%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP079^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n024.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 08:55:22 AM UTC 2026
% Result : Theorem 2.07s 1.40s
% Output : Refutation 2.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 58 ( 12 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 87 ( 7 ~; 0 |; 0 &; 64 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 77 ( 73 usr; 5 con; 0-4 aty)
% ( 6 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 20 ( 16 ^; 4 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_val: $tType ).
thf(type_def_7,type,
set_set_val: $tType ).
thf(type_def_8,type,
val: $tType ).
thf(type_def_9,type,
set_set_set_val: $tType ).
thf(func_def_0,type,
set_set_set_val: $tType ).
thf(func_def_1,type,
set_set_val: $tType ).
thf(func_def_2,type,
set_val: $tType ).
thf(func_def_3,type,
val: $tType ).
thf(func_def_4,type,
uminus1961393973et_val: set_val > set_val ).
thf(func_def_5,type,
if_o_set_val: $o > ( $o > set_val ) > ( $o > set_val ) > $o > set_val ).
thf(func_def_6,type,
if_set_set_val: $o > set_set_val > set_set_val > set_set_val ).
thf(func_def_7,type,
if_set_val: $o > set_val > set_val > set_val ).
thf(func_def_8,type,
if_val: $o > val > val > val ).
thf(func_def_9,type,
sup_sup_set_val: set_val > set_val > set_val ).
thf(func_def_10,type,
ord_less_set_set_val: set_set_val > set_set_val > $o ).
thf(func_def_11,type,
ord_less_set_val: set_val > set_val > $o ).
thf(func_def_12,type,
ord_less_val: val > val > $o ).
thf(func_def_13,type,
ord_le1441829300et_val: ( $o > $o > set_val ) > ( $o > $o > set_val ) > $o ).
thf(func_def_14,type,
ord_le936627147et_val: ( $o > set_set_val ) > ( $o > set_set_val ) > $o ).
thf(func_def_15,type,
ord_le994826475et_val: ( $o > set_val ) > ( $o > set_val ) > $o ).
thf(func_def_16,type,
ord_less_eq_o_val: ( $o > val ) > ( $o > val ) > $o ).
thf(func_def_17,type,
ord_le1135847966et_val: set_set_set_val > set_set_set_val > $o ).
thf(func_def_18,type,
ord_le1742111550et_val: set_set_val > set_set_val > $o ).
thf(func_def_19,type,
ord_less_eq_set_val: set_val > set_val > $o ).
thf(func_def_20,type,
ord_less_eq_val: val > val > $o ).
thf(func_def_21,type,
order_985126002et_val: ( ( $o > set_val ) > $o ) > $o > set_val ).
thf(func_def_22,type,
order_544136439et_val: ( set_set_val > $o ) > set_set_val ).
thf(func_def_23,type,
order_1960465943et_val: ( set_val > $o ) > set_val ).
thf(func_def_24,type,
order_Greatest_val: ( val > $o ) > val ).
thf(func_def_25,type,
order_23236447al_val: ( ( $o > set_val ) > val ) > $o ).
thf(func_def_26,type,
order_650823122et_val: ( set_set_val > set_val ) > $o ).
thf(func_def_27,type,
order_1520822002al_val: ( set_set_val > val ) > $o ).
thf(func_def_28,type,
order_1957703570et_val: ( set_val > set_set_val ) > $o ).
thf(func_def_29,type,
order_1719375026et_val: ( set_val > set_val ) > $o ).
thf(func_def_30,type,
order_1375876562al_val: ( set_val > val ) > $o ).
thf(func_def_31,type,
order_255079095et_val: ( val > $o > set_val ) > $o ).
thf(func_def_32,type,
order_1945059954et_val: ( val > set_set_val ) > $o ).
thf(func_def_33,type,
order_1484138386et_val: ( val > set_val ) > $o ).
thf(func_def_34,type,
order_1689798834al_val: ( val > val ) > $o ).
thf(func_def_35,type,
order_1205732848et_val: ( val > $o > set_val ) > $o ).
thf(func_def_36,type,
order_68692473et_val: ( val > set_set_val ) > $o ).
thf(func_def_37,type,
order_99134233et_val: ( val > set_val ) > $o ).
thf(func_def_38,type,
order_1139042361al_val: ( val > val ) > $o ).
thf(func_def_39,type,
refine1593386065et_val: ( $o > set_val ) > ( $o > set_val ) > $o ).
thf(func_def_40,type,
refine1034950713et_val: set_set_val > set_set_val > $o ).
thf(func_def_41,type,
refine654574649et_val: set_val > set_val > $o ).
thf(func_def_42,type,
refine2021912633al_val: val > val > $o ).
thf(func_def_43,type,
refine511606705et_val: ( $o > set_val ) > ( $o > set_val ) > $o ).
thf(func_def_44,type,
refine1908789496et_val: set_set_val > set_set_val > $o ).
thf(func_def_45,type,
refine1893322264et_val: set_val > set_val > $o ).
thf(func_def_46,type,
refine403244856MP_val: val > val > $o ).
thf(func_def_47,type,
refine1924899106et_val: ( ( $o > set_val ) > $o > set_val ) > ( ( $o > set_val ) > $o > set_val ) > $o ).
thf(func_def_48,type,
refine1169396807et_val: ( ( $o > set_val ) > set_set_val ) > ( set_set_val > $o > set_val ) > $o ).
thf(func_def_49,type,
refine1948536167et_val: ( ( $o > set_val ) > set_val ) > ( set_val > $o > set_val ) > $o ).
thf(func_def_50,type,
refine86398879et_val: ( set_set_val > $o > set_val ) > ( ( $o > set_val ) > set_set_val ) > $o ).
thf(func_def_51,type,
refine855985034et_val: ( set_set_val > set_set_val ) > ( set_set_val > set_set_val ) > $o ).
thf(func_def_52,type,
refine8163498et_val: ( set_set_val > set_val ) > ( set_val > set_set_val ) > $o ).
thf(func_def_53,type,
refine51544255et_val: ( set_val > $o > set_val ) > ( ( $o > set_val ) > set_val ) > $o ).
thf(func_def_54,type,
refine1315043946et_val: ( set_val > set_set_val ) > ( set_set_val > set_val ) > $o ).
thf(func_def_55,type,
refine1929691018et_val: ( set_val > set_val ) > ( set_val > set_val ) > $o ).
thf(func_def_56,type,
refine2057434761et_val: ( set_val > set_val ) > $o ).
thf(func_def_57,type,
refine16560100et_val: ( ( $o > set_val ) > ( $o > set_val ) > $o ) > $o ).
thf(func_def_58,type,
refine1506227973et_val: ( set_set_val > set_set_val > $o ) > $o ).
thf(func_def_59,type,
refine275900453et_val: ( set_val > set_val > $o ) > $o ).
thf(func_def_60,type,
refine67622213oc_val: ( val > val > $o ) > $o ).
thf(func_def_61,type,
collect_set_val: ( set_val > $o ) > set_set_val ).
thf(func_def_62,type,
collect_val: ( val > $o ) > set_val ).
thf(func_def_63,type,
set_or1554624499et_val: set_val > set_val > set_set_val ).
thf(func_def_64,type,
set_or18208019st_val: val > val > set_val ).
thf(func_def_65,type,
set_or1337784553et_val: set_set_val > set_set_set_val ).
thf(func_def_66,type,
set_or650197513et_val: set_val > set_set_val ).
thf(func_def_67,type,
set_ord_atLeast_val: val > set_val ).
thf(func_def_68,type,
set_or867701765et_val: set_val > set_set_val ).
thf(func_def_69,type,
set_ord_atMost_val: val > set_val ).
thf(func_def_70,type,
set_or2126567818an_val: val > val > set_val ).
thf(func_def_71,type,
set_or1288365508an_val: val > set_val ).
thf(func_def_72,type,
set_ord_lessThan_val: val > set_val ).
thf(func_def_73,type,
member_set_val: set_val > set_set_val > $o ).
thf(func_def_74,type,
member_val: val > set_val > $o ).
thf(func_def_75,type,
p: set_val ).
thf(func_def_76,type,
scc: set_val ).
thf(f2035,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f2034]) ).
thf(f2034,plain,
$false = $true,
inference(boolean_simplification,[status(thm)],[f2033]) ).
thf(f2033,plain,
( ( ~ $true ) = $true ),
inference(backward_demodulation,[status(thm)],[f1898,f1333]) ).
thf(f1333,plain,
( $true
= ( !! @ val
@ ^ [Y0: val] :
( ( member_val @ Y0 @ scc )
=> ( member_val @ Y0 @ p ) ) ) ),
inference(cnf_transformation,[status(thm)],[f702]) ).
thf(f702,plain,
( $true
= ( !! @ val
@ ^ [Y0: val] :
( ( member_val @ Y0 @ scc )
=> ( member_val @ Y0 @ p ) ) ) ),
inference(fool_elimination,[status(thm)],[f701]) ).
thf(f701,plain,
! [X0: val] :
( ( member_val @ X0 @ scc )
=> ( member_val @ X0 @ p ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: val] :
( ( member_val @ X0 @ scc )
=> ( member_val @ X0 @ p ) ),
file('/export/starexec/sandbox/tmp/tmp.Tpnd21IUI7/DTF2THF_26920.p',fact_0__092_060open_062_092_060And_062x_O_Ax_A_092_060in_062_Ascc_A_092_060Longrightarrow_062_Ax_A_092_060in_062_AP_092_060close_062) ).
thf(f1898,plain,
( ( ~ ( !! @ val
@ ^ [Y0: val] :
( ( member_val @ Y0 @ scc )
=> ( member_val @ Y0 @ p ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1575]) ).
thf(f1575,plain,
( $true
= ( ~ ( ^ [Y0: set_val,Y1: set_val] :
( !! @ val
@ ^ [Y2: val] :
( ( member_val @ Y2 @ Y0 )
=> ( member_val @ Y2 @ Y1 ) ) )
@ scc
@ p ) ) ),
inference(definition_unfolding,[status(thm)],[f1218,f1109]) ).
thf(f1109,plain,
( ord_less_eq_set_val
= ( ^ [Y0: set_val,Y1: set_val] :
( !! @ val
@ ^ [Y2: val] :
( ( member_val @ Y2 @ Y0 )
=> ( member_val @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f546]) ).
thf(f546,plain,
( ord_less_eq_set_val
= ( ^ [Y0: set_val,Y1: set_val] :
( !! @ val
@ ^ [Y2: val] :
( ( member_val @ Y2 @ Y0 )
=> ( member_val @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f545]) ).
thf(f545,plain,
( ord_less_eq_set_val
= ( ^ [X0: set_val,X1: set_val] :
! [X2: val] :
( ( member_val @ X2 @ X0 )
=> ( member_val @ X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f19]) ).
thf(f19,axiom,
( ord_less_eq_set_val
= ( ^ [X7: set_val,X8: set_val] :
! [X9: val] :
( ( member_val @ X9 @ X7 )
=> ( member_val @ X9 @ X8 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Tpnd21IUI7/DTF2THF_26920.p',fact_18_subset__eq) ).
thf(f1218,plain,
( ( ~ ( ord_less_eq_set_val @ scc @ p ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f928]) ).
thf(f928,plain,
( ( ~ ( ord_less_eq_set_val @ scc @ p ) )
= $true ),
inference(fool_elimination,[status(thm)],[f927]) ).
thf(f927,plain,
~ ( ord_less_eq_set_val @ scc @ p ),
inference(rectify,[status(thm)],[f361]) ).
thf(f361,negated_conjecture,
~ ( ord_less_eq_set_val @ scc @ p ),
inference(negated_conjecture,[status(cth)],[f360]) ).
thf(f360,conjecture,
ord_less_eq_set_val @ scc @ p,
file('/export/starexec/sandbox/tmp/tmp.Tpnd21IUI7/DTF2THF_26920.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : ITP079^1 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n024.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 03:25:10 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.32 ---- Original DTF file ---
% 0.07/0.32 thf(spec,logic,$$dhol).
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 % File : ITP079^1 : TPTP v9.2.1. Released v7.5.0.
% 0.07/0.32 % Domain : Interactive Theorem Proving
% 0.07/0.32 % Problem : Sledgehammer Irreducible problem prob_209__6623758_1
% 0.07/0.32 % Version : Especial.
% 0.07/0.32 % English :
% 0.07/0.32
% 0.07/0.32 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.07/0.32 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.07/0.32 % Source : [Des21]
% 0.07/0.32 % Names : Irreducible/prob_209__6623758_1 [Des21]
% 0.07/0.32
% 0.07/0.32 % Status : Theorem
% 0.07/0.32 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0
% 0.07/0.32 % Syntax : Number of formulae : 437 ( 125 unt; 77 typ; 0 def)
% 0.07/0.32 % Number of atoms : 1207 ( 255 equ; 0 cnn)
% 0.07/0.32 % Maximal formula atoms : 12 ( 3 avg)
% 0.07/0.32 % Number of connectives : 3030 ( 50 ~; 19 |; 37 &;2359 @)
% 0.07/0.32 % ( 0 <=>; 565 =>; 0 <=; 0 <~>)
% 0.07/0.32 % Maximal formula depth : 16 ( 7 avg)
% 0.07/0.32 % Number of types : 5 ( 4 usr)
% 0.07/0.32 % Number of type conns : 567 ( 567 >; 0 *; 0 +; 0 <<)
% 0.07/0.32 % Number of symbols : 76 ( 73 usr; 4 con; 0-4 aty)
% 0.07/0.32 % Number of variables : 1151 ( 131 ^;1020 !; 0 ?;1151 :)
% 0.07/0.32 % SPC : TH0_THM_EQU_NAR
% 0.07/0.32
% 0.07/0.32 % Comments : This file was generated by Sledgehammer 2021-02-23 15:36:10.728
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 % Could-be-implicit typings (4)
% 0.07/0.32 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Set__Oset_Itf__val_J_J_J,type,
% 0.07/0.32 set_set_set_val: $tType ).
% 0.07/0.32
% 0.07/0.32 thf(ty_n_t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 0.07/0.32 set_set_val: $tType ).
% 0.07/0.32
% 0.07/0.32 thf(ty_n_t__Set__Oset_Itf__val_J,type,
% 0.07/0.32 set_val: $tType ).
% 0.07/0.32
% 0.07/0.32 thf(ty_n_tf__val,type,
% 0.07/0.32 val: $tType ).
% 0.07/0.32
% 0.07/0.32 % Explicit typings (73)
% 0.07/0.32 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_Itf__val_J,type,
% 0.07/0.32 uminus1961393973et_val: set_val > set_val ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_If_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J,type,
% 0.07/0.32 if_o_set_val: $o > ( $o > set_val ) > ( $o > set_val ) > $o > set_val ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_If_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 0.07/0.32 if_set_set_val: $o > set_set_val > set_set_val > set_set_val ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_If_001t__Set__Oset_Itf__val_J,type,
% 0.07/0.32 if_set_val: $o > set_val > set_val > set_val ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_If_001tf__val,type,
% 0.07/0.32 if_val: $o > val > val > val ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_Itf__val_J,type,
% 0.07/0.32 sup_sup_set_val: set_val > set_val > set_val ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 0.07/0.32 ord_less_set_set_val: set_set_val > set_set_val > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_Itf__val_J,type,
% 0.07/0.32 ord_less_set_val: set_val > set_val > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oord__class_Oless_001tf__val,type,
% 0.07/0.32 ord_less_val: val > val > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_M_062_I_Eo_Mt__Set__Oset_Itf__val_J_J_J,type,
% 0.07/0.32 ord_le1441829300et_val: ( $o > $o > set_val ) > ( $o > $o > set_val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Set__Oset_It__Set__Oset_Itf__val_J_J_J,type,
% 0.07/0.32 ord_le936627147et_val: ( $o > set_set_val ) > ( $o > set_set_val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J,type,
% 0.07/0.32 ord_le994826475et_val: ( $o > set_val ) > ( $o > set_val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mtf__val_J,type,
% 0.07/0.32 ord_less_eq_o_val: ( $o > val ) > ( $o > val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Set__Oset_Itf__val_J_J_J,type,
% 0.07/0.32 ord_le1135847966et_val: set_set_set_val > set_set_set_val > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 0.07/0.32 ord_le1742111550et_val: set_set_val > set_set_val > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__val_J,type,
% 0.07/0.32 ord_less_eq_set_val: set_val > set_val > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oord__class_Oless__eq_001tf__val,type,
% 0.07/0.32 ord_less_eq_val: val > val > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oorder__class_OGreatest_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J,type,
% 0.07/0.32 order_985126002et_val: ( ( $o > set_val ) > $o ) > $o > set_val ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 0.07/0.32 order_544136439et_val: ( set_set_val > $o ) > set_set_val ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Set__Oset_Itf__val_J,type,
% 0.07/0.32 order_1960465943et_val: ( set_val > $o ) > set_val ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oorder__class_OGreatest_001tf__val,type,
% 0.07/0.32 order_Greatest_val: ( val > $o ) > val ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oorder__class_Oantimono_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J_001tf__val,type,
% 0.07/0.32 order_23236447al_val: ( ( $o > set_val ) > val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oorder__class_Oantimono_001t__Set__Oset_It__Set__Oset_Itf__val_J_J_001t__Set__Oset_Itf__val_J,type,
% 0.07/0.32 order_650823122et_val: ( set_set_val > set_val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oorder__class_Oantimono_001t__Set__Oset_It__Set__Oset_Itf__val_J_J_001tf__val,type,
% 0.07/0.32 order_1520822002al_val: ( set_set_val > val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oorder__class_Oantimono_001t__Set__Oset_Itf__val_J_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 0.07/0.32 order_1957703570et_val: ( set_val > set_set_val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oorder__class_Oantimono_001t__Set__Oset_Itf__val_J_001t__Set__Oset_Itf__val_J,type,
% 0.07/0.32 order_1719375026et_val: ( set_val > set_val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oorder__class_Oantimono_001t__Set__Oset_Itf__val_J_001tf__val,type,
% 0.07/0.32 order_1375876562al_val: ( set_val > val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oorder__class_Oantimono_001tf__val_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J,type,
% 0.07/0.32 order_255079095et_val: ( val > $o > set_val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oorder__class_Oantimono_001tf__val_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 0.07/0.32 order_1945059954et_val: ( val > set_set_val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oorder__class_Oantimono_001tf__val_001t__Set__Oset_Itf__val_J,type,
% 0.07/0.32 order_1484138386et_val: ( val > set_val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oorder__class_Oantimono_001tf__val_001tf__val,type,
% 0.07/0.32 order_1689798834al_val: ( val > val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001tf__val_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J,type,
% 0.07/0.32 order_1205732848et_val: ( val > $o > set_val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001tf__val_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 0.07/0.32 order_68692473et_val: ( val > set_set_val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001tf__val_001t__Set__Oset_Itf__val_J,type,
% 0.07/0.32 order_99134233et_val: ( val > set_val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001tf__val_001tf__val,type,
% 0.07/0.32 order_1139042361al_val: ( val > val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_RefineG__Transfer_OREFINEG__TRANSFER__ALIGN_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J,type,
% 0.07/0.32 refine1593386065et_val: ( $o > set_val ) > ( $o > set_val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_RefineG__Transfer_OREFINEG__TRANSFER__ALIGN_001t__Set__Oset_It__Set__Oset_Itf__val_J_J_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 0.07/0.32 refine1034950713et_val: set_set_val > set_set_val > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_RefineG__Transfer_OREFINEG__TRANSFER__ALIGN_001t__Set__Oset_Itf__val_J_001t__Set__Oset_Itf__val_J,type,
% 0.07/0.32 refine654574649et_val: set_val > set_val > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_RefineG__Transfer_OREFINEG__TRANSFER__ALIGN_001tf__val_001tf__val,type,
% 0.07/0.32 refine2021912633al_val: val > val > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_RefineG__Transfer_OREFINEG__TRANSFER__POST__SIMP_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J,type,
% 0.07/0.32 refine511606705et_val: ( $o > set_val ) > ( $o > set_val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_RefineG__Transfer_OREFINEG__TRANSFER__POST__SIMP_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 0.07/0.32 refine1908789496et_val: set_set_val > set_set_val > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_RefineG__Transfer_OREFINEG__TRANSFER__POST__SIMP_001t__Set__Oset_Itf__val_J,type,
% 0.07/0.32 refine1893322264et_val: set_val > set_val > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_RefineG__Transfer_OREFINEG__TRANSFER__POST__SIMP_001tf__val,type,
% 0.07/0.32 refine403244856MP_val: val > val > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Refine__Misc_Ogalois__connection_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J,type,
% 0.07/0.32 refine1924899106et_val: ( ( $o > set_val ) > $o > set_val ) > ( ( $o > set_val ) > $o > set_val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Refine__Misc_Ogalois__connection_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 0.07/0.32 refine1169396807et_val: ( ( $o > set_val ) > set_set_val ) > ( set_set_val > $o > set_val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Refine__Misc_Ogalois__connection_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J_001t__Set__Oset_Itf__val_J,type,
% 0.07/0.32 refine1948536167et_val: ( ( $o > set_val ) > set_val ) > ( set_val > $o > set_val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Refine__Misc_Ogalois__connection_001t__Set__Oset_It__Set__Oset_Itf__val_J_J_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J,type,
% 0.07/0.32 refine86398879et_val: ( set_set_val > $o > set_val ) > ( ( $o > set_val ) > set_set_val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Refine__Misc_Ogalois__connection_001t__Set__Oset_It__Set__Oset_Itf__val_J_J_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 0.07/0.32 refine855985034et_val: ( set_set_val > set_set_val ) > ( set_set_val > set_set_val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Refine__Misc_Ogalois__connection_001t__Set__Oset_It__Set__Oset_Itf__val_J_J_001t__Set__Oset_Itf__val_J,type,
% 0.07/0.32 refine8163498et_val: ( set_set_val > set_val ) > ( set_val > set_set_val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Refine__Misc_Ogalois__connection_001t__Set__Oset_Itf__val_J_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J,type,
% 0.07/0.32 refine51544255et_val: ( set_val > $o > set_val ) > ( ( $o > set_val ) > set_val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Refine__Misc_Ogalois__connection_001t__Set__Oset_Itf__val_J_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 0.07/0.32 refine1315043946et_val: ( set_val > set_set_val ) > ( set_set_val > set_val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Refine__Misc_Ogalois__connection_001t__Set__Oset_Itf__val_J_001t__Set__Oset_Itf__val_J,type,
% 0.07/0.32 refine1929691018et_val: ( set_val > set_val ) > ( set_val > set_val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Refine__Misc_Oinf__distrib_001t__Set__Oset_Itf__val_J_001t__Set__Oset_Itf__val_J,type,
% 0.07/0.32 refine2057434761et_val: ( set_val > set_val ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Refine__Mono__Prover_Omono__setup__loc_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J,type,
% 0.07/0.32 refine16560100et_val: ( ( $o > set_val ) > ( $o > set_val ) > $o ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Refine__Mono__Prover_Omono__setup__loc_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 0.07/0.32 refine1506227973et_val: ( set_set_val > set_set_val > $o ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Refine__Mono__Prover_Omono__setup__loc_001t__Set__Oset_Itf__val_J,type,
% 0.07/0.32 refine275900453et_val: ( set_val > set_val > $o ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Refine__Mono__Prover_Omono__setup__loc_001tf__val,type,
% 0.07/0.32 refine67622213oc_val: ( val > val > $o ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Set_OCollect_001t__Set__Oset_Itf__val_J,type,
% 0.07/0.32 collect_set_val: ( set_val > $o ) > set_set_val ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Set_OCollect_001tf__val,type,
% 0.07/0.32 collect_val: ( val > $o ) > set_val ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_Itf__val_J,type,
% 0.07/0.32 set_or1554624499et_val: set_val > set_val > set_set_val ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001tf__val,type,
% 0.07/0.32 set_or18208019st_val: val > val > set_val ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 0.07/0.32 set_or1337784553et_val: set_set_val > set_set_set_val ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Set__Oset_Itf__val_J,type,
% 0.07/0.32 set_or650197513et_val: set_val > set_set_val ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Set__Interval_Oord__class_OatLeast_001tf__val,type,
% 0.07/0.32 set_ord_atLeast_val: val > set_val ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_Itf__val_J,type,
% 0.07/0.32 set_or867701765et_val: set_val > set_set_val ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Set__Interval_Oord__class_OatMost_001tf__val,type,
% 0.07/0.32 set_ord_atMost_val: val > set_val ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001tf__val,type,
% 0.07/0.32 set_or2126567818an_val: val > val > set_val ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001tf__val,type,
% 0.07/0.32 set_or1288365508an_val: val > set_val ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Set__Interval_Oord__class_OlessThan_001tf__val,type,
% 0.07/0.32 set_ord_lessThan_val: val > set_val ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_member_001t__Set__Oset_Itf__val_J,type,
% 0.07/0.32 member_set_val: set_val > set_set_val > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_member_001tf__val,type,
% 0.07/0.32 member_val: val > set_val > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_v_P,type,
% 0.07/0.32 p: set_val ).
% 0.07/0.32
% 0.07/0.32 thf(sy_v_scc,type,
% 0.07/0.32 scc: set_val ).
% 0.07/0.32
% 0.07/0.32 % Relevant facts (350)
% 0.07/0.32 thf(fact_0__092_060open_062_092_060And_062x_O_Ax_A_092_060in_062_Ascc_A_092_060Longrightarrow_062_Ax_A_092_060in_062_AP_092_060close_062,axiom,
% 0.07/0.32 ! [X: val] :
% 0.07/0.32 ( ( member_val @ X @ scc )
% 0.07/0.32 => ( member_val @ X @ p ) ) ).
% 0.07/0.32
% 0.07/0.32 % \<open>\<And>x. x \<in> scc \<Longrightarrow> x \<in> P\<close>
% 0.07/0.32 thf(fact_1_subsetI,axiom,
% 0.07/0.32 ! [A: set_set_val,B: set_set_val] :
% 0.07/0.32 ( ! [X2: set_val] :
% 0.07/0.32 ( ( member_set_val @ X2 @ A )
% 0.07/0.32 => ( member_set_val @ X2 @ B ) )
% 0.07/0.32 => ( ord_le1742111550et_val @ A @ B ) ) ).
% 0.07/0.32
% 0.07/0.32 % subsetI
% 0.07/0.32 thf(fact_2_subsetI,axiom,
% 0.07/0.32 ! [A: set_val,B: set_val] :
% 0.07/0.32 ( ! [X2: val] :
% 0.07/0.32 ( ( member_val @ X2 @ A )
% 0.07/0.32 => ( member_val @ X2 @ B ) )
% 0.07/0.32 => ( ord_less_eq_set_val @ A @ B ) ) ).
% 0.07/0.32
% 0.07/0.32 % subsetI
% 0.07/0.32 thf(fact_3_subset__antisym,axiom,
% 0.07/0.32 ! [A: set_set_val,B: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ A @ B )
% 0.07/0.32 => ( ( ord_le1742111550et_val @ B @ A )
% 0.07/0.32 => ( A = B ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % subset_antisym
% 0.07/0.32 thf(fact_4_subset__antisym,axiom,
% 0.07/0.32 ! [A: set_val,B: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A @ B )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ B @ A )
% 0.07/0.32 => ( A = B ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % subset_antisym
% 0.07/0.32 thf(fact_5_order__mono__setup_Orefl,axiom,
% 0.07/0.32 ! [X: $o > set_val] : ( ord_le994826475et_val @ X @ X ) ).
% 0.07/0.32
% 0.07/0.32 % order_mono_setup.refl
% 0.07/0.32 thf(fact_6_order__mono__setup_Orefl,axiom,
% 0.07/0.32 ! [X: val] : ( ord_less_eq_val @ X @ X ) ).
% 0.07/0.32
% 0.07/0.32 % order_mono_setup.refl
% 0.07/0.32 thf(fact_7_order__mono__setup_Orefl,axiom,
% 0.07/0.32 ! [X: set_set_val] : ( ord_le1742111550et_val @ X @ X ) ).
% 0.07/0.32
% 0.07/0.32 % order_mono_setup.refl
% 0.07/0.32 thf(fact_8_order__mono__setup_Orefl,axiom,
% 0.07/0.32 ! [X: set_val] : ( ord_less_eq_set_val @ X @ X ) ).
% 0.07/0.32
% 0.07/0.32 % order_mono_setup.refl
% 0.07/0.32 thf(fact_9_relprop__triggers_I6_J,axiom,
% 0.07/0.32 ! [R: set_set_val,R2: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ R @ R2 )
% 0.07/0.32 => ( ord_le1742111550et_val @ R @ R2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % relprop_triggers(6)
% 0.07/0.32 thf(fact_10_relprop__triggers_I6_J,axiom,
% 0.07/0.32 ! [R: set_val,R2: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ R @ R2 )
% 0.07/0.32 => ( ord_less_eq_set_val @ R @ R2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % relprop_triggers(6)
% 0.07/0.32 thf(fact_11_in__mono,axiom,
% 0.07/0.32 ! [A: set_set_val,B: set_set_val,X: set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ A @ B )
% 0.07/0.32 => ( ( member_set_val @ X @ A )
% 0.07/0.32 => ( member_set_val @ X @ B ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % in_mono
% 0.07/0.32 thf(fact_12_in__mono,axiom,
% 0.07/0.32 ! [A: set_val,B: set_val,X: val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A @ B )
% 0.07/0.32 => ( ( member_val @ X @ A )
% 0.07/0.32 => ( member_val @ X @ B ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % in_mono
% 0.07/0.32 thf(fact_13_subsetD,axiom,
% 0.07/0.32 ! [A: set_set_val,B: set_set_val,C: set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ A @ B )
% 0.07/0.32 => ( ( member_set_val @ C @ A )
% 0.07/0.32 => ( member_set_val @ C @ B ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % subsetD
% 0.07/0.32 thf(fact_14_subsetD,axiom,
% 0.07/0.32 ! [A: set_val,B: set_val,C: val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A @ B )
% 0.07/0.32 => ( ( member_val @ C @ A )
% 0.07/0.32 => ( member_val @ C @ B ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % subsetD
% 0.07/0.32 thf(fact_15_equalityE,axiom,
% 0.07/0.32 ! [A: set_set_val,B: set_set_val] :
% 0.07/0.32 ( ( A = B )
% 0.07/0.32 => ~ ( ( ord_le1742111550et_val @ A @ B )
% 0.07/0.32 => ~ ( ord_le1742111550et_val @ B @ A ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % equalityE
% 0.07/0.32 thf(fact_16_equalityE,axiom,
% 0.07/0.32 ! [A: set_val,B: set_val] :
% 0.07/0.32 ( ( A = B )
% 0.07/0.32 => ~ ( ( ord_less_eq_set_val @ A @ B )
% 0.07/0.32 => ~ ( ord_less_eq_set_val @ B @ A ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % equalityE
% 0.07/0.32 thf(fact_17_subset__eq,axiom,
% 0.07/0.32 ( ord_le1742111550et_val
% 0.07/0.32 = ( ^ [A2: set_set_val,B2: set_set_val] :
% 0.07/0.32 ! [X3: set_val] :
% 0.07/0.32 ( ( member_set_val @ X3 @ A2 )
% 0.07/0.32 => ( member_set_val @ X3 @ B2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % subset_eq
% 0.07/0.32 thf(fact_18_subset__eq,axiom,
% 0.07/0.32 ( ord_less_eq_set_val
% 0.07/0.32 = ( ^ [A2: set_val,B2: set_val] :
% 0.07/0.32 ! [X3: val] :
% 0.07/0.32 ( ( member_val @ X3 @ A2 )
% 0.07/0.32 => ( member_val @ X3 @ B2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % subset_eq
% 0.07/0.32 thf(fact_19_equalityD1,axiom,
% 0.07/0.32 ! [A: set_set_val,B: set_set_val] :
% 0.07/0.32 ( ( A = B )
% 0.07/0.32 => ( ord_le1742111550et_val @ A @ B ) ) ).
% 0.07/0.32
% 0.07/0.32 % equalityD1
% 0.07/0.32 thf(fact_20_equalityD1,axiom,
% 0.07/0.32 ! [A: set_val,B: set_val] :
% 0.07/0.32 ( ( A = B )
% 0.07/0.32 => ( ord_less_eq_set_val @ A @ B ) ) ).
% 0.07/0.32
% 0.07/0.32 % equalityD1
% 0.07/0.32 thf(fact_21_equalityD2,axiom,
% 0.07/0.32 ! [A: set_set_val,B: set_set_val] :
% 0.07/0.32 ( ( A = B )
% 0.07/0.32 => ( ord_le1742111550et_val @ B @ A ) ) ).
% 0.07/0.32
% 0.07/0.32 % equalityD2
% 0.07/0.32 thf(fact_22_equalityD2,axiom,
% 0.07/0.32 ! [A: set_val,B: set_val] :
% 0.07/0.32 ( ( A = B )
% 0.07/0.32 => ( ord_less_eq_set_val @ B @ A ) ) ).
% 0.07/0.32
% 0.07/0.32 % equalityD2
% 0.07/0.32 thf(fact_23_subset__iff,axiom,
% 0.07/0.32 ( ord_le1742111550et_val
% 0.07/0.32 = ( ^ [A2: set_set_val,B2: set_set_val] :
% 0.07/0.32 ! [T: set_val] :
% 0.07/0.32 ( ( member_set_val @ T @ A2 )
% 0.07/0.32 => ( member_set_val @ T @ B2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % subset_iff
% 0.07/0.32 thf(fact_24_subset__iff,axiom,
% 0.07/0.32 ( ord_less_eq_set_val
% 0.07/0.32 = ( ^ [A2: set_val,B2: set_val] :
% 0.07/0.32 ! [T: val] :
% 0.07/0.32 ( ( member_val @ T @ A2 )
% 0.07/0.32 => ( member_val @ T @ B2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % subset_iff
% 0.07/0.32 thf(fact_25_subset__refl,axiom,
% 0.07/0.32 ! [A: set_set_val] : ( ord_le1742111550et_val @ A @ A ) ).
% 0.07/0.32
% 0.07/0.32 % subset_refl
% 0.07/0.32 thf(fact_26_subset__refl,axiom,
% 0.07/0.32 ! [A: set_val] : ( ord_less_eq_set_val @ A @ A ) ).
