%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP047^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:07 AM UTC 2026
% Result : Theorem 3.19s 1.73s
% Output : Refutation 3.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 22 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 106 ( 7 ~; 3 |; 1 &; 94 @)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 36 ( 35 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 186 ( 184 usr; 27 con; 0-7 aty)
% Number of variables : 17 ( 0 ^; 17 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
produc1156025366_r_l_v: $tType ).
thf(type_def_6,type,
expr_r_l_v: $tType ).
thf(type_def_8,type,
l: $tType ).
thf(type_def_9,type,
option_val_r_l_v: $tType ).
thf(type_def_10,type,
const: $tType ).
thf(type_def_11,type,
val_r_l_v: $tType ).
thf(type_def_12,type,
cntxt_r_l_v: $tType ).
thf(type_def_13,type,
r: $tType ).
thf(type_def_14,type,
v: $tType ).
thf(type_def_15,type,
option1457017436_r_l_v: $tType ).
thf(type_def_16,type,
set_option_set_l: $tType ).
thf(type_def_17,type,
set_option_set_r: $tType ).
thf(type_def_18,type,
set_op76482283um_l_l: $tType ).
thf(type_def_19,type,
set_op160472561um_l_r: $tType ).
thf(type_def_20,type,
set_op865065573um_r_l: $tType ).
thf(type_def_21,type,
set_option_l: $tType ).
thf(type_def_22,type,
set_option_r: $tType ).
thf(type_def_23,type,
set_Product_prod_l_l: $tType ).
thf(type_def_24,type,
set_Product_prod_l_r: $tType ).
thf(type_def_25,type,
set_Product_prod_r_l: $tType ).
thf(type_def_26,type,
set_Product_prod_r_r: $tType ).
thf(type_def_27,type,
set_set_l: $tType ).
thf(type_def_28,type,
set_set_r: $tType ).
thf(type_def_29,type,
set_Sum_sum_l_l: $tType ).
thf(type_def_30,type,
set_Sum_sum_l_r: $tType ).
thf(type_def_31,type,
set_Sum_sum_r_l: $tType ).
thf(type_def_32,type,
set_Sum_sum_r_r: $tType ).
thf(type_def_33,type,
set_l: $tType ).
thf(type_def_34,type,
set_r: $tType ).
thf(type_def_35,type,
produc1164766533_r_l_v: $tType ).
thf(type_def_36,type,
produc1489027110_r_l_v: $tType ).
thf(type_def_37,type,
produc1394974636_r_l_v: $tType ).
thf(type_def_38,type,
sum_sum_l_l: $tType ).
thf(type_def_39,type,
sum_sum_l_r: $tType ).
thf(type_def_40,type,
sum_sum_r_l: $tType ).
thf(func_def_0,type,
produc1394974636_r_l_v: $tType ).
thf(func_def_1,type,
produc1489027110_r_l_v: $tType ).
thf(func_def_2,type,
option1457017436_r_l_v: $tType ).
thf(func_def_3,type,
produc1156025366_r_l_v: $tType ).
thf(func_def_4,type,
produc1164766533_r_l_v: $tType ).
thf(func_def_5,type,
set_op865065573um_r_l: $tType ).
thf(func_def_6,type,
set_op160472561um_l_r: $tType ).
thf(func_def_7,type,
set_op76482283um_l_l: $tType ).
thf(func_def_8,type,
set_option_set_r: $tType ).
thf(func_def_9,type,
set_option_set_l: $tType ).
thf(func_def_10,type,
option_val_r_l_v: $tType ).
thf(func_def_11,type,
set_Product_prod_r_r: $tType ).
thf(func_def_12,type,
set_Product_prod_r_l: $tType ).
thf(func_def_13,type,
set_Product_prod_l_r: $tType ).
thf(func_def_14,type,
set_Product_prod_l_l: $tType ).
thf(func_def_15,type,
set_Sum_sum_r_r: $tType ).
thf(func_def_16,type,
set_Sum_sum_r_l: $tType ).
thf(func_def_17,type,
set_Sum_sum_l_r: $tType ).
thf(func_def_18,type,
set_Sum_sum_l_l: $tType ).
thf(func_def_19,type,
set_option_r: $tType ).
thf(func_def_20,type,
set_option_l: $tType ).
thf(func_def_21,type,
cntxt_r_l_v: $tType ).
thf(func_def_22,type,
set_set_r: $tType ).
thf(func_def_23,type,
set_set_l: $tType ).
thf(func_def_24,type,
expr_r_l_v: $tType ).
thf(func_def_25,type,
sum_sum_r_l: $tType ).
thf(func_def_26,type,
sum_sum_l_r: $tType ).
thf(func_def_27,type,
sum_sum_l_l: $tType ).
thf(func_def_28,type,
val_r_l_v: $tType ).
thf(func_def_29,type,
set_r: $tType ).
thf(func_def_30,type,
set_l: $tType ).
thf(func_def_31,type,
const: $tType ).
thf(func_def_32,type,
v: $tType ).
thf(func_def_33,type,
r: $tType ).
thf(func_def_34,type,
l: $tType ).
thf(func_def_35,type,
lID_expression_l_r_v: produc1156025366_r_l_v > expr_r_l_v ).
thf(func_def_36,type,
lID_lo1265057957_l_r_v: produc1156025366_r_l_v > l > option_val_r_l_v ).
thf(func_def_37,type,
lID_snapshot_l_r_v: produc1156025366_r_l_v > l > option_val_r_l_v ).
thf(func_def_38,type,
combine_l_val_r_l_v: ( l > option_val_r_l_v ) > ( l > option_val_r_l_v ) > l > option_val_r_l_v ).
thf(func_def_39,type,
unit: const ).
thf(func_def_40,type,
ref_r_l_v: expr_r_l_v > expr_r_l_v ).
thf(func_def_41,type,
rfork_r_l_v: expr_r_l_v > expr_r_l_v ).
thf(func_def_42,type,
rjoin_r_l_v: expr_r_l_v > expr_r_l_v ).
thf(func_def_43,type,
vE_r_l_v: val_r_l_v > expr_r_l_v ).
thf(func_def_44,type,
plug_r_l_v: cntxt_r_l_v > expr_r_l_v > expr_r_l_v ).
thf(func_def_45,type,
cV_r_l_v: const > val_r_l_v ).
thf(func_def_46,type,
loc_l_r_v: l > val_r_l_v ).
thf(func_def_47,type,
rid_r_l_v: r > val_r_l_v ).
thf(func_def_48,type,
execution_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > expr_r_l_v > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
thf(func_def_49,type,
induct1670415253_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( ( r > option1457017436_r_l_v ) > $o ) > $o ).
thf(func_def_50,type,
reachable_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
thf(func_def_51,type,
finite160708696_set_l: set_option_set_l > $o ).
thf(func_def_52,type,
finite555643486_set_r: set_option_set_r > $o ).
thf(func_def_53,type,
finite1864485196um_l_l: set_op76482283um_l_l > $o ).
thf(func_def_54,type,
finite111936338um_l_r: set_op160472561um_l_r > $o ).
thf(func_def_55,type,
finite1036466630um_r_l: set_op865065573um_r_l > $o ).
thf(func_def_56,type,
finite2114249848tion_l: set_option_l > $o ).
thf(func_def_57,type,
finite16335230tion_r: set_option_r > $o ).
thf(func_def_58,type,
finite785973648od_l_l: set_Product_prod_l_l > $o ).
thf(func_def_59,type,
finite835542678od_l_r: set_Product_prod_l_r > $o ).
thf(func_def_60,type,
finite1457622794od_r_l: set_Product_prod_r_l > $o ).
thf(func_def_61,type,
finite1507191824od_r_r: set_Product_prod_r_r > $o ).
thf(func_def_62,type,
finite_finite_set_l: set_set_l > $o ).
thf(func_def_63,type,
finite_finite_set_r: set_set_r > $o ).
thf(func_def_64,type,
finite1541484284um_l_l: set_Sum_sum_l_l > $o ).
thf(func_def_65,type,
finite1591053314um_l_r: set_Sum_sum_l_r > $o ).
thf(func_def_66,type,
finite65649782um_r_l: set_Sum_sum_r_l > $o ).
thf(func_def_67,type,
finite115218812um_r_r: set_Sum_sum_r_r > $o ).
thf(func_def_68,type,
finite_finite_l: set_l > $o ).
thf(func_def_69,type,
finite_finite_r: set_r > $o ).
thf(func_def_70,type,
bij_betw_l_l: ( l > l ) > set_l > set_l > $o ).
thf(func_def_71,type,
bij_betw_l_r: ( l > r ) > set_l > set_r > $o ).
thf(func_def_72,type,
bij_betw_r_l: ( r > l ) > set_r > set_l > $o ).
thf(func_def_73,type,
bij_betw_r_r: ( r > r ) > set_r > set_r > $o ).
thf(func_def_74,type,
fun_up1835647912_r_l_v: ( l > option_val_r_l_v ) > l > option_val_r_l_v > l > option_val_r_l_v ).
thf(func_def_75,type,
fun_up709272714_r_l_v: ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v > r > option1457017436_r_l_v ).
thf(func_def_76,type,
if_option_val_r_l_v: $o > option_val_r_l_v > option_val_r_l_v > option_val_r_l_v ).
thf(func_def_77,type,
if_opt1153928738_r_l_v: $o > option1457017436_r_l_v > option1457017436_r_l_v > option1457017436_r_l_v ).
thf(func_def_78,type,
lID_G_r_l_v: ( r > option1457017436_r_l_v ) > set_l ).
thf(func_def_79,type,
lID_L_l_r_v: produc1156025366_r_l_v > set_l ).
thf(func_def_80,type,
rID_G_r_l_v: ( r > option1457017436_r_l_v ) > set_r ).
thf(func_def_81,type,
rID_L_l_r_v: produc1156025366_r_l_v > set_r ).
thf(func_def_82,type,
domain87684397_l_r_v: produc1156025366_r_l_v > $o ).
thf(func_def_83,type,
domain1547879849_r_l_v: ( r > option1457017436_r_l_v ) > $o ).
thf(func_def_84,type,
revision_step_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
thf(func_def_85,type,
revisi1291188644_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
thf(func_def_86,type,
subsum148050133_r_l_v: r > r > ( r > option1457017436_r_l_v ) > $o ).
thf(func_def_87,type,
subsum680764357_r_l_v: ( r > option1457017436_r_l_v ) > $o ).
thf(func_def_88,type,
none_val_r_l_v: option_val_r_l_v ).
thf(func_def_89,type,
none_P277133687_r_l_v: option1457017436_r_l_v ).
thf(func_def_90,type,
some_val_r_l_v: val_r_l_v > option_val_r_l_v ).
thf(func_def_91,type,
some_P1807977723_r_l_v: produc1156025366_r_l_v > option1457017436_r_l_v ).
thf(func_def_92,type,
ord_less_eq_set_l: set_l > set_l > $o ).
thf(func_def_93,type,
ord_less_eq_set_r: set_r > set_r > $o ).
thf(func_def_94,type,
top_to471808607_set_l: set_option_set_l ).
thf(func_def_95,type,
top_to555798885_set_r: set_option_set_r ).
thf(func_def_96,type,
top_to1066565019um_l_l: set_op76482283um_l_l ).
thf(func_def_97,type,
top_to1150555297um_l_r: set_op160472561um_l_r ).
thf(func_def_98,type,
top_to1855148309um_r_l: set_op865065573um_r_l ).
thf(func_def_99,type,
top_top_set_option_l: set_option_l ).
thf(func_def_100,type,
top_top_set_option_r: set_option_r ).
thf(func_def_101,type,
top_to320296343od_l_l: set_Product_prod_l_l ).
thf(func_def_102,type,
top_to715231133od_l_r: set_Product_prod_l_r ).
thf(func_def_103,type,
top_to1639761425od_r_l: set_Product_prod_r_l ).
thf(func_def_104,type,
top_to2034696215od_r_r: set_Product_prod_r_r ).
thf(func_def_105,type,
top_top_set_set_l: set_set_l ).
thf(func_def_106,type,
top_top_set_set_r: set_set_r ).
thf(func_def_107,type,
top_to1010946379um_l_l: set_Sum_sum_l_l ).
thf(func_def_108,type,
top_to1405881169um_l_r: set_Sum_sum_l_r ).
thf(func_def_109,type,
top_to182927813um_r_l: set_Sum_sum_r_l ).
thf(func_def_110,type,
top_to577862603um_r_r: set_Sum_sum_r_r ).
thf(func_def_111,type,
top_top_set_l: set_l ).
thf(func_def_112,type,
top_top_set_r: set_r ).
thf(func_def_113,type,
produc1834103605_r_l_v: ( l > option_val_r_l_v ) > expr_r_l_v > produc1164766533_r_l_v ).
thf(func_def_114,type,
produc297528454_r_l_v: ( l > option_val_r_l_v ) > produc1164766533_r_l_v > produc1156025366_r_l_v ).
thf(func_def_115,type,
produc2057232216_r_l_v: ( l > l ) > produc1156025366_r_l_v > produc1489027110_r_l_v ).
thf(func_def_116,type,
produc2111504612_r_l_v: ( r > r ) > produc1489027110_r_l_v > produc1394974636_r_l_v ).
thf(func_def_117,type,
r_G_r_l_v: ( r > r ) > ( l > l ) > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_118,type,
r_L_r_l_v: ( r > r ) > ( l > l ) > produc1156025366_r_l_v > produc1156025366_r_l_v ).
thf(func_def_119,type,
eq_states_r_l_v: ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
thf(func_def_120,type,
is_glo1871033385_r_l_v: ( r > r ) > ( l > l ) > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
thf(func_def_121,type,
collect_set_l: ( set_l > $o ) > set_set_l ).
thf(func_def_122,type,
collect_set_r: ( set_r > $o ) > set_set_r ).
thf(func_def_123,type,
collect_Sum_sum_l_l: ( sum_sum_l_l > $o ) > set_Sum_sum_l_l ).
thf(func_def_124,type,
collect_Sum_sum_l_r: ( sum_sum_l_r > $o ) > set_Sum_sum_l_r ).
thf(func_def_125,type,
collect_Sum_sum_r_l: ( sum_sum_r_l > $o ) > set_Sum_sum_r_l ).
thf(func_def_126,type,
collect_l: ( l > $o ) > set_l ).
thf(func_def_127,type,
collect_r: ( r > $o ) > set_r ).
thf(func_def_128,type,
substitution_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > $o ).
thf(func_def_129,type,
member_set_l: set_l > set_set_l > $o ).
thf(func_def_130,type,
member_set_r: set_r > set_set_r > $o ).
thf(func_def_131,type,
member_l: l > set_l > $o ).
thf(func_def_132,type,
member_r: r > set_r > $o ).
thf(func_def_133,type,
e: cntxt_r_l_v ).
thf(func_def_134,type,
alpha: r > r ).
thf(func_def_135,type,
beta: l > l ).
thf(func_def_136,type,
sigma: l > option_val_r_l_v ).
thf(func_def_137,type,
tau: l > option_val_r_l_v ).
thf(func_def_138,type,
e2: expr_r_l_v ).
thf(func_def_139,type,
r2: r ).
thf(func_def_140,type,
r3: r ).
thf(func_def_141,type,
s: r > option1457017436_r_l_v ).
thf(func_def_142,type,
s2: r > option1457017436_r_l_v ).
thf(func_def_143,type,
subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v ).
thf(func_def_160,type,
sP0: r > ( r > option1457017436_r_l_v ) > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > ( r > option1457017436_r_l_v ) > $o ).
thf(func_def_161,type,
sP1: r > ( r > option1457017436_r_l_v ) > r > ( r > option1457017436_r_l_v ) > $o ).
thf(func_def_162,type,
sK2: ( r > option1457017436_r_l_v ) > r ).
thf(func_def_163,type,
sK3: r > r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_164,type,
sK4: r > r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_165,type,
sK5: ( r > option1457017436_r_l_v ) > r ).
thf(func_def_166,type,
sK6: r > ( r > option1457017436_r_l_v ) > l > option_val_r_l_v ).
thf(func_def_167,type,
sK7: r > ( r > option1457017436_r_l_v ) > expr_r_l_v ).
thf(func_def_168,type,
sK8: r > ( r > option1457017436_r_l_v ) > cntxt_r_l_v ).
thf(func_def_169,type,
sK9: r > ( r > option1457017436_r_l_v ) > l > option_val_r_l_v ).
thf(func_def_170,type,
sK10: ( produc1156025366_r_l_v > $o ) > produc1164766533_r_l_v ).
thf(func_def_171,type,
sK11: ( produc1156025366_r_l_v > $o ) > l > option_val_r_l_v ).
thf(func_def_172,type,
sK12: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > ( r > option1457017436_r_l_v ) > r > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_173,type,
sK13: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > ( r > option1457017436_r_l_v ) > r > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_174,type,
sK14: produc1156025366_r_l_v > expr_r_l_v ).
thf(func_def_175,type,
sK15: produc1156025366_r_l_v > l > option_val_r_l_v ).
thf(func_def_176,type,
sK16: produc1156025366_r_l_v > l > option_val_r_l_v ).
thf(func_def_177,type,
sK17: r > ( r > option1457017436_r_l_v ) > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( r > option1457017436_r_l_v ) > r > r > option1457017436_r_l_v ).
thf(func_def_178,type,
sK18: r > ( r > option1457017436_r_l_v ) > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( r > option1457017436_r_l_v ) > r > r > option1457017436_r_l_v ).
thf(func_def_179,type,
sK19: ( ( r > r ) > ( l > l ) > produc1156025366_r_l_v > $o ) > expr_r_l_v ).
thf(func_def_180,type,
sK20: ( ( r > r ) > ( l > l ) > produc1156025366_r_l_v > $o ) > r > r ).
thf(func_def_181,type,
sK21: ( ( r > r ) > ( l > l ) > produc1156025366_r_l_v > $o ) > l > option_val_r_l_v ).
thf(func_def_182,type,
sK22: ( ( r > r ) > ( l > l ) > produc1156025366_r_l_v > $o ) > l > l ).
thf(func_def_183,type,
sK23: ( ( r > r ) > ( l > l ) > produc1156025366_r_l_v > $o ) > l > option_val_r_l_v ).
thf(func_def_184,type,
sK24: ( produc1164766533_r_l_v > $o ) > l > option_val_r_l_v ).
thf(func_def_185,type,
sK25: ( produc1164766533_r_l_v > $o ) > expr_r_l_v ).
thf(func_def_186,type,
sK26: ( r > option1457017436_r_l_v ) > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( r > option1457017436_r_l_v ) > r > r > r > option1457017436_r_l_v ).
thf(func_def_187,type,
sK27: ( r > option1457017436_r_l_v ) > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( r > option1457017436_r_l_v ) > r > r > r > option1457017436_r_l_v ).
thf(func_def_188,type,
sK28: ( r > option1457017436_r_l_v ) > r > expr_r_l_v ).
thf(func_def_189,type,
sK29: ( r > option1457017436_r_l_v ) > r > l > option_val_r_l_v ).
thf(func_def_190,type,
sK30: ( r > option1457017436_r_l_v ) > r > cntxt_r_l_v ).
thf(func_def_191,type,
sK31: ( r > option1457017436_r_l_v ) > r > l > option_val_r_l_v ).
thf(func_def_192,type,
sK32: ( produc1156025366_r_l_v > $o ) > l > option_val_r_l_v ).
thf(func_def_193,type,
sK33: ( produc1156025366_r_l_v > $o ) > produc1164766533_r_l_v ).
thf(func_def_194,type,
sK34: ( r > option1457017436_r_l_v ) > r > r > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_195,type,
sK35: ( r > option1457017436_r_l_v ) > r > r > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_196,type,
sK36: set_r > r ).
thf(func_def_197,type,
sK37: produc1164766533_r_l_v > expr_r_l_v ).
thf(func_def_198,type,
sK38: produc1164766533_r_l_v > l > option_val_r_l_v ).
thf(func_def_199,type,
sK39: produc1164766533_r_l_v > l > option_val_r_l_v ).
thf(func_def_200,type,
sK40: produc1164766533_r_l_v > expr_r_l_v ).
thf(func_def_201,type,
sK41: ( l > option_val_r_l_v ) > ( r > option1457017436_r_l_v ) > r > ( r > option1457017436_r_l_v ) > cntxt_r_l_v > ( l > option_val_r_l_v ) > expr_r_l_v > r ).
thf(func_def_202,type,
sK42: ( r > option1457017436_r_l_v ) > r > ( r > option1457017436_r_l_v ) > r > r > option1457017436_r_l_v ).
thf(func_def_203,type,
sK43: ( r > option1457017436_r_l_v ) > r > ( r > option1457017436_r_l_v ) > r > r > option1457017436_r_l_v ).
thf(func_def_204,type,
sK44: ( produc1164766533_r_l_v > $o ) > l > option_val_r_l_v ).
thf(func_def_205,type,
sK45: ( produc1164766533_r_l_v > $o ) > expr_r_l_v ).
thf(func_def_206,type,
sK46: r > ( r > option1457017436_r_l_v ) > r > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_207,type,
sK47: r > ( r > option1457017436_r_l_v ) > r > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_208,type,
sK48: produc1156025366_r_l_v > l > option_val_r_l_v ).
thf(func_def_209,type,
sK49: produc1156025366_r_l_v > expr_r_l_v ).
thf(func_def_210,type,
sK50: produc1156025366_r_l_v > l > option_val_r_l_v ).
thf(func_def_211,type,
sK51: ( r > option1457017436_r_l_v ) > l ).
thf(func_def_212,type,
sK52: r > r > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_213,type,
sK53: r > r > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_214,type,
sK54: ( r > option1457017436_r_l_v ) > l ).
thf(func_def_215,type,
sK55: r > r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_216,type,
sK56: r > r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_217,type,
sK57: r > ( l > option_val_r_l_v ) > expr_r_l_v > ( r > option1457017436_r_l_v ) > cntxt_r_l_v > ( r > option1457017436_r_l_v ) > ( l > option_val_r_l_v ) > r ).
thf(func_def_218,type,
sK58: ( produc1156025366_r_l_v > $o ) > l > option_val_r_l_v ).
thf(func_def_219,type,
sK59: ( produc1156025366_r_l_v > $o ) > l > option_val_r_l_v ).
thf(func_def_220,type,
sK60: ( produc1156025366_r_l_v > $o ) > expr_r_l_v ).
thf(func_def_221,type,
sK61: produc1156025366_r_l_v > produc1164766533_r_l_v ).
thf(func_def_222,type,
sK62: produc1156025366_r_l_v > l > option_val_r_l_v ).
thf(func_def_223,type,
sK63: r > r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_224,type,
sK64: r > r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_225,type,
sK65: produc1156025366_r_l_v > l > option_val_r_l_v ).
thf(func_def_226,type,
sK66: produc1156025366_r_l_v > produc1164766533_r_l_v ).
thf(func_def_227,type,
sK67: ( r > option1457017436_r_l_v ) > r > ( r > option1457017436_r_l_v ) > r > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_228,type,
sK68: ( r > option1457017436_r_l_v ) > r > ( r > option1457017436_r_l_v ) > r > ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_229,type,
sK69: ( produc1156025366_r_l_v > $o ) > l > option_val_r_l_v ).
thf(func_def_230,type,
sK70: ( produc1156025366_r_l_v > $o ) > expr_r_l_v ).
thf(func_def_231,type,
sK71: ( produc1156025366_r_l_v > $o ) > l > option_val_r_l_v ).
thf(func_def_232,type,
sK72: ( r > option1457017436_r_l_v ) > r > r > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_233,type,
sK73: ( r > option1457017436_r_l_v ) > r > r > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(func_def_235,type,
ph75:
!>[X0: $tType] : X0 ).
thf(f1394,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1393,f1388]) ).
thf(f1388,plain,
! [X2: r > option1457017436_r_l_v,X0: r] :
( ( fun_up709272714_r_l_v @ X2 @ X0 @ ( X2 @ X0 ) )
= X2 ),
inference(equality_resolution,[status(thm)],[f1296]) ).
thf(f1296,plain,
! [X2: r > option1457017436_r_l_v,X0: r,X1: option1457017436_r_l_v] :
( ( ( fun_up709272714_r_l_v @ X2 @ X0 @ X1 )
= X2 )
| ( ( X2 @ X0 )
!= X1 ) ),
inference(cnf_transformation,[status(thm)],[f1144]) ).
thf(f1144,plain,
! [X0: r,X1: option1457017436_r_l_v,X2: r > option1457017436_r_l_v] :
( ( ( ( X2 @ X0 )
= X1 )
| ( ( fun_up709272714_r_l_v @ X2 @ X0 @ X1 )
!= X2 ) )
& ( ( ( fun_up709272714_r_l_v @ X2 @ X0 @ X1 )
= X2 )
| ( ( X2 @ X0 )
!= X1 ) ) ),
inference(nnf_transformation,[status(thm)],[f651]) ).
thf(f651,plain,
! [X0: r,X1: option1457017436_r_l_v,X2: r > option1457017436_r_l_v] :
( ( ( X2 @ X0 )
= X1 )
<=> ( ( fun_up709272714_r_l_v @ X2 @ X0 @ X1 )
= X2 ) ),
inference(fool_elimination,[status(thm)],[f650]) ).
thf(f650,plain,
! [X0: r,X1: option1457017436_r_l_v,X2: r > option1457017436_r_l_v] :
( ( ( fun_up709272714_r_l_v @ X2 @ X0 @ X1 )
= X2 )
= ( ( X2 @ X0 )
= X1 ) ),
inference(rectify,[status(thm)],[f46]) ).
thf(f46,axiom,
! [X6: r,X7: option1457017436_r_l_v,X5: r > option1457017436_r_l_v] :
( ( ( fun_up709272714_r_l_v @ X5 @ X6 @ X7 )
= X5 )
= ( ( X5 @ X6 )
= X7 ) ),
file('/export/starexec/sandbox/tmp/tmp.6Efo01nBTw/DTF2THF_15893.p',fact_45_fun__upd__idem__iff) ).
thf(f1393,plain,
( s
!= ( fun_up709272714_r_l_v @ s @ r2 @ ( s @ r2 ) ) ),
inference(forward_demodulation,[status(thm)],[f1178,f1292]) ).
thf(f1292,plain,
( ( s @ r2 )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( rfork_r_l_v @ e2 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( s @ r2 )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( rfork_r_l_v @ e2 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6Efo01nBTw/DTF2THF_15893.p',fact_0_local_Ofork_I2_J) ).
thf(f1178,plain,
( s
!= ( fun_up709272714_r_l_v @ s @ r2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( rfork_r_l_v @ e2 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f904]) ).
thf(f904,plain,
( s
!= ( fun_up709272714_r_l_v @ s @ r2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( rfork_r_l_v @ e2 ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f359]) ).
thf(f359,negated_conjecture,
( s
!= ( fun_up709272714_r_l_v @ s @ r2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( rfork_r_l_v @ e2 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f358]) ).
thf(f358,conjecture,
( s
= ( fun_up709272714_r_l_v @ s @ r2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( rfork_r_l_v @ e2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.6Efo01nBTw/DTF2THF_15893.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP047^1 : TPTP v9.2.1. Released v7.5.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.34 % Computer : n031.cluster.edu
% 0.19/0.34 % Model : x86_64 x86_64
% 0.19/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.34 % Memory : 8042.1875MB
% 0.19/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.34 % CPULimit : 300
% 0.19/0.34 % WCLimit : 300
% 0.19/0.34 % DateTime : Tue Feb 24 08:25:33 EST 2026
% 0.19/0.34 % CPUTime :
% 0.19/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.32/0.46 ---- Original DTF file ---
% 0.32/0.47 thf(spec,logic,$$dhol).
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 % File : ITP047^1 : TPTP v9.2.1. Released v7.5.0.
% 0.32/0.47 % Domain : Interactive Theorem Proving
% 0.32/0.47 % Problem : Sledgehammer Determinacy problem prob_914__3357784_1
% 0.32/0.47 % Version : Especial.
% 0.32/0.47 % English :
% 0.32/0.47
% 0.32/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.32/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.32/0.47 % Source : [Des21]
% 0.32/0.47 % Names : Determinacy/prob_914__3357784_1 [Des21]
% 0.32/0.47
% 0.32/0.47 % Status : Theorem
% 0.32/0.47 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0
% 0.32/0.47 % Syntax : Number of formulae : 502 ( 137 unt; 144 typ; 0 def)
% 0.32/0.47 % Number of atoms : 1189 ( 524 equ; 0 cnn)
% 0.32/0.47 % Maximal formula atoms : 13 ( 3 avg)
% 0.32/0.47 % Number of connectives : 4447 ( 181 ~; 60 |; 118 &;3553 @)
% 0.32/0.47 % ( 0 <=>; 535 =>; 0 <=; 0 <~>)
% 0.32/0.47 % Maximal formula depth : 35 ( 8 avg)
% 0.32/0.47 % Number of types : 36 ( 35 usr)
% 0.32/0.47 % Number of type conns : 991 ( 991 >; 0 *; 0 +; 0 <<)
% 0.32/0.47 % Number of symbols : 112 ( 109 usr; 28 con; 0-4 aty)
% 0.32/0.47 % Number of variables : 1427 ( 111 ^;1223 !; 93 ?;1427 :)
% 0.32/0.47 % SPC : TH0_THM_EQU_NAR
% 0.32/0.47
% 0.32/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 15:34:36.700
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 % Could-be-implicit typings (35)
% 0.32/0.47 thf(ty_n_t__Product____Type__Oprod_I_062_Itf__r_Mtf__r_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mtf__l_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J_J,type,
% 0.32/0.47 produc1394974636_r_l_v: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Product____Type__Oprod_I_062_Itf__l_Mtf__l_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J,type,
% 0.32/0.47 produc1489027110_r_l_v: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J,type,
% 0.32/0.47 option1457017436_r_l_v: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J,type,
% 0.32/0.47 produc1156025366_r_l_v: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J,type,
% 0.32/0.47 produc1164766533_r_l_v: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Sum____Type__Osum_Itf__r_Mtf__l_J_J_J,type,
% 0.32/0.47 set_op865065573um_r_l: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Sum____Type__Osum_Itf__l_Mtf__r_J_J_J,type,
% 0.32/0.47 set_op160472561um_l_r: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Sum____Type__Osum_Itf__l_Mtf__l_J_J_J,type,
% 0.32/0.47 set_op76482283um_l_l: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Set__Oset_Itf__r_J_J_J,type,
% 0.32/0.47 set_option_set_r: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Set__Oset_Itf__l_J_J_J,type,
% 0.32/0.47 set_option_set_l: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J,type,
% 0.32/0.47 option_val_r_l_v: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__r_Mtf__r_J_J,type,
% 0.32/0.47 set_Product_prod_r_r: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__r_Mtf__l_J_J,type,
% 0.32/0.47 set_Product_prod_r_l: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__l_Mtf__r_J_J,type,
% 0.32/0.47 set_Product_prod_l_r: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__l_Mtf__l_J_J,type,
% 0.32/0.47 set_Product_prod_l_l: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_Itf__r_Mtf__r_J_J,type,
% 0.32/0.47 set_Sum_sum_r_r: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_Itf__r_Mtf__l_J_J,type,
% 0.32/0.47 set_Sum_sum_r_l: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_Itf__l_Mtf__r_J_J,type,
% 0.32/0.47 set_Sum_sum_l_r: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_Itf__l_Mtf__l_J_J,type,
% 0.32/0.47 set_Sum_sum_l_l: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Set__Oset_It__Option__Ooption_Itf__r_J_J,type,
% 0.32/0.47 set_option_r: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Set__Oset_It__Option__Ooption_Itf__l_J_J,type,
% 0.32/0.47 set_option_l: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Data__Ocntxt_Itf__r_Mtf__l_Mtf__v_J,type,
% 0.32/0.47 cntxt_r_l_v: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Set__Oset_It__Set__Oset_Itf__r_J_J,type,
% 0.32/0.47 set_set_r: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Set__Oset_It__Set__Oset_Itf__l_J_J,type,
% 0.32/0.47 set_set_l: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J,type,
% 0.32/0.47 expr_r_l_v: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Sum____Type__Osum_Itf__r_Mtf__l_J,type,
% 0.32/0.47 sum_sum_r_l: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Sum____Type__Osum_Itf__l_Mtf__r_J,type,
% 0.32/0.47 sum_sum_l_r: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Sum____Type__Osum_Itf__l_Mtf__l_J,type,
% 0.32/0.47 sum_sum_l_l: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,type,
% 0.32/0.47 val_r_l_v: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Set__Oset_Itf__r_J,type,
% 0.32/0.47 set_r: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Set__Oset_Itf__l_J,type,
% 0.32/0.47 set_l: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_t__Data__Oconst,type,
% 0.32/0.47 const: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_tf__v,type,
% 0.32/0.47 v: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_tf__r,type,
% 0.32/0.47 r: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(ty_n_tf__l,type,
% 0.32/0.47 l: $tType ).
% 0.32/0.47
% 0.32/0.47 % Explicit typings (109)
% 0.32/0.47 thf(sy_c_Data_OLID__expression_001tf__l_001tf__r_001tf__v,type,
% 0.32/0.47 lID_expression_l_r_v: produc1156025366_r_l_v > expr_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Data_OLID__local__store_001tf__l_001tf__r_001tf__v,type,
% 0.32/0.47 lID_lo1265057957_l_r_v: produc1156025366_r_l_v > l > option_val_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Data_OLID__snapshot_001tf__l_001tf__r_001tf__v,type,
% 0.32/0.47 lID_snapshot_l_r_v: produc1156025366_r_l_v > l > option_val_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Data_Ocombine_001tf__l_001t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,type,
% 0.32/0.47 combine_l_val_r_l_v: ( l > option_val_r_l_v ) > ( l > option_val_r_l_v ) > l > option_val_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Data_Oconst_OUnit,type,
% 0.32/0.47 unit: const ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Data_Oexpr_ORef_001tf__r_001tf__l_001tf__v,type,
% 0.32/0.47 ref_r_l_v: expr_r_l_v > expr_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Data_Oexpr_ORfork_001tf__r_001tf__l_001tf__v,type,
% 0.32/0.47 rfork_r_l_v: expr_r_l_v > expr_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Data_Oexpr_ORjoin_001tf__r_001tf__l_001tf__v,type,
% 0.32/0.47 rjoin_r_l_v: expr_r_l_v > expr_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Data_Oexpr_OVE_001tf__r_001tf__l_001tf__v,type,
% 0.32/0.47 vE_r_l_v: val_r_l_v > expr_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Data_Oplug_001tf__r_001tf__l_001tf__v,type,
% 0.32/0.47 plug_r_l_v: cntxt_r_l_v > expr_r_l_v > expr_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Data_Oval_OCV_001tf__r_001tf__l_001tf__v,type,
% 0.32/0.47 cV_r_l_v: const > val_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Data_Oval_OLoc_001tf__l_001tf__r_001tf__v,type,
% 0.32/0.47 loc_l_r_v: l > val_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Data_Oval_ORid_001tf__r_001tf__l_001tf__v,type,
% 0.32/0.47 rid_r_l_v: r > val_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Executions_Osubstitution_Oexecution_001tf__r_001tf__l_001tf__v,type,
% 0.32/0.47 execution_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > expr_r_l_v > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Executions_Osubstitution_Oinductive__invariant_001tf__r_001tf__l_001tf__v,type,
% 0.32/0.47 induct1670415253_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( ( r > option1457017436_r_l_v ) > $o ) > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Executions_Osubstitution_Oreachable_001tf__r_001tf__l_001tf__v,type,
% 0.32/0.47 reachable_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_It__Set__Oset_Itf__l_J_J,type,
% 0.32/0.47 finite160708696_set_l: set_option_set_l > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_It__Set__Oset_Itf__r_J_J,type,
% 0.32/0.47 finite555643486_set_r: set_option_set_r > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_It__Sum____Type__Osum_Itf__l_Mtf__l_J_J,type,
% 0.32/0.47 finite1864485196um_l_l: set_op76482283um_l_l > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_It__Sum____Type__Osum_Itf__l_Mtf__r_J_J,type,
% 0.32/0.47 finite111936338um_l_r: set_op160472561um_l_r > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_It__Sum____Type__Osum_Itf__r_Mtf__l_J_J,type,
% 0.32/0.47 finite1036466630um_r_l: set_op865065573um_r_l > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_Itf__l_J,type,
% 0.32/0.47 finite2114249848tion_l: set_option_l > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_Itf__r_J,type,
% 0.32/0.47 finite16335230tion_r: set_option_r > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_Itf__l_Mtf__l_J,type,
% 0.32/0.47 finite785973648od_l_l: set_Product_prod_l_l > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_Itf__l_Mtf__r_J,type,
% 0.32/0.47 finite835542678od_l_r: set_Product_prod_l_r > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_Itf__r_Mtf__l_J,type,
% 0.32/0.47 finite1457622794od_r_l: set_Product_prod_r_l > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_Itf__r_Mtf__r_J,type,
% 0.32/0.47 finite1507191824od_r_r: set_Product_prod_r_r > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_Itf__l_J,type,
% 0.32/0.47 finite_finite_set_l: set_set_l > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_Itf__r_J,type,
% 0.32/0.47 finite_finite_set_r: set_set_r > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Finite__Set_Ofinite_001t__Sum____Type__Osum_Itf__l_Mtf__l_J,type,
% 0.32/0.47 finite1541484284um_l_l: set_Sum_sum_l_l > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Finite__Set_Ofinite_001t__Sum____Type__Osum_Itf__l_Mtf__r_J,type,
% 0.32/0.47 finite1591053314um_l_r: set_Sum_sum_l_r > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Finite__Set_Ofinite_001t__Sum____Type__Osum_Itf__r_Mtf__l_J,type,
% 0.32/0.47 finite65649782um_r_l: set_Sum_sum_r_l > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Finite__Set_Ofinite_001t__Sum____Type__Osum_Itf__r_Mtf__r_J,type,
% 0.32/0.47 finite115218812um_r_r: set_Sum_sum_r_r > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Finite__Set_Ofinite_001tf__l,type,
% 0.32/0.47 finite_finite_l: set_l > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Finite__Set_Ofinite_001tf__r,type,
% 0.32/0.47 finite_finite_r: set_r > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Fun_Obij__betw_001tf__l_001tf__l,type,
% 0.32/0.47 bij_betw_l_l: ( l > l ) > set_l > set_l > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Fun_Obij__betw_001tf__l_001tf__r,type,
% 0.32/0.47 bij_betw_l_r: ( l > r ) > set_l > set_r > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Fun_Obij__betw_001tf__r_001tf__l,type,
% 0.32/0.47 bij_betw_r_l: ( r > l ) > set_r > set_l > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Fun_Obij__betw_001tf__r_001tf__r,type,
% 0.32/0.47 bij_betw_r_r: ( r > r ) > set_r > set_r > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Fun_Ofun__upd_001tf__l_001t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J,type,
% 0.32/0.47 fun_up1835647912_r_l_v: ( l > option_val_r_l_v ) > l > option_val_r_l_v > l > option_val_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Fun_Ofun__upd_001tf__r_001t__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J,type,
% 0.32/0.47 fun_up709272714_r_l_v: ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v > r > option1457017436_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_If_001t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J,type,
% 0.32/0.47 if_option_val_r_l_v: $o > option_val_r_l_v > option_val_r_l_v > option_val_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_If_001t__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J,type,
% 0.32/0.47 if_opt1153928738_r_l_v: $o > option1457017436_r_l_v > option1457017436_r_l_v > option1457017436_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Occurrences_OLID_092_060_094sub_062G_001tf__r_001tf__l_001tf__v,type,
% 0.32/0.47 lID_G_r_l_v: ( r > option1457017436_r_l_v ) > set_l ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Occurrences_OLID_092_060_094sub_062L_001tf__l_001tf__r_001tf__v,type,
% 0.32/0.47 lID_L_l_r_v: produc1156025366_r_l_v > set_l ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Occurrences_ORID_092_060_094sub_062G_001tf__r_001tf__l_001tf__v,type,
% 0.32/0.47 rID_G_r_l_v: ( r > option1457017436_r_l_v ) > set_r ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Occurrences_ORID_092_060_094sub_062L_001tf__l_001tf__r_001tf__v,type,
% 0.32/0.47 rID_L_l_r_v: produc1156025366_r_l_v > set_r ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_OperationalSemantics_Osubstitution_Odomains__subsume_001tf__l_001tf__r_001tf__v,type,
% 0.32/0.47 domain87684397_l_r_v: produc1156025366_r_l_v > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_OperationalSemantics_Osubstitution_Odomains__subsume__globally_001tf__r_001tf__l_001tf__v,type,
% 0.32/0.47 domain1547879849_r_l_v: ( r > option1457017436_r_l_v ) > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_OperationalSemantics_Osubstitution_Orevision__step_001tf__r_001tf__l_001tf__v,type,
% 0.32/0.47 revision_step_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_OperationalSemantics_Osubstitution_Orevision__step__relaxed_001tf__r_001tf__l_001tf__v,type,
% 0.32/0.47 revisi1291188644_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_OperationalSemantics_Osubstitution_Osubsumes__accessible_001tf__r_001tf__l_001tf__v,type,
% 0.32/0.47 subsum148050133_r_l_v: r > r > ( r > option1457017436_r_l_v ) > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_OperationalSemantics_Osubstitution_Osubsumes__accessible__globally_001tf__r_001tf__l_001tf__v,type,
% 0.32/0.47 subsum680764357_r_l_v: ( r > option1457017436_r_l_v ) > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Option_Ooption_ONone_001t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,type,
% 0.32/0.47 none_val_r_l_v: option_val_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J,type,
% 0.32/0.47 none_P277133687_r_l_v: option1457017436_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Option_Ooption_OSome_001t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,type,
% 0.32/0.47 some_val_r_l_v: val_r_l_v > option_val_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J,type,
% 0.32/0.47 some_P1807977723_r_l_v: produc1156025366_r_l_v > option1457017436_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__l_J,type,
% 0.32/0.47 ord_less_eq_set_l: set_l > set_l > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__r_J,type,
% 0.32/0.47 ord_less_eq_set_r: set_r > set_r > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Set__Oset_Itf__l_J_J_J,type,
% 0.32/0.47 top_to471808607_set_l: set_option_set_l ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Set__Oset_Itf__r_J_J_J,type,
% 0.32/0.47 top_to555798885_set_r: set_option_set_r ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Sum____Type__Osum_Itf__l_Mtf__l_J_J_J,type,
% 0.32/0.47 top_to1066565019um_l_l: set_op76482283um_l_l ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Sum____Type__Osum_Itf__l_Mtf__r_J_J_J,type,
% 0.32/0.47 top_to1150555297um_l_r: set_op160472561um_l_r ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Sum____Type__Osum_Itf__r_Mtf__l_J_J_J,type,
% 0.32/0.47 top_to1855148309um_r_l: set_op865065573um_r_l ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_Itf__l_J_J,type,
% 0.32/0.47 top_top_set_option_l: set_option_l ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_Itf__r_J_J,type,
% 0.32/0.47 top_top_set_option_r: set_option_r ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_Itf__l_Mtf__l_J_J,type,
% 0.32/0.47 top_to320296343od_l_l: set_Product_prod_l_l ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_Itf__l_Mtf__r_J_J,type,
% 0.32/0.47 top_to715231133od_l_r: set_Product_prod_l_r ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_Itf__r_Mtf__l_J_J,type,
% 0.32/0.47 top_to1639761425od_r_l: set_Product_prod_r_l ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_Itf__r_Mtf__r_J_J,type,
% 0.32/0.47 top_to2034696215od_r_r: set_Product_prod_r_r ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_Itf__l_J_J,type,
% 0.32/0.47 top_top_set_set_l: set_set_l ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_Itf__r_J_J,type,
% 0.32/0.47 top_top_set_set_r: set_set_r ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Sum____Type__Osum_Itf__l_Mtf__l_J_J,type,
% 0.32/0.47 top_to1010946379um_l_l: set_Sum_sum_l_l ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Sum____Type__Osum_Itf__l_Mtf__r_J_J,type,
% 0.32/0.47 top_to1405881169um_l_r: set_Sum_sum_l_r ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Sum____Type__Osum_Itf__r_Mtf__l_J_J,type,
% 0.32/0.47 top_to182927813um_r_l: set_Sum_sum_r_l ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Sum____Type__Osum_Itf__r_Mtf__r_J_J,type,
% 0.32/0.47 top_to577862603um_r_r: set_Sum_sum_r_r ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__l_J,type,
% 0.32/0.47 top_top_set_l: set_l ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__r_J,type,
% 0.32/0.47 top_top_set_r: set_r ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Product__Type_OPair_001_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_001t__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J,type,
% 0.32/0.47 produc1834103605_r_l_v: ( l > option_val_r_l_v ) > expr_r_l_v > produc1164766533_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Product__Type_OPair_001_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_001t__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J,type,
% 0.32/0.47 produc297528454_r_l_v: ( l > option_val_r_l_v ) > produc1164766533_r_l_v > produc1156025366_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Product__Type_OPair_001_062_Itf__l_Mtf__l_J_001t__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J,type,
% 0.32/0.47 produc2057232216_r_l_v: ( l > l ) > produc1156025366_r_l_v > produc1489027110_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Product__Type_OPair_001_062_Itf__r_Mtf__r_J_001t__Product____Type__Oprod_I_062_Itf__l_Mtf__l_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J,type,
% 0.32/0.47 produc2111504612_r_l_v: ( r > r ) > produc1489027110_r_l_v > produc1394974636_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Renaming_O_092_060R_062_092_060_094sub_062G_001tf__r_001tf__l_001tf__v,type,
% 0.32/0.47 r_G_r_l_v: ( r > r ) > ( l > l ) > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Renaming_O_092_060R_062_092_060_094sub_062L_001tf__r_001tf__l_001tf__v,type,
% 0.32/0.47 r_L_r_l_v: ( r > r ) > ( l > l ) > produc1156025366_r_l_v > produc1156025366_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Renaming_Oeq__states_001tf__r_001tf__l_001tf__v,type,
% 0.32/0.47 eq_states_r_l_v: ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Renaming_Ois__global__renaming_001tf__r_001tf__l_001tf__v,type,
% 0.32/0.47 is_glo1871033385_r_l_v: ( r > r ) > ( l > l ) > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Set_OCollect_001t__Set__Oset_Itf__l_J,type,
% 0.32/0.47 collect_set_l: ( set_l > $o ) > set_set_l ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Set_OCollect_001t__Set__Oset_Itf__r_J,type,
% 0.32/0.47 collect_set_r: ( set_r > $o ) > set_set_r ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Set_OCollect_001t__Sum____Type__Osum_Itf__l_Mtf__l_J,type,
% 0.32/0.47 collect_Sum_sum_l_l: ( sum_sum_l_l > $o ) > set_Sum_sum_l_l ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Set_OCollect_001t__Sum____Type__Osum_Itf__l_Mtf__r_J,type,
% 0.32/0.47 collect_Sum_sum_l_r: ( sum_sum_l_r > $o ) > set_Sum_sum_l_r ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Set_OCollect_001t__Sum____Type__Osum_Itf__r_Mtf__l_J,type,
% 0.32/0.47 collect_Sum_sum_r_l: ( sum_sum_r_l > $o ) > set_Sum_sum_r_l ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Set_OCollect_001tf__l,type,
% 0.32/0.47 collect_l: ( l > $o ) > set_l ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Set_OCollect_001tf__r,type,
% 0.32/0.47 collect_r: ( r > $o ) > set_r ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Substitution_Osubstitution_001tf__r_001tf__l_001tf__v,type,
% 0.32/0.47 substitution_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_member_001t__Set__Oset_Itf__l_J,type,
% 0.32/0.47 member_set_l: set_l > set_set_l > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_member_001t__Set__Oset_Itf__r_J,type,
% 0.32/0.47 member_set_r: set_r > set_set_r > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_member_001tf__l,type,
% 0.32/0.47 member_l: l > set_l > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_member_001tf__r,type,
% 0.32/0.47 member_r: r > set_r > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_v__092_060E_062____,type,
% 0.32/0.47 e: cntxt_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_v__092_060alpha_062,type,
% 0.32/0.47 alpha: r > r ).
% 0.32/0.47
% 0.32/0.47 thf(sy_v__092_060beta_062,type,
% 0.32/0.47 beta: l > l ).
% 0.32/0.47
% 0.32/0.47 thf(sy_v__092_060sigma_062____,type,
% 0.32/0.47 sigma: l > option_val_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_v__092_060tau_062____,type,
% 0.32/0.47 tau: l > option_val_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_v_e____,type,
% 0.32/0.47 e2: expr_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_v_r,type,
% 0.32/0.47 r2: r ).
% 0.32/0.47
% 0.32/0.47 thf(sy_v_r_H____,type,
% 0.32/0.47 r3: r ).
% 0.32/0.47
% 0.32/0.47 thf(sy_v_s,type,
% 0.32/0.47 s: r > option1457017436_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_v_s_H,type,
% 0.32/0.47 s2: r > option1457017436_r_l_v ).
% 0.32/0.47
% 0.32/0.47 thf(sy_v_subst,type,
% 0.32/0.47 subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v ).
% 0.32/0.47
% 0.32/0.47 % Relevant facts (352)
% 0.32/0.47 thf(fact_0_local_Ofork_I2_J,axiom,
% 0.32/0.47 ( ( s @ r2 )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( rfork_r_l_v @ e2 ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % local.fork(2)
% 0.32/0.47 thf(fact_1_expr_Oinject_I7_J,axiom,
% 0.32/0.47 ! [X7: expr_r_l_v,Y7: expr_r_l_v] :
% 0.32/0.47 ( ( ( rfork_r_l_v @ X7 )
% 0.32/0.47 = ( rfork_r_l_v @ Y7 ) )
% 0.32/0.47 = ( X7 = Y7 ) ) ).
% 0.32/0.47
% 0.32/0.47 % expr.inject(7)
% 0.32/0.47 thf(fact_2_injective__cntxt,axiom,
% 0.32/0.47 ! [E: cntxt_r_l_v,E1: expr_r_l_v,E2: expr_r_l_v] :
% 0.32/0.47 ( ( ( plug_r_l_v @ E @ E1 )
% 0.32/0.47 = ( plug_r_l_v @ E @ E2 ) )
% 0.32/0.47 = ( E1 = E2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % injective_cntxt
% 0.32/0.47 thf(fact_3_fun__upd__upd,axiom,
% 0.32/0.47 ! [F: r > option1457017436_r_l_v,X: r,Y: option1457017436_r_l_v,Z: option1457017436_r_l_v] :
% 0.32/0.47 ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ F @ X @ Y ) @ X @ Z )
% 0.32/0.47 = ( fun_up709272714_r_l_v @ F @ X @ Z ) ) ).
% 0.32/0.47
% 0.32/0.47 % fun_upd_upd
% 0.32/0.47 thf(fact_4_fun__upd__upd,axiom,
% 0.32/0.47 ! [F: l > option_val_r_l_v,X: l,Y: option_val_r_l_v,Z: option_val_r_l_v] :
% 0.32/0.47 ( ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ F @ X @ Y ) @ X @ Z )
% 0.32/0.47 = ( fun_up1835647912_r_l_v @ F @ X @ Z ) ) ).
% 0.32/0.47
% 0.32/0.47 % fun_upd_upd
% 0.32/0.47 thf(fact_5_fun__upd__triv,axiom,
% 0.32/0.47 ! [F: r > option1457017436_r_l_v,X: r] :
% 0.32/0.47 ( ( fun_up709272714_r_l_v @ F @ X @ ( F @ X ) )
% 0.32/0.47 = F ) ).
% 0.32/0.47
% 0.32/0.47 % fun_upd_triv
% 0.32/0.47 thf(fact_6_fun__upd__triv,axiom,
% 0.32/0.47 ! [F: l > option_val_r_l_v,X: l] :
% 0.32/0.47 ( ( fun_up1835647912_r_l_v @ F @ X @ ( F @ X ) )
% 0.32/0.47 = F ) ).
% 0.32/0.47
% 0.32/0.47 % fun_upd_triv
% 0.32/0.47 thf(fact_7_fun__upd__apply,axiom,
% 0.32/0.47 ( fun_up709272714_r_l_v
% 0.32/0.47 = ( ^ [F2: r > option1457017436_r_l_v,X2: r,Y2: option1457017436_r_l_v,Z2: r] : ( if_opt1153928738_r_l_v @ ( Z2 = X2 ) @ Y2 @ ( F2 @ Z2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % fun_upd_apply
% 0.32/0.47 thf(fact_8_fun__upd__apply,axiom,
% 0.32/0.47 ( fun_up1835647912_r_l_v
% 0.32/0.47 = ( ^ [F2: l > option_val_r_l_v,X2: l,Y2: option_val_r_l_v,Z2: l] : ( if_option_val_r_l_v @ ( Z2 = X2 ) @ Y2 @ ( F2 @ Z2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % fun_upd_apply
% 0.32/0.47 thf(fact_9_option_Oinject,axiom,
% 0.32/0.47 ! [X22: produc1156025366_r_l_v,Y22: produc1156025366_r_l_v] :
% 0.32/0.47 ( ( ( some_P1807977723_r_l_v @ X22 )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ Y22 ) )
% 0.32/0.47 = ( X22 = Y22 ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.inject
% 0.32/0.47 thf(fact_10_option_Oinject,axiom,
% 0.32/0.47 ! [X22: val_r_l_v,Y22: val_r_l_v] :
% 0.32/0.47 ( ( ( some_val_r_l_v @ X22 )
% 0.32/0.47 = ( some_val_r_l_v @ Y22 ) )
% 0.32/0.47 = ( X22 = Y22 ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.inject
% 0.32/0.47 thf(fact_11_prod_Oinject,axiom,
% 0.32/0.47 ! [X1: r > r,X22: produc1489027110_r_l_v,Y1: r > r,Y22: produc1489027110_r_l_v] :
% 0.32/0.47 ( ( ( produc2111504612_r_l_v @ X1 @ X22 )
% 0.32/0.47 = ( produc2111504612_r_l_v @ Y1 @ Y22 ) )
% 0.32/0.47 = ( ( X1 = Y1 )
% 0.32/0.47 & ( X22 = Y22 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod.inject
% 0.32/0.47 thf(fact_12_prod_Oinject,axiom,
% 0.32/0.47 ! [X1: l > l,X22: produc1156025366_r_l_v,Y1: l > l,Y22: produc1156025366_r_l_v] :
% 0.32/0.47 ( ( ( produc2057232216_r_l_v @ X1 @ X22 )
% 0.32/0.47 = ( produc2057232216_r_l_v @ Y1 @ Y22 ) )
% 0.32/0.47 = ( ( X1 = Y1 )
% 0.32/0.47 & ( X22 = Y22 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod.inject
% 0.32/0.47 thf(fact_13_prod_Oinject,axiom,
% 0.32/0.47 ! [X1: l > option_val_r_l_v,X22: produc1164766533_r_l_v,Y1: l > option_val_r_l_v,Y22: produc1164766533_r_l_v] :
% 0.32/0.47 ( ( ( produc297528454_r_l_v @ X1 @ X22 )
% 0.32/0.47 = ( produc297528454_r_l_v @ Y1 @ Y22 ) )
% 0.32/0.47 = ( ( X1 = Y1 )
% 0.32/0.47 & ( X22 = Y22 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod.inject
% 0.32/0.47 thf(fact_14_prod_Oinject,axiom,
% 0.32/0.47 ! [X1: l > option_val_r_l_v,X22: expr_r_l_v,Y1: l > option_val_r_l_v,Y22: expr_r_l_v] :
% 0.32/0.47 ( ( ( produc1834103605_r_l_v @ X1 @ X22 )
% 0.32/0.47 = ( produc1834103605_r_l_v @ Y1 @ Y22 ) )
% 0.32/0.47 = ( ( X1 = Y1 )
% 0.32/0.47 & ( X22 = Y22 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod.inject
% 0.32/0.47 thf(fact_15_old_Oprod_Oinject,axiom,
% 0.32/0.47 ! [A: r > r,B: produc1489027110_r_l_v,A2: r > r,B2: produc1489027110_r_l_v] :
% 0.32/0.47 ( ( ( produc2111504612_r_l_v @ A @ B )
% 0.32/0.47 = ( produc2111504612_r_l_v @ A2 @ B2 ) )
% 0.32/0.47 = ( ( A = A2 )
% 0.32/0.47 & ( B = B2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % old.prod.inject
% 0.32/0.47 thf(fact_16_old_Oprod_Oinject,axiom,
% 0.32/0.47 ! [A: l > l,B: produc1156025366_r_l_v,A2: l > l,B2: produc1156025366_r_l_v] :
% 0.32/0.47 ( ( ( produc2057232216_r_l_v @ A @ B )
% 0.32/0.47 = ( produc2057232216_r_l_v @ A2 @ B2 ) )
% 0.32/0.47 = ( ( A = A2 )
% 0.32/0.47 & ( B = B2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % old.prod.inject
% 0.32/0.47 thf(fact_17_old_Oprod_Oinject,axiom,
% 0.32/0.47 ! [A: l > option_val_r_l_v,B: produc1164766533_r_l_v,A2: l > option_val_r_l_v,B2: produc1164766533_r_l_v] :
% 0.32/0.47 ( ( ( produc297528454_r_l_v @ A @ B )
% 0.32/0.47 = ( produc297528454_r_l_v @ A2 @ B2 ) )
% 0.32/0.47 = ( ( A = A2 )
% 0.32/0.47 & ( B = B2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % old.prod.inject
% 0.32/0.47 thf(fact_18_old_Oprod_Oinject,axiom,
% 0.32/0.47 ! [A: l > option_val_r_l_v,B: expr_r_l_v,A2: l > option_val_r_l_v,B2: expr_r_l_v] :
% 0.32/0.47 ( ( ( produc1834103605_r_l_v @ A @ B )
% 0.32/0.47 = ( produc1834103605_r_l_v @ A2 @ B2 ) )
% 0.32/0.47 = ( ( A = A2 )
% 0.32/0.47 & ( B = B2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % old.prod.inject
% 0.32/0.47 thf(fact_19_LID__local__store_Ocases,axiom,
% 0.32/0.47 ! [X: produc1156025366_r_l_v] :
% 0.32/0.47 ~ ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E3: expr_r_l_v] :
% 0.32/0.47 ( X
% 0.32/0.47 != ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % LID_local_store.cases
% 0.32/0.47 thf(fact_20_LID__local__store_Oinduct,axiom,
% 0.32/0.47 ! [P: produc1156025366_r_l_v > $o,A0: produc1156025366_r_l_v] :
% 0.32/0.47 ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E3: expr_r_l_v] : ( P @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) )
% 0.32/0.47 => ( P @ A0 ) ) ).
