DT2H2X---1.9.5.THM-Ref.s

%------------------------------------------------------------------------------
% File     : DT2H2X---1.9.5
% Problem  : ITP116^1 : 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 : n012.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 08:55:40 AM UTC 2026

% Result   : Theorem 2.17s 1.68s
% Output   : Refutation 2.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   40 (  33 unt;   0 typ;   0 def)
%            Number of atoms       :  118 (  37 equ;   0 cnn)
%            Maximal formula atoms :    2 (   2 avg)
%            Number of connectives :  409 (  12   ~;   4   |;   9   &; 381   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Number of types       :   21 (  20 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  111 ( 108 usr;   8 con; 0-4 aty)
%            Number of variables   :   84 (  57   ^;  27   !;   0   ?;  84   :)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    finite1489363574real_n: $tType ).

thf(type_def_7,type,
    sigma_1466784463real_n: $tType ).

thf(type_def_8,type,
    set_Fi1058188332real_n: $tType ).

thf(type_def_9,type,
    nat: $tType ).

thf(type_def_10,type,
    set_Fi1326602817real_n: $tType ).

thf(type_def_11,type,
    set_se2111327970real_n: $tType ).

thf(type_def_12,type,
    finite964658038_int_n: $tType ).

thf(type_def_13,type,
    set_nat: $tType ).

thf(type_def_14,type,
    sigma_107786596real_n: $tType ).

thf(type_def_15,type,
    set_Fi1066397675real_n: $tType ).

thf(type_def_16,type,
    set_Fi1491909078real_n: $tType ).

thf(type_def_17,type,
    sigma_1422848389real_n: $tType ).

thf(type_def_18,type,
    set_Fi909698444real_n: $tType ).

thf(type_def_19,type,
    set_Fi1260307670real_n: $tType ).

thf(type_def_20,type,
    set_Fi1645173239real_n: $tType ).

thf(type_def_21,type,
    set_se830533260real_n: $tType ).

thf(type_def_22,type,
    set_se955370231real_n: $tType ).

thf(type_def_23,type,
    set_se1738601133real_n: $tType ).

thf(type_def_24,type,
    set_se221767415real_n: $tType ).

thf(type_def_25,type,
    set_se820660888real_n: $tType ).

thf(func_def_0,type,
    set_Fi1066397675real_n: $tType ).

thf(func_def_1,type,
    set_se830533260real_n: $tType ).

thf(func_def_2,type,
    set_Fi909698444real_n: $tType ).

thf(func_def_3,type,
    set_Fi1260307670real_n: $tType ).

thf(func_def_4,type,
    set_Fi1491909078real_n: $tType ).

thf(func_def_5,type,
    set_se1738601133real_n: $tType ).

thf(func_def_6,type,
    sigma_107786596real_n: $tType ).

thf(func_def_7,type,
    set_se221767415real_n: $tType ).

thf(func_def_8,type,
    set_se955370231real_n: $tType ).

thf(func_def_9,type,
    set_Fi1645173239real_n: $tType ).

thf(func_def_10,type,
    set_Fi1326602817real_n: $tType ).

thf(func_def_11,type,
    sigma_1422848389real_n: $tType ).

thf(func_def_12,type,
    set_se820660888real_n: $tType ).

thf(func_def_13,type,
    sigma_1466784463real_n: $tType ).

thf(func_def_14,type,
    set_se2111327970real_n: $tType ).

thf(func_def_15,type,
    set_Fi1058188332real_n: $tType ).

thf(func_def_16,type,
    finite1489363574real_n: $tType ).

thf(func_def_17,type,
    finite964658038_int_n: $tType ).

thf(func_def_18,type,
    set_nat: $tType ).

thf(func_def_19,type,
    nat: $tType ).

thf(func_def_20,type,
    borel_1962407338real_n: ( finite1489363574real_n > finite1489363574real_n ) > sigma_1466784463real_n > $o ).

thf(func_def_21,type,
    borel_676189912real_n: sigma_1466784463real_n ).

thf(func_def_22,type,
    comple230862828real_n: sigma_1466784463real_n > sigma_1466784463real_n ).

thf(func_def_23,type,
    comple1390568924real_n: sigma_1466784463real_n > set_Fi1058188332real_n > set_Fi1058188332real_n ).

thf(func_def_24,type,
    minus_391085931al_n_o: ( ( finite1489363574real_n > finite1489363574real_n ) > $o ) > ( ( finite1489363574real_n > finite1489363574real_n ) > $o ) > ( finite1489363574real_n > finite1489363574real_n ) > $o ).

thf(func_def_25,type,
    minus_455231168al_n_o: ( finite1489363574real_n > $o ) > ( finite1489363574real_n > $o ) > finite1489363574real_n > $o ).

thf(func_def_26,type,
    minus_1832115082al_n_o: ( set_Fi1058188332real_n > $o ) > ( set_Fi1058188332real_n > $o ) > set_Fi1058188332real_n > $o ).

thf(func_def_27,type,
    minus_1037315151real_n: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ).

thf(func_def_28,type,
    minus_minus_nat: nat > nat > nat ).

thf(func_def_29,type,
    minus_725016986real_n: set_Fi1326602817real_n > set_Fi1326602817real_n > set_Fi1326602817real_n ).

thf(func_def_30,type,
    minus_1686442501real_n: set_Fi1058188332real_n > set_Fi1058188332real_n > set_Fi1058188332real_n ).

thf(func_def_31,type,
    minus_1698615483real_n: set_se2111327970real_n > set_se2111327970real_n > set_se2111327970real_n ).

thf(func_def_32,type,
    plus_p585657087real_n: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ).

thf(func_def_33,type,
    plus_plus_nat: nat > nat > nat ).

thf(func_def_34,type,
    plus_p1606848693real_n: set_Fi1058188332real_n > set_Fi1058188332real_n > set_Fi1058188332real_n ).

thf(func_def_35,type,
    plus_p565022571real_n: set_se2111327970real_n > set_se2111327970real_n > set_se2111327970real_n ).

thf(func_def_36,type,
    zero_z200130687real_n: finite1489363574real_n ).

thf(func_def_37,type,
    zero_zero_nat: nat ).

thf(func_def_38,type,
    if_Fin413489477real_n: $o > ( finite1489363574real_n > finite1489363574real_n ) > ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n ).

thf(func_def_39,type,
    if_Fin127821360real_n: $o > finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ).

thf(func_def_40,type,
    if_set11487206real_n: $o > set_Fi1058188332real_n > set_Fi1058188332real_n > set_Fi1058188332real_n ).

thf(func_def_41,type,
    inf_in32002162al_n_o: ( ( finite1489363574real_n > finite1489363574real_n ) > $o ) > ( ( finite1489363574real_n > finite1489363574real_n ) > $o ) > ( finite1489363574real_n > finite1489363574real_n ) > $o ).

thf(func_def_42,type,
    inf_in1620715847al_n_o: ( finite1489363574real_n > $o ) > ( finite1489363574real_n > $o ) > finite1489363574real_n > $o ).

thf(func_def_43,type,
    inf_in409346577al_n_o: ( set_Fi1058188332real_n > $o ) > ( set_Fi1058188332real_n > $o ) > set_Fi1058188332real_n > $o ).

thf(func_def_44,type,
    inf_in146441683real_n: set_Fi1326602817real_n > set_Fi1326602817real_n > set_Fi1326602817real_n ).

thf(func_def_45,type,
    inf_in1974387902real_n: set_Fi1058188332real_n > set_Fi1058188332real_n > set_Fi1058188332real_n ).

thf(func_def_46,type,
    inf_in632889204real_n: set_se2111327970real_n > set_se2111327970real_n > set_se2111327970real_n ).

thf(func_def_47,type,
    lebesg260170249real_n: sigma_1466784463real_n ).

thf(func_def_48,type,
    minkow1134813771n_real: finite964658038_int_n > finite1489363574real_n ).

thf(func_def_49,type,
    ord_Least_nat: ( nat > $o ) > nat ).

thf(func_def_50,type,
    collec1190264032real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > $o ) > set_Fi1326602817real_n ).

thf(func_def_51,type,
    collec321817931real_n: ( finite1489363574real_n > $o ) > set_Fi1058188332real_n ).

thf(func_def_52,type,
    collec452821761real_n: ( set_Fi1058188332real_n > $o ) > set_se2111327970real_n ).

thf(func_def_53,type,
    image_1123376925real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n ) > set_Fi1326602817real_n > set_Fi1326602817real_n ).

thf(func_def_54,type,
    image_449906696real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n ) > set_Fi1326602817real_n > set_Fi1058188332real_n ).

thf(func_def_55,type,
    image_128879038real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n ) > set_Fi1326602817real_n > set_se2111327970real_n ).

thf(func_def_56,type,
    image_437359496real_n: ( finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n > set_Fi1326602817real_n ).

thf(func_def_57,type,
    image_439535603real_n: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n > set_Fi1058188332real_n ).

thf(func_def_58,type,
    image_545463721real_n: ( finite1489363574real_n > set_Fi1058188332real_n ) > set_Fi1058188332real_n > set_se2111327970real_n ).

thf(func_def_59,type,
    image_nat_nat: ( nat > nat ) > set_nat > set_nat ).

thf(func_def_60,type,
    image_352856126real_n: ( set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n ) > set_se2111327970real_n > set_Fi1326602817real_n ).

thf(func_def_61,type,
    image_1311908777real_n: ( set_Fi1058188332real_n > finite1489363574real_n ) > set_se2111327970real_n > set_Fi1058188332real_n ).

thf(func_def_62,type,
    image_1661509983real_n: ( set_Fi1058188332real_n > set_Fi1058188332real_n ) > set_se2111327970real_n > set_se2111327970real_n ).

thf(func_def_63,type,
    vimage180751827real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n ) > set_Fi1326602817real_n > set_Fi1326602817real_n ).

thf(func_def_64,type,
    vimage1072397758real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n ) > set_Fi1058188332real_n > set_Fi1326602817real_n ).

thf(func_def_65,type,
    vimage2098059032_n_nat: ( ( finite1489363574real_n > finite1489363574real_n ) > nat ) > set_nat > set_Fi1326602817real_n ).

thf(func_def_66,type,
    vimage1910974324real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n ) > set_se2111327970real_n > set_Fi1326602817real_n ).

thf(func_def_67,type,
    vimage1059850558real_n: ( finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ) > set_Fi1326602817real_n > set_Fi1058188332real_n ).

thf(func_def_68,type,
    vimage1233683625real_n: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n > set_Fi1058188332real_n ).

thf(func_def_69,type,
    vimage281029891_n_nat: ( finite1489363574real_n > nat ) > set_nat > set_Fi1058188332real_n ).

thf(func_def_70,type,
    vimage207290975real_n: ( finite1489363574real_n > set_Fi1058188332real_n ) > set_se2111327970real_n > set_Fi1058188332real_n ).

thf(func_def_71,type,
    vimage2134951412real_n: ( set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n ) > set_Fi1326602817real_n > set_se2111327970real_n ).

thf(func_def_72,type,
    vimage973736031real_n: ( set_Fi1058188332real_n > finite1489363574real_n ) > set_Fi1058188332real_n > set_se2111327970real_n ).

thf(func_def_73,type,
    vimage501526201_n_nat: ( set_Fi1058188332real_n > nat ) > set_nat > set_se2111327970real_n ).

thf(func_def_74,type,
    vimage784510485real_n: ( set_Fi1058188332real_n > set_Fi1058188332real_n ) > set_se2111327970real_n > set_se2111327970real_n ).

thf(func_def_75,type,
    sigma_1185134568real_n: sigma_107786596real_n > sigma_107786596real_n > set_Fi1066397675real_n ).

thf(func_def_76,type,
    sigma_2028985427real_n: sigma_107786596real_n > sigma_1466784463real_n > set_Fi1491909078real_n ).

thf(func_def_77,type,
    sigma_364818953real_n: sigma_107786596real_n > sigma_1422848389real_n > set_Fi909698444real_n ).

thf(func_def_78,type,
    sigma_2016438227real_n: sigma_1466784463real_n > sigma_107786596real_n > set_Fi1260307670real_n ).

thf(func_def_79,type,
    sigma_439801790real_n: sigma_1466784463real_n > sigma_1466784463real_n > set_Fi1326602817real_n ).

thf(func_def_80,type,
    sigma_566919540real_n: sigma_1466784463real_n > sigma_1422848389real_n > set_Fi1645173239real_n ).

thf(func_def_81,type,
    sigma_588796041real_n: sigma_1422848389real_n > sigma_107786596real_n > set_se830533260real_n ).

thf(func_def_82,type,
    sigma_1333364596real_n: sigma_1422848389real_n > sigma_1466784463real_n > set_se955370231real_n ).

thf(func_def_83,type,
    sigma_239294762real_n: sigma_1422848389real_n > sigma_1422848389real_n > set_se1738601133real_n ).

thf(func_def_84,type,
    sigma_1052429895real_n: sigma_107786596real_n > set_Fi1326602817real_n > sigma_107786596real_n ).

thf(func_def_85,type,
    sigma_346513458real_n: sigma_1466784463real_n > set_Fi1058188332real_n > sigma_1466784463real_n ).

thf(func_def_86,type,
    sigma_993999336real_n: sigma_1422848389real_n > set_se2111327970real_n > sigma_1422848389real_n ).

thf(func_def_87,type,
    sigma_522684908real_n: sigma_107786596real_n > set_se221767415real_n ).

thf(func_def_88,type,
    sigma_1235138647real_n: sigma_1466784463real_n > set_se2111327970real_n ).

thf(func_def_89,type,
    sigma_433815053real_n: sigma_1422848389real_n > set_se820660888real_n ).

thf(func_def_90,type,
    sigma_1483971331real_n: sigma_107786596real_n > set_Fi1326602817real_n ).

thf(func_def_91,type,
    sigma_476185326real_n: sigma_1466784463real_n > set_Fi1058188332real_n ).

thf(func_def_92,type,
    sigma_607186084real_n: sigma_1422848389real_n > set_se2111327970real_n ).

thf(func_def_93,type,
    sigma_136294295real_n: set_Fi1326602817real_n > ( ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n ) > sigma_1466784463real_n > sigma_107786596real_n ).

thf(func_def_94,type,
    sigma_821351682real_n: set_Fi1058188332real_n > ( finite1489363574real_n > finite1489363574real_n ) > sigma_1466784463real_n > sigma_1466784463real_n ).

thf(func_def_95,type,
    sigma_1384150200real_n: set_se2111327970real_n > ( set_Fi1058188332real_n > finite1489363574real_n ) > sigma_1466784463real_n > sigma_1422848389real_n ).

thf(func_def_96,type,
    member117715276real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n ) > set_Fi1066397675real_n > $o ).

thf(func_def_97,type,
    member1695588023real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n ) > set_Fi1491909078real_n > $o ).

thf(func_def_98,type,
    member640587117real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n ) > set_Fi909698444real_n > $o ).

thf(func_def_99,type,
    member408431031real_n: ( finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ) > set_Fi1260307670real_n > $o ).

thf(func_def_100,type,
    member1746150050real_n: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1326602817real_n > $o ).

thf(func_def_101,type,
    member966061400real_n: ( finite1489363574real_n > set_Fi1058188332real_n ) > set_Fi1645173239real_n > $o ).

thf(func_def_102,type,
    member1764433517real_n: ( set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n ) > set_se830533260real_n > $o ).

thf(func_def_103,type,
    member1759501912real_n: ( set_Fi1058188332real_n > finite1489363574real_n ) > set_se955370231real_n > $o ).

thf(func_def_104,type,
    member1734791438real_n: ( set_Fi1058188332real_n > set_Fi1058188332real_n ) > set_se1738601133real_n > $o ).

thf(func_def_105,type,
    member1352538125real_n: finite1489363574real_n > set_Fi1058188332real_n > $o ).

thf(func_def_106,type,
    member2104752728real_n: set_Fi1326602817real_n > set_se221767415real_n > $o ).

thf(func_def_107,type,
    member223413699real_n: set_Fi1058188332real_n > set_se2111327970real_n > $o ).

thf(func_def_108,type,
    member1475136633real_n: set_se2111327970real_n > set_se820660888real_n > $o ).

thf(func_def_109,type,
    r: finite964658038_int_n > set_Fi1058188332real_n ).

thf(func_def_110,type,
    s: set_Fi1058188332real_n ).

thf(func_def_111,type,
    t: finite964658038_int_n > set_Fi1058188332real_n ).

thf(func_def_112,type,
    t2: finite964658038_int_n > set_Fi1058188332real_n ).

thf(func_def_113,type,
    a: finite964658038_int_n ).

thf(func_def_128,type,
    sK0: ( finite1489363574real_n > $o ) > set_Fi1058188332real_n > ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n ).

thf(func_def_129,type,
    sK1: ( finite1489363574real_n > finite1489363574real_n ) > sigma_1466784463real_n > sigma_1466784463real_n > finite1489363574real_n ).

thf(func_def_130,type,
    sK2: ( finite1489363574real_n > finite1489363574real_n ) > sigma_1466784463real_n > sigma_1466784463real_n > set_Fi1058188332real_n ).

thf(func_def_131,type,
    sK3: set_Fi1058188332real_n > ( finite1489363574real_n > finite1489363574real_n ) > ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n ).

thf(func_def_132,type,
    sK4: ( finite1489363574real_n > $o ) > ( finite1489363574real_n > $o ) > finite1489363574real_n ).

thf(func_def_133,type,
    sK5: ( finite1489363574real_n > finite1489363574real_n ) > ( finite1489363574real_n > $o ) > set_Fi1058188332real_n > finite1489363574real_n ).

thf(func_def_134,type,
    sK6: ( finite1489363574real_n > $o ) > ( finite1489363574real_n > finite1489363574real_n ) > ( finite1489363574real_n > $o ) > finite1489363574real_n ).

thf(func_def_135,type,
    sK7: ( finite1489363574real_n > finite1489363574real_n ) > sigma_1466784463real_n > ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n ).

thf(func_def_136,type,
    sK8: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n ).

thf(func_def_137,type,
    sK9: ( finite1489363574real_n > finite1489363574real_n ) > sigma_1466784463real_n > ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n ).

thf(func_def_138,type,
    sK10: ( finite1489363574real_n > finite1489363574real_n ) > ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n > finite1489363574real_n ).

thf(func_def_139,type,
    sK11: set_Fi1058188332real_n > set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n ).

thf(func_def_140,type,
    sK12: set_Fi1058188332real_n > ( finite1489363574real_n > finite1489363574real_n ) > ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n ).

thf(func_def_142,type,
    ph14: 
      !>[X0: $tType] : X0 ).

thf(f1682,plain,
    $false,
    inference(trivial_inequality_removal,[status(thm)],[f1680]) ).

thf(f1680,plain,
    $true != $true,
    inference(superposition,[status(thm)],[f1412,f1631]) ).

thf(f1631,plain,
    ! [X0: finite964658038_int_n] :
      ( ( member223413699real_n
        @ ( collec321817931real_n
          @ ^ [Y0: finite1489363574real_n] : ( member1352538125real_n @ ( plus_p585657087real_n @ Y0 @ ( minkow1134813771n_real @ X0 ) ) @ ( t2 @ X0 ) ) )
        @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
      = $true ),
    inference(forward_demodulation,[status(thm)],[f1629,f1241]) ).

thf(f1241,plain,
    ! [X0: set_Fi1058188332real_n] :
      ( ( sigma_476185326real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ X0 ) )
      = X0 ),
    inference(cnf_transformation,[status(thm)],[f883]) ).

thf(f883,plain,
    ! [X0: set_Fi1058188332real_n] :
      ( ( sigma_476185326real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ X0 ) )
      = X0 ),
    inference(rectify,[status(thm)],[f276]) ).

thf(f276,axiom,
    ! [X20: set_Fi1058188332real_n] :
      ( ( sigma_476185326real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ X20 ) )
      = X20 ),
    file('/export/starexec/sandbox/tmp/tmp.gWsecxm7AG/DTF2THF_14897.p',fact_275_space__lebesgue__on) ).

thf(f1629,plain,
    ! [X0: finite964658038_int_n] :
      ( $true
      = ( member223413699real_n
        @ ( sigma_476185326real_n
          @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n )
            @ ( collec321817931real_n
              @ ^ [Y0: finite1489363574real_n] : ( member1352538125real_n @ ( plus_p585657087real_n @ Y0 @ ( minkow1134813771n_real @ X0 ) ) @ ( t2 @ X0 ) ) ) ) )
        @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ),
    inference(backward_demodulation,[status(thm)],[f1612,f1383]) ).

thf(f1383,plain,
    ! [X0: set_Fi1058188332real_n,X1: sigma_1466784463real_n] :
      ( ( collec321817931real_n
        @ ^ [Y0: finite1489363574real_n] :
            ( ( member1352538125real_n @ Y0 @ ( sigma_476185326real_n @ X1 ) )
            & ( member1352538125real_n @ Y0 @ X0 ) ) )
      = ( sigma_476185326real_n @ ( sigma_346513458real_n @ X1 @ X0 ) ) ),
    inference(beta_eta_normalization,[status(thm)],[f1315]) ).

thf(f1315,plain,
    ! [X0: set_Fi1058188332real_n,X1: sigma_1466784463real_n] :
      ( ( ^ [Y0: set_Fi1058188332real_n,Y1: set_Fi1058188332real_n] :
            ( collec321817931real_n
            @ ^ [Y2: finite1489363574real_n] :
                ( ( member1352538125real_n @ Y2 @ Y1 )
                & ( member1352538125real_n @ Y2 @ Y0 ) ) )
        @ X0
        @ ( sigma_476185326real_n @ X1 ) )
      = ( sigma_476185326real_n @ ( sigma_346513458real_n @ X1 @ X0 ) ) ),
    inference(definition_unfolding,[status(thm)],[f1137,f1204]) ).

thf(f1204,plain,
    ( inf_in1974387902real_n
    = ( ^ [Y0: set_Fi1058188332real_n,Y1: set_Fi1058188332real_n] :
          ( collec321817931real_n
          @ ^ [Y2: finite1489363574real_n] :
              ( ( member1352538125real_n @ Y2 @ Y1 )
              & ( member1352538125real_n @ Y2 @ Y0 ) ) ) ) ),
    inference(cnf_transformation,[status(thm)],[f797]) ).

thf(f797,plain,
    ( inf_in1974387902real_n
    = ( ^ [Y0: set_Fi1058188332real_n,Y1: set_Fi1058188332real_n] :
          ( collec321817931real_n
          @ ^ [Y2: finite1489363574real_n] :
              ( ( member1352538125real_n @ Y2 @ Y1 )
              & ( member1352538125real_n @ Y2 @ Y0 ) ) ) ) ),
    inference(fool_elimination,[status(thm)],[f796]) ).

thf(f796,plain,
    ( inf_in1974387902real_n
    = ( ^ [X0: set_Fi1058188332real_n,X1: set_Fi1058188332real_n] :
          ( collec321817931real_n
          @ ^ [X2: finite1489363574real_n] :
              ( ( member1352538125real_n @ X2 @ X0 )
              & ( member1352538125real_n @ X2 @ X1 ) ) ) ) ),
    inference(rectify,[status(thm)],[f67]) ).

thf(f67,axiom,
    ( inf_in1974387902real_n
    = ( ^ [X16: set_Fi1058188332real_n,X14: set_Fi1058188332real_n] :
          ( collec321817931real_n
          @ ^ [X2: finite1489363574real_n] :
              ( ( member1352538125real_n @ X2 @ X16 )
              & ( member1352538125real_n @ X2 @ X14 ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.gWsecxm7AG/DTF2THF_14897.p',fact_66_Int__def) ).

thf(f1137,plain,
    ! [X0: set_Fi1058188332real_n,X1: sigma_1466784463real_n] :
      ( ( sigma_476185326real_n @ ( sigma_346513458real_n @ X1 @ X0 ) )
      = ( inf_in1974387902real_n @ X0 @ ( sigma_476185326real_n @ X1 ) ) ),
    inference(cnf_transformation,[status(thm)],[f924]) ).

thf(f924,plain,
    ! [X0: set_Fi1058188332real_n,X1: sigma_1466784463real_n] :
      ( ( sigma_476185326real_n @ ( sigma_346513458real_n @ X1 @ X0 ) )
      = ( inf_in1974387902real_n @ X0 @ ( sigma_476185326real_n @ X1 ) ) ),
    inference(rectify,[status(thm)],[f269]) ).

thf(f269,axiom,
    ! [X39: set_Fi1058188332real_n,X4: sigma_1466784463real_n] :
      ( ( inf_in1974387902real_n @ X39 @ ( sigma_476185326real_n @ X4 ) )
      = ( sigma_476185326real_n @ ( sigma_346513458real_n @ X4 @ X39 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.gWsecxm7AG/DTF2THF_14897.p',fact_268_space__restrict__space) ).

thf(f1612,plain,
    ! [X0: finite964658038_int_n] :
      ( ( member223413699real_n
        @ ( collec321817931real_n
          @ ^ [Y0: finite1489363574real_n] :
              ( ( member1352538125real_n @ Y0 @ ( sigma_476185326real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
              & ( member1352538125real_n @ Y0
                @ ( collec321817931real_n
                  @ ^ [Y1: finite1489363574real_n] : ( member1352538125real_n @ ( plus_p585657087real_n @ Y1 @ ( minkow1134813771n_real @ X0 ) ) @ ( t2 @ X0 ) ) ) ) ) )
        @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
      = $true ),
    inference(subsumption_resolution,[status(thm)],[f1508,f1091]) ).

thf(f1091,plain,
    ! [X0: finite964658038_int_n] :
      ( ( member223413699real_n @ ( t2 @ X0 ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
      = $true ),
    inference(cnf_transformation,[status(thm)],[f550]) ).

thf(f550,plain,
    ! [X0: finite964658038_int_n] :
      ( ( member223413699real_n @ ( t2 @ X0 ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
      = $true ),
    inference(fool_elimination,[status(thm)],[f549]) ).

thf(f549,plain,
    ! [X0: finite964658038_int_n] : ( member223413699real_n @ ( t2 @ X0 ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ),
    inference(rectify,[status(thm)],[f4]) ).

thf(f4,axiom,
    ! [X0: finite964658038_int_n] : ( member223413699real_n @ ( t2 @ X0 ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.gWsecxm7AG/DTF2THF_14897.p',fact_3__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062) ).

thf(f1508,plain,
    ! [X0: finite964658038_int_n] :
      ( ( ( member223413699real_n @ ( t2 @ X0 ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
       != $true )
      | ( ( member223413699real_n
          @ ( collec321817931real_n
            @ ^ [Y0: finite1489363574real_n] :
                ( ( member1352538125real_n @ Y0 @ ( sigma_476185326real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
                & ( member1352538125real_n @ Y0
                  @ ( collec321817931real_n
                    @ ^ [Y1: finite1489363574real_n] : ( member1352538125real_n @ ( plus_p585657087real_n @ Y1 @ ( minkow1134813771n_real @ X0 ) ) @ ( t2 @ X0 ) ) ) ) ) )
          @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
        = $true ) ),
    inference(beta_eta_normalization,[status(thm)],[f1353]) ).

thf(f1353,plain,
    ! [X0: finite964658038_int_n] :
      ( ( ( member223413699real_n
          @ ( ^ [Y0: set_Fi1058188332real_n,Y1: set_Fi1058188332real_n] :
                ( collec321817931real_n
                @ ^ [Y2: finite1489363574real_n] :
                    ( ( member1352538125real_n @ Y2 @ Y1 )
                    & ( member1352538125real_n @ Y2 @ Y0 ) ) )
            @ ( ^ [Y0: finite1489363574real_n > finite1489363574real_n,Y1: set_Fi1058188332real_n] :
                  ( collec321817931real_n
                  @ ^ [Y2: finite1489363574real_n] : ( member1352538125real_n @ ( Y0 @ Y2 ) @ Y1 ) )
              @ ^ [Y0: finite1489363574real_n] : ( plus_p585657087real_n @ Y0 @ ( minkow1134813771n_real @ X0 ) )
              @ ( t2 @ X0 ) )
            @ ( sigma_476185326real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
          @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
        = $true )
      | ( ( member223413699real_n @ ( t2 @ X0 ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
       != $true ) ),
    inference(definition_unfolding,[status(thm)],[f1267,f1204,f1255]) ).

thf(f1255,plain,
    ( vimage1233683625real_n
    = ( ^ [Y0: finite1489363574real_n > finite1489363574real_n,Y1: set_Fi1058188332real_n] :
          ( collec321817931real_n
          @ ^ [Y2: finite1489363574real_n] : ( member1352538125real_n @ ( Y0 @ Y2 ) @ Y1 ) ) ) ),
    inference(cnf_transformation,[status(thm)],[f652]) ).

thf(f652,plain,
    ( vimage1233683625real_n
    = ( ^ [Y0: finite1489363574real_n > finite1489363574real_n,Y1: set_Fi1058188332real_n] :
          ( collec321817931real_n
          @ ^ [Y2: finite1489363574real_n] : ( member1352538125real_n @ ( Y0 @ Y2 ) @ Y1 ) ) ) ),
    inference(fool_elimination,[status(thm)],[f651]) ).

thf(f651,plain,
    ( vimage1233683625real_n
    = ( ^ [X0: finite1489363574real_n > finite1489363574real_n,X1: set_Fi1058188332real_n] :
          ( collec321817931real_n
          @ ^ [X2: finite1489363574real_n] : ( member1352538125real_n @ ( X0 @ X2 ) @ X1 ) ) ) ),
    inference(rectify,[status(thm)],[f27]) ).

thf(f27,axiom,
    ( vimage1233683625real_n
    = ( ^ [X13: finite1489363574real_n > finite1489363574real_n,X14: set_Fi1058188332real_n] :
          ( collec321817931real_n
          @ ^ [X2: finite1489363574real_n] : ( member1352538125real_n @ ( X13 @ X2 ) @ X14 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.gWsecxm7AG/DTF2THF_14897.p',fact_26_vimage__def) ).

thf(f1267,plain,
    ! [X0: finite964658038_int_n] :
      ( ( ( member223413699real_n @ ( t2 @ X0 ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
       != $true )
      | ( ( member223413699real_n
          @ ( inf_in1974387902real_n
            @ ( vimage1233683625real_n
              @ ^ [Y0: finite1489363574real_n] : ( plus_p585657087real_n @ Y0 @ ( minkow1134813771n_real @ X0 ) )
              @ ( t2 @ X0 ) )
            @ ( sigma_476185326real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
          @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
        = $true ) ),
    inference(cnf_transformation,[status(thm)],[f989]) ).

thf(f989,plain,
    ! [X0: finite964658038_int_n] :
      ( ( ( member223413699real_n @ ( t2 @ X0 ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
       != $true )
      | ( ( member223413699real_n
          @ ( inf_in1974387902real_n
            @ ( vimage1233683625real_n
              @ ^ [Y0: finite1489363574real_n] : ( plus_p585657087real_n @ Y0 @ ( minkow1134813771n_real @ X0 ) )
              @ ( t2 @ X0 ) )
            @ ( sigma_476185326real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
          @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
        = $true ) ),
    inference(ennf_transformation,[status(thm)],[f872]) ).

thf(f872,plain,
    ! [X0: finite964658038_int_n] :
      ( ( ( member223413699real_n @ ( t2 @ X0 ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
        = $true )
     => ( ( member223413699real_n
          @ ( inf_in1974387902real_n
            @ ( vimage1233683625real_n
              @ ^ [Y0: finite1489363574real_n] : ( plus_p585657087real_n @ Y0 @ ( minkow1134813771n_real @ X0 ) )
              @ ( t2 @ X0 ) )
            @ ( sigma_476185326real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
          @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
        = $true ) ),
    inference(fool_elimination,[status(thm)],[f871]) ).

thf(f871,plain,
    ! [X0: finite964658038_int_n] :
      ( ( member223413699real_n @ ( t2 @ X0 ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
     => ( member223413699real_n
        @ ( inf_in1974387902real_n
          @ ( vimage1233683625real_n
            @ ^ [X1: finite1489363574real_n] : ( plus_p585657087real_n @ X1 @ ( minkow1134813771n_real @ X0 ) )
            @ ( t2 @ X0 ) )
          @ ( sigma_476185326real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
        @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ),
    inference(rectify,[status(thm)],[f3]) ).

thf(f3,axiom,
    ! [X0: finite964658038_int_n] :
      ( ( member223413699real_n @ ( t2 @ X0 ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
     => ( member223413699real_n
        @ ( inf_in1974387902real_n
          @ ( vimage1233683625real_n
            @ ^ [X2: finite1489363574real_n] : ( plus_p585657087real_n @ X2 @ ( minkow1134813771n_real @ X0 ) )
            @ ( t2 @ X0 ) )
          @ ( sigma_476185326real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
        @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.gWsecxm7AG/DTF2THF_14897.p',fact_2__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_A_092_060Longrightarrow_062_A_I_092_060lambda_062x_O_Ax_A_L_Aof__int__vec_Aa_J_A_N_096_AT_Aa_A_092_060inter_062_Aspace_Alebesgue_A_092_060in_062_Asets_Alebesgue_092_060close_062) ).

thf(f1412,plain,
    ( ( member223413699real_n
      @ ( collec321817931real_n
        @ ^ [Y0: finite1489363574real_n] : ( member1352538125real_n @ ( plus_p585657087real_n @ Y0 @ ( minkow1134813771n_real @ a ) ) @ ( t2 @ a ) ) )
      @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
   != $true ),
    inference(beta_eta_normalization,[status(thm)],[f1312]) ).

thf(f1312,plain,
    ( ( member223413699real_n
      @ ( ^ [Y0: finite1489363574real_n > finite1489363574real_n,Y1: set_Fi1058188332real_n] :
            ( collec321817931real_n
            @ ^ [Y2: finite1489363574real_n] : ( member1352538125real_n @ ( Y0 @ Y2 ) @ Y1 ) )
        @ ^ [Y0: finite1489363574real_n] : ( plus_p585657087real_n @ Y0 @ ( minkow1134813771n_real @ a ) )
        @ ( t2 @ a ) )
      @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
   != $true ),
    inference(definition_unfolding,[status(thm)],[f1132,f1255]) ).

thf(f1132,plain,
    ( ( member223413699real_n
      @ ( vimage1233683625real_n
        @ ^ [Y0: finite1489363574real_n] : ( plus_p585657087real_n @ Y0 @ ( minkow1134813771n_real @ a ) )
        @ ( t2 @ a ) )
      @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
   != $true ),
    inference(cnf_transformation,[status(thm)],[f881]) ).

thf(f881,plain,
    ( ( member223413699real_n
      @ ( vimage1233683625real_n
        @ ^ [Y0: finite1489363574real_n] : ( plus_p585657087real_n @ Y0 @ ( minkow1134813771n_real @ a ) )
        @ ( t2 @ a ) )
      @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
   != $true ),
    inference(flattening,[status(thm)],[f477]) ).

thf(f477,plain,
    ( ( member223413699real_n
      @ ( vimage1233683625real_n
        @ ^ [Y0: finite1489363574real_n] : ( plus_p585657087real_n @ Y0 @ ( minkow1134813771n_real @ a ) )
        @ ( t2 @ a ) )
      @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
   != $true ),
    inference(fool_elimination,[status(thm)],[f476]) ).

thf(f476,plain,
    ~ ( member223413699real_n
      @ ( vimage1233683625real_n
        @ ^ [X0: finite1489363574real_n] : ( plus_p585657087real_n @ X0 @ ( minkow1134813771n_real @ a ) )
        @ ( t2 @ a ) )
      @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ),
    inference(rectify,[status(thm)],[f363]) ).

thf(f363,negated_conjecture,
    ~ ( member223413699real_n
      @ ( vimage1233683625real_n
        @ ^ [X2: finite1489363574real_n] : ( plus_p585657087real_n @ X2 @ ( minkow1134813771n_real @ a ) )
        @ ( t2 @ a ) )
      @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ),
    inference(negated_conjecture,[status(cth)],[f362]) ).