% 0.07/0.32
% 0.07/0.32 % subset_refl
% 0.07/0.32 thf(fact_27_order__mono__setup_Omono__if,axiom,
% 0.07/0.32 ! [T2: $o > set_val,T3: $o > set_val,E: $o > set_val,E2: $o > set_val,B3: $o] :
% 0.07/0.32 ( ( ord_le994826475et_val @ T2 @ T3 )
% 0.07/0.32 => ( ( ord_le994826475et_val @ E @ E2 )
% 0.07/0.32 => ( ord_le994826475et_val @ ( if_o_set_val @ B3 @ T2 @ E ) @ ( if_o_set_val @ B3 @ T3 @ E2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_mono_setup.mono_if
% 0.07/0.32 thf(fact_28_order__mono__setup_Omono__if,axiom,
% 0.07/0.32 ! [T2: val,T3: val,E: val,E2: val,B3: $o] :
% 0.07/0.32 ( ( ord_less_eq_val @ T2 @ T3 )
% 0.07/0.32 => ( ( ord_less_eq_val @ E @ E2 )
% 0.07/0.32 => ( ord_less_eq_val @ ( if_val @ B3 @ T2 @ E ) @ ( if_val @ B3 @ T3 @ E2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_mono_setup.mono_if
% 0.07/0.32 thf(fact_29_order__mono__setup_Omono__if,axiom,
% 0.07/0.32 ! [T2: set_set_val,T3: set_set_val,E: set_set_val,E2: set_set_val,B3: $o] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ T2 @ T3 )
% 0.07/0.32 => ( ( ord_le1742111550et_val @ E @ E2 )
% 0.07/0.32 => ( ord_le1742111550et_val @ ( if_set_set_val @ B3 @ T2 @ E ) @ ( if_set_set_val @ B3 @ T3 @ E2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_mono_setup.mono_if
% 0.07/0.32 thf(fact_30_order__mono__setup_Omono__if,axiom,
% 0.07/0.32 ! [T2: set_val,T3: set_val,E: set_val,E2: set_val,B3: $o] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ T2 @ T3 )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ E @ E2 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( if_set_val @ B3 @ T2 @ E ) @ ( if_set_val @ B3 @ T3 @ E2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_mono_setup.mono_if
% 0.07/0.32 thf(fact_31_Collect__mono__iff,axiom,
% 0.07/0.32 ! [P: set_val > $o,Q: set_val > $o] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ ( collect_set_val @ P ) @ ( collect_set_val @ Q ) )
% 0.07/0.32 = ( ! [X3: set_val] :
% 0.07/0.32 ( ( P @ X3 )
% 0.07/0.32 => ( Q @ X3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Collect_mono_iff
% 0.07/0.32 thf(fact_32_Collect__mono__iff,axiom,
% 0.07/0.32 ! [P: val > $o,Q: val > $o] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ ( collect_val @ P ) @ ( collect_val @ Q ) )
% 0.07/0.32 = ( ! [X3: val] :
% 0.07/0.32 ( ( P @ X3 )
% 0.07/0.32 => ( Q @ X3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Collect_mono_iff
% 0.07/0.32 thf(fact_33_set__eq__subset,axiom,
% 0.07/0.32 ( ( ^ [Y: set_set_val,Z: set_set_val] : ( Y = Z ) )
% 0.07/0.32 = ( ^ [A2: set_set_val,B2: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ A2 @ B2 )
% 0.07/0.32 & ( ord_le1742111550et_val @ B2 @ A2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % set_eq_subset
% 0.07/0.32 thf(fact_34_set__eq__subset,axiom,
% 0.07/0.32 ( ( ^ [Y: set_val,Z: set_val] : ( Y = Z ) )
% 0.07/0.32 = ( ^ [A2: set_val,B2: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A2 @ B2 )
% 0.07/0.32 & ( ord_less_eq_set_val @ B2 @ A2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % set_eq_subset
% 0.07/0.32 thf(fact_35_subset__trans,axiom,
% 0.07/0.32 ! [A: set_set_val,B: set_set_val,C2: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ A @ B )
% 0.07/0.32 => ( ( ord_le1742111550et_val @ B @ C2 )
% 0.07/0.32 => ( ord_le1742111550et_val @ A @ C2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % subset_trans
% 0.07/0.32 thf(fact_36_subset__trans,axiom,
% 0.07/0.32 ! [A: set_val,B: set_val,C2: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A @ B )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ B @ C2 )
% 0.07/0.32 => ( ord_less_eq_set_val @ A @ C2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % subset_trans
% 0.07/0.32 thf(fact_37_Collect__mono,axiom,
% 0.07/0.32 ! [P: set_val > $o,Q: set_val > $o] :
% 0.07/0.32 ( ! [X2: set_val] :
% 0.07/0.32 ( ( P @ X2 )
% 0.07/0.32 => ( Q @ X2 ) )
% 0.07/0.32 => ( ord_le1742111550et_val @ ( collect_set_val @ P ) @ ( collect_set_val @ Q ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Collect_mono
% 0.07/0.32 thf(fact_38_Collect__mono,axiom,
% 0.07/0.32 ! [P: val > $o,Q: val > $o] :
% 0.07/0.32 ( ! [X2: val] :
% 0.07/0.32 ( ( P @ X2 )
% 0.07/0.32 => ( Q @ X2 ) )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( collect_val @ P ) @ ( collect_val @ Q ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Collect_mono
% 0.07/0.32 thf(fact_39_subset__Collect__conv,axiom,
% 0.07/0.32 ! [S: set_set_val,P: set_val > $o] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ S @ ( collect_set_val @ P ) )
% 0.07/0.32 = ( ! [X3: set_val] :
% 0.07/0.32 ( ( member_set_val @ X3 @ S )
% 0.07/0.32 => ( P @ X3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % subset_Collect_conv
% 0.07/0.32 thf(fact_40_subset__Collect__conv,axiom,
% 0.07/0.32 ! [S: set_val,P: val > $o] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ S @ ( collect_val @ P ) )
% 0.07/0.32 = ( ! [X3: val] :
% 0.07/0.32 ( ( member_val @ X3 @ S )
% 0.07/0.32 => ( P @ X3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % subset_Collect_conv
% 0.07/0.32 thf(fact_41_dual__order_Oantisym,axiom,
% 0.07/0.32 ! [B3: $o > set_val,A3: $o > set_val] :
% 0.07/0.32 ( ( ord_le994826475et_val @ B3 @ A3 )
% 0.07/0.32 => ( ( ord_le994826475et_val @ A3 @ B3 )
% 0.07/0.32 => ( A3 = B3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.antisym
% 0.07/0.32 thf(fact_42_dual__order_Oantisym,axiom,
% 0.07/0.32 ! [B3: val,A3: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ B3 @ A3 )
% 0.07/0.32 => ( ( ord_less_eq_val @ A3 @ B3 )
% 0.07/0.32 => ( A3 = B3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.antisym
% 0.07/0.32 thf(fact_43_dual__order_Oantisym,axiom,
% 0.07/0.32 ! [B3: set_set_val,A3: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ B3 @ A3 )
% 0.07/0.32 => ( ( ord_le1742111550et_val @ A3 @ B3 )
% 0.07/0.32 => ( A3 = B3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.antisym
% 0.07/0.32 thf(fact_44_dual__order_Oantisym,axiom,
% 0.07/0.32 ! [B3: set_val,A3: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ B3 @ A3 )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.07/0.32 => ( A3 = B3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.antisym
% 0.07/0.32 thf(fact_45_dual__order_Oeq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y: $o > set_val,Z: $o > set_val] : ( Y = Z ) )
% 0.07/0.32 = ( ^ [A4: $o > set_val,B4: $o > set_val] :
% 0.07/0.32 ( ( ord_le994826475et_val @ B4 @ A4 )
% 0.07/0.32 & ( ord_le994826475et_val @ A4 @ B4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.eq_iff
% 0.07/0.32 thf(fact_46_dual__order_Oeq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y: val,Z: val] : ( Y = Z ) )
% 0.07/0.32 = ( ^ [A4: val,B4: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ B4 @ A4 )
% 0.07/0.32 & ( ord_less_eq_val @ A4 @ B4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.eq_iff
% 0.07/0.32 thf(fact_47_dual__order_Oeq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y: set_set_val,Z: set_set_val] : ( Y = Z ) )
% 0.07/0.32 = ( ^ [A4: set_set_val,B4: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ B4 @ A4 )
% 0.07/0.32 & ( ord_le1742111550et_val @ A4 @ B4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.eq_iff
% 0.07/0.32 thf(fact_48_dual__order_Oeq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y: set_val,Z: set_val] : ( Y = Z ) )
% 0.07/0.32 = ( ^ [A4: set_val,B4: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ B4 @ A4 )
% 0.07/0.32 & ( ord_less_eq_set_val @ A4 @ B4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.eq_iff
% 0.07/0.32 thf(fact_49_dual__order_Otrans,axiom,
% 0.07/0.32 ! [B3: $o > set_val,A3: $o > set_val,C: $o > set_val] :
% 0.07/0.32 ( ( ord_le994826475et_val @ B3 @ A3 )
% 0.07/0.32 => ( ( ord_le994826475et_val @ C @ B3 )
% 0.07/0.32 => ( ord_le994826475et_val @ C @ A3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.trans
% 0.07/0.32 thf(fact_50_dual__order_Otrans,axiom,
% 0.07/0.32 ! [B3: val,A3: val,C: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ B3 @ A3 )
% 0.07/0.32 => ( ( ord_less_eq_val @ C @ B3 )
% 0.07/0.32 => ( ord_less_eq_val @ C @ A3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.trans
% 0.07/0.32 thf(fact_51_dual__order_Otrans,axiom,
% 0.07/0.32 ! [B3: set_set_val,A3: set_set_val,C: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ B3 @ A3 )
% 0.07/0.32 => ( ( ord_le1742111550et_val @ C @ B3 )
% 0.07/0.32 => ( ord_le1742111550et_val @ C @ A3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.trans
% 0.07/0.32 thf(fact_52_dual__order_Otrans,axiom,
% 0.07/0.32 ! [B3: set_val,A3: set_val,C: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ B3 @ A3 )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ C @ B3 )
% 0.07/0.32 => ( ord_less_eq_set_val @ C @ A3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.trans
% 0.07/0.32 thf(fact_53_linorder__wlog,axiom,
% 0.07/0.32 ! [P: val > val > $o,A3: val,B3: val] :
% 0.07/0.32 ( ! [A5: val,B5: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ A5 @ B5 )
% 0.07/0.32 => ( P @ A5 @ B5 ) )
% 0.07/0.32 => ( ! [A5: val,B5: val] :
% 0.07/0.32 ( ( P @ B5 @ A5 )
% 0.07/0.32 => ( P @ A5 @ B5 ) )
% 0.07/0.32 => ( P @ A3 @ B3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % linorder_wlog
% 0.07/0.32 thf(fact_54_dual__order_Orefl,axiom,
% 0.07/0.32 ! [A3: $o > set_val] : ( ord_le994826475et_val @ A3 @ A3 ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.refl
% 0.07/0.32 thf(fact_55_dual__order_Orefl,axiom,
% 0.07/0.32 ! [A3: val] : ( ord_less_eq_val @ A3 @ A3 ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.refl
% 0.07/0.32 thf(fact_56_dual__order_Orefl,axiom,
% 0.07/0.32 ! [A3: set_set_val] : ( ord_le1742111550et_val @ A3 @ A3 ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.refl
% 0.07/0.32 thf(fact_57_dual__order_Orefl,axiom,
% 0.07/0.32 ! [A3: set_val] : ( ord_less_eq_set_val @ A3 @ A3 ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.refl
% 0.07/0.32 thf(fact_58_order__trans,axiom,
% 0.07/0.32 ! [X: $o > set_val,Y2: $o > set_val,Z2: $o > set_val] :
% 0.07/0.32 ( ( ord_le994826475et_val @ X @ Y2 )
% 0.07/0.32 => ( ( ord_le994826475et_val @ Y2 @ Z2 )
% 0.07/0.32 => ( ord_le994826475et_val @ X @ Z2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_trans
% 0.07/0.32 thf(fact_59_order__trans,axiom,
% 0.07/0.32 ! [X: val,Y2: val,Z2: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X @ Y2 )
% 0.07/0.32 => ( ( ord_less_eq_val @ Y2 @ Z2 )
% 0.07/0.32 => ( ord_less_eq_val @ X @ Z2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_trans
% 0.07/0.32 thf(fact_60_order__trans,axiom,
% 0.07/0.32 ! [X: set_set_val,Y2: set_set_val,Z2: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ X @ Y2 )
% 0.07/0.32 => ( ( ord_le1742111550et_val @ Y2 @ Z2 )
% 0.07/0.32 => ( ord_le1742111550et_val @ X @ Z2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_trans
% 0.07/0.32 thf(fact_61_order__trans,axiom,
% 0.07/0.32 ! [X: set_val,Y2: set_val,Z2: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ Y2 @ Z2 )
% 0.07/0.32 => ( ord_less_eq_set_val @ X @ Z2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_trans
% 0.07/0.32 thf(fact_62_order__class_Oorder_Oantisym,axiom,
% 0.07/0.32 ! [A3: $o > set_val,B3: $o > set_val] :
% 0.07/0.32 ( ( ord_le994826475et_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ord_le994826475et_val @ B3 @ A3 )
% 0.07/0.32 => ( A3 = B3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_class.order.antisym
% 0.07/0.32 thf(fact_63_order__class_Oorder_Oantisym,axiom,
% 0.07/0.32 ! [A3: val,B3: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ord_less_eq_val @ B3 @ A3 )
% 0.07/0.32 => ( A3 = B3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_class.order.antisym
% 0.07/0.32 thf(fact_64_order__class_Oorder_Oantisym,axiom,
% 0.07/0.32 ! [A3: set_set_val,B3: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ord_le1742111550et_val @ B3 @ A3 )
% 0.07/0.32 => ( A3 = B3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_class.order.antisym
% 0.07/0.32 thf(fact_65_order__class_Oorder_Oantisym,axiom,
% 0.07/0.32 ! [A3: set_val,B3: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ B3 @ A3 )
% 0.07/0.32 => ( A3 = B3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_class.order.antisym
% 0.07/0.32 thf(fact_66_ord__le__eq__trans,axiom,
% 0.07/0.32 ! [A3: $o > set_val,B3: $o > set_val,C: $o > set_val] :
% 0.07/0.32 ( ( ord_le994826475et_val @ A3 @ B3 )
% 0.07/0.32 => ( ( B3 = C )
% 0.07/0.32 => ( ord_le994826475et_val @ A3 @ C ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_trans
% 0.07/0.32 thf(fact_67_ord__le__eq__trans,axiom,
% 0.07/0.32 ! [A3: val,B3: val,C: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ A3 @ B3 )
% 0.07/0.32 => ( ( B3 = C )
% 0.07/0.32 => ( ord_less_eq_val @ A3 @ C ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_trans
% 0.07/0.32 thf(fact_68_ord__le__eq__trans,axiom,
% 0.07/0.32 ! [A3: set_set_val,B3: set_set_val,C: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ A3 @ B3 )
% 0.07/0.32 => ( ( B3 = C )
% 0.07/0.32 => ( ord_le1742111550et_val @ A3 @ C ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_trans
% 0.07/0.32 thf(fact_69_ord__le__eq__trans,axiom,
% 0.07/0.32 ! [A3: set_val,B3: set_val,C: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.07/0.32 => ( ( B3 = C )
% 0.07/0.32 => ( ord_less_eq_set_val @ A3 @ C ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_trans
% 0.07/0.32 thf(fact_70_le__funD,axiom,
% 0.07/0.32 ! [F: $o > set_val,G: $o > set_val,X: $o] :
% 0.07/0.32 ( ( ord_le994826475et_val @ F @ G )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ X ) @ ( G @ X ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_funD
% 0.07/0.32 thf(fact_71_le__funE,axiom,
% 0.07/0.32 ! [F: $o > set_val,G: $o > set_val,X: $o] :
% 0.07/0.32 ( ( ord_le994826475et_val @ F @ G )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ X ) @ ( G @ X ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_funE
% 0.07/0.32 thf(fact_72_le__funI,axiom,
% 0.07/0.32 ! [F: $o > set_val,G: $o > set_val] :
% 0.07/0.32 ( ! [X2: $o] : ( ord_less_eq_set_val @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.07/0.32 => ( ord_le994826475et_val @ F @ G ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_funI
% 0.07/0.32 thf(fact_73_le__fun__def,axiom,
% 0.07/0.32 ( ord_le994826475et_val
% 0.07/0.32 = ( ^ [F2: $o > set_val,G2: $o > set_val] :
% 0.07/0.32 ! [X3: $o] : ( ord_less_eq_set_val @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_fun_def
% 0.07/0.32 thf(fact_74_order__subst1,axiom,
% 0.07/0.32 ! [A3: set_val,F: set_val > set_val,B3: set_val,C: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A3 @ ( F @ B3 ) )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ B3 @ C )
% 0.07/0.32 => ( ! [X2: set_val,Y3: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_set_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst1
% 0.07/0.32 thf(fact_75_order__subst1,axiom,
% 0.07/0.32 ! [A3: val,F: val > val,B3: val,C: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ A3 @ ( F @ B3 ) )
% 0.07/0.32 => ( ( ord_less_eq_val @ B3 @ C )
% 0.07/0.32 => ( ! [X2: val,Y3: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst1
% 0.07/0.32 thf(fact_76_order__subst1,axiom,
% 0.07/0.32 ! [A3: set_val,F: val > set_val,B3: val,C: val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A3 @ ( F @ B3 ) )
% 0.07/0.32 => ( ( ord_less_eq_val @ B3 @ C )
% 0.07/0.32 => ( ! [X2: val,Y3: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_set_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst1
% 0.07/0.32 thf(fact_77_order__subst1,axiom,
% 0.07/0.32 ! [A3: val,F: set_val > val,B3: set_val,C: set_val] :
% 0.07/0.32 ( ( ord_less_eq_val @ A3 @ ( F @ B3 ) )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ B3 @ C )
% 0.07/0.32 => ( ! [X2: set_val,Y3: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst1
% 0.07/0.32 thf(fact_78_order__subst1,axiom,
% 0.07/0.32 ! [A3: val,F: set_set_val > val,B3: set_set_val,C: set_set_val] :
% 0.07/0.32 ( ( ord_less_eq_val @ A3 @ ( F @ B3 ) )
% 0.07/0.32 => ( ( ord_le1742111550et_val @ B3 @ C )
% 0.07/0.32 => ( ! [X2: set_set_val,Y3: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst1
% 0.07/0.32 thf(fact_79_order__subst1,axiom,
% 0.07/0.32 ! [A3: set_set_val,F: val > set_set_val,B3: val,C: val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ A3 @ ( F @ B3 ) )
% 0.07/0.32 => ( ( ord_less_eq_val @ B3 @ C )
% 0.07/0.32 => ( ! [X2: val,Y3: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le1742111550et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le1742111550et_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst1
% 0.07/0.32 thf(fact_80_order__subst1,axiom,
% 0.07/0.32 ! [A3: set_val,F: set_set_val > set_val,B3: set_set_val,C: set_set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A3 @ ( F @ B3 ) )
% 0.07/0.32 => ( ( ord_le1742111550et_val @ B3 @ C )
% 0.07/0.32 => ( ! [X2: set_set_val,Y3: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_set_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst1
% 0.07/0.32 thf(fact_81_order__subst1,axiom,
% 0.07/0.32 ! [A3: $o > set_val,F: val > $o > set_val,B3: val,C: val] :
% 0.07/0.32 ( ( ord_le994826475et_val @ A3 @ ( F @ B3 ) )
% 0.07/0.32 => ( ( ord_less_eq_val @ B3 @ C )
% 0.07/0.32 => ( ! [X2: val,Y3: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le994826475et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le994826475et_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst1
% 0.07/0.32 thf(fact_82_order__subst1,axiom,
% 0.07/0.32 ! [A3: val,F: ( $o > set_val ) > val,B3: $o > set_val,C: $o > set_val] :
% 0.07/0.32 ( ( ord_less_eq_val @ A3 @ ( F @ B3 ) )
% 0.07/0.32 => ( ( ord_le994826475et_val @ B3 @ C )
% 0.07/0.32 => ( ! [X2: $o > set_val,Y3: $o > set_val] :
% 0.07/0.32 ( ( ord_le994826475et_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst1
% 0.07/0.32 thf(fact_83_order__subst1,axiom,
% 0.07/0.32 ! [A3: set_set_val,F: set_val > set_set_val,B3: set_val,C: set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ A3 @ ( F @ B3 ) )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ B3 @ C )
% 0.07/0.32 => ( ! [X2: set_val,Y3: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le1742111550et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le1742111550et_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst1
% 0.07/0.32 thf(fact_84_order__subst2,axiom,
% 0.07/0.32 ! [A3: set_val,B3: set_val,F: set_val > set_val,C: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ ( F @ B3 ) @ C )
% 0.07/0.32 => ( ! [X2: set_val,Y3: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst2
% 0.07/0.32 thf(fact_85_order__subst2,axiom,
% 0.07/0.32 ! [A3: val,B3: val,F: val > val,C: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ord_less_eq_val @ ( F @ B3 ) @ C )
% 0.07/0.32 => ( ! [X2: val,Y3: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst2
% 0.07/0.32 thf(fact_86_order__subst2,axiom,
% 0.07/0.32 ! [A3: set_val,B3: set_val,F: set_val > val,C: val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ord_less_eq_val @ ( F @ B3 ) @ C )
% 0.07/0.32 => ( ! [X2: set_val,Y3: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst2
% 0.07/0.32 thf(fact_87_order__subst2,axiom,
% 0.07/0.32 ! [A3: val,B3: val,F: val > set_val,C: set_val] :
% 0.07/0.32 ( ( ord_less_eq_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ ( F @ B3 ) @ C )
% 0.07/0.32 => ( ! [X2: val,Y3: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst2
% 0.07/0.32 thf(fact_88_order__subst2,axiom,
% 0.07/0.32 ! [A3: val,B3: val,F: val > set_set_val,C: set_set_val] :
% 0.07/0.32 ( ( ord_less_eq_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ord_le1742111550et_val @ ( F @ B3 ) @ C )
% 0.07/0.32 => ( ! [X2: val,Y3: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le1742111550et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le1742111550et_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst2
% 0.07/0.32 thf(fact_89_order__subst2,axiom,
% 0.07/0.32 ! [A3: set_set_val,B3: set_set_val,F: set_set_val > val,C: val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ord_less_eq_val @ ( F @ B3 ) @ C )
% 0.07/0.32 => ( ! [X2: set_set_val,Y3: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst2
% 0.07/0.32 thf(fact_90_order__subst2,axiom,
% 0.07/0.32 ! [A3: set_val,B3: set_val,F: set_val > set_set_val,C: set_set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ord_le1742111550et_val @ ( F @ B3 ) @ C )
% 0.07/0.32 => ( ! [X2: set_val,Y3: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le1742111550et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le1742111550et_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst2
% 0.07/0.32 thf(fact_91_order__subst2,axiom,
% 0.07/0.32 ! [A3: $o > set_val,B3: $o > set_val,F: ( $o > set_val ) > val,C: val] :
% 0.07/0.32 ( ( ord_le994826475et_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ord_less_eq_val @ ( F @ B3 ) @ C )
% 0.07/0.32 => ( ! [X2: $o > set_val,Y3: $o > set_val] :
% 0.07/0.32 ( ( ord_le994826475et_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst2
% 0.07/0.32 thf(fact_92_order__subst2,axiom,
% 0.07/0.32 ! [A3: val,B3: val,F: val > $o > set_val,C: $o > set_val] :
% 0.07/0.32 ( ( ord_less_eq_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ord_le994826475et_val @ ( F @ B3 ) @ C )
% 0.07/0.32 => ( ! [X2: val,Y3: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le994826475et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le994826475et_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst2
% 0.07/0.32 thf(fact_93_order__subst2,axiom,
% 0.07/0.32 ! [A3: set_set_val,B3: set_set_val,F: set_set_val > set_val,C: set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ ( F @ B3 ) @ C )
% 0.07/0.32 => ( ! [X2: set_set_val,Y3: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst2
% 0.07/0.32 thf(fact_94_ord__eq__le__eq__trans,axiom,
% 0.07/0.32 ! [A3: $o > set_val,B3: $o > set_val,C: $o > set_val,D: $o > set_val] :
% 0.07/0.32 ( ( A3 = B3 )
% 0.07/0.32 => ( ( ord_le994826475et_val @ B3 @ C )
% 0.07/0.32 => ( ( C = D )
% 0.07/0.32 => ( ord_le994826475et_val @ A3 @ D ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_eq_trans
% 0.07/0.32 thf(fact_95_ord__eq__le__eq__trans,axiom,
% 0.07/0.32 ! [A3: val,B3: val,C: val,D: val] :
% 0.07/0.32 ( ( A3 = B3 )
% 0.07/0.32 => ( ( ord_less_eq_val @ B3 @ C )
% 0.07/0.32 => ( ( C = D )
% 0.07/0.32 => ( ord_less_eq_val @ A3 @ D ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_eq_trans
% 0.07/0.32 thf(fact_96_ord__eq__le__eq__trans,axiom,
% 0.07/0.32 ! [A3: set_set_val,B3: set_set_val,C: set_set_val,D: set_set_val] :
% 0.07/0.32 ( ( A3 = B3 )
% 0.07/0.32 => ( ( ord_le1742111550et_val @ B3 @ C )
% 0.07/0.32 => ( ( C = D )
% 0.07/0.32 => ( ord_le1742111550et_val @ A3 @ D ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_eq_trans
% 0.07/0.32 thf(fact_97_ord__eq__le__eq__trans,axiom,
% 0.07/0.32 ! [A3: set_val,B3: set_val,C: set_val,D: set_val] :
% 0.07/0.32 ( ( A3 = B3 )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ B3 @ C )
% 0.07/0.32 => ( ( C = D )
% 0.07/0.32 => ( ord_less_eq_set_val @ A3 @ D ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_eq_trans
% 0.07/0.32 thf(fact_98_ord__eq__le__subst,axiom,
% 0.07/0.32 ! [A3: set_val,F: set_val > set_val,B3: set_val,C: set_val] :
% 0.07/0.32 ( ( A3
% 0.07/0.32 = ( F @ B3 ) )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ B3 @ C )
% 0.07/0.32 => ( ! [X2: set_val,Y3: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_set_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_subst
% 0.07/0.32 thf(fact_99_ord__eq__le__subst,axiom,
% 0.07/0.32 ! [A3: val,F: val > val,B3: val,C: val] :
% 0.07/0.32 ( ( A3
% 0.07/0.32 = ( F @ B3 ) )
% 0.07/0.32 => ( ( ord_less_eq_val @ B3 @ C )
% 0.07/0.32 => ( ! [X2: val,Y3: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_subst
% 0.07/0.32 thf(fact_100_ord__eq__le__subst,axiom,
% 0.07/0.32 ! [A3: val,F: set_val > val,B3: set_val,C: set_val] :
% 0.07/0.32 ( ( A3
% 0.07/0.32 = ( F @ B3 ) )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ B3 @ C )
% 0.07/0.32 => ( ! [X2: set_val,Y3: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_subst
% 0.07/0.32 thf(fact_101_ord__eq__le__subst,axiom,
% 0.07/0.32 ! [A3: set_val,F: val > set_val,B3: val,C: val] :
% 0.07/0.32 ( ( A3
% 0.07/0.32 = ( F @ B3 ) )
% 0.07/0.32 => ( ( ord_less_eq_val @ B3 @ C )
% 0.07/0.32 => ( ! [X2: val,Y3: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_set_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_subst
% 0.07/0.32 thf(fact_102_ord__eq__le__subst,axiom,
% 0.07/0.32 ! [A3: set_set_val,F: val > set_set_val,B3: val,C: val] :
% 0.07/0.32 ( ( A3
% 0.07/0.32 = ( F @ B3 ) )
% 0.07/0.32 => ( ( ord_less_eq_val @ B3 @ C )
% 0.07/0.32 => ( ! [X2: val,Y3: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le1742111550et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le1742111550et_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_subst
% 0.07/0.32 thf(fact_103_ord__eq__le__subst,axiom,
% 0.07/0.32 ! [A3: val,F: set_set_val > val,B3: set_set_val,C: set_set_val] :
% 0.07/0.32 ( ( A3
% 0.07/0.32 = ( F @ B3 ) )
% 0.07/0.32 => ( ( ord_le1742111550et_val @ B3 @ C )
% 0.07/0.32 => ( ! [X2: set_set_val,Y3: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_subst
% 0.07/0.32 thf(fact_104_ord__eq__le__subst,axiom,
% 0.07/0.32 ! [A3: set_set_val,F: set_val > set_set_val,B3: set_val,C: set_val] :
% 0.07/0.32 ( ( A3
% 0.07/0.32 = ( F @ B3 ) )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ B3 @ C )
% 0.07/0.32 => ( ! [X2: set_val,Y3: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le1742111550et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le1742111550et_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_subst
% 0.07/0.32 thf(fact_105_ord__eq__le__subst,axiom,
% 0.07/0.32 ! [A3: val,F: ( $o > set_val ) > val,B3: $o > set_val,C: $o > set_val] :
% 0.07/0.32 ( ( A3
% 0.07/0.32 = ( F @ B3 ) )
% 0.07/0.32 => ( ( ord_le994826475et_val @ B3 @ C )
% 0.07/0.32 => ( ! [X2: $o > set_val,Y3: $o > set_val] :
% 0.07/0.32 ( ( ord_le994826475et_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_subst
% 0.07/0.32 thf(fact_106_ord__eq__le__subst,axiom,
% 0.07/0.32 ! [A3: $o > set_val,F: val > $o > set_val,B3: val,C: val] :
% 0.07/0.32 ( ( A3
% 0.07/0.32 = ( F @ B3 ) )
% 0.07/0.32 => ( ( ord_less_eq_val @ B3 @ C )
% 0.07/0.32 => ( ! [X2: val,Y3: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le994826475et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le994826475et_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_subst
% 0.07/0.32 thf(fact_107_ord__eq__le__subst,axiom,
% 0.07/0.32 ! [A3: set_val,F: set_set_val > set_val,B3: set_set_val,C: set_set_val] :
% 0.07/0.32 ( ( A3
% 0.07/0.32 = ( F @ B3 ) )
% 0.07/0.32 => ( ( ord_le1742111550et_val @ B3 @ C )
% 0.07/0.32 => ( ! [X2: set_set_val,Y3: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_set_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_subst
% 0.07/0.32 thf(fact_108_ord__le__eq__subst,axiom,
% 0.07/0.32 ! [A3: set_val,B3: set_val,F: set_val > set_val,C: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ( F @ B3 )
% 0.07/0.32 = C )
% 0.07/0.32 => ( ! [X2: set_val,Y3: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_subst
% 0.07/0.32 thf(fact_109_ord__le__eq__subst,axiom,
% 0.07/0.32 ! [A3: val,B3: val,F: val > val,C: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ( F @ B3 )
% 0.07/0.32 = C )
% 0.07/0.32 => ( ! [X2: val,Y3: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_subst
% 0.07/0.32 thf(fact_110_ord__le__eq__subst,axiom,
% 0.07/0.32 ! [A3: set_val,B3: set_val,F: set_val > val,C: val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ( F @ B3 )
% 0.07/0.32 = C )
% 0.07/0.32 => ( ! [X2: set_val,Y3: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_subst
% 0.07/0.32 thf(fact_111_ord__le__eq__subst,axiom,
% 0.07/0.32 ! [A3: val,B3: val,F: val > set_val,C: set_val] :
% 0.07/0.32 ( ( ord_less_eq_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ( F @ B3 )
% 0.07/0.32 = C )
% 0.07/0.32 => ( ! [X2: val,Y3: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_subst
% 0.07/0.32 thf(fact_112_ord__le__eq__subst,axiom,
% 0.07/0.32 ! [A3: val,B3: val,F: val > set_set_val,C: set_set_val] :
% 0.07/0.32 ( ( ord_less_eq_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ( F @ B3 )
% 0.07/0.32 = C )
% 0.07/0.32 => ( ! [X2: val,Y3: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le1742111550et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le1742111550et_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_subst
% 0.07/0.32 thf(fact_113_ord__le__eq__subst,axiom,
% 0.07/0.32 ! [A3: set_set_val,B3: set_set_val,F: set_set_val > val,C: val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ( F @ B3 )
% 0.07/0.32 = C )
% 0.07/0.32 => ( ! [X2: set_set_val,Y3: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_subst
% 0.07/0.32 thf(fact_114_ord__le__eq__subst,axiom,
% 0.07/0.32 ! [A3: set_val,B3: set_val,F: set_val > set_set_val,C: set_set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ( F @ B3 )
% 0.07/0.32 = C )
% 0.07/0.32 => ( ! [X2: set_val,Y3: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le1742111550et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le1742111550et_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_subst
% 0.07/0.32 thf(fact_115_ord__le__eq__subst,axiom,
% 0.07/0.32 ! [A3: $o > set_val,B3: $o > set_val,F: ( $o > set_val ) > val,C: val] :
% 0.07/0.32 ( ( ord_le994826475et_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ( F @ B3 )
% 0.07/0.32 = C )
% 0.07/0.32 => ( ! [X2: $o > set_val,Y3: $o > set_val] :
% 0.07/0.32 ( ( ord_le994826475et_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_subst
% 0.07/0.32 thf(fact_116_ord__le__eq__subst,axiom,
% 0.07/0.32 ! [A3: val,B3: val,F: val > $o > set_val,C: $o > set_val] :
% 0.07/0.32 ( ( ord_less_eq_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ( F @ B3 )
% 0.07/0.32 = C )
% 0.07/0.32 => ( ! [X2: val,Y3: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le994826475et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_le994826475et_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_subst
% 0.07/0.32 thf(fact_117_ord__le__eq__subst,axiom,
% 0.07/0.32 ! [A3: set_set_val,B3: set_set_val,F: set_set_val > set_val,C: set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ( F @ B3 )
% 0.07/0.32 = C )
% 0.07/0.32 => ( ! [X2: set_set_val,Y3: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_subst
% 0.07/0.32 thf(fact_118_eq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y: $o > set_val,Z: $o > set_val] : ( Y = Z ) )
% 0.07/0.32 = ( ^ [X3: $o > set_val,Y4: $o > set_val] :
% 0.07/0.32 ( ( ord_le994826475et_val @ X3 @ Y4 )
% 0.07/0.32 & ( ord_le994826475et_val @ Y4 @ X3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_iff
% 0.07/0.32 thf(fact_119_eq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y: val,Z: val] : ( Y = Z ) )
% 0.07/0.32 = ( ^ [X3: val,Y4: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X3 @ Y4 )
% 0.07/0.32 & ( ord_less_eq_val @ Y4 @ X3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_iff
% 0.07/0.32 thf(fact_120_eq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y: set_set_val,Z: set_set_val] : ( Y = Z ) )
% 0.07/0.32 = ( ^ [X3: set_set_val,Y4: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ X3 @ Y4 )
% 0.07/0.32 & ( ord_le1742111550et_val @ Y4 @ X3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_iff
% 0.07/0.32 thf(fact_121_eq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y: set_val,Z: set_val] : ( Y = Z ) )
% 0.07/0.32 = ( ^ [X3: set_val,Y4: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X3 @ Y4 )
% 0.07/0.32 & ( ord_less_eq_set_val @ Y4 @ X3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_iff
% 0.07/0.32 thf(fact_122_antisym,axiom,
% 0.07/0.32 ! [X: $o > set_val,Y2: $o > set_val] :
% 0.07/0.32 ( ( ord_le994826475et_val @ X @ Y2 )
% 0.07/0.32 => ( ( ord_le994826475et_val @ Y2 @ X )
% 0.07/0.32 => ( X = Y2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym
% 0.07/0.32 thf(fact_123_antisym,axiom,
% 0.07/0.32 ! [X: val,Y2: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X @ Y2 )
% 0.07/0.32 => ( ( ord_less_eq_val @ Y2 @ X )
% 0.07/0.32 => ( X = Y2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym
% 0.07/0.32 thf(fact_124_antisym,axiom,
% 0.07/0.32 ! [X: set_set_val,Y2: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ X @ Y2 )
% 0.07/0.32 => ( ( ord_le1742111550et_val @ Y2 @ X )
% 0.07/0.32 => ( X = Y2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym
% 0.07/0.32 thf(fact_125_antisym,axiom,
% 0.07/0.32 ! [X: set_val,Y2: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ Y2 @ X )
% 0.07/0.32 => ( X = Y2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym
% 0.07/0.32 thf(fact_126_linear,axiom,
% 0.07/0.32 ! [X: val,Y2: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X @ Y2 )
% 0.07/0.32 | ( ord_less_eq_val @ Y2 @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % linear
% 0.07/0.32 thf(fact_127_eq__refl,axiom,
% 0.07/0.32 ! [X: $o > set_val,Y2: $o > set_val] :
% 0.07/0.32 ( ( X = Y2 )
% 0.07/0.32 => ( ord_le994826475et_val @ X @ Y2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_refl
% 0.07/0.32 thf(fact_128_eq__refl,axiom,
% 0.07/0.32 ! [X: val,Y2: val] :
% 0.07/0.32 ( ( X = Y2 )
% 0.07/0.32 => ( ord_less_eq_val @ X @ Y2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_refl
% 0.07/0.32 thf(fact_129_eq__refl,axiom,
% 0.07/0.32 ! [X: set_set_val,Y2: set_set_val] :
% 0.07/0.32 ( ( X = Y2 )
% 0.07/0.32 => ( ord_le1742111550et_val @ X @ Y2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_refl
% 0.07/0.32 thf(fact_130_eq__refl,axiom,
% 0.07/0.32 ! [X: set_val,Y2: set_val] :
% 0.07/0.32 ( ( X = Y2 )
% 0.07/0.32 => ( ord_less_eq_set_val @ X @ Y2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_refl
% 0.07/0.32 thf(fact_131_le__cases,axiom,
% 0.07/0.32 ! [X: val,Y2: val] :
% 0.07/0.32 ( ~ ( ord_less_eq_val @ X @ Y2 )
% 0.07/0.32 => ( ord_less_eq_val @ Y2 @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_cases
% 0.07/0.32 thf(fact_132_order_Otrans,axiom,
% 0.07/0.32 ! [A3: $o > set_val,B3: $o > set_val,C: $o > set_val] :
% 0.07/0.32 ( ( ord_le994826475et_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ord_le994826475et_val @ B3 @ C )
% 0.07/0.32 => ( ord_le994826475et_val @ A3 @ C ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order.trans
% 0.07/0.32 thf(fact_133_order_Otrans,axiom,
% 0.07/0.32 ! [A3: val,B3: val,C: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ord_less_eq_val @ B3 @ C )
% 0.07/0.32 => ( ord_less_eq_val @ A3 @ C ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order.trans
% 0.07/0.32 thf(fact_134_order_Otrans,axiom,
% 0.07/0.32 ! [A3: set_set_val,B3: set_set_val,C: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ord_le1742111550et_val @ B3 @ C )
% 0.07/0.32 => ( ord_le1742111550et_val @ A3 @ C ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order.trans
% 0.07/0.32 thf(fact_135_order_Otrans,axiom,
% 0.07/0.32 ! [A3: set_val,B3: set_val,C: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ B3 @ C )
% 0.07/0.32 => ( ord_less_eq_set_val @ A3 @ C ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order.trans
% 0.07/0.32 thf(fact_136_mem__Collect__eq,axiom,
% 0.07/0.32 ! [A3: set_val,P: set_val > $o] :
% 0.07/0.32 ( ( member_set_val @ A3 @ ( collect_set_val @ P ) )
% 0.07/0.32 = ( P @ A3 ) ) ).
% 0.07/0.32
% 0.07/0.32 % mem_Collect_eq
% 0.07/0.32 thf(fact_137_mem__Collect__eq,axiom,
% 0.07/0.32 ! [A3: val,P: val > $o] :
% 0.07/0.32 ( ( member_val @ A3 @ ( collect_val @ P ) )
% 0.07/0.32 = ( P @ A3 ) ) ).
% 0.07/0.32
% 0.07/0.32 % mem_Collect_eq
% 0.07/0.32 thf(fact_138_Collect__mem__eq,axiom,
% 0.07/0.32 ! [A: set_set_val] :
% 0.07/0.32 ( ( collect_set_val
% 0.07/0.32 @ ^ [X3: set_val] : ( member_set_val @ X3 @ A ) )
% 0.07/0.32 = A ) ).
% 0.07/0.32
% 0.07/0.32 % Collect_mem_eq
% 0.07/0.32 thf(fact_139_Collect__mem__eq,axiom,
% 0.07/0.32 ! [A: set_val] :
% 0.07/0.32 ( ( collect_val
% 0.07/0.32 @ ^ [X3: val] : ( member_val @ X3 @ A ) )
% 0.07/0.32 = A ) ).