% 0.32/0.47
% 0.32/0.47 % LID_local_store.induct
% 0.32/0.47 thf(fact_21__092_060R_062_092_060_094sub_062L_Oinduct,axiom,
% 0.32/0.47 ! [P: ( r > r ) > ( l > l ) > produc1156025366_r_l_v > $o,A0: r > r,A1: l > l,A22: produc1156025366_r_l_v] :
% 0.32/0.47 ( ! [Alpha: r > r,Beta: l > l,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E3: expr_r_l_v] : ( P @ Alpha @ Beta @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) )
% 0.32/0.47 => ( P @ A0 @ A1 @ A22 ) ) ).
% 0.32/0.47
% 0.32/0.47 % \<R>\<^sub>L.induct
% 0.32/0.47 thf(fact_22_map__upd__eqD1,axiom,
% 0.32/0.47 ! [M: r > option1457017436_r_l_v,A: r,X: produc1156025366_r_l_v,N: r > option1457017436_r_l_v,Y: produc1156025366_r_l_v] :
% 0.32/0.47 ( ( ( fun_up709272714_r_l_v @ M @ A @ ( some_P1807977723_r_l_v @ X ) )
% 0.32/0.47 = ( fun_up709272714_r_l_v @ N @ A @ ( some_P1807977723_r_l_v @ Y ) ) )
% 0.32/0.47 => ( X = Y ) ) ).
% 0.32/0.47
% 0.32/0.47 % map_upd_eqD1
% 0.32/0.47 thf(fact_23_map__upd__eqD1,axiom,
% 0.32/0.47 ! [M: l > option_val_r_l_v,A: l,X: val_r_l_v,N: l > option_val_r_l_v,Y: val_r_l_v] :
% 0.32/0.47 ( ( ( fun_up1835647912_r_l_v @ M @ A @ ( some_val_r_l_v @ X ) )
% 0.32/0.47 = ( fun_up1835647912_r_l_v @ N @ A @ ( some_val_r_l_v @ Y ) ) )
% 0.32/0.47 => ( X = Y ) ) ).
% 0.32/0.47
% 0.32/0.47 % map_upd_eqD1
% 0.32/0.47 thf(fact_24__092_060R_062_092_060_094sub_062L_Ocases,axiom,
% 0.32/0.47 ! [X: produc1394974636_r_l_v] :
% 0.32/0.47 ~ ! [Alpha: r > r,Beta: l > l,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E3: expr_r_l_v] :
% 0.32/0.47 ( X
% 0.32/0.47 != ( produc2111504612_r_l_v @ Alpha @ ( produc2057232216_r_l_v @ Beta @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % \<R>\<^sub>L.cases
% 0.32/0.47 thf(fact_25_old_Oprod_Oinducts,axiom,
% 0.32/0.47 ! [P: produc1394974636_r_l_v > $o,Prod: produc1394974636_r_l_v] :
% 0.32/0.47 ( ! [A3: r > r,B3: produc1489027110_r_l_v] : ( P @ ( produc2111504612_r_l_v @ A3 @ B3 ) )
% 0.32/0.47 => ( P @ Prod ) ) ).
% 0.32/0.47
% 0.32/0.47 % old.prod.inducts
% 0.32/0.47 thf(fact_26_old_Oprod_Oinducts,axiom,
% 0.32/0.47 ! [P: produc1489027110_r_l_v > $o,Prod: produc1489027110_r_l_v] :
% 0.32/0.47 ( ! [A3: l > l,B3: produc1156025366_r_l_v] : ( P @ ( produc2057232216_r_l_v @ A3 @ B3 ) )
% 0.32/0.47 => ( P @ Prod ) ) ).
% 0.32/0.47
% 0.32/0.47 % old.prod.inducts
% 0.32/0.47 thf(fact_27_old_Oprod_Oinducts,axiom,
% 0.32/0.47 ! [P: produc1156025366_r_l_v > $o,Prod: produc1156025366_r_l_v] :
% 0.32/0.47 ( ! [A3: l > option_val_r_l_v,B3: produc1164766533_r_l_v] : ( P @ ( produc297528454_r_l_v @ A3 @ B3 ) )
% 0.32/0.47 => ( P @ Prod ) ) ).
% 0.32/0.47
% 0.32/0.47 % old.prod.inducts
% 0.32/0.47 thf(fact_28_old_Oprod_Oinducts,axiom,
% 0.32/0.47 ! [P: produc1164766533_r_l_v > $o,Prod: produc1164766533_r_l_v] :
% 0.32/0.47 ( ! [A3: l > option_val_r_l_v,B3: expr_r_l_v] : ( P @ ( produc1834103605_r_l_v @ A3 @ B3 ) )
% 0.32/0.47 => ( P @ Prod ) ) ).
% 0.32/0.47
% 0.32/0.47 % old.prod.inducts
% 0.32/0.47 thf(fact_29_old_Oprod_Oexhaust,axiom,
% 0.32/0.47 ! [Y: produc1394974636_r_l_v] :
% 0.32/0.47 ~ ! [A3: r > r,B3: produc1489027110_r_l_v] :
% 0.32/0.47 ( Y
% 0.32/0.47 != ( produc2111504612_r_l_v @ A3 @ B3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % old.prod.exhaust
% 0.32/0.47 thf(fact_30_old_Oprod_Oexhaust,axiom,
% 0.32/0.47 ! [Y: produc1489027110_r_l_v] :
% 0.32/0.47 ~ ! [A3: l > l,B3: produc1156025366_r_l_v] :
% 0.32/0.47 ( Y
% 0.32/0.47 != ( produc2057232216_r_l_v @ A3 @ B3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % old.prod.exhaust
% 0.32/0.47 thf(fact_31_old_Oprod_Oexhaust,axiom,
% 0.32/0.47 ! [Y: produc1156025366_r_l_v] :
% 0.32/0.47 ~ ! [A3: l > option_val_r_l_v,B3: produc1164766533_r_l_v] :
% 0.32/0.47 ( Y
% 0.32/0.47 != ( produc297528454_r_l_v @ A3 @ B3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % old.prod.exhaust
% 0.32/0.47 thf(fact_32_old_Oprod_Oexhaust,axiom,
% 0.32/0.47 ! [Y: produc1164766533_r_l_v] :
% 0.32/0.47 ~ ! [A3: l > option_val_r_l_v,B3: expr_r_l_v] :
% 0.32/0.47 ( Y
% 0.32/0.47 != ( produc1834103605_r_l_v @ A3 @ B3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % old.prod.exhaust
% 0.32/0.47 thf(fact_33_Pair__inject,axiom,
% 0.32/0.47 ! [A: r > r,B: produc1489027110_r_l_v,A2: r > r,B2: produc1489027110_r_l_v] :
% 0.32/0.47 ( ( ( produc2111504612_r_l_v @ A @ B )
% 0.32/0.47 = ( produc2111504612_r_l_v @ A2 @ B2 ) )
% 0.32/0.47 => ~ ( ( A = A2 )
% 0.32/0.47 => ( B != B2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Pair_inject
% 0.32/0.47 thf(fact_34_Pair__inject,axiom,
% 0.32/0.47 ! [A: l > l,B: produc1156025366_r_l_v,A2: l > l,B2: produc1156025366_r_l_v] :
% 0.32/0.47 ( ( ( produc2057232216_r_l_v @ A @ B )
% 0.32/0.47 = ( produc2057232216_r_l_v @ A2 @ B2 ) )
% 0.32/0.47 => ~ ( ( A = A2 )
% 0.32/0.47 => ( B != B2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Pair_inject
% 0.32/0.47 thf(fact_35_Pair__inject,axiom,
% 0.32/0.47 ! [A: l > option_val_r_l_v,B: produc1164766533_r_l_v,A2: l > option_val_r_l_v,B2: produc1164766533_r_l_v] :
% 0.32/0.47 ( ( ( produc297528454_r_l_v @ A @ B )
% 0.32/0.47 = ( produc297528454_r_l_v @ A2 @ B2 ) )
% 0.32/0.47 => ~ ( ( A = A2 )
% 0.32/0.47 => ( B != B2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Pair_inject
% 0.32/0.47 thf(fact_36_Pair__inject,axiom,
% 0.32/0.47 ! [A: l > option_val_r_l_v,B: expr_r_l_v,A2: l > option_val_r_l_v,B2: expr_r_l_v] :
% 0.32/0.47 ( ( ( produc1834103605_r_l_v @ A @ B )
% 0.32/0.47 = ( produc1834103605_r_l_v @ A2 @ B2 ) )
% 0.32/0.47 => ~ ( ( A = A2 )
% 0.32/0.47 => ( B != B2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Pair_inject
% 0.32/0.47 thf(fact_37_prod__cases,axiom,
% 0.32/0.47 ! [P: produc1394974636_r_l_v > $o,P2: produc1394974636_r_l_v] :
% 0.32/0.47 ( ! [A3: r > r,B3: produc1489027110_r_l_v] : ( P @ ( produc2111504612_r_l_v @ A3 @ B3 ) )
% 0.32/0.47 => ( P @ P2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod_cases
% 0.32/0.47 thf(fact_38_prod__cases,axiom,
% 0.32/0.47 ! [P: produc1489027110_r_l_v > $o,P2: produc1489027110_r_l_v] :
% 0.32/0.47 ( ! [A3: l > l,B3: produc1156025366_r_l_v] : ( P @ ( produc2057232216_r_l_v @ A3 @ B3 ) )
% 0.32/0.47 => ( P @ P2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod_cases
% 0.32/0.47 thf(fact_39_prod__cases,axiom,
% 0.32/0.47 ! [P: produc1156025366_r_l_v > $o,P2: produc1156025366_r_l_v] :
% 0.32/0.47 ( ! [A3: l > option_val_r_l_v,B3: produc1164766533_r_l_v] : ( P @ ( produc297528454_r_l_v @ A3 @ B3 ) )
% 0.32/0.47 => ( P @ P2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod_cases
% 0.32/0.47 thf(fact_40_prod__cases,axiom,
% 0.32/0.47 ! [P: produc1164766533_r_l_v > $o,P2: produc1164766533_r_l_v] :
% 0.32/0.47 ( ! [A3: l > option_val_r_l_v,B3: expr_r_l_v] : ( P @ ( produc1834103605_r_l_v @ A3 @ B3 ) )
% 0.32/0.47 => ( P @ P2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod_cases
% 0.32/0.47 thf(fact_41_surj__pair,axiom,
% 0.32/0.47 ! [P2: produc1394974636_r_l_v] :
% 0.32/0.47 ? [X3: r > r,Y3: produc1489027110_r_l_v] :
% 0.32/0.47 ( P2
% 0.32/0.47 = ( produc2111504612_r_l_v @ X3 @ Y3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % surj_pair
% 0.32/0.47 thf(fact_42_surj__pair,axiom,
% 0.32/0.47 ! [P2: produc1489027110_r_l_v] :
% 0.32/0.47 ? [X3: l > l,Y3: produc1156025366_r_l_v] :
% 0.32/0.47 ( P2
% 0.32/0.47 = ( produc2057232216_r_l_v @ X3 @ Y3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % surj_pair
% 0.32/0.47 thf(fact_43_surj__pair,axiom,
% 0.32/0.47 ! [P2: produc1156025366_r_l_v] :
% 0.32/0.47 ? [X3: l > option_val_r_l_v,Y3: produc1164766533_r_l_v] :
% 0.32/0.47 ( P2
% 0.32/0.47 = ( produc297528454_r_l_v @ X3 @ Y3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % surj_pair
% 0.32/0.47 thf(fact_44_surj__pair,axiom,
% 0.32/0.47 ! [P2: produc1164766533_r_l_v] :
% 0.32/0.47 ? [X3: l > option_val_r_l_v,Y3: expr_r_l_v] :
% 0.32/0.47 ( P2
% 0.32/0.47 = ( produc1834103605_r_l_v @ X3 @ Y3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % surj_pair
% 0.32/0.47 thf(fact_45_fun__upd__idem__iff,axiom,
% 0.32/0.47 ! [F: r > option1457017436_r_l_v,X: r,Y: option1457017436_r_l_v] :
% 0.32/0.47 ( ( ( fun_up709272714_r_l_v @ F @ X @ Y )
% 0.32/0.47 = F )
% 0.32/0.47 = ( ( F @ X )
% 0.32/0.47 = Y ) ) ).
% 0.32/0.47
% 0.32/0.47 % fun_upd_idem_iff
% 0.32/0.47 thf(fact_46_fun__upd__idem__iff,axiom,
% 0.32/0.47 ! [F: l > option_val_r_l_v,X: l,Y: option_val_r_l_v] :
% 0.32/0.47 ( ( ( fun_up1835647912_r_l_v @ F @ X @ Y )
% 0.32/0.47 = F )
% 0.32/0.47 = ( ( F @ X )
% 0.32/0.47 = Y ) ) ).
% 0.32/0.47
% 0.32/0.47 % fun_upd_idem_iff
% 0.32/0.47 thf(fact_47_fun__upd__twist,axiom,
% 0.32/0.47 ! [A: r,C: r,M: r > option1457017436_r_l_v,B: option1457017436_r_l_v,D: option1457017436_r_l_v] :
% 0.32/0.47 ( ( A != C )
% 0.32/0.47 => ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ M @ A @ B ) @ C @ D )
% 0.32/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ M @ C @ D ) @ A @ B ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % fun_upd_twist
% 0.32/0.47 thf(fact_48_fun__upd__twist,axiom,
% 0.32/0.47 ! [A: l,C: l,M: l > option_val_r_l_v,B: option_val_r_l_v,D: option_val_r_l_v] :
% 0.32/0.47 ( ( A != C )
% 0.32/0.47 => ( ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ M @ A @ B ) @ C @ D )
% 0.32/0.47 = ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ M @ C @ D ) @ A @ B ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % fun_upd_twist
% 0.32/0.47 thf(fact_49_fun__upd__other,axiom,
% 0.32/0.47 ! [Z: r,X: r,F: r > option1457017436_r_l_v,Y: option1457017436_r_l_v] :
% 0.32/0.47 ( ( Z != X )
% 0.32/0.47 => ( ( fun_up709272714_r_l_v @ F @ X @ Y @ Z )
% 0.32/0.47 = ( F @ Z ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % fun_upd_other
% 0.32/0.47 thf(fact_50_fun__upd__other,axiom,
% 0.32/0.47 ! [Z: l,X: l,F: l > option_val_r_l_v,Y: option_val_r_l_v] :
% 0.32/0.47 ( ( Z != X )
% 0.32/0.47 => ( ( fun_up1835647912_r_l_v @ F @ X @ Y @ Z )
% 0.32/0.47 = ( F @ Z ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % fun_upd_other
% 0.32/0.47 thf(fact_51_fun__upd__same,axiom,
% 0.32/0.47 ! [F: r > option1457017436_r_l_v,X: r,Y: option1457017436_r_l_v] :
% 0.32/0.47 ( ( fun_up709272714_r_l_v @ F @ X @ Y @ X )
% 0.32/0.47 = Y ) ).
% 0.32/0.47
% 0.32/0.47 % fun_upd_same
% 0.32/0.47 thf(fact_52_fun__upd__same,axiom,
% 0.32/0.47 ! [F: l > option_val_r_l_v,X: l,Y: option_val_r_l_v] :
% 0.32/0.47 ( ( fun_up1835647912_r_l_v @ F @ X @ Y @ X )
% 0.32/0.47 = Y ) ).
% 0.32/0.47
% 0.32/0.47 % fun_upd_same
% 0.32/0.47 thf(fact_53_fun__upd__idem,axiom,
% 0.32/0.47 ! [F: r > option1457017436_r_l_v,X: r,Y: option1457017436_r_l_v] :
% 0.32/0.47 ( ( ( F @ X )
% 0.32/0.47 = Y )
% 0.32/0.47 => ( ( fun_up709272714_r_l_v @ F @ X @ Y )
% 0.32/0.47 = F ) ) ).
% 0.32/0.47
% 0.32/0.47 % fun_upd_idem
% 0.32/0.47 thf(fact_54_fun__upd__idem,axiom,
% 0.32/0.47 ! [F: l > option_val_r_l_v,X: l,Y: option_val_r_l_v] :
% 0.32/0.47 ( ( ( F @ X )
% 0.32/0.47 = Y )
% 0.32/0.47 => ( ( fun_up1835647912_r_l_v @ F @ X @ Y )
% 0.32/0.47 = F ) ) ).
% 0.32/0.47
% 0.32/0.47 % fun_upd_idem
% 0.32/0.47 thf(fact_55_fun__upd__eqD,axiom,
% 0.32/0.47 ! [F: r > option1457017436_r_l_v,X: r,Y: option1457017436_r_l_v,G: r > option1457017436_r_l_v,Z: option1457017436_r_l_v] :
% 0.32/0.47 ( ( ( fun_up709272714_r_l_v @ F @ X @ Y )
% 0.32/0.47 = ( fun_up709272714_r_l_v @ G @ X @ Z ) )
% 0.32/0.47 => ( Y = Z ) ) ).
% 0.32/0.47
% 0.32/0.47 % fun_upd_eqD
% 0.32/0.47 thf(fact_56_fun__upd__eqD,axiom,
% 0.32/0.47 ! [F: l > option_val_r_l_v,X: l,Y: option_val_r_l_v,G: l > option_val_r_l_v,Z: option_val_r_l_v] :
% 0.32/0.47 ( ( ( fun_up1835647912_r_l_v @ F @ X @ Y )
% 0.32/0.47 = ( fun_up1835647912_r_l_v @ G @ X @ Z ) )
% 0.32/0.47 => ( Y = Z ) ) ).
% 0.32/0.47
% 0.32/0.47 % fun_upd_eqD
% 0.32/0.47 thf(fact_57_fun__upd__def,axiom,
% 0.32/0.47 ( fun_up709272714_r_l_v
% 0.32/0.47 = ( ^ [F2: r > option1457017436_r_l_v,A4: r,B4: option1457017436_r_l_v,X2: r] : ( if_opt1153928738_r_l_v @ ( X2 = A4 ) @ B4 @ ( F2 @ X2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % fun_upd_def
% 0.32/0.47 thf(fact_58_fun__upd__def,axiom,
% 0.32/0.47 ( fun_up1835647912_r_l_v
% 0.32/0.47 = ( ^ [F2: l > option_val_r_l_v,A4: l,B4: option_val_r_l_v,X2: l] : ( if_option_val_r_l_v @ ( X2 = A4 ) @ B4 @ ( F2 @ X2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % fun_upd_def
% 0.32/0.47 thf(fact_59_prod__induct5,axiom,
% 0.32/0.47 ! [P: produc1394974636_r_l_v > $o,X: produc1394974636_r_l_v] :
% 0.32/0.47 ( ! [A3: r > r,B3: l > l,C2: l > option_val_r_l_v,D2: l > option_val_r_l_v,E3: expr_r_l_v] : ( P @ ( produc2111504612_r_l_v @ A3 @ ( produc2057232216_r_l_v @ B3 @ ( produc297528454_r_l_v @ C2 @ ( produc1834103605_r_l_v @ D2 @ E3 ) ) ) ) )
% 0.32/0.47 => ( P @ X ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod_induct5
% 0.32/0.47 thf(fact_60_prod__induct4,axiom,
% 0.32/0.47 ! [P: produc1394974636_r_l_v > $o,X: produc1394974636_r_l_v] :
% 0.32/0.47 ( ! [A3: r > r,B3: l > l,C2: l > option_val_r_l_v,D2: produc1164766533_r_l_v] : ( P @ ( produc2111504612_r_l_v @ A3 @ ( produc2057232216_r_l_v @ B3 @ ( produc297528454_r_l_v @ C2 @ D2 ) ) ) )
% 0.32/0.47 => ( P @ X ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod_induct4
% 0.32/0.47 thf(fact_61_prod__induct4,axiom,
% 0.32/0.47 ! [P: produc1489027110_r_l_v > $o,X: produc1489027110_r_l_v] :
% 0.32/0.47 ( ! [A3: l > l,B3: l > option_val_r_l_v,C2: l > option_val_r_l_v,D2: expr_r_l_v] : ( P @ ( produc2057232216_r_l_v @ A3 @ ( produc297528454_r_l_v @ B3 @ ( produc1834103605_r_l_v @ C2 @ D2 ) ) ) )
% 0.32/0.47 => ( P @ X ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod_induct4
% 0.32/0.47 thf(fact_62_prod__induct3,axiom,
% 0.32/0.47 ! [P: produc1394974636_r_l_v > $o,X: produc1394974636_r_l_v] :
% 0.32/0.47 ( ! [A3: r > r,B3: l > l,C2: produc1156025366_r_l_v] : ( P @ ( produc2111504612_r_l_v @ A3 @ ( produc2057232216_r_l_v @ B3 @ C2 ) ) )
% 0.32/0.47 => ( P @ X ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod_induct3
% 0.32/0.47 thf(fact_63_prod__induct3,axiom,
% 0.32/0.47 ! [P: produc1489027110_r_l_v > $o,X: produc1489027110_r_l_v] :
% 0.32/0.47 ( ! [A3: l > l,B3: l > option_val_r_l_v,C2: produc1164766533_r_l_v] : ( P @ ( produc2057232216_r_l_v @ A3 @ ( produc297528454_r_l_v @ B3 @ C2 ) ) )
% 0.32/0.47 => ( P @ X ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod_induct3
% 0.32/0.47 thf(fact_64_prod__induct3,axiom,
% 0.32/0.47 ! [P: produc1156025366_r_l_v > $o,X: produc1156025366_r_l_v] :
% 0.32/0.47 ( ! [A3: l > option_val_r_l_v,B3: l > option_val_r_l_v,C2: expr_r_l_v] : ( P @ ( produc297528454_r_l_v @ A3 @ ( produc1834103605_r_l_v @ B3 @ C2 ) ) )
% 0.32/0.47 => ( P @ X ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod_induct3
% 0.32/0.47 thf(fact_65_prod__cases5,axiom,
% 0.32/0.47 ! [Y: produc1394974636_r_l_v] :
% 0.32/0.47 ~ ! [A3: r > r,B3: l > l,C2: l > option_val_r_l_v,D2: l > option_val_r_l_v,E3: expr_r_l_v] :
% 0.32/0.47 ( Y
% 0.32/0.47 != ( produc2111504612_r_l_v @ A3 @ ( produc2057232216_r_l_v @ B3 @ ( produc297528454_r_l_v @ C2 @ ( produc1834103605_r_l_v @ D2 @ E3 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod_cases5
% 0.32/0.47 thf(fact_66_prod__cases4,axiom,
% 0.32/0.47 ! [Y: produc1394974636_r_l_v] :
% 0.32/0.47 ~ ! [A3: r > r,B3: l > l,C2: l > option_val_r_l_v,D2: produc1164766533_r_l_v] :
% 0.32/0.47 ( Y
% 0.32/0.47 != ( produc2111504612_r_l_v @ A3 @ ( produc2057232216_r_l_v @ B3 @ ( produc297528454_r_l_v @ C2 @ D2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod_cases4
% 0.32/0.47 thf(fact_67_prod__cases4,axiom,
% 0.32/0.47 ! [Y: produc1489027110_r_l_v] :
% 0.32/0.47 ~ ! [A3: l > l,B3: l > option_val_r_l_v,C2: l > option_val_r_l_v,D2: expr_r_l_v] :
% 0.32/0.47 ( Y
% 0.32/0.47 != ( produc2057232216_r_l_v @ A3 @ ( produc297528454_r_l_v @ B3 @ ( produc1834103605_r_l_v @ C2 @ D2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod_cases4
% 0.32/0.47 thf(fact_68_prod__cases3,axiom,
% 0.32/0.47 ! [Y: produc1394974636_r_l_v] :
% 0.32/0.47 ~ ! [A3: r > r,B3: l > l,C2: produc1156025366_r_l_v] :
% 0.32/0.47 ( Y
% 0.32/0.47 != ( produc2111504612_r_l_v @ A3 @ ( produc2057232216_r_l_v @ B3 @ C2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod_cases3
% 0.32/0.47 thf(fact_69_prod__cases3,axiom,
% 0.32/0.47 ! [Y: produc1489027110_r_l_v] :
% 0.32/0.47 ~ ! [A3: l > l,B3: l > option_val_r_l_v,C2: produc1164766533_r_l_v] :
% 0.32/0.47 ( Y
% 0.32/0.47 != ( produc2057232216_r_l_v @ A3 @ ( produc297528454_r_l_v @ B3 @ C2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod_cases3
% 0.32/0.47 thf(fact_70_prod__cases3,axiom,
% 0.32/0.47 ! [Y: produc1156025366_r_l_v] :
% 0.32/0.47 ~ ! [A3: l > option_val_r_l_v,B3: l > option_val_r_l_v,C2: expr_r_l_v] :
% 0.32/0.47 ( Y
% 0.32/0.47 != ( produc297528454_r_l_v @ A3 @ ( produc1834103605_r_l_v @ B3 @ C2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod_cases3
% 0.32/0.47 thf(fact_71_map__upd__Some__unfold,axiom,
% 0.32/0.47 ! [M: r > option1457017436_r_l_v,A: r,B: produc1156025366_r_l_v,X: r,Y: produc1156025366_r_l_v] :
% 0.32/0.47 ( ( ( fun_up709272714_r_l_v @ M @ A @ ( some_P1807977723_r_l_v @ B ) @ X )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ Y ) )
% 0.32/0.47 = ( ( ( X = A )
% 0.32/0.47 & ( B = Y ) )
% 0.32/0.47 | ( ( X != A )
% 0.32/0.47 & ( ( M @ X )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ Y ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % map_upd_Some_unfold
% 0.32/0.47 thf(fact_72_map__upd__Some__unfold,axiom,
% 0.32/0.47 ! [M: l > option_val_r_l_v,A: l,B: val_r_l_v,X: l,Y: val_r_l_v] :
% 0.32/0.47 ( ( ( fun_up1835647912_r_l_v @ M @ A @ ( some_val_r_l_v @ B ) @ X )
% 0.32/0.47 = ( some_val_r_l_v @ Y ) )
% 0.32/0.47 = ( ( ( X = A )
% 0.32/0.47 & ( B = Y ) )
% 0.32/0.47 | ( ( X != A )
% 0.32/0.47 & ( ( M @ X )
% 0.32/0.47 = ( some_val_r_l_v @ Y ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % map_upd_Some_unfold
% 0.32/0.47 thf(fact_73_map__upd__triv,axiom,
% 0.32/0.47 ! [T: r > option1457017436_r_l_v,K: r,X: produc1156025366_r_l_v] :
% 0.32/0.47 ( ( ( T @ K )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ X ) )
% 0.32/0.47 => ( ( fun_up709272714_r_l_v @ T @ K @ ( some_P1807977723_r_l_v @ X ) )
% 0.32/0.47 = T ) ) ).
% 0.32/0.47
% 0.32/0.47 % map_upd_triv
% 0.32/0.47 thf(fact_74_map__upd__triv,axiom,
% 0.32/0.47 ! [T: l > option_val_r_l_v,K: l,X: val_r_l_v] :
% 0.32/0.47 ( ( ( T @ K )
% 0.32/0.47 = ( some_val_r_l_v @ X ) )
% 0.32/0.47 => ( ( fun_up1835647912_r_l_v @ T @ K @ ( some_val_r_l_v @ X ) )
% 0.32/0.47 = T ) ) ).
% 0.32/0.47
% 0.32/0.47 % map_upd_triv
% 0.32/0.47 thf(fact_75_LID__local__store_Osimps,axiom,
% 0.32/0.47 ! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E4: expr_r_l_v] :
% 0.32/0.47 ( ( lID_lo1265057957_l_r_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ E4 ) ) )
% 0.32/0.47 = Tau2 ) ).
% 0.32/0.47
% 0.32/0.47 % LID_local_store.simps
% 0.32/0.47 thf(fact_76_LID__local__store_Oelims,axiom,
% 0.32/0.47 ! [X: produc1156025366_r_l_v,Y: l > option_val_r_l_v] :
% 0.32/0.47 ( ( ( lID_lo1265057957_l_r_v @ X )
% 0.32/0.47 = Y )
% 0.32/0.47 => ~ ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v] :
% 0.32/0.47 ( ? [E3: expr_r_l_v] :
% 0.32/0.47 ( X
% 0.32/0.47 = ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) )
% 0.32/0.47 => ( Y != Tau ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % LID_local_store.elims
% 0.32/0.47 thf(fact_77_LID__expression_Osimps,axiom,
% 0.32/0.47 ! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E4: expr_r_l_v] :
% 0.32/0.47 ( ( lID_expression_l_r_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ E4 ) ) )
% 0.32/0.47 = E4 ) ).
% 0.32/0.47
% 0.32/0.47 % LID_expression.simps
% 0.32/0.47 thf(fact_78_LID__expression_Oelims,axiom,
% 0.32/0.47 ! [X: produc1156025366_r_l_v,Y: expr_r_l_v] :
% 0.32/0.47 ( ( ( lID_expression_l_r_v @ X )
% 0.32/0.47 = Y )
% 0.32/0.47 => ~ ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E3: expr_r_l_v] :
% 0.32/0.47 ( ( X
% 0.32/0.47 = ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) )
% 0.32/0.47 => ( Y != E3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % LID_expression.elims
% 0.32/0.47 thf(fact_79_mem__Collect__eq,axiom,
% 0.32/0.47 ! [A: set_l,P: set_l > $o] :
% 0.32/0.47 ( ( member_set_l @ A @ ( collect_set_l @ P ) )
% 0.32/0.47 = ( P @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % mem_Collect_eq
% 0.32/0.47 thf(fact_80_mem__Collect__eq,axiom,
% 0.32/0.47 ! [A: set_r,P: set_r > $o] :
% 0.32/0.47 ( ( member_set_r @ A @ ( collect_set_r @ P ) )
% 0.32/0.47 = ( P @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % mem_Collect_eq
% 0.32/0.47 thf(fact_81_mem__Collect__eq,axiom,
% 0.32/0.47 ! [A: r,P: r > $o] :
% 0.32/0.47 ( ( member_r @ A @ ( collect_r @ P ) )
% 0.32/0.47 = ( P @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % mem_Collect_eq
% 0.32/0.47 thf(fact_82_mem__Collect__eq,axiom,
% 0.32/0.47 ! [A: l,P: l > $o] :
% 0.32/0.47 ( ( member_l @ A @ ( collect_l @ P ) )
% 0.32/0.47 = ( P @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % mem_Collect_eq
% 0.32/0.47 thf(fact_83_Collect__mem__eq,axiom,
% 0.32/0.47 ! [A5: set_set_l] :
% 0.32/0.47 ( ( collect_set_l
% 0.32/0.47 @ ^ [X2: set_l] : ( member_set_l @ X2 @ A5 ) )
% 0.32/0.47 = A5 ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_mem_eq
% 0.32/0.47 thf(fact_84_Collect__mem__eq,axiom,
% 0.32/0.47 ! [A5: set_set_r] :
% 0.32/0.47 ( ( collect_set_r
% 0.32/0.47 @ ^ [X2: set_r] : ( member_set_r @ X2 @ A5 ) )
% 0.32/0.47 = A5 ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_mem_eq
% 0.32/0.47 thf(fact_85_Collect__mem__eq,axiom,
% 0.32/0.47 ! [A5: set_r] :
% 0.32/0.47 ( ( collect_r
% 0.32/0.47 @ ^ [X2: r] : ( member_r @ X2 @ A5 ) )
% 0.32/0.47 = A5 ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_mem_eq
% 0.32/0.47 thf(fact_86_Collect__mem__eq,axiom,
% 0.32/0.47 ! [A5: set_l] :
% 0.32/0.47 ( ( collect_l
% 0.32/0.47 @ ^ [X2: l] : ( member_l @ X2 @ A5 ) )
% 0.32/0.47 = A5 ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_mem_eq
% 0.32/0.47 thf(fact_87_Collect__cong,axiom,
% 0.32/0.47 ! [P: l > $o,Q: l > $o] :
% 0.32/0.47 ( ! [X3: l] :
% 0.32/0.47 ( ( P @ X3 )
% 0.32/0.47 = ( Q @ X3 ) )
% 0.32/0.47 => ( ( collect_l @ P )
% 0.32/0.47 = ( collect_l @ Q ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_cong
% 0.32/0.47 thf(fact_88_Collect__cong,axiom,
% 0.32/0.47 ! [P: r > $o,Q: r > $o] :
% 0.32/0.47 ( ! [X3: r] :
% 0.32/0.47 ( ( P @ X3 )
% 0.32/0.47 = ( Q @ X3 ) )
% 0.32/0.47 => ( ( collect_r @ P )
% 0.32/0.47 = ( collect_r @ Q ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_cong
% 0.32/0.47 thf(fact_89_Collect__cong,axiom,
% 0.32/0.47 ! [P: set_l > $o,Q: set_l > $o] :
% 0.32/0.47 ( ! [X3: set_l] :
% 0.32/0.47 ( ( P @ X3 )
% 0.32/0.47 = ( Q @ X3 ) )
% 0.32/0.47 => ( ( collect_set_l @ P )
% 0.32/0.47 = ( collect_set_l @ Q ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_cong
% 0.32/0.47 thf(fact_90_Collect__cong,axiom,
% 0.32/0.47 ! [P: set_r > $o,Q: set_r > $o] :
% 0.32/0.47 ( ! [X3: set_r] :
% 0.32/0.47 ( ( P @ X3 )
% 0.32/0.47 = ( Q @ X3 ) )
% 0.32/0.47 => ( ( collect_set_r @ P )
% 0.32/0.47 = ( collect_set_r @ Q ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_cong
% 0.32/0.47 thf(fact_91_local_Ofork_I3_J,axiom,
% 0.32/0.47 ~ ( member_r @ r3 @ ( rID_G_r_l_v @ s ) ) ).
% 0.32/0.47
% 0.32/0.47 % local.fork(3)
% 0.32/0.47 thf(fact_92_LID__snapshot_Osimps,axiom,
% 0.32/0.47 ! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E4: expr_r_l_v] :
% 0.32/0.47 ( ( lID_snapshot_l_r_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ E4 ) ) )
% 0.32/0.47 = Sigma2 ) ).
% 0.32/0.47
% 0.32/0.47 % LID_snapshot.simps
% 0.32/0.47 thf(fact_93_LID__snapshot_Oelims,axiom,
% 0.32/0.47 ! [X: produc1156025366_r_l_v,Y: l > option_val_r_l_v] :
% 0.32/0.47 ( ( ( lID_snapshot_l_r_v @ X )
% 0.32/0.47 = Y )
% 0.32/0.47 => ~ ! [Sigma: l > option_val_r_l_v] :
% 0.32/0.47 ( ? [Tau: l > option_val_r_l_v,E3: expr_r_l_v] :
% 0.32/0.47 ( X
% 0.32/0.47 = ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) )
% 0.32/0.47 => ( Y != Sigma ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % LID_snapshot.elims
% 0.32/0.47 thf(fact_94_local_Ofork_I1_J,axiom,
% 0.32/0.47 ( s2
% 0.32/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s @ r2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r3 ) ) ) ) ) ) ) @ r3
% 0.32/0.47 @ ( some_P1807977723_r_l_v
% 0.32/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
% 0.32/0.47 @ ( produc1834103605_r_l_v
% 0.32/0.47 @ ^ [X2: l] : none_val_r_l_v
% 0.32/0.47 @ e2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % local.fork(1)
% 0.32/0.47 thf(fact_95_expr_Oinject_I1_J,axiom,
% 0.32/0.47 ! [X1: val_r_l_v,Y1: val_r_l_v] :
% 0.32/0.47 ( ( ( vE_r_l_v @ X1 )
% 0.32/0.47 = ( vE_r_l_v @ Y1 ) )
% 0.32/0.47 = ( X1 = Y1 ) ) ).
% 0.32/0.47
% 0.32/0.47 % expr.inject(1)
% 0.32/0.47 thf(fact_96_val_Oinject_I4_J,axiom,
% 0.32/0.47 ! [X4: r,Y4: r] :
% 0.32/0.47 ( ( ( rid_r_l_v @ X4 )
% 0.32/0.47 = ( rid_r_l_v @ Y4 ) )
% 0.32/0.47 = ( X4 = Y4 ) ) ).
% 0.32/0.47
% 0.32/0.47 % val.inject(4)
% 0.32/0.47 thf(fact_97_not__None__eq,axiom,
% 0.32/0.47 ! [X: option1457017436_r_l_v] :
% 0.32/0.47 ( ( X != none_P277133687_r_l_v )
% 0.32/0.47 = ( ? [Y2: produc1156025366_r_l_v] :
% 0.32/0.47 ( X
% 0.32/0.47 = ( some_P1807977723_r_l_v @ Y2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % not_None_eq
% 0.32/0.47 thf(fact_98_not__None__eq,axiom,
% 0.32/0.47 ! [X: option_val_r_l_v] :
% 0.32/0.47 ( ( X != none_val_r_l_v )
% 0.32/0.47 = ( ? [Y2: val_r_l_v] :
% 0.32/0.47 ( X
% 0.32/0.47 = ( some_val_r_l_v @ Y2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % not_None_eq
% 0.32/0.47 thf(fact_99_not__Some__eq,axiom,
% 0.32/0.47 ! [X: option1457017436_r_l_v] :
% 0.32/0.47 ( ( ! [Y2: produc1156025366_r_l_v] :
% 0.32/0.47 ( X
% 0.32/0.47 != ( some_P1807977723_r_l_v @ Y2 ) ) )
% 0.32/0.47 = ( X = none_P277133687_r_l_v ) ) ).
% 0.32/0.47
% 0.32/0.47 % not_Some_eq
% 0.32/0.47 thf(fact_100_not__Some__eq,axiom,
% 0.32/0.47 ! [X: option_val_r_l_v] :
% 0.32/0.47 ( ( ! [Y2: val_r_l_v] :
% 0.32/0.47 ( X
% 0.32/0.47 != ( some_val_r_l_v @ Y2 ) ) )
% 0.32/0.47 = ( X = none_val_r_l_v ) ) ).
% 0.32/0.47
% 0.32/0.47 % not_Some_eq
% 0.32/0.47 thf(fact_101_empty__upd__none,axiom,
% 0.32/0.47 ! [X: l] :
% 0.32/0.47 ( ( fun_up1835647912_r_l_v
% 0.32/0.47 @ ^ [X2: l] : none_val_r_l_v
% 0.32/0.47 @ X
% 0.32/0.47 @ none_val_r_l_v )
% 0.32/0.47 = ( ^ [X2: l] : none_val_r_l_v ) ) ).
% 0.32/0.47
% 0.32/0.47 % empty_upd_none
% 0.32/0.47 thf(fact_102_empty__upd__none,axiom,
% 0.32/0.47 ! [X: r] :
% 0.32/0.47 ( ( fun_up709272714_r_l_v
% 0.32/0.47 @ ^ [X2: r] : none_P277133687_r_l_v
% 0.32/0.47 @ X
% 0.32/0.47 @ none_P277133687_r_l_v )
% 0.32/0.47 = ( ^ [X2: r] : none_P277133687_r_l_v ) ) ).
% 0.32/0.47
% 0.32/0.47 % empty_upd_none
% 0.32/0.47 thf(fact_103_combine_Oelims,axiom,
% 0.32/0.47 ! [X: l > option_val_r_l_v,Xa: l > option_val_r_l_v,Xb: l,Y: option_val_r_l_v] :
% 0.32/0.47 ( ( ( combine_l_val_r_l_v @ X @ Xa @ Xb )
% 0.32/0.47 = Y )
% 0.32/0.47 => ( ( ( ( Xa @ Xb )
% 0.32/0.47 = none_val_r_l_v )
% 0.32/0.47 => ( Y
% 0.32/0.47 = ( X @ Xb ) ) )
% 0.32/0.47 & ( ( ( Xa @ Xb )
% 0.32/0.47 != none_val_r_l_v )
% 0.32/0.47 => ( Y
% 0.32/0.47 = ( Xa @ Xb ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % combine.elims
% 0.32/0.47 thf(fact_104_combine_Osimps,axiom,
% 0.32/0.47 ( combine_l_val_r_l_v
% 0.32/0.47 = ( ^ [F2: l > option_val_r_l_v,G2: l > option_val_r_l_v,X2: l] :
% 0.32/0.47 ( if_option_val_r_l_v
% 0.32/0.47 @ ( ( G2 @ X2 )
% 0.32/0.47 = none_val_r_l_v )
% 0.32/0.47 @ ( F2 @ X2 )
% 0.32/0.47 @ ( G2 @ X2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % combine.simps
% 0.32/0.47 thf(fact_105_option_Odistinct_I1_J,axiom,
% 0.32/0.47 ! [X22: produc1156025366_r_l_v] :
% 0.32/0.47 ( none_P277133687_r_l_v
% 0.32/0.47 != ( some_P1807977723_r_l_v @ X22 ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.distinct(1)
% 0.32/0.47 thf(fact_106_option_Odistinct_I1_J,axiom,
% 0.32/0.47 ! [X22: val_r_l_v] :
% 0.32/0.47 ( none_val_r_l_v
% 0.32/0.47 != ( some_val_r_l_v @ X22 ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.distinct(1)
% 0.32/0.47 thf(fact_107_option_OdiscI,axiom,
% 0.32/0.47 ! [Option: option1457017436_r_l_v,X22: produc1156025366_r_l_v] :
% 0.32/0.47 ( ( Option
% 0.32/0.47 = ( some_P1807977723_r_l_v @ X22 ) )
% 0.32/0.47 => ( Option != none_P277133687_r_l_v ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.discI
% 0.32/0.47 thf(fact_108_option_OdiscI,axiom,
% 0.32/0.47 ! [Option: option_val_r_l_v,X22: val_r_l_v] :
% 0.32/0.47 ( ( Option
% 0.32/0.47 = ( some_val_r_l_v @ X22 ) )
% 0.32/0.47 => ( Option != none_val_r_l_v ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.discI
% 0.32/0.47 thf(fact_109_option_Oexhaust,axiom,
% 0.32/0.47 ! [Y: option1457017436_r_l_v] :
% 0.32/0.47 ( ( Y != none_P277133687_r_l_v )
% 0.32/0.47 => ~ ! [X23: produc1156025366_r_l_v] :
% 0.32/0.47 ( Y
% 0.32/0.47 != ( some_P1807977723_r_l_v @ X23 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.exhaust
% 0.32/0.47 thf(fact_110_option_Oexhaust,axiom,
% 0.32/0.47 ! [Y: option_val_r_l_v] :
% 0.32/0.47 ( ( Y != none_val_r_l_v )
% 0.32/0.47 => ~ ! [X23: val_r_l_v] :
% 0.32/0.47 ( Y
% 0.32/0.47 != ( some_val_r_l_v @ X23 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.exhaust
% 0.32/0.47 thf(fact_111_option_Oinducts,axiom,
% 0.32/0.47 ! [P: option1457017436_r_l_v > $o,Option: option1457017436_r_l_v] :
% 0.32/0.47 ( ( P @ none_P277133687_r_l_v )
% 0.32/0.47 => ( ! [X3: produc1156025366_r_l_v] : ( P @ ( some_P1807977723_r_l_v @ X3 ) )
% 0.32/0.47 => ( P @ Option ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.inducts
% 0.32/0.47 thf(fact_112_option_Oinducts,axiom,
% 0.32/0.47 ! [P: option_val_r_l_v > $o,Option: option_val_r_l_v] :
% 0.32/0.47 ( ( P @ none_val_r_l_v )
% 0.32/0.47 => ( ! [X3: val_r_l_v] : ( P @ ( some_val_r_l_v @ X3 ) )
% 0.32/0.47 => ( P @ Option ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.inducts
% 0.32/0.47 thf(fact_113_split__option__ex,axiom,
% 0.32/0.47 ( ( ^ [P3: option1457017436_r_l_v > $o] :
% 0.32/0.47 ? [X5: option1457017436_r_l_v] : ( P3 @ X5 ) )
% 0.32/0.47 = ( ^ [P4: option1457017436_r_l_v > $o] :
% 0.32/0.47 ( ( P4 @ none_P277133687_r_l_v )
% 0.32/0.47 | ? [X2: produc1156025366_r_l_v] : ( P4 @ ( some_P1807977723_r_l_v @ X2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % split_option_ex
% 0.32/0.47 thf(fact_114_split__option__ex,axiom,
% 0.32/0.47 ( ( ^ [P3: option_val_r_l_v > $o] :
% 0.32/0.47 ? [X5: option_val_r_l_v] : ( P3 @ X5 ) )
% 0.32/0.47 = ( ^ [P4: option_val_r_l_v > $o] :
% 0.32/0.47 ( ( P4 @ none_val_r_l_v )
% 0.32/0.47 | ? [X2: val_r_l_v] : ( P4 @ ( some_val_r_l_v @ X2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % split_option_ex
% 0.32/0.47 thf(fact_115_split__option__all,axiom,
% 0.32/0.47 ( ( ^ [P3: option1457017436_r_l_v > $o] :
% 0.32/0.47 ! [X5: option1457017436_r_l_v] : ( P3 @ X5 ) )
% 0.32/0.47 = ( ^ [P4: option1457017436_r_l_v > $o] :
% 0.32/0.47 ( ( P4 @ none_P277133687_r_l_v )
% 0.32/0.47 & ! [X2: produc1156025366_r_l_v] : ( P4 @ ( some_P1807977723_r_l_v @ X2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % split_option_all
% 0.32/0.47 thf(fact_116_split__option__all,axiom,
% 0.32/0.47 ( ( ^ [P3: option_val_r_l_v > $o] :
% 0.32/0.47 ! [X5: option_val_r_l_v] : ( P3 @ X5 ) )
% 0.32/0.47 = ( ^ [P4: option_val_r_l_v > $o] :
% 0.32/0.47 ( ( P4 @ none_val_r_l_v )
% 0.32/0.47 & ! [X2: val_r_l_v] : ( P4 @ ( some_val_r_l_v @ X2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % split_option_all
% 0.32/0.47 thf(fact_117_combine__options__cases,axiom,
% 0.32/0.47 ! [X: option1457017436_r_l_v,P: option1457017436_r_l_v > option1457017436_r_l_v > $o,Y: option1457017436_r_l_v] :
% 0.32/0.47 ( ( ( X = none_P277133687_r_l_v )
% 0.32/0.47 => ( P @ X @ Y ) )
% 0.32/0.47 => ( ( ( Y = none_P277133687_r_l_v )
% 0.32/0.47 => ( P @ X @ Y ) )
% 0.32/0.47 => ( ! [A3: produc1156025366_r_l_v,B3: produc1156025366_r_l_v] :
% 0.32/0.47 ( ( X
% 0.32/0.47 = ( some_P1807977723_r_l_v @ A3 ) )
% 0.32/0.47 => ( ( Y
% 0.32/0.47 = ( some_P1807977723_r_l_v @ B3 ) )
% 0.32/0.47 => ( P @ X @ Y ) ) )
% 0.32/0.47 => ( P @ X @ Y ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % combine_options_cases
% 0.32/0.47 thf(fact_118_combine__options__cases,axiom,
% 0.32/0.47 ! [X: option1457017436_r_l_v,P: option1457017436_r_l_v > option_val_r_l_v > $o,Y: option_val_r_l_v] :
% 0.32/0.47 ( ( ( X = none_P277133687_r_l_v )
% 0.32/0.47 => ( P @ X @ Y ) )
% 0.32/0.47 => ( ( ( Y = none_val_r_l_v )
% 0.32/0.47 => ( P @ X @ Y ) )
% 0.32/0.47 => ( ! [A3: produc1156025366_r_l_v,B3: val_r_l_v] :
% 0.32/0.47 ( ( X
% 0.32/0.47 = ( some_P1807977723_r_l_v @ A3 ) )
% 0.32/0.47 => ( ( Y
% 0.32/0.47 = ( some_val_r_l_v @ B3 ) )
% 0.32/0.47 => ( P @ X @ Y ) ) )
% 0.32/0.47 => ( P @ X @ Y ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % combine_options_cases
% 0.32/0.47 thf(fact_119_combine__options__cases,axiom,
% 0.32/0.47 ! [X: option_val_r_l_v,P: option_val_r_l_v > option1457017436_r_l_v > $o,Y: option1457017436_r_l_v] :
% 0.32/0.47 ( ( ( X = none_val_r_l_v )
% 0.32/0.47 => ( P @ X @ Y ) )
% 0.32/0.47 => ( ( ( Y = none_P277133687_r_l_v )
% 0.32/0.47 => ( P @ X @ Y ) )
% 0.32/0.47 => ( ! [A3: val_r_l_v,B3: produc1156025366_r_l_v] :
% 0.32/0.47 ( ( X
% 0.32/0.47 = ( some_val_r_l_v @ A3 ) )
% 0.32/0.47 => ( ( Y
% 0.32/0.47 = ( some_P1807977723_r_l_v @ B3 ) )
% 0.32/0.47 => ( P @ X @ Y ) ) )
% 0.32/0.47 => ( P @ X @ Y ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % combine_options_cases
% 0.32/0.47 thf(fact_120_combine__options__cases,axiom,
% 0.32/0.47 ! [X: option_val_r_l_v,P: option_val_r_l_v > option_val_r_l_v > $o,Y: option_val_r_l_v] :
% 0.32/0.47 ( ( ( X = none_val_r_l_v )
% 0.32/0.47 => ( P @ X @ Y ) )
% 0.32/0.47 => ( ( ( Y = none_val_r_l_v )
% 0.32/0.47 => ( P @ X @ Y ) )
% 0.32/0.47 => ( ! [A3: val_r_l_v,B3: val_r_l_v] :
% 0.32/0.47 ( ( X
% 0.32/0.47 = ( some_val_r_l_v @ A3 ) )
% 0.32/0.47 => ( ( Y
% 0.32/0.47 = ( some_val_r_l_v @ B3 ) )
% 0.32/0.47 => ( P @ X @ Y ) ) )
% 0.32/0.47 => ( P @ X @ Y ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % combine_options_cases
% 0.32/0.47 thf(fact_121_expr_Odistinct_I11_J,axiom,
% 0.32/0.47 ! [X1: val_r_l_v,X7: expr_r_l_v] :
% 0.32/0.47 ( ( vE_r_l_v @ X1 )
% 0.32/0.47 != ( rfork_r_l_v @ X7 ) ) ).
% 0.32/0.47
% 0.32/0.47 % expr.distinct(11)
% 0.32/0.47 thf(fact_122_map__upd__nonempty,axiom,
% 0.32/0.47 ! [T: r > option1457017436_r_l_v,K: r,X: produc1156025366_r_l_v] :
% 0.32/0.47 ( ( fun_up709272714_r_l_v @ T @ K @ ( some_P1807977723_r_l_v @ X ) )
% 0.32/0.47 != ( ^ [X2: r] : none_P277133687_r_l_v ) ) ).
% 0.32/0.47
% 0.32/0.47 % map_upd_nonempty
% 0.32/0.47 thf(fact_123_map__upd__nonempty,axiom,
% 0.32/0.47 ! [T: l > option_val_r_l_v,K: l,X: val_r_l_v] :
% 0.32/0.47 ( ( fun_up1835647912_r_l_v @ T @ K @ ( some_val_r_l_v @ X ) )
% 0.32/0.47 != ( ^ [X2: l] : none_val_r_l_v ) ) ).
% 0.32/0.47
% 0.32/0.47 % map_upd_nonempty
% 0.32/0.47 thf(fact_124_restrictions__inwards,axiom,
% 0.32/0.47 ! [X: r,X6: r,F: r > option1457017436_r_l_v,Y: produc1156025366_r_l_v] :
% 0.32/0.47 ( ( X != X6 )
% 0.32/0.47 => ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ F @ X @ ( some_P1807977723_r_l_v @ Y ) ) @ X6 @ none_P277133687_r_l_v )
% 0.32/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ F @ X6 @ none_P277133687_r_l_v ) @ X @ ( some_P1807977723_r_l_v @ Y ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % restrictions_inwards
% 0.32/0.47 thf(fact_125_restrictions__inwards,axiom,
% 0.32/0.47 ! [X: l,X6: l,F: l > option_val_r_l_v,Y: val_r_l_v] :
% 0.32/0.47 ( ( X != X6 )
% 0.32/0.47 => ( ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ F @ X @ ( some_val_r_l_v @ Y ) ) @ X6 @ none_val_r_l_v )
% 0.32/0.47 = ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ F @ X6 @ none_val_r_l_v ) @ X @ ( some_val_r_l_v @ Y ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % restrictions_inwards
% 0.32/0.47 thf(fact_126_RID_092_060_094sub_062GI_I1_J,axiom,
% 0.32/0.47 ! [S: r > option1457017436_r_l_v,R: r,V: produc1156025366_r_l_v] :
% 0.32/0.47 ( ( ( S @ R )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ V ) )
% 0.32/0.47 => ( member_r @ R @ ( rID_G_r_l_v @ S ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % RID\<^sub>GI(1)
% 0.32/0.47 thf(fact_127_revision__step__relaxed_Ofork,axiom,
% 0.32/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,E4: expr_r_l_v,R2: r] :
% 0.32/0.47 ( ( ( S @ R )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 0.32/0.47 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 0.32/0.47 => ( revisi1291188644_r_l_v @ subst @ R @ S
% 0.32/0.47 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) @ R2
% 0.32/0.47 @ ( some_P1807977723_r_l_v
% 0.32/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 0.32/0.47 @ ( produc1834103605_r_l_v
% 0.32/0.47 @ ^ [X2: l] : none_val_r_l_v
% 0.32/0.47 @ E4 ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % revision_step_relaxed.fork
% 0.32/0.47 thf(fact_128_revision__step_Ofork,axiom,
% 0.32/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,E4: expr_r_l_v,R2: r] :
% 0.32/0.47 ( ( ( S @ R )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 0.32/0.47 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 0.32/0.47 => ( revision_step_r_l_v @ subst @ R @ S
% 0.32/0.47 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) @ R2
% 0.32/0.47 @ ( some_P1807977723_r_l_v
% 0.32/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 0.32/0.47 @ ( produc1834103605_r_l_v
% 0.32/0.47 @ ^ [X2: l] : none_val_r_l_v
% 0.32/0.47 @ E4 ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % revision_step.fork
% 0.32/0.47 thf(fact_129__092_060alpha_062r_H__fresh,axiom,
% 0.32/0.47 ~ ( member_r @ ( alpha @ r3 ) @ ( rID_G_r_l_v @ ( r_G_r_l_v @ alpha @ beta @ s ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % \<alpha>r'_fresh
% 0.32/0.47 thf(fact_130_substitution_Orevision__step__relaxed_Ofork,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,E4: expr_r_l_v,R2: r] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( ( S @ R )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 0.32/0.47 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 0.32/0.47 => ( revisi1291188644_r_l_v @ Subst @ R @ S
% 0.32/0.47 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) @ R2
% 0.32/0.47 @ ( some_P1807977723_r_l_v
% 0.32/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 0.32/0.47 @ ( produc1834103605_r_l_v
% 0.32/0.47 @ ^ [X2: l] : none_val_r_l_v
% 0.32/0.47 @ E4 ) ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.revision_step_relaxed.fork
% 0.32/0.47 thf(fact_131_substitution_Ofork__pseudodeterministic,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,E4: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( ( S @ R )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 0.32/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.32/0.47 = ( ? [R3: r] :
% 0.32/0.47 ( ~ ( member_r @ R3 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) ) ) )
% 0.32/0.47 & ( S2
% 0.32/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R3 ) ) ) ) ) ) ) @ R3
% 0.32/0.47 @ ( some_P1807977723_r_l_v
% 0.32/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 0.32/0.47 @ ( produc1834103605_r_l_v
% 0.32/0.47 @ ^ [X2: l] : none_val_r_l_v
% 0.32/0.47 @ E4 ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.fork_pseudodeterministic
% 0.32/0.47 thf(fact_132_local_Ostep,axiom,
% 0.32/0.47 revision_step_r_l_v @ subst @ r2 @ s @ s2 ).
% 0.32/0.47
% 0.32/0.47 % local.step
% 0.32/0.47 thf(fact_133_substitution__axioms,axiom,
% 0.32/0.47 substitution_r_l_v @ subst ).
% 0.32/0.47
% 0.32/0.47 % substitution_axioms
% 0.32/0.47 thf(fact_134_rename__empty_I2_J,axiom,
% 0.32/0.47 ! [Alpha2: r > r,Beta2: l > l] :
% 0.32/0.47 ( ( r_G_r_l_v @ Alpha2 @ Beta2
% 0.32/0.47 @ ^ [X2: r] : none_P277133687_r_l_v )
% 0.32/0.47 = ( ^ [X2: r] : none_P277133687_r_l_v ) ) ).
