 2.71/1.46 => ( ord_less_eq @ A @ C @ ( minus_minus @ A @ ( plus_plus @ A @ B @ C ) @ A2 ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_135_add__le__add__imp__diff__le,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( linordered_semidom @ A )
% 2.71/1.47 => ! [I: A,K: A,N: A,J: A] :
% 2.71/1.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ N )
% 2.71/1.47 => ( ( ord_less_eq @ A @ N @ ( plus_plus @ A @ J @ K ) )
% 2.71/1.47 => ( ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ N )
% 2.71/1.47 => ( ( ord_less_eq @ A @ N @ ( plus_plus @ A @ J @ K ) )
% 2.71/1.47 => ( ord_less_eq @ A @ ( minus_minus @ A @ N @ K ) @ J ) ) ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_136_diff__add,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordere623563068d_diff @ A )
% 2.71/1.47 => ! [A2: A,B: A] :
% 2.71/1.47 ( ( ord_less_eq @ A @ A2 @ B )
% 2.71/1.47 => ( ( plus_plus @ A @ ( minus_minus @ A @ B @ A2 ) @ A2 )
% 2.71/1.47 = B ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_137_add__le__imp__le__diff,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( linordered_semidom @ A )
% 2.71/1.47 => ! [I: A,K: A,N: A] :
% 2.71/1.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ N )
% 2.71/1.47 => ( ord_less_eq @ A @ I @ ( minus_minus @ A @ N @ K ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_138_le__diff__eq,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordered_ab_group_add @ A )
% 2.71/1.47 => ! [A2: A,C: A,B: A] :
% 2.71/1.47 ( ( ord_less_eq @ A @ A2 @ ( minus_minus @ A @ C @ B ) )
% 2.71/1.47 = ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B ) @ C ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_139_diff__le__eq,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordered_ab_group_add @ A )
% 2.71/1.47 => ! [A2: A,B: A,C: A] :
% 2.71/1.47 ( ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ B ) @ C )
% 2.71/1.47 = ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ C @ B ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_140_abs__triangle__ineq,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordere142940540dd_abs @ A )
% 2.71/1.47 => ! [A2: A,B: A] : ( ord_less_eq @ A @ ( abs_abs @ A @ ( plus_plus @ A @ A2 @ B ) ) @ ( plus_plus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_141_abs__triangle__ineq2__sym,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordere142940540dd_abs @ A )
% 2.71/1.47 => ! [A2: A,B: A] : ( ord_less_eq @ A @ ( minus_minus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) @ ( abs_abs @ A @ ( minus_minus @ A @ B @ A2 ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_142_abs__triangle__ineq3,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordere142940540dd_abs @ A )
% 2.71/1.47 => ! [A2: A,B: A] : ( ord_less_eq @ A @ ( abs_abs @ A @ ( minus_minus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) ) @ ( abs_abs @ A @ ( minus_minus @ A @ A2 @ B ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_143_abs__triangle__ineq2,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordere142940540dd_abs @ A )
% 2.71/1.47 => ! [A2: A,B: A] : ( ord_less_eq @ A @ ( minus_minus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) @ ( abs_abs @ A @ ( minus_minus @ A @ A2 @ B ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_144_abs__diff__triangle__ineq,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordere142940540dd_abs @ A )
% 2.71/1.47 => ! [A2: A,B: A,C: A,D: A] : ( ord_less_eq @ A @ ( abs_abs @ A @ ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ ( plus_plus @ A @ C @ D ) ) ) @ ( plus_plus @ A @ ( abs_abs @ A @ ( minus_minus @ A @ A2 @ C ) ) @ ( abs_abs @ A @ ( minus_minus @ A @ B @ D ) ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_145_abs__triangle__ineq4,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordere142940540dd_abs @ A )
% 2.71/1.47 => ! [A2: A,B: A] : ( ord_less_eq @ A @ ( abs_abs @ A @ ( minus_minus @ A @ A2 @ B ) ) @ ( plus_plus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_146_abs__diff__le__iff,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( linordered_idom @ A )
% 2.71/1.47 => ! [X: A,A2: A,R: A] :
% 2.71/1.47 ( ( ord_less_eq @ A @ ( abs_abs @ A @ ( minus_minus @ A @ X @ A2 ) ) @ R )
% 2.71/1.47 = ( ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ R ) @ X )
% 2.71/1.47 & ( ord_less_eq @ A @ X @ ( plus_plus @ A @ A2 @ R ) ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_147_rts1,axiom,
% 2.71/1.47 ! [P: nat,T: real,I3: nat] :
% 2.71/1.47 ( ( ( genClo1015804716orrect @ P @ T )
% 2.71/1.47 & ( ord_less_eq @ real @ ( genClo1163638703lle_te @ P @ ( plus_plus @ nat @ I3 @ ( one_one @ nat ) ) ) @ T ) )
% 2.71/1.47 => ( ord_less_eq @ real @ genClo1651033342e_rmin @ ( minus_minus @ real @ T @ ( genClo1163638703lle_te @ P @ I3 ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_148_rts1d,axiom,
% 2.71/1.47 ! [P2: nat,I: nat] :
% 2.71/1.47 ( ( genClo1015804716orrect @ P2 @ ( genClo1163638703lle_te @ P2 @ ( plus_plus @ nat @ I @ ( one_one @ nat ) ) ) )
% 2.71/1.47 => ( ord_less_eq @ real @ genClo1651033342e_rmin @ ( minus_minus @ real @ ( genClo1163638703lle_te @ P2 @ ( plus_plus @ nat @ I @ ( one_one @ nat ) ) ) @ ( genClo1163638703lle_te @ P2 @ I ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_149_rts0,axiom,
% 2.71/1.47 ! [P: nat,T: real,I3: nat] :
% 2.71/1.47 ( ( ( genClo1015804716orrect @ P @ T )
% 2.71/1.47 & ( ord_less_eq @ real @ T @ ( genClo1163638703lle_te @ P @ ( plus_plus @ nat @ I3 @ ( one_one @ nat ) ) ) ) )
% 2.71/1.47 => ( ord_less_eq @ real @ ( minus_minus @ real @ T @ ( genClo1163638703lle_te @ P @ I3 ) ) @ genClo1650508560e_rmax ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_150_rts0d,axiom,
% 2.71/1.47 ! [P2: nat,I: nat] :
% 2.71/1.47 ( ( genClo1015804716orrect @ P2 @ ( genClo1163638703lle_te @ P2 @ ( plus_plus @ nat @ I @ ( one_one @ nat ) ) ) )
% 2.71/1.47 => ( ord_less_eq @ real @ ( minus_minus @ real @ ( genClo1163638703lle_te @ P2 @ ( plus_plus @ nat @ I @ ( one_one @ nat ) ) ) @ ( genClo1163638703lle_te @ P2 @ I ) ) @ genClo1650508560e_rmax ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_151_okRead2__def,axiom,
% 2.71/1.47 ( genClo293725282kRead2
% 2.71/1.47 = ( ^ [F2: nat > real,G2: nat > real,X2: real,Ppred: nat > $o] :
% 2.71/1.47 ! [P4: nat] :
% 2.71/1.47 ( ( Ppred @ P4 )
% 2.71/1.47 => ( ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ ( F2 @ P4 ) @ ( G2 @ P4 ) ) ) @ X2 ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_152_sin__bound__lemma,axiom,
% 2.71/1.47 ! [X: real,Y: real,U: real,V: real] :
% 2.71/1.47 ( ( X = Y )
% 2.71/1.47 => ( ( ord_less_eq @ real @ ( abs_abs @ real @ U ) @ V )
% 2.71/1.47 => ( ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ ( plus_plus @ real @ X @ U ) @ Y ) ) @ V ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_153_eq__diff__eq_H,axiom,
% 2.71/1.47 ! [X: real,Y: real,Z2: real] :
% 2.71/1.47 ( ( X
% 2.71/1.47 = ( minus_minus @ real @ Y @ Z2 ) )
% 2.71/1.47 = ( Y
% 2.71/1.47 = ( plus_plus @ real @ X @ Z2 ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_154_beta__bound2,axiom,
% 2.71/1.47 ! [P2: nat,I: nat,Q2: nat] :
% 2.71/1.47 ( ( genClo1015804716orrect @ P2 @ ( genClo1163638703lle_te @ P2 @ ( plus_plus @ nat @ I @ ( one_one @ nat ) ) ) )
% 2.71/1.47 => ( ( genClo1015804716orrect @ Q2 @ ( genClo1163638703lle_te @ Q2 @ I ) )
% 2.71/1.47 => ( ord_less_eq @ real @ ( minus_minus @ real @ ( genClo1163638703lle_te @ P2 @ ( plus_plus @ nat @ I @ ( one_one @ nat ) ) ) @ ( genClo1163638703lle_te @ Q2 @ I ) ) @ ( plus_plus @ real @ genClo1650508560e_rmax @ genClo1278781456e_beta ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_155_rts2b,axiom,
% 2.71/1.47 ! [P: nat,Q3: nat,I3: nat] :
% 2.71/1.47 ( ( ( genClo1015804716orrect @ P @ ( genClo1163638703lle_te @ P @ I3 ) )
% 2.71/1.47 & ( genClo1015804716orrect @ Q3 @ ( genClo1163638703lle_te @ Q3 @ I3 ) ) )
% 2.71/1.47 => ( ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ ( genClo1163638703lle_te @ P @ I3 ) @ ( genClo1163638703lle_te @ Q3 @ I3 ) ) ) @ genClo1278781456e_beta ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_156_nat__add__left__cancel__le,axiom,
% 2.71/1.47 ! [K: nat,M: nat,N: nat] :
% 2.71/1.47 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 2.71/1.47 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_157_diff__diff__cancel,axiom,
% 2.71/1.47 ! [I: nat,N: nat] :
% 2.71/1.47 ( ( ord_less_eq @ nat @ I @ N )
% 2.71/1.47 => ( ( minus_minus @ nat @ N @ ( minus_minus @ nat @ N @ I ) )
% 2.71/1.47 = I ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_158_diff__diff__left,axiom,
% 2.71/1.47 ! [I: nat,J: nat,K: nat] :
% 2.71/1.47 ( ( minus_minus @ nat @ ( minus_minus @ nat @ I @ J ) @ K )
% 2.71/1.47 = ( minus_minus @ nat @ I @ ( plus_plus @ nat @ J @ K ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_159_Nat_Odiff__diff__right,axiom,
% 2.71/1.47 ! [K: nat,J: nat,I: nat] :
% 2.71/1.47 ( ( ord_less_eq @ nat @ K @ J )
% 2.71/1.47 => ( ( minus_minus @ nat @ I @ ( minus_minus @ nat @ J @ K ) )
% 2.71/1.47 = ( minus_minus @ nat @ ( plus_plus @ nat @ I @ K ) @ J ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_160_Nat_Oadd__diff__assoc2,axiom,
% 2.71/1.47 ! [K: nat,J: nat,I: nat] :
% 2.71/1.47 ( ( ord_less_eq @ nat @ K @ J )
% 2.71/1.47 => ( ( plus_plus @ nat @ ( minus_minus @ nat @ J @ K ) @ I )
% 2.71/1.47 = ( minus_minus @ nat @ ( plus_plus @ nat @ J @ I ) @ K ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_161_Nat_Oadd__diff__assoc,axiom,
% 2.71/1.47 ! [K: nat,J: nat,I: nat] :
