%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP169^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:56:06 AM UTC 2026
% Result : Theorem 2.69s 1.59s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 16 unt; 0 typ; 2 def)
% Number of atoms : 302 ( 165 equ; 0 cnn)
% Maximal formula atoms : 18 ( 7 avg)
% Number of connectives : 971 ( 94 ~; 80 |; 72 &; 719 @)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 159 ( 156 usr; 18 con; 0-5 aty)
% Number of variables : 14 ( 0 ^; 10 !; 4 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_7,type,
real: $tType ).
thf(type_def_8,type,
cars: $tType ).
thf(type_def_9,type,
traffic: $tType ).
thf(type_def_10,type,
view_e774982825t_unit: $tType ).
thf(type_def_11,type,
real_int: $tType ).
thf(type_def_12,type,
nat_int: $tType ).
thf(func_def_0,type,
view_e774982825t_unit: $tType ).
thf(func_def_1,type,
real_int: $tType ).
thf(func_def_2,type,
nat_int: $tType ).
thf(func_def_3,type,
traffic: $tType ).
thf(func_def_4,type,
real: $tType ).
thf(func_def_5,type,
cars: $tType ).
thf(func_def_6,type,
nat: $tType ).
thf(func_def_7,type,
one_one_nat: nat ).
thf(func_def_8,type,
plus_plus_nat: nat > nat > nat ).
thf(func_def_9,type,
plus_plus_real: real > real > real ).
thf(func_def_10,type,
zero_zero_nat: nat ).
thf(func_def_11,type,
zero_zero_real: real ).
thf(func_def_12,type,
len: ( cars > traffic > cars > real ) > view_e774982825t_unit > traffic > cars > real_int ).
thf(func_def_13,type,
move: traffic > traffic > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_14,type,
nat_card: nat_int > nat ).
thf(func_def_15,type,
bot_bot_nat_int: nat_int ).
thf(func_def_16,type,
ord_less_nat_int: nat_int > nat_int > $o ).
thf(func_def_17,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_18,type,
ord_less_real: real > real > $o ).
thf(func_def_19,type,
ord_less_eq_nat_int: nat_int > nat_int > $o ).
thf(func_def_20,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_21,type,
ord_less_eq_real_int: real_int > real_int > $o ).
thf(func_def_22,type,
ord_less_eq_real: real > real > $o ).
thf(func_def_23,type,
ord_le461438217t_unit: view_e774982825t_unit > view_e774982825t_unit > $o ).
thf(func_def_24,type,
real_length: real_int > real ).
thf(func_def_25,type,
regular_regular: cars > traffic > cars > real ).
thf(func_def_26,type,
restrict: view_e774982825t_unit > ( cars > nat_int ) > cars > nat_int ).
thf(func_def_27,type,
abstract: traffic > traffic > $o ).
thf(func_def_28,type,
clm: traffic > cars > nat_int ).
thf(func_def_29,type,
create_claim: traffic > cars > nat > traffic > $o ).
thf(func_def_30,type,
create_reservation: traffic > cars > traffic > $o ).
thf(func_def_31,type,
res: traffic > cars > nat_int ).
thf(func_def_32,type,
withdraw_claim: traffic > cars > traffic > $o ).
thf(func_def_33,type,
withdraw_reservation: traffic > cars > nat > traffic > $o ).
thf(func_def_34,type,
ext_Product_unit: view_e774982825t_unit > real_int ).
thf(func_def_35,type,
hchop: view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > $o ).
thf(func_def_36,type,
lan_Product_unit: view_e774982825t_unit > nat_int ).
thf(func_def_37,type,
own_Product_unit: view_e774982825t_unit > cars ).
thf(func_def_38,type,
vchop: view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > $o ).
thf(func_def_39,type,
c: cars ).
thf(func_def_40,type,
d: cars ).
thf(func_def_41,type,
e: cars ).
thf(func_def_43,type,
ts: traffic ).
thf(func_def_44,type,
ts2: traffic ).
thf(func_def_45,type,
ts_a: traffic ).
thf(func_def_46,type,
ts3: traffic ).
thf(func_def_47,type,
v: view_e774982825t_unit ).
thf(func_def_66,type,
sP0: view_e774982825t_unit > traffic > cars > $o ).
thf(func_def_67,type,
sP1: ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > traffic > $o ).
thf(func_def_68,type,
sP2: ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > traffic > $o ).
thf(func_def_69,type,
sP3: ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit > $o ).
thf(func_def_70,type,
sP4: ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit > $o ).
thf(func_def_71,type,
sP5: ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit > $o ).
thf(func_def_72,type,
sP6: ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit > $o ).
thf(func_def_73,type,
sP7: ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit > $o ).
thf(func_def_74,type,
sP8: ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > traffic > $o ).
thf(func_def_75,type,
sK9: view_e774982825t_unit > traffic > cars > view_e774982825t_unit ).
thf(func_def_76,type,
sK10: view_e774982825t_unit > traffic > cars > view_e774982825t_unit ).
thf(func_def_77,type,
sK11: view_e774982825t_unit > traffic > cars > view_e774982825t_unit ).
thf(func_def_78,type,
sK12: view_e774982825t_unit > traffic > cars > view_e774982825t_unit ).
thf(func_def_79,type,
sK13: ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > traffic > view_e774982825t_unit ).
thf(func_def_80,type,
sK14: ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > traffic > view_e774982825t_unit ).
thf(func_def_81,type,
sK15: view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_82,type,
sK16: view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_83,type,
sK17: traffic > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_84,type,
sK18: traffic > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_85,type,
sK19: traffic > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_86,type,
sK20: traffic > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_87,type,
sK21: traffic > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_88,type,
sK22: traffic > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_89,type,
sK23: traffic > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_90,type,
sK24: traffic > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_91,type,
sK25: view_e774982825t_unit > traffic > cars > view_e774982825t_unit ).
thf(func_def_92,type,
sK26: view_e774982825t_unit > traffic > cars > view_e774982825t_unit ).
thf(func_def_93,type,
sK27: view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_94,type,
sK28: view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_95,type,
sK29: ( nat > $o ) > nat > nat ).
thf(func_def_96,type,
sK30: nat > view_e774982825t_unit > nat > view_e774982825t_unit ).
thf(func_def_97,type,
sK31: nat > view_e774982825t_unit > nat > view_e774982825t_unit ).
thf(func_def_98,type,
sK32: view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_99,type,
sK33: view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_100,type,
sK34: view_e774982825t_unit > traffic > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit ).
thf(func_def_101,type,
sK35: view_e774982825t_unit > traffic > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit ).
thf(func_def_102,type,
sK36: traffic > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_103,type,
sK37: traffic > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_104,type,
sK38: traffic > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_105,type,
sK39: traffic > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_106,type,
sK40: ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit ).
thf(func_def_107,type,
sK41: ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit ).
thf(func_def_108,type,
sK42: ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit ).
thf(func_def_109,type,
sK43: ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit ).
thf(func_def_110,type,
sK44: view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > traffic > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit ).
thf(func_def_111,type,
sK45: view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > traffic > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit ).
thf(func_def_112,type,
sK46: view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_113,type,
sK47: view_e774982825t_unit ).
thf(func_def_114,type,
sK48: ( nat > $o ) > nat ).
thf(func_def_115,type,
sK49: view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit ).
thf(func_def_116,type,
sK50: view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit ).
thf(func_def_117,type,
sK51: view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_118,type,
sK52: view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_119,type,
sK53: ( nat > $o ) > nat ).
thf(func_def_120,type,
sK54: view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_121,type,
sK55: nat > nat > nat ).
thf(func_def_122,type,
sK56: view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_123,type,
sK57: view_e774982825t_unit > real > view_e774982825t_unit ).
thf(func_def_124,type,
sK58: view_e774982825t_unit > real > view_e774982825t_unit ).
thf(func_def_125,type,
sK59: view_e774982825t_unit > cars > traffic > view_e774982825t_unit ).
thf(func_def_126,type,
sK60: view_e774982825t_unit > cars > traffic > view_e774982825t_unit ).
thf(func_def_127,type,
sK61: ( nat > nat ) > nat ).
thf(func_def_128,type,
sK62: ( nat > nat ) > nat ).
thf(func_def_129,type,
sK63: view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_130,type,
sK64: view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_131,type,
sK65: nat > nat > nat ).
thf(func_def_132,type,
sK66: ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_133,type,
sK67: ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_134,type,
sK68: ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_135,type,
sK69: ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_136,type,
sK70: view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > traffic > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit ).
thf(func_def_137,type,
sK71: view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > traffic > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit ).
thf(func_def_138,type,
sK72: ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_139,type,
sK73: ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_140,type,
sK74: ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_141,type,
sK75: ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_142,type,
sK76: traffic > view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit ).
thf(func_def_143,type,
sK77: traffic > view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit ).
thf(func_def_144,type,
sK78: view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_145,type,
sK79: view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_146,type,
sK80: ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_147,type,
sK81: ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_148,type,
sK82: view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_149,type,
sK83: ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit ).
thf(func_def_150,type,
sK84: ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit ).
thf(func_def_151,type,
sK85: ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_152,type,
sK86: ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_153,type,
sK87: traffic > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_154,type,
sK88: traffic > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_155,type,
sK89: ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit ).
thf(func_def_156,type,
sK90: ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit ).
thf(func_def_157,type,
sK91: ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit ).
thf(func_def_158,type,
sK92: ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit ).
thf(func_def_159,type,
sK93: ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit ).
thf(func_def_160,type,
sK94: ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit ).
thf(func_def_161,type,
sK95: ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit ).
thf(func_def_162,type,
sK96: ( traffic > view_e774982825t_unit > $o ) > ( traffic > view_e774982825t_unit > $o ) > traffic > view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit ).
thf(func_def_163,type,
sK97: ( nat > $o ) > nat ).
thf(func_def_164,type,
sK98: view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_165,type,
sK99: view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_166,type,
sK100: nat > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_167,type,
sK101: nat > view_e774982825t_unit > view_e774982825t_unit ).
thf(func_def_168,type,
sK102: traffic > view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit ).
thf(func_def_169,type,
sK103: traffic > view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit ).
thf(func_def_170,type,
sK104: traffic > view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit ).
thf(func_def_171,type,
sK105: traffic > view_e774982825t_unit > ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit ).
thf(func_def_172,type,
sK106: ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > traffic > view_e774982825t_unit ).
thf(func_def_173,type,
sK107: ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > traffic > view_e774982825t_unit ).
thf(func_def_174,type,
sK108: ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > traffic > view_e774982825t_unit ).
thf(func_def_175,type,
sK109: ( traffic > view_e774982825t_unit > $o ) > view_e774982825t_unit > traffic > view_e774982825t_unit ).
thf(func_def_176,type,
sK110: ( nat > $o ) > nat > nat ).
thf(func_def_177,type,
sK111: ( nat > $o ) > nat ).
thf(func_def_179,type,
ph113:
!>[X0: $tType] : X0 ).
thf(f1648,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1600,f1601,f1641]) ).
thf(f1641,plain,
~ spl112_1,
inference(avatar_contradiction_clause,[status(thm)],[f1640]) ).
thf(f1640,plain,
( $false
| ~ spl112_1 ),
inference(subsumption_resolution,[status(thm)],[f1639,f1298]) ).
thf(f1298,plain,
( ( lan_Product_unit @ sK47 )
= ( restrict @ sK47 @ ( res @ ts ) @ e ) ),
inference(cnf_transformation,[status(thm)],[f1034]) ).
thf(f1034,plain,
( ( one_one_nat
= ( nat_card @ ( lan_Product_unit @ sK47 ) ) )
& ( ( len @ regular_regular @ sK47 @ ts @ c )
= ( ext_Product_unit @ sK47 ) )
& ( ( lan_Product_unit @ sK47 )
= ( restrict @ sK47 @ ( res @ ts ) @ e ) )
& ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ sK47 ) ) )
= $true )
& ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ sK47 ) ) )
= $true )
& ( one_one_nat
= ( nat_card @ ( lan_Product_unit @ sK47 ) ) )
& ( ( len @ regular_regular @ sK47 @ ts @ e )
= ( ext_Product_unit @ sK47 ) )
& ( ( lan_Product_unit @ sK47 )
= ( restrict @ sK47 @ ( res @ ts ) @ c ) )
& ( $true
= ( ord_le461438217t_unit @ sK47 @ ( move @ ts3 @ ts @ v ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK47])],[f729,f1033]) ).
thf(f1033,plain,
( ? [X0: view_e774982825t_unit] :
( ( one_one_nat
= ( nat_card @ ( lan_Product_unit @ X0 ) ) )
& ( ( len @ regular_regular @ X0 @ ts @ c )
= ( ext_Product_unit @ X0 ) )
& ( ( lan_Product_unit @ X0 )
= ( restrict @ X0 @ ( res @ ts ) @ e ) )
& ( $true
= ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X0 ) ) ) )
& ( $true
= ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X0 ) ) ) )
& ( one_one_nat
= ( nat_card @ ( lan_Product_unit @ X0 ) ) )
& ( ( ext_Product_unit @ X0 )
= ( len @ regular_regular @ X0 @ ts @ e ) )
& ( ( restrict @ X0 @ ( res @ ts ) @ c )
= ( lan_Product_unit @ X0 ) )
& ( $true
= ( ord_le461438217t_unit @ X0 @ ( move @ ts3 @ ts @ v ) ) ) )
=> ( ( one_one_nat
= ( nat_card @ ( lan_Product_unit @ sK47 ) ) )
& ( ( len @ regular_regular @ sK47 @ ts @ c )
= ( ext_Product_unit @ sK47 ) )
& ( ( lan_Product_unit @ sK47 )
= ( restrict @ sK47 @ ( res @ ts ) @ e ) )
& ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ sK47 ) ) )
= $true )
& ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ sK47 ) ) )
= $true )
& ( one_one_nat
= ( nat_card @ ( lan_Product_unit @ sK47 ) ) )
& ( ( len @ regular_regular @ sK47 @ ts @ e )
= ( ext_Product_unit @ sK47 ) )
& ( ( lan_Product_unit @ sK47 )
= ( restrict @ sK47 @ ( res @ ts ) @ c ) )
& ( $true
= ( ord_le461438217t_unit @ sK47 @ ( move @ ts3 @ ts @ v ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f729,plain,
? [X0: view_e774982825t_unit] :
( ( one_one_nat
= ( nat_card @ ( lan_Product_unit @ X0 ) ) )
& ( ( len @ regular_regular @ X0 @ ts @ c )
= ( ext_Product_unit @ X0 ) )
& ( ( lan_Product_unit @ X0 )
= ( restrict @ X0 @ ( res @ ts ) @ e ) )
& ( $true
= ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X0 ) ) ) )
& ( $true
= ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X0 ) ) ) )
& ( one_one_nat
= ( nat_card @ ( lan_Product_unit @ X0 ) ) )
& ( ( ext_Product_unit @ X0 )
= ( len @ regular_regular @ X0 @ ts @ e ) )
& ( ( restrict @ X0 @ ( res @ ts ) @ c )
= ( lan_Product_unit @ X0 ) )
& ( $true
= ( ord_le461438217t_unit @ X0 @ ( move @ ts3 @ ts @ v ) ) ) ),
inference(fool_elimination,[status(thm)],[f728]) ).
thf(f728,plain,
? [X0: view_e774982825t_unit] :
( ( ( len @ regular_regular @ X0 @ ts @ c )
= ( ext_Product_unit @ X0 ) )
& ( ( ext_Product_unit @ X0 )
= ( len @ regular_regular @ X0 @ ts @ e ) )
& ( ord_le461438217t_unit @ X0 @ ( move @ ts3 @ ts @ v ) )
& ( ( restrict @ X0 @ ( res @ ts ) @ c )
= ( lan_Product_unit @ X0 ) )
& ( ( lan_Product_unit @ X0 )
= ( restrict @ X0 @ ( res @ ts ) @ e ) )
& ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X0 ) ) )
& ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X0 ) ) )
& ( one_one_nat
= ( nat_card @ ( lan_Product_unit @ X0 ) ) )
& ( one_one_nat
= ( nat_card @ ( lan_Product_unit @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
? [X7: view_e774982825t_unit] :
( ( ( ext_Product_unit @ X7 )
= ( len @ regular_regular @ X7 @ ts @ c ) )
& ( ( ext_Product_unit @ X7 )
= ( len @ regular_regular @ X7 @ ts @ e ) )
& ( ord_le461438217t_unit @ X7 @ ( move @ ts3 @ ts @ v ) )
& ( ( restrict @ X7 @ ( res @ ts ) @ c )
= ( lan_Product_unit @ X7 ) )
& ( ( lan_Product_unit @ X7 )
= ( restrict @ X7 @ ( res @ ts ) @ e ) )
& ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X7 ) ) )
& ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X7 ) ) )
& ( ( nat_card @ ( lan_Product_unit @ X7 ) )
= one_one_nat )
& ( ( nat_card @ ( lan_Product_unit @ X7 ) )
= one_one_nat ) ),
file('/export/starexec/sandbox2/tmp/tmp.pzq8qyAMZ7/DTF2THF_20750.p',fact_4__092_060open_062_092_060exists_062v_H_092_060le_062move_Ats_Ats_H_H_Av_O_A_I0_A_060_A_092_060parallel_062ext_Av_H_092_060parallel_062_A_092_060and_062_Alen_Av_H_Ats_H_H_Ac_A_061_Aext_Av_H_A_092_060and_062_Arestrict_Av_H_A_Ires_Ats_H_H_J_Ac_A_061_Alan_Av_H_A_092_060and_062_A_124lan_Av_H_124_A_061_A1_J_A_092_060and_062_A0_A_060_A_092_060parallel_062ext_Av_H_092_060parallel_062_A_092_060and_062_Alen_Av_H_Ats_H_H_Ae_A_061_Aext_Av_H_A_092_060and_062_Arestrict_Av_H_A_Ires_Ats_H_H_J_Ae_A_061_Alan_Av_H_A_092_060and_062_A_124lan_Av_H_124_A_061_A1_092_060close_062) ).
thf(f1639,plain,
( ( ( lan_Product_unit @ sK47 )
!= ( restrict @ sK47 @ ( res @ ts ) @ e ) )
| ~ spl112_1 ),
inference(subsumption_resolution,[status(thm)],[f1638,f1292]) ).
thf(f1292,plain,
( $true
= ( ord_le461438217t_unit @ sK47 @ ( move @ ts3 @ ts @ v ) ) ),
inference(cnf_transformation,[status(thm)],[f1034]) ).
thf(f1638,plain,
( ( $true
!= ( ord_le461438217t_unit @ sK47 @ ( move @ ts3 @ ts @ v ) ) )
| ( ( lan_Product_unit @ sK47 )
!= ( restrict @ sK47 @ ( res @ ts ) @ e ) )
| ~ spl112_1 ),
inference(subsumption_resolution,[status(thm)],[f1637,f1299]) ).
thf(f1299,plain,
( ( len @ regular_regular @ sK47 @ ts @ c )
= ( ext_Product_unit @ sK47 ) ),
inference(cnf_transformation,[status(thm)],[f1034]) ).
thf(f1637,plain,
( ( ( len @ regular_regular @ sK47 @ ts @ c )
!= ( ext_Product_unit @ sK47 ) )
| ( ( lan_Product_unit @ sK47 )
!= ( restrict @ sK47 @ ( res @ ts ) @ e ) )
| ( $true
!= ( ord_le461438217t_unit @ sK47 @ ( move @ ts3 @ ts @ v ) ) )
| ~ spl112_1 ),
inference(subsumption_resolution,[status(thm)],[f1636,f1293]) ).
thf(f1293,plain,
( ( lan_Product_unit @ sK47 )
= ( restrict @ sK47 @ ( res @ ts ) @ c ) ),
inference(cnf_transformation,[status(thm)],[f1034]) ).
thf(f1636,plain,
( ( ( lan_Product_unit @ sK47 )
!= ( restrict @ sK47 @ ( res @ ts ) @ c ) )
| ( $true
!= ( ord_le461438217t_unit @ sK47 @ ( move @ ts3 @ ts @ v ) ) )
| ( ( len @ regular_regular @ sK47 @ ts @ c )
!= ( ext_Product_unit @ sK47 ) )
| ( ( lan_Product_unit @ sK47 )
!= ( restrict @ sK47 @ ( res @ ts ) @ e ) )
| ~ spl112_1 ),
inference(subsumption_resolution,[status(thm)],[f1627,f1296]) ).
thf(f1296,plain,
( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ sK47 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f1034]) ).
thf(f1627,plain,
( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ sK47 ) ) )
!= $true )
| ( ( len @ regular_regular @ sK47 @ ts @ c )
!= ( ext_Product_unit @ sK47 ) )
| ( ( lan_Product_unit @ sK47 )
!= ( restrict @ sK47 @ ( res @ ts ) @ e ) )
| ( $true
!= ( ord_le461438217t_unit @ sK47 @ ( move @ ts3 @ ts @ v ) ) )
| ( ( lan_Product_unit @ sK47 )
!= ( restrict @ sK47 @ ( res @ ts ) @ c ) )
| ~ spl112_1 ),
inference(trivial_inequality_removal,[status(thm)],[f1618]) ).
thf(f1618,plain,
( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ sK47 ) ) )
!= $true )
| ( $true
!= ( ord_le461438217t_unit @ sK47 @ ( move @ ts3 @ ts @ v ) ) )
| ( ( nat_card @ ( lan_Product_unit @ sK47 ) )
!= ( nat_card @ ( lan_Product_unit @ sK47 ) ) )
| ( ( lan_Product_unit @ sK47 )
!= ( restrict @ sK47 @ ( res @ ts ) @ e ) )
| ( ( ext_Product_unit @ sK47 )
!= ( ext_Product_unit @ sK47 ) )
| ( ( len @ regular_regular @ sK47 @ ts @ c )
!= ( ext_Product_unit @ sK47 ) )
| ( ( lan_Product_unit @ sK47 )
!= ( restrict @ sK47 @ ( res @ ts ) @ c ) )
| ~ spl112_1 ),
inference(superposition,[status(thm)],[f1595,f1294]) ).
thf(f1294,plain,
( ( len @ regular_regular @ sK47 @ ts @ e )
= ( ext_Product_unit @ sK47 ) ),
inference(cnf_transformation,[status(thm)],[f1034]) ).
thf(f1595,plain,
( ! [X0: view_e774982825t_unit] :
( ( ( ext_Product_unit @ X0 )
!= ( len @ regular_regular @ X0 @ ts @ e ) )
| ( $true
!= ( ord_le461438217t_unit @ X0 @ ( move @ ts3 @ ts @ v ) ) )
| ( ( len @ regular_regular @ X0 @ ts @ c )
!= ( ext_Product_unit @ X0 ) )
| ( $true
!= ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X0 ) ) ) )
| ( ( nat_card @ ( lan_Product_unit @ sK47 ) )
!= ( nat_card @ ( lan_Product_unit @ X0 ) ) )
| ( ( restrict @ X0 @ ( res @ ts ) @ c )
!= ( lan_Product_unit @ X0 ) )
| ( ( lan_Product_unit @ X0 )
!= ( restrict @ X0 @ ( res @ ts ) @ e ) ) )
| ~ spl112_1 ),
inference(avatar_component_clause,[status(thm)],[f1594]) ).
thf(f1594,definition,
( spl112_1
<=> ! [X0: view_e774982825t_unit] :
( ( $true
!= ( ord_le461438217t_unit @ X0 @ ( move @ ts3 @ ts @ v ) ) )
| ( ( len @ regular_regular @ X0 @ ts @ c )
!= ( ext_Product_unit @ X0 ) )
| ( ( restrict @ X0 @ ( res @ ts ) @ c )
!= ( lan_Product_unit @ X0 ) )
| ( ( lan_Product_unit @ X0 )
!= ( restrict @ X0 @ ( res @ ts ) @ e ) )
| ( ( ext_Product_unit @ X0 )
!= ( len @ regular_regular @ X0 @ ts @ e ) )
| ( ( nat_card @ ( lan_Product_unit @ sK47 ) )
!= ( nat_card @ ( lan_Product_unit @ X0 ) ) )
| ( $true
!= ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl112_1])],[avatar_definition]) ).
thf(f1601,plain,
~ spl112_2,
inference(avatar_split_clause,[status(thm)],[f1237,f1597]) ).
thf(f1597,definition,
( spl112_2
<=> ( thesis = $true ) ),
introduced(definition,[new_symbols(naming,[spl112_2])],[avatar_definition]) ).
thf(f1237,plain,
thesis != $true,
inference(cnf_transformation,[status(thm)],[f772]) ).
thf(f772,plain,
thesis != $true,
inference(flattening,[status(thm)],[f595]) ).
thf(f595,plain,
thesis != $true,
inference(fool_elimination,[status(thm)],[f594]) ).
thf(f594,plain,
~ thesis,
inference(rectify,[status(thm)],[f286]) ).
thf(f286,negated_conjecture,
~ thesis,
inference(negated_conjecture,[status(cth)],[f285]) ).
thf(f285,conjecture,
thesis,
file('/export/starexec/sandbox2/tmp/tmp.pzq8qyAMZ7/DTF2THF_20750.p',conj_1) ).
thf(f1600,plain,
( spl112_1
| spl112_2 ),
inference(avatar_split_clause,[status(thm)],[f1592,f1597,f1594]) ).
thf(f1592,plain,
! [X0: view_e774982825t_unit] :
( ( thesis = $true )
| ( $true
!= ( ord_le461438217t_unit @ X0 @ ( move @ ts3 @ ts @ v ) ) )
| ( $true
!= ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X0 ) ) ) )
| ( ( nat_card @ ( lan_Product_unit @ sK47 ) )
!= ( nat_card @ ( lan_Product_unit @ X0 ) ) )
| ( ( ext_Product_unit @ X0 )
!= ( len @ regular_regular @ X0 @ ts @ e ) )
| ( ( lan_Product_unit @ X0 )
!= ( restrict @ X0 @ ( res @ ts ) @ e ) )
| ( ( restrict @ X0 @ ( res @ ts ) @ c )
!= ( lan_Product_unit @ X0 ) )
| ( ( len @ regular_regular @ X0 @ ts @ c )
!= ( ext_Product_unit @ X0 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f1518]) ).
thf(f1518,plain,
! [X0: view_e774982825t_unit] :
( ( ( ext_Product_unit @ X0 )
!= ( len @ regular_regular @ X0 @ ts @ e ) )
| ( ( nat_card @ ( lan_Product_unit @ sK47 ) )
!= ( nat_card @ ( lan_Product_unit @ X0 ) ) )
| ( ( len @ regular_regular @ X0 @ ts @ c )
!= ( ext_Product_unit @ X0 ) )
| ( thesis = $true )
| ( ( nat_card @ ( lan_Product_unit @ sK47 ) )
!= ( nat_card @ ( lan_Product_unit @ X0 ) ) )
| ( $true
!= ( ord_le461438217t_unit @ X0 @ ( move @ ts3 @ ts @ v ) ) )
| ( ( lan_Product_unit @ X0 )
!= ( restrict @ X0 @ ( res @ ts ) @ e ) )
| ( ( restrict @ X0 @ ( res @ ts ) @ c )
!= ( lan_Product_unit @ X0 ) )
| ( $true
!= ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X0 ) ) ) )
| ( $true
!= ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X0 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1284,f1300,f1300]) ).
thf(f1300,plain,
( one_one_nat
= ( nat_card @ ( lan_Product_unit @ sK47 ) ) ),
inference(cnf_transformation,[status(thm)],[f1034]) ).
thf(f1284,plain,
! [X0: view_e774982825t_unit] :
( ( ( restrict @ X0 @ ( res @ ts ) @ c )
!= ( lan_Product_unit @ X0 ) )
| ( one_one_nat
!= ( nat_card @ ( lan_Product_unit @ X0 ) ) )
| ( $true
!= ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X0 ) ) ) )
| ( ( ext_Product_unit @ X0 )
!= ( len @ regular_regular @ X0 @ ts @ e ) )
| ( thesis = $true )
| ( $true
!= ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X0 ) ) ) )
| ( one_one_nat
!= ( nat_card @ ( lan_Product_unit @ X0 ) ) )
| ( ( lan_Product_unit @ X0 )
!= ( restrict @ X0 @ ( res @ ts ) @ e ) )
| ( ( len @ regular_regular @ X0 @ ts @ c )
!= ( ext_Product_unit @ X0 ) )
| ( $true
!= ( ord_le461438217t_unit @ X0 @ ( move @ ts3 @ ts @ v ) ) ) ),
inference(cnf_transformation,[status(thm)],[f903]) ).
thf(f903,plain,
! [X0: view_e774982825t_unit] :
( ( ( restrict @ X0 @ ( res @ ts ) @ c )
!= ( lan_Product_unit @ X0 ) )
| ( one_one_nat
!= ( nat_card @ ( lan_Product_unit @ X0 ) ) )
| ( $true
!= ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X0 ) ) ) )
| ( ( ext_Product_unit @ X0 )
!= ( len @ regular_regular @ X0 @ ts @ e ) )
| ( thesis = $true )
| ( $true
!= ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X0 ) ) ) )
| ( one_one_nat
!= ( nat_card @ ( lan_Product_unit @ X0 ) ) )
| ( ( lan_Product_unit @ X0 )
!= ( restrict @ X0 @ ( res @ ts ) @ e ) )
| ( ( len @ regular_regular @ X0 @ ts @ c )
!= ( ext_Product_unit @ X0 ) )
| ( $true
!= ( ord_le461438217t_unit @ X0 @ ( move @ ts3 @ ts @ v ) ) ) ),
inference(flattening,[status(thm)],[f902]) ).
thf(f902,plain,
! [X0: view_e774982825t_unit] :
( ( thesis = $true )
| ( $true
!= ( ord_le461438217t_unit @ X0 @ ( move @ ts3 @ ts @ v ) ) )
| ( ( ext_Product_unit @ X0 )
!= ( len @ regular_regular @ X0 @ ts @ e ) )
| ( ( lan_Product_unit @ X0 )
!= ( restrict @ X0 @ ( res @ ts ) @ e ) )
| ( one_one_nat
!= ( nat_card @ ( lan_Product_unit @ X0 ) ) )
| ( ( restrict @ X0 @ ( res @ ts ) @ c )
!= ( lan_Product_unit @ X0 ) )
| ( ( len @ regular_regular @ X0 @ ts @ c )
!= ( ext_Product_unit @ X0 ) )
| ( one_one_nat
!= ( nat_card @ ( lan_Product_unit @ X0 ) ) )
| ( $true
!= ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X0 ) ) ) )
| ( $true
!= ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f677]) ).
thf(f677,plain,
! [X0: view_e774982825t_unit] :
( ( ( $true
= ( ord_le461438217t_unit @ X0 @ ( move @ ts3 @ ts @ v ) ) )
& ( ( ext_Product_unit @ X0 )
= ( len @ regular_regular @ X0 @ ts @ e ) )
& ( ( lan_Product_unit @ X0 )
= ( restrict @ X0 @ ( res @ ts ) @ e ) )
& ( one_one_nat
= ( nat_card @ ( lan_Product_unit @ X0 ) ) )
& ( ( restrict @ X0 @ ( res @ ts ) @ c )
= ( lan_Product_unit @ X0 ) )
& ( ( len @ regular_regular @ X0 @ ts @ c )
= ( ext_Product_unit @ X0 ) )
& ( one_one_nat
= ( nat_card @ ( lan_Product_unit @ X0 ) ) )
& ( $true
= ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X0 ) ) ) )
& ( $true
= ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X0 ) ) ) ) )
=> ( thesis = $true ) ),
inference(fool_elimination,[status(thm)],[f676]) ).
thf(f676,plain,
! [X0: view_e774982825t_unit] :
( ( ( one_one_nat
= ( nat_card @ ( lan_Product_unit @ X0 ) ) )
& ( ( len @ regular_regular @ X0 @ ts @ c )
= ( ext_Product_unit @ X0 ) )
& ( ( restrict @ X0 @ ( res @ ts ) @ c )
= ( lan_Product_unit @ X0 ) )
& ( ( ext_Product_unit @ X0 )
= ( len @ regular_regular @ X0 @ ts @ e ) )
& ( ord_le461438217t_unit @ X0 @ ( move @ ts3 @ ts @ v ) )
& ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X0 ) ) )
& ( ( lan_Product_unit @ X0 )
= ( restrict @ X0 @ ( res @ ts ) @ e ) )
& ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X0 ) ) )
& ( one_one_nat
= ( nat_card @ ( lan_Product_unit @ X0 ) ) ) )
=> thesis ),
inference(rectify,[status(thm)],[f284]) ).
thf(f284,axiom,
! [X87: view_e774982825t_unit] :
( ( ( one_one_nat
= ( nat_card @ ( lan_Product_unit @ X87 ) ) )
& ( ( ext_Product_unit @ X87 )
= ( len @ regular_regular @ X87 @ ts @ c ) )
& ( ( restrict @ X87 @ ( res @ ts ) @ c )
= ( lan_Product_unit @ X87 ) )
& ( ( ext_Product_unit @ X87 )
= ( len @ regular_regular @ X87 @ ts @ e ) )
& ( ord_le461438217t_unit @ X87 @ ( move @ ts3 @ ts @ v ) )
& ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X87 ) ) )
& ( ( lan_Product_unit @ X87 )
= ( restrict @ X87 @ ( res @ ts ) @ e ) )
& ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ X87 ) ) )
& ( one_one_nat
= ( nat_card @ ( lan_Product_unit @ X87 ) ) ) )
=> thesis ),
file('/export/starexec/sandbox2/tmp/tmp.pzq8qyAMZ7/DTF2THF_20750.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ITP169^1 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.31 % Computer : n013.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Feb 24 08:28:08 EST 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.31 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.41 ---- Original DTF file ---
% 0.15/0.41 thf(spec,logic,$$dhol).
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 % File : ITP169^1 : TPTP v9.2.1. Released v7.5.0.
% 0.15/0.41 % Domain : Interactive Theorem Proving
% 0.15/0.41 % Problem : Sledgehammer Safety_Regular problem prob_273__3352790_1
% 0.15/0.41 % Version : Especial.
% 0.15/0.41 % English :
% 0.15/0.41
% 0.15/0.41 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.15/0.41 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.15/0.41 % Source : [Des21]
% 0.15/0.41 % Names : Safety_Regular/prob_273__3352790_1 [Des21]
% 0.15/0.41
% 0.15/0.41 % Status : Theorem
% 0.15/0.41 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0
% 0.15/0.41 % Syntax : Number of formulae : 333 ( 134 unt; 48 typ; 0 def)
% 0.15/0.41 % Number of atoms : 1026 ( 517 equ; 0 cnn)
% 0.15/0.41 % Maximal formula atoms : 17 ( 3 avg)
% 0.15/0.41 % Number of connectives : 4010 ( 58 ~; 38 |; 438 &;3295 @)
% 0.15/0.41 % ( 0 <=>; 181 =>; 0 <=; 0 <~>)
% 0.15/0.41 % Maximal formula depth : 23 ( 7 avg)
% 0.15/0.41 % Number of types : 8 ( 7 usr)
% 0.15/0.41 % Number of type conns : 141 ( 141 >; 0 *; 0 +; 0 <<)
% 0.15/0.41 % Number of symbols : 42 ( 41 usr; 13 con; 0-4 aty)
% 0.15/0.41 % Number of variables : 936 ( 10 ^; 770 !; 156 ?; 936 :)
% 0.15/0.41 % SPC : TH0_THM_EQU_NAR
% 0.15/0.41
% 0.15/0.41 % Comments : This file was generated by Sledgehammer 2021-02-23 15:37:39.643
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 % Could-be-implicit typings (7)
% 0.15/0.41 thf(ty_n_t__Views__Oview__Oview____ext_It__Product____Type__Ounit_J,type,
% 0.15/0.41 view_e774982825t_unit: $tType ).
% 0.15/0.41
% 0.15/0.41 thf(ty_n_t__RealInt__Oreal____int,type,
% 0.15/0.41 real_int: $tType ).
% 0.15/0.41
% 0.15/0.41 thf(ty_n_t__NatInt__Onat____int,type,
% 0.15/0.41 nat_int: $tType ).
% 0.15/0.41
% 0.15/0.41 thf(ty_n_t__Traffic__Otraffic,type,
% 0.15/0.41 traffic: $tType ).
% 0.15/0.41
% 0.15/0.41 thf(ty_n_t__Real__Oreal,type,
% 0.15/0.41 real: $tType ).
% 0.15/0.41
% 0.15/0.41 thf(ty_n_t__Cars__Ocars,type,
% 0.15/0.41 cars: $tType ).
% 0.15/0.41
% 0.15/0.41 thf(ty_n_t__Nat__Onat,type,
% 0.15/0.41 nat: $tType ).
% 0.15/0.41
% 0.15/0.41 % Explicit typings (41)
% 0.15/0.41 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 0.15/0.41 one_one_nat: nat ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 0.15/0.41 plus_plus_nat: nat > nat > nat ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal,type,
% 0.15/0.41 plus_plus_real: real > real > real ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 0.15/0.41 zero_zero_nat: nat ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal,type,
% 0.15/0.41 zero_zero_real: real ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Length_Osensors_Olen,type,
% 0.15/0.41 len: ( cars > traffic > cars > real ) > view_e774982825t_unit > traffic > cars > real_int ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Move_Otraffic_Omove,type,
% 0.15/0.41 move: traffic > traffic > view_e774982825t_unit > view_e774982825t_unit ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_NatInt_Onat__int_Ocard_H,type,
% 0.15/0.41 nat_card: nat_int > nat ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Orderings_Obot__class_Obot_001t__NatInt__Onat____int,type,
% 0.15/0.41 bot_bot_nat_int: nat_int ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Orderings_Oord__class_Oless_001t__NatInt__Onat____int,type,
% 0.15/0.41 ord_less_nat_int: nat_int > nat_int > $o ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.15/0.41 ord_less_nat: nat > nat > $o ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal,type,
% 0.15/0.41 ord_less_real: real > real > $o ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__NatInt__Onat____int,type,
% 0.15/0.41 ord_less_eq_nat_int: nat_int > nat_int > $o ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.15/0.41 ord_less_eq_nat: nat > nat > $o ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__RealInt__Oreal____int,type,
% 0.15/0.41 ord_less_eq_real_int: real_int > real_int > $o ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type,
% 0.15/0.41 ord_less_eq_real: real > real > $o ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Views__Oview__Oview____ext_It__Product____Type__Ounit_J,type,
% 0.15/0.41 ord_le461438217t_unit: view_e774982825t_unit > view_e774982825t_unit > $o ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_RealInt_Oreal__int_Olength,type,
% 0.15/0.41 real_length: real_int > real ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Regular__Sensors_Oregular,type,
% 0.15/0.41 regular_regular: cars > traffic > cars > real ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Restriction_Orestriction_Orestrict,type,
% 0.15/0.41 restrict: view_e774982825t_unit > ( cars > nat_int ) > cars > nat_int ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Traffic_Otraffic_Oabstract,type,
% 0.15/0.41 abstract: traffic > traffic > $o ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Traffic_Otraffic_Oclm,type,
% 0.15/0.41 clm: traffic > cars > nat_int ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Traffic_Otraffic_Ocreate__claim,type,
% 0.15/0.41 create_claim: traffic > cars > nat > traffic > $o ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Traffic_Otraffic_Ocreate__reservation,type,
% 0.15/0.41 create_reservation: traffic > cars > traffic > $o ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Traffic_Otraffic_Ores,type,
% 0.15/0.41 res: traffic > cars > nat_int ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Traffic_Otraffic_Owithdraw__claim,type,
% 0.15/0.41 withdraw_claim: traffic > cars > traffic > $o ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Traffic_Otraffic_Owithdraw__reservation,type,
% 0.15/0.41 withdraw_reservation: traffic > cars > nat > traffic > $o ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Views_Oview_Oext_001t__Product____Type__Ounit,type,
% 0.15/0.41 ext_Product_unit: view_e774982825t_unit > real_int ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Views_Oview_Ohchop,type,
% 0.15/0.41 hchop: view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > $o ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Views_Oview_Olan_001t__Product____Type__Ounit,type,
% 0.15/0.41 lan_Product_unit: view_e774982825t_unit > nat_int ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Views_Oview_Oown_001t__Product____Type__Ounit,type,
% 0.15/0.41 own_Product_unit: view_e774982825t_unit > cars ).