% 0.32/0.47
% 0.32/0.47 % rename_empty(2)
% 0.32/0.47 thf(fact_135_in__restricted__global__in__unrestricted__global_I1_J,axiom,
% 0.32/0.47 ! [R2: r,S: r > option1457017436_r_l_v,R: r] :
% 0.32/0.47 ( ( member_r @ R2 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 0.32/0.47 => ( member_r @ R2 @ ( rID_G_r_l_v @ S ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % in_restricted_global_in_unrestricted_global(1)
% 0.32/0.47 thf(fact_136_only__fork__introduces__rids_H,axiom,
% 0.32/0.47 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v,R2: r] :
% 0.32/0.47 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.32/0.47 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E5: cntxt_r_l_v,E3: expr_r_l_v] :
% 0.32/0.47 ( ( S @ R )
% 0.32/0.47 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E5 @ ( rfork_r_l_v @ E3 ) ) ) ) ) )
% 0.32/0.47 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 0.32/0.47 => ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % only_fork_introduces_rids'
% 0.32/0.47 thf(fact_137_in__restricted__global__in__updated__global_I1_J,axiom,
% 0.32/0.47 ! [R2: r,S: r > option1457017436_r_l_v,R: r,Ls: produc1156025366_r_l_v] :
% 0.32/0.47 ( ( member_r @ R2 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 0.32/0.47 => ( member_r @ R2 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ Ls ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % in_restricted_global_in_updated_global(1)
% 0.32/0.47 thf(fact_138_fork__pseudodeterministic,axiom,
% 0.32/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,E4: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( ( S @ R )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 0.32/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.32/0.47 = ( ? [R3: r] :
% 0.32/0.47 ( ~ ( member_r @ R3 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) ) ) )
% 0.32/0.47 & ( S2
% 0.32/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R3 ) ) ) ) ) ) ) @ R3
% 0.32/0.47 @ ( some_P1807977723_r_l_v
% 0.32/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 0.32/0.47 @ ( produc1834103605_r_l_v
% 0.32/0.47 @ ^ [X2: l] : none_val_r_l_v
% 0.32/0.47 @ E4 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % fork_pseudodeterministic
% 0.32/0.47 thf(fact_139_substitution_Orevision__step_Ocong,axiom,
% 0.32/0.47 revision_step_r_l_v = revision_step_r_l_v ).
% 0.32/0.47
% 0.32/0.47 % substitution.revision_step.cong
% 0.32/0.47 thf(fact_140_substitution_Orevision__step__relaxed_Ocong,axiom,
% 0.32/0.47 revisi1291188644_r_l_v = revisi1291188644_r_l_v ).
% 0.32/0.47
% 0.32/0.47 % substitution.revision_step_relaxed.cong
% 0.32/0.47 thf(fact_141_substitution_Oonly__fork__introduces__rids_H,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v,R2: r] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.32/0.47 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E5: cntxt_r_l_v,E3: expr_r_l_v] :
% 0.32/0.47 ( ( S @ R )
% 0.32/0.47 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E5 @ ( rfork_r_l_v @ E3 ) ) ) ) ) )
% 0.32/0.47 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 0.32/0.47 => ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S2 ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.only_fork_introduces_rids'
% 0.32/0.47 thf(fact_142_substitution_Orevision__step_Ofork,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,E4: expr_r_l_v,R2: r] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( ( S @ R )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 0.32/0.47 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 0.32/0.47 => ( revision_step_r_l_v @ Subst @ R @ S
% 0.32/0.47 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) @ R2
% 0.32/0.47 @ ( some_P1807977723_r_l_v
% 0.32/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 0.32/0.47 @ ( produc1834103605_r_l_v
% 0.32/0.47 @ ^ [X2: l] : none_val_r_l_v
% 0.32/0.47 @ E4 ) ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.revision_step.fork
% 0.32/0.47 thf(fact_143_local__and__fork__commute,axiom,
% 0.32/0.47 ! [S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,X: produc1156025366_r_l_v,S_22: r > option1457017436_r_l_v,R2: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R4: r,E4: expr_r_l_v] :
% 0.32/0.47 ( ( S_2
% 0.32/0.47 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X ) ) )
% 0.32/0.47 => ( ( S_22
% 0.32/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) @ R4
% 0.32/0.47 @ ( some_P1807977723_r_l_v
% 0.32/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 0.32/0.47 @ ( produc1834103605_r_l_v
% 0.32/0.47 @ ^ [X2: l] : none_val_r_l_v
% 0.32/0.47 @ E4 ) ) ) ) )
% 0.32/0.47 => ( ( ( S_2 @ R2 )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 0.32/0.47 => ( ~ ( member_r @ R4 @ ( rID_G_r_l_v @ S_2 ) )
% 0.32/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S_22
% 0.32/0.47 @ ( fun_up709272714_r_l_v
% 0.32/0.47 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) @ R4
% 0.32/0.47 @ ( some_P1807977723_r_l_v
% 0.32/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 0.32/0.47 @ ( produc1834103605_r_l_v
% 0.32/0.47 @ ^ [X2: l] : none_val_r_l_v
% 0.32/0.47 @ E4 ) ) ) )
% 0.32/0.47 @ R
% 0.32/0.47 @ ( some_P1807977723_r_l_v @ X ) ) )
% 0.32/0.47 => ( ( R != R2 )
% 0.32/0.47 => ( ( R != R4 )
% 0.32/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.32/0.47 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 0.32/0.47 | ( S_2 = S_3 ) )
% 0.32/0.47 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 0.32/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % local_and_fork_commute
% 0.32/0.47 thf(fact_144_revision__step__relaxed_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.32/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r] :
% 0.32/0.47 ( ( ( S @ R )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.32/0.47 => ( ( ( S @ R2 )
% 0.32/0.47 = none_P277133687_r_l_v )
% 0.32/0.47 => ( revisi1291188644_r_l_v @ subst @ R @ S
% 0.32/0.47 @ ^ [X2: r] : none_P277133687_r_l_v ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % revision_step_relaxed.join\<^sub>\<epsilon>
% 0.32/0.47 thf(fact_145_revision__step_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.32/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r] :
% 0.32/0.47 ( ( ( S @ R )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.32/0.47 => ( ( ( S @ R2 )
% 0.32/0.47 = none_P277133687_r_l_v )
% 0.32/0.47 => ( revision_step_r_l_v @ subst @ R @ S
% 0.32/0.47 @ ^ [X2: r] : none_P277133687_r_l_v ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % revision_step.join\<^sub>\<epsilon>
% 0.32/0.47 thf(fact_146_substitution_Olocal__and__fork__commute,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,X: produc1156025366_r_l_v,S_22: r > option1457017436_r_l_v,R2: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R4: r,E4: expr_r_l_v] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( S_2
% 0.32/0.47 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X ) ) )
% 0.32/0.47 => ( ( S_22
% 0.32/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) @ R4
% 0.32/0.47 @ ( some_P1807977723_r_l_v
% 0.32/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 0.32/0.47 @ ( produc1834103605_r_l_v
% 0.32/0.47 @ ^ [X2: l] : none_val_r_l_v
% 0.32/0.47 @ E4 ) ) ) ) )
% 0.32/0.47 => ( ( ( S_2 @ R2 )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 0.32/0.47 => ( ~ ( member_r @ R4 @ ( rID_G_r_l_v @ S_2 ) )
% 0.32/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S_22
% 0.32/0.47 @ ( fun_up709272714_r_l_v
% 0.32/0.47 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) @ R4
% 0.32/0.47 @ ( some_P1807977723_r_l_v
% 0.32/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 0.32/0.47 @ ( produc1834103605_r_l_v
% 0.32/0.47 @ ^ [X2: l] : none_val_r_l_v
% 0.32/0.47 @ E4 ) ) ) )
% 0.32/0.47 @ R
% 0.32/0.47 @ ( some_P1807977723_r_l_v @ X ) ) )
% 0.32/0.47 => ( ( R != R2 )
% 0.32/0.47 => ( ( R != R4 )
% 0.32/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.32/0.47 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 0.32/0.47 | ( S_2 = S_3 ) )
% 0.32/0.47 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 0.32/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.local_and_fork_commute
% 0.32/0.47 thf(fact_147_local__steps__commute,axiom,
% 0.32/0.47 ! [S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,X: produc1156025366_r_l_v,S_22: r > option1457017436_r_l_v,R2: r,Y: produc1156025366_r_l_v] :
% 0.32/0.47 ( ( S_2
% 0.32/0.47 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X ) ) )
% 0.32/0.47 => ( ( S_22
% 0.32/0.47 = ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
% 0.32/0.47 => ( ( revision_step_r_l_v @ subst @ R2 @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X ) ) @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X ) ) @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
% 0.32/0.47 => ( ( revision_step_r_l_v @ subst @ R @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) @ R @ ( some_P1807977723_r_l_v @ X ) ) )
% 0.32/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.32/0.47 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 0.32/0.47 | ( S_2 = S_3 ) )
% 0.32/0.47 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 0.32/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % local_steps_commute
% 0.32/0.47 thf(fact_148_transition__relations__equivalent,axiom,
% 0.32/0.47 ! [S: r > option1457017436_r_l_v,R: r,S2: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( reachable_r_l_v @ subst @ S )
% 0.32/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.32/0.47 = ( revisi1291188644_r_l_v @ subst @ R @ S @ S2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % transition_relations_equivalent
% 0.32/0.47 thf(fact_149_local__determinism,axiom,
% 0.32/0.47 ! [R: r,S_1: r > option1457017436_r_l_v,S_2: r > option1457017436_r_l_v,S_22: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( revision_step_r_l_v @ subst @ R @ S_1 @ S_2 )
% 0.32/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S_1 @ S_22 )
% 0.32/0.47 => ( eq_states_r_l_v @ S_2 @ S_22 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % local_determinism
% 0.32/0.47 thf(fact_150_SLC__sym,axiom,
% 0.32/0.47 ! [R2: r,S_2: r > option1457017436_r_l_v,R: r,S_22: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ? [S_33: r > option1457017436_r_l_v,S_34: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( eq_states_r_l_v @ S_33 @ S_34 )
% 0.32/0.47 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_33 )
% 0.32/0.47 | ( S_2 = S_33 ) )
% 0.32/0.47 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_34 )
% 0.32/0.47 | ( S_22 = S_34 ) ) )
% 0.32/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.32/0.47 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_3 )
% 0.32/0.47 | ( S_22 = S_3 ) )
% 0.32/0.47 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_32 )
% 0.32/0.47 | ( S_2 = S_32 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % SLC_sym
% 0.32/0.47 thf(fact_151_SLC__commute,axiom,
% 0.32/0.47 ! [S_35: r > option1457017436_r_l_v,S_36: r > option1457017436_r_l_v,R2: r,S_2: r > option1457017436_r_l_v,R: r,S_22: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( S_35 = S_36 )
% 0.32/0.47 => ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_35 )
% 0.32/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_36 )
% 0.32/0.47 => ( ( eq_states_r_l_v @ S_35 @ S_36 )
% 0.32/0.47 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_35 )
% 0.32/0.47 | ( S_2 = S_35 ) )
% 0.32/0.47 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_36 )
% 0.32/0.47 | ( S_22 = S_36 ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % SLC_commute
% 0.32/0.47 thf(fact_152_reachability__closed__under__execution__step,axiom,
% 0.32/0.47 ! [S: r > option1457017436_r_l_v,R: r,S2: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( reachable_r_l_v @ subst @ S )
% 0.32/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.32/0.47 => ( reachable_r_l_v @ subst @ S2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % reachability_closed_under_execution_step
% 0.32/0.47 thf(fact_153_expr_Oinject_I8_J,axiom,
% 0.32/0.47 ! [X8: expr_r_l_v,Y8: expr_r_l_v] :
% 0.32/0.47 ( ( ( rjoin_r_l_v @ X8 )
% 0.32/0.47 = ( rjoin_r_l_v @ Y8 ) )
% 0.32/0.47 = ( X8 = Y8 ) ) ).
% 0.32/0.47
% 0.32/0.47 % expr.inject(8)
% 0.32/0.47 thf(fact_154_SLC__join_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.32/0.47 ! [S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R4: r,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( ( S_1 @ R )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 0.32/0.47 => ( ( S_2
% 0.32/0.47 = ( ^ [X2: r] : none_P277133687_r_l_v ) )
% 0.32/0.47 => ( ( ( S_1 @ R4 )
% 0.32/0.47 = none_P277133687_r_l_v )
% 0.32/0.47 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 0.32/0.47 => ( ( R != R2 )
% 0.32/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.32/0.47 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 0.32/0.47 | ( S_2 = S_3 ) )
% 0.32/0.47 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 0.32/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % SLC_join\<^sub>\<epsilon>
% 0.32/0.47 thf(fact_155_reachable__def,axiom,
% 0.32/0.47 ! [S: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( reachable_r_l_v @ subst @ S )
% 0.32/0.47 = ( ? [E6: expr_r_l_v,S3: r > option1457017436_r_l_v] : ( execution_r_l_v @ subst @ E6 @ S3 @ S ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % reachable_def
% 0.32/0.47 thf(fact_156_rjoin_092_060_094sub_062_092_060epsilon_062__deterministic,axiom,
% 0.32/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,S2: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( ( S @ R )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.32/0.47 => ( ( ( S @ R2 )
% 0.32/0.47 = none_P277133687_r_l_v )
% 0.32/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.32/0.47 = ( S2
% 0.32/0.47 = ( ^ [X2: r] : none_P277133687_r_l_v ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rjoin\<^sub>\<epsilon>_deterministic
% 0.32/0.47 thf(fact_157__092_060alpha_062_092_060beta_062__sym,axiom,
% 0.32/0.47 ! [S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( eq_states_r_l_v @ S @ S2 )
% 0.32/0.47 => ( eq_states_r_l_v @ S2 @ S ) ) ).
% 0.32/0.47
% 0.32/0.47 % \<alpha>\<beta>_sym
% 0.32/0.47 thf(fact_158__092_060alpha_062_092_060beta_062__refl,axiom,
% 0.32/0.47 ! [S: r > option1457017436_r_l_v] : ( eq_states_r_l_v @ S @ S ) ).
% 0.32/0.47
% 0.32/0.47 % \<alpha>\<beta>_refl
% 0.32/0.47 thf(fact_159__092_060alpha_062_092_060beta_062__trans,axiom,
% 0.32/0.47 ! [S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v,S4: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( eq_states_r_l_v @ S @ S2 )
% 0.32/0.47 => ( ( eq_states_r_l_v @ S2 @ S4 )
% 0.32/0.47 => ( eq_states_r_l_v @ S @ S4 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % \<alpha>\<beta>_trans
% 0.32/0.47 thf(fact_160_expr_Odistinct_I13_J,axiom,
% 0.32/0.47 ! [X1: val_r_l_v,X8: expr_r_l_v] :
% 0.32/0.47 ( ( vE_r_l_v @ X1 )
% 0.32/0.47 != ( rjoin_r_l_v @ X8 ) ) ).
% 0.32/0.47
% 0.32/0.47 % expr.distinct(13)
% 0.32/0.47 thf(fact_161_expr_Odistinct_I55_J,axiom,
% 0.32/0.47 ! [X7: expr_r_l_v,X8: expr_r_l_v] :
% 0.32/0.47 ( ( rfork_r_l_v @ X7 )
% 0.32/0.47 != ( rjoin_r_l_v @ X8 ) ) ).
% 0.32/0.47
% 0.32/0.47 % expr.distinct(55)
% 0.32/0.47 thf(fact_162_substitution_Olocal__determinism,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S_1: r > option1457017436_r_l_v,S_2: r > option1457017436_r_l_v,S_22: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S_1 @ S_2 )
% 0.32/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S_1 @ S_22 )
% 0.32/0.47 => ( eq_states_r_l_v @ S_2 @ S_22 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.local_determinism
% 0.32/0.47 thf(fact_163_substitution_OSLC__commute,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_35: r > option1457017436_r_l_v,S_36: r > option1457017436_r_l_v,R2: r,S_2: r > option1457017436_r_l_v,R: r,S_22: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( S_35 = S_36 )
% 0.32/0.47 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_35 )
% 0.32/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_36 )
% 0.32/0.47 => ( ( eq_states_r_l_v @ S_35 @ S_36 )
% 0.32/0.47 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_35 )
% 0.32/0.47 | ( S_2 = S_35 ) )
% 0.32/0.47 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_36 )
% 0.32/0.47 | ( S_22 = S_36 ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.SLC_commute
% 0.32/0.47 thf(fact_164_substitution_OSLC__sym,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R2: r,S_2: r > option1457017436_r_l_v,R: r,S_22: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ? [S_33: r > option1457017436_r_l_v,S_34: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( eq_states_r_l_v @ S_33 @ S_34 )
% 0.32/0.47 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_33 )
% 0.32/0.47 | ( S_2 = S_33 ) )
% 0.32/0.47 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_34 )
% 0.32/0.47 | ( S_22 = S_34 ) ) )
% 0.32/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.32/0.47 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_3 )
% 0.32/0.47 | ( S_22 = S_3 ) )
% 0.32/0.47 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_32 )
% 0.32/0.47 | ( S_2 = S_32 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.SLC_sym
% 0.32/0.47 thf(fact_165_substitution_OSLC__join_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R4: r,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( ( S_1 @ R )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 0.32/0.47 => ( ( S_2
% 0.32/0.47 = ( ^ [X2: r] : none_P277133687_r_l_v ) )
% 0.32/0.47 => ( ( ( S_1 @ R4 )
% 0.32/0.47 = none_P277133687_r_l_v )
% 0.32/0.47 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
% 0.32/0.47 => ( ( R != R2 )
% 0.32/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.32/0.47 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 0.32/0.47 | ( S_2 = S_3 ) )
% 0.32/0.47 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 0.32/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.SLC_join\<^sub>\<epsilon>
% 0.32/0.47 thf(fact_166_substitution_Olocal__steps__commute,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,X: produc1156025366_r_l_v,S_22: r > option1457017436_r_l_v,R2: r,Y: produc1156025366_r_l_v] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( S_2
% 0.32/0.47 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X ) ) )
% 0.32/0.47 => ( ( S_22
% 0.32/0.47 = ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
% 0.32/0.47 => ( ( revision_step_r_l_v @ Subst @ R2 @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X ) ) @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X ) ) @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
% 0.32/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) @ R @ ( some_P1807977723_r_l_v @ X ) ) )
% 0.32/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.32/0.47 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 0.32/0.47 | ( S_2 = S_3 ) )
% 0.32/0.47 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 0.32/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.local_steps_commute
% 0.32/0.47 thf(fact_167_substitution_Orjoin_092_060_094sub_062_092_060epsilon_062__deterministic,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,S2: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( ( S @ R )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.32/0.47 => ( ( ( S @ R2 )
% 0.32/0.47 = none_P277133687_r_l_v )
% 0.32/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.32/0.47 = ( S2
% 0.32/0.47 = ( ^ [X2: r] : none_P277133687_r_l_v ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.rjoin\<^sub>\<epsilon>_deterministic
% 0.32/0.47 thf(fact_168_substitution_Orevision__step_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( ( S @ R )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.32/0.47 => ( ( ( S @ R2 )
% 0.32/0.47 = none_P277133687_r_l_v )
% 0.32/0.47 => ( revision_step_r_l_v @ Subst @ R @ S
% 0.32/0.47 @ ^ [X2: r] : none_P277133687_r_l_v ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.revision_step.join\<^sub>\<epsilon>
% 0.32/0.47 thf(fact_169_substitution_Orevision__step__relaxed_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( ( S @ R )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.32/0.47 => ( ( ( S @ R2 )
% 0.32/0.47 = none_P277133687_r_l_v )
% 0.32/0.47 => ( revisi1291188644_r_l_v @ Subst @ R @ S
% 0.32/0.47 @ ^ [X2: r] : none_P277133687_r_l_v ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.revision_step_relaxed.join\<^sub>\<epsilon>
% 0.32/0.47 thf(fact_170_inductive__invariant__is__execution__invariant,axiom,
% 0.32/0.47 ! [S: r > option1457017436_r_l_v,P: ( r > option1457017436_r_l_v ) > $o] :
% 0.32/0.47 ( ( reachable_r_l_v @ subst @ S )
% 0.32/0.47 => ( ( induct1670415253_r_l_v @ subst @ P )
% 0.32/0.47 => ( P @ S ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inductive_invariant_is_execution_invariant
% 0.32/0.47 thf(fact_171_reachable__imp___092_060S_062_092_060_094sub_062G,axiom,
% 0.32/0.47 ! [S: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( reachable_r_l_v @ subst @ S )
% 0.32/0.47 => ( domain1547879849_r_l_v @ S ) ) ).
% 0.32/0.47
% 0.32/0.47 % reachable_imp_\<S>\<^sub>G
% 0.32/0.47 thf(fact_172_substitution_Otransition__relations__equivalent,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,S2: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( reachable_r_l_v @ Subst @ S )
% 0.32/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.32/0.47 = ( revisi1291188644_r_l_v @ Subst @ R @ S @ S2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.transition_relations_equivalent
% 0.32/0.47 thf(fact_173_SLC__fork,axiom,
% 0.32/0.47 ! [S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,E4: expr_r_l_v,S_2: r > option1457017436_r_l_v,Left_forkee: r,R2: r,S_22: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( ( S_1 @ R )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 0.32/0.47 => ( ( S_2
% 0.32/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ Left_forkee ) ) ) ) ) ) ) @ Left_forkee
% 0.32/0.47 @ ( some_P1807977723_r_l_v
% 0.32/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 0.32/0.47 @ ( produc1834103605_r_l_v
% 0.32/0.47 @ ^ [X2: l] : none_val_r_l_v
% 0.32/0.47 @ E4 ) ) ) ) )
% 0.32/0.47 => ( ~ ( member_r @ Left_forkee @ ( rID_G_r_l_v @ S_1 ) )
% 0.32/0.47 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 0.32/0.47 => ( ( R != R2 )
% 0.32/0.47 => ( ( reachable_r_l_v @ subst @ S_1 )
% 0.32/0.47 => ( ~ ( finite_finite_r @ top_top_set_r )
% 0.32/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.32/0.47 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 0.32/0.47 | ( S_2 = S_3 ) )
% 0.32/0.47 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 0.32/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % SLC_fork
% 0.32/0.47 thf(fact_174_join__and__local__commute,axiom,
% 0.32/0.47 ! [S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,E: cntxt_r_l_v,R4: r,S_22: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,Sigma3: l > option_val_r_l_v,V: val_r_l_v] :
% 0.32/0.47 ( ( S_2
% 0.32/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
% 0.32/0.47 => ( ( S_22
% 0.32/0.47 = ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Ls ) ) )
% 0.32/0.47 => ( ( R != R2 )
% 0.32/0.47 => ( ( R2 != R4 )
% 0.32/0.47 => ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) @ R2 @ ( some_P1807977723_r_l_v @ Ls ) ) )
% 0.32/0.47 => ( ( ( S_22 @ R )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 0.32/0.47 => ( ( ( S_22 @ R4 )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.32/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.32/0.47 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 0.32/0.47 | ( S_2 = S_3 ) )
% 0.32/0.47 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 0.32/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % join_and_local_commute
% 0.32/0.47 thf(fact_175_empty__map__finite_I3_J,axiom,
% 0.32/0.47 ( finite_finite_r
% 0.32/0.47 @ ( rID_G_r_l_v
% 0.32/0.47 @ ^ [X2: r] : none_P277133687_r_l_v ) ) ).
% 0.32/0.47
% 0.32/0.47 % empty_map_finite(3)
% 0.32/0.47 thf(fact_176_val_Oinject_I1_J,axiom,
% 0.32/0.47 ! [X1: const,Y1: const] :
% 0.32/0.47 ( ( ( cV_r_l_v @ X1 )
% 0.32/0.47 = ( cV_r_l_v @ Y1 ) )
% 0.32/0.47 = ( X1 = Y1 ) ) ).
% 0.32/0.47
% 0.32/0.47 % val.inject(1)
% 0.32/0.47 thf(fact_177_RID_092_060_094sub_062G__finite__invariant,axiom,
% 0.32/0.47 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.32/0.47 => ( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
% 0.32/0.47 => ( finite_finite_r @ ( rID_G_r_l_v @ S2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % RID\<^sub>G_finite_invariant
% 0.32/0.47 thf(fact_178_reachable__imp__identifiers__finite_I1_J,axiom,
% 0.32/0.47 ! [S: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( reachable_r_l_v @ subst @ S )
% 0.32/0.47 => ( finite_finite_r @ ( rID_G_r_l_v @ S ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % reachable_imp_identifiers_finite(1)
% 0.32/0.47 thf(fact_179_reachable__imp__identifiers__available_I1_J,axiom,
% 0.32/0.47 ! [S: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( reachable_r_l_v @ subst @ S )
% 0.32/0.47 => ( ~ ( finite_finite_r @ top_top_set_r )
% 0.32/0.47 => ? [R5: r] :
% 0.32/0.47 ~ ( member_r @ R5 @ ( rID_G_r_l_v @ S ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % reachable_imp_identifiers_available(1)
% 0.32/0.47 thf(fact_180_finite__option__UNIV,axiom,
% 0.32/0.47 ( ( finite1036466630um_r_l @ top_to1855148309um_r_l )
% 0.32/0.47 = ( finite65649782um_r_l @ top_to182927813um_r_l ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_option_UNIV
% 0.32/0.47 thf(fact_181_finite__option__UNIV,axiom,
% 0.32/0.47 ( ( finite111936338um_l_r @ top_to1150555297um_l_r )
% 0.32/0.47 = ( finite1591053314um_l_r @ top_to1405881169um_l_r ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_option_UNIV
% 0.32/0.47 thf(fact_182_finite__option__UNIV,axiom,
% 0.32/0.47 ( ( finite1864485196um_l_l @ top_to1066565019um_l_l )
% 0.32/0.47 = ( finite1541484284um_l_l @ top_to1010946379um_l_l ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_option_UNIV
% 0.32/0.47 thf(fact_183_finite__option__UNIV,axiom,
% 0.32/0.47 ( ( finite555643486_set_r @ top_to555798885_set_r )
% 0.32/0.47 = ( finite_finite_set_r @ top_top_set_set_r ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_option_UNIV
% 0.32/0.47 thf(fact_184_finite__option__UNIV,axiom,
% 0.32/0.47 ( ( finite160708696_set_l @ top_to471808607_set_l )
% 0.32/0.47 = ( finite_finite_set_l @ top_top_set_set_l ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_option_UNIV
% 0.32/0.47 thf(fact_185_finite__option__UNIV,axiom,
% 0.32/0.47 ( ( finite16335230tion_r @ top_top_set_option_r )
% 0.32/0.47 = ( finite_finite_r @ top_top_set_r ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_option_UNIV
% 0.32/0.47 thf(fact_186_finite__option__UNIV,axiom,
% 0.32/0.47 ( ( finite2114249848tion_l @ top_top_set_option_l )
% 0.32/0.47 = ( finite_finite_l @ top_top_set_l ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_option_UNIV
% 0.32/0.47 thf(fact_187_domains__subsume__globally__def,axiom,
% 0.32/0.47 ( domain1547879849_r_l_v
% 0.32/0.47 = ( ^ [S5: r > option1457017436_r_l_v] :
% 0.32/0.47 ! [R6: r,Ls2: produc1156025366_r_l_v] :
% 0.32/0.47 ( ( ( S5 @ R6 )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ Ls2 ) )
% 0.32/0.47 => ( domain87684397_l_r_v @ Ls2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % domains_subsume_globally_def
% 0.32/0.47 thf(fact_188_finite__state__imp__restriction__finite_I1_J,axiom,
% 0.32/0.47 ! [S: r > option1457017436_r_l_v,R: r] :
% 0.32/0.47 ( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
% 0.32/0.47 => ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_state_imp_restriction_finite(1)
% 0.32/0.47 thf(fact_189_revision__step_Ojoin,axiom,
% 0.32/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v] :
% 0.32/0.47 ( ( ( S @ R )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.32/0.47 => ( ( ( S @ R2 )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.32/0.47 => ( revision_step_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % revision_step.join
% 0.32/0.47 thf(fact_190_revision__step__relaxed_Ojoin,axiom,
% 0.32/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v] :
% 0.32/0.47 ( ( ( S @ R )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.32/0.47 => ( ( ( S @ R2 )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.32/0.47 => ( revisi1291188644_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % revision_step_relaxed.join
% 0.32/0.47 thf(fact_191_SLC__join,axiom,
% 0.32/0.47 ! [S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R4: r,S_2: r > option1457017436_r_l_v,Tau3: l > option_val_r_l_v,Sigma3: l > option_val_r_l_v,V: val_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( ( S_1 @ R )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 0.32/0.47 => ( ( S_2
% 0.32/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
% 0.32/0.47 => ( ( ( S_1 @ R4 )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.32/0.47 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 0.32/0.47 => ( ( R != R2 )
% 0.32/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.32/0.47 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 0.32/0.47 | ( S_2 = S_3 ) )
% 0.32/0.47 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 0.32/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % SLC_join
% 0.32/0.47 thf(fact_192_bij___092_060alpha_062,axiom,
% 0.32/0.47 bij_betw_r_r @ alpha @ top_top_set_r @ top_top_set_r ).
% 0.32/0.47
% 0.32/0.47 % bij_\<alpha>
% 0.32/0.47 thf(fact_193_rjoin__deterministic,axiom,
% 0.32/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( ( S @ R )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.32/0.47 => ( ( ( S @ R2 )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.32/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.32/0.47 = ( S2
% 0.32/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rjoin_deterministic
% 0.32/0.47 thf(fact_194_substitution_Oexecution_Ocong,axiom,
% 0.32/0.47 execution_r_l_v = execution_r_l_v ).
% 0.32/0.47
% 0.32/0.47 % substitution.execution.cong
% 0.32/0.47 thf(fact_195_substitution_Oinductive__invariant_Ocong,axiom,
% 0.32/0.47 induct1670415253_r_l_v = induct1670415253_r_l_v ).
% 0.32/0.47
% 0.32/0.47 % substitution.inductive_invariant.cong
% 0.32/0.47 thf(fact_196_val_Odistinct_I5_J,axiom,
% 0.32/0.47 ! [X1: const,X4: r] :
% 0.32/0.47 ( ( cV_r_l_v @ X1 )
% 0.32/0.47 != ( rid_r_l_v @ X4 ) ) ).
% 0.32/0.47
% 0.32/0.47 % val.distinct(5)
% 0.32/0.47 thf(fact_197_substitution_Oreachable__imp__identifiers__available_I1_J,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( reachable_r_l_v @ Subst @ S )
% 0.32/0.47 => ( ~ ( finite_finite_r @ top_top_set_r )
% 0.32/0.47 => ? [R5: r] :
% 0.32/0.47 ~ ( member_r @ R5 @ ( rID_G_r_l_v @ S ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.reachable_imp_identifiers_available(1)
% 0.32/0.47 thf(fact_198_substitution_Ostrong__local__confluence,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S_1: r > option1457017436_r_l_v,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S_1 @ S_2 )
% 0.32/0.47 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
% 0.32/0.47 => ( ( reachable_r_l_v @ Subst @ S_1 )
% 0.32/0.47 => ( ~ ( finite_finite_l @ top_top_set_l )
% 0.32/0.47 => ( ~ ( finite_finite_r @ top_top_set_r )
% 0.32/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.32/0.47 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 0.32/0.47 | ( S_2 = S_3 ) )
% 0.32/0.47 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 0.32/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.strong_local_confluence
% 0.32/0.47 thf(fact_199_substitution_ORID_092_060_094sub_062G__finite__invariant,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.32/0.47 => ( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
% 0.32/0.47 => ( finite_finite_r @ ( rID_G_r_l_v @ S2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.RID\<^sub>G_finite_invariant
% 0.32/0.47 thf(fact_200_substitution_Oreachable__imp__identifiers__finite_I1_J,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( reachable_r_l_v @ Subst @ S )
% 0.32/0.47 => ( finite_finite_r @ ( rID_G_r_l_v @ S ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.reachable_imp_identifiers_finite(1)
% 0.32/0.47 thf(fact_201_substitution_Oreachable__imp___092_060S_062_092_060_094sub_062G,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( reachable_r_l_v @ Subst @ S )
% 0.32/0.47 => ( domain1547879849_r_l_v @ S ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.reachable_imp_\<S>\<^sub>G
% 0.32/0.47 thf(fact_202_substitution_Oinductive__invariant__is__execution__invariant,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,P: ( r > option1457017436_r_l_v ) > $o] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( reachable_r_l_v @ Subst @ S )
% 0.32/0.47 => ( ( induct1670415253_r_l_v @ Subst @ P )
% 0.32/0.47 => ( P @ S ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.inductive_invariant_is_execution_invariant
% 0.32/0.47 thf(fact_203_substitution_Oempty__map__finite_I3_J,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( finite_finite_r
% 0.32/0.47 @ ( rID_G_r_l_v
% 0.32/0.47 @ ^ [X2: r] : none_P277133687_r_l_v ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.empty_map_finite(3)
% 0.32/0.47 thf(fact_204_substitution_Oreachable__def,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( reachable_r_l_v @ Subst @ S )
% 0.32/0.47 = ( ? [E6: expr_r_l_v,S3: r > option1457017436_r_l_v] : ( execution_r_l_v @ Subst @ E6 @ S3 @ S ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.reachable_def
% 0.32/0.47 thf(fact_205_substitution_Ofinite__state__imp__restriction__finite_I1_J,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
% 0.32/0.47 => ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.finite_state_imp_restriction_finite(1)
% 0.32/0.47 thf(fact_206_substitution_Oreachable_Ocong,axiom,
% 0.32/0.47 reachable_r_l_v = reachable_r_l_v ).
% 0.32/0.47
% 0.32/0.47 % substitution.reachable.cong
% 0.32/0.47 thf(fact_207_substitution_Orevision__step_Ojoin,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( ( S @ R )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.32/0.47 => ( ( ( S @ R2 )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.32/0.47 => ( revision_step_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.revision_step.join
% 0.32/0.47 thf(fact_208_substitution_Orjoin__deterministic,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( ( S @ R )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.32/0.47 => ( ( ( S @ R2 )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.32/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.32/0.47 = ( S2
% 0.32/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.rjoin_deterministic
% 0.32/0.47 thf(fact_209_substitution_Orevision__step__relaxed_Ojoin,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( ( S @ R )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.32/0.47 => ( ( ( S @ R2 )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.32/0.47 => ( revisi1291188644_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.revision_step_relaxed.join
% 0.32/0.47 thf(fact_210_substitution_Ojoin__and__local__commute,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,E: cntxt_r_l_v,R4: r,S_22: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,Sigma3: l > option_val_r_l_v,V: val_r_l_v] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( S_2
% 0.32/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
% 0.32/0.47 => ( ( S_22
% 0.32/0.47 = ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Ls ) ) )
% 0.32/0.47 => ( ( R != R2 )
% 0.32/0.47 => ( ( R2 != R4 )
% 0.32/0.47 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) @ R2 @ ( some_P1807977723_r_l_v @ Ls ) ) )
% 0.32/0.47 => ( ( ( S_22 @ R )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 0.32/0.47 => ( ( ( S_22 @ R4 )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.32/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.32/0.47 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 0.32/0.47 | ( S_2 = S_3 ) )
% 0.32/0.47 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 0.32/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.join_and_local_commute
% 0.32/0.47 thf(fact_211_substitution_OSLC__join,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R4: r,S_2: r > option1457017436_r_l_v,Tau3: l > option_val_r_l_v,Sigma3: l > option_val_r_l_v,V: val_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( ( S_1 @ R )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 0.32/0.47 => ( ( S_2
% 0.32/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
% 0.32/0.47 => ( ( ( S_1 @ R4 )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.32/0.47 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
% 0.32/0.47 => ( ( R != R2 )
% 0.32/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.32/0.47 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 0.32/0.47 | ( S_2 = S_3 ) )
% 0.32/0.47 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 0.32/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.SLC_join
% 0.32/0.47 thf(fact_212_substitution_OSLC__fork,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,E4: expr_r_l_v,S_2: r > option1457017436_r_l_v,Left_forkee: r,R2: r,S_22: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( ( S_1 @ R )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 0.32/0.47 => ( ( S_2
% 0.32/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ Left_forkee ) ) ) ) ) ) ) @ Left_forkee
% 0.32/0.47 @ ( some_P1807977723_r_l_v
% 0.32/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 0.32/0.47 @ ( produc1834103605_r_l_v
% 0.32/0.47 @ ^ [X2: l] : none_val_r_l_v
% 0.32/0.47 @ E4 ) ) ) ) )
% 0.32/0.47 => ( ~ ( member_r @ Left_forkee @ ( rID_G_r_l_v @ S_1 ) )
% 0.32/0.47 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
% 0.32/0.47 => ( ( R != R2 )
% 0.32/0.47 => ( ( reachable_r_l_v @ Subst @ S_1 )
% 0.32/0.47 => ( ~ ( finite_finite_r @ top_top_set_r )
% 0.32/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.32/0.47 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 0.32/0.47 | ( S_2 = S_3 ) )
% 0.32/0.47 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 0.32/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.SLC_fork
% 0.32/0.47 thf(fact_213_substitution_Oreachability__closed__under__execution__step,axiom,
% 0.32/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,S2: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( substitution_r_l_v @ Subst )
% 0.32/0.47 => ( ( reachable_r_l_v @ Subst @ S )
% 0.32/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.32/0.47 => ( reachable_r_l_v @ Subst @ S2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % substitution.reachability_closed_under_execution_step
% 0.32/0.47 thf(fact_214_nice__ind__inv__is__inductive__invariant,axiom,
% 0.32/0.47 ( induct1670415253_r_l_v @ subst
% 0.32/0.47 @ ^ [S5: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( domain1547879849_r_l_v @ S5 )
% 0.32/0.47 & ( subsum680764357_r_l_v @ S5 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % nice_ind_inv_is_inductive_invariant
% 0.32/0.47 thf(fact_215_step__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I2_J,axiom,
% 0.32/0.47 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.32/0.47 => ( ( domain1547879849_r_l_v @ S )
% 0.32/0.47 => ( ( subsum680764357_r_l_v @ S )
% 0.32/0.47 => ( subsum680764357_r_l_v @ S2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % step_preserves_\<S>\<^sub>G_and_\<A>\<^sub>G(2)
% 0.32/0.47 thf(fact_216_step__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I1_J,axiom,
% 0.32/0.47 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.32/0.47 => ( ( domain1547879849_r_l_v @ S )
% 0.32/0.47 => ( ( subsum680764357_r_l_v @ S )
% 0.32/0.47 => ( domain1547879849_r_l_v @ S2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % step_preserves_\<S>\<^sub>G_and_\<A>\<^sub>G(1)
% 0.32/0.47 thf(fact_217_finite__Collect__not,axiom,
% 0.32/0.47 ! [P: sum_sum_r_l > $o] :
% 0.32/0.47 ( ( finite65649782um_r_l @ ( collect_Sum_sum_r_l @ P ) )
% 0.32/0.47 => ( ( finite65649782um_r_l
% 0.32/0.47 @ ( collect_Sum_sum_r_l
% 0.32/0.47 @ ^ [X2: sum_sum_r_l] :
% 0.32/0.47 ~ ( P @ X2 ) ) )
% 0.32/0.47 = ( finite65649782um_r_l @ top_to182927813um_r_l ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_Collect_not
% 0.32/0.47 thf(fact_218_finite__Collect__not,axiom,
% 0.32/0.47 ! [P: sum_sum_l_r > $o] :
% 0.32/0.47 ( ( finite1591053314um_l_r @ ( collect_Sum_sum_l_r @ P ) )
% 0.32/0.47 => ( ( finite1591053314um_l_r
% 0.32/0.47 @ ( collect_Sum_sum_l_r
% 0.32/0.47 @ ^ [X2: sum_sum_l_r] :
% 0.32/0.47 ~ ( P @ X2 ) ) )
% 0.32/0.47 = ( finite1591053314um_l_r @ top_to1405881169um_l_r ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_Collect_not
% 0.32/0.47 thf(fact_219_finite__Collect__not,axiom,
% 0.32/0.47 ! [P: sum_sum_l_l > $o] :
% 0.32/0.47 ( ( finite1541484284um_l_l @ ( collect_Sum_sum_l_l @ P ) )
% 0.32/0.47 => ( ( finite1541484284um_l_l
% 0.32/0.47 @ ( collect_Sum_sum_l_l
% 0.32/0.47 @ ^ [X2: sum_sum_l_l] :
% 0.32/0.47 ~ ( P @ X2 ) ) )
% 0.32/0.47 = ( finite1541484284um_l_l @ top_to1010946379um_l_l ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_Collect_not
% 0.32/0.47 thf(fact_220_finite__Collect__not,axiom,
% 0.32/0.47 ! [P: set_r > $o] :
% 0.32/0.47 ( ( finite_finite_set_r @ ( collect_set_r @ P ) )
% 0.32/0.47 => ( ( finite_finite_set_r
% 0.32/0.47 @ ( collect_set_r
% 0.32/0.47 @ ^ [X2: set_r] :
% 0.32/0.47 ~ ( P @ X2 ) ) )
% 0.32/0.47 = ( finite_finite_set_r @ top_top_set_set_r ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_Collect_not
% 0.32/0.47 thf(fact_221_finite__Collect__not,axiom,
% 0.32/0.47 ! [P: set_l > $o] :
% 0.32/0.47 ( ( finite_finite_set_l @ ( collect_set_l @ P ) )
% 0.32/0.47 => ( ( finite_finite_set_l
% 0.32/0.47 @ ( collect_set_l
% 0.32/0.47 @ ^ [X2: set_l] :
% 0.32/0.47 ~ ( P @ X2 ) ) )
% 0.32/0.47 = ( finite_finite_set_l @ top_top_set_set_l ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_Collect_not
% 0.32/0.47 thf(fact_222_finite__Collect__not,axiom,
% 0.32/0.47 ! [P: r > $o] :
% 0.32/0.47 ( ( finite_finite_r @ ( collect_r @ P ) )
% 0.32/0.47 => ( ( finite_finite_r
% 0.32/0.47 @ ( collect_r
% 0.32/0.47 @ ^ [X2: r] :
% 0.32/0.47 ~ ( P @ X2 ) ) )
% 0.32/0.47 = ( finite_finite_r @ top_top_set_r ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_Collect_not
% 0.32/0.47 thf(fact_223_finite__Collect__not,axiom,
% 0.32/0.47 ! [P: l > $o] :
% 0.32/0.47 ( ( finite_finite_l @ ( collect_l @ P ) )
% 0.32/0.47 => ( ( finite_finite_l
% 0.32/0.47 @ ( collect_l
% 0.32/0.47 @ ^ [X2: l] :
% 0.32/0.47 ~ ( P @ X2 ) ) )
% 0.32/0.47 = ( finite_finite_l @ top_top_set_l ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_Collect_not
% 0.32/0.47 thf(fact_224_in__renamed__in__unlabelled__global_I1_J,axiom,
% 0.32/0.47 ! [Alpha2: r > r,Beta2: l > l,R: r,S: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( bij_betw_r_r @ Alpha2 @ top_top_set_r @ top_top_set_r )
% 0.32/0.47 => ( ( bij_betw_l_l @ Beta2 @ top_top_set_l @ top_top_set_l )
% 0.32/0.47 => ( ( member_r @ ( Alpha2 @ R ) @ ( rID_G_r_l_v @ ( r_G_r_l_v @ Alpha2 @ Beta2 @ S ) ) )
% 0.32/0.47 = ( member_r @ R @ ( rID_G_r_l_v @ S ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % in_renamed_in_unlabelled_global(1)
% 0.32/0.47 thf(fact_225_finite__Collect__conjI,axiom,
% 0.32/0.47 ! [P: sum_sum_r_l > $o,Q: sum_sum_r_l > $o] :
% 0.32/0.47 ( ( ( finite65649782um_r_l @ ( collect_Sum_sum_r_l @ P ) )
% 0.32/0.47 | ( finite65649782um_r_l @ ( collect_Sum_sum_r_l @ Q ) ) )
% 0.32/0.47 => ( finite65649782um_r_l
% 0.32/0.47 @ ( collect_Sum_sum_r_l
% 0.32/0.47 @ ^ [X2: sum_sum_r_l] :
% 0.32/0.47 ( ( P @ X2 )
% 0.32/0.47 & ( Q @ X2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_Collect_conjI
% 0.32/0.47 thf(fact_226_finite__Collect__conjI,axiom,
% 0.32/0.47 ! [P: sum_sum_l_r > $o,Q: sum_sum_l_r > $o] :
% 0.32/0.47 ( ( ( finite1591053314um_l_r @ ( collect_Sum_sum_l_r @ P ) )
% 0.32/0.47 | ( finite1591053314um_l_r @ ( collect_Sum_sum_l_r @ Q ) ) )
% 0.32/0.47 => ( finite1591053314um_l_r
% 0.32/0.47 @ ( collect_Sum_sum_l_r
% 0.32/0.47 @ ^ [X2: sum_sum_l_r] :
% 0.32/0.47 ( ( P @ X2 )
% 0.32/0.47 & ( Q @ X2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_Collect_conjI
% 0.32/0.47 thf(fact_227_finite__Collect__conjI,axiom,
% 0.32/0.47 ! [P: sum_sum_l_l > $o,Q: sum_sum_l_l > $o] :
% 0.32/0.47 ( ( ( finite1541484284um_l_l @ ( collect_Sum_sum_l_l @ P ) )
% 0.32/0.47 | ( finite1541484284um_l_l @ ( collect_Sum_sum_l_l @ Q ) ) )
% 0.32/0.47 => ( finite1541484284um_l_l
% 0.32/0.47 @ ( collect_Sum_sum_l_l
% 0.32/0.47 @ ^ [X2: sum_sum_l_l] :
% 0.32/0.47 ( ( P @ X2 )
% 0.32/0.47 & ( Q @ X2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_Collect_conjI
% 0.32/0.47 thf(fact_228_finite__Collect__conjI,axiom,
% 0.32/0.47 ! [P: set_r > $o,Q: set_r > $o] :
% 0.32/0.47 ( ( ( finite_finite_set_r @ ( collect_set_r @ P ) )
% 0.32/0.47 | ( finite_finite_set_r @ ( collect_set_r @ Q ) ) )
% 0.32/0.47 => ( finite_finite_set_r
% 0.32/0.47 @ ( collect_set_r
% 0.32/0.47 @ ^ [X2: set_r] :
% 0.32/0.47 ( ( P @ X2 )
% 0.32/0.47 & ( Q @ X2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_Collect_conjI
% 0.32/0.47 thf(fact_229_finite__Collect__conjI,axiom,
% 0.32/0.47 ! [P: set_l > $o,Q: set_l > $o] :
% 0.32/0.47 ( ( ( finite_finite_set_l @ ( collect_set_l @ P ) )
% 0.32/0.47 | ( finite_finite_set_l @ ( collect_set_l @ Q ) ) )
% 0.32/0.47 => ( finite_finite_set_l
% 0.32/0.47 @ ( collect_set_l
% 0.32/0.47 @ ^ [X2: set_l] :
% 0.32/0.47 ( ( P @ X2 )
% 0.32/0.47 & ( Q @ X2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_Collect_conjI
% 0.32/0.47 thf(fact_230_finite__Collect__conjI,axiom,
% 0.32/0.47 ! [P: r > $o,Q: r > $o] :
% 0.32/0.47 ( ( ( finite_finite_r @ ( collect_r @ P ) )
% 0.32/0.47 | ( finite_finite_r @ ( collect_r @ Q ) ) )
% 0.32/0.47 => ( finite_finite_r
% 0.32/0.47 @ ( collect_r
% 0.32/0.47 @ ^ [X2: r] :
% 0.32/0.47 ( ( P @ X2 )
% 0.32/0.47 & ( Q @ X2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_Collect_conjI
% 0.32/0.47 thf(fact_231_finite__Collect__conjI,axiom,
% 0.32/0.47 ! [P: l > $o,Q: l > $o] :
% 0.32/0.47 ( ( ( finite_finite_l @ ( collect_l @ P ) )
% 0.32/0.47 | ( finite_finite_l @ ( collect_l @ Q ) ) )
% 0.32/0.47 => ( finite_finite_l
% 0.32/0.47 @ ( collect_l
% 0.32/0.47 @ ^ [X2: l] :
% 0.32/0.47 ( ( P @ X2 )
% 0.32/0.47 & ( Q @ X2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_Collect_conjI
% 0.32/0.47 thf(fact_232_finite__Collect__disjI,axiom,
% 0.32/0.47 ! [P: set_r > $o,Q: set_r > $o] :
% 0.32/0.47 ( ( finite_finite_set_r
% 0.32/0.47 @ ( collect_set_r
% 0.32/0.47 @ ^ [X2: set_r] :
% 0.32/0.47 ( ( P @ X2 )
% 0.32/0.47 | ( Q @ X2 ) ) ) )
% 0.32/0.47 = ( ( finite_finite_set_r @ ( collect_set_r @ P ) )
% 0.32/0.47 & ( finite_finite_set_r @ ( collect_set_r @ Q ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_Collect_disjI
% 0.32/0.47 thf(fact_233_finite__Collect__disjI,axiom,
% 0.32/0.47 ! [P: set_l > $o,Q: set_l > $o] :
% 0.32/0.47 ( ( finite_finite_set_l
% 0.32/0.47 @ ( collect_set_l
% 0.32/0.47 @ ^ [X2: set_l] :
% 0.32/0.47 ( ( P @ X2 )
% 0.32/0.47 | ( Q @ X2 ) ) ) )
% 0.32/0.47 = ( ( finite_finite_set_l @ ( collect_set_l @ P ) )
% 0.32/0.47 & ( finite_finite_set_l @ ( collect_set_l @ Q ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_Collect_disjI
% 0.32/0.47 thf(fact_234_finite__Collect__disjI,axiom,
% 0.32/0.47 ! [P: r > $o,Q: r > $o] :
% 0.32/0.47 ( ( finite_finite_r
% 0.32/0.47 @ ( collect_r
% 0.32/0.47 @ ^ [X2: r] :
% 0.32/0.47 ( ( P @ X2 )
% 0.32/0.47 | ( Q @ X2 ) ) ) )
% 0.32/0.47 = ( ( finite_finite_r @ ( collect_r @ P ) )
% 0.32/0.47 & ( finite_finite_r @ ( collect_r @ Q ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_Collect_disjI
% 0.32/0.47 thf(fact_235_finite__Collect__disjI,axiom,
% 0.32/0.47 ! [P: l > $o,Q: l > $o] :
% 0.32/0.47 ( ( finite_finite_l
% 0.32/0.47 @ ( collect_l
% 0.32/0.47 @ ^ [X2: l] :
% 0.32/0.47 ( ( P @ X2 )
% 0.32/0.47 | ( Q @ X2 ) ) ) )
% 0.32/0.47 = ( ( finite_finite_l @ ( collect_l @ P ) )
% 0.32/0.47 & ( finite_finite_l @ ( collect_l @ Q ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_Collect_disjI
% 0.32/0.47 thf(fact_236_strong__local__confluence,axiom,
% 0.32/0.47 ! [R: r,S_1: r > option1457017436_r_l_v,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( revision_step_r_l_v @ subst @ R @ S_1 @ S_2 )
% 0.32/0.47 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 0.32/0.47 => ( ( reachable_r_l_v @ subst @ S_1 )
% 0.32/0.47 => ( ~ ( finite_finite_l @ top_top_set_l )
% 0.32/0.47 => ( ~ ( finite_finite_r @ top_top_set_r )
% 0.32/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.32/0.47 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 0.32/0.47 | ( S_2 = S_3 ) )
% 0.32/0.47 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 0.32/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % strong_local_confluence
% 0.32/0.47 thf(fact_237_finite__Plus__UNIV__iff,axiom,
% 0.32/0.47 ( ( finite115218812um_r_r @ top_to577862603um_r_r )
% 0.32/0.47 = ( ( finite_finite_r @ top_top_set_r )
% 0.32/0.47 & ( finite_finite_r @ top_top_set_r ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_Plus_UNIV_iff
% 0.32/0.47 thf(fact_238_finite__Plus__UNIV__iff,axiom,
% 0.32/0.47 ( ( finite65649782um_r_l @ top_to182927813um_r_l )
% 0.32/0.47 = ( ( finite_finite_r @ top_top_set_r )
% 0.32/0.47 & ( finite_finite_l @ top_top_set_l ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_Plus_UNIV_iff
% 0.32/0.47 thf(fact_239_finite__Plus__UNIV__iff,axiom,
% 0.32/0.47 ( ( finite1591053314um_l_r @ top_to1405881169um_l_r )
% 0.32/0.47 = ( ( finite_finite_l @ top_top_set_l )
% 0.32/0.47 & ( finite_finite_r @ top_top_set_r ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_Plus_UNIV_iff
% 0.32/0.47 thf(fact_240_finite__Plus__UNIV__iff,axiom,
% 0.32/0.47 ( ( finite1541484284um_l_l @ top_to1010946379um_l_l )
% 0.32/0.47 = ( ( finite_finite_l @ top_top_set_l )
% 0.32/0.47 & ( finite_finite_l @ top_top_set_l ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % finite_Plus_UNIV_iff
% 0.32/0.47 thf(fact_241_eq__statesI,axiom,
% 0.32/0.47 ! [Alpha2: r > r,Beta2: l > l,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ( ( r_G_r_l_v @ Alpha2 @ Beta2 @ S )
% 0.32/0.47 = S2 )
% 0.32/0.47 => ( ( bij_betw_r_r @ Alpha2 @ top_top_set_r @ top_top_set_r )
% 0.32/0.47 => ( ( bij_betw_l_l @ Beta2 @ top_top_set_l @ top_top_set_l )
% 0.32/0.47 => ( eq_states_r_l_v @ S @ S2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % eq_statesI
% 0.32/0.47 thf(fact_242_renaming__distr__global_I2_J,axiom,
% 0.32/0.47 ! [Alpha2: r > r,Beta2: l > l,S: r > option1457017436_r_l_v,R: r] :
% 0.32/0.47 ( ( bij_betw_r_r @ Alpha2 @ top_top_set_r @ top_top_set_r )
% 0.32/0.47 => ( ( r_G_r_l_v @ Alpha2 @ Beta2 @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) )
% 0.32/0.47 = ( fun_up709272714_r_l_v @ ( r_G_r_l_v @ Alpha2 @ Beta2 @ S ) @ ( Alpha2 @ R ) @ none_P277133687_r_l_v ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % renaming_distr_global(2)
% 0.32/0.47 thf(fact_243_domains__subsume__globallyI,axiom,
% 0.32/0.47 ! [S: r > option1457017436_r_l_v] :
% 0.32/0.47 ( ! [R5: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E3: expr_r_l_v] :
% 0.32/0.47 ( ( ( S @ R5 )
% 0.32/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) ) )
% 0.32/0.47 => ( domain87684397_l_r_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) ) )
% 0.32/0.47 => ( domain1547879849_r_l_v @ S ) ) ).
% 0.32/0.47
% 0.32/0.47 % domains_subsume_globallyI
% 0.32/0.47 thf(fact_244_bij___092_060beta_062,axiom,
% 0.32/0.47 bij_betw_l_l @ beta @ top_top_set_l @ top_top_set_l ).