% 2.71/1.47 ( ( ord_less_eq @ nat @ K @ J )
% 2.71/1.47 => ( ( plus_plus @ nat @ I @ ( minus_minus @ nat @ J @ K ) )
% 2.71/1.47 = ( minus_minus @ nat @ ( plus_plus @ nat @ I @ J ) @ K ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_162_Nat_Oex__has__greatest__nat,axiom,
% 2.71/1.47 ! [P3: nat > $o,K: nat,B: nat] :
% 2.71/1.47 ( ( P3 @ K )
% 2.71/1.47 => ( ! [Y2: nat] :
% 2.71/1.47 ( ( P3 @ Y2 )
% 2.71/1.47 => ( ord_less_eq @ nat @ Y2 @ B ) )
% 2.71/1.47 => ? [X3: nat] :
% 2.71/1.47 ( ( P3 @ X3 )
% 2.71/1.47 & ! [Y5: nat] :
% 2.71/1.47 ( ( P3 @ Y5 )
% 2.71/1.47 => ( ord_less_eq @ nat @ Y5 @ X3 ) ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_163_nat__le__linear,axiom,
% 2.71/1.47 ! [M: nat,N: nat] :
% 2.71/1.47 ( ( ord_less_eq @ nat @ M @ N )
% 2.71/1.47 | ( ord_less_eq @ nat @ N @ M ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_164_diff__le__mono2,axiom,
% 2.71/1.47 ! [M: nat,N: nat,L: nat] :
% 2.71/1.47 ( ( ord_less_eq @ nat @ M @ N )
% 2.71/1.47 => ( ord_less_eq @ nat @ ( minus_minus @ nat @ L @ N ) @ ( minus_minus @ nat @ L @ M ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_165_le__diff__iff_H,axiom,
% 2.71/1.47 ! [A2: nat,C: nat,B: nat] :
% 2.71/1.47 ( ( ord_less_eq @ nat @ A2 @ C )
% 2.71/1.47 => ( ( ord_less_eq @ nat @ B @ C )
% 2.71/1.47 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ C @ A2 ) @ ( minus_minus @ nat @ C @ B ) )
% 2.71/1.47 = ( ord_less_eq @ nat @ B @ A2 ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_166_diff__le__self,axiom,
% 2.71/1.47 ! [M: nat,N: nat] : ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ N ) @ M ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_167_diff__le__mono,axiom,
% 2.71/1.47 ! [M: nat,N: nat,L: nat] :
% 2.71/1.47 ( ( ord_less_eq @ nat @ M @ N )
% 2.71/1.47 => ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ L ) @ ( minus_minus @ nat @ N @ L ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_168_Nat_Odiff__diff__eq,axiom,
% 2.71/1.47 ! [K: nat,M: nat,N: nat] :
% 2.71/1.47 ( ( ord_less_eq @ nat @ K @ M )
% 2.71/1.47 => ( ( ord_less_eq @ nat @ K @ N )
% 2.71/1.47 => ( ( minus_minus @ nat @ ( minus_minus @ nat @ M @ K ) @ ( minus_minus @ nat @ N @ K ) )
% 2.71/1.47 = ( minus_minus @ nat @ M @ N ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_169_le__diff__iff,axiom,
% 2.71/1.47 ! [K: nat,M: nat,N: nat] :
% 2.71/1.47 ( ( ord_less_eq @ nat @ K @ M )
% 2.71/1.47 => ( ( ord_less_eq @ nat @ K @ N )
% 2.71/1.47 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ K ) @ ( minus_minus @ nat @ N @ K ) )
% 2.71/1.47 = ( ord_less_eq @ nat @ M @ N ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_170_eq__diff__iff,axiom,
% 2.71/1.47 ! [K: nat,M: nat,N: nat] :
% 2.71/1.47 ( ( ord_less_eq @ nat @ K @ M )
% 2.71/1.47 => ( ( ord_less_eq @ nat @ K @ N )
% 2.71/1.47 => ( ( ( minus_minus @ nat @ M @ K )
% 2.71/1.47 = ( minus_minus @ nat @ N @ K ) )
% 2.71/1.47 = ( M = N ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_171_le__antisym,axiom,
% 2.71/1.47 ! [M: nat,N: nat] :
% 2.71/1.47 ( ( ord_less_eq @ nat @ M @ N )
% 2.71/1.47 => ( ( ord_less_eq @ nat @ N @ M )
% 2.71/1.47 => ( M = N ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_172_eq__imp__le,axiom,
% 2.71/1.47 ! [M: nat,N: nat] :
% 2.71/1.47 ( ( M = N )
% 2.71/1.47 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_173_le__trans,axiom,
% 2.71/1.47 ! [I: nat,J: nat,K: nat] :
% 2.71/1.47 ( ( ord_less_eq @ nat @ I @ J )
% 2.71/1.47 => ( ( ord_less_eq @ nat @ J @ K )
% 2.71/1.47 => ( ord_less_eq @ nat @ I @ K ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_174_le__refl,axiom,
% 2.71/1.47 ! [N: nat] : ( ord_less_eq @ nat @ N @ N ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_175_Nat_Ole__imp__diff__is__add,axiom,
% 2.71/1.47 ! [I: nat,J: nat,K: nat] :
% 2.71/1.47 ( ( ord_less_eq @ nat @ I @ J )
% 2.71/1.47 => ( ( ( minus_minus @ nat @ J @ I )
% 2.71/1.47 = K )
% 2.71/1.47 = ( J
% 2.71/1.47 = ( plus_plus @ nat @ K @ I ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_176_nat__minus__add__max,axiom,
% 2.71/1.47 ! [N: nat,M: nat] :
% 2.71/1.47 ( ( plus_plus @ nat @ ( minus_minus @ nat @ N @ M ) @ M )
% 2.71/1.47 = ( ord_max @ nat @ N @ M ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_177_diff__add__inverse2,axiom,
% 2.71/1.47 ! [M: nat,N: nat] :
% 2.71/1.47 ( ( minus_minus @ nat @ ( plus_plus @ nat @ M @ N ) @ N )
% 2.71/1.47 = M ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_178_diff__add__inverse,axiom,
% 2.71/1.47 ! [N: nat,M: nat] :
% 2.71/1.47 ( ( minus_minus @ nat @ ( plus_plus @ nat @ N @ M ) @ N )
% 2.71/1.47 = M ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_179_Nat_Odiff__add__assoc2,axiom,
% 2.71/1.47 ! [K: nat,J: nat,I: nat] :
% 2.71/1.47 ( ( ord_less_eq @ nat @ K @ J )
% 2.71/1.47 => ( ( minus_minus @ nat @ ( plus_plus @ nat @ J @ I ) @ K )
% 2.71/1.47 = ( plus_plus @ nat @ ( minus_minus @ nat @ J @ K ) @ I ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_180_Nat_Odiff__add__assoc,axiom,
% 2.71/1.47 ! [K: nat,J: nat,I: nat] :
% 2.71/1.47 ( ( ord_less_eq @ nat @ K @ J )
% 2.71/1.47 => ( ( minus_minus @ nat @ ( plus_plus @ nat @ I @ J ) @ K )
% 2.71/1.47 = ( plus_plus @ nat @ I @ ( minus_minus @ nat @ J @ K ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_181_Nat_Ole__diff__conv2,axiom,
% 2.71/1.47 ! [K: nat,J: nat,I: nat] :
% 2.71/1.47 ( ( ord_less_eq @ nat @ K @ J )
% 2.71/1.47 => ( ( ord_less_eq @ nat @ I @ ( minus_minus @ nat @ J @ K ) )
% 2.71/1.47 = ( ord_less_eq @ nat @ ( plus_plus @ nat @ I @ K ) @ J ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_182_le__diff__conv,axiom,
% 2.71/1.47 ! [J: nat,K: nat,I: nat] :
% 2.71/1.47 ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ J @ K ) @ I )
% 2.71/1.47 = ( ord_less_eq @ nat @ J @ ( plus_plus @ nat @ I @ K ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_183_diff__cancel2,axiom,
% 2.71/1.47 ! [M: nat,K: nat,N: nat] :
% 2.71/1.47 ( ( minus_minus @ nat @ ( plus_plus @ nat @ M @ K ) @ ( plus_plus @ nat @ N @ K ) )
% 2.71/1.47 = ( minus_minus @ nat @ M @ N ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_184_Nat_Odiff__cancel,axiom,
% 2.71/1.47 ! [K: nat,M: nat,N: nat] :
% 2.71/1.47 ( ( minus_minus @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 2.71/1.47 = ( minus_minus @ nat @ M @ N ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_185_nat__add__max__right,axiom,
% 2.71/1.47 ! [M: nat,N: nat,Q2: nat] :
% 2.71/1.47 ( ( plus_plus @ nat @ M @ ( ord_max @ nat @ N @ Q2 ) )
% 2.71/1.47 = ( ord_max @ nat @ ( plus_plus @ nat @ M @ N ) @ ( plus_plus @ nat @ M @ Q2 ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_186_nat__add__max__left,axiom,
% 2.71/1.47 ! [M: nat,N: nat,Q2: nat] :
% 2.71/1.47 ( ( plus_plus @ nat @ ( ord_max @ nat @ M @ N ) @ Q2 )
% 2.71/1.47 = ( ord_max @ nat @ ( plus_plus @ nat @ M @ Q2 ) @ ( plus_plus @ nat @ N @ Q2 ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_187_nat__le__iff__add,axiom,
% 2.71/1.47 ( ( ord_less_eq @ nat )
% 2.71/1.47 = ( ^ [M2: nat,N2: nat] :
% 2.71/1.47 ? [K2: nat] :
% 2.71/1.47 ( N2
% 2.71/1.47 = ( plus_plus @ nat @ M2 @ K2 ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_188_trans__le__add2,axiom,
% 2.71/1.47 ! [I: nat,J: nat,M: nat] :
% 2.71/1.47 ( ( ord_less_eq @ nat @ I @ J )
% 2.71/1.47 => ( ord_less_eq @ nat @ I @ ( plus_plus @ nat @ M @ J ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_189_trans__le__add1,axiom,
% 2.71/1.47 ! [I: nat,J: nat,M: nat] :
% 2.71/1.47 ( ( ord_less_eq @ nat @ I @ J )
% 2.71/1.47 => ( ord_less_eq @ nat @ I @ ( plus_plus @ nat @ J @ M ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_190_add__le__mono1,axiom,
% 2.71/1.47 ! [I: nat,J: nat,K: nat] :
% 2.71/1.47 ( ( ord_less_eq @ nat @ I @ J )
% 2.71/1.47 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ K ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_191_add__le__mono,axiom,
% 2.71/1.47 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.71/1.47 ( ( ord_less_eq @ nat @ I @ J )
% 2.71/1.47 => ( ( ord_less_eq @ nat @ K @ L )
% 2.71/1.47 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ L ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_192_le__Suc__ex,axiom,
% 2.71/1.47 ! [K: nat,L: nat] :
% 2.71/1.47 ( ( ord_less_eq @ nat @ K @ L )
% 2.71/1.47 => ? [N3: nat] :
% 2.71/1.47 ( L
% 2.71/1.47 = ( plus_plus @ nat @ K @ N3 ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_193_add__leD2,axiom,
% 2.71/1.47 ! [M: nat,K: nat,N: nat] :
% 2.71/1.47 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K ) @ N )
% 2.71/1.47 => ( ord_less_eq @ nat @ K @ N ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_194_add__leD1,axiom,
% 2.71/1.47 ! [M: nat,K: nat,N: nat] :
% 2.71/1.47 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K ) @ N )
% 2.71/1.47 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_195_le__add2,axiom,
% 2.71/1.47 ! [N: nat,M: nat] : ( ord_less_eq @ nat @ N @ ( plus_plus @ nat @ M @ N ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_196_le__add1,axiom,
% 2.71/1.47 ! [N: nat,M: nat] : ( ord_less_eq @ nat @ N @ ( plus_plus @ nat @ N @ M ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_197_add__leE,axiom,
% 2.71/1.47 ! [M: nat,K: nat,N: nat] :
% 2.71/1.47 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K ) @ N )
% 2.71/1.47 => ~ ( ( ord_less_eq @ nat @ M @ N )
% 2.71/1.47 => ~ ( ord_less_eq @ nat @ K @ N ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_198_nonoverlap,axiom,
% 2.71/1.47 ord_less_eq @ real @ genClo1278781456e_beta @ genClo1651033342e_rmin ).