% 0.15/0.41
% 0.15/0.41 thf(sy_c_Views_Oview_Ovchop,type,
% 0.15/0.41 vchop: view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > $o ).
% 0.15/0.41
% 0.15/0.41 thf(sy_v_c____,type,
% 0.15/0.41 c: cars ).
% 0.15/0.41
% 0.15/0.41 thf(sy_v_d____,type,
% 0.15/0.41 d: cars ).
% 0.15/0.41
% 0.15/0.41 thf(sy_v_e____,type,
% 0.15/0.41 e: cars ).
% 0.15/0.41
% 0.15/0.41 thf(sy_v_thesis____,type,
% 0.15/0.41 thesis: $o ).
% 0.15/0.41
% 0.15/0.41 thf(sy_v_ts_H_H____,type,
% 0.15/0.41 ts: traffic ).
% 0.15/0.41
% 0.15/0.41 thf(sy_v_ts_H____,type,
% 0.15/0.41 ts2: traffic ).
% 0.15/0.41
% 0.15/0.41 thf(sy_v_ts_Ha____,type,
% 0.15/0.41 ts_a: traffic ).
% 0.15/0.41
% 0.15/0.41 thf(sy_v_ts____,type,
% 0.15/0.41 ts3: traffic ).
% 0.15/0.41
% 0.15/0.41 thf(sy_v_v____,type,
% 0.15/0.41 v: view_e774982825t_unit ).
% 0.15/0.41
% 0.15/0.41 % Relevant facts (283)
% 0.15/0.41 thf(fact_0_neg,axiom,
% 0.15/0.41 c != e ).
% 0.15/0.41
% 0.15/0.41 % neg
% 0.15/0.41 thf(fact_1_local_Ohmlsl_Osensors__ge,axiom,
% 0.15/0.41 ! [E: cars,Ts: traffic,C: cars] : ( ord_less_real @ zero_zero_real @ ( regular_regular @ E @ Ts @ C ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.sensors_ge
% 0.15/0.41 thf(fact_2_local_Ohmlsl_Olength__geq__zero,axiom,
% 0.15/0.41 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( real_length @ ( ext_Product_unit @ V ) )
% 0.15/0.41 = zero_zero_real )
% 0.15/0.41 | ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.length_geq_zero
% 0.15/0.41 thf(fact_3_hmlsl_Olen__empty__subview,axiom,
% 0.15/0.41 ! [V2: view_e774982825t_unit,Ts: traffic,C: cars,V3: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( ( real_length @ ( len @ regular_regular @ V2 @ Ts @ C ) )
% 0.15/0.41 = zero_zero_real )
% 0.15/0.41 & ( ord_le461438217t_unit @ V3 @ V2 ) )
% 0.15/0.41 => ( ( real_length @ ( len @ regular_regular @ V3 @ Ts @ C ) )
% 0.15/0.41 = zero_zero_real ) ) ).
% 0.15/0.41
% 0.15/0.41 % hmlsl.len_empty_subview
% 0.15/0.41 thf(fact_4__092_060open_062_092_060exists_062v_H_092_060le_062move_Ats_Ats_H_H_Av_O_A_I0_A_060_A_092_060parallel_062ext_Av_H_092_060parallel_062_A_092_060and_062_Alen_Av_H_Ats_H_H_Ac_A_061_Aext_Av_H_A_092_060and_062_Arestrict_Av_H_A_Ires_Ats_H_H_J_Ac_A_061_Alan_Av_H_A_092_060and_062_A_124lan_Av_H_124_A_061_A1_J_A_092_060and_062_A0_A_060_A_092_060parallel_062ext_Av_H_092_060parallel_062_A_092_060and_062_Alen_Av_H_Ats_H_H_Ae_A_061_Aext_Av_H_A_092_060and_062_Arestrict_Av_H_A_Ires_Ats_H_H_J_Ae_A_061_Alan_Av_H_A_092_060and_062_A_124lan_Av_H_124_A_061_A1_092_060close_062,axiom,
% 0.15/0.41 ? [V4: view_e774982825t_unit] :
% 0.15/0.41 ( ( ord_le461438217t_unit @ V4 @ ( move @ ts3 @ ts @ v ) )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V4 ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V4 @ ts @ c )
% 0.15/0.41 = ( ext_Product_unit @ V4 ) )
% 0.15/0.41 & ( ( restrict @ V4 @ ( res @ ts ) @ c )
% 0.15/0.41 = ( lan_Product_unit @ V4 ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V4 ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V4 ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V4 @ ts @ e )
% 0.15/0.41 = ( ext_Product_unit @ V4 ) )
% 0.15/0.41 & ( ( restrict @ V4 @ ( res @ ts ) @ e )
% 0.15/0.41 = ( lan_Product_unit @ V4 ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V4 ) )
% 0.15/0.41 = one_one_nat ) ) ).
% 0.15/0.41
% 0.15/0.41 % \<open>\<exists>v'\<le>move ts ts'' v. (0 < \<parallel>ext v'\<parallel> \<and> len v' ts'' c = ext v' \<and> restrict v' (res ts'') c = lan v' \<and> |lan v'| = 1) \<and> 0 < \<parallel>ext v'\<parallel> \<and> len v' ts'' e = ext v' \<and> restrict v' (res ts'') e = lan v' \<and> |lan v'| = 1\<close>
% 0.15/0.41 thf(fact_5_local_Ohmlsl_Ores__ge__zero,axiom,
% 0.15/0.41 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ V ) )
% 0.15/0.41 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ V ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat ) )
% 0.15/0.41 => ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.res_ge_zero
% 0.15/0.41 thf(fact_6_local_Ohmlsl_Owidth__res,axiom,
% 0.15/0.41 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ V ) )
% 0.15/0.41 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ V ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat ) )
% 0.15/0.41 => ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.width_res
% 0.15/0.41 thf(fact_7_abs,axiom,
% 0.15/0.41 abstract @ ts3 @ ts2 ).
% 0.15/0.41
% 0.15/0.41 % abs
% 0.15/0.41 thf(fact_8__092_060open_062move_Ats_Ats_H_Av_A_061_Amove_Ats_H_Ats_H_H_A_Imove_Ats_Ats_H_Av_J_092_060close_062,axiom,
% 0.15/0.41 ( ( move @ ts3 @ ts_a @ v )
% 0.15/0.41 = ( move @ ts_a @ ts @ ( move @ ts3 @ ts_a @ v ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % \<open>move ts ts' v = move ts' ts'' (move ts ts' v)\<close>
% 0.15/0.41 thf(fact_9_move__stab,axiom,
% 0.15/0.41 ( ( move @ ts3 @ ts_a @ v )
% 0.15/0.41 = ( move @ ts3 @ ts @ v ) ) ).
% 0.15/0.41
% 0.15/0.41 % move_stab
% 0.15/0.41 thf(fact_10_local_Ohmlsl_Ores__compose,axiom,
% 0.15/0.41 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ? [Va: view_e774982825t_unit,U: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V @ Va @ U )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ Va ) )
% 0.15/0.41 & ( ( restrict @ Va @ ( res @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ Va ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ Va ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ U @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ U ) )
% 0.15/0.41 & ( ( restrict @ U @ ( res @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ U ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ U ) )
% 0.15/0.41 = one_one_nat ) )
% 0.15/0.41 => ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ V ) )
% 0.15/0.41 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ V ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.res_compose
% 0.15/0.41 thf(fact_11_local_Ohmlsl_Ores__decompose,axiom,
% 0.15/0.41 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ V ) )
% 0.15/0.41 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ V ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat ) )
% 0.15/0.41 => ? [Va2: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V @ Va2 @ U2 )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va2 ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ Va2 @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ Va2 ) )
% 0.15/0.41 & ( ( restrict @ Va2 @ ( res @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ Va2 ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ Va2 ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U2 ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ U2 @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ U2 ) )
% 0.15/0.41 & ( ( restrict @ U2 @ ( res @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ U2 ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ U2 ) )
% 0.15/0.41 = one_one_nat ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.res_decompose
% 0.15/0.41 thf(fact_12_local_Ohmlsl_Ores__dense,axiom,
% 0.15/0.41 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ V ) )
% 0.15/0.41 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ V ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat ) )
% 0.15/0.41 = ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V @ W @ U3 )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ W ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ W @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ W ) )
% 0.15/0.41 & ( ( restrict @ W @ ( res @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ W ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ W ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U3 ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ U3 @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ U3 ) )
% 0.15/0.41 & ( ( restrict @ U3 @ ( res @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ U3 ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ U3 ) )
% 0.15/0.41 = one_one_nat ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.res_dense
% 0.15/0.41 thf(fact_13_local_Ohmlsl_Ocar__one__lane__non__empty,axiom,
% 0.15/0.41 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ? [X: cars] :
% 0.15/0.41 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 0.15/0.41 = ( ext_Product_unit @ V ) )
% 0.15/0.41 & ( ( restrict @ V @ ( clm @ Ts2 ) @ X )
% 0.15/0.41 = ( lan_Product_unit @ V ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat ) )
% 0.15/0.41 | ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 0.15/0.41 = ( ext_Product_unit @ V ) )
% 0.15/0.41 & ( ( restrict @ V @ ( res @ Ts2 ) @ X )
% 0.15/0.41 = ( lan_Product_unit @ V ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat ) ) )
% 0.15/0.41 => ( ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.car_one_lane_non_empty
% 0.15/0.41 thf(fact_14_local_Ohmlsl_Oempty__no__car,axiom,
% 0.15/0.41 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( real_length @ ( ext_Product_unit @ V ) )
% 0.15/0.41 = zero_zero_real )
% 0.15/0.41 => ~ ? [X: cars] :
% 0.15/0.41 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 0.15/0.41 = ( ext_Product_unit @ V ) )
% 0.15/0.41 & ( ( restrict @ V @ ( clm @ Ts2 ) @ X )
% 0.15/0.41 = ( lan_Product_unit @ V ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat ) )
% 0.15/0.41 | ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 0.15/0.41 = ( ext_Product_unit @ V ) )
% 0.15/0.41 & ( ( restrict @ V @ ( res @ Ts2 ) @ X )
% 0.15/0.41 = ( lan_Product_unit @ V ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.empty_no_car
% 0.15/0.41 thf(fact_15_local_Ohmlsl_Otwo__lanes__no__car,axiom,
% 0.15/0.41 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 != one_one_nat )
% 0.15/0.41 => ~ ? [X: cars] :
% 0.15/0.41 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 0.15/0.41 = ( ext_Product_unit @ V ) )
% 0.15/0.41 & ( ( restrict @ V @ ( clm @ Ts2 ) @ X )
% 0.15/0.41 = ( lan_Product_unit @ V ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat ) )
% 0.15/0.41 | ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 0.15/0.41 = ( ext_Product_unit @ V ) )
% 0.15/0.41 & ( ( restrict @ V @ ( res @ Ts2 ) @ X )
% 0.15/0.41 = ( lan_Product_unit @ V ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.two_lanes_no_car
% 0.15/0.41 thf(fact_16_local_Ohmlsl_Ores__at__most__two,axiom,
% 0.15/0.41 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ~ ? [Va: view_e774982825t_unit,U: view_e774982825t_unit] :
% 0.15/0.41 ( ( vchop @ V @ Va @ U )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ Va ) )
% 0.15/0.41 & ( ( restrict @ Va @ ( res @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ Va ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ Va ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ? [Vb: view_e774982825t_unit,Ua: view_e774982825t_unit] :
% 0.15/0.41 ( ( vchop @ U @ Vb @ Ua )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Vb ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ Vb @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ Vb ) )
% 0.15/0.41 & ( ( restrict @ Vb @ ( res @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ Vb ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ Vb ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Ua ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ Ua @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ Ua ) )
% 0.15/0.41 & ( ( restrict @ Ua @ ( res @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ Ua ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ Ua ) )
% 0.15/0.41 = one_one_nat ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.res_at_most_two
% 0.15/0.41 thf(fact_17_local_Ohmlsl_Otwo__res__not__res,axiom,
% 0.15/0.41 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ? [Va: view_e774982825t_unit,U: view_e774982825t_unit] :
% 0.15/0.41 ( ( vchop @ V @ Va @ U )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ Va ) )
% 0.15/0.41 & ( ( restrict @ Va @ ( res @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ Va ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ Va ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ U @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ U ) )
% 0.15/0.41 & ( ( restrict @ U @ ( res @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ U ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ U ) )
% 0.15/0.41 = one_one_nat ) )
% 0.15/0.41 => ~ ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ V ) )
% 0.15/0.41 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ V ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.two_res_not_res
% 0.15/0.41 thf(fact_18_local_Ohmlsl_Oclm__ge__zero,axiom,
% 0.15/0.41 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ V ) )
% 0.15/0.41 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ V ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat ) )
% 0.15/0.41 => ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.clm_ge_zero
% 0.15/0.41 thf(fact_19_local_Ohmlsl_Ohchop__weaken2,axiom,
% 0.15/0.41 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( Phi @ Ts2 @ V )
% 0.15/0.41 => ? [Va2: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V @ Va2 @ U2 )
% 0.15/0.41 & ( Phi @ Ts2 @ U2 ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.hchop_weaken2
% 0.15/0.41 thf(fact_20_local_Ohmlsl_Ohchop__weaken1,axiom,
% 0.15/0.41 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( Phi @ Ts2 @ V )
% 0.15/0.41 => ? [Va2: view_e774982825t_unit] :
% 0.15/0.41 ( ? [X_1: view_e774982825t_unit] : ( hchop @ V @ Va2 @ X_1 )
% 0.15/0.41 & ( Phi @ Ts2 @ Va2 ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.hchop_weaken1
% 0.15/0.41 thf(fact_21_local_Ohmlsl_Ohchop__weaken,axiom,
% 0.15/0.41 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( Phi @ Ts2 @ V )
% 0.15/0.41 => ? [Va2: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V @ Va2 @ U2 )
% 0.15/0.41 & ? [Vb2: view_e774982825t_unit] :
% 0.15/0.41 ( ? [X_1: view_e774982825t_unit] : ( hchop @ U2 @ Vb2 @ X_1 )
% 0.15/0.41 & ( Phi @ Ts2 @ Vb2 ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.hchop_weaken
% 0.15/0.41 thf(fact_22_local_Ohmlsl_Ohchop__neg2,axiom,
% 0.15/0.41 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ~ ? [Va2: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V @ Va2 @ U2 )
% 0.15/0.41 & ( Phi @ Ts2 @ U2 ) )
% 0.15/0.41 => ? [Va2: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V @ Va2 @ U2 )
% 0.15/0.41 & ~ ( Phi @ Ts2 @ U2 ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.hchop_neg2
% 0.15/0.41 thf(fact_23_local_Ohmlsl_Ohchop__neg1,axiom,
% 0.15/0.41 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ~ ? [Va2: view_e774982825t_unit] :
% 0.15/0.41 ( ? [X_1: view_e774982825t_unit] : ( hchop @ V @ Va2 @ X_1 )
% 0.15/0.41 & ( Phi @ Ts2 @ Va2 ) )
% 0.15/0.41 => ? [Va2: view_e774982825t_unit] :
% 0.15/0.41 ( ? [X_1: view_e774982825t_unit] : ( hchop @ V @ Va2 @ X_1 )
% 0.15/0.41 & ~ ( Phi @ Ts2 @ Va2 ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.hchop_neg1
% 0.15/0.41 thf(fact_24_local_Ohmlsl_Ohchop__disj__distr2,axiom,
% 0.15/0.41 ! [Psi: traffic > view_e774982825t_unit > $o,Chi: traffic > view_e774982825t_unit > $o,Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V @ W @ U3 )
% 0.15/0.41 & ( ( Psi @ Ts2 @ W )
% 0.15/0.41 | ( Chi @ Ts2 @ W ) )
% 0.15/0.41 & ( Phi @ Ts2 @ U3 ) ) )
% 0.15/0.41 = ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V @ W @ U3 )
% 0.15/0.41 & ( Psi @ Ts2 @ W )
% 0.15/0.41 & ( Phi @ Ts2 @ U3 ) )
% 0.15/0.41 | ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V @ W @ U3 )
% 0.15/0.41 & ( Chi @ Ts2 @ W )
% 0.15/0.41 & ( Phi @ Ts2 @ U3 ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.hchop_disj_distr2
% 0.15/0.41 thf(fact_25_local_Ohmlsl_Ohchop__disj__distr1,axiom,
% 0.15/0.41 ! [Phi: traffic > view_e774982825t_unit > $o,Psi: traffic > view_e774982825t_unit > $o,Chi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V @ W @ U3 )
% 0.15/0.41 & ( Phi @ Ts2 @ W )
% 0.15/0.41 & ( ( Psi @ Ts2 @ U3 )
% 0.15/0.41 | ( Chi @ Ts2 @ U3 ) ) ) )
% 0.15/0.41 = ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V @ W @ U3 )
% 0.15/0.41 & ( Phi @ Ts2 @ W )
% 0.15/0.41 & ( Psi @ Ts2 @ U3 ) )
% 0.15/0.41 | ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V @ W @ U3 )
% 0.15/0.41 & ( Phi @ Ts2 @ W )
% 0.15/0.41 & ( Chi @ Ts2 @ U3 ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.hchop_disj_distr1
% 0.15/0.41 thf(fact_26_local_Ohmlsl_Ohchop__assoc,axiom,
% 0.15/0.41 ! [Phi: traffic > view_e774982825t_unit > $o,Psi: traffic > view_e774982825t_unit > $o,Chi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V @ W @ U3 )
% 0.15/0.41 & ( Phi @ Ts2 @ W )
% 0.15/0.41 & ? [X2: view_e774982825t_unit,Y: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ U3 @ X2 @ Y )
% 0.15/0.41 & ( Psi @ Ts2 @ X2 )
% 0.15/0.41 & ( Chi @ Ts2 @ Y ) ) ) )
% 0.15/0.41 = ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V @ W @ U3 )
% 0.15/0.41 & ? [X2: view_e774982825t_unit,Y: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ W @ X2 @ Y )
% 0.15/0.41 & ( Phi @ Ts2 @ X2 )
% 0.15/0.41 & ( Psi @ Ts2 @ Y ) )
% 0.15/0.41 & ( Chi @ Ts2 @ U3 ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.hchop_assoc
% 0.15/0.41 thf(fact_27_local_Ohmlsl_Ovchop__disj__distr2,axiom,
% 0.15/0.41 ! [Psi: traffic > view_e774982825t_unit > $o,Chi: traffic > view_e774982825t_unit > $o,Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 0.15/0.41 ( ( vchop @ V @ W @ U3 )
% 0.15/0.41 & ( ( Psi @ Ts2 @ W )
% 0.15/0.41 | ( Chi @ Ts2 @ W ) )
% 0.15/0.41 & ( Phi @ Ts2 @ U3 ) ) )
% 0.15/0.41 = ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 0.15/0.41 ( ( vchop @ V @ W @ U3 )
% 0.15/0.41 & ( Psi @ Ts2 @ W )
% 0.15/0.41 & ( Phi @ Ts2 @ U3 ) )
% 0.15/0.41 | ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 0.15/0.41 ( ( vchop @ V @ W @ U3 )
% 0.15/0.41 & ( Chi @ Ts2 @ W )
% 0.15/0.41 & ( Phi @ Ts2 @ U3 ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.vchop_disj_distr2
% 0.15/0.41 thf(fact_28_local_Ohmlsl_Ovchop__disj__distr1,axiom,
% 0.15/0.41 ! [Phi: traffic > view_e774982825t_unit > $o,Psi: traffic > view_e774982825t_unit > $o,Chi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 0.15/0.41 ( ( vchop @ V @ W @ U3 )
% 0.15/0.41 & ( Phi @ Ts2 @ W )
% 0.15/0.41 & ( ( Psi @ Ts2 @ U3 )
% 0.15/0.41 | ( Chi @ Ts2 @ U3 ) ) ) )
% 0.15/0.41 = ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 0.15/0.41 ( ( vchop @ V @ W @ U3 )
% 0.15/0.41 & ( Phi @ Ts2 @ W )
% 0.15/0.41 & ( Psi @ Ts2 @ U3 ) )
% 0.15/0.41 | ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 0.15/0.41 ( ( vchop @ V @ W @ U3 )
% 0.15/0.41 & ( Phi @ Ts2 @ W )
% 0.15/0.41 & ( Chi @ Ts2 @ U3 ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.vchop_disj_distr1
% 0.15/0.41 thf(fact_29_local_Ohmlsl_Ov__chop__weaken2,axiom,
% 0.15/0.41 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( Phi @ Ts2 @ V )
% 0.15/0.41 => ? [Va2: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 0.15/0.41 ( ( vchop @ V @ Va2 @ U2 )
% 0.15/0.41 & ( Phi @ Ts2 @ U2 ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.v_chop_weaken2
% 0.15/0.41 thf(fact_30_local_Ohmlsl_Ov__chop__weaken1,axiom,
% 0.15/0.41 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( Phi @ Ts2 @ V )
% 0.15/0.41 => ? [Va2: view_e774982825t_unit] :
% 0.15/0.41 ( ? [X_1: view_e774982825t_unit] : ( vchop @ V @ Va2 @ X_1 )
% 0.15/0.41 & ( Phi @ Ts2 @ Va2 ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.v_chop_weaken1
% 0.15/0.41 thf(fact_31_local_Ohmlsl_Ov__chop__assoc,axiom,
% 0.15/0.41 ! [Phi: traffic > view_e774982825t_unit > $o,Psi: traffic > view_e774982825t_unit > $o,Chi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 0.15/0.41 ( ( vchop @ V @ W @ U3 )
% 0.15/0.41 & ( Phi @ Ts2 @ W )
% 0.15/0.41 & ? [X2: view_e774982825t_unit,Y: view_e774982825t_unit] :
% 0.15/0.41 ( ( vchop @ U3 @ X2 @ Y )
% 0.15/0.41 & ( Psi @ Ts2 @ X2 )
% 0.15/0.41 & ( Chi @ Ts2 @ Y ) ) ) )
% 0.15/0.41 = ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 0.15/0.41 ( ( vchop @ V @ W @ U3 )
% 0.15/0.41 & ? [X2: view_e774982825t_unit,Y: view_e774982825t_unit] :
% 0.15/0.41 ( ( vchop @ W @ X2 @ Y )
% 0.15/0.41 & ( Phi @ Ts2 @ X2 )
% 0.15/0.41 & ( Psi @ Ts2 @ Y ) )
% 0.15/0.41 & ( Chi @ Ts2 @ U3 ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.v_chop_assoc
% 0.15/0.41 thf(fact_32_local_Ohmlsl_Oglobally__refl,axiom,
% 0.15/0.41 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ! [Ts3: traffic] :
% 0.15/0.41 ( ( abstract @ Ts2 @ Ts3 )
% 0.15/0.41 => ( Phi @ Ts3 @ ( move @ Ts2 @ Ts3 @ V ) ) )
% 0.15/0.41 => ( Phi @ Ts2 @ V ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.globally_refl
% 0.15/0.41 thf(fact_33_local_Ohmlsl_Oglobally__4,axiom,
% 0.15/0.41 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ! [Ts3: traffic] :
% 0.15/0.41 ( ( abstract @ Ts2 @ Ts3 )
% 0.15/0.41 => ( Phi @ Ts3 @ ( move @ Ts2 @ Ts3 @ V ) ) )
% 0.15/0.41 => ! [Ts4: traffic] :
% 0.15/0.41 ( ( abstract @ Ts2 @ Ts4 )
% 0.15/0.41 => ! [Ts_a: traffic] :
% 0.15/0.41 ( ( abstract @ Ts4 @ Ts_a )
% 0.15/0.41 => ( Phi @ Ts_a @ ( move @ Ts4 @ Ts_a @ ( move @ Ts2 @ Ts4 @ V ) ) ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.globally_4
% 0.15/0.41 thf(fact_34_wd__clm_Ohyps_I1_J,axiom,
% 0.15/0.41 abstract @ ts3 @ ts_a ).
% 0.15/0.41
% 0.15/0.41 % wd_clm.hyps(1)
% 0.15/0.41 thf(fact_35_local_Ohmlsl_Owidth__hchop__stable,axiom,
% 0.15/0.41 ! [X3: nat,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = X3 )
% 0.15/0.41 = ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V @ W @ U3 )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ W ) )
% 0.15/0.41 = X3 )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ U3 ) )
% 0.15/0.41 = X3 ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.width_hchop_stable
% 0.15/0.41 thf(fact_36_local_Ohmlsl_Olength__vchop__stable,axiom,
% 0.15/0.41 ! [X3: real,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( real_length @ ( ext_Product_unit @ V ) )
% 0.15/0.41 = X3 )
% 0.15/0.41 = ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 0.15/0.41 ( ( vchop @ V @ W @ U3 )
% 0.15/0.41 & ( ( real_length @ ( ext_Product_unit @ W ) )
% 0.15/0.41 = X3 )
% 0.15/0.41 & ( ( real_length @ ( ext_Product_unit @ U3 ) )
% 0.15/0.41 = X3 ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.length_vchop_stable
% 0.15/0.41 thf(fact_37_hmlsl_Olen__stable__up,axiom,
% 0.15/0.41 ! [V2: view_e774982825t_unit,V1: view_e774982825t_unit,V22: view_e774982825t_unit,Ts: traffic,C: cars] :
% 0.15/0.41 ( ( vchop @ V2 @ V1 @ V22 )
% 0.15/0.41 => ( ( len @ regular_regular @ V2 @ Ts @ C )
% 0.15/0.41 = ( len @ regular_regular @ V22 @ Ts @ C ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % hmlsl.len_stable_up
% 0.15/0.41 thf(fact_38_hmlsl_Olen__stable__down,axiom,
% 0.15/0.41 ! [V2: view_e774982825t_unit,V1: view_e774982825t_unit,V22: view_e774982825t_unit,Ts: traffic,C: cars] :
% 0.15/0.41 ( ( vchop @ V2 @ V1 @ V22 )
% 0.15/0.41 => ( ( len @ regular_regular @ V2 @ Ts @ C )
% 0.15/0.41 = ( len @ regular_regular @ V1 @ Ts @ C ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % hmlsl.len_stable_down
% 0.15/0.41 thf(fact_39_hmlsl_Olen__stable,axiom,
% 0.15/0.41 ! [V2: view_e774982825t_unit,V1: view_e774982825t_unit,V22: view_e774982825t_unit,Ts: traffic,C: cars] :
% 0.15/0.41 ( ( vchop @ V2 @ V1 @ V22 )
% 0.15/0.41 => ( ( len @ regular_regular @ V1 @ Ts @ C )
% 0.15/0.41 = ( len @ regular_regular @ V22 @ Ts @ C ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % hmlsl.len_stable
% 0.15/0.41 thf(fact_40_hmlsl_Olen__view__hchop__right,axiom,
% 0.15/0.41 ! [V2: view_e774982825t_unit,Ts: traffic,C: cars,V1: view_e774982825t_unit,V22: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( ( len @ regular_regular @ V2 @ Ts @ C )
% 0.15/0.41 = ( ext_Product_unit @ V2 ) )
% 0.15/0.41 & ( hchop @ V2 @ V1 @ V22 ) )
% 0.15/0.41 => ( ( len @ regular_regular @ V22 @ Ts @ C )
% 0.15/0.41 = ( ext_Product_unit @ V22 ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % hmlsl.len_view_hchop_right
% 0.15/0.41 thf(fact_41_hmlsl_Olen__view__hchop__left,axiom,
% 0.15/0.41 ! [V2: view_e774982825t_unit,Ts: traffic,C: cars,V1: view_e774982825t_unit,V22: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( ( len @ regular_regular @ V2 @ Ts @ C )
% 0.15/0.41 = ( ext_Product_unit @ V2 ) )
% 0.15/0.41 & ( hchop @ V2 @ V1 @ V22 ) )
% 0.15/0.41 => ( ( len @ regular_regular @ V1 @ Ts @ C )
% 0.15/0.41 = ( ext_Product_unit @ V1 ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % hmlsl.len_view_hchop_left
% 0.15/0.41 thf(fact_42_hmlsl_Olen__compose__hchop,axiom,
% 0.15/0.41 ! [V2: view_e774982825t_unit,V1: view_e774982825t_unit,V22: view_e774982825t_unit,Ts: traffic,C: cars] :
% 0.15/0.41 ( ( ( hchop @ V2 @ V1 @ V22 )
% 0.15/0.41 & ( ( len @ regular_regular @ V1 @ Ts @ C )
% 0.15/0.41 = ( ext_Product_unit @ V1 ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V22 @ Ts @ C )
% 0.15/0.41 = ( ext_Product_unit @ V22 ) ) )
% 0.15/0.41 => ( ( len @ regular_regular @ V2 @ Ts @ C )
% 0.15/0.41 = ( ext_Product_unit @ V2 ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % hmlsl.len_compose_hchop
% 0.15/0.41 thf(fact_43_wd__clm_Ohyps_I2_J,axiom,
% 0.15/0.41 ? [C2: cars] : ( withdraw_claim @ ts_a @ C2 @ ts ) ).
% 0.15/0.41
% 0.15/0.41 % wd_clm.hyps(2)
% 0.15/0.41 thf(fact_44_local_Ohmlsl_Olength__split,axiom,
% 0.15/0.41 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 => ? [Va2: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V @ Va2 @ U2 )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va2 ) ) )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U2 ) ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.length_split
% 0.15/0.41 thf(fact_45_local_Ohmlsl_Olength__meld,axiom,
% 0.15/0.41 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ? [Va: view_e774982825t_unit,U: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V @ Va @ U )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va ) ) )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U ) ) ) )
% 0.15/0.41 => ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.length_meld
% 0.15/0.41 thf(fact_46_local_Ohmlsl_Olength__dense,axiom,
% 0.15/0.41 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 = ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V @ W @ U3 )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ W ) ) )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U3 ) ) ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.length_dense
% 0.15/0.41 thf(fact_47_hmlsl_Olen__empty__on__subview2,axiom,
% 0.15/0.41 ! [V2: view_e774982825t_unit,Ts: traffic,C: cars,V1: view_e774982825t_unit,V22: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( ( real_length @ ( len @ regular_regular @ V2 @ Ts @ C ) )
% 0.15/0.41 = zero_zero_real )
% 0.15/0.41 & ( hchop @ V2 @ V1 @ V22 ) )
% 0.15/0.41 => ( ( real_length @ ( len @ regular_regular @ V22 @ Ts @ C ) )
% 0.15/0.41 = zero_zero_real ) ) ).
% 0.15/0.41
% 0.15/0.41 % hmlsl.len_empty_on_subview2
% 0.15/0.41 thf(fact_48_hmlsl_Olen__empty__on__subview1,axiom,
% 0.15/0.41 ! [V2: view_e774982825t_unit,Ts: traffic,C: cars,V1: view_e774982825t_unit,V22: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( ( real_length @ ( len @ regular_regular @ V2 @ Ts @ C ) )
% 0.15/0.41 = zero_zero_real )
% 0.15/0.41 & ( hchop @ V2 @ V1 @ V22 ) )
% 0.15/0.41 => ( ( real_length @ ( len @ regular_regular @ V1 @ Ts @ C ) )
% 0.15/0.41 = zero_zero_real ) ) ).
% 0.15/0.41
% 0.15/0.41 % hmlsl.len_empty_on_subview1
% 0.15/0.41 thf(fact_49_hmlsl_Olen__fills__subview,axiom,
% 0.15/0.41 ! [V2: view_e774982825t_unit,Ts: traffic,C: cars] :
% 0.15/0.41 ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ V2 @ Ts @ C ) ) )
% 0.15/0.41 => ? [V12: view_e774982825t_unit,V23: view_e774982825t_unit,V32: view_e774982825t_unit,V4: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V2 @ V12 @ V23 )
% 0.15/0.41 & ( hchop @ V23 @ V4 @ V32 )
% 0.15/0.41 & ( ( len @ regular_regular @ V4 @ Ts @ C )
% 0.15/0.41 = ( ext_Product_unit @ V4 ) )
% 0.15/0.41 & ( ( real_length @ ( len @ regular_regular @ V4 @ Ts @ C ) )
% 0.15/0.41 = ( real_length @ ( len @ regular_regular @ V2 @ Ts @ C ) ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % hmlsl.len_fills_subview
% 0.15/0.41 thf(fact_50_d__def,axiom,
% 0.15/0.41 withdraw_claim @ ts_a @ d @ ts ).
% 0.15/0.41
% 0.15/0.41 % d_def
% 0.15/0.41 thf(fact_51_local_Ohmlsl_Owidth__clm,axiom,
% 0.15/0.41 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ V ) )
% 0.15/0.41 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ V ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat ) )
% 0.15/0.41 => ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.width_clm
% 0.15/0.41 thf(fact_52_local_Ohmlsl_Oclm__dense,axiom,
% 0.15/0.41 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ V ) )
% 0.15/0.41 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ V ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat ) )
% 0.15/0.41 = ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V @ W @ U3 )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ W ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ W @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ W ) )
% 0.15/0.41 & ( ( restrict @ W @ ( clm @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ W ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ W ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U3 ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ U3 @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ U3 ) )
% 0.15/0.41 & ( ( restrict @ U3 @ ( clm @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ U3 ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ U3 ) )
% 0.15/0.41 = one_one_nat ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.clm_dense
% 0.15/0.41 thf(fact_53_local_Ohmlsl_Oclm__decompose,axiom,
% 0.15/0.41 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ V ) )
% 0.15/0.41 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ V ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat ) )
% 0.15/0.41 => ? [Va2: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V @ Va2 @ U2 )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va2 ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ Va2 @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ Va2 ) )
% 0.15/0.41 & ( ( restrict @ Va2 @ ( clm @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ Va2 ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ Va2 ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U2 ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ U2 @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ U2 ) )
% 0.15/0.41 & ( ( restrict @ U2 @ ( clm @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ U2 ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ U2 ) )
% 0.15/0.41 = one_one_nat ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.clm_decompose
% 0.15/0.41 thf(fact_54_local_Ohmlsl_Oclm__compose,axiom,
% 0.15/0.41 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ? [Va: view_e774982825t_unit,U: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V @ Va @ U )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ Va ) )
% 0.15/0.41 & ( ( restrict @ Va @ ( clm @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ Va ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ Va ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ U @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ U ) )
% 0.15/0.41 & ( ( restrict @ U @ ( clm @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ U ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ U ) )
% 0.15/0.41 = one_one_nat ) )
% 0.15/0.41 => ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ V ) )
% 0.15/0.41 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ V ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.clm_compose
% 0.15/0.41 thf(fact_55_local_Ohmlsl_Oclm__sing__not__interrupted,axiom,
% 0.15/0.41 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ~ ? [Va: view_e774982825t_unit,U: view_e774982825t_unit] :
% 0.15/0.41 ( ( vchop @ V @ Va @ U )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ Va ) )
% 0.15/0.41 & ( ( restrict @ Va @ ( clm @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ Va ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ Va ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ? [Vb: view_e774982825t_unit,Ua: view_e774982825t_unit] :
% 0.15/0.41 ( ( vchop @ U @ Vb @ Ua )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Ua ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ Ua @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ Ua ) )
% 0.15/0.41 & ( ( restrict @ Ua @ ( clm @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ Ua ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ Ua ) )
% 0.15/0.41 = one_one_nat ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.clm_sing_not_interrupted
% 0.15/0.41 thf(fact_56_local_Ohmlsl_Oclm__sing,axiom,
% 0.15/0.41 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ~ ? [Va: view_e774982825t_unit,U: view_e774982825t_unit] :
% 0.15/0.41 ( ( vchop @ V @ Va @ U )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ Va ) )
% 0.15/0.41 & ( ( restrict @ Va @ ( clm @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ Va ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ Va ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ U @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ U ) )
% 0.15/0.41 & ( ( restrict @ U @ ( clm @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ U ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ U ) )
% 0.15/0.41 = one_one_nat ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.clm_sing
% 0.15/0.41 thf(fact_57_local_Ohmlsl_Ono__clm__before__res2,axiom,
% 0.15/0.41 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ~ ? [Va: view_e774982825t_unit,U: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V @ Va @ U )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ Va ) )
% 0.15/0.41 & ( ( restrict @ Va @ ( clm @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ Va ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ Va ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ? [Vb: view_e774982825t_unit,Ua: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ U @ Vb @ Ua )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Ua ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ Ua @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ Ua ) )
% 0.15/0.41 & ( ( restrict @ Ua @ ( res @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ Ua ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ Ua ) )
% 0.15/0.41 = one_one_nat ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.no_clm_before_res2
% 0.15/0.41 thf(fact_58_local_Ohmlsl_Ono__clm__before__res,axiom,
% 0.15/0.41 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ~ ? [Va: view_e774982825t_unit,U: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V @ Va @ U )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ Va ) )
% 0.15/0.41 & ( ( restrict @ Va @ ( clm @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ Va ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ Va ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ U @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ U ) )
% 0.15/0.41 & ( ( restrict @ U @ ( res @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ U ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ U ) )
% 0.15/0.41 = one_one_nat ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.no_clm_before_res
% 0.15/0.41 thf(fact_59_local_Ohmlsl_Otwo__res__no__car,axiom,
% 0.15/0.41 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ? [Va: view_e774982825t_unit,U: view_e774982825t_unit] :
% 0.15/0.41 ( ( vchop @ V @ Va @ U )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ Va ) )
% 0.15/0.41 & ( ( restrict @ Va @ ( res @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ Va ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ Va ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ U @ Ts2 @ C )
% 0.15/0.41 = ( ext_Product_unit @ U ) )
% 0.15/0.41 & ( ( restrict @ U @ ( res @ Ts2 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ U ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ U ) )
% 0.15/0.41 = one_one_nat ) )
% 0.15/0.41 => ~ ? [X: cars] :
% 0.15/0.41 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 0.15/0.41 = ( ext_Product_unit @ V ) )
% 0.15/0.41 & ( ( restrict @ V @ ( clm @ Ts2 ) @ X )
% 0.15/0.41 = ( lan_Product_unit @ V ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat ) )
% 0.15/0.41 | ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 0.15/0.41 = ( ext_Product_unit @ V ) )
% 0.15/0.41 & ( ( restrict @ V @ ( res @ Ts2 ) @ X )
% 0.15/0.41 = ( lan_Product_unit @ V ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.two_res_no_car
% 0.15/0.41 thf(fact_60__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062d_O_Ats_H_A_092_060_094bold_062_092_060midarrow_062wdc_I_Ad_A_J_A_092_060_094bold_062_092_060rightarrow_062_Ats_H_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.15/0.41 ~ ! [D: cars] :
% 0.15/0.41 ~ ( withdraw_claim @ ts_a @ D @ ts ) ).