% 0.32/0.47
% 0.32/0.47 % bij_\<beta>
% 0.32/0.47 thf(fact_245_bij__betw__finite,axiom,
% 0.32/0.47 ! [F: r > r,A5: set_r,B5: set_r] :
% 0.32/0.47 ( ( bij_betw_r_r @ F @ A5 @ B5 )
% 0.32/0.47 => ( ( finite_finite_r @ A5 )
% 0.32/0.47 = ( finite_finite_r @ B5 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % bij_betw_finite
% 0.32/0.47 thf(fact_246_bij__betw__finite,axiom,
% 0.32/0.47 ! [F: r > l,A5: set_r,B5: set_l] :
% 0.32/0.47 ( ( bij_betw_r_l @ F @ A5 @ B5 )
% 0.32/0.47 => ( ( finite_finite_r @ A5 )
% 0.32/0.47 = ( finite_finite_l @ B5 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % bij_betw_finite
% 0.32/0.47 thf(fact_247_bij__betw__finite,axiom,
% 0.32/0.47 ! [F: l > r,A5: set_l,B5: set_r] :
% 0.32/0.47 ( ( bij_betw_l_r @ F @ A5 @ B5 )
% 0.32/0.47 => ( ( finite_finite_l @ A5 )
% 0.32/0.47 = ( finite_finite_r @ B5 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % bij_betw_finite
% 0.32/0.47 thf(fact_248_bij__betw__finite,axiom,
% 0.32/0.47 ! [F: l > l,A5: set_l,B5: set_l] :
% 0.32/0.47 ( ( bij_betw_l_l @ F @ A5 @ B5 )
% 0.32/0.47 => ( ( finite_finite_l @ A5 )
% 0.32/0.47 = ( finite_finite_l @ B5 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % bij_betw_finite
% 0.32/0.47 thf(fact_249_bij__pointE,axiom,
% 0.32/0.47 ! [F: r > r,Y: r] :
% 0.32/0.47 ( ( bij_betw_r_r @ F @ top_top_set_r @ top_top_set_r )
% 0.32/0.47 => ~ ! [X3: r] :
% 0.32/0.47 ( ( Y
% 0.32/0.47 = ( F @ X3 ) )
% 0.32/0.47 => ~ ! [X9: r] :
% 0.32/0.47 ( ( Y
% 0.32/0.47 = ( F @ X9 ) )
% 0.32/0.47 => ( X9 = X3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % bij_pointE
% 0.32/0.47 thf(fact_250_bij__pointE,axiom,
% 0.32/0.47 ! [F: r > l,Y: l] :
% 0.32/0.47 ( ( bij_betw_r_l @ F @ top_top_set_r @ top_top_set_l )
% 0.32/0.47 => ~ ! [X3: r] :
% 0.32/0.47 ( ( Y
% 0.32/0.47 = ( F @ X3 ) )
% 0.32/0.47 => ~ ! [X9: r] :
% 0.32/0.47 ( ( Y
% 0.32/0.47 = ( F @ X9 ) )
% 0.32/0.47 => ( X9 = X3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % bij_pointE
% 0.32/0.47 thf(fact_251_bij__pointE,axiom,
% 0.32/0.47 ! [F: l > r,Y: r] :
% 0.32/0.47 ( ( bij_betw_l_r @ F @ top_top_set_l @ top_top_set_r )
% 0.32/0.47 => ~ ! [X3: l] :
% 0.32/0.47 ( ( Y
% 0.32/0.47 = ( F @ X3 ) )
% 0.32/0.47 => ~ ! [X9: l] :
% 0.32/0.47 ( ( Y
% 0.32/0.47 = ( F @ X9 ) )
% 0.32/0.47 => ( X9 = X3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % bij_pointE
% 0.32/0.47 thf(fact_252_bij__pointE,axiom,
% 0.32/0.47 ! [F: l > l,Y: l] :
% 0.32/0.47 ( ( bij_betw_l_l @ F @ top_top_set_l @ top_top_set_l )
% 0.32/0.47 => ~ ! [X3: l] :
% 0.32/0.47 ( ( Y
% 0.32/0.47 = ( F @ X3 ) )
% 0.32/0.47 => ~ ! [X9: l] :
% 0.32/0.47 ( ( Y
% 0.32/0.47 = ( F @ X9 ) )
% 0.32/0.47 => ( X9 = X3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % bij_pointE
% 0.32/0.47 thf(fact_253_bij__betwE,axiom,
% 0.32/0.47 ! [F: r > r,A5: set_r,B5: set_r] :
% 0.32/0.47 ( ( bij_betw_r_r @ F @ A5 @ B5 )
% 0.32/0.47 => ! [X10: r] :
% 0.32/0.47 ( ( member_r @ X10 @ A5 )
% 0.32/0.47 => ( member_r @ ( F @ X10 ) @ B5 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % bij_betwE
% 0.32/0.47 thf(fact_254_bij__betwE,axiom,
% 0.32/0.47 ! [F: l > l,A5: set_l,B5: set_l] :
% 0.32/0.47 ( ( bij_betw_l_l @ F @ A5 @ B5 )
% 0.32/0.47 => ! [X10: l] :
% 0.32/0.47 ( ( member_l @ X10 @ A5 )
% 0.32/0.47 => ( member_l @ ( F @ X10 ) @ B5 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % bij_betwE
% 0.32/0.47 thf(fact_255_bij__betw__inv,axiom,
% 0.32/0.47 ! [F: r > r,A5: set_r,B5: set_r] :
% 0.32/0.47 ( ( bij_betw_r_r @ F @ A5 @ B5 )
% 0.32/0.47 => ? [G3: r > r] : ( bij_betw_r_r @ G3 @ B5 @ A5 ) ) ).
% 0.32/0.47
% 0.32/0.47 % bij_betw_inv
% 0.32/0.47 thf(fact_256_bij__betw__inv,axiom,
% 0.32/0.47 ! [F: l > l,A5: set_l,B5: set_l] :
% 0.32/0.48 ( ( bij_betw_l_l @ F @ A5 @ B5 )
% 0.32/0.48 => ? [G3: l > l] : ( bij_betw_l_l @ G3 @ B5 @ A5 ) ) ).
% 0.32/0.48
% 0.32/0.48 % bij_betw_inv
% 0.32/0.48 thf(fact_257_bij__betw__cong,axiom,
% 0.32/0.48 ! [A5: set_r,F: r > r,G: r > r,A6: set_r] :
% 0.32/0.48 ( ! [A3: r] :
% 0.32/0.48 ( ( member_r @ A3 @ A5 )
% 0.32/0.48 => ( ( F @ A3 )
% 0.32/0.48 = ( G @ A3 ) ) )
% 0.32/0.48 => ( ( bij_betw_r_r @ F @ A5 @ A6 )
% 0.32/0.48 = ( bij_betw_r_r @ G @ A5 @ A6 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % bij_betw_cong
% 0.32/0.48 thf(fact_258_bij__betw__cong,axiom,
% 0.32/0.48 ! [A5: set_l,F: l > l,G: l > l,A6: set_l] :
% 0.32/0.48 ( ! [A3: l] :
% 0.32/0.48 ( ( member_l @ A3 @ A5 )
% 0.32/0.48 => ( ( F @ A3 )
% 0.32/0.48 = ( G @ A3 ) ) )
% 0.32/0.48 => ( ( bij_betw_l_l @ F @ A5 @ A6 )
% 0.32/0.48 = ( bij_betw_l_l @ G @ A5 @ A6 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % bij_betw_cong
% 0.32/0.48 thf(fact_259_bij__betw__apply,axiom,
% 0.32/0.48 ! [F: r > l,A5: set_r,B5: set_l,A: r] :
% 0.32/0.48 ( ( bij_betw_r_l @ F @ A5 @ B5 )
% 0.32/0.48 => ( ( member_r @ A @ A5 )
% 0.32/0.48 => ( member_l @ ( F @ A ) @ B5 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % bij_betw_apply
% 0.32/0.48 thf(fact_260_bij__betw__apply,axiom,
% 0.32/0.48 ! [F: l > r,A5: set_l,B5: set_r,A: l] :
% 0.32/0.48 ( ( bij_betw_l_r @ F @ A5 @ B5 )
% 0.32/0.48 => ( ( member_l @ A @ A5 )
% 0.32/0.48 => ( member_r @ ( F @ A ) @ B5 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % bij_betw_apply
% 0.32/0.48 thf(fact_261_bij__betw__apply,axiom,
% 0.32/0.48 ! [F: r > r,A5: set_r,B5: set_r,A: r] :
% 0.32/0.48 ( ( bij_betw_r_r @ F @ A5 @ B5 )
% 0.32/0.48 => ( ( member_r @ A @ A5 )
% 0.32/0.48 => ( member_r @ ( F @ A ) @ B5 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % bij_betw_apply
% 0.32/0.48 thf(fact_262_bij__betw__apply,axiom,
% 0.32/0.48 ! [F: l > l,A5: set_l,B5: set_l,A: l] :
% 0.32/0.48 ( ( bij_betw_l_l @ F @ A5 @ B5 )
% 0.32/0.48 => ( ( member_l @ A @ A5 )
% 0.32/0.48 => ( member_l @ ( F @ A ) @ B5 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % bij_betw_apply
% 0.32/0.48 thf(fact_263_bij__betw__iff__bijections,axiom,
% 0.32/0.48 ( bij_betw_l_r
% 0.32/0.48 = ( ^ [F2: l > r,A7: set_l,B6: set_r] :
% 0.32/0.48 ? [G2: r > l] :
% 0.32/0.48 ( ! [X2: l] :
% 0.32/0.48 ( ( member_l @ X2 @ A7 )
% 0.32/0.48 => ( ( member_r @ ( F2 @ X2 ) @ B6 )
% 0.32/0.48 & ( ( G2 @ ( F2 @ X2 ) )
% 0.32/0.48 = X2 ) ) )
% 0.32/0.48 & ! [X2: r] :
% 0.32/0.48 ( ( member_r @ X2 @ B6 )
% 0.32/0.48 => ( ( member_l @ ( G2 @ X2 ) @ A7 )
% 0.32/0.48 & ( ( F2 @ ( G2 @ X2 ) )
% 0.32/0.48 = X2 ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % bij_betw_iff_bijections
% 0.32/0.48 thf(fact_264_bij__betw__iff__bijections,axiom,
% 0.32/0.48 ( bij_betw_r_l
% 0.32/0.48 = ( ^ [F2: r > l,A7: set_r,B6: set_l] :
% 0.32/0.48 ? [G2: l > r] :
% 0.32/0.48 ( ! [X2: r] :
% 0.32/0.48 ( ( member_r @ X2 @ A7 )
% 0.32/0.48 => ( ( member_l @ ( F2 @ X2 ) @ B6 )
% 0.32/0.48 & ( ( G2 @ ( F2 @ X2 ) )
% 0.32/0.48 = X2 ) ) )
% 0.32/0.48 & ! [X2: l] :
% 0.32/0.48 ( ( member_l @ X2 @ B6 )
% 0.32/0.48 => ( ( member_r @ ( G2 @ X2 ) @ A7 )
% 0.32/0.48 & ( ( F2 @ ( G2 @ X2 ) )
% 0.32/0.48 = X2 ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % bij_betw_iff_bijections
% 0.32/0.48 thf(fact_265_bij__betw__iff__bijections,axiom,
% 0.32/0.48 ( bij_betw_r_r
% 0.32/0.48 = ( ^ [F2: r > r,A7: set_r,B6: set_r] :
% 0.32/0.48 ? [G2: r > r] :
% 0.32/0.48 ( ! [X2: r] :
% 0.32/0.48 ( ( member_r @ X2 @ A7 )
% 0.32/0.48 => ( ( member_r @ ( F2 @ X2 ) @ B6 )
% 0.32/0.48 & ( ( G2 @ ( F2 @ X2 ) )
% 0.32/0.48 = X2 ) ) )
% 0.32/0.48 & ! [X2: r] :
% 0.32/0.48 ( ( member_r @ X2 @ B6 )
% 0.32/0.48 => ( ( member_r @ ( G2 @ X2 ) @ A7 )
% 0.32/0.48 & ( ( F2 @ ( G2 @ X2 ) )
% 0.32/0.48 = X2 ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % bij_betw_iff_bijections
% 0.32/0.48 thf(fact_266_bij__betw__iff__bijections,axiom,
% 0.32/0.48 ( bij_betw_l_l
% 0.32/0.48 = ( ^ [F2: l > l,A7: set_l,B6: set_l] :
% 0.32/0.48 ? [G2: l > l] :
% 0.32/0.48 ( ! [X2: l] :
% 0.32/0.48 ( ( member_l @ X2 @ A7 )
% 0.32/0.48 => ( ( member_l @ ( F2 @ X2 ) @ B6 )
% 0.32/0.48 & ( ( G2 @ ( F2 @ X2 ) )
% 0.32/0.48 = X2 ) ) )
% 0.32/0.48 & ! [X2: l] :
% 0.32/0.48 ( ( member_l @ X2 @ B6 )
% 0.32/0.48 => ( ( member_l @ ( G2 @ X2 ) @ A7 )
% 0.32/0.48 & ( ( F2 @ ( G2 @ X2 ) )
% 0.32/0.48 = X2 ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % bij_betw_iff_bijections
% 0.32/0.48 thf(fact_267_eq__statesE,axiom,
% 0.32/0.48 ! [S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( eq_states_r_l_v @ S @ S2 )
% 0.32/0.48 => ~ ! [Alpha: r > r,Beta: l > l] :
% 0.32/0.48 ( ( ( r_G_r_l_v @ Alpha @ Beta @ S )
% 0.32/0.48 = S2 )
% 0.32/0.48 => ( ( bij_betw_r_r @ Alpha @ top_top_set_r @ top_top_set_r )
% 0.32/0.48 => ~ ( bij_betw_l_l @ Beta @ top_top_set_l @ top_top_set_l ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % eq_statesE
% 0.32/0.48 thf(fact_268_eq__states__def,axiom,
% 0.32/0.48 ( eq_states_r_l_v
% 0.32/0.48 = ( ^ [S5: r > option1457017436_r_l_v,S3: r > option1457017436_r_l_v] :
% 0.32/0.48 ? [Alpha3: r > r,Beta3: l > l] :
% 0.32/0.48 ( ( bij_betw_r_r @ Alpha3 @ top_top_set_r @ top_top_set_r )
% 0.32/0.48 & ( bij_betw_l_l @ Beta3 @ top_top_set_l @ top_top_set_l )
% 0.32/0.48 & ( ( r_G_r_l_v @ Alpha3 @ Beta3 @ S5 )
% 0.32/0.48 = S3 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % eq_states_def
% 0.32/0.48 thf(fact_269_substitution_Oin__renamed__in__unlabelled__global_I1_J,axiom,
% 0.32/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,Alpha2: r > r,Beta2: l > l,R: r,S: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( substitution_r_l_v @ Subst )
% 0.32/0.48 => ( ( bij_betw_r_r @ Alpha2 @ top_top_set_r @ top_top_set_r )
% 0.32/0.48 => ( ( bij_betw_l_l @ Beta2 @ top_top_set_l @ top_top_set_l )
% 0.32/0.48 => ( ( member_r @ ( Alpha2 @ R ) @ ( rID_G_r_l_v @ ( r_G_r_l_v @ Alpha2 @ Beta2 @ S ) ) )
% 0.32/0.48 = ( member_r @ R @ ( rID_G_r_l_v @ S ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % substitution.in_renamed_in_unlabelled_global(1)
% 0.32/0.48 thf(fact_270_not__finite__existsD,axiom,
% 0.32/0.48 ! [P: r > $o] :
% 0.32/0.48 ( ~ ( finite_finite_r @ ( collect_r @ P ) )
% 0.32/0.48 => ? [X_1: r] : ( P @ X_1 ) ) ).
% 0.32/0.48
% 0.32/0.48 % not_finite_existsD
% 0.32/0.48 thf(fact_271_not__finite__existsD,axiom,
% 0.32/0.48 ! [P: l > $o] :
% 0.32/0.48 ( ~ ( finite_finite_l @ ( collect_l @ P ) )
% 0.32/0.48 => ? [X_1: l] : ( P @ X_1 ) ) ).
% 0.32/0.48
% 0.32/0.48 % not_finite_existsD
% 0.32/0.48 thf(fact_272_pigeonhole__infinite__rel,axiom,
% 0.32/0.48 ! [A5: set_r,B5: set_r,R7: r > r > $o] :
% 0.32/0.48 ( ~ ( finite_finite_r @ A5 )
% 0.32/0.48 => ( ( finite_finite_r @ B5 )
% 0.32/0.48 => ( ! [X3: r] :
% 0.32/0.48 ( ( member_r @ X3 @ A5 )
% 0.32/0.48 => ? [Xa2: r] :
% 0.32/0.48 ( ( member_r @ Xa2 @ B5 )
% 0.32/0.48 & ( R7 @ X3 @ Xa2 ) ) )
% 0.32/0.48 => ? [X3: r] :
% 0.32/0.48 ( ( member_r @ X3 @ B5 )
% 0.32/0.48 & ~ ( finite_finite_r
% 0.32/0.48 @ ( collect_r
% 0.32/0.48 @ ^ [A4: r] :
% 0.32/0.48 ( ( member_r @ A4 @ A5 )
% 0.32/0.48 & ( R7 @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % pigeonhole_infinite_rel
% 0.32/0.48 thf(fact_273_pigeonhole__infinite__rel,axiom,
% 0.32/0.48 ! [A5: set_r,B5: set_l,R7: r > l > $o] :
% 0.32/0.48 ( ~ ( finite_finite_r @ A5 )
% 0.32/0.48 => ( ( finite_finite_l @ B5 )
% 0.32/0.48 => ( ! [X3: r] :
% 0.32/0.48 ( ( member_r @ X3 @ A5 )
% 0.32/0.48 => ? [Xa2: l] :
% 0.32/0.48 ( ( member_l @ Xa2 @ B5 )
% 0.32/0.48 & ( R7 @ X3 @ Xa2 ) ) )
% 0.32/0.48 => ? [X3: l] :
% 0.32/0.48 ( ( member_l @ X3 @ B5 )
% 0.32/0.48 & ~ ( finite_finite_r
% 0.32/0.48 @ ( collect_r
% 0.32/0.48 @ ^ [A4: r] :
% 0.32/0.48 ( ( member_r @ A4 @ A5 )
% 0.32/0.48 & ( R7 @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % pigeonhole_infinite_rel
% 0.32/0.48 thf(fact_274_pigeonhole__infinite__rel,axiom,
% 0.32/0.48 ! [A5: set_l,B5: set_r,R7: l > r > $o] :
% 0.32/0.48 ( ~ ( finite_finite_l @ A5 )
% 0.32/0.48 => ( ( finite_finite_r @ B5 )
% 0.32/0.48 => ( ! [X3: l] :
% 0.32/0.48 ( ( member_l @ X3 @ A5 )
% 0.32/0.48 => ? [Xa2: r] :
% 0.32/0.48 ( ( member_r @ Xa2 @ B5 )
% 0.32/0.48 & ( R7 @ X3 @ Xa2 ) ) )
% 0.32/0.48 => ? [X3: r] :
% 0.32/0.48 ( ( member_r @ X3 @ B5 )
% 0.32/0.48 & ~ ( finite_finite_l
% 0.32/0.48 @ ( collect_l
% 0.32/0.48 @ ^ [A4: l] :
% 0.32/0.48 ( ( member_l @ A4 @ A5 )
% 0.32/0.48 & ( R7 @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % pigeonhole_infinite_rel
% 0.32/0.48 thf(fact_275_pigeonhole__infinite__rel,axiom,
% 0.32/0.48 ! [A5: set_l,B5: set_l,R7: l > l > $o] :
% 0.32/0.48 ( ~ ( finite_finite_l @ A5 )
% 0.32/0.48 => ( ( finite_finite_l @ B5 )
% 0.32/0.48 => ( ! [X3: l] :
% 0.32/0.48 ( ( member_l @ X3 @ A5 )
% 0.32/0.48 => ? [Xa2: l] :
% 0.32/0.48 ( ( member_l @ Xa2 @ B5 )
% 0.32/0.48 & ( R7 @ X3 @ Xa2 ) ) )
% 0.32/0.48 => ? [X3: l] :
% 0.32/0.48 ( ( member_l @ X3 @ B5 )
% 0.32/0.48 & ~ ( finite_finite_l
% 0.32/0.48 @ ( collect_l
% 0.32/0.48 @ ^ [A4: l] :
% 0.32/0.48 ( ( member_l @ A4 @ A5 )
% 0.32/0.48 & ( R7 @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % pigeonhole_infinite_rel
% 0.32/0.48 thf(fact_276_finite__Prod__UNIV,axiom,
% 0.32/0.48 ( ( finite_finite_r @ top_top_set_r )
% 0.32/0.48 => ( ( finite_finite_r @ top_top_set_r )
% 0.32/0.48 => ( finite1507191824od_r_r @ top_to2034696215od_r_r ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finite_Prod_UNIV
% 0.32/0.48 thf(fact_277_finite__Prod__UNIV,axiom,
% 0.32/0.48 ( ( finite_finite_r @ top_top_set_r )
% 0.32/0.48 => ( ( finite_finite_l @ top_top_set_l )
% 0.32/0.48 => ( finite1457622794od_r_l @ top_to1639761425od_r_l ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finite_Prod_UNIV
% 0.32/0.48 thf(fact_278_finite__Prod__UNIV,axiom,
% 0.32/0.48 ( ( finite_finite_l @ top_top_set_l )
% 0.32/0.48 => ( ( finite_finite_r @ top_top_set_r )
% 0.32/0.48 => ( finite835542678od_l_r @ top_to715231133od_l_r ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finite_Prod_UNIV
% 0.32/0.48 thf(fact_279_finite__Prod__UNIV,axiom,
% 0.32/0.48 ( ( finite_finite_l @ top_top_set_l )
% 0.32/0.48 => ( ( finite_finite_l @ top_top_set_l )
% 0.32/0.48 => ( finite785973648od_l_l @ top_to320296343od_l_l ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finite_Prod_UNIV
% 0.32/0.48 thf(fact_280_ex__new__if__finite,axiom,
% 0.32/0.48 ! [A5: set_r] :
% 0.32/0.48 ( ~ ( finite_finite_r @ top_top_set_r )
% 0.32/0.48 => ( ( finite_finite_r @ A5 )
% 0.32/0.48 => ? [A3: r] :
% 0.32/0.48 ~ ( member_r @ A3 @ A5 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % ex_new_if_finite
% 0.32/0.48 thf(fact_281_ex__new__if__finite,axiom,
% 0.32/0.48 ! [A5: set_l] :
% 0.32/0.48 ( ~ ( finite_finite_l @ top_top_set_l )
% 0.32/0.48 => ( ( finite_finite_l @ A5 )
% 0.32/0.48 => ? [A3: l] :
% 0.32/0.48 ~ ( member_l @ A3 @ A5 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % ex_new_if_finite
% 0.32/0.48 thf(fact_282_finite__prod,axiom,
% 0.32/0.48 ( ( finite1507191824od_r_r @ top_to2034696215od_r_r )
% 0.32/0.48 = ( ( finite_finite_r @ top_top_set_r )
% 0.32/0.48 & ( finite_finite_r @ top_top_set_r ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finite_prod
% 0.32/0.48 thf(fact_283_finite__prod,axiom,
% 0.32/0.48 ( ( finite1457622794od_r_l @ top_to1639761425od_r_l )
% 0.32/0.48 = ( ( finite_finite_r @ top_top_set_r )
% 0.32/0.48 & ( finite_finite_l @ top_top_set_l ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finite_prod
% 0.32/0.48 thf(fact_284_finite__prod,axiom,
% 0.32/0.48 ( ( finite835542678od_l_r @ top_to715231133od_l_r )
% 0.32/0.48 = ( ( finite_finite_l @ top_top_set_l )
% 0.32/0.48 & ( finite_finite_r @ top_top_set_r ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finite_prod
% 0.32/0.48 thf(fact_285_finite__prod,axiom,
% 0.32/0.48 ( ( finite785973648od_l_l @ top_to320296343od_l_l )
% 0.32/0.48 = ( ( finite_finite_l @ top_top_set_l )
% 0.32/0.48 & ( finite_finite_l @ top_top_set_l ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finite_prod
% 0.32/0.48 thf(fact_286_Finite__Set_Ofinite__set,axiom,
% 0.32/0.48 ( ( finite_finite_set_r @ top_top_set_set_r )
% 0.32/0.48 = ( finite_finite_r @ top_top_set_r ) ) ).
% 0.32/0.48
% 0.32/0.48 % Finite_Set.finite_set
% 0.32/0.48 thf(fact_287_Finite__Set_Ofinite__set,axiom,
% 0.32/0.48 ( ( finite_finite_set_l @ top_top_set_set_l )
% 0.32/0.48 = ( finite_finite_l @ top_top_set_l ) ) ).
% 0.32/0.48
% 0.32/0.48 % Finite_Set.finite_set
% 0.32/0.48 thf(fact_288_substitution_Ostep__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I1_J,axiom,
% 0.32/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( substitution_r_l_v @ Subst )
% 0.32/0.48 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.32/0.48 => ( ( domain1547879849_r_l_v @ S )
% 0.32/0.48 => ( ( subsum680764357_r_l_v @ S )
% 0.32/0.48 => ( domain1547879849_r_l_v @ S2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % substitution.step_preserves_\<S>\<^sub>G_and_\<A>\<^sub>G(1)
% 0.32/0.48 thf(fact_289_substitution_Ostep__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I2_J,axiom,
% 0.32/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( substitution_r_l_v @ Subst )
% 0.32/0.48 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.32/0.48 => ( ( domain1547879849_r_l_v @ S )
% 0.32/0.48 => ( ( subsum680764357_r_l_v @ S )
% 0.32/0.48 => ( subsum680764357_r_l_v @ S2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % substitution.step_preserves_\<S>\<^sub>G_and_\<A>\<^sub>G(2)
% 0.32/0.48 thf(fact_290_finite__update__induct,axiom,
% 0.32/0.48 ! [F: r > option1457017436_r_l_v,C: option1457017436_r_l_v,P: ( r > option1457017436_r_l_v ) > $o] :
% 0.32/0.48 ( ( finite_finite_r
% 0.32/0.48 @ ( collect_r
% 0.32/0.48 @ ^ [A4: r] :
% 0.32/0.48 ( ( F @ A4 )
% 0.32/0.48 != C ) ) )
% 0.32/0.48 => ( ( P
% 0.32/0.48 @ ^ [A4: r] : C )
% 0.32/0.48 => ( ! [A3: r,B3: option1457017436_r_l_v,F3: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( finite_finite_r
% 0.32/0.48 @ ( collect_r
% 0.32/0.48 @ ^ [C3: r] :
% 0.32/0.48 ( ( F3 @ C3 )
% 0.32/0.48 != C ) ) )
% 0.32/0.48 => ( ( ( F3 @ A3 )
% 0.32/0.48 = C )
% 0.32/0.48 => ( ( B3 != C )
% 0.32/0.48 => ( ( P @ F3 )
% 0.32/0.48 => ( P @ ( fun_up709272714_r_l_v @ F3 @ A3 @ B3 ) ) ) ) ) )
% 0.32/0.48 => ( P @ F ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finite_update_induct
% 0.32/0.48 thf(fact_291_finite__update__induct,axiom,
% 0.32/0.48 ! [F: l > option_val_r_l_v,C: option_val_r_l_v,P: ( l > option_val_r_l_v ) > $o] :
% 0.32/0.48 ( ( finite_finite_l
% 0.32/0.48 @ ( collect_l
% 0.32/0.48 @ ^ [A4: l] :
% 0.32/0.48 ( ( F @ A4 )
% 0.32/0.48 != C ) ) )
% 0.32/0.48 => ( ( P
% 0.32/0.48 @ ^ [A4: l] : C )
% 0.32/0.48 => ( ! [A3: l,B3: option_val_r_l_v,F3: l > option_val_r_l_v] :
% 0.32/0.48 ( ( finite_finite_l
% 0.32/0.48 @ ( collect_l
% 0.32/0.48 @ ^ [C3: l] :
% 0.32/0.48 ( ( F3 @ C3 )
% 0.32/0.48 != C ) ) )
% 0.32/0.48 => ( ( ( F3 @ A3 )
% 0.32/0.48 = C )
% 0.32/0.48 => ( ( B3 != C )
% 0.32/0.48 => ( ( P @ F3 )
% 0.32/0.48 => ( P @ ( fun_up1835647912_r_l_v @ F3 @ A3 @ B3 ) ) ) ) ) )
% 0.32/0.48 => ( P @ F ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finite_update_induct
% 0.32/0.48 thf(fact_292_substitution_Onice__ind__inv__is__inductive__invariant,axiom,
% 0.32/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v] :
% 0.32/0.48 ( ( substitution_r_l_v @ Subst )
% 0.32/0.48 => ( induct1670415253_r_l_v @ Subst
% 0.32/0.48 @ ^ [S5: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( domain1547879849_r_l_v @ S5 )
% 0.32/0.48 & ( subsum680764357_r_l_v @ S5 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % substitution.nice_ind_inv_is_inductive_invariant
% 0.32/0.48 thf(fact_293_substitution_Odomains__subsume__globally__def,axiom,
% 0.32/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( substitution_r_l_v @ Subst )
% 0.32/0.48 => ( ( domain1547879849_r_l_v @ S )
% 0.32/0.48 = ( ! [R6: r,Ls2: produc1156025366_r_l_v] :
% 0.32/0.48 ( ( ( S @ R6 )
% 0.32/0.48 = ( some_P1807977723_r_l_v @ Ls2 ) )
% 0.32/0.48 => ( domain87684397_l_r_v @ Ls2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % substitution.domains_subsume_globally_def
% 0.32/0.48 thf(fact_294_substitution_Odomains__subsume__globallyI,axiom,
% 0.32/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( substitution_r_l_v @ Subst )
% 0.32/0.48 => ( ! [R5: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E3: expr_r_l_v] :
% 0.32/0.48 ( ( ( S @ R5 )
% 0.32/0.48 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) ) )
% 0.32/0.48 => ( domain87684397_l_r_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) ) )
% 0.32/0.48 => ( domain1547879849_r_l_v @ S ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % substitution.domains_subsume_globallyI
% 0.32/0.48 thf(fact_295__092_060R_062_092_060_094sub_062GI,axiom,
% 0.32/0.48 ! [Alpha2: r > r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v,Beta2: l > l] :
% 0.32/0.48 ( ( bij_betw_r_r @ Alpha2 @ top_top_set_r @ top_top_set_r )
% 0.32/0.48 => ( ! [R5: r] :
% 0.32/0.48 ( ( ( S @ R5 )
% 0.32/0.48 = none_P277133687_r_l_v )
% 0.32/0.48 => ( ( S2 @ ( Alpha2 @ R5 ) )
% 0.32/0.48 = none_P277133687_r_l_v ) )
% 0.32/0.48 => ( ! [R5: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E3: expr_r_l_v] :
% 0.32/0.48 ( ( ( S @ R5 )
% 0.32/0.48 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) ) )
% 0.32/0.48 => ( ( S2 @ ( Alpha2 @ R5 ) )
% 0.32/0.48 = ( some_P1807977723_r_l_v @ ( r_L_r_l_v @ Alpha2 @ Beta2 @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) ) ) ) )
% 0.32/0.48 => ( ( r_G_r_l_v @ Alpha2 @ Beta2 @ S )
% 0.32/0.48 = S2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % \<R>\<^sub>GI
% 0.32/0.48 thf(fact_296_substitution_Osubsumes__accessible__globallyI,axiom,
% 0.32/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( substitution_r_l_v @ Subst )
% 0.32/0.48 => ( ! [R_1: r,Sigma_1: l > option_val_r_l_v,Tau_1: l > option_val_r_l_v,E_1: expr_r_l_v,R_2: r,Sigma_2: l > option_val_r_l_v,Tau_2: l > option_val_r_l_v,E_2: expr_r_l_v] :
% 0.32/0.48 ( ( ( S @ R_1 )
% 0.32/0.48 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_1 @ ( produc1834103605_r_l_v @ Tau_1 @ E_1 ) ) ) )
% 0.32/0.48 => ( ( ( S @ R_2 )
% 0.32/0.48 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_2 @ ( produc1834103605_r_l_v @ Tau_2 @ E_2 ) ) ) )
% 0.32/0.48 => ( subsum148050133_r_l_v @ R_1 @ R_2 @ S ) ) )
% 0.32/0.48 => ( subsum680764357_r_l_v @ S ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % substitution.subsumes_accessible_globallyI
% 0.32/0.48 thf(fact_297__092_060R_062_092_060_094sub_062G__implements__renaming,axiom,
% 0.32/0.48 ! [Alpha2: r > r,Beta2: l > l,S: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( bij_betw_r_r @ Alpha2 @ top_top_set_r @ top_top_set_r )
% 0.32/0.48 => ( is_glo1871033385_r_l_v @ Alpha2 @ Beta2 @ S @ ( r_G_r_l_v @ Alpha2 @ Beta2 @ S ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % \<R>\<^sub>G_implements_renaming
% 0.32/0.48 thf(fact_298_subsumes__accessible__globallyI,axiom,
% 0.32/0.48 ! [S: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ! [R_1: r,Sigma_1: l > option_val_r_l_v,Tau_1: l > option_val_r_l_v,E_1: expr_r_l_v,R_2: r,Sigma_2: l > option_val_r_l_v,Tau_2: l > option_val_r_l_v,E_2: expr_r_l_v] :
% 0.32/0.48 ( ( ( S @ R_1 )
% 0.32/0.48 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_1 @ ( produc1834103605_r_l_v @ Tau_1 @ E_1 ) ) ) )
% 0.32/0.48 => ( ( ( S @ R_2 )
% 0.32/0.48 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_2 @ ( produc1834103605_r_l_v @ Tau_2 @ E_2 ) ) ) )
% 0.32/0.48 => ( subsum148050133_r_l_v @ R_1 @ R_2 @ S ) ) )
% 0.32/0.48 => ( subsum680764357_r_l_v @ S ) ) ).
% 0.32/0.48
% 0.32/0.48 % subsumes_accessible_globallyI
% 0.32/0.48 thf(fact_299_renaming__distr__global_I1_J,axiom,
% 0.32/0.48 ! [Alpha2: r > r,Beta2: l > l,S: r > option1457017436_r_l_v,R: r,Ls: produc1156025366_r_l_v] :
% 0.32/0.48 ( ( bij_betw_r_r @ Alpha2 @ top_top_set_r @ top_top_set_r )
% 0.32/0.48 => ( ( r_G_r_l_v @ Alpha2 @ Beta2 @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ Ls ) ) )
% 0.32/0.48 = ( fun_up709272714_r_l_v @ ( r_G_r_l_v @ Alpha2 @ Beta2 @ S ) @ ( Alpha2 @ R ) @ ( some_P1807977723_r_l_v @ ( r_L_r_l_v @ Alpha2 @ Beta2 @ Ls ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % renaming_distr_global(1)
% 0.32/0.48 thf(fact_300_RID_092_060_094sub_062GI_I2_J,axiom,
% 0.32/0.48 ! [S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
% 0.32/0.48 ( ( ( S @ R2 )
% 0.32/0.48 = ( some_P1807977723_r_l_v @ Ls ) )
% 0.32/0.48 => ( ( member_r @ R @ ( rID_L_l_r_v @ Ls ) )
% 0.32/0.48 => ( member_r @ R @ ( rID_G_r_l_v @ S ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % RID\<^sub>GI(2)
% 0.32/0.48 thf(fact_301_local__state__of__finite__restricted__global__state__is__finite_I1_J,axiom,
% 0.32/0.48 ! [S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
% 0.32/0.48 ( ( ( S @ R2 )
% 0.32/0.48 = ( some_P1807977723_r_l_v @ Ls ) )
% 0.32/0.48 => ( ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 0.32/0.48 => ( ( R != R2 )
% 0.32/0.48 => ( finite_finite_r @ ( rID_L_l_r_v @ Ls ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % local_state_of_finite_restricted_global_state_is_finite(1)
% 0.32/0.48 thf(fact_302_substitution_Olocal__state__of__finite__restricted__global__state__is__finite_I1_J,axiom,
% 0.32/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
% 0.32/0.48 ( ( substitution_r_l_v @ Subst )
% 0.32/0.48 => ( ( ( S @ R2 )
% 0.32/0.48 = ( some_P1807977723_r_l_v @ Ls ) )
% 0.32/0.48 => ( ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 0.32/0.48 => ( ( R != R2 )
% 0.32/0.48 => ( finite_finite_r @ ( rID_L_l_r_v @ Ls ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % substitution.local_state_of_finite_restricted_global_state_is_finite(1)
% 0.32/0.48 thf(fact_303_reachable__imp__identifiers__available_I2_J,axiom,
% 0.32/0.48 ! [S: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( reachable_r_l_v @ subst @ S )
% 0.32/0.48 => ( ~ ( finite_finite_l @ top_top_set_l )
% 0.32/0.48 => ? [L: l] :
% 0.32/0.48 ~ ( member_l @ L @ ( lID_G_r_l_v @ S ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % reachable_imp_identifiers_available(2)
% 0.32/0.48 thf(fact_304_only__fork__introduces__rids,axiom,
% 0.32/0.48 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.32/0.48 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E5: cntxt_r_l_v,E3: expr_r_l_v] :
% 0.32/0.48 ( ( S @ R )
% 0.32/0.48 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E5 @ ( rfork_r_l_v @ E3 ) ) ) ) ) )
% 0.32/0.48 => ( ord_less_eq_set_r @ ( rID_G_r_l_v @ S2 ) @ ( rID_G_r_l_v @ S ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % only_fork_introduces_rids
% 0.32/0.48 thf(fact_305_empty__map__finite_I4_J,axiom,
% 0.32/0.48 ( finite_finite_l
% 0.32/0.48 @ ( lID_G_r_l_v
% 0.32/0.48 @ ^ [X2: r] : none_P277133687_r_l_v ) ) ).
% 0.32/0.48
% 0.32/0.48 % empty_map_finite(4)
% 0.32/0.48 thf(fact_306_in__renamed__in__unlabelled__global_I2_J,axiom,
% 0.32/0.48 ! [Alpha2: r > r,Beta2: l > l,L2: l,S: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( bij_betw_r_r @ Alpha2 @ top_top_set_r @ top_top_set_r )
% 0.32/0.48 => ( ( bij_betw_l_l @ Beta2 @ top_top_set_l @ top_top_set_l )
% 0.32/0.48 => ( ( member_l @ ( Beta2 @ L2 ) @ ( lID_G_r_l_v @ ( r_G_r_l_v @ Alpha2 @ Beta2 @ S ) ) )
% 0.32/0.48 = ( member_l @ L2 @ ( lID_G_r_l_v @ S ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % in_renamed_in_unlabelled_global(2)
% 0.32/0.48 thf(fact_307_RID_092_060_094sub_062L__finite__invariant,axiom,
% 0.32/0.48 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.32/0.48 => ( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
% 0.32/0.48 => ( finite_finite_l @ ( lID_G_r_l_v @ S2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % RID\<^sub>L_finite_invariant
% 0.32/0.48 thf(fact_308_reachable__imp__identifiers__finite_I2_J,axiom,
% 0.32/0.48 ! [S: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( reachable_r_l_v @ subst @ S )
% 0.32/0.48 => ( finite_finite_l @ ( lID_G_r_l_v @ S ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % reachable_imp_identifiers_finite(2)
% 0.32/0.48 thf(fact_309_in__restricted__global__in__unrestricted__global_I2_J,axiom,
% 0.32/0.48 ! [L2: l,S: r > option1457017436_r_l_v,R: r] :
% 0.32/0.48 ( ( member_l @ L2 @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 0.32/0.48 => ( member_l @ L2 @ ( lID_G_r_l_v @ S ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % in_restricted_global_in_unrestricted_global(2)
% 0.32/0.48 thf(fact_310_LID_092_060_094sub_062GI,axiom,
% 0.32/0.48 ! [S: r > option1457017436_r_l_v,R: r,Ls: produc1156025366_r_l_v,L2: l] :
% 0.32/0.48 ( ( ( S @ R )
% 0.32/0.48 = ( some_P1807977723_r_l_v @ Ls ) )
% 0.32/0.48 => ( ( member_l @ L2 @ ( lID_L_l_r_v @ Ls ) )
% 0.32/0.48 => ( member_l @ L2 @ ( lID_G_r_l_v @ S ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % LID\<^sub>GI
% 0.32/0.48 thf(fact_311_finite__Collect__subsets,axiom,
% 0.32/0.48 ! [A5: set_r] :
% 0.32/0.48 ( ( finite_finite_r @ A5 )
% 0.32/0.48 => ( finite_finite_set_r
% 0.32/0.48 @ ( collect_set_r
% 0.32/0.48 @ ^ [B6: set_r] : ( ord_less_eq_set_r @ B6 @ A5 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finite_Collect_subsets
% 0.32/0.48 thf(fact_312_finite__Collect__subsets,axiom,
% 0.32/0.48 ! [A5: set_l] :
% 0.32/0.48 ( ( finite_finite_l @ A5 )
% 0.32/0.48 => ( finite_finite_set_l
% 0.32/0.48 @ ( collect_set_l
% 0.32/0.48 @ ^ [B6: set_l] : ( ord_less_eq_set_l @ B6 @ A5 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finite_Collect_subsets
% 0.32/0.48 thf(fact_313_finite__state__imp__restriction__finite_I2_J,axiom,
% 0.32/0.48 ! [S: r > option1457017436_r_l_v,R: r] :
% 0.32/0.48 ( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
% 0.32/0.48 => ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finite_state_imp_restriction_finite(2)
% 0.32/0.48 thf(fact_314_in__restricted__global__in__updated__global_I2_J,axiom,
% 0.32/0.48 ! [L2: l,S: r > option1457017436_r_l_v,R: r,Ls: produc1156025366_r_l_v] :
% 0.32/0.48 ( ( member_l @ L2 @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 0.32/0.48 => ( member_l @ L2 @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ Ls ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % in_restricted_global_in_updated_global(2)
% 0.32/0.48 thf(fact_315_local__state__of__finite__restricted__global__state__is__finite_I2_J,axiom,
% 0.32/0.48 ! [S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
% 0.32/0.48 ( ( ( S @ R2 )
% 0.32/0.48 = ( some_P1807977723_r_l_v @ Ls ) )
% 0.32/0.48 => ( ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 0.32/0.48 => ( ( R != R2 )
% 0.32/0.48 => ( finite_finite_l @ ( lID_L_l_r_v @ Ls ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % local_state_of_finite_restricted_global_state_is_finite(2)
% 0.32/0.48 thf(fact_316_ID__restricted__global__subset__unrestricted_I1_J,axiom,
% 0.32/0.48 ! [S: r > option1457017436_r_l_v,R: r] : ( ord_less_eq_set_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) @ ( lID_G_r_l_v @ S ) ) ).
% 0.32/0.48
% 0.32/0.48 % ID_restricted_global_subset_unrestricted(1)
% 0.32/0.48 thf(fact_317_finite__has__minimal2,axiom,
% 0.32/0.48 ! [A5: set_set_r,A: set_r] :
% 0.32/0.48 ( ( finite_finite_set_r @ A5 )
% 0.32/0.48 => ( ( member_set_r @ A @ A5 )
% 0.32/0.48 => ? [X3: set_r] :
% 0.32/0.48 ( ( member_set_r @ X3 @ A5 )
% 0.32/0.48 & ( ord_less_eq_set_r @ X3 @ A )
% 0.32/0.48 & ! [Xa2: set_r] :
% 0.32/0.48 ( ( member_set_r @ Xa2 @ A5 )
% 0.32/0.48 => ( ( ord_less_eq_set_r @ Xa2 @ X3 )
% 0.32/0.48 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finite_has_minimal2
% 0.32/0.48 thf(fact_318_finite__has__minimal2,axiom,
% 0.32/0.48 ! [A5: set_set_l,A: set_l] :
% 0.32/0.48 ( ( finite_finite_set_l @ A5 )
% 0.32/0.48 => ( ( member_set_l @ A @ A5 )
% 0.32/0.48 => ? [X3: set_l] :
% 0.32/0.48 ( ( member_set_l @ X3 @ A5 )
% 0.32/0.48 & ( ord_less_eq_set_l @ X3 @ A )
% 0.32/0.48 & ! [Xa2: set_l] :
% 0.32/0.48 ( ( member_set_l @ Xa2 @ A5 )
% 0.32/0.48 => ( ( ord_less_eq_set_l @ Xa2 @ X3 )
% 0.32/0.48 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finite_has_minimal2
% 0.32/0.48 thf(fact_319_finite__has__maximal2,axiom,
% 0.32/0.48 ! [A5: set_set_r,A: set_r] :
% 0.32/0.48 ( ( finite_finite_set_r @ A5 )
% 0.32/0.48 => ( ( member_set_r @ A @ A5 )
% 0.32/0.48 => ? [X3: set_r] :
% 0.32/0.48 ( ( member_set_r @ X3 @ A5 )
% 0.32/0.48 & ( ord_less_eq_set_r @ A @ X3 )
% 0.32/0.48 & ! [Xa2: set_r] :
% 0.32/0.48 ( ( member_set_r @ Xa2 @ A5 )
% 0.32/0.48 => ( ( ord_less_eq_set_r @ X3 @ Xa2 )
% 0.32/0.48 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finite_has_maximal2
% 0.32/0.48 thf(fact_320_finite__has__maximal2,axiom,
% 0.32/0.48 ! [A5: set_set_l,A: set_l] :
% 0.32/0.48 ( ( finite_finite_set_l @ A5 )
% 0.32/0.48 => ( ( member_set_l @ A @ A5 )
% 0.32/0.48 => ? [X3: set_l] :
% 0.32/0.48 ( ( member_set_l @ X3 @ A5 )
% 0.32/0.48 & ( ord_less_eq_set_l @ A @ X3 )
% 0.32/0.48 & ! [Xa2: set_l] :
% 0.32/0.48 ( ( member_set_l @ Xa2 @ A5 )
% 0.32/0.48 => ( ( ord_less_eq_set_l @ X3 @ Xa2 )
% 0.32/0.48 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finite_has_maximal2
% 0.32/0.48 thf(fact_321_rev__finite__subset,axiom,
% 0.32/0.48 ! [B5: set_r,A5: set_r] :
% 0.32/0.48 ( ( finite_finite_r @ B5 )
% 0.32/0.48 => ( ( ord_less_eq_set_r @ A5 @ B5 )
% 0.32/0.48 => ( finite_finite_r @ A5 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % rev_finite_subset
% 0.32/0.48 thf(fact_322_rev__finite__subset,axiom,
% 0.32/0.48 ! [B5: set_l,A5: set_l] :
% 0.32/0.48 ( ( finite_finite_l @ B5 )
% 0.32/0.48 => ( ( ord_less_eq_set_l @ A5 @ B5 )
% 0.32/0.48 => ( finite_finite_l @ A5 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % rev_finite_subset
% 0.32/0.48 thf(fact_323_infinite__super,axiom,
% 0.32/0.48 ! [S6: set_r,T2: set_r] :
% 0.32/0.48 ( ( ord_less_eq_set_r @ S6 @ T2 )
% 0.32/0.48 => ( ~ ( finite_finite_r @ S6 )
% 0.32/0.48 => ~ ( finite_finite_r @ T2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % infinite_super
% 0.32/0.48 thf(fact_324_infinite__super,axiom,
% 0.32/0.48 ! [S6: set_l,T2: set_l] :
% 0.32/0.48 ( ( ord_less_eq_set_l @ S6 @ T2 )
% 0.32/0.48 => ( ~ ( finite_finite_l @ S6 )
% 0.32/0.48 => ~ ( finite_finite_l @ T2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % infinite_super
% 0.32/0.48 thf(fact_325_finite__subset,axiom,
% 0.32/0.48 ! [A5: set_r,B5: set_r] :
% 0.32/0.48 ( ( ord_less_eq_set_r @ A5 @ B5 )
% 0.32/0.48 => ( ( finite_finite_r @ B5 )
% 0.32/0.48 => ( finite_finite_r @ A5 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finite_subset
% 0.32/0.48 thf(fact_326_finite__subset,axiom,
% 0.32/0.48 ! [A5: set_l,B5: set_l] :
% 0.32/0.48 ( ( ord_less_eq_set_l @ A5 @ B5 )
% 0.32/0.48 => ( ( finite_finite_l @ B5 )
% 0.32/0.48 => ( finite_finite_l @ A5 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % finite_subset
% 0.32/0.48 thf(fact_327_LID_092_060_094sub_062GE,axiom,
% 0.32/0.48 ! [L2: l,S: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( member_l @ L2 @ ( lID_G_r_l_v @ S ) )
% 0.32/0.48 => ~ ! [R5: r,Ls3: produc1156025366_r_l_v] :
% 0.32/0.48 ( ( ( S @ R5 )
% 0.32/0.48 = ( some_P1807977723_r_l_v @ Ls3 ) )
% 0.32/0.48 => ~ ( member_l @ L2 @ ( lID_L_l_r_v @ Ls3 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % LID\<^sub>GE
% 0.32/0.48 thf(fact_328_substitution_ORID_092_060_094sub_062L__finite__invariant,axiom,
% 0.32/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( substitution_r_l_v @ Subst )
% 0.32/0.48 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.32/0.48 => ( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
% 0.32/0.48 => ( finite_finite_l @ ( lID_G_r_l_v @ S2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % substitution.RID\<^sub>L_finite_invariant
% 0.32/0.48 thf(fact_329_ID__restricted__global__subset__unrestricted_I2_J,axiom,
% 0.32/0.48 ! [S: r > option1457017436_r_l_v,R: r] : ( ord_less_eq_set_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) @ ( rID_G_r_l_v @ S ) ) ).
% 0.32/0.48
% 0.32/0.48 % ID_restricted_global_subset_unrestricted(2)
% 0.32/0.48 thf(fact_330_substitution_Oreachable__imp__identifiers__finite_I2_J,axiom,
% 0.32/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( substitution_r_l_v @ Subst )
% 0.32/0.48 => ( ( reachable_r_l_v @ Subst @ S )
% 0.32/0.48 => ( finite_finite_l @ ( lID_G_r_l_v @ S ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % substitution.reachable_imp_identifiers_finite(2)
% 0.32/0.48 thf(fact_331_substitution_Oempty__map__finite_I4_J,axiom,
% 0.32/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v] :
% 0.32/0.48 ( ( substitution_r_l_v @ Subst )
% 0.32/0.48 => ( finite_finite_l
% 0.32/0.48 @ ( lID_G_r_l_v
% 0.32/0.48 @ ^ [X2: r] : none_P277133687_r_l_v ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % substitution.empty_map_finite(4)
% 0.32/0.48 thf(fact_332_substitution_Oreachable__imp__identifiers__available_I2_J,axiom,
% 0.32/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( substitution_r_l_v @ Subst )
% 0.32/0.48 => ( ( reachable_r_l_v @ Subst @ S )
% 0.32/0.48 => ( ~ ( finite_finite_l @ top_top_set_l )
% 0.32/0.48 => ? [L: l] :
% 0.32/0.48 ~ ( member_l @ L @ ( lID_G_r_l_v @ S ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % substitution.reachable_imp_identifiers_available(2)
% 0.32/0.48 thf(fact_333_substitution_Ofinite__state__imp__restriction__finite_I2_J,axiom,
% 0.32/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r] :
% 0.32/0.48 ( ( substitution_r_l_v @ Subst )
% 0.32/0.48 => ( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
% 0.32/0.48 => ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % substitution.finite_state_imp_restriction_finite(2)
% 0.32/0.48 thf(fact_334_substitution_Oin__renamed__in__unlabelled__global_I2_J,axiom,
% 0.32/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,Alpha2: r > r,Beta2: l > l,L2: l,S: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( substitution_r_l_v @ Subst )
% 0.32/0.48 => ( ( bij_betw_r_r @ Alpha2 @ top_top_set_r @ top_top_set_r )
% 0.32/0.48 => ( ( bij_betw_l_l @ Beta2 @ top_top_set_l @ top_top_set_l )
% 0.32/0.48 => ( ( member_l @ ( Beta2 @ L2 ) @ ( lID_G_r_l_v @ ( r_G_r_l_v @ Alpha2 @ Beta2 @ S ) ) )
% 0.32/0.48 = ( member_l @ L2 @ ( lID_G_r_l_v @ S ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % substitution.in_renamed_in_unlabelled_global(2)
% 0.32/0.48 thf(fact_335_substitution_Olocal__state__of__finite__restricted__global__state__is__finite_I2_J,axiom,
% 0.32/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
% 0.32/0.48 ( ( substitution_r_l_v @ Subst )
% 0.32/0.48 => ( ( ( S @ R2 )
% 0.32/0.48 = ( some_P1807977723_r_l_v @ Ls ) )
% 0.32/0.48 => ( ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 0.32/0.48 => ( ( R != R2 )
% 0.32/0.48 => ( finite_finite_l @ ( lID_L_l_r_v @ Ls ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % substitution.local_state_of_finite_restricted_global_state_is_finite(2)
% 0.32/0.48 thf(fact_336_substitution_Oonly__fork__introduces__rids,axiom,
% 0.32/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( substitution_r_l_v @ Subst )
% 0.32/0.48 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.32/0.48 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E5: cntxt_r_l_v,E3: expr_r_l_v] :
% 0.32/0.48 ( ( S @ R )
% 0.32/0.48 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E5 @ ( rfork_r_l_v @ E3 ) ) ) ) ) )
% 0.32/0.48 => ( ord_less_eq_set_r @ ( rID_G_r_l_v @ S2 ) @ ( rID_G_r_l_v @ S ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % substitution.only_fork_introduces_rids
% 0.32/0.48 thf(fact_337_only__new__introduces__lids_H,axiom,
% 0.32/0.48 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v,L2: l] :
% 0.32/0.48 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.32/0.48 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E5: cntxt_r_l_v,V2: val_r_l_v] :
% 0.32/0.48 ( ( S @ R )
% 0.32/0.48 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E5 @ ( ref_r_l_v @ ( vE_r_l_v @ V2 ) ) ) ) ) ) )
% 0.32/0.48 => ( ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S ) )
% 0.32/0.48 => ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % only_new_introduces_lids'
% 0.32/0.48 thf(fact_338_SLC__new,axiom,
% 0.32/0.48 ! [S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,V: val_r_l_v,S_2: r > option1457017436_r_l_v,L2: l,R2: r,S_22: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( ( S_1 @ R )
% 0.32/0.48 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.32/0.48 => ( ( S_2
% 0.32/0.48 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) ) ) ) ) ) )
% 0.32/0.48 => ( ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S_1 ) )
% 0.32/0.48 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 0.32/0.48 => ( ( R != R2 )
% 0.32/0.48 => ( ( reachable_r_l_v @ subst @ S_1 )
% 0.32/0.48 => ( ~ ( finite_finite_l @ top_top_set_l )
% 0.32/0.48 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.32/0.48 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 0.32/0.48 | ( S_2 = S_3 ) )
% 0.32/0.48 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 0.32/0.48 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % SLC_new
% 0.32/0.48 thf(fact_339_val_Oinject_I3_J,axiom,
% 0.32/0.48 ! [X32: l,Y32: l] :
% 0.32/0.48 ( ( ( loc_l_r_v @ X32 )
% 0.32/0.48 = ( loc_l_r_v @ Y32 ) )
% 0.32/0.48 = ( X32 = Y32 ) ) ).
% 0.32/0.48
% 0.32/0.48 % val.inject(3)
% 0.32/0.48 thf(fact_340_expr_Oinject_I4_J,axiom,
% 0.32/0.48 ! [X4: expr_r_l_v,Y4: expr_r_l_v] :
% 0.32/0.48 ( ( ( ref_r_l_v @ X4 )
% 0.32/0.48 = ( ref_r_l_v @ Y4 ) )
% 0.32/0.48 = ( X4 = Y4 ) ) ).
% 0.32/0.48
% 0.32/0.48 % expr.inject(4)
% 0.32/0.48 thf(fact_341_revision__step_Onew,axiom,
% 0.32/0.48 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,V: val_r_l_v,L2: l] :
% 0.32/0.48 ( ( ( S @ R )
% 0.32/0.48 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.32/0.48 => ( ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S ) )
% 0.32/0.48 => ( revision_step_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % revision_step.new
% 0.32/0.48 thf(fact_342_only__new__introduces__lids,axiom,
% 0.32/0.48 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.32/0.48 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E5: cntxt_r_l_v,V2: val_r_l_v] :
% 0.32/0.48 ( ( S @ R )
% 0.32/0.48 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E5 @ ( ref_r_l_v @ ( vE_r_l_v @ V2 ) ) ) ) ) ) )
% 0.32/0.48 => ( ord_less_eq_set_l @ ( lID_G_r_l_v @ S2 ) @ ( lID_G_r_l_v @ S ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % only_new_introduces_lids
% 0.32/0.48 thf(fact_343_new__pseudodeterministic,axiom,
% 0.32/0.48 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( ( S @ R )
% 0.32/0.48 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.32/0.48 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.32/0.48 = ( ? [L3: l] :
% 0.32/0.48 ( ~ ( member_l @ L3 @ ( lID_G_r_l_v @ S ) )
% 0.32/0.48 & ( S2
% 0.32/0.48 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L3 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( loc_l_r_v @ L3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % new_pseudodeterministic
% 0.32/0.48 thf(fact_344_expr_Odistinct_I5_J,axiom,
% 0.32/0.48 ! [X1: val_r_l_v,X4: expr_r_l_v] :
% 0.32/0.48 ( ( vE_r_l_v @ X1 )
% 0.32/0.48 != ( ref_r_l_v @ X4 ) ) ).
% 0.32/0.48
% 0.32/0.48 % expr.distinct(5)
% 0.32/0.48 thf(fact_345_val_Odistinct_I15_J,axiom,
% 0.32/0.48 ! [X32: l,X4: r] :
% 0.32/0.48 ( ( loc_l_r_v @ X32 )
% 0.32/0.48 != ( rid_r_l_v @ X4 ) ) ).
% 0.32/0.48
% 0.32/0.48 % val.distinct(15)
% 0.32/0.48 thf(fact_346_expr_Odistinct_I43_J,axiom,
% 0.32/0.48 ! [X4: expr_r_l_v,X8: expr_r_l_v] :
% 0.32/0.48 ( ( ref_r_l_v @ X4 )
% 0.32/0.48 != ( rjoin_r_l_v @ X8 ) ) ).
% 0.32/0.48
% 0.32/0.48 % expr.distinct(43)
% 0.32/0.48 thf(fact_347_expr_Odistinct_I41_J,axiom,
% 0.32/0.48 ! [X4: expr_r_l_v,X7: expr_r_l_v] :
% 0.32/0.48 ( ( ref_r_l_v @ X4 )
% 0.32/0.48 != ( rfork_r_l_v @ X7 ) ) ).
% 0.32/0.48
% 0.32/0.48 % expr.distinct(41)
% 0.32/0.48 thf(fact_348_val_Odistinct_I3_J,axiom,
% 0.32/0.48 ! [X1: const,X32: l] :
% 0.32/0.48 ( ( cV_r_l_v @ X1 )
% 0.32/0.48 != ( loc_l_r_v @ X32 ) ) ).