% 2.71/1.47
% 2.71/1.47 thf(fact_199_rts2a,axiom,
% 2.71/1.47 ! [P: nat,Q3: nat,T: real,I3: nat] :
% 2.71/1.47 ( ( ( genClo1015804716orrect @ P @ T )
% 2.71/1.47 & ( genClo1015804716orrect @ Q3 @ T )
% 2.71/1.47 & ( ord_less_eq @ real @ ( plus_plus @ real @ ( genClo1163638703lle_te @ Q3 @ I3 ) @ genClo1278781456e_beta ) @ T ) )
% 2.71/1.47 => ( ord_less_eq @ real @ ( genClo1163638703lle_te @ P @ I3 ) @ T ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_200_readerror,axiom,
% 2.71/1.47 ! [P: nat,Q3: nat,I3: nat] :
% 2.71/1.47 ( ( ( genClo1015804716orrect @ P @ ( genClo1163638703lle_te @ P @ ( plus_plus @ nat @ I3 @ ( one_one @ nat ) ) ) )
% 2.71/1.47 & ( genClo1015804716orrect @ Q3 @ ( genClo1163638703lle_te @ P @ ( plus_plus @ nat @ I3 @ ( one_one @ nat ) ) ) ) )
% 2.71/1.47 => ( ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ ( genClo1400225944_theta @ P @ ( plus_plus @ nat @ I3 @ ( one_one @ nat ) ) @ Q3 ) @ ( genClo1160817912lle_IC @ Q3 @ I3 @ ( genClo1163638703lle_te @ P @ ( plus_plus @ nat @ I3 @ ( one_one @ nat ) ) ) ) ) ) @ genClo721845095Lambda ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_201_okRead1__def,axiom,
% 2.71/1.47 ( genClo293725281kRead1
% 2.71/1.47 = ( ^ [F2: nat > real,X2: real,Ppred: nat > $o] :
% 2.71/1.47 ! [L2: nat,M2: nat] :
% 2.71/1.47 ( ( ( Ppred @ L2 )
% 2.71/1.47 & ( Ppred @ M2 ) )
% 2.71/1.47 => ( ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ ( F2 @ L2 ) @ ( F2 @ M2 ) ) ) @ X2 ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_202_beta__bound1,axiom,
% 2.71/1.47 ! [P2: nat,I: nat,Q2: nat] :
% 2.71/1.47 ( ( genClo1015804716orrect @ P2 @ ( genClo1163638703lle_te @ P2 @ ( plus_plus @ nat @ I @ ( one_one @ nat ) ) ) )
% 2.71/1.47 => ( ( genClo1015804716orrect @ Q2 @ ( genClo1163638703lle_te @ P2 @ ( plus_plus @ nat @ I @ ( one_one @ nat ) ) ) )
% 2.71/1.47 => ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( minus_minus @ real @ ( genClo1163638703lle_te @ P2 @ ( plus_plus @ nat @ I @ ( one_one @ nat ) ) ) @ ( genClo1163638703lle_te @ Q2 @ I ) ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_203_le__zero__eq,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( canoni770627133id_add @ A )
% 2.71/1.47 => ! [N: A] :
% 2.71/1.47 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 2.71/1.47 = ( N
% 2.71/1.47 = ( zero_zero @ A ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_204_zero__eq__add__iff__both__eq__0,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( canoni770627133id_add @ A )
% 2.71/1.47 => ! [X: A,Y: A] :
% 2.71/1.47 ( ( ( zero_zero @ A )
% 2.71/1.47 = ( plus_plus @ A @ X @ Y ) )
% 2.71/1.47 = ( ( X
% 2.71/1.47 = ( zero_zero @ A ) )
% 2.71/1.47 & ( Y
% 2.71/1.47 = ( zero_zero @ A ) ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_205_add__eq__0__iff__both__eq__0,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( canoni770627133id_add @ A )
% 2.71/1.47 => ! [X: A,Y: A] :
% 2.71/1.47 ( ( ( plus_plus @ A @ X @ Y )
% 2.71/1.47 = ( zero_zero @ A ) )
% 2.71/1.47 = ( ( X
% 2.71/1.47 = ( zero_zero @ A ) )
% 2.71/1.47 & ( Y
% 2.71/1.47 = ( zero_zero @ A ) ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_206_add__cancel__right__right,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( cancel1352612707id_add @ A )
% 2.71/1.47 => ! [A2: A,B: A] :
% 2.71/1.47 ( ( A2
% 2.71/1.47 = ( plus_plus @ A @ A2 @ B ) )
% 2.71/1.47 = ( B
% 2.71/1.47 = ( zero_zero @ A ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_207_add__cancel__right__left,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( cancel1352612707id_add @ A )
% 2.71/1.47 => ! [A2: A,B: A] :
% 2.71/1.47 ( ( A2
% 2.71/1.47 = ( plus_plus @ A @ B @ A2 ) )
% 2.71/1.47 = ( B
% 2.71/1.47 = ( zero_zero @ A ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_208_add__cancel__left__right,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( cancel1352612707id_add @ A )
% 2.71/1.47 => ! [A2: A,B: A] :
% 2.71/1.47 ( ( ( plus_plus @ A @ A2 @ B )
% 2.71/1.47 = A2 )
% 2.71/1.47 = ( B
% 2.71/1.47 = ( zero_zero @ A ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_209_add__cancel__left__left,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( cancel1352612707id_add @ A )
% 2.71/1.47 => ! [B: A,A2: A] :
% 2.71/1.47 ( ( ( plus_plus @ A @ B @ A2 )
% 2.71/1.47 = A2 )
% 2.71/1.47 = ( B
% 2.71/1.47 = ( zero_zero @ A ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_210_double__zero__sym,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( linord219039673up_add @ A )
% 2.71/1.47 => ! [A2: A] :
% 2.71/1.47 ( ( ( zero_zero @ A )
% 2.71/1.47 = ( plus_plus @ A @ A2 @ A2 ) )
% 2.71/1.47 = ( A2
% 2.71/1.47 = ( zero_zero @ A ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_211_double__zero,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( linord219039673up_add @ A )
% 2.71/1.47 => ! [A2: A] :
% 2.71/1.47 ( ( ( plus_plus @ A @ A2 @ A2 )
% 2.71/1.47 = ( zero_zero @ A ) )
% 2.71/1.47 = ( A2
% 2.71/1.47 = ( zero_zero @ A ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_212_add_Oright__neutral,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( monoid_add @ A )
% 2.71/1.47 => ! [A2: A] :
% 2.71/1.47 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 2.71/1.47 = A2 ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_213_add_Oleft__neutral,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( monoid_add @ A )
% 2.71/1.47 => ! [A2: A] :
% 2.71/1.47 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 2.71/1.47 = A2 ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_214_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( cancel1352612707id_add @ A )
% 2.71/1.47 => ! [A2: A] :
% 2.71/1.47 ( ( minus_minus @ A @ A2 @ A2 )
% 2.71/1.47 = ( zero_zero @ A ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_215_diff__zero,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( cancel1352612707id_add @ A )
% 2.71/1.47 => ! [A2: A] :
% 2.71/1.47 ( ( minus_minus @ A @ A2 @ ( zero_zero @ A ) )
% 2.71/1.47 = A2 ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_216_zero__diff,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( comm_monoid_diff @ A )
% 2.71/1.47 => ! [A2: A] :
% 2.71/1.47 ( ( minus_minus @ A @ ( zero_zero @ A ) @ A2 )
% 2.71/1.47 = ( zero_zero @ A ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_217_diff__0__right,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( group_add @ A )
% 2.71/1.47 => ! [A2: A] :
% 2.71/1.47 ( ( minus_minus @ A @ A2 @ ( zero_zero @ A ) )
% 2.71/1.47 = A2 ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_218_diff__self,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( group_add @ A )
% 2.71/1.47 => ! [A2: A] :
% 2.71/1.47 ( ( minus_minus @ A @ A2 @ A2 )
% 2.71/1.47 = ( zero_zero @ A ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_219_abs__zero,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordere142940540dd_abs @ A )
% 2.71/1.47 => ( ( abs_abs @ A @ ( zero_zero @ A ) )
% 2.71/1.47 = ( zero_zero @ A ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_220_abs__eq__0,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordere142940540dd_abs @ A )
% 2.71/1.47 => ! [A2: A] :
% 2.71/1.47 ( ( ( abs_abs @ A @ A2 )
% 2.71/1.47 = ( zero_zero @ A ) )
% 2.71/1.47 = ( A2
% 2.71/1.47 = ( zero_zero @ A ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_221_abs__0__eq,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordere142940540dd_abs @ A )
% 2.71/1.47 => ! [A2: A] :
% 2.71/1.47 ( ( ( zero_zero @ A )
% 2.71/1.47 = ( abs_abs @ A @ A2 ) )
% 2.71/1.47 = ( A2
% 2.71/1.47 = ( zero_zero @ A ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_222_abs__0,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( idom_abs_sgn @ A )
% 2.71/1.47 => ( ( abs_abs @ A @ ( zero_zero @ A ) )
% 2.71/1.47 = ( zero_zero @ A ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_223_add__le__same__cancel1,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordere516151231imp_le @ A )
% 2.71/1.47 => ! [B: A,A2: A] :
% 2.71/1.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ B @ A2 ) @ B )
% 2.71/1.47 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_224_add__le__same__cancel2,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordere516151231imp_le @ A )
% 2.71/1.47 => ! [A2: A,B: A] :
% 2.71/1.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B ) @ B )
% 2.71/1.47 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_225_le__add__same__cancel1,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordere516151231imp_le @ A )
% 2.71/1.47 => ! [A2: A,B: A] :
% 2.71/1.47 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ A2 @ B ) )
% 2.71/1.47 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_226_le__add__same__cancel2,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordere516151231imp_le @ A )
% 2.71/1.47 => ! [A2: A,B: A] :
% 2.71/1.47 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ B @ A2 ) )
% 2.71/1.47 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_227_double__add__le__zero__iff__single__add__le__zero,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( linord219039673up_add @ A )
% 2.71/1.47 => ! [A2: A] :
% 2.71/1.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ A2 ) @ ( zero_zero @ A ) )
% 2.71/1.47 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_228_zero__le__double__add__iff__zero__le__single__add,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( linord219039673up_add @ A )
% 2.71/1.47 => ! [A2: A] :
% 2.71/1.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ A2 ) )
% 2.71/1.47 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_229_diff__ge__0__iff__ge,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordered_ab_group_add @ A )
% 2.71/1.47 => ! [A2: A,B: A] :
% 2.71/1.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( minus_minus @ A @ A2 @ B ) )
% 2.71/1.47 = ( ord_less_eq @ A @ B @ A2 ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_230_diff__add__zero,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( comm_monoid_diff @ A )
% 2.71/1.47 => ! [A2: A,B: A] :
% 2.71/1.47 ( ( minus_minus @ A @ A2 @ ( plus_plus @ A @ A2 @ B ) )
% 2.71/1.47 = ( zero_zero @ A ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_231_abs__of__nonneg,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordere142940540dd_abs @ A )
% 2.71/1.47 => ! [A2: A] :
% 2.71/1.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.71/1.47 => ( ( abs_abs @ A @ A2 )
% 2.71/1.47 = A2 ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_232_abs__le__self__iff,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordere142940540dd_abs @ A )
% 2.71/1.47 => ! [A2: A] :
% 2.71/1.47 ( ( ord_less_eq @ A @ ( abs_abs @ A @ A2 ) @ A2 )
% 2.71/1.47 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_233_abs__le__zero__iff,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordere142940540dd_abs @ A )
% 2.71/1.47 => ! [A2: A] :
% 2.71/1.47 ( ( ord_less_eq @ A @ ( abs_abs @ A @ A2 ) @ ( zero_zero @ A ) )
% 2.71/1.47 = ( A2
% 2.71/1.47 = ( zero_zero @ A ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_234_zero__le,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( canoni770627133id_add @ A )
% 2.71/1.47 => ! [X: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_235_diff__commute,axiom,
% 2.71/1.47 ! [I: nat,J: nat,K: nat] :
% 2.71/1.47 ( ( minus_minus @ nat @ ( minus_minus @ nat @ I @ J ) @ K )
% 2.71/1.47 = ( minus_minus @ nat @ ( minus_minus @ nat @ I @ K ) @ J ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_236_zero__reorient,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( zero @ A )
% 2.71/1.47 => ! [X: A] :
% 2.71/1.47 ( ( ( zero_zero @ A )
% 2.71/1.47 = X )
% 2.71/1.47 = ( X
% 2.71/1.47 = ( zero_zero @ A ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_237_abs__eq__0__iff,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( idom_abs_sgn @ A )
% 2.71/1.47 => ! [A2: A] :
% 2.71/1.47 ( ( ( abs_abs @ A @ A2 )
% 2.71/1.47 = ( zero_zero @ A ) )
% 2.71/1.47 = ( A2
% 2.71/1.47 = ( zero_zero @ A ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_238_eq__iff__diff__eq__0,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( group_add @ A )
% 2.71/1.47 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 2.71/1.47 = ( ^ [A3: A,B2: A] :
% 2.71/1.47 ( ( minus_minus @ A @ A3 @ B2 )
% 2.71/1.47 = ( zero_zero @ A ) ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_239_zero__neq__one,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( zero_neq_one @ A )
% 2.71/1.47 => ( ( zero_zero @ A )
% 2.71/1.47 != ( one_one @ A ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_240_add_Ogroup__left__neutral,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( group_add @ A )
% 2.71/1.47 => ! [A2: A] :
% 2.71/1.47 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 2.71/1.47 = A2 ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_241_add_Ocomm__neutral,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( comm_monoid_add @ A )
% 2.71/1.47 => ! [A2: A] :