% 0.15/0.41
% 0.15/0.41 % \<open>\<And>thesis. (\<And>d. ts' \<^bold>\<midarrow>wdc( d ) \<^bold>\<rightarrow> ts'' \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.15/0.41 thf(fact_61_local_Ohmlsl_Ofree__dense,axiom,
% 0.15/0.41 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ! [C3: cars] :
% 0.15/0.41 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C3 ) )
% 0.15/0.41 = zero_zero_real )
% 0.15/0.41 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C3 )
% 0.15/0.41 = bot_bot_nat_int )
% 0.15/0.41 & ( ( restrict @ V @ ( res @ Ts2 ) @ C3 )
% 0.15/0.41 = bot_bot_nat_int ) ) ) )
% 0.15/0.41 = ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V @ W @ U3 )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ W ) ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ W ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ! [C3: cars] :
% 0.15/0.41 ( ( ( real_length @ ( len @ regular_regular @ W @ Ts2 @ C3 ) )
% 0.15/0.41 = zero_zero_real )
% 0.15/0.41 | ( ( ( restrict @ W @ ( clm @ Ts2 ) @ C3 )
% 0.15/0.41 = bot_bot_nat_int )
% 0.15/0.41 & ( ( restrict @ W @ ( res @ Ts2 ) @ C3 )
% 0.15/0.41 = bot_bot_nat_int ) ) )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U3 ) ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ U3 ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ! [C3: cars] :
% 0.15/0.41 ( ( ( real_length @ ( len @ regular_regular @ U3 @ Ts2 @ C3 ) )
% 0.15/0.41 = zero_zero_real )
% 0.15/0.41 | ( ( ( restrict @ U3 @ ( clm @ Ts2 ) @ C3 )
% 0.15/0.41 = bot_bot_nat_int )
% 0.15/0.41 & ( ( restrict @ U3 @ ( res @ Ts2 ) @ C3 )
% 0.15/0.41 = bot_bot_nat_int ) ) ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.free_dense
% 0.15/0.41 thf(fact_62_local_Ohmlsl_Ofree__decompose,axiom,
% 0.15/0.41 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ! [C2: cars] :
% 0.15/0.41 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 0.15/0.41 = zero_zero_real )
% 0.15/0.41 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 0.15/0.41 = bot_bot_nat_int )
% 0.15/0.41 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 0.15/0.41 = bot_bot_nat_int ) ) ) )
% 0.15/0.41 => ? [Va2: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V @ Va2 @ U2 )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va2 ) ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ Va2 ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ! [C4: cars] :
% 0.15/0.41 ( ( ( real_length @ ( len @ regular_regular @ Va2 @ Ts2 @ C4 ) )
% 0.15/0.41 = zero_zero_real )
% 0.15/0.41 | ( ( ( restrict @ Va2 @ ( clm @ Ts2 ) @ C4 )
% 0.15/0.41 = bot_bot_nat_int )
% 0.15/0.41 & ( ( restrict @ Va2 @ ( res @ Ts2 ) @ C4 )
% 0.15/0.41 = bot_bot_nat_int ) ) )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U2 ) ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ U2 ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ! [C4: cars] :
% 0.15/0.41 ( ( ( real_length @ ( len @ regular_regular @ U2 @ Ts2 @ C4 ) )
% 0.15/0.41 = zero_zero_real )
% 0.15/0.41 | ( ( ( restrict @ U2 @ ( clm @ Ts2 ) @ C4 )
% 0.15/0.41 = bot_bot_nat_int )
% 0.15/0.41 & ( ( restrict @ U2 @ ( res @ Ts2 ) @ C4 )
% 0.15/0.41 = bot_bot_nat_int ) ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.free_decompose
% 0.15/0.41 thf(fact_63_local_Ohmlsl_Ofree__compose,axiom,
% 0.15/0.41 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ? [Va: view_e774982825t_unit,U: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V @ Va @ U )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va ) ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ Va ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ! [C2: cars] :
% 0.15/0.41 ( ( ( real_length @ ( len @ regular_regular @ Va @ Ts2 @ C2 ) )
% 0.15/0.41 = zero_zero_real )
% 0.15/0.41 | ( ( ( restrict @ Va @ ( clm @ Ts2 ) @ C2 )
% 0.15/0.41 = bot_bot_nat_int )
% 0.15/0.41 & ( ( restrict @ Va @ ( res @ Ts2 ) @ C2 )
% 0.15/0.41 = bot_bot_nat_int ) ) )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U ) ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ U ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ! [C2: cars] :
% 0.15/0.41 ( ( ( real_length @ ( len @ regular_regular @ U @ Ts2 @ C2 ) )
% 0.15/0.41 = zero_zero_real )
% 0.15/0.41 | ( ( ( restrict @ U @ ( clm @ Ts2 ) @ C2 )
% 0.15/0.41 = bot_bot_nat_int )
% 0.15/0.41 & ( ( restrict @ U @ ( res @ Ts2 ) @ C2 )
% 0.15/0.41 = bot_bot_nat_int ) ) ) )
% 0.15/0.41 => ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ! [C4: cars] :
% 0.15/0.41 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C4 ) )
% 0.15/0.41 = zero_zero_real )
% 0.15/0.41 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C4 )
% 0.15/0.41 = bot_bot_nat_int )
% 0.15/0.41 & ( ( restrict @ V @ ( res @ Ts2 ) @ C4 )
% 0.15/0.41 = bot_bot_nat_int ) ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.free_compose
% 0.15/0.41 thf(fact_64_local_Ohmlsl_Owidth__free,axiom,
% 0.15/0.41 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ! [C2: cars] :
% 0.15/0.41 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 0.15/0.41 = zero_zero_real )
% 0.15/0.41 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 0.15/0.41 = bot_bot_nat_int )
% 0.15/0.41 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 0.15/0.41 = bot_bot_nat_int ) ) ) )
% 0.15/0.41 => ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.width_free
% 0.15/0.41 thf(fact_65_local_Ohmlsl_Ores__not__free,axiom,
% 0.15/0.41 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ? [X4: cars] :
% 0.15/0.41 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V @ Ts2 @ X4 )
% 0.15/0.41 = ( ext_Product_unit @ V ) )
% 0.15/0.41 & ( ( restrict @ V @ ( res @ Ts2 ) @ X4 )
% 0.15/0.41 = ( lan_Product_unit @ V ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat ) )
% 0.15/0.41 => ~ ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ! [C2: cars] :
% 0.15/0.41 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 0.15/0.41 = zero_zero_real )
% 0.15/0.41 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 0.15/0.41 = bot_bot_nat_int )
% 0.15/0.41 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 0.15/0.41 = bot_bot_nat_int ) ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.res_not_free
% 0.15/0.41 thf(fact_66_local_Ohmlsl_Ofree__no__res,axiom,
% 0.15/0.41 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ! [C2: cars] :
% 0.15/0.41 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 0.15/0.41 = zero_zero_real )
% 0.15/0.41 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 0.15/0.41 = bot_bot_nat_int )
% 0.15/0.41 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 0.15/0.41 = bot_bot_nat_int ) ) ) )
% 0.15/0.41 => ~ ? [X: cars] :
% 0.15/0.41 ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 0.15/0.41 = ( ext_Product_unit @ V ) )
% 0.15/0.41 & ( ( restrict @ V @ ( res @ Ts2 ) @ X )
% 0.15/0.41 = ( lan_Product_unit @ V ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.free_no_res
% 0.15/0.41 thf(fact_67_local_Ohmlsl_Ofree__no__clm,axiom,
% 0.15/0.41 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ! [C2: cars] :
% 0.15/0.41 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 0.15/0.41 = zero_zero_real )
% 0.15/0.41 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 0.15/0.41 = bot_bot_nat_int )
% 0.15/0.41 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 0.15/0.41 = bot_bot_nat_int ) ) ) )
% 0.15/0.41 => ~ ? [X: cars] :
% 0.15/0.41 ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 0.15/0.41 = ( ext_Product_unit @ V ) )
% 0.15/0.41 & ( ( restrict @ V @ ( clm @ Ts2 ) @ X )
% 0.15/0.41 = ( lan_Product_unit @ V ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.free_no_clm
% 0.15/0.41 thf(fact_68_local_Ohmlsl_Ofree__ge__zero,axiom,
% 0.15/0.41 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ! [C2: cars] :
% 0.15/0.41 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 0.15/0.41 = zero_zero_real )
% 0.15/0.41 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 0.15/0.41 = bot_bot_nat_int )
% 0.15/0.41 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 0.15/0.41 = bot_bot_nat_int ) ) ) )
% 0.15/0.41 => ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.free_ge_zero
% 0.15/0.41 thf(fact_69_local_Ohmlsl_Oclm__not__free,axiom,
% 0.15/0.41 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.41 ? [X4: cars] :
% 0.15/0.41 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V @ Ts2 @ X4 )
% 0.15/0.41 = ( ext_Product_unit @ V ) )
% 0.15/0.41 & ( ( restrict @ V @ ( clm @ Ts2 ) @ X4 )
% 0.15/0.41 = ( lan_Product_unit @ V ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat ) )
% 0.15/0.41 => ~ ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.41 = one_one_nat )
% 0.15/0.41 & ! [C2: cars] :
% 0.15/0.41 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 0.15/0.41 = zero_zero_real )
% 0.15/0.41 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 0.15/0.41 = bot_bot_nat_int )
% 0.15/0.41 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 0.15/0.41 = bot_bot_nat_int ) ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % local.hmlsl.clm_not_free
% 0.15/0.41 thf(fact_70_hmlsl__regular_Obackwards__wdc__res__stab,axiom,
% 0.15/0.41 ! [Ts: traffic,D2: cars,Ts5: traffic,V2: view_e774982825t_unit,C: cars] :
% 0.15/0.41 ( ( ( withdraw_claim @ Ts @ D2 @ Ts5 )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V2 @ Ts5 @ C )
% 0.15/0.41 = ( ext_Product_unit @ V2 ) )
% 0.15/0.41 & ( ( restrict @ V2 @ ( res @ Ts5 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ V2 ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 0.15/0.41 = one_one_nat ) )
% 0.15/0.41 => ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V2 @ Ts @ C )
% 0.15/0.41 = ( ext_Product_unit @ V2 ) )
% 0.15/0.41 & ( ( restrict @ V2 @ ( res @ Ts ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ V2 ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 0.15/0.41 = one_one_nat ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % hmlsl_regular.backwards_wdc_res_stab
% 0.15/0.41 thf(fact_71_view_Ohorizontal__chop__non__empty,axiom,
% 0.15/0.41 ! [V2: view_e774982825t_unit] :
% 0.15/0.41 ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 0.15/0.41 => ? [U2: view_e774982825t_unit,W2: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V2 @ U2 @ W2 )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U2 ) ) )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ W2 ) ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % view.horizontal_chop_non_empty
% 0.15/0.41 thf(fact_72_not__gr__zero,axiom,
% 0.15/0.41 ! [N: nat] :
% 0.15/0.41 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.15/0.41 = ( N = zero_zero_nat ) ) ).
% 0.15/0.41
% 0.15/0.41 % not_gr_zero
% 0.15/0.41 thf(fact_73_le__zero__eq,axiom,
% 0.15/0.41 ! [N: nat] :
% 0.15/0.41 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.15/0.41 = ( N = zero_zero_nat ) ) ).
% 0.15/0.41
% 0.15/0.41 % le_zero_eq
% 0.15/0.41 thf(fact_74_hmlsl__regular_Obackwards__c__res__stab,axiom,
% 0.15/0.41 ! [Ts: traffic,D2: cars,N: nat,Ts5: traffic,V2: view_e774982825t_unit,C: cars] :
% 0.15/0.41 ( ( ( create_claim @ Ts @ D2 @ N @ Ts5 )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V2 @ Ts5 @ C )
% 0.15/0.41 = ( ext_Product_unit @ V2 ) )
% 0.15/0.41 & ( ( restrict @ V2 @ ( res @ Ts5 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ V2 ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 0.15/0.41 = one_one_nat ) )
% 0.15/0.41 => ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V2 @ Ts @ C )
% 0.15/0.41 = ( ext_Product_unit @ V2 ) )
% 0.15/0.41 & ( ( restrict @ V2 @ ( res @ Ts ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ V2 ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 0.15/0.41 = one_one_nat ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % hmlsl_regular.backwards_c_res_stab
% 0.15/0.41 thf(fact_75_hmlsl__regular_Obackwards__wdr__res__stab,axiom,
% 0.15/0.41 ! [Ts: traffic,D2: cars,N: nat,Ts5: traffic,V2: view_e774982825t_unit,C: cars] :
% 0.15/0.41 ( ( ( withdraw_reservation @ Ts @ D2 @ N @ Ts5 )
% 0.15/0.41 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V2 @ Ts5 @ C )
% 0.15/0.41 = ( ext_Product_unit @ V2 ) )
% 0.15/0.41 & ( ( restrict @ V2 @ ( res @ Ts5 ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ V2 ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 0.15/0.41 = one_one_nat ) )
% 0.15/0.41 => ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 0.15/0.41 & ( ( len @ regular_regular @ V2 @ Ts @ C )
% 0.15/0.41 = ( ext_Product_unit @ V2 ) )
% 0.15/0.41 & ( ( restrict @ V2 @ ( res @ Ts ) @ C )
% 0.15/0.41 = ( lan_Product_unit @ V2 ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 0.15/0.41 = one_one_nat ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % hmlsl_regular.backwards_wdr_res_stab
% 0.15/0.41 thf(fact_76_hmlsl_Olen__sub__int,axiom,
% 0.15/0.41 ! [V2: view_e774982825t_unit,Ts: traffic,C: cars] : ( ord_less_eq_real_int @ ( len @ regular_regular @ V2 @ Ts @ C ) @ ( ext_Product_unit @ V2 ) ) ).
% 0.15/0.41
% 0.15/0.41 % hmlsl.len_sub_int
% 0.15/0.41 thf(fact_77_view_Overtical__chop__width__mon,axiom,
% 0.15/0.41 ! [V2: view_e774982825t_unit,V1: view_e774982825t_unit,V22: view_e774982825t_unit,V33: view_e774982825t_unit,V42: view_e774982825t_unit,X3: nat] :
% 0.15/0.41 ( ( ( vchop @ V2 @ V1 @ V22 )
% 0.15/0.41 & ( vchop @ V22 @ V33 @ V42 )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V33 ) )
% 0.15/0.41 = X3 ) )
% 0.15/0.41 => ( ord_less_eq_nat @ X3 @ ( nat_card @ ( lan_Product_unit @ V2 ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % view.vertical_chop_width_mon
% 0.15/0.41 thf(fact_78_zero__reorient,axiom,
% 0.15/0.41 ! [X3: real] :
% 0.15/0.41 ( ( zero_zero_real = X3 )
% 0.15/0.41 = ( X3 = zero_zero_real ) ) ).
% 0.15/0.41
% 0.15/0.41 % zero_reorient
% 0.15/0.41 thf(fact_79_zero__reorient,axiom,
% 0.15/0.41 ! [X3: nat] :
% 0.15/0.41 ( ( zero_zero_nat = X3 )
% 0.15/0.41 = ( X3 = zero_zero_nat ) ) ).
% 0.15/0.41
% 0.15/0.41 % zero_reorient
% 0.15/0.41 thf(fact_80_view_Overtical__chop__singleton,axiom,
% 0.15/0.41 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( vchop @ V2 @ U4 @ W3 )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 0.15/0.41 = one_one_nat ) )
% 0.15/0.41 => ( ( ( nat_card @ ( lan_Product_unit @ U4 ) )
% 0.15/0.41 = zero_zero_nat )
% 0.15/0.41 | ( ( nat_card @ ( lan_Product_unit @ W3 ) )
% 0.15/0.41 = zero_zero_nat ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % view.vertical_chop_singleton
% 0.15/0.41 thf(fact_81_one__reorient,axiom,
% 0.15/0.41 ! [X3: nat] :
% 0.15/0.41 ( ( one_one_nat = X3 )
% 0.15/0.41 = ( X3 = one_one_nat ) ) ).
% 0.15/0.41
% 0.15/0.41 % one_reorient
% 0.15/0.41 thf(fact_82_view_Ohorizontal__chop1,axiom,
% 0.15/0.41 ! [V2: view_e774982825t_unit] :
% 0.15/0.41 ? [U2: view_e774982825t_unit,X_1: view_e774982825t_unit] : ( hchop @ V2 @ U2 @ X_1 ) ).
% 0.15/0.41
% 0.15/0.41 % view.horizontal_chop1
% 0.15/0.41 thf(fact_83_view_Ohorizontal__chop__assoc1,axiom,
% 0.15/0.41 ! [V2: view_e774982825t_unit,V1: view_e774982825t_unit,V22: view_e774982825t_unit,V33: view_e774982825t_unit,V42: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( hchop @ V2 @ V1 @ V22 )
% 0.15/0.41 & ( hchop @ V22 @ V33 @ V42 ) )
% 0.15/0.41 => ? [V4: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V2 @ V4 @ V42 )
% 0.15/0.41 & ( hchop @ V4 @ V1 @ V33 ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % view.horizontal_chop_assoc1
% 0.15/0.41 thf(fact_84_view_Ohorizontal__chop__assoc2,axiom,
% 0.15/0.41 ! [V2: view_e774982825t_unit,V1: view_e774982825t_unit,V22: view_e774982825t_unit,V33: view_e774982825t_unit,V42: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( hchop @ V2 @ V1 @ V22 )
% 0.15/0.41 & ( hchop @ V1 @ V33 @ V42 ) )
% 0.15/0.41 => ? [V4: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V2 @ V33 @ V4 )
% 0.15/0.41 & ( hchop @ V4 @ V42 @ V22 ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % view.horizontal_chop_assoc2
% 0.15/0.41 thf(fact_85_view_Ohorizontal__chop__empty__left,axiom,
% 0.15/0.41 ! [V: view_e774982825t_unit] :
% 0.15/0.41 ? [U2: view_e774982825t_unit] : ( hchop @ V @ U2 @ V ) ).
% 0.15/0.41
% 0.15/0.41 % view.horizontal_chop_empty_left
% 0.15/0.41 thf(fact_86_view_Ohorizontal__chop__empty__right,axiom,
% 0.15/0.41 ! [V: view_e774982825t_unit] :
% 0.15/0.41 ? [X_1: view_e774982825t_unit] : ( hchop @ V @ V @ X_1 ) ).
% 0.15/0.41
% 0.15/0.41 % view.horizontal_chop_empty_right
% 0.15/0.41 thf(fact_87_view_Overtical__chop1,axiom,
% 0.15/0.41 ! [V: view_e774982825t_unit] :
% 0.15/0.41 ? [U2: view_e774982825t_unit,X_1: view_e774982825t_unit] : ( vchop @ V @ U2 @ X_1 ) ).
% 0.15/0.41
% 0.15/0.41 % view.vertical_chop1
% 0.15/0.41 thf(fact_88_view_Overtical__chop__assoc1,axiom,
% 0.15/0.41 ! [V2: view_e774982825t_unit,V1: view_e774982825t_unit,V22: view_e774982825t_unit,V33: view_e774982825t_unit,V42: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( vchop @ V2 @ V1 @ V22 )
% 0.15/0.41 & ( vchop @ V22 @ V33 @ V42 ) )
% 0.15/0.41 => ? [V4: view_e774982825t_unit] :
% 0.15/0.41 ( ( vchop @ V2 @ V4 @ V42 )
% 0.15/0.41 & ( vchop @ V4 @ V1 @ V33 ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % view.vertical_chop_assoc1
% 0.15/0.41 thf(fact_89_view_Overtical__chop__assoc2,axiom,
% 0.15/0.41 ! [V2: view_e774982825t_unit,V1: view_e774982825t_unit,V22: view_e774982825t_unit,V33: view_e774982825t_unit,V42: view_e774982825t_unit] :
% 0.15/0.41 ( ( ( vchop @ V2 @ V1 @ V22 )
% 0.15/0.41 & ( vchop @ V1 @ V33 @ V42 ) )
% 0.15/0.41 => ? [V4: view_e774982825t_unit] :
% 0.15/0.41 ( ( vchop @ V2 @ V33 @ V4 )
% 0.15/0.41 & ( vchop @ V4 @ V42 @ V22 ) ) ) ).
% 0.15/0.41
% 0.15/0.41 % view.vertical_chop_assoc2
% 0.15/0.41 thf(fact_90_view_Overtical__chop__empty__up,axiom,
% 0.15/0.41 ! [V: view_e774982825t_unit] :
% 0.15/0.41 ? [U2: view_e774982825t_unit] : ( vchop @ V @ U2 @ V ) ).
% 0.15/0.41
% 0.15/0.41 % view.vertical_chop_empty_up
% 0.15/0.41 thf(fact_91_view_Overtical__chop__empty__down,axiom,
% 0.15/0.41 ! [V: view_e774982825t_unit] :
% 0.15/0.41 ? [X_1: view_e774982825t_unit] : ( vchop @ V @ V @ X_1 ) ).
% 0.15/0.41
% 0.15/0.41 % view.vertical_chop_empty_down
% 0.15/0.41 thf(fact_92_zero__le,axiom,
% 0.15/0.41 ! [X3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X3 ) ).
% 0.15/0.41
% 0.15/0.41 % zero_le
% 0.15/0.41 thf(fact_93_zero__less__iff__neq__zero,axiom,
% 0.15/0.41 ! [N: nat] :
% 0.15/0.41 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.15/0.41 = ( N != zero_zero_nat ) ) ).
% 0.15/0.41
% 0.15/0.41 % zero_less_iff_neq_zero
% 0.15/0.41 thf(fact_94_gr__implies__not__zero,axiom,
% 0.15/0.41 ! [M: nat,N: nat] :
% 0.15/0.41 ( ( ord_less_nat @ M @ N )
% 0.15/0.41 => ( N != zero_zero_nat ) ) ).
% 0.15/0.41
% 0.15/0.41 % gr_implies_not_zero
% 0.15/0.41 thf(fact_95_not__less__zero,axiom,
% 0.15/0.41 ! [N: nat] :
% 0.15/0.41 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.15/0.41
% 0.15/0.41 % not_less_zero
% 0.15/0.41 thf(fact_96_gr__zeroI,axiom,
% 0.15/0.41 ! [N: nat] :
% 0.15/0.41 ( ( N != zero_zero_nat )
% 0.15/0.41 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.15/0.41
% 0.15/0.41 % gr_zeroI
% 0.15/0.41 thf(fact_97_view_Ohorizontal__chop__leq2,axiom,
% 0.15/0.41 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V2 @ U4 @ W3 )
% 0.15/0.41 => ( ord_le461438217t_unit @ W3 @ V2 ) ) ).
% 0.15/0.41
% 0.15/0.41 % view.horizontal_chop_leq2
% 0.15/0.41 thf(fact_98_view_Ohorizontal__chop__leq1,axiom,
% 0.15/0.41 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V2 @ U4 @ W3 )
% 0.15/0.41 => ( ord_le461438217t_unit @ U4 @ V2 ) ) ).
% 0.15/0.41
% 0.15/0.41 % view.horizontal_chop_leq1
% 0.15/0.41 thf(fact_99_view_Overtical__chop__leq2,axiom,
% 0.15/0.41 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit] :
% 0.15/0.41 ( ( vchop @ V2 @ U4 @ W3 )
% 0.15/0.41 => ( ord_le461438217t_unit @ W3 @ V2 ) ) ).
% 0.15/0.41
% 0.15/0.41 % view.vertical_chop_leq2
% 0.15/0.41 thf(fact_100_view_Overtical__chop__leq1,axiom,
% 0.15/0.41 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit] :
% 0.15/0.41 ( ( vchop @ V2 @ U4 @ W3 )
% 0.15/0.41 => ( ord_le461438217t_unit @ U4 @ V2 ) ) ).
% 0.15/0.41
% 0.15/0.41 % view.vertical_chop_leq1
% 0.15/0.41 thf(fact_101_view_Ohorizontal__chop__width__stable,axiom,
% 0.15/0.41 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit] :
% 0.15/0.41 ( ( hchop @ V2 @ U4 @ W3 )
% 0.15/0.41 => ( ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 0.15/0.41 = ( nat_card @ ( lan_Product_unit @ U4 ) ) )
% 0.15/0.41 & ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 0.15/0.41 = ( nat_card @ ( lan_Product_unit @ W3 ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % view.horizontal_chop_width_stable
% 0.15/0.42 thf(fact_102_view_Overtical__chop__length__stable,axiom,
% 0.15/0.42 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit] :
% 0.15/0.42 ( ( vchop @ V2 @ U4 @ W3 )
% 0.15/0.42 => ( ( ( real_length @ ( ext_Product_unit @ V2 ) )
% 0.15/0.42 = ( real_length @ ( ext_Product_unit @ U4 ) ) )
% 0.15/0.42 & ( ( real_length @ ( ext_Product_unit @ V2 ) )
% 0.15/0.42 = ( real_length @ ( ext_Product_unit @ W3 ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % view.vertical_chop_length_stable
% 0.15/0.42 thf(fact_103_view_Osomewhere__leq,axiom,
% 0.15/0.42 ( ord_le461438217t_unit
% 0.15/0.42 = ( ^ [V5: view_e774982825t_unit,V6: view_e774982825t_unit] :
% 0.15/0.42 ? [V13: view_e774982825t_unit,V24: view_e774982825t_unit,V34: view_e774982825t_unit,Vl: view_e774982825t_unit,Vr: view_e774982825t_unit,Vu: view_e774982825t_unit,Vd: view_e774982825t_unit] :
% 0.15/0.42 ( ( hchop @ V6 @ Vl @ V13 )
% 0.15/0.42 & ( hchop @ V13 @ V24 @ Vr )
% 0.15/0.42 & ( vchop @ V24 @ Vd @ V34 )
% 0.15/0.42 & ( vchop @ V34 @ V5 @ Vu ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % view.somewhere_leq
% 0.15/0.42 thf(fact_104_hmlsl_Oview__leq__len__leq,axiom,
% 0.15/0.42 ! [V2: view_e774982825t_unit,V3: view_e774982825t_unit,Ts: traffic,C: cars] :
% 0.15/0.42 ( ( ( ord_less_eq_real_int @ ( ext_Product_unit @ V2 ) @ ( ext_Product_unit @ V3 ) )
% 0.15/0.42 & ( ( own_Product_unit @ V2 )
% 0.15/0.42 = ( own_Product_unit @ V3 ) )
% 0.15/0.42 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ V2 @ Ts @ C ) ) ) )
% 0.15/0.42 => ( ord_less_eq_real_int @ ( len @ regular_regular @ V2 @ Ts @ C ) @ ( len @ regular_regular @ V3 @ Ts @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % hmlsl.view_leq_len_leq
% 0.15/0.42 thf(fact_105_restriction_Orestriction__card__somewhere__mon,axiom,
% 0.15/0.42 ! [V2: view_e774982825t_unit,Vl2: view_e774982825t_unit,V1: view_e774982825t_unit,V22: view_e774982825t_unit,Vr2: view_e774982825t_unit,Vu2: view_e774982825t_unit,V33: view_e774982825t_unit,V3: view_e774982825t_unit,Vd2: view_e774982825t_unit,F: cars > nat_int,C: cars] :
% 0.15/0.42 ( ( ( hchop @ V2 @ Vl2 @ V1 )
% 0.15/0.42 & ( hchop @ V1 @ V22 @ Vr2 )
% 0.15/0.42 & ( vchop @ V22 @ Vu2 @ V33 )
% 0.15/0.42 & ( vchop @ V33 @ V3 @ Vd2 )
% 0.15/0.42 & ( ( nat_card @ ( restrict @ V3 @ F @ C ) )
% 0.15/0.42 = one_one_nat ) )
% 0.15/0.42 => ( ord_less_eq_nat @ one_one_nat @ ( nat_card @ ( restrict @ V2 @ F @ C ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % restriction.restriction_card_somewhere_mon
% 0.15/0.42 thf(fact_106_hmlsl__regular_Obackwards__res__act,axiom,
% 0.15/0.42 ! [Ts: traffic,C: cars,Ts5: traffic,V2: view_e774982825t_unit] :
% 0.15/0.42 ( ( ( create_reservation @ Ts @ C @ Ts5 )
% 0.15/0.42 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 0.15/0.42 & ( ( len @ regular_regular @ V2 @ Ts5 @ C )
% 0.15/0.42 = ( ext_Product_unit @ V2 ) )
% 0.15/0.42 & ( ( restrict @ V2 @ ( res @ Ts5 ) @ C )
% 0.15/0.42 = ( lan_Product_unit @ V2 ) )
% 0.15/0.42 & ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 0.15/0.42 = one_one_nat ) )
% 0.15/0.42 => ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 0.15/0.42 & ( ( len @ regular_regular @ V2 @ Ts @ C )
% 0.15/0.42 = ( ext_Product_unit @ V2 ) )
% 0.15/0.42 & ( ( restrict @ V2 @ ( res @ Ts ) @ C )
% 0.15/0.42 = ( lan_Product_unit @ V2 ) )
% 0.15/0.42 & ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 0.15/0.42 = one_one_nat ) )
% 0.15/0.42 | ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 0.15/0.42 & ( ( len @ regular_regular @ V2 @ Ts @ C )
% 0.15/0.42 = ( ext_Product_unit @ V2 ) )
% 0.15/0.42 & ( ( restrict @ V2 @ ( clm @ Ts ) @ C )
% 0.15/0.42 = ( lan_Product_unit @ V2 ) )
% 0.15/0.42 & ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 0.15/0.42 = one_one_nat ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % hmlsl_regular.backwards_res_act
% 0.15/0.42 thf(fact_107_hmlsl__regular_Oreservation2,axiom,
% 0.15/0.42 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.42 ( ! [Ts3: traffic] :
% 0.15/0.42 ( ( create_reservation @ Ts2 @ C @ Ts3 )
% 0.15/0.42 => ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.42 & ( ( len @ regular_regular @ V @ Ts3 @ C )
% 0.15/0.42 = ( ext_Product_unit @ V ) )
% 0.15/0.42 & ( ( restrict @ V @ ( res @ Ts3 ) @ C )
% 0.15/0.42 = ( lan_Product_unit @ V ) )
% 0.15/0.42 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.42 = one_one_nat ) ) )
% 0.15/0.42 => ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.42 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.42 = ( ext_Product_unit @ V ) )
% 0.15/0.42 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 0.15/0.42 = ( lan_Product_unit @ V ) )
% 0.15/0.42 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.42 = one_one_nat ) )
% 0.15/0.42 | ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.42 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.42 = ( ext_Product_unit @ V ) )
% 0.15/0.42 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 0.15/0.42 = ( lan_Product_unit @ V ) )
% 0.15/0.42 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.42 = one_one_nat ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % hmlsl_regular.reservation2
% 0.15/0.42 thf(fact_108_hmlsl__regular_Oreservation1,axiom,
% 0.15/0.42 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.42 ( ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.42 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.42 = ( ext_Product_unit @ V ) )
% 0.15/0.42 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 0.15/0.42 = ( lan_Product_unit @ V ) )
% 0.15/0.42 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.42 = one_one_nat ) )
% 0.15/0.42 | ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.42 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.42 = ( ext_Product_unit @ V ) )
% 0.15/0.42 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 0.15/0.42 = ( lan_Product_unit @ V ) )
% 0.15/0.42 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.42 = one_one_nat ) ) )
% 0.15/0.42 => ! [Ts4: traffic] :
% 0.15/0.42 ( ( create_reservation @ Ts2 @ C @ Ts4 )
% 0.15/0.42 => ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.42 & ( ( len @ regular_regular @ V @ Ts4 @ C )
% 0.15/0.42 = ( ext_Product_unit @ V ) )
% 0.15/0.42 & ( ( restrict @ V @ ( res @ Ts4 ) @ C )
% 0.15/0.42 = ( lan_Product_unit @ V ) )
% 0.15/0.42 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.42 = one_one_nat ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % hmlsl_regular.reservation1
% 0.15/0.42 thf(fact_109_hmlsl__regular_Oreservation,axiom,
% 0.15/0.42 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.42 ( ( ! [Ts6: traffic] :
% 0.15/0.42 ( ( create_reservation @ Ts2 @ C @ Ts6 )
% 0.15/0.42 => ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.42 & ( ( len @ regular_regular @ V @ Ts6 @ C )
% 0.15/0.42 = ( ext_Product_unit @ V ) )
% 0.15/0.42 & ( ( restrict @ V @ ( res @ Ts6 ) @ C )
% 0.15/0.42 = ( lan_Product_unit @ V ) )
% 0.15/0.42 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.42 = one_one_nat ) ) ) )
% 0.15/0.42 = ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.42 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.42 = ( ext_Product_unit @ V ) )
% 0.15/0.42 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 0.15/0.42 = ( lan_Product_unit @ V ) )
% 0.15/0.42 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.42 = one_one_nat ) )
% 0.15/0.42 | ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 0.15/0.42 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 0.15/0.42 = ( ext_Product_unit @ V ) )
% 0.15/0.42 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 0.15/0.42 = ( lan_Product_unit @ V ) )
% 0.15/0.42 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.42 = one_one_nat ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % hmlsl_regular.reservation
% 0.15/0.42 thf(fact_110_hmlsl_Oext__eq__len__eq,axiom,
% 0.15/0.42 ! [V2: view_e774982825t_unit,V3: view_e774982825t_unit,Ts: traffic,C: cars] :
% 0.15/0.42 ( ( ( ( ext_Product_unit @ V2 )
% 0.15/0.42 = ( ext_Product_unit @ V3 ) )
% 0.15/0.42 & ( ( own_Product_unit @ V2 )
% 0.15/0.42 = ( own_Product_unit @ V3 ) ) )
% 0.15/0.42 => ( ( len @ regular_regular @ V2 @ Ts @ C )
% 0.15/0.42 = ( len @ regular_regular @ V3 @ Ts @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % hmlsl.ext_eq_len_eq
% 0.15/0.42 thf(fact_111_view_Ohorizontal__chop__own__trans,axiom,
% 0.15/0.42 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit] :
% 0.15/0.42 ( ( hchop @ V2 @ U4 @ W3 )
% 0.15/0.42 => ( ( own_Product_unit @ U4 )
% 0.15/0.42 = ( own_Product_unit @ W3 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % view.horizontal_chop_own_trans
% 0.15/0.42 thf(fact_112_view_Overtical__chop__own__trans,axiom,
% 0.15/0.42 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit] :
% 0.15/0.42 ( ( vchop @ V2 @ U4 @ W3 )
% 0.15/0.42 => ( ( own_Product_unit @ U4 )
% 0.15/0.42 = ( own_Product_unit @ W3 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % view.vertical_chop_own_trans
% 0.15/0.42 thf(fact_113_restriction_Orestrict__subseteq,axiom,
% 0.15/0.42 ! [V2: view_e774982825t_unit,F: cars > nat_int,C: cars] : ( ord_less_eq_nat_int @ ( restrict @ V2 @ F @ C ) @ ( F @ C ) ) ).
% 0.15/0.42
% 0.15/0.42 % restriction.restrict_subseteq
% 0.15/0.42 thf(fact_114_restriction_Orestrict__view,axiom,
% 0.15/0.42 ! [V2: view_e774982825t_unit,F: cars > nat_int,C: cars] : ( ord_less_eq_nat_int @ ( restrict @ V2 @ F @ C ) @ ( lan_Product_unit @ V2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % restriction.restrict_view
% 0.15/0.42 thf(fact_115_restriction_Orestrict__res,axiom,
% 0.15/0.42 ! [V2: view_e774982825t_unit,Ts: traffic,C: cars] : ( ord_less_eq_nat_int @ ( restrict @ V2 @ ( res @ Ts ) @ C ) @ ( res @ Ts @ C ) ) ).
% 0.15/0.42
% 0.15/0.42 % restriction.restrict_res
% 0.15/0.42 thf(fact_116_restriction_Orestriction__stable,axiom,
% 0.15/0.42 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit,F: cars > nat_int,C: cars] :
% 0.15/0.42 ( ( hchop @ V2 @ U4 @ W3 )
% 0.15/0.42 => ( ( restrict @ U4 @ F @ C )
% 0.15/0.42 = ( restrict @ W3 @ F @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % restriction.restriction_stable
% 0.15/0.42 thf(fact_117_restriction_Orestriction__stable1,axiom,
% 0.15/0.42 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit,F: cars > nat_int,C: cars] :
% 0.15/0.42 ( ( hchop @ V2 @ U4 @ W3 )
% 0.15/0.42 => ( ( restrict @ V2 @ F @ C )
% 0.15/0.42 = ( restrict @ U4 @ F @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % restriction.restriction_stable1
% 0.15/0.42 thf(fact_118_restriction_Orestriction__stable2,axiom,
% 0.15/0.42 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit,F: cars > nat_int,C: cars] :
% 0.15/0.42 ( ( hchop @ V2 @ U4 @ W3 )
% 0.15/0.42 => ( ( restrict @ V2 @ F @ C )
% 0.15/0.42 = ( restrict @ W3 @ F @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % restriction.restriction_stable2
% 0.15/0.42 thf(fact_119_restriction_Orestrict__clm,axiom,
% 0.15/0.42 ! [V2: view_e774982825t_unit,Ts: traffic,C: cars] : ( ord_less_eq_nat_int @ ( restrict @ V2 @ ( clm @ Ts ) @ C ) @ ( clm @ Ts @ C ) ) ).
% 0.15/0.42
% 0.15/0.42 % restriction.restrict_clm
% 0.15/0.42 thf(fact_120_restriction_Orestriction__mon2,axiom,
% 0.15/0.42 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit,F: cars > nat_int,C: cars] :
% 0.15/0.42 ( ( vchop @ V2 @ U4 @ W3 )
% 0.15/0.42 => ( ord_less_eq_nat_int @ ( restrict @ W3 @ F @ C ) @ ( restrict @ V2 @ F @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % restriction.restriction_mon2
% 0.15/0.42 thf(fact_121_restriction_Orestriction__mon1,axiom,
% 0.15/0.42 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit,F: cars > nat_int,C: cars] :
% 0.15/0.42 ( ( vchop @ V2 @ U4 @ W3 )
% 0.15/0.42 => ( ord_less_eq_nat_int @ ( restrict @ U4 @ F @ C ) @ ( restrict @ V2 @ F @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % restriction.restriction_mon1
% 0.15/0.42 thf(fact_122_restriction_Orestriction__eq__view__card,axiom,
% 0.15/0.42 ! [V2: view_e774982825t_unit,F: cars > nat_int,C: cars] :
% 0.15/0.42 ( ( ( restrict @ V2 @ F @ C )
% 0.15/0.42 = ( lan_Product_unit @ V2 ) )
% 0.15/0.42 => ( ( nat_card @ ( restrict @ V2 @ F @ C ) )
% 0.15/0.42 = ( nat_card @ ( lan_Product_unit @ V2 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % restriction.restriction_eq_view_card
% 0.15/0.42 thf(fact_123_restriction_Orestrict__eq__lan__subs,axiom,
% 0.15/0.42 ! [V2: view_e774982825t_unit,F: cars > nat_int,C: cars] :
% 0.15/0.42 ( ( ( ( nat_card @ ( restrict @ V2 @ F @ C ) )
% 0.15/0.42 = ( nat_card @ ( lan_Product_unit @ V2 ) ) )
% 0.15/0.42 & ( ord_less_eq_nat_int @ ( restrict @ V2 @ F @ C ) @ ( lan_Product_unit @ V2 ) ) )
% 0.15/0.42 => ( ( restrict @ V2 @ F @ C )
% 0.15/0.42 = ( lan_Product_unit @ V2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % restriction.restrict_eq_lan_subs
% 0.15/0.42 thf(fact_124_restriction_Orestriction__card__mon1,axiom,
% 0.15/0.42 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit,F: cars > nat_int,C: cars] :
% 0.15/0.42 ( ( vchop @ V2 @ U4 @ W3 )
% 0.15/0.42 => ( ord_less_eq_nat @ ( nat_card @ ( restrict @ U4 @ F @ C ) ) @ ( nat_card @ ( restrict @ V2 @ F @ C ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % restriction.restriction_card_mon1
% 0.15/0.42 thf(fact_125_restriction_Orestriction__card__mon2,axiom,
% 0.15/0.42 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit,F: cars > nat_int,C: cars] :
% 0.15/0.42 ( ( vchop @ V2 @ U4 @ W3 )
% 0.15/0.42 => ( ord_less_eq_nat @ ( nat_card @ ( restrict @ W3 @ F @ C ) ) @ ( nat_card @ ( restrict @ V2 @ F @ C ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % restriction.restriction_card_mon2
% 0.15/0.42 thf(fact_126_restriction_Orestriction__clm__leq__one,axiom,
% 0.15/0.42 ! [V2: view_e774982825t_unit,Ts: traffic,C: cars] : ( ord_less_eq_nat @ ( nat_card @ ( restrict @ V2 @ ( clm @ Ts ) @ C ) ) @ one_one_nat ) ).