% 0.07/0.32
% 0.07/0.32 % Collect_mem_eq
% 0.07/0.32 thf(fact_140_Collect__cong,axiom,
% 0.07/0.32 ! [P: val > $o,Q: val > $o] :
% 0.07/0.32 ( ! [X2: val] :
% 0.07/0.32 ( ( P @ X2 )
% 0.07/0.32 = ( Q @ X2 ) )
% 0.07/0.32 => ( ( collect_val @ P )
% 0.07/0.32 = ( collect_val @ Q ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Collect_cong
% 0.07/0.32 thf(fact_141_le__cases3,axiom,
% 0.07/0.32 ! [X: val,Y2: val,Z2: val] :
% 0.07/0.32 ( ( ( ord_less_eq_val @ X @ Y2 )
% 0.07/0.32 => ~ ( ord_less_eq_val @ Y2 @ Z2 ) )
% 0.07/0.32 => ( ( ( ord_less_eq_val @ Y2 @ X )
% 0.07/0.32 => ~ ( ord_less_eq_val @ X @ Z2 ) )
% 0.07/0.32 => ( ( ( ord_less_eq_val @ X @ Z2 )
% 0.07/0.32 => ~ ( ord_less_eq_val @ Z2 @ Y2 ) )
% 0.07/0.32 => ( ( ( ord_less_eq_val @ Z2 @ Y2 )
% 0.07/0.32 => ~ ( ord_less_eq_val @ Y2 @ X ) )
% 0.07/0.32 => ( ( ( ord_less_eq_val @ Y2 @ Z2 )
% 0.07/0.32 => ~ ( ord_less_eq_val @ Z2 @ X ) )
% 0.07/0.32 => ~ ( ( ord_less_eq_val @ Z2 @ X )
% 0.07/0.32 => ~ ( ord_less_eq_val @ X @ Y2 ) ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_cases3
% 0.07/0.32 thf(fact_142_antisym__conv,axiom,
% 0.07/0.32 ! [Y2: $o > set_val,X: $o > set_val] :
% 0.07/0.32 ( ( ord_le994826475et_val @ Y2 @ X )
% 0.07/0.32 => ( ( ord_le994826475et_val @ X @ Y2 )
% 0.07/0.32 = ( X = Y2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym_conv
% 0.07/0.32 thf(fact_143_antisym__conv,axiom,
% 0.07/0.32 ! [Y2: val,X: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ Y2 @ X )
% 0.07/0.32 => ( ( ord_less_eq_val @ X @ Y2 )
% 0.07/0.32 = ( X = Y2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym_conv
% 0.07/0.32 thf(fact_144_antisym__conv,axiom,
% 0.07/0.32 ! [Y2: set_set_val,X: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ Y2 @ X )
% 0.07/0.32 => ( ( ord_le1742111550et_val @ X @ Y2 )
% 0.07/0.32 = ( X = Y2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym_conv
% 0.07/0.32 thf(fact_145_antisym__conv,axiom,
% 0.07/0.32 ! [Y2: set_val,X: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ Y2 @ X )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.07/0.32 = ( X = Y2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym_conv
% 0.07/0.32 thf(fact_146_order__class_Oorder_Oeq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y: $o > set_val,Z: $o > set_val] : ( Y = Z ) )
% 0.07/0.32 = ( ^ [A4: $o > set_val,B4: $o > set_val] :
% 0.07/0.32 ( ( ord_le994826475et_val @ A4 @ B4 )
% 0.07/0.32 & ( ord_le994826475et_val @ B4 @ A4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_class.order.eq_iff
% 0.07/0.32 thf(fact_147_order__class_Oorder_Oeq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y: val,Z: val] : ( Y = Z ) )
% 0.07/0.32 = ( ^ [A4: val,B4: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ A4 @ B4 )
% 0.07/0.32 & ( ord_less_eq_val @ B4 @ A4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_class.order.eq_iff
% 0.07/0.32 thf(fact_148_order__class_Oorder_Oeq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y: set_set_val,Z: set_set_val] : ( Y = Z ) )
% 0.07/0.32 = ( ^ [A4: set_set_val,B4: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ A4 @ B4 )
% 0.07/0.32 & ( ord_le1742111550et_val @ B4 @ A4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_class.order.eq_iff
% 0.07/0.32 thf(fact_149_order__class_Oorder_Oeq__iff,axiom,
% 0.07/0.32 ( ( ^ [Y: set_val,Z: set_val] : ( Y = Z ) )
% 0.07/0.32 = ( ^ [A4: set_val,B4: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A4 @ B4 )
% 0.07/0.32 & ( ord_less_eq_set_val @ B4 @ A4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_class.order.eq_iff
% 0.07/0.32 thf(fact_150_ord__eq__le__trans,axiom,
% 0.07/0.32 ! [A3: $o > set_val,B3: $o > set_val,C: $o > set_val] :
% 0.07/0.32 ( ( A3 = B3 )
% 0.07/0.32 => ( ( ord_le994826475et_val @ B3 @ C )
% 0.07/0.32 => ( ord_le994826475et_val @ A3 @ C ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_trans
% 0.07/0.32 thf(fact_151_ord__eq__le__trans,axiom,
% 0.07/0.32 ! [A3: val,B3: val,C: val] :
% 0.07/0.32 ( ( A3 = B3 )
% 0.07/0.32 => ( ( ord_less_eq_val @ B3 @ C )
% 0.07/0.32 => ( ord_less_eq_val @ A3 @ C ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_trans
% 0.07/0.32 thf(fact_152_ord__eq__le__trans,axiom,
% 0.07/0.32 ! [A3: set_set_val,B3: set_set_val,C: set_set_val] :
% 0.07/0.32 ( ( A3 = B3 )
% 0.07/0.32 => ( ( ord_le1742111550et_val @ B3 @ C )
% 0.07/0.32 => ( ord_le1742111550et_val @ A3 @ C ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_trans
% 0.07/0.32 thf(fact_153_ord__eq__le__trans,axiom,
% 0.07/0.32 ! [A3: set_val,B3: set_val,C: set_val] :
% 0.07/0.32 ( ( A3 = B3 )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ B3 @ C )
% 0.07/0.32 => ( ord_less_eq_set_val @ A3 @ C ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_trans
% 0.07/0.32 thf(fact_154_GreatestI2__order,axiom,
% 0.07/0.32 ! [P: ( $o > set_val ) > $o,X: $o > set_val,Q: ( $o > set_val ) > $o] :
% 0.07/0.32 ( ( P @ X )
% 0.07/0.32 => ( ! [Y3: $o > set_val] :
% 0.07/0.32 ( ( P @ Y3 )
% 0.07/0.32 => ( ord_le994826475et_val @ Y3 @ X ) )
% 0.07/0.32 => ( ! [X2: $o > set_val] :
% 0.07/0.32 ( ( P @ X2 )
% 0.07/0.32 => ( ! [Y5: $o > set_val] :
% 0.07/0.32 ( ( P @ Y5 )
% 0.07/0.32 => ( ord_le994826475et_val @ Y5 @ X2 ) )
% 0.07/0.32 => ( Q @ X2 ) ) )
% 0.07/0.32 => ( Q @ ( order_985126002et_val @ P ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % GreatestI2_order
% 0.07/0.32 thf(fact_155_GreatestI2__order,axiom,
% 0.07/0.32 ! [P: val > $o,X: val,Q: val > $o] :
% 0.07/0.32 ( ( P @ X )
% 0.07/0.32 => ( ! [Y3: val] :
% 0.07/0.32 ( ( P @ Y3 )
% 0.07/0.32 => ( ord_less_eq_val @ Y3 @ X ) )
% 0.07/0.32 => ( ! [X2: val] :
% 0.07/0.32 ( ( P @ X2 )
% 0.07/0.32 => ( ! [Y5: val] :
% 0.07/0.32 ( ( P @ Y5 )
% 0.07/0.32 => ( ord_less_eq_val @ Y5 @ X2 ) )
% 0.07/0.32 => ( Q @ X2 ) ) )
% 0.07/0.32 => ( Q @ ( order_Greatest_val @ P ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % GreatestI2_order
% 0.07/0.32 thf(fact_156_GreatestI2__order,axiom,
% 0.07/0.32 ! [P: set_set_val > $o,X: set_set_val,Q: set_set_val > $o] :
% 0.07/0.32 ( ( P @ X )
% 0.07/0.32 => ( ! [Y3: set_set_val] :
% 0.07/0.32 ( ( P @ Y3 )
% 0.07/0.32 => ( ord_le1742111550et_val @ Y3 @ X ) )
% 0.07/0.32 => ( ! [X2: set_set_val] :
% 0.07/0.32 ( ( P @ X2 )
% 0.07/0.32 => ( ! [Y5: set_set_val] :
% 0.07/0.32 ( ( P @ Y5 )
% 0.07/0.32 => ( ord_le1742111550et_val @ Y5 @ X2 ) )
% 0.07/0.32 => ( Q @ X2 ) ) )
% 0.07/0.32 => ( Q @ ( order_544136439et_val @ P ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % GreatestI2_order
% 0.07/0.32 thf(fact_157_GreatestI2__order,axiom,
% 0.07/0.32 ! [P: set_val > $o,X: set_val,Q: set_val > $o] :
% 0.07/0.32 ( ( P @ X )
% 0.07/0.32 => ( ! [Y3: set_val] :
% 0.07/0.32 ( ( P @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_val @ Y3 @ X ) )
% 0.07/0.32 => ( ! [X2: set_val] :
% 0.07/0.32 ( ( P @ X2 )
% 0.07/0.32 => ( ! [Y5: set_val] :
% 0.07/0.32 ( ( P @ Y5 )
% 0.07/0.32 => ( ord_less_eq_set_val @ Y5 @ X2 ) )
% 0.07/0.32 => ( Q @ X2 ) ) )
% 0.07/0.32 => ( Q @ ( order_1960465943et_val @ P ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % GreatestI2_order
% 0.07/0.32 thf(fact_158_Greatest__equality,axiom,
% 0.07/0.32 ! [P: ( $o > set_val ) > $o,X: $o > set_val] :
% 0.07/0.32 ( ( P @ X )
% 0.07/0.32 => ( ! [Y3: $o > set_val] :
% 0.07/0.32 ( ( P @ Y3 )
% 0.07/0.32 => ( ord_le994826475et_val @ Y3 @ X ) )
% 0.07/0.32 => ( ( order_985126002et_val @ P )
% 0.07/0.32 = X ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Greatest_equality
% 0.07/0.32 thf(fact_159_Greatest__equality,axiom,
% 0.07/0.32 ! [P: val > $o,X: val] :
% 0.07/0.32 ( ( P @ X )
% 0.07/0.32 => ( ! [Y3: val] :
% 0.07/0.32 ( ( P @ Y3 )
% 0.07/0.32 => ( ord_less_eq_val @ Y3 @ X ) )
% 0.07/0.32 => ( ( order_Greatest_val @ P )
% 0.07/0.32 = X ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Greatest_equality
% 0.07/0.32 thf(fact_160_Greatest__equality,axiom,
% 0.07/0.32 ! [P: set_set_val > $o,X: set_set_val] :
% 0.07/0.32 ( ( P @ X )
% 0.07/0.32 => ( ! [Y3: set_set_val] :
% 0.07/0.32 ( ( P @ Y3 )
% 0.07/0.32 => ( ord_le1742111550et_val @ Y3 @ X ) )
% 0.07/0.32 => ( ( order_544136439et_val @ P )
% 0.07/0.32 = X ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Greatest_equality
% 0.07/0.32 thf(fact_161_Greatest__equality,axiom,
% 0.07/0.32 ! [P: set_val > $o,X: set_val] :
% 0.07/0.32 ( ( P @ X )
% 0.07/0.32 => ( ! [Y3: set_val] :
% 0.07/0.32 ( ( P @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_val @ Y3 @ X ) )
% 0.07/0.32 => ( ( order_1960465943et_val @ P )
% 0.07/0.32 = X ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Greatest_equality
% 0.07/0.32 thf(fact_162_Refine__Misc_Oif__mono,axiom,
% 0.07/0.32 ! [B3: $o,M1: $o > set_val,M12: $o > set_val,M2: $o > set_val,M22: $o > set_val] :
% 0.07/0.32 ( ( B3
% 0.07/0.32 => ( ord_le994826475et_val @ M1 @ M12 ) )
% 0.07/0.32 => ( ( ~ B3
% 0.07/0.32 => ( ord_le994826475et_val @ M2 @ M22 ) )
% 0.07/0.32 => ( ord_le994826475et_val @ ( if_o_set_val @ B3 @ M1 @ M2 ) @ ( if_o_set_val @ B3 @ M12 @ M22 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Refine_Misc.if_mono
% 0.07/0.32 thf(fact_163_Refine__Misc_Oif__mono,axiom,
% 0.07/0.32 ! [B3: $o,M1: val,M12: val,M2: val,M22: val] :
% 0.07/0.32 ( ( B3
% 0.07/0.32 => ( ord_less_eq_val @ M1 @ M12 ) )
% 0.07/0.32 => ( ( ~ B3
% 0.07/0.32 => ( ord_less_eq_val @ M2 @ M22 ) )
% 0.07/0.32 => ( ord_less_eq_val @ ( if_val @ B3 @ M1 @ M2 ) @ ( if_val @ B3 @ M12 @ M22 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Refine_Misc.if_mono
% 0.07/0.32 thf(fact_164_Refine__Misc_Oif__mono,axiom,
% 0.07/0.32 ! [B3: $o,M1: set_set_val,M12: set_set_val,M2: set_set_val,M22: set_set_val] :
% 0.07/0.32 ( ( B3
% 0.07/0.32 => ( ord_le1742111550et_val @ M1 @ M12 ) )
% 0.07/0.32 => ( ( ~ B3
% 0.07/0.32 => ( ord_le1742111550et_val @ M2 @ M22 ) )
% 0.07/0.32 => ( ord_le1742111550et_val @ ( if_set_set_val @ B3 @ M1 @ M2 ) @ ( if_set_set_val @ B3 @ M12 @ M22 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Refine_Misc.if_mono
% 0.07/0.32 thf(fact_165_Refine__Misc_Oif__mono,axiom,
% 0.07/0.32 ! [B3: $o,M1: set_val,M12: set_val,M2: set_val,M22: set_val] :
% 0.07/0.32 ( ( B3
% 0.07/0.32 => ( ord_less_eq_set_val @ M1 @ M12 ) )
% 0.07/0.32 => ( ( ~ B3
% 0.07/0.32 => ( ord_less_eq_set_val @ M2 @ M22 ) )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( if_set_val @ B3 @ M1 @ M2 ) @ ( if_set_val @ B3 @ M12 @ M22 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Refine_Misc.if_mono
% 0.07/0.32 thf(fact_166_lhs__step__If,axiom,
% 0.07/0.32 ! [B3: $o,T2: $o > set_val,M: $o > set_val,E: $o > set_val] :
% 0.07/0.32 ( ( B3
% 0.07/0.32 => ( ord_le994826475et_val @ T2 @ M ) )
% 0.07/0.32 => ( ( ~ B3
% 0.07/0.32 => ( ord_le994826475et_val @ E @ M ) )
% 0.07/0.32 => ( ord_le994826475et_val @ ( if_o_set_val @ B3 @ T2 @ E ) @ M ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % lhs_step_If
% 0.07/0.32 thf(fact_167_lhs__step__If,axiom,
% 0.07/0.32 ! [B3: $o,T2: val,M: val,E: val] :
% 0.07/0.32 ( ( B3
% 0.07/0.32 => ( ord_less_eq_val @ T2 @ M ) )
% 0.07/0.32 => ( ( ~ B3
% 0.07/0.32 => ( ord_less_eq_val @ E @ M ) )
% 0.07/0.32 => ( ord_less_eq_val @ ( if_val @ B3 @ T2 @ E ) @ M ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % lhs_step_If
% 0.07/0.32 thf(fact_168_lhs__step__If,axiom,
% 0.07/0.32 ! [B3: $o,T2: set_set_val,M: set_set_val,E: set_set_val] :
% 0.07/0.32 ( ( B3
% 0.07/0.32 => ( ord_le1742111550et_val @ T2 @ M ) )
% 0.07/0.32 => ( ( ~ B3
% 0.07/0.32 => ( ord_le1742111550et_val @ E @ M ) )
% 0.07/0.32 => ( ord_le1742111550et_val @ ( if_set_set_val @ B3 @ T2 @ E ) @ M ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % lhs_step_If
% 0.07/0.32 thf(fact_169_lhs__step__If,axiom,
% 0.07/0.32 ! [B3: $o,T2: set_val,M: set_val,E: set_val] :
% 0.07/0.32 ( ( B3
% 0.07/0.32 => ( ord_less_eq_set_val @ T2 @ M ) )
% 0.07/0.32 => ( ( ~ B3
% 0.07/0.32 => ( ord_less_eq_set_val @ E @ M ) )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( if_set_val @ B3 @ T2 @ E ) @ M ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % lhs_step_If
% 0.07/0.32 thf(fact_170_verit__la__disequality,axiom,
% 0.07/0.32 ! [A3: val,B3: val] :
% 0.07/0.32 ( ( A3 = B3 )
% 0.07/0.32 | ~ ( ord_less_eq_val @ A3 @ B3 )
% 0.07/0.32 | ~ ( ord_less_eq_val @ B3 @ A3 ) ) ).
% 0.07/0.32
% 0.07/0.32 % verit_la_disequality
% 0.07/0.32 thf(fact_171_le__rel__bool__arg__iff,axiom,
% 0.07/0.32 ( ord_le1441829300et_val
% 0.07/0.32 = ( ^ [X4: $o > $o > set_val,Y6: $o > $o > set_val] :
% 0.07/0.32 ( ( ord_le994826475et_val @ ( X4 @ $false ) @ ( Y6 @ $false ) )
% 0.07/0.32 & ( ord_le994826475et_val @ ( X4 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_rel_bool_arg_iff
% 0.07/0.32 thf(fact_172_le__rel__bool__arg__iff,axiom,
% 0.07/0.32 ( ord_less_eq_o_val
% 0.07/0.32 = ( ^ [X4: $o > val,Y6: $o > val] :
% 0.07/0.32 ( ( ord_less_eq_val @ ( X4 @ $false ) @ ( Y6 @ $false ) )
% 0.07/0.32 & ( ord_less_eq_val @ ( X4 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_rel_bool_arg_iff
% 0.07/0.32 thf(fact_173_le__rel__bool__arg__iff,axiom,
% 0.07/0.32 ( ord_le936627147et_val
% 0.07/0.32 = ( ^ [X4: $o > set_set_val,Y6: $o > set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ ( X4 @ $false ) @ ( Y6 @ $false ) )
% 0.07/0.32 & ( ord_le1742111550et_val @ ( X4 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_rel_bool_arg_iff
% 0.07/0.32 thf(fact_174_le__rel__bool__arg__iff,axiom,
% 0.07/0.32 ( ord_le994826475et_val
% 0.07/0.32 = ( ^ [X4: $o > set_val,Y6: $o > set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ ( X4 @ $false ) @ ( Y6 @ $false ) )
% 0.07/0.32 & ( ord_less_eq_set_val @ ( X4 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_rel_bool_arg_iff
% 0.07/0.32 thf(fact_175_antimonoD,axiom,
% 0.07/0.32 ! [F: set_val > set_val,X: set_val,Y2: set_val] :
% 0.07/0.32 ( ( order_1719375026et_val @ F )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoD
% 0.07/0.32 thf(fact_176_antimonoD,axiom,
% 0.07/0.32 ! [F: val > val,X: val,Y2: val] :
% 0.07/0.32 ( ( order_1689798834al_val @ F )
% 0.07/0.32 => ( ( ord_less_eq_val @ X @ Y2 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoD
% 0.07/0.32 thf(fact_177_antimonoD,axiom,
% 0.07/0.32 ! [F: set_val > val,X: set_val,Y2: set_val] :
% 0.07/0.32 ( ( order_1375876562al_val @ F )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoD
% 0.07/0.32 thf(fact_178_antimonoD,axiom,
% 0.07/0.32 ! [F: val > set_val,X: val,Y2: val] :
% 0.07/0.32 ( ( order_1484138386et_val @ F )
% 0.07/0.32 => ( ( ord_less_eq_val @ X @ Y2 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoD
% 0.07/0.32 thf(fact_179_antimonoD,axiom,
% 0.07/0.32 ! [F: val > set_set_val,X: val,Y2: val] :
% 0.07/0.32 ( ( order_1945059954et_val @ F )
% 0.07/0.32 => ( ( ord_less_eq_val @ X @ Y2 )
% 0.07/0.32 => ( ord_le1742111550et_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoD
% 0.07/0.32 thf(fact_180_antimonoD,axiom,
% 0.07/0.32 ! [F: set_set_val > val,X: set_set_val,Y2: set_set_val] :
% 0.07/0.32 ( ( order_1520822002al_val @ F )
% 0.07/0.32 => ( ( ord_le1742111550et_val @ X @ Y2 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoD
% 0.07/0.32 thf(fact_181_antimonoD,axiom,
% 0.07/0.32 ! [F: set_val > set_set_val,X: set_val,Y2: set_val] :
% 0.07/0.32 ( ( order_1957703570et_val @ F )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.07/0.32 => ( ord_le1742111550et_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoD
% 0.07/0.32 thf(fact_182_antimonoD,axiom,
% 0.07/0.32 ! [F: ( $o > set_val ) > val,X: $o > set_val,Y2: $o > set_val] :
% 0.07/0.32 ( ( order_23236447al_val @ F )
% 0.07/0.32 => ( ( ord_le994826475et_val @ X @ Y2 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoD
% 0.07/0.32 thf(fact_183_antimonoD,axiom,
% 0.07/0.32 ! [F: val > $o > set_val,X: val,Y2: val] :
% 0.07/0.32 ( ( order_255079095et_val @ F )
% 0.07/0.32 => ( ( ord_less_eq_val @ X @ Y2 )
% 0.07/0.32 => ( ord_le994826475et_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoD
% 0.07/0.32 thf(fact_184_antimonoD,axiom,
% 0.07/0.32 ! [F: set_set_val > set_val,X: set_set_val,Y2: set_set_val] :
% 0.07/0.32 ( ( order_650823122et_val @ F )
% 0.07/0.32 => ( ( ord_le1742111550et_val @ X @ Y2 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoD
% 0.07/0.32 thf(fact_185_antimonoE,axiom,
% 0.07/0.32 ! [F: set_val > set_val,X: set_val,Y2: set_val] :
% 0.07/0.32 ( ( order_1719375026et_val @ F )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoE
% 0.07/0.32 thf(fact_186_antimonoE,axiom,
% 0.07/0.32 ! [F: val > val,X: val,Y2: val] :
% 0.07/0.32 ( ( order_1689798834al_val @ F )
% 0.07/0.32 => ( ( ord_less_eq_val @ X @ Y2 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoE
% 0.07/0.32 thf(fact_187_antimonoE,axiom,
% 0.07/0.32 ! [F: set_val > val,X: set_val,Y2: set_val] :
% 0.07/0.32 ( ( order_1375876562al_val @ F )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoE
% 0.07/0.32 thf(fact_188_antimonoE,axiom,
% 0.07/0.32 ! [F: val > set_val,X: val,Y2: val] :
% 0.07/0.32 ( ( order_1484138386et_val @ F )
% 0.07/0.32 => ( ( ord_less_eq_val @ X @ Y2 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoE
% 0.07/0.32 thf(fact_189_antimonoE,axiom,
% 0.07/0.32 ! [F: val > set_set_val,X: val,Y2: val] :
% 0.07/0.32 ( ( order_1945059954et_val @ F )
% 0.07/0.32 => ( ( ord_less_eq_val @ X @ Y2 )
% 0.07/0.32 => ( ord_le1742111550et_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoE
% 0.07/0.32 thf(fact_190_antimonoE,axiom,
% 0.07/0.32 ! [F: set_set_val > val,X: set_set_val,Y2: set_set_val] :
% 0.07/0.32 ( ( order_1520822002al_val @ F )
% 0.07/0.32 => ( ( ord_le1742111550et_val @ X @ Y2 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoE
% 0.07/0.32 thf(fact_191_antimonoE,axiom,
% 0.07/0.32 ! [F: set_val > set_set_val,X: set_val,Y2: set_val] :
% 0.07/0.32 ( ( order_1957703570et_val @ F )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.07/0.32 => ( ord_le1742111550et_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoE
% 0.07/0.32 thf(fact_192_antimonoE,axiom,
% 0.07/0.32 ! [F: ( $o > set_val ) > val,X: $o > set_val,Y2: $o > set_val] :
% 0.07/0.32 ( ( order_23236447al_val @ F )
% 0.07/0.32 => ( ( ord_le994826475et_val @ X @ Y2 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoE
% 0.07/0.32 thf(fact_193_antimonoE,axiom,
% 0.07/0.32 ! [F: val > $o > set_val,X: val,Y2: val] :
% 0.07/0.32 ( ( order_255079095et_val @ F )
% 0.07/0.32 => ( ( ord_less_eq_val @ X @ Y2 )
% 0.07/0.32 => ( ord_le994826475et_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoE
% 0.07/0.32 thf(fact_194_antimonoE,axiom,
% 0.07/0.32 ! [F: set_set_val > set_val,X: set_set_val,Y2: set_set_val] :
% 0.07/0.32 ( ( order_650823122et_val @ F )
% 0.07/0.32 => ( ( ord_le1742111550et_val @ X @ Y2 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoE
% 0.07/0.32 thf(fact_195_antimono__def,axiom,
% 0.07/0.32 ( order_1719375026et_val
% 0.07/0.32 = ( ^ [F2: set_val > set_val] :
% 0.07/0.32 ! [X3: set_val,Y4: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X3 @ Y4 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimono_def
% 0.07/0.32 thf(fact_196_antimono__def,axiom,
% 0.07/0.32 ( order_1689798834al_val
% 0.07/0.32 = ( ^ [F2: val > val] :
% 0.07/0.32 ! [X3: val,Y4: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X3 @ Y4 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimono_def
% 0.07/0.32 thf(fact_197_antimono__def,axiom,
% 0.07/0.32 ( order_1375876562al_val
% 0.07/0.32 = ( ^ [F2: set_val > val] :
% 0.07/0.32 ! [X3: set_val,Y4: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X3 @ Y4 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimono_def
% 0.07/0.32 thf(fact_198_antimono__def,axiom,
% 0.07/0.32 ( order_1484138386et_val
% 0.07/0.32 = ( ^ [F2: val > set_val] :
% 0.07/0.32 ! [X3: val,Y4: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X3 @ Y4 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimono_def
% 0.07/0.32 thf(fact_199_antimono__def,axiom,
% 0.07/0.32 ( order_1945059954et_val
% 0.07/0.32 = ( ^ [F2: val > set_set_val] :
% 0.07/0.32 ! [X3: val,Y4: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X3 @ Y4 )
% 0.07/0.32 => ( ord_le1742111550et_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimono_def
% 0.07/0.32 thf(fact_200_antimono__def,axiom,
% 0.07/0.32 ( order_1520822002al_val
% 0.07/0.32 = ( ^ [F2: set_set_val > val] :
% 0.07/0.32 ! [X3: set_set_val,Y4: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ X3 @ Y4 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimono_def
% 0.07/0.32 thf(fact_201_antimono__def,axiom,
% 0.07/0.32 ( order_1957703570et_val
% 0.07/0.32 = ( ^ [F2: set_val > set_set_val] :
% 0.07/0.32 ! [X3: set_val,Y4: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X3 @ Y4 )
% 0.07/0.32 => ( ord_le1742111550et_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimono_def
% 0.07/0.32 thf(fact_202_antimono__def,axiom,
% 0.07/0.32 ( order_23236447al_val
% 0.07/0.32 = ( ^ [F2: ( $o > set_val ) > val] :
% 0.07/0.32 ! [X3: $o > set_val,Y4: $o > set_val] :
% 0.07/0.32 ( ( ord_le994826475et_val @ X3 @ Y4 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimono_def
% 0.07/0.32 thf(fact_203_antimono__def,axiom,
% 0.07/0.32 ( order_255079095et_val
% 0.07/0.32 = ( ^ [F2: val > $o > set_val] :
% 0.07/0.32 ! [X3: val,Y4: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X3 @ Y4 )
% 0.07/0.32 => ( ord_le994826475et_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimono_def
% 0.07/0.32 thf(fact_204_antimono__def,axiom,
% 0.07/0.32 ( order_650823122et_val
% 0.07/0.32 = ( ^ [F2: set_set_val > set_val] :
% 0.07/0.32 ! [X3: set_set_val,Y4: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ X3 @ Y4 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimono_def
% 0.07/0.32 thf(fact_205_antimonoI,axiom,
% 0.07/0.32 ! [F: set_val > set_val] :
% 0.07/0.32 ( ! [X2: set_val,Y3: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 0.07/0.32 => ( order_1719375026et_val @ F ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoI
% 0.07/0.32 thf(fact_206_antimonoI,axiom,
% 0.07/0.32 ! [F: val > val] :
% 0.07/0.32 ( ! [X2: val,Y3: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 0.07/0.32 => ( order_1689798834al_val @ F ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoI
% 0.07/0.32 thf(fact_207_antimonoI,axiom,
% 0.07/0.32 ! [F: set_val > val] :
% 0.07/0.32 ( ! [X2: set_val,Y3: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 0.07/0.32 => ( order_1375876562al_val @ F ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoI
% 0.07/0.32 thf(fact_208_antimonoI,axiom,
% 0.07/0.32 ! [F: val > set_val] :
% 0.07/0.32 ( ! [X2: val,Y3: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 0.07/0.32 => ( order_1484138386et_val @ F ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoI
% 0.07/0.32 thf(fact_209_antimonoI,axiom,
% 0.07/0.32 ! [F: val > set_set_val] :
% 0.07/0.32 ( ! [X2: val,Y3: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le1742111550et_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 0.07/0.32 => ( order_1945059954et_val @ F ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoI
% 0.07/0.32 thf(fact_210_antimonoI,axiom,
% 0.07/0.32 ! [F: set_set_val > val] :
% 0.07/0.32 ( ! [X2: set_set_val,Y3: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 0.07/0.32 => ( order_1520822002al_val @ F ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoI
% 0.07/0.32 thf(fact_211_antimonoI,axiom,
% 0.07/0.32 ! [F: set_val > set_set_val] :
% 0.07/0.32 ( ! [X2: set_val,Y3: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le1742111550et_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 0.07/0.32 => ( order_1957703570et_val @ F ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoI
% 0.07/0.32 thf(fact_212_antimonoI,axiom,
% 0.07/0.32 ! [F: ( $o > set_val ) > val] :
% 0.07/0.32 ( ! [X2: $o > set_val,Y3: $o > set_val] :
% 0.07/0.32 ( ( ord_le994826475et_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 0.07/0.32 => ( order_23236447al_val @ F ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoI
% 0.07/0.32 thf(fact_213_antimonoI,axiom,
% 0.07/0.32 ! [F: val > $o > set_val] :
% 0.07/0.32 ( ! [X2: val,Y3: val] :
% 0.07/0.32 ( ( ord_less_eq_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_le994826475et_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 0.07/0.32 => ( order_255079095et_val @ F ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoI
% 0.07/0.32 thf(fact_214_antimonoI,axiom,
% 0.07/0.32 ! [F: set_set_val > set_val] :
% 0.07/0.32 ( ! [X2: set_set_val,Y3: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 0.07/0.32 => ( order_650823122et_val @ F ) ) ).
% 0.07/0.32
% 0.07/0.32 % antimonoI
% 0.07/0.32 thf(fact_215_order__mono__setup_Omono__setup__loc__axioms,axiom,
% 0.07/0.32 refine16560100et_val @ ord_le994826475et_val ).
% 0.07/0.32
% 0.07/0.32 % order_mono_setup.mono_setup_loc_axioms
% 0.07/0.32 thf(fact_216_order__mono__setup_Omono__setup__loc__axioms,axiom,
% 0.07/0.32 refine67622213oc_val @ ord_less_eq_val ).
% 0.07/0.32
% 0.07/0.32 % order_mono_setup.mono_setup_loc_axioms
% 0.07/0.32 thf(fact_217_order__mono__setup_Omono__setup__loc__axioms,axiom,
% 0.07/0.32 refine1506227973et_val @ ord_le1742111550et_val ).
% 0.07/0.32
% 0.07/0.32 % order_mono_setup.mono_setup_loc_axioms
% 0.07/0.32 thf(fact_218_order__mono__setup_Omono__setup__loc__axioms,axiom,
% 0.07/0.32 refine275900453et_val @ ord_less_eq_set_val ).
% 0.07/0.32
% 0.07/0.32 % order_mono_setup.mono_setup_loc_axioms
% 0.07/0.32 thf(fact_219_galois__connection_O_092_060gamma_062_092_060alpha_062__infl,axiom,
% 0.07/0.32 ! [Alpha: set_val > set_val,Gamma: set_val > set_val,X: set_val] :
% 0.07/0.32 ( ( refine1929691018et_val @ Alpha @ Gamma )
% 0.07/0.32 => ( ord_less_eq_set_val @ X @ ( Gamma @ ( Alpha @ X ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.\<gamma>\<alpha>_infl
% 0.07/0.32 thf(fact_220_galois__connection_O_092_060alpha_062_092_060gamma_062__defl,axiom,
% 0.07/0.32 ! [Alpha: set_val > set_val,Gamma: set_val > set_val,X: set_val] :
% 0.07/0.32 ( ( refine1929691018et_val @ Alpha @ Gamma )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( Alpha @ ( Gamma @ X ) ) @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.\<alpha>\<gamma>_defl
% 0.07/0.32 thf(fact_221_galois__connection_Ogalois,axiom,
% 0.07/0.32 ! [Alpha: set_val > $o > set_val,Gamma: ( $o > set_val ) > set_val,C: set_val,A3: $o > set_val] :
% 0.07/0.32 ( ( refine51544255et_val @ Alpha @ Gamma )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ C @ ( Gamma @ A3 ) )
% 0.07/0.32 = ( ord_le994826475et_val @ ( Alpha @ C ) @ A3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.galois
% 0.07/0.32 thf(fact_222_galois__connection_Ogalois,axiom,
% 0.07/0.32 ! [Alpha: set_val > set_set_val,Gamma: set_set_val > set_val,C: set_val,A3: set_set_val] :
% 0.07/0.32 ( ( refine1315043946et_val @ Alpha @ Gamma )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ C @ ( Gamma @ A3 ) )
% 0.07/0.32 = ( ord_le1742111550et_val @ ( Alpha @ C ) @ A3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.galois
% 0.07/0.32 thf(fact_223_galois__connection_Ogalois,axiom,
% 0.07/0.32 ! [Alpha: ( $o > set_val ) > set_val,Gamma: set_val > $o > set_val,C: $o > set_val,A3: set_val] :
% 0.07/0.32 ( ( refine1948536167et_val @ Alpha @ Gamma )
% 0.07/0.32 => ( ( ord_le994826475et_val @ C @ ( Gamma @ A3 ) )
% 0.07/0.32 = ( ord_less_eq_set_val @ ( Alpha @ C ) @ A3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.galois
% 0.07/0.32 thf(fact_224_galois__connection_Ogalois,axiom,
% 0.07/0.32 ! [Alpha: ( $o > set_val ) > $o > set_val,Gamma: ( $o > set_val ) > $o > set_val,C: $o > set_val,A3: $o > set_val] :
% 0.07/0.32 ( ( refine1924899106et_val @ Alpha @ Gamma )
% 0.07/0.32 => ( ( ord_le994826475et_val @ C @ ( Gamma @ A3 ) )
% 0.07/0.32 = ( ord_le994826475et_val @ ( Alpha @ C ) @ A3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.galois
% 0.07/0.32 thf(fact_225_galois__connection_Ogalois,axiom,
% 0.07/0.32 ! [Alpha: ( $o > set_val ) > set_set_val,Gamma: set_set_val > $o > set_val,C: $o > set_val,A3: set_set_val] :
% 0.07/0.32 ( ( refine1169396807et_val @ Alpha @ Gamma )
% 0.07/0.32 => ( ( ord_le994826475et_val @ C @ ( Gamma @ A3 ) )
% 0.07/0.32 = ( ord_le1742111550et_val @ ( Alpha @ C ) @ A3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.galois
% 0.07/0.32 thf(fact_226_galois__connection_Ogalois,axiom,
% 0.07/0.32 ! [Alpha: set_set_val > set_val,Gamma: set_val > set_set_val,C: set_set_val,A3: set_val] :
% 0.07/0.32 ( ( refine8163498et_val @ Alpha @ Gamma )
% 0.07/0.32 => ( ( ord_le1742111550et_val @ C @ ( Gamma @ A3 ) )
% 0.07/0.32 = ( ord_less_eq_set_val @ ( Alpha @ C ) @ A3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.galois
% 0.07/0.32 thf(fact_227_galois__connection_Ogalois,axiom,
% 0.07/0.32 ! [Alpha: set_set_val > $o > set_val,Gamma: ( $o > set_val ) > set_set_val,C: set_set_val,A3: $o > set_val] :
% 0.07/0.32 ( ( refine86398879et_val @ Alpha @ Gamma )
% 0.07/0.32 => ( ( ord_le1742111550et_val @ C @ ( Gamma @ A3 ) )
% 0.07/0.32 = ( ord_le994826475et_val @ ( Alpha @ C ) @ A3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.galois
% 0.07/0.32 thf(fact_228_galois__connection_Ogalois,axiom,
% 0.07/0.32 ! [Alpha: set_set_val > set_set_val,Gamma: set_set_val > set_set_val,C: set_set_val,A3: set_set_val] :
% 0.07/0.32 ( ( refine855985034et_val @ Alpha @ Gamma )
% 0.07/0.32 => ( ( ord_le1742111550et_val @ C @ ( Gamma @ A3 ) )
% 0.07/0.32 = ( ord_le1742111550et_val @ ( Alpha @ C ) @ A3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.galois
% 0.07/0.32 thf(fact_229_galois__connection_Ogalois,axiom,
% 0.07/0.32 ! [Alpha: set_val > set_val,Gamma: set_val > set_val,C: set_val,A3: set_val] :
% 0.07/0.32 ( ( refine1929691018et_val @ Alpha @ Gamma )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ C @ ( Gamma @ A3 ) )
% 0.07/0.32 = ( ord_less_eq_set_val @ ( Alpha @ C ) @ A3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.galois
% 0.07/0.32 thf(fact_230_galois__connection_Ointro,axiom,
% 0.07/0.32 ! [Gamma: ( $o > set_val ) > set_val,Alpha: set_val > $o > set_val] :
% 0.07/0.32 ( ! [C3: set_val,A5: $o > set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ C3 @ ( Gamma @ A5 ) )
% 0.07/0.32 = ( ord_le994826475et_val @ ( Alpha @ C3 ) @ A5 ) )
% 0.07/0.32 => ( refine51544255et_val @ Alpha @ Gamma ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.intro
% 0.07/0.32 thf(fact_231_galois__connection_Ointro,axiom,
% 0.07/0.32 ! [Gamma: set_set_val > set_val,Alpha: set_val > set_set_val] :
% 0.07/0.32 ( ! [C3: set_val,A5: set_set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ C3 @ ( Gamma @ A5 ) )
% 0.07/0.32 = ( ord_le1742111550et_val @ ( Alpha @ C3 ) @ A5 ) )
% 0.07/0.32 => ( refine1315043946et_val @ Alpha @ Gamma ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.intro
% 0.07/0.32 thf(fact_232_galois__connection_Ointro,axiom,
% 0.07/0.32 ! [Gamma: set_val > $o > set_val,Alpha: ( $o > set_val ) > set_val] :
% 0.07/0.32 ( ! [C3: $o > set_val,A5: set_val] :
% 0.07/0.32 ( ( ord_le994826475et_val @ C3 @ ( Gamma @ A5 ) )
% 0.07/0.32 = ( ord_less_eq_set_val @ ( Alpha @ C3 ) @ A5 ) )
% 0.07/0.32 => ( refine1948536167et_val @ Alpha @ Gamma ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.intro
% 0.07/0.32 thf(fact_233_galois__connection_Ointro,axiom,
% 0.07/0.32 ! [Gamma: ( $o > set_val ) > $o > set_val,Alpha: ( $o > set_val ) > $o > set_val] :
% 0.07/0.32 ( ! [C3: $o > set_val,A5: $o > set_val] :
% 0.07/0.32 ( ( ord_le994826475et_val @ C3 @ ( Gamma @ A5 ) )
% 0.07/0.32 = ( ord_le994826475et_val @ ( Alpha @ C3 ) @ A5 ) )
% 0.07/0.32 => ( refine1924899106et_val @ Alpha @ Gamma ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.intro
% 0.07/0.32 thf(fact_234_galois__connection_Ointro,axiom,
% 0.07/0.32 ! [Gamma: set_set_val > $o > set_val,Alpha: ( $o > set_val ) > set_set_val] :
% 0.07/0.32 ( ! [C3: $o > set_val,A5: set_set_val] :
% 0.07/0.32 ( ( ord_le994826475et_val @ C3 @ ( Gamma @ A5 ) )
% 0.07/0.32 = ( ord_le1742111550et_val @ ( Alpha @ C3 ) @ A5 ) )
% 0.07/0.32 => ( refine1169396807et_val @ Alpha @ Gamma ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.intro
% 0.07/0.32 thf(fact_235_galois__connection_Ointro,axiom,
% 0.07/0.32 ! [Gamma: set_val > set_set_val,Alpha: set_set_val > set_val] :
% 0.07/0.32 ( ! [C3: set_set_val,A5: set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ C3 @ ( Gamma @ A5 ) )
% 0.07/0.32 = ( ord_less_eq_set_val @ ( Alpha @ C3 ) @ A5 ) )
% 0.07/0.32 => ( refine8163498et_val @ Alpha @ Gamma ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.intro
% 0.07/0.32 thf(fact_236_galois__connection_Ointro,axiom,
% 0.07/0.32 ! [Gamma: ( $o > set_val ) > set_set_val,Alpha: set_set_val > $o > set_val] :
% 0.07/0.32 ( ! [C3: set_set_val,A5: $o > set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ C3 @ ( Gamma @ A5 ) )
% 0.07/0.32 = ( ord_le994826475et_val @ ( Alpha @ C3 ) @ A5 ) )
% 0.07/0.32 => ( refine86398879et_val @ Alpha @ Gamma ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.intro
% 0.07/0.32 thf(fact_237_galois__connection_Ointro,axiom,
% 0.07/0.32 ! [Gamma: set_set_val > set_set_val,Alpha: set_set_val > set_set_val] :
% 0.07/0.32 ( ! [C3: set_set_val,A5: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ C3 @ ( Gamma @ A5 ) )
% 0.07/0.32 = ( ord_le1742111550et_val @ ( Alpha @ C3 ) @ A5 ) )
% 0.07/0.32 => ( refine855985034et_val @ Alpha @ Gamma ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.intro
% 0.07/0.32 thf(fact_238_galois__connection_Ointro,axiom,
% 0.07/0.32 ! [Gamma: set_val > set_val,Alpha: set_val > set_val] :
% 0.07/0.32 ( ! [C3: set_val,A5: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ C3 @ ( Gamma @ A5 ) )
% 0.07/0.32 = ( ord_less_eq_set_val @ ( Alpha @ C3 ) @ A5 ) )
% 0.07/0.32 => ( refine1929691018et_val @ Alpha @ Gamma ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.intro
% 0.07/0.32 thf(fact_239_galois__connection__def,axiom,
% 0.07/0.32 ( refine51544255et_val
% 0.07/0.32 = ( ^ [Alpha2: set_val > $o > set_val,Gamma2: ( $o > set_val ) > set_val] :
% 0.07/0.32 ! [C4: set_val,A4: $o > set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ C4 @ ( Gamma2 @ A4 ) )
% 0.07/0.32 = ( ord_le994826475et_val @ ( Alpha2 @ C4 ) @ A4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection_def
% 0.07/0.32 thf(fact_240_galois__connection__def,axiom,
% 0.07/0.32 ( refine1315043946et_val
% 0.07/0.32 = ( ^ [Alpha2: set_val > set_set_val,Gamma2: set_set_val > set_val] :
% 0.07/0.32 ! [C4: set_val,A4: set_set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ C4 @ ( Gamma2 @ A4 ) )
% 0.07/0.32 = ( ord_le1742111550et_val @ ( Alpha2 @ C4 ) @ A4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection_def
% 0.07/0.32 thf(fact_241_galois__connection__def,axiom,
% 0.07/0.32 ( refine1948536167et_val
% 0.07/0.32 = ( ^ [Alpha2: ( $o > set_val ) > set_val,Gamma2: set_val > $o > set_val] :
% 0.07/0.32 ! [C4: $o > set_val,A4: set_val] :
% 0.07/0.32 ( ( ord_le994826475et_val @ C4 @ ( Gamma2 @ A4 ) )
% 0.07/0.32 = ( ord_less_eq_set_val @ ( Alpha2 @ C4 ) @ A4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection_def
% 0.07/0.32 thf(fact_242_galois__connection__def,axiom,
% 0.07/0.32 ( refine1924899106et_val
% 0.07/0.32 = ( ^ [Alpha2: ( $o > set_val ) > $o > set_val,Gamma2: ( $o > set_val ) > $o > set_val] :
% 0.07/0.32 ! [C4: $o > set_val,A4: $o > set_val] :
% 0.07/0.32 ( ( ord_le994826475et_val @ C4 @ ( Gamma2 @ A4 ) )
% 0.07/0.32 = ( ord_le994826475et_val @ ( Alpha2 @ C4 ) @ A4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection_def
% 0.07/0.32 thf(fact_243_galois__connection__def,axiom,
% 0.07/0.32 ( refine1169396807et_val
% 0.07/0.32 = ( ^ [Alpha2: ( $o > set_val ) > set_set_val,Gamma2: set_set_val > $o > set_val] :
% 0.07/0.32 ! [C4: $o > set_val,A4: set_set_val] :
% 0.07/0.32 ( ( ord_le994826475et_val @ C4 @ ( Gamma2 @ A4 ) )
% 0.07/0.32 = ( ord_le1742111550et_val @ ( Alpha2 @ C4 ) @ A4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection_def
% 0.07/0.32 thf(fact_244_galois__connection__def,axiom,
% 0.07/0.32 ( refine8163498et_val
% 0.07/0.32 = ( ^ [Alpha2: set_set_val > set_val,Gamma2: set_val > set_set_val] :
% 0.07/0.32 ! [C4: set_set_val,A4: set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ C4 @ ( Gamma2 @ A4 ) )
% 0.07/0.32 = ( ord_less_eq_set_val @ ( Alpha2 @ C4 ) @ A4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection_def
% 0.07/0.32 thf(fact_245_galois__connection__def,axiom,
% 0.07/0.32 ( refine86398879et_val
% 0.07/0.32 = ( ^ [Alpha2: set_set_val > $o > set_val,Gamma2: ( $o > set_val ) > set_set_val] :
% 0.07/0.32 ! [C4: set_set_val,A4: $o > set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ C4 @ ( Gamma2 @ A4 ) )
% 0.07/0.32 = ( ord_le994826475et_val @ ( Alpha2 @ C4 ) @ A4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection_def
% 0.07/0.32 thf(fact_246_galois__connection__def,axiom,
% 0.07/0.32 ( refine855985034et_val
% 0.07/0.32 = ( ^ [Alpha2: set_set_val > set_set_val,Gamma2: set_set_val > set_set_val] :
% 0.07/0.32 ! [C4: set_set_val,A4: set_set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ C4 @ ( Gamma2 @ A4 ) )
% 0.07/0.32 = ( ord_le1742111550et_val @ ( Alpha2 @ C4 ) @ A4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection_def
% 0.07/0.32 thf(fact_247_galois__connection__def,axiom,
% 0.07/0.32 ( refine1929691018et_val
% 0.07/0.32 = ( ^ [Alpha2: set_val > set_val,Gamma2: set_val > set_val] :
% 0.07/0.32 ! [C4: set_val,A4: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ C4 @ ( Gamma2 @ A4 ) )
% 0.07/0.32 = ( ord_less_eq_set_val @ ( Alpha2 @ C4 ) @ A4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection_def
% 0.07/0.32 thf(fact_248_mono__setup__loc__def,axiom,
% 0.07/0.32 ( refine275900453et_val
% 0.07/0.32 = ( ^ [Le: set_val > set_val > $o] :
% 0.07/0.32 ! [X3: set_val] : ( Le @ X3 @ X3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % mono_setup_loc_def
% 0.07/0.32 thf(fact_249_mono__setup__loc_Orefl,axiom,
% 0.07/0.32 ! [Le2: set_val > set_val > $o,X: set_val] :
% 0.07/0.32 ( ( refine275900453et_val @ Le2 )
% 0.07/0.32 => ( Le2 @ X @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % mono_setup_loc.refl
% 0.07/0.32 thf(fact_250_mono__setup__loc_Ointro,axiom,
% 0.07/0.32 ! [Le2: set_val > set_val > $o] :
% 0.07/0.32 ( ! [X2: set_val] : ( Le2 @ X2 @ X2 )
% 0.07/0.32 => ( refine275900453et_val @ Le2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % mono_setup_loc.intro
% 0.07/0.32 thf(fact_251_mono__setup__loc_Omono__if,axiom,
% 0.07/0.32 ! [Le2: set_val > set_val > $o,T2: set_val,T3: set_val,E: set_val,E2: set_val,B3: $o] :
% 0.07/0.32 ( ( refine275900453et_val @ Le2 )
% 0.07/0.32 => ( ( Le2 @ T2 @ T3 )
% 0.07/0.32 => ( ( Le2 @ E @ E2 )
% 0.07/0.32 => ( Le2 @ ( if_set_val @ B3 @ T2 @ E ) @ ( if_set_val @ B3 @ T3 @ E2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % mono_setup_loc.mono_if
% 0.07/0.32 thf(fact_252_galois__connection_Oinf__dist___092_060alpha_062,axiom,
% 0.07/0.32 ! [Alpha: set_val > set_val,Gamma: set_val > set_val] :
% 0.07/0.32 ( ( refine1929691018et_val @ Alpha @ Gamma )
% 0.07/0.32 => ( refine2057434761et_val @ Alpha ) ) ).