thf(f362,conjecture,
    ( member223413699real_n
    @ ( vimage1233683625real_n
      @ ^ [X2: finite1489363574real_n] : ( plus_p585657087real_n @ X2 @ ( minkow1134813771n_real @ a ) )
      @ ( t2 @ a ) )
    @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.gWsecxm7AG/DTF2THF_14897.p',conj_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06  % Problem  : ITP116^1 : 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 : n012.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 08:26:30 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     : ITP116^1 : TPTP v9.2.1. Released v7.5.0.
% 0.07/0.32  % Domain   : Interactive Theorem Proving
% 0.07/0.32  % Problem  : Sledgehammer Minkowskis_Theorem problem prob_203__6248138_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    : Minkowskis_Theorem/prob_203__6248138_1 [Des21]
% 0.07/0.32  
% 0.07/0.32  % Status   : Theorem
% 0.07/0.32  % Rating   : 0.33 v9.1.0, 0.25 v9.0.0, 0.40 v8.2.0, 0.38 v8.1.0, 0.45 v7.5.0
% 0.07/0.32  % Syntax   : Number of formulae    :  476 ( 175 unt; 114 typ;   0 def)
% 0.07/0.32  %            Number of atoms       :  964 ( 319 equ;   0 cnn)
% 0.07/0.32  %            Maximal formula atoms :    6 (   2 avg)
% 0.07/0.32  %            Number of connectives : 3818 (  35   ~;   4   |; 118   &;3341   @)
% 0.07/0.32  %                                         (   0 <=>; 320  =>;   0  <=;   0 <~>)
% 0.07/0.32  %            Maximal formula depth :   17 (   7 avg)
% 0.07/0.32  %            Number of types       :   21 (  20 usr)
% 0.07/0.32  %            Number of type conns  :  646 ( 646   >;   0   *;   0   +;   0  <<)
% 0.07/0.32  %            Number of symbols     :   97 (  94 usr;   8 con; 0-4 aty)
% 0.07/0.32  %            Number of variables   : 1206 ( 215   ^; 988   !;   3   ?;1206   :)
% 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 15:45:44.564
% 0.07/0.32  %------------------------------------------------------------------------------
% 0.07/0.32  % Could-be-implicit typings (20)
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% 0.07/0.32  thf(ty_n_t__Sigma____Algebra__Omeasure_I_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J,type,
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% 0.07/0.32  thf(ty_n_t__Set__Oset_I_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J_J,type,
% 0.07/0.32      set_Fi1645173239real_n: $tType ).
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% 0.07/0.32  thf(ty_n_t__Set__Oset_I_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J,type,
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% 0.07/0.32  thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
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% 0.07/0.32  thf(ty_n_t__Nat__Onat,type,
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% 0.07/0.32  
% 0.07/0.32  % Explicit typings (94)
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% 0.07/0.32  
% 0.07/0.32  thf(sy_c_member_001_062_I_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_Mt__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J,type,
% 0.07/0.32      member640587117real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n ) > set_Fi909698444real_n > $o ).
% 0.07/0.32  
% 0.07/0.32  thf(sy_c_member_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_M_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J,type,
% 0.07/0.32      member408431031real_n: ( finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ) > set_Fi1260307670real_n > $o ).
% 0.07/0.32  
% 0.07/0.32  thf(sy_c_member_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J,type,
% 0.07/0.32      member1746150050real_n: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1326602817real_n > $o ).
% 0.07/0.32  
% 0.07/0.32  thf(sy_c_member_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J,type,
% 0.07/0.32      member966061400real_n: ( finite1489363574real_n > set_Fi1058188332real_n ) > set_Fi1645173239real_n > $o ).
% 0.07/0.32  
% 0.07/0.32  thf(sy_c_member_001_062_It__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_M_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J,type,
% 0.07/0.32      member1764433517real_n: ( set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n ) > set_se830533260real_n > $o ).
% 0.07/0.32  
% 0.07/0.32  thf(sy_c_member_001_062_It__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J,type,
% 0.07/0.32      member1759501912real_n: ( set_Fi1058188332real_n > finite1489363574real_n ) > set_se955370231real_n > $o ).
% 0.07/0.32  
% 0.07/0.32  thf(sy_c_member_001_062_It__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_Mt__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J,type,
% 0.07/0.32      member1734791438real_n: ( set_Fi1058188332real_n > set_Fi1058188332real_n ) > set_se1738601133real_n > $o ).
% 0.07/0.32  
% 0.07/0.32  thf(sy_c_member_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J,type,
% 0.07/0.32      member1352538125real_n: finite1489363574real_n > set_Fi1058188332real_n > $o ).
% 0.07/0.32  
% 0.07/0.32  thf(sy_c_member_001t__Set__Oset_I_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J,type,
% 0.07/0.32      member2104752728real_n: set_Fi1326602817real_n > set_se221767415real_n > $o ).
% 0.07/0.32  
% 0.07/0.32  thf(sy_c_member_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J,type,
% 0.07/0.32      member223413699real_n: set_Fi1058188332real_n > set_se2111327970real_n > $o ).
% 0.07/0.32  
% 0.07/0.32  thf(sy_c_member_001t__Set__Oset_It__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J,type,
% 0.07/0.32      member1475136633real_n: set_se2111327970real_n > set_se820660888real_n > $o ).
% 0.07/0.32  
% 0.07/0.32  thf(sy_v_R____,type,
% 0.07/0.32      r: finite964658038_int_n > set_Fi1058188332real_n ).
% 0.07/0.32  
% 0.07/0.32  thf(sy_v_S,type,
% 0.07/0.32      s: set_Fi1058188332real_n ).
% 0.07/0.32  
% 0.07/0.32  thf(sy_v_T_H____,type,
% 0.07/0.32      t: finite964658038_int_n > set_Fi1058188332real_n ).
% 0.07/0.32  
% 0.07/0.32  thf(sy_v_T____,type,
% 0.07/0.32      t2: finite964658038_int_n > set_Fi1058188332real_n ).
% 0.07/0.32  
% 0.07/0.32  thf(sy_v_a____,type,
% 0.07/0.32      a: finite964658038_int_n ).
% 0.07/0.32  
% 0.07/0.32  % Relevant facts (354)
% 0.07/0.32  thf(fact_0_assms_I1_J,axiom,
% 0.07/0.32      member223413699real_n @ s @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ).
% 0.07/0.32  
% 0.07/0.32  % assms(1)
% 0.07/0.32  thf(fact_1_of__int__vec__eq__iff,axiom,
% 0.07/0.32      ! [A: finite964658038_int_n,B: finite964658038_int_n] :
% 0.07/0.32        ( ( ( minkow1134813771n_real @ A )
% 0.07/0.32          = ( minkow1134813771n_real @ B ) )
% 0.07/0.32        = ( A = B ) ) ).
% 0.07/0.32  
% 0.07/0.32  % of_int_vec_eq_iff
% 0.07/0.32  thf(fact_2__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_A_092_060Longrightarrow_062_A_I_092_060lambda_062x_O_Ax_A_L_Aof__int__vec_Aa_J_A_N_096_AT_Aa_A_092_060inter_062_Aspace_Alebesgue_A_092_060in_062_Asets_Alebesgue_092_060close_062,axiom,
% 0.07/0.32      ! [A: finite964658038_int_n] :
% 0.07/0.32        ( ( member223413699real_n @ ( t2 @ A ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
% 0.07/0.32       => ( member223413699real_n
% 0.07/0.32          @ ( inf_in1974387902real_n
% 0.07/0.32            @ ( vimage1233683625real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n] : ( plus_p585657087real_n @ X @ ( minkow1134813771n_real @ A ) )
% 0.07/0.32              @ ( t2 @ A ) )
% 0.07/0.32            @ ( sigma_476185326real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
% 0.07/0.32          @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % \<open>\<And>a. T a \<in> sets lebesgue \<Longrightarrow> (\<lambda>x. x + of_int_vec a) -` T a \<inter> space lebesgue \<in> sets lebesgue\<close>
% 0.07/0.32  thf(fact_3__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062,axiom,
% 0.07/0.32      ! [A: finite964658038_int_n] : ( member223413699real_n @ ( t2 @ A ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % \<open>\<And>a. T a \<in> sets lebesgue\<close>
% 0.07/0.32  thf(fact_4_T_H__altdef,axiom,
% 0.07/0.32      ! [A: finite964658038_int_n] :
% 0.07/0.32        ( ( t @ A )
% 0.07/0.32        = ( vimage1233683625real_n
% 0.07/0.32          @ ^ [X: finite1489363574real_n] : ( plus_p585657087real_n @ X @ ( minkow1134813771n_real @ A ) )
% 0.07/0.32          @ ( t2 @ A ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % T'_altdef
% 0.07/0.32  thf(fact_5__092_060open_062_092_060And_062a_O_AR_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062,axiom,
% 0.07/0.32      ! [A: finite964658038_int_n] : ( member223413699real_n @ ( r @ A ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % \<open>\<And>a. R a \<in> sets lebesgue\<close>
% 0.07/0.32  thf(fact_6_sets__completionI__sets,axiom,
% 0.07/0.32      ! [A2: set_Fi1058188332real_n,M: sigma_1466784463real_n] :
% 0.07/0.32        ( ( member223413699real_n @ A2 @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32       => ( member223413699real_n @ A2 @ ( sigma_1235138647real_n @ ( comple230862828real_n @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets_completionI_sets
% 0.07/0.32  thf(fact_7__092_060open_062_092_060And_062a_O_A_I_092_060lambda_062x_O_Ax_A_L_Aof__int__vec_Aa_J_A_092_060in_062_Alebesgue_A_092_060rightarrow_062_092_060_094sub_062M_Alebesgue_092_060close_062,axiom,
% 0.07/0.32      ! [A: finite964658038_int_n] :
% 0.07/0.32        ( member1746150050real_n
% 0.07/0.32        @ ^ [X: finite1489363574real_n] : ( plus_p585657087real_n @ X @ ( minkow1134813771n_real @ A ) )
% 0.07/0.32        @ ( sigma_439801790real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % \<open>\<And>a. (\<lambda>x. x + of_int_vec a) \<in> lebesgue \<rightarrow>\<^sub>M lebesgue\<close>
% 0.07/0.32  thf(fact_8_vimage__ident,axiom,
% 0.07/0.32      ! [Y: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( vimage1233683625real_n
% 0.07/0.32          @ ^ [X: finite1489363574real_n] : X
% 0.07/0.32          @ Y )
% 0.07/0.32        = Y ) ).
% 0.07/0.32  
% 0.07/0.32  % vimage_ident
% 0.07/0.32  thf(fact_9_vimage__Collect__eq,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n,P: finite1489363574real_n > $o] :
% 0.07/0.32        ( ( vimage1233683625real_n @ F @ ( collec321817931real_n @ P ) )
% 0.07/0.32        = ( collec321817931real_n
% 0.07/0.32          @ ^ [Y2: finite1489363574real_n] : ( P @ ( F @ Y2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimage_Collect_eq
% 0.07/0.32  thf(fact_10_vimageI,axiom,
% 0.07/0.32      ! [F: set_Fi1058188332real_n > set_Fi1058188332real_n,A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,B2: set_se2111327970real_n] :
% 0.07/0.32        ( ( ( F @ A )
% 0.07/0.32          = B )
% 0.07/0.32       => ( ( member223413699real_n @ B @ B2 )
% 0.07/0.32         => ( member223413699real_n @ A @ ( vimage784510485real_n @ F @ B2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimageI
% 0.07/0.32  thf(fact_11_vimageI,axiom,
% 0.07/0.32      ! [F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n,B2: set_se2111327970real_n] :
% 0.07/0.32        ( ( ( F @ A )
% 0.07/0.32          = B )
% 0.07/0.32       => ( ( member223413699real_n @ B @ B2 )
% 0.07/0.32         => ( member1746150050real_n @ A @ ( vimage1910974324real_n @ F @ B2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimageI
% 0.07/0.32  thf(fact_12_vimageI,axiom,
% 0.07/0.32      ! [F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,A: set_Fi1058188332real_n,B: finite1489363574real_n > finite1489363574real_n,B2: set_Fi1326602817real_n] :
% 0.07/0.32        ( ( ( F @ A )
% 0.07/0.32          = B )
% 0.07/0.32       => ( ( member1746150050real_n @ B @ B2 )
% 0.07/0.32         => ( member223413699real_n @ A @ ( vimage2134951412real_n @ F @ B2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimageI
% 0.07/0.32  thf(fact_13_vimageI,axiom,
% 0.07/0.32      ! [F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,A: finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n,B2: set_Fi1326602817real_n] :
% 0.07/0.32        ( ( ( F @ A )
% 0.07/0.32          = B )
% 0.07/0.32       => ( ( member1746150050real_n @ B @ B2 )
% 0.07/0.32         => ( member1746150050real_n @ A @ ( vimage180751827real_n @ F @ B2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimageI
% 0.07/0.32  thf(fact_14_vimageI,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n,A: finite1489363574real_n,B: finite1489363574real_n,B2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( ( F @ A )
% 0.07/0.32          = B )
% 0.07/0.32       => ( ( member1352538125real_n @ B @ B2 )
% 0.07/0.32         => ( member1352538125real_n @ A @ ( vimage1233683625real_n @ F @ B2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimageI
% 0.07/0.32  thf(fact_15_vimage__eq,axiom,
% 0.07/0.32      ! [A: set_Fi1058188332real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n,B2: set_se2111327970real_n] :
% 0.07/0.32        ( ( member223413699real_n @ A @ ( vimage784510485real_n @ F @ B2 ) )
% 0.07/0.32        = ( member223413699real_n @ ( F @ A ) @ B2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimage_eq
% 0.07/0.32  thf(fact_16_vimage__eq,axiom,
% 0.07/0.32      ! [A: set_Fi1058188332real_n,F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,B2: set_Fi1326602817real_n] :
% 0.07/0.32        ( ( member223413699real_n @ A @ ( vimage2134951412real_n @ F @ B2 ) )
% 0.07/0.32        = ( member1746150050real_n @ ( F @ A ) @ B2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimage_eq
% 0.07/0.32  thf(fact_17_vimage__eq,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n > finite1489363574real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,B2: set_se2111327970real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ A @ ( vimage1910974324real_n @ F @ B2 ) )
% 0.07/0.32        = ( member223413699real_n @ ( F @ A ) @ B2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimage_eq
% 0.07/0.32  thf(fact_18_vimage__eq,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n > finite1489363574real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,B2: set_Fi1326602817real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ A @ ( vimage180751827real_n @ F @ B2 ) )
% 0.07/0.32        = ( member1746150050real_n @ ( F @ A ) @ B2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimage_eq
% 0.07/0.32  thf(fact_19_vimage__eq,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n,B2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member1352538125real_n @ A @ ( vimage1233683625real_n @ F @ B2 ) )
% 0.07/0.32        = ( member1352538125real_n @ ( F @ A ) @ B2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimage_eq
% 0.07/0.32  thf(fact_20_set__plus__intro,axiom,
% 0.07/0.32      ! [A: set_Fi1058188332real_n,C: set_se2111327970real_n,B: set_Fi1058188332real_n,D: set_se2111327970real_n] :
% 0.07/0.32        ( ( member223413699real_n @ A @ C )
% 0.07/0.32       => ( ( member223413699real_n @ B @ D )
% 0.07/0.32         => ( member223413699real_n @ ( plus_p1606848693real_n @ A @ B ) @ ( plus_p565022571real_n @ C @ D ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % set_plus_intro
% 0.07/0.32  thf(fact_21_set__plus__intro,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,C: set_Fi1058188332real_n,B: finite1489363574real_n,D: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member1352538125real_n @ A @ C )
% 0.07/0.32       => ( ( member1352538125real_n @ B @ D )
% 0.07/0.32         => ( member1352538125real_n @ ( plus_p585657087real_n @ A @ B ) @ ( plus_p1606848693real_n @ C @ D ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % set_plus_intro
% 0.07/0.32  thf(fact_22_add__left__cancel,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] :
% 0.07/0.32        ( ( ( plus_p585657087real_n @ A @ B )
% 0.07/0.32          = ( plus_p585657087real_n @ A @ C2 ) )
% 0.07/0.32        = ( B = C2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % add_left_cancel
% 0.07/0.32  thf(fact_23_add__right__cancel,axiom,
% 0.07/0.32      ! [B: finite1489363574real_n,A: finite1489363574real_n,C2: finite1489363574real_n] :
% 0.07/0.32        ( ( ( plus_p585657087real_n @ B @ A )
% 0.07/0.32          = ( plus_p585657087real_n @ C2 @ A ) )
% 0.07/0.32        = ( B = C2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % add_right_cancel
% 0.07/0.32  thf(fact_24_vimage__def,axiom,
% 0.07/0.32      ( vimage207290975real_n
% 0.07/0.32      = ( ^ [F2: finite1489363574real_n > set_Fi1058188332real_n,B3: set_se2111327970real_n] :
% 0.07/0.32            ( collec321817931real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n] : ( member223413699real_n @ ( F2 @ X ) @ B3 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimage_def
% 0.07/0.32  thf(fact_25_vimage__def,axiom,
% 0.07/0.32      ( vimage1059850558real_n
% 0.07/0.32      = ( ^ [F2: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n,B3: set_Fi1326602817real_n] :
% 0.07/0.32            ( collec321817931real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n] : ( member1746150050real_n @ ( F2 @ X ) @ B3 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimage_def
% 0.07/0.32  thf(fact_26_vimage__def,axiom,
% 0.07/0.32      ( vimage1233683625real_n
% 0.07/0.32      = ( ^ [F2: finite1489363574real_n > finite1489363574real_n,B3: set_Fi1058188332real_n] :
% 0.07/0.32            ( collec321817931real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ ( F2 @ X ) @ B3 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimage_def
% 0.07/0.32  thf(fact_27_vimageD,axiom,
% 0.07/0.32      ! [A: set_Fi1058188332real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n,A2: set_se2111327970real_n] :
% 0.07/0.32        ( ( member223413699real_n @ A @ ( vimage784510485real_n @ F @ A2 ) )
% 0.07/0.32       => ( member223413699real_n @ ( F @ A ) @ A2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimageD
% 0.07/0.32  thf(fact_28_vimageD,axiom,
% 0.07/0.32      ! [A: set_Fi1058188332real_n,F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n] :
% 0.07/0.32        ( ( member223413699real_n @ A @ ( vimage2134951412real_n @ F @ A2 ) )
% 0.07/0.32       => ( member1746150050real_n @ ( F @ A ) @ A2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimageD
% 0.07/0.32  thf(fact_29_vimageD,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n > finite1489363574real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,A2: set_se2111327970real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ A @ ( vimage1910974324real_n @ F @ A2 ) )
% 0.07/0.32       => ( member223413699real_n @ ( F @ A ) @ A2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimageD
% 0.07/0.32  thf(fact_30_vimageD,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n > finite1489363574real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ A @ ( vimage180751827real_n @ F @ A2 ) )
% 0.07/0.32       => ( member1746150050real_n @ ( F @ A ) @ A2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimageD
% 0.07/0.32  thf(fact_31_vimageD,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member1352538125real_n @ A @ ( vimage1233683625real_n @ F @ A2 ) )
% 0.07/0.32       => ( member1352538125real_n @ ( F @ A ) @ A2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimageD
% 0.07/0.32  thf(fact_32_vimageE,axiom,
% 0.07/0.32      ! [A: set_Fi1058188332real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n,B2: set_se2111327970real_n] :
% 0.07/0.32        ( ( member223413699real_n @ A @ ( vimage784510485real_n @ F @ B2 ) )
% 0.07/0.32       => ( member223413699real_n @ ( F @ A ) @ B2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimageE
% 0.07/0.32  thf(fact_33_vimageE,axiom,
% 0.07/0.32      ! [A: set_Fi1058188332real_n,F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,B2: set_Fi1326602817real_n] :
% 0.07/0.32        ( ( member223413699real_n @ A @ ( vimage2134951412real_n @ F @ B2 ) )
% 0.07/0.32       => ( member1746150050real_n @ ( F @ A ) @ B2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimageE
% 0.07/0.32  thf(fact_34_vimageE,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n > finite1489363574real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,B2: set_se2111327970real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ A @ ( vimage1910974324real_n @ F @ B2 ) )
% 0.07/0.32       => ( member223413699real_n @ ( F @ A ) @ B2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimageE
% 0.07/0.32  thf(fact_35_vimageE,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n > finite1489363574real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,B2: set_Fi1326602817real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ A @ ( vimage180751827real_n @ F @ B2 ) )
% 0.07/0.32       => ( member1746150050real_n @ ( F @ A ) @ B2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimageE
% 0.07/0.32  thf(fact_36_vimageE,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n,B2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member1352538125real_n @ A @ ( vimage1233683625real_n @ F @ B2 ) )
% 0.07/0.32       => ( member1352538125real_n @ ( F @ A ) @ B2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimageE
% 0.07/0.32  thf(fact_37_IntI,axiom,
% 0.07/0.32      ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] :
% 0.07/0.32        ( ( member223413699real_n @ C2 @ A2 )
% 0.07/0.32       => ( ( member223413699real_n @ C2 @ B2 )
% 0.07/0.32         => ( member223413699real_n @ C2 @ ( inf_in632889204real_n @ A2 @ B2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % IntI
% 0.07/0.32  thf(fact_38_IntI,axiom,
% 0.07/0.32      ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ C2 @ A2 )
% 0.07/0.32       => ( ( member1746150050real_n @ C2 @ B2 )
% 0.07/0.32         => ( member1746150050real_n @ C2 @ ( inf_in146441683real_n @ A2 @ B2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % IntI
% 0.07/0.32  thf(fact_39_IntI,axiom,
% 0.07/0.32      ! [C2: finite1489363574real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member1352538125real_n @ C2 @ A2 )
% 0.07/0.32       => ( ( member1352538125real_n @ C2 @ B2 )
% 0.07/0.32         => ( member1352538125real_n @ C2 @ ( inf_in1974387902real_n @ A2 @ B2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % IntI
% 0.07/0.32  thf(fact_40_Int__iff,axiom,
% 0.07/0.32      ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] :
% 0.07/0.32        ( ( member223413699real_n @ C2 @ ( inf_in632889204real_n @ A2 @ B2 ) )
% 0.07/0.32        = ( ( member223413699real_n @ C2 @ A2 )
% 0.07/0.32          & ( member223413699real_n @ C2 @ B2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Int_iff
% 0.07/0.32  thf(fact_41_Int__iff,axiom,
% 0.07/0.32      ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ C2 @ ( inf_in146441683real_n @ A2 @ B2 ) )
% 0.07/0.32        = ( ( member1746150050real_n @ C2 @ A2 )
% 0.07/0.32          & ( member1746150050real_n @ C2 @ B2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Int_iff
% 0.07/0.32  thf(fact_42_Int__iff,axiom,
% 0.07/0.32      ! [C2: finite1489363574real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member1352538125real_n @ C2 @ ( inf_in1974387902real_n @ A2 @ B2 ) )
% 0.07/0.32        = ( ( member1352538125real_n @ C2 @ A2 )
% 0.07/0.32          & ( member1352538125real_n @ C2 @ B2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Int_iff
% 0.07/0.32  thf(fact_43_space__completion,axiom,
% 0.07/0.32      ! [M: sigma_1466784463real_n] :
% 0.07/0.32        ( ( sigma_476185326real_n @ ( comple230862828real_n @ M ) )
% 0.07/0.32        = ( sigma_476185326real_n @ M ) ) ).
% 0.07/0.32  
% 0.07/0.32  % space_completion
% 0.07/0.32  thf(fact_44_vimage__Int,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( vimage1233683625real_n @ F @ ( inf_in1974387902real_n @ A2 @ B2 ) )
% 0.07/0.32        = ( inf_in1974387902real_n @ ( vimage1233683625real_n @ F @ A2 ) @ ( vimage1233683625real_n @ F @ B2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimage_Int
% 0.07/0.32  thf(fact_45_T__def,axiom,
% 0.07/0.32      ( t2
% 0.07/0.32      = ( ^ [A3: finite964658038_int_n] : ( inf_in1974387902real_n @ s @ ( r @ A3 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % T_def
% 0.07/0.32  thf(fact_46_IntE,axiom,
% 0.07/0.32      ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] :
% 0.07/0.32        ( ( member223413699real_n @ C2 @ ( inf_in632889204real_n @ A2 @ B2 ) )
% 0.07/0.32       => ~ ( ( member223413699real_n @ C2 @ A2 )
% 0.07/0.32           => ~ ( member223413699real_n @ C2 @ B2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % IntE
% 0.07/0.32  thf(fact_47_IntE,axiom,
% 0.07/0.32      ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ C2 @ ( inf_in146441683real_n @ A2 @ B2 ) )
% 0.07/0.32       => ~ ( ( member1746150050real_n @ C2 @ A2 )
% 0.07/0.32           => ~ ( member1746150050real_n @ C2 @ B2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % IntE
% 0.07/0.32  thf(fact_48_IntE,axiom,
% 0.07/0.32      ! [C2: finite1489363574real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member1352538125real_n @ C2 @ ( inf_in1974387902real_n @ A2 @ B2 ) )
% 0.07/0.32       => ~ ( ( member1352538125real_n @ C2 @ A2 )
% 0.07/0.32           => ~ ( member1352538125real_n @ C2 @ B2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % IntE
% 0.07/0.32  thf(fact_49_IntD1,axiom,
% 0.07/0.32      ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] :
% 0.07/0.32        ( ( member223413699real_n @ C2 @ ( inf_in632889204real_n @ A2 @ B2 ) )
% 0.07/0.32       => ( member223413699real_n @ C2 @ A2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % IntD1
% 0.07/0.32  thf(fact_50_IntD1,axiom,
% 0.07/0.32      ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ C2 @ ( inf_in146441683real_n @ A2 @ B2 ) )
% 0.07/0.32       => ( member1746150050real_n @ C2 @ A2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % IntD1
% 0.07/0.32  thf(fact_51_IntD1,axiom,
% 0.07/0.32      ! [C2: finite1489363574real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member1352538125real_n @ C2 @ ( inf_in1974387902real_n @ A2 @ B2 ) )
% 0.07/0.32       => ( member1352538125real_n @ C2 @ A2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % IntD1
% 0.07/0.32  thf(fact_52_IntD2,axiom,
% 0.07/0.32      ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] :
% 0.07/0.32        ( ( member223413699real_n @ C2 @ ( inf_in632889204real_n @ A2 @ B2 ) )
% 0.07/0.32       => ( member223413699real_n @ C2 @ B2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % IntD2
% 0.07/0.32  thf(fact_53_IntD2,axiom,
% 0.07/0.32      ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ C2 @ ( inf_in146441683real_n @ A2 @ B2 ) )
% 0.07/0.32       => ( member1746150050real_n @ C2 @ B2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % IntD2
% 0.07/0.32  thf(fact_54_IntD2,axiom,
% 0.07/0.32      ! [C2: finite1489363574real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member1352538125real_n @ C2 @ ( inf_in1974387902real_n @ A2 @ B2 ) )
% 0.07/0.32       => ( member1352538125real_n @ C2 @ B2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % IntD2
% 0.07/0.32  thf(fact_55_Int__assoc,axiom,
% 0.07/0.32      ! [A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ A2 @ B2 ) @ C )
% 0.07/0.32        = ( inf_in1974387902real_n @ A2 @ ( inf_in1974387902real_n @ B2 @ C ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Int_assoc
% 0.07/0.32  thf(fact_56_Int__absorb,axiom,
% 0.07/0.32      ! [A2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( inf_in1974387902real_n @ A2 @ A2 )
% 0.07/0.32        = A2 ) ).
% 0.07/0.32  
% 0.07/0.32  % Int_absorb
% 0.07/0.32  thf(fact_57_Int__commute,axiom,
% 0.07/0.32      ( inf_in1974387902real_n
% 0.07/0.32      = ( ^ [A4: set_Fi1058188332real_n,B3: set_Fi1058188332real_n] : ( inf_in1974387902real_n @ B3 @ A4 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Int_commute
% 0.07/0.32  thf(fact_58_Int__left__absorb,axiom,
% 0.07/0.32      ! [A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( inf_in1974387902real_n @ A2 @ ( inf_in1974387902real_n @ A2 @ B2 ) )
% 0.07/0.32        = ( inf_in1974387902real_n @ A2 @ B2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Int_left_absorb
% 0.07/0.32  thf(fact_59_Int__left__commute,axiom,
% 0.07/0.32      ! [A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( inf_in1974387902real_n @ A2 @ ( inf_in1974387902real_n @ B2 @ C ) )
% 0.07/0.32        = ( inf_in1974387902real_n @ B2 @ ( inf_in1974387902real_n @ A2 @ C ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Int_left_commute
% 0.07/0.32  thf(fact_60_Collect__conj__eq,axiom,
% 0.07/0.32      ! [P: finite1489363574real_n > $o,Q: finite1489363574real_n > $o] :
% 0.07/0.32        ( ( collec321817931real_n
% 0.07/0.32          @ ^ [X: finite1489363574real_n] :
% 0.07/0.32              ( ( P @ X )
% 0.07/0.32              & ( Q @ X ) ) )
% 0.07/0.32        = ( inf_in1974387902real_n @ ( collec321817931real_n @ P ) @ ( collec321817931real_n @ Q ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Collect_conj_eq
% 0.07/0.32  thf(fact_61_Int__Collect,axiom,
% 0.07/0.32      ! [X2: set_Fi1058188332real_n,A2: set_se2111327970real_n,P: set_Fi1058188332real_n > $o] :
% 0.07/0.32        ( ( member223413699real_n @ X2 @ ( inf_in632889204real_n @ A2 @ ( collec452821761real_n @ P ) ) )
% 0.07/0.32        = ( ( member223413699real_n @ X2 @ A2 )
% 0.07/0.32          & ( P @ X2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Int_Collect
% 0.07/0.32  thf(fact_62_Int__Collect,axiom,
% 0.07/0.32      ! [X2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
% 0.07/0.32        ( ( member1746150050real_n @ X2 @ ( inf_in146441683real_n @ A2 @ ( collec1190264032real_n @ P ) ) )
% 0.07/0.32        = ( ( member1746150050real_n @ X2 @ A2 )
% 0.07/0.32          & ( P @ X2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Int_Collect
% 0.07/0.32  thf(fact_63_Int__Collect,axiom,
% 0.07/0.32      ! [X2: finite1489363574real_n,A2: set_Fi1058188332real_n,P: finite1489363574real_n > $o] :
% 0.07/0.32        ( ( member1352538125real_n @ X2 @ ( inf_in1974387902real_n @ A2 @ ( collec321817931real_n @ P ) ) )
% 0.07/0.32        = ( ( member1352538125real_n @ X2 @ A2 )
% 0.07/0.32          & ( P @ X2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Int_Collect
% 0.07/0.32  thf(fact_64_Int__def,axiom,
% 0.07/0.32      ( inf_in632889204real_n
% 0.07/0.32      = ( ^ [A4: set_se2111327970real_n,B3: set_se2111327970real_n] :
% 0.07/0.32            ( collec452821761real_n
% 0.07/0.32            @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32                ( ( member223413699real_n @ X @ A4 )
% 0.07/0.32                & ( member223413699real_n @ X @ B3 ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Int_def
% 0.07/0.32  thf(fact_65_Int__def,axiom,
% 0.07/0.32      ( inf_in146441683real_n
% 0.07/0.32      = ( ^ [A4: set_Fi1326602817real_n,B3: set_Fi1326602817real_n] :
% 0.07/0.32            ( collec1190264032real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32                ( ( member1746150050real_n @ X @ A4 )
% 0.07/0.32                & ( member1746150050real_n @ X @ B3 ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Int_def
% 0.07/0.32  thf(fact_66_Int__def,axiom,
% 0.07/0.32      ( inf_in1974387902real_n
% 0.07/0.32      = ( ^ [A4: set_Fi1058188332real_n,B3: set_Fi1058188332real_n] :
% 0.07/0.32            ( collec321817931real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                ( ( member1352538125real_n @ X @ A4 )
% 0.07/0.32                & ( member1352538125real_n @ X @ B3 ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Int_def
% 0.07/0.32  thf(fact_67_measurable__completion,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,N: sigma_1466784463real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ N ) )
% 0.07/0.32       => ( member1746150050real_n @ F @ ( sigma_439801790real_n @ ( comple230862828real_n @ M ) @ N ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_completion
% 0.07/0.32  thf(fact_68_vimage__inter__cong,axiom,
% 0.07/0.32      ! [S: set_Fi1058188332real_n,F: finite1489363574real_n > finite1489363574real_n,G: finite1489363574real_n > finite1489363574real_n,Y3: set_Fi1058188332real_n] :
% 0.07/0.32        ( ! [W: finite1489363574real_n] :
% 0.07/0.32            ( ( member1352538125real_n @ W @ S )
% 0.07/0.32           => ( ( F @ W )
% 0.07/0.32              = ( G @ W ) ) )
% 0.07/0.32       => ( ( inf_in1974387902real_n @ ( vimage1233683625real_n @ F @ Y3 ) @ S )
% 0.07/0.32          = ( inf_in1974387902real_n @ ( vimage1233683625real_n @ G @ Y3 ) @ S ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimage_inter_cong
% 0.07/0.32  thf(fact_69_add__right__imp__eq,axiom,
% 0.07/0.32      ! [B: finite1489363574real_n,A: finite1489363574real_n,C2: finite1489363574real_n] :
% 0.07/0.32        ( ( ( plus_p585657087real_n @ B @ A )
% 0.07/0.32          = ( plus_p585657087real_n @ C2 @ A ) )
% 0.07/0.32       => ( B = C2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % add_right_imp_eq
% 0.07/0.32  thf(fact_70_add__left__imp__eq,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] :
% 0.07/0.32        ( ( ( plus_p585657087real_n @ A @ B )
% 0.07/0.32          = ( plus_p585657087real_n @ A @ C2 ) )
% 0.07/0.32       => ( B = C2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % add_left_imp_eq
% 0.07/0.32  thf(fact_71_add_Oleft__commute,axiom,
% 0.07/0.32      ! [B: finite1489363574real_n,A: finite1489363574real_n,C2: finite1489363574real_n] :
% 0.07/0.32        ( ( plus_p585657087real_n @ B @ ( plus_p585657087real_n @ A @ C2 ) )
% 0.07/0.32        = ( plus_p585657087real_n @ A @ ( plus_p585657087real_n @ B @ C2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % add.left_commute
% 0.07/0.32  thf(fact_72_add_Ocommute,axiom,
% 0.07/0.32      ( plus_p585657087real_n
% 0.07/0.32      = ( ^ [A3: finite1489363574real_n,B4: finite1489363574real_n] : ( plus_p585657087real_n @ B4 @ A3 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % add.commute
% 0.07/0.32  thf(fact_73_add_Oright__cancel,axiom,
% 0.07/0.32      ! [B: finite1489363574real_n,A: finite1489363574real_n,C2: finite1489363574real_n] :
% 0.07/0.32        ( ( ( plus_p585657087real_n @ B @ A )
% 0.07/0.32          = ( plus_p585657087real_n @ C2 @ A ) )
% 0.07/0.32        = ( B = C2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % add.right_cancel
% 0.07/0.32  thf(fact_74_add_Oleft__cancel,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] :
% 0.07/0.32        ( ( ( plus_p585657087real_n @ A @ B )
% 0.07/0.32          = ( plus_p585657087real_n @ A @ C2 ) )
% 0.07/0.32        = ( B = C2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % add.left_cancel
% 0.07/0.32  thf(fact_75_add_Oassoc,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] :
% 0.07/0.32        ( ( plus_p585657087real_n @ ( plus_p585657087real_n @ A @ B ) @ C2 )
% 0.07/0.32        = ( plus_p585657087real_n @ A @ ( plus_p585657087real_n @ B @ C2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % add.assoc
% 0.07/0.32  thf(fact_76_set__plus__elim,axiom,
% 0.07/0.32      ! [X2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] :
% 0.07/0.32        ( ( member223413699real_n @ X2 @ ( plus_p565022571real_n @ A2 @ B2 ) )
% 0.07/0.32       => ~ ! [A5: set_Fi1058188332real_n,B5: set_Fi1058188332real_n] :
% 0.07/0.32              ( ( X2
% 0.07/0.32                = ( plus_p1606848693real_n @ A5 @ B5 ) )
% 0.07/0.32             => ( ( member223413699real_n @ A5 @ A2 )
% 0.07/0.32               => ~ ( member223413699real_n @ B5 @ B2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % set_plus_elim
% 0.07/0.32  thf(fact_77_set__plus__elim,axiom,
% 0.07/0.32      ! [X2: finite1489363574real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member1352538125real_n @ X2 @ ( plus_p1606848693real_n @ A2 @ B2 ) )
% 0.07/0.32       => ~ ! [A5: finite1489363574real_n,B5: finite1489363574real_n] :
% 0.07/0.32              ( ( X2
% 0.07/0.32                = ( plus_p585657087real_n @ A5 @ B5 ) )
% 0.07/0.32             => ( ( member1352538125real_n @ A5 @ A2 )
% 0.07/0.32               => ~ ( member1352538125real_n @ B5 @ B2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % set_plus_elim
% 0.07/0.32  thf(fact_78_group__cancel_Oadd2,axiom,
% 0.07/0.32      ! [B2: finite1489363574real_n,K: finite1489363574real_n,B: finite1489363574real_n,A: finite1489363574real_n] :
% 0.07/0.32        ( ( B2
% 0.07/0.32          = ( plus_p585657087real_n @ K @ B ) )
% 0.07/0.32       => ( ( plus_p585657087real_n @ A @ B2 )
% 0.07/0.32          = ( plus_p585657087real_n @ K @ ( plus_p585657087real_n @ A @ B ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % group_cancel.add2
% 0.07/0.32  thf(fact_79_mem__Collect__eq,axiom,
% 0.07/0.32      ! [A: set_Fi1058188332real_n,P: set_Fi1058188332real_n > $o] :
% 0.07/0.32        ( ( member223413699real_n @ A @ ( collec452821761real_n @ P ) )
% 0.07/0.32        = ( P @ A ) ) ).
% 0.07/0.32  
% 0.07/0.32  % mem_Collect_eq
% 0.07/0.32  thf(fact_80_mem__Collect__eq,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n > finite1489363574real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
% 0.07/0.32        ( ( member1746150050real_n @ A @ ( collec1190264032real_n @ P ) )
% 0.07/0.32        = ( P @ A ) ) ).
% 0.07/0.32  
% 0.07/0.32  % mem_Collect_eq
% 0.07/0.32  thf(fact_81_mem__Collect__eq,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,P: finite1489363574real_n > $o] :
% 0.07/0.32        ( ( member1352538125real_n @ A @ ( collec321817931real_n @ P ) )
% 0.07/0.32        = ( P @ A ) ) ).
% 0.07/0.32  
% 0.07/0.32  % mem_Collect_eq
% 0.07/0.32  thf(fact_82_Collect__mem__eq,axiom,
% 0.07/0.32      ! [A2: set_se2111327970real_n] :
% 0.07/0.32        ( ( collec452821761real_n
% 0.07/0.32          @ ^ [X: set_Fi1058188332real_n] : ( member223413699real_n @ X @ A2 ) )
% 0.07/0.32        = A2 ) ).
% 0.07/0.32  
% 0.07/0.32  % Collect_mem_eq
% 0.07/0.32  thf(fact_83_Collect__mem__eq,axiom,
% 0.07/0.32      ! [A2: set_Fi1326602817real_n] :
% 0.07/0.32        ( ( collec1190264032real_n
% 0.07/0.32          @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ X @ A2 ) )
% 0.07/0.32        = A2 ) ).
% 0.07/0.32  
% 0.07/0.32  % Collect_mem_eq
% 0.07/0.32  thf(fact_84_Collect__mem__eq,axiom,
% 0.07/0.32      ! [A2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( collec321817931real_n
% 0.07/0.32          @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ X @ A2 ) )
% 0.07/0.32        = A2 ) ).
% 0.07/0.32  
% 0.07/0.32  % Collect_mem_eq
% 0.07/0.32  thf(fact_85_Collect__cong,axiom,
% 0.07/0.32      ! [P: finite1489363574real_n > $o,Q: finite1489363574real_n > $o] :
% 0.07/0.32        ( ! [X3: finite1489363574real_n] :
% 0.07/0.32            ( ( P @ X3 )
% 0.07/0.32            = ( Q @ X3 ) )
% 0.07/0.32       => ( ( collec321817931real_n @ P )
% 0.07/0.32          = ( collec321817931real_n @ Q ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Collect_cong
% 0.07/0.32  thf(fact_86_group__cancel_Oadd1,axiom,
% 0.07/0.32      ! [A2: finite1489363574real_n,K: finite1489363574real_n,A: finite1489363574real_n,B: finite1489363574real_n] :
% 0.07/0.32        ( ( A2
% 0.07/0.32          = ( plus_p585657087real_n @ K @ A ) )
% 0.07/0.32       => ( ( plus_p585657087real_n @ A2 @ B )
% 0.07/0.32          = ( plus_p585657087real_n @ K @ ( plus_p585657087real_n @ A @ B ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % group_cancel.add1
% 0.07/0.32  thf(fact_87_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.07/0.32      ! [I: finite1489363574real_n,J: finite1489363574real_n,K: finite1489363574real_n,L: finite1489363574real_n] :
% 0.07/0.32        ( ( ( I = J )
% 0.07/0.32          & ( K = L ) )
% 0.07/0.32       => ( ( plus_p585657087real_n @ I @ K )
% 0.07/0.32          = ( plus_p585657087real_n @ J @ L ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % add_mono_thms_linordered_semiring(4)
% 0.07/0.32  thf(fact_88_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] :
% 0.07/0.32        ( ( plus_p585657087real_n @ ( plus_p585657087real_n @ A @ B ) @ C2 )
% 0.07/0.32        = ( plus_p585657087real_n @ A @ ( plus_p585657087real_n @ B @ C2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % ab_semigroup_add_class.add_ac(1)
% 0.07/0.32  thf(fact_89_vimage__Collect,axiom,
% 0.07/0.32      ! [P: finite1489363574real_n > $o,F: finite1489363574real_n > finite1489363574real_n,Q: finite1489363574real_n > $o] :
% 0.07/0.32        ( ! [X3: finite1489363574real_n] :
% 0.07/0.32            ( ( P @ ( F @ X3 ) )
% 0.07/0.32            = ( Q @ X3 ) )
% 0.07/0.32       => ( ( vimage1233683625real_n @ F @ ( collec321817931real_n @ P ) )
% 0.07/0.32          = ( collec321817931real_n @ Q ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimage_Collect
% 0.07/0.32  thf(fact_90_vimageI2,axiom,
% 0.07/0.32      ! [F: set_Fi1058188332real_n > set_Fi1058188332real_n,A: set_Fi1058188332real_n,A2: set_se2111327970real_n] :
% 0.07/0.32        ( ( member223413699real_n @ ( F @ A ) @ A2 )
% 0.07/0.32       => ( member223413699real_n @ A @ ( vimage784510485real_n @ F @ A2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimageI2
% 0.07/0.32  thf(fact_91_vimageI2,axiom,
% 0.07/0.32      ! [F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,A: finite1489363574real_n > finite1489363574real_n,A2: set_se2111327970real_n] :
% 0.07/0.32        ( ( member223413699real_n @ ( F @ A ) @ A2 )
% 0.07/0.32       => ( member1746150050real_n @ A @ ( vimage1910974324real_n @ F @ A2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimageI2
% 0.07/0.32  thf(fact_92_vimageI2,axiom,
% 0.07/0.32      ! [F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,A: set_Fi1058188332real_n,A2: set_Fi1326602817real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ ( F @ A ) @ A2 )
% 0.07/0.32       => ( member223413699real_n @ A @ ( vimage2134951412real_n @ F @ A2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimageI2
% 0.07/0.32  thf(fact_93_vimageI2,axiom,
% 0.07/0.32      ! [F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,A: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ ( F @ A ) @ A2 )
% 0.07/0.32       => ( member1746150050real_n @ A @ ( vimage180751827real_n @ F @ A2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimageI2
% 0.07/0.32  thf(fact_94_vimageI2,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n,A: finite1489363574real_n,A2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member1352538125real_n @ ( F @ A ) @ A2 )
% 0.07/0.32       => ( member1352538125real_n @ A @ ( vimage1233683625real_n @ F @ A2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimageI2
% 0.07/0.32  thf(fact_95_sets_OInt__space__eq2,axiom,
% 0.07/0.32      ! [X2: set_Fi1058188332real_n,M: sigma_1466784463real_n] :
% 0.07/0.32        ( ( member223413699real_n @ X2 @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32       => ( ( inf_in1974387902real_n @ X2 @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32          = X2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets.Int_space_eq2
% 0.07/0.32  thf(fact_96_sets_OInt__space__eq1,axiom,
% 0.07/0.32      ! [X2: set_Fi1058188332real_n,M: sigma_1466784463real_n] :
% 0.07/0.32        ( ( member223413699real_n @ X2 @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32       => ( ( inf_in1974387902real_n @ ( sigma_476185326real_n @ M ) @ X2 )
% 0.07/0.32          = X2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets.Int_space_eq1
% 0.07/0.32  thf(fact_97_measurable__sets,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,A2: sigma_1466784463real_n,S: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ A2 ) )
% 0.07/0.32       => ( ( member223413699real_n @ S @ ( sigma_1235138647real_n @ A2 ) )
% 0.07/0.32         => ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage1233683625real_n @ F @ S ) @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_sets
% 0.07/0.32  thf(fact_98_measurableI,axiom,
% 0.07/0.32      ! [M: sigma_1422848389real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n,N: sigma_1422848389real_n] :
% 0.07/0.32        ( ! [X3: set_Fi1058188332real_n] :
% 0.07/0.32            ( ( member223413699real_n @ X3 @ ( sigma_607186084real_n @ M ) )
% 0.07/0.32           => ( member223413699real_n @ ( F @ X3 ) @ ( sigma_607186084real_n @ N ) ) )
% 0.07/0.32       => ( ! [A6: set_se2111327970real_n] :
% 0.07/0.32              ( ( member1475136633real_n @ A6 @ ( sigma_433815053real_n @ N ) )
% 0.07/0.32             => ( member1475136633real_n @ ( inf_in632889204real_n @ ( vimage784510485real_n @ F @ A6 ) @ ( sigma_607186084real_n @ M ) ) @ ( sigma_433815053real_n @ M ) ) )
% 0.07/0.32         => ( member1734791438real_n @ F @ ( sigma_239294762real_n @ M @ N ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurableI
% 0.07/0.32  thf(fact_99_measurableI,axiom,
% 0.07/0.32      ! [M: sigma_1422848389real_n,F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,N: sigma_107786596real_n] :
% 0.07/0.32        ( ! [X3: set_Fi1058188332real_n] :
% 0.07/0.32            ( ( member223413699real_n @ X3 @ ( sigma_607186084real_n @ M ) )
% 0.07/0.32           => ( member1746150050real_n @ ( F @ X3 ) @ ( sigma_1483971331real_n @ N ) ) )
% 0.07/0.32       => ( ! [A6: set_Fi1326602817real_n] :
% 0.07/0.32              ( ( member2104752728real_n @ A6 @ ( sigma_522684908real_n @ N ) )
% 0.07/0.32             => ( member1475136633real_n @ ( inf_in632889204real_n @ ( vimage2134951412real_n @ F @ A6 ) @ ( sigma_607186084real_n @ M ) ) @ ( sigma_433815053real_n @ M ) ) )
% 0.07/0.32         => ( member1764433517real_n @ F @ ( sigma_588796041real_n @ M @ N ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurableI
% 0.07/0.32  thf(fact_100_measurableI,axiom,
% 0.07/0.32      ! [M: sigma_107786596real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,N: sigma_1422848389real_n] :
% 0.07/0.32        ( ! [X3: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32            ( ( member1746150050real_n @ X3 @ ( sigma_1483971331real_n @ M ) )
% 0.07/0.32           => ( member223413699real_n @ ( F @ X3 ) @ ( sigma_607186084real_n @ N ) ) )
% 0.07/0.32       => ( ! [A6: set_se2111327970real_n] :
% 0.07/0.32              ( ( member1475136633real_n @ A6 @ ( sigma_433815053real_n @ N ) )
% 0.07/0.32             => ( member2104752728real_n @ ( inf_in146441683real_n @ ( vimage1910974324real_n @ F @ A6 ) @ ( sigma_1483971331real_n @ M ) ) @ ( sigma_522684908real_n @ M ) ) )
% 0.07/0.32         => ( member640587117real_n @ F @ ( sigma_364818953real_n @ M @ N ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurableI
% 0.07/0.32  thf(fact_101_measurableI,axiom,
% 0.07/0.32      ! [M: sigma_107786596real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,N: sigma_107786596real_n] :
% 0.07/0.32        ( ! [X3: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32            ( ( member1746150050real_n @ X3 @ ( sigma_1483971331real_n @ M ) )
% 0.07/0.32           => ( member1746150050real_n @ ( F @ X3 ) @ ( sigma_1483971331real_n @ N ) ) )
% 0.07/0.32       => ( ! [A6: set_Fi1326602817real_n] :
% 0.07/0.32              ( ( member2104752728real_n @ A6 @ ( sigma_522684908real_n @ N ) )
% 0.07/0.32             => ( member2104752728real_n @ ( inf_in146441683real_n @ ( vimage180751827real_n @ F @ A6 ) @ ( sigma_1483971331real_n @ M ) ) @ ( sigma_522684908real_n @ M ) ) )
% 0.07/0.32         => ( member117715276real_n @ F @ ( sigma_1185134568real_n @ M @ N ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurableI
% 0.07/0.32  thf(fact_102_measurableI,axiom,
% 0.07/0.32      ! [M: sigma_1422848389real_n,F: set_Fi1058188332real_n > finite1489363574real_n,N: sigma_1466784463real_n] :
% 0.07/0.32        ( ! [X3: set_Fi1058188332real_n] :
% 0.07/0.32            ( ( member223413699real_n @ X3 @ ( sigma_607186084real_n @ M ) )
% 0.07/0.32           => ( member1352538125real_n @ ( F @ X3 ) @ ( sigma_476185326real_n @ N ) ) )
% 0.07/0.32       => ( ! [A6: set_Fi1058188332real_n] :
% 0.07/0.32              ( ( member223413699real_n @ A6 @ ( sigma_1235138647real_n @ N ) )
% 0.07/0.32             => ( member1475136633real_n @ ( inf_in632889204real_n @ ( vimage973736031real_n @ F @ A6 ) @ ( sigma_607186084real_n @ M ) ) @ ( sigma_433815053real_n @ M ) ) )
% 0.07/0.32         => ( member1759501912real_n @ F @ ( sigma_1333364596real_n @ M @ N ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurableI
% 0.07/0.32  thf(fact_103_measurableI,axiom,
% 0.07/0.32      ! [M: sigma_107786596real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,N: sigma_1466784463real_n] :
% 0.07/0.32        ( ! [X3: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32            ( ( member1746150050real_n @ X3 @ ( sigma_1483971331real_n @ M ) )
% 0.07/0.32           => ( member1352538125real_n @ ( F @ X3 ) @ ( sigma_476185326real_n @ N ) ) )
% 0.07/0.32       => ( ! [A6: set_Fi1058188332real_n] :
% 0.07/0.32              ( ( member223413699real_n @ A6 @ ( sigma_1235138647real_n @ N ) )
% 0.07/0.32             => ( member2104752728real_n @ ( inf_in146441683real_n @ ( vimage1072397758real_n @ F @ A6 ) @ ( sigma_1483971331real_n @ M ) ) @ ( sigma_522684908real_n @ M ) ) )
% 0.07/0.32         => ( member1695588023real_n @ F @ ( sigma_2028985427real_n @ M @ N ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurableI
% 0.07/0.32  thf(fact_104_measurableI,axiom,
% 0.07/0.32      ! [M: sigma_1466784463real_n,F: finite1489363574real_n > set_Fi1058188332real_n,N: sigma_1422848389real_n] :
% 0.07/0.32        ( ! [X3: finite1489363574real_n] :
% 0.07/0.32            ( ( member1352538125real_n @ X3 @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32           => ( member223413699real_n @ ( F @ X3 ) @ ( sigma_607186084real_n @ N ) ) )
% 0.07/0.32       => ( ! [A6: set_se2111327970real_n] :
% 0.07/0.32              ( ( member1475136633real_n @ A6 @ ( sigma_433815053real_n @ N ) )
% 0.07/0.32             => ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage207290975real_n @ F @ A6 ) @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) ) )
% 0.07/0.32         => ( member966061400real_n @ F @ ( sigma_566919540real_n @ M @ N ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurableI
% 0.07/0.32  thf(fact_105_measurableI,axiom,
% 0.07/0.32      ! [M: sigma_1466784463real_n,F: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n,N: sigma_107786596real_n] :
% 0.07/0.32        ( ! [X3: finite1489363574real_n] :
% 0.07/0.32            ( ( member1352538125real_n @ X3 @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32           => ( member1746150050real_n @ ( F @ X3 ) @ ( sigma_1483971331real_n @ N ) ) )
% 0.07/0.32       => ( ! [A6: set_Fi1326602817real_n] :
% 0.07/0.32              ( ( member2104752728real_n @ A6 @ ( sigma_522684908real_n @ N ) )
% 0.07/0.32             => ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage1059850558real_n @ F @ A6 ) @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) ) )
% 0.07/0.32         => ( member408431031real_n @ F @ ( sigma_2016438227real_n @ M @ N ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurableI
% 0.07/0.32  thf(fact_106_measurableI,axiom,
% 0.07/0.32      ! [M: sigma_1466784463real_n,F: finite1489363574real_n > finite1489363574real_n,N: sigma_1466784463real_n] :
% 0.07/0.32        ( ! [X3: finite1489363574real_n] :
% 0.07/0.32            ( ( member1352538125real_n @ X3 @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32           => ( member1352538125real_n @ ( F @ X3 ) @ ( sigma_476185326real_n @ N ) ) )
% 0.07/0.32       => ( ! [A6: set_Fi1058188332real_n] :
% 0.07/0.32              ( ( member223413699real_n @ A6 @ ( sigma_1235138647real_n @ N ) )
% 0.07/0.32             => ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage1233683625real_n @ F @ A6 ) @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) ) )
% 0.07/0.32         => ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ N ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurableI
% 0.07/0.32  thf(fact_107_sets_Otop,axiom,
% 0.07/0.32      ! [M: sigma_1466784463real_n] : ( member223413699real_n @ ( sigma_476185326real_n @ M ) @ ( sigma_1235138647real_n @ M ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets.top
% 0.07/0.32  thf(fact_108_sets_OInt,axiom,
% 0.07/0.32      ! [A: set_Fi1058188332real_n,M: sigma_1466784463real_n,B: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32       => ( ( member223413699real_n @ B @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32         => ( member223413699real_n @ ( inf_in1974387902real_n @ A @ B ) @ ( sigma_1235138647real_n @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets.Int
% 0.07/0.32  thf(fact_109_measurable__If__set,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,M2: sigma_1466784463real_n,G: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ M2 ) )
% 0.07/0.32       => ( ( member1746150050real_n @ G @ ( sigma_439801790real_n @ M @ M2 ) )
% 0.07/0.32         => ( ( member223413699real_n @ ( inf_in1974387902real_n @ A2 @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32           => ( member1746150050real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n] : ( if_Fin127821360real_n @ ( member1352538125real_n @ X @ A2 ) @ ( F @ X ) @ ( G @ X ) )
% 0.07/0.32              @ ( sigma_439801790real_n @ M @ M2 ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_If_set
% 0.07/0.32  thf(fact_110_measurable__sets__Collect,axiom,
% 0.07/0.32      ! [F: set_Fi1058188332real_n > set_Fi1058188332real_n,M: sigma_1422848389real_n,N: sigma_1422848389real_n,P: set_Fi1058188332real_n > $o] :
% 0.07/0.32        ( ( member1734791438real_n @ F @ ( sigma_239294762real_n @ M @ N ) )
% 0.07/0.32       => ( ( member1475136633real_n
% 0.07/0.32            @ ( collec452821761real_n
% 0.07/0.32              @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ N ) )
% 0.07/0.32                  & ( P @ X ) ) )
% 0.07/0.32            @ ( sigma_433815053real_n @ N ) )
% 0.07/0.32         => ( member1475136633real_n
% 0.07/0.32            @ ( collec452821761real_n
% 0.07/0.32              @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 0.07/0.32                  & ( P @ ( F @ X ) ) ) )
% 0.07/0.32            @ ( sigma_433815053real_n @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_sets_Collect
% 0.07/0.32  thf(fact_111_measurable__sets__Collect,axiom,
% 0.07/0.32      ! [F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,M: sigma_107786596real_n,N: sigma_1422848389real_n,P: set_Fi1058188332real_n > $o] :
% 0.07/0.32        ( ( member640587117real_n @ F @ ( sigma_364818953real_n @ M @ N ) )
% 0.07/0.32       => ( ( member1475136633real_n
% 0.07/0.32            @ ( collec452821761real_n
% 0.07/0.32              @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ N ) )
% 0.07/0.32                  & ( P @ X ) ) )
% 0.07/0.32            @ ( sigma_433815053real_n @ N ) )
% 0.07/0.32         => ( member2104752728real_n
% 0.07/0.32            @ ( collec1190264032real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 0.07/0.32                  & ( P @ ( F @ X ) ) ) )
% 0.07/0.32            @ ( sigma_522684908real_n @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_sets_Collect
% 0.07/0.32  thf(fact_112_measurable__sets__Collect,axiom,
% 0.07/0.32      ! [F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,M: sigma_1422848389real_n,N: sigma_107786596real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
% 0.07/0.32        ( ( member1764433517real_n @ F @ ( sigma_588796041real_n @ M @ N ) )
% 0.07/0.32       => ( ( member2104752728real_n
% 0.07/0.32            @ ( collec1190264032real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ N ) )
% 0.07/0.32                  & ( P @ X ) ) )
% 0.07/0.32            @ ( sigma_522684908real_n @ N ) )
% 0.07/0.32         => ( member1475136633real_n
% 0.07/0.32            @ ( collec452821761real_n
% 0.07/0.32              @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 0.07/0.32                  & ( P @ ( F @ X ) ) ) )
% 0.07/0.32            @ ( sigma_433815053real_n @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_sets_Collect
% 0.07/0.32  thf(fact_113_measurable__sets__Collect,axiom,
% 0.07/0.32      ! [F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,M: sigma_107786596real_n,N: sigma_107786596real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
% 0.07/0.32        ( ( member117715276real_n @ F @ ( sigma_1185134568real_n @ M @ N ) )
% 0.07/0.32       => ( ( member2104752728real_n
% 0.07/0.32            @ ( collec1190264032real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ N ) )
% 0.07/0.32                  & ( P @ X ) ) )
% 0.07/0.32            @ ( sigma_522684908real_n @ N ) )
% 0.07/0.32         => ( member2104752728real_n
% 0.07/0.32            @ ( collec1190264032real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 0.07/0.32                  & ( P @ ( F @ X ) ) ) )
% 0.07/0.32            @ ( sigma_522684908real_n @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_sets_Collect
% 0.07/0.32  thf(fact_114_measurable__sets__Collect,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > set_Fi1058188332real_n,M: sigma_1466784463real_n,N: sigma_1422848389real_n,P: set_Fi1058188332real_n > $o] :
% 0.07/0.32        ( ( member966061400real_n @ F @ ( sigma_566919540real_n @ M @ N ) )
% 0.07/0.32       => ( ( member1475136633real_n
% 0.07/0.32            @ ( collec452821761real_n
% 0.07/0.32              @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ N ) )
% 0.07/0.32                  & ( P @ X ) ) )
% 0.07/0.32            @ ( sigma_433815053real_n @ N ) )
% 0.07/0.32         => ( member223413699real_n
% 0.07/0.32            @ ( collec321817931real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32                  & ( P @ ( F @ X ) ) ) )
% 0.07/0.32            @ ( sigma_1235138647real_n @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_sets_Collect
% 0.07/0.32  thf(fact_115_measurable__sets__Collect,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,N: sigma_107786596real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
% 0.07/0.32        ( ( member408431031real_n @ F @ ( sigma_2016438227real_n @ M @ N ) )
% 0.07/0.32       => ( ( member2104752728real_n
% 0.07/0.32            @ ( collec1190264032real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ N ) )
% 0.07/0.32                  & ( P @ X ) ) )
% 0.07/0.32            @ ( sigma_522684908real_n @ N ) )
% 0.07/0.32         => ( member223413699real_n
% 0.07/0.32            @ ( collec321817931real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32                  & ( P @ ( F @ X ) ) ) )
% 0.07/0.32            @ ( sigma_1235138647real_n @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_sets_Collect
% 0.07/0.32  thf(fact_116_measurable__sets__Collect,axiom,
% 0.07/0.32      ! [F: set_Fi1058188332real_n > finite1489363574real_n,M: sigma_1422848389real_n,N: sigma_1466784463real_n,P: finite1489363574real_n > $o] :
% 0.07/0.32        ( ( member1759501912real_n @ F @ ( sigma_1333364596real_n @ M @ N ) )
% 0.07/0.32       => ( ( member223413699real_n
% 0.07/0.32            @ ( collec321817931real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ N ) )
% 0.07/0.32                  & ( P @ X ) ) )
% 0.07/0.32            @ ( sigma_1235138647real_n @ N ) )
% 0.07/0.32         => ( member1475136633real_n
% 0.07/0.32            @ ( collec452821761real_n
% 0.07/0.32              @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 0.07/0.32                  & ( P @ ( F @ X ) ) ) )
% 0.07/0.32            @ ( sigma_433815053real_n @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_sets_Collect
% 0.07/0.32  thf(fact_117_measurable__sets__Collect,axiom,
% 0.07/0.32      ! [F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,M: sigma_107786596real_n,N: sigma_1466784463real_n,P: finite1489363574real_n > $o] :
% 0.07/0.32        ( ( member1695588023real_n @ F @ ( sigma_2028985427real_n @ M @ N ) )
% 0.07/0.32       => ( ( member223413699real_n
% 0.07/0.32            @ ( collec321817931real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ N ) )
% 0.07/0.32                  & ( P @ X ) ) )
% 0.07/0.32            @ ( sigma_1235138647real_n @ N ) )
% 0.07/0.32         => ( member2104752728real_n
% 0.07/0.32            @ ( collec1190264032real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 0.07/0.32                  & ( P @ ( F @ X ) ) ) )
% 0.07/0.32            @ ( sigma_522684908real_n @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_sets_Collect
% 0.07/0.32  thf(fact_118_measurable__sets__Collect,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,N: sigma_1466784463real_n,P: finite1489363574real_n > $o] :
% 0.07/0.32        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ N ) )
% 0.07/0.32       => ( ( member223413699real_n
% 0.07/0.32            @ ( collec321817931real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ N ) )
% 0.07/0.32                  & ( P @ X ) ) )
% 0.07/0.32            @ ( sigma_1235138647real_n @ N ) )
% 0.07/0.32         => ( member223413699real_n
% 0.07/0.32            @ ( collec321817931real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32                  & ( P @ ( F @ X ) ) ) )
% 0.07/0.32            @ ( sigma_1235138647real_n @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_sets_Collect
% 0.07/0.32  thf(fact_119_measurable__If,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,M2: sigma_1466784463real_n,G: finite1489363574real_n > finite1489363574real_n,P: finite1489363574real_n > $o] :
% 0.07/0.32        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ M2 ) )
% 0.07/0.32       => ( ( member1746150050real_n @ G @ ( sigma_439801790real_n @ M @ M2 ) )
% 0.07/0.32         => ( ( member223413699real_n
% 0.07/0.32              @ ( collec321817931real_n
% 0.07/0.32                @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                    ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32                    & ( P @ X ) ) )
% 0.07/0.32              @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32           => ( member1746150050real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n] : ( if_Fin127821360real_n @ ( P @ X ) @ ( F @ X ) @ ( G @ X ) )
% 0.07/0.32              @ ( sigma_439801790real_n @ M @ M2 ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_If
% 0.07/0.32  thf(fact_120_inf__right__idem,axiom,
% 0.07/0.32      ! [X2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ X2 @ Y3 ) @ Y3 )