% 0.15/0.42
% 0.15/0.42 % restriction.restriction_clm_leq_one
% 0.15/0.42 thf(fact_127_restriction_Orestriction__card__mon__trans,axiom,
% 0.15/0.42 ! [V2: view_e774982825t_unit,V1: view_e774982825t_unit,V22: view_e774982825t_unit,V33: view_e774982825t_unit,V42: view_e774982825t_unit,F: cars > nat_int,C: cars] :
% 0.15/0.42 ( ( ( vchop @ V2 @ V1 @ V22 )
% 0.15/0.42 & ( vchop @ V22 @ V33 @ V42 )
% 0.15/0.42 & ( ( nat_card @ ( restrict @ V33 @ F @ C ) )
% 0.15/0.42 = one_one_nat ) )
% 0.15/0.42 => ( ord_less_eq_nat @ one_one_nat @ ( nat_card @ ( restrict @ V2 @ F @ C ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % restriction.restriction_card_mon_trans
% 0.15/0.42 thf(fact_128_hmlsl__regular_Obackwards__res__stab,axiom,
% 0.15/0.42 ! [Ts: traffic,D2: cars,Ts5: traffic,C: cars,V2: view_e774982825t_unit] :
% 0.15/0.42 ( ( ( create_reservation @ Ts @ D2 @ Ts5 )
% 0.15/0.42 & ( D2 != C )
% 0.15/0.42 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 0.15/0.42 & ( ( len @ regular_regular @ V2 @ Ts5 @ C )
% 0.15/0.42 = ( ext_Product_unit @ V2 ) )
% 0.15/0.42 & ( ( restrict @ V2 @ ( res @ Ts5 ) @ C )
% 0.15/0.42 = ( lan_Product_unit @ V2 ) )
% 0.15/0.42 & ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 0.15/0.42 = one_one_nat ) )
% 0.15/0.42 => ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 0.15/0.42 & ( ( len @ regular_regular @ V2 @ Ts @ C )
% 0.15/0.42 = ( ext_Product_unit @ V2 ) )
% 0.15/0.42 & ( ( restrict @ V2 @ ( res @ Ts ) @ C )
% 0.15/0.42 = ( lan_Product_unit @ V2 ) )
% 0.15/0.42 & ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 0.15/0.42 = one_one_nat ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % hmlsl_regular.backwards_res_stab
% 0.15/0.42 thf(fact_129_less__one,axiom,
% 0.15/0.42 ! [N: nat] :
% 0.15/0.42 ( ( ord_less_nat @ N @ one_one_nat )
% 0.15/0.42 = ( N = zero_zero_nat ) ) ).
% 0.15/0.42
% 0.15/0.42 % less_one
% 0.15/0.42 thf(fact_130_le0,axiom,
% 0.15/0.42 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.15/0.42
% 0.15/0.42 % le0
% 0.15/0.42 thf(fact_131_bot__nat__0_Oextremum,axiom,
% 0.15/0.42 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 0.15/0.42
% 0.15/0.42 % bot_nat_0.extremum
% 0.15/0.42 thf(fact_132_card__non__empty__geq__one,axiom,
% 0.15/0.42 ! [I: nat_int] :
% 0.15/0.42 ( ( I != bot_bot_nat_int )
% 0.15/0.42 = ( ord_less_eq_nat @ one_one_nat @ ( nat_card @ I ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % card_non_empty_geq_one
% 0.15/0.42 thf(fact_133_bot__nat__0_Onot__eq__extremum,axiom,
% 0.15/0.42 ! [A: nat] :
% 0.15/0.42 ( ( A != zero_zero_nat )
% 0.15/0.42 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 % bot_nat_0.not_eq_extremum
% 0.15/0.42 thf(fact_134_less__nat__zero__code,axiom,
% 0.15/0.42 ! [N: nat] :
% 0.15/0.42 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.15/0.42
% 0.15/0.42 % less_nat_zero_code
% 0.15/0.42 thf(fact_135_neq0__conv,axiom,
% 0.15/0.42 ! [N: nat] :
% 0.15/0.42 ( ( N != zero_zero_nat )
% 0.15/0.42 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.15/0.42
% 0.15/0.42 % neq0_conv
% 0.15/0.42 thf(fact_136_linorder__neqE__nat,axiom,
% 0.15/0.42 ! [X3: nat,Y2: nat] :
% 0.15/0.42 ( ( X3 != Y2 )
% 0.15/0.42 => ( ~ ( ord_less_nat @ X3 @ Y2 )
% 0.15/0.42 => ( ord_less_nat @ Y2 @ X3 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % linorder_neqE_nat
% 0.15/0.42 thf(fact_137_infinite__descent,axiom,
% 0.15/0.42 ! [P: nat > $o,N: nat] :
% 0.15/0.42 ( ! [N2: nat] :
% 0.15/0.42 ( ~ ( P @ N2 )
% 0.15/0.42 => ? [M2: nat] :
% 0.15/0.42 ( ( ord_less_nat @ M2 @ N2 )
% 0.15/0.42 & ~ ( P @ M2 ) ) )
% 0.15/0.42 => ( P @ N ) ) ).
% 0.15/0.42
% 0.15/0.42 % infinite_descent
% 0.15/0.42 thf(fact_138_nat__less__induct,axiom,
% 0.15/0.42 ! [P: nat > $o,N: nat] :
% 0.15/0.42 ( ! [N2: nat] :
% 0.15/0.42 ( ! [M2: nat] :
% 0.15/0.42 ( ( ord_less_nat @ M2 @ N2 )
% 0.15/0.42 => ( P @ M2 ) )
% 0.15/0.42 => ( P @ N2 ) )
% 0.15/0.42 => ( P @ N ) ) ).
% 0.15/0.42
% 0.15/0.42 % nat_less_induct
% 0.15/0.42 thf(fact_139_less__irrefl__nat,axiom,
% 0.15/0.42 ! [N: nat] :
% 0.15/0.42 ~ ( ord_less_nat @ N @ N ) ).
% 0.15/0.42
% 0.15/0.42 % less_irrefl_nat
% 0.15/0.42 thf(fact_140_less__not__refl3,axiom,
% 0.15/0.42 ! [S: nat,T: nat] :
% 0.15/0.42 ( ( ord_less_nat @ S @ T )
% 0.15/0.42 => ( S != T ) ) ).
% 0.15/0.42
% 0.15/0.42 % less_not_refl3
% 0.15/0.42 thf(fact_141_less__not__refl2,axiom,
% 0.15/0.42 ! [N: nat,M: nat] :
% 0.15/0.42 ( ( ord_less_nat @ N @ M )
% 0.15/0.42 => ( M != N ) ) ).
% 0.15/0.42
% 0.15/0.42 % less_not_refl2
% 0.15/0.42 thf(fact_142_less__not__refl,axiom,
% 0.15/0.42 ! [N: nat] :
% 0.15/0.42 ~ ( ord_less_nat @ N @ N ) ).
% 0.15/0.42
% 0.15/0.42 % less_not_refl
% 0.15/0.42 thf(fact_143_nat__neq__iff,axiom,
% 0.15/0.42 ! [M: nat,N: nat] :
% 0.15/0.42 ( ( M != N )
% 0.15/0.42 = ( ( ord_less_nat @ M @ N )
% 0.15/0.42 | ( ord_less_nat @ N @ M ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % nat_neq_iff
% 0.15/0.42 thf(fact_144_bot__nat__0_Oextremum__strict,axiom,
% 0.15/0.42 ! [A: nat] :
% 0.15/0.42 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 0.15/0.42
% 0.15/0.42 % bot_nat_0.extremum_strict
% 0.15/0.42 thf(fact_145_infinite__descent0,axiom,
% 0.15/0.42 ! [P: nat > $o,N: nat] :
% 0.15/0.42 ( ( P @ zero_zero_nat )
% 0.15/0.42 => ( ! [N2: nat] :
% 0.15/0.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.15/0.42 => ( ~ ( P @ N2 )
% 0.15/0.42 => ? [M2: nat] :
% 0.15/0.42 ( ( ord_less_nat @ M2 @ N2 )
% 0.15/0.42 & ~ ( P @ M2 ) ) ) )
% 0.15/0.42 => ( P @ N ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % infinite_descent0
% 0.15/0.42 thf(fact_146_gr__implies__not0,axiom,
% 0.15/0.42 ! [M: nat,N: nat] :
% 0.15/0.42 ( ( ord_less_nat @ M @ N )
% 0.15/0.42 => ( N != zero_zero_nat ) ) ).
% 0.15/0.42
% 0.15/0.42 % gr_implies_not0
% 0.15/0.42 thf(fact_147_less__zeroE,axiom,
% 0.15/0.42 ! [N: nat] :
% 0.15/0.42 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.15/0.42
% 0.15/0.42 % less_zeroE
% 0.15/0.42 thf(fact_148_not__less0,axiom,
% 0.15/0.42 ! [N: nat] :
% 0.15/0.42 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.15/0.42
% 0.15/0.42 % not_less0
% 0.15/0.42 thf(fact_149_not__gr0,axiom,
% 0.15/0.42 ! [N: nat] :
% 0.15/0.42 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.15/0.42 = ( N = zero_zero_nat ) ) ).
% 0.15/0.42
% 0.15/0.42 % not_gr0
% 0.15/0.42 thf(fact_150_gr0I,axiom,
% 0.15/0.42 ! [N: nat] :
% 0.15/0.42 ( ( N != zero_zero_nat )
% 0.15/0.42 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.15/0.42
% 0.15/0.42 % gr0I
% 0.15/0.42 thf(fact_151_less__mono__imp__le__mono,axiom,
% 0.15/0.42 ! [F: nat > nat,I: nat,J: nat] :
% 0.15/0.42 ( ! [I2: nat,J2: nat] :
% 0.15/0.42 ( ( ord_less_nat @ I2 @ J2 )
% 0.15/0.42 => ( ord_less_nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
% 0.15/0.42 => ( ( ord_less_eq_nat @ I @ J )
% 0.15/0.42 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % less_mono_imp_le_mono
% 0.15/0.42 thf(fact_152_le__neq__implies__less,axiom,
% 0.15/0.42 ! [M: nat,N: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ M @ N )
% 0.15/0.42 => ( ( M != N )
% 0.15/0.42 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % le_neq_implies_less
% 0.15/0.42 thf(fact_153_Nat_Oex__has__greatest__nat,axiom,
% 0.15/0.42 ! [P: nat > $o,K: nat,B: nat] :
% 0.15/0.42 ( ( P @ K )
% 0.15/0.42 => ( ! [Y3: nat] :
% 0.15/0.42 ( ( P @ Y3 )
% 0.15/0.42 => ( ord_less_eq_nat @ Y3 @ B ) )
% 0.15/0.42 => ? [X4: nat] :
% 0.15/0.42 ( ( P @ X4 )
% 0.15/0.42 & ! [Y4: nat] :
% 0.15/0.42 ( ( P @ Y4 )
% 0.15/0.42 => ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % Nat.ex_has_greatest_nat
% 0.15/0.42 thf(fact_154_less__or__eq__imp__le,axiom,
% 0.15/0.42 ! [M: nat,N: nat] :
% 0.15/0.42 ( ( ( ord_less_nat @ M @ N )
% 0.15/0.42 | ( M = N ) )
% 0.15/0.42 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.15/0.42
% 0.15/0.42 % less_or_eq_imp_le
% 0.15/0.42 thf(fact_155_le__eq__less__or__eq,axiom,
% 0.15/0.42 ( ord_less_eq_nat
% 0.15/0.42 = ( ^ [M3: nat,N3: nat] :
% 0.15/0.42 ( ( ord_less_nat @ M3 @ N3 )
% 0.15/0.42 | ( M3 = N3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % le_eq_less_or_eq
% 0.15/0.42 thf(fact_156_less__imp__le__nat,axiom,
% 0.15/0.42 ! [M: nat,N: nat] :
% 0.15/0.42 ( ( ord_less_nat @ M @ N )
% 0.15/0.42 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.15/0.42
% 0.15/0.42 % less_imp_le_nat
% 0.15/0.42 thf(fact_157_nat__le__linear,axiom,
% 0.15/0.42 ! [M: nat,N: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ M @ N )
% 0.15/0.42 | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.15/0.42
% 0.15/0.42 % nat_le_linear
% 0.15/0.42 thf(fact_158_nat__less__le,axiom,
% 0.15/0.42 ( ord_less_nat
% 0.15/0.42 = ( ^ [M3: nat,N3: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ M3 @ N3 )
% 0.15/0.42 & ( M3 != N3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % nat_less_le
% 0.15/0.42 thf(fact_159_le__antisym,axiom,
% 0.15/0.42 ! [M: nat,N: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ M @ N )
% 0.15/0.42 => ( ( ord_less_eq_nat @ N @ M )
% 0.15/0.42 => ( M = N ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % le_antisym
% 0.15/0.42 thf(fact_160_eq__imp__le,axiom,
% 0.15/0.42 ! [M: nat,N: nat] :
% 0.15/0.42 ( ( M = N )
% 0.15/0.42 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.15/0.42
% 0.15/0.42 % eq_imp_le
% 0.15/0.42 thf(fact_161_le__trans,axiom,
% 0.15/0.42 ! [I: nat,J: nat,K: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ I @ J )
% 0.15/0.42 => ( ( ord_less_eq_nat @ J @ K )
% 0.15/0.42 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % le_trans
% 0.15/0.42 thf(fact_162_le__refl,axiom,
% 0.15/0.42 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.15/0.42
% 0.15/0.42 % le_refl
% 0.15/0.42 thf(fact_163_card__subset__less,axiom,
% 0.15/0.42 ! [I: nat_int,I3: nat_int] :
% 0.15/0.42 ( ( ord_less_nat_int @ I @ I3 )
% 0.15/0.42 => ( ord_less_nat @ ( nat_card @ I ) @ ( nat_card @ I3 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % card_subset_less
% 0.15/0.42 thf(fact_164_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.15/0.42 ! [A: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.15/0.42 => ( A = zero_zero_nat ) ) ).
% 0.15/0.42
% 0.15/0.42 % bot_nat_0.extremum_uniqueI
% 0.15/0.42 thf(fact_165_bot__nat__0_Oextremum__unique,axiom,
% 0.15/0.42 ! [A: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.15/0.42 = ( A = zero_zero_nat ) ) ).
% 0.15/0.42
% 0.15/0.42 % bot_nat_0.extremum_unique
% 0.15/0.42 thf(fact_166_ex__least__nat__le,axiom,
% 0.15/0.42 ! [P: nat > $o,N: nat] :
% 0.15/0.42 ( ( P @ N )
% 0.15/0.42 => ( ~ ( P @ zero_zero_nat )
% 0.15/0.42 => ? [K2: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ K2 @ N )
% 0.15/0.42 & ! [I4: nat] :
% 0.15/0.42 ( ( ord_less_nat @ I4 @ K2 )
% 0.15/0.42 => ~ ( P @ I4 ) )
% 0.15/0.42 & ( P @ K2 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % ex_least_nat_le
% 0.15/0.42 thf(fact_167_le__0__eq,axiom,
% 0.15/0.42 ! [N: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.15/0.42 = ( N = zero_zero_nat ) ) ).
% 0.15/0.42
% 0.15/0.42 % le_0_eq
% 0.15/0.42 thf(fact_168_less__eq__nat_Osimps_I1_J,axiom,
% 0.15/0.42 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.15/0.42
% 0.15/0.42 % less_eq_nat.simps(1)
% 0.15/0.42 thf(fact_169_card__subset__le,axiom,
% 0.15/0.42 ! [I: nat_int,I3: nat_int] :
% 0.15/0.42 ( ( ord_less_eq_nat_int @ I @ I3 )
% 0.15/0.42 => ( ord_less_eq_nat @ ( nat_card @ I ) @ ( nat_card @ I3 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % card_subset_le
% 0.15/0.42 thf(fact_170_card__empty__zero,axiom,
% 0.15/0.42 ( ( nat_card @ bot_bot_nat_int )
% 0.15/0.42 = zero_zero_nat ) ).
% 0.15/0.42
% 0.15/0.42 % card_empty_zero
% 0.15/0.42 thf(fact_171_local_Ohmlsl_Owidth__ge,axiom,
% 0.15/0.42 ! [V: view_e774982825t_unit] :
% 0.15/0.42 ( ? [Va: view_e774982825t_unit] :
% 0.15/0.42 ( ? [X_12: view_e774982825t_unit] : ( vchop @ V @ Va @ X_12 )
% 0.15/0.42 & ( ( nat_card @ ( lan_Product_unit @ Va ) )
% 0.15/0.42 = ( plus_plus_nat @ zero_zero_nat @ one_one_nat ) ) )
% 0.15/0.42 => ( ord_less_nat @ zero_zero_nat @ ( nat_card @ ( lan_Product_unit @ V ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.hmlsl.width_ge
% 0.15/0.42 thf(fact_172_traffic_Ocreate__res__subseteq2,axiom,
% 0.15/0.42 ! [Ts: traffic,C: cars,Ts5: traffic] :
% 0.15/0.42 ( ( create_reservation @ Ts @ C @ Ts5 )
% 0.15/0.42 => ( ord_less_eq_nat_int @ ( clm @ Ts @ C ) @ ( res @ Ts5 @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % traffic.create_res_subseteq2
% 0.15/0.42 thf(fact_173_traffic_OatMostOneClm,axiom,
% 0.15/0.42 ! [Ts: traffic,C: cars] : ( ord_less_eq_nat @ ( nat_card @ ( clm @ Ts @ C ) ) @ one_one_nat ) ).
% 0.15/0.42
% 0.15/0.42 % traffic.atMostOneClm
% 0.15/0.42 thf(fact_174_traffic_OatLeastOneRes,axiom,
% 0.15/0.42 ! [Ts: traffic,C: cars] : ( ord_less_eq_nat @ one_one_nat @ ( nat_card @ ( res @ Ts @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % traffic.atLeastOneRes
% 0.15/0.42 thf(fact_175_local_Ohmlsl_Owidth__add1,axiom,
% 0.15/0.42 ! [X3: nat,Y2: nat,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.42 ( ? [Va: view_e774982825t_unit,U: view_e774982825t_unit] :
% 0.15/0.42 ( ( vchop @ V @ Va @ U )
% 0.15/0.42 & ( ( nat_card @ ( lan_Product_unit @ Va ) )
% 0.15/0.42 = X3 )
% 0.15/0.42 & ( ( nat_card @ ( lan_Product_unit @ U ) )
% 0.15/0.42 = Y2 ) )
% 0.15/0.42 => ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.42 = ( plus_plus_nat @ X3 @ Y2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.hmlsl.width_add1
% 0.15/0.42 thf(fact_176_local_Ohmlsl_Owidth__add2,axiom,
% 0.15/0.42 ! [X3: nat,Y2: nat,Ts2: traffic,V: view_e774982825t_unit] :
% 0.15/0.42 ( ( ( nat_card @ ( lan_Product_unit @ V ) )
% 0.15/0.42 = ( plus_plus_nat @ X3 @ Y2 ) )
% 0.15/0.42 => ? [Va2: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 0.15/0.42 ( ( vchop @ V @ Va2 @ U2 )
% 0.15/0.42 & ( ( nat_card @ ( lan_Product_unit @ Va2 ) )
% 0.15/0.42 = X3 )
% 0.15/0.42 & ( ( nat_card @ ( lan_Product_unit @ U2 ) )
% 0.15/0.42 = Y2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % local.hmlsl.width_add2
% 0.15/0.42 thf(fact_177_add__left__cancel,axiom,
% 0.15/0.42 ! [A: real,B: real,C: real] :
% 0.15/0.42 ( ( ( plus_plus_real @ A @ B )
% 0.15/0.42 = ( plus_plus_real @ A @ C ) )
% 0.15/0.42 = ( B = C ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_left_cancel
% 0.15/0.42 thf(fact_178_add__left__cancel,axiom,
% 0.15/0.42 ! [A: nat,B: nat,C: nat] :
% 0.15/0.42 ( ( ( plus_plus_nat @ A @ B )
% 0.15/0.42 = ( plus_plus_nat @ A @ C ) )
% 0.15/0.42 = ( B = C ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_left_cancel
% 0.15/0.42 thf(fact_179_add__right__cancel,axiom,
% 0.15/0.42 ! [B: real,A: real,C: real] :
% 0.15/0.42 ( ( ( plus_plus_real @ B @ A )
% 0.15/0.42 = ( plus_plus_real @ C @ A ) )
% 0.15/0.42 = ( B = C ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_right_cancel
% 0.15/0.42 thf(fact_180_add__right__cancel,axiom,
% 0.15/0.42 ! [B: nat,A: nat,C: nat] :
% 0.15/0.42 ( ( ( plus_plus_nat @ B @ A )
% 0.15/0.42 = ( plus_plus_nat @ C @ A ) )
% 0.15/0.42 = ( B = C ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_right_cancel
% 0.15/0.42 thf(fact_181_add__le__cancel__left,axiom,
% 0.15/0.42 ! [C: real,A: real,B: real] :
% 0.15/0.42 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.15/0.42 = ( ord_less_eq_real @ A @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_le_cancel_left
% 0.15/0.42 thf(fact_182_add__le__cancel__left,axiom,
% 0.15/0.42 ! [C: nat,A: nat,B: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.15/0.42 = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_le_cancel_left
% 0.15/0.42 thf(fact_183_add__le__cancel__right,axiom,
% 0.15/0.42 ! [A: real,C: real,B: real] :
% 0.15/0.42 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.15/0.42 = ( ord_less_eq_real @ A @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_le_cancel_right
% 0.15/0.42 thf(fact_184_add__le__cancel__right,axiom,
% 0.15/0.42 ! [A: nat,C: nat,B: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.15/0.42 = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_le_cancel_right
% 0.15/0.42 thf(fact_185_add_Oleft__neutral,axiom,
% 0.15/0.42 ! [A: real] :
% 0.15/0.42 ( ( plus_plus_real @ zero_zero_real @ A )
% 0.15/0.42 = A ) ).
% 0.15/0.42
% 0.15/0.42 % add.left_neutral
% 0.15/0.42 thf(fact_186_add_Oleft__neutral,axiom,
% 0.15/0.42 ! [A: nat] :
% 0.15/0.42 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.15/0.42 = A ) ).
% 0.15/0.42
% 0.15/0.42 % add.left_neutral
% 0.15/0.42 thf(fact_187_add_Oright__neutral,axiom,
% 0.15/0.42 ! [A: real] :
% 0.15/0.42 ( ( plus_plus_real @ A @ zero_zero_real )
% 0.15/0.42 = A ) ).
% 0.15/0.42
% 0.15/0.42 % add.right_neutral
% 0.15/0.42 thf(fact_188_add_Oright__neutral,axiom,
% 0.15/0.42 ! [A: nat] :
% 0.15/0.42 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.15/0.42 = A ) ).
% 0.15/0.42
% 0.15/0.42 % add.right_neutral
% 0.15/0.42 thf(fact_189_double__zero,axiom,
% 0.15/0.42 ! [A: real] :
% 0.15/0.42 ( ( ( plus_plus_real @ A @ A )
% 0.15/0.42 = zero_zero_real )
% 0.15/0.42 = ( A = zero_zero_real ) ) ).
% 0.15/0.42
% 0.15/0.42 % double_zero
% 0.15/0.42 thf(fact_190_double__zero__sym,axiom,
% 0.15/0.42 ! [A: real] :
% 0.15/0.42 ( ( zero_zero_real
% 0.15/0.42 = ( plus_plus_real @ A @ A ) )
% 0.15/0.42 = ( A = zero_zero_real ) ) ).
% 0.15/0.42
% 0.15/0.42 % double_zero_sym
% 0.15/0.42 thf(fact_191_add__cancel__left__left,axiom,
% 0.15/0.42 ! [B: real,A: real] :
% 0.15/0.42 ( ( ( plus_plus_real @ B @ A )
% 0.15/0.42 = A )
% 0.15/0.42 = ( B = zero_zero_real ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_cancel_left_left
% 0.15/0.42 thf(fact_192_add__cancel__left__left,axiom,
% 0.15/0.42 ! [B: nat,A: nat] :
% 0.15/0.42 ( ( ( plus_plus_nat @ B @ A )
% 0.15/0.42 = A )
% 0.15/0.42 = ( B = zero_zero_nat ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_cancel_left_left
% 0.15/0.42 thf(fact_193_add__cancel__left__right,axiom,
% 0.15/0.42 ! [A: real,B: real] :
% 0.15/0.42 ( ( ( plus_plus_real @ A @ B )
% 0.15/0.42 = A )
% 0.15/0.42 = ( B = zero_zero_real ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_cancel_left_right
% 0.15/0.42 thf(fact_194_add__cancel__left__right,axiom,
% 0.15/0.42 ! [A: nat,B: nat] :
% 0.15/0.42 ( ( ( plus_plus_nat @ A @ B )
% 0.15/0.42 = A )
% 0.15/0.42 = ( B = zero_zero_nat ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_cancel_left_right
% 0.15/0.42 thf(fact_195_add__cancel__right__left,axiom,
% 0.15/0.42 ! [A: real,B: real] :
% 0.15/0.42 ( ( A
% 0.15/0.42 = ( plus_plus_real @ B @ A ) )
% 0.15/0.42 = ( B = zero_zero_real ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_cancel_right_left
% 0.15/0.42 thf(fact_196_add__cancel__right__left,axiom,
% 0.15/0.42 ! [A: nat,B: nat] :
% 0.15/0.42 ( ( A
% 0.15/0.42 = ( plus_plus_nat @ B @ A ) )
% 0.15/0.42 = ( B = zero_zero_nat ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_cancel_right_left
% 0.15/0.42 thf(fact_197_add__cancel__right__right,axiom,
% 0.15/0.42 ! [A: real,B: real] :
% 0.15/0.42 ( ( A
% 0.15/0.42 = ( plus_plus_real @ A @ B ) )
% 0.15/0.42 = ( B = zero_zero_real ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_cancel_right_right
% 0.15/0.42 thf(fact_198_add__cancel__right__right,axiom,
% 0.15/0.42 ! [A: nat,B: nat] :
% 0.15/0.42 ( ( A
% 0.15/0.42 = ( plus_plus_nat @ A @ B ) )
% 0.15/0.42 = ( B = zero_zero_nat ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_cancel_right_right
% 0.15/0.42 thf(fact_199_add__eq__0__iff__both__eq__0,axiom,
% 0.15/0.42 ! [X3: nat,Y2: nat] :
% 0.15/0.42 ( ( ( plus_plus_nat @ X3 @ Y2 )
% 0.15/0.42 = zero_zero_nat )
% 0.15/0.42 = ( ( X3 = zero_zero_nat )
% 0.15/0.42 & ( Y2 = zero_zero_nat ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_eq_0_iff_both_eq_0
% 0.15/0.42 thf(fact_200_zero__eq__add__iff__both__eq__0,axiom,
% 0.15/0.42 ! [X3: nat,Y2: nat] :
% 0.15/0.42 ( ( zero_zero_nat
% 0.15/0.42 = ( plus_plus_nat @ X3 @ Y2 ) )
% 0.15/0.42 = ( ( X3 = zero_zero_nat )
% 0.15/0.42 & ( Y2 = zero_zero_nat ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % zero_eq_add_iff_both_eq_0
% 0.15/0.42 thf(fact_201_add__less__cancel__left,axiom,
% 0.15/0.42 ! [C: real,A: real,B: real] :
% 0.15/0.42 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.15/0.42 = ( ord_less_real @ A @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_less_cancel_left
% 0.15/0.42 thf(fact_202_add__less__cancel__left,axiom,
% 0.15/0.42 ! [C: nat,A: nat,B: nat] :
% 0.15/0.42 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.15/0.42 = ( ord_less_nat @ A @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_less_cancel_left
% 0.15/0.42 thf(fact_203_add__less__cancel__right,axiom,
% 0.15/0.42 ! [A: real,C: real,B: real] :
% 0.15/0.42 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.15/0.42 = ( ord_less_real @ A @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_less_cancel_right
% 0.15/0.42 thf(fact_204_add__less__cancel__right,axiom,
% 0.15/0.42 ! [A: nat,C: nat,B: nat] :
% 0.15/0.42 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.15/0.42 = ( ord_less_nat @ A @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_less_cancel_right
% 0.15/0.42 thf(fact_205_add__is__0,axiom,
% 0.15/0.42 ! [M: nat,N: nat] :
% 0.15/0.42 ( ( ( plus_plus_nat @ M @ N )
% 0.15/0.42 = zero_zero_nat )
% 0.15/0.42 = ( ( M = zero_zero_nat )
% 0.15/0.42 & ( N = zero_zero_nat ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_is_0
% 0.15/0.42 thf(fact_206_Nat_Oadd__0__right,axiom,
% 0.15/0.42 ! [M: nat] :
% 0.15/0.42 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 0.15/0.42 = M ) ).
% 0.15/0.42
% 0.15/0.42 % Nat.add_0_right
% 0.15/0.42 thf(fact_207_nat__add__left__cancel__less,axiom,
% 0.15/0.42 ! [K: nat,M: nat,N: nat] :
% 0.15/0.42 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.15/0.42 = ( ord_less_nat @ M @ N ) ) ).
% 0.15/0.42
% 0.15/0.42 % nat_add_left_cancel_less
% 0.15/0.42 thf(fact_208_nat__add__left__cancel__le,axiom,
% 0.15/0.42 ! [K: nat,M: nat,N: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.15/0.42 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.15/0.42
% 0.15/0.42 % nat_add_left_cancel_le
% 0.15/0.42 thf(fact_209_add__le__same__cancel1,axiom,
% 0.15/0.42 ! [B: real,A: real] :
% 0.15/0.42 ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 0.15/0.42 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_le_same_cancel1
% 0.15/0.42 thf(fact_210_add__le__same__cancel1,axiom,
% 0.15/0.42 ! [B: nat,A: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.15/0.42 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_le_same_cancel1
% 0.15/0.42 thf(fact_211_add__le__same__cancel2,axiom,
% 0.15/0.42 ! [A: real,B: real] :
% 0.15/0.42 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.15/0.42 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_le_same_cancel2
% 0.15/0.42 thf(fact_212_add__le__same__cancel2,axiom,
% 0.15/0.42 ! [A: nat,B: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.15/0.42 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_le_same_cancel2
% 0.15/0.42 thf(fact_213_le__add__same__cancel1,axiom,
% 0.15/0.42 ! [A: real,B: real] :
% 0.15/0.42 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.15/0.42 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % le_add_same_cancel1
% 0.15/0.42 thf(fact_214_le__add__same__cancel1,axiom,
% 0.15/0.42 ! [A: nat,B: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.15/0.42 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % le_add_same_cancel1
% 0.15/0.42 thf(fact_215_le__add__same__cancel2,axiom,
% 0.15/0.42 ! [A: real,B: real] :
% 0.15/0.42 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 0.15/0.42 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % le_add_same_cancel2
% 0.15/0.42 thf(fact_216_le__add__same__cancel2,axiom,
% 0.15/0.42 ! [A: nat,B: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.15/0.42 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % le_add_same_cancel2
% 0.15/0.42 thf(fact_217_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.15/0.42 ! [A: real] :
% 0.15/0.42 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 0.15/0.42 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.15/0.42
% 0.15/0.42 % double_add_le_zero_iff_single_add_le_zero
% 0.15/0.42 thf(fact_218_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.15/0.42 ! [A: real] :
% 0.15/0.42 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 0.15/0.42 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 % zero_le_double_add_iff_zero_le_single_add
% 0.15/0.42 thf(fact_219_add__less__same__cancel1,axiom,
% 0.15/0.42 ! [B: real,A: real] :
% 0.15/0.42 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 0.15/0.42 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_less_same_cancel1
% 0.15/0.42 thf(fact_220_add__less__same__cancel1,axiom,
% 0.15/0.42 ! [B: nat,A: nat] :
% 0.15/0.42 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.15/0.42 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_less_same_cancel1
% 0.15/0.42 thf(fact_221_add__less__same__cancel2,axiom,
% 0.15/0.42 ! [A: real,B: real] :
% 0.15/0.42 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.15/0.42 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_less_same_cancel2
% 0.15/0.42 thf(fact_222_add__less__same__cancel2,axiom,
% 0.15/0.42 ! [A: nat,B: nat] :
% 0.15/0.42 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.15/0.42 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_less_same_cancel2
% 0.15/0.42 thf(fact_223_less__add__same__cancel1,axiom,
% 0.15/0.42 ! [A: real,B: real] :
% 0.15/0.42 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.15/0.42 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % less_add_same_cancel1
% 0.15/0.42 thf(fact_224_less__add__same__cancel1,axiom,
% 0.15/0.42 ! [A: nat,B: nat] :
% 0.15/0.42 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.15/0.42 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % less_add_same_cancel1
% 0.15/0.42 thf(fact_225_less__add__same__cancel2,axiom,
% 0.15/0.42 ! [A: real,B: real] :
% 0.15/0.42 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 0.15/0.42 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % less_add_same_cancel2
% 0.15/0.42 thf(fact_226_less__add__same__cancel2,axiom,
% 0.15/0.42 ! [A: nat,B: nat] :
% 0.15/0.42 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.15/0.42 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % less_add_same_cancel2
% 0.15/0.42 thf(fact_227_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.15/0.42 ! [A: real] :
% 0.15/0.42 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 0.15/0.42 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.15/0.42
% 0.15/0.42 % double_add_less_zero_iff_single_add_less_zero
% 0.15/0.42 thf(fact_228_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.15/0.42 ! [A: real] :
% 0.15/0.42 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 0.15/0.42 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 % zero_less_double_add_iff_zero_less_single_add
% 0.15/0.42 thf(fact_229_add__gr__0,axiom,
% 0.15/0.42 ! [M: nat,N: nat] :
% 0.15/0.42 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 0.15/0.42 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.15/0.42 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_gr_0
% 0.15/0.42 thf(fact_230_add__leE,axiom,
% 0.15/0.42 ! [M: nat,K: nat,N: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.15/0.42 => ~ ( ( ord_less_eq_nat @ M @ N )
% 0.15/0.42 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_leE
% 0.15/0.42 thf(fact_231_le__add1,axiom,
% 0.15/0.42 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 0.15/0.42
% 0.15/0.42 % le_add1
% 0.15/0.42 thf(fact_232_le__add2,axiom,
% 0.15/0.42 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 0.15/0.42
% 0.15/0.42 % le_add2
% 0.15/0.42 thf(fact_233_add__leD1,axiom,
% 0.15/0.42 ! [M: nat,K: nat,N: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.15/0.42 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_leD1
% 0.15/0.42 thf(fact_234_add__leD2,axiom,
% 0.15/0.42 ! [M: nat,K: nat,N: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.15/0.42 => ( ord_less_eq_nat @ K @ N ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_leD2
% 0.15/0.42 thf(fact_235_le__Suc__ex,axiom,
% 0.15/0.42 ! [K: nat,L: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ K @ L )
% 0.15/0.42 => ? [N2: nat] :
% 0.15/0.42 ( L
% 0.15/0.42 = ( plus_plus_nat @ K @ N2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % le_Suc_ex
% 0.15/0.42 thf(fact_236_add__le__mono,axiom,
% 0.15/0.42 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ I @ J )
% 0.15/0.42 => ( ( ord_less_eq_nat @ K @ L )
% 0.15/0.42 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_le_mono
% 0.15/0.42 thf(fact_237_add__le__mono1,axiom,
% 0.15/0.42 ! [I: nat,J: nat,K: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ I @ J )
% 0.15/0.42 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_le_mono1
% 0.15/0.42 thf(fact_238_trans__le__add1,axiom,
% 0.15/0.42 ! [I: nat,J: nat,M: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ I @ J )
% 0.15/0.42 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % trans_le_add1
% 0.15/0.42 thf(fact_239_trans__le__add2,axiom,
% 0.15/0.42 ! [I: nat,J: nat,M: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ I @ J )
% 0.15/0.42 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % trans_le_add2
% 0.15/0.42 thf(fact_240_nat__le__iff__add,axiom,
% 0.15/0.42 ( ord_less_eq_nat
% 0.15/0.42 = ( ^ [M3: nat,N3: nat] :
% 0.15/0.42 ? [K3: nat] :
% 0.15/0.42 ( N3
% 0.15/0.42 = ( plus_plus_nat @ M3 @ K3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % nat_le_iff_add
% 0.15/0.42 thf(fact_241_plus__nat_Oadd__0,axiom,
% 0.15/0.42 ! [N: nat] :
% 0.15/0.42 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 0.15/0.42 = N ) ).