% 0.07/0.32
% 0.07/0.32 % galois_connection.inf_dist_\<alpha>
% 0.07/0.32 thf(fact_253_strict__mono__less__eq,axiom,
% 0.07/0.32 ! [F: val > set_val,X: val,Y2: val] :
% 0.07/0.32 ( ( order_99134233et_val @ F )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ ( F @ X ) @ ( F @ Y2 ) )
% 0.07/0.32 = ( ord_less_eq_val @ X @ Y2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % strict_mono_less_eq
% 0.07/0.32 thf(fact_254_strict__mono__less__eq,axiom,
% 0.07/0.32 ! [F: val > $o > set_val,X: val,Y2: val] :
% 0.07/0.32 ( ( order_1205732848et_val @ F )
% 0.07/0.32 => ( ( ord_le994826475et_val @ ( F @ X ) @ ( F @ Y2 ) )
% 0.07/0.32 = ( ord_less_eq_val @ X @ Y2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % strict_mono_less_eq
% 0.07/0.32 thf(fact_255_strict__mono__less__eq,axiom,
% 0.07/0.32 ! [F: val > val,X: val,Y2: val] :
% 0.07/0.32 ( ( order_1139042361al_val @ F )
% 0.07/0.32 => ( ( ord_less_eq_val @ ( F @ X ) @ ( F @ Y2 ) )
% 0.07/0.32 = ( ord_less_eq_val @ X @ Y2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % strict_mono_less_eq
% 0.07/0.32 thf(fact_256_strict__mono__less__eq,axiom,
% 0.07/0.32 ! [F: val > set_set_val,X: val,Y2: val] :
% 0.07/0.32 ( ( order_68692473et_val @ F )
% 0.07/0.32 => ( ( ord_le1742111550et_val @ ( F @ X ) @ ( F @ Y2 ) )
% 0.07/0.32 = ( ord_less_eq_val @ X @ Y2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % strict_mono_less_eq
% 0.07/0.32 thf(fact_257_greaterThan__subset__iff,axiom,
% 0.07/0.32 ! [X: val,Y2: val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ ( set_or1288365508an_val @ X ) @ ( set_or1288365508an_val @ Y2 ) )
% 0.07/0.32 = ( ord_less_eq_val @ Y2 @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % greaterThan_subset_iff
% 0.07/0.32 thf(fact_258_START__REFINEG__TRANSFER,axiom,
% 0.07/0.32 ! [D: $o > set_val,C: $o > set_val,A3: $o > set_val] :
% 0.07/0.32 ( ( refine1593386065et_val @ D @ C )
% 0.07/0.32 => ( ( ord_le994826475et_val @ C @ A3 )
% 0.07/0.32 => ( ( refine511606705et_val @ C @ D )
% 0.07/0.32 => ( ord_le994826475et_val @ D @ A3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % START_REFINEG_TRANSFER
% 0.07/0.32 thf(fact_259_START__REFINEG__TRANSFER,axiom,
% 0.07/0.32 ! [D: val,C: val,A3: val] :
% 0.07/0.32 ( ( refine2021912633al_val @ D @ C )
% 0.07/0.32 => ( ( ord_less_eq_val @ C @ A3 )
% 0.07/0.32 => ( ( refine403244856MP_val @ C @ D )
% 0.07/0.32 => ( ord_less_eq_val @ D @ A3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % START_REFINEG_TRANSFER
% 0.07/0.32 thf(fact_260_START__REFINEG__TRANSFER,axiom,
% 0.07/0.32 ! [D: set_set_val,C: set_set_val,A3: set_set_val] :
% 0.07/0.32 ( ( refine1034950713et_val @ D @ C )
% 0.07/0.32 => ( ( ord_le1742111550et_val @ C @ A3 )
% 0.07/0.32 => ( ( refine1908789496et_val @ C @ D )
% 0.07/0.32 => ( ord_le1742111550et_val @ D @ A3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % START_REFINEG_TRANSFER
% 0.07/0.32 thf(fact_261_START__REFINEG__TRANSFER,axiom,
% 0.07/0.32 ! [D: set_val,C: set_val,A3: set_val] :
% 0.07/0.32 ( ( refine654574649et_val @ D @ C )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ C @ A3 )
% 0.07/0.32 => ( ( refine1893322264et_val @ C @ D )
% 0.07/0.32 => ( ord_less_eq_set_val @ D @ A3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % START_REFINEG_TRANSFER
% 0.07/0.32 thf(fact_262_lessThan__subset__iff,axiom,
% 0.07/0.32 ! [X: val,Y2: val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ ( set_ord_lessThan_val @ X ) @ ( set_ord_lessThan_val @ Y2 ) )
% 0.07/0.32 = ( ord_less_eq_val @ X @ Y2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % lessThan_subset_iff
% 0.07/0.32 thf(fact_263_atLeast__subset__iff,axiom,
% 0.07/0.32 ! [X: set_set_val,Y2: set_set_val] :
% 0.07/0.32 ( ( ord_le1135847966et_val @ ( set_or1337784553et_val @ X ) @ ( set_or1337784553et_val @ Y2 ) )
% 0.07/0.32 = ( ord_le1742111550et_val @ Y2 @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % atLeast_subset_iff
% 0.07/0.32 thf(fact_264_atLeast__subset__iff,axiom,
% 0.07/0.32 ! [X: set_val,Y2: set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ ( set_or650197513et_val @ X ) @ ( set_or650197513et_val @ Y2 ) )
% 0.07/0.32 = ( ord_less_eq_set_val @ Y2 @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % atLeast_subset_iff
% 0.07/0.32 thf(fact_265_atLeast__subset__iff,axiom,
% 0.07/0.32 ! [X: val,Y2: val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ ( set_ord_atLeast_val @ X ) @ ( set_ord_atLeast_val @ Y2 ) )
% 0.07/0.32 = ( ord_less_eq_val @ Y2 @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % atLeast_subset_iff
% 0.07/0.32 thf(fact_266_atLeast__iff,axiom,
% 0.07/0.32 ! [I: val,K: val] :
% 0.07/0.32 ( ( member_val @ I @ ( set_ord_atLeast_val @ K ) )
% 0.07/0.32 = ( ord_less_eq_val @ K @ I ) ) ).
% 0.07/0.32
% 0.07/0.32 % atLeast_iff
% 0.07/0.32 thf(fact_267_atLeast__iff,axiom,
% 0.07/0.32 ! [I: set_val,K: set_val] :
% 0.07/0.32 ( ( member_set_val @ I @ ( set_or650197513et_val @ K ) )
% 0.07/0.32 = ( ord_less_eq_set_val @ K @ I ) ) ).
% 0.07/0.32
% 0.07/0.32 % atLeast_iff
% 0.07/0.32 thf(fact_268_Ioi__le__Ico,axiom,
% 0.07/0.32 ! [A3: val] : ( ord_less_eq_set_val @ ( set_or1288365508an_val @ A3 ) @ ( set_ord_atLeast_val @ A3 ) ) ).
% 0.07/0.32
% 0.07/0.32 % Ioi_le_Ico
% 0.07/0.32 thf(fact_269_Ici__subset__Ioi__iff,axiom,
% 0.07/0.32 ! [A3: val,B3: val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ ( set_ord_atLeast_val @ A3 ) @ ( set_or1288365508an_val @ B3 ) )
% 0.07/0.32 = ( ord_less_val @ B3 @ A3 ) ) ).
% 0.07/0.32
% 0.07/0.32 % Ici_subset_Ioi_iff
% 0.07/0.32 thf(fact_270_Icc__subset__Ici__iff,axiom,
% 0.07/0.32 ! [L: set_val,H: set_val,L2: set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ ( set_or1554624499et_val @ L @ H ) @ ( set_or650197513et_val @ L2 ) )
% 0.07/0.32 = ( ~ ( ord_less_eq_set_val @ L @ H )
% 0.07/0.32 | ( ord_less_eq_set_val @ L2 @ L ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Icc_subset_Ici_iff
% 0.07/0.32 thf(fact_271_Icc__subset__Ici__iff,axiom,
% 0.07/0.32 ! [L: val,H: val,L2: val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ ( set_or18208019st_val @ L @ H ) @ ( set_ord_atLeast_val @ L2 ) )
% 0.07/0.32 = ( ~ ( ord_less_eq_val @ L @ H )
% 0.07/0.32 | ( ord_less_eq_val @ L2 @ L ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Icc_subset_Ici_iff
% 0.07/0.32 thf(fact_272_atMost__subset__iff,axiom,
% 0.07/0.32 ! [X: set_val,Y2: set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ ( set_or867701765et_val @ X ) @ ( set_or867701765et_val @ Y2 ) )
% 0.07/0.32 = ( ord_less_eq_set_val @ X @ Y2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % atMost_subset_iff
% 0.07/0.32 thf(fact_273_atMost__subset__iff,axiom,
% 0.07/0.32 ! [X: val,Y2: val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ ( set_ord_atMost_val @ X ) @ ( set_ord_atMost_val @ Y2 ) )
% 0.07/0.32 = ( ord_less_eq_val @ X @ Y2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % atMost_subset_iff
% 0.07/0.32 thf(fact_274_psubsetI,axiom,
% 0.07/0.32 ! [A: set_val,B: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A @ B )
% 0.07/0.32 => ( ( A != B )
% 0.07/0.32 => ( ord_less_set_val @ A @ B ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % psubsetI
% 0.07/0.32 thf(fact_275_ComplI,axiom,
% 0.07/0.32 ! [C: val,A: set_val] :
% 0.07/0.32 ( ~ ( member_val @ C @ A )
% 0.07/0.32 => ( member_val @ C @ ( uminus1961393973et_val @ A ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ComplI
% 0.07/0.32 thf(fact_276_Compl__iff,axiom,
% 0.07/0.32 ! [C: val,A: set_val] :
% 0.07/0.32 ( ( member_val @ C @ ( uminus1961393973et_val @ A ) )
% 0.07/0.32 = ( ~ ( member_val @ C @ A ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Compl_iff
% 0.07/0.32 thf(fact_277_atLeastAtMost__iff,axiom,
% 0.07/0.32 ! [I: val,L: val,U: val] :
% 0.07/0.32 ( ( member_val @ I @ ( set_or18208019st_val @ L @ U ) )
% 0.07/0.32 = ( ( ord_less_eq_val @ L @ I )
% 0.07/0.32 & ( ord_less_eq_val @ I @ U ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % atLeastAtMost_iff
% 0.07/0.32 thf(fact_278_atLeastAtMost__iff,axiom,
% 0.07/0.32 ! [I: set_val,L: set_val,U: set_val] :
% 0.07/0.32 ( ( member_set_val @ I @ ( set_or1554624499et_val @ L @ U ) )
% 0.07/0.32 = ( ( ord_less_eq_set_val @ L @ I )
% 0.07/0.32 & ( ord_less_eq_set_val @ I @ U ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % atLeastAtMost_iff
% 0.07/0.32 thf(fact_279_Icc__eq__Icc,axiom,
% 0.07/0.32 ! [L: set_val,H: set_val,L2: set_val,H2: set_val] :
% 0.07/0.32 ( ( ( set_or1554624499et_val @ L @ H )
% 0.07/0.32 = ( set_or1554624499et_val @ L2 @ H2 ) )
% 0.07/0.32 = ( ( ( L = L2 )
% 0.07/0.32 & ( H = H2 ) )
% 0.07/0.32 | ( ~ ( ord_less_eq_set_val @ L @ H )
% 0.07/0.32 & ~ ( ord_less_eq_set_val @ L2 @ H2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Icc_eq_Icc
% 0.07/0.32 thf(fact_280_atMost__iff,axiom,
% 0.07/0.32 ! [I: val,K: val] :
% 0.07/0.32 ( ( member_val @ I @ ( set_ord_atMost_val @ K ) )
% 0.07/0.32 = ( ord_less_eq_val @ I @ K ) ) ).
% 0.07/0.32
% 0.07/0.32 % atMost_iff
% 0.07/0.32 thf(fact_281_atMost__iff,axiom,
% 0.07/0.32 ! [I: set_val,K: set_val] :
% 0.07/0.32 ( ( member_set_val @ I @ ( set_or867701765et_val @ K ) )
% 0.07/0.32 = ( ord_less_eq_set_val @ I @ K ) ) ).
% 0.07/0.32
% 0.07/0.32 % atMost_iff
% 0.07/0.32 thf(fact_282_lessThan__iff,axiom,
% 0.07/0.32 ! [I: val,K: val] :
% 0.07/0.32 ( ( member_val @ I @ ( set_ord_lessThan_val @ K ) )
% 0.07/0.32 = ( ord_less_val @ I @ K ) ) ).
% 0.07/0.32
% 0.07/0.32 % lessThan_iff
% 0.07/0.32 thf(fact_283_Compl__anti__mono,axiom,
% 0.07/0.32 ! [A: set_val,B: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A @ B )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( uminus1961393973et_val @ B ) @ ( uminus1961393973et_val @ A ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Compl_anti_mono
% 0.07/0.32 thf(fact_284_Compl__subset__Compl__iff,axiom,
% 0.07/0.32 ! [A: set_val,B: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ ( uminus1961393973et_val @ A ) @ ( uminus1961393973et_val @ B ) )
% 0.07/0.32 = ( ord_less_eq_set_val @ B @ A ) ) ).
% 0.07/0.32
% 0.07/0.32 % Compl_subset_Compl_iff
% 0.07/0.32 thf(fact_285_greaterThan__iff,axiom,
% 0.07/0.32 ! [I: val,K: val] :
% 0.07/0.32 ( ( member_val @ I @ ( set_or1288365508an_val @ K ) )
% 0.07/0.32 = ( ord_less_val @ K @ I ) ) ).
% 0.07/0.32
% 0.07/0.32 % greaterThan_iff
% 0.07/0.32 thf(fact_286_atLeastatMost__subset__iff,axiom,
% 0.07/0.32 ! [A3: set_val,B3: set_val,C: set_val,D: set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ ( set_or1554624499et_val @ A3 @ B3 ) @ ( set_or1554624499et_val @ C @ D ) )
% 0.07/0.32 = ( ~ ( ord_less_eq_set_val @ A3 @ B3 )
% 0.07/0.32 | ( ( ord_less_eq_set_val @ C @ A3 )
% 0.07/0.32 & ( ord_less_eq_set_val @ B3 @ D ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % atLeastatMost_subset_iff
% 0.07/0.32 thf(fact_287_atLeastatMost__subset__iff,axiom,
% 0.07/0.32 ! [A3: val,B3: val,C: val,D: val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ ( set_or18208019st_val @ A3 @ B3 ) @ ( set_or18208019st_val @ C @ D ) )
% 0.07/0.32 = ( ~ ( ord_less_eq_val @ A3 @ B3 )
% 0.07/0.32 | ( ( ord_less_eq_val @ C @ A3 )
% 0.07/0.32 & ( ord_less_eq_val @ B3 @ D ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % atLeastatMost_subset_iff
% 0.07/0.32 thf(fact_288_Icc__subset__Iic__iff,axiom,
% 0.07/0.32 ! [L: set_val,H: set_val,H2: set_val] :
% 0.07/0.32 ( ( ord_le1742111550et_val @ ( set_or1554624499et_val @ L @ H ) @ ( set_or867701765et_val @ H2 ) )
% 0.07/0.32 = ( ~ ( ord_less_eq_set_val @ L @ H )
% 0.07/0.32 | ( ord_less_eq_set_val @ H @ H2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Icc_subset_Iic_iff
% 0.07/0.32 thf(fact_289_Icc__subset__Iic__iff,axiom,
% 0.07/0.32 ! [L: val,H: val,H2: val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ ( set_or18208019st_val @ L @ H ) @ ( set_ord_atMost_val @ H2 ) )
% 0.07/0.32 = ( ~ ( ord_less_eq_val @ L @ H )
% 0.07/0.32 | ( ord_less_eq_val @ H @ H2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Icc_subset_Iic_iff
% 0.07/0.32 thf(fact_290_atLeastatMost__psubset__iff,axiom,
% 0.07/0.32 ! [A3: set_val,B3: set_val,C: set_val,D: set_val] :
% 0.07/0.32 ( ( ord_less_set_set_val @ ( set_or1554624499et_val @ A3 @ B3 ) @ ( set_or1554624499et_val @ C @ D ) )
% 0.07/0.32 = ( ( ~ ( ord_less_eq_set_val @ A3 @ B3 )
% 0.07/0.32 | ( ( ord_less_eq_set_val @ C @ A3 )
% 0.07/0.32 & ( ord_less_eq_set_val @ B3 @ D )
% 0.07/0.32 & ( ( ord_less_set_val @ C @ A3 )
% 0.07/0.32 | ( ord_less_set_val @ B3 @ D ) ) ) )
% 0.07/0.32 & ( ord_less_eq_set_val @ C @ D ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % atLeastatMost_psubset_iff
% 0.07/0.32 thf(fact_291_ComplD,axiom,
% 0.07/0.32 ! [C: val,A: set_val] :
% 0.07/0.32 ( ( member_val @ C @ ( uminus1961393973et_val @ A ) )
% 0.07/0.32 => ~ ( member_val @ C @ A ) ) ).
% 0.07/0.32
% 0.07/0.32 % ComplD
% 0.07/0.32 thf(fact_292_Iic__subset__Iio__iff,axiom,
% 0.07/0.32 ! [A3: val,B3: val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ ( set_ord_atMost_val @ A3 ) @ ( set_ord_lessThan_val @ B3 ) )
% 0.07/0.32 = ( ord_less_val @ A3 @ B3 ) ) ).
% 0.07/0.32
% 0.07/0.32 % Iic_subset_Iio_iff
% 0.07/0.32 thf(fact_293_leD,axiom,
% 0.07/0.32 ! [Y2: set_val,X: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ Y2 @ X )
% 0.07/0.32 => ~ ( ord_less_set_val @ X @ Y2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % leD
% 0.07/0.32 thf(fact_294_le__less,axiom,
% 0.07/0.32 ( ord_less_eq_set_val
% 0.07/0.32 = ( ^ [X3: set_val,Y4: set_val] :
% 0.07/0.32 ( ( ord_less_set_val @ X3 @ Y4 )
% 0.07/0.32 | ( X3 = Y4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_less
% 0.07/0.32 thf(fact_295_less__le,axiom,
% 0.07/0.32 ( ord_less_set_val
% 0.07/0.32 = ( ^ [X3: set_val,Y4: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X3 @ Y4 )
% 0.07/0.32 & ( X3 != Y4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % less_le
% 0.07/0.32 thf(fact_296_order__le__less__subst2,axiom,
% 0.07/0.32 ! [A3: set_val,B3: set_val,F: set_val > set_val,C: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ord_less_set_val @ ( F @ B3 ) @ C )
% 0.07/0.32 => ( ! [X2: set_val,Y3: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_set_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_le_less_subst2
% 0.07/0.32 thf(fact_297_order__less__le__subst1,axiom,
% 0.07/0.32 ! [A3: set_val,F: set_val > set_val,B3: set_val,C: set_val] :
% 0.07/0.32 ( ( ord_less_set_val @ A3 @ ( F @ B3 ) )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ B3 @ C )
% 0.07/0.32 => ( ! [X2: set_val,Y3: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_set_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_less_le_subst1
% 0.07/0.32 thf(fact_298_le__neq__trans,axiom,
% 0.07/0.32 ! [A3: set_val,B3: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.07/0.32 => ( ( A3 != B3 )
% 0.07/0.32 => ( ord_less_set_val @ A3 @ B3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_neq_trans
% 0.07/0.32 thf(fact_299_antisym__conv1,axiom,
% 0.07/0.32 ! [X: set_val,Y2: set_val] :
% 0.07/0.32 ( ~ ( ord_less_set_val @ X @ Y2 )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.07/0.32 = ( X = Y2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym_conv1
% 0.07/0.32 thf(fact_300_antisym__conv2,axiom,
% 0.07/0.32 ! [X: set_val,Y2: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.07/0.32 => ( ( ~ ( ord_less_set_val @ X @ Y2 ) )
% 0.07/0.32 = ( X = Y2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym_conv2
% 0.07/0.32 thf(fact_301_less__imp__le,axiom,
% 0.07/0.32 ! [X: set_val,Y2: set_val] :
% 0.07/0.32 ( ( ord_less_set_val @ X @ Y2 )
% 0.07/0.32 => ( ord_less_eq_set_val @ X @ Y2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % less_imp_le
% 0.07/0.32 thf(fact_302_le__less__trans,axiom,
% 0.07/0.32 ! [X: set_val,Y2: set_val,Z2: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.07/0.32 => ( ( ord_less_set_val @ Y2 @ Z2 )
% 0.07/0.32 => ( ord_less_set_val @ X @ Z2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_less_trans
% 0.07/0.32 thf(fact_303_less__le__trans,axiom,
% 0.07/0.32 ! [X: set_val,Y2: set_val,Z2: set_val] :
% 0.07/0.32 ( ( ord_less_set_val @ X @ Y2 )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ Y2 @ Z2 )
% 0.07/0.32 => ( ord_less_set_val @ X @ Z2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % less_le_trans
% 0.07/0.32 thf(fact_304_le__imp__less__or__eq,axiom,
% 0.07/0.32 ! [X: set_val,Y2: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.07/0.32 => ( ( ord_less_set_val @ X @ Y2 )
% 0.07/0.32 | ( X = Y2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_imp_less_or_eq
% 0.07/0.32 thf(fact_305_less__le__not__le,axiom,
% 0.07/0.32 ( ord_less_set_val
% 0.07/0.32 = ( ^ [X3: set_val,Y4: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X3 @ Y4 )
% 0.07/0.32 & ~ ( ord_less_eq_set_val @ Y4 @ X3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % less_le_not_le
% 0.07/0.32 thf(fact_306_order_Ostrict__trans1,axiom,
% 0.07/0.32 ! [A3: set_val,B3: set_val,C: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ord_less_set_val @ B3 @ C )
% 0.07/0.32 => ( ord_less_set_val @ A3 @ C ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order.strict_trans1
% 0.07/0.32 thf(fact_307_order_Ostrict__trans2,axiom,
% 0.07/0.32 ! [A3: set_val,B3: set_val,C: set_val] :
% 0.07/0.32 ( ( ord_less_set_val @ A3 @ B3 )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ B3 @ C )
% 0.07/0.32 => ( ord_less_set_val @ A3 @ C ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order.strict_trans2
% 0.07/0.32 thf(fact_308_order_Oorder__iff__strict,axiom,
% 0.07/0.32 ( ord_less_eq_set_val
% 0.07/0.32 = ( ^ [A4: set_val,B4: set_val] :
% 0.07/0.32 ( ( ord_less_set_val @ A4 @ B4 )
% 0.07/0.32 | ( A4 = B4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order.order_iff_strict
% 0.07/0.32 thf(fact_309_order_Ostrict__iff__order,axiom,
% 0.07/0.32 ( ord_less_set_val
% 0.07/0.32 = ( ^ [A4: set_val,B4: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A4 @ B4 )
% 0.07/0.32 & ( A4 != B4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order.strict_iff_order
% 0.07/0.32 thf(fact_310_dual__order_Ostrict__trans1,axiom,
% 0.07/0.32 ! [B3: set_val,A3: set_val,C: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ B3 @ A3 )
% 0.07/0.32 => ( ( ord_less_set_val @ C @ B3 )
% 0.07/0.32 => ( ord_less_set_val @ C @ A3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.strict_trans1
% 0.07/0.32 thf(fact_311_dual__order_Ostrict__trans2,axiom,
% 0.07/0.32 ! [B3: set_val,A3: set_val,C: set_val] :
% 0.07/0.32 ( ( ord_less_set_val @ B3 @ A3 )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ C @ B3 )
% 0.07/0.32 => ( ord_less_set_val @ C @ A3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.strict_trans2
% 0.07/0.32 thf(fact_312_order_Ostrict__implies__order,axiom,
% 0.07/0.32 ! [A3: set_val,B3: set_val] :
% 0.07/0.32 ( ( ord_less_set_val @ A3 @ B3 )
% 0.07/0.32 => ( ord_less_eq_set_val @ A3 @ B3 ) ) ).
% 0.07/0.32
% 0.07/0.32 % order.strict_implies_order
% 0.07/0.32 thf(fact_313_dual__order_Oorder__iff__strict,axiom,
% 0.07/0.32 ( ord_less_eq_set_val
% 0.07/0.32 = ( ^ [B4: set_val,A4: set_val] :
% 0.07/0.32 ( ( ord_less_set_val @ B4 @ A4 )
% 0.07/0.32 | ( A4 = B4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.order_iff_strict
% 0.07/0.32 thf(fact_314_dual__order_Ostrict__iff__order,axiom,
% 0.07/0.32 ( ord_less_set_val
% 0.07/0.32 = ( ^ [B4: set_val,A4: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ B4 @ A4 )
% 0.07/0.32 & ( A4 != B4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.strict_iff_order
% 0.07/0.32 thf(fact_315_dual__order_Ostrict__implies__order,axiom,
% 0.07/0.32 ! [B3: set_val,A3: set_val] :
% 0.07/0.32 ( ( ord_less_set_val @ B3 @ A3 )
% 0.07/0.32 => ( ord_less_eq_set_val @ B3 @ A3 ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.strict_implies_order
% 0.07/0.32 thf(fact_316_order_Onot__eq__order__implies__strict,axiom,
% 0.07/0.32 ! [A3: set_val,B3: set_val] :
% 0.07/0.32 ( ( A3 != B3 )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.07/0.32 => ( ord_less_set_val @ A3 @ B3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order.not_eq_order_implies_strict
% 0.07/0.32 thf(fact_317_psubsetE,axiom,
% 0.07/0.32 ! [A: set_val,B: set_val] :
% 0.07/0.32 ( ( ord_less_set_val @ A @ B )
% 0.07/0.32 => ~ ( ( ord_less_eq_set_val @ A @ B )
% 0.07/0.32 => ( ord_less_eq_set_val @ B @ A ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % psubsetE
% 0.07/0.32 thf(fact_318_psubset__eq,axiom,
% 0.07/0.32 ( ord_less_set_val
% 0.07/0.32 = ( ^ [A2: set_val,B2: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A2 @ B2 )
% 0.07/0.32 & ( A2 != B2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % psubset_eq
% 0.07/0.32 thf(fact_319_psubset__imp__subset,axiom,
% 0.07/0.32 ! [A: set_val,B: set_val] :
% 0.07/0.32 ( ( ord_less_set_val @ A @ B )
% 0.07/0.32 => ( ord_less_eq_set_val @ A @ B ) ) ).
% 0.07/0.32
% 0.07/0.32 % psubset_imp_subset
% 0.07/0.32 thf(fact_320_psubset__subset__trans,axiom,
% 0.07/0.32 ! [A: set_val,B: set_val,C2: set_val] :
% 0.07/0.32 ( ( ord_less_set_val @ A @ B )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ B @ C2 )
% 0.07/0.32 => ( ord_less_set_val @ A @ C2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % psubset_subset_trans
% 0.07/0.32 thf(fact_321_subset__not__subset__eq,axiom,
% 0.07/0.32 ( ord_less_set_val
% 0.07/0.32 = ( ^ [A2: set_val,B2: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A2 @ B2 )
% 0.07/0.32 & ~ ( ord_less_eq_set_val @ B2 @ A2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % subset_not_subset_eq
% 0.07/0.32 thf(fact_322_subset__psubset__trans,axiom,
% 0.07/0.32 ! [A: set_val,B: set_val,C2: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A @ B )
% 0.07/0.32 => ( ( ord_less_set_val @ B @ C2 )
% 0.07/0.32 => ( ord_less_set_val @ A @ C2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % subset_psubset_trans
% 0.07/0.32 thf(fact_323_subset__iff__psubset__eq,axiom,
% 0.07/0.32 ( ord_less_eq_set_val
% 0.07/0.32 = ( ^ [A2: set_val,B2: set_val] :
% 0.07/0.32 ( ( ord_less_set_val @ A2 @ B2 )
% 0.07/0.32 | ( A2 = B2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % subset_iff_psubset_eq
% 0.07/0.32 thf(fact_324_compl__le__compl__iff,axiom,
% 0.07/0.32 ! [X: set_val,Y2: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ ( uminus1961393973et_val @ X ) @ ( uminus1961393973et_val @ Y2 ) )
% 0.07/0.32 = ( ord_less_eq_set_val @ Y2 @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % compl_le_compl_iff
% 0.07/0.32 thf(fact_325_compl__mono,axiom,
% 0.07/0.32 ! [X: set_val,Y2: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( uminus1961393973et_val @ Y2 ) @ ( uminus1961393973et_val @ X ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % compl_mono
% 0.07/0.32 thf(fact_326_compl__le__swap1,axiom,
% 0.07/0.32 ! [Y2: set_val,X: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ Y2 @ ( uminus1961393973et_val @ X ) )
% 0.07/0.32 => ( ord_less_eq_set_val @ X @ ( uminus1961393973et_val @ Y2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % compl_le_swap1
% 0.07/0.32 thf(fact_327_compl__le__swap2,axiom,
% 0.07/0.32 ! [Y2: set_val,X: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ ( uminus1961393973et_val @ Y2 ) @ X )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( uminus1961393973et_val @ X ) @ Y2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % compl_le_swap2
% 0.07/0.32 thf(fact_328_psubsetD,axiom,
% 0.07/0.32 ! [A: set_val,B: set_val,C: val] :
% 0.07/0.32 ( ( ord_less_set_val @ A @ B )
% 0.07/0.32 => ( ( member_val @ C @ A )
% 0.07/0.32 => ( member_val @ C @ B ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % psubsetD
% 0.07/0.32 thf(fact_329_UnCI,axiom,
% 0.07/0.32 ! [C: val,B: set_val,A: set_val] :
% 0.07/0.32 ( ( ~ ( member_val @ C @ B )
% 0.07/0.32 => ( member_val @ C @ A ) )
% 0.07/0.32 => ( member_val @ C @ ( sup_sup_set_val @ A @ B ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % UnCI
% 0.07/0.32 thf(fact_330_Un__iff,axiom,
% 0.07/0.32 ! [C: val,A: set_val,B: set_val] :
% 0.07/0.32 ( ( member_val @ C @ ( sup_sup_set_val @ A @ B ) )
% 0.07/0.32 = ( ( member_val @ C @ A )
% 0.07/0.32 | ( member_val @ C @ B ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Un_iff
% 0.07/0.32 thf(fact_331_le__sup__iff,axiom,
% 0.07/0.32 ! [X: set_val,Y2: set_val,Z2: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ ( sup_sup_set_val @ X @ Y2 ) @ Z2 )
% 0.07/0.32 = ( ( ord_less_eq_set_val @ X @ Z2 )
% 0.07/0.32 & ( ord_less_eq_set_val @ Y2 @ Z2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_sup_iff
% 0.07/0.32 thf(fact_332_sup_Obounded__iff,axiom,
% 0.07/0.32 ! [B3: set_val,C: set_val,A3: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ ( sup_sup_set_val @ B3 @ C ) @ A3 )
% 0.07/0.32 = ( ( ord_less_eq_set_val @ B3 @ A3 )
% 0.07/0.32 & ( ord_less_eq_set_val @ C @ A3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % sup.bounded_iff
% 0.07/0.32 thf(fact_333_Un__subset__iff,axiom,
% 0.07/0.32 ! [A: set_val,B: set_val,C2: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ B ) @ C2 )
% 0.07/0.32 = ( ( ord_less_eq_set_val @ A @ C2 )
% 0.07/0.32 & ( ord_less_eq_set_val @ B @ C2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % Un_subset_iff
% 0.07/0.32 thf(fact_334_greaterThanLessThan__iff,axiom,
% 0.07/0.32 ! [I: val,L: val,U: val] :
% 0.07/0.32 ( ( member_val @ I @ ( set_or2126567818an_val @ L @ U ) )
% 0.07/0.32 = ( ( ord_less_val @ L @ I )
% 0.07/0.32 & ( ord_less_val @ I @ U ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % greaterThanLessThan_iff
% 0.07/0.32 thf(fact_335_sup_OcoboundedI2,axiom,
% 0.07/0.32 ! [C: set_val,B3: set_val,A3: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ C @ B3 )
% 0.07/0.32 => ( ord_less_eq_set_val @ C @ ( sup_sup_set_val @ A3 @ B3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % sup.coboundedI2
% 0.07/0.32 thf(fact_336_sup_OcoboundedI1,axiom,
% 0.07/0.32 ! [C: set_val,A3: set_val,B3: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ C @ A3 )
% 0.07/0.32 => ( ord_less_eq_set_val @ C @ ( sup_sup_set_val @ A3 @ B3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % sup.coboundedI1
% 0.07/0.32 thf(fact_337_sup_Oabsorb__iff2,axiom,
% 0.07/0.32 ( ord_less_eq_set_val
% 0.07/0.32 = ( ^ [A4: set_val,B4: set_val] :
% 0.07/0.32 ( ( sup_sup_set_val @ A4 @ B4 )
% 0.07/0.32 = B4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % sup.absorb_iff2
% 0.07/0.32 thf(fact_338_sup_Oabsorb__iff1,axiom,
% 0.07/0.32 ( ord_less_eq_set_val
% 0.07/0.32 = ( ^ [B4: set_val,A4: set_val] :
% 0.07/0.32 ( ( sup_sup_set_val @ A4 @ B4 )
% 0.07/0.32 = A4 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % sup.absorb_iff1
% 0.07/0.32 thf(fact_339_sup_Ocobounded2,axiom,
% 0.07/0.32 ! [B3: set_val,A3: set_val] : ( ord_less_eq_set_val @ B3 @ ( sup_sup_set_val @ A3 @ B3 ) ) ).
% 0.07/0.32
% 0.07/0.32 % sup.cobounded2
% 0.07/0.32 thf(fact_340_sup_Ocobounded1,axiom,
% 0.07/0.32 ! [A3: set_val,B3: set_val] : ( ord_less_eq_set_val @ A3 @ ( sup_sup_set_val @ A3 @ B3 ) ) ).
% 0.07/0.32
% 0.07/0.32 % sup.cobounded1
% 0.07/0.32 thf(fact_341_sup_Oorder__iff,axiom,
% 0.07/0.32 ( ord_less_eq_set_val
% 0.07/0.32 = ( ^ [B4: set_val,A4: set_val] :
% 0.07/0.32 ( A4
% 0.07/0.32 = ( sup_sup_set_val @ A4 @ B4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % sup.order_iff
% 0.07/0.32 thf(fact_342_sup_OboundedI,axiom,
% 0.07/0.32 ! [B3: set_val,A3: set_val,C: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ B3 @ A3 )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ C @ A3 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( sup_sup_set_val @ B3 @ C ) @ A3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % sup.boundedI
% 0.07/0.32 thf(fact_343_sup_OboundedE,axiom,
% 0.07/0.32 ! [B3: set_val,C: set_val,A3: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ ( sup_sup_set_val @ B3 @ C ) @ A3 )
% 0.07/0.32 => ~ ( ( ord_less_eq_set_val @ B3 @ A3 )
% 0.07/0.32 => ~ ( ord_less_eq_set_val @ C @ A3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % sup.boundedE
% 0.07/0.32 thf(fact_344_sup__absorb2,axiom,
% 0.07/0.32 ! [X: set_val,Y2: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ X @ Y2 )
% 0.07/0.32 => ( ( sup_sup_set_val @ X @ Y2 )
% 0.07/0.32 = Y2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % sup_absorb2
% 0.07/0.32 thf(fact_345_sup__absorb1,axiom,
% 0.07/0.32 ! [Y2: set_val,X: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ Y2 @ X )
% 0.07/0.32 => ( ( sup_sup_set_val @ X @ Y2 )
% 0.07/0.32 = X ) ) ).
% 0.07/0.32
% 0.07/0.32 % sup_absorb1
% 0.07/0.32 thf(fact_346_sup_Oabsorb2,axiom,
% 0.07/0.32 ! [A3: set_val,B3: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 0.07/0.32 => ( ( sup_sup_set_val @ A3 @ B3 )
% 0.07/0.32 = B3 ) ) ).
% 0.07/0.32
% 0.07/0.32 % sup.absorb2
% 0.07/0.32 thf(fact_347_sup_Oabsorb1,axiom,
% 0.07/0.32 ! [B3: set_val,A3: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ B3 @ A3 )
% 0.07/0.32 => ( ( sup_sup_set_val @ A3 @ B3 )
% 0.07/0.32 = A3 ) ) ).
% 0.07/0.32
% 0.07/0.32 % sup.absorb1
% 0.07/0.32 thf(fact_348_sup__unique,axiom,
% 0.07/0.32 ! [F: set_val > set_val > set_val,X: set_val,Y2: set_val] :
% 0.07/0.32 ( ! [X2: set_val,Y3: set_val] : ( ord_less_eq_set_val @ X2 @ ( F @ X2 @ Y3 ) )
% 0.07/0.32 => ( ! [X2: set_val,Y3: set_val] : ( ord_less_eq_set_val @ Y3 @ ( F @ X2 @ Y3 ) )
% 0.07/0.32 => ( ! [X2: set_val,Y3: set_val,Z3: set_val] :
% 0.07/0.32 ( ( ord_less_eq_set_val @ Y3 @ X2 )
% 0.07/0.32 => ( ( ord_less_eq_set_val @ Z3 @ X2 )
% 0.07/0.32 => ( ord_less_eq_set_val @ ( F @ Y3 @ Z3 ) @ X2 ) ) )
% 0.07/0.32 => ( ( sup_sup_set_val @ X @ Y2 )
% 0.07/0.32 = ( F @ X @ Y2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % sup_unique
% 0.07/0.32 thf(fact_349_sup_OorderI,axiom,
% 0.07/0.32 ! [A3: set_val,B3: set_val] :
% 0.07/0.32 ( ( A3
% 0.07/0.32 = ( sup_sup_set_val @ A3 @ B3 ) )
% 0.07/0.32 => ( ord_less_eq_set_val @ B3 @ A3 ) ) ).
% 0.07/0.32
% 0.07/0.32 % sup.orderI
% 0.07/0.32
% 0.07/0.32 % Helper facts (9)
% 0.07/0.32 thf(help_If_2_1_If_001tf__val_T,axiom,
% 0.07/0.32 ! [X: val,Y2: val] :
% 0.07/0.32 ( ( if_val @ $false @ X @ Y2 )
% 0.07/0.32 = Y2 ) ).
% 0.07/0.32
% 0.07/0.32 thf(help_If_1_1_If_001tf__val_T,axiom,
% 0.07/0.32 ! [X: val,Y2: val] :
% 0.07/0.32 ( ( if_val @ $true @ X @ Y2 )
% 0.07/0.32 = X ) ).
% 0.07/0.32
% 0.07/0.32 thf(help_If_2_1_If_001t__Set__Oset_Itf__val_J_T,axiom,
% 0.07/0.32 ! [X: set_val,Y2: set_val] :
% 0.07/0.32 ( ( if_set_val @ $false @ X @ Y2 )
% 0.07/0.32 = Y2 ) ).
% 0.07/0.32
% 0.07/0.32 thf(help_If_1_1_If_001t__Set__Oset_Itf__val_J_T,axiom,
% 0.07/0.32 ! [X: set_val,Y2: set_val] :
% 0.07/0.32 ( ( if_set_val @ $true @ X @ Y2 )
% 0.07/0.32 = X ) ).
% 0.07/0.32
% 0.07/0.32 thf(help_If_2_1_If_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J_T,axiom,
% 0.07/0.32 ! [X: $o > set_val,Y2: $o > set_val] :
% 0.07/0.32 ( ( if_o_set_val @ $false @ X @ Y2 )
% 0.07/0.32 = Y2 ) ).
% 0.07/0.32
% 0.07/0.32 thf(help_If_1_1_If_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J_T,axiom,
% 0.07/0.32 ! [X: $o > set_val,Y2: $o > set_val] :
% 0.07/0.32 ( ( if_o_set_val @ $true @ X @ Y2 )
% 0.07/0.32 = X ) ).
% 0.07/0.32
% 0.07/0.32 thf(help_If_3_1_If_001t__Set__Oset_It__Set__Oset_Itf__val_J_J_T,axiom,
% 0.07/0.32 ! [P: $o] :
% 0.07/0.32 ( ( P = $true )
% 0.07/0.32 | ( P = $false ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(help_If_2_1_If_001t__Set__Oset_It__Set__Oset_Itf__val_J_J_T,axiom,
% 0.07/0.32 ! [X: set_set_val,Y2: set_set_val] :
% 0.07/0.32 ( ( if_set_set_val @ $false @ X @ Y2 )
% 0.07/0.32 = Y2 ) ).
% 0.07/0.32
% 0.07/0.32 thf(help_If_1_1_If_001t__Set__Oset_It__Set__Oset_Itf__val_J_J_T,axiom,
% 0.07/0.32 ! [X: set_set_val,Y2: set_set_val] :
% 0.07/0.32 ( ( if_set_set_val @ $true @ X @ Y2 )
% 0.07/0.32 = X ) ).
% 0.07/0.32
% 0.07/0.32 % Conjectures (1)
% 0.07/0.32 thf(conj_0,conjecture,
% 0.07/0.32 ord_less_eq_set_val @ scc @ p ).
% 0.07/0.32
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 ------------------------
% 1.96/1.16 ---- Embedded in THF ---
% 1.96/1.16 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.96/1.16 %%% Generated on Tue Feb 24 03:25:11 EST 2026
% 1.96/1.16 %%% using '$$dhol' embedding, version 1.3.0.
% 1.96/1.16 %%% Logic specification used:
% 1.96/1.16 %%% thf(spec, logic, $$dhol).
% 1.96/1.16
% 1.96/1.16 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Tpnd21IUI7/DTF2DTF26920.p
% See solution above
% 1.96/1.16 ------------------------
% 1.96/1.19 ---- Cleaned THF ---
% 1.96/1.19 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Set__Oset_Itf__val_J_J_J,type,
% 1.96/1.19 set_set_set_val: $tType ).