% 0.07/0.32        = ( inf_in1974387902real_n @ X2 @ Y3 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % inf_right_idem
% 0.07/0.32  thf(fact_121_inf_Oright__idem,axiom,
% 0.07/0.32      ! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ A @ B ) @ B )
% 0.07/0.32        = ( inf_in1974387902real_n @ A @ B ) ) ).
% 0.07/0.32  
% 0.07/0.32  % inf.right_idem
% 0.07/0.32  thf(fact_122_inf__left__idem,axiom,
% 0.07/0.32      ! [X2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( inf_in1974387902real_n @ X2 @ ( inf_in1974387902real_n @ X2 @ Y3 ) )
% 0.07/0.32        = ( inf_in1974387902real_n @ X2 @ Y3 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % inf_left_idem
% 0.07/0.32  thf(fact_123_inf_Oleft__idem,axiom,
% 0.07/0.32      ! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ A @ B ) )
% 0.07/0.32        = ( inf_in1974387902real_n @ A @ B ) ) ).
% 0.07/0.32  
% 0.07/0.32  % inf.left_idem
% 0.07/0.32  thf(fact_124_inf__idem,axiom,
% 0.07/0.32      ! [X2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( inf_in1974387902real_n @ X2 @ X2 )
% 0.07/0.32        = X2 ) ).
% 0.07/0.32  
% 0.07/0.32  % inf_idem
% 0.07/0.32  thf(fact_125_inf_Oidem,axiom,
% 0.07/0.32      ! [A: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( inf_in1974387902real_n @ A @ A )
% 0.07/0.32        = A ) ).
% 0.07/0.32  
% 0.07/0.32  % inf.idem
% 0.07/0.32  thf(fact_126_inf__set__def,axiom,
% 0.07/0.32      ( inf_in632889204real_n
% 0.07/0.32      = ( ^ [A4: set_se2111327970real_n,B3: set_se2111327970real_n] :
% 0.07/0.32            ( collec452821761real_n
% 0.07/0.32            @ ( inf_in409346577al_n_o
% 0.07/0.32              @ ^ [X: set_Fi1058188332real_n] : ( member223413699real_n @ X @ A4 )
% 0.07/0.32              @ ^ [X: set_Fi1058188332real_n] : ( member223413699real_n @ X @ B3 ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % inf_set_def
% 0.07/0.32  thf(fact_127_inf__set__def,axiom,
% 0.07/0.32      ( inf_in146441683real_n
% 0.07/0.32      = ( ^ [A4: set_Fi1326602817real_n,B3: set_Fi1326602817real_n] :
% 0.07/0.32            ( collec1190264032real_n
% 0.07/0.32            @ ( inf_in32002162al_n_o
% 0.07/0.32              @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ X @ A4 )
% 0.07/0.32              @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ X @ B3 ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % inf_set_def
% 0.07/0.32  thf(fact_128_inf__set__def,axiom,
% 0.07/0.32      ( inf_in1974387902real_n
% 0.07/0.32      = ( ^ [A4: set_Fi1058188332real_n,B3: set_Fi1058188332real_n] :
% 0.07/0.32            ( collec321817931real_n
% 0.07/0.32            @ ( inf_in1620715847al_n_o
% 0.07/0.32              @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ X @ A4 )
% 0.07/0.32              @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ X @ B3 ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % inf_set_def
% 0.07/0.32  thf(fact_129_inf__left__commute,axiom,
% 0.07/0.32      ! [X2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n,Z: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( inf_in1974387902real_n @ X2 @ ( inf_in1974387902real_n @ Y3 @ Z ) )
% 0.07/0.32        = ( inf_in1974387902real_n @ Y3 @ ( inf_in1974387902real_n @ X2 @ Z ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % inf_left_commute
% 0.07/0.32  thf(fact_130_inf_Oleft__commute,axiom,
% 0.07/0.32      ! [B: set_Fi1058188332real_n,A: set_Fi1058188332real_n,C2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( inf_in1974387902real_n @ B @ ( inf_in1974387902real_n @ A @ C2 ) )
% 0.07/0.32        = ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ B @ C2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % inf.left_commute
% 0.07/0.32  thf(fact_131_inf__commute,axiom,
% 0.07/0.32      ( inf_in1974387902real_n
% 0.07/0.32      = ( ^ [X: set_Fi1058188332real_n,Y2: set_Fi1058188332real_n] : ( inf_in1974387902real_n @ Y2 @ X ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % inf_commute
% 0.07/0.32  thf(fact_132_inf_Ocommute,axiom,
% 0.07/0.32      ( inf_in1974387902real_n
% 0.07/0.32      = ( ^ [A3: set_Fi1058188332real_n,B4: set_Fi1058188332real_n] : ( inf_in1974387902real_n @ B4 @ A3 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % inf.commute
% 0.07/0.32  thf(fact_133_inf__assoc,axiom,
% 0.07/0.32      ! [X2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n,Z: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ X2 @ Y3 ) @ Z )
% 0.07/0.32        = ( inf_in1974387902real_n @ X2 @ ( inf_in1974387902real_n @ Y3 @ Z ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % inf_assoc
% 0.07/0.32  thf(fact_134_inf_Oassoc,axiom,
% 0.07/0.32      ! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ A @ B ) @ C2 )
% 0.07/0.32        = ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ B @ C2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % inf.assoc
% 0.07/0.32  thf(fact_135_boolean__algebra__cancel_Oinf2,axiom,
% 0.07/0.32      ! [B2: set_Fi1058188332real_n,K: set_Fi1058188332real_n,B: set_Fi1058188332real_n,A: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( B2
% 0.07/0.32          = ( inf_in1974387902real_n @ K @ B ) )
% 0.07/0.32       => ( ( inf_in1974387902real_n @ A @ B2 )
% 0.07/0.32          = ( inf_in1974387902real_n @ K @ ( inf_in1974387902real_n @ A @ B ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % boolean_algebra_cancel.inf2
% 0.07/0.32  thf(fact_136_boolean__algebra__cancel_Oinf1,axiom,
% 0.07/0.32      ! [A2: set_Fi1058188332real_n,K: set_Fi1058188332real_n,A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( A2
% 0.07/0.32          = ( inf_in1974387902real_n @ K @ A ) )
% 0.07/0.32       => ( ( inf_in1974387902real_n @ A2 @ B )
% 0.07/0.32          = ( inf_in1974387902real_n @ K @ ( inf_in1974387902real_n @ A @ B ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % boolean_algebra_cancel.inf1
% 0.07/0.32  thf(fact_137_inf__sup__aci_I1_J,axiom,
% 0.07/0.32      ( inf_in1974387902real_n
% 0.07/0.32      = ( ^ [X: set_Fi1058188332real_n,Y2: set_Fi1058188332real_n] : ( inf_in1974387902real_n @ Y2 @ X ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % inf_sup_aci(1)
% 0.07/0.32  thf(fact_138_inf__sup__aci_I2_J,axiom,
% 0.07/0.32      ! [X2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n,Z: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ X2 @ Y3 ) @ Z )
% 0.07/0.32        = ( inf_in1974387902real_n @ X2 @ ( inf_in1974387902real_n @ Y3 @ Z ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % inf_sup_aci(2)
% 0.07/0.32  thf(fact_139_inf__sup__aci_I3_J,axiom,
% 0.07/0.32      ! [X2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n,Z: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( inf_in1974387902real_n @ X2 @ ( inf_in1974387902real_n @ Y3 @ Z ) )
% 0.07/0.32        = ( inf_in1974387902real_n @ Y3 @ ( inf_in1974387902real_n @ X2 @ Z ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % inf_sup_aci(3)
% 0.07/0.32  thf(fact_140_inf__sup__aci_I4_J,axiom,
% 0.07/0.32      ! [X2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( inf_in1974387902real_n @ X2 @ ( inf_in1974387902real_n @ X2 @ Y3 ) )
% 0.07/0.32        = ( inf_in1974387902real_n @ X2 @ Y3 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % inf_sup_aci(4)
% 0.07/0.32  thf(fact_141_measurable__compose__rev,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n,L2: sigma_1466784463real_n,N: sigma_1466784463real_n,G: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ L2 @ N ) )
% 0.07/0.32       => ( ( member1746150050real_n @ G @ ( sigma_439801790real_n @ M @ L2 ) )
% 0.07/0.32         => ( member1746150050real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n] : ( F @ ( G @ X ) )
% 0.07/0.32            @ ( sigma_439801790real_n @ M @ N ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_compose_rev
% 0.07/0.32  thf(fact_142_measurable__compose,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,N: sigma_1466784463real_n,G: finite1489363574real_n > finite1489363574real_n,L2: sigma_1466784463real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ N ) )
% 0.07/0.32       => ( ( member1746150050real_n @ G @ ( sigma_439801790real_n @ N @ L2 ) )
% 0.07/0.32         => ( member1746150050real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n] : ( G @ ( F @ X ) )
% 0.07/0.32            @ ( sigma_439801790real_n @ M @ L2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_compose
% 0.07/0.32  thf(fact_143_measurable__id,axiom,
% 0.07/0.32      ! [M: sigma_1466784463real_n] :
% 0.07/0.32        ( member1746150050real_n
% 0.07/0.32        @ ^ [X: finite1489363574real_n] : X
% 0.07/0.32        @ ( sigma_439801790real_n @ M @ M ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_id
% 0.07/0.32  thf(fact_144_measurable__cong__sets,axiom,
% 0.07/0.32      ! [M: sigma_1466784463real_n,M2: sigma_1466784463real_n,N: sigma_1466784463real_n,N2: sigma_1466784463real_n] :
% 0.07/0.32        ( ( ( sigma_1235138647real_n @ M )
% 0.07/0.32          = ( sigma_1235138647real_n @ M2 ) )
% 0.07/0.32       => ( ( ( sigma_1235138647real_n @ N )
% 0.07/0.32            = ( sigma_1235138647real_n @ N2 ) )
% 0.07/0.32         => ( ( sigma_439801790real_n @ M @ N )
% 0.07/0.32            = ( sigma_439801790real_n @ M2 @ N2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_cong_sets
% 0.07/0.32  thf(fact_145_sets__eq__imp__space__eq,axiom,
% 0.07/0.32      ! [M: sigma_1466784463real_n,M2: sigma_1466784463real_n] :
% 0.07/0.32        ( ( ( sigma_1235138647real_n @ M )
% 0.07/0.32          = ( sigma_1235138647real_n @ M2 ) )
% 0.07/0.32       => ( ( sigma_476185326real_n @ M )
% 0.07/0.32          = ( sigma_476185326real_n @ M2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets_eq_imp_space_eq
% 0.07/0.32  thf(fact_146_measurable__cong__simp,axiom,
% 0.07/0.32      ! [M: sigma_1466784463real_n,N: sigma_1466784463real_n,M2: sigma_1466784463real_n,N2: sigma_1466784463real_n,F: finite1489363574real_n > finite1489363574real_n,G: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32        ( ( M = N )
% 0.07/0.32       => ( ( M2 = N2 )
% 0.07/0.32         => ( ! [W: finite1489363574real_n] :
% 0.07/0.32                ( ( member1352538125real_n @ W @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32               => ( ( F @ W )
% 0.07/0.32                  = ( G @ W ) ) )
% 0.07/0.32           => ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ M2 ) )
% 0.07/0.32              = ( member1746150050real_n @ G @ ( sigma_439801790real_n @ N @ N2 ) ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_cong_simp
% 0.07/0.32  thf(fact_147_measurable__space,axiom,
% 0.07/0.32      ! [F: set_Fi1058188332real_n > set_Fi1058188332real_n,M: sigma_1422848389real_n,A2: sigma_1422848389real_n,X2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member1734791438real_n @ F @ ( sigma_239294762real_n @ M @ A2 ) )
% 0.07/0.32       => ( ( member223413699real_n @ X2 @ ( sigma_607186084real_n @ M ) )
% 0.07/0.32         => ( member223413699real_n @ ( F @ X2 ) @ ( sigma_607186084real_n @ A2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_space
% 0.07/0.32  thf(fact_148_measurable__space,axiom,
% 0.07/0.32      ! [F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,M: sigma_1422848389real_n,A2: sigma_107786596real_n,X2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member1764433517real_n @ F @ ( sigma_588796041real_n @ M @ A2 ) )
% 0.07/0.32       => ( ( member223413699real_n @ X2 @ ( sigma_607186084real_n @ M ) )
% 0.07/0.32         => ( member1746150050real_n @ ( F @ X2 ) @ ( sigma_1483971331real_n @ A2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_space
% 0.07/0.32  thf(fact_149_measurable__space,axiom,
% 0.07/0.32      ! [F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,M: sigma_107786596real_n,A2: sigma_1422848389real_n,X2: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32        ( ( member640587117real_n @ F @ ( sigma_364818953real_n @ M @ A2 ) )
% 0.07/0.32       => ( ( member1746150050real_n @ X2 @ ( sigma_1483971331real_n @ M ) )
% 0.07/0.32         => ( member223413699real_n @ ( F @ X2 ) @ ( sigma_607186084real_n @ A2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_space
% 0.07/0.32  thf(fact_150_measurable__space,axiom,
% 0.07/0.32      ! [F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,M: sigma_107786596real_n,A2: sigma_107786596real_n,X2: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32        ( ( member117715276real_n @ F @ ( sigma_1185134568real_n @ M @ A2 ) )
% 0.07/0.32       => ( ( member1746150050real_n @ X2 @ ( sigma_1483971331real_n @ M ) )
% 0.07/0.32         => ( member1746150050real_n @ ( F @ X2 ) @ ( sigma_1483971331real_n @ A2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_space
% 0.07/0.32  thf(fact_151_measurable__space,axiom,
% 0.07/0.32      ! [F: set_Fi1058188332real_n > finite1489363574real_n,M: sigma_1422848389real_n,A2: sigma_1466784463real_n,X2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member1759501912real_n @ F @ ( sigma_1333364596real_n @ M @ A2 ) )
% 0.07/0.32       => ( ( member223413699real_n @ X2 @ ( sigma_607186084real_n @ M ) )
% 0.07/0.32         => ( member1352538125real_n @ ( F @ X2 ) @ ( sigma_476185326real_n @ A2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_space
% 0.07/0.32  thf(fact_152_measurable__space,axiom,
% 0.07/0.32      ! [F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,M: sigma_107786596real_n,A2: sigma_1466784463real_n,X2: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32        ( ( member1695588023real_n @ F @ ( sigma_2028985427real_n @ M @ A2 ) )
% 0.07/0.32       => ( ( member1746150050real_n @ X2 @ ( sigma_1483971331real_n @ M ) )
% 0.07/0.32         => ( member1352538125real_n @ ( F @ X2 ) @ ( sigma_476185326real_n @ A2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_space
% 0.07/0.32  thf(fact_153_measurable__space,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > set_Fi1058188332real_n,M: sigma_1466784463real_n,A2: sigma_1422848389real_n,X2: finite1489363574real_n] :
% 0.07/0.32        ( ( member966061400real_n @ F @ ( sigma_566919540real_n @ M @ A2 ) )
% 0.07/0.32       => ( ( member1352538125real_n @ X2 @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32         => ( member223413699real_n @ ( F @ X2 ) @ ( sigma_607186084real_n @ A2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_space
% 0.07/0.32  thf(fact_154_measurable__space,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,A2: sigma_107786596real_n,X2: finite1489363574real_n] :
% 0.07/0.32        ( ( member408431031real_n @ F @ ( sigma_2016438227real_n @ M @ A2 ) )
% 0.07/0.32       => ( ( member1352538125real_n @ X2 @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32         => ( member1746150050real_n @ ( F @ X2 ) @ ( sigma_1483971331real_n @ A2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_space
% 0.07/0.32  thf(fact_155_measurable__space,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,A2: sigma_1466784463real_n,X2: finite1489363574real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ A2 ) )
% 0.07/0.32       => ( ( member1352538125real_n @ X2 @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32         => ( member1352538125real_n @ ( F @ X2 ) @ ( sigma_476185326real_n @ A2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_space
% 0.07/0.32  thf(fact_156_measurable__cong,axiom,
% 0.07/0.32      ! [M: sigma_1466784463real_n,F: finite1489363574real_n > finite1489363574real_n,G: finite1489363574real_n > finite1489363574real_n,M2: sigma_1466784463real_n] :
% 0.07/0.32        ( ! [W: finite1489363574real_n] :
% 0.07/0.32            ( ( member1352538125real_n @ W @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32           => ( ( F @ W )
% 0.07/0.32              = ( G @ W ) ) )
% 0.07/0.32       => ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ M2 ) )
% 0.07/0.32          = ( member1746150050real_n @ G @ ( sigma_439801790real_n @ M @ M2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_cong
% 0.07/0.32  thf(fact_157_measurable__ident__sets,axiom,
% 0.07/0.32      ! [M: sigma_1466784463real_n,M2: sigma_1466784463real_n] :
% 0.07/0.32        ( ( ( sigma_1235138647real_n @ M )
% 0.07/0.32          = ( sigma_1235138647real_n @ M2 ) )
% 0.07/0.32       => ( member1746150050real_n
% 0.07/0.32          @ ^ [X: finite1489363574real_n] : X
% 0.07/0.32          @ ( sigma_439801790real_n @ M @ M2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_ident_sets
% 0.07/0.32  thf(fact_158_sets_Osets__Collect_I5_J,axiom,
% 0.07/0.32      ! [M: sigma_1422848389real_n,Pb: $o] :
% 0.07/0.32        ( member1475136633real_n
% 0.07/0.32        @ ( collec452821761real_n
% 0.07/0.32          @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32              ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 0.07/0.32              & Pb ) )
% 0.07/0.32        @ ( sigma_433815053real_n @ M ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets.sets_Collect(5)
% 0.07/0.32  thf(fact_159_sets_Osets__Collect_I5_J,axiom,
% 0.07/0.32      ! [M: sigma_107786596real_n,Pb: $o] :
% 0.07/0.32        ( member2104752728real_n
% 0.07/0.32        @ ( collec1190264032real_n
% 0.07/0.32          @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32              ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 0.07/0.32              & Pb ) )
% 0.07/0.32        @ ( sigma_522684908real_n @ M ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets.sets_Collect(5)
% 0.07/0.32  thf(fact_160_sets_Osets__Collect_I5_J,axiom,
% 0.07/0.32      ! [M: sigma_1466784463real_n,Pb: $o] :
% 0.07/0.32        ( member223413699real_n
% 0.07/0.32        @ ( collec321817931real_n
% 0.07/0.32          @ ^ [X: finite1489363574real_n] :
% 0.07/0.32              ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32              & Pb ) )
% 0.07/0.32        @ ( sigma_1235138647real_n @ M ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets.sets_Collect(5)
% 0.07/0.32  thf(fact_161_sets_Osets__Collect__imp,axiom,
% 0.07/0.32      ! [M: sigma_1422848389real_n,P: set_Fi1058188332real_n > $o,Q: set_Fi1058188332real_n > $o] :
% 0.07/0.32        ( ( member1475136633real_n
% 0.07/0.32          @ ( collec452821761real_n
% 0.07/0.32            @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32                ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 0.07/0.32                & ( P @ X ) ) )
% 0.07/0.32          @ ( sigma_433815053real_n @ M ) )
% 0.07/0.32       => ( ( member1475136633real_n
% 0.07/0.32            @ ( collec452821761real_n
% 0.07/0.32              @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 0.07/0.32                  & ( Q @ X ) ) )
% 0.07/0.32            @ ( sigma_433815053real_n @ M ) )
% 0.07/0.32         => ( member1475136633real_n
% 0.07/0.32            @ ( collec452821761real_n
% 0.07/0.32              @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 0.07/0.32                  & ( ( Q @ X )
% 0.07/0.32                   => ( P @ X ) ) ) )
% 0.07/0.32            @ ( sigma_433815053real_n @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets.sets_Collect_imp
% 0.07/0.32  thf(fact_162_sets_Osets__Collect__imp,axiom,
% 0.07/0.32      ! [M: sigma_107786596real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o,Q: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
% 0.07/0.32        ( ( member2104752728real_n
% 0.07/0.32          @ ( collec1190264032real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32                ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 0.07/0.32                & ( P @ X ) ) )
% 0.07/0.32          @ ( sigma_522684908real_n @ M ) )
% 0.07/0.32       => ( ( member2104752728real_n
% 0.07/0.32            @ ( collec1190264032real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 0.07/0.32                  & ( Q @ X ) ) )
% 0.07/0.32            @ ( sigma_522684908real_n @ M ) )
% 0.07/0.32         => ( member2104752728real_n
% 0.07/0.32            @ ( collec1190264032real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 0.07/0.32                  & ( ( Q @ X )
% 0.07/0.32                   => ( P @ X ) ) ) )
% 0.07/0.32            @ ( sigma_522684908real_n @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets.sets_Collect_imp
% 0.07/0.32  thf(fact_163_sets_Osets__Collect__imp,axiom,
% 0.07/0.32      ! [M: sigma_1466784463real_n,P: finite1489363574real_n > $o,Q: finite1489363574real_n > $o] :
% 0.07/0.32        ( ( member223413699real_n
% 0.07/0.32          @ ( collec321817931real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32                & ( P @ X ) ) )
% 0.07/0.32          @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32       => ( ( member223413699real_n
% 0.07/0.32            @ ( collec321817931real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32                  & ( Q @ X ) ) )
% 0.07/0.32            @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32         => ( member223413699real_n
% 0.07/0.32            @ ( collec321817931real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32                  & ( ( Q @ X )
% 0.07/0.32                   => ( P @ X ) ) ) )
% 0.07/0.32            @ ( sigma_1235138647real_n @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets.sets_Collect_imp
% 0.07/0.32  thf(fact_164_sets_Osets__Collect__neg,axiom,
% 0.07/0.32      ! [M: sigma_1422848389real_n,P: set_Fi1058188332real_n > $o] :
% 0.07/0.32        ( ( member1475136633real_n
% 0.07/0.32          @ ( collec452821761real_n
% 0.07/0.32            @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32                ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 0.07/0.32                & ( P @ X ) ) )
% 0.07/0.32          @ ( sigma_433815053real_n @ M ) )
% 0.07/0.32       => ( member1475136633real_n
% 0.07/0.32          @ ( collec452821761real_n
% 0.07/0.32            @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32                ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 0.07/0.32                & ~ ( P @ X ) ) )
% 0.07/0.32          @ ( sigma_433815053real_n @ M ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets.sets_Collect_neg
% 0.07/0.32  thf(fact_165_sets_Osets__Collect__neg,axiom,
% 0.07/0.32      ! [M: sigma_107786596real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
% 0.07/0.32        ( ( member2104752728real_n
% 0.07/0.32          @ ( collec1190264032real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32                ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 0.07/0.32                & ( P @ X ) ) )
% 0.07/0.32          @ ( sigma_522684908real_n @ M ) )
% 0.07/0.32       => ( member2104752728real_n
% 0.07/0.32          @ ( collec1190264032real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32                ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 0.07/0.32                & ~ ( P @ X ) ) )
% 0.07/0.32          @ ( sigma_522684908real_n @ M ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets.sets_Collect_neg
% 0.07/0.32  thf(fact_166_sets_Osets__Collect__neg,axiom,
% 0.07/0.32      ! [M: sigma_1466784463real_n,P: finite1489363574real_n > $o] :
% 0.07/0.32        ( ( member223413699real_n
% 0.07/0.32          @ ( collec321817931real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32                & ( P @ X ) ) )
% 0.07/0.32          @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32       => ( member223413699real_n
% 0.07/0.32          @ ( collec321817931real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32                & ~ ( P @ X ) ) )
% 0.07/0.32          @ ( sigma_1235138647real_n @ M ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets.sets_Collect_neg
% 0.07/0.32  thf(fact_167_sets_Osets__Collect__conj,axiom,
% 0.07/0.32      ! [M: sigma_1422848389real_n,P: set_Fi1058188332real_n > $o,Q: set_Fi1058188332real_n > $o] :
% 0.07/0.32        ( ( member1475136633real_n
% 0.07/0.32          @ ( collec452821761real_n
% 0.07/0.32            @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32                ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 0.07/0.32                & ( P @ X ) ) )
% 0.07/0.32          @ ( sigma_433815053real_n @ M ) )
% 0.07/0.32       => ( ( member1475136633real_n
% 0.07/0.32            @ ( collec452821761real_n
% 0.07/0.32              @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 0.07/0.32                  & ( Q @ X ) ) )
% 0.07/0.32            @ ( sigma_433815053real_n @ M ) )
% 0.07/0.32         => ( member1475136633real_n
% 0.07/0.32            @ ( collec452821761real_n
% 0.07/0.32              @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 0.07/0.32                  & ( Q @ X )
% 0.07/0.32                  & ( P @ X ) ) )
% 0.07/0.32            @ ( sigma_433815053real_n @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets.sets_Collect_conj
% 0.07/0.32  thf(fact_168_sets_Osets__Collect__conj,axiom,
% 0.07/0.32      ! [M: sigma_107786596real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o,Q: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
% 0.07/0.32        ( ( member2104752728real_n
% 0.07/0.32          @ ( collec1190264032real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32                ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 0.07/0.32                & ( P @ X ) ) )
% 0.07/0.32          @ ( sigma_522684908real_n @ M ) )
% 0.07/0.32       => ( ( member2104752728real_n
% 0.07/0.32            @ ( collec1190264032real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 0.07/0.32                  & ( Q @ X ) ) )
% 0.07/0.32            @ ( sigma_522684908real_n @ M ) )
% 0.07/0.32         => ( member2104752728real_n
% 0.07/0.32            @ ( collec1190264032real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 0.07/0.32                  & ( Q @ X )
% 0.07/0.32                  & ( P @ X ) ) )
% 0.07/0.32            @ ( sigma_522684908real_n @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets.sets_Collect_conj
% 0.07/0.32  thf(fact_169_sets_Osets__Collect__conj,axiom,
% 0.07/0.32      ! [M: sigma_1466784463real_n,P: finite1489363574real_n > $o,Q: finite1489363574real_n > $o] :
% 0.07/0.32        ( ( member223413699real_n
% 0.07/0.32          @ ( collec321817931real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32                & ( P @ X ) ) )
% 0.07/0.32          @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32       => ( ( member223413699real_n
% 0.07/0.32            @ ( collec321817931real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32                  & ( Q @ X ) ) )
% 0.07/0.32            @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32         => ( member223413699real_n
% 0.07/0.32            @ ( collec321817931real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32                  & ( Q @ X )
% 0.07/0.32                  & ( P @ X ) ) )
% 0.07/0.32            @ ( sigma_1235138647real_n @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets.sets_Collect_conj
% 0.07/0.32  thf(fact_170_sets_Osets__Collect__disj,axiom,
% 0.07/0.32      ! [M: sigma_1422848389real_n,P: set_Fi1058188332real_n > $o,Q: set_Fi1058188332real_n > $o] :
% 0.07/0.32        ( ( member1475136633real_n
% 0.07/0.32          @ ( collec452821761real_n
% 0.07/0.32            @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32                ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 0.07/0.32                & ( P @ X ) ) )
% 0.07/0.32          @ ( sigma_433815053real_n @ M ) )
% 0.07/0.32       => ( ( member1475136633real_n
% 0.07/0.32            @ ( collec452821761real_n
% 0.07/0.32              @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 0.07/0.32                  & ( Q @ X ) ) )
% 0.07/0.32            @ ( sigma_433815053real_n @ M ) )
% 0.07/0.32         => ( member1475136633real_n
% 0.07/0.32            @ ( collec452821761real_n
% 0.07/0.32              @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 0.07/0.32                  & ( ( Q @ X )
% 0.07/0.32                    | ( P @ X ) ) ) )
% 0.07/0.32            @ ( sigma_433815053real_n @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets.sets_Collect_disj
% 0.07/0.32  thf(fact_171_sets_Osets__Collect__disj,axiom,
% 0.07/0.32      ! [M: sigma_107786596real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o,Q: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
% 0.07/0.32        ( ( member2104752728real_n
% 0.07/0.32          @ ( collec1190264032real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32                ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 0.07/0.32                & ( P @ X ) ) )
% 0.07/0.32          @ ( sigma_522684908real_n @ M ) )
% 0.07/0.32       => ( ( member2104752728real_n
% 0.07/0.32            @ ( collec1190264032real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 0.07/0.32                  & ( Q @ X ) ) )
% 0.07/0.32            @ ( sigma_522684908real_n @ M ) )
% 0.07/0.32         => ( member2104752728real_n
% 0.07/0.32            @ ( collec1190264032real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 0.07/0.32                  & ( ( Q @ X )
% 0.07/0.32                    | ( P @ X ) ) ) )
% 0.07/0.32            @ ( sigma_522684908real_n @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets.sets_Collect_disj
% 0.07/0.32  thf(fact_172_sets_Osets__Collect__disj,axiom,
% 0.07/0.32      ! [M: sigma_1466784463real_n,P: finite1489363574real_n > $o,Q: finite1489363574real_n > $o] :
% 0.07/0.32        ( ( member223413699real_n
% 0.07/0.32          @ ( collec321817931real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32                & ( P @ X ) ) )
% 0.07/0.32          @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32       => ( ( member223413699real_n
% 0.07/0.32            @ ( collec321817931real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32                  & ( Q @ X ) ) )
% 0.07/0.32            @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32         => ( member223413699real_n
% 0.07/0.32            @ ( collec321817931real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32                  & ( ( Q @ X )
% 0.07/0.32                    | ( P @ X ) ) ) )
% 0.07/0.32            @ ( sigma_1235138647real_n @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets.sets_Collect_disj
% 0.07/0.32  thf(fact_173_sets_Osets__Collect__const,axiom,
% 0.07/0.32      ! [M: sigma_1422848389real_n,P: $o] :
% 0.07/0.32        ( member1475136633real_n
% 0.07/0.32        @ ( collec452821761real_n
% 0.07/0.32          @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32              ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 0.07/0.32              & P ) )
% 0.07/0.32        @ ( sigma_433815053real_n @ M ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets.sets_Collect_const
% 0.07/0.32  thf(fact_174_sets_Osets__Collect__const,axiom,
% 0.07/0.32      ! [M: sigma_107786596real_n,P: $o] :
% 0.07/0.32        ( member2104752728real_n
% 0.07/0.32        @ ( collec1190264032real_n
% 0.07/0.32          @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32              ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 0.07/0.32              & P ) )
% 0.07/0.32        @ ( sigma_522684908real_n @ M ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets.sets_Collect_const
% 0.07/0.32  thf(fact_175_sets_Osets__Collect__const,axiom,
% 0.07/0.32      ! [M: sigma_1466784463real_n,P: $o] :
% 0.07/0.32        ( member223413699real_n
% 0.07/0.32        @ ( collec321817931real_n
% 0.07/0.32          @ ^ [X: finite1489363574real_n] :
% 0.07/0.32              ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32              & P ) )
% 0.07/0.32        @ ( sigma_1235138647real_n @ M ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets.sets_Collect_const
% 0.07/0.32  thf(fact_176_measurable__const,axiom,
% 0.07/0.32      ! [C2: finite1489363574real_n,M2: sigma_1466784463real_n,M: sigma_1466784463real_n] :
% 0.07/0.32        ( ( member1352538125real_n @ C2 @ ( sigma_476185326real_n @ M2 ) )
% 0.07/0.32       => ( member1746150050real_n
% 0.07/0.32          @ ^ [X: finite1489363574real_n] : C2
% 0.07/0.32          @ ( sigma_439801790real_n @ M @ M2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_const
% 0.07/0.32  thf(fact_177_T_H__def,axiom,
% 0.07/0.32      ( t
% 0.07/0.32      = ( ^ [A3: finite964658038_int_n] :
% 0.07/0.32            ( image_439535603real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ X @ ( minkow1134813771n_real @ A3 ) )
% 0.07/0.32            @ ( t2 @ A3 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % T'_def
% 0.07/0.32  thf(fact_178_inf__Int__eq,axiom,
% 0.07/0.32      ! [R: set_se2111327970real_n,S: set_se2111327970real_n] :
% 0.07/0.32        ( ( inf_in409346577al_n_o
% 0.07/0.32          @ ^ [X: set_Fi1058188332real_n] : ( member223413699real_n @ X @ R )
% 0.07/0.32          @ ^ [X: set_Fi1058188332real_n] : ( member223413699real_n @ X @ S ) )
% 0.07/0.32        = ( ^ [X: set_Fi1058188332real_n] : ( member223413699real_n @ X @ ( inf_in632889204real_n @ R @ S ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % inf_Int_eq
% 0.07/0.32  thf(fact_179_inf__Int__eq,axiom,
% 0.07/0.32      ! [R: set_Fi1326602817real_n,S: set_Fi1326602817real_n] :
% 0.07/0.32        ( ( inf_in32002162al_n_o
% 0.07/0.32          @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ X @ R )
% 0.07/0.32          @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ X @ S ) )
% 0.07/0.32        = ( ^ [X: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ X @ ( inf_in146441683real_n @ R @ S ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % inf_Int_eq
% 0.07/0.32  thf(fact_180_inf__Int__eq,axiom,
% 0.07/0.32      ! [R: set_Fi1058188332real_n,S: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( inf_in1620715847al_n_o
% 0.07/0.32          @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ X @ R )
% 0.07/0.32          @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ X @ S ) )
% 0.07/0.32        = ( ^ [X: finite1489363574real_n] : ( member1352538125real_n @ X @ ( inf_in1974387902real_n @ R @ S ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % inf_Int_eq
% 0.07/0.32  thf(fact_181_main__part__sets,axiom,
% 0.07/0.32      ! [S: set_Fi1058188332real_n,M: sigma_1466784463real_n] :
% 0.07/0.32        ( ( member223413699real_n @ S @ ( sigma_1235138647real_n @ ( comple230862828real_n @ M ) ) )
% 0.07/0.32       => ( member223413699real_n @ ( comple1390568924real_n @ M @ S ) @ ( sigma_1235138647real_n @ M ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % main_part_sets
% 0.07/0.32  thf(fact_182_measurable__restrict__space__iff,axiom,
% 0.07/0.32      ! [Omega: set_se2111327970real_n,M: sigma_1422848389real_n,C2: set_Fi1058188332real_n,N: sigma_1422848389real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member1475136633real_n @ ( inf_in632889204real_n @ Omega @ ( sigma_607186084real_n @ M ) ) @ ( sigma_433815053real_n @ M ) )
% 0.07/0.32       => ( ( member223413699real_n @ C2 @ ( sigma_607186084real_n @ N ) )
% 0.07/0.32         => ( ( member1734791438real_n @ F @ ( sigma_239294762real_n @ ( sigma_993999336real_n @ M @ Omega ) @ N ) )
% 0.07/0.32            = ( member1734791438real_n
% 0.07/0.32              @ ^ [X: set_Fi1058188332real_n] : ( if_set11487206real_n @ ( member223413699real_n @ X @ Omega ) @ ( F @ X ) @ C2 )
% 0.07/0.32              @ ( sigma_239294762real_n @ M @ N ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_restrict_space_iff
% 0.07/0.32  thf(fact_183_measurable__restrict__space__iff,axiom,
% 0.07/0.32      ! [Omega: set_Fi1326602817real_n,M: sigma_107786596real_n,C2: set_Fi1058188332real_n,N: sigma_1422848389real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member2104752728real_n @ ( inf_in146441683real_n @ Omega @ ( sigma_1483971331real_n @ M ) ) @ ( sigma_522684908real_n @ M ) )
% 0.07/0.32       => ( ( member223413699real_n @ C2 @ ( sigma_607186084real_n @ N ) )
% 0.07/0.32         => ( ( member640587117real_n @ F @ ( sigma_364818953real_n @ ( sigma_1052429895real_n @ M @ Omega ) @ N ) )
% 0.07/0.32            = ( member640587117real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( if_set11487206real_n @ ( member1746150050real_n @ X @ Omega ) @ ( F @ X ) @ C2 )
% 0.07/0.32              @ ( sigma_364818953real_n @ M @ N ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_restrict_space_iff
% 0.07/0.32  thf(fact_184_measurable__restrict__space__iff,axiom,
% 0.07/0.32      ! [Omega: set_se2111327970real_n,M: sigma_1422848389real_n,C2: finite1489363574real_n > finite1489363574real_n,N: sigma_107786596real_n,F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32        ( ( member1475136633real_n @ ( inf_in632889204real_n @ Omega @ ( sigma_607186084real_n @ M ) ) @ ( sigma_433815053real_n @ M ) )
% 0.07/0.32       => ( ( member1746150050real_n @ C2 @ ( sigma_1483971331real_n @ N ) )
% 0.07/0.32         => ( ( member1764433517real_n @ F @ ( sigma_588796041real_n @ ( sigma_993999336real_n @ M @ Omega ) @ N ) )
% 0.07/0.32            = ( member1764433517real_n
% 0.07/0.32              @ ^ [X: set_Fi1058188332real_n] : ( if_Fin413489477real_n @ ( member223413699real_n @ X @ Omega ) @ ( F @ X ) @ C2 )
% 0.07/0.32              @ ( sigma_588796041real_n @ M @ N ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_restrict_space_iff
% 0.07/0.32  thf(fact_185_measurable__restrict__space__iff,axiom,
% 0.07/0.32      ! [Omega: set_Fi1326602817real_n,M: sigma_107786596real_n,C2: finite1489363574real_n > finite1489363574real_n,N: sigma_107786596real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32        ( ( member2104752728real_n @ ( inf_in146441683real_n @ Omega @ ( sigma_1483971331real_n @ M ) ) @ ( sigma_522684908real_n @ M ) )
% 0.07/0.32       => ( ( member1746150050real_n @ C2 @ ( sigma_1483971331real_n @ N ) )
% 0.07/0.32         => ( ( member117715276real_n @ F @ ( sigma_1185134568real_n @ ( sigma_1052429895real_n @ M @ Omega ) @ N ) )
% 0.07/0.32            = ( member117715276real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( if_Fin413489477real_n @ ( member1746150050real_n @ X @ Omega ) @ ( F @ X ) @ C2 )
% 0.07/0.32              @ ( sigma_1185134568real_n @ M @ N ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_restrict_space_iff
% 0.07/0.32  thf(fact_186_measurable__restrict__space__iff,axiom,
% 0.07/0.32      ! [Omega: set_se2111327970real_n,M: sigma_1422848389real_n,C2: finite1489363574real_n,N: sigma_1466784463real_n,F: set_Fi1058188332real_n > finite1489363574real_n] :
% 0.07/0.32        ( ( member1475136633real_n @ ( inf_in632889204real_n @ Omega @ ( sigma_607186084real_n @ M ) ) @ ( sigma_433815053real_n @ M ) )
% 0.07/0.32       => ( ( member1352538125real_n @ C2 @ ( sigma_476185326real_n @ N ) )
% 0.07/0.32         => ( ( member1759501912real_n @ F @ ( sigma_1333364596real_n @ ( sigma_993999336real_n @ M @ Omega ) @ N ) )
% 0.07/0.32            = ( member1759501912real_n
% 0.07/0.32              @ ^ [X: set_Fi1058188332real_n] : ( if_Fin127821360real_n @ ( member223413699real_n @ X @ Omega ) @ ( F @ X ) @ C2 )
% 0.07/0.32              @ ( sigma_1333364596real_n @ M @ N ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_restrict_space_iff
% 0.07/0.32  thf(fact_187_measurable__restrict__space__iff,axiom,
% 0.07/0.32      ! [Omega: set_Fi1326602817real_n,M: sigma_107786596real_n,C2: finite1489363574real_n,N: sigma_1466784463real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n] :
% 0.07/0.32        ( ( member2104752728real_n @ ( inf_in146441683real_n @ Omega @ ( sigma_1483971331real_n @ M ) ) @ ( sigma_522684908real_n @ M ) )
% 0.07/0.32       => ( ( member1352538125real_n @ C2 @ ( sigma_476185326real_n @ N ) )
% 0.07/0.32         => ( ( member1695588023real_n @ F @ ( sigma_2028985427real_n @ ( sigma_1052429895real_n @ M @ Omega ) @ N ) )
% 0.07/0.32            = ( member1695588023real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( if_Fin127821360real_n @ ( member1746150050real_n @ X @ Omega ) @ ( F @ X ) @ C2 )
% 0.07/0.32              @ ( sigma_2028985427real_n @ M @ N ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_restrict_space_iff
% 0.07/0.32  thf(fact_188_measurable__restrict__space__iff,axiom,
% 0.07/0.32      ! [Omega: set_Fi1058188332real_n,M: sigma_1466784463real_n,C2: set_Fi1058188332real_n,N: sigma_1422848389real_n,F: finite1489363574real_n > set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member223413699real_n @ ( inf_in1974387902real_n @ Omega @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32       => ( ( member223413699real_n @ C2 @ ( sigma_607186084real_n @ N ) )
% 0.07/0.32         => ( ( member966061400real_n @ F @ ( sigma_566919540real_n @ ( sigma_346513458real_n @ M @ Omega ) @ N ) )
% 0.07/0.32            = ( member966061400real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n] : ( if_set11487206real_n @ ( member1352538125real_n @ X @ Omega ) @ ( F @ X ) @ C2 )
% 0.07/0.32              @ ( sigma_566919540real_n @ M @ N ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_restrict_space_iff
% 0.07/0.32  thf(fact_189_measurable__restrict__space__iff,axiom,
% 0.07/0.32      ! [Omega: set_Fi1058188332real_n,M: sigma_1466784463real_n,C2: finite1489363574real_n > finite1489363574real_n,N: sigma_107786596real_n,F: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32        ( ( member223413699real_n @ ( inf_in1974387902real_n @ Omega @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32       => ( ( member1746150050real_n @ C2 @ ( sigma_1483971331real_n @ N ) )
% 0.07/0.32         => ( ( member408431031real_n @ F @ ( sigma_2016438227real_n @ ( sigma_346513458real_n @ M @ Omega ) @ N ) )
% 0.07/0.32            = ( member408431031real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n] : ( if_Fin413489477real_n @ ( member1352538125real_n @ X @ Omega ) @ ( F @ X ) @ C2 )
% 0.07/0.32              @ ( sigma_2016438227real_n @ M @ N ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_restrict_space_iff
% 0.07/0.32  thf(fact_190_measurable__restrict__space__iff,axiom,
% 0.07/0.32      ! [Omega: set_Fi1058188332real_n,M: sigma_1466784463real_n,C2: finite1489363574real_n,N: sigma_1466784463real_n,F: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32        ( ( member223413699real_n @ ( inf_in1974387902real_n @ Omega @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32       => ( ( member1352538125real_n @ C2 @ ( sigma_476185326real_n @ N ) )
% 0.07/0.32         => ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ M @ Omega ) @ N ) )
% 0.07/0.32            = ( member1746150050real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n] : ( if_Fin127821360real_n @ ( member1352538125real_n @ X @ Omega ) @ ( F @ X ) @ C2 )
% 0.07/0.32              @ ( sigma_439801790real_n @ M @ N ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_restrict_space_iff
% 0.07/0.32  thf(fact_191_sets__Least,axiom,
% 0.07/0.32      ! [M: sigma_1422848389real_n,P: nat > set_Fi1058188332real_n > $o,A2: set_nat] :
% 0.07/0.32        ( ! [I2: nat] :
% 0.07/0.32            ( member1475136633real_n
% 0.07/0.32            @ ( collec452821761real_n
% 0.07/0.32              @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 0.07/0.32                  & ( P @ I2 @ X ) ) )
% 0.07/0.32            @ ( sigma_433815053real_n @ M ) )
% 0.07/0.32       => ( member1475136633real_n
% 0.07/0.32          @ ( inf_in632889204real_n
% 0.07/0.32            @ ( vimage501526201_n_nat
% 0.07/0.32              @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32                  ( ord_Least_nat
% 0.07/0.32                  @ ^ [J2: nat] : ( P @ J2 @ X ) )
% 0.07/0.32              @ A2 )
% 0.07/0.32            @ ( sigma_607186084real_n @ M ) )
% 0.07/0.32          @ ( sigma_433815053real_n @ M ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets_Least
% 0.07/0.32  thf(fact_192_sets__Least,axiom,
% 0.07/0.32      ! [M: sigma_107786596real_n,P: nat > ( finite1489363574real_n > finite1489363574real_n ) > $o,A2: set_nat] :
% 0.07/0.32        ( ! [I2: nat] :
% 0.07/0.32            ( member2104752728real_n
% 0.07/0.32            @ ( collec1190264032real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 0.07/0.32                  & ( P @ I2 @ X ) ) )
% 0.07/0.32            @ ( sigma_522684908real_n @ M ) )
% 0.07/0.32       => ( member2104752728real_n
% 0.07/0.32          @ ( inf_in146441683real_n
% 0.07/0.32            @ ( vimage2098059032_n_nat
% 0.07/0.32              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32                  ( ord_Least_nat
% 0.07/0.32                  @ ^ [J2: nat] : ( P @ J2 @ X ) )
% 0.07/0.32              @ A2 )
% 0.07/0.32            @ ( sigma_1483971331real_n @ M ) )
% 0.07/0.32          @ ( sigma_522684908real_n @ M ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets_Least
% 0.07/0.32  thf(fact_193_sets__Least,axiom,
% 0.07/0.32      ! [M: sigma_1466784463real_n,P: nat > finite1489363574real_n > $o,A2: set_nat] :
% 0.07/0.32        ( ! [I2: nat] :
% 0.07/0.32            ( member223413699real_n
% 0.07/0.32            @ ( collec321817931real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32                  & ( P @ I2 @ X ) ) )
% 0.07/0.32            @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32       => ( member223413699real_n
% 0.07/0.32          @ ( inf_in1974387902real_n
% 0.07/0.32            @ ( vimage281029891_n_nat
% 0.07/0.32              @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                  ( ord_Least_nat
% 0.07/0.32                  @ ^ [J2: nat] : ( P @ J2 @ X ) )
% 0.07/0.32              @ A2 )
% 0.07/0.32            @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32          @ ( sigma_1235138647real_n @ M ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets_Least
% 0.07/0.32  thf(fact_194_in__vimage__algebra,axiom,
% 0.07/0.32      ! [A2: set_Fi1058188332real_n,M: sigma_1466784463real_n,F: finite1489363574real_n > finite1489363574real_n,X4: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member223413699real_n @ A2 @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32       => ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage1233683625real_n @ F @ A2 ) @ X4 ) @ ( sigma_1235138647real_n @ ( sigma_821351682real_n @ X4 @ F @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % in_vimage_algebra
% 0.07/0.32  thf(fact_195_in__borel__measurable__borel,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) )
% 0.07/0.32        = ( ! [X: set_Fi1058188332real_n] :
% 0.07/0.32              ( ( member223413699real_n @ X @ ( sigma_1235138647real_n @ borel_676189912real_n ) )
% 0.07/0.32             => ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage1233683625real_n @ F @ X ) @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % in_borel_measurable_borel
% 0.07/0.32  thf(fact_196_image__eqI,axiom,
% 0.07/0.32      ! [B: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n,X2: finite1489363574real_n,A2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( B
% 0.07/0.32          = ( F @ X2 ) )
% 0.07/0.32       => ( ( member1352538125real_n @ X2 @ A2 )
% 0.07/0.32         => ( member1352538125real_n @ B @ ( image_439535603real_n @ F @ A2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % image_eqI
% 0.07/0.32  thf(fact_197_image__eqI,axiom,
% 0.07/0.32      ! [B: set_Fi1058188332real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n,X2: set_Fi1058188332real_n,A2: set_se2111327970real_n] :
% 0.07/0.32        ( ( B
% 0.07/0.32          = ( F @ X2 ) )
% 0.07/0.32       => ( ( member223413699real_n @ X2 @ A2 )
% 0.07/0.32         => ( member223413699real_n @ B @ ( image_1661509983real_n @ F @ A2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % image_eqI
% 0.07/0.32  thf(fact_198_image__eqI,axiom,
% 0.07/0.32      ! [B: finite1489363574real_n > finite1489363574real_n,F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,X2: set_Fi1058188332real_n,A2: set_se2111327970real_n] :
% 0.07/0.32        ( ( B
% 0.07/0.32          = ( F @ X2 ) )
% 0.07/0.32       => ( ( member223413699real_n @ X2 @ A2 )
% 0.07/0.32         => ( member1746150050real_n @ B @ ( image_352856126real_n @ F @ A2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % image_eqI
% 0.07/0.32  thf(fact_199_image__eqI,axiom,
% 0.07/0.32      ! [B: set_Fi1058188332real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,X2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n] :
% 0.07/0.32        ( ( B
% 0.07/0.32          = ( F @ X2 ) )
% 0.07/0.32       => ( ( member1746150050real_n @ X2 @ A2 )
% 0.07/0.32         => ( member223413699real_n @ B @ ( image_128879038real_n @ F @ A2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % image_eqI
% 0.07/0.32  thf(fact_200_image__eqI,axiom,
% 0.07/0.32      ! [B: finite1489363574real_n > finite1489363574real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,X2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n] :
% 0.07/0.32        ( ( B
% 0.07/0.32          = ( F @ X2 ) )
% 0.07/0.32       => ( ( member1746150050real_n @ X2 @ A2 )
% 0.07/0.32         => ( member1746150050real_n @ B @ ( image_1123376925real_n @ F @ A2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % image_eqI
% 0.07/0.32  thf(fact_201_image__ident,axiom,
% 0.07/0.32      ! [Y: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( image_439535603real_n
% 0.07/0.32          @ ^ [X: finite1489363574real_n] : X
% 0.07/0.32          @ Y )
% 0.07/0.32        = Y ) ).
% 0.07/0.32  
% 0.07/0.32  % image_ident
% 0.07/0.32  thf(fact_202_add__diff__cancel__right_H,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,B: finite1489363574real_n] :
% 0.07/0.32        ( ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ B ) @ B )
% 0.07/0.32        = A ) ).
% 0.07/0.32  
% 0.07/0.32  % add_diff_cancel_right'
% 0.07/0.32  thf(fact_203_add__diff__cancel__right_H,axiom,
% 0.07/0.32      ! [A: nat,B: nat] :
% 0.07/0.32        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.07/0.32        = A ) ).
% 0.07/0.32  
% 0.07/0.32  % add_diff_cancel_right'
% 0.07/0.32  thf(fact_204_add__diff__cancel__right,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,C2: finite1489363574real_n,B: finite1489363574real_n] :
% 0.07/0.32        ( ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ C2 ) @ ( plus_p585657087real_n @ B @ C2 ) )
% 0.07/0.32        = ( minus_1037315151real_n @ A @ B ) ) ).
% 0.07/0.32  
% 0.07/0.32  % add_diff_cancel_right
% 0.07/0.32  thf(fact_205_add__diff__cancel__right,axiom,
% 0.07/0.32      ! [A: nat,C2: nat,B: nat] :
% 0.07/0.32        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 0.07/0.32        = ( minus_minus_nat @ A @ B ) ) ).
% 0.07/0.32  
% 0.07/0.32  % add_diff_cancel_right
% 0.07/0.32  thf(fact_206_add__diff__cancel__left_H,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,B: finite1489363574real_n] :
% 0.07/0.32        ( ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ B ) @ A )
% 0.07/0.32        = B ) ).
% 0.07/0.32  
% 0.07/0.32  % add_diff_cancel_left'
% 0.07/0.32  thf(fact_207_add__diff__cancel__left_H,axiom,
% 0.07/0.32      ! [A: nat,B: nat] :
% 0.07/0.32        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 0.07/0.32        = B ) ).
% 0.07/0.32  
% 0.07/0.32  % add_diff_cancel_left'
% 0.07/0.32  thf(fact_208_add__diff__cancel__left,axiom,
% 0.07/0.32      ! [C2: finite1489363574real_n,A: finite1489363574real_n,B: finite1489363574real_n] :
% 0.07/0.32        ( ( minus_1037315151real_n @ ( plus_p585657087real_n @ C2 @ A ) @ ( plus_p585657087real_n @ C2 @ B ) )
% 0.07/0.32        = ( minus_1037315151real_n @ A @ B ) ) ).
% 0.07/0.32  
% 0.07/0.32  % add_diff_cancel_left
% 0.07/0.32  thf(fact_209_add__diff__cancel__left,axiom,
% 0.07/0.32      ! [C2: nat,A: nat,B: nat] :
% 0.07/0.32        ( ( minus_minus_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 0.07/0.32        = ( minus_minus_nat @ A @ B ) ) ).
% 0.07/0.32  
% 0.07/0.32  % add_diff_cancel_left
% 0.07/0.32  thf(fact_210_diff__add__cancel,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,B: finite1489363574real_n] :
% 0.07/0.32        ( ( plus_p585657087real_n @ ( minus_1037315151real_n @ A @ B ) @ B )
% 0.07/0.32        = A ) ).
% 0.07/0.32  
% 0.07/0.32  % diff_add_cancel
% 0.07/0.32  thf(fact_211_add__diff__cancel,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,B: finite1489363574real_n] :
% 0.07/0.32        ( ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ B ) @ B )
% 0.07/0.32        = A ) ).
% 0.07/0.32  
% 0.07/0.32  % add_diff_cancel
% 0.07/0.32  thf(fact_212_main__part,axiom,
% 0.07/0.32      ! [S: set_Fi1058188332real_n,M: sigma_1466784463real_n] :
% 0.07/0.32        ( ( member223413699real_n @ S @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32       => ( ( comple1390568924real_n @ M @ S )
% 0.07/0.32          = S ) ) ).
% 0.07/0.32  
% 0.07/0.32  % main_part
% 0.07/0.32  thf(fact_213_space__restrict__space2,axiom,
% 0.07/0.32      ! [Omega: set_Fi1058188332real_n,M: sigma_1466784463real_n] :
% 0.07/0.32        ( ( member223413699real_n @ Omega @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32       => ( ( sigma_476185326real_n @ ( sigma_346513458real_n @ M @ Omega ) )
% 0.07/0.32          = Omega ) ) ).
% 0.07/0.32  
% 0.07/0.32  % space_restrict_space2
% 0.07/0.32  thf(fact_214_borel__measurable__diff,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,G: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) )
% 0.07/0.32       => ( ( member1746150050real_n @ G @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) )
% 0.07/0.32         => ( member1746150050real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ ( F @ X ) @ ( G @ X ) )
% 0.07/0.32            @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % borel_measurable_diff
% 0.07/0.32  thf(fact_215_Compr__image__eq,axiom,
% 0.07/0.32      ! [F: set_Fi1058188332real_n > set_Fi1058188332real_n,A2: set_se2111327970real_n,P: set_Fi1058188332real_n > $o] :
% 0.07/0.32        ( ( collec452821761real_n
% 0.07/0.32          @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32              ( ( member223413699real_n @ X @ ( image_1661509983real_n @ F @ A2 ) )
% 0.07/0.32              & ( P @ X ) ) )
% 0.07/0.32        = ( image_1661509983real_n @ F
% 0.07/0.32          @ ( collec452821761real_n
% 0.07/0.32            @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32                ( ( member223413699real_n @ X @ A2 )
% 0.07/0.32                & ( P @ ( F @ X ) ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Compr_image_eq
% 0.07/0.32  thf(fact_216_Compr__image__eq,axiom,
% 0.07/0.32      ! [F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,A2: set_Fi1326602817real_n,P: set_Fi1058188332real_n > $o] :
% 0.07/0.32        ( ( collec452821761real_n
% 0.07/0.32          @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32              ( ( member223413699real_n @ X @ ( image_128879038real_n @ F @ A2 ) )
% 0.07/0.32              & ( P @ X ) ) )
% 0.07/0.32        = ( image_128879038real_n @ F
% 0.07/0.32          @ ( collec1190264032real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32                ( ( member1746150050real_n @ X @ A2 )
% 0.07/0.32                & ( P @ ( F @ X ) ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Compr_image_eq
% 0.07/0.32  thf(fact_217_Compr__image__eq,axiom,
% 0.07/0.32      ! [F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,A2: set_se2111327970real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
% 0.07/0.32        ( ( collec1190264032real_n
% 0.07/0.32          @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32              ( ( member1746150050real_n @ X @ ( image_352856126real_n @ F @ A2 ) )
% 0.07/0.32              & ( P @ X ) ) )
% 0.07/0.32        = ( image_352856126real_n @ F
% 0.07/0.32          @ ( collec452821761real_n
% 0.07/0.32            @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32                ( ( member223413699real_n @ X @ A2 )
% 0.07/0.32                & ( P @ ( F @ X ) ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Compr_image_eq
% 0.07/0.32  thf(fact_218_Compr__image__eq,axiom,
% 0.07/0.32      ! [F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
% 0.07/0.32        ( ( collec1190264032real_n
% 0.07/0.32          @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32              ( ( member1746150050real_n @ X @ ( image_1123376925real_n @ F @ A2 ) )
% 0.07/0.32              & ( P @ X ) ) )
% 0.07/0.32        = ( image_1123376925real_n @ F
% 0.07/0.32          @ ( collec1190264032real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32                ( ( member1746150050real_n @ X @ A2 )
% 0.07/0.32                & ( P @ ( F @ X ) ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Compr_image_eq
% 0.07/0.32  thf(fact_219_Compr__image__eq,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > set_Fi1058188332real_n,A2: set_Fi1058188332real_n,P: set_Fi1058188332real_n > $o] :
% 0.07/0.32        ( ( collec452821761real_n
% 0.07/0.32          @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32              ( ( member223413699real_n @ X @ ( image_545463721real_n @ F @ A2 ) )
% 0.07/0.32              & ( P @ X ) ) )
% 0.07/0.32        = ( image_545463721real_n @ F
% 0.07/0.32          @ ( collec321817931real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                ( ( member1352538125real_n @ X @ A2 )
% 0.07/0.32                & ( P @ ( F @ X ) ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Compr_image_eq
% 0.07/0.32  thf(fact_220_Compr__image__eq,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
% 0.07/0.32        ( ( collec1190264032real_n
% 0.07/0.32          @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32              ( ( member1746150050real_n @ X @ ( image_437359496real_n @ F @ A2 ) )
% 0.07/0.32              & ( P @ X ) ) )
% 0.07/0.32        = ( image_437359496real_n @ F
% 0.07/0.32          @ ( collec321817931real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                ( ( member1352538125real_n @ X @ A2 )
% 0.07/0.32                & ( P @ ( F @ X ) ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Compr_image_eq
% 0.07/0.32  thf(fact_221_Compr__image__eq,axiom,
% 0.07/0.32      ! [F: set_Fi1058188332real_n > finite1489363574real_n,A2: set_se2111327970real_n,P: finite1489363574real_n > $o] :
% 0.07/0.32        ( ( collec321817931real_n
% 0.07/0.32          @ ^ [X: finite1489363574real_n] :
% 0.07/0.32              ( ( member1352538125real_n @ X @ ( image_1311908777real_n @ F @ A2 ) )
% 0.07/0.32              & ( P @ X ) ) )
% 0.07/0.32        = ( image_1311908777real_n @ F
% 0.07/0.32          @ ( collec452821761real_n
% 0.07/0.32            @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32                ( ( member223413699real_n @ X @ A2 )
% 0.07/0.32                & ( P @ ( F @ X ) ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Compr_image_eq
% 0.07/0.32  thf(fact_222_Compr__image__eq,axiom,
% 0.07/0.32      ! [F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,A2: set_Fi1326602817real_n,P: finite1489363574real_n > $o] :
% 0.07/0.32        ( ( collec321817931real_n
% 0.07/0.32          @ ^ [X: finite1489363574real_n] :
% 0.07/0.32              ( ( member1352538125real_n @ X @ ( image_449906696real_n @ F @ A2 ) )
% 0.07/0.32              & ( P @ X ) ) )
% 0.07/0.32        = ( image_449906696real_n @ F
% 0.07/0.32          @ ( collec1190264032real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32                ( ( member1746150050real_n @ X @ A2 )
% 0.07/0.32                & ( P @ ( F @ X ) ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Compr_image_eq
% 0.07/0.32  thf(fact_223_Compr__image__eq,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n,P: finite1489363574real_n > $o] :
% 0.07/0.32        ( ( collec321817931real_n
% 0.07/0.32          @ ^ [X: finite1489363574real_n] :
% 0.07/0.32              ( ( member1352538125real_n @ X @ ( image_439535603real_n @ F @ A2 ) )
% 0.07/0.32              & ( P @ X ) ) )
% 0.07/0.32        = ( image_439535603real_n @ F
% 0.07/0.32          @ ( collec321817931real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                ( ( member1352538125real_n @ X @ A2 )
% 0.07/0.32                & ( P @ ( F @ X ) ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Compr_image_eq
% 0.07/0.32  thf(fact_224_image__image,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n,G: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( image_439535603real_n @ F @ ( image_439535603real_n @ G @ A2 ) )
% 0.07/0.32        = ( image_439535603real_n
% 0.07/0.32          @ ^ [X: finite1489363574real_n] : ( F @ ( G @ X ) )
% 0.07/0.32          @ A2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % image_image
% 0.07/0.32  thf(fact_225_imageE,axiom,
% 0.07/0.32      ! [B: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member1352538125real_n @ B @ ( image_439535603real_n @ F @ A2 ) )
% 0.07/0.32       => ~ ! [X3: finite1489363574real_n] :
% 0.07/0.32              ( ( B
% 0.07/0.32                = ( F @ X3 ) )
% 0.07/0.32             => ~ ( member1352538125real_n @ X3 @ A2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % imageE
% 0.07/0.32  thf(fact_226_imageE,axiom,
% 0.07/0.32      ! [B: set_Fi1058188332real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n,A2: set_se2111327970real_n] :
% 0.07/0.32        ( ( member223413699real_n @ B @ ( image_1661509983real_n @ F @ A2 ) )
% 0.07/0.32       => ~ ! [X3: set_Fi1058188332real_n] :
% 0.07/0.32              ( ( B
% 0.07/0.32                = ( F @ X3 ) )
% 0.07/0.32             => ~ ( member223413699real_n @ X3 @ A2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % imageE
% 0.07/0.32  thf(fact_227_imageE,axiom,
% 0.07/0.32      ! [B: set_Fi1058188332real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,A2: set_Fi1326602817real_n] :
% 0.07/0.32        ( ( member223413699real_n @ B @ ( image_128879038real_n @ F @ A2 ) )
% 0.07/0.32       => ~ ! [X3: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32              ( ( B
% 0.07/0.32                = ( F @ X3 ) )
% 0.07/0.32             => ~ ( member1746150050real_n @ X3 @ A2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % imageE
% 0.07/0.32  thf(fact_228_imageE,axiom,
% 0.07/0.32      ! [B: finite1489363574real_n > finite1489363574real_n,F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,A2: set_se2111327970real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ B @ ( image_352856126real_n @ F @ A2 ) )