% 0.15/0.42
% 0.15/0.42 % plus_nat.add_0
% 0.15/0.42 thf(fact_242_add__eq__self__zero,axiom,
% 0.15/0.42 ! [M: nat,N: nat] :
% 0.15/0.42 ( ( ( plus_plus_nat @ M @ N )
% 0.15/0.42 = M )
% 0.15/0.42 => ( N = zero_zero_nat ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_eq_self_zero
% 0.15/0.42 thf(fact_243_add__le__imp__le__right,axiom,
% 0.15/0.42 ! [A: real,C: real,B: real] :
% 0.15/0.42 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.15/0.42 => ( ord_less_eq_real @ A @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_le_imp_le_right
% 0.15/0.42 thf(fact_244_add__le__imp__le__right,axiom,
% 0.15/0.42 ! [A: nat,C: nat,B: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.15/0.42 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_le_imp_le_right
% 0.15/0.42 thf(fact_245_add__le__imp__le__left,axiom,
% 0.15/0.42 ! [C: real,A: real,B: real] :
% 0.15/0.42 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.15/0.42 => ( ord_less_eq_real @ A @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_le_imp_le_left
% 0.15/0.42 thf(fact_246_add__le__imp__le__left,axiom,
% 0.15/0.42 ! [C: nat,A: nat,B: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.15/0.42 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_le_imp_le_left
% 0.15/0.42 thf(fact_247_le__iff__add,axiom,
% 0.15/0.42 ( ord_less_eq_nat
% 0.15/0.42 = ( ^ [A2: nat,B2: nat] :
% 0.15/0.42 ? [C3: nat] :
% 0.15/0.42 ( B2
% 0.15/0.42 = ( plus_plus_nat @ A2 @ C3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % le_iff_add
% 0.15/0.42 thf(fact_248_add__right__mono,axiom,
% 0.15/0.42 ! [A: real,B: real,C: real] :
% 0.15/0.42 ( ( ord_less_eq_real @ A @ B )
% 0.15/0.42 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_right_mono
% 0.15/0.42 thf(fact_249_add__right__mono,axiom,
% 0.15/0.42 ! [A: nat,B: nat,C: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ A @ B )
% 0.15/0.42 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_right_mono
% 0.15/0.42 thf(fact_250_less__eqE,axiom,
% 0.15/0.42 ! [A: nat,B: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ A @ B )
% 0.15/0.42 => ~ ! [C2: nat] :
% 0.15/0.42 ( B
% 0.15/0.42 != ( plus_plus_nat @ A @ C2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % less_eqE
% 0.15/0.42 thf(fact_251_add__left__mono,axiom,
% 0.15/0.42 ! [A: real,B: real,C: real] :
% 0.15/0.42 ( ( ord_less_eq_real @ A @ B )
% 0.15/0.42 => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_left_mono
% 0.15/0.42 thf(fact_252_add__left__mono,axiom,
% 0.15/0.42 ! [A: nat,B: nat,C: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ A @ B )
% 0.15/0.42 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_left_mono
% 0.15/0.42 thf(fact_253_add__mono,axiom,
% 0.15/0.42 ! [A: real,B: real,C: real,D2: real] :
% 0.15/0.42 ( ( ord_less_eq_real @ A @ B )
% 0.15/0.42 => ( ( ord_less_eq_real @ C @ D2 )
% 0.15/0.42 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_mono
% 0.15/0.42 thf(fact_254_add__mono,axiom,
% 0.15/0.42 ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.15/0.42 ( ( ord_less_eq_nat @ A @ B )
% 0.15/0.42 => ( ( ord_less_eq_nat @ C @ D2 )
% 0.15/0.42 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_mono
% 0.15/0.42 thf(fact_255_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.15/0.42 ! [I: real,J: real,K: real,L: real] :
% 0.15/0.42 ( ( ( ord_less_eq_real @ I @ J )
% 0.15/0.42 & ( ord_less_eq_real @ K @ L ) )
% 0.15/0.42 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_mono_thms_linordered_semiring(1)
% 0.15/0.42 thf(fact_256_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.15/0.42 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.15/0.42 ( ( ( ord_less_eq_nat @ I @ J )
% 0.15/0.42 & ( ord_less_eq_nat @ K @ L ) )
% 0.15/0.42 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_mono_thms_linordered_semiring(1)
% 0.15/0.42 thf(fact_257_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.15/0.42 ! [I: real,J: real,K: real,L: real] :
% 0.15/0.42 ( ( ( I = J )
% 0.15/0.42 & ( ord_less_eq_real @ K @ L ) )
% 0.15/0.42 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_mono_thms_linordered_semiring(2)
% 0.15/0.42 thf(fact_258_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.15/0.42 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.15/0.42 ( ( ( I = J )
% 0.15/0.42 & ( ord_less_eq_nat @ K @ L ) )
% 0.15/0.42 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_mono_thms_linordered_semiring(2)
% 0.15/0.42 thf(fact_259_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.15/0.42 ! [I: real,J: real,K: real,L: real] :
% 0.15/0.42 ( ( ( ord_less_eq_real @ I @ J )
% 0.15/0.42 & ( K = L ) )
% 0.15/0.42 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_mono_thms_linordered_semiring(3)
% 0.15/0.42 thf(fact_260_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.15/0.42 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.15/0.42 ( ( ( ord_less_eq_nat @ I @ J )
% 0.15/0.42 & ( K = L ) )
% 0.15/0.42 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_mono_thms_linordered_semiring(3)
% 0.15/0.42 thf(fact_261_add__less__imp__less__right,axiom,
% 0.15/0.42 ! [A: real,C: real,B: real] :
% 0.15/0.42 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.15/0.42 => ( ord_less_real @ A @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_less_imp_less_right
% 0.15/0.42 thf(fact_262_add__less__imp__less__right,axiom,
% 0.15/0.42 ! [A: nat,C: nat,B: nat] :
% 0.15/0.42 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.15/0.42 => ( ord_less_nat @ A @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_less_imp_less_right
% 0.15/0.42 thf(fact_263_add__less__imp__less__left,axiom,
% 0.15/0.42 ! [C: real,A: real,B: real] :
% 0.15/0.42 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.15/0.42 => ( ord_less_real @ A @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_less_imp_less_left
% 0.15/0.42 thf(fact_264_add__less__imp__less__left,axiom,
% 0.15/0.42 ! [C: nat,A: nat,B: nat] :
% 0.15/0.42 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.15/0.42 => ( ord_less_nat @ A @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_less_imp_less_left
% 0.15/0.42 thf(fact_265_add__strict__right__mono,axiom,
% 0.15/0.42 ! [A: real,B: real,C: real] :
% 0.15/0.42 ( ( ord_less_real @ A @ B )
% 0.15/0.42 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_strict_right_mono
% 0.15/0.42 thf(fact_266_add__strict__right__mono,axiom,
% 0.15/0.42 ! [A: nat,B: nat,C: nat] :
% 0.15/0.42 ( ( ord_less_nat @ A @ B )
% 0.15/0.42 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_strict_right_mono
% 0.15/0.42 thf(fact_267_add__strict__left__mono,axiom,
% 0.15/0.42 ! [A: real,B: real,C: real] :
% 0.15/0.42 ( ( ord_less_real @ A @ B )
% 0.15/0.42 => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_strict_left_mono
% 0.15/0.42 thf(fact_268_add__strict__left__mono,axiom,
% 0.15/0.42 ! [A: nat,B: nat,C: nat] :
% 0.15/0.42 ( ( ord_less_nat @ A @ B )
% 0.15/0.42 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_strict_left_mono
% 0.15/0.42 thf(fact_269_add__strict__mono,axiom,
% 0.15/0.42 ! [A: real,B: real,C: real,D2: real] :
% 0.15/0.42 ( ( ord_less_real @ A @ B )
% 0.15/0.42 => ( ( ord_less_real @ C @ D2 )
% 0.15/0.42 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_strict_mono
% 0.15/0.42 thf(fact_270_add__strict__mono,axiom,
% 0.15/0.42 ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.15/0.42 ( ( ord_less_nat @ A @ B )
% 0.15/0.42 => ( ( ord_less_nat @ C @ D2 )
% 0.15/0.42 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_strict_mono
% 0.15/0.42 thf(fact_271_add__mono__thms__linordered__field_I1_J,axiom,
% 0.15/0.42 ! [I: real,J: real,K: real,L: real] :
% 0.15/0.42 ( ( ( ord_less_real @ I @ J )
% 0.15/0.42 & ( K = L ) )
% 0.15/0.42 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_mono_thms_linordered_field(1)
% 0.15/0.42 thf(fact_272_add__mono__thms__linordered__field_I1_J,axiom,
% 0.15/0.42 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.15/0.42 ( ( ( ord_less_nat @ I @ J )
% 0.15/0.42 & ( K = L ) )
% 0.15/0.42 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_mono_thms_linordered_field(1)
% 0.15/0.42 thf(fact_273_add__mono__thms__linordered__field_I2_J,axiom,
% 0.15/0.42 ! [I: real,J: real,K: real,L: real] :
% 0.15/0.42 ( ( ( I = J )
% 0.15/0.42 & ( ord_less_real @ K @ L ) )
% 0.15/0.42 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_mono_thms_linordered_field(2)
% 0.15/0.42 thf(fact_274_add__mono__thms__linordered__field_I2_J,axiom,
% 0.15/0.42 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.15/0.42 ( ( ( I = J )
% 0.15/0.42 & ( ord_less_nat @ K @ L ) )
% 0.15/0.42 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_mono_thms_linordered_field(2)
% 0.15/0.42 thf(fact_275_add__mono__thms__linordered__field_I5_J,axiom,
% 0.15/0.42 ! [I: real,J: real,K: real,L: real] :
% 0.15/0.42 ( ( ( ord_less_real @ I @ J )
% 0.15/0.42 & ( ord_less_real @ K @ L ) )
% 0.15/0.42 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_mono_thms_linordered_field(5)
% 0.15/0.42 thf(fact_276_add__mono__thms__linordered__field_I5_J,axiom,
% 0.15/0.42 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.15/0.42 ( ( ( ord_less_nat @ I @ J )
% 0.15/0.42 & ( ord_less_nat @ K @ L ) )
% 0.15/0.42 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_mono_thms_linordered_field(5)
% 0.15/0.42 thf(fact_277_less__add__eq__less,axiom,
% 0.15/0.42 ! [K: nat,L: nat,M: nat,N: nat] :
% 0.15/0.42 ( ( ord_less_nat @ K @ L )
% 0.15/0.42 => ( ( ( plus_plus_nat @ M @ L )
% 0.15/0.42 = ( plus_plus_nat @ K @ N ) )
% 0.15/0.42 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % less_add_eq_less
% 0.15/0.42 thf(fact_278_trans__less__add2,axiom,
% 0.15/0.42 ! [I: nat,J: nat,M: nat] :
% 0.15/0.42 ( ( ord_less_nat @ I @ J )
% 0.15/0.42 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % trans_less_add2
% 0.15/0.42 thf(fact_279_trans__less__add1,axiom,
% 0.15/0.42 ! [I: nat,J: nat,M: nat] :
% 0.15/0.42 ( ( ord_less_nat @ I @ J )
% 0.15/0.42 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % trans_less_add1
% 0.15/0.42 thf(fact_280_add__less__mono1,axiom,
% 0.15/0.42 ! [I: nat,J: nat,K: nat] :
% 0.15/0.42 ( ( ord_less_nat @ I @ J )
% 0.15/0.42 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % add_less_mono1
% 0.15/0.42 thf(fact_281_not__add__less2,axiom,
% 0.15/0.42 ! [J: nat,I: nat] :
% 0.15/0.42 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 0.15/0.42
% 0.15/0.42 % not_add_less2
% 0.15/0.42 thf(fact_282_not__add__less1,axiom,
% 0.15/0.42 ! [I: nat,J: nat] :
% 0.15/0.42 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 0.15/0.42
% 0.15/0.42 % not_add_less1
% 0.15/0.42
% 0.15/0.42 % Conjectures (2)
% 0.15/0.42 thf(conj_0,hypothesis,
% 0.15/0.42 ! [V7: view_e774982825t_unit] :
% 0.15/0.42 ( ( ( ord_le461438217t_unit @ V7 @ ( move @ ts3 @ ts @ v ) )
% 0.15/0.42 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V7 ) ) )
% 0.15/0.42 & ( ( len @ regular_regular @ V7 @ ts @ c )
% 0.15/0.42 = ( ext_Product_unit @ V7 ) )
% 0.15/0.42 & ( ( restrict @ V7 @ ( res @ ts ) @ c )
% 0.15/0.42 = ( lan_Product_unit @ V7 ) )
% 0.15/0.42 & ( ( nat_card @ ( lan_Product_unit @ V7 ) )
% 0.15/0.42 = one_one_nat )
% 0.15/0.42 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V7 ) ) )
% 0.15/0.42 & ( ( len @ regular_regular @ V7 @ ts @ e )
% 0.15/0.42 = ( ext_Product_unit @ V7 ) )
% 0.15/0.42 & ( ( restrict @ V7 @ ( res @ ts ) @ e )
% 0.15/0.42 = ( lan_Product_unit @ V7 ) )
% 0.15/0.42 & ( ( nat_card @ ( lan_Product_unit @ V7 ) )
% 0.15/0.42 = one_one_nat ) )
% 0.15/0.42 => thesis ) ).
% 0.15/0.42
% 0.15/0.42 thf(conj_1,conjecture,
% 0.15/0.42 thesis ).
% 0.15/0.42
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 ------------------------
% 2.57/1.45 ---- Embedded in THF ---
% 2.57/1.45 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.57/1.45 %%% Generated on Tue Feb 24 08:28:09 EST 2026
% 2.57/1.45 %%% using '$$dhol' embedding, version 1.3.0.
% 2.57/1.45 %%% Logic specification used:
% 2.57/1.45 %%% thf(spec, logic, $$dhol).
% 2.57/1.45
% 2.57/1.45 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.pzq8qyAMZ7/DTF2DTF20750.p
% See solution above
% 2.57/1.45 ------------------------
% 2.57/1.49 ---- Cleaned THF ---
% 2.57/1.49 thf(ty_n_t__Views__Oview__Oview____ext_It__Product____Type__Ounit_J,type,
% 2.57/1.49 view_e774982825t_unit: $tType ).
% 2.57/1.49
% 2.57/1.49 thf(ty_n_t__RealInt__Oreal____int,type,
% 2.57/1.49 real_int: $tType ).
% 2.57/1.49
% 2.57/1.49 thf(ty_n_t__NatInt__Onat____int,type,
% 2.57/1.49 nat_int: $tType ).
% 2.57/1.49
% 2.57/1.49 thf(ty_n_t__Traffic__Otraffic,type,
% 2.57/1.49 traffic: $tType ).
% 2.57/1.49
% 2.57/1.49 thf(ty_n_t__Real__Oreal,type,
% 2.57/1.49 real: $tType ).
% 2.57/1.49
% 2.57/1.49 thf(ty_n_t__Cars__Ocars,type,
% 2.57/1.49 cars: $tType ).
% 2.57/1.49
% 2.57/1.49 thf(ty_n_t__Nat__Onat,type,
% 2.57/1.49 nat: $tType ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 2.57/1.49 one_one_nat: nat ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 2.57/1.49 plus_plus_nat: nat > nat > nat ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal,type,
% 2.57/1.49 plus_plus_real: real > real > real ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 2.57/1.49 zero_zero_nat: nat ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal,type,
% 2.57/1.49 zero_zero_real: real ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Length_Osensors_Olen,type,
% 2.57/1.49 len: ( cars > traffic > cars > real ) > view_e774982825t_unit > traffic > cars > real_int ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Move_Otraffic_Omove,type,
% 2.57/1.49 move: traffic > traffic > view_e774982825t_unit > view_e774982825t_unit ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_NatInt_Onat__int_Ocard_H,type,
% 2.57/1.49 nat_card: nat_int > nat ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Orderings_Obot__class_Obot_001t__NatInt__Onat____int,type,
% 2.57/1.49 bot_bot_nat_int: nat_int ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Orderings_Oord__class_Oless_001t__NatInt__Onat____int,type,
% 2.57/1.49 ord_less_nat_int: nat_int > nat_int > $o ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 2.57/1.49 ord_less_nat: nat > nat > $o ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal,type,
% 2.57/1.49 ord_less_real: real > real > $o ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__NatInt__Onat____int,type,
% 2.57/1.49 ord_less_eq_nat_int: nat_int > nat_int > $o ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 2.57/1.49 ord_less_eq_nat: nat > nat > $o ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__RealInt__Oreal____int,type,
% 2.57/1.49 ord_less_eq_real_int: real_int > real_int > $o ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type,
% 2.57/1.49 ord_less_eq_real: real > real > $o ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Views__Oview__Oview____ext_It__Product____Type__Ounit_J,type,
% 2.57/1.49 ord_le461438217t_unit: view_e774982825t_unit > view_e774982825t_unit > $o ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_RealInt_Oreal__int_Olength,type,
% 2.57/1.49 real_length: real_int > real ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Regular__Sensors_Oregular,type,
% 2.57/1.49 regular_regular: cars > traffic > cars > real ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Restriction_Orestriction_Orestrict,type,
% 2.57/1.49 restrict: view_e774982825t_unit > ( cars > nat_int ) > cars > nat_int ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Traffic_Otraffic_Oabstract,type,
% 2.57/1.49 abstract: traffic > traffic > $o ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Traffic_Otraffic_Oclm,type,
% 2.57/1.49 clm: traffic > cars > nat_int ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Traffic_Otraffic_Ocreate__claim,type,
% 2.57/1.49 create_claim: traffic > cars > nat > traffic > $o ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Traffic_Otraffic_Ocreate__reservation,type,
% 2.57/1.49 create_reservation: traffic > cars > traffic > $o ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Traffic_Otraffic_Ores,type,
% 2.57/1.49 res: traffic > cars > nat_int ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Traffic_Otraffic_Owithdraw__claim,type,
% 2.57/1.49 withdraw_claim: traffic > cars > traffic > $o ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Traffic_Otraffic_Owithdraw__reservation,type,
% 2.57/1.49 withdraw_reservation: traffic > cars > nat > traffic > $o ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Views_Oview_Oext_001t__Product____Type__Ounit,type,
% 2.57/1.49 ext_Product_unit: view_e774982825t_unit > real_int ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Views_Oview_Ohchop,type,
% 2.57/1.49 hchop: view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > $o ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Views_Oview_Olan_001t__Product____Type__Ounit,type,
% 2.57/1.49 lan_Product_unit: view_e774982825t_unit > nat_int ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Views_Oview_Oown_001t__Product____Type__Ounit,type,
% 2.57/1.49 own_Product_unit: view_e774982825t_unit > cars ).
% 2.57/1.49
% 2.57/1.49 thf(sy_c_Views_Oview_Ovchop,type,
% 2.57/1.49 vchop: view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > $o ).
% 2.57/1.49
% 2.57/1.49 thf(sy_v_c____,type,
% 2.57/1.49 c: cars ).
% 2.57/1.49
% 2.57/1.49 thf(sy_v_d____,type,
% 2.57/1.49 d: cars ).
% 2.57/1.49
% 2.57/1.49 thf(sy_v_e____,type,
% 2.57/1.49 e: cars ).
% 2.57/1.49
% 2.57/1.49 thf(sy_v_thesis____,type,
% 2.57/1.49 thesis: $o ).
% 2.57/1.49
% 2.57/1.49 thf(sy_v_ts_H_H____,type,
% 2.57/1.49 ts: traffic ).
% 2.57/1.49
% 2.57/1.49 thf(sy_v_ts_H____,type,
% 2.57/1.49 ts2: traffic ).
% 2.57/1.49
% 2.57/1.49 thf(sy_v_ts_Ha____,type,
% 2.57/1.49 ts_a: traffic ).
% 2.57/1.49
% 2.57/1.49 thf(sy_v_ts____,type,
% 2.57/1.49 ts3: traffic ).
% 2.57/1.49
% 2.57/1.49 thf(sy_v_v____,type,
% 2.57/1.49 v: view_e774982825t_unit ).
% 2.57/1.49
% 2.57/1.49 thf(fact_0_neg,axiom,
% 2.57/1.49 c != e ).
% 2.57/1.49
% 2.57/1.49 thf(fact_1_local_Ohmlsl_Osensors__ge,axiom,
% 2.57/1.49 ! [E: cars,Ts: traffic,C: cars] : ( ord_less_real @ zero_zero_real @ ( regular_regular @ E @ Ts @ C ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_2_local_Ohmlsl_Olength__geq__zero,axiom,
% 2.57/1.49 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( real_length @ ( ext_Product_unit @ V ) )
% 2.57/1.49 = zero_zero_real )
% 2.57/1.49 | ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_3_hmlsl_Olen__empty__subview,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,Ts: traffic,C: cars,V3: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( ( real_length @ ( len @ regular_regular @ V2 @ Ts @ C ) )
% 2.57/1.49 = zero_zero_real )
% 2.57/1.49 & ( ord_le461438217t_unit @ V3 @ V2 ) )
% 2.57/1.49 => ( ( real_length @ ( len @ regular_regular @ V3 @ Ts @ C ) )
% 2.57/1.49 = zero_zero_real ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_4__092_060open_062_092_060exists_062v_H_092_060le_062move_Ats_Ats_H_H_Av_O_A_I0_A_060_A_092_060parallel_062ext_Av_H_092_060parallel_062_A_092_060and_062_Alen_Av_H_Ats_H_H_Ac_A_061_Aext_Av_H_A_092_060and_062_Arestrict_Av_H_A_Ires_Ats_H_H_J_Ac_A_061_Alan_Av_H_A_092_060and_062_A_124lan_Av_H_124_A_061_A1_J_A_092_060and_062_A0_A_060_A_092_060parallel_062ext_Av_H_092_060parallel_062_A_092_060and_062_Alen_Av_H_Ats_H_H_Ae_A_061_Aext_Av_H_A_092_060and_062_Arestrict_Av_H_A_Ires_Ats_H_H_J_Ae_A_061_Alan_Av_H_A_092_060and_062_A_124lan_Av_H_124_A_061_A1_092_060close_062,axiom,
% 2.57/1.49 ? [V4: view_e774982825t_unit] :
% 2.57/1.49 ( ( ord_le461438217t_unit @ V4 @ ( move @ ts3 @ ts @ v ) )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V4 ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V4 @ ts @ c )
% 2.57/1.49 = ( ext_Product_unit @ V4 ) )
% 2.57/1.49 & ( ( restrict @ V4 @ ( res @ ts ) @ c )
% 2.57/1.49 = ( lan_Product_unit @ V4 ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V4 ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V4 ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V4 @ ts @ e )
% 2.57/1.49 = ( ext_Product_unit @ V4 ) )
% 2.57/1.49 & ( ( restrict @ V4 @ ( res @ ts ) @ e )
% 2.57/1.49 = ( lan_Product_unit @ V4 ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V4 ) )
% 2.57/1.49 = one_one_nat ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_5_local_Ohmlsl_Ores__ge__zero,axiom,
% 2.57/1.49 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 => ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_6_local_Ohmlsl_Owidth__res,axiom,
% 2.57/1.49 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 => ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_7_abs,axiom,
% 2.57/1.49 abstract @ ts3 @ ts2 ).
% 2.57/1.49
% 2.57/1.49 thf(fact_8__092_060open_062move_Ats_Ats_H_Av_A_061_Amove_Ats_H_Ats_H_H_A_Imove_Ats_Ats_H_Av_J_092_060close_062,axiom,
% 2.57/1.49 ( ( move @ ts3 @ ts_a @ v )
% 2.57/1.49 = ( move @ ts_a @ ts @ ( move @ ts3 @ ts_a @ v ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_9_move__stab,axiom,
% 2.57/1.49 ( ( move @ ts3 @ ts_a @ v )
% 2.57/1.49 = ( move @ ts3 @ ts @ v ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_10_local_Ohmlsl_Ores__compose,axiom,
% 2.57/1.49 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ? [Va: view_e774982825t_unit,U: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V @ Va @ U )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ Va ) )
% 2.57/1.49 & ( ( restrict @ Va @ ( res @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ Va ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ Va ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ U @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ U ) )
% 2.57/1.49 & ( ( restrict @ U @ ( res @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ U ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ U ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 => ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_11_local_Ohmlsl_Ores__decompose,axiom,
% 2.57/1.49 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 => ? [Va2: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V @ Va2 @ U2 )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va2 ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ Va2 @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ Va2 ) )
% 2.57/1.49 & ( ( restrict @ Va2 @ ( res @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ Va2 ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ Va2 ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U2 ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ U2 @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ U2 ) )
% 2.57/1.49 & ( ( restrict @ U2 @ ( res @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ U2 ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ U2 ) )
% 2.57/1.49 = one_one_nat ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_12_local_Ohmlsl_Ores__dense,axiom,
% 2.57/1.49 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 = ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V @ W @ U3 )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ W ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ W @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ W ) )
% 2.57/1.49 & ( ( restrict @ W @ ( res @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ W ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ W ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U3 ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ U3 @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ U3 ) )
% 2.57/1.49 & ( ( restrict @ U3 @ ( res @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ U3 ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ U3 ) )
% 2.57/1.49 = one_one_nat ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_13_local_Ohmlsl_Ocar__one__lane__non__empty,axiom,
% 2.57/1.49 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ? [X: cars] :
% 2.57/1.49 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( clm @ Ts2 ) @ X )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 | ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ X )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) ) )
% 2.57/1.49 => ( ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_14_local_Ohmlsl_Oempty__no__car,axiom,
% 2.57/1.49 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( real_length @ ( ext_Product_unit @ V ) )
% 2.57/1.49 = zero_zero_real )
% 2.57/1.49 => ~ ? [X: cars] :
% 2.57/1.49 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( clm @ Ts2 ) @ X )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 | ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ X )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_15_local_Ohmlsl_Otwo__lanes__no__car,axiom,
% 2.57/1.49 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 != one_one_nat )
% 2.57/1.49 => ~ ? [X: cars] :
% 2.57/1.49 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( clm @ Ts2 ) @ X )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 | ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ X )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_16_local_Ohmlsl_Ores__at__most__two,axiom,
% 2.57/1.49 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ~ ? [Va: view_e774982825t_unit,U: view_e774982825t_unit] :
% 2.57/1.49 ( ( vchop @ V @ Va @ U )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ Va ) )
% 2.57/1.49 & ( ( restrict @ Va @ ( res @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ Va ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ Va ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ? [Vb: view_e774982825t_unit,Ua: view_e774982825t_unit] :
% 2.57/1.49 ( ( vchop @ U @ Vb @ Ua )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Vb ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ Vb @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ Vb ) )
% 2.57/1.49 & ( ( restrict @ Vb @ ( res @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ Vb ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ Vb ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Ua ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ Ua @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ Ua ) )
% 2.57/1.49 & ( ( restrict @ Ua @ ( res @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ Ua ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ Ua ) )
% 2.57/1.49 = one_one_nat ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_17_local_Ohmlsl_Otwo__res__not__res,axiom,
% 2.57/1.49 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ? [Va: view_e774982825t_unit,U: view_e774982825t_unit] :
% 2.57/1.49 ( ( vchop @ V @ Va @ U )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ Va ) )
% 2.57/1.49 & ( ( restrict @ Va @ ( res @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ Va ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ Va ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ U @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ U ) )
% 2.57/1.49 & ( ( restrict @ U @ ( res @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ U ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ U ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 => ~ ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_18_local_Ohmlsl_Oclm__ge__zero,axiom,
% 2.57/1.49 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 => ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_19_local_Ohmlsl_Ohchop__weaken2,axiom,
% 2.57/1.49 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( Phi @ Ts2 @ V )
% 2.57/1.49 => ? [Va2: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V @ Va2 @ U2 )
% 2.57/1.49 & ( Phi @ Ts2 @ U2 ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_20_local_Ohmlsl_Ohchop__weaken1,axiom,
% 2.57/1.49 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( Phi @ Ts2 @ V )
% 2.57/1.49 => ? [Va2: view_e774982825t_unit] :
% 2.57/1.49 ( ? [X_1: view_e774982825t_unit] : ( hchop @ V @ Va2 @ X_1 )
% 2.57/1.49 & ( Phi @ Ts2 @ Va2 ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_21_local_Ohmlsl_Ohchop__weaken,axiom,
% 2.57/1.49 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( Phi @ Ts2 @ V )
% 2.57/1.49 => ? [Va2: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V @ Va2 @ U2 )
% 2.57/1.49 & ? [Vb2: view_e774982825t_unit] :
% 2.57/1.49 ( ? [X_1: view_e774982825t_unit] : ( hchop @ U2 @ Vb2 @ X_1 )
% 2.57/1.49 & ( Phi @ Ts2 @ Vb2 ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_22_local_Ohmlsl_Ohchop__neg2,axiom,
% 2.57/1.49 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ~ ? [Va2: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V @ Va2 @ U2 )
% 2.57/1.49 & ( Phi @ Ts2 @ U2 ) )
% 2.57/1.49 => ? [Va2: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V @ Va2 @ U2 )
% 2.57/1.49 & ~ ( Phi @ Ts2 @ U2 ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_23_local_Ohmlsl_Ohchop__neg1,axiom,
% 2.57/1.49 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ~ ? [Va2: view_e774982825t_unit] :
% 2.57/1.49 ( ? [X_1: view_e774982825t_unit] : ( hchop @ V @ Va2 @ X_1 )
% 2.57/1.49 & ( Phi @ Ts2 @ Va2 ) )
% 2.57/1.49 => ? [Va2: view_e774982825t_unit] :
% 2.57/1.49 ( ? [X_1: view_e774982825t_unit] : ( hchop @ V @ Va2 @ X_1 )
% 2.57/1.49 & ~ ( Phi @ Ts2 @ Va2 ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_24_local_Ohmlsl_Ohchop__disj__distr2,axiom,
% 2.57/1.49 ! [Psi: traffic > view_e774982825t_unit > $o,Chi: traffic > view_e774982825t_unit > $o,Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V @ W @ U3 )
% 2.57/1.49 & ( ( Psi @ Ts2 @ W )
% 2.57/1.49 | ( Chi @ Ts2 @ W ) )
% 2.57/1.49 & ( Phi @ Ts2 @ U3 ) ) )
% 2.57/1.49 = ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V @ W @ U3 )
% 2.57/1.49 & ( Psi @ Ts2 @ W )
% 2.57/1.49 & ( Phi @ Ts2 @ U3 ) )
% 2.57/1.49 | ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V @ W @ U3 )
% 2.57/1.49 & ( Chi @ Ts2 @ W )
% 2.57/1.49 & ( Phi @ Ts2 @ U3 ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_25_local_Ohmlsl_Ohchop__disj__distr1,axiom,
% 2.57/1.49 ! [Phi: traffic > view_e774982825t_unit > $o,Psi: traffic > view_e774982825t_unit > $o,Chi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V @ W @ U3 )
% 2.57/1.49 & ( Phi @ Ts2 @ W )
% 2.57/1.49 & ( ( Psi @ Ts2 @ U3 )
% 2.57/1.49 | ( Chi @ Ts2 @ U3 ) ) ) )
% 2.57/1.49 = ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V @ W @ U3 )
% 2.57/1.49 & ( Phi @ Ts2 @ W )
% 2.57/1.49 & ( Psi @ Ts2 @ U3 ) )
% 2.57/1.49 | ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V @ W @ U3 )
% 2.57/1.49 & ( Phi @ Ts2 @ W )
% 2.57/1.49 & ( Chi @ Ts2 @ U3 ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_26_local_Ohmlsl_Ohchop__assoc,axiom,
% 2.57/1.49 ! [Phi: traffic > view_e774982825t_unit > $o,Psi: traffic > view_e774982825t_unit > $o,Chi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V @ W @ U3 )
% 2.57/1.49 & ( Phi @ Ts2 @ W )
% 2.57/1.49 & ? [X2: view_e774982825t_unit,Y: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ U3 @ X2 @ Y )
% 2.57/1.49 & ( Psi @ Ts2 @ X2 )
% 2.57/1.49 & ( Chi @ Ts2 @ Y ) ) ) )
% 2.57/1.49 = ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V @ W @ U3 )
% 2.57/1.49 & ? [X2: view_e774982825t_unit,Y: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ W @ X2 @ Y )
% 2.57/1.49 & ( Phi @ Ts2 @ X2 )
% 2.57/1.49 & ( Psi @ Ts2 @ Y ) )
% 2.57/1.49 & ( Chi @ Ts2 @ U3 ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_27_local_Ohmlsl_Ovchop__disj__distr2,axiom,
% 2.57/1.49 ! [Psi: traffic > view_e774982825t_unit > $o,Chi: traffic > view_e774982825t_unit > $o,Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 2.57/1.49 ( ( vchop @ V @ W @ U3 )
% 2.57/1.49 & ( ( Psi @ Ts2 @ W )
% 2.57/1.49 | ( Chi @ Ts2 @ W ) )
% 2.57/1.49 & ( Phi @ Ts2 @ U3 ) ) )
% 2.57/1.49 = ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 2.57/1.49 ( ( vchop @ V @ W @ U3 )
% 2.57/1.49 & ( Psi @ Ts2 @ W )
% 2.57/1.49 & ( Phi @ Ts2 @ U3 ) )
% 2.57/1.49 | ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 2.57/1.49 ( ( vchop @ V @ W @ U3 )
% 2.57/1.49 & ( Chi @ Ts2 @ W )
% 2.57/1.49 & ( Phi @ Ts2 @ U3 ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_28_local_Ohmlsl_Ovchop__disj__distr1,axiom,
% 2.57/1.49 ! [Phi: traffic > view_e774982825t_unit > $o,Psi: traffic > view_e774982825t_unit > $o,Chi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 2.57/1.49 ( ( vchop @ V @ W @ U3 )
% 2.57/1.49 & ( Phi @ Ts2 @ W )
% 2.57/1.49 & ( ( Psi @ Ts2 @ U3 )
% 2.57/1.49 | ( Chi @ Ts2 @ U3 ) ) ) )
% 2.57/1.49 = ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 2.57/1.49 ( ( vchop @ V @ W @ U3 )
% 2.57/1.49 & ( Phi @ Ts2 @ W )
% 2.57/1.49 & ( Psi @ Ts2 @ U3 ) )
% 2.57/1.49 | ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 2.57/1.49 ( ( vchop @ V @ W @ U3 )
% 2.57/1.49 & ( Phi @ Ts2 @ W )
% 2.57/1.49 & ( Chi @ Ts2 @ U3 ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_29_local_Ohmlsl_Ov__chop__weaken2,axiom,
% 2.57/1.49 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( Phi @ Ts2 @ V )
% 2.57/1.49 => ? [Va2: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 2.57/1.49 ( ( vchop @ V @ Va2 @ U2 )
% 2.57/1.49 & ( Phi @ Ts2 @ U2 ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_30_local_Ohmlsl_Ov__chop__weaken1,axiom,
% 2.57/1.49 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( Phi @ Ts2 @ V )
% 2.57/1.49 => ? [Va2: view_e774982825t_unit] :
% 2.57/1.49 ( ? [X_1: view_e774982825t_unit] : ( vchop @ V @ Va2 @ X_1 )
% 2.57/1.49 & ( Phi @ Ts2 @ Va2 ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_31_local_Ohmlsl_Ov__chop__assoc,axiom,
% 2.57/1.49 ! [Phi: traffic > view_e774982825t_unit > $o,Psi: traffic > view_e774982825t_unit > $o,Chi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 2.57/1.49 ( ( vchop @ V @ W @ U3 )
% 2.57/1.49 & ( Phi @ Ts2 @ W )
% 2.57/1.49 & ? [X2: view_e774982825t_unit,Y: view_e774982825t_unit] :
% 2.57/1.49 ( ( vchop @ U3 @ X2 @ Y )
% 2.57/1.49 & ( Psi @ Ts2 @ X2 )
% 2.57/1.49 & ( Chi @ Ts2 @ Y ) ) ) )
% 2.57/1.49 = ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 2.57/1.49 ( ( vchop @ V @ W @ U3 )
% 2.57/1.49 & ? [X2: view_e774982825t_unit,Y: view_e774982825t_unit] :
% 2.57/1.49 ( ( vchop @ W @ X2 @ Y )
% 2.57/1.49 & ( Phi @ Ts2 @ X2 )
% 2.57/1.49 & ( Psi @ Ts2 @ Y ) )
% 2.57/1.49 & ( Chi @ Ts2 @ U3 ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_32_local_Ohmlsl_Oglobally__refl,axiom,
% 2.57/1.49 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ! [Ts3: traffic] :
% 2.57/1.49 ( ( abstract @ Ts2 @ Ts3 )
% 2.57/1.49 => ( Phi @ Ts3 @ ( move @ Ts2 @ Ts3 @ V ) ) )
% 2.57/1.49 => ( Phi @ Ts2 @ V ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_33_local_Ohmlsl_Oglobally__4,axiom,
% 2.57/1.49 ! [Phi: traffic > view_e774982825t_unit > $o,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ! [Ts3: traffic] :
% 2.57/1.49 ( ( abstract @ Ts2 @ Ts3 )
% 2.57/1.49 => ( Phi @ Ts3 @ ( move @ Ts2 @ Ts3 @ V ) ) )
% 2.57/1.49 => ! [Ts4: traffic] :
% 2.57/1.49 ( ( abstract @ Ts2 @ Ts4 )
% 2.57/1.49 => ! [Ts_a: traffic] :
% 2.57/1.49 ( ( abstract @ Ts4 @ Ts_a )
% 2.57/1.49 => ( Phi @ Ts_a @ ( move @ Ts4 @ Ts_a @ ( move @ Ts2 @ Ts4 @ V ) ) ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_34_wd__clm_Ohyps_I1_J,axiom,
% 2.57/1.49 abstract @ ts3 @ ts_a ).
% 2.57/1.49
% 2.57/1.49 thf(fact_35_local_Ohmlsl_Owidth__hchop__stable,axiom,
% 2.57/1.49 ! [X3: nat,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = X3 )
% 2.57/1.49 = ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V @ W @ U3 )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ W ) )
% 2.57/1.49 = X3 )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ U3 ) )
% 2.57/1.49 = X3 ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_36_local_Ohmlsl_Olength__vchop__stable,axiom,
% 2.57/1.49 ! [X3: real,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( real_length @ ( ext_Product_unit @ V ) )
% 2.57/1.49 = X3 )
% 2.57/1.49 = ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 2.57/1.49 ( ( vchop @ V @ W @ U3 )
% 2.57/1.49 & ( ( real_length @ ( ext_Product_unit @ W ) )
% 2.57/1.49 = X3 )
% 2.57/1.49 & ( ( real_length @ ( ext_Product_unit @ U3 ) )
% 2.57/1.49 = X3 ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_37_hmlsl_Olen__stable__up,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,V1: view_e774982825t_unit,V22: view_e774982825t_unit,Ts: traffic,C: cars] :
% 2.57/1.49 ( ( vchop @ V2 @ V1 @ V22 )
% 2.57/1.49 => ( ( len @ regular_regular @ V2 @ Ts @ C )
% 2.57/1.49 = ( len @ regular_regular @ V22 @ Ts @ C ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_38_hmlsl_Olen__stable__down,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,V1: view_e774982825t_unit,V22: view_e774982825t_unit,Ts: traffic,C: cars] :
% 2.57/1.49 ( ( vchop @ V2 @ V1 @ V22 )
% 2.57/1.49 => ( ( len @ regular_regular @ V2 @ Ts @ C )
% 2.57/1.49 = ( len @ regular_regular @ V1 @ Ts @ C ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_39_hmlsl_Olen__stable,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,V1: view_e774982825t_unit,V22: view_e774982825t_unit,Ts: traffic,C: cars] :
% 2.57/1.49 ( ( vchop @ V2 @ V1 @ V22 )
% 2.57/1.49 => ( ( len @ regular_regular @ V1 @ Ts @ C )
% 2.57/1.49 = ( len @ regular_regular @ V22 @ Ts @ C ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_40_hmlsl_Olen__view__hchop__right,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,Ts: traffic,C: cars,V1: view_e774982825t_unit,V22: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( ( len @ regular_regular @ V2 @ Ts @ C )
% 2.57/1.49 = ( ext_Product_unit @ V2 ) )
% 2.57/1.49 & ( hchop @ V2 @ V1 @ V22 ) )
% 2.57/1.49 => ( ( len @ regular_regular @ V22 @ Ts @ C )
% 2.57/1.49 = ( ext_Product_unit @ V22 ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_41_hmlsl_Olen__view__hchop__left,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,Ts: traffic,C: cars,V1: view_e774982825t_unit,V22: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( ( len @ regular_regular @ V2 @ Ts @ C )
% 2.57/1.49 = ( ext_Product_unit @ V2 ) )
% 2.57/1.49 & ( hchop @ V2 @ V1 @ V22 ) )
% 2.57/1.49 => ( ( len @ regular_regular @ V1 @ Ts @ C )
% 2.57/1.49 = ( ext_Product_unit @ V1 ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_42_hmlsl_Olen__compose__hchop,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,V1: view_e774982825t_unit,V22: view_e774982825t_unit,Ts: traffic,C: cars] :
% 2.57/1.49 ( ( ( hchop @ V2 @ V1 @ V22 )
% 2.57/1.49 & ( ( len @ regular_regular @ V1 @ Ts @ C )
% 2.57/1.49 = ( ext_Product_unit @ V1 ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V22 @ Ts @ C )
% 2.57/1.49 = ( ext_Product_unit @ V22 ) ) )
% 2.57/1.49 => ( ( len @ regular_regular @ V2 @ Ts @ C )
% 2.57/1.49 = ( ext_Product_unit @ V2 ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_43_wd__clm_Ohyps_I2_J,axiom,
% 2.57/1.49 ? [C2: cars] : ( withdraw_claim @ ts_a @ C2 @ ts ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_44_local_Ohmlsl_Olength__split,axiom,
% 2.57/1.49 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 => ? [Va2: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V @ Va2 @ U2 )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va2 ) ) )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U2 ) ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_45_local_Ohmlsl_Olength__meld,axiom,
% 2.57/1.49 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ? [Va: view_e774982825t_unit,U: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V @ Va @ U )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va ) ) )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U ) ) ) )
% 2.57/1.49 => ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_46_local_Ohmlsl_Olength__dense,axiom,
% 2.57/1.49 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 = ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V @ W @ U3 )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ W ) ) )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U3 ) ) ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_47_hmlsl_Olen__empty__on__subview2,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,Ts: traffic,C: cars,V1: view_e774982825t_unit,V22: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( ( real_length @ ( len @ regular_regular @ V2 @ Ts @ C ) )
% 2.57/1.49 = zero_zero_real )
% 2.57/1.49 & ( hchop @ V2 @ V1 @ V22 ) )
% 2.57/1.49 => ( ( real_length @ ( len @ regular_regular @ V22 @ Ts @ C ) )
% 2.57/1.49 = zero_zero_real ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_48_hmlsl_Olen__empty__on__subview1,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,Ts: traffic,C: cars,V1: view_e774982825t_unit,V22: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( ( real_length @ ( len @ regular_regular @ V2 @ Ts @ C ) )
% 2.57/1.49 = zero_zero_real )
% 2.57/1.49 & ( hchop @ V2 @ V1 @ V22 ) )
% 2.57/1.49 => ( ( real_length @ ( len @ regular_regular @ V1 @ Ts @ C ) )
% 2.57/1.49 = zero_zero_real ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_49_hmlsl_Olen__fills__subview,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,Ts: traffic,C: cars] :
% 2.57/1.49 ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ V2 @ Ts @ C ) ) )
% 2.57/1.49 => ? [V12: view_e774982825t_unit,V23: view_e774982825t_unit,V32: view_e774982825t_unit,V4: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V2 @ V12 @ V23 )
% 2.57/1.49 & ( hchop @ V23 @ V4 @ V32 )
% 2.57/1.49 & ( ( len @ regular_regular @ V4 @ Ts @ C )
% 2.57/1.49 = ( ext_Product_unit @ V4 ) )
% 2.57/1.49 & ( ( real_length @ ( len @ regular_regular @ V4 @ Ts @ C ) )
% 2.57/1.49 = ( real_length @ ( len @ regular_regular @ V2 @ Ts @ C ) ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_50_d__def,axiom,
% 2.57/1.49 withdraw_claim @ ts_a @ d @ ts ).