% 1.96/1.19
% 1.96/1.19 thf(ty_n_t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 1.96/1.19 set_set_val: $tType ).
% 1.96/1.19
% 1.96/1.19 thf(ty_n_t__Set__Oset_Itf__val_J,type,
% 1.96/1.19 set_val: $tType ).
% 1.96/1.19
% 1.96/1.19 thf(ty_n_tf__val,type,
% 1.96/1.19 val: $tType ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_Itf__val_J,type,
% 1.96/1.19 uminus1961393973et_val: set_val > set_val ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_If_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J,type,
% 1.96/1.19 if_o_set_val: $o > ( $o > set_val ) > ( $o > set_val ) > $o > set_val ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_If_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 1.96/1.19 if_set_set_val: $o > set_set_val > set_set_val > set_set_val ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_If_001t__Set__Oset_Itf__val_J,type,
% 1.96/1.19 if_set_val: $o > set_val > set_val > set_val ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_If_001tf__val,type,
% 1.96/1.19 if_val: $o > val > val > val ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_Itf__val_J,type,
% 1.96/1.19 sup_sup_set_val: set_val > set_val > set_val ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 1.96/1.19 ord_less_set_set_val: set_set_val > set_set_val > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_Itf__val_J,type,
% 1.96/1.19 ord_less_set_val: set_val > set_val > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oord__class_Oless_001tf__val,type,
% 1.96/1.19 ord_less_val: val > val > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_M_062_I_Eo_Mt__Set__Oset_Itf__val_J_J_J,type,
% 1.96/1.19 ord_le1441829300et_val: ( $o > $o > set_val ) > ( $o > $o > set_val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Set__Oset_It__Set__Oset_Itf__val_J_J_J,type,
% 1.96/1.19 ord_le936627147et_val: ( $o > set_set_val ) > ( $o > set_set_val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J,type,
% 1.96/1.19 ord_le994826475et_val: ( $o > set_val ) > ( $o > set_val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mtf__val_J,type,
% 1.96/1.19 ord_less_eq_o_val: ( $o > val ) > ( $o > val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Set__Oset_Itf__val_J_J_J,type,
% 1.96/1.19 ord_le1135847966et_val: set_set_set_val > set_set_set_val > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 1.96/1.19 ord_le1742111550et_val: set_set_val > set_set_val > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__val_J,type,
% 1.96/1.19 ord_less_eq_set_val: set_val > set_val > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oord__class_Oless__eq_001tf__val,type,
% 1.96/1.19 ord_less_eq_val: val > val > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oorder__class_OGreatest_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J,type,
% 1.96/1.19 order_985126002et_val: ( ( $o > set_val ) > $o ) > $o > set_val ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 1.96/1.19 order_544136439et_val: ( set_set_val > $o ) > set_set_val ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Set__Oset_Itf__val_J,type,
% 1.96/1.19 order_1960465943et_val: ( set_val > $o ) > set_val ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oorder__class_OGreatest_001tf__val,type,
% 1.96/1.19 order_Greatest_val: ( val > $o ) > val ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oorder__class_Oantimono_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J_001tf__val,type,
% 1.96/1.19 order_23236447al_val: ( ( $o > set_val ) > val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oorder__class_Oantimono_001t__Set__Oset_It__Set__Oset_Itf__val_J_J_001t__Set__Oset_Itf__val_J,type,
% 1.96/1.19 order_650823122et_val: ( set_set_val > set_val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oorder__class_Oantimono_001t__Set__Oset_It__Set__Oset_Itf__val_J_J_001tf__val,type,
% 1.96/1.19 order_1520822002al_val: ( set_set_val > val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oorder__class_Oantimono_001t__Set__Oset_Itf__val_J_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 1.96/1.19 order_1957703570et_val: ( set_val > set_set_val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oorder__class_Oantimono_001t__Set__Oset_Itf__val_J_001t__Set__Oset_Itf__val_J,type,
% 1.96/1.19 order_1719375026et_val: ( set_val > set_val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oorder__class_Oantimono_001t__Set__Oset_Itf__val_J_001tf__val,type,
% 1.96/1.19 order_1375876562al_val: ( set_val > val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oorder__class_Oantimono_001tf__val_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J,type,
% 1.96/1.19 order_255079095et_val: ( val > $o > set_val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oorder__class_Oantimono_001tf__val_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 1.96/1.19 order_1945059954et_val: ( val > set_set_val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oorder__class_Oantimono_001tf__val_001t__Set__Oset_Itf__val_J,type,
% 1.96/1.19 order_1484138386et_val: ( val > set_val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oorder__class_Oantimono_001tf__val_001tf__val,type,
% 1.96/1.19 order_1689798834al_val: ( val > val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001tf__val_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J,type,
% 1.96/1.19 order_1205732848et_val: ( val > $o > set_val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001tf__val_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 1.96/1.19 order_68692473et_val: ( val > set_set_val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001tf__val_001t__Set__Oset_Itf__val_J,type,
% 1.96/1.19 order_99134233et_val: ( val > set_val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001tf__val_001tf__val,type,
% 1.96/1.19 order_1139042361al_val: ( val > val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_RefineG__Transfer_OREFINEG__TRANSFER__ALIGN_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J,type,
% 1.96/1.19 refine1593386065et_val: ( $o > set_val ) > ( $o > set_val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_RefineG__Transfer_OREFINEG__TRANSFER__ALIGN_001t__Set__Oset_It__Set__Oset_Itf__val_J_J_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 1.96/1.19 refine1034950713et_val: set_set_val > set_set_val > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_RefineG__Transfer_OREFINEG__TRANSFER__ALIGN_001t__Set__Oset_Itf__val_J_001t__Set__Oset_Itf__val_J,type,
% 1.96/1.19 refine654574649et_val: set_val > set_val > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_RefineG__Transfer_OREFINEG__TRANSFER__ALIGN_001tf__val_001tf__val,type,
% 1.96/1.19 refine2021912633al_val: val > val > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_RefineG__Transfer_OREFINEG__TRANSFER__POST__SIMP_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J,type,
% 1.96/1.19 refine511606705et_val: ( $o > set_val ) > ( $o > set_val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_RefineG__Transfer_OREFINEG__TRANSFER__POST__SIMP_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 1.96/1.19 refine1908789496et_val: set_set_val > set_set_val > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_RefineG__Transfer_OREFINEG__TRANSFER__POST__SIMP_001t__Set__Oset_Itf__val_J,type,
% 1.96/1.19 refine1893322264et_val: set_val > set_val > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_RefineG__Transfer_OREFINEG__TRANSFER__POST__SIMP_001tf__val,type,
% 1.96/1.19 refine403244856MP_val: val > val > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Refine__Misc_Ogalois__connection_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J,type,
% 1.96/1.19 refine1924899106et_val: ( ( $o > set_val ) > $o > set_val ) > ( ( $o > set_val ) > $o > set_val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Refine__Misc_Ogalois__connection_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 1.96/1.19 refine1169396807et_val: ( ( $o > set_val ) > set_set_val ) > ( set_set_val > $o > set_val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Refine__Misc_Ogalois__connection_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J_001t__Set__Oset_Itf__val_J,type,
% 1.96/1.19 refine1948536167et_val: ( ( $o > set_val ) > set_val ) > ( set_val > $o > set_val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Refine__Misc_Ogalois__connection_001t__Set__Oset_It__Set__Oset_Itf__val_J_J_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J,type,
% 1.96/1.19 refine86398879et_val: ( set_set_val > $o > set_val ) > ( ( $o > set_val ) > set_set_val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Refine__Misc_Ogalois__connection_001t__Set__Oset_It__Set__Oset_Itf__val_J_J_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 1.96/1.19 refine855985034et_val: ( set_set_val > set_set_val ) > ( set_set_val > set_set_val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Refine__Misc_Ogalois__connection_001t__Set__Oset_It__Set__Oset_Itf__val_J_J_001t__Set__Oset_Itf__val_J,type,
% 1.96/1.19 refine8163498et_val: ( set_set_val > set_val ) > ( set_val > set_set_val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Refine__Misc_Ogalois__connection_001t__Set__Oset_Itf__val_J_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J,type,
% 1.96/1.19 refine51544255et_val: ( set_val > $o > set_val ) > ( ( $o > set_val ) > set_val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Refine__Misc_Ogalois__connection_001t__Set__Oset_Itf__val_J_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 1.96/1.19 refine1315043946et_val: ( set_val > set_set_val ) > ( set_set_val > set_val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Refine__Misc_Ogalois__connection_001t__Set__Oset_Itf__val_J_001t__Set__Oset_Itf__val_J,type,
% 1.96/1.19 refine1929691018et_val: ( set_val > set_val ) > ( set_val > set_val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Refine__Misc_Oinf__distrib_001t__Set__Oset_Itf__val_J_001t__Set__Oset_Itf__val_J,type,
% 1.96/1.19 refine2057434761et_val: ( set_val > set_val ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Refine__Mono__Prover_Omono__setup__loc_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J,type,
% 1.96/1.19 refine16560100et_val: ( ( $o > set_val ) > ( $o > set_val ) > $o ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Refine__Mono__Prover_Omono__setup__loc_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 1.96/1.19 refine1506227973et_val: ( set_set_val > set_set_val > $o ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Refine__Mono__Prover_Omono__setup__loc_001t__Set__Oset_Itf__val_J,type,
% 1.96/1.19 refine275900453et_val: ( set_val > set_val > $o ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Refine__Mono__Prover_Omono__setup__loc_001tf__val,type,
% 1.96/1.19 refine67622213oc_val: ( val > val > $o ) > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Set_OCollect_001t__Set__Oset_Itf__val_J,type,
% 1.96/1.19 collect_set_val: ( set_val > $o ) > set_set_val ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Set_OCollect_001tf__val,type,
% 1.96/1.19 collect_val: ( val > $o ) > set_val ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_Itf__val_J,type,
% 1.96/1.19 set_or1554624499et_val: set_val > set_val > set_set_val ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001tf__val,type,
% 1.96/1.19 set_or18208019st_val: val > val > set_val ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 1.96/1.19 set_or1337784553et_val: set_set_val > set_set_set_val ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Set__Oset_Itf__val_J,type,
% 1.96/1.19 set_or650197513et_val: set_val > set_set_val ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Set__Interval_Oord__class_OatLeast_001tf__val,type,
% 1.96/1.19 set_ord_atLeast_val: val > set_val ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_Itf__val_J,type,
% 1.96/1.19 set_or867701765et_val: set_val > set_set_val ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Set__Interval_Oord__class_OatMost_001tf__val,type,
% 1.96/1.19 set_ord_atMost_val: val > set_val ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001tf__val,type,
% 1.96/1.19 set_or2126567818an_val: val > val > set_val ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001tf__val,type,
% 1.96/1.19 set_or1288365508an_val: val > set_val ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_Set__Interval_Oord__class_OlessThan_001tf__val,type,
% 1.96/1.19 set_ord_lessThan_val: val > set_val ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_member_001t__Set__Oset_Itf__val_J,type,
% 1.96/1.19 member_set_val: set_val > set_set_val > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_c_member_001tf__val,type,
% 1.96/1.19 member_val: val > set_val > $o ).
% 1.96/1.19
% 1.96/1.19 thf(sy_v_P,type,
% 1.96/1.19 p: set_val ).
% 1.96/1.19
% 1.96/1.19 thf(sy_v_scc,type,
% 1.96/1.19 scc: set_val ).
% 1.96/1.19
% 1.96/1.19 thf(fact_0__092_060open_062_092_060And_062x_O_Ax_A_092_060in_062_Ascc_A_092_060Longrightarrow_062_Ax_A_092_060in_062_AP_092_060close_062,axiom,
% 1.96/1.19 ! [X: val] :
% 1.96/1.19 ( ( member_val @ X @ scc )
% 1.96/1.19 => ( member_val @ X @ p ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_1_subsetI,axiom,
% 1.96/1.19 ! [A: set_set_val,B: set_set_val] :
% 1.96/1.19 ( ! [X2: set_val] :
% 1.96/1.19 ( ( member_set_val @ X2 @ A )
% 1.96/1.19 => ( member_set_val @ X2 @ B ) )
% 1.96/1.19 => ( ord_le1742111550et_val @ A @ B ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_2_subsetI,axiom,
% 1.96/1.19 ! [A: set_val,B: set_val] :
% 1.96/1.19 ( ! [X2: val] :
% 1.96/1.19 ( ( member_val @ X2 @ A )
% 1.96/1.19 => ( member_val @ X2 @ B ) )
% 1.96/1.19 => ( ord_less_eq_set_val @ A @ B ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_3_subset__antisym,axiom,
% 1.96/1.19 ! [A: set_set_val,B: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ A @ B )
% 1.96/1.19 => ( ( ord_le1742111550et_val @ B @ A )
% 1.96/1.19 => ( A = B ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_4_subset__antisym,axiom,
% 1.96/1.19 ! [A: set_val,B: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A @ B )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ B @ A )
% 1.96/1.19 => ( A = B ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_5_order__mono__setup_Orefl,axiom,
% 1.96/1.19 ! [X: $o > set_val] : ( ord_le994826475et_val @ X @ X ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_6_order__mono__setup_Orefl,axiom,
% 1.96/1.19 ! [X: val] : ( ord_less_eq_val @ X @ X ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_7_order__mono__setup_Orefl,axiom,
% 1.96/1.19 ! [X: set_set_val] : ( ord_le1742111550et_val @ X @ X ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_8_order__mono__setup_Orefl,axiom,
% 1.96/1.19 ! [X: set_val] : ( ord_less_eq_set_val @ X @ X ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_9_relprop__triggers_I6_J,axiom,
% 1.96/1.19 ! [R: set_set_val,R2: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ R @ R2 )
% 1.96/1.19 => ( ord_le1742111550et_val @ R @ R2 ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_10_relprop__triggers_I6_J,axiom,
% 1.96/1.19 ! [R: set_val,R2: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ R @ R2 )
% 1.96/1.19 => ( ord_less_eq_set_val @ R @ R2 ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_11_in__mono,axiom,
% 1.96/1.19 ! [A: set_set_val,B: set_set_val,X: set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ A @ B )
% 1.96/1.19 => ( ( member_set_val @ X @ A )
% 1.96/1.19 => ( member_set_val @ X @ B ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_12_in__mono,axiom,
% 1.96/1.19 ! [A: set_val,B: set_val,X: val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A @ B )
% 1.96/1.19 => ( ( member_val @ X @ A )
% 1.96/1.19 => ( member_val @ X @ B ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_13_subsetD,axiom,
% 1.96/1.19 ! [A: set_set_val,B: set_set_val,C: set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ A @ B )
% 1.96/1.19 => ( ( member_set_val @ C @ A )
% 1.96/1.19 => ( member_set_val @ C @ B ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_14_subsetD,axiom,
% 1.96/1.19 ! [A: set_val,B: set_val,C: val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A @ B )
% 1.96/1.19 => ( ( member_val @ C @ A )
% 1.96/1.19 => ( member_val @ C @ B ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_15_equalityE,axiom,
% 1.96/1.19 ! [A: set_set_val,B: set_set_val] :
% 1.96/1.19 ( ( A = B )
% 1.96/1.19 => ~ ( ( ord_le1742111550et_val @ A @ B )
% 1.96/1.19 => ~ ( ord_le1742111550et_val @ B @ A ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_16_equalityE,axiom,
% 1.96/1.19 ! [A: set_val,B: set_val] :
% 1.96/1.19 ( ( A = B )
% 1.96/1.19 => ~ ( ( ord_less_eq_set_val @ A @ B )
% 1.96/1.19 => ~ ( ord_less_eq_set_val @ B @ A ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_17_subset__eq,axiom,
% 1.96/1.19 ( ord_le1742111550et_val
% 1.96/1.19 = ( ^ [A2: set_set_val,B2: set_set_val] :
% 1.96/1.19 ! [X3: set_val] :
% 1.96/1.19 ( ( member_set_val @ X3 @ A2 )
% 1.96/1.19 => ( member_set_val @ X3 @ B2 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_18_subset__eq,axiom,
% 1.96/1.19 ( ord_less_eq_set_val
% 1.96/1.19 = ( ^ [A2: set_val,B2: set_val] :
% 1.96/1.19 ! [X3: val] :
% 1.96/1.19 ( ( member_val @ X3 @ A2 )
% 1.96/1.19 => ( member_val @ X3 @ B2 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_19_equalityD1,axiom,
% 1.96/1.19 ! [A: set_set_val,B: set_set_val] :
% 1.96/1.19 ( ( A = B )
% 1.96/1.19 => ( ord_le1742111550et_val @ A @ B ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_20_equalityD1,axiom,
% 1.96/1.19 ! [A: set_val,B: set_val] :
% 1.96/1.19 ( ( A = B )
% 1.96/1.19 => ( ord_less_eq_set_val @ A @ B ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_21_equalityD2,axiom,
% 1.96/1.19 ! [A: set_set_val,B: set_set_val] :
% 1.96/1.19 ( ( A = B )
% 1.96/1.19 => ( ord_le1742111550et_val @ B @ A ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_22_equalityD2,axiom,
% 1.96/1.19 ! [A: set_val,B: set_val] :
% 1.96/1.19 ( ( A = B )
% 1.96/1.19 => ( ord_less_eq_set_val @ B @ A ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_23_subset__iff,axiom,
% 1.96/1.19 ( ord_le1742111550et_val
% 1.96/1.19 = ( ^ [A2: set_set_val,B2: set_set_val] :
% 1.96/1.19 ! [T: set_val] :
% 1.96/1.19 ( ( member_set_val @ T @ A2 )
% 1.96/1.19 => ( member_set_val @ T @ B2 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_24_subset__iff,axiom,
% 1.96/1.19 ( ord_less_eq_set_val
% 1.96/1.19 = ( ^ [A2: set_val,B2: set_val] :
% 1.96/1.19 ! [T: val] :
% 1.96/1.19 ( ( member_val @ T @ A2 )
% 1.96/1.19 => ( member_val @ T @ B2 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_25_subset__refl,axiom,
% 1.96/1.19 ! [A: set_set_val] : ( ord_le1742111550et_val @ A @ A ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_26_subset__refl,axiom,
% 1.96/1.19 ! [A: set_val] : ( ord_less_eq_set_val @ A @ A ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_27_order__mono__setup_Omono__if,axiom,
% 1.96/1.19 ! [T2: $o > set_val,T3: $o > set_val,E: $o > set_val,E2: $o > set_val,B3: $o] :
% 1.96/1.19 ( ( ord_le994826475et_val @ T2 @ T3 )
% 1.96/1.19 => ( ( ord_le994826475et_val @ E @ E2 )
% 1.96/1.19 => ( ord_le994826475et_val @ ( if_o_set_val @ B3 @ T2 @ E ) @ ( if_o_set_val @ B3 @ T3 @ E2 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_28_order__mono__setup_Omono__if,axiom,
% 1.96/1.19 ! [T2: val,T3: val,E: val,E2: val,B3: $o] :
% 1.96/1.19 ( ( ord_less_eq_val @ T2 @ T3 )
% 1.96/1.19 => ( ( ord_less_eq_val @ E @ E2 )
% 1.96/1.19 => ( ord_less_eq_val @ ( if_val @ B3 @ T2 @ E ) @ ( if_val @ B3 @ T3 @ E2 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_29_order__mono__setup_Omono__if,axiom,
% 1.96/1.19 ! [T2: set_set_val,T3: set_set_val,E: set_set_val,E2: set_set_val,B3: $o] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ T2 @ T3 )
% 1.96/1.19 => ( ( ord_le1742111550et_val @ E @ E2 )
% 1.96/1.19 => ( ord_le1742111550et_val @ ( if_set_set_val @ B3 @ T2 @ E ) @ ( if_set_set_val @ B3 @ T3 @ E2 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_30_order__mono__setup_Omono__if,axiom,
% 1.96/1.19 ! [T2: set_val,T3: set_val,E: set_val,E2: set_val,B3: $o] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ T2 @ T3 )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ E @ E2 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( if_set_val @ B3 @ T2 @ E ) @ ( if_set_val @ B3 @ T3 @ E2 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_31_Collect__mono__iff,axiom,
% 1.96/1.19 ! [P: set_val > $o,Q: set_val > $o] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ ( collect_set_val @ P ) @ ( collect_set_val @ Q ) )
% 1.96/1.19 = ( ! [X3: set_val] :
% 1.96/1.19 ( ( P @ X3 )
% 1.96/1.19 => ( Q @ X3 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_32_Collect__mono__iff,axiom,
% 1.96/1.19 ! [P: val > $o,Q: val > $o] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ ( collect_val @ P ) @ ( collect_val @ Q ) )
% 1.96/1.19 = ( ! [X3: val] :
% 1.96/1.19 ( ( P @ X3 )
% 1.96/1.19 => ( Q @ X3 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_33_set__eq__subset,axiom,
% 1.96/1.19 ( ( ^ [Y: set_set_val,Z: set_set_val] : ( Y = Z ) )
% 1.96/1.19 = ( ^ [A2: set_set_val,B2: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ A2 @ B2 )
% 1.96/1.19 & ( ord_le1742111550et_val @ B2 @ A2 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_34_set__eq__subset,axiom,
% 1.96/1.19 ( ( ^ [Y: set_val,Z: set_val] : ( Y = Z ) )
% 1.96/1.19 = ( ^ [A2: set_val,B2: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A2 @ B2 )
% 1.96/1.19 & ( ord_less_eq_set_val @ B2 @ A2 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_35_subset__trans,axiom,
% 1.96/1.19 ! [A: set_set_val,B: set_set_val,C2: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ A @ B )
% 1.96/1.19 => ( ( ord_le1742111550et_val @ B @ C2 )
% 1.96/1.19 => ( ord_le1742111550et_val @ A @ C2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_36_subset__trans,axiom,
% 1.96/1.19 ! [A: set_val,B: set_val,C2: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A @ B )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ B @ C2 )
% 1.96/1.19 => ( ord_less_eq_set_val @ A @ C2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_37_Collect__mono,axiom,
% 1.96/1.19 ! [P: set_val > $o,Q: set_val > $o] :
% 1.96/1.19 ( ! [X2: set_val] :
% 1.96/1.19 ( ( P @ X2 )
% 1.96/1.19 => ( Q @ X2 ) )
% 1.96/1.19 => ( ord_le1742111550et_val @ ( collect_set_val @ P ) @ ( collect_set_val @ Q ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_38_Collect__mono,axiom,
% 1.96/1.19 ! [P: val > $o,Q: val > $o] :
% 1.96/1.19 ( ! [X2: val] :
% 1.96/1.19 ( ( P @ X2 )
% 1.96/1.19 => ( Q @ X2 ) )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( collect_val @ P ) @ ( collect_val @ Q ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_39_subset__Collect__conv,axiom,
% 1.96/1.19 ! [S: set_set_val,P: set_val > $o] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ S @ ( collect_set_val @ P ) )
% 1.96/1.19 = ( ! [X3: set_val] :
% 1.96/1.19 ( ( member_set_val @ X3 @ S )
% 1.96/1.19 => ( P @ X3 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_40_subset__Collect__conv,axiom,
% 1.96/1.19 ! [S: set_val,P: val > $o] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ S @ ( collect_val @ P ) )
% 1.96/1.19 = ( ! [X3: val] :
% 1.96/1.19 ( ( member_val @ X3 @ S )
% 1.96/1.19 => ( P @ X3 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_41_dual__order_Oantisym,axiom,
% 1.96/1.19 ! [B3: $o > set_val,A3: $o > set_val] :
% 1.96/1.19 ( ( ord_le994826475et_val @ B3 @ A3 )
% 1.96/1.19 => ( ( ord_le994826475et_val @ A3 @ B3 )
% 1.96/1.19 => ( A3 = B3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_42_dual__order_Oantisym,axiom,
% 1.96/1.19 ! [B3: val,A3: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ B3 @ A3 )
% 1.96/1.19 => ( ( ord_less_eq_val @ A3 @ B3 )
% 1.96/1.19 => ( A3 = B3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_43_dual__order_Oantisym,axiom,
% 1.96/1.19 ! [B3: set_set_val,A3: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ B3 @ A3 )
% 1.96/1.19 => ( ( ord_le1742111550et_val @ A3 @ B3 )
% 1.96/1.19 => ( A3 = B3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_44_dual__order_Oantisym,axiom,
% 1.96/1.19 ! [B3: set_val,A3: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ B3 @ A3 )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ A3 @ B3 )
% 1.96/1.19 => ( A3 = B3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_45_dual__order_Oeq__iff,axiom,
% 1.96/1.19 ( ( ^ [Y: $o > set_val,Z: $o > set_val] : ( Y = Z ) )
% 1.96/1.19 = ( ^ [A4: $o > set_val,B4: $o > set_val] :
% 1.96/1.19 ( ( ord_le994826475et_val @ B4 @ A4 )
% 1.96/1.19 & ( ord_le994826475et_val @ A4 @ B4 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_46_dual__order_Oeq__iff,axiom,
% 1.96/1.19 ( ( ^ [Y: val,Z: val] : ( Y = Z ) )
% 1.96/1.19 = ( ^ [A4: val,B4: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ B4 @ A4 )
% 1.96/1.19 & ( ord_less_eq_val @ A4 @ B4 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_47_dual__order_Oeq__iff,axiom,
% 1.96/1.19 ( ( ^ [Y: set_set_val,Z: set_set_val] : ( Y = Z ) )
% 1.96/1.19 = ( ^ [A4: set_set_val,B4: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ B4 @ A4 )
% 1.96/1.19 & ( ord_le1742111550et_val @ A4 @ B4 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_48_dual__order_Oeq__iff,axiom,
% 1.96/1.19 ( ( ^ [Y: set_val,Z: set_val] : ( Y = Z ) )
% 1.96/1.19 = ( ^ [A4: set_val,B4: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ B4 @ A4 )
% 1.96/1.19 & ( ord_less_eq_set_val @ A4 @ B4 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_49_dual__order_Otrans,axiom,
% 1.96/1.19 ! [B3: $o > set_val,A3: $o > set_val,C: $o > set_val] :
% 1.96/1.19 ( ( ord_le994826475et_val @ B3 @ A3 )
% 1.96/1.19 => ( ( ord_le994826475et_val @ C @ B3 )
% 1.96/1.19 => ( ord_le994826475et_val @ C @ A3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_50_dual__order_Otrans,axiom,
% 1.96/1.19 ! [B3: val,A3: val,C: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ B3 @ A3 )
% 1.96/1.19 => ( ( ord_less_eq_val @ C @ B3 )
% 1.96/1.19 => ( ord_less_eq_val @ C @ A3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_51_dual__order_Otrans,axiom,
% 1.96/1.19 ! [B3: set_set_val,A3: set_set_val,C: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ B3 @ A3 )
% 1.96/1.19 => ( ( ord_le1742111550et_val @ C @ B3 )
% 1.96/1.19 => ( ord_le1742111550et_val @ C @ A3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_52_dual__order_Otrans,axiom,
% 1.96/1.19 ! [B3: set_val,A3: set_val,C: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ B3 @ A3 )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ C @ B3 )
% 1.96/1.19 => ( ord_less_eq_set_val @ C @ A3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_53_linorder__wlog,axiom,
% 1.96/1.19 ! [P: val > val > $o,A3: val,B3: val] :
% 1.96/1.19 ( ! [A5: val,B5: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ A5 @ B5 )
% 1.96/1.19 => ( P @ A5 @ B5 ) )
% 1.96/1.19 => ( ! [A5: val,B5: val] :
% 1.96/1.19 ( ( P @ B5 @ A5 )
% 1.96/1.19 => ( P @ A5 @ B5 ) )
% 1.96/1.19 => ( P @ A3 @ B3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_54_dual__order_Orefl,axiom,
% 1.96/1.19 ! [A3: $o > set_val] : ( ord_le994826475et_val @ A3 @ A3 ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_55_dual__order_Orefl,axiom,
% 1.96/1.19 ! [A3: val] : ( ord_less_eq_val @ A3 @ A3 ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_56_dual__order_Orefl,axiom,
% 1.96/1.19 ! [A3: set_set_val] : ( ord_le1742111550et_val @ A3 @ A3 ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_57_dual__order_Orefl,axiom,
% 1.96/1.19 ! [A3: set_val] : ( ord_less_eq_set_val @ A3 @ A3 ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_58_order__trans,axiom,
% 1.96/1.19 ! [X: $o > set_val,Y2: $o > set_val,Z2: $o > set_val] :
% 1.96/1.19 ( ( ord_le994826475et_val @ X @ Y2 )
% 1.96/1.19 => ( ( ord_le994826475et_val @ Y2 @ Z2 )
% 1.96/1.19 => ( ord_le994826475et_val @ X @ Z2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_59_order__trans,axiom,
% 1.96/1.19 ! [X: val,Y2: val,Z2: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X @ Y2 )
% 1.96/1.19 => ( ( ord_less_eq_val @ Y2 @ Z2 )
% 1.96/1.19 => ( ord_less_eq_val @ X @ Z2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_60_order__trans,axiom,
% 1.96/1.19 ! [X: set_set_val,Y2: set_set_val,Z2: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ X @ Y2 )
% 1.96/1.19 => ( ( ord_le1742111550et_val @ Y2 @ Z2 )
% 1.96/1.19 => ( ord_le1742111550et_val @ X @ Z2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_61_order__trans,axiom,
% 1.96/1.19 ! [X: set_val,Y2: set_val,Z2: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X @ Y2 )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ Y2 @ Z2 )
% 1.96/1.19 => ( ord_less_eq_set_val @ X @ Z2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_62_order__class_Oorder_Oantisym,axiom,
% 1.96/1.19 ! [A3: $o > set_val,B3: $o > set_val] :
% 1.96/1.19 ( ( ord_le994826475et_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ord_le994826475et_val @ B3 @ A3 )
% 1.96/1.19 => ( A3 = B3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_63_order__class_Oorder_Oantisym,axiom,
% 1.96/1.19 ! [A3: val,B3: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ord_less_eq_val @ B3 @ A3 )
% 1.96/1.19 => ( A3 = B3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_64_order__class_Oorder_Oantisym,axiom,
% 1.96/1.19 ! [A3: set_set_val,B3: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ord_le1742111550et_val @ B3 @ A3 )
% 1.96/1.19 => ( A3 = B3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_65_order__class_Oorder_Oantisym,axiom,
% 1.96/1.19 ! [A3: set_val,B3: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ B3 @ A3 )
% 1.96/1.19 => ( A3 = B3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_66_ord__le__eq__trans,axiom,
% 1.96/1.19 ! [A3: $o > set_val,B3: $o > set_val,C: $o > set_val] :
% 1.96/1.19 ( ( ord_le994826475et_val @ A3 @ B3 )
% 1.96/1.19 => ( ( B3 = C )
% 1.96/1.19 => ( ord_le994826475et_val @ A3 @ C ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_67_ord__le__eq__trans,axiom,
% 1.96/1.19 ! [A3: val,B3: val,C: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ A3 @ B3 )
% 1.96/1.19 => ( ( B3 = C )
% 1.96/1.19 => ( ord_less_eq_val @ A3 @ C ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_68_ord__le__eq__trans,axiom,
% 1.96/1.19 ! [A3: set_set_val,B3: set_set_val,C: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ A3 @ B3 )
% 1.96/1.19 => ( ( B3 = C )
% 1.96/1.19 => ( ord_le1742111550et_val @ A3 @ C ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_69_ord__le__eq__trans,axiom,
% 1.96/1.19 ! [A3: set_val,B3: set_val,C: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 1.96/1.19 => ( ( B3 = C )
% 1.96/1.19 => ( ord_less_eq_set_val @ A3 @ C ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_70_le__funD,axiom,
% 1.96/1.19 ! [F: $o > set_val,G: $o > set_val,X: $o] :
% 1.96/1.19 ( ( ord_le994826475et_val @ F @ G )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ X ) @ ( G @ X ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_71_le__funE,axiom,
% 1.96/1.19 ! [F: $o > set_val,G: $o > set_val,X: $o] :
% 1.96/1.19 ( ( ord_le994826475et_val @ F @ G )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ X ) @ ( G @ X ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_72_le__funI,axiom,
% 1.96/1.19 ! [F: $o > set_val,G: $o > set_val] :
% 1.96/1.19 ( ! [X2: $o] : ( ord_less_eq_set_val @ ( F @ X2 ) @ ( G @ X2 ) )
% 1.96/1.19 => ( ord_le994826475et_val @ F @ G ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_73_le__fun__def,axiom,
% 1.96/1.19 ( ord_le994826475et_val
% 1.96/1.19 = ( ^ [F2: $o > set_val,G2: $o > set_val] :
% 1.96/1.19 ! [X3: $o] : ( ord_less_eq_set_val @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_74_order__subst1,axiom,
% 1.96/1.19 ! [A3: set_val,F: set_val > set_val,B3: set_val,C: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A3 @ ( F @ B3 ) )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ B3 @ C )
% 1.96/1.19 => ( ! [X2: set_val,Y3: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_set_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_75_order__subst1,axiom,
% 1.96/1.19 ! [A3: val,F: val > val,B3: val,C: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ A3 @ ( F @ B3 ) )
% 1.96/1.19 => ( ( ord_less_eq_val @ B3 @ C )
% 1.96/1.19 => ( ! [X2: val,Y3: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_76_order__subst1,axiom,
% 1.96/1.19 ! [A3: set_val,F: val > set_val,B3: val,C: val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A3 @ ( F @ B3 ) )
% 1.96/1.19 => ( ( ord_less_eq_val @ B3 @ C )
% 1.96/1.19 => ( ! [X2: val,Y3: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_set_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_77_order__subst1,axiom,
% 1.96/1.19 ! [A3: val,F: set_val > val,B3: set_val,C: set_val] :
% 1.96/1.19 ( ( ord_less_eq_val @ A3 @ ( F @ B3 ) )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ B3 @ C )
% 1.96/1.19 => ( ! [X2: set_val,Y3: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_78_order__subst1,axiom,
% 1.96/1.19 ! [A3: val,F: set_set_val > val,B3: set_set_val,C: set_set_val] :
% 1.96/1.19 ( ( ord_less_eq_val @ A3 @ ( F @ B3 ) )
% 1.96/1.19 => ( ( ord_le1742111550et_val @ B3 @ C )
% 1.96/1.19 => ( ! [X2: set_set_val,Y3: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_79_order__subst1,axiom,
% 1.96/1.19 ! [A3: set_set_val,F: val > set_set_val,B3: val,C: val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ A3 @ ( F @ B3 ) )
% 1.96/1.19 => ( ( ord_less_eq_val @ B3 @ C )
% 1.96/1.19 => ( ! [X2: val,Y3: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_le1742111550et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_le1742111550et_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_80_order__subst1,axiom,
% 1.96/1.19 ! [A3: set_val,F: set_set_val > set_val,B3: set_set_val,C: set_set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A3 @ ( F @ B3 ) )
% 1.96/1.19 => ( ( ord_le1742111550et_val @ B3 @ C )
% 1.96/1.19 => ( ! [X2: set_set_val,Y3: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_set_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_81_order__subst1,axiom,
% 1.96/1.19 ! [A3: $o > set_val,F: val > $o > set_val,B3: val,C: val] :
% 1.96/1.19 ( ( ord_le994826475et_val @ A3 @ ( F @ B3 ) )
% 1.96/1.19 => ( ( ord_less_eq_val @ B3 @ C )
% 1.96/1.19 => ( ! [X2: val,Y3: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_le994826475et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_le994826475et_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_82_order__subst1,axiom,
% 1.96/1.19 ! [A3: val,F: ( $o > set_val ) > val,B3: $o > set_val,C: $o > set_val] :
% 1.96/1.19 ( ( ord_less_eq_val @ A3 @ ( F @ B3 ) )
% 1.96/1.19 => ( ( ord_le994826475et_val @ B3 @ C )
% 1.96/1.19 => ( ! [X2: $o > set_val,Y3: $o > set_val] :
% 1.96/1.19 ( ( ord_le994826475et_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_83_order__subst1,axiom,
% 1.96/1.19 ! [A3: set_set_val,F: set_val > set_set_val,B3: set_val,C: set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ A3 @ ( F @ B3 ) )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ B3 @ C )
% 1.96/1.19 => ( ! [X2: set_val,Y3: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_le1742111550et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_le1742111550et_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_84_order__subst2,axiom,
% 1.96/1.19 ! [A3: set_val,B3: set_val,F: set_val > set_val,C: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ ( F @ B3 ) @ C )
% 1.96/1.19 => ( ! [X2: set_val,Y3: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_85_order__subst2,axiom,
% 1.96/1.19 ! [A3: val,B3: val,F: val > val,C: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ord_less_eq_val @ ( F @ B3 ) @ C )
% 1.96/1.19 => ( ! [X2: val,Y3: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_86_order__subst2,axiom,
% 1.96/1.19 ! [A3: set_val,B3: set_val,F: set_val > val,C: val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ord_less_eq_val @ ( F @ B3 ) @ C )
% 1.96/1.19 => ( ! [X2: set_val,Y3: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_87_order__subst2,axiom,
% 1.96/1.19 ! [A3: val,B3: val,F: val > set_val,C: set_val] :
% 1.96/1.19 ( ( ord_less_eq_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ ( F @ B3 ) @ C )
% 1.96/1.19 => ( ! [X2: val,Y3: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_88_order__subst2,axiom,
% 1.96/1.19 ! [A3: val,B3: val,F: val > set_set_val,C: set_set_val] :
% 1.96/1.19 ( ( ord_less_eq_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ord_le1742111550et_val @ ( F @ B3 ) @ C )
% 1.96/1.19 => ( ! [X2: val,Y3: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_le1742111550et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_le1742111550et_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_89_order__subst2,axiom,
% 1.96/1.19 ! [A3: set_set_val,B3: set_set_val,F: set_set_val > val,C: val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ord_less_eq_val @ ( F @ B3 ) @ C )
% 1.96/1.19 => ( ! [X2: set_set_val,Y3: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_90_order__subst2,axiom,
% 1.96/1.19 ! [A3: set_val,B3: set_val,F: set_val > set_set_val,C: set_set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ord_le1742111550et_val @ ( F @ B3 ) @ C )
% 1.96/1.19 => ( ! [X2: set_val,Y3: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_le1742111550et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_le1742111550et_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_91_order__subst2,axiom,