% 0.07/0.32       => ~ ! [X3: set_Fi1058188332real_n] :
% 0.07/0.32              ( ( B
% 0.07/0.32                = ( F @ X3 ) )
% 0.07/0.32             => ~ ( member223413699real_n @ X3 @ A2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % imageE
% 0.07/0.32  thf(fact_229_imageE,axiom,
% 0.07/0.32      ! [B: finite1489363574real_n > finite1489363574real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ B @ ( image_1123376925real_n @ F @ A2 ) )
% 0.07/0.32       => ~ ! [X3: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32              ( ( B
% 0.07/0.32                = ( F @ X3 ) )
% 0.07/0.32             => ~ ( member1746150050real_n @ X3 @ A2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % imageE
% 0.07/0.32  thf(fact_230_diff__right__commute,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,C2: finite1489363574real_n,B: finite1489363574real_n] :
% 0.07/0.32        ( ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ C2 ) @ B )
% 0.07/0.32        = ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ B ) @ C2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % diff_right_commute
% 0.07/0.32  thf(fact_231_diff__right__commute,axiom,
% 0.07/0.32      ! [A: nat,C2: nat,B: nat] :
% 0.07/0.32        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C2 ) @ B )
% 0.07/0.32        = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % diff_right_commute
% 0.07/0.32  thf(fact_232_diff__eq__diff__eq,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n,D2: finite1489363574real_n] :
% 0.07/0.32        ( ( ( minus_1037315151real_n @ A @ B )
% 0.07/0.32          = ( minus_1037315151real_n @ C2 @ D2 ) )
% 0.07/0.32       => ( ( A = B )
% 0.07/0.32          = ( C2 = D2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % diff_eq_diff_eq
% 0.07/0.32  thf(fact_233_rev__image__eqI,axiom,
% 0.07/0.32      ! [X2: finite1489363574real_n,A2: set_Fi1058188332real_n,B: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32        ( ( member1352538125real_n @ X2 @ A2 )
% 0.07/0.32       => ( ( B
% 0.07/0.32            = ( F @ X2 ) )
% 0.07/0.32         => ( member1352538125real_n @ B @ ( image_439535603real_n @ F @ A2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % rev_image_eqI
% 0.07/0.32  thf(fact_234_rev__image__eqI,axiom,
% 0.07/0.32      ! [X2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B: set_Fi1058188332real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member223413699real_n @ X2 @ A2 )
% 0.07/0.32       => ( ( B
% 0.07/0.32            = ( F @ X2 ) )
% 0.07/0.32         => ( member223413699real_n @ B @ ( image_1661509983real_n @ F @ A2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % rev_image_eqI
% 0.07/0.32  thf(fact_235_rev__image__eqI,axiom,
% 0.07/0.32      ! [X2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B: finite1489363574real_n > finite1489363574real_n,F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32        ( ( member223413699real_n @ X2 @ A2 )
% 0.07/0.32       => ( ( B
% 0.07/0.32            = ( F @ X2 ) )
% 0.07/0.32         => ( member1746150050real_n @ B @ ( image_352856126real_n @ F @ A2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % rev_image_eqI
% 0.07/0.32  thf(fact_236_rev__image__eqI,axiom,
% 0.07/0.32      ! [X2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B: set_Fi1058188332real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ X2 @ A2 )
% 0.07/0.32       => ( ( B
% 0.07/0.32            = ( F @ X2 ) )
% 0.07/0.32         => ( member223413699real_n @ B @ ( image_128879038real_n @ F @ A2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % rev_image_eqI
% 0.07/0.32  thf(fact_237_rev__image__eqI,axiom,
% 0.07/0.32      ! [X2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B: finite1489363574real_n > finite1489363574real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ X2 @ A2 )
% 0.07/0.32       => ( ( B
% 0.07/0.32            = ( F @ X2 ) )
% 0.07/0.32         => ( member1746150050real_n @ B @ ( image_1123376925real_n @ F @ A2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % rev_image_eqI
% 0.07/0.32  thf(fact_238_ball__imageD,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n,P: finite1489363574real_n > $o] :
% 0.07/0.32        ( ! [X3: finite1489363574real_n] :
% 0.07/0.32            ( ( member1352538125real_n @ X3 @ ( image_439535603real_n @ F @ A2 ) )
% 0.07/0.32           => ( P @ X3 ) )
% 0.07/0.32       => ! [X5: finite1489363574real_n] :
% 0.07/0.32            ( ( member1352538125real_n @ X5 @ A2 )
% 0.07/0.32           => ( P @ ( F @ X5 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % ball_imageD
% 0.07/0.32  thf(fact_239_image__cong,axiom,
% 0.07/0.32      ! [M: set_Fi1058188332real_n,N: set_Fi1058188332real_n,F: finite1489363574real_n > finite1489363574real_n,G: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32        ( ( M = N )
% 0.07/0.32       => ( ! [X3: finite1489363574real_n] :
% 0.07/0.32              ( ( member1352538125real_n @ X3 @ N )
% 0.07/0.32             => ( ( F @ X3 )
% 0.07/0.32                = ( G @ X3 ) ) )
% 0.07/0.32         => ( ( image_439535603real_n @ F @ M )
% 0.07/0.32            = ( image_439535603real_n @ G @ N ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % image_cong
% 0.07/0.32  thf(fact_240_bex__imageD,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n,P: finite1489363574real_n > $o] :
% 0.07/0.32        ( ? [X5: finite1489363574real_n] :
% 0.07/0.32            ( ( member1352538125real_n @ X5 @ ( image_439535603real_n @ F @ A2 ) )
% 0.07/0.32            & ( P @ X5 ) )
% 0.07/0.32       => ? [X3: finite1489363574real_n] :
% 0.07/0.32            ( ( member1352538125real_n @ X3 @ A2 )
% 0.07/0.32            & ( P @ ( F @ X3 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % bex_imageD
% 0.07/0.32  thf(fact_241_image__iff,axiom,
% 0.07/0.32      ! [Z: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member1352538125real_n @ Z @ ( image_439535603real_n @ F @ A2 ) )
% 0.07/0.32        = ( ? [X: finite1489363574real_n] :
% 0.07/0.32              ( ( member1352538125real_n @ X @ A2 )
% 0.07/0.32              & ( Z
% 0.07/0.32                = ( F @ X ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % image_iff
% 0.07/0.32  thf(fact_242_imageI,axiom,
% 0.07/0.32      ! [X2: finite1489363574real_n,A2: set_Fi1058188332real_n,F: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32        ( ( member1352538125real_n @ X2 @ A2 )
% 0.07/0.32       => ( member1352538125real_n @ ( F @ X2 ) @ ( image_439535603real_n @ F @ A2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % imageI
% 0.07/0.32  thf(fact_243_imageI,axiom,
% 0.07/0.32      ! [X2: set_Fi1058188332real_n,A2: set_se2111327970real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member223413699real_n @ X2 @ A2 )
% 0.07/0.32       => ( member223413699real_n @ ( F @ X2 ) @ ( image_1661509983real_n @ F @ A2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % imageI
% 0.07/0.32  thf(fact_244_imageI,axiom,
% 0.07/0.32      ! [X2: set_Fi1058188332real_n,A2: set_se2111327970real_n,F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32        ( ( member223413699real_n @ X2 @ A2 )
% 0.07/0.32       => ( member1746150050real_n @ ( F @ X2 ) @ ( image_352856126real_n @ F @ A2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % imageI
% 0.07/0.32  thf(fact_245_imageI,axiom,
% 0.07/0.32      ! [X2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ X2 @ A2 )
% 0.07/0.32       => ( member223413699real_n @ ( F @ X2 ) @ ( image_128879038real_n @ F @ A2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % imageI
% 0.07/0.32  thf(fact_246_imageI,axiom,
% 0.07/0.32      ! [X2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ X2 @ A2 )
% 0.07/0.32       => ( member1746150050real_n @ ( F @ X2 ) @ ( image_1123376925real_n @ F @ A2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % imageI
% 0.07/0.32  thf(fact_247_borel__measurable__const,axiom,
% 0.07/0.32      ! [C2: finite1489363574real_n,M: sigma_1466784463real_n] :
% 0.07/0.32        ( member1746150050real_n
% 0.07/0.32        @ ^ [X: finite1489363574real_n] : C2
% 0.07/0.32        @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) ) ).
% 0.07/0.32  
% 0.07/0.32  % borel_measurable_const
% 0.07/0.32  thf(fact_248_sets__restrict__space__cong,axiom,
% 0.07/0.32      ! [M: sigma_1466784463real_n,N: sigma_1466784463real_n,Omega: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( ( sigma_1235138647real_n @ M )
% 0.07/0.32          = ( sigma_1235138647real_n @ N ) )
% 0.07/0.32       => ( ( sigma_1235138647real_n @ ( sigma_346513458real_n @ M @ Omega ) )
% 0.07/0.32          = ( sigma_1235138647real_n @ ( sigma_346513458real_n @ N @ Omega ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets_restrict_space_cong
% 0.07/0.32  thf(fact_249_restrict__space__sets__cong,axiom,
% 0.07/0.32      ! [A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n,M: sigma_1466784463real_n,N: sigma_1466784463real_n] :
% 0.07/0.32        ( ( A2 = B2 )
% 0.07/0.32       => ( ( ( sigma_1235138647real_n @ M )
% 0.07/0.32            = ( sigma_1235138647real_n @ N ) )
% 0.07/0.32         => ( ( sigma_1235138647real_n @ ( sigma_346513458real_n @ M @ A2 ) )
% 0.07/0.32            = ( sigma_1235138647real_n @ ( sigma_346513458real_n @ N @ B2 ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % restrict_space_sets_cong
% 0.07/0.32  thf(fact_250_measurable__restrict__space1,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,N: sigma_1466784463real_n,Omega: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ N ) )
% 0.07/0.32       => ( member1746150050real_n @ F @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ M @ Omega ) @ N ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_restrict_space1
% 0.07/0.32  thf(fact_251_add__implies__diff,axiom,
% 0.07/0.32      ! [C2: finite1489363574real_n,B: finite1489363574real_n,A: finite1489363574real_n] :
% 0.07/0.32        ( ( ( plus_p585657087real_n @ C2 @ B )
% 0.07/0.32          = A )
% 0.07/0.32       => ( C2
% 0.07/0.32          = ( minus_1037315151real_n @ A @ B ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % add_implies_diff
% 0.07/0.32  thf(fact_252_add__implies__diff,axiom,
% 0.07/0.32      ! [C2: nat,B: nat,A: nat] :
% 0.07/0.32        ( ( ( plus_plus_nat @ C2 @ B )
% 0.07/0.32          = A )
% 0.07/0.32       => ( C2
% 0.07/0.32          = ( minus_minus_nat @ A @ B ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % add_implies_diff
% 0.07/0.32  thf(fact_253_diff__diff__add,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] :
% 0.07/0.32        ( ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ B ) @ C2 )
% 0.07/0.32        = ( minus_1037315151real_n @ A @ ( plus_p585657087real_n @ B @ C2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % diff_diff_add
% 0.07/0.32  thf(fact_254_diff__diff__add,axiom,
% 0.07/0.32      ! [A: nat,B: nat,C2: nat] :
% 0.07/0.32        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C2 )
% 0.07/0.32        = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % diff_diff_add
% 0.07/0.32  thf(fact_255_diff__add__eq__diff__diff__swap,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] :
% 0.07/0.32        ( ( minus_1037315151real_n @ A @ ( plus_p585657087real_n @ B @ C2 ) )
% 0.07/0.32        = ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ C2 ) @ B ) ) ).
% 0.07/0.32  
% 0.07/0.32  % diff_add_eq_diff_diff_swap
% 0.07/0.32  thf(fact_256_diff__add__eq,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] :
% 0.07/0.32        ( ( plus_p585657087real_n @ ( minus_1037315151real_n @ A @ B ) @ C2 )
% 0.07/0.32        = ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ C2 ) @ B ) ) ).
% 0.07/0.32  
% 0.07/0.32  % diff_add_eq
% 0.07/0.32  thf(fact_257_diff__diff__eq2,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] :
% 0.07/0.32        ( ( minus_1037315151real_n @ A @ ( minus_1037315151real_n @ B @ C2 ) )
% 0.07/0.32        = ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ C2 ) @ B ) ) ).
% 0.07/0.32  
% 0.07/0.32  % diff_diff_eq2
% 0.07/0.32  thf(fact_258_add__diff__eq,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] :
% 0.07/0.32        ( ( plus_p585657087real_n @ A @ ( minus_1037315151real_n @ B @ C2 ) )
% 0.07/0.32        = ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ B ) @ C2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % add_diff_eq
% 0.07/0.32  thf(fact_259_eq__diff__eq,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,C2: finite1489363574real_n,B: finite1489363574real_n] :
% 0.07/0.32        ( ( A
% 0.07/0.32          = ( minus_1037315151real_n @ C2 @ B ) )
% 0.07/0.32        = ( ( plus_p585657087real_n @ A @ B )
% 0.07/0.32          = C2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % eq_diff_eq
% 0.07/0.32  thf(fact_260_diff__eq__eq,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] :
% 0.07/0.32        ( ( ( minus_1037315151real_n @ A @ B )
% 0.07/0.32          = C2 )
% 0.07/0.32        = ( A
% 0.07/0.32          = ( plus_p585657087real_n @ C2 @ B ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % diff_eq_eq
% 0.07/0.32  thf(fact_261_group__cancel_Osub1,axiom,
% 0.07/0.32      ! [A2: finite1489363574real_n,K: finite1489363574real_n,A: finite1489363574real_n,B: finite1489363574real_n] :
% 0.07/0.32        ( ( A2
% 0.07/0.32          = ( plus_p585657087real_n @ K @ A ) )
% 0.07/0.32       => ( ( minus_1037315151real_n @ A2 @ B )
% 0.07/0.32          = ( plus_p585657087real_n @ K @ ( minus_1037315151real_n @ A @ B ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % group_cancel.sub1
% 0.07/0.32  thf(fact_262_sets__vimage__algebra__cong,axiom,
% 0.07/0.32      ! [M: sigma_1466784463real_n,N: sigma_1466784463real_n,X4: set_Fi1058188332real_n,F: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32        ( ( ( sigma_1235138647real_n @ M )
% 0.07/0.32          = ( sigma_1235138647real_n @ N ) )
% 0.07/0.32       => ( ( sigma_1235138647real_n @ ( sigma_821351682real_n @ X4 @ F @ M ) )
% 0.07/0.32          = ( sigma_1235138647real_n @ ( sigma_821351682real_n @ X4 @ F @ N ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets_vimage_algebra_cong
% 0.07/0.32  thf(fact_263_vimage__algebra__cong,axiom,
% 0.07/0.32      ! [X4: set_se2111327970real_n,Y: set_se2111327970real_n,F: set_Fi1058188332real_n > finite1489363574real_n,G: set_Fi1058188332real_n > finite1489363574real_n,M: sigma_1466784463real_n,N: sigma_1466784463real_n] :
% 0.07/0.32        ( ( X4 = Y )
% 0.07/0.32       => ( ! [X3: set_Fi1058188332real_n] :
% 0.07/0.32              ( ( member223413699real_n @ X3 @ Y )
% 0.07/0.32             => ( ( F @ X3 )
% 0.07/0.32                = ( G @ X3 ) ) )
% 0.07/0.32         => ( ( ( sigma_1235138647real_n @ M )
% 0.07/0.32              = ( sigma_1235138647real_n @ N ) )
% 0.07/0.32           => ( ( sigma_1384150200real_n @ X4 @ F @ M )
% 0.07/0.32              = ( sigma_1384150200real_n @ Y @ G @ N ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimage_algebra_cong
% 0.07/0.32  thf(fact_264_vimage__algebra__cong,axiom,
% 0.07/0.32      ! [X4: set_Fi1326602817real_n,Y: set_Fi1326602817real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,G: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,M: sigma_1466784463real_n,N: sigma_1466784463real_n] :
% 0.07/0.32        ( ( X4 = Y )
% 0.07/0.32       => ( ! [X3: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32              ( ( member1746150050real_n @ X3 @ Y )
% 0.07/0.32             => ( ( F @ X3 )
% 0.07/0.32                = ( G @ X3 ) ) )
% 0.07/0.32         => ( ( ( sigma_1235138647real_n @ M )
% 0.07/0.32              = ( sigma_1235138647real_n @ N ) )
% 0.07/0.32           => ( ( sigma_136294295real_n @ X4 @ F @ M )
% 0.07/0.32              = ( sigma_136294295real_n @ Y @ G @ N ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimage_algebra_cong
% 0.07/0.32  thf(fact_265_borel__measurable__const__add,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,A: finite1489363574real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) )
% 0.07/0.32       => ( member1746150050real_n
% 0.07/0.32          @ ^ [X: finite1489363574real_n] : ( plus_p585657087real_n @ A @ ( F @ X ) )
% 0.07/0.32          @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % borel_measurable_const_add
% 0.07/0.32  thf(fact_266_borel__measurable__add,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,G: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) )
% 0.07/0.32       => ( ( member1746150050real_n @ G @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) )
% 0.07/0.32         => ( member1746150050real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n] : ( plus_p585657087real_n @ ( F @ X ) @ ( G @ X ) )
% 0.07/0.32            @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % borel_measurable_add
% 0.07/0.32  thf(fact_267_sets__restrict__restrict__space,axiom,
% 0.07/0.32      ! [M: sigma_1466784463real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( sigma_1235138647real_n @ ( sigma_346513458real_n @ ( sigma_346513458real_n @ M @ A2 ) @ B2 ) )
% 0.07/0.32        = ( sigma_1235138647real_n @ ( sigma_346513458real_n @ M @ ( inf_in1974387902real_n @ A2 @ B2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets_restrict_restrict_space
% 0.07/0.32  thf(fact_268_space__restrict__space,axiom,
% 0.07/0.32      ! [M: sigma_1466784463real_n,Omega: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( sigma_476185326real_n @ ( sigma_346513458real_n @ M @ Omega ) )
% 0.07/0.32        = ( inf_in1974387902real_n @ Omega @ ( sigma_476185326real_n @ M ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % space_restrict_space
% 0.07/0.32  thf(fact_269_measurable__sets__borel,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,A2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ borel_676189912real_n @ M ) )
% 0.07/0.32       => ( ( member223413699real_n @ A2 @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32         => ( member223413699real_n @ ( vimage1233683625real_n @ F @ A2 ) @ ( sigma_1235138647real_n @ borel_676189912real_n ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_sets_borel
% 0.07/0.32  thf(fact_270_sets__Collect__restrict__space__iff,axiom,
% 0.07/0.32      ! [S: set_se2111327970real_n,M: sigma_1422848389real_n,P: set_Fi1058188332real_n > $o] :
% 0.07/0.32        ( ( member1475136633real_n @ S @ ( sigma_433815053real_n @ M ) )
% 0.07/0.32       => ( ( member1475136633real_n
% 0.07/0.32            @ ( collec452821761real_n
% 0.07/0.32              @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ ( sigma_993999336real_n @ M @ S ) ) )
% 0.07/0.32                  & ( P @ X ) ) )
% 0.07/0.32            @ ( sigma_433815053real_n @ ( sigma_993999336real_n @ M @ S ) ) )
% 0.07/0.32          = ( member1475136633real_n
% 0.07/0.32            @ ( collec452821761real_n
% 0.07/0.32              @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 0.07/0.32                  & ( member223413699real_n @ X @ S )
% 0.07/0.32                  & ( P @ X ) ) )
% 0.07/0.32            @ ( sigma_433815053real_n @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets_Collect_restrict_space_iff
% 0.07/0.32  thf(fact_271_sets__Collect__restrict__space__iff,axiom,
% 0.07/0.32      ! [S: set_Fi1326602817real_n,M: sigma_107786596real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
% 0.07/0.32        ( ( member2104752728real_n @ S @ ( sigma_522684908real_n @ M ) )
% 0.07/0.32       => ( ( member2104752728real_n
% 0.07/0.32            @ ( collec1190264032real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ ( sigma_1052429895real_n @ M @ S ) ) )
% 0.07/0.32                  & ( P @ X ) ) )
% 0.07/0.32            @ ( sigma_522684908real_n @ ( sigma_1052429895real_n @ M @ S ) ) )
% 0.07/0.32          = ( member2104752728real_n
% 0.07/0.32            @ ( collec1190264032real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 0.07/0.32                  & ( member1746150050real_n @ X @ S )
% 0.07/0.32                  & ( P @ X ) ) )
% 0.07/0.32            @ ( sigma_522684908real_n @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets_Collect_restrict_space_iff
% 0.07/0.32  thf(fact_272_sets__Collect__restrict__space__iff,axiom,
% 0.07/0.32      ! [S: set_Fi1058188332real_n,M: sigma_1466784463real_n,P: finite1489363574real_n > $o] :
% 0.07/0.32        ( ( member223413699real_n @ S @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32       => ( ( member223413699real_n
% 0.07/0.32            @ ( collec321817931real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ ( sigma_346513458real_n @ M @ S ) ) )
% 0.07/0.32                  & ( P @ X ) ) )
% 0.07/0.32            @ ( sigma_1235138647real_n @ ( sigma_346513458real_n @ M @ S ) ) )
% 0.07/0.32          = ( member223413699real_n
% 0.07/0.32            @ ( collec321817931real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32                  & ( member1352538125real_n @ X @ S )
% 0.07/0.32                  & ( P @ X ) ) )
% 0.07/0.32            @ ( sigma_1235138647real_n @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets_Collect_restrict_space_iff
% 0.07/0.32  thf(fact_273_measurable__equality__set,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,G: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) )
% 0.07/0.32       => ( ( member1746150050real_n @ G @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) )
% 0.07/0.32         => ( member223413699real_n
% 0.07/0.32            @ ( collec321817931real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32                  & ( ( F @ X )
% 0.07/0.32                    = ( G @ X ) ) ) )
% 0.07/0.32            @ ( sigma_1235138647real_n @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_equality_set
% 0.07/0.32  thf(fact_274_measurable__If__restrict__space__iff,axiom,
% 0.07/0.32      ! [M: sigma_1466784463real_n,P: finite1489363574real_n > $o,F: finite1489363574real_n > finite1489363574real_n,G: finite1489363574real_n > finite1489363574real_n,N: sigma_1466784463real_n] :
% 0.07/0.32        ( ( member223413699real_n
% 0.07/0.32          @ ( collec321817931real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32                & ( P @ X ) ) )
% 0.07/0.32          @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32       => ( ( member1746150050real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n] : ( if_Fin127821360real_n @ ( P @ X ) @ ( F @ X ) @ ( G @ X ) )
% 0.07/0.32            @ ( sigma_439801790real_n @ M @ N ) )
% 0.07/0.32          = ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ M @ ( collec321817931real_n @ P ) ) @ N ) )
% 0.07/0.32            & ( member1746150050real_n @ G
% 0.07/0.32              @ ( sigma_439801790real_n
% 0.07/0.32                @ ( sigma_346513458real_n @ M
% 0.07/0.32                  @ ( collec321817931real_n
% 0.07/0.32                    @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                        ~ ( P @ X ) ) )
% 0.07/0.32                @ N ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_If_restrict_space_iff
% 0.07/0.32  thf(fact_275_space__lebesgue__on,axiom,
% 0.07/0.32      ! [S: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( sigma_476185326real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ S ) )
% 0.07/0.32        = S ) ).
% 0.07/0.32  
% 0.07/0.32  % space_lebesgue_on
% 0.07/0.32  thf(fact_276_sets__lebesgue__on__refl,axiom,
% 0.07/0.32      ! [S: set_Fi1058188332real_n] : ( member223413699real_n @ S @ ( sigma_1235138647real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ S ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets_lebesgue_on_refl
% 0.07/0.32  thf(fact_277_space__lborel,axiom,
% 0.07/0.32      ( ( sigma_476185326real_n @ lebesg260170249real_n )
% 0.07/0.32      = ( sigma_476185326real_n @ borel_676189912real_n ) ) ).
% 0.07/0.32  
% 0.07/0.32  % space_lborel
% 0.07/0.32  thf(fact_278_measurable__lborel1,axiom,
% 0.07/0.32      ! [M: sigma_1466784463real_n] :
% 0.07/0.32        ( ( sigma_439801790real_n @ M @ lebesg260170249real_n )
% 0.07/0.32        = ( sigma_439801790real_n @ M @ borel_676189912real_n ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_lborel1
% 0.07/0.32  thf(fact_279_measurable__lborel2,axiom,
% 0.07/0.32      ! [M: sigma_1466784463real_n] :
% 0.07/0.32        ( ( sigma_439801790real_n @ lebesg260170249real_n @ M )
% 0.07/0.32        = ( sigma_439801790real_n @ borel_676189912real_n @ M ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_lborel2
% 0.07/0.32  thf(fact_280_sets_ODiff,axiom,
% 0.07/0.32      ! [A: set_Fi1058188332real_n,M: sigma_1466784463real_n,B: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32       => ( ( member223413699real_n @ B @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32         => ( member223413699real_n @ ( minus_1686442501real_n @ A @ B ) @ ( sigma_1235138647real_n @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets.Diff
% 0.07/0.32  thf(fact_281_sets_Ocompl__sets,axiom,
% 0.07/0.32      ! [A: set_Fi1058188332real_n,M: sigma_1466784463real_n] :
% 0.07/0.32        ( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32       => ( member223413699real_n @ ( minus_1686442501real_n @ ( sigma_476185326real_n @ M ) @ A ) @ ( sigma_1235138647real_n @ M ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets.compl_sets
% 0.07/0.32  thf(fact_282_sets__lborel,axiom,
% 0.07/0.32      ( ( sigma_1235138647real_n @ lebesg260170249real_n )
% 0.07/0.32      = ( sigma_1235138647real_n @ borel_676189912real_n ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets_lborel
% 0.07/0.32  thf(fact_283_Int__Diff,axiom,
% 0.07/0.32      ! [A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( minus_1686442501real_n @ ( inf_in1974387902real_n @ A2 @ B2 ) @ C )
% 0.07/0.32        = ( inf_in1974387902real_n @ A2 @ ( minus_1686442501real_n @ B2 @ C ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Int_Diff
% 0.07/0.32  thf(fact_284_Diff__Int2,axiom,
% 0.07/0.32      ! [A2: set_Fi1058188332real_n,C: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( minus_1686442501real_n @ ( inf_in1974387902real_n @ A2 @ C ) @ ( inf_in1974387902real_n @ B2 @ C ) )
% 0.07/0.32        = ( minus_1686442501real_n @ ( inf_in1974387902real_n @ A2 @ C ) @ B2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Diff_Int2
% 0.07/0.32  thf(fact_285_Diff__Diff__Int,axiom,
% 0.07/0.32      ! [A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( minus_1686442501real_n @ A2 @ ( minus_1686442501real_n @ A2 @ B2 ) )
% 0.07/0.32        = ( inf_in1974387902real_n @ A2 @ B2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Diff_Diff_Int
% 0.07/0.32  thf(fact_286_Diff__Int__distrib,axiom,
% 0.07/0.32      ! [C: set_Fi1058188332real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( inf_in1974387902real_n @ C @ ( minus_1686442501real_n @ A2 @ B2 ) )
% 0.07/0.32        = ( minus_1686442501real_n @ ( inf_in1974387902real_n @ C @ A2 ) @ ( inf_in1974387902real_n @ C @ B2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Diff_Int_distrib
% 0.07/0.32  thf(fact_287_Diff__Int__distrib2,axiom,
% 0.07/0.32      ! [A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( inf_in1974387902real_n @ ( minus_1686442501real_n @ A2 @ B2 ) @ C )
% 0.07/0.32        = ( minus_1686442501real_n @ ( inf_in1974387902real_n @ A2 @ C ) @ ( inf_in1974387902real_n @ B2 @ C ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Diff_Int_distrib2
% 0.07/0.32  thf(fact_288_vimage__Diff,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( vimage1233683625real_n @ F @ ( minus_1686442501real_n @ A2 @ B2 ) )
% 0.07/0.32        = ( minus_1686442501real_n @ ( vimage1233683625real_n @ F @ A2 ) @ ( vimage1233683625real_n @ F @ B2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % vimage_Diff
% 0.07/0.32  thf(fact_289_sets__restrict__space,axiom,
% 0.07/0.32      ! [M: sigma_1466784463real_n,Omega: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( sigma_1235138647real_n @ ( sigma_346513458real_n @ M @ Omega ) )
% 0.07/0.32        = ( image_1661509983real_n @ ( inf_in1974387902real_n @ Omega ) @ ( sigma_1235138647real_n @ M ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % sets_restrict_space
% 0.07/0.32  thf(fact_290_lborelD,axiom,
% 0.07/0.32      ! [A2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member223413699real_n @ A2 @ ( sigma_1235138647real_n @ borel_676189912real_n ) )
% 0.07/0.32       => ( member223413699real_n @ A2 @ ( sigma_1235138647real_n @ lebesg260170249real_n ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % lborelD
% 0.07/0.32  thf(fact_291_measurable__lebesgue__cong,axiom,
% 0.07/0.32      ! [S: set_Fi1058188332real_n,F: finite1489363574real_n > finite1489363574real_n,G: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n] :
% 0.07/0.32        ( ! [X3: finite1489363574real_n] :
% 0.07/0.32            ( ( member1352538125real_n @ X3 @ S )
% 0.07/0.32           => ( ( F @ X3 )
% 0.07/0.32              = ( G @ X3 ) ) )
% 0.07/0.32       => ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ S ) @ M ) )
% 0.07/0.32          = ( member1746150050real_n @ G @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ S ) @ M ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % measurable_lebesgue_cong
% 0.07/0.32  thf(fact_292_lborelD__Collect,axiom,
% 0.07/0.32      ! [P: finite1489363574real_n > $o] :
% 0.07/0.32        ( ( member223413699real_n
% 0.07/0.32          @ ( collec321817931real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ borel_676189912real_n ) )
% 0.07/0.32                & ( P @ X ) ) )
% 0.07/0.32          @ ( sigma_1235138647real_n @ borel_676189912real_n ) )
% 0.07/0.32       => ( member223413699real_n
% 0.07/0.32          @ ( collec321817931real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ lebesg260170249real_n ) )
% 0.07/0.32                & ( P @ X ) ) )
% 0.07/0.32          @ ( sigma_1235138647real_n @ lebesg260170249real_n ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % lborelD_Collect
% 0.07/0.32  thf(fact_293_lebesgue__sets__translation,axiom,
% 0.07/0.32      ! [S: set_Fi1058188332real_n,A: finite1489363574real_n] :
% 0.07/0.32        ( ( member223413699real_n @ S @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
% 0.07/0.32       => ( member223413699real_n @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ S ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % lebesgue_sets_translation
% 0.07/0.32  thf(fact_294_lebesgue__measurable__vimage__borel,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n,T: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ borel_676189912real_n ) )
% 0.07/0.32       => ( ( member223413699real_n @ T @ ( sigma_1235138647real_n @ borel_676189912real_n ) )
% 0.07/0.32         => ( member223413699real_n
% 0.07/0.32            @ ( collec321817931real_n
% 0.07/0.32              @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ ( F @ X ) @ T ) )
% 0.07/0.32            @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % lebesgue_measurable_vimage_borel
% 0.07/0.32  thf(fact_295_borel__measurable__lebesgue__preimage__borel,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ borel_676189912real_n ) )
% 0.07/0.32        = ( ! [T2: set_Fi1058188332real_n] :
% 0.07/0.32              ( ( member223413699real_n @ T2 @ ( sigma_1235138647real_n @ borel_676189912real_n ) )
% 0.07/0.32             => ( member223413699real_n
% 0.07/0.32                @ ( collec321817931real_n
% 0.07/0.32                  @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ ( F @ X ) @ T2 ) )
% 0.07/0.32                @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % borel_measurable_lebesgue_preimage_borel
% 0.07/0.32  thf(fact_296_borel__measurable__vimage__borel,axiom,
% 0.07/0.32      ! [F: finite1489363574real_n > finite1489363574real_n,S: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ S ) @ borel_676189912real_n ) )
% 0.07/0.32        = ( ! [T2: set_Fi1058188332real_n] :
% 0.07/0.32              ( ( member223413699real_n @ T2 @ ( sigma_1235138647real_n @ borel_676189912real_n ) )
% 0.07/0.32             => ( member223413699real_n
% 0.07/0.32                @ ( collec321817931real_n
% 0.07/0.32                  @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                      ( ( member1352538125real_n @ X @ S )
% 0.07/0.32                      & ( member1352538125real_n @ ( F @ X ) @ T2 ) ) )
% 0.07/0.32                @ ( sigma_1235138647real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ S ) ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % borel_measurable_vimage_borel
% 0.07/0.32  thf(fact_297_restrict__space__eq__vimage__algebra_H,axiom,
% 0.07/0.32      ! [M: sigma_1466784463real_n,Omega: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( sigma_1235138647real_n @ ( sigma_346513458real_n @ M @ Omega ) )
% 0.07/0.32        = ( sigma_1235138647real_n
% 0.07/0.32          @ ( sigma_821351682real_n @ ( inf_in1974387902real_n @ Omega @ ( sigma_476185326real_n @ M ) )
% 0.07/0.32            @ ^ [X: finite1489363574real_n] : X
% 0.07/0.32            @ M ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % restrict_space_eq_vimage_algebra'
% 0.07/0.32  thf(fact_298_restrict__restrict__space,axiom,
% 0.07/0.32      ! [A2: set_Fi1058188332real_n,M: sigma_1466784463real_n,B2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( member223413699real_n @ ( inf_in1974387902real_n @ A2 @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32       => ( ( member223413699real_n @ ( inf_in1974387902real_n @ B2 @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) )
% 0.07/0.32         => ( ( sigma_346513458real_n @ ( sigma_346513458real_n @ M @ A2 ) @ B2 )
% 0.07/0.32            = ( sigma_346513458real_n @ M @ ( inf_in1974387902real_n @ A2 @ B2 ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % restrict_restrict_space
% 0.07/0.32  thf(fact_299_is__borel__def,axiom,
% 0.07/0.32      ( borel_1962407338real_n
% 0.07/0.32      = ( ^ [F2: finite1489363574real_n > finite1489363574real_n,M3: sigma_1466784463real_n] : ( member1746150050real_n @ F2 @ ( sigma_439801790real_n @ M3 @ borel_676189912real_n ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % is_borel_def
% 0.07/0.32  thf(fact_300_Diff__iff,axiom,
% 0.07/0.32      ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] :
% 0.07/0.32        ( ( member223413699real_n @ C2 @ ( minus_1698615483real_n @ A2 @ B2 ) )
% 0.07/0.32        = ( ( member223413699real_n @ C2 @ A2 )
% 0.07/0.32          & ~ ( member223413699real_n @ C2 @ B2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Diff_iff
% 0.07/0.32  thf(fact_301_Diff__iff,axiom,
% 0.07/0.32      ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ C2 @ ( minus_725016986real_n @ A2 @ B2 ) )
% 0.07/0.32        = ( ( member1746150050real_n @ C2 @ A2 )
% 0.07/0.32          & ~ ( member1746150050real_n @ C2 @ B2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % Diff_iff
% 0.07/0.32  thf(fact_302_DiffI,axiom,
% 0.07/0.32      ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] :
% 0.07/0.32        ( ( member223413699real_n @ C2 @ A2 )
% 0.07/0.32       => ( ~ ( member223413699real_n @ C2 @ B2 )
% 0.07/0.32         => ( member223413699real_n @ C2 @ ( minus_1698615483real_n @ A2 @ B2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % DiffI
% 0.07/0.32  thf(fact_303_DiffI,axiom,
% 0.07/0.32      ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ C2 @ A2 )
% 0.07/0.32       => ( ~ ( member1746150050real_n @ C2 @ B2 )
% 0.07/0.32         => ( member1746150050real_n @ C2 @ ( minus_725016986real_n @ A2 @ B2 ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % DiffI
% 0.07/0.32  thf(fact_304_set__diff__eq,axiom,
% 0.07/0.32      ( minus_1698615483real_n
% 0.07/0.32      = ( ^ [A4: set_se2111327970real_n,B3: set_se2111327970real_n] :
% 0.07/0.32            ( collec452821761real_n
% 0.07/0.32            @ ^ [X: set_Fi1058188332real_n] :
% 0.07/0.32                ( ( member223413699real_n @ X @ A4 )
% 0.07/0.32                & ~ ( member223413699real_n @ X @ B3 ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % set_diff_eq
% 0.07/0.32  thf(fact_305_set__diff__eq,axiom,
% 0.07/0.32      ( minus_725016986real_n
% 0.07/0.32      = ( ^ [A4: set_Fi1326602817real_n,B3: set_Fi1326602817real_n] :
% 0.07/0.32            ( collec1190264032real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32                ( ( member1746150050real_n @ X @ A4 )
% 0.07/0.32                & ~ ( member1746150050real_n @ X @ B3 ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % set_diff_eq
% 0.07/0.32  thf(fact_306_set__diff__eq,axiom,
% 0.07/0.32      ( minus_1686442501real_n
% 0.07/0.32      = ( ^ [A4: set_Fi1058188332real_n,B3: set_Fi1058188332real_n] :
% 0.07/0.32            ( collec321817931real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n] :
% 0.07/0.32                ( ( member1352538125real_n @ X @ A4 )
% 0.07/0.32                & ~ ( member1352538125real_n @ X @ B3 ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % set_diff_eq
% 0.07/0.32  thf(fact_307_minus__set__def,axiom,
% 0.07/0.32      ( minus_1698615483real_n
% 0.07/0.32      = ( ^ [A4: set_se2111327970real_n,B3: set_se2111327970real_n] :
% 0.07/0.32            ( collec452821761real_n
% 0.07/0.32            @ ( minus_1832115082al_n_o
% 0.07/0.32              @ ^ [X: set_Fi1058188332real_n] : ( member223413699real_n @ X @ A4 )
% 0.07/0.32              @ ^ [X: set_Fi1058188332real_n] : ( member223413699real_n @ X @ B3 ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % minus_set_def
% 0.07/0.32  thf(fact_308_minus__set__def,axiom,
% 0.07/0.32      ( minus_725016986real_n
% 0.07/0.32      = ( ^ [A4: set_Fi1326602817real_n,B3: set_Fi1326602817real_n] :
% 0.07/0.32            ( collec1190264032real_n
% 0.07/0.32            @ ( minus_391085931al_n_o
% 0.07/0.32              @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ X @ A4 )
% 0.07/0.32              @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ X @ B3 ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % minus_set_def
% 0.07/0.32  thf(fact_309_minus__set__def,axiom,
% 0.07/0.32      ( minus_1686442501real_n
% 0.07/0.32      = ( ^ [A4: set_Fi1058188332real_n,B3: set_Fi1058188332real_n] :
% 0.07/0.32            ( collec321817931real_n
% 0.07/0.32            @ ( minus_455231168al_n_o
% 0.07/0.32              @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ X @ A4 )
% 0.07/0.32              @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ X @ B3 ) ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % minus_set_def
% 0.07/0.32  thf(fact_310_DiffD2,axiom,
% 0.07/0.32      ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] :
% 0.07/0.32        ( ( member223413699real_n @ C2 @ ( minus_1698615483real_n @ A2 @ B2 ) )
% 0.07/0.32       => ~ ( member223413699real_n @ C2 @ B2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % DiffD2
% 0.07/0.32  thf(fact_311_DiffD2,axiom,
% 0.07/0.32      ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ C2 @ ( minus_725016986real_n @ A2 @ B2 ) )
% 0.07/0.32       => ~ ( member1746150050real_n @ C2 @ B2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % DiffD2
% 0.07/0.32  thf(fact_312_DiffD1,axiom,
% 0.07/0.32      ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] :
% 0.07/0.32        ( ( member223413699real_n @ C2 @ ( minus_1698615483real_n @ A2 @ B2 ) )
% 0.07/0.32       => ( member223413699real_n @ C2 @ A2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % DiffD1
% 0.07/0.32  thf(fact_313_DiffD1,axiom,
% 0.07/0.32      ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ C2 @ ( minus_725016986real_n @ A2 @ B2 ) )
% 0.07/0.32       => ( member1746150050real_n @ C2 @ A2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % DiffD1
% 0.07/0.32  thf(fact_314_DiffE,axiom,
% 0.07/0.32      ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] :
% 0.07/0.32        ( ( member223413699real_n @ C2 @ ( minus_1698615483real_n @ A2 @ B2 ) )
% 0.07/0.32       => ~ ( ( member223413699real_n @ C2 @ A2 )
% 0.07/0.32           => ( member223413699real_n @ C2 @ B2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % DiffE
% 0.07/0.32  thf(fact_315_DiffE,axiom,
% 0.07/0.32      ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] :
% 0.07/0.32        ( ( member1746150050real_n @ C2 @ ( minus_725016986real_n @ A2 @ B2 ) )
% 0.07/0.32       => ~ ( ( member1746150050real_n @ C2 @ A2 )
% 0.07/0.32           => ( member1746150050real_n @ C2 @ B2 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % DiffE
% 0.07/0.32  thf(fact_316_translation__subtract__diff,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,S2: set_Fi1058188332real_n,T3: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( image_439535603real_n
% 0.07/0.32          @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ X @ A )
% 0.07/0.32          @ ( minus_1686442501real_n @ S2 @ T3 ) )
% 0.07/0.32        = ( minus_1686442501real_n
% 0.07/0.32          @ ( image_439535603real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ X @ A )
% 0.07/0.32            @ S2 )
% 0.07/0.32          @ ( image_439535603real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ X @ A )
% 0.07/0.32            @ T3 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % translation_subtract_diff
% 0.07/0.32  thf(fact_317_translation__subtract__Int,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,S2: set_Fi1058188332real_n,T3: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( image_439535603real_n
% 0.07/0.32          @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ X @ A )
% 0.07/0.32          @ ( inf_in1974387902real_n @ S2 @ T3 ) )
% 0.07/0.32        = ( inf_in1974387902real_n
% 0.07/0.32          @ ( image_439535603real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ X @ A )
% 0.07/0.32            @ S2 )
% 0.07/0.32          @ ( image_439535603real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ X @ A )
% 0.07/0.32            @ T3 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % translation_subtract_Int
% 0.07/0.32  thf(fact_318_translation__diff,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,S2: set_Fi1058188332real_n,T3: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ ( minus_1686442501real_n @ S2 @ T3 ) )
% 0.07/0.32        = ( minus_1686442501real_n @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ S2 ) @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ T3 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % translation_diff
% 0.07/0.32  thf(fact_319_translation__Int,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,S2: set_Fi1058188332real_n,T3: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ ( inf_in1974387902real_n @ S2 @ T3 ) )
% 0.07/0.32        = ( inf_in1974387902real_n @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ S2 ) @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ T3 ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % translation_Int
% 0.07/0.32  thf(fact_320_translation__invert,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ A2 )
% 0.07/0.32          = ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ B2 ) )
% 0.07/0.32       => ( A2 = B2 ) ) ).
% 0.07/0.32  
% 0.07/0.32  % translation_invert
% 0.07/0.32  thf(fact_321_translation__assoc,axiom,
% 0.07/0.32      ! [B: finite1489363574real_n,A: finite1489363574real_n,S: set_Fi1058188332real_n] :
% 0.07/0.32        ( ( image_439535603real_n @ ( plus_p585657087real_n @ B ) @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ S ) )
% 0.07/0.32        = ( image_439535603real_n @ ( plus_p585657087real_n @ ( plus_p585657087real_n @ A @ B ) ) @ S ) ) ).
% 0.07/0.32  
% 0.07/0.32  % translation_assoc
% 0.07/0.32  thf(fact_322_affine__parallel__expl__aux,axiom,
% 0.07/0.32      ! [S: set_Fi1058188332real_n,A: finite1489363574real_n,T: set_Fi1058188332real_n] :
% 0.07/0.32        ( ! [X3: finite1489363574real_n] :
% 0.07/0.32            ( ( member1352538125real_n @ X3 @ S )
% 0.07/0.32            = ( member1352538125real_n @ ( plus_p585657087real_n @ A @ X3 ) @ T ) )
% 0.07/0.32       => ( T
% 0.07/0.32          = ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ S ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % affine_parallel_expl_aux
% 0.07/0.32  thf(fact_323_borel__measurable__if,axiom,
% 0.07/0.32      ! [S: set_Fi1058188332real_n,F: finite1489363574real_n > finite1489363574real_n] :
% 0.07/0.32        ( ( member223413699real_n @ S @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
% 0.07/0.32       => ( ( member1746150050real_n
% 0.07/0.32            @ ^ [X: finite1489363574real_n] : ( if_Fin127821360real_n @ ( member1352538125real_n @ X @ S ) @ ( F @ X ) @ zero_z200130687real_n )
% 0.07/0.32            @ ( sigma_439801790real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ borel_676189912real_n ) )
% 0.07/0.32          = ( member1746150050real_n @ F @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ S ) @ borel_676189912real_n ) ) ) ) ).
% 0.07/0.32  
% 0.07/0.32  % borel_measurable_if
% 0.07/0.32  thf(fact_324_add_Oleft__neutral,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n] :
% 0.07/0.32        ( ( plus_p585657087real_n @ zero_z200130687real_n @ A )
% 0.07/0.32        = A ) ).
% 0.07/0.32  
% 0.07/0.32  % add.left_neutral
% 0.07/0.32  thf(fact_325_add_Oleft__neutral,axiom,
% 0.07/0.32      ! [A: nat] :
% 0.07/0.32        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.07/0.32        = A ) ).
% 0.07/0.32  
% 0.07/0.32  % add.left_neutral
% 0.07/0.32  thf(fact_326_add_Oright__neutral,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n] :
% 0.07/0.32        ( ( plus_p585657087real_n @ A @ zero_z200130687real_n )
% 0.07/0.32        = A ) ).
% 0.07/0.32  
% 0.07/0.32  % add.right_neutral
% 0.07/0.32  thf(fact_327_add_Oright__neutral,axiom,
% 0.07/0.32      ! [A: nat] :
% 0.07/0.32        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.07/0.32        = A ) ).
% 0.07/0.32  
% 0.07/0.32  % add.right_neutral
% 0.07/0.32  thf(fact_328_add__cancel__left__left,axiom,
% 0.07/0.32      ! [B: finite1489363574real_n,A: finite1489363574real_n] :
% 0.07/0.32        ( ( ( plus_p585657087real_n @ B @ A )
% 0.07/0.32          = A )
% 0.07/0.32        = ( B = zero_z200130687real_n ) ) ).
% 0.07/0.32  
% 0.07/0.32  % add_cancel_left_left
% 0.07/0.32  thf(fact_329_add__cancel__left__left,axiom,
% 0.07/0.32      ! [B: nat,A: nat] :
% 0.07/0.32        ( ( ( plus_plus_nat @ B @ A )
% 0.07/0.32          = A )
% 0.07/0.32        = ( B = zero_zero_nat ) ) ).
% 0.07/0.32  
% 0.07/0.32  % add_cancel_left_left
% 0.07/0.32  thf(fact_330_add__cancel__left__right,axiom,
% 0.07/0.32      ! [A: finite1489363574real_n,B: finite1489363574real_n] :
% 0.14/0.32        ( ( ( plus_p585657087real_n @ A @ B )
% 0.14/0.32          = A )
% 0.14/0.32        = ( B = zero_z200130687real_n ) ) ).
% 0.14/0.32  
% 0.14/0.32  % add_cancel_left_right
% 0.14/0.32  thf(fact_331_add__cancel__left__right,axiom,
% 0.14/0.32      ! [A: nat,B: nat] :
% 0.14/0.32        ( ( ( plus_plus_nat @ A @ B )
% 0.14/0.32          = A )
% 0.14/0.32        = ( B = zero_zero_nat ) ) ).
% 0.14/0.32  
% 0.14/0.32  % add_cancel_left_right
% 0.14/0.32  thf(fact_332_add__cancel__right__left,axiom,
% 0.14/0.32      ! [A: finite1489363574real_n,B: finite1489363574real_n] :
% 0.14/0.32        ( ( A
% 0.14/0.32          = ( plus_p585657087real_n @ B @ A ) )
% 0.14/0.32        = ( B = zero_z200130687real_n ) ) ).
% 0.14/0.32  
% 0.14/0.32  % add_cancel_right_left
% 0.14/0.32  thf(fact_333_add__cancel__right__left,axiom,
% 0.14/0.32      ! [A: nat,B: nat] :
% 0.14/0.32        ( ( A
% 0.14/0.32          = ( plus_plus_nat @ B @ A ) )
% 0.14/0.32        = ( B = zero_zero_nat ) ) ).
% 0.14/0.32  
% 0.14/0.32  % add_cancel_right_left
% 0.14/0.32  thf(fact_334_add__cancel__right__right,axiom,
% 0.14/0.32      ! [A: finite1489363574real_n,B: finite1489363574real_n] :
% 0.14/0.32        ( ( A
% 0.14/0.32          = ( plus_p585657087real_n @ A @ B ) )
% 0.14/0.32        = ( B = zero_z200130687real_n ) ) ).
% 0.14/0.32  
% 0.14/0.32  % add_cancel_right_right
% 0.14/0.32  thf(fact_335_add__cancel__right__right,axiom,
% 0.14/0.32      ! [A: nat,B: nat] :
% 0.14/0.32        ( ( A
% 0.14/0.32          = ( plus_plus_nat @ A @ B ) )
% 0.14/0.32        = ( B = zero_zero_nat ) ) ).
% 0.14/0.32  
% 0.14/0.32  % add_cancel_right_right
% 0.14/0.32  thf(fact_336_add__eq__0__iff__both__eq__0,axiom,
% 0.14/0.32      ! [X2: nat,Y3: nat] :
% 0.14/0.32        ( ( ( plus_plus_nat @ X2 @ Y3 )
% 0.14/0.32          = zero_zero_nat )
% 0.14/0.32        = ( ( X2 = zero_zero_nat )
% 0.14/0.32          & ( Y3 = zero_zero_nat ) ) ) ).
% 0.14/0.32  
% 0.14/0.32  % add_eq_0_iff_both_eq_0
% 0.14/0.32  thf(fact_337_zero__eq__add__iff__both__eq__0,axiom,
% 0.14/0.32      ! [X2: nat,Y3: nat] :
% 0.14/0.32        ( ( zero_zero_nat
% 0.14/0.32          = ( plus_plus_nat @ X2 @ Y3 ) )
% 0.14/0.32        = ( ( X2 = zero_zero_nat )
% 0.14/0.32          & ( Y3 = zero_zero_nat ) ) ) ).
% 0.14/0.32  
% 0.14/0.32  % zero_eq_add_iff_both_eq_0
% 0.14/0.32  thf(fact_338_diff__self,axiom,
% 0.14/0.32      ! [A: finite1489363574real_n] :
% 0.14/0.32        ( ( minus_1037315151real_n @ A @ A )
% 0.14/0.32        = zero_z200130687real_n ) ).
% 0.14/0.32  
% 0.14/0.32  % diff_self
% 0.14/0.32  thf(fact_339_diff__0__right,axiom,
% 0.14/0.32      ! [A: finite1489363574real_n] :
% 0.14/0.32        ( ( minus_1037315151real_n @ A @ zero_z200130687real_n )
% 0.14/0.32        = A ) ).
% 0.14/0.32  
% 0.14/0.32  % diff_0_right
% 0.14/0.32  thf(fact_340_zero__diff,axiom,
% 0.14/0.32      ! [A: nat] :
% 0.14/0.32        ( ( minus_minus_nat @ zero_zero_nat @ A )
% 0.14/0.32        = zero_zero_nat ) ).
% 0.14/0.32  
% 0.14/0.32  % zero_diff
% 0.14/0.32  thf(fact_341_diff__zero,axiom,
% 0.14/0.32      ! [A: finite1489363574real_n] :
% 0.14/0.32        ( ( minus_1037315151real_n @ A @ zero_z200130687real_n )
% 0.14/0.32        = A ) ).
% 0.14/0.32  
% 0.14/0.32  % diff_zero
% 0.14/0.32  thf(fact_342_diff__zero,axiom,
% 0.14/0.32      ! [A: nat] :
% 0.14/0.32        ( ( minus_minus_nat @ A @ zero_zero_nat )
% 0.14/0.32        = A ) ).
% 0.14/0.32  
% 0.14/0.32  % diff_zero
% 0.14/0.32  thf(fact_343_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.14/0.32      ! [A: finite1489363574real_n] :
% 0.14/0.32        ( ( minus_1037315151real_n @ A @ A )
% 0.14/0.32        = zero_z200130687real_n ) ).
% 0.14/0.32  
% 0.14/0.32  % cancel_comm_monoid_add_class.diff_cancel
% 0.14/0.32  thf(fact_344_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.14/0.32      ! [A: nat] :
% 0.14/0.32        ( ( minus_minus_nat @ A @ A )
% 0.14/0.32        = zero_zero_nat ) ).
% 0.14/0.32  
% 0.14/0.32  % cancel_comm_monoid_add_class.diff_cancel
% 0.14/0.32  thf(fact_345_image__add__0,axiom,
% 0.14/0.32      ! [S: set_Fi1058188332real_n] :
% 0.14/0.32        ( ( image_439535603real_n @ ( plus_p585657087real_n @ zero_z200130687real_n ) @ S )
% 0.14/0.32        = S ) ).
% 0.14/0.32  
% 0.14/0.32  % image_add_0
% 0.14/0.32  thf(fact_346_image__add__0,axiom,
% 0.14/0.32      ! [S: set_nat] :
% 0.14/0.32        ( ( image_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ S )
% 0.14/0.32        = S ) ).
% 0.14/0.32  
% 0.14/0.32  % image_add_0
% 0.14/0.32  thf(fact_347_diff__add__zero,axiom,
% 0.14/0.32      ! [A: nat,B: nat] :
% 0.14/0.32        ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.14/0.32        = zero_zero_nat ) ).
% 0.14/0.32  
% 0.14/0.32  % diff_add_zero
% 0.14/0.32  thf(fact_348_eq__add__iff,axiom,
% 0.14/0.32      ! [X2: finite1489363574real_n,Y3: finite1489363574real_n] :
% 0.14/0.32        ( ( X2
% 0.14/0.32          = ( plus_p585657087real_n @ X2 @ Y3 ) )
% 0.14/0.32        = ( Y3 = zero_z200130687real_n ) ) ).
% 0.14/0.32  
% 0.14/0.32  % eq_add_iff
% 0.14/0.32  thf(fact_349_Least__eq__0,axiom,
% 0.14/0.32      ! [P: nat > $o] :
% 0.14/0.32        ( ( P @ zero_zero_nat )
% 0.14/0.32       => ( ( ord_Least_nat @ P )
% 0.14/0.32          = zero_zero_nat ) ) ).
% 0.14/0.32  
% 0.14/0.32  % Least_eq_0
% 0.14/0.32  thf(fact_350_diff__0__eq__0,axiom,
% 0.14/0.32      ! [N3: nat] :
% 0.14/0.32        ( ( minus_minus_nat @ zero_zero_nat @ N3 )
% 0.14/0.32        = zero_zero_nat ) ).
% 0.14/0.32  
% 0.14/0.32  % diff_0_eq_0
% 0.14/0.32  thf(fact_351_diff__self__eq__0,axiom,
% 0.14/0.32      ! [M4: nat] :
% 0.14/0.32        ( ( minus_minus_nat @ M4 @ M4 )
% 0.14/0.32        = zero_zero_nat ) ).
% 0.14/0.32  
% 0.14/0.32  % diff_self_eq_0
% 0.14/0.32  thf(fact_352_diffs0__imp__equal,axiom,
% 0.14/0.32      ! [M4: nat,N3: nat] :
% 0.14/0.32        ( ( ( minus_minus_nat @ M4 @ N3 )
% 0.14/0.32          = zero_zero_nat )
% 0.14/0.32       => ( ( ( minus_minus_nat @ N3 @ M4 )
% 0.14/0.32            = zero_zero_nat )
% 0.14/0.32         => ( M4 = N3 ) ) ) ).
% 0.14/0.32  
% 0.14/0.32  % diffs0_imp_equal
% 0.14/0.32  thf(fact_353_minus__nat_Odiff__0,axiom,
% 0.14/0.32      ! [M4: nat] :
% 0.14/0.32        ( ( minus_minus_nat @ M4 @ zero_zero_nat )
% 0.14/0.32        = M4 ) ).
% 0.14/0.32  
% 0.14/0.32  % minus_nat.diff_0
% 0.14/0.32  
% 0.14/0.32  % Helper facts (7)
% 0.14/0.32  thf(help_If_2_1_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_T,axiom,
% 0.14/0.32      ! [X2: finite1489363574real_n,Y3: finite1489363574real_n] :
% 0.14/0.32        ( ( if_Fin127821360real_n @ $false @ X2 @ Y3 )
% 0.14/0.32        = Y3 ) ).
% 0.14/0.32  
% 0.14/0.32  thf(help_If_1_1_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_T,axiom,
% 0.14/0.32      ! [X2: finite1489363574real_n,Y3: finite1489363574real_n] :
% 0.14/0.32        ( ( if_Fin127821360real_n @ $true @ X2 @ Y3 )
% 0.14/0.32        = X2 ) ).
% 0.14/0.32  
% 0.14/0.32  thf(help_If_2_1_If_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_T,axiom,
% 0.14/0.32      ! [X2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n] :
% 0.14/0.32        ( ( if_set11487206real_n @ $false @ X2 @ Y3 )
% 0.14/0.32        = Y3 ) ).
% 0.14/0.32  
% 0.14/0.32  thf(help_If_1_1_If_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_T,axiom,
% 0.14/0.32      ! [X2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n] :
% 0.14/0.32        ( ( if_set11487206real_n @ $true @ X2 @ Y3 )
% 0.14/0.32        = X2 ) ).
% 0.14/0.32  
% 0.14/0.32  thf(help_If_3_1_If_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_T,axiom,
% 0.14/0.32      ! [P: $o] :
% 0.14/0.32        ( ( P = $true )
% 0.14/0.32        | ( P = $false ) ) ).
% 0.14/0.32  
% 0.14/0.32  thf(help_If_2_1_If_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_T,axiom,
% 0.14/0.32      ! [X2: finite1489363574real_n > finite1489363574real_n,Y3: finite1489363574real_n > finite1489363574real_n] :
% 0.14/0.32        ( ( if_Fin413489477real_n @ $false @ X2 @ Y3 )
% 0.14/0.32        = Y3 ) ).
% 0.14/0.32  
% 0.14/0.32  thf(help_If_1_1_If_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_T,axiom,
% 0.14/0.32      ! [X2: finite1489363574real_n > finite1489363574real_n,Y3: finite1489363574real_n > finite1489363574real_n] :
% 0.14/0.32        ( ( if_Fin413489477real_n @ $true @ X2 @ Y3 )
% 0.14/0.32        = X2 ) ).
% 0.14/0.32  
% 0.14/0.32  % Conjectures (1)
% 0.14/0.32  thf(conj_0,conjecture,
% 0.14/0.32      ( member223413699real_n
% 0.14/0.32      @ ( vimage1233683625real_n
% 0.14/0.32        @ ^ [X: finite1489363574real_n] : ( plus_p585657087real_n @ X @ ( minkow1134813771n_real @ a ) )
% 0.14/0.32        @ ( t2 @ a ) )
% 0.14/0.32      @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ).
% 0.14/0.32  
% 0.14/0.32  %------------------------------------------------------------------------------
% 0.14/0.32  ------------------------
% 2.12/1.13  ---- Embedded in THF ---
% 2.12/1.13  %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.12/1.13  %%% Generated on Tue Feb 24 08:26:31 EST 2026
% 2.12/1.13  %%% using '$$dhol' embedding, version 1.3.0.
% 2.12/1.13  %%% Logic specification used:
% 2.12/1.13  %%% thf(spec, logic, $$dhol).
% 2.12/1.13  
% 2.12/1.13  % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.gWsecxm7AG/DTF2DTF14897.p
% See solution above
% 2.12/1.13  ------------------------
% 2.12/1.16  ---- Cleaned THF ---
% 2.12/1.16  thf(ty_n_t__Set__Oset_I_062_I_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_M_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J_J,type,
% 2.12/1.16      set_Fi1066397675real_n: $tType ).
% 2.12/1.16  
% 2.12/1.16  thf(ty_n_t__Set__Oset_I_062_It__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_M_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J_J,type,
% 2.12/1.16      set_se830533260real_n: $tType ).
% 2.12/1.16  
% 2.12/1.16  thf(ty_n_t__Set__Oset_I_062_I_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_Mt__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J_J,type,
% 2.12/1.16      set_Fi909698444real_n: $tType ).
% 2.12/1.16  
% 2.12/1.16  thf(ty_n_t__Set__Oset_I_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_M_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J_J,type,
% 2.12/1.16      set_Fi1260307670real_n: $tType ).
% 2.12/1.16  
% 2.12/1.16  thf(ty_n_t__Set__Oset_I_062_I_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J,type,
% 2.12/1.16      set_Fi1491909078real_n: $tType ).
% 2.12/1.16  
% 2.12/1.16  thf(ty_n_t__Set__Oset_I_062_It__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_Mt__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J_J,type,
% 2.12/1.16      set_se1738601133real_n: $tType ).
% 2.12/1.16  
% 2.12/1.16  thf(ty_n_t__Sigma____Algebra__Omeasure_I_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J,type,
% 2.12/1.16      sigma_107786596real_n: $tType ).
% 2.12/1.16  
% 2.12/1.16  thf(ty_n_t__Set__Oset_It__Set__Oset_I_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J_J,type,
% 2.12/1.16      set_se221767415real_n: $tType ).
% 2.12/1.16  
% 2.12/1.16  thf(ty_n_t__Set__Oset_I_062_It__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J,type,
% 2.12/1.16      set_se955370231real_n: $tType ).
% 2.12/1.16  
% 2.12/1.16  thf(ty_n_t__Set__Oset_I_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J_J,type,
% 2.12/1.16      set_Fi1645173239real_n: $tType ).
% 2.12/1.16  
% 2.12/1.16  thf(ty_n_t__Set__Oset_I_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J,type,
% 2.12/1.16      set_Fi1326602817real_n: $tType ).
% 2.12/1.16  
% 2.12/1.16  thf(ty_n_t__Sigma____Algebra__Omeasure_It__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J,type,
% 2.12/1.16      sigma_1422848389real_n: $tType ).
% 2.12/1.16  
% 2.12/1.16  thf(ty_n_t__Set__Oset_It__Set__Oset_It__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J_J,type,
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% 2.12/1.16  
% 2.12/1.16  thf(ty_n_t__Sigma____Algebra__Omeasure_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J,type,
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% 2.12/1.16  
% 2.12/1.16  thf(ty_n_t__Set__Oset_It__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J,type,
% 2.12/1.16      set_se2111327970real_n: $tType ).
% 2.12/1.16  
% 2.12/1.16  thf(ty_n_t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J,type,
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% 2.12/1.16  thf(ty_n_t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J,type,
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% 2.12/1.16  
% 2.12/1.16  thf(ty_n_t__Finite____Cartesian____Product__Ovec_It__Int__Oint_Mtf__n_J,type,
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% 2.12/1.16  
% 2.12/1.16  thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 2.12/1.16      set_nat: $tType ).
% 2.12/1.16  
% 2.12/1.16  thf(ty_n_t__Nat__Onat,type,
% 2.12/1.16      nat: $tType ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Borel__Space_Ois__borel_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J,type,
% 2.12/1.16      borel_1962407338real_n: ( finite1489363574real_n > finite1489363574real_n ) > sigma_1466784463real_n > $o ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Borel__Space_Otopological__space__class_Oborel_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J,type,
% 2.12/1.16      borel_676189912real_n: sigma_1466784463real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Complete__Measure_Ocompletion_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J,type,
% 2.12/1.16      comple230862828real_n: sigma_1466784463real_n > sigma_1466784463real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Complete__Measure_Omain__part_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J,type,
% 2.12/1.16      comple1390568924real_n: sigma_1466784463real_n > set_Fi1058188332real_n > set_Fi1058188332real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Groups_Ominus__class_Ominus_001_062_I_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_M_Eo_J,type,
% 2.12/1.16      minus_391085931al_n_o: ( ( finite1489363574real_n > finite1489363574real_n ) > $o ) > ( ( finite1489363574real_n > finite1489363574real_n ) > $o ) > ( finite1489363574real_n > finite1489363574real_n ) > $o ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_M_Eo_J,type,
% 2.12/1.16      minus_455231168al_n_o: ( finite1489363574real_n > $o ) > ( finite1489363574real_n > $o ) > finite1489363574real_n > $o ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_M_Eo_J,type,
% 2.12/1.16      minus_1832115082al_n_o: ( set_Fi1058188332real_n > $o ) > ( set_Fi1058188332real_n > $o ) > set_Fi1058188332real_n > $o ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Groups_Ominus__class_Ominus_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J,type,
% 2.12/1.16      minus_1037315151real_n: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 2.12/1.16      minus_minus_nat: nat > nat > nat ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_I_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J,type,
% 2.12/1.16      minus_725016986real_n: set_Fi1326602817real_n > set_Fi1326602817real_n > set_Fi1326602817real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J,type,
% 2.12/1.16      minus_1686442501real_n: set_Fi1058188332real_n > set_Fi1058188332real_n > set_Fi1058188332real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J,type,
% 2.12/1.16      minus_1698615483real_n: set_se2111327970real_n > set_se2111327970real_n > set_se2111327970real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Groups_Oplus__class_Oplus_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J,type,
% 2.12/1.16      plus_p585657087real_n: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 2.12/1.16      plus_plus_nat: nat > nat > nat ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Groups_Oplus__class_Oplus_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J,type,