% 2.57/1.49
% 2.57/1.49 thf(fact_51_local_Ohmlsl_Owidth__clm,axiom,
% 2.57/1.49 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 => ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_52_local_Ohmlsl_Oclm__dense,axiom,
% 2.57/1.49 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 = ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V @ W @ U3 )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ W ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ W @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ W ) )
% 2.57/1.49 & ( ( restrict @ W @ ( clm @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ W ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ W ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U3 ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ U3 @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ U3 ) )
% 2.57/1.49 & ( ( restrict @ U3 @ ( clm @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ U3 ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ U3 ) )
% 2.57/1.49 = one_one_nat ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_53_local_Ohmlsl_Oclm__decompose,axiom,
% 2.57/1.49 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 => ? [Va2: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V @ Va2 @ U2 )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va2 ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ Va2 @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ Va2 ) )
% 2.57/1.49 & ( ( restrict @ Va2 @ ( clm @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ Va2 ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ Va2 ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U2 ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ U2 @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ U2 ) )
% 2.57/1.49 & ( ( restrict @ U2 @ ( clm @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ U2 ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ U2 ) )
% 2.57/1.49 = one_one_nat ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_54_local_Ohmlsl_Oclm__compose,axiom,
% 2.57/1.49 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ? [Va: view_e774982825t_unit,U: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V @ Va @ U )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ Va ) )
% 2.57/1.49 & ( ( restrict @ Va @ ( clm @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ Va ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ Va ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ U @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ U ) )
% 2.57/1.49 & ( ( restrict @ U @ ( clm @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ U ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ U ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 => ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_55_local_Ohmlsl_Oclm__sing__not__interrupted,axiom,
% 2.57/1.49 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ~ ? [Va: view_e774982825t_unit,U: view_e774982825t_unit] :
% 2.57/1.49 ( ( vchop @ V @ Va @ U )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ Va ) )
% 2.57/1.49 & ( ( restrict @ Va @ ( clm @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ Va ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ Va ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ? [Vb: view_e774982825t_unit,Ua: view_e774982825t_unit] :
% 2.57/1.49 ( ( vchop @ U @ Vb @ Ua )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Ua ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ Ua @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ Ua ) )
% 2.57/1.49 & ( ( restrict @ Ua @ ( clm @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ Ua ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ Ua ) )
% 2.57/1.49 = one_one_nat ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_56_local_Ohmlsl_Oclm__sing,axiom,
% 2.57/1.49 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ~ ? [Va: view_e774982825t_unit,U: view_e774982825t_unit] :
% 2.57/1.49 ( ( vchop @ V @ Va @ U )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ Va ) )
% 2.57/1.49 & ( ( restrict @ Va @ ( clm @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ Va ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ Va ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ U @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ U ) )
% 2.57/1.49 & ( ( restrict @ U @ ( clm @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ U ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ U ) )
% 2.57/1.49 = one_one_nat ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_57_local_Ohmlsl_Ono__clm__before__res2,axiom,
% 2.57/1.49 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ~ ? [Va: view_e774982825t_unit,U: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V @ Va @ U )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ Va ) )
% 2.57/1.49 & ( ( restrict @ Va @ ( clm @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ Va ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ Va ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ? [Vb: view_e774982825t_unit,Ua: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ U @ Vb @ Ua )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Ua ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ Ua @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ Ua ) )
% 2.57/1.49 & ( ( restrict @ Ua @ ( res @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ Ua ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ Ua ) )
% 2.57/1.49 = one_one_nat ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_58_local_Ohmlsl_Ono__clm__before__res,axiom,
% 2.57/1.49 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ~ ? [Va: view_e774982825t_unit,U: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V @ Va @ U )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ Va ) )
% 2.57/1.49 & ( ( restrict @ Va @ ( clm @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ Va ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ Va ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ U @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ U ) )
% 2.57/1.49 & ( ( restrict @ U @ ( res @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ U ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ U ) )
% 2.57/1.49 = one_one_nat ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_59_local_Ohmlsl_Otwo__res__no__car,axiom,
% 2.57/1.49 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ? [Va: view_e774982825t_unit,U: view_e774982825t_unit] :
% 2.57/1.49 ( ( vchop @ V @ Va @ U )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ Va @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ Va ) )
% 2.57/1.49 & ( ( restrict @ Va @ ( res @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ Va ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ Va ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ U @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ U ) )
% 2.57/1.49 & ( ( restrict @ U @ ( res @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ U ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ U ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 => ~ ? [X: cars] :
% 2.57/1.49 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( clm @ Ts2 ) @ X )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 | ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ X )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_60__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062d_O_Ats_H_A_092_060_094bold_062_092_060midarrow_062wdc_I_Ad_A_J_A_092_060_094bold_062_092_060rightarrow_062_Ats_H_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.57/1.49 ~ ! [D: cars] :
% 2.57/1.49 ~ ( withdraw_claim @ ts_a @ D @ ts ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_61_local_Ohmlsl_Ofree__dense,axiom,
% 2.57/1.49 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ! [C3: cars] :
% 2.57/1.49 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C3 ) )
% 2.57/1.49 = zero_zero_real )
% 2.57/1.49 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C3 )
% 2.57/1.49 = bot_bot_nat_int )
% 2.57/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C3 )
% 2.57/1.49 = bot_bot_nat_int ) ) ) )
% 2.57/1.49 = ( ? [W: view_e774982825t_unit,U3: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V @ W @ U3 )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ W ) ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ W ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ! [C3: cars] :
% 2.57/1.49 ( ( ( real_length @ ( len @ regular_regular @ W @ Ts2 @ C3 ) )
% 2.57/1.49 = zero_zero_real )
% 2.57/1.49 | ( ( ( restrict @ W @ ( clm @ Ts2 ) @ C3 )
% 2.57/1.49 = bot_bot_nat_int )
% 2.57/1.49 & ( ( restrict @ W @ ( res @ Ts2 ) @ C3 )
% 2.57/1.49 = bot_bot_nat_int ) ) )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U3 ) ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ U3 ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ! [C3: cars] :
% 2.57/1.49 ( ( ( real_length @ ( len @ regular_regular @ U3 @ Ts2 @ C3 ) )
% 2.57/1.49 = zero_zero_real )
% 2.57/1.49 | ( ( ( restrict @ U3 @ ( clm @ Ts2 ) @ C3 )
% 2.57/1.49 = bot_bot_nat_int )
% 2.57/1.49 & ( ( restrict @ U3 @ ( res @ Ts2 ) @ C3 )
% 2.57/1.49 = bot_bot_nat_int ) ) ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_62_local_Ohmlsl_Ofree__decompose,axiom,
% 2.57/1.49 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ! [C2: cars] :
% 2.57/1.49 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 2.57/1.49 = zero_zero_real )
% 2.57/1.49 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 2.57/1.49 = bot_bot_nat_int )
% 2.57/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 2.57/1.49 = bot_bot_nat_int ) ) ) )
% 2.57/1.49 => ? [Va2: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V @ Va2 @ U2 )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va2 ) ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ Va2 ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ! [C4: cars] :
% 2.57/1.49 ( ( ( real_length @ ( len @ regular_regular @ Va2 @ Ts2 @ C4 ) )
% 2.57/1.49 = zero_zero_real )
% 2.57/1.49 | ( ( ( restrict @ Va2 @ ( clm @ Ts2 ) @ C4 )
% 2.57/1.49 = bot_bot_nat_int )
% 2.57/1.49 & ( ( restrict @ Va2 @ ( res @ Ts2 ) @ C4 )
% 2.57/1.49 = bot_bot_nat_int ) ) )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U2 ) ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ U2 ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ! [C4: cars] :
% 2.57/1.49 ( ( ( real_length @ ( len @ regular_regular @ U2 @ Ts2 @ C4 ) )
% 2.57/1.49 = zero_zero_real )
% 2.57/1.49 | ( ( ( restrict @ U2 @ ( clm @ Ts2 ) @ C4 )
% 2.57/1.49 = bot_bot_nat_int )
% 2.57/1.49 & ( ( restrict @ U2 @ ( res @ Ts2 ) @ C4 )
% 2.57/1.49 = bot_bot_nat_int ) ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_63_local_Ohmlsl_Ofree__compose,axiom,
% 2.57/1.49 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ? [Va: view_e774982825t_unit,U: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V @ Va @ U )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ Va ) ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ Va ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ! [C2: cars] :
% 2.57/1.49 ( ( ( real_length @ ( len @ regular_regular @ Va @ Ts2 @ C2 ) )
% 2.57/1.49 = zero_zero_real )
% 2.57/1.49 | ( ( ( restrict @ Va @ ( clm @ Ts2 ) @ C2 )
% 2.57/1.49 = bot_bot_nat_int )
% 2.57/1.49 & ( ( restrict @ Va @ ( res @ Ts2 ) @ C2 )
% 2.57/1.49 = bot_bot_nat_int ) ) )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U ) ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ U ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ! [C2: cars] :
% 2.57/1.49 ( ( ( real_length @ ( len @ regular_regular @ U @ Ts2 @ C2 ) )
% 2.57/1.49 = zero_zero_real )
% 2.57/1.49 | ( ( ( restrict @ U @ ( clm @ Ts2 ) @ C2 )
% 2.57/1.49 = bot_bot_nat_int )
% 2.57/1.49 & ( ( restrict @ U @ ( res @ Ts2 ) @ C2 )
% 2.57/1.49 = bot_bot_nat_int ) ) ) )
% 2.57/1.49 => ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ! [C4: cars] :
% 2.57/1.49 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C4 ) )
% 2.57/1.49 = zero_zero_real )
% 2.57/1.49 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C4 )
% 2.57/1.49 = bot_bot_nat_int )
% 2.57/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C4 )
% 2.57/1.49 = bot_bot_nat_int ) ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_64_local_Ohmlsl_Owidth__free,axiom,
% 2.57/1.49 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ! [C2: cars] :
% 2.57/1.49 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 2.57/1.49 = zero_zero_real )
% 2.57/1.49 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 2.57/1.49 = bot_bot_nat_int )
% 2.57/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 2.57/1.49 = bot_bot_nat_int ) ) ) )
% 2.57/1.49 => ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_65_local_Ohmlsl_Ores__not__free,axiom,
% 2.57/1.49 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ? [X4: cars] :
% 2.57/1.49 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ X4 )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ X4 )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 => ~ ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ! [C2: cars] :
% 2.57/1.49 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 2.57/1.49 = zero_zero_real )
% 2.57/1.49 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 2.57/1.49 = bot_bot_nat_int )
% 2.57/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 2.57/1.49 = bot_bot_nat_int ) ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_66_local_Ohmlsl_Ofree__no__res,axiom,
% 2.57/1.49 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ! [C2: cars] :
% 2.57/1.49 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 2.57/1.49 = zero_zero_real )
% 2.57/1.49 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 2.57/1.49 = bot_bot_nat_int )
% 2.57/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 2.57/1.49 = bot_bot_nat_int ) ) ) )
% 2.57/1.49 => ~ ? [X: cars] :
% 2.57/1.49 ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ X )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_67_local_Ohmlsl_Ofree__no__clm,axiom,
% 2.57/1.49 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ! [C2: cars] :
% 2.57/1.49 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 2.57/1.49 = zero_zero_real )
% 2.57/1.49 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 2.57/1.49 = bot_bot_nat_int )
% 2.57/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 2.57/1.49 = bot_bot_nat_int ) ) ) )
% 2.57/1.49 => ~ ? [X: cars] :
% 2.57/1.49 ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ X )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( clm @ Ts2 ) @ X )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_68_local_Ohmlsl_Ofree__ge__zero,axiom,
% 2.57/1.49 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ! [C2: cars] :
% 2.57/1.49 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 2.57/1.49 = zero_zero_real )
% 2.57/1.49 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 2.57/1.49 = bot_bot_nat_int )
% 2.57/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 2.57/1.49 = bot_bot_nat_int ) ) ) )
% 2.57/1.49 => ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_69_local_Ohmlsl_Oclm__not__free,axiom,
% 2.57/1.49 ! [Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ? [X4: cars] :
% 2.57/1.49 ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ X4 )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( clm @ Ts2 ) @ X4 )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 => ~ ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ! [C2: cars] :
% 2.57/1.49 ( ( ( real_length @ ( len @ regular_regular @ V @ Ts2 @ C2 ) )
% 2.57/1.49 = zero_zero_real )
% 2.57/1.49 | ( ( ( restrict @ V @ ( clm @ Ts2 ) @ C2 )
% 2.57/1.49 = bot_bot_nat_int )
% 2.57/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C2 )
% 2.57/1.49 = bot_bot_nat_int ) ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_70_hmlsl__regular_Obackwards__wdc__res__stab,axiom,
% 2.57/1.49 ! [Ts: traffic,D2: cars,Ts5: traffic,V2: view_e774982825t_unit,C: cars] :
% 2.57/1.49 ( ( ( withdraw_claim @ Ts @ D2 @ Ts5 )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V2 @ Ts5 @ C )
% 2.57/1.49 = ( ext_Product_unit @ V2 ) )
% 2.57/1.49 & ( ( restrict @ V2 @ ( res @ Ts5 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V2 ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 => ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V2 @ Ts @ C )
% 2.57/1.49 = ( ext_Product_unit @ V2 ) )
% 2.57/1.49 & ( ( restrict @ V2 @ ( res @ Ts ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V2 ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 2.57/1.49 = one_one_nat ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_71_view_Ohorizontal__chop__non__empty,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit] :
% 2.57/1.49 ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 2.57/1.49 => ? [U2: view_e774982825t_unit,W2: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V2 @ U2 @ W2 )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ U2 ) ) )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ W2 ) ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_72_not__gr__zero,axiom,
% 2.57/1.49 ! [N: nat] :
% 2.57/1.49 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 2.57/1.49 = ( N = zero_zero_nat ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_73_le__zero__eq,axiom,
% 2.57/1.49 ! [N: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 2.57/1.49 = ( N = zero_zero_nat ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_74_hmlsl__regular_Obackwards__c__res__stab,axiom,
% 2.57/1.49 ! [Ts: traffic,D2: cars,N: nat,Ts5: traffic,V2: view_e774982825t_unit,C: cars] :
% 2.57/1.49 ( ( ( create_claim @ Ts @ D2 @ N @ Ts5 )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V2 @ Ts5 @ C )
% 2.57/1.49 = ( ext_Product_unit @ V2 ) )
% 2.57/1.49 & ( ( restrict @ V2 @ ( res @ Ts5 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V2 ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 => ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V2 @ Ts @ C )
% 2.57/1.49 = ( ext_Product_unit @ V2 ) )
% 2.57/1.49 & ( ( restrict @ V2 @ ( res @ Ts ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V2 ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 2.57/1.49 = one_one_nat ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_75_hmlsl__regular_Obackwards__wdr__res__stab,axiom,
% 2.57/1.49 ! [Ts: traffic,D2: cars,N: nat,Ts5: traffic,V2: view_e774982825t_unit,C: cars] :
% 2.57/1.49 ( ( ( withdraw_reservation @ Ts @ D2 @ N @ Ts5 )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V2 @ Ts5 @ C )
% 2.57/1.49 = ( ext_Product_unit @ V2 ) )
% 2.57/1.49 & ( ( restrict @ V2 @ ( res @ Ts5 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V2 ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 => ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V2 @ Ts @ C )
% 2.57/1.49 = ( ext_Product_unit @ V2 ) )
% 2.57/1.49 & ( ( restrict @ V2 @ ( res @ Ts ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V2 ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 2.57/1.49 = one_one_nat ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_76_hmlsl_Olen__sub__int,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,Ts: traffic,C: cars] : ( ord_less_eq_real_int @ ( len @ regular_regular @ V2 @ Ts @ C ) @ ( ext_Product_unit @ V2 ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_77_view_Overtical__chop__width__mon,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,V1: view_e774982825t_unit,V22: view_e774982825t_unit,V33: view_e774982825t_unit,V42: view_e774982825t_unit,X3: nat] :
% 2.57/1.49 ( ( ( vchop @ V2 @ V1 @ V22 )
% 2.57/1.49 & ( vchop @ V22 @ V33 @ V42 )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V33 ) )
% 2.57/1.49 = X3 ) )
% 2.57/1.49 => ( ord_less_eq_nat @ X3 @ ( nat_card @ ( lan_Product_unit @ V2 ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_78_zero__reorient,axiom,
% 2.57/1.49 ! [X3: real] :
% 2.57/1.49 ( ( zero_zero_real = X3 )
% 2.57/1.49 = ( X3 = zero_zero_real ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_79_zero__reorient,axiom,
% 2.57/1.49 ! [X3: nat] :
% 2.57/1.49 ( ( zero_zero_nat = X3 )
% 2.57/1.49 = ( X3 = zero_zero_nat ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_80_view_Overtical__chop__singleton,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( vchop @ V2 @ U4 @ W3 )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 => ( ( ( nat_card @ ( lan_Product_unit @ U4 ) )
% 2.57/1.49 = zero_zero_nat )
% 2.57/1.49 | ( ( nat_card @ ( lan_Product_unit @ W3 ) )
% 2.57/1.49 = zero_zero_nat ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_81_one__reorient,axiom,
% 2.57/1.49 ! [X3: nat] :
% 2.57/1.49 ( ( one_one_nat = X3 )
% 2.57/1.49 = ( X3 = one_one_nat ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_82_view_Ohorizontal__chop1,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit] :
% 2.57/1.49 ? [U2: view_e774982825t_unit,X_1: view_e774982825t_unit] : ( hchop @ V2 @ U2 @ X_1 ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_83_view_Ohorizontal__chop__assoc1,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,V1: view_e774982825t_unit,V22: view_e774982825t_unit,V33: view_e774982825t_unit,V42: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( hchop @ V2 @ V1 @ V22 )
% 2.57/1.49 & ( hchop @ V22 @ V33 @ V42 ) )
% 2.57/1.49 => ? [V4: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V2 @ V4 @ V42 )
% 2.57/1.49 & ( hchop @ V4 @ V1 @ V33 ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_84_view_Ohorizontal__chop__assoc2,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,V1: view_e774982825t_unit,V22: view_e774982825t_unit,V33: view_e774982825t_unit,V42: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( hchop @ V2 @ V1 @ V22 )
% 2.57/1.49 & ( hchop @ V1 @ V33 @ V42 ) )
% 2.57/1.49 => ? [V4: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V2 @ V33 @ V4 )
% 2.57/1.49 & ( hchop @ V4 @ V42 @ V22 ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_85_view_Ohorizontal__chop__empty__left,axiom,
% 2.57/1.49 ! [V: view_e774982825t_unit] :
% 2.57/1.49 ? [U2: view_e774982825t_unit] : ( hchop @ V @ U2 @ V ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_86_view_Ohorizontal__chop__empty__right,axiom,
% 2.57/1.49 ! [V: view_e774982825t_unit] :
% 2.57/1.49 ? [X_1: view_e774982825t_unit] : ( hchop @ V @ V @ X_1 ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_87_view_Overtical__chop1,axiom,
% 2.57/1.49 ! [V: view_e774982825t_unit] :
% 2.57/1.49 ? [U2: view_e774982825t_unit,X_1: view_e774982825t_unit] : ( vchop @ V @ U2 @ X_1 ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_88_view_Overtical__chop__assoc1,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,V1: view_e774982825t_unit,V22: view_e774982825t_unit,V33: view_e774982825t_unit,V42: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( vchop @ V2 @ V1 @ V22 )
% 2.57/1.49 & ( vchop @ V22 @ V33 @ V42 ) )
% 2.57/1.49 => ? [V4: view_e774982825t_unit] :
% 2.57/1.49 ( ( vchop @ V2 @ V4 @ V42 )
% 2.57/1.49 & ( vchop @ V4 @ V1 @ V33 ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_89_view_Overtical__chop__assoc2,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,V1: view_e774982825t_unit,V22: view_e774982825t_unit,V33: view_e774982825t_unit,V42: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( vchop @ V2 @ V1 @ V22 )
% 2.57/1.49 & ( vchop @ V1 @ V33 @ V42 ) )
% 2.57/1.49 => ? [V4: view_e774982825t_unit] :
% 2.57/1.49 ( ( vchop @ V2 @ V33 @ V4 )
% 2.57/1.49 & ( vchop @ V4 @ V42 @ V22 ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_90_view_Overtical__chop__empty__up,axiom,
% 2.57/1.49 ! [V: view_e774982825t_unit] :
% 2.57/1.49 ? [U2: view_e774982825t_unit] : ( vchop @ V @ U2 @ V ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_91_view_Overtical__chop__empty__down,axiom,
% 2.57/1.49 ! [V: view_e774982825t_unit] :
% 2.57/1.49 ? [X_1: view_e774982825t_unit] : ( vchop @ V @ V @ X_1 ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_92_zero__le,axiom,
% 2.57/1.49 ! [X3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X3 ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_93_zero__less__iff__neq__zero,axiom,
% 2.57/1.49 ! [N: nat] :
% 2.57/1.49 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.57/1.49 = ( N != zero_zero_nat ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_94_gr__implies__not__zero,axiom,
% 2.57/1.49 ! [M: nat,N: nat] :
% 2.57/1.49 ( ( ord_less_nat @ M @ N )
% 2.57/1.49 => ( N != zero_zero_nat ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_95_not__less__zero,axiom,
% 2.57/1.49 ! [N: nat] :
% 2.57/1.49 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_96_gr__zeroI,axiom,
% 2.57/1.49 ! [N: nat] :
% 2.57/1.49 ( ( N != zero_zero_nat )
% 2.57/1.49 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_97_view_Ohorizontal__chop__leq2,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V2 @ U4 @ W3 )
% 2.57/1.49 => ( ord_le461438217t_unit @ W3 @ V2 ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_98_view_Ohorizontal__chop__leq1,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V2 @ U4 @ W3 )
% 2.57/1.49 => ( ord_le461438217t_unit @ U4 @ V2 ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_99_view_Overtical__chop__leq2,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit] :
% 2.57/1.49 ( ( vchop @ V2 @ U4 @ W3 )
% 2.57/1.49 => ( ord_le461438217t_unit @ W3 @ V2 ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_100_view_Overtical__chop__leq1,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit] :
% 2.57/1.49 ( ( vchop @ V2 @ U4 @ W3 )
% 2.57/1.49 => ( ord_le461438217t_unit @ U4 @ V2 ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_101_view_Ohorizontal__chop__width__stable,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V2 @ U4 @ W3 )
% 2.57/1.49 => ( ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 2.57/1.49 = ( nat_card @ ( lan_Product_unit @ U4 ) ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 2.57/1.49 = ( nat_card @ ( lan_Product_unit @ W3 ) ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_102_view_Overtical__chop__length__stable,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit] :
% 2.57/1.49 ( ( vchop @ V2 @ U4 @ W3 )
% 2.57/1.49 => ( ( ( real_length @ ( ext_Product_unit @ V2 ) )
% 2.57/1.49 = ( real_length @ ( ext_Product_unit @ U4 ) ) )
% 2.57/1.49 & ( ( real_length @ ( ext_Product_unit @ V2 ) )
% 2.57/1.49 = ( real_length @ ( ext_Product_unit @ W3 ) ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_103_view_Osomewhere__leq,axiom,
% 2.57/1.49 ( ord_le461438217t_unit
% 2.57/1.49 = ( ^ [V5: view_e774982825t_unit,V6: view_e774982825t_unit] :
% 2.57/1.49 ? [V13: view_e774982825t_unit,V24: view_e774982825t_unit,V34: view_e774982825t_unit,Vl: view_e774982825t_unit,Vr: view_e774982825t_unit,Vu: view_e774982825t_unit,Vd: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V6 @ Vl @ V13 )
% 2.57/1.49 & ( hchop @ V13 @ V24 @ Vr )
% 2.57/1.49 & ( vchop @ V24 @ Vd @ V34 )
% 2.57/1.49 & ( vchop @ V34 @ V5 @ Vu ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_104_hmlsl_Oview__leq__len__leq,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,V3: view_e774982825t_unit,Ts: traffic,C: cars] :
% 2.57/1.49 ( ( ( ord_less_eq_real_int @ ( ext_Product_unit @ V2 ) @ ( ext_Product_unit @ V3 ) )
% 2.57/1.49 & ( ( own_Product_unit @ V2 )
% 2.57/1.49 = ( own_Product_unit @ V3 ) )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( len @ regular_regular @ V2 @ Ts @ C ) ) ) )
% 2.57/1.49 => ( ord_less_eq_real_int @ ( len @ regular_regular @ V2 @ Ts @ C ) @ ( len @ regular_regular @ V3 @ Ts @ C ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_105_restriction_Orestriction__card__somewhere__mon,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,Vl2: view_e774982825t_unit,V1: view_e774982825t_unit,V22: view_e774982825t_unit,Vr2: view_e774982825t_unit,Vu2: view_e774982825t_unit,V33: view_e774982825t_unit,V3: view_e774982825t_unit,Vd2: view_e774982825t_unit,F: cars > nat_int,C: cars] :
% 2.57/1.49 ( ( ( hchop @ V2 @ Vl2 @ V1 )
% 2.57/1.49 & ( hchop @ V1 @ V22 @ Vr2 )
% 2.57/1.49 & ( vchop @ V22 @ Vu2 @ V33 )
% 2.57/1.49 & ( vchop @ V33 @ V3 @ Vd2 )
% 2.57/1.49 & ( ( nat_card @ ( restrict @ V3 @ F @ C ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 => ( ord_less_eq_nat @ one_one_nat @ ( nat_card @ ( restrict @ V2 @ F @ C ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_106_hmlsl__regular_Obackwards__res__act,axiom,
% 2.57/1.49 ! [Ts: traffic,C: cars,Ts5: traffic,V2: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( create_reservation @ Ts @ C @ Ts5 )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V2 @ Ts5 @ C )
% 2.57/1.49 = ( ext_Product_unit @ V2 ) )
% 2.57/1.49 & ( ( restrict @ V2 @ ( res @ Ts5 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V2 ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 => ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V2 @ Ts @ C )
% 2.57/1.49 = ( ext_Product_unit @ V2 ) )
% 2.57/1.49 & ( ( restrict @ V2 @ ( res @ Ts ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V2 ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 | ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V2 @ Ts @ C )
% 2.57/1.49 = ( ext_Product_unit @ V2 ) )
% 2.57/1.49 & ( ( restrict @ V2 @ ( clm @ Ts ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V2 ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 2.57/1.49 = one_one_nat ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_107_hmlsl__regular_Oreservation2,axiom,
% 2.57/1.49 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ! [Ts3: traffic] :
% 2.57/1.49 ( ( create_reservation @ Ts2 @ C @ Ts3 )
% 2.57/1.49 => ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts3 @ C )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( res @ Ts3 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) ) )
% 2.57/1.49 => ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 | ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_108_hmlsl__regular_Oreservation1,axiom,
% 2.57/1.49 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 | ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) ) )
% 2.57/1.49 => ! [Ts4: traffic] :
% 2.57/1.49 ( ( create_reservation @ Ts2 @ C @ Ts4 )
% 2.57/1.49 => ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts4 @ C )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( res @ Ts4 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_109_hmlsl__regular_Oreservation,axiom,
% 2.57/1.49 ! [C: cars,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ! [Ts6: traffic] :
% 2.57/1.49 ( ( create_reservation @ Ts2 @ C @ Ts6 )
% 2.57/1.49 => ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts6 @ C )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( res @ Ts6 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) ) ) )
% 2.57/1.49 = ( ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( res @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 | ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V @ Ts2 @ C )
% 2.57/1.49 = ( ext_Product_unit @ V ) )
% 2.57/1.49 & ( ( restrict @ V @ ( clm @ Ts2 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = one_one_nat ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_110_hmlsl_Oext__eq__len__eq,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,V3: view_e774982825t_unit,Ts: traffic,C: cars] :
% 2.57/1.49 ( ( ( ( ext_Product_unit @ V2 )
% 2.57/1.49 = ( ext_Product_unit @ V3 ) )
% 2.57/1.49 & ( ( own_Product_unit @ V2 )
% 2.57/1.49 = ( own_Product_unit @ V3 ) ) )
% 2.57/1.49 => ( ( len @ regular_regular @ V2 @ Ts @ C )
% 2.57/1.49 = ( len @ regular_regular @ V3 @ Ts @ C ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_111_view_Ohorizontal__chop__own__trans,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit] :
% 2.57/1.49 ( ( hchop @ V2 @ U4 @ W3 )
% 2.57/1.49 => ( ( own_Product_unit @ U4 )
% 2.57/1.49 = ( own_Product_unit @ W3 ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_112_view_Overtical__chop__own__trans,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit] :
% 2.57/1.49 ( ( vchop @ V2 @ U4 @ W3 )
% 2.57/1.49 => ( ( own_Product_unit @ U4 )
% 2.57/1.49 = ( own_Product_unit @ W3 ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_113_restriction_Orestrict__subseteq,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,F: cars > nat_int,C: cars] : ( ord_less_eq_nat_int @ ( restrict @ V2 @ F @ C ) @ ( F @ C ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_114_restriction_Orestrict__view,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,F: cars > nat_int,C: cars] : ( ord_less_eq_nat_int @ ( restrict @ V2 @ F @ C ) @ ( lan_Product_unit @ V2 ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_115_restriction_Orestrict__res,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,Ts: traffic,C: cars] : ( ord_less_eq_nat_int @ ( restrict @ V2 @ ( res @ Ts ) @ C ) @ ( res @ Ts @ C ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_116_restriction_Orestriction__stable,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit,F: cars > nat_int,C: cars] :
% 2.57/1.49 ( ( hchop @ V2 @ U4 @ W3 )
% 2.57/1.49 => ( ( restrict @ U4 @ F @ C )
% 2.57/1.49 = ( restrict @ W3 @ F @ C ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_117_restriction_Orestriction__stable1,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit,F: cars > nat_int,C: cars] :
% 2.57/1.49 ( ( hchop @ V2 @ U4 @ W3 )
% 2.57/1.49 => ( ( restrict @ V2 @ F @ C )
% 2.57/1.49 = ( restrict @ U4 @ F @ C ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_118_restriction_Orestriction__stable2,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit,F: cars > nat_int,C: cars] :
% 2.57/1.49 ( ( hchop @ V2 @ U4 @ W3 )
% 2.57/1.49 => ( ( restrict @ V2 @ F @ C )
% 2.57/1.49 = ( restrict @ W3 @ F @ C ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_119_restriction_Orestrict__clm,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,Ts: traffic,C: cars] : ( ord_less_eq_nat_int @ ( restrict @ V2 @ ( clm @ Ts ) @ C ) @ ( clm @ Ts @ C ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_120_restriction_Orestriction__mon2,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit,F: cars > nat_int,C: cars] :
% 2.57/1.49 ( ( vchop @ V2 @ U4 @ W3 )
% 2.57/1.49 => ( ord_less_eq_nat_int @ ( restrict @ W3 @ F @ C ) @ ( restrict @ V2 @ F @ C ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_121_restriction_Orestriction__mon1,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit,F: cars > nat_int,C: cars] :
% 2.57/1.49 ( ( vchop @ V2 @ U4 @ W3 )
% 2.57/1.49 => ( ord_less_eq_nat_int @ ( restrict @ U4 @ F @ C ) @ ( restrict @ V2 @ F @ C ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_122_restriction_Orestriction__eq__view__card,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,F: cars > nat_int,C: cars] :
% 2.57/1.49 ( ( ( restrict @ V2 @ F @ C )
% 2.57/1.49 = ( lan_Product_unit @ V2 ) )
% 2.57/1.49 => ( ( nat_card @ ( restrict @ V2 @ F @ C ) )
% 2.57/1.49 = ( nat_card @ ( lan_Product_unit @ V2 ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_123_restriction_Orestrict__eq__lan__subs,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,F: cars > nat_int,C: cars] :
% 2.57/1.49 ( ( ( ( nat_card @ ( restrict @ V2 @ F @ C ) )
% 2.57/1.49 = ( nat_card @ ( lan_Product_unit @ V2 ) ) )
% 2.57/1.49 & ( ord_less_eq_nat_int @ ( restrict @ V2 @ F @ C ) @ ( lan_Product_unit @ V2 ) ) )
% 2.57/1.49 => ( ( restrict @ V2 @ F @ C )
% 2.57/1.49 = ( lan_Product_unit @ V2 ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_124_restriction_Orestriction__card__mon1,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit,F: cars > nat_int,C: cars] :
% 2.57/1.49 ( ( vchop @ V2 @ U4 @ W3 )
% 2.57/1.49 => ( ord_less_eq_nat @ ( nat_card @ ( restrict @ U4 @ F @ C ) ) @ ( nat_card @ ( restrict @ V2 @ F @ C ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_125_restriction_Orestriction__card__mon2,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,U4: view_e774982825t_unit,W3: view_e774982825t_unit,F: cars > nat_int,C: cars] :
% 2.57/1.49 ( ( vchop @ V2 @ U4 @ W3 )
% 2.57/1.49 => ( ord_less_eq_nat @ ( nat_card @ ( restrict @ W3 @ F @ C ) ) @ ( nat_card @ ( restrict @ V2 @ F @ C ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_126_restriction_Orestriction__clm__leq__one,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,Ts: traffic,C: cars] : ( ord_less_eq_nat @ ( nat_card @ ( restrict @ V2 @ ( clm @ Ts ) @ C ) ) @ one_one_nat ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_127_restriction_Orestriction__card__mon__trans,axiom,
% 2.57/1.49 ! [V2: view_e774982825t_unit,V1: view_e774982825t_unit,V22: view_e774982825t_unit,V33: view_e774982825t_unit,V42: view_e774982825t_unit,F: cars > nat_int,C: cars] :
% 2.57/1.49 ( ( ( vchop @ V2 @ V1 @ V22 )
% 2.57/1.49 & ( vchop @ V22 @ V33 @ V42 )
% 2.57/1.49 & ( ( nat_card @ ( restrict @ V33 @ F @ C ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 => ( ord_less_eq_nat @ one_one_nat @ ( nat_card @ ( restrict @ V2 @ F @ C ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_128_hmlsl__regular_Obackwards__res__stab,axiom,
% 2.57/1.49 ! [Ts: traffic,D2: cars,Ts5: traffic,C: cars,V2: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( create_reservation @ Ts @ D2 @ Ts5 )
% 2.57/1.49 & ( D2 != C )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V2 @ Ts5 @ C )
% 2.57/1.49 = ( ext_Product_unit @ V2 ) )
% 2.57/1.49 & ( ( restrict @ V2 @ ( res @ Ts5 ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V2 ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 => ( ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V2 ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V2 @ Ts @ C )
% 2.57/1.49 = ( ext_Product_unit @ V2 ) )
% 2.57/1.49 & ( ( restrict @ V2 @ ( res @ Ts ) @ C )
% 2.57/1.49 = ( lan_Product_unit @ V2 ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V2 ) )
% 2.57/1.49 = one_one_nat ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_129_less__one,axiom,
% 2.57/1.49 ! [N: nat] :
% 2.57/1.49 ( ( ord_less_nat @ N @ one_one_nat )
% 2.57/1.49 = ( N = zero_zero_nat ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_130_le0,axiom,
% 2.57/1.49 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_131_bot__nat__0_Oextremum,axiom,
% 2.57/1.49 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_132_card__non__empty__geq__one,axiom,
% 2.57/1.49 ! [I: nat_int] :
% 2.57/1.49 ( ( I != bot_bot_nat_int )
% 2.57/1.49 = ( ord_less_eq_nat @ one_one_nat @ ( nat_card @ I ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_133_bot__nat__0_Onot__eq__extremum,axiom,
% 2.57/1.49 ! [A: nat] :
% 2.57/1.49 ( ( A != zero_zero_nat )
% 2.57/1.49 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_134_less__nat__zero__code,axiom,
% 2.57/1.49 ! [N: nat] :
% 2.57/1.49 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_135_neq0__conv,axiom,
% 2.57/1.49 ! [N: nat] :
% 2.57/1.49 ( ( N != zero_zero_nat )
% 2.57/1.49 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_136_linorder__neqE__nat,axiom,
% 2.57/1.49 ! [X3: nat,Y2: nat] :
% 2.57/1.49 ( ( X3 != Y2 )
% 2.57/1.49 => ( ~ ( ord_less_nat @ X3 @ Y2 )
% 2.57/1.49 => ( ord_less_nat @ Y2 @ X3 ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_137_infinite__descent,axiom,
% 2.57/1.49 ! [P: nat > $o,N: nat] :
% 2.57/1.49 ( ! [N2: nat] :
% 2.57/1.49 ( ~ ( P @ N2 )
% 2.57/1.49 => ? [M2: nat] :
% 2.57/1.49 ( ( ord_less_nat @ M2 @ N2 )
% 2.57/1.49 & ~ ( P @ M2 ) ) )
% 2.57/1.49 => ( P @ N ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_138_nat__less__induct,axiom,
% 2.57/1.49 ! [P: nat > $o,N: nat] :
% 2.57/1.49 ( ! [N2: nat] :
% 2.57/1.49 ( ! [M2: nat] :
% 2.57/1.49 ( ( ord_less_nat @ M2 @ N2 )
% 2.57/1.49 => ( P @ M2 ) )
% 2.57/1.49 => ( P @ N2 ) )
% 2.57/1.49 => ( P @ N ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_139_less__irrefl__nat,axiom,
% 2.57/1.49 ! [N: nat] :
% 2.57/1.49 ~ ( ord_less_nat @ N @ N ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_140_less__not__refl3,axiom,
% 2.57/1.49 ! [S: nat,T: nat] :
% 2.57/1.49 ( ( ord_less_nat @ S @ T )
% 2.57/1.49 => ( S != T ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_141_less__not__refl2,axiom,
% 2.57/1.49 ! [N: nat,M: nat] :
% 2.57/1.49 ( ( ord_less_nat @ N @ M )
% 2.57/1.49 => ( M != N ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_142_less__not__refl,axiom,