% 2.71/1.47 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 2.71/1.47 = A2 ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_242_comm__monoid__add__class_Oadd__0,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( comm_monoid_add @ A )
% 2.71/1.47 => ! [A2: A] :
% 2.71/1.47 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 2.71/1.47 = A2 ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_243_add__decreasing,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordere216010020id_add @ A )
% 2.71/1.47 => ! [A2: A,C: A,B: A] :
% 2.71/1.47 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.71/1.47 => ( ( ord_less_eq @ A @ C @ B )
% 2.71/1.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ B ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_244_add__increasing,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordere216010020id_add @ A )
% 2.71/1.47 => ! [A2: A,B: A,C: A] :
% 2.71/1.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.71/1.47 => ( ( ord_less_eq @ A @ B @ C )
% 2.71/1.47 => ( ord_less_eq @ A @ B @ ( plus_plus @ A @ A2 @ C ) ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_245_add__decreasing2,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordere216010020id_add @ A )
% 2.71/1.47 => ! [C: A,A2: A,B: A] :
% 2.71/1.47 ( ( ord_less_eq @ A @ C @ ( zero_zero @ A ) )
% 2.71/1.47 => ( ( ord_less_eq @ A @ A2 @ B )
% 2.71/1.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ B ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_246_add__increasing2,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordere216010020id_add @ A )
% 2.71/1.47 => ! [C: A,B: A,A2: A] :
% 2.71/1.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 2.71/1.47 => ( ( ord_less_eq @ A @ B @ A2 )
% 2.71/1.47 => ( ord_less_eq @ A @ B @ ( plus_plus @ A @ A2 @ C ) ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_247_add__nonneg__nonneg,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordere216010020id_add @ A )
% 2.71/1.47 => ! [A2: A,B: A] :
% 2.71/1.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.71/1.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B )
% 2.71/1.47 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ B ) ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_248_add__nonpos__nonpos,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordere216010020id_add @ A )
% 2.71/1.47 => ! [A2: A,B: A] :
% 2.71/1.47 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.71/1.47 => ( ( ord_less_eq @ A @ B @ ( zero_zero @ A ) )
% 2.71/1.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_249_add__nonneg__eq__0__iff,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordere216010020id_add @ A )
% 2.71/1.47 => ! [X: A,Y: A] :
% 2.71/1.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X )
% 2.71/1.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ Y )
% 2.71/1.47 => ( ( ( plus_plus @ A @ X @ Y )
% 2.71/1.47 = ( zero_zero @ A ) )
% 2.71/1.47 = ( ( X
% 2.71/1.47 = ( zero_zero @ A ) )
% 2.71/1.47 & ( Y
% 2.71/1.47 = ( zero_zero @ A ) ) ) ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_250_add__nonpos__eq__0__iff,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordere216010020id_add @ A )
% 2.71/1.47 => ! [X: A,Y: A] :
% 2.71/1.47 ( ( ord_less_eq @ A @ X @ ( zero_zero @ A ) )
% 2.71/1.47 => ( ( ord_less_eq @ A @ Y @ ( zero_zero @ A ) )
% 2.71/1.47 => ( ( ( plus_plus @ A @ X @ Y )
% 2.71/1.47 = ( zero_zero @ A ) )
% 2.71/1.47 = ( ( X
% 2.71/1.47 = ( zero_zero @ A ) )
% 2.71/1.47 & ( Y
% 2.71/1.47 = ( zero_zero @ A ) ) ) ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_251_zero__le__one,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( linord1659791738miring @ A )
% 2.71/1.47 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_252_not__one__le__zero,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( linord1659791738miring @ A )
% 2.71/1.47 => ~ ( ord_less_eq @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(fact_253_le__iff__diff__le__0,axiom,
% 2.71/1.47 ! [A: $tType] :
% 2.71/1.47 ( ( ordered_ab_group_add @ A )
% 2.71/1.47 => ( ( ord_less_eq @ A )
% 2.71/1.47 = ( ^ [A3: A,B2: A] : ( ord_less_eq @ A @ ( minus_minus @ A @ A3 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.71/1.47 ! [A7: $tType,A8: $tType] :
% 2.71/1.47 ( ( preorder @ A8 )
% 2.71/1.47 => ( preorder @ ( A7 > A8 ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.71/1.47 ! [A7: $tType,A8: $tType] :
% 2.71/1.47 ( ( order @ A8 )
% 2.71/1.47 => ( order @ ( A7 > A8 ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_fun___Orderings_Oord,axiom,
% 2.71/1.47 ! [A7: $tType,A8: $tType] :
% 2.71/1.47 ( ( ord @ A8 )
% 2.71/1.47 => ( ord @ ( A7 > A8 ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_fun___Groups_Ominus,axiom,
% 2.71/1.47 ! [A7: $tType,A8: $tType] :
% 2.71/1.47 ( ( minus @ A8 )
% 2.71/1.47 => ( minus @ ( A7 > A8 ) ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le,axiom,
% 2.71/1.47 ordere516151231imp_le @ nat ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Nat_Onat___Groups_Oordered__cancel__comm__monoid__diff,axiom,
% 2.71/1.47 ordere623563068d_diff @ nat ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 2.71/1.47 ordere236663937imp_le @ nat ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 2.71/1.47 canoni770627133id_add @ nat ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring,axiom,
% 2.71/1.47 linord1659791738miring @ nat ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
% 2.71/1.47 ordere779506340up_add @ nat ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Nat_Onat___Groups_Oordered__comm__monoid__add,axiom,
% 2.71/1.47 ordere216010020id_add @ nat ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
% 2.71/1.47 cancel146912293up_add @ nat ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add,axiom,
% 2.71/1.47 cancel1352612707id_add @ nat ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
% 2.71/1.47 cancel_semigroup_add @ nat ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Nat_Onat___Rings_Olinordered__semidom,axiom,
% 2.71/1.47 linordered_semidom @ nat ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__diff,axiom,
% 2.71/1.47 comm_monoid_diff @ nat ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add,axiom,
% 2.71/1.47 ab_semigroup_add @ nat ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
% 2.71/1.47 comm_monoid_add @ nat ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Nat_Onat___Groups_Osemigroup__add,axiom,
% 2.71/1.47 semigroup_add @ nat ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Nat_Onat___Rings_Ozero__neq__one,axiom,
% 2.71/1.47 zero_neq_one @ nat ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 2.71/1.47 preorder @ nat ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 2.71/1.47 linorder @ nat ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Nat_Onat___Groups_Omonoid__add,axiom,
% 2.71/1.47 monoid_add @ nat ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 2.71/1.47 order @ nat ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 2.71/1.47 ord @ nat ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Nat_Onat___Groups_Ominus_4,axiom,
% 2.71/1.47 minus @ nat ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 2.71/1.47 zero @ nat ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 2.71/1.47 one @ nat ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_HOL_Obool___Orderings_Opreorder_5,axiom,
% 2.71/1.47 preorder @ $o ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_HOL_Obool___Orderings_Olinorder_6,axiom,
% 2.71/1.47 linorder @ $o ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_HOL_Obool___Orderings_Oorder_7,axiom,
% 2.71/1.47 order @ $o ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_HOL_Obool___Orderings_Oord_8,axiom,
% 2.71/1.47 ord @ $o ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_HOL_Obool___Groups_Ominus_9,axiom,
% 2.71/1.47 minus @ $o ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__monoid__add__imp__le_10,axiom,
% 2.71/1.47 ordere516151231imp_le @ real ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le_11,axiom,
% 2.71/1.47 ordere236663937imp_le @ real ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_12,axiom,
% 2.71/1.47 linord1659791738miring @ real ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add_13,axiom,
% 2.71/1.47 ordere779506340up_add @ real ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Groups_Oordered__ab__group__add__abs,axiom,
% 2.71/1.47 ordere142940540dd_abs @ real ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Groups_Oordered__comm__monoid__add_14,axiom,
% 2.71/1.47 ordere216010020id_add @ real ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Groups_Olinordered__ab__group__add,axiom,
% 2.71/1.47 linord219039673up_add @ real ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Groups_Ocancel__ab__semigroup__add_15,axiom,
% 2.71/1.47 cancel146912293up_add @ real ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add_16,axiom,
% 2.71/1.47 cancel1352612707id_add @ real ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Groups_Oordered__ab__group__add,axiom,
% 2.71/1.47 ordered_ab_group_add @ real ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Groups_Ocancel__semigroup__add_17,axiom,
% 2.71/1.47 cancel_semigroup_add @ real ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Rings_Olinordered__semidom_18,axiom,
% 2.71/1.47 linordered_semidom @ real ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Groups_Oab__semigroup__add_19,axiom,
% 2.71/1.47 ab_semigroup_add @ real ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Groups_Ocomm__monoid__add_20,axiom,
% 2.71/1.47 comm_monoid_add @ real ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Rings_Olinordered__idom,axiom,
% 2.71/1.47 linordered_idom @ real ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Groups_Osemigroup__add_21,axiom,
% 2.71/1.47 semigroup_add @ real ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Groups_Oab__group__add,axiom,
% 2.71/1.47 ab_group_add @ real ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Rings_Ozero__neq__one_22,axiom,
% 2.71/1.47 zero_neq_one @ real ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Rings_Oidom__abs__sgn,axiom,
% 2.71/1.47 idom_abs_sgn @ real ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Orderings_Opreorder_23,axiom,
% 2.71/1.47 preorder @ real ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Orderings_Olinorder_24,axiom,
% 2.71/1.47 linorder @ real ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Groups_Omonoid__add_25,axiom,
% 2.71/1.47 monoid_add @ real ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Groups_Ogroup__add,axiom,
% 2.71/1.47 group_add @ real ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Orderings_Oorder_26,axiom,
% 2.71/1.47 order @ real ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Orderings_Oord_27,axiom,
% 2.71/1.47 ord @ real ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Groups_Ominus_28,axiom,
% 2.71/1.47 minus @ real ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Groups_Ozero_29,axiom,
% 2.71/1.47 zero @ real ).
% 2.71/1.47
% 2.71/1.47 thf(tcon_Real_Oreal___Groups_Oone_30,axiom,
% 2.71/1.47 one @ real ).
% 2.71/1.47
% 2.71/1.47 thf(help_If_3_1_T,axiom,
% 2.71/1.47 ! [P3: $o] :
% 2.71/1.47 ( ( P3 = $true )
% 2.71/1.47 | ( P3 = $false ) ) ).
% 2.71/1.47
% 2.71/1.47 thf(help_If_2_1_T,axiom,
% 2.71/1.47 ! [A: $tType,X: A,Y: A] :
% 2.71/1.47 ( ( if @ A @ $false @ X @ Y )
% 2.71/1.47 = Y ) ).
% 2.71/1.47
% 2.71/1.47 thf(help_If_1_1_T,axiom,
% 2.71/1.47 ! [A: $tType,X: A,Y: A] :
% 2.71/1.47 ( ( if @ A @ $true @ X @ Y )
% 2.71/1.47 = X ) ).
% 2.71/1.47
% 2.71/1.47 thf(conj_0,conjecture,
% 2.71/1.47 genClo1015804716orrect @ m @ ( ord_max @ real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) ).
% 2.71/1.47 ------------------------
% 2.71/1.49 % (982)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/2Mi)
% 2.71/1.50 % (982)Instruction limit reached!
% 2.71/1.50 % (982)------------------------------
% 2.71/1.50 % (982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.50 % (982)Termination reason: Unknown
% 2.71/1.50 % (982)Termination phase: shuffling
% 2.71/1.50
% 2.71/1.50 % (982)Memory used [KB]: 1279
% 2.71/1.50 % (982)Time elapsed: 0.002 s
% 2.71/1.50 % (982)Instructions burned: 2 (million)
% 2.71/1.50 % (982)------------------------------
% 2.71/1.50 % (982)------------------------------
% 2.71/1.50 % (980)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/4Mi)
% 2.71/1.50 % (981)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/27Mi)
% 2.71/1.50 % (983)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/2Mi)
% 2.79/1.50 % (983)Instruction limit reached!
% 2.79/1.50 % (983)------------------------------
% 2.79/1.50 % (983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.50 % (983)Termination reason: Unknown
% 2.79/1.50 % (983)Termination phase: shuffling
% 2.79/1.50
% 2.79/1.50 % (983)Memory used [KB]: 1279
% 2.79/1.50 % (983)Time elapsed: 0.002 s
% 2.79/1.50 % (983)Instructions burned: 2 (million)
% 2.79/1.50 % (983)------------------------------
% 2.79/1.50 % (983)------------------------------
% 2.79/1.50 % (980)Instruction limit reached!