% 2.12/1.16      plus_p1606848693real_n: set_Fi1058188332real_n > set_Fi1058188332real_n > set_Fi1058188332real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Groups_Oplus__class_Oplus_001t__Set__Oset_It__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J,type,
% 2.12/1.16      plus_p565022571real_n: set_se2111327970real_n > set_se2111327970real_n > set_se2111327970real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Groups_Ozero__class_Ozero_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J,type,
% 2.12/1.16      zero_z200130687real_n: finite1489363574real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 2.12/1.16      zero_zero_nat: nat ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_If_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J,type,
% 2.12/1.16      if_Fin413489477real_n: $o > ( finite1489363574real_n > finite1489363574real_n ) > ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J,type,
% 2.12/1.16      if_Fin127821360real_n: $o > finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_If_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J,type,
% 2.12/1.16      if_set11487206real_n: $o > set_Fi1058188332real_n > set_Fi1058188332real_n > set_Fi1058188332real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_M_Eo_J,type,
% 2.12/1.16      inf_in32002162al_n_o: ( ( finite1489363574real_n > finite1489363574real_n ) > $o ) > ( ( finite1489363574real_n > finite1489363574real_n ) > $o ) > ( finite1489363574real_n > finite1489363574real_n ) > $o ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_M_Eo_J,type,
% 2.12/1.16      inf_in1620715847al_n_o: ( finite1489363574real_n > $o ) > ( finite1489363574real_n > $o ) > finite1489363574real_n > $o ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_M_Eo_J,type,
% 2.12/1.16      inf_in409346577al_n_o: ( set_Fi1058188332real_n > $o ) > ( set_Fi1058188332real_n > $o ) > set_Fi1058188332real_n > $o ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J,type,
% 2.12/1.16      inf_in146441683real_n: set_Fi1326602817real_n > set_Fi1326602817real_n > set_Fi1326602817real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J,type,
% 2.12/1.16      inf_in1974387902real_n: set_Fi1058188332real_n > set_Fi1058188332real_n > set_Fi1058188332real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_J,type,
% 2.12/1.16      inf_in632889204real_n: set_se2111327970real_n > set_se2111327970real_n > set_se2111327970real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Lebesgue__Measure_Olborel_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J,type,
% 2.12/1.16      lebesg260170249real_n: sigma_1466784463real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Minkowskis__Theorem__Mirabelle__uzuvqgwfeb_Oof__int__vec_001tf__n_001t__Real__Oreal,type,
% 2.12/1.16      minkow1134813771n_real: finite964658038_int_n > finite1489363574real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Orderings_Oord__class_OLeast_001t__Nat__Onat,type,
% 2.12/1.16      ord_Least_nat: ( nat > $o ) > nat ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Set_OCollect_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J,type,
% 2.12/1.16      collec1190264032real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > $o ) > set_Fi1326602817real_n ).
% 2.12/1.16  
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% 2.12/1.16      collec321817931real_n: ( finite1489363574real_n > $o ) > set_Fi1058188332real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Set_OCollect_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J,type,
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% 2.12/1.16  
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% 2.12/1.16      image_1123376925real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n ) > set_Fi1326602817real_n > set_Fi1326602817real_n ).
% 2.12/1.16  
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% 2.12/1.16      image_449906696real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n ) > set_Fi1326602817real_n > set_Fi1058188332real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Set_Oimage_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J,type,
% 2.12/1.16      image_128879038real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n ) > set_Fi1326602817real_n > set_se2111327970real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Set_Oimage_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J,type,
% 2.12/1.16      image_437359496real_n: ( finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n > set_Fi1326602817real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Set_Oimage_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J,type,
% 2.12/1.16      image_439535603real_n: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n > set_Fi1058188332real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Set_Oimage_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J,type,
% 2.12/1.16      image_545463721real_n: ( finite1489363574real_n > set_Fi1058188332real_n ) > set_Fi1058188332real_n > set_se2111327970real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.12/1.16      image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Set_Oimage_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J,type,
% 2.12/1.16      image_352856126real_n: ( set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n ) > set_se2111327970real_n > set_Fi1326602817real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Set_Oimage_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J,type,
% 2.12/1.16      image_1311908777real_n: ( set_Fi1058188332real_n > finite1489363574real_n ) > set_se2111327970real_n > set_Fi1058188332real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Set_Oimage_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J,type,
% 2.12/1.16      image_1661509983real_n: ( set_Fi1058188332real_n > set_Fi1058188332real_n ) > set_se2111327970real_n > set_se2111327970real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Set_Ovimage_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J,type,
% 2.12/1.16      vimage180751827real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n ) > set_Fi1326602817real_n > set_Fi1326602817real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Set_Ovimage_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J,type,
% 2.12/1.16      vimage1072397758real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n ) > set_Fi1058188332real_n > set_Fi1326602817real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Set_Ovimage_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_001t__Nat__Onat,type,
% 2.12/1.16      vimage2098059032_n_nat: ( ( finite1489363574real_n > finite1489363574real_n ) > nat ) > set_nat > set_Fi1326602817real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Set_Ovimage_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J,type,
% 2.12/1.16      vimage1910974324real_n: ( ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n ) > set_se2111327970real_n > set_Fi1326602817real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Set_Ovimage_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J,type,
% 2.12/1.16      vimage1059850558real_n: ( finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ) > set_Fi1326602817real_n > set_Fi1058188332real_n ).
% 2.12/1.16  
% 2.12/1.16  thf(sy_c_Set_Ovimage_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J,type,
% 2.12/1.16      vimage1233683625real_n: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n > set_Fi1058188332real_n ).
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% 2.12/1.16        ( ( ( minkow1134813771n_real @ A )
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% 2.12/1.16  
% 2.12/1.16  thf(fact_6_sets__completionI__sets,axiom,
% 2.12/1.16      ! [A2: set_Fi1058188332real_n,M: sigma_1466784463real_n] :
% 2.12/1.16        ( ( member223413699real_n @ A2 @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.16       => ( member223413699real_n @ A2 @ ( sigma_1235138647real_n @ ( comple230862828real_n @ M ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_7__092_060open_062_092_060And_062a_O_A_I_092_060lambda_062x_O_Ax_A_L_Aof__int__vec_Aa_J_A_092_060in_062_Alebesgue_A_092_060rightarrow_062_092_060_094sub_062M_Alebesgue_092_060close_062,axiom,
% 2.12/1.16      ! [A: finite964658038_int_n] :
% 2.12/1.16        ( member1746150050real_n
% 2.12/1.16        @ ^ [X: finite1489363574real_n] : ( plus_p585657087real_n @ X @ ( minkow1134813771n_real @ A ) )
% 2.12/1.16        @ ( sigma_439801790real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_8_vimage__ident,axiom,
% 2.12/1.16      ! [Y: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( vimage1233683625real_n
% 2.12/1.16          @ ^ [X: finite1489363574real_n] : X
% 2.12/1.16          @ Y )
% 2.12/1.16        = Y ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_9_vimage__Collect__eq,axiom,
% 2.12/1.16      ! [F: finite1489363574real_n > finite1489363574real_n,P: finite1489363574real_n > $o] :
% 2.12/1.16        ( ( vimage1233683625real_n @ F @ ( collec321817931real_n @ P ) )
% 2.12/1.16        = ( collec321817931real_n
% 2.12/1.16          @ ^ [Y2: finite1489363574real_n] : ( P @ ( F @ Y2 ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_10_vimageI,axiom,
% 2.12/1.16      ! [F: set_Fi1058188332real_n > set_Fi1058188332real_n,A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,B2: set_se2111327970real_n] :
% 2.12/1.16        ( ( ( F @ A )
% 2.12/1.16          = B )
% 2.12/1.16       => ( ( member223413699real_n @ B @ B2 )
% 2.12/1.16         => ( member223413699real_n @ A @ ( vimage784510485real_n @ F @ B2 ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_11_vimageI,axiom,
% 2.12/1.16      ! [F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,A: finite1489363574real_n > finite1489363574real_n,B: set_Fi1058188332real_n,B2: set_se2111327970real_n] :
% 2.12/1.16        ( ( ( F @ A )
% 2.12/1.16          = B )
% 2.12/1.16       => ( ( member223413699real_n @ B @ B2 )
% 2.12/1.16         => ( member1746150050real_n @ A @ ( vimage1910974324real_n @ F @ B2 ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_12_vimageI,axiom,
% 2.12/1.16      ! [F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,A: set_Fi1058188332real_n,B: finite1489363574real_n > finite1489363574real_n,B2: set_Fi1326602817real_n] :
% 2.12/1.16        ( ( ( F @ A )
% 2.12/1.16          = B )
% 2.12/1.16       => ( ( member1746150050real_n @ B @ B2 )
% 2.12/1.16         => ( member223413699real_n @ A @ ( vimage2134951412real_n @ F @ B2 ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_13_vimageI,axiom,
% 2.12/1.16      ! [F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,A: finite1489363574real_n > finite1489363574real_n,B: finite1489363574real_n > finite1489363574real_n,B2: set_Fi1326602817real_n] :
% 2.12/1.16        ( ( ( F @ A )
% 2.12/1.16          = B )
% 2.12/1.16       => ( ( member1746150050real_n @ B @ B2 )
% 2.12/1.16         => ( member1746150050real_n @ A @ ( vimage180751827real_n @ F @ B2 ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_14_vimageI,axiom,
% 2.12/1.16      ! [F: finite1489363574real_n > finite1489363574real_n,A: finite1489363574real_n,B: finite1489363574real_n,B2: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( ( F @ A )
% 2.12/1.16          = B )
% 2.12/1.16       => ( ( member1352538125real_n @ B @ B2 )
% 2.12/1.16         => ( member1352538125real_n @ A @ ( vimage1233683625real_n @ F @ B2 ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_15_vimage__eq,axiom,
% 2.12/1.16      ! [A: set_Fi1058188332real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n,B2: set_se2111327970real_n] :
% 2.12/1.16        ( ( member223413699real_n @ A @ ( vimage784510485real_n @ F @ B2 ) )
% 2.12/1.16        = ( member223413699real_n @ ( F @ A ) @ B2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_16_vimage__eq,axiom,
% 2.12/1.16      ! [A: set_Fi1058188332real_n,F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,B2: set_Fi1326602817real_n] :
% 2.12/1.16        ( ( member223413699real_n @ A @ ( vimage2134951412real_n @ F @ B2 ) )
% 2.12/1.16        = ( member1746150050real_n @ ( F @ A ) @ B2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_17_vimage__eq,axiom,
% 2.12/1.16      ! [A: finite1489363574real_n > finite1489363574real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,B2: set_se2111327970real_n] :
% 2.12/1.16        ( ( member1746150050real_n @ A @ ( vimage1910974324real_n @ F @ B2 ) )
% 2.12/1.16        = ( member223413699real_n @ ( F @ A ) @ B2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_18_vimage__eq,axiom,
% 2.12/1.16      ! [A: finite1489363574real_n > finite1489363574real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,B2: set_Fi1326602817real_n] :
% 2.12/1.16        ( ( member1746150050real_n @ A @ ( vimage180751827real_n @ F @ B2 ) )
% 2.12/1.16        = ( member1746150050real_n @ ( F @ A ) @ B2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_19_vimage__eq,axiom,
% 2.12/1.16      ! [A: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n,B2: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( member1352538125real_n @ A @ ( vimage1233683625real_n @ F @ B2 ) )
% 2.12/1.16        = ( member1352538125real_n @ ( F @ A ) @ B2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_20_set__plus__intro,axiom,
% 2.12/1.16      ! [A: set_Fi1058188332real_n,C: set_se2111327970real_n,B: set_Fi1058188332real_n,D: set_se2111327970real_n] :
% 2.12/1.16        ( ( member223413699real_n @ A @ C )
% 2.12/1.16       => ( ( member223413699real_n @ B @ D )
% 2.12/1.16         => ( member223413699real_n @ ( plus_p1606848693real_n @ A @ B ) @ ( plus_p565022571real_n @ C @ D ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_21_set__plus__intro,axiom,
% 2.12/1.16      ! [A: finite1489363574real_n,C: set_Fi1058188332real_n,B: finite1489363574real_n,D: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( member1352538125real_n @ A @ C )
% 2.12/1.16       => ( ( member1352538125real_n @ B @ D )
% 2.12/1.16         => ( member1352538125real_n @ ( plus_p585657087real_n @ A @ B ) @ ( plus_p1606848693real_n @ C @ D ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_22_add__left__cancel,axiom,
% 2.12/1.16      ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] :
% 2.12/1.16        ( ( ( plus_p585657087real_n @ A @ B )
% 2.12/1.16          = ( plus_p585657087real_n @ A @ C2 ) )
% 2.12/1.16        = ( B = C2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_23_add__right__cancel,axiom,
% 2.12/1.16      ! [B: finite1489363574real_n,A: finite1489363574real_n,C2: finite1489363574real_n] :
% 2.12/1.16        ( ( ( plus_p585657087real_n @ B @ A )
% 2.12/1.16          = ( plus_p585657087real_n @ C2 @ A ) )
% 2.12/1.16        = ( B = C2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_24_vimage__def,axiom,
% 2.12/1.16      ( vimage207290975real_n
% 2.12/1.16      = ( ^ [F2: finite1489363574real_n > set_Fi1058188332real_n,B3: set_se2111327970real_n] :
% 2.12/1.16            ( collec321817931real_n
% 2.12/1.16            @ ^ [X: finite1489363574real_n] : ( member223413699real_n @ ( F2 @ X ) @ B3 ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_25_vimage__def,axiom,
% 2.12/1.16      ( vimage1059850558real_n
% 2.12/1.16      = ( ^ [F2: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n,B3: set_Fi1326602817real_n] :
% 2.12/1.16            ( collec321817931real_n
% 2.12/1.16            @ ^ [X: finite1489363574real_n] : ( member1746150050real_n @ ( F2 @ X ) @ B3 ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_26_vimage__def,axiom,
% 2.12/1.16      ( vimage1233683625real_n
% 2.12/1.16      = ( ^ [F2: finite1489363574real_n > finite1489363574real_n,B3: set_Fi1058188332real_n] :
% 2.12/1.16            ( collec321817931real_n
% 2.12/1.16            @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ ( F2 @ X ) @ B3 ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_27_vimageD,axiom,
% 2.12/1.16      ! [A: set_Fi1058188332real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n,A2: set_se2111327970real_n] :
% 2.12/1.16        ( ( member223413699real_n @ A @ ( vimage784510485real_n @ F @ A2 ) )
% 2.12/1.16       => ( member223413699real_n @ ( F @ A ) @ A2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_28_vimageD,axiom,
% 2.12/1.16      ! [A: set_Fi1058188332real_n,F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n] :
% 2.12/1.16        ( ( member223413699real_n @ A @ ( vimage2134951412real_n @ F @ A2 ) )
% 2.12/1.16       => ( member1746150050real_n @ ( F @ A ) @ A2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_29_vimageD,axiom,
% 2.12/1.16      ! [A: finite1489363574real_n > finite1489363574real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,A2: set_se2111327970real_n] :
% 2.12/1.16        ( ( member1746150050real_n @ A @ ( vimage1910974324real_n @ F @ A2 ) )
% 2.12/1.16       => ( member223413699real_n @ ( F @ A ) @ A2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_30_vimageD,axiom,
% 2.12/1.16      ! [A: finite1489363574real_n > finite1489363574real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n] :
% 2.12/1.16        ( ( member1746150050real_n @ A @ ( vimage180751827real_n @ F @ A2 ) )
% 2.12/1.16       => ( member1746150050real_n @ ( F @ A ) @ A2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_31_vimageD,axiom,
% 2.12/1.16      ! [A: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( member1352538125real_n @ A @ ( vimage1233683625real_n @ F @ A2 ) )
% 2.12/1.16       => ( member1352538125real_n @ ( F @ A ) @ A2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_32_vimageE,axiom,
% 2.12/1.16      ! [A: set_Fi1058188332real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n,B2: set_se2111327970real_n] :
% 2.12/1.16        ( ( member223413699real_n @ A @ ( vimage784510485real_n @ F @ B2 ) )
% 2.12/1.16       => ( member223413699real_n @ ( F @ A ) @ B2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_33_vimageE,axiom,
% 2.12/1.16      ! [A: set_Fi1058188332real_n,F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,B2: set_Fi1326602817real_n] :
% 2.12/1.16        ( ( member223413699real_n @ A @ ( vimage2134951412real_n @ F @ B2 ) )
% 2.12/1.16       => ( member1746150050real_n @ ( F @ A ) @ B2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_34_vimageE,axiom,
% 2.12/1.16      ! [A: finite1489363574real_n > finite1489363574real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,B2: set_se2111327970real_n] :
% 2.12/1.16        ( ( member1746150050real_n @ A @ ( vimage1910974324real_n @ F @ B2 ) )
% 2.12/1.16       => ( member223413699real_n @ ( F @ A ) @ B2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_35_vimageE,axiom,
% 2.12/1.16      ! [A: finite1489363574real_n > finite1489363574real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,B2: set_Fi1326602817real_n] :
% 2.12/1.16        ( ( member1746150050real_n @ A @ ( vimage180751827real_n @ F @ B2 ) )
% 2.12/1.16       => ( member1746150050real_n @ ( F @ A ) @ B2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_36_vimageE,axiom,
% 2.12/1.16      ! [A: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n,B2: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( member1352538125real_n @ A @ ( vimage1233683625real_n @ F @ B2 ) )
% 2.12/1.16       => ( member1352538125real_n @ ( F @ A ) @ B2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_37_IntI,axiom,
% 2.12/1.16      ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] :
% 2.12/1.16        ( ( member223413699real_n @ C2 @ A2 )
% 2.12/1.16       => ( ( member223413699real_n @ C2 @ B2 )
% 2.12/1.16         => ( member223413699real_n @ C2 @ ( inf_in632889204real_n @ A2 @ B2 ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_38_IntI,axiom,
% 2.12/1.16      ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] :
% 2.12/1.16        ( ( member1746150050real_n @ C2 @ A2 )
% 2.12/1.16       => ( ( member1746150050real_n @ C2 @ B2 )
% 2.12/1.16         => ( member1746150050real_n @ C2 @ ( inf_in146441683real_n @ A2 @ B2 ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_39_IntI,axiom,
% 2.12/1.16      ! [C2: finite1489363574real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( member1352538125real_n @ C2 @ A2 )
% 2.12/1.16       => ( ( member1352538125real_n @ C2 @ B2 )
% 2.12/1.16         => ( member1352538125real_n @ C2 @ ( inf_in1974387902real_n @ A2 @ B2 ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_40_Int__iff,axiom,
% 2.12/1.16      ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] :
% 2.12/1.16        ( ( member223413699real_n @ C2 @ ( inf_in632889204real_n @ A2 @ B2 ) )
% 2.12/1.16        = ( ( member223413699real_n @ C2 @ A2 )
% 2.12/1.16          & ( member223413699real_n @ C2 @ B2 ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_41_Int__iff,axiom,
% 2.12/1.16      ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] :
% 2.12/1.16        ( ( member1746150050real_n @ C2 @ ( inf_in146441683real_n @ A2 @ B2 ) )
% 2.12/1.16        = ( ( member1746150050real_n @ C2 @ A2 )
% 2.12/1.16          & ( member1746150050real_n @ C2 @ B2 ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_42_Int__iff,axiom,
% 2.12/1.16      ! [C2: finite1489363574real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( member1352538125real_n @ C2 @ ( inf_in1974387902real_n @ A2 @ B2 ) )
% 2.12/1.16        = ( ( member1352538125real_n @ C2 @ A2 )
% 2.12/1.16          & ( member1352538125real_n @ C2 @ B2 ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_43_space__completion,axiom,
% 2.12/1.16      ! [M: sigma_1466784463real_n] :
% 2.12/1.16        ( ( sigma_476185326real_n @ ( comple230862828real_n @ M ) )
% 2.12/1.16        = ( sigma_476185326real_n @ M ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_44_vimage__Int,axiom,
% 2.12/1.16      ! [F: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( vimage1233683625real_n @ F @ ( inf_in1974387902real_n @ A2 @ B2 ) )
% 2.12/1.16        = ( inf_in1974387902real_n @ ( vimage1233683625real_n @ F @ A2 ) @ ( vimage1233683625real_n @ F @ B2 ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_45_T__def,axiom,
% 2.12/1.16      ( t2
% 2.12/1.16      = ( ^ [A3: finite964658038_int_n] : ( inf_in1974387902real_n @ s @ ( r @ A3 ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_46_IntE,axiom,
% 2.12/1.16      ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] :
% 2.12/1.16        ( ( member223413699real_n @ C2 @ ( inf_in632889204real_n @ A2 @ B2 ) )
% 2.12/1.16       => ~ ( ( member223413699real_n @ C2 @ A2 )
% 2.12/1.16           => ~ ( member223413699real_n @ C2 @ B2 ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_47_IntE,axiom,
% 2.12/1.16      ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] :
% 2.12/1.16        ( ( member1746150050real_n @ C2 @ ( inf_in146441683real_n @ A2 @ B2 ) )
% 2.12/1.16       => ~ ( ( member1746150050real_n @ C2 @ A2 )
% 2.12/1.16           => ~ ( member1746150050real_n @ C2 @ B2 ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_48_IntE,axiom,
% 2.12/1.16      ! [C2: finite1489363574real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( member1352538125real_n @ C2 @ ( inf_in1974387902real_n @ A2 @ B2 ) )
% 2.12/1.16       => ~ ( ( member1352538125real_n @ C2 @ A2 )
% 2.12/1.16           => ~ ( member1352538125real_n @ C2 @ B2 ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_49_IntD1,axiom,
% 2.12/1.16      ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] :
% 2.12/1.16        ( ( member223413699real_n @ C2 @ ( inf_in632889204real_n @ A2 @ B2 ) )
% 2.12/1.16       => ( member223413699real_n @ C2 @ A2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_50_IntD1,axiom,
% 2.12/1.16      ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] :
% 2.12/1.16        ( ( member1746150050real_n @ C2 @ ( inf_in146441683real_n @ A2 @ B2 ) )
% 2.12/1.16       => ( member1746150050real_n @ C2 @ A2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_51_IntD1,axiom,
% 2.12/1.16      ! [C2: finite1489363574real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( member1352538125real_n @ C2 @ ( inf_in1974387902real_n @ A2 @ B2 ) )
% 2.12/1.16       => ( member1352538125real_n @ C2 @ A2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_52_IntD2,axiom,
% 2.12/1.16      ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] :
% 2.12/1.16        ( ( member223413699real_n @ C2 @ ( inf_in632889204real_n @ A2 @ B2 ) )
% 2.12/1.16       => ( member223413699real_n @ C2 @ B2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_53_IntD2,axiom,
% 2.12/1.16      ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] :
% 2.12/1.16        ( ( member1746150050real_n @ C2 @ ( inf_in146441683real_n @ A2 @ B2 ) )
% 2.12/1.16       => ( member1746150050real_n @ C2 @ B2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_54_IntD2,axiom,
% 2.12/1.16      ! [C2: finite1489363574real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( member1352538125real_n @ C2 @ ( inf_in1974387902real_n @ A2 @ B2 ) )
% 2.12/1.16       => ( member1352538125real_n @ C2 @ B2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_55_Int__assoc,axiom,
% 2.12/1.16      ! [A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ A2 @ B2 ) @ C )
% 2.12/1.16        = ( inf_in1974387902real_n @ A2 @ ( inf_in1974387902real_n @ B2 @ C ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_56_Int__absorb,axiom,
% 2.12/1.16      ! [A2: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( inf_in1974387902real_n @ A2 @ A2 )
% 2.12/1.16        = A2 ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_57_Int__commute,axiom,
% 2.12/1.16      ( inf_in1974387902real_n
% 2.12/1.16      = ( ^ [A4: set_Fi1058188332real_n,B3: set_Fi1058188332real_n] : ( inf_in1974387902real_n @ B3 @ A4 ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_58_Int__left__absorb,axiom,
% 2.12/1.16      ! [A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( inf_in1974387902real_n @ A2 @ ( inf_in1974387902real_n @ A2 @ B2 ) )
% 2.12/1.16        = ( inf_in1974387902real_n @ A2 @ B2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_59_Int__left__commute,axiom,
% 2.12/1.16      ! [A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( inf_in1974387902real_n @ A2 @ ( inf_in1974387902real_n @ B2 @ C ) )
% 2.12/1.16        = ( inf_in1974387902real_n @ B2 @ ( inf_in1974387902real_n @ A2 @ C ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_60_Collect__conj__eq,axiom,
% 2.12/1.16      ! [P: finite1489363574real_n > $o,Q: finite1489363574real_n > $o] :
% 2.12/1.16        ( ( collec321817931real_n
% 2.12/1.16          @ ^ [X: finite1489363574real_n] :
% 2.12/1.16              ( ( P @ X )
% 2.12/1.16              & ( Q @ X ) ) )
% 2.12/1.16        = ( inf_in1974387902real_n @ ( collec321817931real_n @ P ) @ ( collec321817931real_n @ Q ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_61_Int__Collect,axiom,
% 2.12/1.16      ! [X2: set_Fi1058188332real_n,A2: set_se2111327970real_n,P: set_Fi1058188332real_n > $o] :
% 2.12/1.16        ( ( member223413699real_n @ X2 @ ( inf_in632889204real_n @ A2 @ ( collec452821761real_n @ P ) ) )
% 2.12/1.16        = ( ( member223413699real_n @ X2 @ A2 )
% 2.12/1.16          & ( P @ X2 ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_62_Int__Collect,axiom,
% 2.12/1.16      ! [X2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
% 2.12/1.16        ( ( member1746150050real_n @ X2 @ ( inf_in146441683real_n @ A2 @ ( collec1190264032real_n @ P ) ) )
% 2.12/1.16        = ( ( member1746150050real_n @ X2 @ A2 )
% 2.12/1.16          & ( P @ X2 ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_63_Int__Collect,axiom,
% 2.12/1.16      ! [X2: finite1489363574real_n,A2: set_Fi1058188332real_n,P: finite1489363574real_n > $o] :
% 2.12/1.16        ( ( member1352538125real_n @ X2 @ ( inf_in1974387902real_n @ A2 @ ( collec321817931real_n @ P ) ) )
% 2.12/1.16        = ( ( member1352538125real_n @ X2 @ A2 )
% 2.12/1.16          & ( P @ X2 ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_64_Int__def,axiom,
% 2.12/1.16      ( inf_in632889204real_n
% 2.12/1.16      = ( ^ [A4: set_se2111327970real_n,B3: set_se2111327970real_n] :
% 2.12/1.16            ( collec452821761real_n
% 2.12/1.16            @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.16                ( ( member223413699real_n @ X @ A4 )
% 2.12/1.16                & ( member223413699real_n @ X @ B3 ) ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_65_Int__def,axiom,
% 2.12/1.16      ( inf_in146441683real_n
% 2.12/1.16      = ( ^ [A4: set_Fi1326602817real_n,B3: set_Fi1326602817real_n] :
% 2.12/1.16            ( collec1190264032real_n
% 2.12/1.16            @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.16                ( ( member1746150050real_n @ X @ A4 )
% 2.12/1.16                & ( member1746150050real_n @ X @ B3 ) ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_66_Int__def,axiom,
% 2.12/1.16      ( inf_in1974387902real_n
% 2.12/1.16      = ( ^ [A4: set_Fi1058188332real_n,B3: set_Fi1058188332real_n] :
% 2.12/1.16            ( collec321817931real_n
% 2.12/1.16            @ ^ [X: finite1489363574real_n] :
% 2.12/1.16                ( ( member1352538125real_n @ X @ A4 )
% 2.12/1.16                & ( member1352538125real_n @ X @ B3 ) ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_67_measurable__completion,axiom,
% 2.12/1.16      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,N: sigma_1466784463real_n] :
% 2.12/1.16        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ N ) )
% 2.12/1.16       => ( member1746150050real_n @ F @ ( sigma_439801790real_n @ ( comple230862828real_n @ M ) @ N ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_68_vimage__inter__cong,axiom,
% 2.12/1.16      ! [S: set_Fi1058188332real_n,F: finite1489363574real_n > finite1489363574real_n,G: finite1489363574real_n > finite1489363574real_n,Y3: set_Fi1058188332real_n] :
% 2.12/1.16        ( ! [W: finite1489363574real_n] :
% 2.12/1.16            ( ( member1352538125real_n @ W @ S )
% 2.12/1.16           => ( ( F @ W )
% 2.12/1.16              = ( G @ W ) ) )
% 2.12/1.16       => ( ( inf_in1974387902real_n @ ( vimage1233683625real_n @ F @ Y3 ) @ S )
% 2.12/1.16          = ( inf_in1974387902real_n @ ( vimage1233683625real_n @ G @ Y3 ) @ S ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_69_add__right__imp__eq,axiom,
% 2.12/1.16      ! [B: finite1489363574real_n,A: finite1489363574real_n,C2: finite1489363574real_n] :
% 2.12/1.16        ( ( ( plus_p585657087real_n @ B @ A )
% 2.12/1.16          = ( plus_p585657087real_n @ C2 @ A ) )
% 2.12/1.16       => ( B = C2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_70_add__left__imp__eq,axiom,
% 2.12/1.16      ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] :
% 2.12/1.16        ( ( ( plus_p585657087real_n @ A @ B )
% 2.12/1.16          = ( plus_p585657087real_n @ A @ C2 ) )
% 2.12/1.16       => ( B = C2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_71_add_Oleft__commute,axiom,
% 2.12/1.16      ! [B: finite1489363574real_n,A: finite1489363574real_n,C2: finite1489363574real_n] :
% 2.12/1.16        ( ( plus_p585657087real_n @ B @ ( plus_p585657087real_n @ A @ C2 ) )
% 2.12/1.16        = ( plus_p585657087real_n @ A @ ( plus_p585657087real_n @ B @ C2 ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_72_add_Ocommute,axiom,
% 2.12/1.16      ( plus_p585657087real_n
% 2.12/1.16      = ( ^ [A3: finite1489363574real_n,B4: finite1489363574real_n] : ( plus_p585657087real_n @ B4 @ A3 ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_73_add_Oright__cancel,axiom,
% 2.12/1.16      ! [B: finite1489363574real_n,A: finite1489363574real_n,C2: finite1489363574real_n] :
% 2.12/1.16        ( ( ( plus_p585657087real_n @ B @ A )
% 2.12/1.16          = ( plus_p585657087real_n @ C2 @ A ) )
% 2.12/1.16        = ( B = C2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_74_add_Oleft__cancel,axiom,
% 2.12/1.16      ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] :
% 2.12/1.16        ( ( ( plus_p585657087real_n @ A @ B )
% 2.12/1.16          = ( plus_p585657087real_n @ A @ C2 ) )
% 2.12/1.16        = ( B = C2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_75_add_Oassoc,axiom,
% 2.12/1.16      ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] :
% 2.12/1.16        ( ( plus_p585657087real_n @ ( plus_p585657087real_n @ A @ B ) @ C2 )
% 2.12/1.16        = ( plus_p585657087real_n @ A @ ( plus_p585657087real_n @ B @ C2 ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_76_set__plus__elim,axiom,
% 2.12/1.16      ! [X2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] :
% 2.12/1.16        ( ( member223413699real_n @ X2 @ ( plus_p565022571real_n @ A2 @ B2 ) )
% 2.12/1.16       => ~ ! [A5: set_Fi1058188332real_n,B5: set_Fi1058188332real_n] :
% 2.12/1.16              ( ( X2
% 2.12/1.16                = ( plus_p1606848693real_n @ A5 @ B5 ) )
% 2.12/1.16             => ( ( member223413699real_n @ A5 @ A2 )
% 2.12/1.16               => ~ ( member223413699real_n @ B5 @ B2 ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_77_set__plus__elim,axiom,
% 2.12/1.16      ! [X2: finite1489363574real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( member1352538125real_n @ X2 @ ( plus_p1606848693real_n @ A2 @ B2 ) )
% 2.12/1.16       => ~ ! [A5: finite1489363574real_n,B5: finite1489363574real_n] :
% 2.12/1.16              ( ( X2
% 2.12/1.16                = ( plus_p585657087real_n @ A5 @ B5 ) )
% 2.12/1.16             => ( ( member1352538125real_n @ A5 @ A2 )
% 2.12/1.16               => ~ ( member1352538125real_n @ B5 @ B2 ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_78_group__cancel_Oadd2,axiom,
% 2.12/1.16      ! [B2: finite1489363574real_n,K: finite1489363574real_n,B: finite1489363574real_n,A: finite1489363574real_n] :
% 2.12/1.16        ( ( B2
% 2.12/1.16          = ( plus_p585657087real_n @ K @ B ) )
% 2.12/1.16       => ( ( plus_p585657087real_n @ A @ B2 )
% 2.12/1.16          = ( plus_p585657087real_n @ K @ ( plus_p585657087real_n @ A @ B ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_79_mem__Collect__eq,axiom,
% 2.12/1.16      ! [A: set_Fi1058188332real_n,P: set_Fi1058188332real_n > $o] :
% 2.12/1.16        ( ( member223413699real_n @ A @ ( collec452821761real_n @ P ) )
% 2.12/1.16        = ( P @ A ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_80_mem__Collect__eq,axiom,
% 2.12/1.16      ! [A: finite1489363574real_n > finite1489363574real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
% 2.12/1.16        ( ( member1746150050real_n @ A @ ( collec1190264032real_n @ P ) )
% 2.12/1.16        = ( P @ A ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_81_mem__Collect__eq,axiom,
% 2.12/1.16      ! [A: finite1489363574real_n,P: finite1489363574real_n > $o] :
% 2.12/1.16        ( ( member1352538125real_n @ A @ ( collec321817931real_n @ P ) )
% 2.12/1.16        = ( P @ A ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_82_Collect__mem__eq,axiom,
% 2.12/1.16      ! [A2: set_se2111327970real_n] :
% 2.12/1.16        ( ( collec452821761real_n
% 2.12/1.16          @ ^ [X: set_Fi1058188332real_n] : ( member223413699real_n @ X @ A2 ) )
% 2.12/1.16        = A2 ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_83_Collect__mem__eq,axiom,
% 2.12/1.16      ! [A2: set_Fi1326602817real_n] :
% 2.12/1.16        ( ( collec1190264032real_n
% 2.12/1.16          @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ X @ A2 ) )
% 2.12/1.16        = A2 ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_84_Collect__mem__eq,axiom,
% 2.12/1.16      ! [A2: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( collec321817931real_n
% 2.12/1.16          @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ X @ A2 ) )
% 2.12/1.16        = A2 ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_85_Collect__cong,axiom,
% 2.12/1.16      ! [P: finite1489363574real_n > $o,Q: finite1489363574real_n > $o] :
% 2.12/1.16        ( ! [X3: finite1489363574real_n] :
% 2.12/1.16            ( ( P @ X3 )
% 2.12/1.16            = ( Q @ X3 ) )
% 2.12/1.16       => ( ( collec321817931real_n @ P )
% 2.12/1.16          = ( collec321817931real_n @ Q ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_86_group__cancel_Oadd1,axiom,
% 2.12/1.16      ! [A2: finite1489363574real_n,K: finite1489363574real_n,A: finite1489363574real_n,B: finite1489363574real_n] :
% 2.12/1.16        ( ( A2
% 2.12/1.16          = ( plus_p585657087real_n @ K @ A ) )
% 2.12/1.16       => ( ( plus_p585657087real_n @ A2 @ B )
% 2.12/1.16          = ( plus_p585657087real_n @ K @ ( plus_p585657087real_n @ A @ B ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_87_add__mono__thms__linordered__semiring_I4_J,axiom,
% 2.12/1.16      ! [I: finite1489363574real_n,J: finite1489363574real_n,K: finite1489363574real_n,L: finite1489363574real_n] :
% 2.12/1.16        ( ( ( I = J )
% 2.12/1.16          & ( K = L ) )
% 2.12/1.16       => ( ( plus_p585657087real_n @ I @ K )
% 2.12/1.16          = ( plus_p585657087real_n @ J @ L ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_88_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 2.12/1.16      ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] :
% 2.12/1.16        ( ( plus_p585657087real_n @ ( plus_p585657087real_n @ A @ B ) @ C2 )
% 2.12/1.16        = ( plus_p585657087real_n @ A @ ( plus_p585657087real_n @ B @ C2 ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_89_vimage__Collect,axiom,
% 2.12/1.16      ! [P: finite1489363574real_n > $o,F: finite1489363574real_n > finite1489363574real_n,Q: finite1489363574real_n > $o] :
% 2.12/1.16        ( ! [X3: finite1489363574real_n] :
% 2.12/1.16            ( ( P @ ( F @ X3 ) )
% 2.12/1.16            = ( Q @ X3 ) )
% 2.12/1.16       => ( ( vimage1233683625real_n @ F @ ( collec321817931real_n @ P ) )
% 2.12/1.16          = ( collec321817931real_n @ Q ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_90_vimageI2,axiom,
% 2.12/1.16      ! [F: set_Fi1058188332real_n > set_Fi1058188332real_n,A: set_Fi1058188332real_n,A2: set_se2111327970real_n] :
% 2.12/1.16        ( ( member223413699real_n @ ( F @ A ) @ A2 )
% 2.12/1.16       => ( member223413699real_n @ A @ ( vimage784510485real_n @ F @ A2 ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_91_vimageI2,axiom,
% 2.12/1.16      ! [F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,A: finite1489363574real_n > finite1489363574real_n,A2: set_se2111327970real_n] :
% 2.12/1.16        ( ( member223413699real_n @ ( F @ A ) @ A2 )
% 2.12/1.16       => ( member1746150050real_n @ A @ ( vimage1910974324real_n @ F @ A2 ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_92_vimageI2,axiom,
% 2.12/1.16      ! [F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,A: set_Fi1058188332real_n,A2: set_Fi1326602817real_n] :
% 2.12/1.16        ( ( member1746150050real_n @ ( F @ A ) @ A2 )
% 2.12/1.16       => ( member223413699real_n @ A @ ( vimage2134951412real_n @ F @ A2 ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_93_vimageI2,axiom,
% 2.12/1.16      ! [F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,A: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n] :
% 2.12/1.16        ( ( member1746150050real_n @ ( F @ A ) @ A2 )
% 2.12/1.16       => ( member1746150050real_n @ A @ ( vimage180751827real_n @ F @ A2 ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_94_vimageI2,axiom,
% 2.12/1.16      ! [F: finite1489363574real_n > finite1489363574real_n,A: finite1489363574real_n,A2: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( member1352538125real_n @ ( F @ A ) @ A2 )
% 2.12/1.16       => ( member1352538125real_n @ A @ ( vimage1233683625real_n @ F @ A2 ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_95_sets_OInt__space__eq2,axiom,
% 2.12/1.16      ! [X2: set_Fi1058188332real_n,M: sigma_1466784463real_n] :
% 2.12/1.16        ( ( member223413699real_n @ X2 @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.16       => ( ( inf_in1974387902real_n @ X2 @ ( sigma_476185326real_n @ M ) )
% 2.12/1.16          = X2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_96_sets_OInt__space__eq1,axiom,
% 2.12/1.16      ! [X2: set_Fi1058188332real_n,M: sigma_1466784463real_n] :
% 2.12/1.16        ( ( member223413699real_n @ X2 @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.16       => ( ( inf_in1974387902real_n @ ( sigma_476185326real_n @ M ) @ X2 )
% 2.12/1.16          = X2 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_97_measurable__sets,axiom,
% 2.12/1.16      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,A2: sigma_1466784463real_n,S: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ A2 ) )
% 2.12/1.16       => ( ( member223413699real_n @ S @ ( sigma_1235138647real_n @ A2 ) )
% 2.12/1.16         => ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage1233683625real_n @ F @ S ) @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_98_measurableI,axiom,
% 2.12/1.16      ! [M: sigma_1422848389real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n,N: sigma_1422848389real_n] :
% 2.12/1.16        ( ! [X3: set_Fi1058188332real_n] :
% 2.12/1.16            ( ( member223413699real_n @ X3 @ ( sigma_607186084real_n @ M ) )
% 2.12/1.16           => ( member223413699real_n @ ( F @ X3 ) @ ( sigma_607186084real_n @ N ) ) )
% 2.12/1.16       => ( ! [A6: set_se2111327970real_n] :
% 2.12/1.16              ( ( member1475136633real_n @ A6 @ ( sigma_433815053real_n @ N ) )
% 2.12/1.16             => ( member1475136633real_n @ ( inf_in632889204real_n @ ( vimage784510485real_n @ F @ A6 ) @ ( sigma_607186084real_n @ M ) ) @ ( sigma_433815053real_n @ M ) ) )
% 2.12/1.16         => ( member1734791438real_n @ F @ ( sigma_239294762real_n @ M @ N ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_99_measurableI,axiom,
% 2.12/1.16      ! [M: sigma_1422848389real_n,F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,N: sigma_107786596real_n] :
% 2.12/1.16        ( ! [X3: set_Fi1058188332real_n] :
% 2.12/1.16            ( ( member223413699real_n @ X3 @ ( sigma_607186084real_n @ M ) )
% 2.12/1.16           => ( member1746150050real_n @ ( F @ X3 ) @ ( sigma_1483971331real_n @ N ) ) )
% 2.12/1.16       => ( ! [A6: set_Fi1326602817real_n] :
% 2.12/1.16              ( ( member2104752728real_n @ A6 @ ( sigma_522684908real_n @ N ) )
% 2.12/1.16             => ( member1475136633real_n @ ( inf_in632889204real_n @ ( vimage2134951412real_n @ F @ A6 ) @ ( sigma_607186084real_n @ M ) ) @ ( sigma_433815053real_n @ M ) ) )
% 2.12/1.16         => ( member1764433517real_n @ F @ ( sigma_588796041real_n @ M @ N ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_100_measurableI,axiom,
% 2.12/1.16      ! [M: sigma_107786596real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,N: sigma_1422848389real_n] :
% 2.12/1.16        ( ! [X3: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.16            ( ( member1746150050real_n @ X3 @ ( sigma_1483971331real_n @ M ) )
% 2.12/1.16           => ( member223413699real_n @ ( F @ X3 ) @ ( sigma_607186084real_n @ N ) ) )
% 2.12/1.16       => ( ! [A6: set_se2111327970real_n] :
% 2.12/1.16              ( ( member1475136633real_n @ A6 @ ( sigma_433815053real_n @ N ) )
% 2.12/1.16             => ( member2104752728real_n @ ( inf_in146441683real_n @ ( vimage1910974324real_n @ F @ A6 ) @ ( sigma_1483971331real_n @ M ) ) @ ( sigma_522684908real_n @ M ) ) )
% 2.12/1.16         => ( member640587117real_n @ F @ ( sigma_364818953real_n @ M @ N ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_101_measurableI,axiom,
% 2.12/1.16      ! [M: sigma_107786596real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,N: sigma_107786596real_n] :
% 2.12/1.16        ( ! [X3: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.16            ( ( member1746150050real_n @ X3 @ ( sigma_1483971331real_n @ M ) )
% 2.12/1.16           => ( member1746150050real_n @ ( F @ X3 ) @ ( sigma_1483971331real_n @ N ) ) )
% 2.12/1.16       => ( ! [A6: set_Fi1326602817real_n] :
% 2.12/1.16              ( ( member2104752728real_n @ A6 @ ( sigma_522684908real_n @ N ) )
% 2.12/1.16             => ( member2104752728real_n @ ( inf_in146441683real_n @ ( vimage180751827real_n @ F @ A6 ) @ ( sigma_1483971331real_n @ M ) ) @ ( sigma_522684908real_n @ M ) ) )
% 2.12/1.16         => ( member117715276real_n @ F @ ( sigma_1185134568real_n @ M @ N ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_102_measurableI,axiom,
% 2.12/1.16      ! [M: sigma_1422848389real_n,F: set_Fi1058188332real_n > finite1489363574real_n,N: sigma_1466784463real_n] :
% 2.12/1.16        ( ! [X3: set_Fi1058188332real_n] :
% 2.12/1.16            ( ( member223413699real_n @ X3 @ ( sigma_607186084real_n @ M ) )
% 2.12/1.16           => ( member1352538125real_n @ ( F @ X3 ) @ ( sigma_476185326real_n @ N ) ) )
% 2.12/1.16       => ( ! [A6: set_Fi1058188332real_n] :
% 2.12/1.16              ( ( member223413699real_n @ A6 @ ( sigma_1235138647real_n @ N ) )
% 2.12/1.16             => ( member1475136633real_n @ ( inf_in632889204real_n @ ( vimage973736031real_n @ F @ A6 ) @ ( sigma_607186084real_n @ M ) ) @ ( sigma_433815053real_n @ M ) ) )
% 2.12/1.16         => ( member1759501912real_n @ F @ ( sigma_1333364596real_n @ M @ N ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_103_measurableI,axiom,
% 2.12/1.16      ! [M: sigma_107786596real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,N: sigma_1466784463real_n] :
% 2.12/1.16        ( ! [X3: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.16            ( ( member1746150050real_n @ X3 @ ( sigma_1483971331real_n @ M ) )
% 2.12/1.16           => ( member1352538125real_n @ ( F @ X3 ) @ ( sigma_476185326real_n @ N ) ) )
% 2.12/1.16       => ( ! [A6: set_Fi1058188332real_n] :
% 2.12/1.16              ( ( member223413699real_n @ A6 @ ( sigma_1235138647real_n @ N ) )
% 2.12/1.16             => ( member2104752728real_n @ ( inf_in146441683real_n @ ( vimage1072397758real_n @ F @ A6 ) @ ( sigma_1483971331real_n @ M ) ) @ ( sigma_522684908real_n @ M ) ) )
% 2.12/1.16         => ( member1695588023real_n @ F @ ( sigma_2028985427real_n @ M @ N ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_104_measurableI,axiom,
% 2.12/1.16      ! [M: sigma_1466784463real_n,F: finite1489363574real_n > set_Fi1058188332real_n,N: sigma_1422848389real_n] :
% 2.12/1.16        ( ! [X3: finite1489363574real_n] :
% 2.12/1.16            ( ( member1352538125real_n @ X3 @ ( sigma_476185326real_n @ M ) )
% 2.12/1.16           => ( member223413699real_n @ ( F @ X3 ) @ ( sigma_607186084real_n @ N ) ) )
% 2.12/1.16       => ( ! [A6: set_se2111327970real_n] :
% 2.12/1.16              ( ( member1475136633real_n @ A6 @ ( sigma_433815053real_n @ N ) )
% 2.12/1.16             => ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage207290975real_n @ F @ A6 ) @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) ) )
% 2.12/1.16         => ( member966061400real_n @ F @ ( sigma_566919540real_n @ M @ N ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_105_measurableI,axiom,
% 2.12/1.16      ! [M: sigma_1466784463real_n,F: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n,N: sigma_107786596real_n] :
% 2.12/1.16        ( ! [X3: finite1489363574real_n] :
% 2.12/1.16            ( ( member1352538125real_n @ X3 @ ( sigma_476185326real_n @ M ) )
% 2.12/1.16           => ( member1746150050real_n @ ( F @ X3 ) @ ( sigma_1483971331real_n @ N ) ) )
% 2.12/1.16       => ( ! [A6: set_Fi1326602817real_n] :
% 2.12/1.16              ( ( member2104752728real_n @ A6 @ ( sigma_522684908real_n @ N ) )
% 2.12/1.16             => ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage1059850558real_n @ F @ A6 ) @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) ) )
% 2.12/1.16         => ( member408431031real_n @ F @ ( sigma_2016438227real_n @ M @ N ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_106_measurableI,axiom,
% 2.12/1.16      ! [M: sigma_1466784463real_n,F: finite1489363574real_n > finite1489363574real_n,N: sigma_1466784463real_n] :
% 2.12/1.16        ( ! [X3: finite1489363574real_n] :
% 2.12/1.16            ( ( member1352538125real_n @ X3 @ ( sigma_476185326real_n @ M ) )
% 2.12/1.16           => ( member1352538125real_n @ ( F @ X3 ) @ ( sigma_476185326real_n @ N ) ) )
% 2.12/1.16       => ( ! [A6: set_Fi1058188332real_n] :
% 2.12/1.16              ( ( member223413699real_n @ A6 @ ( sigma_1235138647real_n @ N ) )
% 2.12/1.16             => ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage1233683625real_n @ F @ A6 ) @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) ) )
% 2.12/1.16         => ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ N ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_107_sets_Otop,axiom,
% 2.12/1.16      ! [M: sigma_1466784463real_n] : ( member223413699real_n @ ( sigma_476185326real_n @ M ) @ ( sigma_1235138647real_n @ M ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_108_sets_OInt,axiom,
% 2.12/1.16      ! [A: set_Fi1058188332real_n,M: sigma_1466784463real_n,B: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.16       => ( ( member223413699real_n @ B @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.16         => ( member223413699real_n @ ( inf_in1974387902real_n @ A @ B ) @ ( sigma_1235138647real_n @ M ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_109_measurable__If__set,axiom,
% 2.12/1.16      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,M2: sigma_1466784463real_n,G: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ M2 ) )
% 2.12/1.16       => ( ( member1746150050real_n @ G @ ( sigma_439801790real_n @ M @ M2 ) )
% 2.12/1.16         => ( ( member223413699real_n @ ( inf_in1974387902real_n @ A2 @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.16           => ( member1746150050real_n
% 2.12/1.16              @ ^ [X: finite1489363574real_n] : ( if_Fin127821360real_n @ ( member1352538125real_n @ X @ A2 ) @ ( F @ X ) @ ( G @ X ) )
% 2.12/1.16              @ ( sigma_439801790real_n @ M @ M2 ) ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_110_measurable__sets__Collect,axiom,
% 2.12/1.16      ! [F: set_Fi1058188332real_n > set_Fi1058188332real_n,M: sigma_1422848389real_n,N: sigma_1422848389real_n,P: set_Fi1058188332real_n > $o] :
% 2.12/1.16        ( ( member1734791438real_n @ F @ ( sigma_239294762real_n @ M @ N ) )
% 2.12/1.16       => ( ( member1475136633real_n
% 2.12/1.16            @ ( collec452821761real_n
% 2.12/1.16              @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.16                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ N ) )
% 2.12/1.16                  & ( P @ X ) ) )
% 2.12/1.16            @ ( sigma_433815053real_n @ N ) )
% 2.12/1.16         => ( member1475136633real_n
% 2.12/1.16            @ ( collec452821761real_n
% 2.12/1.16              @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.16                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 2.12/1.16                  & ( P @ ( F @ X ) ) ) )
% 2.12/1.16            @ ( sigma_433815053real_n @ M ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_111_measurable__sets__Collect,axiom,
% 2.12/1.16      ! [F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,M: sigma_107786596real_n,N: sigma_1422848389real_n,P: set_Fi1058188332real_n > $o] :
% 2.12/1.16        ( ( member640587117real_n @ F @ ( sigma_364818953real_n @ M @ N ) )
% 2.12/1.16       => ( ( member1475136633real_n
% 2.12/1.16            @ ( collec452821761real_n
% 2.12/1.16              @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.16                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ N ) )
% 2.12/1.16                  & ( P @ X ) ) )
% 2.12/1.16            @ ( sigma_433815053real_n @ N ) )
% 2.12/1.16         => ( member2104752728real_n
% 2.12/1.16            @ ( collec1190264032real_n
% 2.12/1.16              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.16                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 2.12/1.16                  & ( P @ ( F @ X ) ) ) )
% 2.12/1.16            @ ( sigma_522684908real_n @ M ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_112_measurable__sets__Collect,axiom,
% 2.12/1.16      ! [F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,M: sigma_1422848389real_n,N: sigma_107786596real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
% 2.12/1.16        ( ( member1764433517real_n @ F @ ( sigma_588796041real_n @ M @ N ) )
% 2.12/1.16       => ( ( member2104752728real_n
% 2.12/1.16            @ ( collec1190264032real_n
% 2.12/1.16              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.16                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ N ) )
% 2.12/1.16                  & ( P @ X ) ) )
% 2.12/1.16            @ ( sigma_522684908real_n @ N ) )
% 2.12/1.16         => ( member1475136633real_n
% 2.12/1.16            @ ( collec452821761real_n
% 2.12/1.16              @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.16                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 2.12/1.16                  & ( P @ ( F @ X ) ) ) )
% 2.12/1.16            @ ( sigma_433815053real_n @ M ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_113_measurable__sets__Collect,axiom,
% 2.12/1.16      ! [F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,M: sigma_107786596real_n,N: sigma_107786596real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
% 2.12/1.16        ( ( member117715276real_n @ F @ ( sigma_1185134568real_n @ M @ N ) )
% 2.12/1.16       => ( ( member2104752728real_n
% 2.12/1.16            @ ( collec1190264032real_n
% 2.12/1.16              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.16                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ N ) )
% 2.12/1.16                  & ( P @ X ) ) )
% 2.12/1.16            @ ( sigma_522684908real_n @ N ) )
% 2.12/1.16         => ( member2104752728real_n
% 2.12/1.16            @ ( collec1190264032real_n
% 2.12/1.16              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.16                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 2.12/1.16                  & ( P @ ( F @ X ) ) ) )
% 2.12/1.16            @ ( sigma_522684908real_n @ M ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_114_measurable__sets__Collect,axiom,
% 2.12/1.16      ! [F: finite1489363574real_n > set_Fi1058188332real_n,M: sigma_1466784463real_n,N: sigma_1422848389real_n,P: set_Fi1058188332real_n > $o] :
% 2.12/1.16        ( ( member966061400real_n @ F @ ( sigma_566919540real_n @ M @ N ) )
% 2.12/1.16       => ( ( member1475136633real_n
% 2.12/1.16            @ ( collec452821761real_n
% 2.12/1.16              @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.16                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ N ) )
% 2.12/1.16                  & ( P @ X ) ) )
% 2.12/1.16            @ ( sigma_433815053real_n @ N ) )
% 2.12/1.16         => ( member223413699real_n
% 2.12/1.16            @ ( collec321817931real_n
% 2.12/1.16              @ ^ [X: finite1489363574real_n] :
% 2.12/1.16                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 2.12/1.16                  & ( P @ ( F @ X ) ) ) )
% 2.12/1.16            @ ( sigma_1235138647real_n @ M ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_115_measurable__sets__Collect,axiom,
% 2.12/1.16      ! [F: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,N: sigma_107786596real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
% 2.12/1.16        ( ( member408431031real_n @ F @ ( sigma_2016438227real_n @ M @ N ) )
% 2.12/1.16       => ( ( member2104752728real_n
% 2.12/1.16            @ ( collec1190264032real_n
% 2.12/1.16              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.16                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ N ) )
% 2.12/1.16                  & ( P @ X ) ) )
% 2.12/1.16            @ ( sigma_522684908real_n @ N ) )
% 2.12/1.16         => ( member223413699real_n
% 2.12/1.16            @ ( collec321817931real_n
% 2.12/1.16              @ ^ [X: finite1489363574real_n] :
% 2.12/1.16                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 2.12/1.16                  & ( P @ ( F @ X ) ) ) )
% 2.12/1.16            @ ( sigma_1235138647real_n @ M ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_116_measurable__sets__Collect,axiom,
% 2.12/1.16      ! [F: set_Fi1058188332real_n > finite1489363574real_n,M: sigma_1422848389real_n,N: sigma_1466784463real_n,P: finite1489363574real_n > $o] :
% 2.12/1.16        ( ( member1759501912real_n @ F @ ( sigma_1333364596real_n @ M @ N ) )
% 2.12/1.16       => ( ( member223413699real_n
% 2.12/1.16            @ ( collec321817931real_n
% 2.12/1.16              @ ^ [X: finite1489363574real_n] :
% 2.12/1.16                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ N ) )
% 2.12/1.16                  & ( P @ X ) ) )
% 2.12/1.16            @ ( sigma_1235138647real_n @ N ) )
% 2.12/1.16         => ( member1475136633real_n
% 2.12/1.16            @ ( collec452821761real_n
% 2.12/1.16              @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.16                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 2.12/1.16                  & ( P @ ( F @ X ) ) ) )
% 2.12/1.16            @ ( sigma_433815053real_n @ M ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_117_measurable__sets__Collect,axiom,
% 2.12/1.16      ! [F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,M: sigma_107786596real_n,N: sigma_1466784463real_n,P: finite1489363574real_n > $o] :
% 2.12/1.16        ( ( member1695588023real_n @ F @ ( sigma_2028985427real_n @ M @ N ) )
% 2.12/1.16       => ( ( member223413699real_n
% 2.12/1.16            @ ( collec321817931real_n
% 2.12/1.16              @ ^ [X: finite1489363574real_n] :
% 2.12/1.16                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ N ) )
% 2.12/1.16                  & ( P @ X ) ) )
% 2.12/1.16            @ ( sigma_1235138647real_n @ N ) )
% 2.12/1.16         => ( member2104752728real_n
% 2.12/1.16            @ ( collec1190264032real_n
% 2.12/1.16              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.16                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 2.12/1.16                  & ( P @ ( F @ X ) ) ) )
% 2.12/1.16            @ ( sigma_522684908real_n @ M ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_118_measurable__sets__Collect,axiom,
% 2.12/1.16      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,N: sigma_1466784463real_n,P: finite1489363574real_n > $o] :
% 2.12/1.16        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ N ) )
% 2.12/1.16       => ( ( member223413699real_n
% 2.12/1.16            @ ( collec321817931real_n
% 2.12/1.16              @ ^ [X: finite1489363574real_n] :
% 2.12/1.16                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ N ) )
% 2.12/1.16                  & ( P @ X ) ) )
% 2.12/1.16            @ ( sigma_1235138647real_n @ N ) )
% 2.12/1.16         => ( member223413699real_n
% 2.12/1.16            @ ( collec321817931real_n
% 2.12/1.16              @ ^ [X: finite1489363574real_n] :
% 2.12/1.16                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 2.12/1.16                  & ( P @ ( F @ X ) ) ) )
% 2.12/1.16            @ ( sigma_1235138647real_n @ M ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_119_measurable__If,axiom,
% 2.12/1.16      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,M2: sigma_1466784463real_n,G: finite1489363574real_n > finite1489363574real_n,P: finite1489363574real_n > $o] :
% 2.12/1.16        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ M2 ) )
% 2.12/1.16       => ( ( member1746150050real_n @ G @ ( sigma_439801790real_n @ M @ M2 ) )
% 2.12/1.16         => ( ( member223413699real_n
% 2.12/1.16              @ ( collec321817931real_n
% 2.12/1.16                @ ^ [X: finite1489363574real_n] :
% 2.12/1.16                    ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 2.12/1.16                    & ( P @ X ) ) )
% 2.12/1.16              @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.16           => ( member1746150050real_n
% 2.12/1.16              @ ^ [X: finite1489363574real_n] : ( if_Fin127821360real_n @ ( P @ X ) @ ( F @ X ) @ ( G @ X ) )
% 2.12/1.16              @ ( sigma_439801790real_n @ M @ M2 ) ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_120_inf__right__idem,axiom,
% 2.12/1.16      ! [X2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ X2 @ Y3 ) @ Y3 )
% 2.12/1.16        = ( inf_in1974387902real_n @ X2 @ Y3 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_121_inf_Oright__idem,axiom,
% 2.12/1.16      ! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ A @ B ) @ B )
% 2.12/1.16        = ( inf_in1974387902real_n @ A @ B ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_122_inf__left__idem,axiom,
% 2.12/1.16      ! [X2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( inf_in1974387902real_n @ X2 @ ( inf_in1974387902real_n @ X2 @ Y3 ) )
% 2.12/1.16        = ( inf_in1974387902real_n @ X2 @ Y3 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_123_inf_Oleft__idem,axiom,
% 2.12/1.16      ! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ A @ B ) )
% 2.12/1.16        = ( inf_in1974387902real_n @ A @ B ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_124_inf__idem,axiom,
% 2.12/1.16      ! [X2: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( inf_in1974387902real_n @ X2 @ X2 )
% 2.12/1.16        = X2 ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_125_inf_Oidem,axiom,
% 2.12/1.16      ! [A: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( inf_in1974387902real_n @ A @ A )
% 2.12/1.16        = A ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_126_inf__set__def,axiom,
% 2.12/1.16      ( inf_in632889204real_n
% 2.12/1.16      = ( ^ [A4: set_se2111327970real_n,B3: set_se2111327970real_n] :
% 2.12/1.16            ( collec452821761real_n
% 2.12/1.16            @ ( inf_in409346577al_n_o
% 2.12/1.16              @ ^ [X: set_Fi1058188332real_n] : ( member223413699real_n @ X @ A4 )
% 2.12/1.16              @ ^ [X: set_Fi1058188332real_n] : ( member223413699real_n @ X @ B3 ) ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_127_inf__set__def,axiom,
% 2.12/1.16      ( inf_in146441683real_n
% 2.12/1.16      = ( ^ [A4: set_Fi1326602817real_n,B3: set_Fi1326602817real_n] :