% 2.57/1.49 ! [N: nat] :
% 2.57/1.49 ~ ( ord_less_nat @ N @ N ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_143_nat__neq__iff,axiom,
% 2.57/1.49 ! [M: nat,N: nat] :
% 2.57/1.49 ( ( M != N )
% 2.57/1.49 = ( ( ord_less_nat @ M @ N )
% 2.57/1.49 | ( ord_less_nat @ N @ M ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_144_bot__nat__0_Oextremum__strict,axiom,
% 2.57/1.49 ! [A: nat] :
% 2.57/1.49 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_145_infinite__descent0,axiom,
% 2.57/1.49 ! [P: nat > $o,N: nat] :
% 2.57/1.49 ( ( P @ zero_zero_nat )
% 2.57/1.49 => ( ! [N2: nat] :
% 2.57/1.49 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 2.57/1.49 => ( ~ ( P @ N2 )
% 2.57/1.49 => ? [M2: nat] :
% 2.57/1.49 ( ( ord_less_nat @ M2 @ N2 )
% 2.57/1.49 & ~ ( P @ M2 ) ) ) )
% 2.57/1.49 => ( P @ N ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_146_gr__implies__not0,axiom,
% 2.57/1.49 ! [M: nat,N: nat] :
% 2.57/1.49 ( ( ord_less_nat @ M @ N )
% 2.57/1.49 => ( N != zero_zero_nat ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_147_less__zeroE,axiom,
% 2.57/1.49 ! [N: nat] :
% 2.57/1.49 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_148_not__less0,axiom,
% 2.57/1.49 ! [N: nat] :
% 2.57/1.49 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_149_not__gr0,axiom,
% 2.57/1.49 ! [N: nat] :
% 2.57/1.49 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 2.57/1.49 = ( N = zero_zero_nat ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_150_gr0I,axiom,
% 2.57/1.49 ! [N: nat] :
% 2.57/1.49 ( ( N != zero_zero_nat )
% 2.57/1.49 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_151_less__mono__imp__le__mono,axiom,
% 2.57/1.49 ! [F: nat > nat,I: nat,J: nat] :
% 2.57/1.49 ( ! [I2: nat,J2: nat] :
% 2.57/1.49 ( ( ord_less_nat @ I2 @ J2 )
% 2.57/1.49 => ( ord_less_nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
% 2.57/1.49 => ( ( ord_less_eq_nat @ I @ J )
% 2.57/1.49 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_152_le__neq__implies__less,axiom,
% 2.57/1.49 ! [M: nat,N: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ M @ N )
% 2.57/1.49 => ( ( M != N )
% 2.57/1.49 => ( ord_less_nat @ M @ N ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_153_Nat_Oex__has__greatest__nat,axiom,
% 2.57/1.49 ! [P: nat > $o,K: nat,B: nat] :
% 2.57/1.49 ( ( P @ K )
% 2.57/1.49 => ( ! [Y3: nat] :
% 2.57/1.49 ( ( P @ Y3 )
% 2.57/1.49 => ( ord_less_eq_nat @ Y3 @ B ) )
% 2.57/1.49 => ? [X4: nat] :
% 2.57/1.49 ( ( P @ X4 )
% 2.57/1.49 & ! [Y4: nat] :
% 2.57/1.49 ( ( P @ Y4 )
% 2.57/1.49 => ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_154_less__or__eq__imp__le,axiom,
% 2.57/1.49 ! [M: nat,N: nat] :
% 2.57/1.49 ( ( ( ord_less_nat @ M @ N )
% 2.57/1.49 | ( M = N ) )
% 2.57/1.49 => ( ord_less_eq_nat @ M @ N ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_155_le__eq__less__or__eq,axiom,
% 2.57/1.49 ( ord_less_eq_nat
% 2.57/1.49 = ( ^ [M3: nat,N3: nat] :
% 2.57/1.49 ( ( ord_less_nat @ M3 @ N3 )
% 2.57/1.49 | ( M3 = N3 ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_156_less__imp__le__nat,axiom,
% 2.57/1.49 ! [M: nat,N: nat] :
% 2.57/1.49 ( ( ord_less_nat @ M @ N )
% 2.57/1.49 => ( ord_less_eq_nat @ M @ N ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_157_nat__le__linear,axiom,
% 2.57/1.49 ! [M: nat,N: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ M @ N )
% 2.57/1.49 | ( ord_less_eq_nat @ N @ M ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_158_nat__less__le,axiom,
% 2.57/1.49 ( ord_less_nat
% 2.57/1.49 = ( ^ [M3: nat,N3: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ M3 @ N3 )
% 2.57/1.49 & ( M3 != N3 ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_159_le__antisym,axiom,
% 2.57/1.49 ! [M: nat,N: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ M @ N )
% 2.57/1.49 => ( ( ord_less_eq_nat @ N @ M )
% 2.57/1.49 => ( M = N ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_160_eq__imp__le,axiom,
% 2.57/1.49 ! [M: nat,N: nat] :
% 2.57/1.49 ( ( M = N )
% 2.57/1.49 => ( ord_less_eq_nat @ M @ N ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_161_le__trans,axiom,
% 2.57/1.49 ! [I: nat,J: nat,K: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ I @ J )
% 2.57/1.49 => ( ( ord_less_eq_nat @ J @ K )
% 2.57/1.49 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_162_le__refl,axiom,
% 2.57/1.49 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_163_card__subset__less,axiom,
% 2.57/1.49 ! [I: nat_int,I3: nat_int] :
% 2.57/1.49 ( ( ord_less_nat_int @ I @ I3 )
% 2.57/1.49 => ( ord_less_nat @ ( nat_card @ I ) @ ( nat_card @ I3 ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_164_bot__nat__0_Oextremum__uniqueI,axiom,
% 2.57/1.49 ! [A: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 2.57/1.49 => ( A = zero_zero_nat ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_165_bot__nat__0_Oextremum__unique,axiom,
% 2.57/1.49 ! [A: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 2.57/1.49 = ( A = zero_zero_nat ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_166_ex__least__nat__le,axiom,
% 2.57/1.49 ! [P: nat > $o,N: nat] :
% 2.57/1.49 ( ( P @ N )
% 2.57/1.49 => ( ~ ( P @ zero_zero_nat )
% 2.57/1.49 => ? [K2: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ K2 @ N )
% 2.57/1.49 & ! [I4: nat] :
% 2.57/1.49 ( ( ord_less_nat @ I4 @ K2 )
% 2.57/1.49 => ~ ( P @ I4 ) )
% 2.57/1.49 & ( P @ K2 ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_167_le__0__eq,axiom,
% 2.57/1.49 ! [N: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 2.57/1.49 = ( N = zero_zero_nat ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_168_less__eq__nat_Osimps_I1_J,axiom,
% 2.57/1.49 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_169_card__subset__le,axiom,
% 2.57/1.49 ! [I: nat_int,I3: nat_int] :
% 2.57/1.49 ( ( ord_less_eq_nat_int @ I @ I3 )
% 2.57/1.49 => ( ord_less_eq_nat @ ( nat_card @ I ) @ ( nat_card @ I3 ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_170_card__empty__zero,axiom,
% 2.57/1.49 ( ( nat_card @ bot_bot_nat_int )
% 2.57/1.49 = zero_zero_nat ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_171_local_Ohmlsl_Owidth__ge,axiom,
% 2.57/1.49 ! [V: view_e774982825t_unit] :
% 2.57/1.49 ( ? [Va: view_e774982825t_unit] :
% 2.57/1.49 ( ? [X_12: view_e774982825t_unit] : ( vchop @ V @ Va @ X_12 )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ Va ) )
% 2.57/1.49 = ( plus_plus_nat @ zero_zero_nat @ one_one_nat ) ) )
% 2.57/1.49 => ( ord_less_nat @ zero_zero_nat @ ( nat_card @ ( lan_Product_unit @ V ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_172_traffic_Ocreate__res__subseteq2,axiom,
% 2.57/1.49 ! [Ts: traffic,C: cars,Ts5: traffic] :
% 2.57/1.49 ( ( create_reservation @ Ts @ C @ Ts5 )
% 2.57/1.49 => ( ord_less_eq_nat_int @ ( clm @ Ts @ C ) @ ( res @ Ts5 @ C ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_173_traffic_OatMostOneClm,axiom,
% 2.57/1.49 ! [Ts: traffic,C: cars] : ( ord_less_eq_nat @ ( nat_card @ ( clm @ Ts @ C ) ) @ one_one_nat ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_174_traffic_OatLeastOneRes,axiom,
% 2.57/1.49 ! [Ts: traffic,C: cars] : ( ord_less_eq_nat @ one_one_nat @ ( nat_card @ ( res @ Ts @ C ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_175_local_Ohmlsl_Owidth__add1,axiom,
% 2.57/1.49 ! [X3: nat,Y2: nat,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ? [Va: view_e774982825t_unit,U: view_e774982825t_unit] :
% 2.57/1.49 ( ( vchop @ V @ Va @ U )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ Va ) )
% 2.57/1.49 = X3 )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ U ) )
% 2.57/1.49 = Y2 ) )
% 2.57/1.49 => ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = ( plus_plus_nat @ X3 @ Y2 ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_176_local_Ohmlsl_Owidth__add2,axiom,
% 2.57/1.49 ! [X3: nat,Y2: nat,Ts2: traffic,V: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( nat_card @ ( lan_Product_unit @ V ) )
% 2.57/1.49 = ( plus_plus_nat @ X3 @ Y2 ) )
% 2.57/1.49 => ? [Va2: view_e774982825t_unit,U2: view_e774982825t_unit] :
% 2.57/1.49 ( ( vchop @ V @ Va2 @ U2 )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ Va2 ) )
% 2.57/1.49 = X3 )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ U2 ) )
% 2.57/1.49 = Y2 ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_177_add__left__cancel,axiom,
% 2.57/1.49 ! [A: real,B: real,C: real] :
% 2.57/1.49 ( ( ( plus_plus_real @ A @ B )
% 2.57/1.49 = ( plus_plus_real @ A @ C ) )
% 2.57/1.49 = ( B = C ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_178_add__left__cancel,axiom,
% 2.57/1.49 ! [A: nat,B: nat,C: nat] :
% 2.57/1.49 ( ( ( plus_plus_nat @ A @ B )
% 2.57/1.49 = ( plus_plus_nat @ A @ C ) )
% 2.57/1.49 = ( B = C ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_179_add__right__cancel,axiom,
% 2.57/1.49 ! [B: real,A: real,C: real] :
% 2.57/1.49 ( ( ( plus_plus_real @ B @ A )
% 2.57/1.49 = ( plus_plus_real @ C @ A ) )
% 2.57/1.49 = ( B = C ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_180_add__right__cancel,axiom,
% 2.57/1.49 ! [B: nat,A: nat,C: nat] :
% 2.57/1.49 ( ( ( plus_plus_nat @ B @ A )
% 2.57/1.49 = ( plus_plus_nat @ C @ A ) )
% 2.57/1.49 = ( B = C ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_181_add__le__cancel__left,axiom,
% 2.57/1.49 ! [C: real,A: real,B: real] :
% 2.57/1.49 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 2.57/1.49 = ( ord_less_eq_real @ A @ B ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_182_add__le__cancel__left,axiom,
% 2.57/1.49 ! [C: nat,A: nat,B: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 2.57/1.49 = ( ord_less_eq_nat @ A @ B ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_183_add__le__cancel__right,axiom,
% 2.57/1.49 ! [A: real,C: real,B: real] :
% 2.57/1.49 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 2.57/1.49 = ( ord_less_eq_real @ A @ B ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_184_add__le__cancel__right,axiom,
% 2.57/1.49 ! [A: nat,C: nat,B: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 2.57/1.49 = ( ord_less_eq_nat @ A @ B ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_185_add_Oleft__neutral,axiom,
% 2.57/1.49 ! [A: real] :
% 2.57/1.49 ( ( plus_plus_real @ zero_zero_real @ A )
% 2.57/1.49 = A ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_186_add_Oleft__neutral,axiom,
% 2.57/1.49 ! [A: nat] :
% 2.57/1.49 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 2.57/1.49 = A ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_187_add_Oright__neutral,axiom,
% 2.57/1.49 ! [A: real] :
% 2.57/1.49 ( ( plus_plus_real @ A @ zero_zero_real )
% 2.57/1.49 = A ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_188_add_Oright__neutral,axiom,
% 2.57/1.49 ! [A: nat] :
% 2.57/1.49 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 2.57/1.49 = A ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_189_double__zero,axiom,
% 2.57/1.49 ! [A: real] :
% 2.57/1.49 ( ( ( plus_plus_real @ A @ A )
% 2.57/1.49 = zero_zero_real )
% 2.57/1.49 = ( A = zero_zero_real ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_190_double__zero__sym,axiom,
% 2.57/1.49 ! [A: real] :
% 2.57/1.49 ( ( zero_zero_real
% 2.57/1.49 = ( plus_plus_real @ A @ A ) )
% 2.57/1.49 = ( A = zero_zero_real ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_191_add__cancel__left__left,axiom,
% 2.57/1.49 ! [B: real,A: real] :
% 2.57/1.49 ( ( ( plus_plus_real @ B @ A )
% 2.57/1.49 = A )
% 2.57/1.49 = ( B = zero_zero_real ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_192_add__cancel__left__left,axiom,
% 2.57/1.49 ! [B: nat,A: nat] :
% 2.57/1.49 ( ( ( plus_plus_nat @ B @ A )
% 2.57/1.49 = A )
% 2.57/1.49 = ( B = zero_zero_nat ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_193_add__cancel__left__right,axiom,
% 2.57/1.49 ! [A: real,B: real] :
% 2.57/1.49 ( ( ( plus_plus_real @ A @ B )
% 2.57/1.49 = A )
% 2.57/1.49 = ( B = zero_zero_real ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_194_add__cancel__left__right,axiom,
% 2.57/1.49 ! [A: nat,B: nat] :
% 2.57/1.49 ( ( ( plus_plus_nat @ A @ B )
% 2.57/1.49 = A )
% 2.57/1.49 = ( B = zero_zero_nat ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_195_add__cancel__right__left,axiom,
% 2.57/1.49 ! [A: real,B: real] :
% 2.57/1.49 ( ( A
% 2.57/1.49 = ( plus_plus_real @ B @ A ) )
% 2.57/1.49 = ( B = zero_zero_real ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_196_add__cancel__right__left,axiom,
% 2.57/1.49 ! [A: nat,B: nat] :
% 2.57/1.49 ( ( A
% 2.57/1.49 = ( plus_plus_nat @ B @ A ) )
% 2.57/1.49 = ( B = zero_zero_nat ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_197_add__cancel__right__right,axiom,
% 2.57/1.49 ! [A: real,B: real] :
% 2.57/1.49 ( ( A
% 2.57/1.49 = ( plus_plus_real @ A @ B ) )
% 2.57/1.49 = ( B = zero_zero_real ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_198_add__cancel__right__right,axiom,
% 2.57/1.49 ! [A: nat,B: nat] :
% 2.57/1.49 ( ( A
% 2.57/1.49 = ( plus_plus_nat @ A @ B ) )
% 2.57/1.49 = ( B = zero_zero_nat ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_199_add__eq__0__iff__both__eq__0,axiom,
% 2.57/1.49 ! [X3: nat,Y2: nat] :
% 2.57/1.49 ( ( ( plus_plus_nat @ X3 @ Y2 )
% 2.57/1.49 = zero_zero_nat )
% 2.57/1.49 = ( ( X3 = zero_zero_nat )
% 2.57/1.49 & ( Y2 = zero_zero_nat ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_200_zero__eq__add__iff__both__eq__0,axiom,
% 2.57/1.49 ! [X3: nat,Y2: nat] :
% 2.57/1.49 ( ( zero_zero_nat
% 2.57/1.49 = ( plus_plus_nat @ X3 @ Y2 ) )
% 2.57/1.49 = ( ( X3 = zero_zero_nat )
% 2.57/1.49 & ( Y2 = zero_zero_nat ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_201_add__less__cancel__left,axiom,
% 2.57/1.49 ! [C: real,A: real,B: real] :
% 2.57/1.49 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 2.57/1.49 = ( ord_less_real @ A @ B ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_202_add__less__cancel__left,axiom,
% 2.57/1.49 ! [C: nat,A: nat,B: nat] :
% 2.57/1.49 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 2.57/1.49 = ( ord_less_nat @ A @ B ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_203_add__less__cancel__right,axiom,
% 2.57/1.49 ! [A: real,C: real,B: real] :
% 2.57/1.49 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 2.57/1.49 = ( ord_less_real @ A @ B ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_204_add__less__cancel__right,axiom,
% 2.57/1.49 ! [A: nat,C: nat,B: nat] :
% 2.57/1.49 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 2.57/1.49 = ( ord_less_nat @ A @ B ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_205_add__is__0,axiom,
% 2.57/1.49 ! [M: nat,N: nat] :
% 2.57/1.49 ( ( ( plus_plus_nat @ M @ N )
% 2.57/1.49 = zero_zero_nat )
% 2.57/1.49 = ( ( M = zero_zero_nat )
% 2.57/1.49 & ( N = zero_zero_nat ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_206_Nat_Oadd__0__right,axiom,
% 2.57/1.49 ! [M: nat] :
% 2.57/1.49 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 2.57/1.49 = M ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_207_nat__add__left__cancel__less,axiom,
% 2.57/1.49 ! [K: nat,M: nat,N: nat] :
% 2.57/1.49 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 2.57/1.49 = ( ord_less_nat @ M @ N ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_208_nat__add__left__cancel__le,axiom,
% 2.57/1.49 ! [K: nat,M: nat,N: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 2.57/1.49 = ( ord_less_eq_nat @ M @ N ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_209_add__le__same__cancel1,axiom,
% 2.57/1.49 ! [B: real,A: real] :
% 2.57/1.49 ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 2.57/1.49 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_210_add__le__same__cancel1,axiom,
% 2.57/1.49 ! [B: nat,A: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 2.57/1.49 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_211_add__le__same__cancel2,axiom,
% 2.57/1.49 ! [A: real,B: real] :
% 2.57/1.49 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 2.57/1.49 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_212_add__le__same__cancel2,axiom,
% 2.57/1.49 ! [A: nat,B: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 2.57/1.49 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_213_le__add__same__cancel1,axiom,
% 2.57/1.49 ! [A: real,B: real] :
% 2.57/1.49 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 2.57/1.49 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_214_le__add__same__cancel1,axiom,
% 2.57/1.49 ! [A: nat,B: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 2.57/1.49 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_215_le__add__same__cancel2,axiom,
% 2.57/1.49 ! [A: real,B: real] :
% 2.57/1.49 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 2.57/1.49 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_216_le__add__same__cancel2,axiom,
% 2.57/1.49 ! [A: nat,B: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 2.57/1.49 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_217_double__add__le__zero__iff__single__add__le__zero,axiom,
% 2.57/1.49 ! [A: real] :
% 2.57/1.49 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 2.57/1.49 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_218_zero__le__double__add__iff__zero__le__single__add,axiom,
% 2.57/1.49 ! [A: real] :
% 2.57/1.49 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 2.57/1.49 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_219_add__less__same__cancel1,axiom,
% 2.57/1.49 ! [B: real,A: real] :
% 2.57/1.49 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 2.57/1.49 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_220_add__less__same__cancel1,axiom,
% 2.57/1.49 ! [B: nat,A: nat] :
% 2.57/1.49 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 2.57/1.49 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_221_add__less__same__cancel2,axiom,
% 2.57/1.49 ! [A: real,B: real] :
% 2.57/1.49 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 2.57/1.49 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_222_add__less__same__cancel2,axiom,
% 2.57/1.49 ! [A: nat,B: nat] :
% 2.57/1.49 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 2.57/1.49 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_223_less__add__same__cancel1,axiom,
% 2.57/1.49 ! [A: real,B: real] :
% 2.57/1.49 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 2.57/1.49 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_224_less__add__same__cancel1,axiom,
% 2.57/1.49 ! [A: nat,B: nat] :
% 2.57/1.49 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 2.57/1.49 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_225_less__add__same__cancel2,axiom,
% 2.57/1.49 ! [A: real,B: real] :
% 2.57/1.49 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 2.57/1.49 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_226_less__add__same__cancel2,axiom,
% 2.57/1.49 ! [A: nat,B: nat] :
% 2.57/1.49 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 2.57/1.49 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_227_double__add__less__zero__iff__single__add__less__zero,axiom,
% 2.57/1.49 ! [A: real] :
% 2.57/1.49 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 2.57/1.49 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_228_zero__less__double__add__iff__zero__less__single__add,axiom,
% 2.57/1.49 ! [A: real] :
% 2.57/1.49 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 2.57/1.49 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_229_add__gr__0,axiom,
% 2.57/1.49 ! [M: nat,N: nat] :
% 2.57/1.49 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 2.57/1.49 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 2.57/1.49 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_230_add__leE,axiom,
% 2.57/1.49 ! [M: nat,K: nat,N: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 2.57/1.49 => ~ ( ( ord_less_eq_nat @ M @ N )
% 2.57/1.49 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_231_le__add1,axiom,
% 2.57/1.49 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_232_le__add2,axiom,
% 2.57/1.49 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_233_add__leD1,axiom,
% 2.57/1.49 ! [M: nat,K: nat,N: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 2.57/1.49 => ( ord_less_eq_nat @ M @ N ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_234_add__leD2,axiom,
% 2.57/1.49 ! [M: nat,K: nat,N: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 2.57/1.49 => ( ord_less_eq_nat @ K @ N ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_235_le__Suc__ex,axiom,
% 2.57/1.49 ! [K: nat,L: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ K @ L )
% 2.57/1.49 => ? [N2: nat] :
% 2.57/1.49 ( L
% 2.57/1.49 = ( plus_plus_nat @ K @ N2 ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_236_add__le__mono,axiom,
% 2.57/1.49 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ I @ J )
% 2.57/1.49 => ( ( ord_less_eq_nat @ K @ L )
% 2.57/1.49 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_237_add__le__mono1,axiom,
% 2.57/1.49 ! [I: nat,J: nat,K: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ I @ J )
% 2.57/1.49 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_238_trans__le__add1,axiom,
% 2.57/1.49 ! [I: nat,J: nat,M: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ I @ J )
% 2.57/1.49 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_239_trans__le__add2,axiom,
% 2.57/1.49 ! [I: nat,J: nat,M: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ I @ J )
% 2.57/1.49 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_240_nat__le__iff__add,axiom,
% 2.57/1.49 ( ord_less_eq_nat
% 2.57/1.49 = ( ^ [M3: nat,N3: nat] :
% 2.57/1.49 ? [K3: nat] :
% 2.57/1.49 ( N3
% 2.57/1.49 = ( plus_plus_nat @ M3 @ K3 ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_241_plus__nat_Oadd__0,axiom,
% 2.57/1.49 ! [N: nat] :
% 2.57/1.49 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 2.57/1.49 = N ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_242_add__eq__self__zero,axiom,
% 2.57/1.49 ! [M: nat,N: nat] :
% 2.57/1.49 ( ( ( plus_plus_nat @ M @ N )
% 2.57/1.49 = M )
% 2.57/1.49 => ( N = zero_zero_nat ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_243_add__le__imp__le__right,axiom,
% 2.57/1.49 ! [A: real,C: real,B: real] :
% 2.57/1.49 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 2.57/1.49 => ( ord_less_eq_real @ A @ B ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_244_add__le__imp__le__right,axiom,
% 2.57/1.49 ! [A: nat,C: nat,B: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 2.57/1.49 => ( ord_less_eq_nat @ A @ B ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_245_add__le__imp__le__left,axiom,
% 2.57/1.49 ! [C: real,A: real,B: real] :
% 2.57/1.49 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 2.57/1.49 => ( ord_less_eq_real @ A @ B ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_246_add__le__imp__le__left,axiom,
% 2.57/1.49 ! [C: nat,A: nat,B: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 2.57/1.49 => ( ord_less_eq_nat @ A @ B ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_247_le__iff__add,axiom,
% 2.57/1.49 ( ord_less_eq_nat
% 2.57/1.49 = ( ^ [A2: nat,B2: nat] :
% 2.57/1.49 ? [C3: nat] :
% 2.57/1.49 ( B2
% 2.57/1.49 = ( plus_plus_nat @ A2 @ C3 ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_248_add__right__mono,axiom,
% 2.57/1.49 ! [A: real,B: real,C: real] :
% 2.57/1.49 ( ( ord_less_eq_real @ A @ B )
% 2.57/1.49 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_249_add__right__mono,axiom,
% 2.57/1.49 ! [A: nat,B: nat,C: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ A @ B )
% 2.57/1.49 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_250_less__eqE,axiom,
% 2.57/1.49 ! [A: nat,B: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ A @ B )
% 2.57/1.49 => ~ ! [C2: nat] :
% 2.57/1.49 ( B
% 2.57/1.49 != ( plus_plus_nat @ A @ C2 ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_251_add__left__mono,axiom,
% 2.57/1.49 ! [A: real,B: real,C: real] :
% 2.57/1.49 ( ( ord_less_eq_real @ A @ B )
% 2.57/1.49 => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_252_add__left__mono,axiom,
% 2.57/1.49 ! [A: nat,B: nat,C: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ A @ B )
% 2.57/1.49 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_253_add__mono,axiom,
% 2.57/1.49 ! [A: real,B: real,C: real,D2: real] :
% 2.57/1.49 ( ( ord_less_eq_real @ A @ B )
% 2.57/1.49 => ( ( ord_less_eq_real @ C @ D2 )
% 2.57/1.49 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_254_add__mono,axiom,
% 2.57/1.49 ! [A: nat,B: nat,C: nat,D2: nat] :
% 2.57/1.49 ( ( ord_less_eq_nat @ A @ B )
% 2.57/1.49 => ( ( ord_less_eq_nat @ C @ D2 )
% 2.57/1.49 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_255_add__mono__thms__linordered__semiring_I1_J,axiom,
% 2.57/1.49 ! [I: real,J: real,K: real,L: real] :
% 2.57/1.49 ( ( ( ord_less_eq_real @ I @ J )
% 2.57/1.49 & ( ord_less_eq_real @ K @ L ) )
% 2.57/1.49 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_256_add__mono__thms__linordered__semiring_I1_J,axiom,
% 2.57/1.49 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.57/1.49 ( ( ( ord_less_eq_nat @ I @ J )
% 2.57/1.49 & ( ord_less_eq_nat @ K @ L ) )
% 2.57/1.49 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_257_add__mono__thms__linordered__semiring_I2_J,axiom,
% 2.57/1.49 ! [I: real,J: real,K: real,L: real] :
% 2.57/1.49 ( ( ( I = J )
% 2.57/1.49 & ( ord_less_eq_real @ K @ L ) )
% 2.57/1.49 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_258_add__mono__thms__linordered__semiring_I2_J,axiom,
% 2.57/1.49 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.57/1.49 ( ( ( I = J )
% 2.57/1.49 & ( ord_less_eq_nat @ K @ L ) )
% 2.57/1.49 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_259_add__mono__thms__linordered__semiring_I3_J,axiom,
% 2.57/1.49 ! [I: real,J: real,K: real,L: real] :
% 2.57/1.49 ( ( ( ord_less_eq_real @ I @ J )
% 2.57/1.49 & ( K = L ) )
% 2.57/1.49 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_260_add__mono__thms__linordered__semiring_I3_J,axiom,
% 2.57/1.49 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.57/1.49 ( ( ( ord_less_eq_nat @ I @ J )
% 2.57/1.49 & ( K = L ) )
% 2.57/1.49 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_261_add__less__imp__less__right,axiom,
% 2.57/1.49 ! [A: real,C: real,B: real] :
% 2.57/1.49 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 2.57/1.49 => ( ord_less_real @ A @ B ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_262_add__less__imp__less__right,axiom,
% 2.57/1.49 ! [A: nat,C: nat,B: nat] :
% 2.57/1.49 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 2.57/1.49 => ( ord_less_nat @ A @ B ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_263_add__less__imp__less__left,axiom,
% 2.57/1.49 ! [C: real,A: real,B: real] :
% 2.57/1.49 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 2.57/1.49 => ( ord_less_real @ A @ B ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_264_add__less__imp__less__left,axiom,
% 2.57/1.49 ! [C: nat,A: nat,B: nat] :
% 2.57/1.49 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 2.57/1.49 => ( ord_less_nat @ A @ B ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_265_add__strict__right__mono,axiom,
% 2.57/1.49 ! [A: real,B: real,C: real] :
% 2.57/1.49 ( ( ord_less_real @ A @ B )
% 2.57/1.49 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_266_add__strict__right__mono,axiom,
% 2.57/1.49 ! [A: nat,B: nat,C: nat] :
% 2.57/1.49 ( ( ord_less_nat @ A @ B )
% 2.57/1.49 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_267_add__strict__left__mono,axiom,
% 2.57/1.49 ! [A: real,B: real,C: real] :
% 2.57/1.49 ( ( ord_less_real @ A @ B )
% 2.57/1.49 => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_268_add__strict__left__mono,axiom,
% 2.57/1.49 ! [A: nat,B: nat,C: nat] :
% 2.57/1.49 ( ( ord_less_nat @ A @ B )
% 2.57/1.49 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_269_add__strict__mono,axiom,
% 2.57/1.49 ! [A: real,B: real,C: real,D2: real] :
% 2.57/1.49 ( ( ord_less_real @ A @ B )
% 2.57/1.49 => ( ( ord_less_real @ C @ D2 )
% 2.57/1.49 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_270_add__strict__mono,axiom,
% 2.57/1.49 ! [A: nat,B: nat,C: nat,D2: nat] :
% 2.57/1.49 ( ( ord_less_nat @ A @ B )
% 2.57/1.49 => ( ( ord_less_nat @ C @ D2 )
% 2.57/1.49 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_271_add__mono__thms__linordered__field_I1_J,axiom,
% 2.57/1.49 ! [I: real,J: real,K: real,L: real] :
% 2.57/1.49 ( ( ( ord_less_real @ I @ J )
% 2.57/1.49 & ( K = L ) )
% 2.57/1.49 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_272_add__mono__thms__linordered__field_I1_J,axiom,
% 2.57/1.49 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.57/1.49 ( ( ( ord_less_nat @ I @ J )
% 2.57/1.49 & ( K = L ) )
% 2.57/1.49 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_273_add__mono__thms__linordered__field_I2_J,axiom,
% 2.57/1.49 ! [I: real,J: real,K: real,L: real] :
% 2.57/1.49 ( ( ( I = J )
% 2.57/1.49 & ( ord_less_real @ K @ L ) )
% 2.57/1.49 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_274_add__mono__thms__linordered__field_I2_J,axiom,
% 2.57/1.49 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.57/1.49 ( ( ( I = J )
% 2.57/1.49 & ( ord_less_nat @ K @ L ) )
% 2.57/1.49 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_275_add__mono__thms__linordered__field_I5_J,axiom,
% 2.57/1.49 ! [I: real,J: real,K: real,L: real] :
% 2.57/1.49 ( ( ( ord_less_real @ I @ J )
% 2.57/1.49 & ( ord_less_real @ K @ L ) )
% 2.57/1.49 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_276_add__mono__thms__linordered__field_I5_J,axiom,
% 2.57/1.49 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.57/1.49 ( ( ( ord_less_nat @ I @ J )
% 2.57/1.49 & ( ord_less_nat @ K @ L ) )
% 2.57/1.49 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_277_less__add__eq__less,axiom,
% 2.57/1.49 ! [K: nat,L: nat,M: nat,N: nat] :
% 2.57/1.49 ( ( ord_less_nat @ K @ L )
% 2.57/1.49 => ( ( ( plus_plus_nat @ M @ L )
% 2.57/1.49 = ( plus_plus_nat @ K @ N ) )
% 2.57/1.49 => ( ord_less_nat @ M @ N ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_278_trans__less__add2,axiom,
% 2.57/1.49 ! [I: nat,J: nat,M: nat] :
% 2.57/1.49 ( ( ord_less_nat @ I @ J )
% 2.57/1.49 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_279_trans__less__add1,axiom,
% 2.57/1.49 ! [I: nat,J: nat,M: nat] :
% 2.57/1.49 ( ( ord_less_nat @ I @ J )
% 2.57/1.49 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_280_add__less__mono1,axiom,
% 2.57/1.49 ! [I: nat,J: nat,K: nat] :
% 2.57/1.49 ( ( ord_less_nat @ I @ J )
% 2.57/1.49 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_281_not__add__less2,axiom,
% 2.57/1.49 ! [J: nat,I: nat] :
% 2.57/1.49 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 2.57/1.49
% 2.57/1.49 thf(fact_282_not__add__less1,axiom,
% 2.57/1.49 ! [I: nat,J: nat] :
% 2.57/1.49 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 2.57/1.49
% 2.57/1.49 thf(conj_0,hypothesis,
% 2.57/1.49 ! [V7: view_e774982825t_unit] :
% 2.57/1.49 ( ( ( ord_le461438217t_unit @ V7 @ ( move @ ts3 @ ts @ v ) )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V7 ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V7 @ ts @ c )
% 2.57/1.49 = ( ext_Product_unit @ V7 ) )
% 2.57/1.49 & ( ( restrict @ V7 @ ( res @ ts ) @ c )
% 2.57/1.49 = ( lan_Product_unit @ V7 ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V7 ) )
% 2.57/1.49 = one_one_nat )
% 2.57/1.49 & ( ord_less_real @ zero_zero_real @ ( real_length @ ( ext_Product_unit @ V7 ) ) )
% 2.57/1.49 & ( ( len @ regular_regular @ V7 @ ts @ e )
% 2.57/1.49 = ( ext_Product_unit @ V7 ) )
% 2.57/1.49 & ( ( restrict @ V7 @ ( res @ ts ) @ e )
% 2.57/1.49 = ( lan_Product_unit @ V7 ) )
% 2.57/1.49 & ( ( nat_card @ ( lan_Product_unit @ V7 ) )
% 2.57/1.49 = one_one_nat ) )
% 2.57/1.49 => thesis ) ).
% 2.57/1.49
% 2.57/1.49 thf(conj_1,conjecture,
% 2.57/1.49 thesis ).
% 2.57/1.49 ------------------------
% 2.69/1.52 % (20861)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_20750 for (2999ds/2Mi)
% 2.69/1.52 % (20857)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20750 for (2999ds/183Mi)
% 2.69/1.52 % (20859)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_20750 for (2999ds/27Mi)
% 2.69/1.52 % (20863)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20750 for (2999ds/18Mi)
% 2.69/1.52 % (20858)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_20750 for (2999ds/4Mi)
% 2.69/1.52 % (20862)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_20750 for (2999ds/275Mi)
% 2.69/1.52 % (20860)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20750 for (2999ds/2Mi)
% 2.69/1.52 % (20858)Instruction limit reached!
% 2.69/1.52 % (20858)------------------------------
% 2.69/1.52 % (20858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.52 % (20858)Termination reason: Unknown
% 2.69/1.52 % (20858)Termination phase: shuffling
% 2.69/1.52
% 2.69/1.52 % (20858)Memory used [KB]: 1407
% 2.69/1.52 % (20858)Time elapsed: 0.003 s
% 2.69/1.52 % (20858)Instructions burned: 4 (million)
% 2.69/1.52 % (20858)------------------------------
% 2.69/1.52 % (20858)------------------------------
% 2.69/1.52 % (20860)Instruction limit reached!
% 2.69/1.52 % (20860)------------------------------
% 2.69/1.52 % (20860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.52 % (20860)Termination reason: Unknown
% 2.69/1.52 % (20860)Termination phase: shuffling
% 2.69/1.52
% 2.69/1.52 % (20860)Memory used [KB]: 1407
% 2.69/1.52 % (20860)Time elapsed: 0.003 s
% 2.69/1.52 % (20860)Instructions burned: 4 (million)
% 2.69/1.52 % (20860)------------------------------
% 2.69/1.52 % (20860)------------------------------
% 2.69/1.52 % (20861)Instruction limit reached!
% 2.69/1.52 % (20861)------------------------------
% 2.69/1.52 % (20861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.52 % (20861)Termination reason: Unknown
% 2.69/1.52 % (20861)Termination phase: shuffling
% 2.69/1.52
% 2.69/1.52 % (20861)Memory used [KB]: 1407
% 2.69/1.52 % (20861)Time elapsed: 0.003 s
% 2.69/1.52 % (20861)Instructions burned: 4 (million)
% 2.69/1.52 % (20861)------------------------------
% 2.69/1.52 % (20861)------------------------------
% 2.69/1.52 % (20863)Instruction limit reached!
% 2.69/1.52 % (20863)------------------------------
% 2.69/1.52 % (20863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.52 % (20863)Termination reason: Unknown
% 2.69/1.52 % (20863)Termination phase: shuffling
% 2.69/1.52
% 2.69/1.52 % (20863)Memory used [KB]: 1663
% 2.69/1.52 % (20863)Time elapsed: 0.008 s
% 2.69/1.52 % (20863)Instructions burned: 20 (million)
% 2.69/1.52 % (20863)------------------------------
% 2.69/1.52 % (20863)------------------------------
% 2.69/1.53 % (20859)Instruction limit reached!
% 2.69/1.53 % (20859)------------------------------
% 2.69/1.53 % (20859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.53 % (20859)Termination reason: Unknown
% 2.69/1.53 % (20859)Termination phase: shuffling
% 2.69/1.53
% 2.69/1.53 % (20859)Memory used [KB]: 1791
% 2.69/1.53 % (20859)Time elapsed: 0.011 s
% 2.69/1.53 % (20859)Instructions burned: 29 (million)
% 2.69/1.53 % (20859)------------------------------
% 2.69/1.53 % (20859)------------------------------
% 2.69/1.53 % (20868)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20750 for (2999ds/3Mi)
% 2.69/1.53 % (20870)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_20750 for (2999ds/15Mi)
% 2.69/1.53 % (20869)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_20750 for (2999ds/37Mi)
% 2.69/1.53 % (20868)Instruction limit reached!
% 2.69/1.53 % (20868)------------------------------
% 2.69/1.53 % (20868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.53 % (20868)Termination reason: Unknown
% 2.69/1.53 % (20868)Termination phase: shuffling
% 2.69/1.53
% 2.69/1.53 % (20868)Memory used [KB]: 1407
% 2.69/1.53 % (20868)Time elapsed: 0.002 s
% 2.69/1.53 % (20868)Instructions burned: 3 (million)
% 2.69/1.53 % (20868)------------------------------
% 2.69/1.53 % (20868)------------------------------
% 2.69/1.53 % (20870)Instruction limit reached!
% 2.69/1.53 % (20870)------------------------------
% 2.69/1.53 % (20870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.53 % (20870)Termination reason: Unknown
% 2.69/1.53 % (20870)Termination phase: shuffling
% 2.69/1.53
% 2.69/1.53 % (20870)Memory used [KB]: 1535
% 2.69/1.53 % (20870)Time elapsed: 0.006 s
% 2.69/1.53 % (20870)Instructions burned: 15 (million)
% 2.69/1.53 % (20870)------------------------------
% 2.69/1.53 % (20870)------------------------------
% 2.69/1.53 % (20873)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_20750 for (2999ds/3Mi)
% 2.69/1.53 % (20873)Instruction limit reached!
% 2.69/1.53 % (20873)------------------------------
% 2.69/1.53 % (20873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.53 % (20873)Termination reason: Unknown
% 2.69/1.53 % (20873)Termination phase: shuffling
% 2.69/1.53
% 2.69/1.53 % (20873)Memory used [KB]: 1407
% 2.69/1.53 % (20873)Time elapsed: 0.002 s
% 2.69/1.53 % (20873)Instructions burned: 3 (million)
% 2.69/1.53 % (20873)------------------------------
% 2.69/1.53 % (20873)------------------------------
% 2.69/1.54 % (20876)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_20750 for (2999ds/1041Mi)
% 2.69/1.54 % (20878)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_20750 for (2999ds/7Mi)
% 2.69/1.54 % (20869)Instruction limit reached!
% 2.69/1.54 % (20869)------------------------------
% 2.69/1.54 % (20869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.54 % (20869)Termination reason: Unknown
% 2.69/1.54 % (20869)Termination phase: shuffling
% 2.69/1.54
% 2.69/1.54 % (20869)Memory used [KB]: 2046
% 2.69/1.54 % (20869)Time elapsed: 0.012 s
% 2.69/1.54 % (20869)Instructions burned: 40 (million)
% 2.69/1.54 % (20869)------------------------------
% 2.69/1.54 % (20869)------------------------------
% 2.69/1.54 % (20878)Instruction limit reached!
% 2.69/1.54 % (20878)------------------------------
% 2.69/1.54 % (20878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.54 % (20878)Termination reason: Unknown
% 2.69/1.54 % (20878)Termination phase: shuffling
% 2.69/1.54
% 2.69/1.54 % (20878)Memory used [KB]: 1407
% 2.69/1.54 % (20878)Time elapsed: 0.004 s
% 2.69/1.54 % (20878)Instructions burned: 8 (million)
% 2.69/1.54 % (20878)------------------------------
% 2.69/1.54 % (20878)------------------------------
% 2.69/1.54 % (20880)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_20750 for (2999ds/16Mi)
% 2.69/1.54 % (20882)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_20750 for (2999ds/3Mi)
% 2.69/1.54 % (20882)Instruction limit reached!
% 2.69/1.54 % (20882)------------------------------
% 2.69/1.54 % (20882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.54 % (20882)Termination reason: Unknown
% 2.69/1.54 % (20882)Termination phase: shuffling
% 2.69/1.54
% 2.69/1.54 % (20882)Memory used [KB]: 1407
% 2.69/1.54 % (20882)Time elapsed: 0.003 s
% 2.69/1.54 % (20882)Instructions burned: 5 (million)
% 2.69/1.54 % (20882)------------------------------
% 2.69/1.54 % (20882)------------------------------
% 2.69/1.55 % (20880)Instruction limit reached!
% 2.69/1.55 % (20880)------------------------------
% 2.69/1.55 % (20880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.55 % (20880)Termination reason: Unknown
% 2.69/1.55 % (20880)Termination phase: shuffling
% 2.69/1.55
% 2.69/1.55 % (20880)Memory used [KB]: 1535
% 2.69/1.55 % (20880)Time elapsed: 0.007 s
% 2.69/1.55 % (20880)Instructions burned: 18 (million)
% 2.69/1.55 % (20880)------------------------------
% 2.69/1.55 % (20880)------------------------------
% 2.69/1.55 % (20885)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_20750 for (2999ds/3Mi)
% 2.69/1.55 % (20885)Instruction limit reached!
% 2.69/1.55 % (20885)------------------------------
% 2.69/1.55 % (20885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.55 % (20885)Termination reason: Unknown
% 2.69/1.55 % (20885)Termination phase: shuffling
% 2.69/1.55
% 2.69/1.55 % (20885)Memory used [KB]: 1407
% 2.69/1.55 % (20885)Time elapsed: 0.003 s
% 2.69/1.55 % (20885)Instructions burned: 5 (million)
% 2.69/1.55 % (20885)------------------------------
% 2.69/1.55 % (20885)------------------------------
% 2.69/1.55 % (20887)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_20750 for (2999ds/7Mi)
% 2.69/1.55 % (20887)Instruction limit reached!