% 2.79/1.50 % (980)------------------------------
% 2.79/1.50 % (980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.50 % (980)Termination reason: Unknown
% 2.79/1.50 % (980)Termination phase: shuffling
% 2.79/1.50
% 2.79/1.50 % (980)Memory used [KB]: 1407
% 2.79/1.50 % (980)Time elapsed: 0.003 s
% 2.79/1.50 % (980)Instructions burned: 6 (million)
% 2.79/1.50 % (980)------------------------------
% 2.79/1.50 % (980)------------------------------
% 2.79/1.50 % (979)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/183Mi)
% 2.79/1.50 % (985)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/18Mi)
% 2.79/1.50 % (984)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/275Mi)
% 2.79/1.50 % (986)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/3Mi)
% 2.79/1.51 % (981)Instruction limit reached!
% 2.79/1.51 % (981)------------------------------
% 2.79/1.51 % (981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.51 % (981)Termination reason: Unknown
% 2.79/1.51 % (981)Termination phase: Property scanning
% 2.79/1.51
% 2.79/1.51 % (981)Memory used [KB]: 1663
% 2.79/1.51 % (981)Time elapsed: 0.011 s
% 2.79/1.51 % (981)Instructions burned: 30 (million)
% 2.79/1.51 % (981)------------------------------
% 2.79/1.51 % (981)------------------------------
% 2.79/1.51 % (986)Instruction limit reached!
% 2.79/1.51 % (986)------------------------------
% 2.79/1.51 % (986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.51 % (986)Termination reason: Unknown
% 2.79/1.51 % (986)Termination phase: shuffling
% 2.79/1.51
% 2.79/1.51 % (986)Memory used [KB]: 1279
% 2.79/1.51 % (986)Time elapsed: 0.002 s
% 2.79/1.51 % (986)Instructions burned: 3 (million)
% 2.79/1.51 % (986)------------------------------
% 2.79/1.51 % (986)------------------------------
% 2.79/1.51 % (987)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/37Mi)
% 2.79/1.51 % (988)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/15Mi)
% 2.79/1.51 % (988)Instruction limit reached!
% 2.79/1.51 % (988)------------------------------
% 2.79/1.51 % (988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.51 % (988)Termination reason: Unknown
% 2.79/1.51 % (988)Termination phase: shuffling
% 2.79/1.51
% 2.79/1.51 % (988)Memory used [KB]: 1535
% 2.79/1.51 % (988)Time elapsed: 0.007 s
% 2.79/1.51 % (988)Instructions burned: 16 (million)
% 2.79/1.51 % (988)------------------------------
% 2.79/1.51 % (988)------------------------------
% 2.79/1.51 % (985)Instruction limit reached!
% 2.79/1.51 % (985)------------------------------
% 2.79/1.51 % (985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.51 % (985)Termination reason: Unknown
% 2.79/1.51 % (985)Termination phase: shuffling
% 2.79/1.51
% 2.79/1.51 % (985)Memory used [KB]: 1663
% 2.79/1.51 % (985)Time elapsed: 0.014 s
% 2.79/1.51 % (985)Instructions burned: 19 (million)
% 2.79/1.51 % (985)------------------------------
% 2.79/1.51 % (985)------------------------------
% 2.79/1.52 % (992)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/1041Mi)
% 2.79/1.52 % (991)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/3Mi)
% 2.79/1.52 % (991)Instruction limit reached!
% 2.79/1.52 % (991)------------------------------
% 2.79/1.52 % (991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.52 % (991)Termination reason: Unknown
% 2.79/1.52 % (991)Termination phase: shuffling
% 2.79/1.52
% 2.79/1.52 % (991)Memory used [KB]: 1407
% 2.79/1.52 % (991)Time elapsed: 0.003 s
% 2.79/1.52 % (991)Instructions burned: 3 (million)
% 2.79/1.52 % (991)------------------------------
% 2.79/1.52 % (991)------------------------------
% 2.79/1.52 % (987)Instruction limit reached!
% 2.79/1.52 % (987)------------------------------
% 2.79/1.52 % (987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.52 % (987)Termination reason: Unknown
% 2.79/1.52 % (987)Termination phase: Property scanning
% 2.79/1.52
% 2.79/1.52 % (987)Memory used [KB]: 2046
% 2.79/1.52 % (987)Time elapsed: 0.013 s
% 2.79/1.52 % (987)Instructions burned: 38 (million)
% 2.79/1.52 % (987)------------------------------
% 2.79/1.52 % (987)------------------------------
% 2.79/1.52 % (993)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/7Mi)
% 2.79/1.52 % (993)Instruction limit reached!
% 2.79/1.52 % (993)------------------------------
% 2.79/1.52 % (993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.52 % (993)Termination reason: Unknown
% 2.79/1.52 % (993)Termination phase: shuffling
% 2.79/1.52
% 2.79/1.52 % (993)Memory used [KB]: 1407
% 2.79/1.52 % (993)Time elapsed: 0.004 s
% 2.79/1.52 % (993)Instructions burned: 9 (million)
% 2.79/1.52 % (993)------------------------------
% 2.79/1.52 % (993)------------------------------
% 2.79/1.53 % (995)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/3Mi)
% 2.79/1.53 % (995)Instruction limit reached!
% 2.79/1.53 % (995)------------------------------
% 2.79/1.53 % (995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.53 % (995)Termination reason: Unknown
% 2.79/1.53 % (995)Termination phase: shuffling
% 2.79/1.53
% 2.79/1.53 % (995)Memory used [KB]: 1407
% 2.79/1.53 % (995)Time elapsed: 0.003 s
% 2.79/1.53 % (995)Instructions burned: 4 (million)
% 2.79/1.53 % (995)------------------------------
% 2.79/1.53 % (995)------------------------------
% 2.79/1.53 % (996)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/3Mi)
% 2.79/1.53 % (984)Refutation not found, incomplete strategy
% 2.79/1.53 % (984)------------------------------
% 2.79/1.53 % (984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.53 % (984)Termination reason: Refutation not found, incomplete strategy
% 2.79/1.53
% 2.79/1.53
% 2.79/1.53 % (984)Memory used [KB]: 6396
% 2.79/1.53 % (984)Time elapsed: 0.027 s
% 2.79/1.53 % (984)Instructions burned: 46 (million)
% 2.79/1.53 % (984)------------------------------
% 2.79/1.53 % (984)------------------------------
% 2.79/1.53 % (996)Instruction limit reached!
% 2.79/1.53 % (996)------------------------------
% 2.79/1.53 % (996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.53 % (996)Termination reason: Unknown
% 2.79/1.53 % (996)Termination phase: shuffling
% 2.79/1.53
% 2.79/1.53 % (996)Memory used [KB]: 1407
% 2.79/1.53 % (996)Time elapsed: 0.003 s
% 2.79/1.53 % (996)Instructions burned: 3 (million)
% 2.79/1.53 % (996)------------------------------
% 2.79/1.53 % (996)------------------------------
% 2.79/1.53 % (994)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/16Mi)
% 2.79/1.53 % (997)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/7Mi)
% 2.79/1.54 % (997)Instruction limit reached!
% 2.79/1.54 % (997)------------------------------
% 2.79/1.54 % (997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.54 % (997)Termination reason: Unknown
% 2.79/1.54 % (997)Termination phase: shuffling
% 2.79/1.54
% 2.79/1.54 % (997)Memory used [KB]: 1407
% 2.79/1.54 % (997)Time elapsed: 0.004 s
% 2.79/1.54 % (997)Instructions burned: 9 (million)
% 2.79/1.54 % (997)------------------------------
% 2.79/1.54 % (997)------------------------------
% 2.79/1.54 % (998)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/3Mi)
% 2.79/1.54 % (999)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/4Mi)
% 2.79/1.54 % (998)Instruction limit reached!
% 2.79/1.54 % (998)------------------------------
% 2.79/1.54 % (998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.54 % (998)Termination reason: Unknown
% 2.79/1.54 % (998)Termination phase: shuffling
% 2.79/1.54
% 2.79/1.54 % (998)Memory used [KB]: 1407
% 2.79/1.54 % (998)Time elapsed: 0.003 s
% 2.79/1.54 % (998)Instructions burned: 4 (million)
% 2.79/1.54 % (998)------------------------------
% 2.79/1.54 % (998)------------------------------
% 2.79/1.54 % (1000)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/18Mi)
% 2.79/1.54 % (999)Instruction limit reached!
% 2.79/1.54 % (999)------------------------------
% 2.79/1.54 % (999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.54 % (999)Termination reason: Unknown
% 2.79/1.54 % (999)Termination phase: shuffling
% 2.79/1.54
% 2.79/1.54 % (999)Memory used [KB]: 1407
% 2.79/1.54 % (999)Time elapsed: 0.004 s
% 2.79/1.54 % (999)Instructions burned: 6 (million)
% 2.79/1.54 % (999)------------------------------
% 2.79/1.54 % (999)------------------------------
% 2.79/1.54 % (994)Instruction limit reached!
% 2.79/1.54 % (994)------------------------------
% 2.79/1.54 % (994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.54 % (994)Termination reason: Unknown
% 2.79/1.54 % (994)Termination phase: shuffling
% 2.79/1.54
% 2.79/1.54 % (994)Memory used [KB]: 1663
% 2.79/1.54 % (994)Time elapsed: 0.012 s
% 2.79/1.54 % (994)Instructions burned: 16 (million)
% 2.79/1.54 % (994)------------------------------
% 2.79/1.54 % (994)------------------------------
% 2.79/1.55 % (1000)Instruction limit reached!
% 2.79/1.55 % (1000)------------------------------
% 2.79/1.55 % (1000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.55 % (1000)Termination reason: Unknown
% 2.79/1.55 % (1000)Termination phase: shuffling
% 2.79/1.55
% 2.79/1.55 % (1000)Memory used [KB]: 1663
% 2.79/1.55 % (1000)Time elapsed: 0.008 s
% 2.79/1.55 % (1000)Instructions burned: 18 (million)
% 2.79/1.55 % (1000)------------------------------
% 2.79/1.55 % (1000)------------------------------
% 2.79/1.55 % (1001)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/710Mi)
% 2.79/1.55 % (1002)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/6Mi)
% 2.79/1.55 % (1003)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/902Mi)
% 2.79/1.55 % (1002)Instruction limit reached!
% 2.79/1.55 % (1002)------------------------------
% 2.79/1.55 % (1002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.55 % (1002)Termination reason: Unknown
% 2.79/1.55 % (1002)Termination phase: shuffling
% 2.79/1.55
% 2.79/1.55 % (1002)Memory used [KB]: 1407
% 2.79/1.55 % (1002)Time elapsed: 0.004 s
% 2.79/1.55 % (1002)Instructions burned: 7 (million)
% 2.79/1.55 % (1002)------------------------------
% 2.79/1.55 % (1002)------------------------------
% 2.79/1.56 % (1005)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/5Mi)
% 2.79/1.56 % (1005)Instruction limit reached!
% 2.79/1.56 % (1005)------------------------------
% 2.79/1.56 % (1005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.56 % (1005)Termination reason: Unknown
% 2.79/1.56 % (1005)Termination phase: shuffling
% 2.79/1.56
% 2.79/1.56 % (1005)Memory used [KB]: 1407
% 2.79/1.56 % (1005)Time elapsed: 0.004 s
% 2.79/1.56 % (1005)Instructions burned: 8 (million)
% 2.79/1.56 % (1005)------------------------------
% 2.79/1.56 % (1005)------------------------------
% 2.79/1.56 % (1004)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/21Mi)
% 2.79/1.56 % (1006)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/6Mi)
% 2.79/1.56 % (1006)Instruction limit reached!
% 2.79/1.56 % (1006)------------------------------
% 2.79/1.56 % (1006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.56 % (1006)Termination reason: Unknown
% 2.79/1.56 % (1006)Termination phase: shuffling
% 2.79/1.56
% 2.79/1.56 % (1006)Memory used [KB]: 1407
% 2.79/1.56 % (1006)Time elapsed: 0.004 s
% 2.79/1.56 % (1006)Instructions burned: 7 (million)
% 2.79/1.56 % (1006)------------------------------
% 2.79/1.56 % (1006)------------------------------
% 2.79/1.57 % (1007)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/377Mi)
% 2.79/1.57 % (979)Instruction limit reached!