% 0.32/0.48
% 0.32/0.48 % val.distinct(3)
% 0.32/0.48 thf(fact_349_substitution_Onew__pseudodeterministic,axiom,
% 0.32/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( substitution_r_l_v @ Subst )
% 0.32/0.48 => ( ( ( S @ R )
% 0.32/0.48 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.32/0.48 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.32/0.48 = ( ? [L3: l] :
% 0.32/0.48 ( ~ ( member_l @ L3 @ ( lID_G_r_l_v @ S ) )
% 0.32/0.48 & ( S2
% 0.32/0.48 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L3 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( loc_l_r_v @ L3 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % substitution.new_pseudodeterministic
% 0.32/0.48 thf(fact_350_substitution_Orevision__step_Onew,axiom,
% 0.32/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,V: val_r_l_v,L2: l] :
% 0.32/0.48 ( ( substitution_r_l_v @ Subst )
% 0.32/0.48 => ( ( ( S @ R )
% 0.32/0.48 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.32/0.48 => ( ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S ) )
% 0.32/0.48 => ( revision_step_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % substitution.revision_step.new
% 0.32/0.48 thf(fact_351_substitution_OSLC__new,axiom,
% 0.32/0.48 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,V: val_r_l_v,S_2: r > option1457017436_r_l_v,L2: l,R2: r,S_22: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( substitution_r_l_v @ Subst )
% 0.32/0.48 => ( ( ( S_1 @ R )
% 0.32/0.48 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.32/0.48 => ( ( S_2
% 0.32/0.48 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) ) ) ) ) ) )
% 0.32/0.48 => ( ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S_1 ) )
% 0.32/0.48 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
% 0.32/0.48 => ( ( R != R2 )
% 0.32/0.48 => ( ( reachable_r_l_v @ Subst @ S_1 )
% 0.32/0.48 => ( ~ ( finite_finite_l @ top_top_set_l )
% 0.32/0.48 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.32/0.48 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.32/0.48 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 0.32/0.48 | ( S_2 = S_3 ) )
% 0.32/0.48 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 0.32/0.48 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % substitution.SLC_new
% 0.32/0.48
% 0.32/0.48 % Helper facts (5)
% 0.32/0.48 thf(help_If_2_1_If_001t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_T,axiom,
% 0.32/0.48 ! [X: option_val_r_l_v,Y: option_val_r_l_v] :
% 0.32/0.48 ( ( if_option_val_r_l_v @ $false @ X @ Y )
% 0.32/0.48 = Y ) ).
% 0.32/0.48
% 0.32/0.48 thf(help_If_1_1_If_001t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_T,axiom,
% 0.32/0.48 ! [X: option_val_r_l_v,Y: option_val_r_l_v] :
% 0.32/0.48 ( ( if_option_val_r_l_v @ $true @ X @ Y )
% 0.32/0.48 = X ) ).
% 0.32/0.48
% 0.32/0.48 thf(help_If_3_1_If_001t__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J_T,axiom,
% 0.32/0.48 ! [P: $o] :
% 0.32/0.48 ( ( P = $true )
% 0.32/0.48 | ( P = $false ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(help_If_2_1_If_001t__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J_T,axiom,
% 0.32/0.48 ! [X: option1457017436_r_l_v,Y: option1457017436_r_l_v] :
% 0.32/0.48 ( ( if_opt1153928738_r_l_v @ $false @ X @ Y )
% 0.32/0.48 = Y ) ).
% 0.32/0.48
% 0.32/0.48 thf(help_If_1_1_If_001t__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J_T,axiom,
% 0.32/0.48 ! [X: option1457017436_r_l_v,Y: option1457017436_r_l_v] :
% 0.32/0.48 ( ( if_opt1153928738_r_l_v @ $true @ X @ Y )
% 0.32/0.48 = X ) ).
% 0.32/0.48
% 0.32/0.48 % Conjectures (1)
% 0.32/0.48 thf(conj_0,conjecture,
% 0.32/0.48 ( s
% 0.32/0.48 = ( fun_up709272714_r_l_v @ s @ r2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( rfork_r_l_v @ e2 ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 ------------------------
% 2.96/1.56 ---- Embedded in THF ---
% 2.96/1.56 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.96/1.56 %%% Generated on Tue Feb 24 08:25:34 EST 2026
% 2.96/1.56 %%% using '$$dhol' embedding, version 1.3.0.
% 2.96/1.56 %%% Logic specification used:
% 2.96/1.56 %%% thf(spec, logic, $$dhol).
% 2.96/1.56
% 2.96/1.56 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.6Efo01nBTw/DTF2DTF15893.p
% See solution above
% 2.96/1.56 ------------------------
% 2.96/1.60 ---- Cleaned THF ---
% 3.19/1.60 thf(ty_n_t__Product____Type__Oprod_I_062_Itf__r_Mtf__r_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mtf__l_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J_J,type,
% 3.19/1.60 produc1394974636_r_l_v: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Product____Type__Oprod_I_062_Itf__l_Mtf__l_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J,type,
% 3.19/1.60 produc1489027110_r_l_v: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J,type,
% 3.19/1.60 option1457017436_r_l_v: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J,type,
% 3.19/1.60 produc1156025366_r_l_v: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J,type,
% 3.19/1.60 produc1164766533_r_l_v: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Sum____Type__Osum_Itf__r_Mtf__l_J_J_J,type,
% 3.19/1.60 set_op865065573um_r_l: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Sum____Type__Osum_Itf__l_Mtf__r_J_J_J,type,
% 3.19/1.60 set_op160472561um_l_r: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Sum____Type__Osum_Itf__l_Mtf__l_J_J_J,type,
% 3.19/1.60 set_op76482283um_l_l: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Set__Oset_Itf__r_J_J_J,type,
% 3.19/1.60 set_option_set_r: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Set__Oset_Itf__l_J_J_J,type,
% 3.19/1.60 set_option_set_l: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J,type,
% 3.19/1.60 option_val_r_l_v: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__r_Mtf__r_J_J,type,
% 3.19/1.60 set_Product_prod_r_r: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__r_Mtf__l_J_J,type,
% 3.19/1.60 set_Product_prod_r_l: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__l_Mtf__r_J_J,type,
% 3.19/1.60 set_Product_prod_l_r: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__l_Mtf__l_J_J,type,
% 3.19/1.60 set_Product_prod_l_l: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_Itf__r_Mtf__r_J_J,type,
% 3.19/1.60 set_Sum_sum_r_r: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_Itf__r_Mtf__l_J_J,type,
% 3.19/1.60 set_Sum_sum_r_l: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_Itf__l_Mtf__r_J_J,type,
% 3.19/1.60 set_Sum_sum_l_r: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_Itf__l_Mtf__l_J_J,type,
% 3.19/1.60 set_Sum_sum_l_l: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Set__Oset_It__Option__Ooption_Itf__r_J_J,type,
% 3.19/1.60 set_option_r: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Set__Oset_It__Option__Ooption_Itf__l_J_J,type,
% 3.19/1.60 set_option_l: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Data__Ocntxt_Itf__r_Mtf__l_Mtf__v_J,type,
% 3.19/1.60 cntxt_r_l_v: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Set__Oset_It__Set__Oset_Itf__r_J_J,type,
% 3.19/1.60 set_set_r: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Set__Oset_It__Set__Oset_Itf__l_J_J,type,
% 3.19/1.60 set_set_l: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J,type,
% 3.19/1.60 expr_r_l_v: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Sum____Type__Osum_Itf__r_Mtf__l_J,type,
% 3.19/1.60 sum_sum_r_l: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Sum____Type__Osum_Itf__l_Mtf__r_J,type,
% 3.19/1.60 sum_sum_l_r: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Sum____Type__Osum_Itf__l_Mtf__l_J,type,
% 3.19/1.60 sum_sum_l_l: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,type,
% 3.19/1.60 val_r_l_v: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Set__Oset_Itf__r_J,type,
% 3.19/1.60 set_r: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Set__Oset_Itf__l_J,type,
% 3.19/1.60 set_l: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_t__Data__Oconst,type,
% 3.19/1.60 const: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_tf__v,type,
% 3.19/1.60 v: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_tf__r,type,
% 3.19/1.60 r: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(ty_n_tf__l,type,
% 3.19/1.60 l: $tType ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Data_OLID__expression_001tf__l_001tf__r_001tf__v,type,
% 3.19/1.60 lID_expression_l_r_v: produc1156025366_r_l_v > expr_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Data_OLID__local__store_001tf__l_001tf__r_001tf__v,type,
% 3.19/1.60 lID_lo1265057957_l_r_v: produc1156025366_r_l_v > l > option_val_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Data_OLID__snapshot_001tf__l_001tf__r_001tf__v,type,
% 3.19/1.60 lID_snapshot_l_r_v: produc1156025366_r_l_v > l > option_val_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Data_Ocombine_001tf__l_001t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,type,
% 3.19/1.60 combine_l_val_r_l_v: ( l > option_val_r_l_v ) > ( l > option_val_r_l_v ) > l > option_val_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Data_Oconst_OUnit,type,
% 3.19/1.60 unit: const ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Data_Oexpr_ORef_001tf__r_001tf__l_001tf__v,type,
% 3.19/1.60 ref_r_l_v: expr_r_l_v > expr_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Data_Oexpr_ORfork_001tf__r_001tf__l_001tf__v,type,
% 3.19/1.60 rfork_r_l_v: expr_r_l_v > expr_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Data_Oexpr_ORjoin_001tf__r_001tf__l_001tf__v,type,
% 3.19/1.60 rjoin_r_l_v: expr_r_l_v > expr_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Data_Oexpr_OVE_001tf__r_001tf__l_001tf__v,type,
% 3.19/1.60 vE_r_l_v: val_r_l_v > expr_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Data_Oplug_001tf__r_001tf__l_001tf__v,type,
% 3.19/1.60 plug_r_l_v: cntxt_r_l_v > expr_r_l_v > expr_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Data_Oval_OCV_001tf__r_001tf__l_001tf__v,type,
% 3.19/1.60 cV_r_l_v: const > val_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Data_Oval_OLoc_001tf__l_001tf__r_001tf__v,type,
% 3.19/1.60 loc_l_r_v: l > val_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Data_Oval_ORid_001tf__r_001tf__l_001tf__v,type,
% 3.19/1.60 rid_r_l_v: r > val_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Executions_Osubstitution_Oexecution_001tf__r_001tf__l_001tf__v,type,
% 3.19/1.60 execution_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > expr_r_l_v > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Executions_Osubstitution_Oinductive__invariant_001tf__r_001tf__l_001tf__v,type,
% 3.19/1.60 induct1670415253_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( ( r > option1457017436_r_l_v ) > $o ) > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Executions_Osubstitution_Oreachable_001tf__r_001tf__l_001tf__v,type,
% 3.19/1.60 reachable_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_It__Set__Oset_Itf__l_J_J,type,
% 3.19/1.60 finite160708696_set_l: set_option_set_l > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_It__Set__Oset_Itf__r_J_J,type,
% 3.19/1.60 finite555643486_set_r: set_option_set_r > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_It__Sum____Type__Osum_Itf__l_Mtf__l_J_J,type,
% 3.19/1.60 finite1864485196um_l_l: set_op76482283um_l_l > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_It__Sum____Type__Osum_Itf__l_Mtf__r_J_J,type,
% 3.19/1.60 finite111936338um_l_r: set_op160472561um_l_r > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_It__Sum____Type__Osum_Itf__r_Mtf__l_J_J,type,
% 3.19/1.60 finite1036466630um_r_l: set_op865065573um_r_l > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_Itf__l_J,type,
% 3.19/1.60 finite2114249848tion_l: set_option_l > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_Itf__r_J,type,
% 3.19/1.60 finite16335230tion_r: set_option_r > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_Itf__l_Mtf__l_J,type,
% 3.19/1.60 finite785973648od_l_l: set_Product_prod_l_l > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_Itf__l_Mtf__r_J,type,
% 3.19/1.60 finite835542678od_l_r: set_Product_prod_l_r > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_Itf__r_Mtf__l_J,type,
% 3.19/1.60 finite1457622794od_r_l: set_Product_prod_r_l > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_Itf__r_Mtf__r_J,type,
% 3.19/1.60 finite1507191824od_r_r: set_Product_prod_r_r > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_Itf__l_J,type,
% 3.19/1.60 finite_finite_set_l: set_set_l > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_Itf__r_J,type,
% 3.19/1.60 finite_finite_set_r: set_set_r > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Finite__Set_Ofinite_001t__Sum____Type__Osum_Itf__l_Mtf__l_J,type,
% 3.19/1.60 finite1541484284um_l_l: set_Sum_sum_l_l > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Finite__Set_Ofinite_001t__Sum____Type__Osum_Itf__l_Mtf__r_J,type,
% 3.19/1.60 finite1591053314um_l_r: set_Sum_sum_l_r > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Finite__Set_Ofinite_001t__Sum____Type__Osum_Itf__r_Mtf__l_J,type,
% 3.19/1.60 finite65649782um_r_l: set_Sum_sum_r_l > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Finite__Set_Ofinite_001t__Sum____Type__Osum_Itf__r_Mtf__r_J,type,
% 3.19/1.60 finite115218812um_r_r: set_Sum_sum_r_r > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Finite__Set_Ofinite_001tf__l,type,
% 3.19/1.60 finite_finite_l: set_l > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Finite__Set_Ofinite_001tf__r,type,
% 3.19/1.60 finite_finite_r: set_r > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Fun_Obij__betw_001tf__l_001tf__l,type,
% 3.19/1.60 bij_betw_l_l: ( l > l ) > set_l > set_l > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Fun_Obij__betw_001tf__l_001tf__r,type,
% 3.19/1.60 bij_betw_l_r: ( l > r ) > set_l > set_r > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Fun_Obij__betw_001tf__r_001tf__l,type,
% 3.19/1.60 bij_betw_r_l: ( r > l ) > set_r > set_l > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Fun_Obij__betw_001tf__r_001tf__r,type,
% 3.19/1.60 bij_betw_r_r: ( r > r ) > set_r > set_r > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Fun_Ofun__upd_001tf__l_001t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J,type,
% 3.19/1.60 fun_up1835647912_r_l_v: ( l > option_val_r_l_v ) > l > option_val_r_l_v > l > option_val_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Fun_Ofun__upd_001tf__r_001t__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J,type,
% 3.19/1.60 fun_up709272714_r_l_v: ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v > r > option1457017436_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_If_001t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J,type,
% 3.19/1.60 if_option_val_r_l_v: $o > option_val_r_l_v > option_val_r_l_v > option_val_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_If_001t__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J,type,
% 3.19/1.60 if_opt1153928738_r_l_v: $o > option1457017436_r_l_v > option1457017436_r_l_v > option1457017436_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Occurrences_OLID_092_060_094sub_062G_001tf__r_001tf__l_001tf__v,type,
% 3.19/1.60 lID_G_r_l_v: ( r > option1457017436_r_l_v ) > set_l ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Occurrences_OLID_092_060_094sub_062L_001tf__l_001tf__r_001tf__v,type,
% 3.19/1.60 lID_L_l_r_v: produc1156025366_r_l_v > set_l ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Occurrences_ORID_092_060_094sub_062G_001tf__r_001tf__l_001tf__v,type,
% 3.19/1.60 rID_G_r_l_v: ( r > option1457017436_r_l_v ) > set_r ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Occurrences_ORID_092_060_094sub_062L_001tf__l_001tf__r_001tf__v,type,
% 3.19/1.60 rID_L_l_r_v: produc1156025366_r_l_v > set_r ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_OperationalSemantics_Osubstitution_Odomains__subsume_001tf__l_001tf__r_001tf__v,type,
% 3.19/1.60 domain87684397_l_r_v: produc1156025366_r_l_v > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_OperationalSemantics_Osubstitution_Odomains__subsume__globally_001tf__r_001tf__l_001tf__v,type,
% 3.19/1.60 domain1547879849_r_l_v: ( r > option1457017436_r_l_v ) > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_OperationalSemantics_Osubstitution_Orevision__step_001tf__r_001tf__l_001tf__v,type,
% 3.19/1.60 revision_step_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_OperationalSemantics_Osubstitution_Orevision__step__relaxed_001tf__r_001tf__l_001tf__v,type,
% 3.19/1.60 revisi1291188644_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > r > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_OperationalSemantics_Osubstitution_Osubsumes__accessible_001tf__r_001tf__l_001tf__v,type,
% 3.19/1.60 subsum148050133_r_l_v: r > r > ( r > option1457017436_r_l_v ) > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_OperationalSemantics_Osubstitution_Osubsumes__accessible__globally_001tf__r_001tf__l_001tf__v,type,
% 3.19/1.60 subsum680764357_r_l_v: ( r > option1457017436_r_l_v ) > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Option_Ooption_ONone_001t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,type,
% 3.19/1.60 none_val_r_l_v: option_val_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J,type,
% 3.19/1.60 none_P277133687_r_l_v: option1457017436_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Option_Ooption_OSome_001t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,type,
% 3.19/1.60 some_val_r_l_v: val_r_l_v > option_val_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J,type,
% 3.19/1.60 some_P1807977723_r_l_v: produc1156025366_r_l_v > option1457017436_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__l_J,type,
% 3.19/1.60 ord_less_eq_set_l: set_l > set_l > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__r_J,type,
% 3.19/1.60 ord_less_eq_set_r: set_r > set_r > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Set__Oset_Itf__l_J_J_J,type,
% 3.19/1.60 top_to471808607_set_l: set_option_set_l ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Set__Oset_Itf__r_J_J_J,type,
% 3.19/1.60 top_to555798885_set_r: set_option_set_r ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Sum____Type__Osum_Itf__l_Mtf__l_J_J_J,type,
% 3.19/1.60 top_to1066565019um_l_l: set_op76482283um_l_l ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Sum____Type__Osum_Itf__l_Mtf__r_J_J_J,type,
% 3.19/1.60 top_to1150555297um_l_r: set_op160472561um_l_r ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Sum____Type__Osum_Itf__r_Mtf__l_J_J_J,type,
% 3.19/1.60 top_to1855148309um_r_l: set_op865065573um_r_l ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_Itf__l_J_J,type,
% 3.19/1.60 top_top_set_option_l: set_option_l ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_Itf__r_J_J,type,
% 3.19/1.60 top_top_set_option_r: set_option_r ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_Itf__l_Mtf__l_J_J,type,
% 3.19/1.60 top_to320296343od_l_l: set_Product_prod_l_l ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_Itf__l_Mtf__r_J_J,type,
% 3.19/1.60 top_to715231133od_l_r: set_Product_prod_l_r ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_Itf__r_Mtf__l_J_J,type,
% 3.19/1.60 top_to1639761425od_r_l: set_Product_prod_r_l ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_Itf__r_Mtf__r_J_J,type,
% 3.19/1.60 top_to2034696215od_r_r: set_Product_prod_r_r ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_Itf__l_J_J,type,
% 3.19/1.60 top_top_set_set_l: set_set_l ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_Itf__r_J_J,type,
% 3.19/1.60 top_top_set_set_r: set_set_r ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Sum____Type__Osum_Itf__l_Mtf__l_J_J,type,
% 3.19/1.60 top_to1010946379um_l_l: set_Sum_sum_l_l ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Sum____Type__Osum_Itf__l_Mtf__r_J_J,type,
% 3.19/1.60 top_to1405881169um_l_r: set_Sum_sum_l_r ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Sum____Type__Osum_Itf__r_Mtf__l_J_J,type,
% 3.19/1.60 top_to182927813um_r_l: set_Sum_sum_r_l ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Sum____Type__Osum_Itf__r_Mtf__r_J_J,type,
% 3.19/1.60 top_to577862603um_r_r: set_Sum_sum_r_r ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__l_J,type,
% 3.19/1.60 top_top_set_l: set_l ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__r_J,type,
% 3.19/1.60 top_top_set_r: set_r ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Product__Type_OPair_001_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_001t__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J,type,
% 3.19/1.60 produc1834103605_r_l_v: ( l > option_val_r_l_v ) > expr_r_l_v > produc1164766533_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Product__Type_OPair_001_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_001t__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J,type,
% 3.19/1.60 produc297528454_r_l_v: ( l > option_val_r_l_v ) > produc1164766533_r_l_v > produc1156025366_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Product__Type_OPair_001_062_Itf__l_Mtf__l_J_001t__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J,type,
% 3.19/1.60 produc2057232216_r_l_v: ( l > l ) > produc1156025366_r_l_v > produc1489027110_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Product__Type_OPair_001_062_Itf__r_Mtf__r_J_001t__Product____Type__Oprod_I_062_Itf__l_Mtf__l_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J,type,
% 3.19/1.60 produc2111504612_r_l_v: ( r > r ) > produc1489027110_r_l_v > produc1394974636_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Renaming_O_092_060R_062_092_060_094sub_062G_001tf__r_001tf__l_001tf__v,type,
% 3.19/1.60 r_G_r_l_v: ( r > r ) > ( l > l ) > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Renaming_O_092_060R_062_092_060_094sub_062L_001tf__r_001tf__l_001tf__v,type,
% 3.19/1.60 r_L_r_l_v: ( r > r ) > ( l > l ) > produc1156025366_r_l_v > produc1156025366_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Renaming_Oeq__states_001tf__r_001tf__l_001tf__v,type,
% 3.19/1.60 eq_states_r_l_v: ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Renaming_Ois__global__renaming_001tf__r_001tf__l_001tf__v,type,
% 3.19/1.60 is_glo1871033385_r_l_v: ( r > r ) > ( l > l ) > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Set_OCollect_001t__Set__Oset_Itf__l_J,type,
% 3.19/1.60 collect_set_l: ( set_l > $o ) > set_set_l ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Set_OCollect_001t__Set__Oset_Itf__r_J,type,
% 3.19/1.60 collect_set_r: ( set_r > $o ) > set_set_r ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Set_OCollect_001t__Sum____Type__Osum_Itf__l_Mtf__l_J,type,
% 3.19/1.60 collect_Sum_sum_l_l: ( sum_sum_l_l > $o ) > set_Sum_sum_l_l ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Set_OCollect_001t__Sum____Type__Osum_Itf__l_Mtf__r_J,type,
% 3.19/1.60 collect_Sum_sum_l_r: ( sum_sum_l_r > $o ) > set_Sum_sum_l_r ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Set_OCollect_001t__Sum____Type__Osum_Itf__r_Mtf__l_J,type,
% 3.19/1.60 collect_Sum_sum_r_l: ( sum_sum_r_l > $o ) > set_Sum_sum_r_l ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Set_OCollect_001tf__l,type,
% 3.19/1.60 collect_l: ( l > $o ) > set_l ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Set_OCollect_001tf__r,type,
% 3.19/1.60 collect_r: ( r > $o ) > set_r ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_Substitution_Osubstitution_001tf__r_001tf__l_001tf__v,type,
% 3.19/1.60 substitution_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_member_001t__Set__Oset_Itf__l_J,type,
% 3.19/1.60 member_set_l: set_l > set_set_l > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_member_001t__Set__Oset_Itf__r_J,type,
% 3.19/1.60 member_set_r: set_r > set_set_r > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_member_001tf__l,type,
% 3.19/1.60 member_l: l > set_l > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_c_member_001tf__r,type,
% 3.19/1.60 member_r: r > set_r > $o ).
% 3.19/1.60
% 3.19/1.60 thf(sy_v__092_060E_062____,type,
% 3.19/1.60 e: cntxt_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_v__092_060alpha_062,type,
% 3.19/1.60 alpha: r > r ).
% 3.19/1.60
% 3.19/1.60 thf(sy_v__092_060beta_062,type,
% 3.19/1.60 beta: l > l ).
% 3.19/1.60
% 3.19/1.60 thf(sy_v__092_060sigma_062____,type,
% 3.19/1.60 sigma: l > option_val_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_v__092_060tau_062____,type,
% 3.19/1.60 tau: l > option_val_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_v_e____,type,
% 3.19/1.60 e2: expr_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_v_r,type,
% 3.19/1.60 r2: r ).
% 3.19/1.60
% 3.19/1.60 thf(sy_v_r_H____,type,
% 3.19/1.60 r3: r ).
% 3.19/1.60
% 3.19/1.60 thf(sy_v_s,type,
% 3.19/1.60 s: r > option1457017436_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_v_s_H,type,
% 3.19/1.60 s2: r > option1457017436_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(sy_v_subst,type,
% 3.19/1.60 subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(fact_0_local_Ofork_I2_J,axiom,
% 3.19/1.60 ( ( s @ r2 )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( rfork_r_l_v @ e2 ) ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_1_expr_Oinject_I7_J,axiom,
% 3.19/1.60 ! [X7: expr_r_l_v,Y7: expr_r_l_v] :
% 3.19/1.60 ( ( ( rfork_r_l_v @ X7 )
% 3.19/1.60 = ( rfork_r_l_v @ Y7 ) )
% 3.19/1.60 = ( X7 = Y7 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_2_injective__cntxt,axiom,
% 3.19/1.60 ! [E: cntxt_r_l_v,E1: expr_r_l_v,E2: expr_r_l_v] :
% 3.19/1.60 ( ( ( plug_r_l_v @ E @ E1 )
% 3.19/1.60 = ( plug_r_l_v @ E @ E2 ) )
% 3.19/1.60 = ( E1 = E2 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_3_fun__upd__upd,axiom,
% 3.19/1.60 ! [F: r > option1457017436_r_l_v,X: r,Y: option1457017436_r_l_v,Z: option1457017436_r_l_v] :
% 3.19/1.60 ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ F @ X @ Y ) @ X @ Z )
% 3.19/1.60 = ( fun_up709272714_r_l_v @ F @ X @ Z ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_4_fun__upd__upd,axiom,
% 3.19/1.60 ! [F: l > option_val_r_l_v,X: l,Y: option_val_r_l_v,Z: option_val_r_l_v] :
% 3.19/1.60 ( ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ F @ X @ Y ) @ X @ Z )
% 3.19/1.60 = ( fun_up1835647912_r_l_v @ F @ X @ Z ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_5_fun__upd__triv,axiom,
% 3.19/1.60 ! [F: r > option1457017436_r_l_v,X: r] :
% 3.19/1.60 ( ( fun_up709272714_r_l_v @ F @ X @ ( F @ X ) )
% 3.19/1.60 = F ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_6_fun__upd__triv,axiom,
% 3.19/1.60 ! [F: l > option_val_r_l_v,X: l] :
% 3.19/1.60 ( ( fun_up1835647912_r_l_v @ F @ X @ ( F @ X ) )
% 3.19/1.60 = F ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_7_fun__upd__apply,axiom,
% 3.19/1.60 ( fun_up709272714_r_l_v
% 3.19/1.60 = ( ^ [F2: r > option1457017436_r_l_v,X2: r,Y2: option1457017436_r_l_v,Z2: r] : ( if_opt1153928738_r_l_v @ ( Z2 = X2 ) @ Y2 @ ( F2 @ Z2 ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_8_fun__upd__apply,axiom,
% 3.19/1.60 ( fun_up1835647912_r_l_v
% 3.19/1.60 = ( ^ [F2: l > option_val_r_l_v,X2: l,Y2: option_val_r_l_v,Z2: l] : ( if_option_val_r_l_v @ ( Z2 = X2 ) @ Y2 @ ( F2 @ Z2 ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_9_option_Oinject,axiom,
% 3.19/1.60 ! [X22: produc1156025366_r_l_v,Y22: produc1156025366_r_l_v] :
% 3.19/1.60 ( ( ( some_P1807977723_r_l_v @ X22 )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ Y22 ) )
% 3.19/1.60 = ( X22 = Y22 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_10_option_Oinject,axiom,
% 3.19/1.60 ! [X22: val_r_l_v,Y22: val_r_l_v] :
% 3.19/1.60 ( ( ( some_val_r_l_v @ X22 )
% 3.19/1.60 = ( some_val_r_l_v @ Y22 ) )
% 3.19/1.60 = ( X22 = Y22 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_11_prod_Oinject,axiom,
% 3.19/1.60 ! [X1: r > r,X22: produc1489027110_r_l_v,Y1: r > r,Y22: produc1489027110_r_l_v] :
% 3.19/1.60 ( ( ( produc2111504612_r_l_v @ X1 @ X22 )
% 3.19/1.60 = ( produc2111504612_r_l_v @ Y1 @ Y22 ) )
% 3.19/1.60 = ( ( X1 = Y1 )
% 3.19/1.60 & ( X22 = Y22 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_12_prod_Oinject,axiom,
% 3.19/1.60 ! [X1: l > l,X22: produc1156025366_r_l_v,Y1: l > l,Y22: produc1156025366_r_l_v] :
% 3.19/1.60 ( ( ( produc2057232216_r_l_v @ X1 @ X22 )
% 3.19/1.60 = ( produc2057232216_r_l_v @ Y1 @ Y22 ) )
% 3.19/1.60 = ( ( X1 = Y1 )
% 3.19/1.60 & ( X22 = Y22 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_13_prod_Oinject,axiom,
% 3.19/1.60 ! [X1: l > option_val_r_l_v,X22: produc1164766533_r_l_v,Y1: l > option_val_r_l_v,Y22: produc1164766533_r_l_v] :
% 3.19/1.60 ( ( ( produc297528454_r_l_v @ X1 @ X22 )
% 3.19/1.60 = ( produc297528454_r_l_v @ Y1 @ Y22 ) )
% 3.19/1.60 = ( ( X1 = Y1 )
% 3.19/1.60 & ( X22 = Y22 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_14_prod_Oinject,axiom,
% 3.19/1.60 ! [X1: l > option_val_r_l_v,X22: expr_r_l_v,Y1: l > option_val_r_l_v,Y22: expr_r_l_v] :
% 3.19/1.60 ( ( ( produc1834103605_r_l_v @ X1 @ X22 )
% 3.19/1.60 = ( produc1834103605_r_l_v @ Y1 @ Y22 ) )
% 3.19/1.60 = ( ( X1 = Y1 )
% 3.19/1.60 & ( X22 = Y22 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_15_old_Oprod_Oinject,axiom,
% 3.19/1.60 ! [A: r > r,B: produc1489027110_r_l_v,A2: r > r,B2: produc1489027110_r_l_v] :
% 3.19/1.60 ( ( ( produc2111504612_r_l_v @ A @ B )
% 3.19/1.60 = ( produc2111504612_r_l_v @ A2 @ B2 ) )
% 3.19/1.60 = ( ( A = A2 )
% 3.19/1.60 & ( B = B2 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_16_old_Oprod_Oinject,axiom,
% 3.19/1.60 ! [A: l > l,B: produc1156025366_r_l_v,A2: l > l,B2: produc1156025366_r_l_v] :
% 3.19/1.60 ( ( ( produc2057232216_r_l_v @ A @ B )
% 3.19/1.60 = ( produc2057232216_r_l_v @ A2 @ B2 ) )
% 3.19/1.60 = ( ( A = A2 )
% 3.19/1.60 & ( B = B2 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_17_old_Oprod_Oinject,axiom,
% 3.19/1.60 ! [A: l > option_val_r_l_v,B: produc1164766533_r_l_v,A2: l > option_val_r_l_v,B2: produc1164766533_r_l_v] :
% 3.19/1.60 ( ( ( produc297528454_r_l_v @ A @ B )
% 3.19/1.60 = ( produc297528454_r_l_v @ A2 @ B2 ) )
% 3.19/1.60 = ( ( A = A2 )
% 3.19/1.60 & ( B = B2 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_18_old_Oprod_Oinject,axiom,
% 3.19/1.60 ! [A: l > option_val_r_l_v,B: expr_r_l_v,A2: l > option_val_r_l_v,B2: expr_r_l_v] :
% 3.19/1.60 ( ( ( produc1834103605_r_l_v @ A @ B )
% 3.19/1.60 = ( produc1834103605_r_l_v @ A2 @ B2 ) )
% 3.19/1.60 = ( ( A = A2 )
% 3.19/1.60 & ( B = B2 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_19_LID__local__store_Ocases,axiom,
% 3.19/1.60 ! [X: produc1156025366_r_l_v] :
% 3.19/1.60 ~ ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E3: expr_r_l_v] :
% 3.19/1.60 ( X
% 3.19/1.60 != ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_20_LID__local__store_Oinduct,axiom,
% 3.19/1.60 ! [P: produc1156025366_r_l_v > $o,A0: produc1156025366_r_l_v] :
% 3.19/1.60 ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E3: expr_r_l_v] : ( P @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) )
% 3.19/1.60 => ( P @ A0 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_21__092_060R_062_092_060_094sub_062L_Oinduct,axiom,
% 3.19/1.60 ! [P: ( r > r ) > ( l > l ) > produc1156025366_r_l_v > $o,A0: r > r,A1: l > l,A22: produc1156025366_r_l_v] :
% 3.19/1.60 ( ! [Alpha: r > r,Beta: l > l,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E3: expr_r_l_v] : ( P @ Alpha @ Beta @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) )
% 3.19/1.60 => ( P @ A0 @ A1 @ A22 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_22_map__upd__eqD1,axiom,
% 3.19/1.60 ! [M: r > option1457017436_r_l_v,A: r,X: produc1156025366_r_l_v,N: r > option1457017436_r_l_v,Y: produc1156025366_r_l_v] :
% 3.19/1.60 ( ( ( fun_up709272714_r_l_v @ M @ A @ ( some_P1807977723_r_l_v @ X ) )
% 3.19/1.60 = ( fun_up709272714_r_l_v @ N @ A @ ( some_P1807977723_r_l_v @ Y ) ) )
% 3.19/1.60 => ( X = Y ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_23_map__upd__eqD1,axiom,
% 3.19/1.60 ! [M: l > option_val_r_l_v,A: l,X: val_r_l_v,N: l > option_val_r_l_v,Y: val_r_l_v] :
% 3.19/1.60 ( ( ( fun_up1835647912_r_l_v @ M @ A @ ( some_val_r_l_v @ X ) )
% 3.19/1.60 = ( fun_up1835647912_r_l_v @ N @ A @ ( some_val_r_l_v @ Y ) ) )
% 3.19/1.60 => ( X = Y ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_24__092_060R_062_092_060_094sub_062L_Ocases,axiom,
% 3.19/1.60 ! [X: produc1394974636_r_l_v] :
% 3.19/1.60 ~ ! [Alpha: r > r,Beta: l > l,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E3: expr_r_l_v] :
% 3.19/1.60 ( X
% 3.19/1.60 != ( produc2111504612_r_l_v @ Alpha @ ( produc2057232216_r_l_v @ Beta @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_25_old_Oprod_Oinducts,axiom,
% 3.19/1.60 ! [P: produc1394974636_r_l_v > $o,Prod: produc1394974636_r_l_v] :
% 3.19/1.60 ( ! [A3: r > r,B3: produc1489027110_r_l_v] : ( P @ ( produc2111504612_r_l_v @ A3 @ B3 ) )
% 3.19/1.60 => ( P @ Prod ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_26_old_Oprod_Oinducts,axiom,
% 3.19/1.60 ! [P: produc1489027110_r_l_v > $o,Prod: produc1489027110_r_l_v] :
% 3.19/1.60 ( ! [A3: l > l,B3: produc1156025366_r_l_v] : ( P @ ( produc2057232216_r_l_v @ A3 @ B3 ) )
% 3.19/1.60 => ( P @ Prod ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_27_old_Oprod_Oinducts,axiom,
% 3.19/1.60 ! [P: produc1156025366_r_l_v > $o,Prod: produc1156025366_r_l_v] :
% 3.19/1.60 ( ! [A3: l > option_val_r_l_v,B3: produc1164766533_r_l_v] : ( P @ ( produc297528454_r_l_v @ A3 @ B3 ) )
% 3.19/1.60 => ( P @ Prod ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_28_old_Oprod_Oinducts,axiom,
% 3.19/1.60 ! [P: produc1164766533_r_l_v > $o,Prod: produc1164766533_r_l_v] :
% 3.19/1.60 ( ! [A3: l > option_val_r_l_v,B3: expr_r_l_v] : ( P @ ( produc1834103605_r_l_v @ A3 @ B3 ) )
% 3.19/1.60 => ( P @ Prod ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_29_old_Oprod_Oexhaust,axiom,
% 3.19/1.60 ! [Y: produc1394974636_r_l_v] :
% 3.19/1.60 ~ ! [A3: r > r,B3: produc1489027110_r_l_v] :
% 3.19/1.60 ( Y
% 3.19/1.60 != ( produc2111504612_r_l_v @ A3 @ B3 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_30_old_Oprod_Oexhaust,axiom,
% 3.19/1.60 ! [Y: produc1489027110_r_l_v] :
% 3.19/1.60 ~ ! [A3: l > l,B3: produc1156025366_r_l_v] :
% 3.19/1.60 ( Y
% 3.19/1.60 != ( produc2057232216_r_l_v @ A3 @ B3 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_31_old_Oprod_Oexhaust,axiom,
% 3.19/1.60 ! [Y: produc1156025366_r_l_v] :
% 3.19/1.60 ~ ! [A3: l > option_val_r_l_v,B3: produc1164766533_r_l_v] :
% 3.19/1.60 ( Y
% 3.19/1.60 != ( produc297528454_r_l_v @ A3 @ B3 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_32_old_Oprod_Oexhaust,axiom,
% 3.19/1.60 ! [Y: produc1164766533_r_l_v] :
% 3.19/1.60 ~ ! [A3: l > option_val_r_l_v,B3: expr_r_l_v] :
% 3.19/1.60 ( Y
% 3.19/1.60 != ( produc1834103605_r_l_v @ A3 @ B3 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_33_Pair__inject,axiom,
% 3.19/1.60 ! [A: r > r,B: produc1489027110_r_l_v,A2: r > r,B2: produc1489027110_r_l_v] :
% 3.19/1.60 ( ( ( produc2111504612_r_l_v @ A @ B )
% 3.19/1.60 = ( produc2111504612_r_l_v @ A2 @ B2 ) )
% 3.19/1.60 => ~ ( ( A = A2 )
% 3.19/1.60 => ( B != B2 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_34_Pair__inject,axiom,
% 3.19/1.60 ! [A: l > l,B: produc1156025366_r_l_v,A2: l > l,B2: produc1156025366_r_l_v] :
% 3.19/1.60 ( ( ( produc2057232216_r_l_v @ A @ B )
% 3.19/1.60 = ( produc2057232216_r_l_v @ A2 @ B2 ) )
% 3.19/1.60 => ~ ( ( A = A2 )
% 3.19/1.60 => ( B != B2 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_35_Pair__inject,axiom,
% 3.19/1.60 ! [A: l > option_val_r_l_v,B: produc1164766533_r_l_v,A2: l > option_val_r_l_v,B2: produc1164766533_r_l_v] :
% 3.19/1.60 ( ( ( produc297528454_r_l_v @ A @ B )
% 3.19/1.60 = ( produc297528454_r_l_v @ A2 @ B2 ) )
% 3.19/1.60 => ~ ( ( A = A2 )
% 3.19/1.60 => ( B != B2 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_36_Pair__inject,axiom,
% 3.19/1.60 ! [A: l > option_val_r_l_v,B: expr_r_l_v,A2: l > option_val_r_l_v,B2: expr_r_l_v] :
% 3.19/1.60 ( ( ( produc1834103605_r_l_v @ A @ B )
% 3.19/1.60 = ( produc1834103605_r_l_v @ A2 @ B2 ) )
% 3.19/1.60 => ~ ( ( A = A2 )
% 3.19/1.60 => ( B != B2 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_37_prod__cases,axiom,
% 3.19/1.60 ! [P: produc1394974636_r_l_v > $o,P2: produc1394974636_r_l_v] :
% 3.19/1.60 ( ! [A3: r > r,B3: produc1489027110_r_l_v] : ( P @ ( produc2111504612_r_l_v @ A3 @ B3 ) )
% 3.19/1.60 => ( P @ P2 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_38_prod__cases,axiom,
% 3.19/1.60 ! [P: produc1489027110_r_l_v > $o,P2: produc1489027110_r_l_v] :
% 3.19/1.60 ( ! [A3: l > l,B3: produc1156025366_r_l_v] : ( P @ ( produc2057232216_r_l_v @ A3 @ B3 ) )
% 3.19/1.60 => ( P @ P2 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_39_prod__cases,axiom,
% 3.19/1.60 ! [P: produc1156025366_r_l_v > $o,P2: produc1156025366_r_l_v] :
% 3.19/1.60 ( ! [A3: l > option_val_r_l_v,B3: produc1164766533_r_l_v] : ( P @ ( produc297528454_r_l_v @ A3 @ B3 ) )
% 3.19/1.60 => ( P @ P2 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_40_prod__cases,axiom,
% 3.19/1.60 ! [P: produc1164766533_r_l_v > $o,P2: produc1164766533_r_l_v] :
% 3.19/1.60 ( ! [A3: l > option_val_r_l_v,B3: expr_r_l_v] : ( P @ ( produc1834103605_r_l_v @ A3 @ B3 ) )
% 3.19/1.60 => ( P @ P2 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_41_surj__pair,axiom,
% 3.19/1.60 ! [P2: produc1394974636_r_l_v] :
% 3.19/1.60 ? [X3: r > r,Y3: produc1489027110_r_l_v] :
% 3.19/1.60 ( P2
% 3.19/1.60 = ( produc2111504612_r_l_v @ X3 @ Y3 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_42_surj__pair,axiom,
% 3.19/1.60 ! [P2: produc1489027110_r_l_v] :
% 3.19/1.60 ? [X3: l > l,Y3: produc1156025366_r_l_v] :
% 3.19/1.60 ( P2
% 3.19/1.60 = ( produc2057232216_r_l_v @ X3 @ Y3 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_43_surj__pair,axiom,
% 3.19/1.60 ! [P2: produc1156025366_r_l_v] :
% 3.19/1.60 ? [X3: l > option_val_r_l_v,Y3: produc1164766533_r_l_v] :
% 3.19/1.60 ( P2
% 3.19/1.60 = ( produc297528454_r_l_v @ X3 @ Y3 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_44_surj__pair,axiom,
% 3.19/1.60 ! [P2: produc1164766533_r_l_v] :
% 3.19/1.60 ? [X3: l > option_val_r_l_v,Y3: expr_r_l_v] :
% 3.19/1.60 ( P2
% 3.19/1.60 = ( produc1834103605_r_l_v @ X3 @ Y3 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_45_fun__upd__idem__iff,axiom,
% 3.19/1.60 ! [F: r > option1457017436_r_l_v,X: r,Y: option1457017436_r_l_v] :
% 3.19/1.60 ( ( ( fun_up709272714_r_l_v @ F @ X @ Y )
% 3.19/1.60 = F )
% 3.19/1.60 = ( ( F @ X )
% 3.19/1.60 = Y ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_46_fun__upd__idem__iff,axiom,
% 3.19/1.60 ! [F: l > option_val_r_l_v,X: l,Y: option_val_r_l_v] :
% 3.19/1.60 ( ( ( fun_up1835647912_r_l_v @ F @ X @ Y )
% 3.19/1.60 = F )
% 3.19/1.60 = ( ( F @ X )
% 3.19/1.60 = Y ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_47_fun__upd__twist,axiom,
% 3.19/1.60 ! [A: r,C: r,M: r > option1457017436_r_l_v,B: option1457017436_r_l_v,D: option1457017436_r_l_v] :
% 3.19/1.60 ( ( A != C )
% 3.19/1.60 => ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ M @ A @ B ) @ C @ D )
% 3.19/1.60 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ M @ C @ D ) @ A @ B ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_48_fun__upd__twist,axiom,
% 3.19/1.60 ! [A: l,C: l,M: l > option_val_r_l_v,B: option_val_r_l_v,D: option_val_r_l_v] :
% 3.19/1.60 ( ( A != C )
% 3.19/1.60 => ( ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ M @ A @ B ) @ C @ D )
% 3.19/1.60 = ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ M @ C @ D ) @ A @ B ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_49_fun__upd__other,axiom,
% 3.19/1.60 ! [Z: r,X: r,F: r > option1457017436_r_l_v,Y: option1457017436_r_l_v] :
% 3.19/1.60 ( ( Z != X )
% 3.19/1.60 => ( ( fun_up709272714_r_l_v @ F @ X @ Y @ Z )
% 3.19/1.60 = ( F @ Z ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_50_fun__upd__other,axiom,
% 3.19/1.60 ! [Z: l,X: l,F: l > option_val_r_l_v,Y: option_val_r_l_v] :
% 3.19/1.60 ( ( Z != X )
% 3.19/1.60 => ( ( fun_up1835647912_r_l_v @ F @ X @ Y @ Z )
% 3.19/1.60 = ( F @ Z ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_51_fun__upd__same,axiom,
% 3.19/1.60 ! [F: r > option1457017436_r_l_v,X: r,Y: option1457017436_r_l_v] :
% 3.19/1.60 ( ( fun_up709272714_r_l_v @ F @ X @ Y @ X )
% 3.19/1.60 = Y ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_52_fun__upd__same,axiom,
% 3.19/1.60 ! [F: l > option_val_r_l_v,X: l,Y: option_val_r_l_v] :
% 3.19/1.60 ( ( fun_up1835647912_r_l_v @ F @ X @ Y @ X )
% 3.19/1.60 = Y ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_53_fun__upd__idem,axiom,
% 3.19/1.60 ! [F: r > option1457017436_r_l_v,X: r,Y: option1457017436_r_l_v] :
% 3.19/1.60 ( ( ( F @ X )
% 3.19/1.60 = Y )
% 3.19/1.60 => ( ( fun_up709272714_r_l_v @ F @ X @ Y )
% 3.19/1.60 = F ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_54_fun__upd__idem,axiom,
% 3.19/1.60 ! [F: l > option_val_r_l_v,X: l,Y: option_val_r_l_v] :
% 3.19/1.60 ( ( ( F @ X )
% 3.19/1.60 = Y )
% 3.19/1.60 => ( ( fun_up1835647912_r_l_v @ F @ X @ Y )
% 3.19/1.60 = F ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_55_fun__upd__eqD,axiom,
% 3.19/1.60 ! [F: r > option1457017436_r_l_v,X: r,Y: option1457017436_r_l_v,G: r > option1457017436_r_l_v,Z: option1457017436_r_l_v] :
% 3.19/1.60 ( ( ( fun_up709272714_r_l_v @ F @ X @ Y )
% 3.19/1.60 = ( fun_up709272714_r_l_v @ G @ X @ Z ) )
% 3.19/1.60 => ( Y = Z ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_56_fun__upd__eqD,axiom,
% 3.19/1.60 ! [F: l > option_val_r_l_v,X: l,Y: option_val_r_l_v,G: l > option_val_r_l_v,Z: option_val_r_l_v] :
% 3.19/1.60 ( ( ( fun_up1835647912_r_l_v @ F @ X @ Y )
% 3.19/1.60 = ( fun_up1835647912_r_l_v @ G @ X @ Z ) )
% 3.19/1.60 => ( Y = Z ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_57_fun__upd__def,axiom,
% 3.19/1.60 ( fun_up709272714_r_l_v
% 3.19/1.60 = ( ^ [F2: r > option1457017436_r_l_v,A4: r,B4: option1457017436_r_l_v,X2: r] : ( if_opt1153928738_r_l_v @ ( X2 = A4 ) @ B4 @ ( F2 @ X2 ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_58_fun__upd__def,axiom,
% 3.19/1.60 ( fun_up1835647912_r_l_v
% 3.19/1.60 = ( ^ [F2: l > option_val_r_l_v,A4: l,B4: option_val_r_l_v,X2: l] : ( if_option_val_r_l_v @ ( X2 = A4 ) @ B4 @ ( F2 @ X2 ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_59_prod__induct5,axiom,
% 3.19/1.60 ! [P: produc1394974636_r_l_v > $o,X: produc1394974636_r_l_v] :
% 3.19/1.60 ( ! [A3: r > r,B3: l > l,C2: l > option_val_r_l_v,D2: l > option_val_r_l_v,E3: expr_r_l_v] : ( P @ ( produc2111504612_r_l_v @ A3 @ ( produc2057232216_r_l_v @ B3 @ ( produc297528454_r_l_v @ C2 @ ( produc1834103605_r_l_v @ D2 @ E3 ) ) ) ) )
% 3.19/1.60 => ( P @ X ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_60_prod__induct4,axiom,
% 3.19/1.60 ! [P: produc1394974636_r_l_v > $o,X: produc1394974636_r_l_v] :
% 3.19/1.60 ( ! [A3: r > r,B3: l > l,C2: l > option_val_r_l_v,D2: produc1164766533_r_l_v] : ( P @ ( produc2111504612_r_l_v @ A3 @ ( produc2057232216_r_l_v @ B3 @ ( produc297528454_r_l_v @ C2 @ D2 ) ) ) )
% 3.19/1.60 => ( P @ X ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_61_prod__induct4,axiom,
% 3.19/1.60 ! [P: produc1489027110_r_l_v > $o,X: produc1489027110_r_l_v] :
% 3.19/1.60 ( ! [A3: l > l,B3: l > option_val_r_l_v,C2: l > option_val_r_l_v,D2: expr_r_l_v] : ( P @ ( produc2057232216_r_l_v @ A3 @ ( produc297528454_r_l_v @ B3 @ ( produc1834103605_r_l_v @ C2 @ D2 ) ) ) )
% 3.19/1.60 => ( P @ X ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_62_prod__induct3,axiom,
% 3.19/1.60 ! [P: produc1394974636_r_l_v > $o,X: produc1394974636_r_l_v] :
% 3.19/1.60 ( ! [A3: r > r,B3: l > l,C2: produc1156025366_r_l_v] : ( P @ ( produc2111504612_r_l_v @ A3 @ ( produc2057232216_r_l_v @ B3 @ C2 ) ) )
% 3.19/1.60 => ( P @ X ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_63_prod__induct3,axiom,
% 3.19/1.60 ! [P: produc1489027110_r_l_v > $o,X: produc1489027110_r_l_v] :
% 3.19/1.60 ( ! [A3: l > l,B3: l > option_val_r_l_v,C2: produc1164766533_r_l_v] : ( P @ ( produc2057232216_r_l_v @ A3 @ ( produc297528454_r_l_v @ B3 @ C2 ) ) )
% 3.19/1.60 => ( P @ X ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_64_prod__induct3,axiom,
% 3.19/1.60 ! [P: produc1156025366_r_l_v > $o,X: produc1156025366_r_l_v] :
% 3.19/1.60 ( ! [A3: l > option_val_r_l_v,B3: l > option_val_r_l_v,C2: expr_r_l_v] : ( P @ ( produc297528454_r_l_v @ A3 @ ( produc1834103605_r_l_v @ B3 @ C2 ) ) )
% 3.19/1.60 => ( P @ X ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_65_prod__cases5,axiom,
% 3.19/1.60 ! [Y: produc1394974636_r_l_v] :
% 3.19/1.60 ~ ! [A3: r > r,B3: l > l,C2: l > option_val_r_l_v,D2: l > option_val_r_l_v,E3: expr_r_l_v] :
% 3.19/1.60 ( Y
% 3.19/1.60 != ( produc2111504612_r_l_v @ A3 @ ( produc2057232216_r_l_v @ B3 @ ( produc297528454_r_l_v @ C2 @ ( produc1834103605_r_l_v @ D2 @ E3 ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_66_prod__cases4,axiom,
% 3.19/1.60 ! [Y: produc1394974636_r_l_v] :
% 3.19/1.60 ~ ! [A3: r > r,B3: l > l,C2: l > option_val_r_l_v,D2: produc1164766533_r_l_v] :
% 3.19/1.60 ( Y
% 3.19/1.60 != ( produc2111504612_r_l_v @ A3 @ ( produc2057232216_r_l_v @ B3 @ ( produc297528454_r_l_v @ C2 @ D2 ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_67_prod__cases4,axiom,
% 3.19/1.60 ! [Y: produc1489027110_r_l_v] :
% 3.19/1.60 ~ ! [A3: l > l,B3: l > option_val_r_l_v,C2: l > option_val_r_l_v,D2: expr_r_l_v] :
% 3.19/1.60 ( Y
% 3.19/1.60 != ( produc2057232216_r_l_v @ A3 @ ( produc297528454_r_l_v @ B3 @ ( produc1834103605_r_l_v @ C2 @ D2 ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_68_prod__cases3,axiom,
% 3.19/1.60 ! [Y: produc1394974636_r_l_v] :
% 3.19/1.60 ~ ! [A3: r > r,B3: l > l,C2: produc1156025366_r_l_v] :
% 3.19/1.60 ( Y
% 3.19/1.60 != ( produc2111504612_r_l_v @ A3 @ ( produc2057232216_r_l_v @ B3 @ C2 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_69_prod__cases3,axiom,
% 3.19/1.60 ! [Y: produc1489027110_r_l_v] :
% 3.19/1.60 ~ ! [A3: l > l,B3: l > option_val_r_l_v,C2: produc1164766533_r_l_v] :
% 3.19/1.60 ( Y
% 3.19/1.60 != ( produc2057232216_r_l_v @ A3 @ ( produc297528454_r_l_v @ B3 @ C2 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_70_prod__cases3,axiom,
% 3.19/1.60 ! [Y: produc1156025366_r_l_v] :
% 3.19/1.60 ~ ! [A3: l > option_val_r_l_v,B3: l > option_val_r_l_v,C2: expr_r_l_v] :
% 3.19/1.60 ( Y
% 3.19/1.60 != ( produc297528454_r_l_v @ A3 @ ( produc1834103605_r_l_v @ B3 @ C2 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_71_map__upd__Some__unfold,axiom,
% 3.19/1.60 ! [M: r > option1457017436_r_l_v,A: r,B: produc1156025366_r_l_v,X: r,Y: produc1156025366_r_l_v] :
% 3.19/1.60 ( ( ( fun_up709272714_r_l_v @ M @ A @ ( some_P1807977723_r_l_v @ B ) @ X )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ Y ) )
% 3.19/1.60 = ( ( ( X = A )
% 3.19/1.60 & ( B = Y ) )
% 3.19/1.60 | ( ( X != A )
% 3.19/1.60 & ( ( M @ X )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ Y ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_72_map__upd__Some__unfold,axiom,
% 3.19/1.60 ! [M: l > option_val_r_l_v,A: l,B: val_r_l_v,X: l,Y: val_r_l_v] :
% 3.19/1.60 ( ( ( fun_up1835647912_r_l_v @ M @ A @ ( some_val_r_l_v @ B ) @ X )
% 3.19/1.60 = ( some_val_r_l_v @ Y ) )
% 3.19/1.60 = ( ( ( X = A )
% 3.19/1.60 & ( B = Y ) )
% 3.19/1.60 | ( ( X != A )
% 3.19/1.60 & ( ( M @ X )
% 3.19/1.60 = ( some_val_r_l_v @ Y ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_73_map__upd__triv,axiom,
% 3.19/1.60 ! [T: r > option1457017436_r_l_v,K: r,X: produc1156025366_r_l_v] :
% 3.19/1.60 ( ( ( T @ K )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ X ) )
% 3.19/1.60 => ( ( fun_up709272714_r_l_v @ T @ K @ ( some_P1807977723_r_l_v @ X ) )
% 3.19/1.60 = T ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_74_map__upd__triv,axiom,
% 3.19/1.60 ! [T: l > option_val_r_l_v,K: l,X: val_r_l_v] :
% 3.19/1.60 ( ( ( T @ K )
% 3.19/1.60 = ( some_val_r_l_v @ X ) )
% 3.19/1.60 => ( ( fun_up1835647912_r_l_v @ T @ K @ ( some_val_r_l_v @ X ) )
% 3.19/1.60 = T ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_75_LID__local__store_Osimps,axiom,
% 3.19/1.60 ! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E4: expr_r_l_v] :
% 3.19/1.60 ( ( lID_lo1265057957_l_r_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ E4 ) ) )
% 3.19/1.60 = Tau2 ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_76_LID__local__store_Oelims,axiom,
% 3.19/1.60 ! [X: produc1156025366_r_l_v,Y: l > option_val_r_l_v] :
% 3.19/1.60 ( ( ( lID_lo1265057957_l_r_v @ X )
% 3.19/1.60 = Y )
% 3.19/1.60 => ~ ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v] :
% 3.19/1.60 ( ? [E3: expr_r_l_v] :
% 3.19/1.60 ( X
% 3.19/1.60 = ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) )
% 3.19/1.60 => ( Y != Tau ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_77_LID__expression_Osimps,axiom,
% 3.19/1.60 ! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E4: expr_r_l_v] :
% 3.19/1.60 ( ( lID_expression_l_r_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ E4 ) ) )
% 3.19/1.60 = E4 ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_78_LID__expression_Oelims,axiom,
% 3.19/1.60 ! [X: produc1156025366_r_l_v,Y: expr_r_l_v] :
% 3.19/1.60 ( ( ( lID_expression_l_r_v @ X )
% 3.19/1.60 = Y )
% 3.19/1.60 => ~ ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E3: expr_r_l_v] :
% 3.19/1.60 ( ( X
% 3.19/1.60 = ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) )
% 3.19/1.60 => ( Y != E3 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_79_mem__Collect__eq,axiom,
% 3.19/1.60 ! [A: set_l,P: set_l > $o] :
% 3.19/1.60 ( ( member_set_l @ A @ ( collect_set_l @ P ) )