% 2.69/1.55 % (20887)------------------------------
% 2.69/1.55 % (20887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.55 % (20887)Termination reason: Unknown
% 2.69/1.55 % (20887)Termination phase: shuffling
% 2.69/1.55
% 2.69/1.55 % (20887)Memory used [KB]: 1535
% 2.69/1.55 % (20887)Time elapsed: 0.004 s
% 2.69/1.55 % (20887)Instructions burned: 9 (million)
% 2.69/1.55 % (20887)------------------------------
% 2.69/1.55 % (20887)------------------------------
% 2.69/1.55 % (20891)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_20750 for (2999ds/3Mi)
% 2.69/1.56 % (20891)Instruction limit reached!
% 2.69/1.56 % (20891)------------------------------
% 2.69/1.56 % (20891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.56 % (20891)Termination reason: Unknown
% 2.69/1.56 % (20891)Termination phase: shuffling
% 2.69/1.56
% 2.69/1.56 % (20891)Memory used [KB]: 1407
% 2.69/1.56 % (20891)Time elapsed: 0.002 s
% 2.69/1.56 % (20891)Instructions burned: 3 (million)
% 2.69/1.56 % (20891)------------------------------
% 2.69/1.56 % (20891)------------------------------
% 2.69/1.56 % (20893)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_20750 for (2999ds/4Mi)
% 2.69/1.56 % (20893)Instruction limit reached!
% 2.69/1.56 % (20893)------------------------------
% 2.69/1.56 % (20893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.56 % (20893)Termination reason: Unknown
% 2.69/1.56 % (20893)Termination phase: shuffling
% 2.69/1.56
% 2.69/1.56 % (20893)Memory used [KB]: 1407
% 2.69/1.56 % (20893)Time elapsed: 0.003 s
% 2.69/1.56 % (20893)Instructions burned: 6 (million)
% 2.69/1.56 % (20893)------------------------------
% 2.69/1.56 % (20893)------------------------------
% 2.69/1.56 % (20895)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_20750 for (2999ds/18Mi)
% 2.69/1.56 % (20897)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_20750 for (2999ds/710Mi)
% 2.69/1.56 % (20899)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_20750 for (2999ds/6Mi)
% 2.69/1.57 % (20895)Instruction limit reached!
% 2.69/1.57 % (20895)------------------------------
% 2.69/1.57 % (20895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.57 % (20895)Termination reason: Unknown
% 2.69/1.57 % (20895)Termination phase: shuffling
% 2.69/1.57
% 2.69/1.57 % (20895)Memory used [KB]: 1535
% 2.69/1.57 % (20895)Time elapsed: 0.007 s
% 2.69/1.57 % (20895)Instructions burned: 19 (million)
% 2.69/1.57 % (20895)------------------------------
% 2.69/1.57 % (20895)------------------------------
% 2.69/1.57 % (20899)Instruction limit reached!
% 2.69/1.57 % (20899)------------------------------
% 2.69/1.57 % (20899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.57 % (20899)Termination reason: Unknown
% 2.69/1.57 % (20899)Termination phase: shuffling
% 2.69/1.57
% 2.69/1.57 % (20899)Memory used [KB]: 1407
% 2.69/1.57 % (20899)Time elapsed: 0.003 s
% 2.69/1.57 % (20899)Instructions burned: 6 (million)
% 2.69/1.57 % (20899)------------------------------
% 2.69/1.57 % (20899)------------------------------
% 2.69/1.57 % (20857)Instruction limit reached!
% 2.69/1.57 % (20857)------------------------------
% 2.69/1.57 % (20857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.57 % (20857)Termination reason: Unknown
% 2.69/1.57 % (20857)Termination phase: Saturation
% 2.69/1.57
% 2.69/1.57 % (20857)Memory used [KB]: 7036
% 2.69/1.57 % (20857)Time elapsed: 0.052 s
% 2.69/1.57 % (20857)Instructions burned: 184 (million)
% 2.69/1.57 % (20857)------------------------------
% 2.69/1.57 % (20857)------------------------------
% 2.69/1.57 % (20901)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_20750 for (2999ds/902Mi)
% 2.69/1.57 % (20905)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_20750 for (2999ds/21Mi)
% 2.69/1.58 % (20907)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_20750 for (2999ds/5Mi)
% 2.69/1.58 % (20908)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_20750 for (2999ds/6Mi)
% 2.69/1.58 % (20907)Instruction limit reached!
% 2.69/1.58 % (20907)------------------------------
% 2.69/1.58 % (20907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.58 % (20907)Termination reason: Unknown
% 2.69/1.58 % (20907)Termination phase: shuffling
% 2.69/1.58
% 2.69/1.58 % (20907)Memory used [KB]: 1407
% 2.69/1.58 % (20907)Time elapsed: 0.003 s
% 2.69/1.58 % (20907)Instructions burned: 7 (million)
% 2.69/1.58 % (20907)------------------------------
% 2.69/1.58 % (20907)------------------------------
% 2.69/1.58 % (20908)Instruction limit reached!
% 2.69/1.58 % (20908)------------------------------
% 2.69/1.58 % (20908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.58 % (20908)Termination reason: Unknown
% 2.69/1.58 % (20908)Termination phase: shuffling
% 2.69/1.58
% 2.69/1.58 % (20908)Memory used [KB]: 1407
% 2.69/1.58 % (20908)Time elapsed: 0.003 s
% 2.69/1.58 % (20908)Instructions burned: 7 (million)
% 2.69/1.58 % (20908)------------------------------
% 2.69/1.58 % (20908)------------------------------
% 2.69/1.58 % (20905)Instruction limit reached!
% 2.69/1.58 % (20905)------------------------------
% 2.69/1.58 % (20905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.58 % (20905)Termination reason: Unknown
% 2.69/1.58 % (20905)Termination phase: shuffling
% 2.69/1.58
% 2.69/1.58 % (20905)Memory used [KB]: 1791
% 2.69/1.58 % (20905)Time elapsed: 0.008 s
% 2.69/1.58 % (20905)Instructions burned: 22 (million)
% 2.69/1.58 % (20905)------------------------------
% 2.69/1.58 % (20905)------------------------------
% 2.69/1.58 % (20862)First to succeed.
% 2.69/1.59 % (20916)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_20750 for (2999ds/377Mi)
% 2.69/1.59 % (20917)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_20750 for (2999ds/779Mi)
% 2.69/1.59 % (20862)Refutation found. Thanks to Tanya!
% 2.69/1.59 % SZS status Theorem for DTF2THF_20750
% 2.69/1.59 % SZS output start Proof for DTF2THF_20750
% 2.69/1.59 thf(type_def_5, type, nat: $tType).
% 2.69/1.59 thf(type_def_7, type, real: $tType).
% 2.69/1.59 thf(type_def_8, type, cars: $tType).
% 2.69/1.59 thf(type_def_9, type, traffic: $tType).
% 2.69/1.59 thf(type_def_10, type, view_e774982825t_unit: $tType).
% 2.69/1.59 thf(type_def_11, type, real_int: $tType).
% 2.69/1.59 thf(type_def_12, type, nat_int: $tType).
% 2.69/1.59 thf(func_def_0, type, view_e774982825t_unit: $tType).
% 2.69/1.59 thf(func_def_1, type, real_int: $tType).
% 2.69/1.59 thf(func_def_2, type, nat_int: $tType).
% 2.69/1.59 thf(func_def_3, type, traffic: $tType).
% 2.69/1.59 thf(func_def_4, type, real: $tType).
% 2.69/1.59 thf(func_def_5, type, cars: $tType).
% 2.69/1.59 thf(func_def_6, type, nat: $tType).
% 2.69/1.59 thf(func_def_7, type, one_one_nat: nat).
% 2.69/1.59 thf(func_def_8, type, plus_plus_nat: nat > nat > nat).
% 2.69/1.59 thf(func_def_9, type, plus_plus_real: real > real > real).
% 2.69/1.59 thf(func_def_10, type, zero_zero_nat: nat).
% 2.69/1.59 thf(func_def_11, type, zero_zero_real: real).
% 2.69/1.59 thf(func_def_12, type, len: (cars > traffic > cars > real) > view_e774982825t_unit > traffic > cars > real_int).
% 2.69/1.59 thf(func_def_13, type, move: traffic > traffic > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_14, type, nat_card: nat_int > nat).
% 2.69/1.59 thf(func_def_15, type, bot_bot_nat_int: nat_int).
% 2.69/1.59 thf(func_def_16, type, ord_less_nat_int: nat_int > nat_int > $o).
% 2.69/1.59 thf(func_def_17, type, ord_less_nat: nat > nat > $o).
% 2.69/1.59 thf(func_def_18, type, ord_less_real: real > real > $o).
% 2.69/1.59 thf(func_def_19, type, ord_less_eq_nat_int: nat_int > nat_int > $o).
% 2.69/1.59 thf(func_def_20, type, ord_less_eq_nat: nat > nat > $o).
% 2.69/1.59 thf(func_def_21, type, ord_less_eq_real_int: real_int > real_int > $o).
% 2.69/1.59 thf(func_def_22, type, ord_less_eq_real: real > real > $o).
% 2.69/1.59 thf(func_def_23, type, ord_le461438217t_unit: view_e774982825t_unit > view_e774982825t_unit > $o).
% 2.69/1.59 thf(func_def_24, type, real_length: real_int > real).
% 2.69/1.59 thf(func_def_25, type, regular_regular: cars > traffic > cars > real).
% 2.69/1.59 thf(func_def_26, type, restrict: view_e774982825t_unit > (cars > nat_int) > cars > nat_int).
% 2.69/1.59 thf(func_def_27, type, abstract: traffic > traffic > $o).
% 2.69/1.59 thf(func_def_28, type, clm: traffic > cars > nat_int).
% 2.69/1.59 thf(func_def_29, type, create_claim: traffic > cars > nat > traffic > $o).
% 2.69/1.59 thf(func_def_30, type, create_reservation: traffic > cars > traffic > $o).
% 2.69/1.59 thf(func_def_31, type, res: traffic > cars > nat_int).
% 2.69/1.59 thf(func_def_32, type, withdraw_claim: traffic > cars > traffic > $o).
% 2.69/1.59 thf(func_def_33, type, withdraw_reservation: traffic > cars > nat > traffic > $o).
% 2.69/1.59 thf(func_def_34, type, ext_Product_unit: view_e774982825t_unit > real_int).
% 2.69/1.59 thf(func_def_35, type, hchop: view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > $o).
% 2.69/1.59 thf(func_def_36, type, lan_Product_unit: view_e774982825t_unit > nat_int).
% 2.69/1.59 thf(func_def_37, type, own_Product_unit: view_e774982825t_unit > cars).
% 2.69/1.59 thf(func_def_38, type, vchop: view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > $o).
% 2.69/1.59 thf(func_def_39, type, c: cars).
% 2.69/1.59 thf(func_def_40, type, d: cars).
% 2.69/1.59 thf(func_def_41, type, e: cars).
% 2.69/1.59 thf(func_def_43, type, ts: traffic).
% 2.69/1.59 thf(func_def_44, type, ts2: traffic).
% 2.69/1.59 thf(func_def_45, type, ts_a: traffic).
% 2.69/1.59 thf(func_def_46, type, ts3: traffic).
% 2.69/1.59 thf(func_def_47, type, v: view_e774982825t_unit).
% 2.69/1.59 thf(func_def_66, type, sP0: view_e774982825t_unit > traffic > cars > $o).
% 2.69/1.59 thf(func_def_67, type, sP1: (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > traffic > $o).
% 2.69/1.59 thf(func_def_68, type, sP2: (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > traffic > $o).
% 2.69/1.59 thf(func_def_69, type, sP3: (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit > $o).
% 2.69/1.59 thf(func_def_70, type, sP4: (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit > $o).
% 2.69/1.59 thf(func_def_71, type, sP5: (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit > $o).
% 2.69/1.59 thf(func_def_72, type, sP6: (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit > $o).
% 2.69/1.59 thf(func_def_73, type, sP7: (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit > $o).
% 2.69/1.59 thf(func_def_74, type, sP8: (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > traffic > $o).
% 2.69/1.59 thf(func_def_75, type, sK9: view_e774982825t_unit > traffic > cars > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_76, type, sK10: view_e774982825t_unit > traffic > cars > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_77, type, sK11: view_e774982825t_unit > traffic > cars > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_78, type, sK12: view_e774982825t_unit > traffic > cars > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_79, type, sK13: (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > traffic > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_80, type, sK14: (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > traffic > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_81, type, sK15: view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_82, type, sK16: view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_83, type, sK17: traffic > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_84, type, sK18: traffic > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_85, type, sK19: traffic > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_86, type, sK20: traffic > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_87, type, sK21: traffic > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_88, type, sK22: traffic > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_89, type, sK23: traffic > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_90, type, sK24: traffic > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_91, type, sK25: view_e774982825t_unit > traffic > cars > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_92, type, sK26: view_e774982825t_unit > traffic > cars > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_93, type, sK27: view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_94, type, sK28: view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_95, type, sK29: (nat > $o) > nat > nat).
% 2.69/1.59 thf(func_def_96, type, sK30: nat > view_e774982825t_unit > nat > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_97, type, sK31: nat > view_e774982825t_unit > nat > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_98, type, sK32: view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_99, type, sK33: view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_100, type, sK34: view_e774982825t_unit > traffic > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_101, type, sK35: view_e774982825t_unit > traffic > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_102, type, sK36: traffic > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_103, type, sK37: traffic > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_104, type, sK38: traffic > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_105, type, sK39: traffic > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_106, type, sK40: (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_107, type, sK41: (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_108, type, sK42: (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_109, type, sK43: (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_110, type, sK44: view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > traffic > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_111, type, sK45: view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > traffic > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_112, type, sK46: view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_113, type, sK47: view_e774982825t_unit).
% 2.69/1.59 thf(func_def_114, type, sK48: (nat > $o) > nat).
% 2.69/1.59 thf(func_def_115, type, sK49: view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_116, type, sK50: view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_117, type, sK51: view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_118, type, sK52: view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_119, type, sK53: (nat > $o) > nat).
% 2.69/1.59 thf(func_def_120, type, sK54: view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_121, type, sK55: nat > nat > nat).
% 2.69/1.59 thf(func_def_122, type, sK56: view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_123, type, sK57: view_e774982825t_unit > real > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_124, type, sK58: view_e774982825t_unit > real > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_125, type, sK59: view_e774982825t_unit > cars > traffic > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_126, type, sK60: view_e774982825t_unit > cars > traffic > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_127, type, sK61: (nat > nat) > nat).
% 2.69/1.59 thf(func_def_128, type, sK62: (nat > nat) > nat).
% 2.69/1.59 thf(func_def_129, type, sK63: view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_130, type, sK64: view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_131, type, sK65: nat > nat > nat).
% 2.69/1.59 thf(func_def_132, type, sK66: (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_133, type, sK67: (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_134, type, sK68: (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_135, type, sK69: (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_136, type, sK70: view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > traffic > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_137, type, sK71: view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > traffic > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_138, type, sK72: (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_139, type, sK73: (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_140, type, sK74: (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_141, type, sK75: (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_142, type, sK76: traffic > view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_143, type, sK77: traffic > view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_144, type, sK78: view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_145, type, sK79: view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_146, type, sK80: (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_147, type, sK81: (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_148, type, sK82: view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_149, type, sK83: (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_150, type, sK84: (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_151, type, sK85: (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_152, type, sK86: (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_153, type, sK87: traffic > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_154, type, sK88: traffic > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_155, type, sK89: (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_156, type, sK90: (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_157, type, sK91: (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_158, type, sK92: (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_159, type, sK93: (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_160, type, sK94: (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_161, type, sK95: (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_162, type, sK96: (traffic > view_e774982825t_unit > $o) > (traffic > view_e774982825t_unit > $o) > traffic > view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_163, type, sK97: (nat > $o) > nat).
% 2.69/1.59 thf(func_def_164, type, sK98: view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_165, type, sK99: view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_166, type, sK100: nat > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_167, type, sK101: nat > view_e774982825t_unit > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_168, type, sK102: traffic > view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_169, type, sK103: traffic > view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_170, type, sK104: traffic > view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_171, type, sK105: traffic > view_e774982825t_unit > (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_172, type, sK106: (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > traffic > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_173, type, sK107: (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > traffic > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_174, type, sK108: (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > traffic > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_175, type, sK109: (traffic > view_e774982825t_unit > $o) > view_e774982825t_unit > traffic > view_e774982825t_unit).
% 2.69/1.59 thf(func_def_176, type, sK110: (nat > $o) > nat > nat).
% 2.69/1.59 thf(func_def_177, type, sK111: (nat > $o) > nat).
% 2.69/1.59 thf(func_def_179, type, ph113: !>[X0: $tType]:(X0)).
% 2.69/1.59 thf(f1648,plain,(
% 2.69/1.59 $false),
% 2.69/1.59 inference(avatar_sat_refutation,[status(thm)],[f1600,f1601,f1641])).
% 2.69/1.59 thf(f1641,plain,(
% 2.69/1.59 ~spl112_1),
% 2.69/1.59 inference(avatar_contradiction_clause,[status(thm)],[f1640])).
% 2.69/1.59 thf(f1640,plain,(
% 2.69/1.59 $false | ~spl112_1),
% 2.69/1.59 inference(subsumption_resolution,[status(thm)],[f1639,f1298])).
% 2.69/1.59 thf(f1298,plain,(
% 2.69/1.59 ((lan_Product_unit @ sK47) = (restrict @ sK47 @ (res @ ts) @ e))),
% 2.69/1.59 inference(cnf_transformation,[status(thm)],[f1034])).
% 2.69/1.59 thf(f1034,plain,(
% 2.69/1.59 (one_one_nat = (nat_card @ (lan_Product_unit @ sK47))) & ((len @ regular_regular @ sK47 @ ts @ c) = (ext_Product_unit @ sK47)) & ((lan_Product_unit @ sK47) = (restrict @ sK47 @ (res @ ts) @ e)) & ((ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ sK47))) = $true) & ((ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ sK47))) = $true) & (one_one_nat = (nat_card @ (lan_Product_unit @ sK47))) & ((len @ regular_regular @ sK47 @ ts @ e) = (ext_Product_unit @ sK47)) & ((lan_Product_unit @ sK47) = (restrict @ sK47 @ (res @ ts) @ c)) & ($true = (ord_le461438217t_unit @ sK47 @ (move @ ts3 @ ts @ v)))),
% 2.69/1.59 inference(skolemisation,[status(esa),new_symbols(skolem,[sK47])],[f729,f1033])).
% 2.69/1.59 thf(f1033,plain,(
% 2.69/1.59 ? [X0 : view_e774982825t_unit] : ((one_one_nat = (nat_card @ (lan_Product_unit @ X0))) & ((len @ regular_regular @ X0 @ ts @ c) = (ext_Product_unit @ X0)) & ((lan_Product_unit @ X0) = (restrict @ X0 @ (res @ ts) @ e)) & ($true = (ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ X0)))) & ($true = (ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ X0)))) & (one_one_nat = (nat_card @ (lan_Product_unit @ X0))) & ((ext_Product_unit @ X0) = (len @ regular_regular @ X0 @ ts @ e)) & ((restrict @ X0 @ (res @ ts) @ c) = (lan_Product_unit @ X0)) & ($true = (ord_le461438217t_unit @ X0 @ (move @ ts3 @ ts @ v)))) => ((one_one_nat = (nat_card @ (lan_Product_unit @ sK47))) & ((len @ regular_regular @ sK47 @ ts @ c) = (ext_Product_unit @ sK47)) & ((lan_Product_unit @ sK47) = (restrict @ sK47 @ (res @ ts) @ e)) & ((ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ sK47))) = $true) & ((ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ sK47))) = $true) & (one_one_nat = (nat_card @ (lan_Product_unit @ sK47))) & ((len @ regular_regular @ sK47 @ ts @ e) = (ext_Product_unit @ sK47)) & ((lan_Product_unit @ sK47) = (restrict @ sK47 @ (res @ ts) @ c)) & ($true = (ord_le461438217t_unit @ sK47 @ (move @ ts3 @ ts @ v))))),
% 2.69/1.59 introduced(definition,[],[choice_axiom])).
% 2.69/1.59 thf(f729,plain,(
% 2.69/1.59 ? [X0 : view_e774982825t_unit] : ((one_one_nat = (nat_card @ (lan_Product_unit @ X0))) & ((len @ regular_regular @ X0 @ ts @ c) = (ext_Product_unit @ X0)) & ((lan_Product_unit @ X0) = (restrict @ X0 @ (res @ ts) @ e)) & ($true = (ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ X0)))) & ($true = (ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ X0)))) & (one_one_nat = (nat_card @ (lan_Product_unit @ X0))) & ((ext_Product_unit @ X0) = (len @ regular_regular @ X0 @ ts @ e)) & ((restrict @ X0 @ (res @ ts) @ c) = (lan_Product_unit @ X0)) & ($true = (ord_le461438217t_unit @ X0 @ (move @ ts3 @ ts @ v))))),
% 2.69/1.59 inference(fool_elimination,[status(thm)],[f728])).
% 2.69/1.59 thf(f728,plain,(
% 2.69/1.59 ? [X0 : view_e774982825t_unit] : (((len @ regular_regular @ X0 @ ts @ c) = (ext_Product_unit @ X0)) & ((ext_Product_unit @ X0) = (len @ regular_regular @ X0 @ ts @ e)) & (ord_le461438217t_unit @ X0 @ (move @ ts3 @ ts @ v)) & ((restrict @ X0 @ (res @ ts) @ c) = (lan_Product_unit @ X0)) & ((lan_Product_unit @ X0) = (restrict @ X0 @ (res @ ts) @ e)) & (ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ X0))) & (ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ X0))) & (one_one_nat = (nat_card @ (lan_Product_unit @ X0))) & (one_one_nat = (nat_card @ (lan_Product_unit @ X0))))),
% 2.69/1.59 inference(rectify,[status(thm)],[f5])).
% 2.69/1.59 thf(f5,axiom,(
% 2.69/1.59 ? [X7 : view_e774982825t_unit] : (((ext_Product_unit @ X7) = (len @ regular_regular @ X7 @ ts @ c)) & ((ext_Product_unit @ X7) = (len @ regular_regular @ X7 @ ts @ e)) & (ord_le461438217t_unit @ X7 @ (move @ ts3 @ ts @ v)) & ((restrict @ X7 @ (res @ ts) @ c) = (lan_Product_unit @ X7)) & ((lan_Product_unit @ X7) = (restrict @ X7 @ (res @ ts) @ e)) & (ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ X7))) & (ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ X7))) & ((nat_card @ (lan_Product_unit @ X7)) = one_one_nat) & ((nat_card @ (lan_Product_unit @ X7)) = one_one_nat))),
% 2.69/1.59 file('/export/starexec/sandbox2/tmp/tmp.pzq8qyAMZ7/DTF2THF_20750.p',fact_4__092_060open_062_092_060exists_062v_H_092_060le_062move_Ats_Ats_H_H_Av_O_A_I0_A_060_A_092_060parallel_062ext_Av_H_092_060parallel_062_A_092_060and_062_Alen_Av_H_Ats_H_H_Ac_A_061_Aext_Av_H_A_092_060and_062_Arestrict_Av_H_A_Ires_Ats_H_H_J_Ac_A_061_Alan_Av_H_A_092_060and_062_A_124lan_Av_H_124_A_061_A1_J_A_092_060and_062_A0_A_060_A_092_060parallel_062ext_Av_H_092_060parallel_062_A_092_060and_062_Alen_Av_H_Ats_H_H_Ae_A_061_Aext_Av_H_A_092_060and_062_Arestrict_Av_H_A_Ires_Ats_H_H_J_Ae_A_061_Alan_Av_H_A_092_060and_062_A_124lan_Av_H_124_A_061_A1_092_060close_062)).
% 2.69/1.59 thf(f1639,plain,(
% 2.69/1.59 ((lan_Product_unit @ sK47) != (restrict @ sK47 @ (res @ ts) @ e)) | ~spl112_1),
% 2.69/1.59 inference(subsumption_resolution,[status(thm)],[f1638,f1292])).
% 2.69/1.59 thf(f1292,plain,(
% 2.69/1.59 ($true = (ord_le461438217t_unit @ sK47 @ (move @ ts3 @ ts @ v)))),
% 2.69/1.59 inference(cnf_transformation,[status(thm)],[f1034])).
% 2.69/1.59 thf(f1638,plain,(
% 2.69/1.59 ($true != (ord_le461438217t_unit @ sK47 @ (move @ ts3 @ ts @ v))) | ((lan_Product_unit @ sK47) != (restrict @ sK47 @ (res @ ts) @ e)) | ~spl112_1),
% 2.69/1.59 inference(subsumption_resolution,[status(thm)],[f1637,f1299])).
% 2.69/1.59 thf(f1299,plain,(
% 2.69/1.59 ((len @ regular_regular @ sK47 @ ts @ c) = (ext_Product_unit @ sK47))),
% 2.69/1.59 inference(cnf_transformation,[status(thm)],[f1034])).
% 2.69/1.59 thf(f1637,plain,(
% 2.69/1.59 ((len @ regular_regular @ sK47 @ ts @ c) != (ext_Product_unit @ sK47)) | ((lan_Product_unit @ sK47) != (restrict @ sK47 @ (res @ ts) @ e)) | ($true != (ord_le461438217t_unit @ sK47 @ (move @ ts3 @ ts @ v))) | ~spl112_1),
% 2.69/1.59 inference(subsumption_resolution,[status(thm)],[f1636,f1293])).
% 2.69/1.59 thf(f1293,plain,(
% 2.69/1.59 ((lan_Product_unit @ sK47) = (restrict @ sK47 @ (res @ ts) @ c))),
% 2.69/1.59 inference(cnf_transformation,[status(thm)],[f1034])).
% 2.69/1.59 thf(f1636,plain,(
% 2.69/1.59 ((lan_Product_unit @ sK47) != (restrict @ sK47 @ (res @ ts) @ c)) | ($true != (ord_le461438217t_unit @ sK47 @ (move @ ts3 @ ts @ v))) | ((len @ regular_regular @ sK47 @ ts @ c) != (ext_Product_unit @ sK47)) | ((lan_Product_unit @ sK47) != (restrict @ sK47 @ (res @ ts) @ e)) | ~spl112_1),
% 2.69/1.59 inference(subsumption_resolution,[status(thm)],[f1627,f1296])).
% 2.69/1.59 thf(f1296,plain,(
% 2.69/1.59 ((ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ sK47))) = $true)),
% 2.69/1.59 inference(cnf_transformation,[status(thm)],[f1034])).
% 2.69/1.59 thf(f1627,plain,(
% 2.69/1.59 ((ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ sK47))) != $true) | ((len @ regular_regular @ sK47 @ ts @ c) != (ext_Product_unit @ sK47)) | ((lan_Product_unit @ sK47) != (restrict @ sK47 @ (res @ ts) @ e)) | ($true != (ord_le461438217t_unit @ sK47 @ (move @ ts3 @ ts @ v))) | ((lan_Product_unit @ sK47) != (restrict @ sK47 @ (res @ ts) @ c)) | ~spl112_1),
% 2.69/1.59 inference(trivial_inequality_removal,[status(thm)],[f1618])).
% 2.69/1.59 thf(f1618,plain,(
% 2.69/1.59 ((ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ sK47))) != $true) | ($true != (ord_le461438217t_unit @ sK47 @ (move @ ts3 @ ts @ v))) | ((nat_card @ (lan_Product_unit @ sK47)) != (nat_card @ (lan_Product_unit @ sK47))) | ((lan_Product_unit @ sK47) != (restrict @ sK47 @ (res @ ts) @ e)) | ((ext_Product_unit @ sK47) != (ext_Product_unit @ sK47)) | ((len @ regular_regular @ sK47 @ ts @ c) != (ext_Product_unit @ sK47)) | ((lan_Product_unit @ sK47) != (restrict @ sK47 @ (res @ ts) @ c)) | ~spl112_1),
% 2.69/1.59 inference(superposition,[status(thm)],[f1595,f1294])).
% 2.69/1.59 thf(f1294,plain,(
% 2.69/1.59 ((len @ regular_regular @ sK47 @ ts @ e) = (ext_Product_unit @ sK47))),
% 2.69/1.59 inference(cnf_transformation,[status(thm)],[f1034])).
% 2.69/1.59 thf(f1595,plain,(
% 2.69/1.59 ( ! [X0 : view_e774982825t_unit] : (((ext_Product_unit @ X0) != (len @ regular_regular @ X0 @ ts @ e)) | ($true != (ord_le461438217t_unit @ X0 @ (move @ ts3 @ ts @ v))) | ((len @ regular_regular @ X0 @ ts @ c) != (ext_Product_unit @ X0)) | ($true != (ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ X0)))) | ((nat_card @ (lan_Product_unit @ sK47)) != (nat_card @ (lan_Product_unit @ X0))) | ((restrict @ X0 @ (res @ ts) @ c) != (lan_Product_unit @ X0)) | ((lan_Product_unit @ X0) != (restrict @ X0 @ (res @ ts) @ e))) ) | ~spl112_1),
% 2.69/1.59 inference(avatar_component_clause,[status(thm)],[f1594])).
% 2.69/1.59 thf(f1594,definition,(
% 2.69/1.59 spl112_1 <=> ! [X0 : view_e774982825t_unit] : (($true != (ord_le461438217t_unit @ X0 @ (move @ ts3 @ ts @ v))) | ((len @ regular_regular @ X0 @ ts @ c) != (ext_Product_unit @ X0)) | ((restrict @ X0 @ (res @ ts) @ c) != (lan_Product_unit @ X0)) | ((lan_Product_unit @ X0) != (restrict @ X0 @ (res @ ts) @ e)) | ((ext_Product_unit @ X0) != (len @ regular_regular @ X0 @ ts @ e)) | ((nat_card @ (lan_Product_unit @ sK47)) != (nat_card @ (lan_Product_unit @ X0))) | ($true != (ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ X0)))))),
% 2.69/1.59 introduced(definition,[new_symbols(naming,[spl112_1])],[avatar_definition])).
% 2.69/1.59 thf(f1601,plain,(
% 2.69/1.59 ~spl112_2),
% 2.69/1.59 inference(avatar_split_clause,[status(thm)],[f1237,f1597])).
% 2.69/1.59 thf(f1597,definition,(
% 2.69/1.59 spl112_2 <=> (thesis = $true)),
% 2.69/1.59 introduced(definition,[new_symbols(naming,[spl112_2])],[avatar_definition])).
% 2.69/1.59 thf(f1237,plain,(
% 2.69/1.59 (thesis != $true)),
% 2.69/1.59 inference(cnf_transformation,[status(thm)],[f772])).
% 2.69/1.59 thf(f772,plain,(
% 2.69/1.59 (thesis != $true)),
% 2.69/1.59 inference(flattening,[status(thm)],[f595])).
% 2.69/1.59 thf(f595,plain,(
% 2.69/1.59 ~(thesis = $true)),
% 2.69/1.59 inference(fool_elimination,[status(thm)],[f594])).
% 2.69/1.59 thf(f594,plain,(
% 2.69/1.59 ~thesis),
% 2.69/1.59 inference(rectify,[status(thm)],[f286])).
% 2.69/1.59 thf(f286,negated_conjecture,(
% 2.69/1.59 ~thesis),
% 2.69/1.59 inference(negated_conjecture,[status(cth)],[f285])).
% 2.69/1.59 thf(f285,conjecture,(
% 2.69/1.59 thesis),
% 2.69/1.59 file('/export/starexec/sandbox2/tmp/tmp.pzq8qyAMZ7/DTF2THF_20750.p',conj_1)).
% 2.69/1.59 thf(f1600,plain,(
% 2.69/1.59 spl112_1 | spl112_2),
% 2.69/1.59 inference(avatar_split_clause,[status(thm)],[f1592,f1597,f1594])).
% 2.69/1.59 thf(f1592,plain,(
% 2.69/1.59 ( ! [X0 : view_e774982825t_unit] : ((thesis = $true) | ($true != (ord_le461438217t_unit @ X0 @ (move @ ts3 @ ts @ v))) | ($true != (ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ X0)))) | ((nat_card @ (lan_Product_unit @ sK47)) != (nat_card @ (lan_Product_unit @ X0))) | ((ext_Product_unit @ X0) != (len @ regular_regular @ X0 @ ts @ e)) | ((lan_Product_unit @ X0) != (restrict @ X0 @ (res @ ts) @ e)) | ((restrict @ X0 @ (res @ ts) @ c) != (lan_Product_unit @ X0)) | ((len @ regular_regular @ X0 @ ts @ c) != (ext_Product_unit @ X0))) )),
% 2.69/1.59 inference(duplicate_literal_removal,[status(thm)],[f1518])).
% 2.69/1.59 thf(f1518,plain,(
% 2.69/1.59 ( ! [X0 : view_e774982825t_unit] : (((ext_Product_unit @ X0) != (len @ regular_regular @ X0 @ ts @ e)) | ((nat_card @ (lan_Product_unit @ sK47)) != (nat_card @ (lan_Product_unit @ X0))) | ((len @ regular_regular @ X0 @ ts @ c) != (ext_Product_unit @ X0)) | (thesis = $true) | ((nat_card @ (lan_Product_unit @ sK47)) != (nat_card @ (lan_Product_unit @ X0))) | ($true != (ord_le461438217t_unit @ X0 @ (move @ ts3 @ ts @ v))) | ((lan_Product_unit @ X0) != (restrict @ X0 @ (res @ ts) @ e)) | ((restrict @ X0 @ (res @ ts) @ c) != (lan_Product_unit @ X0)) | ($true != (ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ X0)))) | ($true != (ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ X0))))) )),
% 2.69/1.59 inference(definition_unfolding,[status(thm)],[f1284,f1300,f1300])).
% 2.69/1.59 thf(f1300,plain,(
% 2.69/1.59 (one_one_nat = (nat_card @ (lan_Product_unit @ sK47)))),
% 2.69/1.59 inference(cnf_transformation,[status(thm)],[f1034])).
% 2.69/1.59 thf(f1284,plain,(
% 2.69/1.59 ( ! [X0 : view_e774982825t_unit] : (((restrict @ X0 @ (res @ ts) @ c) != (lan_Product_unit @ X0)) | (one_one_nat != (nat_card @ (lan_Product_unit @ X0))) | ($true != (ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ X0)))) | ((ext_Product_unit @ X0) != (len @ regular_regular @ X0 @ ts @ e)) | (thesis = $true) | ($true != (ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ X0)))) | (one_one_nat != (nat_card @ (lan_Product_unit @ X0))) | ((lan_Product_unit @ X0) != (restrict @ X0 @ (res @ ts) @ e)) | ((len @ regular_regular @ X0 @ ts @ c) != (ext_Product_unit @ X0)) | ($true != (ord_le461438217t_unit @ X0 @ (move @ ts3 @ ts @ v)))) )),
% 2.69/1.59 inference(cnf_transformation,[status(thm)],[f903])).
% 2.69/1.59 thf(f903,plain,(
% 2.69/1.59 ! [X0 : view_e774982825t_unit] : (((restrict @ X0 @ (res @ ts) @ c) != (lan_Product_unit @ X0)) | (one_one_nat != (nat_card @ (lan_Product_unit @ X0))) | ($true != (ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ X0)))) | ((ext_Product_unit @ X0) != (len @ regular_regular @ X0 @ ts @ e)) | (thesis = $true) | ($true != (ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ X0)))) | (one_one_nat != (nat_card @ (lan_Product_unit @ X0))) | ((lan_Product_unit @ X0) != (restrict @ X0 @ (res @ ts) @ e)) | ((len @ regular_regular @ X0 @ ts @ c) != (ext_Product_unit @ X0)) | ($true != (ord_le461438217t_unit @ X0 @ (move @ ts3 @ ts @ v))))),
% 2.69/1.59 inference(flattening,[status(thm)],[f902])).
% 2.69/1.59 thf(f902,plain,(
% 2.69/1.59 ! [X0 : view_e774982825t_unit] : ((thesis = $true) | (($true != (ord_le461438217t_unit @ X0 @ (move @ ts3 @ ts @ v))) | ((ext_Product_unit @ X0) != (len @ regular_regular @ X0 @ ts @ e)) | ((lan_Product_unit @ X0) != (restrict @ X0 @ (res @ ts) @ e)) | (one_one_nat != (nat_card @ (lan_Product_unit @ X0))) | ((restrict @ X0 @ (res @ ts) @ c) != (lan_Product_unit @ X0)) | ((len @ regular_regular @ X0 @ ts @ c) != (ext_Product_unit @ X0)) | (one_one_nat != (nat_card @ (lan_Product_unit @ X0))) | ($true != (ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ X0)))) | ($true != (ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ X0))))))),
% 2.69/1.59 inference(ennf_transformation,[status(thm)],[f677])).
% 2.69/1.59 thf(f677,plain,(
% 2.69/1.59 ! [X0 : view_e774982825t_unit] : ((($true = (ord_le461438217t_unit @ X0 @ (move @ ts3 @ ts @ v))) & ((ext_Product_unit @ X0) = (len @ regular_regular @ X0 @ ts @ e)) & ((lan_Product_unit @ X0) = (restrict @ X0 @ (res @ ts) @ e)) & (one_one_nat = (nat_card @ (lan_Product_unit @ X0))) & ((restrict @ X0 @ (res @ ts) @ c) = (lan_Product_unit @ X0)) & ((len @ regular_regular @ X0 @ ts @ c) = (ext_Product_unit @ X0)) & (one_one_nat = (nat_card @ (lan_Product_unit @ X0))) & ($true = (ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ X0)))) & ($true = (ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ X0))))) => (thesis = $true))),
% 2.69/1.59 inference(fool_elimination,[status(thm)],[f676])).
% 2.69/1.59 thf(f676,plain,(
% 2.69/1.59 ! [X0 : view_e774982825t_unit] : (((one_one_nat = (nat_card @ (lan_Product_unit @ X0))) & ((len @ regular_regular @ X0 @ ts @ c) = (ext_Product_unit @ X0)) & ((restrict @ X0 @ (res @ ts) @ c) = (lan_Product_unit @ X0)) & ((ext_Product_unit @ X0) = (len @ regular_regular @ X0 @ ts @ e)) & (ord_le461438217t_unit @ X0 @ (move @ ts3 @ ts @ v)) & (ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ X0))) & ((lan_Product_unit @ X0) = (restrict @ X0 @ (res @ ts) @ e)) & (ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ X0))) & (one_one_nat = (nat_card @ (lan_Product_unit @ X0)))) => thesis)),
% 2.69/1.59 inference(rectify,[status(thm)],[f284])).
% 2.69/1.59 thf(f284,axiom,(
% 2.69/1.59 ! [X87 : view_e774982825t_unit] : (((one_one_nat = (nat_card @ (lan_Product_unit @ X87))) & ((ext_Product_unit @ X87) = (len @ regular_regular @ X87 @ ts @ c)) & ((restrict @ X87 @ (res @ ts) @ c) = (lan_Product_unit @ X87)) & ((ext_Product_unit @ X87) = (len @ regular_regular @ X87 @ ts @ e)) & (ord_le461438217t_unit @ X87 @ (move @ ts3 @ ts @ v)) & (ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ X87))) & ((lan_Product_unit @ X87) = (restrict @ X87 @ (res @ ts) @ e)) & (ord_less_real @ zero_zero_real @ (real_length @ (ext_Product_unit @ X87))) & (one_one_nat = (nat_card @ (lan_Product_unit @ X87)))) => thesis)),
% 2.69/1.59 file('/export/starexec/sandbox2/tmp/tmp.pzq8qyAMZ7/DTF2THF_20750.p',conj_0)).
% 2.69/1.59 % SZS output end Proof for DTF2THF_20750
% 2.69/1.59 % (20862)------------------------------
% 2.69/1.59 % (20862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.59 % (20862)Termination reason: Refutation
% 2.69/1.59
% 2.69/1.59 % (20862)Memory used [KB]: 7547
% 2.69/1.59 % (20862)Time elapsed: 0.070 s
% 2.69/1.59 % (20862)Instructions burned: 231 (million)
% 2.69/1.59 % (20862)------------------------------
% 2.69/1.59 % (20862)------------------------------
% 2.69/1.59 % (20855)Success in time 0.085 s
%------------------------------------------------------------------------------