% 2.79/1.57 % (979)------------------------------
% 2.79/1.57 % (979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.57 % (979)Termination reason: Unknown
% 2.79/1.57 % (979)Termination phase: Saturation
% 2.79/1.57
% 2.79/1.57 % (979)Memory used [KB]: 6780
% 2.79/1.57 % (979)Time elapsed: 0.069 s
% 2.79/1.57 % (979)Instructions burned: 183 (million)
% 2.79/1.57 % (979)------------------------------
% 2.79/1.57 % (979)------------------------------
% 2.79/1.57 % (1004)Instruction limit reached!
% 2.79/1.57 % (1004)------------------------------
% 2.79/1.57 % (1004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.57 % (1004)Termination reason: Unknown
% 2.79/1.57 % (1004)Termination phase: Property scanning
% 2.79/1.57
% 2.79/1.57 % (1004)Memory used [KB]: 1663
% 2.79/1.57 % (1004)Time elapsed: 0.015 s
% 2.79/1.57 % (1004)Instructions burned: 21 (million)
% 2.79/1.57 % (1004)------------------------------
% 2.79/1.57 % (1004)------------------------------
% 2.79/1.57 % (1008)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/779Mi)
% 2.79/1.58 % (1009)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/19Mi)
% 2.79/1.58 % (1009)Instruction limit reached!
% 2.79/1.58 % (1009)------------------------------
% 2.79/1.58 % (1009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.58 % (1009)Termination reason: Unknown
% 2.79/1.58 % (1009)Termination phase: shuffling
% 2.79/1.58
% 2.79/1.58 % (1009)Memory used [KB]: 1791
% 2.79/1.58 % (1009)Time elapsed: 0.007 s
% 2.79/1.58 % (1009)Instructions burned: 22 (million)
% 2.79/1.58 % (1009)------------------------------
% 2.79/1.58 % (1009)------------------------------
% 2.79/1.59 % (1010)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_740 for (2999ds/879Mi)
% 2.79/1.59 % (1011)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_740 for (2998ds/17Mi)
% 2.79/1.60 % (1011)Instruction limit reached!
% 2.79/1.60 % (1011)------------------------------
% 2.79/1.60 % (1011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.60 % (1011)Termination reason: Unknown
% 2.79/1.60 % (1011)Termination phase: shuffling
% 2.79/1.60
% 2.79/1.60 % (1011)Memory used [KB]: 1663
% 2.79/1.60 % (1011)Time elapsed: 0.007 s
% 2.79/1.60 % (1011)Instructions burned: 19 (million)
% 2.79/1.60 % (1011)------------------------------
% 2.79/1.60 % (1011)------------------------------
% 2.79/1.61 % (1014)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_740 for (2998ds/3Mi)
% 2.79/1.61 % (1014)Instruction limit reached!
% 2.79/1.61 % (1014)------------------------------
% 2.79/1.61 % (1014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.61 % (1014)Termination reason: Unknown
% 2.79/1.61 % (1014)Termination phase: shuffling
% 2.79/1.61
% 2.79/1.61 % (1014)Memory used [KB]: 1407
% 2.79/1.61 % (1014)Time elapsed: 0.003 s
% 2.79/1.61 % (1014)Instructions burned: 5 (million)
% 2.79/1.61 % (1014)------------------------------
% 2.79/1.61 % (1014)------------------------------
% 2.79/1.62 % (1016)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_740 for (2998ds/30Mi)
% 2.79/1.63 % (1016)Instruction limit reached!
% 2.79/1.63 % (1016)------------------------------
% 2.79/1.63 % (1016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.63 % (1016)Termination reason: Unknown
% 2.79/1.63 % (1016)Termination phase: Property scanning
% 2.79/1.63
% 2.79/1.63 % (1016)Memory used [KB]: 1663
% 2.79/1.63 % (1016)Time elapsed: 0.010 s
% 2.79/1.63 % (1016)Instructions burned: 30 (million)
% 2.79/1.63 % (1016)------------------------------
% 2.79/1.63 % (1016)------------------------------
% 2.79/1.64 % (1018)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_740 for (2998ds/127Mi)
% 2.79/1.68 % (1018)Instruction limit reached!
% 2.79/1.68 % (1018)------------------------------
% 2.79/1.68 % (1018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.68 % (1018)Termination reason: Unknown
% 2.79/1.68 % (1018)Termination phase: Saturation
% 2.79/1.68
% 2.79/1.68 % (1018)Memory used [KB]: 6652
% 2.79/1.68 % (1018)Time elapsed: 0.040 s
% 2.79/1.68 % (1018)Instructions burned: 129 (million)
% 2.79/1.68 % (1018)------------------------------
% 2.79/1.68 % (1018)------------------------------
% 2.79/1.69 % (1021)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_740 for (2998ds/100Mi)
% 2.79/1.69 % (1007)Instruction limit reached!
% 2.79/1.69 % (1007)------------------------------
% 2.79/1.69 % (1007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.69 % (1007)Termination reason: Unknown
% 2.79/1.69 % (1007)Termination phase: Saturation
% 2.79/1.69
% 2.79/1.69 % (1007)Memory used [KB]: 7419
% 2.79/1.69 % (1007)Time elapsed: 0.125 s
% 2.79/1.69 % (1007)Instructions burned: 377 (million)
% 2.79/1.69 % (1007)------------------------------
% 2.79/1.69 % (1007)------------------------------
% 2.79/1.70 % (1022)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_740 for (2997ds/3Mi)
% 2.79/1.70 % (1022)Instruction limit reached!
% 2.79/1.70 % (1022)------------------------------
% 2.79/1.70 % (1022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.70 % (1022)Termination reason: Unknown
% 2.79/1.70 % (1022)Termination phase: shuffling
% 2.79/1.70
% 2.79/1.70 % (1022)Memory used [KB]: 1279
% 2.79/1.70 % (1022)Time elapsed: 0.002 s
% 2.79/1.70 % (1022)Instructions burned: 3 (million)
% 2.79/1.70 % (1022)------------------------------
% 2.79/1.70 % (1022)------------------------------
% 2.79/1.71 % (1023)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_740 for (2997ds/20Mi)
% 2.79/1.71 % (1021)Instruction limit reached!
% 2.79/1.71 % (1021)------------------------------
% 2.79/1.71 % (1021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.71 % (1021)Termination reason: Unknown
% 2.79/1.71 % (1021)Termination phase: Property scanning
% 2.79/1.71
% 2.79/1.71 % (1021)Memory used [KB]: 2174
% 2.79/1.71 % (1021)Time elapsed: 0.028 s
% 2.79/1.71 % (1021)Instructions burned: 101 (million)
% 2.79/1.71 % (1021)------------------------------
% 2.79/1.71 % (1021)------------------------------
% 2.79/1.72 % (1023)Instruction limit reached!
% 2.79/1.72 % (1023)------------------------------
% 2.79/1.72 % (1023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.72 % (1023)Termination reason: Unknown
% 2.79/1.72 % (1023)Termination phase: Property scanning
% 2.79/1.72
% 2.79/1.72 % (1023)Memory used [KB]: 1663
% 2.79/1.72 % (1023)Time elapsed: 0.008 s
% 2.79/1.72 % (1023)Instructions burned: 20 (million)
% 2.79/1.72 % (1023)------------------------------
% 2.79/1.72 % (1023)------------------------------
% 2.79/1.72 % (1024)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_740 for (2997ds/86Mi)
% 2.79/1.73 % (1025)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_740 for (2997ds/107Mi)
% 2.79/1.75 % (1024)Instruction limit reached!
% 2.79/1.75 % (1024)------------------------------
% 2.79/1.75 % (1024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.75 % (1024)Termination reason: Unknown
% 2.79/1.75 % (1024)Termination phase: Saturation
% 2.79/1.75
% 2.79/1.75 % (1024)Memory used [KB]: 6524
% 2.79/1.75 % (1024)Time elapsed: 0.026 s
% 2.79/1.75 % (1024)Instructions burned: 86 (million)
% 2.79/1.75 % (1024)------------------------------
% 2.79/1.75 % (1024)------------------------------
% 2.79/1.76 % (1026)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_740 for (2997ds/39Mi)
% 2.79/1.76 % (1025)Instruction limit reached!
% 2.79/1.76 % (1025)------------------------------
% 2.79/1.76 % (1025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.76 % (1025)Termination reason: Unknown
% 2.79/1.76 % (1025)Termination phase: Saturation
% 2.79/1.76
% 2.79/1.76 % (1025)Memory used [KB]: 6652
% 2.79/1.76 % (1025)Time elapsed: 0.034 s
% 2.79/1.76 % (1025)Instructions burned: 109 (million)
% 2.79/1.76 % (1025)------------------------------
% 2.79/1.76 % (1025)------------------------------
% 2.79/1.76 % (1001)Instruction limit reached!
% 2.79/1.76 % (1001)------------------------------
% 2.79/1.76 % (1001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.76 % (1001)Termination reason: Unknown
% 2.79/1.76 % (1001)Termination phase: Saturation
% 2.79/1.76
% 2.79/1.76 % (1001)Memory used [KB]: 7675
% 2.79/1.76 % (1001)Time elapsed: 0.219 s
% 2.79/1.76 % (1001)Instructions burned: 711 (million)
% 2.79/1.76 % (1001)------------------------------
% 2.79/1.76 % (1001)------------------------------
% 2.79/1.77 % (1026)Instruction limit reached!
% 2.79/1.77 % (1026)------------------------------
% 2.79/1.77 % (1026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.77 % (1026)Termination reason: Unknown
% 2.79/1.77 % (1026)Termination phase: Property scanning
% 2.79/1.77
% 2.79/1.77 % (1026)Memory used [KB]: 2046
% 2.79/1.77 % (1026)Time elapsed: 0.012 s
% 2.79/1.77 % (1026)Instructions burned: 40 (million)
% 2.79/1.77 % (1026)------------------------------
% 2.79/1.77 % (1026)------------------------------
% 2.79/1.77 % (1027)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_740 for (2997ds/448Mi)
% 2.79/1.77 % (1028)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_740 for (2997ds/46Mi)
% 2.79/1.78 % (1029)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_740 for (2997ds/98Mi)
% 2.79/1.79 % (1028)Instruction limit reached!
% 2.79/1.79 % (1028)------------------------------
% 2.79/1.79 % (1028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.79 % (1028)Termination reason: Unknown
% 2.79/1.79 % (1028)Termination phase: Property scanning
% 2.79/1.79
% 2.79/1.79 % (1028)Memory used [KB]: 1791
% 2.79/1.79 % (1028)Time elapsed: 0.015 s
% 2.79/1.79 % (1028)Instructions burned: 47 (million)
% 2.79/1.79 % (1028)------------------------------
% 2.79/1.79 % (1028)------------------------------
% 2.79/1.80 % (1030)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_740 for (2996ds/507Mi)
% 2.79/1.80 % (1029)Instruction limit reached!
% 2.79/1.80 % (1029)------------------------------
% 2.79/1.80 % (1029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.80 % (1029)Termination reason: Unknown
% 2.79/1.80 % (1029)Termination phase: Property scanning
% 2.79/1.80
% 2.79/1.80 % (1029)Memory used [KB]: 2174
% 2.79/1.80 % (1029)Time elapsed: 0.027 s
% 2.79/1.80 % (1029)Instructions burned: 100 (million)
% 2.79/1.80 % (1029)------------------------------
% 2.79/1.80 % (1029)------------------------------
% 2.79/1.81 % (1036)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_740 for (2996ds/149Mi)
% 2.79/1.82 % (1008)Instruction limit reached!
% 2.79/1.82 % (1008)------------------------------
% 2.79/1.82 % (1008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.82 % (1008)Termination reason: Unknown
% 2.79/1.82 % (1008)Termination phase: Saturation
% 2.79/1.82
% 2.79/1.82 % (1008)Memory used [KB]: 7803
% 2.79/1.82 % (1008)Time elapsed: 0.246 s
% 2.79/1.82 % (1008)Instructions burned: 780 (million)
% 2.79/1.82 % (1008)------------------------------
% 2.79/1.82 % (1008)------------------------------
% 2.79/1.83 % (1037)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_740 for (2996ds/39Mi)
% 2.79/1.83 % (992)Instruction limit reached!
% 2.79/1.83 % (992)------------------------------
% 2.79/1.83 % (992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.83 % (992)Termination reason: Unknown
% 2.79/1.83 % (992)Termination phase: Saturation
% 2.79/1.83
% 2.79/1.83 % (992)Memory used [KB]: 9338
% 2.79/1.83 % (992)Time elapsed: 0.314 s
% 2.79/1.83 % (992)Instructions burned: 1044 (million)
% 2.79/1.83 % (992)------------------------------
% 2.79/1.83 % (992)------------------------------
% 2.79/1.84 % (1003)Instruction limit reached!