% 3.19/1.60 = ( P @ A ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_80_mem__Collect__eq,axiom,
% 3.19/1.60 ! [A: set_r,P: set_r > $o] :
% 3.19/1.60 ( ( member_set_r @ A @ ( collect_set_r @ P ) )
% 3.19/1.60 = ( P @ A ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_81_mem__Collect__eq,axiom,
% 3.19/1.60 ! [A: r,P: r > $o] :
% 3.19/1.60 ( ( member_r @ A @ ( collect_r @ P ) )
% 3.19/1.60 = ( P @ A ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_82_mem__Collect__eq,axiom,
% 3.19/1.60 ! [A: l,P: l > $o] :
% 3.19/1.60 ( ( member_l @ A @ ( collect_l @ P ) )
% 3.19/1.60 = ( P @ A ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_83_Collect__mem__eq,axiom,
% 3.19/1.60 ! [A5: set_set_l] :
% 3.19/1.60 ( ( collect_set_l
% 3.19/1.60 @ ^ [X2: set_l] : ( member_set_l @ X2 @ A5 ) )
% 3.19/1.60 = A5 ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_84_Collect__mem__eq,axiom,
% 3.19/1.60 ! [A5: set_set_r] :
% 3.19/1.60 ( ( collect_set_r
% 3.19/1.60 @ ^ [X2: set_r] : ( member_set_r @ X2 @ A5 ) )
% 3.19/1.60 = A5 ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_85_Collect__mem__eq,axiom,
% 3.19/1.60 ! [A5: set_r] :
% 3.19/1.60 ( ( collect_r
% 3.19/1.60 @ ^ [X2: r] : ( member_r @ X2 @ A5 ) )
% 3.19/1.60 = A5 ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_86_Collect__mem__eq,axiom,
% 3.19/1.60 ! [A5: set_l] :
% 3.19/1.60 ( ( collect_l
% 3.19/1.60 @ ^ [X2: l] : ( member_l @ X2 @ A5 ) )
% 3.19/1.60 = A5 ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_87_Collect__cong,axiom,
% 3.19/1.60 ! [P: l > $o,Q: l > $o] :
% 3.19/1.60 ( ! [X3: l] :
% 3.19/1.60 ( ( P @ X3 )
% 3.19/1.60 = ( Q @ X3 ) )
% 3.19/1.60 => ( ( collect_l @ P )
% 3.19/1.60 = ( collect_l @ Q ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_88_Collect__cong,axiom,
% 3.19/1.60 ! [P: r > $o,Q: r > $o] :
% 3.19/1.60 ( ! [X3: r] :
% 3.19/1.60 ( ( P @ X3 )
% 3.19/1.60 = ( Q @ X3 ) )
% 3.19/1.60 => ( ( collect_r @ P )
% 3.19/1.60 = ( collect_r @ Q ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_89_Collect__cong,axiom,
% 3.19/1.60 ! [P: set_l > $o,Q: set_l > $o] :
% 3.19/1.60 ( ! [X3: set_l] :
% 3.19/1.60 ( ( P @ X3 )
% 3.19/1.60 = ( Q @ X3 ) )
% 3.19/1.60 => ( ( collect_set_l @ P )
% 3.19/1.60 = ( collect_set_l @ Q ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_90_Collect__cong,axiom,
% 3.19/1.60 ! [P: set_r > $o,Q: set_r > $o] :
% 3.19/1.60 ( ! [X3: set_r] :
% 3.19/1.60 ( ( P @ X3 )
% 3.19/1.60 = ( Q @ X3 ) )
% 3.19/1.60 => ( ( collect_set_r @ P )
% 3.19/1.60 = ( collect_set_r @ Q ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_91_local_Ofork_I3_J,axiom,
% 3.19/1.60 ~ ( member_r @ r3 @ ( rID_G_r_l_v @ s ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_92_LID__snapshot_Osimps,axiom,
% 3.19/1.60 ! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E4: expr_r_l_v] :
% 3.19/1.60 ( ( lID_snapshot_l_r_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ E4 ) ) )
% 3.19/1.60 = Sigma2 ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_93_LID__snapshot_Oelims,axiom,
% 3.19/1.60 ! [X: produc1156025366_r_l_v,Y: l > option_val_r_l_v] :
% 3.19/1.60 ( ( ( lID_snapshot_l_r_v @ X )
% 3.19/1.60 = Y )
% 3.19/1.60 => ~ ! [Sigma: l > option_val_r_l_v] :
% 3.19/1.60 ( ? [Tau: l > option_val_r_l_v,E3: expr_r_l_v] :
% 3.19/1.60 ( X
% 3.19/1.60 = ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) )
% 3.19/1.60 => ( Y != Sigma ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_94_local_Ofork_I1_J,axiom,
% 3.19/1.60 ( s2
% 3.19/1.60 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s @ r2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r3 ) ) ) ) ) ) ) @ r3
% 3.19/1.60 @ ( some_P1807977723_r_l_v
% 3.19/1.60 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
% 3.19/1.60 @ ( produc1834103605_r_l_v
% 3.19/1.60 @ ^ [X2: l] : none_val_r_l_v
% 3.19/1.60 @ e2 ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_95_expr_Oinject_I1_J,axiom,
% 3.19/1.60 ! [X1: val_r_l_v,Y1: val_r_l_v] :
% 3.19/1.60 ( ( ( vE_r_l_v @ X1 )
% 3.19/1.60 = ( vE_r_l_v @ Y1 ) )
% 3.19/1.60 = ( X1 = Y1 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_96_val_Oinject_I4_J,axiom,
% 3.19/1.60 ! [X4: r,Y4: r] :
% 3.19/1.60 ( ( ( rid_r_l_v @ X4 )
% 3.19/1.60 = ( rid_r_l_v @ Y4 ) )
% 3.19/1.60 = ( X4 = Y4 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_97_not__None__eq,axiom,
% 3.19/1.60 ! [X: option1457017436_r_l_v] :
% 3.19/1.60 ( ( X != none_P277133687_r_l_v )
% 3.19/1.60 = ( ? [Y2: produc1156025366_r_l_v] :
% 3.19/1.60 ( X
% 3.19/1.60 = ( some_P1807977723_r_l_v @ Y2 ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_98_not__None__eq,axiom,
% 3.19/1.60 ! [X: option_val_r_l_v] :
% 3.19/1.60 ( ( X != none_val_r_l_v )
% 3.19/1.60 = ( ? [Y2: val_r_l_v] :
% 3.19/1.60 ( X
% 3.19/1.60 = ( some_val_r_l_v @ Y2 ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_99_not__Some__eq,axiom,
% 3.19/1.60 ! [X: option1457017436_r_l_v] :
% 3.19/1.60 ( ( ! [Y2: produc1156025366_r_l_v] :
% 3.19/1.60 ( X
% 3.19/1.60 != ( some_P1807977723_r_l_v @ Y2 ) ) )
% 3.19/1.60 = ( X = none_P277133687_r_l_v ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_100_not__Some__eq,axiom,
% 3.19/1.60 ! [X: option_val_r_l_v] :
% 3.19/1.60 ( ( ! [Y2: val_r_l_v] :
% 3.19/1.60 ( X
% 3.19/1.60 != ( some_val_r_l_v @ Y2 ) ) )
% 3.19/1.60 = ( X = none_val_r_l_v ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_101_empty__upd__none,axiom,
% 3.19/1.60 ! [X: l] :
% 3.19/1.60 ( ( fun_up1835647912_r_l_v
% 3.19/1.60 @ ^ [X2: l] : none_val_r_l_v
% 3.19/1.60 @ X
% 3.19/1.60 @ none_val_r_l_v )
% 3.19/1.60 = ( ^ [X2: l] : none_val_r_l_v ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_102_empty__upd__none,axiom,
% 3.19/1.60 ! [X: r] :
% 3.19/1.60 ( ( fun_up709272714_r_l_v
% 3.19/1.60 @ ^ [X2: r] : none_P277133687_r_l_v
% 3.19/1.60 @ X
% 3.19/1.60 @ none_P277133687_r_l_v )
% 3.19/1.60 = ( ^ [X2: r] : none_P277133687_r_l_v ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_103_combine_Oelims,axiom,
% 3.19/1.60 ! [X: l > option_val_r_l_v,Xa: l > option_val_r_l_v,Xb: l,Y: option_val_r_l_v] :
% 3.19/1.60 ( ( ( combine_l_val_r_l_v @ X @ Xa @ Xb )
% 3.19/1.60 = Y )
% 3.19/1.60 => ( ( ( ( Xa @ Xb )
% 3.19/1.60 = none_val_r_l_v )
% 3.19/1.60 => ( Y
% 3.19/1.60 = ( X @ Xb ) ) )
% 3.19/1.60 & ( ( ( Xa @ Xb )
% 3.19/1.60 != none_val_r_l_v )
% 3.19/1.60 => ( Y
% 3.19/1.60 = ( Xa @ Xb ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_104_combine_Osimps,axiom,
% 3.19/1.60 ( combine_l_val_r_l_v
% 3.19/1.60 = ( ^ [F2: l > option_val_r_l_v,G2: l > option_val_r_l_v,X2: l] :
% 3.19/1.60 ( if_option_val_r_l_v
% 3.19/1.60 @ ( ( G2 @ X2 )
% 3.19/1.60 = none_val_r_l_v )
% 3.19/1.60 @ ( F2 @ X2 )
% 3.19/1.60 @ ( G2 @ X2 ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_105_option_Odistinct_I1_J,axiom,
% 3.19/1.60 ! [X22: produc1156025366_r_l_v] :
% 3.19/1.60 ( none_P277133687_r_l_v
% 3.19/1.60 != ( some_P1807977723_r_l_v @ X22 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_106_option_Odistinct_I1_J,axiom,
% 3.19/1.60 ! [X22: val_r_l_v] :
% 3.19/1.60 ( none_val_r_l_v
% 3.19/1.60 != ( some_val_r_l_v @ X22 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_107_option_OdiscI,axiom,
% 3.19/1.60 ! [Option: option1457017436_r_l_v,X22: produc1156025366_r_l_v] :
% 3.19/1.60 ( ( Option
% 3.19/1.60 = ( some_P1807977723_r_l_v @ X22 ) )
% 3.19/1.60 => ( Option != none_P277133687_r_l_v ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_108_option_OdiscI,axiom,
% 3.19/1.60 ! [Option: option_val_r_l_v,X22: val_r_l_v] :
% 3.19/1.60 ( ( Option
% 3.19/1.60 = ( some_val_r_l_v @ X22 ) )
% 3.19/1.60 => ( Option != none_val_r_l_v ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_109_option_Oexhaust,axiom,
% 3.19/1.60 ! [Y: option1457017436_r_l_v] :
% 3.19/1.60 ( ( Y != none_P277133687_r_l_v )
% 3.19/1.60 => ~ ! [X23: produc1156025366_r_l_v] :
% 3.19/1.60 ( Y
% 3.19/1.60 != ( some_P1807977723_r_l_v @ X23 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_110_option_Oexhaust,axiom,
% 3.19/1.60 ! [Y: option_val_r_l_v] :
% 3.19/1.60 ( ( Y != none_val_r_l_v )
% 3.19/1.60 => ~ ! [X23: val_r_l_v] :
% 3.19/1.60 ( Y
% 3.19/1.60 != ( some_val_r_l_v @ X23 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_111_option_Oinducts,axiom,
% 3.19/1.60 ! [P: option1457017436_r_l_v > $o,Option: option1457017436_r_l_v] :
% 3.19/1.60 ( ( P @ none_P277133687_r_l_v )
% 3.19/1.60 => ( ! [X3: produc1156025366_r_l_v] : ( P @ ( some_P1807977723_r_l_v @ X3 ) )
% 3.19/1.60 => ( P @ Option ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_112_option_Oinducts,axiom,
% 3.19/1.60 ! [P: option_val_r_l_v > $o,Option: option_val_r_l_v] :
% 3.19/1.60 ( ( P @ none_val_r_l_v )
% 3.19/1.60 => ( ! [X3: val_r_l_v] : ( P @ ( some_val_r_l_v @ X3 ) )
% 3.19/1.60 => ( P @ Option ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_113_split__option__ex,axiom,
% 3.19/1.60 ( ( ^ [P3: option1457017436_r_l_v > $o] :
% 3.19/1.60 ? [X5: option1457017436_r_l_v] : ( P3 @ X5 ) )
% 3.19/1.60 = ( ^ [P4: option1457017436_r_l_v > $o] :
% 3.19/1.60 ( ( P4 @ none_P277133687_r_l_v )
% 3.19/1.60 | ? [X2: produc1156025366_r_l_v] : ( P4 @ ( some_P1807977723_r_l_v @ X2 ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_114_split__option__ex,axiom,
% 3.19/1.60 ( ( ^ [P3: option_val_r_l_v > $o] :
% 3.19/1.60 ? [X5: option_val_r_l_v] : ( P3 @ X5 ) )
% 3.19/1.60 = ( ^ [P4: option_val_r_l_v > $o] :
% 3.19/1.60 ( ( P4 @ none_val_r_l_v )
% 3.19/1.60 | ? [X2: val_r_l_v] : ( P4 @ ( some_val_r_l_v @ X2 ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_115_split__option__all,axiom,
% 3.19/1.60 ( ( ^ [P3: option1457017436_r_l_v > $o] :
% 3.19/1.60 ! [X5: option1457017436_r_l_v] : ( P3 @ X5 ) )
% 3.19/1.60 = ( ^ [P4: option1457017436_r_l_v > $o] :
% 3.19/1.60 ( ( P4 @ none_P277133687_r_l_v )
% 3.19/1.60 & ! [X2: produc1156025366_r_l_v] : ( P4 @ ( some_P1807977723_r_l_v @ X2 ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_116_split__option__all,axiom,
% 3.19/1.60 ( ( ^ [P3: option_val_r_l_v > $o] :
% 3.19/1.60 ! [X5: option_val_r_l_v] : ( P3 @ X5 ) )
% 3.19/1.60 = ( ^ [P4: option_val_r_l_v > $o] :
% 3.19/1.60 ( ( P4 @ none_val_r_l_v )
% 3.19/1.60 & ! [X2: val_r_l_v] : ( P4 @ ( some_val_r_l_v @ X2 ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_117_combine__options__cases,axiom,
% 3.19/1.60 ! [X: option1457017436_r_l_v,P: option1457017436_r_l_v > option1457017436_r_l_v > $o,Y: option1457017436_r_l_v] :
% 3.19/1.60 ( ( ( X = none_P277133687_r_l_v )
% 3.19/1.60 => ( P @ X @ Y ) )
% 3.19/1.60 => ( ( ( Y = none_P277133687_r_l_v )
% 3.19/1.60 => ( P @ X @ Y ) )
% 3.19/1.60 => ( ! [A3: produc1156025366_r_l_v,B3: produc1156025366_r_l_v] :
% 3.19/1.60 ( ( X
% 3.19/1.60 = ( some_P1807977723_r_l_v @ A3 ) )
% 3.19/1.60 => ( ( Y
% 3.19/1.60 = ( some_P1807977723_r_l_v @ B3 ) )
% 3.19/1.60 => ( P @ X @ Y ) ) )
% 3.19/1.60 => ( P @ X @ Y ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_118_combine__options__cases,axiom,
% 3.19/1.60 ! [X: option1457017436_r_l_v,P: option1457017436_r_l_v > option_val_r_l_v > $o,Y: option_val_r_l_v] :
% 3.19/1.60 ( ( ( X = none_P277133687_r_l_v )
% 3.19/1.60 => ( P @ X @ Y ) )
% 3.19/1.60 => ( ( ( Y = none_val_r_l_v )
% 3.19/1.60 => ( P @ X @ Y ) )
% 3.19/1.60 => ( ! [A3: produc1156025366_r_l_v,B3: val_r_l_v] :
% 3.19/1.60 ( ( X
% 3.19/1.60 = ( some_P1807977723_r_l_v @ A3 ) )
% 3.19/1.60 => ( ( Y
% 3.19/1.60 = ( some_val_r_l_v @ B3 ) )
% 3.19/1.60 => ( P @ X @ Y ) ) )
% 3.19/1.60 => ( P @ X @ Y ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_119_combine__options__cases,axiom,
% 3.19/1.60 ! [X: option_val_r_l_v,P: option_val_r_l_v > option1457017436_r_l_v > $o,Y: option1457017436_r_l_v] :
% 3.19/1.60 ( ( ( X = none_val_r_l_v )
% 3.19/1.60 => ( P @ X @ Y ) )
% 3.19/1.60 => ( ( ( Y = none_P277133687_r_l_v )
% 3.19/1.60 => ( P @ X @ Y ) )
% 3.19/1.60 => ( ! [A3: val_r_l_v,B3: produc1156025366_r_l_v] :
% 3.19/1.60 ( ( X
% 3.19/1.60 = ( some_val_r_l_v @ A3 ) )
% 3.19/1.60 => ( ( Y
% 3.19/1.60 = ( some_P1807977723_r_l_v @ B3 ) )
% 3.19/1.60 => ( P @ X @ Y ) ) )
% 3.19/1.60 => ( P @ X @ Y ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_120_combine__options__cases,axiom,
% 3.19/1.60 ! [X: option_val_r_l_v,P: option_val_r_l_v > option_val_r_l_v > $o,Y: option_val_r_l_v] :
% 3.19/1.60 ( ( ( X = none_val_r_l_v )
% 3.19/1.60 => ( P @ X @ Y ) )
% 3.19/1.60 => ( ( ( Y = none_val_r_l_v )
% 3.19/1.60 => ( P @ X @ Y ) )
% 3.19/1.60 => ( ! [A3: val_r_l_v,B3: val_r_l_v] :
% 3.19/1.60 ( ( X
% 3.19/1.60 = ( some_val_r_l_v @ A3 ) )
% 3.19/1.60 => ( ( Y
% 3.19/1.60 = ( some_val_r_l_v @ B3 ) )
% 3.19/1.60 => ( P @ X @ Y ) ) )
% 3.19/1.60 => ( P @ X @ Y ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_121_expr_Odistinct_I11_J,axiom,
% 3.19/1.60 ! [X1: val_r_l_v,X7: expr_r_l_v] :
% 3.19/1.60 ( ( vE_r_l_v @ X1 )
% 3.19/1.60 != ( rfork_r_l_v @ X7 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_122_map__upd__nonempty,axiom,
% 3.19/1.60 ! [T: r > option1457017436_r_l_v,K: r,X: produc1156025366_r_l_v] :
% 3.19/1.60 ( ( fun_up709272714_r_l_v @ T @ K @ ( some_P1807977723_r_l_v @ X ) )
% 3.19/1.60 != ( ^ [X2: r] : none_P277133687_r_l_v ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_123_map__upd__nonempty,axiom,
% 3.19/1.60 ! [T: l > option_val_r_l_v,K: l,X: val_r_l_v] :
% 3.19/1.60 ( ( fun_up1835647912_r_l_v @ T @ K @ ( some_val_r_l_v @ X ) )
% 3.19/1.60 != ( ^ [X2: l] : none_val_r_l_v ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_124_restrictions__inwards,axiom,
% 3.19/1.60 ! [X: r,X6: r,F: r > option1457017436_r_l_v,Y: produc1156025366_r_l_v] :
% 3.19/1.60 ( ( X != X6 )
% 3.19/1.60 => ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ F @ X @ ( some_P1807977723_r_l_v @ Y ) ) @ X6 @ none_P277133687_r_l_v )
% 3.19/1.60 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ F @ X6 @ none_P277133687_r_l_v ) @ X @ ( some_P1807977723_r_l_v @ Y ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_125_restrictions__inwards,axiom,
% 3.19/1.60 ! [X: l,X6: l,F: l > option_val_r_l_v,Y: val_r_l_v] :
% 3.19/1.60 ( ( X != X6 )
% 3.19/1.60 => ( ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ F @ X @ ( some_val_r_l_v @ Y ) ) @ X6 @ none_val_r_l_v )
% 3.19/1.60 = ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ F @ X6 @ none_val_r_l_v ) @ X @ ( some_val_r_l_v @ Y ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_126_RID_092_060_094sub_062GI_I1_J,axiom,
% 3.19/1.60 ! [S: r > option1457017436_r_l_v,R: r,V: produc1156025366_r_l_v] :
% 3.19/1.60 ( ( ( S @ R )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ V ) )
% 3.19/1.60 => ( member_r @ R @ ( rID_G_r_l_v @ S ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_127_revision__step__relaxed_Ofork,axiom,
% 3.19/1.60 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,E4: expr_r_l_v,R2: r] :
% 3.19/1.60 ( ( ( S @ R )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 3.19/1.60 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 3.19/1.60 => ( revisi1291188644_r_l_v @ subst @ R @ S
% 3.19/1.60 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) @ R2
% 3.19/1.60 @ ( some_P1807977723_r_l_v
% 3.19/1.60 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 3.19/1.60 @ ( produc1834103605_r_l_v
% 3.19/1.60 @ ^ [X2: l] : none_val_r_l_v
% 3.19/1.60 @ E4 ) ) ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_128_revision__step_Ofork,axiom,
% 3.19/1.60 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,E4: expr_r_l_v,R2: r] :
% 3.19/1.60 ( ( ( S @ R )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 3.19/1.60 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 3.19/1.60 => ( revision_step_r_l_v @ subst @ R @ S
% 3.19/1.60 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) @ R2
% 3.19/1.60 @ ( some_P1807977723_r_l_v
% 3.19/1.60 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 3.19/1.60 @ ( produc1834103605_r_l_v
% 3.19/1.60 @ ^ [X2: l] : none_val_r_l_v
% 3.19/1.60 @ E4 ) ) ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_129__092_060alpha_062r_H__fresh,axiom,
% 3.19/1.60 ~ ( member_r @ ( alpha @ r3 ) @ ( rID_G_r_l_v @ ( r_G_r_l_v @ alpha @ beta @ s ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_130_substitution_Orevision__step__relaxed_Ofork,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,E4: expr_r_l_v,R2: r] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( ( S @ R )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 3.19/1.60 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 3.19/1.60 => ( revisi1291188644_r_l_v @ Subst @ R @ S
% 3.19/1.60 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) @ R2
% 3.19/1.60 @ ( some_P1807977723_r_l_v
% 3.19/1.60 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 3.19/1.60 @ ( produc1834103605_r_l_v
% 3.19/1.60 @ ^ [X2: l] : none_val_r_l_v
% 3.19/1.60 @ E4 ) ) ) ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_131_substitution_Ofork__pseudodeterministic,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,E4: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( ( S @ R )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 3.19/1.60 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.19/1.60 = ( ? [R3: r] :
% 3.19/1.60 ( ~ ( member_r @ R3 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) ) ) )
% 3.19/1.60 & ( S2
% 3.19/1.60 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R3 ) ) ) ) ) ) ) @ R3
% 3.19/1.60 @ ( some_P1807977723_r_l_v
% 3.19/1.60 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 3.19/1.60 @ ( produc1834103605_r_l_v
% 3.19/1.60 @ ^ [X2: l] : none_val_r_l_v
% 3.19/1.60 @ E4 ) ) ) ) ) ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_132_local_Ostep,axiom,
% 3.19/1.60 revision_step_r_l_v @ subst @ r2 @ s @ s2 ).
% 3.19/1.60
% 3.19/1.60 thf(fact_133_substitution__axioms,axiom,
% 3.19/1.60 substitution_r_l_v @ subst ).
% 3.19/1.60
% 3.19/1.60 thf(fact_134_rename__empty_I2_J,axiom,
% 3.19/1.60 ! [Alpha2: r > r,Beta2: l > l] :
% 3.19/1.60 ( ( r_G_r_l_v @ Alpha2 @ Beta2
% 3.19/1.60 @ ^ [X2: r] : none_P277133687_r_l_v )
% 3.19/1.60 = ( ^ [X2: r] : none_P277133687_r_l_v ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_135_in__restricted__global__in__unrestricted__global_I1_J,axiom,
% 3.19/1.60 ! [R2: r,S: r > option1457017436_r_l_v,R: r] :
% 3.19/1.60 ( ( member_r @ R2 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 3.19/1.60 => ( member_r @ R2 @ ( rID_G_r_l_v @ S ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_136_only__fork__introduces__rids_H,axiom,
% 3.19/1.60 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v,R2: r] :
% 3.19/1.60 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.19/1.60 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E5: cntxt_r_l_v,E3: expr_r_l_v] :
% 3.19/1.60 ( ( S @ R )
% 3.19/1.60 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E5 @ ( rfork_r_l_v @ E3 ) ) ) ) ) )
% 3.19/1.60 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 3.19/1.60 => ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S2 ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_137_in__restricted__global__in__updated__global_I1_J,axiom,
% 3.19/1.60 ! [R2: r,S: r > option1457017436_r_l_v,R: r,Ls: produc1156025366_r_l_v] :
% 3.19/1.60 ( ( member_r @ R2 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 3.19/1.60 => ( member_r @ R2 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ Ls ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_138_fork__pseudodeterministic,axiom,
% 3.19/1.60 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,E4: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( ( S @ R )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 3.19/1.60 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.19/1.60 = ( ? [R3: r] :
% 3.19/1.60 ( ~ ( member_r @ R3 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) ) ) )
% 3.19/1.60 & ( S2
% 3.19/1.60 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R3 ) ) ) ) ) ) ) @ R3
% 3.19/1.60 @ ( some_P1807977723_r_l_v
% 3.19/1.60 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 3.19/1.60 @ ( produc1834103605_r_l_v
% 3.19/1.60 @ ^ [X2: l] : none_val_r_l_v
% 3.19/1.60 @ E4 ) ) ) ) ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_139_substitution_Orevision__step_Ocong,axiom,
% 3.19/1.60 revision_step_r_l_v = revision_step_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(fact_140_substitution_Orevision__step__relaxed_Ocong,axiom,
% 3.19/1.60 revisi1291188644_r_l_v = revisi1291188644_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(fact_141_substitution_Oonly__fork__introduces__rids_H,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v,R2: r] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.19/1.60 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E5: cntxt_r_l_v,E3: expr_r_l_v] :
% 3.19/1.60 ( ( S @ R )
% 3.19/1.60 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E5 @ ( rfork_r_l_v @ E3 ) ) ) ) ) )
% 3.19/1.60 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 3.19/1.60 => ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S2 ) ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_142_substitution_Orevision__step_Ofork,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,E4: expr_r_l_v,R2: r] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( ( S @ R )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 3.19/1.60 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 3.19/1.60 => ( revision_step_r_l_v @ Subst @ R @ S
% 3.19/1.60 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) @ R2
% 3.19/1.60 @ ( some_P1807977723_r_l_v
% 3.19/1.60 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 3.19/1.60 @ ( produc1834103605_r_l_v
% 3.19/1.60 @ ^ [X2: l] : none_val_r_l_v
% 3.19/1.60 @ E4 ) ) ) ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_143_local__and__fork__commute,axiom,
% 3.19/1.60 ! [S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,X: produc1156025366_r_l_v,S_22: r > option1457017436_r_l_v,R2: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R4: r,E4: expr_r_l_v] :
% 3.19/1.60 ( ( S_2
% 3.19/1.60 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X ) ) )
% 3.19/1.60 => ( ( S_22
% 3.19/1.60 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) @ R4
% 3.19/1.60 @ ( some_P1807977723_r_l_v
% 3.19/1.60 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 3.19/1.60 @ ( produc1834103605_r_l_v
% 3.19/1.60 @ ^ [X2: l] : none_val_r_l_v
% 3.19/1.60 @ E4 ) ) ) ) )
% 3.19/1.60 => ( ( ( S_2 @ R2 )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 3.19/1.60 => ( ~ ( member_r @ R4 @ ( rID_G_r_l_v @ S_2 ) )
% 3.19/1.60 => ( ( revision_step_r_l_v @ subst @ R @ S_22
% 3.19/1.60 @ ( fun_up709272714_r_l_v
% 3.19/1.60 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) @ R4
% 3.19/1.60 @ ( some_P1807977723_r_l_v
% 3.19/1.60 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 3.19/1.60 @ ( produc1834103605_r_l_v
% 3.19/1.60 @ ^ [X2: l] : none_val_r_l_v
% 3.19/1.60 @ E4 ) ) ) )
% 3.19/1.60 @ R
% 3.19/1.60 @ ( some_P1807977723_r_l_v @ X ) ) )
% 3.19/1.60 => ( ( R != R2 )
% 3.19/1.60 => ( ( R != R4 )
% 3.19/1.60 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.19/1.60 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 3.19/1.60 | ( S_2 = S_3 ) )
% 3.19/1.60 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 3.19/1.60 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_144_revision__step__relaxed_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 3.19/1.60 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r] :
% 3.19/1.60 ( ( ( S @ R )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 3.19/1.60 => ( ( ( S @ R2 )
% 3.19/1.60 = none_P277133687_r_l_v )
% 3.19/1.60 => ( revisi1291188644_r_l_v @ subst @ R @ S
% 3.19/1.60 @ ^ [X2: r] : none_P277133687_r_l_v ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_145_revision__step_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 3.19/1.60 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r] :
% 3.19/1.60 ( ( ( S @ R )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 3.19/1.60 => ( ( ( S @ R2 )
% 3.19/1.60 = none_P277133687_r_l_v )
% 3.19/1.60 => ( revision_step_r_l_v @ subst @ R @ S
% 3.19/1.60 @ ^ [X2: r] : none_P277133687_r_l_v ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_146_substitution_Olocal__and__fork__commute,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,X: produc1156025366_r_l_v,S_22: r > option1457017436_r_l_v,R2: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R4: r,E4: expr_r_l_v] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( S_2
% 3.19/1.60 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X ) ) )
% 3.19/1.60 => ( ( S_22
% 3.19/1.60 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) @ R4
% 3.19/1.60 @ ( some_P1807977723_r_l_v
% 3.19/1.60 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 3.19/1.60 @ ( produc1834103605_r_l_v
% 3.19/1.60 @ ^ [X2: l] : none_val_r_l_v
% 3.19/1.60 @ E4 ) ) ) ) )
% 3.19/1.60 => ( ( ( S_2 @ R2 )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 3.19/1.60 => ( ~ ( member_r @ R4 @ ( rID_G_r_l_v @ S_2 ) )
% 3.19/1.60 => ( ( revision_step_r_l_v @ Subst @ R @ S_22
% 3.19/1.60 @ ( fun_up709272714_r_l_v
% 3.19/1.60 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) @ R4
% 3.19/1.60 @ ( some_P1807977723_r_l_v
% 3.19/1.60 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 3.19/1.60 @ ( produc1834103605_r_l_v
% 3.19/1.60 @ ^ [X2: l] : none_val_r_l_v
% 3.19/1.60 @ E4 ) ) ) )
% 3.19/1.60 @ R
% 3.19/1.60 @ ( some_P1807977723_r_l_v @ X ) ) )
% 3.19/1.60 => ( ( R != R2 )
% 3.19/1.60 => ( ( R != R4 )
% 3.19/1.60 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.19/1.60 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 3.19/1.60 | ( S_2 = S_3 ) )
% 3.19/1.60 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 3.19/1.60 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_147_local__steps__commute,axiom,
% 3.19/1.60 ! [S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,X: produc1156025366_r_l_v,S_22: r > option1457017436_r_l_v,R2: r,Y: produc1156025366_r_l_v] :
% 3.19/1.60 ( ( S_2
% 3.19/1.60 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X ) ) )
% 3.19/1.60 => ( ( S_22
% 3.19/1.60 = ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
% 3.19/1.60 => ( ( revision_step_r_l_v @ subst @ R2 @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X ) ) @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X ) ) @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
% 3.19/1.60 => ( ( revision_step_r_l_v @ subst @ R @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) @ R @ ( some_P1807977723_r_l_v @ X ) ) )
% 3.19/1.60 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.19/1.60 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 3.19/1.60 | ( S_2 = S_3 ) )
% 3.19/1.60 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 3.19/1.60 | ( S_22 = S_32 ) ) ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_148_transition__relations__equivalent,axiom,
% 3.19/1.60 ! [S: r > option1457017436_r_l_v,R: r,S2: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( reachable_r_l_v @ subst @ S )
% 3.19/1.60 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.19/1.60 = ( revisi1291188644_r_l_v @ subst @ R @ S @ S2 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_149_local__determinism,axiom,
% 3.19/1.60 ! [R: r,S_1: r > option1457017436_r_l_v,S_2: r > option1457017436_r_l_v,S_22: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( revision_step_r_l_v @ subst @ R @ S_1 @ S_2 )
% 3.19/1.60 => ( ( revision_step_r_l_v @ subst @ R @ S_1 @ S_22 )
% 3.19/1.60 => ( eq_states_r_l_v @ S_2 @ S_22 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_150_SLC__sym,axiom,
% 3.19/1.60 ! [R2: r,S_2: r > option1457017436_r_l_v,R: r,S_22: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ? [S_33: r > option1457017436_r_l_v,S_34: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( eq_states_r_l_v @ S_33 @ S_34 )
% 3.19/1.60 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_33 )
% 3.19/1.60 | ( S_2 = S_33 ) )
% 3.19/1.60 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_34 )
% 3.19/1.60 | ( S_22 = S_34 ) ) )
% 3.19/1.60 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.19/1.60 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_3 )
% 3.19/1.60 | ( S_22 = S_3 ) )
% 3.19/1.60 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_32 )
% 3.19/1.60 | ( S_2 = S_32 ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_151_SLC__commute,axiom,
% 3.19/1.60 ! [S_35: r > option1457017436_r_l_v,S_36: r > option1457017436_r_l_v,R2: r,S_2: r > option1457017436_r_l_v,R: r,S_22: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( S_35 = S_36 )
% 3.19/1.60 => ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_35 )
% 3.19/1.60 => ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_36 )
% 3.19/1.60 => ( ( eq_states_r_l_v @ S_35 @ S_36 )
% 3.19/1.60 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_35 )
% 3.19/1.60 | ( S_2 = S_35 ) )
% 3.19/1.60 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_36 )
% 3.19/1.60 | ( S_22 = S_36 ) ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_152_reachability__closed__under__execution__step,axiom,
% 3.19/1.60 ! [S: r > option1457017436_r_l_v,R: r,S2: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( reachable_r_l_v @ subst @ S )
% 3.19/1.60 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.19/1.60 => ( reachable_r_l_v @ subst @ S2 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_153_expr_Oinject_I8_J,axiom,
% 3.19/1.60 ! [X8: expr_r_l_v,Y8: expr_r_l_v] :
% 3.19/1.60 ( ( ( rjoin_r_l_v @ X8 )
% 3.19/1.60 = ( rjoin_r_l_v @ Y8 ) )
% 3.19/1.60 = ( X8 = Y8 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_154_SLC__join_092_060_094sub_062_092_060epsilon_062,axiom,
% 3.19/1.60 ! [S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R4: r,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( ( S_1 @ R )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 3.19/1.60 => ( ( S_2
% 3.19/1.60 = ( ^ [X2: r] : none_P277133687_r_l_v ) )
% 3.19/1.60 => ( ( ( S_1 @ R4 )
% 3.19/1.60 = none_P277133687_r_l_v )
% 3.19/1.60 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 3.19/1.60 => ( ( R != R2 )
% 3.19/1.60 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.19/1.60 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 3.19/1.60 | ( S_2 = S_3 ) )
% 3.19/1.60 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 3.19/1.60 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_155_reachable__def,axiom,
% 3.19/1.60 ! [S: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( reachable_r_l_v @ subst @ S )
% 3.19/1.60 = ( ? [E6: expr_r_l_v,S3: r > option1457017436_r_l_v] : ( execution_r_l_v @ subst @ E6 @ S3 @ S ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_156_rjoin_092_060_094sub_062_092_060epsilon_062__deterministic,axiom,
% 3.19/1.60 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,S2: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( ( S @ R )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 3.19/1.60 => ( ( ( S @ R2 )
% 3.19/1.60 = none_P277133687_r_l_v )
% 3.19/1.60 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.19/1.60 = ( S2
% 3.19/1.60 = ( ^ [X2: r] : none_P277133687_r_l_v ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_157__092_060alpha_062_092_060beta_062__sym,axiom,
% 3.19/1.60 ! [S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( eq_states_r_l_v @ S @ S2 )
% 3.19/1.60 => ( eq_states_r_l_v @ S2 @ S ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_158__092_060alpha_062_092_060beta_062__refl,axiom,
% 3.19/1.60 ! [S: r > option1457017436_r_l_v] : ( eq_states_r_l_v @ S @ S ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_159__092_060alpha_062_092_060beta_062__trans,axiom,
% 3.19/1.60 ! [S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v,S4: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( eq_states_r_l_v @ S @ S2 )
% 3.19/1.60 => ( ( eq_states_r_l_v @ S2 @ S4 )
% 3.19/1.60 => ( eq_states_r_l_v @ S @ S4 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_160_expr_Odistinct_I13_J,axiom,
% 3.19/1.60 ! [X1: val_r_l_v,X8: expr_r_l_v] :
% 3.19/1.60 ( ( vE_r_l_v @ X1 )
% 3.19/1.60 != ( rjoin_r_l_v @ X8 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_161_expr_Odistinct_I55_J,axiom,
% 3.19/1.60 ! [X7: expr_r_l_v,X8: expr_r_l_v] :
% 3.19/1.60 ( ( rfork_r_l_v @ X7 )
% 3.19/1.60 != ( rjoin_r_l_v @ X8 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_162_substitution_Olocal__determinism,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S_1: r > option1457017436_r_l_v,S_2: r > option1457017436_r_l_v,S_22: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( revision_step_r_l_v @ Subst @ R @ S_1 @ S_2 )
% 3.19/1.60 => ( ( revision_step_r_l_v @ Subst @ R @ S_1 @ S_22 )
% 3.19/1.60 => ( eq_states_r_l_v @ S_2 @ S_22 ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_163_substitution_OSLC__commute,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_35: r > option1457017436_r_l_v,S_36: r > option1457017436_r_l_v,R2: r,S_2: r > option1457017436_r_l_v,R: r,S_22: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( S_35 = S_36 )
% 3.19/1.60 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_35 )
% 3.19/1.60 => ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_36 )
% 3.19/1.60 => ( ( eq_states_r_l_v @ S_35 @ S_36 )
% 3.19/1.60 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_35 )
% 3.19/1.60 | ( S_2 = S_35 ) )
% 3.19/1.60 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_36 )
% 3.19/1.60 | ( S_22 = S_36 ) ) ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_164_substitution_OSLC__sym,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R2: r,S_2: r > option1457017436_r_l_v,R: r,S_22: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ? [S_33: r > option1457017436_r_l_v,S_34: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( eq_states_r_l_v @ S_33 @ S_34 )
% 3.19/1.60 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_33 )
% 3.19/1.60 | ( S_2 = S_33 ) )
% 3.19/1.60 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_34 )
% 3.19/1.60 | ( S_22 = S_34 ) ) )
% 3.19/1.60 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.19/1.60 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_3 )
% 3.19/1.60 | ( S_22 = S_3 ) )
% 3.19/1.60 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_32 )
% 3.19/1.60 | ( S_2 = S_32 ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_165_substitution_OSLC__join_092_060_094sub_062_092_060epsilon_062,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R4: r,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( ( S_1 @ R )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 3.19/1.60 => ( ( S_2
% 3.19/1.60 = ( ^ [X2: r] : none_P277133687_r_l_v ) )
% 3.19/1.60 => ( ( ( S_1 @ R4 )
% 3.19/1.60 = none_P277133687_r_l_v )
% 3.19/1.60 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
% 3.19/1.60 => ( ( R != R2 )
% 3.19/1.60 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.19/1.60 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 3.19/1.60 | ( S_2 = S_3 ) )
% 3.19/1.60 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 3.19/1.60 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_166_substitution_Olocal__steps__commute,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,X: produc1156025366_r_l_v,S_22: r > option1457017436_r_l_v,R2: r,Y: produc1156025366_r_l_v] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( S_2
% 3.19/1.60 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X ) ) )
% 3.19/1.60 => ( ( S_22
% 3.19/1.60 = ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
% 3.19/1.60 => ( ( revision_step_r_l_v @ Subst @ R2 @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X ) ) @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X ) ) @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
% 3.19/1.60 => ( ( revision_step_r_l_v @ Subst @ R @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) @ R @ ( some_P1807977723_r_l_v @ X ) ) )
% 3.19/1.60 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.19/1.60 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 3.19/1.60 | ( S_2 = S_3 ) )
% 3.19/1.60 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 3.19/1.60 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_167_substitution_Orjoin_092_060_094sub_062_092_060epsilon_062__deterministic,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,S2: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( ( S @ R )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 3.19/1.60 => ( ( ( S @ R2 )
% 3.19/1.60 = none_P277133687_r_l_v )
% 3.19/1.60 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.19/1.60 = ( S2
% 3.19/1.60 = ( ^ [X2: r] : none_P277133687_r_l_v ) ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_168_substitution_Orevision__step_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( ( S @ R )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 3.19/1.60 => ( ( ( S @ R2 )
% 3.19/1.60 = none_P277133687_r_l_v )
% 3.19/1.60 => ( revision_step_r_l_v @ Subst @ R @ S
% 3.19/1.60 @ ^ [X2: r] : none_P277133687_r_l_v ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_169_substitution_Orevision__step__relaxed_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( ( S @ R )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 3.19/1.60 => ( ( ( S @ R2 )
% 3.19/1.60 = none_P277133687_r_l_v )
% 3.19/1.60 => ( revisi1291188644_r_l_v @ Subst @ R @ S
% 3.19/1.60 @ ^ [X2: r] : none_P277133687_r_l_v ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_170_inductive__invariant__is__execution__invariant,axiom,
% 3.19/1.60 ! [S: r > option1457017436_r_l_v,P: ( r > option1457017436_r_l_v ) > $o] :
% 3.19/1.60 ( ( reachable_r_l_v @ subst @ S )
% 3.19/1.60 => ( ( induct1670415253_r_l_v @ subst @ P )
% 3.19/1.60 => ( P @ S ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_171_reachable__imp___092_060S_062_092_060_094sub_062G,axiom,
% 3.19/1.60 ! [S: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( reachable_r_l_v @ subst @ S )
% 3.19/1.60 => ( domain1547879849_r_l_v @ S ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_172_substitution_Otransition__relations__equivalent,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,S2: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( reachable_r_l_v @ Subst @ S )
% 3.19/1.60 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.19/1.60 = ( revisi1291188644_r_l_v @ Subst @ R @ S @ S2 ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_173_SLC__fork,axiom,
% 3.19/1.60 ! [S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,E4: expr_r_l_v,S_2: r > option1457017436_r_l_v,Left_forkee: r,R2: r,S_22: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( ( S_1 @ R )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 3.19/1.60 => ( ( S_2
% 3.19/1.60 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ Left_forkee ) ) ) ) ) ) ) @ Left_forkee
% 3.19/1.60 @ ( some_P1807977723_r_l_v
% 3.19/1.60 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 3.19/1.60 @ ( produc1834103605_r_l_v
% 3.19/1.60 @ ^ [X2: l] : none_val_r_l_v
% 3.19/1.60 @ E4 ) ) ) ) )
% 3.19/1.60 => ( ~ ( member_r @ Left_forkee @ ( rID_G_r_l_v @ S_1 ) )
% 3.19/1.60 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 3.19/1.60 => ( ( R != R2 )
% 3.19/1.60 => ( ( reachable_r_l_v @ subst @ S_1 )
% 3.19/1.60 => ( ~ ( finite_finite_r @ top_top_set_r )
% 3.19/1.60 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.19/1.60 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 3.19/1.60 | ( S_2 = S_3 ) )
% 3.19/1.60 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 3.19/1.60 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_174_join__and__local__commute,axiom,
% 3.19/1.60 ! [S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,E: cntxt_r_l_v,R4: r,S_22: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,Sigma3: l > option_val_r_l_v,V: val_r_l_v] :
% 3.19/1.60 ( ( S_2
% 3.19/1.60 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
% 3.19/1.60 => ( ( S_22
% 3.19/1.60 = ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Ls ) ) )
% 3.19/1.60 => ( ( R != R2 )
% 3.19/1.60 => ( ( R2 != R4 )
% 3.19/1.60 => ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) @ R2 @ ( some_P1807977723_r_l_v @ Ls ) ) )
% 3.19/1.60 => ( ( ( S_22 @ R )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 3.19/1.60 => ( ( ( S_22 @ R4 )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 3.19/1.60 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.19/1.60 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 3.19/1.60 | ( S_2 = S_3 ) )
% 3.19/1.60 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 3.19/1.60 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_175_empty__map__finite_I3_J,axiom,
% 3.19/1.60 ( finite_finite_r
% 3.19/1.60 @ ( rID_G_r_l_v
% 3.19/1.60 @ ^ [X2: r] : none_P277133687_r_l_v ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_176_val_Oinject_I1_J,axiom,
% 3.19/1.60 ! [X1: const,Y1: const] :
% 3.19/1.60 ( ( ( cV_r_l_v @ X1 )
% 3.19/1.60 = ( cV_r_l_v @ Y1 ) )
% 3.19/1.60 = ( X1 = Y1 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_177_RID_092_060_094sub_062G__finite__invariant,axiom,
% 3.19/1.60 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.19/1.60 => ( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
% 3.19/1.60 => ( finite_finite_r @ ( rID_G_r_l_v @ S2 ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_178_reachable__imp__identifiers__finite_I1_J,axiom,
% 3.19/1.60 ! [S: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( reachable_r_l_v @ subst @ S )
% 3.19/1.60 => ( finite_finite_r @ ( rID_G_r_l_v @ S ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_179_reachable__imp__identifiers__available_I1_J,axiom,
% 3.19/1.60 ! [S: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( reachable_r_l_v @ subst @ S )
% 3.19/1.60 => ( ~ ( finite_finite_r @ top_top_set_r )
% 3.19/1.60 => ? [R5: r] :
% 3.19/1.60 ~ ( member_r @ R5 @ ( rID_G_r_l_v @ S ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_180_finite__option__UNIV,axiom,
% 3.19/1.60 ( ( finite1036466630um_r_l @ top_to1855148309um_r_l )
% 3.19/1.60 = ( finite65649782um_r_l @ top_to182927813um_r_l ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_181_finite__option__UNIV,axiom,
% 3.19/1.60 ( ( finite111936338um_l_r @ top_to1150555297um_l_r )
% 3.19/1.60 = ( finite1591053314um_l_r @ top_to1405881169um_l_r ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_182_finite__option__UNIV,axiom,
% 3.19/1.60 ( ( finite1864485196um_l_l @ top_to1066565019um_l_l )
% 3.19/1.60 = ( finite1541484284um_l_l @ top_to1010946379um_l_l ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_183_finite__option__UNIV,axiom,
% 3.19/1.60 ( ( finite555643486_set_r @ top_to555798885_set_r )
% 3.19/1.60 = ( finite_finite_set_r @ top_top_set_set_r ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_184_finite__option__UNIV,axiom,
% 3.19/1.60 ( ( finite160708696_set_l @ top_to471808607_set_l )
% 3.19/1.60 = ( finite_finite_set_l @ top_top_set_set_l ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_185_finite__option__UNIV,axiom,
% 3.19/1.60 ( ( finite16335230tion_r @ top_top_set_option_r )
% 3.19/1.60 = ( finite_finite_r @ top_top_set_r ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_186_finite__option__UNIV,axiom,
% 3.19/1.60 ( ( finite2114249848tion_l @ top_top_set_option_l )
% 3.19/1.60 = ( finite_finite_l @ top_top_set_l ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_187_domains__subsume__globally__def,axiom,
% 3.19/1.60 ( domain1547879849_r_l_v
% 3.19/1.60 = ( ^ [S5: r > option1457017436_r_l_v] :
% 3.19/1.60 ! [R6: r,Ls2: produc1156025366_r_l_v] :
% 3.19/1.60 ( ( ( S5 @ R6 )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ Ls2 ) )
% 3.19/1.60 => ( domain87684397_l_r_v @ Ls2 ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_188_finite__state__imp__restriction__finite_I1_J,axiom,
% 3.19/1.60 ! [S: r > option1457017436_r_l_v,R: r] :
% 3.19/1.60 ( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
% 3.19/1.60 => ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_189_revision__step_Ojoin,axiom,
% 3.19/1.60 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v] :
% 3.19/1.60 ( ( ( S @ R )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 3.19/1.60 => ( ( ( S @ R2 )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 3.19/1.60 => ( revision_step_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_190_revision__step__relaxed_Ojoin,axiom,
% 3.19/1.60 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v] :
% 3.19/1.60 ( ( ( S @ R )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 3.19/1.60 => ( ( ( S @ R2 )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 3.19/1.60 => ( revisi1291188644_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_191_SLC__join,axiom,
% 3.19/1.60 ! [S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R4: r,S_2: r > option1457017436_r_l_v,Tau3: l > option_val_r_l_v,Sigma3: l > option_val_r_l_v,V: val_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( ( S_1 @ R )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 3.19/1.60 => ( ( S_2
% 3.19/1.60 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
% 3.19/1.60 => ( ( ( S_1 @ R4 )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 3.19/1.60 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 3.19/1.60 => ( ( R != R2 )
% 3.19/1.60 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.19/1.60 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 3.19/1.60 | ( S_2 = S_3 ) )
% 3.19/1.60 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 3.19/1.60 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_192_bij___092_060alpha_062,axiom,
% 3.19/1.60 bij_betw_r_r @ alpha @ top_top_set_r @ top_top_set_r ).
% 3.19/1.60
% 3.19/1.60 thf(fact_193_rjoin__deterministic,axiom,
% 3.19/1.60 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( ( S @ R )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 3.19/1.60 => ( ( ( S @ R2 )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 3.19/1.60 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.19/1.60 = ( S2
% 3.19/1.60 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_194_substitution_Oexecution_Ocong,axiom,
% 3.19/1.60 execution_r_l_v = execution_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(fact_195_substitution_Oinductive__invariant_Ocong,axiom,
% 3.19/1.60 induct1670415253_r_l_v = induct1670415253_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(fact_196_val_Odistinct_I5_J,axiom,
% 3.19/1.60 ! [X1: const,X4: r] :
% 3.19/1.60 ( ( cV_r_l_v @ X1 )
% 3.19/1.60 != ( rid_r_l_v @ X4 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_197_substitution_Oreachable__imp__identifiers__available_I1_J,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( reachable_r_l_v @ Subst @ S )
% 3.19/1.60 => ( ~ ( finite_finite_r @ top_top_set_r )
% 3.19/1.60 => ? [R5: r] :
% 3.19/1.60 ~ ( member_r @ R5 @ ( rID_G_r_l_v @ S ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_198_substitution_Ostrong__local__confluence,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S_1: r > option1457017436_r_l_v,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( revision_step_r_l_v @ Subst @ R @ S_1 @ S_2 )
% 3.19/1.60 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
% 3.19/1.60 => ( ( reachable_r_l_v @ Subst @ S_1 )
% 3.19/1.60 => ( ~ ( finite_finite_l @ top_top_set_l )
% 3.19/1.60 => ( ~ ( finite_finite_r @ top_top_set_r )
% 3.19/1.60 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.19/1.60 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 3.19/1.60 | ( S_2 = S_3 ) )
% 3.19/1.60 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 3.19/1.60 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_199_substitution_ORID_092_060_094sub_062G__finite__invariant,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.19/1.60 => ( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
% 3.19/1.60 => ( finite_finite_r @ ( rID_G_r_l_v @ S2 ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_200_substitution_Oreachable__imp__identifiers__finite_I1_J,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( reachable_r_l_v @ Subst @ S )
% 3.19/1.60 => ( finite_finite_r @ ( rID_G_r_l_v @ S ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_201_substitution_Oreachable__imp___092_060S_062_092_060_094sub_062G,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( reachable_r_l_v @ Subst @ S )
% 3.19/1.60 => ( domain1547879849_r_l_v @ S ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_202_substitution_Oinductive__invariant__is__execution__invariant,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,P: ( r > option1457017436_r_l_v ) > $o] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( reachable_r_l_v @ Subst @ S )
% 3.19/1.60 => ( ( induct1670415253_r_l_v @ Subst @ P )
% 3.19/1.60 => ( P @ S ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_203_substitution_Oempty__map__finite_I3_J,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( finite_finite_r
% 3.19/1.60 @ ( rID_G_r_l_v
% 3.19/1.60 @ ^ [X2: r] : none_P277133687_r_l_v ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_204_substitution_Oreachable__def,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( reachable_r_l_v @ Subst @ S )
% 3.19/1.60 = ( ? [E6: expr_r_l_v,S3: r > option1457017436_r_l_v] : ( execution_r_l_v @ Subst @ E6 @ S3 @ S ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_205_substitution_Ofinite__state__imp__restriction__finite_I1_J,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
% 3.19/1.60 => ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_206_substitution_Oreachable_Ocong,axiom,
% 3.19/1.60 reachable_r_l_v = reachable_r_l_v ).