% 1.96/1.19 ! [A3: $o > set_val,B3: $o > set_val,F: ( $o > set_val ) > val,C: val] :
% 1.96/1.19 ( ( ord_le994826475et_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ord_less_eq_val @ ( F @ B3 ) @ C )
% 1.96/1.19 => ( ! [X2: $o > set_val,Y3: $o > set_val] :
% 1.96/1.19 ( ( ord_le994826475et_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_92_order__subst2,axiom,
% 1.96/1.19 ! [A3: val,B3: val,F: val > $o > set_val,C: $o > set_val] :
% 1.96/1.19 ( ( ord_less_eq_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ord_le994826475et_val @ ( F @ B3 ) @ C )
% 1.96/1.19 => ( ! [X2: val,Y3: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_le994826475et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_le994826475et_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_93_order__subst2,axiom,
% 1.96/1.19 ! [A3: set_set_val,B3: set_set_val,F: set_set_val > set_val,C: set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ ( F @ B3 ) @ C )
% 1.96/1.19 => ( ! [X2: set_set_val,Y3: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_94_ord__eq__le__eq__trans,axiom,
% 1.96/1.19 ! [A3: $o > set_val,B3: $o > set_val,C: $o > set_val,D: $o > set_val] :
% 1.96/1.19 ( ( A3 = B3 )
% 1.96/1.19 => ( ( ord_le994826475et_val @ B3 @ C )
% 1.96/1.19 => ( ( C = D )
% 1.96/1.19 => ( ord_le994826475et_val @ A3 @ D ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_95_ord__eq__le__eq__trans,axiom,
% 1.96/1.19 ! [A3: val,B3: val,C: val,D: val] :
% 1.96/1.19 ( ( A3 = B3 )
% 1.96/1.19 => ( ( ord_less_eq_val @ B3 @ C )
% 1.96/1.19 => ( ( C = D )
% 1.96/1.19 => ( ord_less_eq_val @ A3 @ D ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_96_ord__eq__le__eq__trans,axiom,
% 1.96/1.19 ! [A3: set_set_val,B3: set_set_val,C: set_set_val,D: set_set_val] :
% 1.96/1.19 ( ( A3 = B3 )
% 1.96/1.19 => ( ( ord_le1742111550et_val @ B3 @ C )
% 1.96/1.19 => ( ( C = D )
% 1.96/1.19 => ( ord_le1742111550et_val @ A3 @ D ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_97_ord__eq__le__eq__trans,axiom,
% 1.96/1.19 ! [A3: set_val,B3: set_val,C: set_val,D: set_val] :
% 1.96/1.19 ( ( A3 = B3 )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ B3 @ C )
% 1.96/1.19 => ( ( C = D )
% 1.96/1.19 => ( ord_less_eq_set_val @ A3 @ D ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_98_ord__eq__le__subst,axiom,
% 1.96/1.19 ! [A3: set_val,F: set_val > set_val,B3: set_val,C: set_val] :
% 1.96/1.19 ( ( A3
% 1.96/1.19 = ( F @ B3 ) )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ B3 @ C )
% 1.96/1.19 => ( ! [X2: set_val,Y3: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_set_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_99_ord__eq__le__subst,axiom,
% 1.96/1.19 ! [A3: val,F: val > val,B3: val,C: val] :
% 1.96/1.19 ( ( A3
% 1.96/1.19 = ( F @ B3 ) )
% 1.96/1.19 => ( ( ord_less_eq_val @ B3 @ C )
% 1.96/1.19 => ( ! [X2: val,Y3: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_100_ord__eq__le__subst,axiom,
% 1.96/1.19 ! [A3: val,F: set_val > val,B3: set_val,C: set_val] :
% 1.96/1.19 ( ( A3
% 1.96/1.19 = ( F @ B3 ) )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ B3 @ C )
% 1.96/1.19 => ( ! [X2: set_val,Y3: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_101_ord__eq__le__subst,axiom,
% 1.96/1.19 ! [A3: set_val,F: val > set_val,B3: val,C: val] :
% 1.96/1.19 ( ( A3
% 1.96/1.19 = ( F @ B3 ) )
% 1.96/1.19 => ( ( ord_less_eq_val @ B3 @ C )
% 1.96/1.19 => ( ! [X2: val,Y3: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_set_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_102_ord__eq__le__subst,axiom,
% 1.96/1.19 ! [A3: set_set_val,F: val > set_set_val,B3: val,C: val] :
% 1.96/1.19 ( ( A3
% 1.96/1.19 = ( F @ B3 ) )
% 1.96/1.19 => ( ( ord_less_eq_val @ B3 @ C )
% 1.96/1.19 => ( ! [X2: val,Y3: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_le1742111550et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_le1742111550et_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_103_ord__eq__le__subst,axiom,
% 1.96/1.19 ! [A3: val,F: set_set_val > val,B3: set_set_val,C: set_set_val] :
% 1.96/1.19 ( ( A3
% 1.96/1.19 = ( F @ B3 ) )
% 1.96/1.19 => ( ( ord_le1742111550et_val @ B3 @ C )
% 1.96/1.19 => ( ! [X2: set_set_val,Y3: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_104_ord__eq__le__subst,axiom,
% 1.96/1.19 ! [A3: set_set_val,F: set_val > set_set_val,B3: set_val,C: set_val] :
% 1.96/1.19 ( ( A3
% 1.96/1.19 = ( F @ B3 ) )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ B3 @ C )
% 1.96/1.19 => ( ! [X2: set_val,Y3: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_le1742111550et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_le1742111550et_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_105_ord__eq__le__subst,axiom,
% 1.96/1.19 ! [A3: val,F: ( $o > set_val ) > val,B3: $o > set_val,C: $o > set_val] :
% 1.96/1.19 ( ( A3
% 1.96/1.19 = ( F @ B3 ) )
% 1.96/1.19 => ( ( ord_le994826475et_val @ B3 @ C )
% 1.96/1.19 => ( ! [X2: $o > set_val,Y3: $o > set_val] :
% 1.96/1.19 ( ( ord_le994826475et_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_106_ord__eq__le__subst,axiom,
% 1.96/1.19 ! [A3: $o > set_val,F: val > $o > set_val,B3: val,C: val] :
% 1.96/1.19 ( ( A3
% 1.96/1.19 = ( F @ B3 ) )
% 1.96/1.19 => ( ( ord_less_eq_val @ B3 @ C )
% 1.96/1.19 => ( ! [X2: val,Y3: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_le994826475et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_le994826475et_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_107_ord__eq__le__subst,axiom,
% 1.96/1.19 ! [A3: set_val,F: set_set_val > set_val,B3: set_set_val,C: set_set_val] :
% 1.96/1.19 ( ( A3
% 1.96/1.19 = ( F @ B3 ) )
% 1.96/1.19 => ( ( ord_le1742111550et_val @ B3 @ C )
% 1.96/1.19 => ( ! [X2: set_set_val,Y3: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_set_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_108_ord__le__eq__subst,axiom,
% 1.96/1.19 ! [A3: set_val,B3: set_val,F: set_val > set_val,C: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ( F @ B3 )
% 1.96/1.19 = C )
% 1.96/1.19 => ( ! [X2: set_val,Y3: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_109_ord__le__eq__subst,axiom,
% 1.96/1.19 ! [A3: val,B3: val,F: val > val,C: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ( F @ B3 )
% 1.96/1.19 = C )
% 1.96/1.19 => ( ! [X2: val,Y3: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_110_ord__le__eq__subst,axiom,
% 1.96/1.19 ! [A3: set_val,B3: set_val,F: set_val > val,C: val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ( F @ B3 )
% 1.96/1.19 = C )
% 1.96/1.19 => ( ! [X2: set_val,Y3: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_111_ord__le__eq__subst,axiom,
% 1.96/1.19 ! [A3: val,B3: val,F: val > set_val,C: set_val] :
% 1.96/1.19 ( ( ord_less_eq_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ( F @ B3 )
% 1.96/1.19 = C )
% 1.96/1.19 => ( ! [X2: val,Y3: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_112_ord__le__eq__subst,axiom,
% 1.96/1.19 ! [A3: val,B3: val,F: val > set_set_val,C: set_set_val] :
% 1.96/1.19 ( ( ord_less_eq_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ( F @ B3 )
% 1.96/1.19 = C )
% 1.96/1.19 => ( ! [X2: val,Y3: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_le1742111550et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_le1742111550et_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_113_ord__le__eq__subst,axiom,
% 1.96/1.19 ! [A3: set_set_val,B3: set_set_val,F: set_set_val > val,C: val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ( F @ B3 )
% 1.96/1.19 = C )
% 1.96/1.19 => ( ! [X2: set_set_val,Y3: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_114_ord__le__eq__subst,axiom,
% 1.96/1.19 ! [A3: set_val,B3: set_val,F: set_val > set_set_val,C: set_set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ( F @ B3 )
% 1.96/1.19 = C )
% 1.96/1.19 => ( ! [X2: set_val,Y3: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_le1742111550et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_le1742111550et_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_115_ord__le__eq__subst,axiom,
% 1.96/1.19 ! [A3: $o > set_val,B3: $o > set_val,F: ( $o > set_val ) > val,C: val] :
% 1.96/1.19 ( ( ord_le994826475et_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ( F @ B3 )
% 1.96/1.19 = C )
% 1.96/1.19 => ( ! [X2: $o > set_val,Y3: $o > set_val] :
% 1.96/1.19 ( ( ord_le994826475et_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_116_ord__le__eq__subst,axiom,
% 1.96/1.19 ! [A3: val,B3: val,F: val > $o > set_val,C: $o > set_val] :
% 1.96/1.19 ( ( ord_less_eq_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ( F @ B3 )
% 1.96/1.19 = C )
% 1.96/1.19 => ( ! [X2: val,Y3: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_le994826475et_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_le994826475et_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_117_ord__le__eq__subst,axiom,
% 1.96/1.19 ! [A3: set_set_val,B3: set_set_val,F: set_set_val > set_val,C: set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ( F @ B3 )
% 1.96/1.19 = C )
% 1.96/1.19 => ( ! [X2: set_set_val,Y3: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_118_eq__iff,axiom,
% 1.96/1.19 ( ( ^ [Y: $o > set_val,Z: $o > set_val] : ( Y = Z ) )
% 1.96/1.19 = ( ^ [X3: $o > set_val,Y4: $o > set_val] :
% 1.96/1.19 ( ( ord_le994826475et_val @ X3 @ Y4 )
% 1.96/1.19 & ( ord_le994826475et_val @ Y4 @ X3 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_119_eq__iff,axiom,
% 1.96/1.19 ( ( ^ [Y: val,Z: val] : ( Y = Z ) )
% 1.96/1.19 = ( ^ [X3: val,Y4: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X3 @ Y4 )
% 1.96/1.19 & ( ord_less_eq_val @ Y4 @ X3 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_120_eq__iff,axiom,
% 1.96/1.19 ( ( ^ [Y: set_set_val,Z: set_set_val] : ( Y = Z ) )
% 1.96/1.19 = ( ^ [X3: set_set_val,Y4: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ X3 @ Y4 )
% 1.96/1.19 & ( ord_le1742111550et_val @ Y4 @ X3 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_121_eq__iff,axiom,
% 1.96/1.19 ( ( ^ [Y: set_val,Z: set_val] : ( Y = Z ) )
% 1.96/1.19 = ( ^ [X3: set_val,Y4: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X3 @ Y4 )
% 1.96/1.19 & ( ord_less_eq_set_val @ Y4 @ X3 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_122_antisym,axiom,
% 1.96/1.19 ! [X: $o > set_val,Y2: $o > set_val] :
% 1.96/1.19 ( ( ord_le994826475et_val @ X @ Y2 )
% 1.96/1.19 => ( ( ord_le994826475et_val @ Y2 @ X )
% 1.96/1.19 => ( X = Y2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_123_antisym,axiom,
% 1.96/1.19 ! [X: val,Y2: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X @ Y2 )
% 1.96/1.19 => ( ( ord_less_eq_val @ Y2 @ X )
% 1.96/1.19 => ( X = Y2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_124_antisym,axiom,
% 1.96/1.19 ! [X: set_set_val,Y2: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ X @ Y2 )
% 1.96/1.19 => ( ( ord_le1742111550et_val @ Y2 @ X )
% 1.96/1.19 => ( X = Y2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_125_antisym,axiom,
% 1.96/1.19 ! [X: set_val,Y2: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X @ Y2 )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ Y2 @ X )
% 1.96/1.19 => ( X = Y2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_126_linear,axiom,
% 1.96/1.19 ! [X: val,Y2: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X @ Y2 )
% 1.96/1.19 | ( ord_less_eq_val @ Y2 @ X ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_127_eq__refl,axiom,
% 1.96/1.19 ! [X: $o > set_val,Y2: $o > set_val] :
% 1.96/1.19 ( ( X = Y2 )
% 1.96/1.19 => ( ord_le994826475et_val @ X @ Y2 ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_128_eq__refl,axiom,
% 1.96/1.19 ! [X: val,Y2: val] :
% 1.96/1.19 ( ( X = Y2 )
% 1.96/1.19 => ( ord_less_eq_val @ X @ Y2 ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_129_eq__refl,axiom,
% 1.96/1.19 ! [X: set_set_val,Y2: set_set_val] :
% 1.96/1.19 ( ( X = Y2 )
% 1.96/1.19 => ( ord_le1742111550et_val @ X @ Y2 ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_130_eq__refl,axiom,
% 1.96/1.19 ! [X: set_val,Y2: set_val] :
% 1.96/1.19 ( ( X = Y2 )
% 1.96/1.19 => ( ord_less_eq_set_val @ X @ Y2 ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_131_le__cases,axiom,
% 1.96/1.19 ! [X: val,Y2: val] :
% 1.96/1.19 ( ~ ( ord_less_eq_val @ X @ Y2 )
% 1.96/1.19 => ( ord_less_eq_val @ Y2 @ X ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_132_order_Otrans,axiom,
% 1.96/1.19 ! [A3: $o > set_val,B3: $o > set_val,C: $o > set_val] :
% 1.96/1.19 ( ( ord_le994826475et_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ord_le994826475et_val @ B3 @ C )
% 1.96/1.19 => ( ord_le994826475et_val @ A3 @ C ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_133_order_Otrans,axiom,
% 1.96/1.19 ! [A3: val,B3: val,C: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ord_less_eq_val @ B3 @ C )
% 1.96/1.19 => ( ord_less_eq_val @ A3 @ C ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_134_order_Otrans,axiom,
% 1.96/1.19 ! [A3: set_set_val,B3: set_set_val,C: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ord_le1742111550et_val @ B3 @ C )
% 1.96/1.19 => ( ord_le1742111550et_val @ A3 @ C ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_135_order_Otrans,axiom,
% 1.96/1.19 ! [A3: set_val,B3: set_val,C: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ B3 @ C )
% 1.96/1.19 => ( ord_less_eq_set_val @ A3 @ C ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_136_mem__Collect__eq,axiom,
% 1.96/1.19 ! [A3: set_val,P: set_val > $o] :
% 1.96/1.19 ( ( member_set_val @ A3 @ ( collect_set_val @ P ) )
% 1.96/1.19 = ( P @ A3 ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_137_mem__Collect__eq,axiom,
% 1.96/1.19 ! [A3: val,P: val > $o] :
% 1.96/1.19 ( ( member_val @ A3 @ ( collect_val @ P ) )
% 1.96/1.19 = ( P @ A3 ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_138_Collect__mem__eq,axiom,
% 1.96/1.19 ! [A: set_set_val] :
% 1.96/1.19 ( ( collect_set_val
% 1.96/1.19 @ ^ [X3: set_val] : ( member_set_val @ X3 @ A ) )
% 1.96/1.19 = A ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_139_Collect__mem__eq,axiom,
% 1.96/1.19 ! [A: set_val] :
% 1.96/1.19 ( ( collect_val
% 1.96/1.19 @ ^ [X3: val] : ( member_val @ X3 @ A ) )
% 1.96/1.19 = A ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_140_Collect__cong,axiom,
% 1.96/1.19 ! [P: val > $o,Q: val > $o] :
% 1.96/1.19 ( ! [X2: val] :
% 1.96/1.19 ( ( P @ X2 )
% 1.96/1.19 = ( Q @ X2 ) )
% 1.96/1.19 => ( ( collect_val @ P )
% 1.96/1.19 = ( collect_val @ Q ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_141_le__cases3,axiom,
% 1.96/1.19 ! [X: val,Y2: val,Z2: val] :
% 1.96/1.19 ( ( ( ord_less_eq_val @ X @ Y2 )
% 1.96/1.19 => ~ ( ord_less_eq_val @ Y2 @ Z2 ) )
% 1.96/1.19 => ( ( ( ord_less_eq_val @ Y2 @ X )
% 1.96/1.19 => ~ ( ord_less_eq_val @ X @ Z2 ) )
% 1.96/1.19 => ( ( ( ord_less_eq_val @ X @ Z2 )
% 1.96/1.19 => ~ ( ord_less_eq_val @ Z2 @ Y2 ) )
% 1.96/1.19 => ( ( ( ord_less_eq_val @ Z2 @ Y2 )
% 1.96/1.19 => ~ ( ord_less_eq_val @ Y2 @ X ) )
% 1.96/1.19 => ( ( ( ord_less_eq_val @ Y2 @ Z2 )
% 1.96/1.19 => ~ ( ord_less_eq_val @ Z2 @ X ) )
% 1.96/1.19 => ~ ( ( ord_less_eq_val @ Z2 @ X )
% 1.96/1.19 => ~ ( ord_less_eq_val @ X @ Y2 ) ) ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_142_antisym__conv,axiom,
% 1.96/1.19 ! [Y2: $o > set_val,X: $o > set_val] :
% 1.96/1.19 ( ( ord_le994826475et_val @ Y2 @ X )
% 1.96/1.19 => ( ( ord_le994826475et_val @ X @ Y2 )
% 1.96/1.19 = ( X = Y2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_143_antisym__conv,axiom,
% 1.96/1.19 ! [Y2: val,X: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ Y2 @ X )
% 1.96/1.19 => ( ( ord_less_eq_val @ X @ Y2 )
% 1.96/1.19 = ( X = Y2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_144_antisym__conv,axiom,
% 1.96/1.19 ! [Y2: set_set_val,X: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ Y2 @ X )
% 1.96/1.19 => ( ( ord_le1742111550et_val @ X @ Y2 )
% 1.96/1.19 = ( X = Y2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_145_antisym__conv,axiom,
% 1.96/1.19 ! [Y2: set_val,X: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ Y2 @ X )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ X @ Y2 )
% 1.96/1.19 = ( X = Y2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_146_order__class_Oorder_Oeq__iff,axiom,
% 1.96/1.19 ( ( ^ [Y: $o > set_val,Z: $o > set_val] : ( Y = Z ) )
% 1.96/1.19 = ( ^ [A4: $o > set_val,B4: $o > set_val] :
% 1.96/1.19 ( ( ord_le994826475et_val @ A4 @ B4 )
% 1.96/1.19 & ( ord_le994826475et_val @ B4 @ A4 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_147_order__class_Oorder_Oeq__iff,axiom,
% 1.96/1.19 ( ( ^ [Y: val,Z: val] : ( Y = Z ) )
% 1.96/1.19 = ( ^ [A4: val,B4: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ A4 @ B4 )
% 1.96/1.19 & ( ord_less_eq_val @ B4 @ A4 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_148_order__class_Oorder_Oeq__iff,axiom,
% 1.96/1.19 ( ( ^ [Y: set_set_val,Z: set_set_val] : ( Y = Z ) )
% 1.96/1.19 = ( ^ [A4: set_set_val,B4: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ A4 @ B4 )
% 1.96/1.19 & ( ord_le1742111550et_val @ B4 @ A4 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_149_order__class_Oorder_Oeq__iff,axiom,
% 1.96/1.19 ( ( ^ [Y: set_val,Z: set_val] : ( Y = Z ) )
% 1.96/1.19 = ( ^ [A4: set_val,B4: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A4 @ B4 )
% 1.96/1.19 & ( ord_less_eq_set_val @ B4 @ A4 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_150_ord__eq__le__trans,axiom,
% 1.96/1.19 ! [A3: $o > set_val,B3: $o > set_val,C: $o > set_val] :
% 1.96/1.19 ( ( A3 = B3 )
% 1.96/1.19 => ( ( ord_le994826475et_val @ B3 @ C )
% 1.96/1.19 => ( ord_le994826475et_val @ A3 @ C ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_151_ord__eq__le__trans,axiom,
% 1.96/1.19 ! [A3: val,B3: val,C: val] :
% 1.96/1.19 ( ( A3 = B3 )
% 1.96/1.19 => ( ( ord_less_eq_val @ B3 @ C )
% 1.96/1.19 => ( ord_less_eq_val @ A3 @ C ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_152_ord__eq__le__trans,axiom,
% 1.96/1.19 ! [A3: set_set_val,B3: set_set_val,C: set_set_val] :
% 1.96/1.19 ( ( A3 = B3 )
% 1.96/1.19 => ( ( ord_le1742111550et_val @ B3 @ C )
% 1.96/1.19 => ( ord_le1742111550et_val @ A3 @ C ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_153_ord__eq__le__trans,axiom,
% 1.96/1.19 ! [A3: set_val,B3: set_val,C: set_val] :
% 1.96/1.19 ( ( A3 = B3 )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ B3 @ C )
% 1.96/1.19 => ( ord_less_eq_set_val @ A3 @ C ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_154_GreatestI2__order,axiom,
% 1.96/1.19 ! [P: ( $o > set_val ) > $o,X: $o > set_val,Q: ( $o > set_val ) > $o] :
% 1.96/1.19 ( ( P @ X )
% 1.96/1.19 => ( ! [Y3: $o > set_val] :
% 1.96/1.19 ( ( P @ Y3 )
% 1.96/1.19 => ( ord_le994826475et_val @ Y3 @ X ) )
% 1.96/1.19 => ( ! [X2: $o > set_val] :
% 1.96/1.19 ( ( P @ X2 )
% 1.96/1.19 => ( ! [Y5: $o > set_val] :
% 1.96/1.19 ( ( P @ Y5 )
% 1.96/1.19 => ( ord_le994826475et_val @ Y5 @ X2 ) )
% 1.96/1.19 => ( Q @ X2 ) ) )
% 1.96/1.19 => ( Q @ ( order_985126002et_val @ P ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_155_GreatestI2__order,axiom,
% 1.96/1.19 ! [P: val > $o,X: val,Q: val > $o] :
% 1.96/1.19 ( ( P @ X )
% 1.96/1.19 => ( ! [Y3: val] :
% 1.96/1.19 ( ( P @ Y3 )
% 1.96/1.19 => ( ord_less_eq_val @ Y3 @ X ) )
% 1.96/1.19 => ( ! [X2: val] :
% 1.96/1.19 ( ( P @ X2 )
% 1.96/1.19 => ( ! [Y5: val] :
% 1.96/1.19 ( ( P @ Y5 )
% 1.96/1.19 => ( ord_less_eq_val @ Y5 @ X2 ) )
% 1.96/1.19 => ( Q @ X2 ) ) )
% 1.96/1.19 => ( Q @ ( order_Greatest_val @ P ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_156_GreatestI2__order,axiom,
% 1.96/1.19 ! [P: set_set_val > $o,X: set_set_val,Q: set_set_val > $o] :
% 1.96/1.19 ( ( P @ X )
% 1.96/1.19 => ( ! [Y3: set_set_val] :
% 1.96/1.19 ( ( P @ Y3 )
% 1.96/1.19 => ( ord_le1742111550et_val @ Y3 @ X ) )
% 1.96/1.19 => ( ! [X2: set_set_val] :
% 1.96/1.19 ( ( P @ X2 )
% 1.96/1.19 => ( ! [Y5: set_set_val] :
% 1.96/1.19 ( ( P @ Y5 )
% 1.96/1.19 => ( ord_le1742111550et_val @ Y5 @ X2 ) )
% 1.96/1.19 => ( Q @ X2 ) ) )
% 1.96/1.19 => ( Q @ ( order_544136439et_val @ P ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_157_GreatestI2__order,axiom,
% 1.96/1.19 ! [P: set_val > $o,X: set_val,Q: set_val > $o] :
% 1.96/1.19 ( ( P @ X )
% 1.96/1.19 => ( ! [Y3: set_val] :
% 1.96/1.19 ( ( P @ Y3 )
% 1.96/1.19 => ( ord_less_eq_set_val @ Y3 @ X ) )
% 1.96/1.19 => ( ! [X2: set_val] :
% 1.96/1.19 ( ( P @ X2 )
% 1.96/1.19 => ( ! [Y5: set_val] :
% 1.96/1.19 ( ( P @ Y5 )
% 1.96/1.19 => ( ord_less_eq_set_val @ Y5 @ X2 ) )
% 1.96/1.19 => ( Q @ X2 ) ) )
% 1.96/1.19 => ( Q @ ( order_1960465943et_val @ P ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_158_Greatest__equality,axiom,
% 1.96/1.19 ! [P: ( $o > set_val ) > $o,X: $o > set_val] :
% 1.96/1.19 ( ( P @ X )
% 1.96/1.19 => ( ! [Y3: $o > set_val] :
% 1.96/1.19 ( ( P @ Y3 )
% 1.96/1.19 => ( ord_le994826475et_val @ Y3 @ X ) )
% 1.96/1.19 => ( ( order_985126002et_val @ P )
% 1.96/1.19 = X ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_159_Greatest__equality,axiom,
% 1.96/1.19 ! [P: val > $o,X: val] :
% 1.96/1.19 ( ( P @ X )
% 1.96/1.19 => ( ! [Y3: val] :
% 1.96/1.19 ( ( P @ Y3 )
% 1.96/1.19 => ( ord_less_eq_val @ Y3 @ X ) )
% 1.96/1.19 => ( ( order_Greatest_val @ P )
% 1.96/1.19 = X ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_160_Greatest__equality,axiom,
% 1.96/1.19 ! [P: set_set_val > $o,X: set_set_val] :
% 1.96/1.19 ( ( P @ X )
% 1.96/1.19 => ( ! [Y3: set_set_val] :
% 1.96/1.19 ( ( P @ Y3 )
% 1.96/1.19 => ( ord_le1742111550et_val @ Y3 @ X ) )
% 1.96/1.19 => ( ( order_544136439et_val @ P )
% 1.96/1.19 = X ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_161_Greatest__equality,axiom,
% 1.96/1.19 ! [P: set_val > $o,X: set_val] :
% 1.96/1.19 ( ( P @ X )
% 1.96/1.19 => ( ! [Y3: set_val] :
% 1.96/1.19 ( ( P @ Y3 )
% 1.96/1.19 => ( ord_less_eq_set_val @ Y3 @ X ) )
% 1.96/1.19 => ( ( order_1960465943et_val @ P )
% 1.96/1.19 = X ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_162_Refine__Misc_Oif__mono,axiom,
% 1.96/1.19 ! [B3: $o,M1: $o > set_val,M12: $o > set_val,M2: $o > set_val,M22: $o > set_val] :
% 1.96/1.19 ( ( B3
% 1.96/1.19 => ( ord_le994826475et_val @ M1 @ M12 ) )
% 1.96/1.19 => ( ( ~ B3
% 1.96/1.19 => ( ord_le994826475et_val @ M2 @ M22 ) )
% 1.96/1.19 => ( ord_le994826475et_val @ ( if_o_set_val @ B3 @ M1 @ M2 ) @ ( if_o_set_val @ B3 @ M12 @ M22 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_163_Refine__Misc_Oif__mono,axiom,
% 1.96/1.19 ! [B3: $o,M1: val,M12: val,M2: val,M22: val] :
% 1.96/1.19 ( ( B3
% 1.96/1.19 => ( ord_less_eq_val @ M1 @ M12 ) )
% 1.96/1.19 => ( ( ~ B3
% 1.96/1.19 => ( ord_less_eq_val @ M2 @ M22 ) )
% 1.96/1.19 => ( ord_less_eq_val @ ( if_val @ B3 @ M1 @ M2 ) @ ( if_val @ B3 @ M12 @ M22 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_164_Refine__Misc_Oif__mono,axiom,
% 1.96/1.19 ! [B3: $o,M1: set_set_val,M12: set_set_val,M2: set_set_val,M22: set_set_val] :
% 1.96/1.19 ( ( B3
% 1.96/1.19 => ( ord_le1742111550et_val @ M1 @ M12 ) )
% 1.96/1.19 => ( ( ~ B3
% 1.96/1.19 => ( ord_le1742111550et_val @ M2 @ M22 ) )
% 1.96/1.19 => ( ord_le1742111550et_val @ ( if_set_set_val @ B3 @ M1 @ M2 ) @ ( if_set_set_val @ B3 @ M12 @ M22 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_165_Refine__Misc_Oif__mono,axiom,
% 1.96/1.19 ! [B3: $o,M1: set_val,M12: set_val,M2: set_val,M22: set_val] :
% 1.96/1.19 ( ( B3
% 1.96/1.19 => ( ord_less_eq_set_val @ M1 @ M12 ) )
% 1.96/1.19 => ( ( ~ B3
% 1.96/1.19 => ( ord_less_eq_set_val @ M2 @ M22 ) )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( if_set_val @ B3 @ M1 @ M2 ) @ ( if_set_val @ B3 @ M12 @ M22 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_166_lhs__step__If,axiom,
% 1.96/1.19 ! [B3: $o,T2: $o > set_val,M: $o > set_val,E: $o > set_val] :
% 1.96/1.19 ( ( B3
% 1.96/1.19 => ( ord_le994826475et_val @ T2 @ M ) )
% 1.96/1.19 => ( ( ~ B3
% 1.96/1.19 => ( ord_le994826475et_val @ E @ M ) )
% 1.96/1.19 => ( ord_le994826475et_val @ ( if_o_set_val @ B3 @ T2 @ E ) @ M ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_167_lhs__step__If,axiom,
% 1.96/1.19 ! [B3: $o,T2: val,M: val,E: val] :
% 1.96/1.19 ( ( B3
% 1.96/1.19 => ( ord_less_eq_val @ T2 @ M ) )
% 1.96/1.19 => ( ( ~ B3
% 1.96/1.19 => ( ord_less_eq_val @ E @ M ) )
% 1.96/1.19 => ( ord_less_eq_val @ ( if_val @ B3 @ T2 @ E ) @ M ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_168_lhs__step__If,axiom,
% 1.96/1.19 ! [B3: $o,T2: set_set_val,M: set_set_val,E: set_set_val] :
% 1.96/1.19 ( ( B3
% 1.96/1.19 => ( ord_le1742111550et_val @ T2 @ M ) )
% 1.96/1.19 => ( ( ~ B3
% 1.96/1.19 => ( ord_le1742111550et_val @ E @ M ) )
% 1.96/1.19 => ( ord_le1742111550et_val @ ( if_set_set_val @ B3 @ T2 @ E ) @ M ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_169_lhs__step__If,axiom,
% 1.96/1.19 ! [B3: $o,T2: set_val,M: set_val,E: set_val] :
% 1.96/1.19 ( ( B3
% 1.96/1.19 => ( ord_less_eq_set_val @ T2 @ M ) )
% 1.96/1.19 => ( ( ~ B3
% 1.96/1.19 => ( ord_less_eq_set_val @ E @ M ) )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( if_set_val @ B3 @ T2 @ E ) @ M ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_170_verit__la__disequality,axiom,
% 1.96/1.19 ! [A3: val,B3: val] :
% 1.96/1.19 ( ( A3 = B3 )
% 1.96/1.19 | ~ ( ord_less_eq_val @ A3 @ B3 )
% 1.96/1.19 | ~ ( ord_less_eq_val @ B3 @ A3 ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_171_le__rel__bool__arg__iff,axiom,
% 1.96/1.19 ( ord_le1441829300et_val
% 1.96/1.19 = ( ^ [X4: $o > $o > set_val,Y6: $o > $o > set_val] :
% 1.96/1.19 ( ( ord_le994826475et_val @ ( X4 @ $false ) @ ( Y6 @ $false ) )
% 1.96/1.19 & ( ord_le994826475et_val @ ( X4 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_172_le__rel__bool__arg__iff,axiom,
% 1.96/1.19 ( ord_less_eq_o_val
% 1.96/1.19 = ( ^ [X4: $o > val,Y6: $o > val] :
% 1.96/1.19 ( ( ord_less_eq_val @ ( X4 @ $false ) @ ( Y6 @ $false ) )
% 1.96/1.19 & ( ord_less_eq_val @ ( X4 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_173_le__rel__bool__arg__iff,axiom,
% 1.96/1.19 ( ord_le936627147et_val
% 1.96/1.19 = ( ^ [X4: $o > set_set_val,Y6: $o > set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ ( X4 @ $false ) @ ( Y6 @ $false ) )
% 1.96/1.19 & ( ord_le1742111550et_val @ ( X4 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_174_le__rel__bool__arg__iff,axiom,
% 1.96/1.19 ( ord_le994826475et_val
% 1.96/1.19 = ( ^ [X4: $o > set_val,Y6: $o > set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ ( X4 @ $false ) @ ( Y6 @ $false ) )
% 1.96/1.19 & ( ord_less_eq_set_val @ ( X4 @ $true ) @ ( Y6 @ $true ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_175_antimonoD,axiom,
% 1.96/1.19 ! [F: set_val > set_val,X: set_val,Y2: set_val] :
% 1.96/1.19 ( ( order_1719375026et_val @ F )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ X @ Y2 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_176_antimonoD,axiom,
% 1.96/1.19 ! [F: val > val,X: val,Y2: val] :
% 1.96/1.19 ( ( order_1689798834al_val @ F )
% 1.96/1.19 => ( ( ord_less_eq_val @ X @ Y2 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_177_antimonoD,axiom,
% 1.96/1.19 ! [F: set_val > val,X: set_val,Y2: set_val] :
% 1.96/1.19 ( ( order_1375876562al_val @ F )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ X @ Y2 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_178_antimonoD,axiom,
% 1.96/1.19 ! [F: val > set_val,X: val,Y2: val] :
% 1.96/1.19 ( ( order_1484138386et_val @ F )
% 1.96/1.19 => ( ( ord_less_eq_val @ X @ Y2 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_179_antimonoD,axiom,
% 1.96/1.19 ! [F: val > set_set_val,X: val,Y2: val] :
% 1.96/1.19 ( ( order_1945059954et_val @ F )
% 1.96/1.19 => ( ( ord_less_eq_val @ X @ Y2 )
% 1.96/1.19 => ( ord_le1742111550et_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_180_antimonoD,axiom,
% 1.96/1.19 ! [F: set_set_val > val,X: set_set_val,Y2: set_set_val] :
% 1.96/1.19 ( ( order_1520822002al_val @ F )
% 1.96/1.19 => ( ( ord_le1742111550et_val @ X @ Y2 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_181_antimonoD,axiom,
% 1.96/1.19 ! [F: set_val > set_set_val,X: set_val,Y2: set_val] :
% 1.96/1.19 ( ( order_1957703570et_val @ F )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ X @ Y2 )
% 1.96/1.19 => ( ord_le1742111550et_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_182_antimonoD,axiom,
% 1.96/1.19 ! [F: ( $o > set_val ) > val,X: $o > set_val,Y2: $o > set_val] :
% 1.96/1.19 ( ( order_23236447al_val @ F )
% 1.96/1.19 => ( ( ord_le994826475et_val @ X @ Y2 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_183_antimonoD,axiom,
% 1.96/1.19 ! [F: val > $o > set_val,X: val,Y2: val] :
% 1.96/1.19 ( ( order_255079095et_val @ F )
% 1.96/1.19 => ( ( ord_less_eq_val @ X @ Y2 )
% 1.96/1.19 => ( ord_le994826475et_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_184_antimonoD,axiom,
% 1.96/1.19 ! [F: set_set_val > set_val,X: set_set_val,Y2: set_set_val] :
% 1.96/1.19 ( ( order_650823122et_val @ F )
% 1.96/1.19 => ( ( ord_le1742111550et_val @ X @ Y2 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_185_antimonoE,axiom,
% 1.96/1.19 ! [F: set_val > set_val,X: set_val,Y2: set_val] :
% 1.96/1.19 ( ( order_1719375026et_val @ F )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ X @ Y2 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_186_antimonoE,axiom,
% 1.96/1.19 ! [F: val > val,X: val,Y2: val] :
% 1.96/1.19 ( ( order_1689798834al_val @ F )
% 1.96/1.19 => ( ( ord_less_eq_val @ X @ Y2 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_187_antimonoE,axiom,
% 1.96/1.19 ! [F: set_val > val,X: set_val,Y2: set_val] :
% 1.96/1.19 ( ( order_1375876562al_val @ F )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ X @ Y2 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_188_antimonoE,axiom,
% 1.96/1.19 ! [F: val > set_val,X: val,Y2: val] :
% 1.96/1.19 ( ( order_1484138386et_val @ F )
% 1.96/1.19 => ( ( ord_less_eq_val @ X @ Y2 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_189_antimonoE,axiom,
% 1.96/1.19 ! [F: val > set_set_val,X: val,Y2: val] :
% 1.96/1.19 ( ( order_1945059954et_val @ F )
% 1.96/1.19 => ( ( ord_less_eq_val @ X @ Y2 )
% 1.96/1.19 => ( ord_le1742111550et_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_190_antimonoE,axiom,
% 1.96/1.19 ! [F: set_set_val > val,X: set_set_val,Y2: set_set_val] :
% 1.96/1.19 ( ( order_1520822002al_val @ F )
% 1.96/1.19 => ( ( ord_le1742111550et_val @ X @ Y2 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_191_antimonoE,axiom,
% 1.96/1.19 ! [F: set_val > set_set_val,X: set_val,Y2: set_val] :
% 1.96/1.19 ( ( order_1957703570et_val @ F )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ X @ Y2 )
% 1.96/1.19 => ( ord_le1742111550et_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_192_antimonoE,axiom,
% 1.96/1.19 ! [F: ( $o > set_val ) > val,X: $o > set_val,Y2: $o > set_val] :
% 1.96/1.19 ( ( order_23236447al_val @ F )
% 1.96/1.19 => ( ( ord_le994826475et_val @ X @ Y2 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_193_antimonoE,axiom,
% 1.96/1.19 ! [F: val > $o > set_val,X: val,Y2: val] :
% 1.96/1.19 ( ( order_255079095et_val @ F )
% 1.96/1.19 => ( ( ord_less_eq_val @ X @ Y2 )
% 1.96/1.19 => ( ord_le994826475et_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_194_antimonoE,axiom,
% 1.96/1.19 ! [F: set_set_val > set_val,X: set_set_val,Y2: set_set_val] :
% 1.96/1.19 ( ( order_650823122et_val @ F )
% 1.96/1.19 => ( ( ord_le1742111550et_val @ X @ Y2 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ Y2 ) @ ( F @ X ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_195_antimono__def,axiom,
% 1.96/1.19 ( order_1719375026et_val
% 1.96/1.19 = ( ^ [F2: set_val > set_val] :
% 1.96/1.19 ! [X3: set_val,Y4: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X3 @ Y4 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_196_antimono__def,axiom,
% 1.96/1.19 ( order_1689798834al_val
% 1.96/1.19 = ( ^ [F2: val > val] :
% 1.96/1.19 ! [X3: val,Y4: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X3 @ Y4 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_197_antimono__def,axiom,
% 1.96/1.19 ( order_1375876562al_val
% 1.96/1.19 = ( ^ [F2: set_val > val] :
% 1.96/1.19 ! [X3: set_val,Y4: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X3 @ Y4 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_198_antimono__def,axiom,
% 1.96/1.19 ( order_1484138386et_val
% 1.96/1.19 = ( ^ [F2: val > set_val] :
% 1.96/1.19 ! [X3: val,Y4: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X3 @ Y4 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_199_antimono__def,axiom,
% 1.96/1.19 ( order_1945059954et_val
% 1.96/1.19 = ( ^ [F2: val > set_set_val] :
% 1.96/1.19 ! [X3: val,Y4: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X3 @ Y4 )
% 1.96/1.19 => ( ord_le1742111550et_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_200_antimono__def,axiom,
% 1.96/1.19 ( order_1520822002al_val
% 1.96/1.19 = ( ^ [F2: set_set_val > val] :
% 1.96/1.19 ! [X3: set_set_val,Y4: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ X3 @ Y4 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_201_antimono__def,axiom,
% 1.96/1.19 ( order_1957703570et_val
% 1.96/1.19 = ( ^ [F2: set_val > set_set_val] :
% 1.96/1.19 ! [X3: set_val,Y4: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X3 @ Y4 )
% 1.96/1.19 => ( ord_le1742111550et_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_202_antimono__def,axiom,
% 1.96/1.19 ( order_23236447al_val
% 1.96/1.19 = ( ^ [F2: ( $o > set_val ) > val] :
% 1.96/1.19 ! [X3: $o > set_val,Y4: $o > set_val] :
% 1.96/1.19 ( ( ord_le994826475et_val @ X3 @ Y4 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_203_antimono__def,axiom,
% 1.96/1.19 ( order_255079095et_val
% 1.96/1.19 = ( ^ [F2: val > $o > set_val] :
% 1.96/1.19 ! [X3: val,Y4: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X3 @ Y4 )
% 1.96/1.19 => ( ord_le994826475et_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_204_antimono__def,axiom,
% 1.96/1.19 ( order_650823122et_val
% 1.96/1.19 = ( ^ [F2: set_set_val > set_val] :
% 1.96/1.19 ! [X3: set_set_val,Y4: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ X3 @ Y4 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F2 @ Y4 ) @ ( F2 @ X3 ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_205_antimonoI,axiom,
% 1.96/1.19 ! [F: set_val > set_val] :
% 1.96/1.19 ( ! [X2: set_val,Y3: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 1.96/1.19 => ( order_1719375026et_val @ F ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_206_antimonoI,axiom,
% 1.96/1.19 ! [F: val > val] :
% 1.96/1.19 ( ! [X2: val,Y3: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 1.96/1.19 => ( order_1689798834al_val @ F ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_207_antimonoI,axiom,
% 1.96/1.19 ! [F: set_val > val] :
% 1.96/1.19 ( ! [X2: set_val,Y3: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 1.96/1.19 => ( order_1375876562al_val @ F ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_208_antimonoI,axiom,
% 1.96/1.19 ! [F: val > set_val] :
% 1.96/1.19 ( ! [X2: val,Y3: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 1.96/1.19 => ( order_1484138386et_val @ F ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_209_antimonoI,axiom,
% 1.96/1.19 ! [F: val > set_set_val] :
% 1.96/1.19 ( ! [X2: val,Y3: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_le1742111550et_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 1.96/1.19 => ( order_1945059954et_val @ F ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_210_antimonoI,axiom,
% 1.96/1.19 ! [F: set_set_val > val] :
% 1.96/1.19 ( ! [X2: set_set_val,Y3: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 1.96/1.19 => ( order_1520822002al_val @ F ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_211_antimonoI,axiom,
% 1.96/1.19 ! [F: set_val > set_set_val] :
% 1.96/1.19 ( ! [X2: set_val,Y3: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_le1742111550et_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 1.96/1.19 => ( order_1957703570et_val @ F ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_212_antimonoI,axiom,
% 1.96/1.19 ! [F: ( $o > set_val ) > val] :
% 1.96/1.19 ( ! [X2: $o > set_val,Y3: $o > set_val] :
% 1.96/1.19 ( ( ord_le994826475et_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 1.96/1.19 => ( order_23236447al_val @ F ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_213_antimonoI,axiom,
% 1.96/1.19 ! [F: val > $o > set_val] :
% 1.96/1.19 ( ! [X2: val,Y3: val] :
% 1.96/1.19 ( ( ord_less_eq_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_le994826475et_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 1.96/1.19 => ( order_255079095et_val @ F ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_214_antimonoI,axiom,
% 1.96/1.19 ! [F: set_set_val > set_val] :
% 1.96/1.19 ( ! [X2: set_set_val,Y3: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 1.96/1.19 => ( order_650823122et_val @ F ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_215_order__mono__setup_Omono__setup__loc__axioms,axiom,
% 1.96/1.19 refine16560100et_val @ ord_le994826475et_val ).
% 1.96/1.19
% 1.96/1.19 thf(fact_216_order__mono__setup_Omono__setup__loc__axioms,axiom,
% 1.96/1.19 refine67622213oc_val @ ord_less_eq_val ).
% 1.96/1.19
% 1.96/1.19 thf(fact_217_order__mono__setup_Omono__setup__loc__axioms,axiom,
% 1.96/1.19 refine1506227973et_val @ ord_le1742111550et_val ).
% 1.96/1.19
% 1.96/1.19 thf(fact_218_order__mono__setup_Omono__setup__loc__axioms,axiom,
% 1.96/1.19 refine275900453et_val @ ord_less_eq_set_val ).