% 2.12/1.16            ( collec1190264032real_n
% 2.12/1.16            @ ( inf_in32002162al_n_o
% 2.12/1.16              @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ X @ A4 )
% 2.12/1.16              @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ X @ B3 ) ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_128_inf__set__def,axiom,
% 2.12/1.16      ( inf_in1974387902real_n
% 2.12/1.16      = ( ^ [A4: set_Fi1058188332real_n,B3: set_Fi1058188332real_n] :
% 2.12/1.16            ( collec321817931real_n
% 2.12/1.16            @ ( inf_in1620715847al_n_o
% 2.12/1.16              @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ X @ A4 )
% 2.12/1.16              @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ X @ B3 ) ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_129_inf__left__commute,axiom,
% 2.12/1.16      ! [X2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n,Z: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( inf_in1974387902real_n @ X2 @ ( inf_in1974387902real_n @ Y3 @ Z ) )
% 2.12/1.16        = ( inf_in1974387902real_n @ Y3 @ ( inf_in1974387902real_n @ X2 @ Z ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_130_inf_Oleft__commute,axiom,
% 2.12/1.16      ! [B: set_Fi1058188332real_n,A: set_Fi1058188332real_n,C2: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( inf_in1974387902real_n @ B @ ( inf_in1974387902real_n @ A @ C2 ) )
% 2.12/1.16        = ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ B @ C2 ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_131_inf__commute,axiom,
% 2.12/1.16      ( inf_in1974387902real_n
% 2.12/1.16      = ( ^ [X: set_Fi1058188332real_n,Y2: set_Fi1058188332real_n] : ( inf_in1974387902real_n @ Y2 @ X ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_132_inf_Ocommute,axiom,
% 2.12/1.16      ( inf_in1974387902real_n
% 2.12/1.16      = ( ^ [A3: set_Fi1058188332real_n,B4: set_Fi1058188332real_n] : ( inf_in1974387902real_n @ B4 @ A3 ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_133_inf__assoc,axiom,
% 2.12/1.16      ! [X2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n,Z: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ X2 @ Y3 ) @ Z )
% 2.12/1.16        = ( inf_in1974387902real_n @ X2 @ ( inf_in1974387902real_n @ Y3 @ Z ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_134_inf_Oassoc,axiom,
% 2.12/1.16      ! [A: set_Fi1058188332real_n,B: set_Fi1058188332real_n,C2: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ A @ B ) @ C2 )
% 2.12/1.16        = ( inf_in1974387902real_n @ A @ ( inf_in1974387902real_n @ B @ C2 ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_135_boolean__algebra__cancel_Oinf2,axiom,
% 2.12/1.16      ! [B2: set_Fi1058188332real_n,K: set_Fi1058188332real_n,B: set_Fi1058188332real_n,A: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( B2
% 2.12/1.16          = ( inf_in1974387902real_n @ K @ B ) )
% 2.12/1.16       => ( ( inf_in1974387902real_n @ A @ B2 )
% 2.12/1.16          = ( inf_in1974387902real_n @ K @ ( inf_in1974387902real_n @ A @ B ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_136_boolean__algebra__cancel_Oinf1,axiom,
% 2.12/1.16      ! [A2: set_Fi1058188332real_n,K: set_Fi1058188332real_n,A: set_Fi1058188332real_n,B: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( A2
% 2.12/1.16          = ( inf_in1974387902real_n @ K @ A ) )
% 2.12/1.16       => ( ( inf_in1974387902real_n @ A2 @ B )
% 2.12/1.16          = ( inf_in1974387902real_n @ K @ ( inf_in1974387902real_n @ A @ B ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_137_inf__sup__aci_I1_J,axiom,
% 2.12/1.16      ( inf_in1974387902real_n
% 2.12/1.16      = ( ^ [X: set_Fi1058188332real_n,Y2: set_Fi1058188332real_n] : ( inf_in1974387902real_n @ Y2 @ X ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_138_inf__sup__aci_I2_J,axiom,
% 2.12/1.16      ! [X2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n,Z: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( inf_in1974387902real_n @ ( inf_in1974387902real_n @ X2 @ Y3 ) @ Z )
% 2.12/1.16        = ( inf_in1974387902real_n @ X2 @ ( inf_in1974387902real_n @ Y3 @ Z ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_139_inf__sup__aci_I3_J,axiom,
% 2.12/1.16      ! [X2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n,Z: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( inf_in1974387902real_n @ X2 @ ( inf_in1974387902real_n @ Y3 @ Z ) )
% 2.12/1.16        = ( inf_in1974387902real_n @ Y3 @ ( inf_in1974387902real_n @ X2 @ Z ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_140_inf__sup__aci_I4_J,axiom,
% 2.12/1.16      ! [X2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( inf_in1974387902real_n @ X2 @ ( inf_in1974387902real_n @ X2 @ Y3 ) )
% 2.12/1.16        = ( inf_in1974387902real_n @ X2 @ Y3 ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_141_measurable__compose__rev,axiom,
% 2.12/1.16      ! [F: finite1489363574real_n > finite1489363574real_n,L2: sigma_1466784463real_n,N: sigma_1466784463real_n,G: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n] :
% 2.12/1.16        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ L2 @ N ) )
% 2.12/1.16       => ( ( member1746150050real_n @ G @ ( sigma_439801790real_n @ M @ L2 ) )
% 2.12/1.16         => ( member1746150050real_n
% 2.12/1.16            @ ^ [X: finite1489363574real_n] : ( F @ ( G @ X ) )
% 2.12/1.16            @ ( sigma_439801790real_n @ M @ N ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_142_measurable__compose,axiom,
% 2.12/1.16      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,N: sigma_1466784463real_n,G: finite1489363574real_n > finite1489363574real_n,L2: sigma_1466784463real_n] :
% 2.12/1.16        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ N ) )
% 2.12/1.16       => ( ( member1746150050real_n @ G @ ( sigma_439801790real_n @ N @ L2 ) )
% 2.12/1.16         => ( member1746150050real_n
% 2.12/1.16            @ ^ [X: finite1489363574real_n] : ( G @ ( F @ X ) )
% 2.12/1.16            @ ( sigma_439801790real_n @ M @ L2 ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_143_measurable__id,axiom,
% 2.12/1.16      ! [M: sigma_1466784463real_n] :
% 2.12/1.16        ( member1746150050real_n
% 2.12/1.16        @ ^ [X: finite1489363574real_n] : X
% 2.12/1.16        @ ( sigma_439801790real_n @ M @ M ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_144_measurable__cong__sets,axiom,
% 2.12/1.16      ! [M: sigma_1466784463real_n,M2: sigma_1466784463real_n,N: sigma_1466784463real_n,N2: sigma_1466784463real_n] :
% 2.12/1.16        ( ( ( sigma_1235138647real_n @ M )
% 2.12/1.16          = ( sigma_1235138647real_n @ M2 ) )
% 2.12/1.16       => ( ( ( sigma_1235138647real_n @ N )
% 2.12/1.16            = ( sigma_1235138647real_n @ N2 ) )
% 2.12/1.16         => ( ( sigma_439801790real_n @ M @ N )
% 2.12/1.16            = ( sigma_439801790real_n @ M2 @ N2 ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_145_sets__eq__imp__space__eq,axiom,
% 2.12/1.16      ! [M: sigma_1466784463real_n,M2: sigma_1466784463real_n] :
% 2.12/1.16        ( ( ( sigma_1235138647real_n @ M )
% 2.12/1.16          = ( sigma_1235138647real_n @ M2 ) )
% 2.12/1.16       => ( ( sigma_476185326real_n @ M )
% 2.12/1.16          = ( sigma_476185326real_n @ M2 ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_146_measurable__cong__simp,axiom,
% 2.12/1.16      ! [M: sigma_1466784463real_n,N: sigma_1466784463real_n,M2: sigma_1466784463real_n,N2: sigma_1466784463real_n,F: finite1489363574real_n > finite1489363574real_n,G: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.16        ( ( M = N )
% 2.12/1.16       => ( ( M2 = N2 )
% 2.12/1.16         => ( ! [W: finite1489363574real_n] :
% 2.12/1.16                ( ( member1352538125real_n @ W @ ( sigma_476185326real_n @ M ) )
% 2.12/1.16               => ( ( F @ W )
% 2.12/1.16                  = ( G @ W ) ) )
% 2.12/1.16           => ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ M2 ) )
% 2.12/1.16              = ( member1746150050real_n @ G @ ( sigma_439801790real_n @ N @ N2 ) ) ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_147_measurable__space,axiom,
% 2.12/1.16      ! [F: set_Fi1058188332real_n > set_Fi1058188332real_n,M: sigma_1422848389real_n,A2: sigma_1422848389real_n,X2: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( member1734791438real_n @ F @ ( sigma_239294762real_n @ M @ A2 ) )
% 2.12/1.16       => ( ( member223413699real_n @ X2 @ ( sigma_607186084real_n @ M ) )
% 2.12/1.16         => ( member223413699real_n @ ( F @ X2 ) @ ( sigma_607186084real_n @ A2 ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_148_measurable__space,axiom,
% 2.12/1.16      ! [F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,M: sigma_1422848389real_n,A2: sigma_107786596real_n,X2: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( member1764433517real_n @ F @ ( sigma_588796041real_n @ M @ A2 ) )
% 2.12/1.16       => ( ( member223413699real_n @ X2 @ ( sigma_607186084real_n @ M ) )
% 2.12/1.16         => ( member1746150050real_n @ ( F @ X2 ) @ ( sigma_1483971331real_n @ A2 ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_149_measurable__space,axiom,
% 2.12/1.16      ! [F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,M: sigma_107786596real_n,A2: sigma_1422848389real_n,X2: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.16        ( ( member640587117real_n @ F @ ( sigma_364818953real_n @ M @ A2 ) )
% 2.12/1.16       => ( ( member1746150050real_n @ X2 @ ( sigma_1483971331real_n @ M ) )
% 2.12/1.16         => ( member223413699real_n @ ( F @ X2 ) @ ( sigma_607186084real_n @ A2 ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_150_measurable__space,axiom,
% 2.12/1.16      ! [F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,M: sigma_107786596real_n,A2: sigma_107786596real_n,X2: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.16        ( ( member117715276real_n @ F @ ( sigma_1185134568real_n @ M @ A2 ) )
% 2.12/1.16       => ( ( member1746150050real_n @ X2 @ ( sigma_1483971331real_n @ M ) )
% 2.12/1.16         => ( member1746150050real_n @ ( F @ X2 ) @ ( sigma_1483971331real_n @ A2 ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_151_measurable__space,axiom,
% 2.12/1.16      ! [F: set_Fi1058188332real_n > finite1489363574real_n,M: sigma_1422848389real_n,A2: sigma_1466784463real_n,X2: set_Fi1058188332real_n] :
% 2.12/1.16        ( ( member1759501912real_n @ F @ ( sigma_1333364596real_n @ M @ A2 ) )
% 2.12/1.16       => ( ( member223413699real_n @ X2 @ ( sigma_607186084real_n @ M ) )
% 2.12/1.16         => ( member1352538125real_n @ ( F @ X2 ) @ ( sigma_476185326real_n @ A2 ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_152_measurable__space,axiom,
% 2.12/1.16      ! [F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,M: sigma_107786596real_n,A2: sigma_1466784463real_n,X2: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.16        ( ( member1695588023real_n @ F @ ( sigma_2028985427real_n @ M @ A2 ) )
% 2.12/1.16       => ( ( member1746150050real_n @ X2 @ ( sigma_1483971331real_n @ M ) )
% 2.12/1.16         => ( member1352538125real_n @ ( F @ X2 ) @ ( sigma_476185326real_n @ A2 ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_153_measurable__space,axiom,
% 2.12/1.16      ! [F: finite1489363574real_n > set_Fi1058188332real_n,M: sigma_1466784463real_n,A2: sigma_1422848389real_n,X2: finite1489363574real_n] :
% 2.12/1.16        ( ( member966061400real_n @ F @ ( sigma_566919540real_n @ M @ A2 ) )
% 2.12/1.16       => ( ( member1352538125real_n @ X2 @ ( sigma_476185326real_n @ M ) )
% 2.12/1.16         => ( member223413699real_n @ ( F @ X2 ) @ ( sigma_607186084real_n @ A2 ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_154_measurable__space,axiom,
% 2.12/1.16      ! [F: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,A2: sigma_107786596real_n,X2: finite1489363574real_n] :
% 2.12/1.16        ( ( member408431031real_n @ F @ ( sigma_2016438227real_n @ M @ A2 ) )
% 2.12/1.16       => ( ( member1352538125real_n @ X2 @ ( sigma_476185326real_n @ M ) )
% 2.12/1.16         => ( member1746150050real_n @ ( F @ X2 ) @ ( sigma_1483971331real_n @ A2 ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_155_measurable__space,axiom,
% 2.12/1.16      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,A2: sigma_1466784463real_n,X2: finite1489363574real_n] :
% 2.12/1.16        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ A2 ) )
% 2.12/1.16       => ( ( member1352538125real_n @ X2 @ ( sigma_476185326real_n @ M ) )
% 2.12/1.16         => ( member1352538125real_n @ ( F @ X2 ) @ ( sigma_476185326real_n @ A2 ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_156_measurable__cong,axiom,
% 2.12/1.16      ! [M: sigma_1466784463real_n,F: finite1489363574real_n > finite1489363574real_n,G: finite1489363574real_n > finite1489363574real_n,M2: sigma_1466784463real_n] :
% 2.12/1.16        ( ! [W: finite1489363574real_n] :
% 2.12/1.16            ( ( member1352538125real_n @ W @ ( sigma_476185326real_n @ M ) )
% 2.12/1.16           => ( ( F @ W )
% 2.12/1.16              = ( G @ W ) ) )
% 2.12/1.16       => ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ M2 ) )
% 2.12/1.16          = ( member1746150050real_n @ G @ ( sigma_439801790real_n @ M @ M2 ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_157_measurable__ident__sets,axiom,
% 2.12/1.16      ! [M: sigma_1466784463real_n,M2: sigma_1466784463real_n] :
% 2.12/1.16        ( ( ( sigma_1235138647real_n @ M )
% 2.12/1.16          = ( sigma_1235138647real_n @ M2 ) )
% 2.12/1.16       => ( member1746150050real_n
% 2.12/1.16          @ ^ [X: finite1489363574real_n] : X
% 2.12/1.16          @ ( sigma_439801790real_n @ M @ M2 ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_158_sets_Osets__Collect_I5_J,axiom,
% 2.12/1.16      ! [M: sigma_1422848389real_n,Pb: $o] :
% 2.12/1.16        ( member1475136633real_n
% 2.12/1.16        @ ( collec452821761real_n
% 2.12/1.16          @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.16              ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 2.12/1.16              & Pb ) )
% 2.12/1.16        @ ( sigma_433815053real_n @ M ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_159_sets_Osets__Collect_I5_J,axiom,
% 2.12/1.16      ! [M: sigma_107786596real_n,Pb: $o] :
% 2.12/1.16        ( member2104752728real_n
% 2.12/1.16        @ ( collec1190264032real_n
% 2.12/1.16          @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.16              ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 2.12/1.16              & Pb ) )
% 2.12/1.16        @ ( sigma_522684908real_n @ M ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_160_sets_Osets__Collect_I5_J,axiom,
% 2.12/1.16      ! [M: sigma_1466784463real_n,Pb: $o] :
% 2.12/1.16        ( member223413699real_n
% 2.12/1.16        @ ( collec321817931real_n
% 2.12/1.16          @ ^ [X: finite1489363574real_n] :
% 2.12/1.16              ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 2.12/1.16              & Pb ) )
% 2.12/1.16        @ ( sigma_1235138647real_n @ M ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_161_sets_Osets__Collect__imp,axiom,
% 2.12/1.16      ! [M: sigma_1422848389real_n,P: set_Fi1058188332real_n > $o,Q: set_Fi1058188332real_n > $o] :
% 2.12/1.16        ( ( member1475136633real_n
% 2.12/1.16          @ ( collec452821761real_n
% 2.12/1.16            @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.16                ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 2.12/1.16                & ( P @ X ) ) )
% 2.12/1.16          @ ( sigma_433815053real_n @ M ) )
% 2.12/1.16       => ( ( member1475136633real_n
% 2.12/1.16            @ ( collec452821761real_n
% 2.12/1.16              @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.16                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 2.12/1.16                  & ( Q @ X ) ) )
% 2.12/1.16            @ ( sigma_433815053real_n @ M ) )
% 2.12/1.16         => ( member1475136633real_n
% 2.12/1.16            @ ( collec452821761real_n
% 2.12/1.16              @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.16                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 2.12/1.16                  & ( ( Q @ X )
% 2.12/1.16                   => ( P @ X ) ) ) )
% 2.12/1.16            @ ( sigma_433815053real_n @ M ) ) ) ) ).
% 2.12/1.16  
% 2.12/1.16  thf(fact_162_sets_Osets__Collect__imp,axiom,
% 2.12/1.16      ! [M: sigma_107786596real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o,Q: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
% 2.12/1.17        ( ( member2104752728real_n
% 2.12/1.17          @ ( collec1190264032real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17                ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 2.12/1.17                & ( P @ X ) ) )
% 2.12/1.17          @ ( sigma_522684908real_n @ M ) )
% 2.12/1.17       => ( ( member2104752728real_n
% 2.12/1.17            @ ( collec1190264032real_n
% 2.12/1.17              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 2.12/1.17                  & ( Q @ X ) ) )
% 2.12/1.17            @ ( sigma_522684908real_n @ M ) )
% 2.12/1.17         => ( member2104752728real_n
% 2.12/1.17            @ ( collec1190264032real_n
% 2.12/1.17              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 2.12/1.17                  & ( ( Q @ X )
% 2.12/1.17                   => ( P @ X ) ) ) )
% 2.12/1.17            @ ( sigma_522684908real_n @ M ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_163_sets_Osets__Collect__imp,axiom,
% 2.12/1.17      ! [M: sigma_1466784463real_n,P: finite1489363574real_n > $o,Q: finite1489363574real_n > $o] :
% 2.12/1.17        ( ( member223413699real_n
% 2.12/1.17          @ ( collec321817931real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n] :
% 2.12/1.17                ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 2.12/1.17                & ( P @ X ) ) )
% 2.12/1.17          @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.17       => ( ( member223413699real_n
% 2.12/1.17            @ ( collec321817931real_n
% 2.12/1.17              @ ^ [X: finite1489363574real_n] :
% 2.12/1.17                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 2.12/1.17                  & ( Q @ X ) ) )
% 2.12/1.17            @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.17         => ( member223413699real_n
% 2.12/1.17            @ ( collec321817931real_n
% 2.12/1.17              @ ^ [X: finite1489363574real_n] :
% 2.12/1.17                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 2.12/1.17                  & ( ( Q @ X )
% 2.12/1.17                   => ( P @ X ) ) ) )
% 2.12/1.17            @ ( sigma_1235138647real_n @ M ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_164_sets_Osets__Collect__neg,axiom,
% 2.12/1.17      ! [M: sigma_1422848389real_n,P: set_Fi1058188332real_n > $o] :
% 2.12/1.17        ( ( member1475136633real_n
% 2.12/1.17          @ ( collec452821761real_n
% 2.12/1.17            @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.17                ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 2.12/1.17                & ( P @ X ) ) )
% 2.12/1.17          @ ( sigma_433815053real_n @ M ) )
% 2.12/1.17       => ( member1475136633real_n
% 2.12/1.17          @ ( collec452821761real_n
% 2.12/1.17            @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.17                ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 2.12/1.17                & ~ ( P @ X ) ) )
% 2.12/1.17          @ ( sigma_433815053real_n @ M ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_165_sets_Osets__Collect__neg,axiom,
% 2.12/1.17      ! [M: sigma_107786596real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
% 2.12/1.17        ( ( member2104752728real_n
% 2.12/1.17          @ ( collec1190264032real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17                ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 2.12/1.17                & ( P @ X ) ) )
% 2.12/1.17          @ ( sigma_522684908real_n @ M ) )
% 2.12/1.17       => ( member2104752728real_n
% 2.12/1.17          @ ( collec1190264032real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17                ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 2.12/1.17                & ~ ( P @ X ) ) )
% 2.12/1.17          @ ( sigma_522684908real_n @ M ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_166_sets_Osets__Collect__neg,axiom,
% 2.12/1.17      ! [M: sigma_1466784463real_n,P: finite1489363574real_n > $o] :
% 2.12/1.17        ( ( member223413699real_n
% 2.12/1.17          @ ( collec321817931real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n] :
% 2.12/1.17                ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 2.12/1.17                & ( P @ X ) ) )
% 2.12/1.17          @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.17       => ( member223413699real_n
% 2.12/1.17          @ ( collec321817931real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n] :
% 2.12/1.17                ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 2.12/1.17                & ~ ( P @ X ) ) )
% 2.12/1.17          @ ( sigma_1235138647real_n @ M ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_167_sets_Osets__Collect__conj,axiom,
% 2.12/1.17      ! [M: sigma_1422848389real_n,P: set_Fi1058188332real_n > $o,Q: set_Fi1058188332real_n > $o] :
% 2.12/1.17        ( ( member1475136633real_n
% 2.12/1.17          @ ( collec452821761real_n
% 2.12/1.17            @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.17                ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 2.12/1.17                & ( P @ X ) ) )
% 2.12/1.17          @ ( sigma_433815053real_n @ M ) )
% 2.12/1.17       => ( ( member1475136633real_n
% 2.12/1.17            @ ( collec452821761real_n
% 2.12/1.17              @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.17                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 2.12/1.17                  & ( Q @ X ) ) )
% 2.12/1.17            @ ( sigma_433815053real_n @ M ) )
% 2.12/1.17         => ( member1475136633real_n
% 2.12/1.17            @ ( collec452821761real_n
% 2.12/1.17              @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.17                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 2.12/1.17                  & ( Q @ X )
% 2.12/1.17                  & ( P @ X ) ) )
% 2.12/1.17            @ ( sigma_433815053real_n @ M ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_168_sets_Osets__Collect__conj,axiom,
% 2.12/1.17      ! [M: sigma_107786596real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o,Q: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
% 2.12/1.17        ( ( member2104752728real_n
% 2.12/1.17          @ ( collec1190264032real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17                ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 2.12/1.17                & ( P @ X ) ) )
% 2.12/1.17          @ ( sigma_522684908real_n @ M ) )
% 2.12/1.17       => ( ( member2104752728real_n
% 2.12/1.17            @ ( collec1190264032real_n
% 2.12/1.17              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 2.12/1.17                  & ( Q @ X ) ) )
% 2.12/1.17            @ ( sigma_522684908real_n @ M ) )
% 2.12/1.17         => ( member2104752728real_n
% 2.12/1.17            @ ( collec1190264032real_n
% 2.12/1.17              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 2.12/1.17                  & ( Q @ X )
% 2.12/1.17                  & ( P @ X ) ) )
% 2.12/1.17            @ ( sigma_522684908real_n @ M ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_169_sets_Osets__Collect__conj,axiom,
% 2.12/1.17      ! [M: sigma_1466784463real_n,P: finite1489363574real_n > $o,Q: finite1489363574real_n > $o] :
% 2.12/1.17        ( ( member223413699real_n
% 2.12/1.17          @ ( collec321817931real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n] :
% 2.12/1.17                ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 2.12/1.17                & ( P @ X ) ) )
% 2.12/1.17          @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.17       => ( ( member223413699real_n
% 2.12/1.17            @ ( collec321817931real_n
% 2.12/1.17              @ ^ [X: finite1489363574real_n] :
% 2.12/1.17                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 2.12/1.17                  & ( Q @ X ) ) )
% 2.12/1.17            @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.17         => ( member223413699real_n
% 2.12/1.17            @ ( collec321817931real_n
% 2.12/1.17              @ ^ [X: finite1489363574real_n] :
% 2.12/1.17                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 2.12/1.17                  & ( Q @ X )
% 2.12/1.17                  & ( P @ X ) ) )
% 2.12/1.17            @ ( sigma_1235138647real_n @ M ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_170_sets_Osets__Collect__disj,axiom,
% 2.12/1.17      ! [M: sigma_1422848389real_n,P: set_Fi1058188332real_n > $o,Q: set_Fi1058188332real_n > $o] :
% 2.12/1.17        ( ( member1475136633real_n
% 2.12/1.17          @ ( collec452821761real_n
% 2.12/1.17            @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.17                ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 2.12/1.17                & ( P @ X ) ) )
% 2.12/1.17          @ ( sigma_433815053real_n @ M ) )
% 2.12/1.17       => ( ( member1475136633real_n
% 2.12/1.17            @ ( collec452821761real_n
% 2.12/1.17              @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.17                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 2.12/1.17                  & ( Q @ X ) ) )
% 2.12/1.17            @ ( sigma_433815053real_n @ M ) )
% 2.12/1.17         => ( member1475136633real_n
% 2.12/1.17            @ ( collec452821761real_n
% 2.12/1.17              @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.17                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 2.12/1.17                  & ( ( Q @ X )
% 2.12/1.17                    | ( P @ X ) ) ) )
% 2.12/1.17            @ ( sigma_433815053real_n @ M ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_171_sets_Osets__Collect__disj,axiom,
% 2.12/1.17      ! [M: sigma_107786596real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o,Q: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
% 2.12/1.17        ( ( member2104752728real_n
% 2.12/1.17          @ ( collec1190264032real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17                ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 2.12/1.17                & ( P @ X ) ) )
% 2.12/1.17          @ ( sigma_522684908real_n @ M ) )
% 2.12/1.17       => ( ( member2104752728real_n
% 2.12/1.17            @ ( collec1190264032real_n
% 2.12/1.17              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 2.12/1.17                  & ( Q @ X ) ) )
% 2.12/1.17            @ ( sigma_522684908real_n @ M ) )
% 2.12/1.17         => ( member2104752728real_n
% 2.12/1.17            @ ( collec1190264032real_n
% 2.12/1.17              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 2.12/1.17                  & ( ( Q @ X )
% 2.12/1.17                    | ( P @ X ) ) ) )
% 2.12/1.17            @ ( sigma_522684908real_n @ M ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_172_sets_Osets__Collect__disj,axiom,
% 2.12/1.17      ! [M: sigma_1466784463real_n,P: finite1489363574real_n > $o,Q: finite1489363574real_n > $o] :
% 2.12/1.17        ( ( member223413699real_n
% 2.12/1.17          @ ( collec321817931real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n] :
% 2.12/1.17                ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 2.12/1.17                & ( P @ X ) ) )
% 2.12/1.17          @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.17       => ( ( member223413699real_n
% 2.12/1.17            @ ( collec321817931real_n
% 2.12/1.17              @ ^ [X: finite1489363574real_n] :
% 2.12/1.17                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 2.12/1.17                  & ( Q @ X ) ) )
% 2.12/1.17            @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.17         => ( member223413699real_n
% 2.12/1.17            @ ( collec321817931real_n
% 2.12/1.17              @ ^ [X: finite1489363574real_n] :
% 2.12/1.17                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 2.12/1.17                  & ( ( Q @ X )
% 2.12/1.17                    | ( P @ X ) ) ) )
% 2.12/1.17            @ ( sigma_1235138647real_n @ M ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_173_sets_Osets__Collect__const,axiom,
% 2.12/1.17      ! [M: sigma_1422848389real_n,P: $o] :
% 2.12/1.17        ( member1475136633real_n
% 2.12/1.17        @ ( collec452821761real_n
% 2.12/1.17          @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.17              ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 2.12/1.17              & P ) )
% 2.12/1.17        @ ( sigma_433815053real_n @ M ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_174_sets_Osets__Collect__const,axiom,
% 2.12/1.17      ! [M: sigma_107786596real_n,P: $o] :
% 2.12/1.17        ( member2104752728real_n
% 2.12/1.17        @ ( collec1190264032real_n
% 2.12/1.17          @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17              ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 2.12/1.17              & P ) )
% 2.12/1.17        @ ( sigma_522684908real_n @ M ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_175_sets_Osets__Collect__const,axiom,
% 2.12/1.17      ! [M: sigma_1466784463real_n,P: $o] :
% 2.12/1.17        ( member223413699real_n
% 2.12/1.17        @ ( collec321817931real_n
% 2.12/1.17          @ ^ [X: finite1489363574real_n] :
% 2.12/1.17              ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 2.12/1.17              & P ) )
% 2.12/1.17        @ ( sigma_1235138647real_n @ M ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_176_measurable__const,axiom,
% 2.12/1.17      ! [C2: finite1489363574real_n,M2: sigma_1466784463real_n,M: sigma_1466784463real_n] :
% 2.12/1.17        ( ( member1352538125real_n @ C2 @ ( sigma_476185326real_n @ M2 ) )
% 2.12/1.17       => ( member1746150050real_n
% 2.12/1.17          @ ^ [X: finite1489363574real_n] : C2
% 2.12/1.17          @ ( sigma_439801790real_n @ M @ M2 ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_177_T_H__def,axiom,
% 2.12/1.17      ( t
% 2.12/1.17      = ( ^ [A3: finite964658038_int_n] :
% 2.12/1.17            ( image_439535603real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ X @ ( minkow1134813771n_real @ A3 ) )
% 2.12/1.17            @ ( t2 @ A3 ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_178_inf__Int__eq,axiom,
% 2.12/1.17      ! [R: set_se2111327970real_n,S: set_se2111327970real_n] :
% 2.12/1.17        ( ( inf_in409346577al_n_o
% 2.12/1.17          @ ^ [X: set_Fi1058188332real_n] : ( member223413699real_n @ X @ R )
% 2.12/1.17          @ ^ [X: set_Fi1058188332real_n] : ( member223413699real_n @ X @ S ) )
% 2.12/1.17        = ( ^ [X: set_Fi1058188332real_n] : ( member223413699real_n @ X @ ( inf_in632889204real_n @ R @ S ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_179_inf__Int__eq,axiom,
% 2.12/1.17      ! [R: set_Fi1326602817real_n,S: set_Fi1326602817real_n] :
% 2.12/1.17        ( ( inf_in32002162al_n_o
% 2.12/1.17          @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ X @ R )
% 2.12/1.17          @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ X @ S ) )
% 2.12/1.17        = ( ^ [X: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ X @ ( inf_in146441683real_n @ R @ S ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_180_inf__Int__eq,axiom,
% 2.12/1.17      ! [R: set_Fi1058188332real_n,S: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( inf_in1620715847al_n_o
% 2.12/1.17          @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ X @ R )
% 2.12/1.17          @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ X @ S ) )
% 2.12/1.17        = ( ^ [X: finite1489363574real_n] : ( member1352538125real_n @ X @ ( inf_in1974387902real_n @ R @ S ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_181_main__part__sets,axiom,
% 2.12/1.17      ! [S: set_Fi1058188332real_n,M: sigma_1466784463real_n] :
% 2.12/1.17        ( ( member223413699real_n @ S @ ( sigma_1235138647real_n @ ( comple230862828real_n @ M ) ) )
% 2.12/1.17       => ( member223413699real_n @ ( comple1390568924real_n @ M @ S ) @ ( sigma_1235138647real_n @ M ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_182_measurable__restrict__space__iff,axiom,
% 2.12/1.17      ! [Omega: set_se2111327970real_n,M: sigma_1422848389real_n,C2: set_Fi1058188332real_n,N: sigma_1422848389real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n] :
% 2.12/1.17        ( ( member1475136633real_n @ ( inf_in632889204real_n @ Omega @ ( sigma_607186084real_n @ M ) ) @ ( sigma_433815053real_n @ M ) )
% 2.12/1.17       => ( ( member223413699real_n @ C2 @ ( sigma_607186084real_n @ N ) )
% 2.12/1.17         => ( ( member1734791438real_n @ F @ ( sigma_239294762real_n @ ( sigma_993999336real_n @ M @ Omega ) @ N ) )
% 2.12/1.17            = ( member1734791438real_n
% 2.12/1.17              @ ^ [X: set_Fi1058188332real_n] : ( if_set11487206real_n @ ( member223413699real_n @ X @ Omega ) @ ( F @ X ) @ C2 )
% 2.12/1.17              @ ( sigma_239294762real_n @ M @ N ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_183_measurable__restrict__space__iff,axiom,
% 2.12/1.17      ! [Omega: set_Fi1326602817real_n,M: sigma_107786596real_n,C2: set_Fi1058188332real_n,N: sigma_1422848389real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n] :
% 2.12/1.17        ( ( member2104752728real_n @ ( inf_in146441683real_n @ Omega @ ( sigma_1483971331real_n @ M ) ) @ ( sigma_522684908real_n @ M ) )
% 2.12/1.17       => ( ( member223413699real_n @ C2 @ ( sigma_607186084real_n @ N ) )
% 2.12/1.17         => ( ( member640587117real_n @ F @ ( sigma_364818953real_n @ ( sigma_1052429895real_n @ M @ Omega ) @ N ) )
% 2.12/1.17            = ( member640587117real_n
% 2.12/1.17              @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( if_set11487206real_n @ ( member1746150050real_n @ X @ Omega ) @ ( F @ X ) @ C2 )
% 2.12/1.17              @ ( sigma_364818953real_n @ M @ N ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_184_measurable__restrict__space__iff,axiom,
% 2.12/1.17      ! [Omega: set_se2111327970real_n,M: sigma_1422848389real_n,C2: finite1489363574real_n > finite1489363574real_n,N: sigma_107786596real_n,F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17        ( ( member1475136633real_n @ ( inf_in632889204real_n @ Omega @ ( sigma_607186084real_n @ M ) ) @ ( sigma_433815053real_n @ M ) )
% 2.12/1.17       => ( ( member1746150050real_n @ C2 @ ( sigma_1483971331real_n @ N ) )
% 2.12/1.17         => ( ( member1764433517real_n @ F @ ( sigma_588796041real_n @ ( sigma_993999336real_n @ M @ Omega ) @ N ) )
% 2.12/1.17            = ( member1764433517real_n
% 2.12/1.17              @ ^ [X: set_Fi1058188332real_n] : ( if_Fin413489477real_n @ ( member223413699real_n @ X @ Omega ) @ ( F @ X ) @ C2 )
% 2.12/1.17              @ ( sigma_588796041real_n @ M @ N ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_185_measurable__restrict__space__iff,axiom,
% 2.12/1.17      ! [Omega: set_Fi1326602817real_n,M: sigma_107786596real_n,C2: finite1489363574real_n > finite1489363574real_n,N: sigma_107786596real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17        ( ( member2104752728real_n @ ( inf_in146441683real_n @ Omega @ ( sigma_1483971331real_n @ M ) ) @ ( sigma_522684908real_n @ M ) )
% 2.12/1.17       => ( ( member1746150050real_n @ C2 @ ( sigma_1483971331real_n @ N ) )
% 2.12/1.17         => ( ( member117715276real_n @ F @ ( sigma_1185134568real_n @ ( sigma_1052429895real_n @ M @ Omega ) @ N ) )
% 2.12/1.17            = ( member117715276real_n
% 2.12/1.17              @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( if_Fin413489477real_n @ ( member1746150050real_n @ X @ Omega ) @ ( F @ X ) @ C2 )
% 2.12/1.17              @ ( sigma_1185134568real_n @ M @ N ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_186_measurable__restrict__space__iff,axiom,
% 2.12/1.17      ! [Omega: set_se2111327970real_n,M: sigma_1422848389real_n,C2: finite1489363574real_n,N: sigma_1466784463real_n,F: set_Fi1058188332real_n > finite1489363574real_n] :
% 2.12/1.17        ( ( member1475136633real_n @ ( inf_in632889204real_n @ Omega @ ( sigma_607186084real_n @ M ) ) @ ( sigma_433815053real_n @ M ) )
% 2.12/1.17       => ( ( member1352538125real_n @ C2 @ ( sigma_476185326real_n @ N ) )
% 2.12/1.17         => ( ( member1759501912real_n @ F @ ( sigma_1333364596real_n @ ( sigma_993999336real_n @ M @ Omega ) @ N ) )
% 2.12/1.17            = ( member1759501912real_n
% 2.12/1.17              @ ^ [X: set_Fi1058188332real_n] : ( if_Fin127821360real_n @ ( member223413699real_n @ X @ Omega ) @ ( F @ X ) @ C2 )
% 2.12/1.17              @ ( sigma_1333364596real_n @ M @ N ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_187_measurable__restrict__space__iff,axiom,
% 2.12/1.17      ! [Omega: set_Fi1326602817real_n,M: sigma_107786596real_n,C2: finite1489363574real_n,N: sigma_1466784463real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n] :
% 2.12/1.17        ( ( member2104752728real_n @ ( inf_in146441683real_n @ Omega @ ( sigma_1483971331real_n @ M ) ) @ ( sigma_522684908real_n @ M ) )
% 2.12/1.17       => ( ( member1352538125real_n @ C2 @ ( sigma_476185326real_n @ N ) )
% 2.12/1.17         => ( ( member1695588023real_n @ F @ ( sigma_2028985427real_n @ ( sigma_1052429895real_n @ M @ Omega ) @ N ) )
% 2.12/1.17            = ( member1695588023real_n
% 2.12/1.17              @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( if_Fin127821360real_n @ ( member1746150050real_n @ X @ Omega ) @ ( F @ X ) @ C2 )
% 2.12/1.17              @ ( sigma_2028985427real_n @ M @ N ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_188_measurable__restrict__space__iff,axiom,
% 2.12/1.17      ! [Omega: set_Fi1058188332real_n,M: sigma_1466784463real_n,C2: set_Fi1058188332real_n,N: sigma_1422848389real_n,F: finite1489363574real_n > set_Fi1058188332real_n] :
% 2.12/1.17        ( ( member223413699real_n @ ( inf_in1974387902real_n @ Omega @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.17       => ( ( member223413699real_n @ C2 @ ( sigma_607186084real_n @ N ) )
% 2.12/1.17         => ( ( member966061400real_n @ F @ ( sigma_566919540real_n @ ( sigma_346513458real_n @ M @ Omega ) @ N ) )
% 2.12/1.17            = ( member966061400real_n
% 2.12/1.17              @ ^ [X: finite1489363574real_n] : ( if_set11487206real_n @ ( member1352538125real_n @ X @ Omega ) @ ( F @ X ) @ C2 )
% 2.12/1.17              @ ( sigma_566919540real_n @ M @ N ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_189_measurable__restrict__space__iff,axiom,
% 2.12/1.17      ! [Omega: set_Fi1058188332real_n,M: sigma_1466784463real_n,C2: finite1489363574real_n > finite1489363574real_n,N: sigma_107786596real_n,F: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17        ( ( member223413699real_n @ ( inf_in1974387902real_n @ Omega @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.17       => ( ( member1746150050real_n @ C2 @ ( sigma_1483971331real_n @ N ) )
% 2.12/1.17         => ( ( member408431031real_n @ F @ ( sigma_2016438227real_n @ ( sigma_346513458real_n @ M @ Omega ) @ N ) )
% 2.12/1.17            = ( member408431031real_n
% 2.12/1.17              @ ^ [X: finite1489363574real_n] : ( if_Fin413489477real_n @ ( member1352538125real_n @ X @ Omega ) @ ( F @ X ) @ C2 )
% 2.12/1.17              @ ( sigma_2016438227real_n @ M @ N ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_190_measurable__restrict__space__iff,axiom,
% 2.12/1.17      ! [Omega: set_Fi1058188332real_n,M: sigma_1466784463real_n,C2: finite1489363574real_n,N: sigma_1466784463real_n,F: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17        ( ( member223413699real_n @ ( inf_in1974387902real_n @ Omega @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.17       => ( ( member1352538125real_n @ C2 @ ( sigma_476185326real_n @ N ) )
% 2.12/1.17         => ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ M @ Omega ) @ N ) )
% 2.12/1.17            = ( member1746150050real_n
% 2.12/1.17              @ ^ [X: finite1489363574real_n] : ( if_Fin127821360real_n @ ( member1352538125real_n @ X @ Omega ) @ ( F @ X ) @ C2 )
% 2.12/1.17              @ ( sigma_439801790real_n @ M @ N ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_191_sets__Least,axiom,
% 2.12/1.17      ! [M: sigma_1422848389real_n,P: nat > set_Fi1058188332real_n > $o,A2: set_nat] :
% 2.12/1.17        ( ! [I2: nat] :
% 2.12/1.17            ( member1475136633real_n
% 2.12/1.17            @ ( collec452821761real_n
% 2.12/1.17              @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.17                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 2.12/1.17                  & ( P @ I2 @ X ) ) )
% 2.12/1.17            @ ( sigma_433815053real_n @ M ) )
% 2.12/1.17       => ( member1475136633real_n
% 2.12/1.17          @ ( inf_in632889204real_n
% 2.12/1.17            @ ( vimage501526201_n_nat
% 2.12/1.17              @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.17                  ( ord_Least_nat
% 2.12/1.17                  @ ^ [J2: nat] : ( P @ J2 @ X ) )
% 2.12/1.17              @ A2 )
% 2.12/1.17            @ ( sigma_607186084real_n @ M ) )
% 2.12/1.17          @ ( sigma_433815053real_n @ M ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_192_sets__Least,axiom,
% 2.12/1.17      ! [M: sigma_107786596real_n,P: nat > ( finite1489363574real_n > finite1489363574real_n ) > $o,A2: set_nat] :
% 2.12/1.17        ( ! [I2: nat] :
% 2.12/1.17            ( member2104752728real_n
% 2.12/1.17            @ ( collec1190264032real_n
% 2.12/1.17              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 2.12/1.17                  & ( P @ I2 @ X ) ) )
% 2.12/1.17            @ ( sigma_522684908real_n @ M ) )
% 2.12/1.17       => ( member2104752728real_n
% 2.12/1.17          @ ( inf_in146441683real_n
% 2.12/1.17            @ ( vimage2098059032_n_nat
% 2.12/1.17              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17                  ( ord_Least_nat
% 2.12/1.17                  @ ^ [J2: nat] : ( P @ J2 @ X ) )
% 2.12/1.17              @ A2 )
% 2.12/1.17            @ ( sigma_1483971331real_n @ M ) )
% 2.12/1.17          @ ( sigma_522684908real_n @ M ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_193_sets__Least,axiom,
% 2.12/1.17      ! [M: sigma_1466784463real_n,P: nat > finite1489363574real_n > $o,A2: set_nat] :
% 2.12/1.17        ( ! [I2: nat] :
% 2.12/1.17            ( member223413699real_n
% 2.12/1.17            @ ( collec321817931real_n
% 2.12/1.17              @ ^ [X: finite1489363574real_n] :
% 2.12/1.17                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 2.12/1.17                  & ( P @ I2 @ X ) ) )
% 2.12/1.17            @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.17       => ( member223413699real_n
% 2.12/1.17          @ ( inf_in1974387902real_n
% 2.12/1.17            @ ( vimage281029891_n_nat
% 2.12/1.17              @ ^ [X: finite1489363574real_n] :
% 2.12/1.17                  ( ord_Least_nat
% 2.12/1.17                  @ ^ [J2: nat] : ( P @ J2 @ X ) )
% 2.12/1.17              @ A2 )
% 2.12/1.17            @ ( sigma_476185326real_n @ M ) )
% 2.12/1.17          @ ( sigma_1235138647real_n @ M ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_194_in__vimage__algebra,axiom,
% 2.12/1.17      ! [A2: set_Fi1058188332real_n,M: sigma_1466784463real_n,F: finite1489363574real_n > finite1489363574real_n,X4: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( member223413699real_n @ A2 @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.17       => ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage1233683625real_n @ F @ A2 ) @ X4 ) @ ( sigma_1235138647real_n @ ( sigma_821351682real_n @ X4 @ F @ M ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_195_in__borel__measurable__borel,axiom,
% 2.12/1.17      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n] :
% 2.12/1.17        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) )
% 2.12/1.17        = ( ! [X: set_Fi1058188332real_n] :
% 2.12/1.17              ( ( member223413699real_n @ X @ ( sigma_1235138647real_n @ borel_676189912real_n ) )
% 2.12/1.17             => ( member223413699real_n @ ( inf_in1974387902real_n @ ( vimage1233683625real_n @ F @ X ) @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_196_image__eqI,axiom,
% 2.12/1.17      ! [B: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n,X2: finite1489363574real_n,A2: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( B
% 2.12/1.17          = ( F @ X2 ) )
% 2.12/1.17       => ( ( member1352538125real_n @ X2 @ A2 )
% 2.12/1.17         => ( member1352538125real_n @ B @ ( image_439535603real_n @ F @ A2 ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_197_image__eqI,axiom,
% 2.12/1.17      ! [B: set_Fi1058188332real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n,X2: set_Fi1058188332real_n,A2: set_se2111327970real_n] :
% 2.12/1.17        ( ( B
% 2.12/1.17          = ( F @ X2 ) )
% 2.12/1.17       => ( ( member223413699real_n @ X2 @ A2 )
% 2.12/1.17         => ( member223413699real_n @ B @ ( image_1661509983real_n @ F @ A2 ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_198_image__eqI,axiom,
% 2.12/1.17      ! [B: finite1489363574real_n > finite1489363574real_n,F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,X2: set_Fi1058188332real_n,A2: set_se2111327970real_n] :
% 2.12/1.17        ( ( B
% 2.12/1.17          = ( F @ X2 ) )
% 2.12/1.17       => ( ( member223413699real_n @ X2 @ A2 )
% 2.12/1.17         => ( member1746150050real_n @ B @ ( image_352856126real_n @ F @ A2 ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_199_image__eqI,axiom,
% 2.12/1.17      ! [B: set_Fi1058188332real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,X2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n] :
% 2.12/1.17        ( ( B
% 2.12/1.17          = ( F @ X2 ) )
% 2.12/1.17       => ( ( member1746150050real_n @ X2 @ A2 )
% 2.12/1.17         => ( member223413699real_n @ B @ ( image_128879038real_n @ F @ A2 ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_200_image__eqI,axiom,
% 2.12/1.17      ! [B: finite1489363574real_n > finite1489363574real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,X2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n] :
% 2.12/1.17        ( ( B
% 2.12/1.17          = ( F @ X2 ) )
% 2.12/1.17       => ( ( member1746150050real_n @ X2 @ A2 )
% 2.12/1.17         => ( member1746150050real_n @ B @ ( image_1123376925real_n @ F @ A2 ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_201_image__ident,axiom,
% 2.12/1.17      ! [Y: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( image_439535603real_n
% 2.12/1.17          @ ^ [X: finite1489363574real_n] : X
% 2.12/1.17          @ Y )
% 2.12/1.17        = Y ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_202_add__diff__cancel__right_H,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n,B: finite1489363574real_n] :
% 2.12/1.17        ( ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ B ) @ B )
% 2.12/1.17        = A ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_203_add__diff__cancel__right_H,axiom,
% 2.12/1.17      ! [A: nat,B: nat] :
% 2.12/1.17        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 2.12/1.17        = A ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_204_add__diff__cancel__right,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n,C2: finite1489363574real_n,B: finite1489363574real_n] :
% 2.12/1.17        ( ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ C2 ) @ ( plus_p585657087real_n @ B @ C2 ) )
% 2.12/1.17        = ( minus_1037315151real_n @ A @ B ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_205_add__diff__cancel__right,axiom,
% 2.12/1.17      ! [A: nat,C2: nat,B: nat] :
% 2.12/1.17        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 2.12/1.17        = ( minus_minus_nat @ A @ B ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_206_add__diff__cancel__left_H,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n,B: finite1489363574real_n] :
% 2.12/1.17        ( ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ B ) @ A )
% 2.12/1.17        = B ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_207_add__diff__cancel__left_H,axiom,
% 2.12/1.17      ! [A: nat,B: nat] :
% 2.12/1.17        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 2.12/1.17        = B ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_208_add__diff__cancel__left,axiom,
% 2.12/1.17      ! [C2: finite1489363574real_n,A: finite1489363574real_n,B: finite1489363574real_n] :
% 2.12/1.17        ( ( minus_1037315151real_n @ ( plus_p585657087real_n @ C2 @ A ) @ ( plus_p585657087real_n @ C2 @ B ) )
% 2.12/1.17        = ( minus_1037315151real_n @ A @ B ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_209_add__diff__cancel__left,axiom,
% 2.12/1.17      ! [C2: nat,A: nat,B: nat] :
% 2.12/1.17        ( ( minus_minus_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 2.12/1.17        = ( minus_minus_nat @ A @ B ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_210_diff__add__cancel,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n,B: finite1489363574real_n] :
% 2.12/1.17        ( ( plus_p585657087real_n @ ( minus_1037315151real_n @ A @ B ) @ B )
% 2.12/1.17        = A ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_211_add__diff__cancel,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n,B: finite1489363574real_n] :
% 2.12/1.17        ( ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ B ) @ B )
% 2.12/1.17        = A ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_212_main__part,axiom,
% 2.12/1.17      ! [S: set_Fi1058188332real_n,M: sigma_1466784463real_n] :
% 2.12/1.17        ( ( member223413699real_n @ S @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.17       => ( ( comple1390568924real_n @ M @ S )
% 2.12/1.17          = S ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_213_space__restrict__space2,axiom,
% 2.12/1.17      ! [Omega: set_Fi1058188332real_n,M: sigma_1466784463real_n] :
% 2.12/1.17        ( ( member223413699real_n @ Omega @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.17       => ( ( sigma_476185326real_n @ ( sigma_346513458real_n @ M @ Omega ) )
% 2.12/1.17          = Omega ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_214_borel__measurable__diff,axiom,
% 2.12/1.17      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,G: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) )
% 2.12/1.17       => ( ( member1746150050real_n @ G @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) )
% 2.12/1.17         => ( member1746150050real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ ( F @ X ) @ ( G @ X ) )
% 2.12/1.17            @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_215_Compr__image__eq,axiom,
% 2.12/1.17      ! [F: set_Fi1058188332real_n > set_Fi1058188332real_n,A2: set_se2111327970real_n,P: set_Fi1058188332real_n > $o] :
% 2.12/1.17        ( ( collec452821761real_n
% 2.12/1.17          @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.17              ( ( member223413699real_n @ X @ ( image_1661509983real_n @ F @ A2 ) )
% 2.12/1.17              & ( P @ X ) ) )
% 2.12/1.17        = ( image_1661509983real_n @ F
% 2.12/1.17          @ ( collec452821761real_n
% 2.12/1.17            @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.17                ( ( member223413699real_n @ X @ A2 )
% 2.12/1.17                & ( P @ ( F @ X ) ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_216_Compr__image__eq,axiom,
% 2.12/1.17      ! [F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,A2: set_Fi1326602817real_n,P: set_Fi1058188332real_n > $o] :
% 2.12/1.17        ( ( collec452821761real_n
% 2.12/1.17          @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.17              ( ( member223413699real_n @ X @ ( image_128879038real_n @ F @ A2 ) )
% 2.12/1.17              & ( P @ X ) ) )
% 2.12/1.17        = ( image_128879038real_n @ F
% 2.12/1.17          @ ( collec1190264032real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17                ( ( member1746150050real_n @ X @ A2 )
% 2.12/1.17                & ( P @ ( F @ X ) ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_217_Compr__image__eq,axiom,
% 2.12/1.17      ! [F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,A2: set_se2111327970real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
% 2.12/1.17        ( ( collec1190264032real_n
% 2.12/1.17          @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17              ( ( member1746150050real_n @ X @ ( image_352856126real_n @ F @ A2 ) )
% 2.12/1.17              & ( P @ X ) ) )
% 2.12/1.17        = ( image_352856126real_n @ F
% 2.12/1.17          @ ( collec452821761real_n
% 2.12/1.17            @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.17                ( ( member223413699real_n @ X @ A2 )
% 2.12/1.17                & ( P @ ( F @ X ) ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_218_Compr__image__eq,axiom,
% 2.12/1.17      ! [F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
% 2.12/1.17        ( ( collec1190264032real_n
% 2.12/1.17          @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17              ( ( member1746150050real_n @ X @ ( image_1123376925real_n @ F @ A2 ) )
% 2.12/1.17              & ( P @ X ) ) )
% 2.12/1.17        = ( image_1123376925real_n @ F
% 2.12/1.17          @ ( collec1190264032real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17                ( ( member1746150050real_n @ X @ A2 )
% 2.12/1.17                & ( P @ ( F @ X ) ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_219_Compr__image__eq,axiom,
% 2.12/1.17      ! [F: finite1489363574real_n > set_Fi1058188332real_n,A2: set_Fi1058188332real_n,P: set_Fi1058188332real_n > $o] :
% 2.12/1.17        ( ( collec452821761real_n
% 2.12/1.17          @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.17              ( ( member223413699real_n @ X @ ( image_545463721real_n @ F @ A2 ) )
% 2.12/1.17              & ( P @ X ) ) )
% 2.12/1.17        = ( image_545463721real_n @ F
% 2.12/1.17          @ ( collec321817931real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n] :
% 2.12/1.17                ( ( member1352538125real_n @ X @ A2 )
% 2.12/1.17                & ( P @ ( F @ X ) ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_220_Compr__image__eq,axiom,
% 2.12/1.17      ! [F: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
% 2.12/1.17        ( ( collec1190264032real_n
% 2.12/1.17          @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17              ( ( member1746150050real_n @ X @ ( image_437359496real_n @ F @ A2 ) )
% 2.12/1.17              & ( P @ X ) ) )
% 2.12/1.17        = ( image_437359496real_n @ F
% 2.12/1.17          @ ( collec321817931real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n] :
% 2.12/1.17                ( ( member1352538125real_n @ X @ A2 )
% 2.12/1.17                & ( P @ ( F @ X ) ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_221_Compr__image__eq,axiom,
% 2.12/1.17      ! [F: set_Fi1058188332real_n > finite1489363574real_n,A2: set_se2111327970real_n,P: finite1489363574real_n > $o] :
% 2.12/1.17        ( ( collec321817931real_n
% 2.12/1.17          @ ^ [X: finite1489363574real_n] :
% 2.12/1.17              ( ( member1352538125real_n @ X @ ( image_1311908777real_n @ F @ A2 ) )
% 2.12/1.17              & ( P @ X ) ) )
% 2.12/1.17        = ( image_1311908777real_n @ F
% 2.12/1.17          @ ( collec452821761real_n
% 2.12/1.17            @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.17                ( ( member223413699real_n @ X @ A2 )
% 2.12/1.17                & ( P @ ( F @ X ) ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_222_Compr__image__eq,axiom,
% 2.12/1.17      ! [F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,A2: set_Fi1326602817real_n,P: finite1489363574real_n > $o] :
% 2.12/1.17        ( ( collec321817931real_n
% 2.12/1.17          @ ^ [X: finite1489363574real_n] :
% 2.12/1.17              ( ( member1352538125real_n @ X @ ( image_449906696real_n @ F @ A2 ) )
% 2.12/1.17              & ( P @ X ) ) )
% 2.12/1.17        = ( image_449906696real_n @ F
% 2.12/1.17          @ ( collec1190264032real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17                ( ( member1746150050real_n @ X @ A2 )
% 2.12/1.17                & ( P @ ( F @ X ) ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_223_Compr__image__eq,axiom,
% 2.12/1.17      ! [F: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n,P: finite1489363574real_n > $o] :
% 2.12/1.17        ( ( collec321817931real_n
% 2.12/1.17          @ ^ [X: finite1489363574real_n] :
% 2.12/1.17              ( ( member1352538125real_n @ X @ ( image_439535603real_n @ F @ A2 ) )
% 2.12/1.17              & ( P @ X ) ) )
% 2.12/1.17        = ( image_439535603real_n @ F
% 2.12/1.17          @ ( collec321817931real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n] :
% 2.12/1.17                ( ( member1352538125real_n @ X @ A2 )
% 2.12/1.17                & ( P @ ( F @ X ) ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_224_image__image,axiom,
% 2.12/1.17      ! [F: finite1489363574real_n > finite1489363574real_n,G: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( image_439535603real_n @ F @ ( image_439535603real_n @ G @ A2 ) )
% 2.12/1.17        = ( image_439535603real_n
% 2.12/1.17          @ ^ [X: finite1489363574real_n] : ( F @ ( G @ X ) )
% 2.12/1.17          @ A2 ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_225_imageE,axiom,
% 2.12/1.17      ! [B: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( member1352538125real_n @ B @ ( image_439535603real_n @ F @ A2 ) )
% 2.12/1.17       => ~ ! [X3: finite1489363574real_n] :
% 2.12/1.17              ( ( B
% 2.12/1.17                = ( F @ X3 ) )
% 2.12/1.17             => ~ ( member1352538125real_n @ X3 @ A2 ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_226_imageE,axiom,
% 2.12/1.17      ! [B: set_Fi1058188332real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n,A2: set_se2111327970real_n] :
% 2.12/1.17        ( ( member223413699real_n @ B @ ( image_1661509983real_n @ F @ A2 ) )
% 2.12/1.17       => ~ ! [X3: set_Fi1058188332real_n] :
% 2.12/1.17              ( ( B
% 2.12/1.17                = ( F @ X3 ) )
% 2.12/1.17             => ~ ( member223413699real_n @ X3 @ A2 ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_227_imageE,axiom,
% 2.12/1.17      ! [B: set_Fi1058188332real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n,A2: set_Fi1326602817real_n] :
% 2.12/1.17        ( ( member223413699real_n @ B @ ( image_128879038real_n @ F @ A2 ) )
% 2.12/1.17       => ~ ! [X3: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17              ( ( B
% 2.12/1.17                = ( F @ X3 ) )
% 2.12/1.17             => ~ ( member1746150050real_n @ X3 @ A2 ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_228_imageE,axiom,
% 2.12/1.17      ! [B: finite1489363574real_n > finite1489363574real_n,F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n,A2: set_se2111327970real_n] :
% 2.12/1.17        ( ( member1746150050real_n @ B @ ( image_352856126real_n @ F @ A2 ) )
% 2.12/1.17       => ~ ! [X3: set_Fi1058188332real_n] :
% 2.12/1.17              ( ( B
% 2.12/1.17                = ( F @ X3 ) )
% 2.12/1.17             => ~ ( member223413699real_n @ X3 @ A2 ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_229_imageE,axiom,
% 2.12/1.17      ! [B: finite1489363574real_n > finite1489363574real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n] :
% 2.12/1.17        ( ( member1746150050real_n @ B @ ( image_1123376925real_n @ F @ A2 ) )
% 2.12/1.17       => ~ ! [X3: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17              ( ( B
% 2.12/1.17                = ( F @ X3 ) )
% 2.12/1.17             => ~ ( member1746150050real_n @ X3 @ A2 ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_230_diff__right__commute,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n,C2: finite1489363574real_n,B: finite1489363574real_n] :
% 2.12/1.17        ( ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ C2 ) @ B )
% 2.12/1.17        = ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ B ) @ C2 ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_231_diff__right__commute,axiom,
% 2.12/1.17      ! [A: nat,C2: nat,B: nat] :
% 2.12/1.17        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C2 ) @ B )
% 2.12/1.17        = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C2 ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_232_diff__eq__diff__eq,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n,D2: finite1489363574real_n] :
% 2.12/1.17        ( ( ( minus_1037315151real_n @ A @ B )
% 2.12/1.17          = ( minus_1037315151real_n @ C2 @ D2 ) )
% 2.12/1.17       => ( ( A = B )
% 2.12/1.17          = ( C2 = D2 ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_233_rev__image__eqI,axiom,
% 2.12/1.17      ! [X2: finite1489363574real_n,A2: set_Fi1058188332real_n,B: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17        ( ( member1352538125real_n @ X2 @ A2 )
% 2.12/1.17       => ( ( B
% 2.12/1.17            = ( F @ X2 ) )
% 2.12/1.17         => ( member1352538125real_n @ B @ ( image_439535603real_n @ F @ A2 ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_234_rev__image__eqI,axiom,
% 2.12/1.17      ! [X2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B: set_Fi1058188332real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n] :
% 2.12/1.17        ( ( member223413699real_n @ X2 @ A2 )
% 2.12/1.17       => ( ( B
% 2.12/1.17            = ( F @ X2 ) )
% 2.12/1.17         => ( member223413699real_n @ B @ ( image_1661509983real_n @ F @ A2 ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_235_rev__image__eqI,axiom,
% 2.12/1.17      ! [X2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B: finite1489363574real_n > finite1489363574real_n,F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17        ( ( member223413699real_n @ X2 @ A2 )