% 3.19/1.60
% 3.19/1.60 thf(fact_207_substitution_Orevision__step_Ojoin,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( ( S @ R )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 3.19/1.60 => ( ( ( S @ R2 )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 3.19/1.60 => ( revision_step_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_208_substitution_Orjoin__deterministic,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( ( S @ R )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 3.19/1.60 => ( ( ( S @ R2 )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 3.19/1.60 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.19/1.60 = ( S2
% 3.19/1.60 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_209_substitution_Orevision__step__relaxed_Ojoin,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( ( S @ R )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 3.19/1.60 => ( ( ( S @ R2 )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 3.19/1.60 => ( revisi1291188644_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_210_substitution_Ojoin__and__local__commute,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,E: cntxt_r_l_v,R4: r,S_22: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,Sigma3: l > option_val_r_l_v,V: val_r_l_v] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( S_2
% 3.19/1.60 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
% 3.19/1.60 => ( ( S_22
% 3.19/1.60 = ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Ls ) ) )
% 3.19/1.60 => ( ( R != R2 )
% 3.19/1.60 => ( ( R2 != R4 )
% 3.19/1.60 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) @ R2 @ ( some_P1807977723_r_l_v @ Ls ) ) )
% 3.19/1.60 => ( ( ( S_22 @ R )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 3.19/1.60 => ( ( ( S_22 @ R4 )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 3.19/1.60 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.19/1.60 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 3.19/1.60 | ( S_2 = S_3 ) )
% 3.19/1.60 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 3.19/1.60 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_211_substitution_OSLC__join,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R4: r,S_2: r > option1457017436_r_l_v,Tau3: l > option_val_r_l_v,Sigma3: l > option_val_r_l_v,V: val_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( ( S_1 @ R )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 3.19/1.60 => ( ( S_2
% 3.19/1.60 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
% 3.19/1.60 => ( ( ( S_1 @ R4 )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 3.19/1.60 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
% 3.19/1.60 => ( ( R != R2 )
% 3.19/1.60 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.19/1.60 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 3.19/1.60 | ( S_2 = S_3 ) )
% 3.19/1.60 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 3.19/1.60 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_212_substitution_OSLC__fork,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,E4: expr_r_l_v,S_2: r > option1457017436_r_l_v,Left_forkee: r,R2: r,S_22: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( ( S_1 @ R )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 3.19/1.60 => ( ( S_2
% 3.19/1.60 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ Left_forkee ) ) ) ) ) ) ) @ Left_forkee
% 3.19/1.60 @ ( some_P1807977723_r_l_v
% 3.19/1.60 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
% 3.19/1.60 @ ( produc1834103605_r_l_v
% 3.19/1.60 @ ^ [X2: l] : none_val_r_l_v
% 3.19/1.60 @ E4 ) ) ) ) )
% 3.19/1.60 => ( ~ ( member_r @ Left_forkee @ ( rID_G_r_l_v @ S_1 ) )
% 3.19/1.60 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
% 3.19/1.60 => ( ( R != R2 )
% 3.19/1.60 => ( ( reachable_r_l_v @ Subst @ S_1 )
% 3.19/1.60 => ( ~ ( finite_finite_r @ top_top_set_r )
% 3.19/1.60 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.19/1.60 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 3.19/1.60 | ( S_2 = S_3 ) )
% 3.19/1.60 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 3.19/1.60 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_213_substitution_Oreachability__closed__under__execution__step,axiom,
% 3.19/1.60 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,S2: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( substitution_r_l_v @ Subst )
% 3.19/1.60 => ( ( reachable_r_l_v @ Subst @ S )
% 3.19/1.60 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.19/1.60 => ( reachable_r_l_v @ Subst @ S2 ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_214_nice__ind__inv__is__inductive__invariant,axiom,
% 3.19/1.60 ( induct1670415253_r_l_v @ subst
% 3.19/1.60 @ ^ [S5: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( domain1547879849_r_l_v @ S5 )
% 3.19/1.60 & ( subsum680764357_r_l_v @ S5 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_215_step__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I2_J,axiom,
% 3.19/1.60 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.19/1.60 => ( ( domain1547879849_r_l_v @ S )
% 3.19/1.60 => ( ( subsum680764357_r_l_v @ S )
% 3.19/1.60 => ( subsum680764357_r_l_v @ S2 ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_216_step__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I1_J,axiom,
% 3.19/1.60 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.19/1.60 => ( ( domain1547879849_r_l_v @ S )
% 3.19/1.60 => ( ( subsum680764357_r_l_v @ S )
% 3.19/1.60 => ( domain1547879849_r_l_v @ S2 ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_217_finite__Collect__not,axiom,
% 3.19/1.60 ! [P: sum_sum_r_l > $o] :
% 3.19/1.60 ( ( finite65649782um_r_l @ ( collect_Sum_sum_r_l @ P ) )
% 3.19/1.60 => ( ( finite65649782um_r_l
% 3.19/1.60 @ ( collect_Sum_sum_r_l
% 3.19/1.60 @ ^ [X2: sum_sum_r_l] :
% 3.19/1.60 ~ ( P @ X2 ) ) )
% 3.19/1.60 = ( finite65649782um_r_l @ top_to182927813um_r_l ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_218_finite__Collect__not,axiom,
% 3.19/1.60 ! [P: sum_sum_l_r > $o] :
% 3.19/1.60 ( ( finite1591053314um_l_r @ ( collect_Sum_sum_l_r @ P ) )
% 3.19/1.60 => ( ( finite1591053314um_l_r
% 3.19/1.60 @ ( collect_Sum_sum_l_r
% 3.19/1.60 @ ^ [X2: sum_sum_l_r] :
% 3.19/1.60 ~ ( P @ X2 ) ) )
% 3.19/1.60 = ( finite1591053314um_l_r @ top_to1405881169um_l_r ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_219_finite__Collect__not,axiom,
% 3.19/1.60 ! [P: sum_sum_l_l > $o] :
% 3.19/1.60 ( ( finite1541484284um_l_l @ ( collect_Sum_sum_l_l @ P ) )
% 3.19/1.60 => ( ( finite1541484284um_l_l
% 3.19/1.60 @ ( collect_Sum_sum_l_l
% 3.19/1.60 @ ^ [X2: sum_sum_l_l] :
% 3.19/1.60 ~ ( P @ X2 ) ) )
% 3.19/1.60 = ( finite1541484284um_l_l @ top_to1010946379um_l_l ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_220_finite__Collect__not,axiom,
% 3.19/1.60 ! [P: set_r > $o] :
% 3.19/1.60 ( ( finite_finite_set_r @ ( collect_set_r @ P ) )
% 3.19/1.60 => ( ( finite_finite_set_r
% 3.19/1.60 @ ( collect_set_r
% 3.19/1.60 @ ^ [X2: set_r] :
% 3.19/1.60 ~ ( P @ X2 ) ) )
% 3.19/1.60 = ( finite_finite_set_r @ top_top_set_set_r ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_221_finite__Collect__not,axiom,
% 3.19/1.60 ! [P: set_l > $o] :
% 3.19/1.60 ( ( finite_finite_set_l @ ( collect_set_l @ P ) )
% 3.19/1.60 => ( ( finite_finite_set_l
% 3.19/1.60 @ ( collect_set_l
% 3.19/1.60 @ ^ [X2: set_l] :
% 3.19/1.60 ~ ( P @ X2 ) ) )
% 3.19/1.60 = ( finite_finite_set_l @ top_top_set_set_l ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_222_finite__Collect__not,axiom,
% 3.19/1.60 ! [P: r > $o] :
% 3.19/1.60 ( ( finite_finite_r @ ( collect_r @ P ) )
% 3.19/1.60 => ( ( finite_finite_r
% 3.19/1.60 @ ( collect_r
% 3.19/1.60 @ ^ [X2: r] :
% 3.19/1.60 ~ ( P @ X2 ) ) )
% 3.19/1.60 = ( finite_finite_r @ top_top_set_r ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_223_finite__Collect__not,axiom,
% 3.19/1.60 ! [P: l > $o] :
% 3.19/1.60 ( ( finite_finite_l @ ( collect_l @ P ) )
% 3.19/1.60 => ( ( finite_finite_l
% 3.19/1.60 @ ( collect_l
% 3.19/1.60 @ ^ [X2: l] :
% 3.19/1.60 ~ ( P @ X2 ) ) )
% 3.19/1.60 = ( finite_finite_l @ top_top_set_l ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_224_in__renamed__in__unlabelled__global_I1_J,axiom,
% 3.19/1.60 ! [Alpha2: r > r,Beta2: l > l,R: r,S: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( bij_betw_r_r @ Alpha2 @ top_top_set_r @ top_top_set_r )
% 3.19/1.60 => ( ( bij_betw_l_l @ Beta2 @ top_top_set_l @ top_top_set_l )
% 3.19/1.60 => ( ( member_r @ ( Alpha2 @ R ) @ ( rID_G_r_l_v @ ( r_G_r_l_v @ Alpha2 @ Beta2 @ S ) ) )
% 3.19/1.60 = ( member_r @ R @ ( rID_G_r_l_v @ S ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_225_finite__Collect__conjI,axiom,
% 3.19/1.60 ! [P: sum_sum_r_l > $o,Q: sum_sum_r_l > $o] :
% 3.19/1.60 ( ( ( finite65649782um_r_l @ ( collect_Sum_sum_r_l @ P ) )
% 3.19/1.60 | ( finite65649782um_r_l @ ( collect_Sum_sum_r_l @ Q ) ) )
% 3.19/1.60 => ( finite65649782um_r_l
% 3.19/1.60 @ ( collect_Sum_sum_r_l
% 3.19/1.60 @ ^ [X2: sum_sum_r_l] :
% 3.19/1.60 ( ( P @ X2 )
% 3.19/1.60 & ( Q @ X2 ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_226_finite__Collect__conjI,axiom,
% 3.19/1.60 ! [P: sum_sum_l_r > $o,Q: sum_sum_l_r > $o] :
% 3.19/1.60 ( ( ( finite1591053314um_l_r @ ( collect_Sum_sum_l_r @ P ) )
% 3.19/1.60 | ( finite1591053314um_l_r @ ( collect_Sum_sum_l_r @ Q ) ) )
% 3.19/1.60 => ( finite1591053314um_l_r
% 3.19/1.60 @ ( collect_Sum_sum_l_r
% 3.19/1.60 @ ^ [X2: sum_sum_l_r] :
% 3.19/1.60 ( ( P @ X2 )
% 3.19/1.60 & ( Q @ X2 ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_227_finite__Collect__conjI,axiom,
% 3.19/1.60 ! [P: sum_sum_l_l > $o,Q: sum_sum_l_l > $o] :
% 3.19/1.60 ( ( ( finite1541484284um_l_l @ ( collect_Sum_sum_l_l @ P ) )
% 3.19/1.60 | ( finite1541484284um_l_l @ ( collect_Sum_sum_l_l @ Q ) ) )
% 3.19/1.60 => ( finite1541484284um_l_l
% 3.19/1.60 @ ( collect_Sum_sum_l_l
% 3.19/1.60 @ ^ [X2: sum_sum_l_l] :
% 3.19/1.60 ( ( P @ X2 )
% 3.19/1.60 & ( Q @ X2 ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_228_finite__Collect__conjI,axiom,
% 3.19/1.60 ! [P: set_r > $o,Q: set_r > $o] :
% 3.19/1.60 ( ( ( finite_finite_set_r @ ( collect_set_r @ P ) )
% 3.19/1.60 | ( finite_finite_set_r @ ( collect_set_r @ Q ) ) )
% 3.19/1.60 => ( finite_finite_set_r
% 3.19/1.60 @ ( collect_set_r
% 3.19/1.60 @ ^ [X2: set_r] :
% 3.19/1.60 ( ( P @ X2 )
% 3.19/1.60 & ( Q @ X2 ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_229_finite__Collect__conjI,axiom,
% 3.19/1.60 ! [P: set_l > $o,Q: set_l > $o] :
% 3.19/1.60 ( ( ( finite_finite_set_l @ ( collect_set_l @ P ) )
% 3.19/1.60 | ( finite_finite_set_l @ ( collect_set_l @ Q ) ) )
% 3.19/1.60 => ( finite_finite_set_l
% 3.19/1.60 @ ( collect_set_l
% 3.19/1.60 @ ^ [X2: set_l] :
% 3.19/1.60 ( ( P @ X2 )
% 3.19/1.60 & ( Q @ X2 ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_230_finite__Collect__conjI,axiom,
% 3.19/1.60 ! [P: r > $o,Q: r > $o] :
% 3.19/1.60 ( ( ( finite_finite_r @ ( collect_r @ P ) )
% 3.19/1.60 | ( finite_finite_r @ ( collect_r @ Q ) ) )
% 3.19/1.60 => ( finite_finite_r
% 3.19/1.60 @ ( collect_r
% 3.19/1.60 @ ^ [X2: r] :
% 3.19/1.60 ( ( P @ X2 )
% 3.19/1.60 & ( Q @ X2 ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_231_finite__Collect__conjI,axiom,
% 3.19/1.60 ! [P: l > $o,Q: l > $o] :
% 3.19/1.60 ( ( ( finite_finite_l @ ( collect_l @ P ) )
% 3.19/1.60 | ( finite_finite_l @ ( collect_l @ Q ) ) )
% 3.19/1.60 => ( finite_finite_l
% 3.19/1.60 @ ( collect_l
% 3.19/1.60 @ ^ [X2: l] :
% 3.19/1.60 ( ( P @ X2 )
% 3.19/1.60 & ( Q @ X2 ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_232_finite__Collect__disjI,axiom,
% 3.19/1.60 ! [P: set_r > $o,Q: set_r > $o] :
% 3.19/1.60 ( ( finite_finite_set_r
% 3.19/1.60 @ ( collect_set_r
% 3.19/1.60 @ ^ [X2: set_r] :
% 3.19/1.60 ( ( P @ X2 )
% 3.19/1.60 | ( Q @ X2 ) ) ) )
% 3.19/1.60 = ( ( finite_finite_set_r @ ( collect_set_r @ P ) )
% 3.19/1.60 & ( finite_finite_set_r @ ( collect_set_r @ Q ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_233_finite__Collect__disjI,axiom,
% 3.19/1.60 ! [P: set_l > $o,Q: set_l > $o] :
% 3.19/1.60 ( ( finite_finite_set_l
% 3.19/1.60 @ ( collect_set_l
% 3.19/1.60 @ ^ [X2: set_l] :
% 3.19/1.60 ( ( P @ X2 )
% 3.19/1.60 | ( Q @ X2 ) ) ) )
% 3.19/1.60 = ( ( finite_finite_set_l @ ( collect_set_l @ P ) )
% 3.19/1.60 & ( finite_finite_set_l @ ( collect_set_l @ Q ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_234_finite__Collect__disjI,axiom,
% 3.19/1.60 ! [P: r > $o,Q: r > $o] :
% 3.19/1.60 ( ( finite_finite_r
% 3.19/1.60 @ ( collect_r
% 3.19/1.60 @ ^ [X2: r] :
% 3.19/1.60 ( ( P @ X2 )
% 3.19/1.60 | ( Q @ X2 ) ) ) )
% 3.19/1.60 = ( ( finite_finite_r @ ( collect_r @ P ) )
% 3.19/1.60 & ( finite_finite_r @ ( collect_r @ Q ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_235_finite__Collect__disjI,axiom,
% 3.19/1.60 ! [P: l > $o,Q: l > $o] :
% 3.19/1.60 ( ( finite_finite_l
% 3.19/1.60 @ ( collect_l
% 3.19/1.60 @ ^ [X2: l] :
% 3.19/1.60 ( ( P @ X2 )
% 3.19/1.60 | ( Q @ X2 ) ) ) )
% 3.19/1.60 = ( ( finite_finite_l @ ( collect_l @ P ) )
% 3.19/1.60 & ( finite_finite_l @ ( collect_l @ Q ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_236_strong__local__confluence,axiom,
% 3.19/1.60 ! [R: r,S_1: r > option1457017436_r_l_v,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( revision_step_r_l_v @ subst @ R @ S_1 @ S_2 )
% 3.19/1.60 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 3.19/1.60 => ( ( reachable_r_l_v @ subst @ S_1 )
% 3.19/1.60 => ( ~ ( finite_finite_l @ top_top_set_l )
% 3.19/1.60 => ( ~ ( finite_finite_r @ top_top_set_r )
% 3.19/1.60 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.19/1.60 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 3.19/1.60 | ( S_2 = S_3 ) )
% 3.19/1.60 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 3.19/1.60 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_237_finite__Plus__UNIV__iff,axiom,
% 3.19/1.60 ( ( finite115218812um_r_r @ top_to577862603um_r_r )
% 3.19/1.60 = ( ( finite_finite_r @ top_top_set_r )
% 3.19/1.60 & ( finite_finite_r @ top_top_set_r ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_238_finite__Plus__UNIV__iff,axiom,
% 3.19/1.60 ( ( finite65649782um_r_l @ top_to182927813um_r_l )
% 3.19/1.60 = ( ( finite_finite_r @ top_top_set_r )
% 3.19/1.60 & ( finite_finite_l @ top_top_set_l ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_239_finite__Plus__UNIV__iff,axiom,
% 3.19/1.60 ( ( finite1591053314um_l_r @ top_to1405881169um_l_r )
% 3.19/1.60 = ( ( finite_finite_l @ top_top_set_l )
% 3.19/1.60 & ( finite_finite_r @ top_top_set_r ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_240_finite__Plus__UNIV__iff,axiom,
% 3.19/1.60 ( ( finite1541484284um_l_l @ top_to1010946379um_l_l )
% 3.19/1.60 = ( ( finite_finite_l @ top_top_set_l )
% 3.19/1.60 & ( finite_finite_l @ top_top_set_l ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_241_eq__statesI,axiom,
% 3.19/1.60 ! [Alpha2: r > r,Beta2: l > l,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ( ( r_G_r_l_v @ Alpha2 @ Beta2 @ S )
% 3.19/1.60 = S2 )
% 3.19/1.60 => ( ( bij_betw_r_r @ Alpha2 @ top_top_set_r @ top_top_set_r )
% 3.19/1.60 => ( ( bij_betw_l_l @ Beta2 @ top_top_set_l @ top_top_set_l )
% 3.19/1.60 => ( eq_states_r_l_v @ S @ S2 ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_242_renaming__distr__global_I2_J,axiom,
% 3.19/1.60 ! [Alpha2: r > r,Beta2: l > l,S: r > option1457017436_r_l_v,R: r] :
% 3.19/1.60 ( ( bij_betw_r_r @ Alpha2 @ top_top_set_r @ top_top_set_r )
% 3.19/1.60 => ( ( r_G_r_l_v @ Alpha2 @ Beta2 @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) )
% 3.19/1.60 = ( fun_up709272714_r_l_v @ ( r_G_r_l_v @ Alpha2 @ Beta2 @ S ) @ ( Alpha2 @ R ) @ none_P277133687_r_l_v ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_243_domains__subsume__globallyI,axiom,
% 3.19/1.60 ! [S: r > option1457017436_r_l_v] :
% 3.19/1.60 ( ! [R5: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E3: expr_r_l_v] :
% 3.19/1.60 ( ( ( S @ R5 )
% 3.19/1.60 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) ) )
% 3.19/1.60 => ( domain87684397_l_r_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) ) )
% 3.19/1.60 => ( domain1547879849_r_l_v @ S ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_244_bij___092_060beta_062,axiom,
% 3.19/1.60 bij_betw_l_l @ beta @ top_top_set_l @ top_top_set_l ).
% 3.19/1.60
% 3.19/1.60 thf(fact_245_bij__betw__finite,axiom,
% 3.19/1.60 ! [F: r > r,A5: set_r,B5: set_r] :
% 3.19/1.60 ( ( bij_betw_r_r @ F @ A5 @ B5 )
% 3.19/1.60 => ( ( finite_finite_r @ A5 )
% 3.19/1.60 = ( finite_finite_r @ B5 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_246_bij__betw__finite,axiom,
% 3.19/1.60 ! [F: r > l,A5: set_r,B5: set_l] :
% 3.19/1.60 ( ( bij_betw_r_l @ F @ A5 @ B5 )
% 3.19/1.60 => ( ( finite_finite_r @ A5 )
% 3.19/1.60 = ( finite_finite_l @ B5 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_247_bij__betw__finite,axiom,
% 3.19/1.60 ! [F: l > r,A5: set_l,B5: set_r] :
% 3.19/1.60 ( ( bij_betw_l_r @ F @ A5 @ B5 )
% 3.19/1.60 => ( ( finite_finite_l @ A5 )
% 3.19/1.60 = ( finite_finite_r @ B5 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_248_bij__betw__finite,axiom,
% 3.19/1.60 ! [F: l > l,A5: set_l,B5: set_l] :
% 3.19/1.60 ( ( bij_betw_l_l @ F @ A5 @ B5 )
% 3.19/1.60 => ( ( finite_finite_l @ A5 )
% 3.19/1.60 = ( finite_finite_l @ B5 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_249_bij__pointE,axiom,
% 3.19/1.60 ! [F: r > r,Y: r] :
% 3.19/1.60 ( ( bij_betw_r_r @ F @ top_top_set_r @ top_top_set_r )
% 3.19/1.60 => ~ ! [X3: r] :
% 3.19/1.60 ( ( Y
% 3.19/1.60 = ( F @ X3 ) )
% 3.19/1.60 => ~ ! [X9: r] :
% 3.19/1.60 ( ( Y
% 3.19/1.60 = ( F @ X9 ) )
% 3.19/1.60 => ( X9 = X3 ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_250_bij__pointE,axiom,
% 3.19/1.60 ! [F: r > l,Y: l] :
% 3.19/1.60 ( ( bij_betw_r_l @ F @ top_top_set_r @ top_top_set_l )
% 3.19/1.60 => ~ ! [X3: r] :
% 3.19/1.60 ( ( Y
% 3.19/1.60 = ( F @ X3 ) )
% 3.19/1.60 => ~ ! [X9: r] :
% 3.19/1.60 ( ( Y
% 3.19/1.60 = ( F @ X9 ) )
% 3.19/1.60 => ( X9 = X3 ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_251_bij__pointE,axiom,
% 3.19/1.60 ! [F: l > r,Y: r] :
% 3.19/1.60 ( ( bij_betw_l_r @ F @ top_top_set_l @ top_top_set_r )
% 3.19/1.60 => ~ ! [X3: l] :
% 3.19/1.60 ( ( Y
% 3.19/1.60 = ( F @ X3 ) )
% 3.19/1.60 => ~ ! [X9: l] :
% 3.19/1.60 ( ( Y
% 3.19/1.60 = ( F @ X9 ) )
% 3.19/1.60 => ( X9 = X3 ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_252_bij__pointE,axiom,
% 3.19/1.60 ! [F: l > l,Y: l] :
% 3.19/1.60 ( ( bij_betw_l_l @ F @ top_top_set_l @ top_top_set_l )
% 3.19/1.60 => ~ ! [X3: l] :
% 3.19/1.60 ( ( Y
% 3.19/1.60 = ( F @ X3 ) )
% 3.19/1.60 => ~ ! [X9: l] :
% 3.19/1.60 ( ( Y
% 3.19/1.60 = ( F @ X9 ) )
% 3.19/1.60 => ( X9 = X3 ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_253_bij__betwE,axiom,
% 3.19/1.60 ! [F: r > r,A5: set_r,B5: set_r] :
% 3.19/1.60 ( ( bij_betw_r_r @ F @ A5 @ B5 )
% 3.19/1.60 => ! [X10: r] :
% 3.19/1.60 ( ( member_r @ X10 @ A5 )
% 3.19/1.60 => ( member_r @ ( F @ X10 ) @ B5 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_254_bij__betwE,axiom,
% 3.19/1.60 ! [F: l > l,A5: set_l,B5: set_l] :
% 3.19/1.60 ( ( bij_betw_l_l @ F @ A5 @ B5 )
% 3.19/1.60 => ! [X10: l] :
% 3.19/1.60 ( ( member_l @ X10 @ A5 )
% 3.19/1.60 => ( member_l @ ( F @ X10 ) @ B5 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_255_bij__betw__inv,axiom,
% 3.19/1.60 ! [F: r > r,A5: set_r,B5: set_r] :
% 3.19/1.60 ( ( bij_betw_r_r @ F @ A5 @ B5 )
% 3.19/1.60 => ? [G3: r > r] : ( bij_betw_r_r @ G3 @ B5 @ A5 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_256_bij__betw__inv,axiom,
% 3.19/1.60 ! [F: l > l,A5: set_l,B5: set_l] :
% 3.19/1.60 ( ( bij_betw_l_l @ F @ A5 @ B5 )
% 3.19/1.60 => ? [G3: l > l] : ( bij_betw_l_l @ G3 @ B5 @ A5 ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_257_bij__betw__cong,axiom,
% 3.19/1.60 ! [A5: set_r,F: r > r,G: r > r,A6: set_r] :
% 3.19/1.60 ( ! [A3: r] :
% 3.19/1.60 ( ( member_r @ A3 @ A5 )
% 3.19/1.60 => ( ( F @ A3 )
% 3.19/1.60 = ( G @ A3 ) ) )
% 3.19/1.60 => ( ( bij_betw_r_r @ F @ A5 @ A6 )
% 3.19/1.60 = ( bij_betw_r_r @ G @ A5 @ A6 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_258_bij__betw__cong,axiom,
% 3.19/1.60 ! [A5: set_l,F: l > l,G: l > l,A6: set_l] :
% 3.19/1.60 ( ! [A3: l] :
% 3.19/1.60 ( ( member_l @ A3 @ A5 )
% 3.19/1.60 => ( ( F @ A3 )
% 3.19/1.60 = ( G @ A3 ) ) )
% 3.19/1.60 => ( ( bij_betw_l_l @ F @ A5 @ A6 )
% 3.19/1.60 = ( bij_betw_l_l @ G @ A5 @ A6 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_259_bij__betw__apply,axiom,
% 3.19/1.60 ! [F: r > l,A5: set_r,B5: set_l,A: r] :
% 3.19/1.60 ( ( bij_betw_r_l @ F @ A5 @ B5 )
% 3.19/1.60 => ( ( member_r @ A @ A5 )
% 3.19/1.60 => ( member_l @ ( F @ A ) @ B5 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_260_bij__betw__apply,axiom,
% 3.19/1.60 ! [F: l > r,A5: set_l,B5: set_r,A: l] :
% 3.19/1.60 ( ( bij_betw_l_r @ F @ A5 @ B5 )
% 3.19/1.60 => ( ( member_l @ A @ A5 )
% 3.19/1.60 => ( member_r @ ( F @ A ) @ B5 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_261_bij__betw__apply,axiom,
% 3.19/1.60 ! [F: r > r,A5: set_r,B5: set_r,A: r] :
% 3.19/1.60 ( ( bij_betw_r_r @ F @ A5 @ B5 )
% 3.19/1.60 => ( ( member_r @ A @ A5 )
% 3.19/1.60 => ( member_r @ ( F @ A ) @ B5 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_262_bij__betw__apply,axiom,
% 3.19/1.60 ! [F: l > l,A5: set_l,B5: set_l,A: l] :
% 3.19/1.60 ( ( bij_betw_l_l @ F @ A5 @ B5 )
% 3.19/1.60 => ( ( member_l @ A @ A5 )
% 3.19/1.60 => ( member_l @ ( F @ A ) @ B5 ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_263_bij__betw__iff__bijections,axiom,
% 3.19/1.60 ( bij_betw_l_r
% 3.19/1.60 = ( ^ [F2: l > r,A7: set_l,B6: set_r] :
% 3.19/1.60 ? [G2: r > l] :
% 3.19/1.60 ( ! [X2: l] :
% 3.19/1.60 ( ( member_l @ X2 @ A7 )
% 3.19/1.60 => ( ( member_r @ ( F2 @ X2 ) @ B6 )
% 3.19/1.60 & ( ( G2 @ ( F2 @ X2 ) )
% 3.19/1.60 = X2 ) ) )
% 3.19/1.60 & ! [X2: r] :
% 3.19/1.60 ( ( member_r @ X2 @ B6 )
% 3.19/1.60 => ( ( member_l @ ( G2 @ X2 ) @ A7 )
% 3.19/1.60 & ( ( F2 @ ( G2 @ X2 ) )
% 3.19/1.60 = X2 ) ) ) ) ) ) ).
% 3.19/1.60
% 3.19/1.60 thf(fact_264_bij__betw__iff__bijections,axiom,
% 3.19/1.60 ( bij_betw_r_l
% 3.19/1.60 = ( ^ [F2: r > l,A7: set_r,B6: set_l] :
% 3.19/1.60 ? [G2: l > r] :
% 3.19/1.60 ( ! [X2: r] :
% 3.19/1.60 ( ( member_r @ X2 @ A7 )
% 3.19/1.60 => ( ( member_l @ ( F2 @ X2 ) @ B6 )
% 3.19/1.60 & ( ( G2 @ ( F2 @ X2 ) )
% 3.19/1.61 = X2 ) ) )
% 3.19/1.61 & ! [X2: l] :
% 3.19/1.61 ( ( member_l @ X2 @ B6 )
% 3.19/1.61 => ( ( member_r @ ( G2 @ X2 ) @ A7 )
% 3.19/1.61 & ( ( F2 @ ( G2 @ X2 ) )
% 3.19/1.61 = X2 ) ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_265_bij__betw__iff__bijections,axiom,
% 3.19/1.61 ( bij_betw_r_r
% 3.19/1.61 = ( ^ [F2: r > r,A7: set_r,B6: set_r] :
% 3.19/1.61 ? [G2: r > r] :
% 3.19/1.61 ( ! [X2: r] :
% 3.19/1.61 ( ( member_r @ X2 @ A7 )
% 3.19/1.61 => ( ( member_r @ ( F2 @ X2 ) @ B6 )
% 3.19/1.61 & ( ( G2 @ ( F2 @ X2 ) )
% 3.19/1.61 = X2 ) ) )
% 3.19/1.61 & ! [X2: r] :
% 3.19/1.61 ( ( member_r @ X2 @ B6 )
% 3.19/1.61 => ( ( member_r @ ( G2 @ X2 ) @ A7 )
% 3.19/1.61 & ( ( F2 @ ( G2 @ X2 ) )
% 3.19/1.61 = X2 ) ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_266_bij__betw__iff__bijections,axiom,
% 3.19/1.61 ( bij_betw_l_l
% 3.19/1.61 = ( ^ [F2: l > l,A7: set_l,B6: set_l] :
% 3.19/1.61 ? [G2: l > l] :
% 3.19/1.61 ( ! [X2: l] :
% 3.19/1.61 ( ( member_l @ X2 @ A7 )
% 3.19/1.61 => ( ( member_l @ ( F2 @ X2 ) @ B6 )
% 3.19/1.61 & ( ( G2 @ ( F2 @ X2 ) )
% 3.19/1.61 = X2 ) ) )
% 3.19/1.61 & ! [X2: l] :
% 3.19/1.61 ( ( member_l @ X2 @ B6 )
% 3.19/1.61 => ( ( member_l @ ( G2 @ X2 ) @ A7 )
% 3.19/1.61 & ( ( F2 @ ( G2 @ X2 ) )
% 3.19/1.61 = X2 ) ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_267_eq__statesE,axiom,
% 3.19/1.61 ! [S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( eq_states_r_l_v @ S @ S2 )
% 3.19/1.61 => ~ ! [Alpha: r > r,Beta: l > l] :
% 3.19/1.61 ( ( ( r_G_r_l_v @ Alpha @ Beta @ S )
% 3.19/1.61 = S2 )
% 3.19/1.61 => ( ( bij_betw_r_r @ Alpha @ top_top_set_r @ top_top_set_r )
% 3.19/1.61 => ~ ( bij_betw_l_l @ Beta @ top_top_set_l @ top_top_set_l ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_268_eq__states__def,axiom,
% 3.19/1.61 ( eq_states_r_l_v
% 3.19/1.61 = ( ^ [S5: r > option1457017436_r_l_v,S3: r > option1457017436_r_l_v] :
% 3.19/1.61 ? [Alpha3: r > r,Beta3: l > l] :
% 3.19/1.61 ( ( bij_betw_r_r @ Alpha3 @ top_top_set_r @ top_top_set_r )
% 3.19/1.61 & ( bij_betw_l_l @ Beta3 @ top_top_set_l @ top_top_set_l )
% 3.19/1.61 & ( ( r_G_r_l_v @ Alpha3 @ Beta3 @ S5 )
% 3.19/1.61 = S3 ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_269_substitution_Oin__renamed__in__unlabelled__global_I1_J,axiom,
% 3.19/1.61 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,Alpha2: r > r,Beta2: l > l,R: r,S: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( substitution_r_l_v @ Subst )
% 3.19/1.61 => ( ( bij_betw_r_r @ Alpha2 @ top_top_set_r @ top_top_set_r )
% 3.19/1.61 => ( ( bij_betw_l_l @ Beta2 @ top_top_set_l @ top_top_set_l )
% 3.19/1.61 => ( ( member_r @ ( Alpha2 @ R ) @ ( rID_G_r_l_v @ ( r_G_r_l_v @ Alpha2 @ Beta2 @ S ) ) )
% 3.19/1.61 = ( member_r @ R @ ( rID_G_r_l_v @ S ) ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_270_not__finite__existsD,axiom,
% 3.19/1.61 ! [P: r > $o] :
% 3.19/1.61 ( ~ ( finite_finite_r @ ( collect_r @ P ) )
% 3.19/1.61 => ? [X_1: r] : ( P @ X_1 ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_271_not__finite__existsD,axiom,
% 3.19/1.61 ! [P: l > $o] :
% 3.19/1.61 ( ~ ( finite_finite_l @ ( collect_l @ P ) )
% 3.19/1.61 => ? [X_1: l] : ( P @ X_1 ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_272_pigeonhole__infinite__rel,axiom,
% 3.19/1.61 ! [A5: set_r,B5: set_r,R7: r > r > $o] :
% 3.19/1.61 ( ~ ( finite_finite_r @ A5 )
% 3.19/1.61 => ( ( finite_finite_r @ B5 )
% 3.19/1.61 => ( ! [X3: r] :
% 3.19/1.61 ( ( member_r @ X3 @ A5 )
% 3.19/1.61 => ? [Xa2: r] :
% 3.19/1.61 ( ( member_r @ Xa2 @ B5 )
% 3.19/1.61 & ( R7 @ X3 @ Xa2 ) ) )
% 3.19/1.61 => ? [X3: r] :
% 3.19/1.61 ( ( member_r @ X3 @ B5 )
% 3.19/1.61 & ~ ( finite_finite_r
% 3.19/1.61 @ ( collect_r
% 3.19/1.61 @ ^ [A4: r] :
% 3.19/1.61 ( ( member_r @ A4 @ A5 )
% 3.19/1.61 & ( R7 @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_273_pigeonhole__infinite__rel,axiom,
% 3.19/1.61 ! [A5: set_r,B5: set_l,R7: r > l > $o] :
% 3.19/1.61 ( ~ ( finite_finite_r @ A5 )
% 3.19/1.61 => ( ( finite_finite_l @ B5 )
% 3.19/1.61 => ( ! [X3: r] :
% 3.19/1.61 ( ( member_r @ X3 @ A5 )
% 3.19/1.61 => ? [Xa2: l] :
% 3.19/1.61 ( ( member_l @ Xa2 @ B5 )
% 3.19/1.61 & ( R7 @ X3 @ Xa2 ) ) )
% 3.19/1.61 => ? [X3: l] :
% 3.19/1.61 ( ( member_l @ X3 @ B5 )
% 3.19/1.61 & ~ ( finite_finite_r
% 3.19/1.61 @ ( collect_r
% 3.19/1.61 @ ^ [A4: r] :
% 3.19/1.61 ( ( member_r @ A4 @ A5 )
% 3.19/1.61 & ( R7 @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_274_pigeonhole__infinite__rel,axiom,
% 3.19/1.61 ! [A5: set_l,B5: set_r,R7: l > r > $o] :
% 3.19/1.61 ( ~ ( finite_finite_l @ A5 )
% 3.19/1.61 => ( ( finite_finite_r @ B5 )
% 3.19/1.61 => ( ! [X3: l] :
% 3.19/1.61 ( ( member_l @ X3 @ A5 )
% 3.19/1.61 => ? [Xa2: r] :
% 3.19/1.61 ( ( member_r @ Xa2 @ B5 )
% 3.19/1.61 & ( R7 @ X3 @ Xa2 ) ) )
% 3.19/1.61 => ? [X3: r] :
% 3.19/1.61 ( ( member_r @ X3 @ B5 )
% 3.19/1.61 & ~ ( finite_finite_l
% 3.19/1.61 @ ( collect_l
% 3.19/1.61 @ ^ [A4: l] :
% 3.19/1.61 ( ( member_l @ A4 @ A5 )
% 3.19/1.61 & ( R7 @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_275_pigeonhole__infinite__rel,axiom,
% 3.19/1.61 ! [A5: set_l,B5: set_l,R7: l > l > $o] :
% 3.19/1.61 ( ~ ( finite_finite_l @ A5 )
% 3.19/1.61 => ( ( finite_finite_l @ B5 )
% 3.19/1.61 => ( ! [X3: l] :
% 3.19/1.61 ( ( member_l @ X3 @ A5 )
% 3.19/1.61 => ? [Xa2: l] :
% 3.19/1.61 ( ( member_l @ Xa2 @ B5 )
% 3.19/1.61 & ( R7 @ X3 @ Xa2 ) ) )
% 3.19/1.61 => ? [X3: l] :
% 3.19/1.61 ( ( member_l @ X3 @ B5 )
% 3.19/1.61 & ~ ( finite_finite_l
% 3.19/1.61 @ ( collect_l
% 3.19/1.61 @ ^ [A4: l] :
% 3.19/1.61 ( ( member_l @ A4 @ A5 )
% 3.19/1.61 & ( R7 @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_276_finite__Prod__UNIV,axiom,
% 3.19/1.61 ( ( finite_finite_r @ top_top_set_r )
% 3.19/1.61 => ( ( finite_finite_r @ top_top_set_r )
% 3.19/1.61 => ( finite1507191824od_r_r @ top_to2034696215od_r_r ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_277_finite__Prod__UNIV,axiom,
% 3.19/1.61 ( ( finite_finite_r @ top_top_set_r )
% 3.19/1.61 => ( ( finite_finite_l @ top_top_set_l )
% 3.19/1.61 => ( finite1457622794od_r_l @ top_to1639761425od_r_l ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_278_finite__Prod__UNIV,axiom,
% 3.19/1.61 ( ( finite_finite_l @ top_top_set_l )
% 3.19/1.61 => ( ( finite_finite_r @ top_top_set_r )
% 3.19/1.61 => ( finite835542678od_l_r @ top_to715231133od_l_r ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_279_finite__Prod__UNIV,axiom,
% 3.19/1.61 ( ( finite_finite_l @ top_top_set_l )
% 3.19/1.61 => ( ( finite_finite_l @ top_top_set_l )
% 3.19/1.61 => ( finite785973648od_l_l @ top_to320296343od_l_l ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_280_ex__new__if__finite,axiom,
% 3.19/1.61 ! [A5: set_r] :
% 3.19/1.61 ( ~ ( finite_finite_r @ top_top_set_r )
% 3.19/1.61 => ( ( finite_finite_r @ A5 )
% 3.19/1.61 => ? [A3: r] :
% 3.19/1.61 ~ ( member_r @ A3 @ A5 ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_281_ex__new__if__finite,axiom,
% 3.19/1.61 ! [A5: set_l] :
% 3.19/1.61 ( ~ ( finite_finite_l @ top_top_set_l )
% 3.19/1.61 => ( ( finite_finite_l @ A5 )
% 3.19/1.61 => ? [A3: l] :
% 3.19/1.61 ~ ( member_l @ A3 @ A5 ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_282_finite__prod,axiom,
% 3.19/1.61 ( ( finite1507191824od_r_r @ top_to2034696215od_r_r )
% 3.19/1.61 = ( ( finite_finite_r @ top_top_set_r )
% 3.19/1.61 & ( finite_finite_r @ top_top_set_r ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_283_finite__prod,axiom,
% 3.19/1.61 ( ( finite1457622794od_r_l @ top_to1639761425od_r_l )
% 3.19/1.61 = ( ( finite_finite_r @ top_top_set_r )
% 3.19/1.61 & ( finite_finite_l @ top_top_set_l ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_284_finite__prod,axiom,
% 3.19/1.61 ( ( finite835542678od_l_r @ top_to715231133od_l_r )
% 3.19/1.61 = ( ( finite_finite_l @ top_top_set_l )
% 3.19/1.61 & ( finite_finite_r @ top_top_set_r ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_285_finite__prod,axiom,
% 3.19/1.61 ( ( finite785973648od_l_l @ top_to320296343od_l_l )
% 3.19/1.61 = ( ( finite_finite_l @ top_top_set_l )
% 3.19/1.61 & ( finite_finite_l @ top_top_set_l ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_286_Finite__Set_Ofinite__set,axiom,
% 3.19/1.61 ( ( finite_finite_set_r @ top_top_set_set_r )
% 3.19/1.61 = ( finite_finite_r @ top_top_set_r ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_287_Finite__Set_Ofinite__set,axiom,
% 3.19/1.61 ( ( finite_finite_set_l @ top_top_set_set_l )
% 3.19/1.61 = ( finite_finite_l @ top_top_set_l ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_288_substitution_Ostep__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I1_J,axiom,
% 3.19/1.61 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( substitution_r_l_v @ Subst )
% 3.19/1.61 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.19/1.61 => ( ( domain1547879849_r_l_v @ S )
% 3.19/1.61 => ( ( subsum680764357_r_l_v @ S )
% 3.19/1.61 => ( domain1547879849_r_l_v @ S2 ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_289_substitution_Ostep__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I2_J,axiom,
% 3.19/1.61 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( substitution_r_l_v @ Subst )
% 3.19/1.61 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.19/1.61 => ( ( domain1547879849_r_l_v @ S )
% 3.19/1.61 => ( ( subsum680764357_r_l_v @ S )
% 3.19/1.61 => ( subsum680764357_r_l_v @ S2 ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_290_finite__update__induct,axiom,
% 3.19/1.61 ! [F: r > option1457017436_r_l_v,C: option1457017436_r_l_v,P: ( r > option1457017436_r_l_v ) > $o] :
% 3.19/1.61 ( ( finite_finite_r
% 3.19/1.61 @ ( collect_r
% 3.19/1.61 @ ^ [A4: r] :
% 3.19/1.61 ( ( F @ A4 )
% 3.19/1.61 != C ) ) )
% 3.19/1.61 => ( ( P
% 3.19/1.61 @ ^ [A4: r] : C )
% 3.19/1.61 => ( ! [A3: r,B3: option1457017436_r_l_v,F3: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( finite_finite_r
% 3.19/1.61 @ ( collect_r
% 3.19/1.61 @ ^ [C3: r] :
% 3.19/1.61 ( ( F3 @ C3 )
% 3.19/1.61 != C ) ) )
% 3.19/1.61 => ( ( ( F3 @ A3 )
% 3.19/1.61 = C )
% 3.19/1.61 => ( ( B3 != C )
% 3.19/1.61 => ( ( P @ F3 )
% 3.19/1.61 => ( P @ ( fun_up709272714_r_l_v @ F3 @ A3 @ B3 ) ) ) ) ) )
% 3.19/1.61 => ( P @ F ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_291_finite__update__induct,axiom,
% 3.19/1.61 ! [F: l > option_val_r_l_v,C: option_val_r_l_v,P: ( l > option_val_r_l_v ) > $o] :
% 3.19/1.61 ( ( finite_finite_l
% 3.19/1.61 @ ( collect_l
% 3.19/1.61 @ ^ [A4: l] :
% 3.19/1.61 ( ( F @ A4 )
% 3.19/1.61 != C ) ) )
% 3.19/1.61 => ( ( P
% 3.19/1.61 @ ^ [A4: l] : C )
% 3.19/1.61 => ( ! [A3: l,B3: option_val_r_l_v,F3: l > option_val_r_l_v] :
% 3.19/1.61 ( ( finite_finite_l
% 3.19/1.61 @ ( collect_l
% 3.19/1.61 @ ^ [C3: l] :
% 3.19/1.61 ( ( F3 @ C3 )
% 3.19/1.61 != C ) ) )
% 3.19/1.61 => ( ( ( F3 @ A3 )
% 3.19/1.61 = C )
% 3.19/1.61 => ( ( B3 != C )
% 3.19/1.61 => ( ( P @ F3 )
% 3.19/1.61 => ( P @ ( fun_up1835647912_r_l_v @ F3 @ A3 @ B3 ) ) ) ) ) )
% 3.19/1.61 => ( P @ F ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_292_substitution_Onice__ind__inv__is__inductive__invariant,axiom,
% 3.19/1.61 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v] :
% 3.19/1.61 ( ( substitution_r_l_v @ Subst )
% 3.19/1.61 => ( induct1670415253_r_l_v @ Subst
% 3.19/1.61 @ ^ [S5: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( domain1547879849_r_l_v @ S5 )
% 3.19/1.61 & ( subsum680764357_r_l_v @ S5 ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_293_substitution_Odomains__subsume__globally__def,axiom,
% 3.19/1.61 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( substitution_r_l_v @ Subst )
% 3.19/1.61 => ( ( domain1547879849_r_l_v @ S )
% 3.19/1.61 = ( ! [R6: r,Ls2: produc1156025366_r_l_v] :
% 3.19/1.61 ( ( ( S @ R6 )
% 3.19/1.61 = ( some_P1807977723_r_l_v @ Ls2 ) )
% 3.19/1.61 => ( domain87684397_l_r_v @ Ls2 ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_294_substitution_Odomains__subsume__globallyI,axiom,
% 3.19/1.61 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( substitution_r_l_v @ Subst )
% 3.19/1.61 => ( ! [R5: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E3: expr_r_l_v] :
% 3.19/1.61 ( ( ( S @ R5 )
% 3.19/1.61 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) ) )
% 3.19/1.61 => ( domain87684397_l_r_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) ) )
% 3.19/1.61 => ( domain1547879849_r_l_v @ S ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_295__092_060R_062_092_060_094sub_062GI,axiom,
% 3.19/1.61 ! [Alpha2: r > r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v,Beta2: l > l] :
% 3.19/1.61 ( ( bij_betw_r_r @ Alpha2 @ top_top_set_r @ top_top_set_r )
% 3.19/1.61 => ( ! [R5: r] :
% 3.19/1.61 ( ( ( S @ R5 )
% 3.19/1.61 = none_P277133687_r_l_v )
% 3.19/1.61 => ( ( S2 @ ( Alpha2 @ R5 ) )
% 3.19/1.61 = none_P277133687_r_l_v ) )
% 3.19/1.61 => ( ! [R5: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E3: expr_r_l_v] :
% 3.19/1.61 ( ( ( S @ R5 )
% 3.19/1.61 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) ) )
% 3.19/1.61 => ( ( S2 @ ( Alpha2 @ R5 ) )
% 3.19/1.61 = ( some_P1807977723_r_l_v @ ( r_L_r_l_v @ Alpha2 @ Beta2 @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) ) ) ) )
% 3.19/1.61 => ( ( r_G_r_l_v @ Alpha2 @ Beta2 @ S )
% 3.19/1.61 = S2 ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_296_substitution_Osubsumes__accessible__globallyI,axiom,
% 3.19/1.61 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( substitution_r_l_v @ Subst )
% 3.19/1.61 => ( ! [R_1: r,Sigma_1: l > option_val_r_l_v,Tau_1: l > option_val_r_l_v,E_1: expr_r_l_v,R_2: r,Sigma_2: l > option_val_r_l_v,Tau_2: l > option_val_r_l_v,E_2: expr_r_l_v] :
% 3.19/1.61 ( ( ( S @ R_1 )
% 3.19/1.61 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_1 @ ( produc1834103605_r_l_v @ Tau_1 @ E_1 ) ) ) )
% 3.19/1.61 => ( ( ( S @ R_2 )
% 3.19/1.61 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_2 @ ( produc1834103605_r_l_v @ Tau_2 @ E_2 ) ) ) )
% 3.19/1.61 => ( subsum148050133_r_l_v @ R_1 @ R_2 @ S ) ) )
% 3.19/1.61 => ( subsum680764357_r_l_v @ S ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_297__092_060R_062_092_060_094sub_062G__implements__renaming,axiom,
% 3.19/1.61 ! [Alpha2: r > r,Beta2: l > l,S: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( bij_betw_r_r @ Alpha2 @ top_top_set_r @ top_top_set_r )
% 3.19/1.61 => ( is_glo1871033385_r_l_v @ Alpha2 @ Beta2 @ S @ ( r_G_r_l_v @ Alpha2 @ Beta2 @ S ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_298_subsumes__accessible__globallyI,axiom,
% 3.19/1.61 ! [S: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ! [R_1: r,Sigma_1: l > option_val_r_l_v,Tau_1: l > option_val_r_l_v,E_1: expr_r_l_v,R_2: r,Sigma_2: l > option_val_r_l_v,Tau_2: l > option_val_r_l_v,E_2: expr_r_l_v] :
% 3.19/1.61 ( ( ( S @ R_1 )
% 3.19/1.61 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_1 @ ( produc1834103605_r_l_v @ Tau_1 @ E_1 ) ) ) )
% 3.19/1.61 => ( ( ( S @ R_2 )
% 3.19/1.61 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_2 @ ( produc1834103605_r_l_v @ Tau_2 @ E_2 ) ) ) )
% 3.19/1.61 => ( subsum148050133_r_l_v @ R_1 @ R_2 @ S ) ) )
% 3.19/1.61 => ( subsum680764357_r_l_v @ S ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_299_renaming__distr__global_I1_J,axiom,
% 3.19/1.61 ! [Alpha2: r > r,Beta2: l > l,S: r > option1457017436_r_l_v,R: r,Ls: produc1156025366_r_l_v] :
% 3.19/1.61 ( ( bij_betw_r_r @ Alpha2 @ top_top_set_r @ top_top_set_r )
% 3.19/1.61 => ( ( r_G_r_l_v @ Alpha2 @ Beta2 @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ Ls ) ) )
% 3.19/1.61 = ( fun_up709272714_r_l_v @ ( r_G_r_l_v @ Alpha2 @ Beta2 @ S ) @ ( Alpha2 @ R ) @ ( some_P1807977723_r_l_v @ ( r_L_r_l_v @ Alpha2 @ Beta2 @ Ls ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_300_RID_092_060_094sub_062GI_I2_J,axiom,
% 3.19/1.61 ! [S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
% 3.19/1.61 ( ( ( S @ R2 )
% 3.19/1.61 = ( some_P1807977723_r_l_v @ Ls ) )
% 3.19/1.61 => ( ( member_r @ R @ ( rID_L_l_r_v @ Ls ) )
% 3.19/1.61 => ( member_r @ R @ ( rID_G_r_l_v @ S ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_301_local__state__of__finite__restricted__global__state__is__finite_I1_J,axiom,
% 3.19/1.61 ! [S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
% 3.19/1.61 ( ( ( S @ R2 )
% 3.19/1.61 = ( some_P1807977723_r_l_v @ Ls ) )
% 3.19/1.61 => ( ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 3.19/1.61 => ( ( R != R2 )
% 3.19/1.61 => ( finite_finite_r @ ( rID_L_l_r_v @ Ls ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_302_substitution_Olocal__state__of__finite__restricted__global__state__is__finite_I1_J,axiom,
% 3.19/1.61 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
% 3.19/1.61 ( ( substitution_r_l_v @ Subst )
% 3.19/1.61 => ( ( ( S @ R2 )
% 3.19/1.61 = ( some_P1807977723_r_l_v @ Ls ) )
% 3.19/1.61 => ( ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 3.19/1.61 => ( ( R != R2 )
% 3.19/1.61 => ( finite_finite_r @ ( rID_L_l_r_v @ Ls ) ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_303_reachable__imp__identifiers__available_I2_J,axiom,
% 3.19/1.61 ! [S: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( reachable_r_l_v @ subst @ S )
% 3.19/1.61 => ( ~ ( finite_finite_l @ top_top_set_l )
% 3.19/1.61 => ? [L: l] :
% 3.19/1.61 ~ ( member_l @ L @ ( lID_G_r_l_v @ S ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_304_only__fork__introduces__rids,axiom,
% 3.19/1.61 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.19/1.61 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E5: cntxt_r_l_v,E3: expr_r_l_v] :
% 3.19/1.61 ( ( S @ R )
% 3.19/1.61 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E5 @ ( rfork_r_l_v @ E3 ) ) ) ) ) )
% 3.19/1.61 => ( ord_less_eq_set_r @ ( rID_G_r_l_v @ S2 ) @ ( rID_G_r_l_v @ S ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_305_empty__map__finite_I4_J,axiom,
% 3.19/1.61 ( finite_finite_l
% 3.19/1.61 @ ( lID_G_r_l_v
% 3.19/1.61 @ ^ [X2: r] : none_P277133687_r_l_v ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_306_in__renamed__in__unlabelled__global_I2_J,axiom,
% 3.19/1.61 ! [Alpha2: r > r,Beta2: l > l,L2: l,S: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( bij_betw_r_r @ Alpha2 @ top_top_set_r @ top_top_set_r )
% 3.19/1.61 => ( ( bij_betw_l_l @ Beta2 @ top_top_set_l @ top_top_set_l )
% 3.19/1.61 => ( ( member_l @ ( Beta2 @ L2 ) @ ( lID_G_r_l_v @ ( r_G_r_l_v @ Alpha2 @ Beta2 @ S ) ) )
% 3.19/1.61 = ( member_l @ L2 @ ( lID_G_r_l_v @ S ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_307_RID_092_060_094sub_062L__finite__invariant,axiom,
% 3.19/1.61 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.19/1.61 => ( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
% 3.19/1.61 => ( finite_finite_l @ ( lID_G_r_l_v @ S2 ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_308_reachable__imp__identifiers__finite_I2_J,axiom,
% 3.19/1.61 ! [S: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( reachable_r_l_v @ subst @ S )
% 3.19/1.61 => ( finite_finite_l @ ( lID_G_r_l_v @ S ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_309_in__restricted__global__in__unrestricted__global_I2_J,axiom,
% 3.19/1.61 ! [L2: l,S: r > option1457017436_r_l_v,R: r] :
% 3.19/1.61 ( ( member_l @ L2 @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 3.19/1.61 => ( member_l @ L2 @ ( lID_G_r_l_v @ S ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_310_LID_092_060_094sub_062GI,axiom,
% 3.19/1.61 ! [S: r > option1457017436_r_l_v,R: r,Ls: produc1156025366_r_l_v,L2: l] :
% 3.19/1.61 ( ( ( S @ R )
% 3.19/1.61 = ( some_P1807977723_r_l_v @ Ls ) )
% 3.19/1.61 => ( ( member_l @ L2 @ ( lID_L_l_r_v @ Ls ) )
% 3.19/1.61 => ( member_l @ L2 @ ( lID_G_r_l_v @ S ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_311_finite__Collect__subsets,axiom,
% 3.19/1.61 ! [A5: set_r] :
% 3.19/1.61 ( ( finite_finite_r @ A5 )
% 3.19/1.61 => ( finite_finite_set_r
% 3.19/1.61 @ ( collect_set_r
% 3.19/1.61 @ ^ [B6: set_r] : ( ord_less_eq_set_r @ B6 @ A5 ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_312_finite__Collect__subsets,axiom,
% 3.19/1.61 ! [A5: set_l] :
% 3.19/1.61 ( ( finite_finite_l @ A5 )
% 3.19/1.61 => ( finite_finite_set_l
% 3.19/1.61 @ ( collect_set_l
% 3.19/1.61 @ ^ [B6: set_l] : ( ord_less_eq_set_l @ B6 @ A5 ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_313_finite__state__imp__restriction__finite_I2_J,axiom,
% 3.19/1.61 ! [S: r > option1457017436_r_l_v,R: r] :
% 3.19/1.61 ( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
% 3.19/1.61 => ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_314_in__restricted__global__in__updated__global_I2_J,axiom,
% 3.19/1.61 ! [L2: l,S: r > option1457017436_r_l_v,R: r,Ls: produc1156025366_r_l_v] :
% 3.19/1.61 ( ( member_l @ L2 @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 3.19/1.61 => ( member_l @ L2 @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ Ls ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_315_local__state__of__finite__restricted__global__state__is__finite_I2_J,axiom,
% 3.19/1.61 ! [S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
% 3.19/1.61 ( ( ( S @ R2 )
% 3.19/1.61 = ( some_P1807977723_r_l_v @ Ls ) )
% 3.19/1.61 => ( ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 3.19/1.61 => ( ( R != R2 )
% 3.19/1.61 => ( finite_finite_l @ ( lID_L_l_r_v @ Ls ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_316_ID__restricted__global__subset__unrestricted_I1_J,axiom,
% 3.19/1.61 ! [S: r > option1457017436_r_l_v,R: r] : ( ord_less_eq_set_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) @ ( lID_G_r_l_v @ S ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_317_finite__has__minimal2,axiom,
% 3.19/1.61 ! [A5: set_set_r,A: set_r] :
% 3.19/1.61 ( ( finite_finite_set_r @ A5 )
% 3.19/1.61 => ( ( member_set_r @ A @ A5 )
% 3.19/1.61 => ? [X3: set_r] :
% 3.19/1.61 ( ( member_set_r @ X3 @ A5 )
% 3.19/1.61 & ( ord_less_eq_set_r @ X3 @ A )
% 3.19/1.61 & ! [Xa2: set_r] :
% 3.19/1.61 ( ( member_set_r @ Xa2 @ A5 )
% 3.19/1.61 => ( ( ord_less_eq_set_r @ Xa2 @ X3 )
% 3.19/1.61 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_318_finite__has__minimal2,axiom,
% 3.19/1.61 ! [A5: set_set_l,A: set_l] :
% 3.19/1.61 ( ( finite_finite_set_l @ A5 )
% 3.19/1.61 => ( ( member_set_l @ A @ A5 )
% 3.19/1.61 => ? [X3: set_l] :
% 3.19/1.61 ( ( member_set_l @ X3 @ A5 )
% 3.19/1.61 & ( ord_less_eq_set_l @ X3 @ A )
% 3.19/1.61 & ! [Xa2: set_l] :
% 3.19/1.61 ( ( member_set_l @ Xa2 @ A5 )
% 3.19/1.61 => ( ( ord_less_eq_set_l @ Xa2 @ X3 )
% 3.19/1.61 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_319_finite__has__maximal2,axiom,
% 3.19/1.61 ! [A5: set_set_r,A: set_r] :
% 3.19/1.61 ( ( finite_finite_set_r @ A5 )
% 3.19/1.61 => ( ( member_set_r @ A @ A5 )
% 3.19/1.61 => ? [X3: set_r] :
% 3.19/1.61 ( ( member_set_r @ X3 @ A5 )
% 3.19/1.61 & ( ord_less_eq_set_r @ A @ X3 )
% 3.19/1.61 & ! [Xa2: set_r] :
% 3.19/1.61 ( ( member_set_r @ Xa2 @ A5 )
% 3.19/1.61 => ( ( ord_less_eq_set_r @ X3 @ Xa2 )
% 3.19/1.61 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_320_finite__has__maximal2,axiom,
% 3.19/1.61 ! [A5: set_set_l,A: set_l] :
% 3.19/1.61 ( ( finite_finite_set_l @ A5 )
% 3.19/1.61 => ( ( member_set_l @ A @ A5 )
% 3.19/1.61 => ? [X3: set_l] :
% 3.19/1.61 ( ( member_set_l @ X3 @ A5 )
% 3.19/1.61 & ( ord_less_eq_set_l @ A @ X3 )
% 3.19/1.61 & ! [Xa2: set_l] :
% 3.19/1.61 ( ( member_set_l @ Xa2 @ A5 )
% 3.19/1.61 => ( ( ord_less_eq_set_l @ X3 @ Xa2 )
% 3.19/1.61 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_321_rev__finite__subset,axiom,
% 3.19/1.61 ! [B5: set_r,A5: set_r] :
% 3.19/1.61 ( ( finite_finite_r @ B5 )
% 3.19/1.61 => ( ( ord_less_eq_set_r @ A5 @ B5 )
% 3.19/1.61 => ( finite_finite_r @ A5 ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_322_rev__finite__subset,axiom,
% 3.19/1.61 ! [B5: set_l,A5: set_l] :
% 3.19/1.61 ( ( finite_finite_l @ B5 )
% 3.19/1.61 => ( ( ord_less_eq_set_l @ A5 @ B5 )
% 3.19/1.61 => ( finite_finite_l @ A5 ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_323_infinite__super,axiom,
% 3.19/1.61 ! [S6: set_r,T2: set_r] :
% 3.19/1.61 ( ( ord_less_eq_set_r @ S6 @ T2 )
% 3.19/1.61 => ( ~ ( finite_finite_r @ S6 )
% 3.19/1.61 => ~ ( finite_finite_r @ T2 ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_324_infinite__super,axiom,
% 3.19/1.61 ! [S6: set_l,T2: set_l] :
% 3.19/1.61 ( ( ord_less_eq_set_l @ S6 @ T2 )
% 3.19/1.61 => ( ~ ( finite_finite_l @ S6 )
% 3.19/1.61 => ~ ( finite_finite_l @ T2 ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_325_finite__subset,axiom,
% 3.19/1.61 ! [A5: set_r,B5: set_r] :
% 3.19/1.61 ( ( ord_less_eq_set_r @ A5 @ B5 )
% 3.19/1.61 => ( ( finite_finite_r @ B5 )
% 3.19/1.61 => ( finite_finite_r @ A5 ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_326_finite__subset,axiom,
% 3.19/1.61 ! [A5: set_l,B5: set_l] :
% 3.19/1.61 ( ( ord_less_eq_set_l @ A5 @ B5 )
% 3.19/1.61 => ( ( finite_finite_l @ B5 )
% 3.19/1.61 => ( finite_finite_l @ A5 ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_327_LID_092_060_094sub_062GE,axiom,
% 3.19/1.61 ! [L2: l,S: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( member_l @ L2 @ ( lID_G_r_l_v @ S ) )
% 3.19/1.61 => ~ ! [R5: r,Ls3: produc1156025366_r_l_v] :
% 3.19/1.61 ( ( ( S @ R5 )
% 3.19/1.61 = ( some_P1807977723_r_l_v @ Ls3 ) )
% 3.19/1.61 => ~ ( member_l @ L2 @ ( lID_L_l_r_v @ Ls3 ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_328_substitution_ORID_092_060_094sub_062L__finite__invariant,axiom,
% 3.19/1.61 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( substitution_r_l_v @ Subst )
% 3.19/1.61 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.19/1.61 => ( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
% 3.19/1.61 => ( finite_finite_l @ ( lID_G_r_l_v @ S2 ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_329_ID__restricted__global__subset__unrestricted_I2_J,axiom,
% 3.19/1.61 ! [S: r > option1457017436_r_l_v,R: r] : ( ord_less_eq_set_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) @ ( rID_G_r_l_v @ S ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_330_substitution_Oreachable__imp__identifiers__finite_I2_J,axiom,
% 3.19/1.61 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( substitution_r_l_v @ Subst )
% 3.19/1.61 => ( ( reachable_r_l_v @ Subst @ S )
% 3.19/1.61 => ( finite_finite_l @ ( lID_G_r_l_v @ S ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_331_substitution_Oempty__map__finite_I4_J,axiom,
% 3.19/1.61 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v] :
% 3.19/1.61 ( ( substitution_r_l_v @ Subst )
% 3.19/1.61 => ( finite_finite_l
% 3.19/1.61 @ ( lID_G_r_l_v
% 3.19/1.61 @ ^ [X2: r] : none_P277133687_r_l_v ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_332_substitution_Oreachable__imp__identifiers__available_I2_J,axiom,
% 3.19/1.61 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( substitution_r_l_v @ Subst )
% 3.19/1.61 => ( ( reachable_r_l_v @ Subst @ S )
% 3.19/1.61 => ( ~ ( finite_finite_l @ top_top_set_l )
% 3.19/1.61 => ? [L: l] :
% 3.19/1.61 ~ ( member_l @ L @ ( lID_G_r_l_v @ S ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_333_substitution_Ofinite__state__imp__restriction__finite_I2_J,axiom,
% 3.19/1.61 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r] :
% 3.19/1.61 ( ( substitution_r_l_v @ Subst )
% 3.19/1.61 => ( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
% 3.19/1.61 => ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_334_substitution_Oin__renamed__in__unlabelled__global_I2_J,axiom,
% 3.19/1.61 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,Alpha2: r > r,Beta2: l > l,L2: l,S: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( substitution_r_l_v @ Subst )
% 3.19/1.61 => ( ( bij_betw_r_r @ Alpha2 @ top_top_set_r @ top_top_set_r )
% 3.19/1.61 => ( ( bij_betw_l_l @ Beta2 @ top_top_set_l @ top_top_set_l )
% 3.19/1.61 => ( ( member_l @ ( Beta2 @ L2 ) @ ( lID_G_r_l_v @ ( r_G_r_l_v @ Alpha2 @ Beta2 @ S ) ) )
% 3.19/1.61 = ( member_l @ L2 @ ( lID_G_r_l_v @ S ) ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_335_substitution_Olocal__state__of__finite__restricted__global__state__is__finite_I2_J,axiom,
% 3.19/1.61 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
% 3.19/1.61 ( ( substitution_r_l_v @ Subst )
% 3.19/1.61 => ( ( ( S @ R2 )
% 3.19/1.61 = ( some_P1807977723_r_l_v @ Ls ) )
% 3.19/1.61 => ( ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 3.19/1.61 => ( ( R != R2 )
% 3.19/1.61 => ( finite_finite_l @ ( lID_L_l_r_v @ Ls ) ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_336_substitution_Oonly__fork__introduces__rids,axiom,
% 3.19/1.61 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( substitution_r_l_v @ Subst )
% 3.19/1.61 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.19/1.61 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E5: cntxt_r_l_v,E3: expr_r_l_v] :
% 3.19/1.61 ( ( S @ R )
% 3.19/1.61 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E5 @ ( rfork_r_l_v @ E3 ) ) ) ) ) )
% 3.19/1.61 => ( ord_less_eq_set_r @ ( rID_G_r_l_v @ S2 ) @ ( rID_G_r_l_v @ S ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_337_only__new__introduces__lids_H,axiom,
% 3.19/1.61 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v,L2: l] :
% 3.19/1.61 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.19/1.61 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E5: cntxt_r_l_v,V2: val_r_l_v] :
% 3.19/1.61 ( ( S @ R )
% 3.19/1.61 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E5 @ ( ref_r_l_v @ ( vE_r_l_v @ V2 ) ) ) ) ) ) )
% 3.19/1.61 => ( ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S ) )
% 3.19/1.61 => ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S2 ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_338_SLC__new,axiom,
% 3.19/1.61 ! [S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,V: val_r_l_v,S_2: r > option1457017436_r_l_v,L2: l,R2: r,S_22: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( ( S_1 @ R )
% 3.19/1.61 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 3.19/1.61 => ( ( S_2
% 3.19/1.61 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) ) ) ) ) ) )
% 3.19/1.61 => ( ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S_1 ) )
% 3.19/1.61 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 3.19/1.61 => ( ( R != R2 )
% 3.19/1.61 => ( ( reachable_r_l_v @ subst @ S_1 )
% 3.19/1.61 => ( ~ ( finite_finite_l @ top_top_set_l )
% 3.19/1.61 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.19/1.61 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 3.19/1.61 | ( S_2 = S_3 ) )
% 3.19/1.61 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 3.19/1.61 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_339_val_Oinject_I3_J,axiom,
% 3.19/1.61 ! [X32: l,Y32: l] :
% 3.19/1.61 ( ( ( loc_l_r_v @ X32 )
% 3.19/1.61 = ( loc_l_r_v @ Y32 ) )
% 3.19/1.61 = ( X32 = Y32 ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_340_expr_Oinject_I4_J,axiom,
% 3.19/1.61 ! [X4: expr_r_l_v,Y4: expr_r_l_v] :
% 3.19/1.61 ( ( ( ref_r_l_v @ X4 )
% 3.19/1.61 = ( ref_r_l_v @ Y4 ) )
% 3.19/1.61 = ( X4 = Y4 ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_341_revision__step_Onew,axiom,
% 3.19/1.61 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,V: val_r_l_v,L2: l] :
% 3.19/1.61 ( ( ( S @ R )
% 3.19/1.61 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 3.19/1.61 => ( ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S ) )
% 3.19/1.61 => ( revision_step_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) ) ) ) ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_342_only__new__introduces__lids,axiom,
% 3.19/1.61 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.19/1.61 => ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E5: cntxt_r_l_v,V2: val_r_l_v] :
% 3.19/1.61 ( ( S @ R )
% 3.19/1.61 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E5 @ ( ref_r_l_v @ ( vE_r_l_v @ V2 ) ) ) ) ) ) )
% 3.19/1.61 => ( ord_less_eq_set_l @ ( lID_G_r_l_v @ S2 ) @ ( lID_G_r_l_v @ S ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_343_new__pseudodeterministic,axiom,
% 3.19/1.61 ! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( ( S @ R )
% 3.19/1.61 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 3.19/1.61 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.19/1.61 = ( ? [L3: l] :
% 3.19/1.61 ( ~ ( member_l @ L3 @ ( lID_G_r_l_v @ S ) )
% 3.19/1.61 & ( S2
% 3.19/1.61 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L3 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( loc_l_r_v @ L3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_344_expr_Odistinct_I5_J,axiom,
% 3.19/1.61 ! [X1: val_r_l_v,X4: expr_r_l_v] :
% 3.19/1.61 ( ( vE_r_l_v @ X1 )
% 3.19/1.61 != ( ref_r_l_v @ X4 ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_345_val_Odistinct_I15_J,axiom,
% 3.19/1.61 ! [X32: l,X4: r] :
% 3.19/1.61 ( ( loc_l_r_v @ X32 )
% 3.19/1.61 != ( rid_r_l_v @ X4 ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_346_expr_Odistinct_I43_J,axiom,
% 3.19/1.61 ! [X4: expr_r_l_v,X8: expr_r_l_v] :
% 3.19/1.61 ( ( ref_r_l_v @ X4 )
% 3.19/1.61 != ( rjoin_r_l_v @ X8 ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_347_expr_Odistinct_I41_J,axiom,
% 3.19/1.61 ! [X4: expr_r_l_v,X7: expr_r_l_v] :
% 3.19/1.61 ( ( ref_r_l_v @ X4 )
% 3.19/1.61 != ( rfork_r_l_v @ X7 ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_348_val_Odistinct_I3_J,axiom,
% 3.19/1.61 ! [X1: const,X32: l] :
% 3.19/1.61 ( ( cV_r_l_v @ X1 )
% 3.19/1.61 != ( loc_l_r_v @ X32 ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_349_substitution_Onew__pseudodeterministic,axiom,
% 3.19/1.61 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( substitution_r_l_v @ Subst )
% 3.19/1.61 => ( ( ( S @ R )
% 3.19/1.61 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 3.19/1.61 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.19/1.61 = ( ? [L3: l] :
% 3.19/1.61 ( ~ ( member_l @ L3 @ ( lID_G_r_l_v @ S ) )
% 3.19/1.61 & ( S2
% 3.19/1.61 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L3 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( loc_l_r_v @ L3 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_350_substitution_Orevision__step_Onew,axiom,
% 3.19/1.61 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,V: val_r_l_v,L2: l] :
% 3.19/1.61 ( ( substitution_r_l_v @ Subst )
% 3.19/1.61 => ( ( ( S @ R )
% 3.19/1.61 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 3.19/1.61 => ( ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S ) )
% 3.19/1.61 => ( revision_step_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(fact_351_substitution_OSLC__new,axiom,
% 3.19/1.61 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,V: val_r_l_v,S_2: r > option1457017436_r_l_v,L2: l,R2: r,S_22: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( substitution_r_l_v @ Subst )
% 3.19/1.61 => ( ( ( S_1 @ R )
% 3.19/1.61 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 3.19/1.61 => ( ( S_2
% 3.19/1.61 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) ) ) ) ) ) )
% 3.19/1.61 => ( ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S_1 ) )
% 3.19/1.61 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
% 3.19/1.61 => ( ( R != R2 )
% 3.19/1.61 => ( ( reachable_r_l_v @ Subst @ S_1 )
% 3.19/1.61 => ( ~ ( finite_finite_l @ top_top_set_l )
% 3.19/1.61 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.19/1.61 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.19/1.61 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 3.19/1.61 | ( S_2 = S_3 ) )
% 3.19/1.61 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 3.19/1.61 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(help_If_2_1_If_001t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_T,axiom,
% 3.19/1.61 ! [X: option_val_r_l_v,Y: option_val_r_l_v] :
% 3.19/1.61 ( ( if_option_val_r_l_v @ $false @ X @ Y )
% 3.19/1.61 = Y ) ).