% 1.96/1.19
% 1.96/1.19 thf(fact_219_galois__connection_O_092_060gamma_062_092_060alpha_062__infl,axiom,
% 1.96/1.19 ! [Alpha: set_val > set_val,Gamma: set_val > set_val,X: set_val] :
% 1.96/1.19 ( ( refine1929691018et_val @ Alpha @ Gamma )
% 1.96/1.19 => ( ord_less_eq_set_val @ X @ ( Gamma @ ( Alpha @ X ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_220_galois__connection_O_092_060alpha_062_092_060gamma_062__defl,axiom,
% 1.96/1.19 ! [Alpha: set_val > set_val,Gamma: set_val > set_val,X: set_val] :
% 1.96/1.19 ( ( refine1929691018et_val @ Alpha @ Gamma )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( Alpha @ ( Gamma @ X ) ) @ X ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_221_galois__connection_Ogalois,axiom,
% 1.96/1.19 ! [Alpha: set_val > $o > set_val,Gamma: ( $o > set_val ) > set_val,C: set_val,A3: $o > set_val] :
% 1.96/1.19 ( ( refine51544255et_val @ Alpha @ Gamma )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ C @ ( Gamma @ A3 ) )
% 1.96/1.19 = ( ord_le994826475et_val @ ( Alpha @ C ) @ A3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_222_galois__connection_Ogalois,axiom,
% 1.96/1.19 ! [Alpha: set_val > set_set_val,Gamma: set_set_val > set_val,C: set_val,A3: set_set_val] :
% 1.96/1.19 ( ( refine1315043946et_val @ Alpha @ Gamma )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ C @ ( Gamma @ A3 ) )
% 1.96/1.19 = ( ord_le1742111550et_val @ ( Alpha @ C ) @ A3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_223_galois__connection_Ogalois,axiom,
% 1.96/1.19 ! [Alpha: ( $o > set_val ) > set_val,Gamma: set_val > $o > set_val,C: $o > set_val,A3: set_val] :
% 1.96/1.19 ( ( refine1948536167et_val @ Alpha @ Gamma )
% 1.96/1.19 => ( ( ord_le994826475et_val @ C @ ( Gamma @ A3 ) )
% 1.96/1.19 = ( ord_less_eq_set_val @ ( Alpha @ C ) @ A3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_224_galois__connection_Ogalois,axiom,
% 1.96/1.19 ! [Alpha: ( $o > set_val ) > $o > set_val,Gamma: ( $o > set_val ) > $o > set_val,C: $o > set_val,A3: $o > set_val] :
% 1.96/1.19 ( ( refine1924899106et_val @ Alpha @ Gamma )
% 1.96/1.19 => ( ( ord_le994826475et_val @ C @ ( Gamma @ A3 ) )
% 1.96/1.19 = ( ord_le994826475et_val @ ( Alpha @ C ) @ A3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_225_galois__connection_Ogalois,axiom,
% 1.96/1.19 ! [Alpha: ( $o > set_val ) > set_set_val,Gamma: set_set_val > $o > set_val,C: $o > set_val,A3: set_set_val] :
% 1.96/1.19 ( ( refine1169396807et_val @ Alpha @ Gamma )
% 1.96/1.19 => ( ( ord_le994826475et_val @ C @ ( Gamma @ A3 ) )
% 1.96/1.19 = ( ord_le1742111550et_val @ ( Alpha @ C ) @ A3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_226_galois__connection_Ogalois,axiom,
% 1.96/1.19 ! [Alpha: set_set_val > set_val,Gamma: set_val > set_set_val,C: set_set_val,A3: set_val] :
% 1.96/1.19 ( ( refine8163498et_val @ Alpha @ Gamma )
% 1.96/1.19 => ( ( ord_le1742111550et_val @ C @ ( Gamma @ A3 ) )
% 1.96/1.19 = ( ord_less_eq_set_val @ ( Alpha @ C ) @ A3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_227_galois__connection_Ogalois,axiom,
% 1.96/1.19 ! [Alpha: set_set_val > $o > set_val,Gamma: ( $o > set_val ) > set_set_val,C: set_set_val,A3: $o > set_val] :
% 1.96/1.19 ( ( refine86398879et_val @ Alpha @ Gamma )
% 1.96/1.19 => ( ( ord_le1742111550et_val @ C @ ( Gamma @ A3 ) )
% 1.96/1.19 = ( ord_le994826475et_val @ ( Alpha @ C ) @ A3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_228_galois__connection_Ogalois,axiom,
% 1.96/1.19 ! [Alpha: set_set_val > set_set_val,Gamma: set_set_val > set_set_val,C: set_set_val,A3: set_set_val] :
% 1.96/1.19 ( ( refine855985034et_val @ Alpha @ Gamma )
% 1.96/1.19 => ( ( ord_le1742111550et_val @ C @ ( Gamma @ A3 ) )
% 1.96/1.19 = ( ord_le1742111550et_val @ ( Alpha @ C ) @ A3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_229_galois__connection_Ogalois,axiom,
% 1.96/1.19 ! [Alpha: set_val > set_val,Gamma: set_val > set_val,C: set_val,A3: set_val] :
% 1.96/1.19 ( ( refine1929691018et_val @ Alpha @ Gamma )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ C @ ( Gamma @ A3 ) )
% 1.96/1.19 = ( ord_less_eq_set_val @ ( Alpha @ C ) @ A3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_230_galois__connection_Ointro,axiom,
% 1.96/1.19 ! [Gamma: ( $o > set_val ) > set_val,Alpha: set_val > $o > set_val] :
% 1.96/1.19 ( ! [C3: set_val,A5: $o > set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ C3 @ ( Gamma @ A5 ) )
% 1.96/1.19 = ( ord_le994826475et_val @ ( Alpha @ C3 ) @ A5 ) )
% 1.96/1.19 => ( refine51544255et_val @ Alpha @ Gamma ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_231_galois__connection_Ointro,axiom,
% 1.96/1.19 ! [Gamma: set_set_val > set_val,Alpha: set_val > set_set_val] :
% 1.96/1.19 ( ! [C3: set_val,A5: set_set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ C3 @ ( Gamma @ A5 ) )
% 1.96/1.19 = ( ord_le1742111550et_val @ ( Alpha @ C3 ) @ A5 ) )
% 1.96/1.19 => ( refine1315043946et_val @ Alpha @ Gamma ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_232_galois__connection_Ointro,axiom,
% 1.96/1.19 ! [Gamma: set_val > $o > set_val,Alpha: ( $o > set_val ) > set_val] :
% 1.96/1.19 ( ! [C3: $o > set_val,A5: set_val] :
% 1.96/1.19 ( ( ord_le994826475et_val @ C3 @ ( Gamma @ A5 ) )
% 1.96/1.19 = ( ord_less_eq_set_val @ ( Alpha @ C3 ) @ A5 ) )
% 1.96/1.19 => ( refine1948536167et_val @ Alpha @ Gamma ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_233_galois__connection_Ointro,axiom,
% 1.96/1.19 ! [Gamma: ( $o > set_val ) > $o > set_val,Alpha: ( $o > set_val ) > $o > set_val] :
% 1.96/1.19 ( ! [C3: $o > set_val,A5: $o > set_val] :
% 1.96/1.19 ( ( ord_le994826475et_val @ C3 @ ( Gamma @ A5 ) )
% 1.96/1.19 = ( ord_le994826475et_val @ ( Alpha @ C3 ) @ A5 ) )
% 1.96/1.19 => ( refine1924899106et_val @ Alpha @ Gamma ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_234_galois__connection_Ointro,axiom,
% 1.96/1.19 ! [Gamma: set_set_val > $o > set_val,Alpha: ( $o > set_val ) > set_set_val] :
% 1.96/1.19 ( ! [C3: $o > set_val,A5: set_set_val] :
% 1.96/1.19 ( ( ord_le994826475et_val @ C3 @ ( Gamma @ A5 ) )
% 1.96/1.19 = ( ord_le1742111550et_val @ ( Alpha @ C3 ) @ A5 ) )
% 1.96/1.19 => ( refine1169396807et_val @ Alpha @ Gamma ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_235_galois__connection_Ointro,axiom,
% 1.96/1.19 ! [Gamma: set_val > set_set_val,Alpha: set_set_val > set_val] :
% 1.96/1.19 ( ! [C3: set_set_val,A5: set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ C3 @ ( Gamma @ A5 ) )
% 1.96/1.19 = ( ord_less_eq_set_val @ ( Alpha @ C3 ) @ A5 ) )
% 1.96/1.19 => ( refine8163498et_val @ Alpha @ Gamma ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_236_galois__connection_Ointro,axiom,
% 1.96/1.19 ! [Gamma: ( $o > set_val ) > set_set_val,Alpha: set_set_val > $o > set_val] :
% 1.96/1.19 ( ! [C3: set_set_val,A5: $o > set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ C3 @ ( Gamma @ A5 ) )
% 1.96/1.19 = ( ord_le994826475et_val @ ( Alpha @ C3 ) @ A5 ) )
% 1.96/1.19 => ( refine86398879et_val @ Alpha @ Gamma ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_237_galois__connection_Ointro,axiom,
% 1.96/1.19 ! [Gamma: set_set_val > set_set_val,Alpha: set_set_val > set_set_val] :
% 1.96/1.19 ( ! [C3: set_set_val,A5: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ C3 @ ( Gamma @ A5 ) )
% 1.96/1.19 = ( ord_le1742111550et_val @ ( Alpha @ C3 ) @ A5 ) )
% 1.96/1.19 => ( refine855985034et_val @ Alpha @ Gamma ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_238_galois__connection_Ointro,axiom,
% 1.96/1.19 ! [Gamma: set_val > set_val,Alpha: set_val > set_val] :
% 1.96/1.19 ( ! [C3: set_val,A5: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ C3 @ ( Gamma @ A5 ) )
% 1.96/1.19 = ( ord_less_eq_set_val @ ( Alpha @ C3 ) @ A5 ) )
% 1.96/1.19 => ( refine1929691018et_val @ Alpha @ Gamma ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_239_galois__connection__def,axiom,
% 1.96/1.19 ( refine51544255et_val
% 1.96/1.19 = ( ^ [Alpha2: set_val > $o > set_val,Gamma2: ( $o > set_val ) > set_val] :
% 1.96/1.19 ! [C4: set_val,A4: $o > set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ C4 @ ( Gamma2 @ A4 ) )
% 1.96/1.19 = ( ord_le994826475et_val @ ( Alpha2 @ C4 ) @ A4 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_240_galois__connection__def,axiom,
% 1.96/1.19 ( refine1315043946et_val
% 1.96/1.19 = ( ^ [Alpha2: set_val > set_set_val,Gamma2: set_set_val > set_val] :
% 1.96/1.19 ! [C4: set_val,A4: set_set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ C4 @ ( Gamma2 @ A4 ) )
% 1.96/1.19 = ( ord_le1742111550et_val @ ( Alpha2 @ C4 ) @ A4 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_241_galois__connection__def,axiom,
% 1.96/1.19 ( refine1948536167et_val
% 1.96/1.19 = ( ^ [Alpha2: ( $o > set_val ) > set_val,Gamma2: set_val > $o > set_val] :
% 1.96/1.19 ! [C4: $o > set_val,A4: set_val] :
% 1.96/1.19 ( ( ord_le994826475et_val @ C4 @ ( Gamma2 @ A4 ) )
% 1.96/1.19 = ( ord_less_eq_set_val @ ( Alpha2 @ C4 ) @ A4 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_242_galois__connection__def,axiom,
% 1.96/1.19 ( refine1924899106et_val
% 1.96/1.19 = ( ^ [Alpha2: ( $o > set_val ) > $o > set_val,Gamma2: ( $o > set_val ) > $o > set_val] :
% 1.96/1.19 ! [C4: $o > set_val,A4: $o > set_val] :
% 1.96/1.19 ( ( ord_le994826475et_val @ C4 @ ( Gamma2 @ A4 ) )
% 1.96/1.19 = ( ord_le994826475et_val @ ( Alpha2 @ C4 ) @ A4 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_243_galois__connection__def,axiom,
% 1.96/1.19 ( refine1169396807et_val
% 1.96/1.19 = ( ^ [Alpha2: ( $o > set_val ) > set_set_val,Gamma2: set_set_val > $o > set_val] :
% 1.96/1.19 ! [C4: $o > set_val,A4: set_set_val] :
% 1.96/1.19 ( ( ord_le994826475et_val @ C4 @ ( Gamma2 @ A4 ) )
% 1.96/1.19 = ( ord_le1742111550et_val @ ( Alpha2 @ C4 ) @ A4 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_244_galois__connection__def,axiom,
% 1.96/1.19 ( refine8163498et_val
% 1.96/1.19 = ( ^ [Alpha2: set_set_val > set_val,Gamma2: set_val > set_set_val] :
% 1.96/1.19 ! [C4: set_set_val,A4: set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ C4 @ ( Gamma2 @ A4 ) )
% 1.96/1.19 = ( ord_less_eq_set_val @ ( Alpha2 @ C4 ) @ A4 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_245_galois__connection__def,axiom,
% 1.96/1.19 ( refine86398879et_val
% 1.96/1.19 = ( ^ [Alpha2: set_set_val > $o > set_val,Gamma2: ( $o > set_val ) > set_set_val] :
% 1.96/1.19 ! [C4: set_set_val,A4: $o > set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ C4 @ ( Gamma2 @ A4 ) )
% 1.96/1.19 = ( ord_le994826475et_val @ ( Alpha2 @ C4 ) @ A4 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_246_galois__connection__def,axiom,
% 1.96/1.19 ( refine855985034et_val
% 1.96/1.19 = ( ^ [Alpha2: set_set_val > set_set_val,Gamma2: set_set_val > set_set_val] :
% 1.96/1.19 ! [C4: set_set_val,A4: set_set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ C4 @ ( Gamma2 @ A4 ) )
% 1.96/1.19 = ( ord_le1742111550et_val @ ( Alpha2 @ C4 ) @ A4 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_247_galois__connection__def,axiom,
% 1.96/1.19 ( refine1929691018et_val
% 1.96/1.19 = ( ^ [Alpha2: set_val > set_val,Gamma2: set_val > set_val] :
% 1.96/1.19 ! [C4: set_val,A4: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ C4 @ ( Gamma2 @ A4 ) )
% 1.96/1.19 = ( ord_less_eq_set_val @ ( Alpha2 @ C4 ) @ A4 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_248_mono__setup__loc__def,axiom,
% 1.96/1.19 ( refine275900453et_val
% 1.96/1.19 = ( ^ [Le: set_val > set_val > $o] :
% 1.96/1.19 ! [X3: set_val] : ( Le @ X3 @ X3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_249_mono__setup__loc_Orefl,axiom,
% 1.96/1.19 ! [Le2: set_val > set_val > $o,X: set_val] :
% 1.96/1.19 ( ( refine275900453et_val @ Le2 )
% 1.96/1.19 => ( Le2 @ X @ X ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_250_mono__setup__loc_Ointro,axiom,
% 1.96/1.19 ! [Le2: set_val > set_val > $o] :
% 1.96/1.19 ( ! [X2: set_val] : ( Le2 @ X2 @ X2 )
% 1.96/1.19 => ( refine275900453et_val @ Le2 ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_251_mono__setup__loc_Omono__if,axiom,
% 1.96/1.19 ! [Le2: set_val > set_val > $o,T2: set_val,T3: set_val,E: set_val,E2: set_val,B3: $o] :
% 1.96/1.19 ( ( refine275900453et_val @ Le2 )
% 1.96/1.19 => ( ( Le2 @ T2 @ T3 )
% 1.96/1.19 => ( ( Le2 @ E @ E2 )
% 1.96/1.19 => ( Le2 @ ( if_set_val @ B3 @ T2 @ E ) @ ( if_set_val @ B3 @ T3 @ E2 ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_252_galois__connection_Oinf__dist___092_060alpha_062,axiom,
% 1.96/1.19 ! [Alpha: set_val > set_val,Gamma: set_val > set_val] :
% 1.96/1.19 ( ( refine1929691018et_val @ Alpha @ Gamma )
% 1.96/1.19 => ( refine2057434761et_val @ Alpha ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_253_strict__mono__less__eq,axiom,
% 1.96/1.19 ! [F: val > set_val,X: val,Y2: val] :
% 1.96/1.19 ( ( order_99134233et_val @ F )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ ( F @ X ) @ ( F @ Y2 ) )
% 1.96/1.19 = ( ord_less_eq_val @ X @ Y2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_254_strict__mono__less__eq,axiom,
% 1.96/1.19 ! [F: val > $o > set_val,X: val,Y2: val] :
% 1.96/1.19 ( ( order_1205732848et_val @ F )
% 1.96/1.19 => ( ( ord_le994826475et_val @ ( F @ X ) @ ( F @ Y2 ) )
% 1.96/1.19 = ( ord_less_eq_val @ X @ Y2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_255_strict__mono__less__eq,axiom,
% 1.96/1.19 ! [F: val > val,X: val,Y2: val] :
% 1.96/1.19 ( ( order_1139042361al_val @ F )
% 1.96/1.19 => ( ( ord_less_eq_val @ ( F @ X ) @ ( F @ Y2 ) )
% 1.96/1.19 = ( ord_less_eq_val @ X @ Y2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_256_strict__mono__less__eq,axiom,
% 1.96/1.19 ! [F: val > set_set_val,X: val,Y2: val] :
% 1.96/1.19 ( ( order_68692473et_val @ F )
% 1.96/1.19 => ( ( ord_le1742111550et_val @ ( F @ X ) @ ( F @ Y2 ) )
% 1.96/1.19 = ( ord_less_eq_val @ X @ Y2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_257_greaterThan__subset__iff,axiom,
% 1.96/1.19 ! [X: val,Y2: val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ ( set_or1288365508an_val @ X ) @ ( set_or1288365508an_val @ Y2 ) )
% 1.96/1.19 = ( ord_less_eq_val @ Y2 @ X ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_258_START__REFINEG__TRANSFER,axiom,
% 1.96/1.19 ! [D: $o > set_val,C: $o > set_val,A3: $o > set_val] :
% 1.96/1.19 ( ( refine1593386065et_val @ D @ C )
% 1.96/1.19 => ( ( ord_le994826475et_val @ C @ A3 )
% 1.96/1.19 => ( ( refine511606705et_val @ C @ D )
% 1.96/1.19 => ( ord_le994826475et_val @ D @ A3 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_259_START__REFINEG__TRANSFER,axiom,
% 1.96/1.19 ! [D: val,C: val,A3: val] :
% 1.96/1.19 ( ( refine2021912633al_val @ D @ C )
% 1.96/1.19 => ( ( ord_less_eq_val @ C @ A3 )
% 1.96/1.19 => ( ( refine403244856MP_val @ C @ D )
% 1.96/1.19 => ( ord_less_eq_val @ D @ A3 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_260_START__REFINEG__TRANSFER,axiom,
% 1.96/1.19 ! [D: set_set_val,C: set_set_val,A3: set_set_val] :
% 1.96/1.19 ( ( refine1034950713et_val @ D @ C )
% 1.96/1.19 => ( ( ord_le1742111550et_val @ C @ A3 )
% 1.96/1.19 => ( ( refine1908789496et_val @ C @ D )
% 1.96/1.19 => ( ord_le1742111550et_val @ D @ A3 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_261_START__REFINEG__TRANSFER,axiom,
% 1.96/1.19 ! [D: set_val,C: set_val,A3: set_val] :
% 1.96/1.19 ( ( refine654574649et_val @ D @ C )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ C @ A3 )
% 1.96/1.19 => ( ( refine1893322264et_val @ C @ D )
% 1.96/1.19 => ( ord_less_eq_set_val @ D @ A3 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_262_lessThan__subset__iff,axiom,
% 1.96/1.19 ! [X: val,Y2: val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ ( set_ord_lessThan_val @ X ) @ ( set_ord_lessThan_val @ Y2 ) )
% 1.96/1.19 = ( ord_less_eq_val @ X @ Y2 ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_263_atLeast__subset__iff,axiom,
% 1.96/1.19 ! [X: set_set_val,Y2: set_set_val] :
% 1.96/1.19 ( ( ord_le1135847966et_val @ ( set_or1337784553et_val @ X ) @ ( set_or1337784553et_val @ Y2 ) )
% 1.96/1.19 = ( ord_le1742111550et_val @ Y2 @ X ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_264_atLeast__subset__iff,axiom,
% 1.96/1.19 ! [X: set_val,Y2: set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ ( set_or650197513et_val @ X ) @ ( set_or650197513et_val @ Y2 ) )
% 1.96/1.19 = ( ord_less_eq_set_val @ Y2 @ X ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_265_atLeast__subset__iff,axiom,
% 1.96/1.19 ! [X: val,Y2: val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ ( set_ord_atLeast_val @ X ) @ ( set_ord_atLeast_val @ Y2 ) )
% 1.96/1.19 = ( ord_less_eq_val @ Y2 @ X ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_266_atLeast__iff,axiom,
% 1.96/1.19 ! [I: val,K: val] :
% 1.96/1.19 ( ( member_val @ I @ ( set_ord_atLeast_val @ K ) )
% 1.96/1.19 = ( ord_less_eq_val @ K @ I ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_267_atLeast__iff,axiom,
% 1.96/1.19 ! [I: set_val,K: set_val] :
% 1.96/1.19 ( ( member_set_val @ I @ ( set_or650197513et_val @ K ) )
% 1.96/1.19 = ( ord_less_eq_set_val @ K @ I ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_268_Ioi__le__Ico,axiom,
% 1.96/1.19 ! [A3: val] : ( ord_less_eq_set_val @ ( set_or1288365508an_val @ A3 ) @ ( set_ord_atLeast_val @ A3 ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_269_Ici__subset__Ioi__iff,axiom,
% 1.96/1.19 ! [A3: val,B3: val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ ( set_ord_atLeast_val @ A3 ) @ ( set_or1288365508an_val @ B3 ) )
% 1.96/1.19 = ( ord_less_val @ B3 @ A3 ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_270_Icc__subset__Ici__iff,axiom,
% 1.96/1.19 ! [L: set_val,H: set_val,L2: set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ ( set_or1554624499et_val @ L @ H ) @ ( set_or650197513et_val @ L2 ) )
% 1.96/1.19 = ( ~ ( ord_less_eq_set_val @ L @ H )
% 1.96/1.19 | ( ord_less_eq_set_val @ L2 @ L ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_271_Icc__subset__Ici__iff,axiom,
% 1.96/1.19 ! [L: val,H: val,L2: val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ ( set_or18208019st_val @ L @ H ) @ ( set_ord_atLeast_val @ L2 ) )
% 1.96/1.19 = ( ~ ( ord_less_eq_val @ L @ H )
% 1.96/1.19 | ( ord_less_eq_val @ L2 @ L ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_272_atMost__subset__iff,axiom,
% 1.96/1.19 ! [X: set_val,Y2: set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ ( set_or867701765et_val @ X ) @ ( set_or867701765et_val @ Y2 ) )
% 1.96/1.19 = ( ord_less_eq_set_val @ X @ Y2 ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_273_atMost__subset__iff,axiom,
% 1.96/1.19 ! [X: val,Y2: val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ ( set_ord_atMost_val @ X ) @ ( set_ord_atMost_val @ Y2 ) )
% 1.96/1.19 = ( ord_less_eq_val @ X @ Y2 ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_274_psubsetI,axiom,
% 1.96/1.19 ! [A: set_val,B: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A @ B )
% 1.96/1.19 => ( ( A != B )
% 1.96/1.19 => ( ord_less_set_val @ A @ B ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_275_ComplI,axiom,
% 1.96/1.19 ! [C: val,A: set_val] :
% 1.96/1.19 ( ~ ( member_val @ C @ A )
% 1.96/1.19 => ( member_val @ C @ ( uminus1961393973et_val @ A ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_276_Compl__iff,axiom,
% 1.96/1.19 ! [C: val,A: set_val] :
% 1.96/1.19 ( ( member_val @ C @ ( uminus1961393973et_val @ A ) )
% 1.96/1.19 = ( ~ ( member_val @ C @ A ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_277_atLeastAtMost__iff,axiom,
% 1.96/1.19 ! [I: val,L: val,U: val] :
% 1.96/1.19 ( ( member_val @ I @ ( set_or18208019st_val @ L @ U ) )
% 1.96/1.19 = ( ( ord_less_eq_val @ L @ I )
% 1.96/1.19 & ( ord_less_eq_val @ I @ U ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_278_atLeastAtMost__iff,axiom,
% 1.96/1.19 ! [I: set_val,L: set_val,U: set_val] :
% 1.96/1.19 ( ( member_set_val @ I @ ( set_or1554624499et_val @ L @ U ) )
% 1.96/1.19 = ( ( ord_less_eq_set_val @ L @ I )
% 1.96/1.19 & ( ord_less_eq_set_val @ I @ U ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_279_Icc__eq__Icc,axiom,
% 1.96/1.19 ! [L: set_val,H: set_val,L2: set_val,H2: set_val] :
% 1.96/1.19 ( ( ( set_or1554624499et_val @ L @ H )
% 1.96/1.19 = ( set_or1554624499et_val @ L2 @ H2 ) )
% 1.96/1.19 = ( ( ( L = L2 )
% 1.96/1.19 & ( H = H2 ) )
% 1.96/1.19 | ( ~ ( ord_less_eq_set_val @ L @ H )
% 1.96/1.19 & ~ ( ord_less_eq_set_val @ L2 @ H2 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_280_atMost__iff,axiom,
% 1.96/1.19 ! [I: val,K: val] :
% 1.96/1.19 ( ( member_val @ I @ ( set_ord_atMost_val @ K ) )
% 1.96/1.19 = ( ord_less_eq_val @ I @ K ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_281_atMost__iff,axiom,
% 1.96/1.19 ! [I: set_val,K: set_val] :
% 1.96/1.19 ( ( member_set_val @ I @ ( set_or867701765et_val @ K ) )
% 1.96/1.19 = ( ord_less_eq_set_val @ I @ K ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_282_lessThan__iff,axiom,
% 1.96/1.19 ! [I: val,K: val] :
% 1.96/1.19 ( ( member_val @ I @ ( set_ord_lessThan_val @ K ) )
% 1.96/1.19 = ( ord_less_val @ I @ K ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_283_Compl__anti__mono,axiom,
% 1.96/1.19 ! [A: set_val,B: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A @ B )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( uminus1961393973et_val @ B ) @ ( uminus1961393973et_val @ A ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_284_Compl__subset__Compl__iff,axiom,
% 1.96/1.19 ! [A: set_val,B: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ ( uminus1961393973et_val @ A ) @ ( uminus1961393973et_val @ B ) )
% 1.96/1.19 = ( ord_less_eq_set_val @ B @ A ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_285_greaterThan__iff,axiom,
% 1.96/1.19 ! [I: val,K: val] :
% 1.96/1.19 ( ( member_val @ I @ ( set_or1288365508an_val @ K ) )
% 1.96/1.19 = ( ord_less_val @ K @ I ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_286_atLeastatMost__subset__iff,axiom,
% 1.96/1.19 ! [A3: set_val,B3: set_val,C: set_val,D: set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ ( set_or1554624499et_val @ A3 @ B3 ) @ ( set_or1554624499et_val @ C @ D ) )
% 1.96/1.19 = ( ~ ( ord_less_eq_set_val @ A3 @ B3 )
% 1.96/1.19 | ( ( ord_less_eq_set_val @ C @ A3 )
% 1.96/1.19 & ( ord_less_eq_set_val @ B3 @ D ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_287_atLeastatMost__subset__iff,axiom,
% 1.96/1.19 ! [A3: val,B3: val,C: val,D: val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ ( set_or18208019st_val @ A3 @ B3 ) @ ( set_or18208019st_val @ C @ D ) )
% 1.96/1.19 = ( ~ ( ord_less_eq_val @ A3 @ B3 )
% 1.96/1.19 | ( ( ord_less_eq_val @ C @ A3 )
% 1.96/1.19 & ( ord_less_eq_val @ B3 @ D ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_288_Icc__subset__Iic__iff,axiom,
% 1.96/1.19 ! [L: set_val,H: set_val,H2: set_val] :
% 1.96/1.19 ( ( ord_le1742111550et_val @ ( set_or1554624499et_val @ L @ H ) @ ( set_or867701765et_val @ H2 ) )
% 1.96/1.19 = ( ~ ( ord_less_eq_set_val @ L @ H )
% 1.96/1.19 | ( ord_less_eq_set_val @ H @ H2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_289_Icc__subset__Iic__iff,axiom,
% 1.96/1.19 ! [L: val,H: val,H2: val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ ( set_or18208019st_val @ L @ H ) @ ( set_ord_atMost_val @ H2 ) )
% 1.96/1.19 = ( ~ ( ord_less_eq_val @ L @ H )
% 1.96/1.19 | ( ord_less_eq_val @ H @ H2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_290_atLeastatMost__psubset__iff,axiom,
% 1.96/1.19 ! [A3: set_val,B3: set_val,C: set_val,D: set_val] :
% 1.96/1.19 ( ( ord_less_set_set_val @ ( set_or1554624499et_val @ A3 @ B3 ) @ ( set_or1554624499et_val @ C @ D ) )
% 1.96/1.19 = ( ( ~ ( ord_less_eq_set_val @ A3 @ B3 )
% 1.96/1.19 | ( ( ord_less_eq_set_val @ C @ A3 )
% 1.96/1.19 & ( ord_less_eq_set_val @ B3 @ D )
% 1.96/1.19 & ( ( ord_less_set_val @ C @ A3 )
% 1.96/1.19 | ( ord_less_set_val @ B3 @ D ) ) ) )
% 1.96/1.19 & ( ord_less_eq_set_val @ C @ D ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_291_ComplD,axiom,
% 1.96/1.19 ! [C: val,A: set_val] :
% 1.96/1.19 ( ( member_val @ C @ ( uminus1961393973et_val @ A ) )
% 1.96/1.19 => ~ ( member_val @ C @ A ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_292_Iic__subset__Iio__iff,axiom,
% 1.96/1.19 ! [A3: val,B3: val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ ( set_ord_atMost_val @ A3 ) @ ( set_ord_lessThan_val @ B3 ) )
% 1.96/1.19 = ( ord_less_val @ A3 @ B3 ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_293_leD,axiom,
% 1.96/1.19 ! [Y2: set_val,X: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ Y2 @ X )
% 1.96/1.19 => ~ ( ord_less_set_val @ X @ Y2 ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_294_le__less,axiom,
% 1.96/1.19 ( ord_less_eq_set_val
% 1.96/1.19 = ( ^ [X3: set_val,Y4: set_val] :
% 1.96/1.19 ( ( ord_less_set_val @ X3 @ Y4 )
% 1.96/1.19 | ( X3 = Y4 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_295_less__le,axiom,
% 1.96/1.19 ( ord_less_set_val
% 1.96/1.19 = ( ^ [X3: set_val,Y4: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X3 @ Y4 )
% 1.96/1.19 & ( X3 != Y4 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_296_order__le__less__subst2,axiom,
% 1.96/1.19 ! [A3: set_val,B3: set_val,F: set_val > set_val,C: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ord_less_set_val @ ( F @ B3 ) @ C )
% 1.96/1.19 => ( ! [X2: set_val,Y3: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_set_val @ ( F @ A3 ) @ C ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_297_order__less__le__subst1,axiom,
% 1.96/1.19 ! [A3: set_val,F: set_val > set_val,B3: set_val,C: set_val] :
% 1.96/1.19 ( ( ord_less_set_val @ A3 @ ( F @ B3 ) )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ B3 @ C )
% 1.96/1.19 => ( ! [X2: set_val,Y3: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 1.96/1.19 => ( ord_less_set_val @ A3 @ ( F @ C ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_298_le__neq__trans,axiom,
% 1.96/1.19 ! [A3: set_val,B3: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 1.96/1.19 => ( ( A3 != B3 )
% 1.96/1.19 => ( ord_less_set_val @ A3 @ B3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_299_antisym__conv1,axiom,
% 1.96/1.19 ! [X: set_val,Y2: set_val] :
% 1.96/1.19 ( ~ ( ord_less_set_val @ X @ Y2 )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ X @ Y2 )
% 1.96/1.19 = ( X = Y2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_300_antisym__conv2,axiom,
% 1.96/1.19 ! [X: set_val,Y2: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X @ Y2 )
% 1.96/1.19 => ( ( ~ ( ord_less_set_val @ X @ Y2 ) )
% 1.96/1.19 = ( X = Y2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_301_less__imp__le,axiom,
% 1.96/1.19 ! [X: set_val,Y2: set_val] :
% 1.96/1.19 ( ( ord_less_set_val @ X @ Y2 )
% 1.96/1.19 => ( ord_less_eq_set_val @ X @ Y2 ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_302_le__less__trans,axiom,
% 1.96/1.19 ! [X: set_val,Y2: set_val,Z2: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X @ Y2 )
% 1.96/1.19 => ( ( ord_less_set_val @ Y2 @ Z2 )
% 1.96/1.19 => ( ord_less_set_val @ X @ Z2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_303_less__le__trans,axiom,
% 1.96/1.19 ! [X: set_val,Y2: set_val,Z2: set_val] :
% 1.96/1.19 ( ( ord_less_set_val @ X @ Y2 )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ Y2 @ Z2 )
% 1.96/1.19 => ( ord_less_set_val @ X @ Z2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_304_le__imp__less__or__eq,axiom,
% 1.96/1.19 ! [X: set_val,Y2: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X @ Y2 )
% 1.96/1.19 => ( ( ord_less_set_val @ X @ Y2 )
% 1.96/1.19 | ( X = Y2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_305_less__le__not__le,axiom,
% 1.96/1.19 ( ord_less_set_val
% 1.96/1.19 = ( ^ [X3: set_val,Y4: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X3 @ Y4 )
% 1.96/1.19 & ~ ( ord_less_eq_set_val @ Y4 @ X3 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_306_order_Ostrict__trans1,axiom,
% 1.96/1.19 ! [A3: set_val,B3: set_val,C: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ord_less_set_val @ B3 @ C )
% 1.96/1.19 => ( ord_less_set_val @ A3 @ C ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_307_order_Ostrict__trans2,axiom,
% 1.96/1.19 ! [A3: set_val,B3: set_val,C: set_val] :
% 1.96/1.19 ( ( ord_less_set_val @ A3 @ B3 )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ B3 @ C )
% 1.96/1.19 => ( ord_less_set_val @ A3 @ C ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_308_order_Oorder__iff__strict,axiom,
% 1.96/1.19 ( ord_less_eq_set_val
% 1.96/1.19 = ( ^ [A4: set_val,B4: set_val] :
% 1.96/1.19 ( ( ord_less_set_val @ A4 @ B4 )
% 1.96/1.19 | ( A4 = B4 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_309_order_Ostrict__iff__order,axiom,
% 1.96/1.19 ( ord_less_set_val
% 1.96/1.19 = ( ^ [A4: set_val,B4: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A4 @ B4 )
% 1.96/1.19 & ( A4 != B4 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_310_dual__order_Ostrict__trans1,axiom,
% 1.96/1.19 ! [B3: set_val,A3: set_val,C: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ B3 @ A3 )
% 1.96/1.19 => ( ( ord_less_set_val @ C @ B3 )
% 1.96/1.19 => ( ord_less_set_val @ C @ A3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_311_dual__order_Ostrict__trans2,axiom,
% 1.96/1.19 ! [B3: set_val,A3: set_val,C: set_val] :
% 1.96/1.19 ( ( ord_less_set_val @ B3 @ A3 )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ C @ B3 )
% 1.96/1.19 => ( ord_less_set_val @ C @ A3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_312_order_Ostrict__implies__order,axiom,
% 1.96/1.19 ! [A3: set_val,B3: set_val] :
% 1.96/1.19 ( ( ord_less_set_val @ A3 @ B3 )
% 1.96/1.19 => ( ord_less_eq_set_val @ A3 @ B3 ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_313_dual__order_Oorder__iff__strict,axiom,
% 1.96/1.19 ( ord_less_eq_set_val
% 1.96/1.19 = ( ^ [B4: set_val,A4: set_val] :
% 1.96/1.19 ( ( ord_less_set_val @ B4 @ A4 )
% 1.96/1.19 | ( A4 = B4 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_314_dual__order_Ostrict__iff__order,axiom,
% 1.96/1.19 ( ord_less_set_val
% 1.96/1.19 = ( ^ [B4: set_val,A4: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ B4 @ A4 )
% 1.96/1.19 & ( A4 != B4 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_315_dual__order_Ostrict__implies__order,axiom,
% 1.96/1.19 ! [B3: set_val,A3: set_val] :
% 1.96/1.19 ( ( ord_less_set_val @ B3 @ A3 )
% 1.96/1.19 => ( ord_less_eq_set_val @ B3 @ A3 ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_316_order_Onot__eq__order__implies__strict,axiom,
% 1.96/1.19 ! [A3: set_val,B3: set_val] :
% 1.96/1.19 ( ( A3 != B3 )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ A3 @ B3 )
% 1.96/1.19 => ( ord_less_set_val @ A3 @ B3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_317_psubsetE,axiom,
% 1.96/1.19 ! [A: set_val,B: set_val] :
% 1.96/1.19 ( ( ord_less_set_val @ A @ B )
% 1.96/1.19 => ~ ( ( ord_less_eq_set_val @ A @ B )
% 1.96/1.19 => ( ord_less_eq_set_val @ B @ A ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_318_psubset__eq,axiom,
% 1.96/1.19 ( ord_less_set_val
% 1.96/1.19 = ( ^ [A2: set_val,B2: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A2 @ B2 )
% 1.96/1.19 & ( A2 != B2 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_319_psubset__imp__subset,axiom,
% 1.96/1.19 ! [A: set_val,B: set_val] :
% 1.96/1.19 ( ( ord_less_set_val @ A @ B )
% 1.96/1.19 => ( ord_less_eq_set_val @ A @ B ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_320_psubset__subset__trans,axiom,
% 1.96/1.19 ! [A: set_val,B: set_val,C2: set_val] :
% 1.96/1.19 ( ( ord_less_set_val @ A @ B )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ B @ C2 )
% 1.96/1.19 => ( ord_less_set_val @ A @ C2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_321_subset__not__subset__eq,axiom,
% 1.96/1.19 ( ord_less_set_val
% 1.96/1.19 = ( ^ [A2: set_val,B2: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A2 @ B2 )
% 1.96/1.19 & ~ ( ord_less_eq_set_val @ B2 @ A2 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_322_subset__psubset__trans,axiom,
% 1.96/1.19 ! [A: set_val,B: set_val,C2: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A @ B )
% 1.96/1.19 => ( ( ord_less_set_val @ B @ C2 )
% 1.96/1.19 => ( ord_less_set_val @ A @ C2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_323_subset__iff__psubset__eq,axiom,
% 1.96/1.19 ( ord_less_eq_set_val
% 1.96/1.19 = ( ^ [A2: set_val,B2: set_val] :
% 1.96/1.19 ( ( ord_less_set_val @ A2 @ B2 )
% 1.96/1.19 | ( A2 = B2 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_324_compl__le__compl__iff,axiom,
% 1.96/1.19 ! [X: set_val,Y2: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ ( uminus1961393973et_val @ X ) @ ( uminus1961393973et_val @ Y2 ) )
% 1.96/1.19 = ( ord_less_eq_set_val @ Y2 @ X ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_325_compl__mono,axiom,
% 1.96/1.19 ! [X: set_val,Y2: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X @ Y2 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( uminus1961393973et_val @ Y2 ) @ ( uminus1961393973et_val @ X ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_326_compl__le__swap1,axiom,
% 1.96/1.19 ! [Y2: set_val,X: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ Y2 @ ( uminus1961393973et_val @ X ) )
% 1.96/1.19 => ( ord_less_eq_set_val @ X @ ( uminus1961393973et_val @ Y2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_327_compl__le__swap2,axiom,
% 1.96/1.19 ! [Y2: set_val,X: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ ( uminus1961393973et_val @ Y2 ) @ X )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( uminus1961393973et_val @ X ) @ Y2 ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_328_psubsetD,axiom,
% 1.96/1.19 ! [A: set_val,B: set_val,C: val] :
% 1.96/1.19 ( ( ord_less_set_val @ A @ B )
% 1.96/1.19 => ( ( member_val @ C @ A )
% 1.96/1.19 => ( member_val @ C @ B ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_329_UnCI,axiom,
% 1.96/1.19 ! [C: val,B: set_val,A: set_val] :
% 1.96/1.19 ( ( ~ ( member_val @ C @ B )
% 1.96/1.19 => ( member_val @ C @ A ) )
% 1.96/1.19 => ( member_val @ C @ ( sup_sup_set_val @ A @ B ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_330_Un__iff,axiom,
% 1.96/1.19 ! [C: val,A: set_val,B: set_val] :
% 1.96/1.19 ( ( member_val @ C @ ( sup_sup_set_val @ A @ B ) )
% 1.96/1.19 = ( ( member_val @ C @ A )
% 1.96/1.19 | ( member_val @ C @ B ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_331_le__sup__iff,axiom,
% 1.96/1.19 ! [X: set_val,Y2: set_val,Z2: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ ( sup_sup_set_val @ X @ Y2 ) @ Z2 )
% 1.96/1.19 = ( ( ord_less_eq_set_val @ X @ Z2 )
% 1.96/1.19 & ( ord_less_eq_set_val @ Y2 @ Z2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_332_sup_Obounded__iff,axiom,
% 1.96/1.19 ! [B3: set_val,C: set_val,A3: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ ( sup_sup_set_val @ B3 @ C ) @ A3 )
% 1.96/1.19 = ( ( ord_less_eq_set_val @ B3 @ A3 )
% 1.96/1.19 & ( ord_less_eq_set_val @ C @ A3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_333_Un__subset__iff,axiom,
% 1.96/1.19 ! [A: set_val,B: set_val,C2: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ B ) @ C2 )
% 1.96/1.19 = ( ( ord_less_eq_set_val @ A @ C2 )
% 1.96/1.19 & ( ord_less_eq_set_val @ B @ C2 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_334_greaterThanLessThan__iff,axiom,
% 1.96/1.19 ! [I: val,L: val,U: val] :
% 1.96/1.19 ( ( member_val @ I @ ( set_or2126567818an_val @ L @ U ) )
% 1.96/1.19 = ( ( ord_less_val @ L @ I )
% 1.96/1.19 & ( ord_less_val @ I @ U ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_335_sup_OcoboundedI2,axiom,
% 1.96/1.19 ! [C: set_val,B3: set_val,A3: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ C @ B3 )
% 1.96/1.19 => ( ord_less_eq_set_val @ C @ ( sup_sup_set_val @ A3 @ B3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_336_sup_OcoboundedI1,axiom,
% 1.96/1.19 ! [C: set_val,A3: set_val,B3: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ C @ A3 )
% 1.96/1.19 => ( ord_less_eq_set_val @ C @ ( sup_sup_set_val @ A3 @ B3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_337_sup_Oabsorb__iff2,axiom,
% 1.96/1.19 ( ord_less_eq_set_val
% 1.96/1.19 = ( ^ [A4: set_val,B4: set_val] :
% 1.96/1.19 ( ( sup_sup_set_val @ A4 @ B4 )
% 1.96/1.19 = B4 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_338_sup_Oabsorb__iff1,axiom,
% 1.96/1.19 ( ord_less_eq_set_val
% 1.96/1.19 = ( ^ [B4: set_val,A4: set_val] :
% 1.96/1.19 ( ( sup_sup_set_val @ A4 @ B4 )
% 1.96/1.19 = A4 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_339_sup_Ocobounded2,axiom,
% 1.96/1.19 ! [B3: set_val,A3: set_val] : ( ord_less_eq_set_val @ B3 @ ( sup_sup_set_val @ A3 @ B3 ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_340_sup_Ocobounded1,axiom,
% 1.96/1.19 ! [A3: set_val,B3: set_val] : ( ord_less_eq_set_val @ A3 @ ( sup_sup_set_val @ A3 @ B3 ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_341_sup_Oorder__iff,axiom,
% 1.96/1.19 ( ord_less_eq_set_val
% 1.96/1.19 = ( ^ [B4: set_val,A4: set_val] :
% 1.96/1.19 ( A4
% 1.96/1.19 = ( sup_sup_set_val @ A4 @ B4 ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_342_sup_OboundedI,axiom,
% 1.96/1.19 ! [B3: set_val,A3: set_val,C: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ B3 @ A3 )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ C @ A3 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( sup_sup_set_val @ B3 @ C ) @ A3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_343_sup_OboundedE,axiom,
% 1.96/1.19 ! [B3: set_val,C: set_val,A3: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ ( sup_sup_set_val @ B3 @ C ) @ A3 )
% 1.96/1.19 => ~ ( ( ord_less_eq_set_val @ B3 @ A3 )
% 1.96/1.19 => ~ ( ord_less_eq_set_val @ C @ A3 ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_344_sup__absorb2,axiom,
% 1.96/1.19 ! [X: set_val,Y2: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ X @ Y2 )
% 1.96/1.19 => ( ( sup_sup_set_val @ X @ Y2 )
% 1.96/1.19 = Y2 ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_345_sup__absorb1,axiom,
% 1.96/1.19 ! [Y2: set_val,X: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ Y2 @ X )
% 1.96/1.19 => ( ( sup_sup_set_val @ X @ Y2 )
% 1.96/1.19 = X ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_346_sup_Oabsorb2,axiom,
% 1.96/1.19 ! [A3: set_val,B3: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ A3 @ B3 )
% 1.96/1.19 => ( ( sup_sup_set_val @ A3 @ B3 )
% 1.96/1.19 = B3 ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_347_sup_Oabsorb1,axiom,
% 1.96/1.19 ! [B3: set_val,A3: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ B3 @ A3 )
% 1.96/1.19 => ( ( sup_sup_set_val @ A3 @ B3 )
% 1.96/1.19 = A3 ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_348_sup__unique,axiom,
% 1.96/1.19 ! [F: set_val > set_val > set_val,X: set_val,Y2: set_val] :
% 1.96/1.19 ( ! [X2: set_val,Y3: set_val] : ( ord_less_eq_set_val @ X2 @ ( F @ X2 @ Y3 ) )
% 1.96/1.19 => ( ! [X2: set_val,Y3: set_val] : ( ord_less_eq_set_val @ Y3 @ ( F @ X2 @ Y3 ) )
% 1.96/1.19 => ( ! [X2: set_val,Y3: set_val,Z3: set_val] :
% 1.96/1.19 ( ( ord_less_eq_set_val @ Y3 @ X2 )
% 1.96/1.19 => ( ( ord_less_eq_set_val @ Z3 @ X2 )
% 1.96/1.19 => ( ord_less_eq_set_val @ ( F @ Y3 @ Z3 ) @ X2 ) ) )
% 1.96/1.19 => ( ( sup_sup_set_val @ X @ Y2 )
% 1.96/1.19 = ( F @ X @ Y2 ) ) ) ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(fact_349_sup_OorderI,axiom,
% 1.96/1.19 ! [A3: set_val,B3: set_val] :
% 1.96/1.19 ( ( A3
% 1.96/1.19 = ( sup_sup_set_val @ A3 @ B3 ) )
% 1.96/1.19 => ( ord_less_eq_set_val @ B3 @ A3 ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(help_If_2_1_If_001tf__val_T,axiom,
% 1.96/1.19 ! [X: val,Y2: val] :
% 1.96/1.19 ( ( if_val @ $false @ X @ Y2 )
% 1.96/1.19 = Y2 ) ).