% 2.79/1.84 % (1003)------------------------------
% 2.79/1.84 % (1003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.84 % (1003)Termination reason: Unknown
% 2.79/1.84 % (1003)Termination phase: Saturation
% 2.79/1.84
% 2.79/1.84 % (1003)Memory used [KB]: 7675
% 2.79/1.84 % (1003)Time elapsed: 0.287 s
% 2.79/1.84 % (1003)Instructions burned: 902 (million)
% 2.79/1.84 % (1003)------------------------------
% 2.79/1.84 % (1003)------------------------------
% 2.79/1.84 % (1038)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_740 for (2996ds/6Mi)
% 2.79/1.84 % (1038)Instruction limit reached!
% 2.79/1.84 % (1038)------------------------------
% 2.79/1.84 % (1038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.84 % (1038)Termination reason: Unknown
% 2.79/1.84 % (1038)Termination phase: shuffling
% 2.79/1.84
% 2.79/1.84 % (1038)Memory used [KB]: 1407
% 2.79/1.84 % (1038)Time elapsed: 0.003 s
% 2.79/1.84 % (1038)Instructions burned: 7 (million)
% 2.79/1.84 % (1037)Instruction limit reached!
% 2.79/1.84 % (1037)------------------------------
% 2.79/1.84 % (1037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.84 % (1038)------------------------------
% 2.79/1.84 % (1038)------------------------------
% 2.79/1.84 % (1037)Termination reason: Unknown
% 2.79/1.84 % (1037)Termination phase: Preprocessing 3
% 2.79/1.84
% 2.79/1.84 % (1037)Memory used [KB]: 1791
% 2.79/1.84 % (1037)Time elapsed: 0.013 s
% 2.79/1.84 % (1037)Instructions burned: 40 (million)
% 2.79/1.84 % (1037)------------------------------
% 2.79/1.84 % (1037)------------------------------
% 2.79/1.85 % (1039)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_740 for (2996ds/1087Mi)
% 2.79/1.85 % (1040)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_740 for (2996ds/47Mi)
% 2.79/1.85 % (1041)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_740 for (2996ds/44Mi)
% 2.79/1.86 % (1036)Instruction limit reached!
% 2.79/1.86 % (1036)------------------------------
% 2.79/1.86 % (1036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.86 % (1036)Termination reason: Unknown
% 2.79/1.86 % (1036)Termination phase: Saturation
% 2.79/1.86
% 2.79/1.86 % (1036)Memory used [KB]: 6780
% 2.79/1.86 % (1036)Time elapsed: 0.048 s
% 2.79/1.86 % (1036)Instructions burned: 150 (million)
% 2.79/1.86 % (1036)------------------------------
% 2.79/1.86 % (1036)------------------------------
% 2.79/1.86 % (1041)Instruction limit reached!
% 2.79/1.86 % (1041)------------------------------
% 2.79/1.86 % (1041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.86 % (1041)Termination reason: Unknown
% 2.79/1.86 % (1041)Termination phase: Property scanning
% 2.79/1.86
% 2.79/1.86 % (1041)Memory used [KB]: 2046
% 2.79/1.86 % (1041)Time elapsed: 0.014 s
% 2.79/1.86 % (1041)Instructions burned: 46 (million)
% 2.79/1.86 % (1041)------------------------------
% 2.79/1.86 % (1041)------------------------------
% 2.79/1.86 % (1040)Instruction limit reached!
% 2.79/1.86 % (1040)------------------------------
% 2.79/1.86 % (1040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.86 % (1040)Termination reason: Unknown
% 2.79/1.86 % (1040)Termination phase: Property scanning
% 2.79/1.86
% 2.79/1.86 % (1040)Memory used [KB]: 1918
% 2.79/1.86 % (1040)Time elapsed: 0.016 s
% 2.79/1.86 % (1040)Instructions burned: 49 (million)
% 2.79/1.86 % (1040)------------------------------
% 2.79/1.86 % (1040)------------------------------
% 2.79/1.87 % (1042)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_740 for (2996ds/432Mi)
% 2.79/1.87 % (1043)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_740 for (2996ds/62Mi)
% 2.79/1.87 % (1045)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_740 for (2996ds/31Mi)
% 2.79/1.88 % (1010)Instruction limit reached!
% 2.79/1.88 % (1010)------------------------------
% 2.79/1.88 % (1010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.88 % (1010)Termination reason: Unknown
% 2.79/1.88 % (1010)Termination phase: Saturation
% 2.79/1.88
% 2.79/1.88 % (1010)Memory used [KB]: 7931
% 2.79/1.88 % (1010)Time elapsed: 0.291 s
% 2.79/1.88 % (1010)Instructions burned: 881 (million)
% 2.79/1.88 % (1010)------------------------------
% 2.79/1.88 % (1010)------------------------------
% 2.79/1.88 % (1045)Instruction limit reached!
% 2.79/1.88 % (1045)------------------------------
% 2.79/1.88 % (1045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.88 % (1045)Termination reason: Unknown
% 2.79/1.88 % (1045)Termination phase: shuffling
% 2.79/1.88
% 2.79/1.88 % (1045)Memory used [KB]: 1663
% 2.79/1.88 % (1045)Time elapsed: 0.011 s
% 2.79/1.88 % (1045)Instructions burned: 34 (million)
% 2.79/1.88 % (1045)------------------------------
% 2.79/1.88 % (1045)------------------------------
% 2.79/1.89 % (1043)Instruction limit reached!
% 2.79/1.89 % (1043)------------------------------
% 2.79/1.89 % (1043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.89 % (1043)Termination reason: Unknown
% 2.79/1.89 % (1043)Termination phase: Preprocessing 3
% 2.79/1.89
% 2.79/1.89 % (1043)Memory used [KB]: 2174
% 2.79/1.89 % (1043)Time elapsed: 0.018 s
% 2.79/1.89 % (1043)Instructions burned: 64 (million)
% 2.79/1.89 % (1043)------------------------------
% 2.79/1.89 % (1043)------------------------------
% 2.79/1.89 % (1046)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_740 for (2996ds/96Mi)
% 2.79/1.89 % (1050)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_740 for (2996ds/453Mi)
% 2.79/1.90 % (1051)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_740 for (2995ds/71Mi)
% 2.79/1.90 % (1027)First to succeed.
% 2.79/1.90 % (1027)Refutation found. Thanks to Tanya!
% 2.79/1.90 % SZS status Theorem for DTF2THF_740
% 2.79/1.90 % SZS output start Proof for DTF2THF_740
% 2.79/1.90 thf(type_def_5, type, nat: $tType).
% 2.79/1.90 thf(type_def_6, type, real: $tType).
% 2.79/1.90 thf(func_def_0, type, real: $tType).
% 2.79/1.90 thf(func_def_1, type, nat: $tType).
% 2.79/1.90 thf(func_def_2, type, type: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_3, type, one: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_4, type, zero: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_5, type, minus: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_6, type, ord: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_7, type, order: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_8, type, group_add: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_9, type, monoid_add: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_10, type, linorder: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_11, type, preorder: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_12, type, idom_abs_sgn: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_13, type, zero_neq_one: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_14, type, ab_group_add: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_15, type, semigroup_add: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_16, type, linordered_idom: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_17, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_18, type, ab_semigroup_add: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_19, type, comm_monoid_diff: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_20, type, linordered_semidom: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_21, type, cancel_semigroup_add: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_22, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_23, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_24, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_25, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_26, type, ordere216010020id_add: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_27, type, ordere142940540dd_abs: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_28, type, ordere779506340up_add: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_29, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_30, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_31, type, ordere236663937imp_le: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_32, type, ordere623563068d_diff: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_33, type, ordere516151231imp_le: !>[X0: $tType]:($o)).
% 2.79/1.90 thf(func_def_34, type, genClo1160817912lle_IC: nat > nat > real > real).
% 2.79/1.90 thf(func_def_35, type, genClo721845095Lambda: real).
% 2.79/1.90 thf(func_def_36, type, genClo1278781456e_beta: real).
% 2.79/1.90 thf(func_def_37, type, genClo1400225944_theta: nat > nat > nat > real).
% 2.79/1.90 thf(func_def_38, type, genClo1015804716orrect: nat > real > $o).
% 2.79/1.90 thf(func_def_39, type, genClo293725281kRead1: (nat > real) > real > (nat > $o) > $o).
% 2.79/1.90 thf(func_def_40, type, genClo293725282kRead2: (nat > real) > (nat > real) > real > (nat > $o) > $o).
% 2.79/1.90 thf(func_def_41, type, genClo208577157axsync: nat > real > $o).
% 2.79/1.90 thf(func_def_42, type, genClo1650508560e_rmax: real).
% 2.79/1.90 thf(func_def_43, type, genClo1651033342e_rmin: real).
% 2.79/1.90 thf(func_def_44, type, genClo1163638703lle_te: nat > nat > real).
% 2.79/1.90 thf(func_def_45, type, abs_abs: !>[X0: $tType]:(X0 > X0)).
% 2.79/1.90 thf(func_def_46, type, minus_minus: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.79/1.90 thf(func_def_47, type, one_one: !>[X0: $tType]:(X0)).
% 2.79/1.90 thf(func_def_48, type, plus_plus: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.79/1.90 thf(func_def_49, type, zero_zero: !>[X0: $tType]:(X0)).
% 2.79/1.90 thf(func_def_50, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 2.79/1.90 thf(func_def_51, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.79/1.90 thf(func_def_52, type, ord_max: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.79/1.90 thf(func_def_53, type, delta_S: real).
% 2.79/1.90 thf(func_def_54, type, i: nat).
% 2.79/1.90 thf(func_def_55, type, l: nat).
% 2.79/1.90 thf(func_def_56, type, m: nat).
% 2.79/1.90 thf(func_def_57, type, p: nat).
% 2.79/1.90 thf(func_def_75, type, sK1: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.79/1.90 thf(func_def_76, type, sK2: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.79/1.90 thf(func_def_77, type, sK3: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.79/1.90 thf(func_def_78, type, sK4: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.79/1.90 thf(func_def_79, type, sK5: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.79/1.90 thf(func_def_80, type, sK6: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.79/1.90 thf(func_def_81, type, sK7: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.79/1.90 thf(func_def_82, type, sK8: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.79/1.90 thf(func_def_83, type, ph9: !>[X0: $tType]:(X0)).
% 2.79/1.90 thf(f3267,plain,(
% 2.79/1.90 $false),
% 2.79/1.90 inference(avatar_sat_refutation,[status(thm)],[f3022,f3266])).
% 2.79/1.90 thf(f3266,plain,(
% 2.79/1.90 spl0_6),
% 2.79/1.90 inference(avatar_split_clause,[status(thm)],[f3261,f2988])).
% 2.79/1.90 thf(f2988,definition,(
% 2.79/1.90 spl0_6 <=> ((genClo1015804716orrect @ m @ (genClo1163638703lle_te @ p @ (plus_plus @ nat @ i @ one_one @ nat))) = $false)),
% 2.79/1.90 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 2.79/1.90 thf(f3261,plain,(
% 2.79/1.90 ((genClo1015804716orrect @ m @ (genClo1163638703lle_te @ p @ (plus_plus @ nat @ i @ one_one @ nat))) = $false)),
% 2.79/1.90 inference(trivial_inequality_removal,[status(thm)],[f3253])).
% 2.79/1.90 thf(f3253,plain,(
% 2.79/1.90 ($true = $false) | ((genClo1015804716orrect @ m @ (genClo1163638703lle_te @ p @ (plus_plus @ nat @ i @ one_one @ nat))) = $false)),
% 2.79/1.90 inference(superposition,[status(thm)],[f1053,f2492])).
% 2.79/1.90 thf(f2492,plain,(
% 2.79/1.90 ( ! [X0 : real] : (((ord_less_eq @ real @ (ord_max @ real @ (genClo1163638703lle_te @ l @ i) @ (genClo1163638703lle_te @ m @ i)) @ X0) = $false) | ($false = (genClo1015804716orrect @ m @ X0))) )),
% 2.79/1.90 inference(trivial_inequality_removal,[status(thm)],[f2471])).
% 2.79/1.90 thf(f2471,plain,(
% 2.79/1.90 ( ! [X0 : real] : (($false = (genClo1015804716orrect @ m @ X0)) | ($true = $false) | ((ord_less_eq @ real @ (ord_max @ real @ (genClo1163638703lle_te @ l @ i) @ (genClo1163638703lle_te @ m @ i)) @ X0) = $false)) )),
% 2.79/1.90 inference(superposition,[status(thm)],[f2119,f1983])).