% 3.19/1.61
% 3.19/1.61 thf(help_If_1_1_If_001t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_T,axiom,
% 3.19/1.61 ! [X: option_val_r_l_v,Y: option_val_r_l_v] :
% 3.19/1.61 ( ( if_option_val_r_l_v @ $true @ X @ Y )
% 3.19/1.61 = X ) ).
% 3.19/1.61
% 3.19/1.61 thf(help_If_3_1_If_001t__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J_T,axiom,
% 3.19/1.61 ! [P: $o] :
% 3.19/1.61 ( ( P = $true )
% 3.19/1.61 | ( P = $false ) ) ).
% 3.19/1.61
% 3.19/1.61 thf(help_If_2_1_If_001t__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J_T,axiom,
% 3.19/1.61 ! [X: option1457017436_r_l_v,Y: option1457017436_r_l_v] :
% 3.19/1.61 ( ( if_opt1153928738_r_l_v @ $false @ X @ Y )
% 3.19/1.61 = Y ) ).
% 3.19/1.61
% 3.19/1.61 thf(help_If_1_1_If_001t__Option__Ooption_It__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J_T,axiom,
% 3.19/1.61 ! [X: option1457017436_r_l_v,Y: option1457017436_r_l_v] :
% 3.19/1.61 ( ( if_opt1153928738_r_l_v @ $true @ X @ Y )
% 3.19/1.61 = X ) ).
% 3.19/1.61
% 3.19/1.61 thf(conj_0,conjecture,
% 3.19/1.61 ( s
% 3.19/1.61 = ( fun_up709272714_r_l_v @ s @ r2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( rfork_r_l_v @ e2 ) ) ) ) ) ) ) ).
% 3.19/1.61 ------------------------
% 3.19/1.63 % (16216)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15893 for (2999ds/183Mi)
% 3.19/1.63 % (16220)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_15893 for (2999ds/2Mi)
% 3.19/1.63 % (16220)Instruction limit reached!
% 3.19/1.63 % (16220)------------------------------
% 3.19/1.63 % (16220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.63 % (16220)Termination reason: Unknown
% 3.19/1.63 % (16220)Termination phase: shuffling
% 3.19/1.63
% 3.19/1.63 % (16220)Memory used [KB]: 1535
% 3.19/1.63 % (16220)Time elapsed: 0.002 s
% 3.19/1.63 % (16220)Instructions burned: 2 (million)
% 3.19/1.63 % (16220)------------------------------
% 3.19/1.63 % (16220)------------------------------
% 3.19/1.64 % (16217)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_15893 for (2999ds/4Mi)
% 3.19/1.64 % (16218)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_15893 for (2999ds/27Mi)
% 3.19/1.64 % (16219)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15893 for (2999ds/2Mi)
% 3.19/1.64 % (16221)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_15893 for (2999ds/275Mi)
% 3.19/1.64 % (16222)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15893 for (2999ds/18Mi)
% 3.19/1.64 % (16219)Instruction limit reached!
% 3.19/1.64 % (16219)------------------------------
% 3.19/1.64 % (16219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.64 % (16219)Termination reason: Unknown
% 3.19/1.64 % (16219)Termination phase: shuffling
% 3.19/1.64
% 3.19/1.64 % (16219)Memory used [KB]: 1535
% 3.19/1.64 % (16219)Time elapsed: 0.004 s
% 3.19/1.64 % (16219)Instructions burned: 2 (million)
% 3.19/1.64 % (16219)------------------------------
% 3.19/1.64 % (16219)------------------------------
% 3.19/1.64 % (16217)Instruction limit reached!
% 3.19/1.64 % (16217)------------------------------
% 3.19/1.64 % (16217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.64 % (16217)Termination reason: Unknown
% 3.19/1.64 % (16217)Termination phase: shuffling
% 3.19/1.64
% 3.19/1.64 % (16217)Memory used [KB]: 1663
% 3.19/1.64 % (16217)Time elapsed: 0.005 s
% 3.19/1.64 % (16217)Instructions burned: 4 (million)
% 3.19/1.64 % (16217)------------------------------
% 3.19/1.64 % (16217)------------------------------
% 3.19/1.64 % (16223)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15893 for (2999ds/3Mi)
% 3.19/1.64 % (16223)Instruction limit reached!
% 3.19/1.64 % (16223)------------------------------
% 3.19/1.64 % (16223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.64 % (16223)Termination reason: Unknown
% 3.19/1.64 % (16223)Termination phase: shuffling
% 3.19/1.64
% 3.19/1.64 % (16223)Memory used [KB]: 1535
% 3.19/1.64 % (16223)Time elapsed: 0.003 s
% 3.19/1.64 % (16223)Instructions burned: 3 (million)
% 3.19/1.64 % (16223)------------------------------
% 3.19/1.64 % (16223)------------------------------
% 3.19/1.65 % (16222)Instruction limit reached!
% 3.19/1.65 % (16222)------------------------------
% 3.19/1.65 % (16222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.65 % (16222)Termination reason: Unknown
% 3.19/1.65 % (16222)Termination phase: shuffling
% 3.19/1.65
% 3.19/1.65 % (16222)Memory used [KB]: 1918
% 3.19/1.65 % (16222)Time elapsed: 0.014 s
% 3.19/1.65 % (16222)Instructions burned: 19 (million)
% 3.19/1.65 % (16222)------------------------------
% 3.19/1.65 % (16222)------------------------------
% 3.19/1.65 % (16226)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_15893 for (2999ds/3Mi)
% 3.19/1.66 % (16226)Instruction limit reached!
% 3.19/1.66 % (16226)------------------------------
% 3.19/1.66 % (16226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.66 % (16226)Termination reason: Unknown
% 3.19/1.66 % (16226)Termination phase: shuffling
% 3.19/1.66
% 3.19/1.66 % (16226)Memory used [KB]: 1535
% 3.19/1.66 % (16226)Time elapsed: 0.003 s
% 3.19/1.66 % (16226)Instructions burned: 3 (million)
% 3.19/1.66 % (16226)------------------------------
% 3.19/1.66 % (16226)------------------------------
% 3.19/1.66 % (16218)Instruction limit reached!
% 3.19/1.66 % (16218)------------------------------
% 3.19/1.66 % (16218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.66 % (16218)Termination reason: Unknown
% 3.19/1.66 % (16218)Termination phase: shuffling
% 3.19/1.66
% 3.19/1.66 % (16218)Memory used [KB]: 2046
% 3.19/1.66 % (16218)Time elapsed: 0.019 s
% 3.19/1.66 % (16218)Instructions burned: 27 (million)
% 3.19/1.66 % (16218)------------------------------
% 3.19/1.66 % (16218)------------------------------
% 3.19/1.66 % (16224)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_15893 for (2999ds/37Mi)
% 3.19/1.66 % (16225)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_15893 for (2999ds/15Mi)
% 3.19/1.67 % (16228)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_15893 for (2999ds/7Mi)
% 3.19/1.67 % (16227)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_15893 for (2999ds/1041Mi)
% 3.19/1.67 % (16225)Instruction limit reached!
% 3.19/1.67 % (16225)------------------------------
% 3.19/1.67 % (16225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.67 % (16225)Termination reason: Unknown
% 3.19/1.67 % (16225)Termination phase: shuffling
% 3.19/1.67
% 3.19/1.67 % (16225)Memory used [KB]: 1791
% 3.19/1.67 % (16225)Time elapsed: 0.011 s
% 3.19/1.67 % (16225)Instructions burned: 15 (million)
% 3.19/1.67 % (16225)------------------------------
% 3.19/1.67 % (16225)------------------------------
% 3.19/1.67 % (16228)Instruction limit reached!
% 3.19/1.67 % (16228)------------------------------
% 3.19/1.67 % (16228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.67 % (16228)Termination reason: Unknown
% 3.19/1.67 % (16228)Termination phase: shuffling
% 3.19/1.67
% 3.19/1.67 % (16228)Memory used [KB]: 1791
% 3.19/1.67 % (16228)Time elapsed: 0.005 s
% 3.19/1.67 % (16228)Instructions burned: 9 (million)
% 3.19/1.67 % (16228)------------------------------
% 3.19/1.67 % (16228)------------------------------
% 3.19/1.67 % (16229)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_15893 for (2999ds/16Mi)
% 3.19/1.68 % (16224)Instruction limit reached!
% 3.19/1.68 % (16224)------------------------------
% 3.19/1.68 % (16224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.68 % (16224)Termination reason: Unknown
% 3.19/1.68 % (16224)Termination phase: shuffling
% 3.19/1.68
% 3.19/1.68 % (16224)Memory used [KB]: 2302
% 3.19/1.68 % (16224)Time elapsed: 0.021 s
% 3.19/1.68 % (16224)Instructions burned: 38 (million)
% 3.19/1.68 % (16224)------------------------------
% 3.19/1.68 % (16224)------------------------------
% 3.19/1.68 % (16231)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_15893 for (2999ds/3Mi)
% 3.19/1.68 % (16231)Instruction limit reached!
% 3.19/1.68 % (16231)------------------------------
% 3.19/1.68 % (16231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.68 % (16231)Termination reason: Unknown
% 3.19/1.68 % (16231)Termination phase: shuffling
% 3.19/1.68
% 3.19/1.68 % (16231)Memory used [KB]: 1535
% 3.19/1.68 % (16231)Time elapsed: 0.003 s
% 3.19/1.68 % (16231)Instructions burned: 3 (million)
% 3.19/1.68 % (16231)------------------------------
% 3.19/1.68 % (16231)------------------------------
% 3.19/1.68 % (16216)Instruction limit reached!
% 3.19/1.68 % (16216)------------------------------
% 3.19/1.68 % (16216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.68 % (16216)Termination reason: Unknown
% 3.19/1.68 % (16216)Termination phase: Property scanning
% 3.19/1.68
% 3.19/1.68 % (16216)Memory used [KB]: 3326
% 3.19/1.68 % (16216)Time elapsed: 0.052 s
% 3.19/1.68 % (16216)Instructions burned: 183 (million)
% 3.19/1.68 % (16216)------------------------------
% 3.19/1.68 % (16216)------------------------------
% 3.19/1.68 % (16229)Instruction limit reached!
% 3.19/1.68 % (16229)------------------------------
% 3.19/1.68 % (16229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.68 % (16229)Termination reason: Unknown
% 3.19/1.68 % (16229)Termination phase: shuffling
% 3.19/1.68
% 3.19/1.68 % (16229)Memory used [KB]: 1918
% 3.19/1.68 % (16229)Time elapsed: 0.012 s
% 3.19/1.68 % (16229)Instructions burned: 17 (million)
% 3.19/1.68 % (16229)------------------------------
% 3.19/1.68 % (16229)------------------------------
% 3.19/1.69 % (16230)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_15893 for (2999ds/3Mi)
% 3.19/1.69 % (16230)Instruction limit reached!
% 3.19/1.69 % (16230)------------------------------
% 3.19/1.69 % (16230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.69 % (16230)Termination reason: Unknown
% 3.19/1.69 % (16230)Termination phase: shuffling
% 3.19/1.69
% 3.19/1.69 % (16230)Memory used [KB]: 1535
% 3.19/1.69 % (16230)Time elapsed: 0.004 s
% 3.19/1.69 % (16230)Instructions burned: 3 (million)
% 3.19/1.69 % (16230)------------------------------
% 3.19/1.69 % (16230)------------------------------
% 3.19/1.69 % (16232)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_15893 for (2999ds/7Mi)
% 3.19/1.69 % (16233)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_15893 for (2999ds/3Mi)
% 3.19/1.69 % (16232)Instruction limit reached!
% 3.19/1.69 % (16232)------------------------------
% 3.19/1.69 % (16232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.69 % (16232)Termination reason: Unknown
% 3.19/1.69 % (16232)Termination phase: shuffling
% 3.19/1.69
% 3.19/1.69 % (16232)Memory used [KB]: 1663
% 3.19/1.69 % (16232)Time elapsed: 0.004 s
% 3.19/1.69 % (16232)Instructions burned: 8 (million)
% 3.19/1.69 % (16232)------------------------------
% 3.19/1.69 % (16232)------------------------------
% 3.19/1.69 % (16234)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_15893 for (2999ds/4Mi)
% 3.19/1.69 % (16233)Instruction limit reached!
% 3.19/1.69 % (16233)------------------------------
% 3.19/1.69 % (16233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.69 % (16233)Termination reason: Unknown
% 3.19/1.69 % (16233)Termination phase: shuffling
% 3.19/1.69
% 3.19/1.69 % (16233)Memory used [KB]: 1663
% 3.19/1.69 % (16233)Time elapsed: 0.003 s
% 3.19/1.69 % (16233)Instructions burned: 3 (million)
% 3.19/1.69 % (16233)------------------------------
% 3.19/1.69 % (16233)------------------------------
% 3.19/1.69 % (16234)Instruction limit reached!
% 3.19/1.69 % (16234)------------------------------
% 3.19/1.69 % (16234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.69 % (16234)Termination reason: Unknown
% 3.19/1.69 % (16234)Termination phase: shuffling
% 3.19/1.69
% 3.19/1.69 % (16234)Memory used [KB]: 1663
% 3.19/1.69 % (16234)Time elapsed: 0.003 s
% 3.19/1.69 % (16234)Instructions burned: 6 (million)
% 3.19/1.69 % (16234)------------------------------
% 3.19/1.69 % (16234)------------------------------
% 3.19/1.70 % (16235)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_15893 for (2999ds/18Mi)
% 3.19/1.70 % (16237)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_15893 for (2999ds/6Mi)
% 3.19/1.70 % (16238)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_15893 for (2999ds/902Mi)
% 3.19/1.70 % (16236)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_15893 for (2999ds/710Mi)
% 3.19/1.70 % (16237)Instruction limit reached!
% 3.19/1.70 % (16237)------------------------------
% 3.19/1.70 % (16237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.70 % (16237)Termination reason: Unknown
% 3.19/1.70 % (16237)Termination phase: shuffling
% 3.19/1.70
% 3.19/1.70 % (16237)Memory used [KB]: 1663
% 3.19/1.70 % (16237)Time elapsed: 0.003 s
% 3.19/1.70 % (16237)Instructions burned: 6 (million)
% 3.19/1.70 % (16237)------------------------------
% 3.19/1.70 % (16237)------------------------------
% 3.19/1.70 % (16239)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_15893 for (2999ds/21Mi)
% 3.19/1.70 % (16235)Instruction limit reached!
% 3.19/1.70 % (16235)------------------------------
% 3.19/1.70 % (16235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.70 % (16235)Termination reason: Unknown
% 3.19/1.70 % (16235)Termination phase: shuffling
% 3.19/1.70
% 3.19/1.70 % (16235)Memory used [KB]: 1918
% 3.19/1.70 % (16235)Time elapsed: 0.008 s
% 3.19/1.70 % (16235)Instructions burned: 18 (million)
% 3.19/1.70 % (16235)------------------------------
% 3.19/1.70 % (16235)------------------------------
% 3.19/1.71 % (16239)Instruction limit reached!
% 3.19/1.71 % (16239)------------------------------
% 3.19/1.71 % (16239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.71 % (16239)Termination reason: Unknown
% 3.19/1.71 % (16239)Termination phase: shuffling
% 3.19/1.71
% 3.19/1.71 % (16239)Memory used [KB]: 1918
% 3.19/1.71 % (16239)Time elapsed: 0.008 s
% 3.19/1.71 % (16239)Instructions burned: 22 (million)
% 3.19/1.71 % (16239)------------------------------
% 3.19/1.71 % (16239)------------------------------
% 3.19/1.71 % (16240)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_15893 for (2999ds/5Mi)
% 3.19/1.71 % (16240)Instruction limit reached!
% 3.19/1.71 % (16240)------------------------------
% 3.19/1.71 % (16240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.71 % (16240)Termination reason: Unknown
% 3.19/1.71 % (16240)Termination phase: shuffling
% 3.19/1.71
% 3.19/1.71 % (16240)Memory used [KB]: 1663
% 3.19/1.71 % (16240)Time elapsed: 0.003 s
% 3.19/1.71 % (16240)Instructions burned: 6 (million)
% 3.19/1.71 % (16240)------------------------------
% 3.19/1.71 % (16240)------------------------------
% 3.19/1.71 % (16241)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_15893 for (2999ds/6Mi)
% 3.19/1.72 % (16241)Instruction limit reached!
% 3.19/1.72 % (16241)------------------------------
% 3.19/1.72 % (16241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.72 % (16241)Termination reason: Unknown
% 3.19/1.72 % (16241)Termination phase: shuffling
% 3.19/1.72
% 3.19/1.72 % (16241)Memory used [KB]: 1791
% 3.19/1.72 % (16241)Time elapsed: 0.004 s
% 3.19/1.72 % (16241)Instructions burned: 7 (million)
% 3.19/1.72 % (16241)------------------------------
% 3.19/1.72 % (16241)------------------------------
% 3.19/1.72 % (16242)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_15893 for (2999ds/377Mi)
% 3.19/1.72 % (16243)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_15893 for (2999ds/779Mi)
% 3.19/1.72 % (16221)First to succeed.
% 3.19/1.73 % (16221)Refutation found. Thanks to Tanya!
% 3.19/1.73 % SZS status Theorem for DTF2THF_15893
% 3.19/1.73 % SZS output start Proof for DTF2THF_15893
% 3.19/1.73 thf(type_def_5, type, produc1156025366_r_l_v: $tType).
% 3.19/1.73 thf(type_def_6, type, expr_r_l_v: $tType).
% 3.19/1.73 thf(type_def_8, type, l: $tType).
% 3.19/1.73 thf(type_def_9, type, option_val_r_l_v: $tType).
% 3.19/1.73 thf(type_def_10, type, const: $tType).
% 3.19/1.73 thf(type_def_11, type, val_r_l_v: $tType).
% 3.19/1.73 thf(type_def_12, type, cntxt_r_l_v: $tType).
% 3.19/1.73 thf(type_def_13, type, r: $tType).
% 3.19/1.73 thf(type_def_14, type, v: $tType).
% 3.19/1.73 thf(type_def_15, type, option1457017436_r_l_v: $tType).
% 3.19/1.73 thf(type_def_16, type, set_option_set_l: $tType).
% 3.19/1.73 thf(type_def_17, type, set_option_set_r: $tType).
% 3.19/1.73 thf(type_def_18, type, set_op76482283um_l_l: $tType).
% 3.19/1.73 thf(type_def_19, type, set_op160472561um_l_r: $tType).
% 3.19/1.73 thf(type_def_20, type, set_op865065573um_r_l: $tType).
% 3.19/1.73 thf(type_def_21, type, set_option_l: $tType).
% 3.19/1.73 thf(type_def_22, type, set_option_r: $tType).
% 3.19/1.73 thf(type_def_23, type, set_Product_prod_l_l: $tType).
% 3.19/1.73 thf(type_def_24, type, set_Product_prod_l_r: $tType).
% 3.19/1.73 thf(type_def_25, type, set_Product_prod_r_l: $tType).
% 3.19/1.73 thf(type_def_26, type, set_Product_prod_r_r: $tType).
% 3.19/1.73 thf(type_def_27, type, set_set_l: $tType).
% 3.19/1.73 thf(type_def_28, type, set_set_r: $tType).
% 3.19/1.73 thf(type_def_29, type, set_Sum_sum_l_l: $tType).
% 3.19/1.73 thf(type_def_30, type, set_Sum_sum_l_r: $tType).
% 3.19/1.73 thf(type_def_31, type, set_Sum_sum_r_l: $tType).
% 3.19/1.73 thf(type_def_32, type, set_Sum_sum_r_r: $tType).
% 3.19/1.73 thf(type_def_33, type, set_l: $tType).
% 3.19/1.73 thf(type_def_34, type, set_r: $tType).
% 3.19/1.73 thf(type_def_35, type, produc1164766533_r_l_v: $tType).
% 3.19/1.73 thf(type_def_36, type, produc1489027110_r_l_v: $tType).
% 3.19/1.73 thf(type_def_37, type, produc1394974636_r_l_v: $tType).
% 3.19/1.73 thf(type_def_38, type, sum_sum_l_l: $tType).
% 3.19/1.73 thf(type_def_39, type, sum_sum_l_r: $tType).
% 3.19/1.73 thf(type_def_40, type, sum_sum_r_l: $tType).
% 3.19/1.73 thf(func_def_0, type, produc1394974636_r_l_v: $tType).
% 3.19/1.73 thf(func_def_1, type, produc1489027110_r_l_v: $tType).
% 3.19/1.73 thf(func_def_2, type, option1457017436_r_l_v: $tType).
% 3.19/1.73 thf(func_def_3, type, produc1156025366_r_l_v: $tType).
% 3.19/1.73 thf(func_def_4, type, produc1164766533_r_l_v: $tType).
% 3.19/1.73 thf(func_def_5, type, set_op865065573um_r_l: $tType).
% 3.19/1.73 thf(func_def_6, type, set_op160472561um_l_r: $tType).
% 3.19/1.73 thf(func_def_7, type, set_op76482283um_l_l: $tType).
% 3.19/1.73 thf(func_def_8, type, set_option_set_r: $tType).
% 3.19/1.73 thf(func_def_9, type, set_option_set_l: $tType).
% 3.19/1.73 thf(func_def_10, type, option_val_r_l_v: $tType).
% 3.19/1.73 thf(func_def_11, type, set_Product_prod_r_r: $tType).
% 3.19/1.73 thf(func_def_12, type, set_Product_prod_r_l: $tType).
% 3.19/1.73 thf(func_def_13, type, set_Product_prod_l_r: $tType).
% 3.19/1.73 thf(func_def_14, type, set_Product_prod_l_l: $tType).
% 3.19/1.73 thf(func_def_15, type, set_Sum_sum_r_r: $tType).
% 3.19/1.73 thf(func_def_16, type, set_Sum_sum_r_l: $tType).
% 3.19/1.73 thf(func_def_17, type, set_Sum_sum_l_r: $tType).
% 3.19/1.73 thf(func_def_18, type, set_Sum_sum_l_l: $tType).
% 3.19/1.73 thf(func_def_19, type, set_option_r: $tType).
% 3.19/1.73 thf(func_def_20, type, set_option_l: $tType).
% 3.19/1.73 thf(func_def_21, type, cntxt_r_l_v: $tType).
% 3.19/1.73 thf(func_def_22, type, set_set_r: $tType).
% 3.19/1.73 thf(func_def_23, type, set_set_l: $tType).
% 3.19/1.73 thf(func_def_24, type, expr_r_l_v: $tType).
% 3.19/1.73 thf(func_def_25, type, sum_sum_r_l: $tType).
% 3.19/1.73 thf(func_def_26, type, sum_sum_l_r: $tType).
% 3.19/1.73 thf(func_def_27, type, sum_sum_l_l: $tType).
% 3.19/1.73 thf(func_def_28, type, val_r_l_v: $tType).
% 3.19/1.73 thf(func_def_29, type, set_r: $tType).
% 3.19/1.73 thf(func_def_30, type, set_l: $tType).
% 3.19/1.73 thf(func_def_31, type, const: $tType).
% 3.19/1.73 thf(func_def_32, type, v: $tType).
% 3.19/1.73 thf(func_def_33, type, r: $tType).
% 3.19/1.73 thf(func_def_34, type, l: $tType).
% 3.19/1.73 thf(func_def_35, type, lID_expression_l_r_v: produc1156025366_r_l_v > expr_r_l_v).
% 3.19/1.73 thf(func_def_36, type, lID_lo1265057957_l_r_v: produc1156025366_r_l_v > l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_37, type, lID_snapshot_l_r_v: produc1156025366_r_l_v > l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_38, type, combine_l_val_r_l_v: (l > option_val_r_l_v) > (l > option_val_r_l_v) > l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_39, type, unit: const).
% 3.19/1.73 thf(func_def_40, type, ref_r_l_v: expr_r_l_v > expr_r_l_v).
% 3.19/1.73 thf(func_def_41, type, rfork_r_l_v: expr_r_l_v > expr_r_l_v).
% 3.19/1.73 thf(func_def_42, type, rjoin_r_l_v: expr_r_l_v > expr_r_l_v).
% 3.19/1.73 thf(func_def_43, type, vE_r_l_v: val_r_l_v > expr_r_l_v).
% 3.19/1.73 thf(func_def_44, type, plug_r_l_v: cntxt_r_l_v > expr_r_l_v > expr_r_l_v).
% 3.19/1.73 thf(func_def_45, type, cV_r_l_v: const > val_r_l_v).
% 3.19/1.73 thf(func_def_46, type, loc_l_r_v: l > val_r_l_v).
% 3.19/1.73 thf(func_def_47, type, rid_r_l_v: r > val_r_l_v).
% 3.19/1.73 thf(func_def_48, type, execution_r_l_v: (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > expr_r_l_v > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > $o).
% 3.19/1.73 thf(func_def_49, type, induct1670415253_r_l_v: (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > ((r > option1457017436_r_l_v) > $o) > $o).
% 3.19/1.73 thf(func_def_50, type, reachable_r_l_v: (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > (r > option1457017436_r_l_v) > $o).
% 3.19/1.73 thf(func_def_51, type, finite160708696_set_l: set_option_set_l > $o).
% 3.19/1.73 thf(func_def_52, type, finite555643486_set_r: set_option_set_r > $o).
% 3.19/1.73 thf(func_def_53, type, finite1864485196um_l_l: set_op76482283um_l_l > $o).
% 3.19/1.73 thf(func_def_54, type, finite111936338um_l_r: set_op160472561um_l_r > $o).
% 3.19/1.73 thf(func_def_55, type, finite1036466630um_r_l: set_op865065573um_r_l > $o).
% 3.19/1.73 thf(func_def_56, type, finite2114249848tion_l: set_option_l > $o).
% 3.19/1.73 thf(func_def_57, type, finite16335230tion_r: set_option_r > $o).
% 3.19/1.73 thf(func_def_58, type, finite785973648od_l_l: set_Product_prod_l_l > $o).
% 3.19/1.73 thf(func_def_59, type, finite835542678od_l_r: set_Product_prod_l_r > $o).
% 3.19/1.73 thf(func_def_60, type, finite1457622794od_r_l: set_Product_prod_r_l > $o).
% 3.19/1.73 thf(func_def_61, type, finite1507191824od_r_r: set_Product_prod_r_r > $o).
% 3.19/1.73 thf(func_def_62, type, finite_finite_set_l: set_set_l > $o).
% 3.19/1.73 thf(func_def_63, type, finite_finite_set_r: set_set_r > $o).
% 3.19/1.73 thf(func_def_64, type, finite1541484284um_l_l: set_Sum_sum_l_l > $o).
% 3.19/1.73 thf(func_def_65, type, finite1591053314um_l_r: set_Sum_sum_l_r > $o).
% 3.19/1.73 thf(func_def_66, type, finite65649782um_r_l: set_Sum_sum_r_l > $o).
% 3.19/1.73 thf(func_def_67, type, finite115218812um_r_r: set_Sum_sum_r_r > $o).
% 3.19/1.73 thf(func_def_68, type, finite_finite_l: set_l > $o).
% 3.19/1.73 thf(func_def_69, type, finite_finite_r: set_r > $o).
% 3.19/1.73 thf(func_def_70, type, bij_betw_l_l: (l > l) > set_l > set_l > $o).
% 3.19/1.73 thf(func_def_71, type, bij_betw_l_r: (l > r) > set_l > set_r > $o).
% 3.19/1.73 thf(func_def_72, type, bij_betw_r_l: (r > l) > set_r > set_l > $o).
% 3.19/1.73 thf(func_def_73, type, bij_betw_r_r: (r > r) > set_r > set_r > $o).
% 3.19/1.73 thf(func_def_74, type, fun_up1835647912_r_l_v: (l > option_val_r_l_v) > l > option_val_r_l_v > l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_75, type, fun_up709272714_r_l_v: (r > option1457017436_r_l_v) > r > option1457017436_r_l_v > r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_76, type, if_option_val_r_l_v: $o > option_val_r_l_v > option_val_r_l_v > option_val_r_l_v).
% 3.19/1.73 thf(func_def_77, type, if_opt1153928738_r_l_v: $o > option1457017436_r_l_v > option1457017436_r_l_v > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_78, type, lID_G_r_l_v: (r > option1457017436_r_l_v) > set_l).
% 3.19/1.73 thf(func_def_79, type, lID_L_l_r_v: produc1156025366_r_l_v > set_l).
% 3.19/1.73 thf(func_def_80, type, rID_G_r_l_v: (r > option1457017436_r_l_v) > set_r).
% 3.19/1.73 thf(func_def_81, type, rID_L_l_r_v: produc1156025366_r_l_v > set_r).
% 3.19/1.73 thf(func_def_82, type, domain87684397_l_r_v: produc1156025366_r_l_v > $o).
% 3.19/1.73 thf(func_def_83, type, domain1547879849_r_l_v: (r > option1457017436_r_l_v) > $o).
% 3.19/1.73 thf(func_def_84, type, revision_step_r_l_v: (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > $o).
% 3.19/1.73 thf(func_def_85, type, revisi1291188644_r_l_v: (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > $o).
% 3.19/1.73 thf(func_def_86, type, subsum148050133_r_l_v: r > r > (r > option1457017436_r_l_v) > $o).
% 3.19/1.73 thf(func_def_87, type, subsum680764357_r_l_v: (r > option1457017436_r_l_v) > $o).
% 3.19/1.73 thf(func_def_88, type, none_val_r_l_v: option_val_r_l_v).
% 3.19/1.73 thf(func_def_89, type, none_P277133687_r_l_v: option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_90, type, some_val_r_l_v: val_r_l_v > option_val_r_l_v).
% 3.19/1.73 thf(func_def_91, type, some_P1807977723_r_l_v: produc1156025366_r_l_v > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_92, type, ord_less_eq_set_l: set_l > set_l > $o).
% 3.19/1.73 thf(func_def_93, type, ord_less_eq_set_r: set_r > set_r > $o).
% 3.19/1.73 thf(func_def_94, type, top_to471808607_set_l: set_option_set_l).
% 3.19/1.73 thf(func_def_95, type, top_to555798885_set_r: set_option_set_r).
% 3.19/1.73 thf(func_def_96, type, top_to1066565019um_l_l: set_op76482283um_l_l).
% 3.19/1.73 thf(func_def_97, type, top_to1150555297um_l_r: set_op160472561um_l_r).
% 3.19/1.73 thf(func_def_98, type, top_to1855148309um_r_l: set_op865065573um_r_l).
% 3.19/1.73 thf(func_def_99, type, top_top_set_option_l: set_option_l).
% 3.19/1.73 thf(func_def_100, type, top_top_set_option_r: set_option_r).
% 3.19/1.73 thf(func_def_101, type, top_to320296343od_l_l: set_Product_prod_l_l).
% 3.19/1.73 thf(func_def_102, type, top_to715231133od_l_r: set_Product_prod_l_r).
% 3.19/1.73 thf(func_def_103, type, top_to1639761425od_r_l: set_Product_prod_r_l).
% 3.19/1.73 thf(func_def_104, type, top_to2034696215od_r_r: set_Product_prod_r_r).
% 3.19/1.73 thf(func_def_105, type, top_top_set_set_l: set_set_l).
% 3.19/1.73 thf(func_def_106, type, top_top_set_set_r: set_set_r).
% 3.19/1.73 thf(func_def_107, type, top_to1010946379um_l_l: set_Sum_sum_l_l).
% 3.19/1.73 thf(func_def_108, type, top_to1405881169um_l_r: set_Sum_sum_l_r).
% 3.19/1.73 thf(func_def_109, type, top_to182927813um_r_l: set_Sum_sum_r_l).
% 3.19/1.73 thf(func_def_110, type, top_to577862603um_r_r: set_Sum_sum_r_r).
% 3.19/1.73 thf(func_def_111, type, top_top_set_l: set_l).
% 3.19/1.73 thf(func_def_112, type, top_top_set_r: set_r).
% 3.19/1.73 thf(func_def_113, type, produc1834103605_r_l_v: (l > option_val_r_l_v) > expr_r_l_v > produc1164766533_r_l_v).
% 3.19/1.73 thf(func_def_114, type, produc297528454_r_l_v: (l > option_val_r_l_v) > produc1164766533_r_l_v > produc1156025366_r_l_v).
% 3.19/1.73 thf(func_def_115, type, produc2057232216_r_l_v: (l > l) > produc1156025366_r_l_v > produc1489027110_r_l_v).
% 3.19/1.73 thf(func_def_116, type, produc2111504612_r_l_v: (r > r) > produc1489027110_r_l_v > produc1394974636_r_l_v).
% 3.19/1.73 thf(func_def_117, type, r_G_r_l_v: (r > r) > (l > l) > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_118, type, r_L_r_l_v: (r > r) > (l > l) > produc1156025366_r_l_v > produc1156025366_r_l_v).
% 3.19/1.73 thf(func_def_119, type, eq_states_r_l_v: (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > $o).
% 3.19/1.73 thf(func_def_120, type, is_glo1871033385_r_l_v: (r > r) > (l > l) > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > $o).
% 3.19/1.73 thf(func_def_121, type, collect_set_l: (set_l > $o) > set_set_l).
% 3.19/1.73 thf(func_def_122, type, collect_set_r: (set_r > $o) > set_set_r).
% 3.19/1.73 thf(func_def_123, type, collect_Sum_sum_l_l: (sum_sum_l_l > $o) > set_Sum_sum_l_l).
% 3.19/1.73 thf(func_def_124, type, collect_Sum_sum_l_r: (sum_sum_l_r > $o) > set_Sum_sum_l_r).
% 3.19/1.73 thf(func_def_125, type, collect_Sum_sum_r_l: (sum_sum_r_l > $o) > set_Sum_sum_r_l).
% 3.19/1.73 thf(func_def_126, type, collect_l: (l > $o) > set_l).
% 3.19/1.73 thf(func_def_127, type, collect_r: (r > $o) > set_r).
% 3.19/1.73 thf(func_def_128, type, substitution_r_l_v: (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > $o).
% 3.19/1.73 thf(func_def_129, type, member_set_l: set_l > set_set_l > $o).
% 3.19/1.73 thf(func_def_130, type, member_set_r: set_r > set_set_r > $o).
% 3.19/1.73 thf(func_def_131, type, member_l: l > set_l > $o).
% 3.19/1.73 thf(func_def_132, type, member_r: r > set_r > $o).
% 3.19/1.73 thf(func_def_133, type, e: cntxt_r_l_v).
% 3.19/1.73 thf(func_def_134, type, alpha: r > r).
% 3.19/1.73 thf(func_def_135, type, beta: l > l).
% 3.19/1.73 thf(func_def_136, type, sigma: l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_137, type, tau: l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_138, type, e2: expr_r_l_v).
% 3.19/1.73 thf(func_def_139, type, r2: r).
% 3.19/1.73 thf(func_def_140, type, r3: r).
% 3.19/1.73 thf(func_def_141, type, s: r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_142, type, s2: r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_143, type, subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v).
% 3.19/1.73 thf(func_def_160, type, sP0: r > (r > option1457017436_r_l_v) > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > r > (r > option1457017436_r_l_v) > $o).
% 3.19/1.73 thf(func_def_161, type, sP1: r > (r > option1457017436_r_l_v) > r > (r > option1457017436_r_l_v) > $o).
% 3.19/1.73 thf(func_def_162, type, sK2: (r > option1457017436_r_l_v) > r).
% 3.19/1.73 thf(func_def_163, type, sK3: r > r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_164, type, sK4: r > r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_165, type, sK5: (r > option1457017436_r_l_v) > r).
% 3.19/1.73 thf(func_def_166, type, sK6: r > (r > option1457017436_r_l_v) > l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_167, type, sK7: r > (r > option1457017436_r_l_v) > expr_r_l_v).
% 3.19/1.73 thf(func_def_168, type, sK8: r > (r > option1457017436_r_l_v) > cntxt_r_l_v).
% 3.19/1.73 thf(func_def_169, type, sK9: r > (r > option1457017436_r_l_v) > l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_170, type, sK10: (produc1156025366_r_l_v > $o) > produc1164766533_r_l_v).
% 3.19/1.73 thf(func_def_171, type, sK11: (produc1156025366_r_l_v > $o) > l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_172, type, sK12: (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > r > (r > option1457017436_r_l_v) > r > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_173, type, sK13: (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > r > (r > option1457017436_r_l_v) > r > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_174, type, sK14: produc1156025366_r_l_v > expr_r_l_v).
% 3.19/1.73 thf(func_def_175, type, sK15: produc1156025366_r_l_v > l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_176, type, sK16: produc1156025366_r_l_v > l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_177, type, sK17: r > (r > option1457017436_r_l_v) > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > (r > option1457017436_r_l_v) > r > r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_178, type, sK18: r > (r > option1457017436_r_l_v) > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > (r > option1457017436_r_l_v) > r > r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_179, type, sK19: ((r > r) > (l > l) > produc1156025366_r_l_v > $o) > expr_r_l_v).
% 3.19/1.73 thf(func_def_180, type, sK20: ((r > r) > (l > l) > produc1156025366_r_l_v > $o) > r > r).
% 3.19/1.73 thf(func_def_181, type, sK21: ((r > r) > (l > l) > produc1156025366_r_l_v > $o) > l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_182, type, sK22: ((r > r) > (l > l) > produc1156025366_r_l_v > $o) > l > l).
% 3.19/1.73 thf(func_def_183, type, sK23: ((r > r) > (l > l) > produc1156025366_r_l_v > $o) > l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_184, type, sK24: (produc1164766533_r_l_v > $o) > l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_185, type, sK25: (produc1164766533_r_l_v > $o) > expr_r_l_v).
% 3.19/1.73 thf(func_def_186, type, sK26: (r > option1457017436_r_l_v) > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > (r > option1457017436_r_l_v) > r > r > r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_187, type, sK27: (r > option1457017436_r_l_v) > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > (r > option1457017436_r_l_v) > r > r > r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_188, type, sK28: (r > option1457017436_r_l_v) > r > expr_r_l_v).
% 3.19/1.73 thf(func_def_189, type, sK29: (r > option1457017436_r_l_v) > r > l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_190, type, sK30: (r > option1457017436_r_l_v) > r > cntxt_r_l_v).
% 3.19/1.73 thf(func_def_191, type, sK31: (r > option1457017436_r_l_v) > r > l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_192, type, sK32: (produc1156025366_r_l_v > $o) > l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_193, type, sK33: (produc1156025366_r_l_v > $o) > produc1164766533_r_l_v).
% 3.19/1.73 thf(func_def_194, type, sK34: (r > option1457017436_r_l_v) > r > r > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_195, type, sK35: (r > option1457017436_r_l_v) > r > r > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_196, type, sK36: set_r > r).
% 3.19/1.73 thf(func_def_197, type, sK37: produc1164766533_r_l_v > expr_r_l_v).
% 3.19/1.73 thf(func_def_198, type, sK38: produc1164766533_r_l_v > l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_199, type, sK39: produc1164766533_r_l_v > l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_200, type, sK40: produc1164766533_r_l_v > expr_r_l_v).
% 3.19/1.73 thf(func_def_201, type, sK41: (l > option_val_r_l_v) > (r > option1457017436_r_l_v) > r > (r > option1457017436_r_l_v) > cntxt_r_l_v > (l > option_val_r_l_v) > expr_r_l_v > r).
% 3.19/1.73 thf(func_def_202, type, sK42: (r > option1457017436_r_l_v) > r > (r > option1457017436_r_l_v) > r > r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_203, type, sK43: (r > option1457017436_r_l_v) > r > (r > option1457017436_r_l_v) > r > r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_204, type, sK44: (produc1164766533_r_l_v > $o) > l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_205, type, sK45: (produc1164766533_r_l_v > $o) > expr_r_l_v).
% 3.19/1.73 thf(func_def_206, type, sK46: r > (r > option1457017436_r_l_v) > r > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_207, type, sK47: r > (r > option1457017436_r_l_v) > r > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_208, type, sK48: produc1156025366_r_l_v > l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_209, type, sK49: produc1156025366_r_l_v > expr_r_l_v).
% 3.19/1.73 thf(func_def_210, type, sK50: produc1156025366_r_l_v > l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_211, type, sK51: (r > option1457017436_r_l_v) > l).
% 3.19/1.73 thf(func_def_212, type, sK52: r > r > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_213, type, sK53: r > r > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_214, type, sK54: (r > option1457017436_r_l_v) > l).
% 3.19/1.73 thf(func_def_215, type, sK55: r > r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_216, type, sK56: r > r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_217, type, sK57: r > (l > option_val_r_l_v) > expr_r_l_v > (r > option1457017436_r_l_v) > cntxt_r_l_v > (r > option1457017436_r_l_v) > (l > option_val_r_l_v) > r).
% 3.19/1.73 thf(func_def_218, type, sK58: (produc1156025366_r_l_v > $o) > l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_219, type, sK59: (produc1156025366_r_l_v > $o) > l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_220, type, sK60: (produc1156025366_r_l_v > $o) > expr_r_l_v).
% 3.19/1.73 thf(func_def_221, type, sK61: produc1156025366_r_l_v > produc1164766533_r_l_v).
% 3.19/1.73 thf(func_def_222, type, sK62: produc1156025366_r_l_v > l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_223, type, sK63: r > r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_224, type, sK64: r > r > (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_225, type, sK65: produc1156025366_r_l_v > l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_226, type, sK66: produc1156025366_r_l_v > produc1164766533_r_l_v).
% 3.19/1.73 thf(func_def_227, type, sK67: (r > option1457017436_r_l_v) > r > (r > option1457017436_r_l_v) > r > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_228, type, sK68: (r > option1457017436_r_l_v) > r > (r > option1457017436_r_l_v) > r > (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_229, type, sK69: (produc1156025366_r_l_v > $o) > l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_230, type, sK70: (produc1156025366_r_l_v > $o) > expr_r_l_v).
% 3.19/1.73 thf(func_def_231, type, sK71: (produc1156025366_r_l_v > $o) > l > option_val_r_l_v).
% 3.19/1.73 thf(func_def_232, type, sK72: (r > option1457017436_r_l_v) > r > r > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_233, type, sK73: (r > option1457017436_r_l_v) > r > r > (r > option1457017436_r_l_v) > r > option1457017436_r_l_v).
% 3.19/1.73 thf(func_def_235, type, ph75: !>[X0: $tType]:(X0)).
% 3.19/1.73 thf(f1394,plain,(
% 3.19/1.73 $false),
% 3.19/1.73 inference(subsumption_resolution,[status(thm)],[f1393,f1388])).
% 3.19/1.73 thf(f1388,plain,(
% 3.19/1.73 ( ! [X2 : r > option1457017436_r_l_v,X0 : r] : (((fun_up709272714_r_l_v @ X2 @ X0 @ (X2 @ X0)) = X2)) )),
% 3.19/1.73 inference(equality_resolution,[status(thm)],[f1296])).
% 3.19/1.73 thf(f1296,plain,(
% 3.19/1.73 ( ! [X2 : r > option1457017436_r_l_v,X0 : r,X1 : option1457017436_r_l_v] : (((fun_up709272714_r_l_v @ X2 @ X0 @ X1) = X2) | ((X2 @ X0) != X1)) )),
% 3.19/1.73 inference(cnf_transformation,[status(thm)],[f1144])).
% 3.19/1.73 thf(f1144,plain,(
% 3.19/1.73 ! [X0 : r,X1 : option1457017436_r_l_v,X2 : r > option1457017436_r_l_v] : ((((X2 @ X0) = X1) | ((fun_up709272714_r_l_v @ X2 @ X0 @ X1) != X2)) & (((fun_up709272714_r_l_v @ X2 @ X0 @ X1) = X2) | ((X2 @ X0) != X1)))),
% 3.19/1.73 inference(nnf_transformation,[status(thm)],[f651])).
% 3.19/1.73 thf(f651,plain,(
% 3.19/1.73 ! [X0 : r,X1 : option1457017436_r_l_v,X2 : r > option1457017436_r_l_v] : (((X2 @ X0) = X1) <=> ((fun_up709272714_r_l_v @ X2 @ X0 @ X1) = X2))),
% 3.19/1.73 inference(fool_elimination,[status(thm)],[f650])).
% 3.19/1.73 thf(f650,plain,(
% 3.19/1.73 ! [X0 : r,X1 : option1457017436_r_l_v,X2 : r > option1457017436_r_l_v] : (((fun_up709272714_r_l_v @ X2 @ X0 @ X1) = X2) = ((X2 @ X0) = X1))),
% 3.19/1.73 inference(rectify,[status(thm)],[f46])).
% 3.19/1.73 thf(f46,axiom,(
% 3.19/1.73 ! [X6 : r,X7 : option1457017436_r_l_v,X5 : r > option1457017436_r_l_v] : (((fun_up709272714_r_l_v @ X5 @ X6 @ X7) = X5) = ((X5 @ X6) = X7))),
% 3.19/1.73 file('/export/starexec/sandbox/tmp/tmp.6Efo01nBTw/DTF2THF_15893.p',fact_45_fun__upd__idem__iff)).
% 3.19/1.73 thf(f1393,plain,(
% 3.19/1.73 (s != (fun_up709272714_r_l_v @ s @ r2 @ (s @ r2)))),
% 3.19/1.73 inference(forward_demodulation,[status(thm)],[f1178,f1292])).
% 3.19/1.73 thf(f1292,plain,(
% 3.19/1.73 ((s @ r2) = (some_P1807977723_r_l_v @ (produc297528454_r_l_v @ sigma @ (produc1834103605_r_l_v @ tau @ (plug_r_l_v @ e @ (rfork_r_l_v @ e2))))))),
% 3.19/1.73 inference(cnf_transformation,[status(thm)],[f1])).
% 3.19/1.73 thf(f1,axiom,(
% 3.19/1.73 ((s @ r2) = (some_P1807977723_r_l_v @ (produc297528454_r_l_v @ sigma @ (produc1834103605_r_l_v @ tau @ (plug_r_l_v @ e @ (rfork_r_l_v @ e2))))))),
% 3.19/1.73 file('/export/starexec/sandbox/tmp/tmp.6Efo01nBTw/DTF2THF_15893.p',fact_0_local_Ofork_I2_J)).
% 3.19/1.73 thf(f1178,plain,(
% 3.19/1.73 (s != (fun_up709272714_r_l_v @ s @ r2 @ (some_P1807977723_r_l_v @ (produc297528454_r_l_v @ sigma @ (produc1834103605_r_l_v @ tau @ (plug_r_l_v @ e @ (rfork_r_l_v @ e2)))))))),
% 3.19/1.73 inference(cnf_transformation,[status(thm)],[f904])).
% 3.19/1.73 thf(f904,plain,(
% 3.19/1.73 (s != (fun_up709272714_r_l_v @ s @ r2 @ (some_P1807977723_r_l_v @ (produc297528454_r_l_v @ sigma @ (produc1834103605_r_l_v @ tau @ (plug_r_l_v @ e @ (rfork_r_l_v @ e2)))))))),
% 3.19/1.73 inference(flattening,[status(thm)],[f359])).
% 3.19/1.73 thf(f359,negated_conjecture,(
% 3.19/1.73 ~(s = (fun_up709272714_r_l_v @ s @ r2 @ (some_P1807977723_r_l_v @ (produc297528454_r_l_v @ sigma @ (produc1834103605_r_l_v @ tau @ (plug_r_l_v @ e @ (rfork_r_l_v @ e2)))))))),
% 3.19/1.73 inference(negated_conjecture,[status(cth)],[f358])).
% 3.19/1.73 thf(f358,conjecture,(
% 3.19/1.73 (s = (fun_up709272714_r_l_v @ s @ r2 @ (some_P1807977723_r_l_v @ (produc297528454_r_l_v @ sigma @ (produc1834103605_r_l_v @ tau @ (plug_r_l_v @ e @ (rfork_r_l_v @ e2)))))))),
% 3.19/1.73 file('/export/starexec/sandbox/tmp/tmp.6Efo01nBTw/DTF2THF_15893.p',conj_0)).
% 3.19/1.73 % SZS output end Proof for DTF2THF_15893
% 3.19/1.73 % (16221)------------------------------
% 3.19/1.73 % (16221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.73 % (16221)Termination reason: Refutation
% 3.19/1.73
% 3.19/1.73 % (16221)Memory used [KB]: 7675
% 3.19/1.73 % (16221)Time elapsed: 0.087 s
% 3.19/1.73 % (16221)Instructions burned: 151 (million)
% 3.19/1.73 % (16221)------------------------------
% 3.19/1.73 % (16221)------------------------------
% 3.19/1.73 % (16215)Success in time 0.105 s
%------------------------------------------------------------------------------