% 1.96/1.19
% 1.96/1.19 thf(help_If_1_1_If_001tf__val_T,axiom,
% 1.96/1.19 ! [X: val,Y2: val] :
% 1.96/1.19 ( ( if_val @ $true @ X @ Y2 )
% 1.96/1.19 = X ) ).
% 1.96/1.19
% 1.96/1.19 thf(help_If_2_1_If_001t__Set__Oset_Itf__val_J_T,axiom,
% 1.96/1.19 ! [X: set_val,Y2: set_val] :
% 1.96/1.19 ( ( if_set_val @ $false @ X @ Y2 )
% 1.96/1.19 = Y2 ) ).
% 1.96/1.19
% 1.96/1.19 thf(help_If_1_1_If_001t__Set__Oset_Itf__val_J_T,axiom,
% 1.96/1.19 ! [X: set_val,Y2: set_val] :
% 1.96/1.19 ( ( if_set_val @ $true @ X @ Y2 )
% 1.96/1.19 = X ) ).
% 1.96/1.19
% 1.96/1.19 thf(help_If_2_1_If_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J_T,axiom,
% 1.96/1.19 ! [X: $o > set_val,Y2: $o > set_val] :
% 1.96/1.19 ( ( if_o_set_val @ $false @ X @ Y2 )
% 1.96/1.19 = Y2 ) ).
% 1.96/1.19
% 1.96/1.19 thf(help_If_1_1_If_001_062_I_Eo_Mt__Set__Oset_Itf__val_J_J_T,axiom,
% 1.96/1.19 ! [X: $o > set_val,Y2: $o > set_val] :
% 1.96/1.19 ( ( if_o_set_val @ $true @ X @ Y2 )
% 1.96/1.19 = X ) ).
% 1.96/1.19
% 1.96/1.19 thf(help_If_3_1_If_001t__Set__Oset_It__Set__Oset_Itf__val_J_J_T,axiom,
% 1.96/1.19 ! [P: $o] :
% 1.96/1.19 ( ( P = $true )
% 1.96/1.19 | ( P = $false ) ) ).
% 1.96/1.19
% 1.96/1.19 thf(help_If_2_1_If_001t__Set__Oset_It__Set__Oset_Itf__val_J_J_T,axiom,
% 1.96/1.19 ! [X: set_set_val,Y2: set_set_val] :
% 1.96/1.19 ( ( if_set_set_val @ $false @ X @ Y2 )
% 1.96/1.19 = Y2 ) ).
% 1.96/1.19
% 1.96/1.19 thf(help_If_1_1_If_001t__Set__Oset_It__Set__Oset_Itf__val_J_J_T,axiom,
% 1.96/1.19 ! [X: set_set_val,Y2: set_set_val] :
% 1.96/1.19 ( ( if_set_set_val @ $true @ X @ Y2 )
% 1.96/1.19 = X ) ).
% 1.96/1.19
% 1.96/1.19 thf(conj_0,conjecture,
% 1.96/1.19 ord_less_eq_set_val @ scc @ p ).
% 1.96/1.19 ------------------------
% 2.07/1.22 % (27129)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26920 for (2999ds/183Mi)
% 2.07/1.22 % (27135)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26920 for (2999ds/18Mi)
% 2.07/1.22 % (27132)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26920 for (2999ds/2Mi)
% 2.07/1.22 % (27131)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_26920 for (2999ds/27Mi)
% 2.07/1.22 % (27134)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_26920 for (2999ds/275Mi)
% 2.07/1.22 % (27133)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_26920 for (2999ds/2Mi)
% 2.07/1.22 % (27132)Instruction limit reached!
% 2.07/1.22 % (27132)------------------------------
% 2.07/1.22 % (27132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.22 % (27132)Termination reason: Unknown
% 2.07/1.22 % (27132)Termination phase: shuffling
% 2.07/1.22
% 2.07/1.22 % (27132)Memory used [KB]: 1535
% 2.07/1.22 % (27132)Time elapsed: 0.002 s
% 2.07/1.22 % (27132)Instructions burned: 2 (million)
% 2.07/1.22 % (27132)------------------------------
% 2.07/1.22 % (27132)------------------------------
% 2.07/1.22 % (27133)Instruction limit reached!
% 2.07/1.22 % (27133)------------------------------
% 2.07/1.22 % (27133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.22 % (27133)Termination reason: Unknown
% 2.07/1.22 % (27133)Termination phase: shuffling
% 2.07/1.22
% 2.07/1.22 % (27133)Memory used [KB]: 1535
% 2.07/1.22 % (27133)Time elapsed: 0.003 s
% 2.07/1.22 % (27133)Instructions burned: 3 (million)
% 2.07/1.22 % (27133)------------------------------
% 2.07/1.22 % (27133)------------------------------
% 2.07/1.22 % (27135)Instruction limit reached!
% 2.07/1.22 % (27135)------------------------------
% 2.07/1.22 % (27135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.22 % (27135)Termination reason: Unknown
% 2.07/1.22 % (27135)Termination phase: shuffling
% 2.07/1.22
% 2.07/1.22 % (27135)Memory used [KB]: 1918
% 2.07/1.22 % (27135)Time elapsed: 0.009 s
% 2.07/1.22 % (27135)Instructions burned: 19 (million)
% 2.07/1.22 % (27135)------------------------------
% 2.07/1.22 % (27135)------------------------------
% 2.07/1.22 % (27130)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_26920 for (2999ds/4Mi)
% 2.07/1.23 % (27130)Instruction limit reached!
% 2.07/1.23 % (27130)------------------------------
% 2.07/1.23 % (27130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.23 % (27130)Termination reason: Unknown
% 2.07/1.23 % (27130)Termination phase: shuffling
% 2.07/1.23
% 2.07/1.23 % (27130)Memory used [KB]: 1663
% 2.07/1.23 % (27130)Time elapsed: 0.003 s
% 2.07/1.23 % (27130)Instructions burned: 6 (million)
% 2.07/1.23 % (27130)------------------------------
% 2.07/1.23 % (27130)------------------------------
% 2.07/1.23 % (27131)Instruction limit reached!
% 2.07/1.23 % (27131)------------------------------
% 2.07/1.23 % (27131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.23 % (27131)Termination reason: Unknown
% 2.07/1.23 % (27131)Termination phase: shuffling
% 2.07/1.23
% 2.07/1.23 % (27131)Memory used [KB]: 2046
% 2.07/1.23 % (27131)Time elapsed: 0.015 s
% 2.07/1.23 % (27131)Instructions burned: 27 (million)
% 2.07/1.23 % (27131)------------------------------
% 2.07/1.23 % (27131)------------------------------
% 2.07/1.24 % (27140)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26920 for (2999ds/3Mi)
% 2.07/1.24 % (27144)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_26920 for (2999ds/3Mi)
% 2.07/1.24 % (27140)Instruction limit reached!
% 2.07/1.24 % (27140)------------------------------
% 2.07/1.24 % (27140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.24 % (27140)Termination reason: Unknown
% 2.07/1.24 % (27140)Termination phase: shuffling
% 2.07/1.24
% 2.07/1.24 % (27140)Memory used [KB]: 1535
% 2.07/1.24 % (27140)Time elapsed: 0.003 s
% 2.07/1.24 % (27140)Instructions burned: 3 (million)
% 2.07/1.24 % (27140)------------------------------
% 2.07/1.24 % (27140)------------------------------
% 2.07/1.24 % (27141)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_26920 for (2999ds/37Mi)
% 2.07/1.24 % (27143)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_26920 for (2999ds/15Mi)
% 2.07/1.24 % (27144)Instruction limit reached!
% 2.07/1.24 % (27144)------------------------------
% 2.07/1.24 % (27144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.24 % (27144)Termination reason: Unknown
% 2.07/1.24 % (27144)Termination phase: shuffling
% 2.07/1.24
% 2.07/1.24 % (27144)Memory used [KB]: 1535
% 2.07/1.24 % (27144)Time elapsed: 0.002 s
% 2.07/1.24 % (27144)Instructions burned: 3 (million)
% 2.07/1.24 % (27144)------------------------------
% 2.07/1.24 % (27144)------------------------------
% 2.07/1.24 % (27143)Instruction limit reached!
% 2.07/1.24 % (27143)------------------------------
% 2.07/1.24 % (27143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.24 % (27143)Termination reason: Unknown
% 2.07/1.24 % (27143)Termination phase: shuffling
% 2.07/1.24
% 2.07/1.24 % (27143)Memory used [KB]: 1791
% 2.07/1.24 % (27143)Time elapsed: 0.009 s
% 2.07/1.24 % (27143)Instructions burned: 15 (million)
% 2.07/1.24 % (27143)------------------------------
% 2.07/1.24 % (27143)------------------------------
% 2.07/1.25 % (27147)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_26920 for (2999ds/1041Mi)
% 2.07/1.25 % (27148)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_26920 for (2999ds/7Mi)
% 2.07/1.25 % (27149)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_26920 for (2999ds/16Mi)
% 2.07/1.25 % (27141)Instruction limit reached!
% 2.07/1.25 % (27141)------------------------------
% 2.07/1.25 % (27141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.25 % (27141)Termination reason: Unknown
% 2.07/1.25 % (27141)Termination phase: shuffling
% 2.07/1.25
% 2.07/1.25 % (27141)Memory used [KB]: 2302
% 2.07/1.25 % (27141)Time elapsed: 0.016 s
% 2.07/1.25 % (27141)Instructions burned: 37 (million)
% 2.07/1.25 % (27141)------------------------------
% 2.07/1.25 % (27141)------------------------------
% 2.07/1.25 % (27148)Instruction limit reached!
% 2.07/1.25 % (27148)------------------------------
% 2.07/1.25 % (27148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.25 % (27148)Termination reason: Unknown
% 2.07/1.25 % (27148)Termination phase: shuffling
% 2.07/1.25
% 2.07/1.25 % (27148)Memory used [KB]: 1535
% 2.07/1.25 % (27148)Time elapsed: 0.005 s
% 2.07/1.25 % (27148)Instructions burned: 7 (million)
% 2.07/1.25 % (27148)------------------------------
% 2.07/1.25 % (27148)------------------------------
% 2.07/1.26 % (27149)Instruction limit reached!
% 2.07/1.26 % (27149)------------------------------
% 2.07/1.26 % (27149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.26 % (27149)Termination reason: Unknown
% 2.07/1.26 % (27149)Termination phase: shuffling
% 2.07/1.26
% 2.07/1.26 % (27149)Memory used [KB]: 1791
% 2.07/1.26 % (27149)Time elapsed: 0.010 s
% 2.07/1.26 % (27149)Instructions burned: 16 (million)
% 2.07/1.26 % (27149)------------------------------
% 2.07/1.26 % (27149)------------------------------
% 2.07/1.26 % (27153)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_26920 for (2999ds/3Mi)
% 2.07/1.27 % (27153)Instruction limit reached!
% 2.07/1.27 % (27153)------------------------------
% 2.07/1.27 % (27153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.27 % (27153)Termination reason: Unknown
% 2.07/1.27 % (27153)Termination phase: shuffling
% 2.07/1.27
% 2.07/1.27 % (27153)Memory used [KB]: 1535
% 2.07/1.27 % (27153)Time elapsed: 0.004 s
% 2.07/1.27 % (27153)Instructions burned: 4 (million)
% 2.07/1.27 % (27153)------------------------------
% 2.07/1.27 % (27153)------------------------------
% 2.07/1.27 % (27156)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_26920 for (2999ds/3Mi)
% 2.07/1.27 % (27159)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_26920 for (2999ds/3Mi)
% 2.07/1.27 % (27157)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_26920 for (2999ds/7Mi)
% 2.07/1.27 % (27156)Instruction limit reached!
% 2.07/1.27 % (27156)------------------------------
% 2.07/1.27 % (27156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.27 % (27156)Termination reason: Unknown
% 2.07/1.27 % (27159)Instruction limit reached!
% 2.07/1.27 % (27159)------------------------------
% 2.07/1.27 % (27159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.27 % (27159)Termination reason: Unknown
% 2.07/1.27 % (27159)Termination phase: shuffling
% 2.07/1.27
% 2.07/1.27 % (27159)Memory used [KB]: 1535
% 2.07/1.27 % (27159)Time elapsed: 0.002 s
% 2.07/1.27 % (27159)Instructions burned: 3 (million)
% 2.07/1.27 % (27159)------------------------------
% 2.07/1.27 % (27159)------------------------------
% 2.07/1.27 % (27156)Termination phase: shuffling
% 2.07/1.27
% 2.07/1.27 % (27156)Memory used [KB]: 1535
% 2.07/1.27 % (27156)Time elapsed: 0.003 s
% 2.07/1.27 % (27156)Instructions burned: 3 (million)
% 2.07/1.27 % (27156)------------------------------
% 2.07/1.27 % (27156)------------------------------
% 2.07/1.27 % (27157)Instruction limit reached!
% 2.07/1.27 % (27157)------------------------------
% 2.07/1.27 % (27157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.27 % (27157)Termination reason: Unknown
% 2.07/1.27 % (27157)Termination phase: shuffling
% 2.07/1.27
% 2.07/1.27 % (27157)Memory used [KB]: 1663
% 2.07/1.27 % (27157)Time elapsed: 0.005 s
% 2.07/1.27 % (27157)Instructions burned: 8 (million)
% 2.07/1.27 % (27157)------------------------------
% 2.07/1.27 % (27157)------------------------------
% 2.07/1.28 % (27164)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_26920 for (2999ds/18Mi)
% 2.07/1.28 % (27162)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_26920 for (2999ds/4Mi)
% 2.07/1.28 % (27162)Instruction limit reached!
% 2.07/1.28 % (27162)------------------------------
% 2.07/1.28 % (27162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.28 % (27162)Termination reason: Unknown
% 2.07/1.28 % (27162)Termination phase: shuffling
% 2.07/1.28
% 2.07/1.28 % (27162)Memory used [KB]: 1535
% 2.07/1.28 % (27162)Time elapsed: 0.004 s
% 2.07/1.28 % (27162)Instructions burned: 5 (million)
% 2.07/1.28 % (27162)------------------------------
% 2.07/1.28 % (27162)------------------------------
% 2.07/1.29 % (27164)Instruction limit reached!
% 2.07/1.29 % (27164)------------------------------
% 2.07/1.29 % (27164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.29 % (27164)Termination reason: Unknown
% 2.07/1.29 % (27164)Termination phase: shuffling
% 2.07/1.29
% 2.07/1.29 % (27164)Memory used [KB]: 1791
% 2.07/1.29 % (27164)Time elapsed: 0.007 s
% 2.07/1.29 % (27164)Instructions burned: 18 (million)
% 2.07/1.29 % (27164)------------------------------
% 2.07/1.29 % (27164)------------------------------
% 2.07/1.29 % (27165)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_26920 for (2999ds/710Mi)
% 2.07/1.29 % (27166)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_26920 for (2999ds/6Mi)
% 2.07/1.29 % (27166)Instruction limit reached!
% 2.07/1.29 % (27166)------------------------------
% 2.07/1.29 % (27166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.29 % (27166)Termination reason: Unknown
% 2.07/1.29 % (27166)Termination phase: shuffling
% 2.07/1.29
% 2.07/1.29 % (27166)Memory used [KB]: 1535
% 2.07/1.29 % (27166)Time elapsed: 0.005 s
% 2.07/1.29 % (27166)Instructions burned: 7 (million)
% 2.07/1.29 % (27166)------------------------------
% 2.07/1.29 % (27166)------------------------------
% 2.07/1.30 % (27171)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_26920 for (2999ds/21Mi)
% 2.07/1.30 % (27129)Instruction limit reached!
% 2.07/1.30 % (27129)------------------------------
% 2.07/1.30 % (27129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.30 % (27129)Termination reason: Unknown
% 2.07/1.30 % (27129)Termination phase: Saturation
% 2.07/1.30
% 2.07/1.30 % (27129)Memory used [KB]: 7547
% 2.07/1.30 % (27129)Time elapsed: 0.086 s
% 2.07/1.30 % (27129)Instructions burned: 183 (million)
% 2.07/1.30 % (27129)------------------------------
% 2.07/1.30 % (27129)------------------------------
% 2.07/1.30 % (27170)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_26920 for (2999ds/902Mi)
% 2.07/1.31 % (27173)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_26920 for (2998ds/5Mi)
% 2.07/1.31 % (27171)Instruction limit reached!
% 2.07/1.31 % (27171)------------------------------
% 2.07/1.31 % (27171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.31 % (27171)Termination reason: Unknown
% 2.07/1.31 % (27171)Termination phase: shuffling
% 2.07/1.31
% 2.07/1.31 % (27171)Memory used [KB]: 1918
% 2.07/1.31 % (27171)Time elapsed: 0.012 s
% 2.07/1.31 % (27171)Instructions burned: 21 (million)
% 2.07/1.31 % (27171)------------------------------
% 2.07/1.31 % (27171)------------------------------
% 2.07/1.31 % (27173)Instruction limit reached!
% 2.07/1.31 % (27173)------------------------------
% 2.07/1.31 % (27173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.31 % (27173)Termination reason: Unknown
% 2.07/1.31 % (27173)Termination phase: shuffling
% 2.07/1.31
% 2.07/1.31 % (27173)Memory used [KB]: 1663
% 2.07/1.31 % (27173)Time elapsed: 0.004 s
% 2.07/1.31 % (27173)Instructions burned: 6 (million)
% 2.07/1.31 % (27173)------------------------------
% 2.07/1.31 % (27173)------------------------------
% 2.07/1.32 % (27174)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_26920 for (2998ds/6Mi)
% 2.07/1.32 % (27174)Instruction limit reached!
% 2.07/1.32 % (27174)------------------------------
% 2.07/1.32 % (27174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.32 % (27174)Termination reason: Unknown
% 2.07/1.32 % (27174)Termination phase: shuffling
% 2.07/1.32
% 2.07/1.32 % (27174)Memory used [KB]: 1663
% 2.07/1.32 % (27174)Time elapsed: 0.005 s
% 2.07/1.32 % (27174)Instructions burned: 7 (million)
% 2.07/1.32 % (27174)------------------------------
% 2.07/1.32 % (27174)------------------------------
% 2.07/1.33 % (27177)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_26920 for (2998ds/779Mi)
% 2.07/1.33 % (27178)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_26920 for (2998ds/19Mi)
% 2.07/1.34 % (27134)Instruction limit reached!
% 2.07/1.34 % (27134)------------------------------
% 2.07/1.34 % (27134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.34 % (27134)Termination reason: Unknown
% 2.07/1.34 % (27134)Termination phase: Saturation
% 2.07/1.34
% 2.07/1.34 % (27134)Memory used [KB]: 6780
% 2.07/1.34 % (27134)Time elapsed: 0.117 s
% 2.07/1.34 % (27134)Instructions burned: 276 (million)
% 2.07/1.34 % (27134)------------------------------
% 2.07/1.34 % (27134)------------------------------
% 2.07/1.34 % (27175)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_26920 for (2998ds/377Mi)
% 2.07/1.34 % (27178)Instruction limit reached!
% 2.07/1.34 % (27178)------------------------------
% 2.07/1.34 % (27178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.34 % (27178)Termination reason: Unknown
% 2.07/1.34 % (27178)Termination phase: shuffling
% 2.07/1.34
% 2.07/1.34 % (27178)Memory used [KB]: 1918
% 2.07/1.34 % (27178)Time elapsed: 0.010 s
% 2.07/1.34 % (27178)Instructions burned: 19 (million)
% 2.07/1.34 % (27178)------------------------------
% 2.07/1.34 % (27178)------------------------------
% 2.07/1.35 % (27180)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_26920 for (2998ds/879Mi)
% 2.07/1.37 % (27181)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_26920 for (2998ds/17Mi)
% 2.07/1.37 % (27181)Instruction limit reached!
% 2.07/1.37 % (27181)------------------------------
% 2.07/1.37 % (27181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.37 % (27181)Termination reason: Unknown
% 2.07/1.37 % (27181)Termination phase: shuffling
% 2.07/1.37
% 2.07/1.37 % (27181)Memory used [KB]: 1791
% 2.07/1.37 % (27181)Time elapsed: 0.010 s
% 2.07/1.37 % (27181)Instructions burned: 17 (million)
% 2.07/1.37 % (27181)------------------------------
% 2.07/1.37 % (27181)------------------------------
% 2.07/1.38 % (27180)Refutation not found, incomplete strategy
% 2.07/1.38 % (27180)------------------------------
% 2.07/1.38 % (27180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.38 % (27180)Termination reason: Refutation not found, incomplete strategy
% 2.07/1.38
% 2.07/1.38
% 2.07/1.38 % (27180)Memory used [KB]: 6652
% 2.07/1.38 % (27180)Time elapsed: 0.027 s
% 2.07/1.38 % (27180)Instructions burned: 69 (million)
% 2.07/1.38 % (27180)------------------------------
% 2.07/1.38 % (27180)------------------------------
% 2.07/1.39 % (27185)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_26920 for (2998ds/30Mi)
% 2.07/1.39 % (27184)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_26920 for (2998ds/3Mi)
% 2.07/1.39 % (27184)Instruction limit reached!
% 2.07/1.39 % (27184)------------------------------
% 2.07/1.39 % (27184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.39 % (27184)Termination reason: Unknown
% 2.07/1.39 % (27184)Termination phase: shuffling
% 2.07/1.39
% 2.07/1.39 % (27184)Memory used [KB]: 1535
% 2.07/1.39 % (27184)Time elapsed: 0.003 s
% 2.07/1.39 % (27184)Instructions burned: 3 (million)
% 2.07/1.39 % (27184)------------------------------
% 2.07/1.39 % (27184)------------------------------
% 2.07/1.40 % (27147)First to succeed.
% 2.07/1.40 % (27147)Refutation found. Thanks to Tanya!
% 2.07/1.40 % SZS status Theorem for DTF2THF_26920
% 2.07/1.40 % SZS output start Proof for DTF2THF_26920
% 2.07/1.40 thf(type_def_5, type, set_val: $tType).
% 2.07/1.40 thf(type_def_7, type, set_set_val: $tType).
% 2.07/1.40 thf(type_def_8, type, val: $tType).
% 2.07/1.40 thf(type_def_9, type, set_set_set_val: $tType).
% 2.07/1.40 thf(func_def_0, type, set_set_set_val: $tType).
% 2.07/1.40 thf(func_def_1, type, set_set_val: $tType).
% 2.07/1.40 thf(func_def_2, type, set_val: $tType).
% 2.07/1.40 thf(func_def_3, type, val: $tType).
% 2.07/1.40 thf(func_def_4, type, uminus1961393973et_val: set_val > set_val).
% 2.07/1.40 thf(func_def_5, type, if_o_set_val: $o > ($o > set_val) > ($o > set_val) > $o > set_val).
% 2.07/1.40 thf(func_def_6, type, if_set_set_val: $o > set_set_val > set_set_val > set_set_val).
% 2.07/1.40 thf(func_def_7, type, if_set_val: $o > set_val > set_val > set_val).
% 2.07/1.40 thf(func_def_8, type, if_val: $o > val > val > val).
% 2.07/1.40 thf(func_def_9, type, sup_sup_set_val: set_val > set_val > set_val).
% 2.07/1.40 thf(func_def_10, type, ord_less_set_set_val: set_set_val > set_set_val > $o).
% 2.07/1.40 thf(func_def_11, type, ord_less_set_val: set_val > set_val > $o).
% 2.07/1.40 thf(func_def_12, type, ord_less_val: val > val > $o).
% 2.07/1.40 thf(func_def_13, type, ord_le1441829300et_val: ($o > $o > set_val) > ($o > $o > set_val) > $o).
% 2.07/1.40 thf(func_def_14, type, ord_le936627147et_val: ($o > set_set_val) > ($o > set_set_val) > $o).
% 2.07/1.40 thf(func_def_15, type, ord_le994826475et_val: ($o > set_val) > ($o > set_val) > $o).
% 2.07/1.40 thf(func_def_16, type, ord_less_eq_o_val: ($o > val) > ($o > val) > $o).
% 2.07/1.40 thf(func_def_17, type, ord_le1135847966et_val: set_set_set_val > set_set_set_val > $o).
% 2.07/1.40 thf(func_def_18, type, ord_le1742111550et_val: set_set_val > set_set_val > $o).
% 2.07/1.40 thf(func_def_19, type, ord_less_eq_set_val: set_val > set_val > $o).
% 2.07/1.40 thf(func_def_20, type, ord_less_eq_val: val > val > $o).
% 2.07/1.40 thf(func_def_21, type, order_985126002et_val: (($o > set_val) > $o) > $o > set_val).
% 2.07/1.40 thf(func_def_22, type, order_544136439et_val: (set_set_val > $o) > set_set_val).
% 2.07/1.40 thf(func_def_23, type, order_1960465943et_val: (set_val > $o) > set_val).
% 2.07/1.40 thf(func_def_24, type, order_Greatest_val: (val > $o) > val).
% 2.07/1.40 thf(func_def_25, type, order_23236447al_val: (($o > set_val) > val) > $o).
% 2.07/1.40 thf(func_def_26, type, order_650823122et_val: (set_set_val > set_val) > $o).
% 2.07/1.40 thf(func_def_27, type, order_1520822002al_val: (set_set_val > val) > $o).
% 2.07/1.40 thf(func_def_28, type, order_1957703570et_val: (set_val > set_set_val) > $o).
% 2.07/1.40 thf(func_def_29, type, order_1719375026et_val: (set_val > set_val) > $o).
% 2.07/1.40 thf(func_def_30, type, order_1375876562al_val: (set_val > val) > $o).
% 2.07/1.40 thf(func_def_31, type, order_255079095et_val: (val > $o > set_val) > $o).
% 2.07/1.40 thf(func_def_32, type, order_1945059954et_val: (val > set_set_val) > $o).
% 2.07/1.40 thf(func_def_33, type, order_1484138386et_val: (val > set_val) > $o).
% 2.07/1.40 thf(func_def_34, type, order_1689798834al_val: (val > val) > $o).
% 2.07/1.40 thf(func_def_35, type, order_1205732848et_val: (val > $o > set_val) > $o).
% 2.07/1.40 thf(func_def_36, type, order_68692473et_val: (val > set_set_val) > $o).
% 2.07/1.40 thf(func_def_37, type, order_99134233et_val: (val > set_val) > $o).
% 2.07/1.40 thf(func_def_38, type, order_1139042361al_val: (val > val) > $o).
% 2.07/1.40 thf(func_def_39, type, refine1593386065et_val: ($o > set_val) > ($o > set_val) > $o).
% 2.07/1.40 thf(func_def_40, type, refine1034950713et_val: set_set_val > set_set_val > $o).
% 2.07/1.40 thf(func_def_41, type, refine654574649et_val: set_val > set_val > $o).
% 2.07/1.40 thf(func_def_42, type, refine2021912633al_val: val > val > $o).
% 2.07/1.40 thf(func_def_43, type, refine511606705et_val: ($o > set_val) > ($o > set_val) > $o).
% 2.07/1.40 thf(func_def_44, type, refine1908789496et_val: set_set_val > set_set_val > $o).
% 2.07/1.40 thf(func_def_45, type, refine1893322264et_val: set_val > set_val > $o).
% 2.07/1.40 thf(func_def_46, type, refine403244856MP_val: val > val > $o).
% 2.07/1.40 thf(func_def_47, type, refine1924899106et_val: (($o > set_val) > $o > set_val) > (($o > set_val) > $o > set_val) > $o).
% 2.07/1.40 thf(func_def_48, type, refine1169396807et_val: (($o > set_val) > set_set_val) > (set_set_val > $o > set_val) > $o).
% 2.07/1.40 thf(func_def_49, type, refine1948536167et_val: (($o > set_val) > set_val) > (set_val > $o > set_val) > $o).
% 2.07/1.40 thf(func_def_50, type, refine86398879et_val: (set_set_val > $o > set_val) > (($o > set_val) > set_set_val) > $o).
% 2.07/1.40 thf(func_def_51, type, refine855985034et_val: (set_set_val > set_set_val) > (set_set_val > set_set_val) > $o).
% 2.07/1.40 thf(func_def_52, type, refine8163498et_val: (set_set_val > set_val) > (set_val > set_set_val) > $o).
% 2.07/1.40 thf(func_def_53, type, refine51544255et_val: (set_val > $o > set_val) > (($o > set_val) > set_val) > $o).
% 2.07/1.40 thf(func_def_54, type, refine1315043946et_val: (set_val > set_set_val) > (set_set_val > set_val) > $o).
% 2.07/1.40 thf(func_def_55, type, refine1929691018et_val: (set_val > set_val) > (set_val > set_val) > $o).
% 2.07/1.40 thf(func_def_56, type, refine2057434761et_val: (set_val > set_val) > $o).
% 2.07/1.40 thf(func_def_57, type, refine16560100et_val: (($o > set_val) > ($o > set_val) > $o) > $o).
% 2.07/1.40 thf(func_def_58, type, refine1506227973et_val: (set_set_val > set_set_val > $o) > $o).
% 2.07/1.40 thf(func_def_59, type, refine275900453et_val: (set_val > set_val > $o) > $o).
% 2.07/1.40 thf(func_def_60, type, refine67622213oc_val: (val > val > $o) > $o).
% 2.07/1.40 thf(func_def_61, type, collect_set_val: (set_val > $o) > set_set_val).
% 2.07/1.40 thf(func_def_62, type, collect_val: (val > $o) > set_val).
% 2.07/1.40 thf(func_def_63, type, set_or1554624499et_val: set_val > set_val > set_set_val).
% 2.07/1.40 thf(func_def_64, type, set_or18208019st_val: val > val > set_val).
% 2.07/1.40 thf(func_def_65, type, set_or1337784553et_val: set_set_val > set_set_set_val).
% 2.07/1.40 thf(func_def_66, type, set_or650197513et_val: set_val > set_set_val).
% 2.07/1.40 thf(func_def_67, type, set_ord_atLeast_val: val > set_val).
% 2.07/1.40 thf(func_def_68, type, set_or867701765et_val: set_val > set_set_val).
% 2.07/1.40 thf(func_def_69, type, set_ord_atMost_val: val > set_val).
% 2.07/1.40 thf(func_def_70, type, set_or2126567818an_val: val > val > set_val).
% 2.07/1.40 thf(func_def_71, type, set_or1288365508an_val: val > set_val).
% 2.07/1.40 thf(func_def_72, type, set_ord_lessThan_val: val > set_val).
% 2.07/1.40 thf(func_def_73, type, member_set_val: set_val > set_set_val > $o).
% 2.07/1.40 thf(func_def_74, type, member_val: val > set_val > $o).
% 2.07/1.40 thf(func_def_75, type, p: set_val).
% 2.07/1.40 thf(func_def_76, type, scc: set_val).
% 2.07/1.40 thf(f2035,plain,(
% 2.07/1.40 $false),
% 2.07/1.40 inference(trivial_inequality_removal,[status(thm)],[f2034])).
% 2.07/1.40 thf(f2034,plain,(
% 2.07/1.40 ($false = $true)),
% 2.07/1.40 inference(boolean_simplification,[status(thm)],[f2033])).
% 2.07/1.40 thf(f2033,plain,(
% 2.07/1.40 ((~ $true) = $true)),
% 2.07/1.40 inference(backward_demodulation,[status(thm)],[f1898,f1333])).
% 2.07/1.40 thf(f1333,plain,(
% 2.07/1.40 ($true = (!! @ val @ (^[Y0 : val]: ((member_val @ Y0 @ scc) => (member_val @ Y0 @ p)))))),
% 2.07/1.40 inference(cnf_transformation,[status(thm)],[f702])).
% 2.07/1.40 thf(f702,plain,(
% 2.07/1.40 ($true = (!! @ val @ (^[Y0 : val]: ((member_val @ Y0 @ scc) => (member_val @ Y0 @ p)))))),
% 2.07/1.40 inference(fool_elimination,[status(thm)],[f701])).
% 2.07/1.40 thf(f701,plain,(
% 2.07/1.40 ! [X0 : val] : ((member_val @ X0 @ scc) => (member_val @ X0 @ p))),
% 2.07/1.40 inference(rectify,[status(thm)],[f1])).
% 2.07/1.40 thf(f1,axiom,(
% 2.07/1.40 ! [X0 : val] : ((member_val @ X0 @ scc) => (member_val @ X0 @ p))),
% 2.07/1.40 file('/export/starexec/sandbox/tmp/tmp.Tpnd21IUI7/DTF2THF_26920.p',fact_0__092_060open_062_092_060And_062x_O_Ax_A_092_060in_062_Ascc_A_092_060Longrightarrow_062_Ax_A_092_060in_062_AP_092_060close_062)).
% 2.07/1.40 thf(f1898,plain,(
% 2.07/1.40 ((~ (!! @ val @ (^[Y0 : val]: ((member_val @ Y0 @ scc) => (member_val @ Y0 @ p))))) = $true)),
% 2.07/1.40 inference(beta_eta_normalization,[status(thm)],[f1575])).
% 2.07/1.40 thf(f1575,plain,(
% 2.07/1.40 ($true = (~ ((^[Y0 : set_val]: ((^[Y1 : set_val]: (!! @ val @ (^[Y2 : val]: ((member_val @ Y2 @ Y0) => (member_val @ Y2 @ Y1))))))) @ scc @ p)))),
% 2.07/1.40 inference(definition_unfolding,[status(thm)],[f1218,f1109])).
% 2.07/1.40 thf(f1109,plain,(
% 2.07/1.40 (ord_less_eq_set_val = (^[Y0 : set_val]: ((^[Y1 : set_val]: (!! @ val @ (^[Y2 : val]: ((member_val @ Y2 @ Y0) => (member_val @ Y2 @ Y1))))))))),
% 2.07/1.40 inference(cnf_transformation,[status(thm)],[f546])).
% 2.07/1.40 thf(f546,plain,(
% 2.07/1.40 (ord_less_eq_set_val = (^[Y0 : set_val]: ((^[Y1 : set_val]: (!! @ val @ (^[Y2 : val]: ((member_val @ Y2 @ Y0) => (member_val @ Y2 @ Y1))))))))),
% 2.07/1.40 inference(fool_elimination,[status(thm)],[f545])).
% 2.07/1.40 thf(f545,plain,(
% 2.07/1.40 (ord_less_eq_set_val = (^[X0 : set_val, X1 : set_val] : (! [X2 : val] : ((member_val @ X2 @ X0) => (member_val @ X2 @ X1)))))),
% 2.07/1.40 inference(rectify,[status(thm)],[f19])).
% 2.07/1.40 thf(f19,axiom,(
% 2.07/1.40 (ord_less_eq_set_val = (^[X7 : set_val, X8 : set_val] : (! [X9 : val] : ((member_val @ X9 @ X7) => (member_val @ X9 @ X8)))))),
% 2.07/1.40 file('/export/starexec/sandbox/tmp/tmp.Tpnd21IUI7/DTF2THF_26920.p',fact_18_subset__eq)).
% 2.07/1.40 thf(f1218,plain,(
% 2.07/1.40 ((~ (ord_less_eq_set_val @ scc @ p)) = $true)),
% 2.07/1.40 inference(cnf_transformation,[status(thm)],[f928])).
% 2.07/1.40 thf(f928,plain,(
% 2.07/1.40 ((~ (ord_less_eq_set_val @ scc @ p)) = $true)),
% 2.07/1.40 inference(fool_elimination,[status(thm)],[f927])).
% 2.07/1.40 thf(f927,plain,(
% 2.07/1.40 ~(ord_less_eq_set_val @ scc @ p)),
% 2.07/1.40 inference(rectify,[status(thm)],[f361])).
% 2.07/1.40 thf(f361,negated_conjecture,(
% 2.07/1.40 ~(ord_less_eq_set_val @ scc @ p)),
% 2.07/1.40 inference(negated_conjecture,[status(cth)],[f360])).
% 2.07/1.40 thf(f360,conjecture,(
% 2.07/1.40 (ord_less_eq_set_val @ scc @ p)),
% 2.07/1.40 file('/export/starexec/sandbox/tmp/tmp.Tpnd21IUI7/DTF2THF_26920.p',conj_0)).
% 2.07/1.40 % SZS output end Proof for DTF2THF_26920
% 2.07/1.40 % (27147)------------------------------
% 2.07/1.40 % (27147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.40 % (27147)Termination reason: Refutation
% 2.07/1.40
% 2.07/1.40 % (27147)Memory used [KB]: 8571
% 2.07/1.40 % (27147)Time elapsed: 0.151 s
% 2.07/1.40 % (27147)Instructions burned: 342 (million)
% 2.07/1.40 % (27147)------------------------------
% 2.07/1.40 % (27147)------------------------------
% 2.07/1.40 % (27118)Success in time 0.207 s
%------------------------------------------------------------------------------