% 2.12/1.17       => ( ( B
% 2.12/1.17            = ( F @ X2 ) )
% 2.12/1.17         => ( member1746150050real_n @ B @ ( image_352856126real_n @ F @ A2 ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_236_rev__image__eqI,axiom,
% 2.12/1.17      ! [X2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B: set_Fi1058188332real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n] :
% 2.12/1.17        ( ( member1746150050real_n @ X2 @ A2 )
% 2.12/1.17       => ( ( B
% 2.12/1.17            = ( F @ X2 ) )
% 2.12/1.17         => ( member223413699real_n @ B @ ( image_128879038real_n @ F @ A2 ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_237_rev__image__eqI,axiom,
% 2.12/1.17      ! [X2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B: finite1489363574real_n > finite1489363574real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17        ( ( member1746150050real_n @ X2 @ A2 )
% 2.12/1.17       => ( ( B
% 2.12/1.17            = ( F @ X2 ) )
% 2.12/1.17         => ( member1746150050real_n @ B @ ( image_1123376925real_n @ F @ A2 ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_238_ball__imageD,axiom,
% 2.12/1.17      ! [F: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n,P: finite1489363574real_n > $o] :
% 2.12/1.17        ( ! [X3: finite1489363574real_n] :
% 2.12/1.17            ( ( member1352538125real_n @ X3 @ ( image_439535603real_n @ F @ A2 ) )
% 2.12/1.17           => ( P @ X3 ) )
% 2.12/1.17       => ! [X5: finite1489363574real_n] :
% 2.12/1.17            ( ( member1352538125real_n @ X5 @ A2 )
% 2.12/1.17           => ( P @ ( F @ X5 ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_239_image__cong,axiom,
% 2.12/1.17      ! [M: set_Fi1058188332real_n,N: set_Fi1058188332real_n,F: finite1489363574real_n > finite1489363574real_n,G: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17        ( ( M = N )
% 2.12/1.17       => ( ! [X3: finite1489363574real_n] :
% 2.12/1.17              ( ( member1352538125real_n @ X3 @ N )
% 2.12/1.17             => ( ( F @ X3 )
% 2.12/1.17                = ( G @ X3 ) ) )
% 2.12/1.17         => ( ( image_439535603real_n @ F @ M )
% 2.12/1.17            = ( image_439535603real_n @ G @ N ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_240_bex__imageD,axiom,
% 2.12/1.17      ! [F: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n,P: finite1489363574real_n > $o] :
% 2.12/1.17        ( ? [X5: finite1489363574real_n] :
% 2.12/1.17            ( ( member1352538125real_n @ X5 @ ( image_439535603real_n @ F @ A2 ) )
% 2.12/1.17            & ( P @ X5 ) )
% 2.12/1.17       => ? [X3: finite1489363574real_n] :
% 2.12/1.17            ( ( member1352538125real_n @ X3 @ A2 )
% 2.12/1.17            & ( P @ ( F @ X3 ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_241_image__iff,axiom,
% 2.12/1.17      ! [Z: finite1489363574real_n,F: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( member1352538125real_n @ Z @ ( image_439535603real_n @ F @ A2 ) )
% 2.12/1.17        = ( ? [X: finite1489363574real_n] :
% 2.12/1.17              ( ( member1352538125real_n @ X @ A2 )
% 2.12/1.17              & ( Z
% 2.12/1.17                = ( F @ X ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_242_imageI,axiom,
% 2.12/1.17      ! [X2: finite1489363574real_n,A2: set_Fi1058188332real_n,F: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17        ( ( member1352538125real_n @ X2 @ A2 )
% 2.12/1.17       => ( member1352538125real_n @ ( F @ X2 ) @ ( image_439535603real_n @ F @ A2 ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_243_imageI,axiom,
% 2.12/1.17      ! [X2: set_Fi1058188332real_n,A2: set_se2111327970real_n,F: set_Fi1058188332real_n > set_Fi1058188332real_n] :
% 2.12/1.17        ( ( member223413699real_n @ X2 @ A2 )
% 2.12/1.17       => ( member223413699real_n @ ( F @ X2 ) @ ( image_1661509983real_n @ F @ A2 ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_244_imageI,axiom,
% 2.12/1.17      ! [X2: set_Fi1058188332real_n,A2: set_se2111327970real_n,F: set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17        ( ( member223413699real_n @ X2 @ A2 )
% 2.12/1.17       => ( member1746150050real_n @ ( F @ X2 ) @ ( image_352856126real_n @ F @ A2 ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_245_imageI,axiom,
% 2.12/1.17      ! [X2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n] :
% 2.12/1.17        ( ( member1746150050real_n @ X2 @ A2 )
% 2.12/1.17       => ( member223413699real_n @ ( F @ X2 ) @ ( image_128879038real_n @ F @ A2 ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_246_imageI,axiom,
% 2.12/1.17      ! [X2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17        ( ( member1746150050real_n @ X2 @ A2 )
% 2.12/1.17       => ( member1746150050real_n @ ( F @ X2 ) @ ( image_1123376925real_n @ F @ A2 ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_247_borel__measurable__const,axiom,
% 2.12/1.17      ! [C2: finite1489363574real_n,M: sigma_1466784463real_n] :
% 2.12/1.17        ( member1746150050real_n
% 2.12/1.17        @ ^ [X: finite1489363574real_n] : C2
% 2.12/1.17        @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_248_sets__restrict__space__cong,axiom,
% 2.12/1.17      ! [M: sigma_1466784463real_n,N: sigma_1466784463real_n,Omega: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( ( sigma_1235138647real_n @ M )
% 2.12/1.17          = ( sigma_1235138647real_n @ N ) )
% 2.12/1.17       => ( ( sigma_1235138647real_n @ ( sigma_346513458real_n @ M @ Omega ) )
% 2.12/1.17          = ( sigma_1235138647real_n @ ( sigma_346513458real_n @ N @ Omega ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_249_restrict__space__sets__cong,axiom,
% 2.12/1.17      ! [A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n,M: sigma_1466784463real_n,N: sigma_1466784463real_n] :
% 2.12/1.17        ( ( A2 = B2 )
% 2.12/1.17       => ( ( ( sigma_1235138647real_n @ M )
% 2.12/1.17            = ( sigma_1235138647real_n @ N ) )
% 2.12/1.17         => ( ( sigma_1235138647real_n @ ( sigma_346513458real_n @ M @ A2 ) )
% 2.12/1.17            = ( sigma_1235138647real_n @ ( sigma_346513458real_n @ N @ B2 ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_250_measurable__restrict__space1,axiom,
% 2.12/1.17      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,N: sigma_1466784463real_n,Omega: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ N ) )
% 2.12/1.17       => ( member1746150050real_n @ F @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ M @ Omega ) @ N ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_251_add__implies__diff,axiom,
% 2.12/1.17      ! [C2: finite1489363574real_n,B: finite1489363574real_n,A: finite1489363574real_n] :
% 2.12/1.17        ( ( ( plus_p585657087real_n @ C2 @ B )
% 2.12/1.17          = A )
% 2.12/1.17       => ( C2
% 2.12/1.17          = ( minus_1037315151real_n @ A @ B ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_252_add__implies__diff,axiom,
% 2.12/1.17      ! [C2: nat,B: nat,A: nat] :
% 2.12/1.17        ( ( ( plus_plus_nat @ C2 @ B )
% 2.12/1.17          = A )
% 2.12/1.17       => ( C2
% 2.12/1.17          = ( minus_minus_nat @ A @ B ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_253_diff__diff__add,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] :
% 2.12/1.17        ( ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ B ) @ C2 )
% 2.12/1.17        = ( minus_1037315151real_n @ A @ ( plus_p585657087real_n @ B @ C2 ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_254_diff__diff__add,axiom,
% 2.12/1.17      ! [A: nat,B: nat,C2: nat] :
% 2.12/1.17        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C2 )
% 2.12/1.17        = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_255_diff__add__eq__diff__diff__swap,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] :
% 2.12/1.17        ( ( minus_1037315151real_n @ A @ ( plus_p585657087real_n @ B @ C2 ) )
% 2.12/1.17        = ( minus_1037315151real_n @ ( minus_1037315151real_n @ A @ C2 ) @ B ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_256_diff__add__eq,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] :
% 2.12/1.17        ( ( plus_p585657087real_n @ ( minus_1037315151real_n @ A @ B ) @ C2 )
% 2.12/1.17        = ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ C2 ) @ B ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_257_diff__diff__eq2,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] :
% 2.12/1.17        ( ( minus_1037315151real_n @ A @ ( minus_1037315151real_n @ B @ C2 ) )
% 2.12/1.17        = ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ C2 ) @ B ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_258_add__diff__eq,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] :
% 2.12/1.17        ( ( plus_p585657087real_n @ A @ ( minus_1037315151real_n @ B @ C2 ) )
% 2.12/1.17        = ( minus_1037315151real_n @ ( plus_p585657087real_n @ A @ B ) @ C2 ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_259_eq__diff__eq,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n,C2: finite1489363574real_n,B: finite1489363574real_n] :
% 2.12/1.17        ( ( A
% 2.12/1.17          = ( minus_1037315151real_n @ C2 @ B ) )
% 2.12/1.17        = ( ( plus_p585657087real_n @ A @ B )
% 2.12/1.17          = C2 ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_260_diff__eq__eq,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n,B: finite1489363574real_n,C2: finite1489363574real_n] :
% 2.12/1.17        ( ( ( minus_1037315151real_n @ A @ B )
% 2.12/1.17          = C2 )
% 2.12/1.17        = ( A
% 2.12/1.17          = ( plus_p585657087real_n @ C2 @ B ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_261_group__cancel_Osub1,axiom,
% 2.12/1.17      ! [A2: finite1489363574real_n,K: finite1489363574real_n,A: finite1489363574real_n,B: finite1489363574real_n] :
% 2.12/1.17        ( ( A2
% 2.12/1.17          = ( plus_p585657087real_n @ K @ A ) )
% 2.12/1.17       => ( ( minus_1037315151real_n @ A2 @ B )
% 2.12/1.17          = ( plus_p585657087real_n @ K @ ( minus_1037315151real_n @ A @ B ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_262_sets__vimage__algebra__cong,axiom,
% 2.12/1.17      ! [M: sigma_1466784463real_n,N: sigma_1466784463real_n,X4: set_Fi1058188332real_n,F: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17        ( ( ( sigma_1235138647real_n @ M )
% 2.12/1.17          = ( sigma_1235138647real_n @ N ) )
% 2.12/1.17       => ( ( sigma_1235138647real_n @ ( sigma_821351682real_n @ X4 @ F @ M ) )
% 2.12/1.17          = ( sigma_1235138647real_n @ ( sigma_821351682real_n @ X4 @ F @ N ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_263_vimage__algebra__cong,axiom,
% 2.12/1.17      ! [X4: set_se2111327970real_n,Y: set_se2111327970real_n,F: set_Fi1058188332real_n > finite1489363574real_n,G: set_Fi1058188332real_n > finite1489363574real_n,M: sigma_1466784463real_n,N: sigma_1466784463real_n] :
% 2.12/1.17        ( ( X4 = Y )
% 2.12/1.17       => ( ! [X3: set_Fi1058188332real_n] :
% 2.12/1.17              ( ( member223413699real_n @ X3 @ Y )
% 2.12/1.17             => ( ( F @ X3 )
% 2.12/1.17                = ( G @ X3 ) ) )
% 2.12/1.17         => ( ( ( sigma_1235138647real_n @ M )
% 2.12/1.17              = ( sigma_1235138647real_n @ N ) )
% 2.12/1.17           => ( ( sigma_1384150200real_n @ X4 @ F @ M )
% 2.12/1.17              = ( sigma_1384150200real_n @ Y @ G @ N ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_264_vimage__algebra__cong,axiom,
% 2.12/1.17      ! [X4: set_Fi1326602817real_n,Y: set_Fi1326602817real_n,F: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,G: ( finite1489363574real_n > finite1489363574real_n ) > finite1489363574real_n,M: sigma_1466784463real_n,N: sigma_1466784463real_n] :
% 2.12/1.17        ( ( X4 = Y )
% 2.12/1.17       => ( ! [X3: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17              ( ( member1746150050real_n @ X3 @ Y )
% 2.12/1.17             => ( ( F @ X3 )
% 2.12/1.17                = ( G @ X3 ) ) )
% 2.12/1.17         => ( ( ( sigma_1235138647real_n @ M )
% 2.12/1.17              = ( sigma_1235138647real_n @ N ) )
% 2.12/1.17           => ( ( sigma_136294295real_n @ X4 @ F @ M )
% 2.12/1.17              = ( sigma_136294295real_n @ Y @ G @ N ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_265_borel__measurable__const__add,axiom,
% 2.12/1.17      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,A: finite1489363574real_n] :
% 2.12/1.17        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) )
% 2.12/1.17       => ( member1746150050real_n
% 2.12/1.17          @ ^ [X: finite1489363574real_n] : ( plus_p585657087real_n @ A @ ( F @ X ) )
% 2.12/1.17          @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_266_borel__measurable__add,axiom,
% 2.12/1.17      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,G: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) )
% 2.12/1.17       => ( ( member1746150050real_n @ G @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) )
% 2.12/1.17         => ( member1746150050real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n] : ( plus_p585657087real_n @ ( F @ X ) @ ( G @ X ) )
% 2.12/1.17            @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_267_sets__restrict__restrict__space,axiom,
% 2.12/1.17      ! [M: sigma_1466784463real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( sigma_1235138647real_n @ ( sigma_346513458real_n @ ( sigma_346513458real_n @ M @ A2 ) @ B2 ) )
% 2.12/1.17        = ( sigma_1235138647real_n @ ( sigma_346513458real_n @ M @ ( inf_in1974387902real_n @ A2 @ B2 ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_268_space__restrict__space,axiom,
% 2.12/1.17      ! [M: sigma_1466784463real_n,Omega: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( sigma_476185326real_n @ ( sigma_346513458real_n @ M @ Omega ) )
% 2.12/1.17        = ( inf_in1974387902real_n @ Omega @ ( sigma_476185326real_n @ M ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_269_measurable__sets__borel,axiom,
% 2.12/1.17      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,A2: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ borel_676189912real_n @ M ) )
% 2.12/1.17       => ( ( member223413699real_n @ A2 @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.17         => ( member223413699real_n @ ( vimage1233683625real_n @ F @ A2 ) @ ( sigma_1235138647real_n @ borel_676189912real_n ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_270_sets__Collect__restrict__space__iff,axiom,
% 2.12/1.17      ! [S: set_se2111327970real_n,M: sigma_1422848389real_n,P: set_Fi1058188332real_n > $o] :
% 2.12/1.17        ( ( member1475136633real_n @ S @ ( sigma_433815053real_n @ M ) )
% 2.12/1.17       => ( ( member1475136633real_n
% 2.12/1.17            @ ( collec452821761real_n
% 2.12/1.17              @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.17                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ ( sigma_993999336real_n @ M @ S ) ) )
% 2.12/1.17                  & ( P @ X ) ) )
% 2.12/1.17            @ ( sigma_433815053real_n @ ( sigma_993999336real_n @ M @ S ) ) )
% 2.12/1.17          = ( member1475136633real_n
% 2.12/1.17            @ ( collec452821761real_n
% 2.12/1.17              @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.17                  ( ( member223413699real_n @ X @ ( sigma_607186084real_n @ M ) )
% 2.12/1.17                  & ( member223413699real_n @ X @ S )
% 2.12/1.17                  & ( P @ X ) ) )
% 2.12/1.17            @ ( sigma_433815053real_n @ M ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_271_sets__Collect__restrict__space__iff,axiom,
% 2.12/1.17      ! [S: set_Fi1326602817real_n,M: sigma_107786596real_n,P: ( finite1489363574real_n > finite1489363574real_n ) > $o] :
% 2.12/1.17        ( ( member2104752728real_n @ S @ ( sigma_522684908real_n @ M ) )
% 2.12/1.17       => ( ( member2104752728real_n
% 2.12/1.17            @ ( collec1190264032real_n
% 2.12/1.17              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ ( sigma_1052429895real_n @ M @ S ) ) )
% 2.12/1.17                  & ( P @ X ) ) )
% 2.12/1.17            @ ( sigma_522684908real_n @ ( sigma_1052429895real_n @ M @ S ) ) )
% 2.12/1.17          = ( member2104752728real_n
% 2.12/1.17            @ ( collec1190264032real_n
% 2.12/1.17              @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17                  ( ( member1746150050real_n @ X @ ( sigma_1483971331real_n @ M ) )
% 2.12/1.17                  & ( member1746150050real_n @ X @ S )
% 2.12/1.17                  & ( P @ X ) ) )
% 2.12/1.17            @ ( sigma_522684908real_n @ M ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_272_sets__Collect__restrict__space__iff,axiom,
% 2.12/1.17      ! [S: set_Fi1058188332real_n,M: sigma_1466784463real_n,P: finite1489363574real_n > $o] :
% 2.12/1.17        ( ( member223413699real_n @ S @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.17       => ( ( member223413699real_n
% 2.12/1.17            @ ( collec321817931real_n
% 2.12/1.17              @ ^ [X: finite1489363574real_n] :
% 2.12/1.17                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ ( sigma_346513458real_n @ M @ S ) ) )
% 2.12/1.17                  & ( P @ X ) ) )
% 2.12/1.17            @ ( sigma_1235138647real_n @ ( sigma_346513458real_n @ M @ S ) ) )
% 2.12/1.17          = ( member223413699real_n
% 2.12/1.17            @ ( collec321817931real_n
% 2.12/1.17              @ ^ [X: finite1489363574real_n] :
% 2.12/1.17                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 2.12/1.17                  & ( member1352538125real_n @ X @ S )
% 2.12/1.17                  & ( P @ X ) ) )
% 2.12/1.17            @ ( sigma_1235138647real_n @ M ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_273_measurable__equality__set,axiom,
% 2.12/1.17      ! [F: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n,G: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) )
% 2.12/1.17       => ( ( member1746150050real_n @ G @ ( sigma_439801790real_n @ M @ borel_676189912real_n ) )
% 2.12/1.17         => ( member223413699real_n
% 2.12/1.17            @ ( collec321817931real_n
% 2.12/1.17              @ ^ [X: finite1489363574real_n] :
% 2.12/1.17                  ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 2.12/1.17                  & ( ( F @ X )
% 2.12/1.17                    = ( G @ X ) ) ) )
% 2.12/1.17            @ ( sigma_1235138647real_n @ M ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_274_measurable__If__restrict__space__iff,axiom,
% 2.12/1.17      ! [M: sigma_1466784463real_n,P: finite1489363574real_n > $o,F: finite1489363574real_n > finite1489363574real_n,G: finite1489363574real_n > finite1489363574real_n,N: sigma_1466784463real_n] :
% 2.12/1.17        ( ( member223413699real_n
% 2.12/1.17          @ ( collec321817931real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n] :
% 2.12/1.17                ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ M ) )
% 2.12/1.17                & ( P @ X ) ) )
% 2.12/1.17          @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.17       => ( ( member1746150050real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n] : ( if_Fin127821360real_n @ ( P @ X ) @ ( F @ X ) @ ( G @ X ) )
% 2.12/1.17            @ ( sigma_439801790real_n @ M @ N ) )
% 2.12/1.17          = ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ M @ ( collec321817931real_n @ P ) ) @ N ) )
% 2.12/1.17            & ( member1746150050real_n @ G
% 2.12/1.17              @ ( sigma_439801790real_n
% 2.12/1.17                @ ( sigma_346513458real_n @ M
% 2.12/1.17                  @ ( collec321817931real_n
% 2.12/1.17                    @ ^ [X: finite1489363574real_n] :
% 2.12/1.17                        ~ ( P @ X ) ) )
% 2.12/1.17                @ N ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_275_space__lebesgue__on,axiom,
% 2.12/1.17      ! [S: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( sigma_476185326real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ S ) )
% 2.12/1.17        = S ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_276_sets__lebesgue__on__refl,axiom,
% 2.12/1.17      ! [S: set_Fi1058188332real_n] : ( member223413699real_n @ S @ ( sigma_1235138647real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ S ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_277_space__lborel,axiom,
% 2.12/1.17      ( ( sigma_476185326real_n @ lebesg260170249real_n )
% 2.12/1.17      = ( sigma_476185326real_n @ borel_676189912real_n ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_278_measurable__lborel1,axiom,
% 2.12/1.17      ! [M: sigma_1466784463real_n] :
% 2.12/1.17        ( ( sigma_439801790real_n @ M @ lebesg260170249real_n )
% 2.12/1.17        = ( sigma_439801790real_n @ M @ borel_676189912real_n ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_279_measurable__lborel2,axiom,
% 2.12/1.17      ! [M: sigma_1466784463real_n] :
% 2.12/1.17        ( ( sigma_439801790real_n @ lebesg260170249real_n @ M )
% 2.12/1.17        = ( sigma_439801790real_n @ borel_676189912real_n @ M ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_280_sets_ODiff,axiom,
% 2.12/1.17      ! [A: set_Fi1058188332real_n,M: sigma_1466784463real_n,B: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.17       => ( ( member223413699real_n @ B @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.17         => ( member223413699real_n @ ( minus_1686442501real_n @ A @ B ) @ ( sigma_1235138647real_n @ M ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_281_sets_Ocompl__sets,axiom,
% 2.12/1.17      ! [A: set_Fi1058188332real_n,M: sigma_1466784463real_n] :
% 2.12/1.17        ( ( member223413699real_n @ A @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.17       => ( member223413699real_n @ ( minus_1686442501real_n @ ( sigma_476185326real_n @ M ) @ A ) @ ( sigma_1235138647real_n @ M ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_282_sets__lborel,axiom,
% 2.12/1.17      ( ( sigma_1235138647real_n @ lebesg260170249real_n )
% 2.12/1.17      = ( sigma_1235138647real_n @ borel_676189912real_n ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_283_Int__Diff,axiom,
% 2.12/1.17      ! [A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( minus_1686442501real_n @ ( inf_in1974387902real_n @ A2 @ B2 ) @ C )
% 2.12/1.17        = ( inf_in1974387902real_n @ A2 @ ( minus_1686442501real_n @ B2 @ C ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_284_Diff__Int2,axiom,
% 2.12/1.17      ! [A2: set_Fi1058188332real_n,C: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( minus_1686442501real_n @ ( inf_in1974387902real_n @ A2 @ C ) @ ( inf_in1974387902real_n @ B2 @ C ) )
% 2.12/1.17        = ( minus_1686442501real_n @ ( inf_in1974387902real_n @ A2 @ C ) @ B2 ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_285_Diff__Diff__Int,axiom,
% 2.12/1.17      ! [A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( minus_1686442501real_n @ A2 @ ( minus_1686442501real_n @ A2 @ B2 ) )
% 2.12/1.17        = ( inf_in1974387902real_n @ A2 @ B2 ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_286_Diff__Int__distrib,axiom,
% 2.12/1.17      ! [C: set_Fi1058188332real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( inf_in1974387902real_n @ C @ ( minus_1686442501real_n @ A2 @ B2 ) )
% 2.12/1.17        = ( minus_1686442501real_n @ ( inf_in1974387902real_n @ C @ A2 ) @ ( inf_in1974387902real_n @ C @ B2 ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_287_Diff__Int__distrib2,axiom,
% 2.12/1.17      ! [A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n,C: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( inf_in1974387902real_n @ ( minus_1686442501real_n @ A2 @ B2 ) @ C )
% 2.12/1.17        = ( minus_1686442501real_n @ ( inf_in1974387902real_n @ A2 @ C ) @ ( inf_in1974387902real_n @ B2 @ C ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_288_vimage__Diff,axiom,
% 2.12/1.17      ! [F: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( vimage1233683625real_n @ F @ ( minus_1686442501real_n @ A2 @ B2 ) )
% 2.12/1.17        = ( minus_1686442501real_n @ ( vimage1233683625real_n @ F @ A2 ) @ ( vimage1233683625real_n @ F @ B2 ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_289_sets__restrict__space,axiom,
% 2.12/1.17      ! [M: sigma_1466784463real_n,Omega: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( sigma_1235138647real_n @ ( sigma_346513458real_n @ M @ Omega ) )
% 2.12/1.17        = ( image_1661509983real_n @ ( inf_in1974387902real_n @ Omega ) @ ( sigma_1235138647real_n @ M ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_290_lborelD,axiom,
% 2.12/1.17      ! [A2: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( member223413699real_n @ A2 @ ( sigma_1235138647real_n @ borel_676189912real_n ) )
% 2.12/1.17       => ( member223413699real_n @ A2 @ ( sigma_1235138647real_n @ lebesg260170249real_n ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_291_measurable__lebesgue__cong,axiom,
% 2.12/1.17      ! [S: set_Fi1058188332real_n,F: finite1489363574real_n > finite1489363574real_n,G: finite1489363574real_n > finite1489363574real_n,M: sigma_1466784463real_n] :
% 2.12/1.17        ( ! [X3: finite1489363574real_n] :
% 2.12/1.17            ( ( member1352538125real_n @ X3 @ S )
% 2.12/1.17           => ( ( F @ X3 )
% 2.12/1.17              = ( G @ X3 ) ) )
% 2.12/1.17       => ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ S ) @ M ) )
% 2.12/1.17          = ( member1746150050real_n @ G @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ S ) @ M ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_292_lborelD__Collect,axiom,
% 2.12/1.17      ! [P: finite1489363574real_n > $o] :
% 2.12/1.17        ( ( member223413699real_n
% 2.12/1.17          @ ( collec321817931real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n] :
% 2.12/1.17                ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ borel_676189912real_n ) )
% 2.12/1.17                & ( P @ X ) ) )
% 2.12/1.17          @ ( sigma_1235138647real_n @ borel_676189912real_n ) )
% 2.12/1.17       => ( member223413699real_n
% 2.12/1.17          @ ( collec321817931real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n] :
% 2.12/1.17                ( ( member1352538125real_n @ X @ ( sigma_476185326real_n @ lebesg260170249real_n ) )
% 2.12/1.17                & ( P @ X ) ) )
% 2.12/1.17          @ ( sigma_1235138647real_n @ lebesg260170249real_n ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_293_lebesgue__sets__translation,axiom,
% 2.12/1.17      ! [S: set_Fi1058188332real_n,A: finite1489363574real_n] :
% 2.12/1.17        ( ( member223413699real_n @ S @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
% 2.12/1.17       => ( member223413699real_n @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ S ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_294_lebesgue__measurable__vimage__borel,axiom,
% 2.12/1.17      ! [F: finite1489363574real_n > finite1489363574real_n,T: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ borel_676189912real_n ) )
% 2.12/1.17       => ( ( member223413699real_n @ T @ ( sigma_1235138647real_n @ borel_676189912real_n ) )
% 2.12/1.17         => ( member223413699real_n
% 2.12/1.17            @ ( collec321817931real_n
% 2.12/1.17              @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ ( F @ X ) @ T ) )
% 2.12/1.17            @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_295_borel__measurable__lebesgue__preimage__borel,axiom,
% 2.12/1.17      ! [F: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ borel_676189912real_n ) )
% 2.12/1.17        = ( ! [T2: set_Fi1058188332real_n] :
% 2.12/1.17              ( ( member223413699real_n @ T2 @ ( sigma_1235138647real_n @ borel_676189912real_n ) )
% 2.12/1.17             => ( member223413699real_n
% 2.12/1.17                @ ( collec321817931real_n
% 2.12/1.17                  @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ ( F @ X ) @ T2 ) )
% 2.12/1.17                @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_296_borel__measurable__vimage__borel,axiom,
% 2.12/1.17      ! [F: finite1489363574real_n > finite1489363574real_n,S: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( member1746150050real_n @ F @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ S ) @ borel_676189912real_n ) )
% 2.12/1.17        = ( ! [T2: set_Fi1058188332real_n] :
% 2.12/1.17              ( ( member223413699real_n @ T2 @ ( sigma_1235138647real_n @ borel_676189912real_n ) )
% 2.12/1.17             => ( member223413699real_n
% 2.12/1.17                @ ( collec321817931real_n
% 2.12/1.17                  @ ^ [X: finite1489363574real_n] :
% 2.12/1.17                      ( ( member1352538125real_n @ X @ S )
% 2.12/1.17                      & ( member1352538125real_n @ ( F @ X ) @ T2 ) ) )
% 2.12/1.17                @ ( sigma_1235138647real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ S ) ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_297_restrict__space__eq__vimage__algebra_H,axiom,
% 2.12/1.17      ! [M: sigma_1466784463real_n,Omega: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( sigma_1235138647real_n @ ( sigma_346513458real_n @ M @ Omega ) )
% 2.12/1.17        = ( sigma_1235138647real_n
% 2.12/1.17          @ ( sigma_821351682real_n @ ( inf_in1974387902real_n @ Omega @ ( sigma_476185326real_n @ M ) )
% 2.12/1.17            @ ^ [X: finite1489363574real_n] : X
% 2.12/1.17            @ M ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_298_restrict__restrict__space,axiom,
% 2.12/1.17      ! [A2: set_Fi1058188332real_n,M: sigma_1466784463real_n,B2: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( member223413699real_n @ ( inf_in1974387902real_n @ A2 @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.17       => ( ( member223413699real_n @ ( inf_in1974387902real_n @ B2 @ ( sigma_476185326real_n @ M ) ) @ ( sigma_1235138647real_n @ M ) )
% 2.12/1.17         => ( ( sigma_346513458real_n @ ( sigma_346513458real_n @ M @ A2 ) @ B2 )
% 2.12/1.17            = ( sigma_346513458real_n @ M @ ( inf_in1974387902real_n @ A2 @ B2 ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_299_is__borel__def,axiom,
% 2.12/1.17      ( borel_1962407338real_n
% 2.12/1.17      = ( ^ [F2: finite1489363574real_n > finite1489363574real_n,M3: sigma_1466784463real_n] : ( member1746150050real_n @ F2 @ ( sigma_439801790real_n @ M3 @ borel_676189912real_n ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_300_Diff__iff,axiom,
% 2.12/1.17      ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] :
% 2.12/1.17        ( ( member223413699real_n @ C2 @ ( minus_1698615483real_n @ A2 @ B2 ) )
% 2.12/1.17        = ( ( member223413699real_n @ C2 @ A2 )
% 2.12/1.17          & ~ ( member223413699real_n @ C2 @ B2 ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_301_Diff__iff,axiom,
% 2.12/1.17      ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] :
% 2.12/1.17        ( ( member1746150050real_n @ C2 @ ( minus_725016986real_n @ A2 @ B2 ) )
% 2.12/1.17        = ( ( member1746150050real_n @ C2 @ A2 )
% 2.12/1.17          & ~ ( member1746150050real_n @ C2 @ B2 ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_302_DiffI,axiom,
% 2.12/1.17      ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] :
% 2.12/1.17        ( ( member223413699real_n @ C2 @ A2 )
% 2.12/1.17       => ( ~ ( member223413699real_n @ C2 @ B2 )
% 2.12/1.17         => ( member223413699real_n @ C2 @ ( minus_1698615483real_n @ A2 @ B2 ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_303_DiffI,axiom,
% 2.12/1.17      ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] :
% 2.12/1.17        ( ( member1746150050real_n @ C2 @ A2 )
% 2.12/1.17       => ( ~ ( member1746150050real_n @ C2 @ B2 )
% 2.12/1.17         => ( member1746150050real_n @ C2 @ ( minus_725016986real_n @ A2 @ B2 ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_304_set__diff__eq,axiom,
% 2.12/1.17      ( minus_1698615483real_n
% 2.12/1.17      = ( ^ [A4: set_se2111327970real_n,B3: set_se2111327970real_n] :
% 2.12/1.17            ( collec452821761real_n
% 2.12/1.17            @ ^ [X: set_Fi1058188332real_n] :
% 2.12/1.17                ( ( member223413699real_n @ X @ A4 )
% 2.12/1.17                & ~ ( member223413699real_n @ X @ B3 ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_305_set__diff__eq,axiom,
% 2.12/1.17      ( minus_725016986real_n
% 2.12/1.17      = ( ^ [A4: set_Fi1326602817real_n,B3: set_Fi1326602817real_n] :
% 2.12/1.17            ( collec1190264032real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17                ( ( member1746150050real_n @ X @ A4 )
% 2.12/1.17                & ~ ( member1746150050real_n @ X @ B3 ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_306_set__diff__eq,axiom,
% 2.12/1.17      ( minus_1686442501real_n
% 2.12/1.17      = ( ^ [A4: set_Fi1058188332real_n,B3: set_Fi1058188332real_n] :
% 2.12/1.17            ( collec321817931real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n] :
% 2.12/1.17                ( ( member1352538125real_n @ X @ A4 )
% 2.12/1.17                & ~ ( member1352538125real_n @ X @ B3 ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_307_minus__set__def,axiom,
% 2.12/1.17      ( minus_1698615483real_n
% 2.12/1.17      = ( ^ [A4: set_se2111327970real_n,B3: set_se2111327970real_n] :
% 2.12/1.17            ( collec452821761real_n
% 2.12/1.17            @ ( minus_1832115082al_n_o
% 2.12/1.17              @ ^ [X: set_Fi1058188332real_n] : ( member223413699real_n @ X @ A4 )
% 2.12/1.17              @ ^ [X: set_Fi1058188332real_n] : ( member223413699real_n @ X @ B3 ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_308_minus__set__def,axiom,
% 2.12/1.17      ( minus_725016986real_n
% 2.12/1.17      = ( ^ [A4: set_Fi1326602817real_n,B3: set_Fi1326602817real_n] :
% 2.12/1.17            ( collec1190264032real_n
% 2.12/1.17            @ ( minus_391085931al_n_o
% 2.12/1.17              @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ X @ A4 )
% 2.12/1.17              @ ^ [X: finite1489363574real_n > finite1489363574real_n] : ( member1746150050real_n @ X @ B3 ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_309_minus__set__def,axiom,
% 2.12/1.17      ( minus_1686442501real_n
% 2.12/1.17      = ( ^ [A4: set_Fi1058188332real_n,B3: set_Fi1058188332real_n] :
% 2.12/1.17            ( collec321817931real_n
% 2.12/1.17            @ ( minus_455231168al_n_o
% 2.12/1.17              @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ X @ A4 )
% 2.12/1.17              @ ^ [X: finite1489363574real_n] : ( member1352538125real_n @ X @ B3 ) ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_310_DiffD2,axiom,
% 2.12/1.17      ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] :
% 2.12/1.17        ( ( member223413699real_n @ C2 @ ( minus_1698615483real_n @ A2 @ B2 ) )
% 2.12/1.17       => ~ ( member223413699real_n @ C2 @ B2 ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_311_DiffD2,axiom,
% 2.12/1.17      ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] :
% 2.12/1.17        ( ( member1746150050real_n @ C2 @ ( minus_725016986real_n @ A2 @ B2 ) )
% 2.12/1.17       => ~ ( member1746150050real_n @ C2 @ B2 ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_312_DiffD1,axiom,
% 2.12/1.17      ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] :
% 2.12/1.17        ( ( member223413699real_n @ C2 @ ( minus_1698615483real_n @ A2 @ B2 ) )
% 2.12/1.17       => ( member223413699real_n @ C2 @ A2 ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_313_DiffD1,axiom,
% 2.12/1.17      ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] :
% 2.12/1.17        ( ( member1746150050real_n @ C2 @ ( minus_725016986real_n @ A2 @ B2 ) )
% 2.12/1.17       => ( member1746150050real_n @ C2 @ A2 ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_314_DiffE,axiom,
% 2.12/1.17      ! [C2: set_Fi1058188332real_n,A2: set_se2111327970real_n,B2: set_se2111327970real_n] :
% 2.12/1.17        ( ( member223413699real_n @ C2 @ ( minus_1698615483real_n @ A2 @ B2 ) )
% 2.12/1.17       => ~ ( ( member223413699real_n @ C2 @ A2 )
% 2.12/1.17           => ( member223413699real_n @ C2 @ B2 ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_315_DiffE,axiom,
% 2.12/1.17      ! [C2: finite1489363574real_n > finite1489363574real_n,A2: set_Fi1326602817real_n,B2: set_Fi1326602817real_n] :
% 2.12/1.17        ( ( member1746150050real_n @ C2 @ ( minus_725016986real_n @ A2 @ B2 ) )
% 2.12/1.17       => ~ ( ( member1746150050real_n @ C2 @ A2 )
% 2.12/1.17           => ( member1746150050real_n @ C2 @ B2 ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_316_translation__subtract__diff,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n,S2: set_Fi1058188332real_n,T3: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( image_439535603real_n
% 2.12/1.17          @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ X @ A )
% 2.12/1.17          @ ( minus_1686442501real_n @ S2 @ T3 ) )
% 2.12/1.17        = ( minus_1686442501real_n
% 2.12/1.17          @ ( image_439535603real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ X @ A )
% 2.12/1.17            @ S2 )
% 2.12/1.17          @ ( image_439535603real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ X @ A )
% 2.12/1.17            @ T3 ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_317_translation__subtract__Int,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n,S2: set_Fi1058188332real_n,T3: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( image_439535603real_n
% 2.12/1.17          @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ X @ A )
% 2.12/1.17          @ ( inf_in1974387902real_n @ S2 @ T3 ) )
% 2.12/1.17        = ( inf_in1974387902real_n
% 2.12/1.17          @ ( image_439535603real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ X @ A )
% 2.12/1.17            @ S2 )
% 2.12/1.17          @ ( image_439535603real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n] : ( minus_1037315151real_n @ X @ A )
% 2.12/1.17            @ T3 ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_318_translation__diff,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n,S2: set_Fi1058188332real_n,T3: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ ( minus_1686442501real_n @ S2 @ T3 ) )
% 2.12/1.17        = ( minus_1686442501real_n @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ S2 ) @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ T3 ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_319_translation__Int,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n,S2: set_Fi1058188332real_n,T3: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ ( inf_in1974387902real_n @ S2 @ T3 ) )
% 2.12/1.17        = ( inf_in1974387902real_n @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ S2 ) @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ T3 ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_320_translation__invert,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n,A2: set_Fi1058188332real_n,B2: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ A2 )
% 2.12/1.17          = ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ B2 ) )
% 2.12/1.17       => ( A2 = B2 ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_321_translation__assoc,axiom,
% 2.12/1.17      ! [B: finite1489363574real_n,A: finite1489363574real_n,S: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( image_439535603real_n @ ( plus_p585657087real_n @ B ) @ ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ S ) )
% 2.12/1.17        = ( image_439535603real_n @ ( plus_p585657087real_n @ ( plus_p585657087real_n @ A @ B ) ) @ S ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_322_affine__parallel__expl__aux,axiom,
% 2.12/1.17      ! [S: set_Fi1058188332real_n,A: finite1489363574real_n,T: set_Fi1058188332real_n] :
% 2.12/1.17        ( ! [X3: finite1489363574real_n] :
% 2.12/1.17            ( ( member1352538125real_n @ X3 @ S )
% 2.12/1.17            = ( member1352538125real_n @ ( plus_p585657087real_n @ A @ X3 ) @ T ) )
% 2.12/1.17       => ( T
% 2.12/1.17          = ( image_439535603real_n @ ( plus_p585657087real_n @ A ) @ S ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_323_borel__measurable__if,axiom,
% 2.12/1.17      ! [S: set_Fi1058188332real_n,F: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17        ( ( member223413699real_n @ S @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
% 2.12/1.17       => ( ( member1746150050real_n
% 2.12/1.17            @ ^ [X: finite1489363574real_n] : ( if_Fin127821360real_n @ ( member1352538125real_n @ X @ S ) @ ( F @ X ) @ zero_z200130687real_n )
% 2.12/1.17            @ ( sigma_439801790real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ borel_676189912real_n ) )
% 2.12/1.17          = ( member1746150050real_n @ F @ ( sigma_439801790real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ S ) @ borel_676189912real_n ) ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_324_add_Oleft__neutral,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n] :
% 2.12/1.17        ( ( plus_p585657087real_n @ zero_z200130687real_n @ A )
% 2.12/1.17        = A ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_325_add_Oleft__neutral,axiom,
% 2.12/1.17      ! [A: nat] :
% 2.12/1.17        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 2.12/1.17        = A ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_326_add_Oright__neutral,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n] :
% 2.12/1.17        ( ( plus_p585657087real_n @ A @ zero_z200130687real_n )
% 2.12/1.17        = A ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_327_add_Oright__neutral,axiom,
% 2.12/1.17      ! [A: nat] :
% 2.12/1.17        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 2.12/1.17        = A ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_328_add__cancel__left__left,axiom,
% 2.12/1.17      ! [B: finite1489363574real_n,A: finite1489363574real_n] :
% 2.12/1.17        ( ( ( plus_p585657087real_n @ B @ A )
% 2.12/1.17          = A )
% 2.12/1.17        = ( B = zero_z200130687real_n ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_329_add__cancel__left__left,axiom,
% 2.12/1.17      ! [B: nat,A: nat] :
% 2.12/1.17        ( ( ( plus_plus_nat @ B @ A )
% 2.12/1.17          = A )
% 2.12/1.17        = ( B = zero_zero_nat ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_330_add__cancel__left__right,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n,B: finite1489363574real_n] :
% 2.12/1.17        ( ( ( plus_p585657087real_n @ A @ B )
% 2.12/1.17          = A )
% 2.12/1.17        = ( B = zero_z200130687real_n ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_331_add__cancel__left__right,axiom,
% 2.12/1.17      ! [A: nat,B: nat] :
% 2.12/1.17        ( ( ( plus_plus_nat @ A @ B )
% 2.12/1.17          = A )
% 2.12/1.17        = ( B = zero_zero_nat ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_332_add__cancel__right__left,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n,B: finite1489363574real_n] :
% 2.12/1.17        ( ( A
% 2.12/1.17          = ( plus_p585657087real_n @ B @ A ) )
% 2.12/1.17        = ( B = zero_z200130687real_n ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_333_add__cancel__right__left,axiom,
% 2.12/1.17      ! [A: nat,B: nat] :
% 2.12/1.17        ( ( A
% 2.12/1.17          = ( plus_plus_nat @ B @ A ) )
% 2.12/1.17        = ( B = zero_zero_nat ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_334_add__cancel__right__right,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n,B: finite1489363574real_n] :
% 2.12/1.17        ( ( A
% 2.12/1.17          = ( plus_p585657087real_n @ A @ B ) )
% 2.12/1.17        = ( B = zero_z200130687real_n ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_335_add__cancel__right__right,axiom,
% 2.12/1.17      ! [A: nat,B: nat] :
% 2.12/1.17        ( ( A
% 2.12/1.17          = ( plus_plus_nat @ A @ B ) )
% 2.12/1.17        = ( B = zero_zero_nat ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_336_add__eq__0__iff__both__eq__0,axiom,
% 2.12/1.17      ! [X2: nat,Y3: nat] :
% 2.12/1.17        ( ( ( plus_plus_nat @ X2 @ Y3 )
% 2.12/1.17          = zero_zero_nat )
% 2.12/1.17        = ( ( X2 = zero_zero_nat )
% 2.12/1.17          & ( Y3 = zero_zero_nat ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_337_zero__eq__add__iff__both__eq__0,axiom,
% 2.12/1.17      ! [X2: nat,Y3: nat] :
% 2.12/1.17        ( ( zero_zero_nat
% 2.12/1.17          = ( plus_plus_nat @ X2 @ Y3 ) )
% 2.12/1.17        = ( ( X2 = zero_zero_nat )
% 2.12/1.17          & ( Y3 = zero_zero_nat ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_338_diff__self,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n] :
% 2.12/1.17        ( ( minus_1037315151real_n @ A @ A )
% 2.12/1.17        = zero_z200130687real_n ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_339_diff__0__right,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n] :
% 2.12/1.17        ( ( minus_1037315151real_n @ A @ zero_z200130687real_n )
% 2.12/1.17        = A ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_340_zero__diff,axiom,
% 2.12/1.17      ! [A: nat] :
% 2.12/1.17        ( ( minus_minus_nat @ zero_zero_nat @ A )
% 2.12/1.17        = zero_zero_nat ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_341_diff__zero,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n] :
% 2.12/1.17        ( ( minus_1037315151real_n @ A @ zero_z200130687real_n )
% 2.12/1.17        = A ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_342_diff__zero,axiom,
% 2.12/1.17      ! [A: nat] :
% 2.12/1.17        ( ( minus_minus_nat @ A @ zero_zero_nat )
% 2.12/1.17        = A ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_343_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 2.12/1.17      ! [A: finite1489363574real_n] :
% 2.12/1.17        ( ( minus_1037315151real_n @ A @ A )
% 2.12/1.17        = zero_z200130687real_n ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_344_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 2.12/1.17      ! [A: nat] :
% 2.12/1.17        ( ( minus_minus_nat @ A @ A )
% 2.12/1.17        = zero_zero_nat ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_345_image__add__0,axiom,
% 2.12/1.17      ! [S: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( image_439535603real_n @ ( plus_p585657087real_n @ zero_z200130687real_n ) @ S )
% 2.12/1.17        = S ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_346_image__add__0,axiom,
% 2.12/1.17      ! [S: set_nat] :
% 2.12/1.17        ( ( image_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ S )
% 2.12/1.17        = S ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_347_diff__add__zero,axiom,
% 2.12/1.17      ! [A: nat,B: nat] :
% 2.12/1.17        ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 2.12/1.17        = zero_zero_nat ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_348_eq__add__iff,axiom,
% 2.12/1.17      ! [X2: finite1489363574real_n,Y3: finite1489363574real_n] :
% 2.12/1.17        ( ( X2
% 2.12/1.17          = ( plus_p585657087real_n @ X2 @ Y3 ) )
% 2.12/1.17        = ( Y3 = zero_z200130687real_n ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_349_Least__eq__0,axiom,
% 2.12/1.17      ! [P: nat > $o] :
% 2.12/1.17        ( ( P @ zero_zero_nat )
% 2.12/1.17       => ( ( ord_Least_nat @ P )
% 2.12/1.17          = zero_zero_nat ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_350_diff__0__eq__0,axiom,
% 2.12/1.17      ! [N3: nat] :
% 2.12/1.17        ( ( minus_minus_nat @ zero_zero_nat @ N3 )
% 2.12/1.17        = zero_zero_nat ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_351_diff__self__eq__0,axiom,
% 2.12/1.17      ! [M4: nat] :
% 2.12/1.17        ( ( minus_minus_nat @ M4 @ M4 )
% 2.12/1.17        = zero_zero_nat ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_352_diffs0__imp__equal,axiom,
% 2.12/1.17      ! [M4: nat,N3: nat] :
% 2.12/1.17        ( ( ( minus_minus_nat @ M4 @ N3 )
% 2.12/1.17          = zero_zero_nat )
% 2.12/1.17       => ( ( ( minus_minus_nat @ N3 @ M4 )
% 2.12/1.17            = zero_zero_nat )
% 2.12/1.17         => ( M4 = N3 ) ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(fact_353_minus__nat_Odiff__0,axiom,
% 2.12/1.17      ! [M4: nat] :
% 2.12/1.17        ( ( minus_minus_nat @ M4 @ zero_zero_nat )
% 2.12/1.17        = M4 ) ).
% 2.12/1.17  
% 2.12/1.17  thf(help_If_2_1_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_T,axiom,
% 2.12/1.17      ! [X2: finite1489363574real_n,Y3: finite1489363574real_n] :
% 2.12/1.17        ( ( if_Fin127821360real_n @ $false @ X2 @ Y3 )
% 2.12/1.17        = Y3 ) ).
% 2.12/1.17  
% 2.12/1.17  thf(help_If_1_1_If_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_T,axiom,
% 2.12/1.17      ! [X2: finite1489363574real_n,Y3: finite1489363574real_n] :
% 2.12/1.17        ( ( if_Fin127821360real_n @ $true @ X2 @ Y3 )
% 2.12/1.17        = X2 ) ).
% 2.12/1.17  
% 2.12/1.17  thf(help_If_2_1_If_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_T,axiom,
% 2.12/1.17      ! [X2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( if_set11487206real_n @ $false @ X2 @ Y3 )
% 2.12/1.17        = Y3 ) ).
% 2.12/1.17  
% 2.12/1.17  thf(help_If_1_1_If_001t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_T,axiom,
% 2.12/1.17      ! [X2: set_Fi1058188332real_n,Y3: set_Fi1058188332real_n] :
% 2.12/1.17        ( ( if_set11487206real_n @ $true @ X2 @ Y3 )
% 2.12/1.17        = X2 ) ).
% 2.12/1.17  
% 2.12/1.17  thf(help_If_3_1_If_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_T,axiom,
% 2.12/1.17      ! [P: $o] :
% 2.12/1.17        ( ( P = $true )
% 2.12/1.17        | ( P = $false ) ) ).
% 2.12/1.17  
% 2.12/1.17  thf(help_If_2_1_If_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_T,axiom,
% 2.12/1.17      ! [X2: finite1489363574real_n > finite1489363574real_n,Y3: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17        ( ( if_Fin413489477real_n @ $false @ X2 @ Y3 )
% 2.12/1.17        = Y3 ) ).
% 2.12/1.17  
% 2.12/1.17  thf(help_If_1_1_If_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__n_J_J_T,axiom,
% 2.12/1.17      ! [X2: finite1489363574real_n > finite1489363574real_n,Y3: finite1489363574real_n > finite1489363574real_n] :
% 2.12/1.17        ( ( if_Fin413489477real_n @ $true @ X2 @ Y3 )
% 2.12/1.17        = X2 ) ).
% 2.12/1.17  
% 2.12/1.17  thf(conj_0,conjecture,
% 2.12/1.17      ( member223413699real_n
% 2.12/1.17      @ ( vimage1233683625real_n
% 2.12/1.17        @ ^ [X: finite1489363574real_n] : ( plus_p585657087real_n @ X @ ( minkow1134813771n_real @ a ) )
% 2.12/1.17        @ ( t2 @ a ) )
% 2.12/1.17      @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ).
% 2.12/1.17  ------------------------
% 2.12/1.19  % (15162)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_14897 for (2999ds/4Mi)
% 2.12/1.19  % (15164)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14897 for (2999ds/2Mi)
% 2.12/1.19  % (15163)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_14897 for (2999ds/27Mi)
% 2.12/1.19  % (15161)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14897 for (2999ds/183Mi)
% 2.12/1.19  % (15165)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_14897 for (2999ds/2Mi)
% 2.12/1.19  % (15166)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_14897 for (2999ds/275Mi)
% 2.12/1.19  % (15167)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14897 for (2999ds/18Mi)
% 2.12/1.19  % (15164)Instruction limit reached!
% 2.12/1.19  % (15164)------------------------------
% 2.12/1.19  % (15164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.19  % (15164)Termination reason: Unknown
% 2.12/1.19  % (15164)Termination phase: shuffling
% 2.12/1.19  
% 2.12/1.19  % (15164)Memory used [KB]: 1535
% 2.12/1.19  % (15164)Time elapsed: 0.002 s
% 2.12/1.19  % (15164)Instructions burned: 2 (million)
% 2.12/1.19  % (15164)------------------------------
% 2.12/1.19  % (15164)------------------------------
% 2.12/1.19  % (15165)Instruction limit reached!
% 2.12/1.19  % (15165)------------------------------
% 2.12/1.19  % (15165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.19  % (15165)Termination reason: Unknown
% 2.12/1.19  % (15165)Termination phase: shuffling
% 2.12/1.19  
% 2.12/1.19  % (15165)Memory used [KB]: 1535
% 2.12/1.19  % (15165)Time elapsed: 0.002 s
% 2.12/1.19  % (15165)Instructions burned: 2 (million)
% 2.12/1.19  % (15165)------------------------------
% 2.12/1.19  % (15165)------------------------------
% 2.12/1.19  % (15162)Instruction limit reached!
% 2.12/1.19  % (15162)------------------------------
% 2.12/1.19  % (15162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.12/1.19  % (15162)Termination reason: Unknown
% 2.12/1.19  % (15162)Termination phase: shuffling
% 2.12/1.19  
% 2.12/1.19  % (15162)Memory used [KB]: 1663
% 2.12/1.19  % (15162)Time elapsed: 0.003 s
% 2.12/1.19  % (15162)Instructions burned: 6 (million)
% 2.12/1.19  % (15162)------------------------------
% 2.12/1.19  % (15162)------------------------------
% 2.17/1.20  % (15167)Instruction limit reached!
% 2.17/1.20  % (15167)------------------------------
% 2.17/1.20  % (15167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.20  % (15167)Termination reason: Unknown
% 2.17/1.20  % (15167)Termination phase: shuffling
% 2.17/1.20  
% 2.17/1.20  % (15167)Memory used [KB]: 1791
% 2.17/1.20  % (15167)Time elapsed: 0.007 s
% 2.17/1.20  % (15167)Instructions burned: 19 (million)
% 2.17/1.20  % (15167)------------------------------
% 2.17/1.20  % (15167)------------------------------
% 2.17/1.20  % (15163)Instruction limit reached!
% 2.17/1.20  % (15163)------------------------------
% 2.17/1.20  % (15163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.20  % (15163)Termination reason: Unknown
% 2.17/1.20  % (15163)Termination phase: shuffling
% 2.17/1.20  
% 2.17/1.20  % (15163)Memory used [KB]: 1918
% 2.17/1.20  % (15163)Time elapsed: 0.010 s
% 2.17/1.20  % (15163)Instructions burned: 28 (million)
% 2.17/1.20  % (15163)------------------------------
% 2.17/1.20  % (15163)------------------------------
% 2.17/1.20  % (15168)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14897 for (2999ds/3Mi)
% 2.17/1.20  % (15169)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_14897 for (2999ds/37Mi)
% 2.17/1.20  % (15170)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_14897 for (2999ds/15Mi)
% 2.17/1.20  % (15168)Instruction limit reached!
% 2.17/1.20  % (15168)------------------------------
% 2.17/1.20  % (15168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.20  % (15168)Termination reason: Unknown
% 2.17/1.20  % (15168)Termination phase: shuffling
% 2.17/1.20  
% 2.17/1.20  % (15168)Memory used [KB]: 1535
% 2.17/1.20  % (15168)Time elapsed: 0.003 s
% 2.17/1.20  % (15168)Instructions burned: 6 (million)
% 2.17/1.20  % (15168)------------------------------
% 2.17/1.20  % (15168)------------------------------
% 2.17/1.21  % (15171)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_14897 for (2999ds/3Mi)
% 2.17/1.21  % (15170)Instruction limit reached!
% 2.17/1.21  % (15170)------------------------------
% 2.17/1.21  % (15170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.21  % (15170)Termination reason: Unknown
% 2.17/1.21  % (15170)Termination phase: shuffling
% 2.17/1.21  
% 2.17/1.21  % (15170)Memory used [KB]: 1791
% 2.17/1.21  % (15170)Time elapsed: 0.006 s
% 2.17/1.21  % (15170)Instructions burned: 15 (million)
% 2.17/1.21  % (15170)------------------------------
% 2.17/1.21  % (15170)------------------------------
% 2.17/1.21  % (15171)Instruction limit reached!
% 2.17/1.21  % (15171)------------------------------
% 2.17/1.21  % (15171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.21  % (15171)Termination reason: Unknown
% 2.17/1.21  % (15171)Termination phase: shuffling
% 2.17/1.21  
% 2.17/1.21  % (15171)Memory used [KB]: 1535
% 2.17/1.21  % (15171)Time elapsed: 0.003 s
% 2.17/1.21  % (15171)Instructions burned: 5 (million)
% 2.17/1.21  % (15171)------------------------------
% 2.17/1.21  % (15171)------------------------------
% 2.17/1.21  % (15172)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_14897 for (2999ds/1041Mi)
% 2.17/1.21  % (15169)Instruction limit reached!
% 2.17/1.21  % (15169)------------------------------
% 2.17/1.21  % (15169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.21  % (15169)Termination reason: Unknown
% 2.17/1.21  % (15169)Termination phase: shuffling
% 2.17/1.21  
% 2.17/1.21  % (15169)Memory used [KB]: 2302
% 2.17/1.21  % (15169)Time elapsed: 0.012 s
% 2.17/1.21  % (15169)Instructions burned: 40 (million)
% 2.17/1.21  % (15169)------------------------------
% 2.17/1.21  % (15169)------------------------------
% 2.17/1.21  % (15173)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_14897 for (2999ds/7Mi)
% 2.17/1.22  % (15173)Instruction limit reached!
% 2.17/1.22  % (15173)------------------------------
% 2.17/1.22  % (15173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.22  % (15173)Termination reason: Unknown
% 2.17/1.22  % (15173)Termination phase: shuffling
% 2.17/1.22  
% 2.17/1.22  % (15173)Memory used [KB]: 1663
% 2.17/1.22  % (15173)Time elapsed: 0.004 s
% 2.17/1.22  % (15173)Instructions burned: 9 (million)
% 2.17/1.22  % (15173)------------------------------
% 2.17/1.22  % (15173)------------------------------
% 2.17/1.22  % (15175)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_14897 for (2999ds/16Mi)
% 2.17/1.22  % (15176)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_14897 for (2999ds/3Mi)
% 2.17/1.22  % (15176)Instruction limit reached!
% 2.17/1.22  % (15176)------------------------------
% 2.17/1.22  % (15176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.22  % (15176)Termination reason: Unknown
% 2.17/1.22  % (15176)Termination phase: shuffling
% 2.17/1.22  
% 2.17/1.22  % (15176)Memory used [KB]: 1535
% 2.17/1.22  % (15176)Time elapsed: 0.002 s
% 2.17/1.22  % (15176)Instructions burned: 3 (million)
% 2.17/1.22  % (15176)------------------------------
% 2.17/1.22  % (15176)------------------------------
% 2.17/1.22  % (15177)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_14897 for (2999ds/3Mi)
% 2.17/1.22  % (15175)Instruction limit reached!
% 2.17/1.22  % (15175)------------------------------
% 2.17/1.22  % (15175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.22  % (15175)Termination reason: Unknown
% 2.17/1.22  % (15175)Termination phase: shuffling
% 2.17/1.22  
% 2.17/1.22  % (15175)Memory used [KB]: 1791
% 2.17/1.22  % (15175)Time elapsed: 0.007 s
% 2.17/1.22  % (15175)Instructions burned: 19 (million)
% 2.17/1.22  % (15175)------------------------------
% 2.17/1.22  % (15175)------------------------------
% 2.17/1.22  % (15177)Instruction limit reached!
% 2.17/1.22  % (15177)------------------------------
% 2.17/1.22  % (15177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.22  % (15177)Termination reason: Unknown
% 2.17/1.22  % (15177)Termination phase: shuffling
% 2.17/1.22  
% 2.17/1.22  % (15177)Memory used [KB]: 1535
% 2.17/1.22  % (15177)Time elapsed: 0.003 s
% 2.17/1.22  % (15177)Instructions burned: 6 (million)
% 2.17/1.22  % (15177)------------------------------
% 2.17/1.22  % (15177)------------------------------
% 2.17/1.23  % (15178)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_14897 for (2999ds/7Mi)
% 2.17/1.23  % (15178)Instruction limit reached!
% 2.17/1.23  % (15178)------------------------------
% 2.17/1.23  % (15178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.23  % (15178)Termination reason: Unknown
% 2.17/1.23  % (15178)Termination phase: shuffling
% 2.17/1.23  
% 2.17/1.23  % (15178)Memory used [KB]: 1663
% 2.17/1.23  % (15178)Time elapsed: 0.004 s
% 2.17/1.23  % (15178)Instructions burned: 9 (million)
% 2.17/1.23  % (15178)------------------------------
% 2.17/1.23  % (15178)------------------------------
% 2.17/1.23  % (15179)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_14897 for (2999ds/3Mi)
% 2.17/1.23  % (15179)Instruction limit reached!
% 2.17/1.23  % (15179)------------------------------
% 2.17/1.23  % (15179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.23  % (15179)Termination reason: Unknown
% 2.17/1.23  % (15179)Termination phase: shuffling
% 2.17/1.23  
% 2.17/1.23  % (15179)Memory used [KB]: 1535
% 2.17/1.23  % (15179)Time elapsed: 0.002 s
% 2.17/1.23  % (15179)Instructions burned: 3 (million)
% 2.17/1.23  % (15179)------------------------------
% 2.17/1.23  % (15179)------------------------------
% 2.17/1.23  % (15180)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_14897 for (2999ds/4Mi)
% 2.17/1.23  % (15181)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_14897 for (2999ds/18Mi)
% 2.17/1.23  % (15180)Instruction limit reached!
% 2.17/1.23  % (15180)------------------------------
% 2.17/1.23  % (15180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.23  % (15180)Termination reason: Unknown
% 2.17/1.23  % (15180)Termination phase: shuffling
% 2.17/1.23  
% 2.17/1.23  % (15180)Memory used [KB]: 1535
% 2.17/1.23  % (15180)Time elapsed: 0.003 s
% 2.17/1.23  % (15180)Instructions burned: 6 (million)
% 2.17/1.23  % (15180)------------------------------
% 2.17/1.23  % (15180)------------------------------
% 2.17/1.24  % (15182)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_14897 for (2999ds/710Mi)
% 2.17/1.24  % (15183)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_14897 for (2999ds/6Mi)
% 2.17/1.24  % (15181)Instruction limit reached!
% 2.17/1.24  % (15181)------------------------------
% 2.17/1.24  % (15181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.24  % (15181)Termination reason: Unknown
% 2.17/1.24  % (15181)Termination phase: shuffling
% 2.17/1.24  
% 2.17/1.24  % (15181)Memory used [KB]: 1791
% 2.17/1.24  % (15181)Time elapsed: 0.007 s
% 2.17/1.24  % (15181)Instructions burned: 19 (million)
% 2.17/1.24  % (15181)------------------------------
% 2.17/1.24  % (15181)------------------------------
% 2.17/1.24  % (15183)Instruction limit reached!
% 2.17/1.24  % (15183)------------------------------
% 2.17/1.24  % (15183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.24  % (15183)Termination reason: Unknown
% 2.17/1.24  % (15183)Termination phase: shuffling
% 2.17/1.24  
% 2.17/1.24  % (15183)Memory used [KB]: 1535
% 2.17/1.24  % (15183)Time elapsed: 0.003 s
% 2.17/1.24  % (15183)Instructions burned: 6 (million)
% 2.17/1.24  % (15183)------------------------------
% 2.17/1.24  % (15183)------------------------------