% 2.79/1.90 thf(f1983,plain,(
% 2.79/1.90 ((genClo1015804716orrect @ m @ (ord_max @ real @ (genClo1163638703lle_te @ l @ i) @ (genClo1163638703lle_te @ m @ i))) = $false)),
% 2.79/1.90 inference(not_proxy_clausification,[status(thm)],[f1118])).
% 2.79/1.90 thf(f1118,plain,(
% 2.79/1.90 ($true = (~ (genClo1015804716orrect @ m @ (ord_max @ real @ (genClo1163638703lle_te @ l @ i) @ (genClo1163638703lle_te @ m @ i)))))),
% 2.79/1.90 inference(cnf_transformation,[status(thm)],[f791])).
% 2.79/1.90 thf(f791,plain,(
% 2.79/1.90 ($true = (~ (genClo1015804716orrect @ m @ (ord_max @ real @ (genClo1163638703lle_te @ l @ i) @ (genClo1163638703lle_te @ m @ i)))))),
% 2.79/1.90 inference(fool_elimination,[status(thm)],[f790])).
% 2.79/1.90 thf(f790,plain,(
% 2.79/1.90 ~(genClo1015804716orrect @ m @ (ord_max @ real @ (genClo1163638703lle_te @ l @ i) @ (genClo1163638703lle_te @ m @ i)))),
% 2.79/1.90 inference(rectify,[status(thm)],[f320])).
% 2.79/1.90 thf(f320,negated_conjecture,(
% 2.79/1.90 ~(genClo1015804716orrect @ m @ (ord_max @ real @ (genClo1163638703lle_te @ l @ i) @ (genClo1163638703lle_te @ m @ i)))),
% 2.79/1.90 inference(negated_conjecture,[status(cth)],[f319])).
% 2.79/1.90 thf(f319,conjecture,(
% 2.79/1.90 (genClo1015804716orrect @ m @ (ord_max @ real @ (genClo1163638703lle_te @ l @ i) @ (genClo1163638703lle_te @ m @ i)))),
% 2.79/1.90 file('/export/starexec/sandbox2/tmp/tmp.Kaf6658Iwd/DTF2THF_740.p',conj_0)).
% 2.79/1.90 thf(f2119,plain,(
% 2.79/1.90 ( ! [X2 : real,X3 : nat,X1 : real] : (((genClo1015804716orrect @ X3 @ X1) = $false) | ((ord_less_eq @ real @ X2 @ X1) = $false) | ((genClo1015804716orrect @ X3 @ X2) = $true)) )),
% 2.79/1.90 inference(binary_proxy_clausification,[status(thm)],[f2118])).
% 2.79/1.90 thf(f2118,plain,(
% 2.79/1.90 ( ! [X2 : real,X3 : nat,X1 : real] : (((genClo1015804716orrect @ X3 @ X2) = $true) | (((ord_less_eq @ real @ X2 @ X1) & (genClo1015804716orrect @ X3 @ X1)) = $false)) )),
% 2.79/1.90 inference(binary_proxy_clausification,[status(thm)],[f2117])).
% 2.79/1.90 thf(f2117,plain,(
% 2.79/1.90 ( ! [X2 : real,X3 : nat,X1 : real] : (((((ord_less_eq @ real @ X2 @ X1) & (genClo1015804716orrect @ X3 @ X1)) => (genClo1015804716orrect @ X3 @ X2)) = $true)) )),
% 2.79/1.90 inference(beta_eta_normalization,[status(thm)],[f2116])).
% 2.79/1.90 thf(f2116,plain,(
% 2.79/1.90 ( ! [X2 : real,X3 : nat,X1 : real] : ((((^[Y0 : nat]: (((ord_less_eq @ real @ X2 @ X1) & (genClo1015804716orrect @ Y0 @ X1)) => (genClo1015804716orrect @ Y0 @ X2))) @ X3) = $true)) )),
% 2.79/1.90 inference(pi_clausification,[status(thm)],[f2115])).
% 2.79/1.90 thf(f2115,plain,(
% 2.79/1.90 ( ! [X2 : real,X1 : real] : (((!! @ nat @ (^[Y0 : nat]: (((ord_less_eq @ real @ X2 @ X1) & (genClo1015804716orrect @ Y0 @ X1)) => (genClo1015804716orrect @ Y0 @ X2)))) = $true)) )),
% 2.79/1.90 inference(beta_eta_normalization,[status(thm)],[f2114])).
% 2.79/1.90 thf(f2114,plain,(
% 2.79/1.90 ( ! [X2 : real,X1 : real] : ((((^[Y0 : real]: (!! @ nat @ (^[Y1 : nat]: (((ord_less_eq @ real @ Y0 @ X1) & (genClo1015804716orrect @ Y1 @ X1)) => (genClo1015804716orrect @ Y1 @ Y0))))) @ X2) = $true)) )),
% 2.79/1.90 inference(pi_clausification,[status(thm)],[f2113])).
% 2.79/1.90 thf(f2113,plain,(
% 2.79/1.90 ( ! [X1 : real] : (((!! @ real @ (^[Y0 : real]: (!! @ nat @ (^[Y1 : nat]: (((ord_less_eq @ real @ Y0 @ X1) & (genClo1015804716orrect @ Y1 @ X1)) => (genClo1015804716orrect @ Y1 @ Y0)))))) = $true)) )),
% 2.79/1.90 inference(beta_eta_normalization,[status(thm)],[f2112])).
% 2.79/1.90 thf(f2112,plain,(
% 2.79/1.90 ( ! [X1 : real] : ((((^[Y0 : real]: (!! @ real @ (^[Y1 : real]: (!! @ nat @ (^[Y2 : nat]: (((ord_less_eq @ real @ Y1 @ Y0) & (genClo1015804716orrect @ Y2 @ Y0)) => (genClo1015804716orrect @ Y2 @ Y1))))))) @ X1) = $true)) )),
% 2.79/1.90 inference(pi_clausification,[status(thm)],[f1063])).
% 2.79/1.90 thf(f1063,plain,(
% 2.79/1.90 ((!! @ real @ (^[Y0 : real]: (!! @ real @ (^[Y1 : real]: (!! @ nat @ (^[Y2 : nat]: (((ord_less_eq @ real @ Y1 @ Y0) & (genClo1015804716orrect @ Y2 @ Y0)) => (genClo1015804716orrect @ Y2 @ Y1)))))))) = $true)),
% 2.79/1.90 inference(cnf_transformation,[status(thm)],[f495])).
% 2.79/1.90 thf(f495,plain,(
% 2.79/1.90 ((!! @ real @ (^[Y0 : real]: (!! @ real @ (^[Y1 : real]: (!! @ nat @ (^[Y2 : nat]: (((ord_less_eq @ real @ Y1 @ Y0) & (genClo1015804716orrect @ Y2 @ Y0)) => (genClo1015804716orrect @ Y2 @ Y1)))))))) = $true)),
% 2.79/1.90 inference(fool_elimination,[status(thm)],[f494])).
% 2.79/1.90 thf(f494,plain,(
% 2.79/1.90 ! [X0 : nat,X1 : real,X2 : real] : (((genClo1015804716orrect @ X0 @ X2) & (ord_less_eq @ real @ X1 @ X2)) => (genClo1015804716orrect @ X0 @ X1))),
% 2.79/1.90 inference(rectify,[status(thm)],[f1])).
% 2.79/1.90 thf(f1,axiom,(
% 2.79/1.90 ! [X1 : nat,X2 : real,X3 : real] : (((genClo1015804716orrect @ X1 @ X3) & (ord_less_eq @ real @ X2 @ X3)) => (genClo1015804716orrect @ X1 @ X2))),
% 2.79/1.90 file('/export/starexec/sandbox2/tmp/tmp.Kaf6658Iwd/DTF2THF_740.p',fact_0_correct__closed)).
% 2.79/1.90 thf(f1053,plain,(
% 2.79/1.90 ((ord_less_eq @ real @ (ord_max @ real @ (genClo1163638703lle_te @ l @ i) @ (genClo1163638703lle_te @ m @ i)) @ (genClo1163638703lle_te @ p @ (plus_plus @ nat @ i @ one_one @ nat))) = $true)),
% 2.79/1.90 inference(cnf_transformation,[status(thm)],[f703])).
% 2.79/1.90 thf(f703,plain,(
% 2.79/1.90 ((ord_less_eq @ real @ (ord_max @ real @ (genClo1163638703lle_te @ l @ i) @ (genClo1163638703lle_te @ m @ i)) @ (genClo1163638703lle_te @ p @ (plus_plus @ nat @ i @ one_one @ nat))) = $true)),
% 2.79/1.90 inference(fool_elimination,[status(thm)],[f702])).
% 2.79/1.90 thf(f702,plain,(
% 2.79/1.90 (ord_less_eq @ real @ (ord_max @ real @ (genClo1163638703lle_te @ l @ i) @ (genClo1163638703lle_te @ m @ i)) @ (genClo1163638703lle_te @ p @ (plus_plus @ nat @ i @ one_one @ nat)))),
% 2.79/1.90 inference(rectify,[status(thm)],[f4])).
% 2.79/1.90 thf(f4,axiom,(
% 2.79/1.90 (ord_less_eq @ real @ (ord_max @ real @ (genClo1163638703lle_te @ l @ i) @ (genClo1163638703lle_te @ m @ i)) @ (genClo1163638703lle_te @ p @ (plus_plus @ nat @ i @ one_one @ nat)))),
% 2.79/1.90 file('/export/starexec/sandbox2/tmp/tmp.Kaf6658Iwd/DTF2THF_740.p',fact_3_tml__le__tp)).
% 2.79/1.90 thf(f3022,plain,(
% 2.79/1.90 ~spl0_6),
% 2.79/1.90 inference(avatar_contradiction_clause,[status(thm)],[f3021])).
% 2.79/1.90 thf(f3021,plain,(
% 2.79/1.90 $false | ~spl0_6),
% 2.79/1.90 inference(trivial_inequality_removal,[status(thm)],[f3015])).
% 2.79/1.90 thf(f3015,plain,(
% 2.79/1.90 ($true = $false) | ~spl0_6),
% 2.79/1.90 inference(backward_demodulation,[status(thm)],[f1131,f2990])).
% 2.79/1.90 thf(f2990,plain,(
% 2.79/1.90 ((genClo1015804716orrect @ m @ (genClo1163638703lle_te @ p @ (plus_plus @ nat @ i @ one_one @ nat))) = $false) | ~spl0_6),
% 2.79/1.90 inference(avatar_component_clause,[status(thm)],[f2988])).
% 2.79/1.90 thf(f1131,plain,(
% 2.79/1.90 ((genClo1015804716orrect @ m @ (genClo1163638703lle_te @ p @ (plus_plus @ nat @ i @ one_one @ nat))) = $true)),
% 2.79/1.90 inference(cnf_transformation,[status(thm)],[f621])).
% 2.79/1.90 thf(f621,plain,(
% 2.79/1.90 ((genClo1015804716orrect @ m @ (genClo1163638703lle_te @ p @ (plus_plus @ nat @ i @ one_one @ nat))) = $true)),
% 2.79/1.90 inference(fool_elimination,[status(thm)],[f620])).
% 2.79/1.90 thf(f620,plain,(
% 2.79/1.90 (genClo1015804716orrect @ m @ (genClo1163638703lle_te @ p @ (plus_plus @ nat @ i @ one_one @ nat)))),
% 2.79/1.90 inference(rectify,[status(thm)],[f2])).
% 2.79/1.90 thf(f2,axiom,(
% 2.79/1.90 (genClo1015804716orrect @ m @ (genClo1163638703lle_te @ p @ (plus_plus @ nat @ i @ one_one @ nat)))),
% 2.79/1.90 file('/export/starexec/sandbox2/tmp/tmp.Kaf6658Iwd/DTF2THF_740.p',fact_1_corr__m)).
% 2.79/1.90 % SZS output end Proof for DTF2THF_740
% 2.79/1.90 % (1027)------------------------------
% 2.79/1.90 % (1027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.90 % (1027)Termination reason: Refutation
% 2.79/1.90
% 2.79/1.90 % (1027)Memory used [KB]: 7547
% 2.79/1.90 % (1027)Time elapsed: 0.133 s
% 2.79/1.90 % (1027)Instructions burned: 432 (million)
% 2.79/1.90 % (1027)------------------------------
% 2.79/1.90 % (1027)------------------------------
% 2.79/1.90 % (978)Success in time 0.434 s
%------------------------------------------------------------------------------