% 2.17/1.24  % (15161)Instruction limit reached!
% 2.17/1.24  % (15161)------------------------------
% 2.17/1.24  % (15161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.24  % (15161)Termination reason: Unknown
% 2.17/1.24  % (15161)Termination phase: Saturation
% 2.17/1.24  
% 2.17/1.24  % (15161)Memory used [KB]: 7419
% 2.17/1.24  % (15161)Time elapsed: 0.053 s
% 2.17/1.24  % (15161)Instructions burned: 185 (million)
% 2.17/1.24  % (15161)------------------------------
% 2.17/1.24  % (15161)------------------------------
% 2.17/1.24  % (15184)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_14897 for (2999ds/902Mi)
% 2.17/1.25  % (15185)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_14897 for (2999ds/21Mi)
% 2.17/1.25  % (15186)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_14897 for (2999ds/5Mi)
% 2.17/1.25  % (15186)Instruction limit reached!
% 2.17/1.25  % (15186)------------------------------
% 2.17/1.25  % (15186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.25  % (15186)Termination reason: Unknown
% 2.17/1.25  % (15186)Termination phase: shuffling
% 2.17/1.25  
% 2.17/1.25  % (15186)Memory used [KB]: 1663
% 2.17/1.25  % (15186)Time elapsed: 0.003 s
% 2.17/1.25  % (15186)Instructions burned: 6 (million)
% 2.17/1.25  % (15186)------------------------------
% 2.17/1.25  % (15186)------------------------------
% 2.17/1.25  % (15187)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_14897 for (2999ds/6Mi)
% 2.17/1.26  % (15187)Instruction limit reached!
% 2.17/1.26  % (15187)------------------------------
% 2.17/1.26  % (15187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.26  % (15187)Termination reason: Unknown
% 2.17/1.26  % (15187)Termination phase: shuffling
% 2.17/1.26  
% 2.17/1.26  % (15187)Memory used [KB]: 1663
% 2.17/1.26  % (15187)Time elapsed: 0.003 s
% 2.17/1.26  % (15187)Instructions burned: 6 (million)
% 2.17/1.26  % (15187)------------------------------
% 2.17/1.26  % (15187)------------------------------
% 2.17/1.26  % (15185)Instruction limit reached!
% 2.17/1.26  % (15185)------------------------------
% 2.17/1.26  % (15185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.26  % (15185)Termination reason: Unknown
% 2.17/1.26  % (15185)Termination phase: shuffling
% 2.17/1.26  
% 2.17/1.26  % (15185)Memory used [KB]: 1918
% 2.17/1.26  % (15185)Time elapsed: 0.008 s
% 2.17/1.26  % (15185)Instructions burned: 22 (million)
% 2.17/1.26  % (15185)------------------------------
% 2.17/1.26  % (15185)------------------------------
% 2.17/1.26  % (15188)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_14897 for (2999ds/377Mi)
% 2.17/1.26  % (15189)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_14897 for (2999ds/779Mi)
% 2.17/1.27  % (15190)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_14897 for (2999ds/19Mi)
% 2.17/1.27  % (15190)Instruction limit reached!
% 2.17/1.27  % (15190)------------------------------
% 2.17/1.27  % (15190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.27  % (15190)Termination reason: Unknown
% 2.17/1.27  % (15190)Termination phase: shuffling
% 2.17/1.27  
% 2.17/1.27  % (15190)Memory used [KB]: 2046
% 2.17/1.27  % (15190)Time elapsed: 0.007 s
% 2.17/1.27  % (15190)Instructions burned: 21 (million)
% 2.17/1.27  % (15190)------------------------------
% 2.17/1.27  % (15190)------------------------------
% 2.17/1.28  % (15166)Instruction limit reached!
% 2.17/1.28  % (15166)------------------------------
% 2.17/1.28  % (15166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.28  % (15166)Termination reason: Unknown
% 2.17/1.28  % (15166)Termination phase: Saturation
% 2.17/1.28  
% 2.17/1.28  % (15166)Memory used [KB]: 7419
% 2.17/1.28  % (15166)Time elapsed: 0.086 s
% 2.17/1.28  % (15166)Instructions burned: 275 (million)
% 2.17/1.28  % (15166)------------------------------
% 2.17/1.28  % (15166)------------------------------
% 2.17/1.28  % (15191)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_14897 for (2999ds/879Mi)
% 2.17/1.29  % (15192)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_14897 for (2999ds/17Mi)
% 2.17/1.29  % (15184)Refutation not found, incomplete strategy
% 2.17/1.29  % (15184)------------------------------
% 2.17/1.29  % (15184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.29  % (15184)Termination reason: Refutation not found, incomplete strategy
% 2.17/1.29  
% 2.17/1.29  
% 2.17/1.29  % (15184)Memory used [KB]: 7547
% 2.17/1.29  % (15184)Time elapsed: 0.047 s
% 2.17/1.29  % (15184)Instructions burned: 160 (million)
% 2.17/1.29  % (15184)------------------------------
% 2.17/1.29  % (15184)------------------------------
% 2.17/1.29  % (15192)Instruction limit reached!
% 2.17/1.29  % (15192)------------------------------
% 2.17/1.29  % (15192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.29  % (15192)Termination reason: Unknown
% 2.17/1.29  % (15192)Termination phase: shuffling
% 2.17/1.29  
% 2.17/1.29  % (15192)Memory used [KB]: 1791
% 2.17/1.29  % (15192)Time elapsed: 0.007 s
% 2.17/1.29  % (15192)Instructions burned: 17 (million)
% 2.17/1.29  % (15192)------------------------------
% 2.17/1.29  % (15192)------------------------------
% 2.17/1.30  % (15193)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_14897 for (2998ds/3Mi)
% 2.17/1.30  % (15193)Instruction limit reached!
% 2.17/1.30  % (15193)------------------------------
% 2.17/1.30  % (15193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.30  % (15193)Termination reason: Unknown
% 2.17/1.30  % (15193)Termination phase: shuffling
% 2.17/1.30  
% 2.17/1.30  % (15193)Memory used [KB]: 1535
% 2.17/1.30  % (15193)Time elapsed: 0.002 s
% 2.17/1.30  % (15193)Instructions burned: 3 (million)
% 2.17/1.30  % (15193)------------------------------
% 2.17/1.30  % (15193)------------------------------
% 2.17/1.30  % (15194)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_14897 for (2998ds/30Mi)
% 2.17/1.31  % (15195)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_14897 for (2998ds/127Mi)
% 2.17/1.31  % (15194)Instruction limit reached!
% 2.17/1.31  % (15194)------------------------------
% 2.17/1.31  % (15194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.31  % (15194)Termination reason: Unknown
% 2.17/1.31  % (15194)Termination phase: shuffling
% 2.17/1.31  
% 2.17/1.31  % (15194)Memory used [KB]: 2046
% 2.17/1.31  % (15194)Time elapsed: 0.011 s
% 2.17/1.31  % (15194)Instructions burned: 32 (million)
% 2.17/1.31  % (15194)------------------------------
% 2.17/1.31  % (15194)------------------------------
% 2.17/1.32  % (15196)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_14897 for (2998ds/100Mi)
% 2.17/1.35  % (15195)Instruction limit reached!
% 2.17/1.35  % (15195)------------------------------
% 2.17/1.35  % (15195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.35  % (15195)Termination reason: Unknown
% 2.17/1.35  % (15195)Termination phase: Property scanning
% 2.17/1.35  
% 2.17/1.35  % (15195)Memory used [KB]: 2558
% 2.17/1.35  % (15195)Time elapsed: 0.036 s
% 2.17/1.35  % (15195)Instructions burned: 128 (million)
% 2.17/1.35  % (15195)------------------------------
% 2.17/1.35  % (15195)------------------------------
% 2.17/1.35  % (15196)Instruction limit reached!
% 2.17/1.35  % (15196)------------------------------
% 2.17/1.35  % (15196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.35  % (15196)Termination reason: Unknown
% 2.17/1.35  % (15196)Termination phase: Property scanning
% 2.17/1.35  
% 2.17/1.35  % (15196)Memory used [KB]: 2814
% 2.17/1.35  % (15196)Time elapsed: 0.027 s
% 2.17/1.35  % (15196)Instructions burned: 100 (million)
% 2.17/1.35  % (15196)------------------------------
% 2.17/1.35  % (15196)------------------------------
% 2.17/1.36  % (15197)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_14897 for (2998ds/3Mi)
% 2.17/1.36  % (15198)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_14897 for (2998ds/20Mi)
% 2.17/1.36  % (15197)Instruction limit reached!
% 2.17/1.36  % (15197)------------------------------
% 2.17/1.36  % (15197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.36  % (15197)Termination reason: Unknown
% 2.17/1.36  % (15197)Termination phase: shuffling
% 2.17/1.36  
% 2.17/1.36  % (15197)Memory used [KB]: 1535
% 2.17/1.36  % (15197)Time elapsed: 0.003 s
% 2.17/1.36  % (15197)Instructions burned: 5 (million)
% 2.17/1.36  % (15197)------------------------------
% 2.17/1.36  % (15197)------------------------------
% 2.17/1.36  % (15198)Instruction limit reached!
% 2.17/1.36  % (15198)------------------------------
% 2.17/1.36  % (15198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.36  % (15198)Termination reason: Unknown
% 2.17/1.36  % (15198)Termination phase: shuffling
% 2.17/1.36  
% 2.17/1.36  % (15198)Memory used [KB]: 1918
% 2.17/1.36  % (15198)Time elapsed: 0.008 s
% 2.17/1.36  % (15198)Instructions burned: 21 (million)
% 2.17/1.36  % (15198)------------------------------
% 2.17/1.36  % (15198)------------------------------
% 2.17/1.37  % (15199)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_14897 for (2998ds/86Mi)
% 2.17/1.37  % (15200)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_14897 for (2998ds/107Mi)
% 2.17/1.38  % (15188)Instruction limit reached!
% 2.17/1.38  % (15188)------------------------------
% 2.17/1.38  % (15188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.38  % (15188)Termination reason: Unknown
% 2.17/1.38  % (15188)Termination phase: Saturation
% 2.17/1.38  
% 2.17/1.38  % (15188)Memory used [KB]: 8315
% 2.17/1.38  % (15188)Time elapsed: 0.115 s
% 2.17/1.38  % (15188)Instructions burned: 380 (million)
% 2.17/1.38  % (15188)------------------------------
% 2.17/1.38  % (15188)------------------------------
% 2.17/1.39  % (15201)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_14897 for (2998ds/39Mi)
% 2.17/1.39  % (15199)Instruction limit reached!
% 2.17/1.39  % (15199)------------------------------
% 2.17/1.39  % (15199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.39  % (15199)Termination reason: Unknown
% 2.17/1.39  % (15199)Termination phase: Property scanning
% 2.17/1.39  
% 2.17/1.39  % (15199)Memory used [KB]: 2558
% 2.17/1.39  % (15199)Time elapsed: 0.026 s
% 2.17/1.39  % (15199)Instructions burned: 86 (million)
% 2.17/1.39  % (15199)------------------------------
% 2.17/1.39  % (15199)------------------------------
% 2.17/1.40  % (15201)Instruction limit reached!
% 2.17/1.40  % (15201)------------------------------
% 2.17/1.40  % (15201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.40  % (15201)Termination reason: Unknown
% 2.17/1.40  % (15201)Termination phase: shuffling
% 2.17/1.40  
% 2.17/1.40  % (15201)Memory used [KB]: 2302
% 2.17/1.40  % (15201)Time elapsed: 0.012 s
% 2.17/1.40  % (15201)Instructions burned: 39 (million)
% 2.17/1.40  % (15201)------------------------------
% 2.17/1.40  % (15201)------------------------------
% 2.17/1.40  % (15202)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_14897 for (2997ds/448Mi)
% 2.17/1.40  % (15200)Instruction limit reached!
% 2.17/1.40  % (15200)------------------------------
% 2.17/1.40  % (15200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.40  % (15200)Termination reason: Unknown
% 2.17/1.40  % (15200)Termination phase: Saturation
% 2.17/1.40  
% 2.17/1.40  % (15200)Memory used [KB]: 6908
% 2.17/1.40  % (15200)Time elapsed: 0.032 s
% 2.17/1.40  % (15200)Instructions burned: 109 (million)
% 2.17/1.40  % (15200)------------------------------
% 2.17/1.40  % (15200)------------------------------
% 2.17/1.41  % (15203)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_14897 for (2997ds/46Mi)
% 2.17/1.41  % (15204)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_14897 for (2997ds/98Mi)
% 2.17/1.42  % (15203)Instruction limit reached!
% 2.17/1.42  % (15203)------------------------------
% 2.17/1.42  % (15203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.42  % (15203)Termination reason: Unknown
% 2.17/1.42  % (15203)Termination phase: Property scanning
% 2.17/1.42  
% 2.17/1.42  % (15203)Memory used [KB]: 2046
% 2.17/1.42  % (15203)Time elapsed: 0.016 s
% 2.17/1.42  % (15203)Instructions burned: 49 (million)
% 2.17/1.42  % (15203)------------------------------
% 2.17/1.42  % (15203)------------------------------
% 2.17/1.43  % (15205)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_14897 for (2997ds/507Mi)
% 2.17/1.44  % (15204)Instruction limit reached!
% 2.17/1.44  % (15204)------------------------------
% 2.17/1.44  % (15204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.44  % (15204)Termination reason: Unknown
% 2.17/1.44  % (15204)Termination phase: Property scanning
% 2.17/1.44  
% 2.17/1.44  % (15204)Memory used [KB]: 2814
% 2.17/1.44  % (15204)Time elapsed: 0.027 s
% 2.17/1.44  % (15204)Instructions burned: 98 (million)
% 2.17/1.44  % (15204)------------------------------
% 2.17/1.44  % (15204)------------------------------
% 2.17/1.45  % (15182)Refutation not found, non-redundant clauses discarded% (15182)------------------------------
% 2.17/1.45  % (15182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.45  % (15182)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.17/1.45  
% 2.17/1.45  % (15182)Memory used [KB]: 7547
% 2.17/1.45  % (15182)Time elapsed: 0.210 s
% 2.17/1.45  % (15182)Instructions burned: 708 (million)
% 2.17/1.45  % (15182)------------------------------
% 2.17/1.45  % (15182)------------------------------
% 2.17/1.45  % (15206)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_14897 for (2997ds/149Mi)
% 2.17/1.46  % (15207)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_14897 for (2997ds/39Mi)
% 2.17/1.47  % (15207)Instruction limit reached!
% 2.17/1.47  % (15207)------------------------------
% 2.17/1.47  % (15207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.47  % (15207)Termination reason: Unknown
% 2.17/1.47  % (15207)Termination phase: Property scanning
% 2.17/1.47  
% 2.17/1.47  % (15207)Memory used [KB]: 2046
% 2.17/1.47  % (15207)Time elapsed: 0.014 s
% 2.17/1.47  % (15207)Instructions burned: 41 (million)
% 2.17/1.47  % (15207)------------------------------
% 2.17/1.47  % (15207)------------------------------
% 2.17/1.48  % (15208)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_14897 for (2996ds/6Mi)
% 2.17/1.48  % (15208)Instruction limit reached!
% 2.17/1.48  % (15208)------------------------------
% 2.17/1.48  % (15208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.48  % (15208)Termination reason: Unknown
% 2.17/1.48  % (15208)Termination phase: shuffling
% 2.17/1.48  
% 2.17/1.48  % (15208)Memory used [KB]: 1663
% 2.17/1.48  % (15208)Time elapsed: 0.003 s
% 2.17/1.48  % (15208)Instructions burned: 7 (million)
% 2.17/1.48  % (15208)------------------------------
% 2.17/1.48  % (15208)------------------------------
% 2.17/1.49  % (15206)Instruction limit reached!
% 2.17/1.49  % (15206)------------------------------
% 2.17/1.49  % (15206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.49  % (15206)Termination reason: Unknown
% 2.17/1.49  % (15206)Termination phase: Saturation
% 2.17/1.49  
% 2.17/1.49  % (15206)Memory used [KB]: 7164
% 2.17/1.49  % (15206)Time elapsed: 0.042 s
% 2.17/1.49  % (15206)Instructions burned: 149 (million)
% 2.17/1.49  % (15206)------------------------------
% 2.17/1.49  % (15206)------------------------------
% 2.17/1.49  % (15209)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_14897 for (2996ds/1087Mi)
% 2.17/1.50  % (15189)Instruction limit reached!
% 2.17/1.50  % (15189)------------------------------
% 2.17/1.50  % (15189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.50  % (15189)Termination reason: Unknown
% 2.17/1.50  % (15189)Termination phase: Saturation
% 2.17/1.50  
% 2.17/1.50  % (15189)Memory used [KB]: 9083
% 2.17/1.50  % (15189)Time elapsed: 0.233 s
% 2.17/1.50  % (15189)Instructions burned: 780 (million)
% 2.17/1.50  % (15189)------------------------------
% 2.17/1.50  % (15189)------------------------------
% 2.17/1.50  % (15210)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_14897 for (2996ds/47Mi)
% 2.17/1.51  % (15211)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_14897 for (2996ds/44Mi)
% 2.17/1.51  % (15210)Instruction limit reached!
% 2.17/1.51  % (15210)------------------------------
% 2.17/1.51  % (15210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.51  % (15210)Termination reason: Unknown
% 2.17/1.51  % (15210)Termination phase: Property scanning
% 2.17/1.51  
% 2.17/1.51  % (15210)Memory used [KB]: 2046
% 2.17/1.51  % (15210)Time elapsed: 0.016 s
% 2.17/1.51  % (15210)Instructions burned: 50 (million)
% 2.17/1.51  % (15210)------------------------------
% 2.17/1.51  % (15210)------------------------------
% 2.17/1.52  % (15211)Instruction limit reached!
% 2.17/1.52  % (15211)------------------------------
% 2.17/1.52  % (15211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.52  % (15211)Termination reason: Unknown
% 2.17/1.52  % (15211)Termination phase: shuffling
% 2.17/1.52  
% 2.17/1.52  % (15211)Memory used [KB]: 2302
% 2.17/1.52  % (15211)Time elapsed: 0.013 s
% 2.17/1.52  % (15211)Instructions burned: 44 (million)
% 2.17/1.52  % (15211)------------------------------
% 2.17/1.52  % (15211)------------------------------
% 2.17/1.52  % (15172)Instruction limit reached!
% 2.17/1.52  % (15172)------------------------------
% 2.17/1.52  % (15172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.52  % (15172)Termination reason: Unknown
% 2.17/1.52  % (15172)Termination phase: Saturation
% 2.17/1.52  
% 2.17/1.52  % (15172)Memory used [KB]: 10234
% 2.17/1.52  % (15172)Time elapsed: 0.310 s
% 2.17/1.52  % (15172)Instructions burned: 1044 (million)
% 2.17/1.52  % (15172)------------------------------
% 2.17/1.52  % (15172)------------------------------
% 2.17/1.52  % (15212)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_14897 for (2996ds/432Mi)
% 2.17/1.53  % (15213)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_14897 for (2996ds/62Mi)
% 2.17/1.53  % (15202)Instruction limit reached!
% 2.17/1.53  % (15202)------------------------------
% 2.17/1.53  % (15202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.53  % (15202)Termination reason: Unknown
% 2.17/1.53  % (15202)Termination phase: Saturation
% 2.17/1.53  
% 2.17/1.53  % (15202)Memory used [KB]: 8827
% 2.17/1.53  % (15202)Time elapsed: 0.129 s
% 2.17/1.53  % (15202)Instructions burned: 449 (million)
% 2.17/1.53  % (15202)------------------------------
% 2.17/1.53  % (15202)------------------------------
% 2.17/1.53  % (15214)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_14897 for (2996ds/31Mi)
% 2.17/1.54  % (15214)Instruction limit reached!
% 2.17/1.54  % (15214)------------------------------
% 2.17/1.54  % (15214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.54  % (15214)Termination reason: Unknown
% 2.17/1.54  % (15214)Termination phase: shuffling
% 2.17/1.54  
% 2.17/1.54  % (15214)Memory used [KB]: 2046
% 2.17/1.54  % (15214)Time elapsed: 0.011 s
% 2.17/1.54  % (15214)Instructions burned: 31 (million)
% 2.17/1.54  % (15214)------------------------------
% 2.17/1.54  % (15214)------------------------------
% 2.17/1.54  % (15215)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_14897 for (2996ds/96Mi)
% 2.17/1.54  % (15213)Instruction limit reached!
% 2.17/1.54  % (15213)------------------------------
% 2.17/1.54  % (15213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.54  % (15213)Termination reason: Unknown
% 2.17/1.54  % (15213)Termination phase: shuffling
% 2.17/1.54  
% 2.17/1.54  % (15213)Memory used [KB]: 2814
% 2.17/1.54  % (15213)Time elapsed: 0.018 s
% 2.17/1.54  % (15213)Instructions burned: 62 (million)
% 2.17/1.54  % (15213)------------------------------
% 2.17/1.54  % (15213)------------------------------
% 2.17/1.55  % (15216)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_14897 for (2996ds/453Mi)
% 2.17/1.55  % (15217)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_14897 for (2996ds/71Mi)
% 2.17/1.55  % (15191)Instruction limit reached!
% 2.17/1.55  % (15191)------------------------------
% 2.17/1.55  % (15191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.55  % (15191)Termination reason: Unknown
% 2.17/1.55  % (15191)Termination phase: Saturation
% 2.17/1.55  
% 2.17/1.55  % (15191)Memory used [KB]: 7931
% 2.17/1.55  % (15191)Time elapsed: 0.274 s
% 2.17/1.55  % (15191)Instructions burned: 881 (million)
% 2.17/1.55  % (15191)------------------------------
% 2.17/1.55  % (15191)------------------------------
% 2.17/1.56  % (15218)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_14897 for (2996ds/83Mi)
% 2.17/1.57  % (15215)Instruction limit reached!
% 2.17/1.57  % (15215)------------------------------
% 2.17/1.57  % (15215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.57  % (15215)Termination reason: Unknown
% 2.17/1.57  % (15215)Termination phase: Function definition elimination
% 2.17/1.57  
% 2.17/1.57  % (15215)Memory used [KB]: 2558
% 2.17/1.57  % (15215)Time elapsed: 0.029 s
% 2.17/1.57  % (15215)Instructions burned: 97 (million)
% 2.17/1.57  % (15215)------------------------------
% 2.17/1.57  % (15215)------------------------------
% 2.17/1.58  % (15219)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_14897 for (2996ds/11Mi)
% 2.17/1.58  % (15217)Instruction limit reached!
% 2.17/1.58  % (15217)------------------------------
% 2.17/1.58  % (15217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.58  % (15217)Termination reason: Unknown
% 2.17/1.58  % (15217)Termination phase: Preprocessing 3
% 2.17/1.58  
% 2.17/1.58  % (15217)Memory used [KB]: 2430
% 2.17/1.58  % (15217)Time elapsed: 0.023 s
% 2.17/1.58  % (15217)Instructions burned: 74 (million)
% 2.17/1.58  % (15217)------------------------------
% 2.17/1.58  % (15217)------------------------------
% 2.17/1.58  % (15219)Instruction limit reached!
% 2.17/1.58  % (15219)------------------------------
% 2.17/1.58  % (15219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.58  % (15219)Termination reason: Unknown
% 2.17/1.58  % (15219)Termination phase: shuffling
% 2.17/1.58  
% 2.17/1.58  % (15219)Memory used [KB]: 1791
% 2.17/1.58  % (15219)Time elapsed: 0.004 s
% 2.17/1.58  % (15219)Instructions burned: 11 (million)
% 2.17/1.58  % (15219)------------------------------
% 2.17/1.58  % (15219)------------------------------
% 2.17/1.58  % (15205)Instruction limit reached!
% 2.17/1.58  % (15205)------------------------------
% 2.17/1.58  % (15205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.58  % (15205)Termination reason: Unknown
% 2.17/1.58  % (15205)Termination phase: Saturation
% 2.17/1.58  
% 2.17/1.58  % (15205)Memory used [KB]: 8571
% 2.17/1.58  % (15205)Time elapsed: 0.152 s
% 2.17/1.58  % (15205)Instructions burned: 510 (million)
% 2.17/1.58  % (15205)------------------------------
% 2.17/1.58  % (15205)------------------------------
% 2.17/1.59  % (15220)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_14897 for (2995ds/41Mi)
% 2.17/1.59  % (15221)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_14897 for (2995ds/6Mi)
% 2.17/1.59  % (15218)Instruction limit reached!
% 2.17/1.59  % (15218)------------------------------
% 2.17/1.59  % (15218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.59  % (15218)Termination reason: Unknown
% 2.17/1.59  % (15218)Termination phase: Property scanning
% 2.17/1.59  
% 2.17/1.59  % (15218)Memory used [KB]: 2302
% 2.17/1.59  % (15218)Time elapsed: 0.026 s
% 2.17/1.59  % (15218)Instructions burned: 86 (million)
% 2.17/1.59  % (15218)------------------------------
% 2.17/1.59  % (15218)------------------------------
% 2.17/1.59  % (15221)Instruction limit reached!
% 2.17/1.59  % (15221)------------------------------
% 2.17/1.59  % (15221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.59  % (15221)Termination reason: Unknown
% 2.17/1.59  % (15221)Termination phase: shuffling
% 2.17/1.59  
% 2.17/1.59  % (15221)Memory used [KB]: 1535
% 2.17/1.59  % (15221)Time elapsed: 0.003 s
% 2.17/1.59  % (15221)Instructions burned: 6 (million)
% 2.17/1.59  % (15221)------------------------------
% 2.17/1.59  % (15221)------------------------------
% 2.17/1.59  % (15222)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_14897 for (2995ds/150Mi)
% 2.17/1.60  % (15220)Instruction limit reached!
% 2.17/1.60  % (15220)------------------------------
% 2.17/1.60  % (15220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.60  % (15220)Termination reason: Unknown
% 2.17/1.60  % (15220)Termination phase: shuffling
% 2.17/1.60  
% 2.17/1.60  % (15220)Memory used [KB]: 2302
% 2.17/1.60  % (15220)Time elapsed: 0.013 s
% 2.17/1.60  % (15220)Instructions burned: 43 (million)
% 2.17/1.60  % (15220)------------------------------
% 2.17/1.60  % (15220)------------------------------
% 2.17/1.60  % (15223)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_14897 for (2995ds/343Mi)
% 2.17/1.60  % (15224)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_14897 for (2995ds/109Mi)
% 2.17/1.61  % (15225)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_14897 for (2995ds/253Mi)
% 2.17/1.63  % (15224)Instruction limit reached!
% 2.17/1.63  % (15224)------------------------------
% 2.17/1.63  % (15224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.63  % (15224)Termination reason: Unknown
% 2.17/1.63  % (15224)Termination phase: shuffling
% 2.17/1.63  
% 2.17/1.63  % (15224)Memory used [KB]: 2558
% 2.17/1.63  % (15224)Time elapsed: 0.033 s
% 2.17/1.63  % (15224)Instructions burned: 110 (million)
% 2.17/1.63  % (15224)------------------------------
% 2.17/1.63  % (15224)------------------------------
% 2.17/1.63  % (15222)Instruction limit reached!
% 2.17/1.63  % (15222)------------------------------
% 2.17/1.63  % (15222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.63  % (15222)Termination reason: Unknown
% 2.17/1.63  % (15222)Termination phase: Saturation
% 2.17/1.63  
% 2.17/1.63  % (15222)Memory used [KB]: 7164
% 2.17/1.63  % (15222)Time elapsed: 0.043 s
% 2.17/1.63  % (15222)Instructions burned: 150 (million)
% 2.17/1.63  % (15222)------------------------------
% 2.17/1.63  % (15222)------------------------------
% 2.17/1.64  % (15226)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_14897 for (2995ds/140Mi)
% 2.17/1.64  % (15227)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_14897 for (2995ds/614Mi)
% 2.17/1.65  % (15212)Instruction limit reached!
% 2.17/1.65  % (15212)------------------------------
% 2.17/1.65  % (15212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.65  % (15212)Termination reason: Unknown
% 2.17/1.65  % (15212)Termination phase: Saturation
% 2.17/1.65  
% 2.17/1.65  % (15212)Memory used [KB]: 4733
% 2.17/1.65  % (15212)Time elapsed: 0.124 s
% 2.17/1.65  % (15212)Instructions burned: 432 (million)
% 2.17/1.65  % (15212)------------------------------
% 2.17/1.65  % (15212)------------------------------
% 2.17/1.66  % (15228)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_14897 for (2995ds/202Mi)
% 2.17/1.67  % (15223)First to succeed.
% 2.17/1.67  % (15216)Instruction limit reached!
% 2.17/1.67  % (15216)------------------------------
% 2.17/1.67  % (15216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.67  % (15216)Termination reason: Unknown
% 2.17/1.67  % (15216)Termination phase: Saturation
% 2.17/1.67  
% 2.17/1.67  % (15216)Memory used [KB]: 8187
% 2.17/1.67  % (15216)Time elapsed: 0.126 s
% 2.17/1.67  % (15216)Instructions burned: 453 (million)
% 2.17/1.67  % (15216)------------------------------
% 2.17/1.67  % (15216)------------------------------
% 2.17/1.68  % (15223)Refutation found. Thanks to Tanya!
% 2.17/1.68  % SZS status Theorem for DTF2THF_14897
% 2.17/1.68  % SZS output start Proof for DTF2THF_14897
% 2.17/1.68  thf(type_def_5, type, finite1489363574real_n: $tType).
% 2.17/1.68  thf(type_def_7, type, sigma_1466784463real_n: $tType).
% 2.17/1.68  thf(type_def_8, type, set_Fi1058188332real_n: $tType).
% 2.17/1.68  thf(type_def_9, type, nat: $tType).
% 2.17/1.68  thf(type_def_10, type, set_Fi1326602817real_n: $tType).
% 2.17/1.68  thf(type_def_11, type, set_se2111327970real_n: $tType).
% 2.17/1.68  thf(type_def_12, type, finite964658038_int_n: $tType).
% 2.17/1.68  thf(type_def_13, type, set_nat: $tType).
% 2.17/1.68  thf(type_def_14, type, sigma_107786596real_n: $tType).
% 2.17/1.68  thf(type_def_15, type, set_Fi1066397675real_n: $tType).
% 2.17/1.68  thf(type_def_16, type, set_Fi1491909078real_n: $tType).
% 2.17/1.68  thf(type_def_17, type, sigma_1422848389real_n: $tType).
% 2.17/1.68  thf(type_def_18, type, set_Fi909698444real_n: $tType).
% 2.17/1.68  thf(type_def_19, type, set_Fi1260307670real_n: $tType).
% 2.17/1.68  thf(type_def_20, type, set_Fi1645173239real_n: $tType).
% 2.17/1.68  thf(type_def_21, type, set_se830533260real_n: $tType).
% 2.17/1.68  thf(type_def_22, type, set_se955370231real_n: $tType).
% 2.17/1.68  thf(type_def_23, type, set_se1738601133real_n: $tType).
% 2.17/1.68  thf(type_def_24, type, set_se221767415real_n: $tType).
% 2.17/1.68  thf(type_def_25, type, set_se820660888real_n: $tType).
% 2.17/1.68  thf(func_def_0, type, set_Fi1066397675real_n: $tType).
% 2.17/1.68  thf(func_def_1, type, set_se830533260real_n: $tType).
% 2.17/1.68  thf(func_def_2, type, set_Fi909698444real_n: $tType).
% 2.17/1.68  thf(func_def_3, type, set_Fi1260307670real_n: $tType).
% 2.17/1.68  thf(func_def_4, type, set_Fi1491909078real_n: $tType).
% 2.17/1.68  thf(func_def_5, type, set_se1738601133real_n: $tType).
% 2.17/1.68  thf(func_def_6, type, sigma_107786596real_n: $tType).
% 2.17/1.68  thf(func_def_7, type, set_se221767415real_n: $tType).
% 2.17/1.68  thf(func_def_8, type, set_se955370231real_n: $tType).
% 2.17/1.68  thf(func_def_9, type, set_Fi1645173239real_n: $tType).
% 2.17/1.68  thf(func_def_10, type, set_Fi1326602817real_n: $tType).
% 2.17/1.68  thf(func_def_11, type, sigma_1422848389real_n: $tType).
% 2.17/1.68  thf(func_def_12, type, set_se820660888real_n: $tType).
% 2.17/1.68  thf(func_def_13, type, sigma_1466784463real_n: $tType).
% 2.17/1.68  thf(func_def_14, type, set_se2111327970real_n: $tType).
% 2.17/1.68  thf(func_def_15, type, set_Fi1058188332real_n: $tType).
% 2.17/1.68  thf(func_def_16, type, finite1489363574real_n: $tType).
% 2.17/1.68  thf(func_def_17, type, finite964658038_int_n: $tType).
% 2.17/1.68  thf(func_def_18, type, set_nat: $tType).
% 2.17/1.68  thf(func_def_19, type, nat: $tType).
% 2.17/1.68  thf(func_def_20, type, borel_1962407338real_n: (finite1489363574real_n > finite1489363574real_n) > sigma_1466784463real_n > $o).
% 2.17/1.68  thf(func_def_21, type, borel_676189912real_n: sigma_1466784463real_n).
% 2.17/1.68  thf(func_def_22, type, comple230862828real_n: sigma_1466784463real_n > sigma_1466784463real_n).
% 2.17/1.68  thf(func_def_23, type, comple1390568924real_n: sigma_1466784463real_n > set_Fi1058188332real_n > set_Fi1058188332real_n).
% 2.17/1.68  thf(func_def_24, type, minus_391085931al_n_o: ((finite1489363574real_n > finite1489363574real_n) > $o) > ((finite1489363574real_n > finite1489363574real_n) > $o) > (finite1489363574real_n > finite1489363574real_n) > $o).
% 2.17/1.68  thf(func_def_25, type, minus_455231168al_n_o: (finite1489363574real_n > $o) > (finite1489363574real_n > $o) > finite1489363574real_n > $o).
% 2.17/1.68  thf(func_def_26, type, minus_1832115082al_n_o: (set_Fi1058188332real_n > $o) > (set_Fi1058188332real_n > $o) > set_Fi1058188332real_n > $o).
% 2.17/1.68  thf(func_def_27, type, minus_1037315151real_n: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n).
% 2.17/1.68  thf(func_def_28, type, minus_minus_nat: nat > nat > nat).
% 2.17/1.68  thf(func_def_29, type, minus_725016986real_n: set_Fi1326602817real_n > set_Fi1326602817real_n > set_Fi1326602817real_n).
% 2.17/1.68  thf(func_def_30, type, minus_1686442501real_n: set_Fi1058188332real_n > set_Fi1058188332real_n > set_Fi1058188332real_n).
% 2.17/1.68  thf(func_def_31, type, minus_1698615483real_n: set_se2111327970real_n > set_se2111327970real_n > set_se2111327970real_n).
% 2.17/1.68  thf(func_def_32, type, plus_p585657087real_n: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n).
% 2.17/1.68  thf(func_def_33, type, plus_plus_nat: nat > nat > nat).
% 2.17/1.68  thf(func_def_34, type, plus_p1606848693real_n: set_Fi1058188332real_n > set_Fi1058188332real_n > set_Fi1058188332real_n).
% 2.17/1.68  thf(func_def_35, type, plus_p565022571real_n: set_se2111327970real_n > set_se2111327970real_n > set_se2111327970real_n).
% 2.17/1.68  thf(func_def_36, type, zero_z200130687real_n: finite1489363574real_n).
% 2.17/1.68  thf(func_def_37, type, zero_zero_nat: nat).
% 2.17/1.68  thf(func_def_38, type, if_Fin413489477real_n: $o > (finite1489363574real_n > finite1489363574real_n) > (finite1489363574real_n > finite1489363574real_n) > finite1489363574real_n > finite1489363574real_n).
% 2.17/1.68  thf(func_def_39, type, if_Fin127821360real_n: $o > finite1489363574real_n > finite1489363574real_n > finite1489363574real_n).
% 2.17/1.68  thf(func_def_40, type, if_set11487206real_n: $o > set_Fi1058188332real_n > set_Fi1058188332real_n > set_Fi1058188332real_n).
% 2.17/1.68  thf(func_def_41, type, inf_in32002162al_n_o: ((finite1489363574real_n > finite1489363574real_n) > $o) > ((finite1489363574real_n > finite1489363574real_n) > $o) > (finite1489363574real_n > finite1489363574real_n) > $o).
% 2.17/1.68  thf(func_def_42, type, inf_in1620715847al_n_o: (finite1489363574real_n > $o) > (finite1489363574real_n > $o) > finite1489363574real_n > $o).
% 2.17/1.68  thf(func_def_43, type, inf_in409346577al_n_o: (set_Fi1058188332real_n > $o) > (set_Fi1058188332real_n > $o) > set_Fi1058188332real_n > $o).
% 2.17/1.68  thf(func_def_44, type, inf_in146441683real_n: set_Fi1326602817real_n > set_Fi1326602817real_n > set_Fi1326602817real_n).
% 2.17/1.68  thf(func_def_45, type, inf_in1974387902real_n: set_Fi1058188332real_n > set_Fi1058188332real_n > set_Fi1058188332real_n).
% 2.17/1.68  thf(func_def_46, type, inf_in632889204real_n: set_se2111327970real_n > set_se2111327970real_n > set_se2111327970real_n).
% 2.17/1.68  thf(func_def_47, type, lebesg260170249real_n: sigma_1466784463real_n).
% 2.17/1.68  thf(func_def_48, type, minkow1134813771n_real: finite964658038_int_n > finite1489363574real_n).
% 2.17/1.68  thf(func_def_49, type, ord_Least_nat: (nat > $o) > nat).
% 2.17/1.68  thf(func_def_50, type, collec1190264032real_n: ((finite1489363574real_n > finite1489363574real_n) > $o) > set_Fi1326602817real_n).
% 2.17/1.68  thf(func_def_51, type, collec321817931real_n: (finite1489363574real_n > $o) > set_Fi1058188332real_n).
% 2.17/1.68  thf(func_def_52, type, collec452821761real_n: (set_Fi1058188332real_n > $o) > set_se2111327970real_n).
% 2.17/1.68  thf(func_def_53, type, image_1123376925real_n: ((finite1489363574real_n > finite1489363574real_n) > finite1489363574real_n > finite1489363574real_n) > set_Fi1326602817real_n > set_Fi1326602817real_n).
% 2.17/1.68  thf(func_def_54, type, image_449906696real_n: ((finite1489363574real_n > finite1489363574real_n) > finite1489363574real_n) > set_Fi1326602817real_n > set_Fi1058188332real_n).
% 2.17/1.68  thf(func_def_55, type, image_128879038real_n: ((finite1489363574real_n > finite1489363574real_n) > set_Fi1058188332real_n) > set_Fi1326602817real_n > set_se2111327970real_n).
% 2.17/1.68  thf(func_def_56, type, image_437359496real_n: (finite1489363574real_n > finite1489363574real_n > finite1489363574real_n) > set_Fi1058188332real_n > set_Fi1326602817real_n).
% 2.17/1.68  thf(func_def_57, type, image_439535603real_n: (finite1489363574real_n > finite1489363574real_n) > set_Fi1058188332real_n > set_Fi1058188332real_n).
% 2.17/1.68  thf(func_def_58, type, image_545463721real_n: (finite1489363574real_n > set_Fi1058188332real_n) > set_Fi1058188332real_n > set_se2111327970real_n).
% 2.17/1.68  thf(func_def_59, type, image_nat_nat: (nat > nat) > set_nat > set_nat).
% 2.17/1.68  thf(func_def_60, type, image_352856126real_n: (set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n) > set_se2111327970real_n > set_Fi1326602817real_n).
% 2.17/1.68  thf(func_def_61, type, image_1311908777real_n: (set_Fi1058188332real_n > finite1489363574real_n) > set_se2111327970real_n > set_Fi1058188332real_n).
% 2.17/1.68  thf(func_def_62, type, image_1661509983real_n: (set_Fi1058188332real_n > set_Fi1058188332real_n) > set_se2111327970real_n > set_se2111327970real_n).
% 2.17/1.68  thf(func_def_63, type, vimage180751827real_n: ((finite1489363574real_n > finite1489363574real_n) > finite1489363574real_n > finite1489363574real_n) > set_Fi1326602817real_n > set_Fi1326602817real_n).
% 2.17/1.68  thf(func_def_64, type, vimage1072397758real_n: ((finite1489363574real_n > finite1489363574real_n) > finite1489363574real_n) > set_Fi1058188332real_n > set_Fi1326602817real_n).
% 2.17/1.68  thf(func_def_65, type, vimage2098059032_n_nat: ((finite1489363574real_n > finite1489363574real_n) > nat) > set_nat > set_Fi1326602817real_n).
% 2.17/1.68  thf(func_def_66, type, vimage1910974324real_n: ((finite1489363574real_n > finite1489363574real_n) > set_Fi1058188332real_n) > set_se2111327970real_n > set_Fi1326602817real_n).
% 2.17/1.68  thf(func_def_67, type, vimage1059850558real_n: (finite1489363574real_n > finite1489363574real_n > finite1489363574real_n) > set_Fi1326602817real_n > set_Fi1058188332real_n).
% 2.17/1.68  thf(func_def_68, type, vimage1233683625real_n: (finite1489363574real_n > finite1489363574real_n) > set_Fi1058188332real_n > set_Fi1058188332real_n).
% 2.17/1.68  thf(func_def_69, type, vimage281029891_n_nat: (finite1489363574real_n > nat) > set_nat > set_Fi1058188332real_n).
% 2.17/1.68  thf(func_def_70, type, vimage207290975real_n: (finite1489363574real_n > set_Fi1058188332real_n) > set_se2111327970real_n > set_Fi1058188332real_n).
% 2.17/1.68  thf(func_def_71, type, vimage2134951412real_n: (set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n) > set_Fi1326602817real_n > set_se2111327970real_n).
% 2.17/1.68  thf(func_def_72, type, vimage973736031real_n: (set_Fi1058188332real_n > finite1489363574real_n) > set_Fi1058188332real_n > set_se2111327970real_n).
% 2.17/1.68  thf(func_def_73, type, vimage501526201_n_nat: (set_Fi1058188332real_n > nat) > set_nat > set_se2111327970real_n).
% 2.17/1.68  thf(func_def_74, type, vimage784510485real_n: (set_Fi1058188332real_n > set_Fi1058188332real_n) > set_se2111327970real_n > set_se2111327970real_n).
% 2.17/1.68  thf(func_def_75, type, sigma_1185134568real_n: sigma_107786596real_n > sigma_107786596real_n > set_Fi1066397675real_n).
% 2.17/1.68  thf(func_def_76, type, sigma_2028985427real_n: sigma_107786596real_n > sigma_1466784463real_n > set_Fi1491909078real_n).
% 2.17/1.68  thf(func_def_77, type, sigma_364818953real_n: sigma_107786596real_n > sigma_1422848389real_n > set_Fi909698444real_n).
% 2.17/1.68  thf(func_def_78, type, sigma_2016438227real_n: sigma_1466784463real_n > sigma_107786596real_n > set_Fi1260307670real_n).
% 2.17/1.68  thf(func_def_79, type, sigma_439801790real_n: sigma_1466784463real_n > sigma_1466784463real_n > set_Fi1326602817real_n).
% 2.17/1.68  thf(func_def_80, type, sigma_566919540real_n: sigma_1466784463real_n > sigma_1422848389real_n > set_Fi1645173239real_n).
% 2.17/1.68  thf(func_def_81, type, sigma_588796041real_n: sigma_1422848389real_n > sigma_107786596real_n > set_se830533260real_n).
% 2.17/1.68  thf(func_def_82, type, sigma_1333364596real_n: sigma_1422848389real_n > sigma_1466784463real_n > set_se955370231real_n).
% 2.17/1.68  thf(func_def_83, type, sigma_239294762real_n: sigma_1422848389real_n > sigma_1422848389real_n > set_se1738601133real_n).
% 2.17/1.68  thf(func_def_84, type, sigma_1052429895real_n: sigma_107786596real_n > set_Fi1326602817real_n > sigma_107786596real_n).
% 2.17/1.68  thf(func_def_85, type, sigma_346513458real_n: sigma_1466784463real_n > set_Fi1058188332real_n > sigma_1466784463real_n).
% 2.17/1.68  thf(func_def_86, type, sigma_993999336real_n: sigma_1422848389real_n > set_se2111327970real_n > sigma_1422848389real_n).
% 2.17/1.68  thf(func_def_87, type, sigma_522684908real_n: sigma_107786596real_n > set_se221767415real_n).
% 2.17/1.68  thf(func_def_88, type, sigma_1235138647real_n: sigma_1466784463real_n > set_se2111327970real_n).
% 2.17/1.68  thf(func_def_89, type, sigma_433815053real_n: sigma_1422848389real_n > set_se820660888real_n).
% 2.17/1.68  thf(func_def_90, type, sigma_1483971331real_n: sigma_107786596real_n > set_Fi1326602817real_n).
% 2.17/1.68  thf(func_def_91, type, sigma_476185326real_n: sigma_1466784463real_n > set_Fi1058188332real_n).
% 2.17/1.68  thf(func_def_92, type, sigma_607186084real_n: sigma_1422848389real_n > set_se2111327970real_n).
% 2.17/1.68  thf(func_def_93, type, sigma_136294295real_n: set_Fi1326602817real_n > ((finite1489363574real_n > finite1489363574real_n) > finite1489363574real_n) > sigma_1466784463real_n > sigma_107786596real_n).
% 2.17/1.68  thf(func_def_94, type, sigma_821351682real_n: set_Fi1058188332real_n > (finite1489363574real_n > finite1489363574real_n) > sigma_1466784463real_n > sigma_1466784463real_n).
% 2.17/1.68  thf(func_def_95, type, sigma_1384150200real_n: set_se2111327970real_n > (set_Fi1058188332real_n > finite1489363574real_n) > sigma_1466784463real_n > sigma_1422848389real_n).
% 2.17/1.68  thf(func_def_96, type, member117715276real_n: ((finite1489363574real_n > finite1489363574real_n) > finite1489363574real_n > finite1489363574real_n) > set_Fi1066397675real_n > $o).
% 2.17/1.68  thf(func_def_97, type, member1695588023real_n: ((finite1489363574real_n > finite1489363574real_n) > finite1489363574real_n) > set_Fi1491909078real_n > $o).
% 2.17/1.68  thf(func_def_98, type, member640587117real_n: ((finite1489363574real_n > finite1489363574real_n) > set_Fi1058188332real_n) > set_Fi909698444real_n > $o).
% 2.17/1.68  thf(func_def_99, type, member408431031real_n: (finite1489363574real_n > finite1489363574real_n > finite1489363574real_n) > set_Fi1260307670real_n > $o).
% 2.17/1.68  thf(func_def_100, type, member1746150050real_n: (finite1489363574real_n > finite1489363574real_n) > set_Fi1326602817real_n > $o).
% 2.17/1.68  thf(func_def_101, type, member966061400real_n: (finite1489363574real_n > set_Fi1058188332real_n) > set_Fi1645173239real_n > $o).
% 2.17/1.68  thf(func_def_102, type, member1764433517real_n: (set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n) > set_se830533260real_n > $o).
% 2.17/1.68  thf(func_def_103, type, member1759501912real_n: (set_Fi1058188332real_n > finite1489363574real_n) > set_se955370231real_n > $o).
% 2.17/1.68  thf(func_def_104, type, member1734791438real_n: (set_Fi1058188332real_n > set_Fi1058188332real_n) > set_se1738601133real_n > $o).
% 2.17/1.68  thf(func_def_105, type, member1352538125real_n: finite1489363574real_n > set_Fi1058188332real_n > $o).
% 2.17/1.68  thf(func_def_106, type, member2104752728real_n: set_Fi1326602817real_n > set_se221767415real_n > $o).
% 2.17/1.68  thf(func_def_107, type, member223413699real_n: set_Fi1058188332real_n > set_se2111327970real_n > $o).
% 2.17/1.68  thf(func_def_108, type, member1475136633real_n: set_se2111327970real_n > set_se820660888real_n > $o).
% 2.17/1.68  thf(func_def_109, type, r: finite964658038_int_n > set_Fi1058188332real_n).
% 2.17/1.68  thf(func_def_110, type, s: set_Fi1058188332real_n).
% 2.17/1.68  thf(func_def_111, type, t: finite964658038_int_n > set_Fi1058188332real_n).
% 2.17/1.68  thf(func_def_112, type, t2: finite964658038_int_n > set_Fi1058188332real_n).
% 2.17/1.68  thf(func_def_113, type, a: finite964658038_int_n).
% 2.17/1.68  thf(func_def_128, type, sK0: (finite1489363574real_n > $o) > set_Fi1058188332real_n > (finite1489363574real_n > finite1489363574real_n) > finite1489363574real_n).
% 2.17/1.68  thf(func_def_129, type, sK1: (finite1489363574real_n > finite1489363574real_n) > sigma_1466784463real_n > sigma_1466784463real_n > finite1489363574real_n).
% 2.17/1.68  thf(func_def_130, type, sK2: (finite1489363574real_n > finite1489363574real_n) > sigma_1466784463real_n > sigma_1466784463real_n > set_Fi1058188332real_n).
% 2.17/1.68  thf(func_def_131, type, sK3: set_Fi1058188332real_n > (finite1489363574real_n > finite1489363574real_n) > (finite1489363574real_n > finite1489363574real_n) > finite1489363574real_n).
% 2.17/1.68  thf(func_def_132, type, sK4: (finite1489363574real_n > $o) > (finite1489363574real_n > $o) > finite1489363574real_n).
% 2.17/1.68  thf(func_def_133, type, sK5: (finite1489363574real_n > finite1489363574real_n) > (finite1489363574real_n > $o) > set_Fi1058188332real_n > finite1489363574real_n).
% 2.17/1.68  thf(func_def_134, type, sK6: (finite1489363574real_n > $o) > (finite1489363574real_n > finite1489363574real_n) > (finite1489363574real_n > $o) > finite1489363574real_n).
% 2.17/1.68  thf(func_def_135, type, sK7: (finite1489363574real_n > finite1489363574real_n) > sigma_1466784463real_n > (finite1489363574real_n > finite1489363574real_n) > finite1489363574real_n).
% 2.17/1.68  thf(func_def_136, type, sK8: (finite1489363574real_n > finite1489363574real_n) > set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n).
% 2.17/1.68  thf(func_def_137, type, sK9: (finite1489363574real_n > finite1489363574real_n) > sigma_1466784463real_n > (finite1489363574real_n > finite1489363574real_n) > finite1489363574real_n).
% 2.17/1.68  thf(func_def_138, type, sK10: (finite1489363574real_n > finite1489363574real_n) > (finite1489363574real_n > finite1489363574real_n) > set_Fi1058188332real_n > finite1489363574real_n).
% 2.17/1.68  thf(func_def_139, type, sK11: set_Fi1058188332real_n > set_Fi1058188332real_n > finite1489363574real_n > finite1489363574real_n).
% 2.17/1.68  thf(func_def_140, type, sK12: set_Fi1058188332real_n > (finite1489363574real_n > finite1489363574real_n) > (finite1489363574real_n > finite1489363574real_n) > finite1489363574real_n).
% 2.17/1.68  thf(func_def_142, type, ph14: !>[X0: $tType]:(X0)).
% 2.17/1.68  thf(f1682,plain,(
% 2.17/1.68    $false),
% 2.17/1.68    inference(trivial_inequality_removal,[status(thm)],[f1680])).
% 2.17/1.68  thf(f1680,plain,(
% 2.17/1.68    ($true != $true)),
% 2.17/1.68    inference(superposition,[status(thm)],[f1412,f1631])).
% 2.17/1.68  thf(f1631,plain,(
% 2.17/1.68    ( ! [X0 : finite964658038_int_n] : (((member223413699real_n @ (collec321817931real_n @ (^[Y0 : finite1489363574real_n]: (member1352538125real_n @ (plus_p585657087real_n @ Y0 @ (minkow1134813771n_real @ X0)) @ (t2 @ X0)))) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))) = $true)) )),
% 2.17/1.68    inference(forward_demodulation,[status(thm)],[f1629,f1241])).
% 2.17/1.68  thf(f1241,plain,(
% 2.17/1.68    ( ! [X0 : set_Fi1058188332real_n] : (((sigma_476185326real_n @ (sigma_346513458real_n @ (comple230862828real_n @ lebesg260170249real_n) @ X0)) = X0)) )),
% 2.17/1.68    inference(cnf_transformation,[status(thm)],[f883])).
% 2.17/1.68  thf(f883,plain,(
% 2.17/1.68    ! [X0 : set_Fi1058188332real_n] : ((sigma_476185326real_n @ (sigma_346513458real_n @ (comple230862828real_n @ lebesg260170249real_n) @ X0)) = X0)),
% 2.17/1.68    inference(rectify,[status(thm)],[f276])).
% 2.17/1.68  thf(f276,axiom,(
% 2.17/1.68    ! [X20 : set_Fi1058188332real_n] : ((sigma_476185326real_n @ (sigma_346513458real_n @ (comple230862828real_n @ lebesg260170249real_n) @ X20)) = X20)),
% 2.17/1.68    file('/export/starexec/sandbox/tmp/tmp.gWsecxm7AG/DTF2THF_14897.p',fact_275_space__lebesgue__on)).
% 2.17/1.68  thf(f1629,plain,(
% 2.17/1.68    ( ! [X0 : finite964658038_int_n] : (($true = (member223413699real_n @ (sigma_476185326real_n @ (sigma_346513458real_n @ (comple230862828real_n @ lebesg260170249real_n) @ (collec321817931real_n @ (^[Y0 : finite1489363574real_n]: (member1352538125real_n @ (plus_p585657087real_n @ Y0 @ (minkow1134813771n_real @ X0)) @ (t2 @ X0)))))) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))))) )),
% 2.17/1.68    inference(backward_demodulation,[status(thm)],[f1612,f1383])).
% 2.17/1.68  thf(f1383,plain,(
% 2.17/1.68    ( ! [X0 : set_Fi1058188332real_n,X1 : sigma_1466784463real_n] : (((collec321817931real_n @ (^[Y0 : finite1489363574real_n]: ((member1352538125real_n @ Y0 @ (sigma_476185326real_n @ X1)) & (member1352538125real_n @ Y0 @ X0)))) = (sigma_476185326real_n @ (sigma_346513458real_n @ X1 @ X0)))) )),
% 2.17/1.68    inference(beta_eta_normalization,[status(thm)],[f1315])).
% 2.17/1.68  thf(f1315,plain,(
% 2.17/1.68    ( ! [X0 : set_Fi1058188332real_n,X1 : sigma_1466784463real_n] : ((((^[Y0 : set_Fi1058188332real_n]: ((^[Y1 : set_Fi1058188332real_n]: (collec321817931real_n @ (^[Y2 : finite1489363574real_n]: ((member1352538125real_n @ Y2 @ Y1) & (member1352538125real_n @ Y2 @ Y0))))))) @ X0 @ (sigma_476185326real_n @ X1)) = (sigma_476185326real_n @ (sigma_346513458real_n @ X1 @ X0)))) )),
% 2.17/1.68    inference(definition_unfolding,[status(thm)],[f1137,f1204])).
% 2.17/1.68  thf(f1204,plain,(
% 2.17/1.68    (inf_in1974387902real_n = (^[Y0 : set_Fi1058188332real_n]: ((^[Y1 : set_Fi1058188332real_n]: (collec321817931real_n @ (^[Y2 : finite1489363574real_n]: ((member1352538125real_n @ Y2 @ Y1) & (member1352538125real_n @ Y2 @ Y0))))))))),
% 2.17/1.68    inference(cnf_transformation,[status(thm)],[f797])).
% 2.17/1.68  thf(f797,plain,(
% 2.17/1.68    (inf_in1974387902real_n = (^[Y0 : set_Fi1058188332real_n]: ((^[Y1 : set_Fi1058188332real_n]: (collec321817931real_n @ (^[Y2 : finite1489363574real_n]: ((member1352538125real_n @ Y2 @ Y1) & (member1352538125real_n @ Y2 @ Y0))))))))),
% 2.17/1.68    inference(fool_elimination,[status(thm)],[f796])).
% 2.17/1.68  thf(f796,plain,(
% 2.17/1.68    (inf_in1974387902real_n = (^[X0 : set_Fi1058188332real_n, X1 : set_Fi1058188332real_n] : (collec321817931real_n @ (^[X2 : finite1489363574real_n] : ((member1352538125real_n @ X2 @ X0) & (member1352538125real_n @ X2 @ X1))))))),
% 2.17/1.68    inference(rectify,[status(thm)],[f67])).
% 2.17/1.68  thf(f67,axiom,(
% 2.17/1.68    (inf_in1974387902real_n = (^[X16 : set_Fi1058188332real_n, X14 : set_Fi1058188332real_n] : (collec321817931real_n @ (^[X2 : finite1489363574real_n] : ((member1352538125real_n @ X2 @ X16) & (member1352538125real_n @ X2 @ X14))))))),
% 2.17/1.68    file('/export/starexec/sandbox/tmp/tmp.gWsecxm7AG/DTF2THF_14897.p',fact_66_Int__def)).
% 2.17/1.68  thf(f1137,plain,(
% 2.17/1.68    ( ! [X0 : set_Fi1058188332real_n,X1 : sigma_1466784463real_n] : (((sigma_476185326real_n @ (sigma_346513458real_n @ X1 @ X0)) = (inf_in1974387902real_n @ X0 @ (sigma_476185326real_n @ X1)))) )),
% 2.17/1.68    inference(cnf_transformation,[status(thm)],[f924])).
% 2.17/1.68  thf(f924,plain,(
% 2.17/1.68    ! [X0 : set_Fi1058188332real_n,X1 : sigma_1466784463real_n] : ((sigma_476185326real_n @ (sigma_346513458real_n @ X1 @ X0)) = (inf_in1974387902real_n @ X0 @ (sigma_476185326real_n @ X1)))),
% 2.17/1.68    inference(rectify,[status(thm)],[f269])).
% 2.17/1.68  thf(f269,axiom,(
% 2.17/1.68    ! [X39 : set_Fi1058188332real_n,X4 : sigma_1466784463real_n] : ((inf_in1974387902real_n @ X39 @ (sigma_476185326real_n @ X4)) = (sigma_476185326real_n @ (sigma_346513458real_n @ X4 @ X39)))),
% 2.17/1.68    file('/export/starexec/sandbox/tmp/tmp.gWsecxm7AG/DTF2THF_14897.p',fact_268_space__restrict__space)).
% 2.17/1.68  thf(f1612,plain,(
% 2.17/1.68    ( ! [X0 : finite964658038_int_n] : (((member223413699real_n @ (collec321817931real_n @ (^[Y0 : finite1489363574real_n]: ((member1352538125real_n @ Y0 @ (sigma_476185326real_n @ (comple230862828real_n @ lebesg260170249real_n))) & (member1352538125real_n @ Y0 @ (collec321817931real_n @ (^[Y1 : finite1489363574real_n]: (member1352538125real_n @ (plus_p585657087real_n @ Y1 @ (minkow1134813771n_real @ X0)) @ (t2 @ X0)))))))) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))) = $true)) )),
% 2.17/1.68    inference(subsumption_resolution,[status(thm)],[f1508,f1091])).
% 2.17/1.68  thf(f1091,plain,(
% 2.17/1.68    ( ! [X0 : finite964658038_int_n] : (((member223413699real_n @ (t2 @ X0) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))) = $true)) )),
% 2.17/1.68    inference(cnf_transformation,[status(thm)],[f550])).
% 2.17/1.68  thf(f550,plain,(
% 2.17/1.68    ! [X0 : finite964658038_int_n] : ((member223413699real_n @ (t2 @ X0) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))) = $true)),
% 2.17/1.68    inference(fool_elimination,[status(thm)],[f549])).
% 2.17/1.68  thf(f549,plain,(
% 2.17/1.68    ! [X0 : finite964658038_int_n] : (member223413699real_n @ (t2 @ X0) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n)))),
% 2.17/1.68    inference(rectify,[status(thm)],[f4])).
% 2.17/1.68  thf(f4,axiom,(
% 2.17/1.68    ! [X0 : finite964658038_int_n] : (member223413699real_n @ (t2 @ X0) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n)))),
% 2.17/1.68    file('/export/starexec/sandbox/tmp/tmp.gWsecxm7AG/DTF2THF_14897.p',fact_3__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062)).
% 2.17/1.68  thf(f1508,plain,(
% 2.17/1.68    ( ! [X0 : finite964658038_int_n] : (((member223413699real_n @ (t2 @ X0) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))) != $true) | ((member223413699real_n @ (collec321817931real_n @ (^[Y0 : finite1489363574real_n]: ((member1352538125real_n @ Y0 @ (sigma_476185326real_n @ (comple230862828real_n @ lebesg260170249real_n))) & (member1352538125real_n @ Y0 @ (collec321817931real_n @ (^[Y1 : finite1489363574real_n]: (member1352538125real_n @ (plus_p585657087real_n @ Y1 @ (minkow1134813771n_real @ X0)) @ (t2 @ X0)))))))) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))) = $true)) )),
% 2.17/1.68    inference(beta_eta_normalization,[status(thm)],[f1353])).
% 2.17/1.68  thf(f1353,plain,(
% 2.17/1.68    ( ! [X0 : finite964658038_int_n] : (((member223413699real_n @ ((^[Y0 : set_Fi1058188332real_n]: ((^[Y1 : set_Fi1058188332real_n]: (collec321817931real_n @ (^[Y2 : finite1489363574real_n]: ((member1352538125real_n @ Y2 @ Y1) & (member1352538125real_n @ Y2 @ Y0))))))) @ ((^[Y0 : finite1489363574real_n > finite1489363574real_n]: ((^[Y1 : set_Fi1058188332real_n]: (collec321817931real_n @ (^[Y2 : finite1489363574real_n]: (member1352538125real_n @ (Y0 @ Y2) @ Y1)))))) @ (^[Y0 : finite1489363574real_n]: (plus_p585657087real_n @ Y0 @ (minkow1134813771n_real @ X0))) @ (t2 @ X0)) @ (sigma_476185326real_n @ (comple230862828real_n @ lebesg260170249real_n))) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))) = $true) | ((member223413699real_n @ (t2 @ X0) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))) != $true)) )),
% 2.17/1.68    inference(definition_unfolding,[status(thm)],[f1267,f1204,f1255])).
% 2.17/1.68  thf(f1255,plain,(
% 2.17/1.68    (vimage1233683625real_n = (^[Y0 : finite1489363574real_n > finite1489363574real_n]: ((^[Y1 : set_Fi1058188332real_n]: (collec321817931real_n @ (^[Y2 : finite1489363574real_n]: (member1352538125real_n @ (Y0 @ Y2) @ Y1)))))))),
% 2.17/1.68    inference(cnf_transformation,[status(thm)],[f652])).
% 2.17/1.68  thf(f652,plain,(
% 2.17/1.68    (vimage1233683625real_n = (^[Y0 : finite1489363574real_n > finite1489363574real_n]: ((^[Y1 : set_Fi1058188332real_n]: (collec321817931real_n @ (^[Y2 : finite1489363574real_n]: (member1352538125real_n @ (Y0 @ Y2) @ Y1)))))))),
% 2.17/1.68    inference(fool_elimination,[status(thm)],[f651])).
% 2.17/1.68  thf(f651,plain,(
% 2.17/1.68    (vimage1233683625real_n = (^[X0 : finite1489363574real_n > finite1489363574real_n, X1 : set_Fi1058188332real_n] : (collec321817931real_n @ (^[X2 : finite1489363574real_n] : (member1352538125real_n @ (X0 @ X2) @ X1)))))),
% 2.17/1.68    inference(rectify,[status(thm)],[f27])).
% 2.17/1.68  thf(f27,axiom,(
% 2.17/1.68    (vimage1233683625real_n = (^[X13 : finite1489363574real_n > finite1489363574real_n, X14 : set_Fi1058188332real_n] : (collec321817931real_n @ (^[X2 : finite1489363574real_n] : (member1352538125real_n @ (X13 @ X2) @ X14)))))),
% 2.17/1.68    file('/export/starexec/sandbox/tmp/tmp.gWsecxm7AG/DTF2THF_14897.p',fact_26_vimage__def)).
% 2.17/1.68  thf(f1267,plain,(
% 2.17/1.68    ( ! [X0 : finite964658038_int_n] : (((member223413699real_n @ (t2 @ X0) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))) != $true) | ((member223413699real_n @ (inf_in1974387902real_n @ (vimage1233683625real_n @ (^[Y0 : finite1489363574real_n]: (plus_p585657087real_n @ Y0 @ (minkow1134813771n_real @ X0))) @ (t2 @ X0)) @ (sigma_476185326real_n @ (comple230862828real_n @ lebesg260170249real_n))) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))) = $true)) )),
% 2.17/1.68    inference(cnf_transformation,[status(thm)],[f989])).
% 2.17/1.68  thf(f989,plain,(
% 2.17/1.68    ! [X0 : finite964658038_int_n] : (((member223413699real_n @ (t2 @ X0) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))) != $true) | ((member223413699real_n @ (inf_in1974387902real_n @ (vimage1233683625real_n @ (^[Y0 : finite1489363574real_n]: (plus_p585657087real_n @ Y0 @ (minkow1134813771n_real @ X0))) @ (t2 @ X0)) @ (sigma_476185326real_n @ (comple230862828real_n @ lebesg260170249real_n))) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))) = $true))),
% 2.17/1.68    inference(ennf_transformation,[status(thm)],[f872])).
% 2.17/1.68  thf(f872,plain,(
% 2.17/1.68    ! [X0 : finite964658038_int_n] : (((member223413699real_n @ (t2 @ X0) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))) = $true) => ((member223413699real_n @ (inf_in1974387902real_n @ (vimage1233683625real_n @ (^[Y0 : finite1489363574real_n]: (plus_p585657087real_n @ Y0 @ (minkow1134813771n_real @ X0))) @ (t2 @ X0)) @ (sigma_476185326real_n @ (comple230862828real_n @ lebesg260170249real_n))) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))) = $true))),
% 2.17/1.68    inference(fool_elimination,[status(thm)],[f871])).
% 2.17/1.68  thf(f871,plain,(
% 2.17/1.68    ! [X0 : finite964658038_int_n] : ((member223413699real_n @ (t2 @ X0) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))) => (member223413699real_n @ (inf_in1974387902real_n @ (vimage1233683625real_n @ (^[X1 : finite1489363574real_n] : (plus_p585657087real_n @ X1 @ (minkow1134813771n_real @ X0))) @ (t2 @ X0)) @ (sigma_476185326real_n @ (comple230862828real_n @ lebesg260170249real_n))) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))))),
% 2.17/1.68    inference(rectify,[status(thm)],[f3])).
% 2.17/1.68  thf(f3,axiom,(
% 2.17/1.68    ! [X0 : finite964658038_int_n] : ((member223413699real_n @ (t2 @ X0) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))) => (member223413699real_n @ (inf_in1974387902real_n @ (vimage1233683625real_n @ (^[X2 : finite1489363574real_n] : (plus_p585657087real_n @ X2 @ (minkow1134813771n_real @ X0))) @ (t2 @ X0)) @ (sigma_476185326real_n @ (comple230862828real_n @ lebesg260170249real_n))) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))))),
% 2.17/1.68    file('/export/starexec/sandbox/tmp/tmp.gWsecxm7AG/DTF2THF_14897.p',fact_2__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_A_092_060Longrightarrow_062_A_I_092_060lambda_062x_O_Ax_A_L_Aof__int__vec_Aa_J_A_N_096_AT_Aa_A_092_060inter_062_Aspace_Alebesgue_A_092_060in_062_Asets_Alebesgue_092_060close_062)).
% 2.17/1.68  thf(f1412,plain,(
% 2.17/1.68    ((member223413699real_n @ (collec321817931real_n @ (^[Y0 : finite1489363574real_n]: (member1352538125real_n @ (plus_p585657087real_n @ Y0 @ (minkow1134813771n_real @ a)) @ (t2 @ a)))) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))) != $true)),
% 2.17/1.68    inference(beta_eta_normalization,[status(thm)],[f1312])).
% 2.17/1.68  thf(f1312,plain,(
% 2.17/1.68    ((member223413699real_n @ ((^[Y0 : finite1489363574real_n > finite1489363574real_n]: ((^[Y1 : set_Fi1058188332real_n]: (collec321817931real_n @ (^[Y2 : finite1489363574real_n]: (member1352538125real_n @ (Y0 @ Y2) @ Y1)))))) @ (^[Y0 : finite1489363574real_n]: (plus_p585657087real_n @ Y0 @ (minkow1134813771n_real @ a))) @ (t2 @ a)) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))) != $true)),
% 2.17/1.68    inference(definition_unfolding,[status(thm)],[f1132,f1255])).
% 2.17/1.68  thf(f1132,plain,(
% 2.17/1.68    ((member223413699real_n @ (vimage1233683625real_n @ (^[Y0 : finite1489363574real_n]: (plus_p585657087real_n @ Y0 @ (minkow1134813771n_real @ a))) @ (t2 @ a)) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))) != $true)),
% 2.17/1.68    inference(cnf_transformation,[status(thm)],[f881])).
% 2.17/1.68  thf(f881,plain,(
% 2.17/1.68    ((member223413699real_n @ (vimage1233683625real_n @ (^[Y0 : finite1489363574real_n]: (plus_p585657087real_n @ Y0 @ (minkow1134813771n_real @ a))) @ (t2 @ a)) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))) != $true)),
% 2.17/1.68    inference(flattening,[status(thm)],[f477])).
% 2.17/1.68  thf(f477,plain,(
% 2.17/1.68    ~((member223413699real_n @ (vimage1233683625real_n @ (^[Y0 : finite1489363574real_n]: (plus_p585657087real_n @ Y0 @ (minkow1134813771n_real @ a))) @ (t2 @ a)) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n))) = $true)),
% 2.17/1.68    inference(fool_elimination,[status(thm)],[f476])).
% 2.17/1.68  thf(f476,plain,(
% 2.17/1.68    ~(member223413699real_n @ (vimage1233683625real_n @ (^[X0 : finite1489363574real_n] : (plus_p585657087real_n @ X0 @ (minkow1134813771n_real @ a))) @ (t2 @ a)) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n)))),
% 2.17/1.68    inference(rectify,[status(thm)],[f363])).
% 2.17/1.68  thf(f363,negated_conjecture,(
% 2.17/1.68    ~(member223413699real_n @ (vimage1233683625real_n @ (^[X2 : finite1489363574real_n] : (plus_p585657087real_n @ X2 @ (minkow1134813771n_real @ a))) @ (t2 @ a)) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n)))),
% 2.17/1.68    inference(negated_conjecture,[status(cth)],[f362])).
% 2.17/1.68  thf(f362,conjecture,(
% 2.17/1.68    (member223413699real_n @ (vimage1233683625real_n @ (^[X2 : finite1489363574real_n] : (plus_p585657087real_n @ X2 @ (minkow1134813771n_real @ a))) @ (t2 @ a)) @ (sigma_1235138647real_n @ (comple230862828real_n @ lebesg260170249real_n)))),
% 2.17/1.68    file('/export/starexec/sandbox/tmp/tmp.gWsecxm7AG/DTF2THF_14897.p',conj_0)).
% 2.17/1.68  % SZS output end Proof for DTF2THF_14897
% 2.17/1.68  % (15223)------------------------------
% 2.17/1.68  % (15223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.68  % (15223)Termination reason: Refutation
% 2.17/1.68  
% 2.17/1.68  % (15223)Memory used [KB]: 7547
% 2.17/1.68  % (15223)Time elapsed: 0.077 s
% 2.17/1.68  % (15223)Instructions burned: 243 (million)
% 2.17/1.68  % (15223)------------------------------
% 2.17/1.68  % (15223)------------------------------
% 2.17/1.68  % (15160)Success in time 0.497 s
%------------------------------------------------------------------------------