%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP045^1 : 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 : n023.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 08:55:06 AM UTC 2026
% Result : Theorem 3.16s 1.69s
% Output : Refutation 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 24 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 536 ( 14 ~; 4 |; 0 &; 516 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 27 ( 26 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 141 ( 139 usr; 20 con; 0-4 aty)
% Number of variables : 38 ( 18 ^; 20 !; 0 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
l: $tType ).
thf(type_def_6,type,
option_val_r_l_v: $tType ).
thf(type_def_8,type,
const: $tType ).
thf(type_def_9,type,
produc1156025366_r_l_v: $tType ).
thf(type_def_10,type,
set_l: $tType ).
thf(type_def_11,type,
expr_r_l_v: $tType ).
thf(type_def_12,type,
val_r_l_v: $tType ).
thf(type_def_13,type,
cntxt_r_l_v: $tType ).
thf(type_def_14,type,
r: $tType ).
thf(type_def_15,type,
v: $tType ).
thf(type_def_16,type,
option1457017436_r_l_v: $tType ).
thf(type_def_17,type,
set_Pr1409704485_r_l_v: $tType ).
thf(type_def_18,type,
set_option_l: $tType ).
thf(type_def_19,type,
set_option_r: $tType ).
thf(type_def_20,type,
set_set_option_l: $tType ).
thf(type_def_21,type,
set_set_option_r: $tType ).
thf(type_def_22,type,
set_se888453765_r_l_v: $tType ).
thf(type_def_23,type,
set_set_set_l: $tType ).
thf(type_def_24,type,
set_set_set_r: $tType ).
thf(type_def_25,type,
set_set_l: $tType ).
thf(type_def_26,type,
set_set_r: $tType ).
thf(type_def_27,type,
set_r: $tType ).
thf(type_def_28,type,
produc1389397445_r_l_v: $tType ).
thf(type_def_29,type,
produc1164766533_r_l_v: $tType ).
thf(type_def_30,type,
option_l: $tType ).
thf(type_def_31,type,
option_r: $tType ).
thf(func_def_0,type,
set_se888453765_r_l_v: $tType ).
thf(func_def_1,type,
set_Pr1409704485_r_l_v: $tType ).
thf(func_def_2,type,
produc1389397445_r_l_v: $tType ).
thf(func_def_3,type,
option1457017436_r_l_v: $tType ).
thf(func_def_4,type,
produc1156025366_r_l_v: $tType ).
thf(func_def_5,type,
produc1164766533_r_l_v: $tType ).
thf(func_def_6,type,
set_set_option_r: $tType ).
thf(func_def_7,type,
set_set_option_l: $tType ).
thf(func_def_8,type,
option_val_r_l_v: $tType ).
thf(func_def_9,type,
set_set_set_r: $tType ).
thf(func_def_10,type,
set_set_set_l: $tType ).
thf(func_def_11,type,
set_option_r: $tType ).
thf(func_def_12,type,
set_option_l: $tType ).
thf(func_def_13,type,
cntxt_r_l_v: $tType ).
thf(func_def_14,type,
set_set_r: $tType ).
thf(func_def_15,type,
set_set_l: $tType ).
thf(func_def_16,type,
expr_r_l_v: $tType ).
thf(func_def_17,type,
val_r_l_v: $tType ).
thf(func_def_18,type,
option_r: $tType ).
thf(func_def_19,type,
option_l: $tType ).
thf(func_def_20,type,
set_r: $tType ).
thf(func_def_21,type,
set_l: $tType ).
thf(func_def_22,type,
const: $tType ).
thf(func_def_23,type,
v: $tType ).
thf(func_def_24,type,
r: $tType ).
thf(func_def_25,type,
l: $tType ).
thf(func_def_26,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_27,type,
f: const ).
thf(func_def_28,type,
t: const ).
thf(func_def_29,type,
unit: const ).
thf(func_def_30,type,
doms_l_r_v: produc1156025366_r_l_v > set_l ).
thf(func_def_31,type,
assign_r_l_v: expr_r_l_v > expr_r_l_v > expr_r_l_v ).
thf(func_def_32,type,
ite_r_l_v: expr_r_l_v > expr_r_l_v > expr_r_l_v > expr_r_l_v ).
thf(func_def_33,type,
read_r_l_v: expr_r_l_v > expr_r_l_v ).
thf(func_def_34,type,
ref_r_l_v: expr_r_l_v > expr_r_l_v ).
thf(func_def_35,type,
rfork_r_l_v: expr_r_l_v > expr_r_l_v ).
thf(func_def_36,type,
rjoin_r_l_v: expr_r_l_v > expr_r_l_v ).
thf(func_def_37,type,
vE_r_l_v: val_r_l_v > expr_r_l_v ).
thf(func_def_38,type,
plug_r_l_v: cntxt_r_l_v > expr_r_l_v > expr_r_l_v ).
thf(func_def_39,type,
cV_r_l_v: const > val_r_l_v ).
thf(func_def_40,type,
loc_l_r_v: l > val_r_l_v ).
thf(func_def_41,type,
rid_r_l_v: r > val_r_l_v ).
thf(func_def_42,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_43,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_44,type,
maxima311842975_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_45,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_46,type,
steps_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > set_Pr1409704485_r_l_v ).
thf(func_def_47,type,
terminates_in_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 ) > $o ).
thf(func_def_48,type,
finite2114249848tion_l: set_option_l > $o ).
thf(func_def_49,type,
finite16335230tion_r: set_option_r > $o ).
thf(func_def_50,type,
finite1853159534_r_l_v: set_Pr1409704485_r_l_v > $o ).
thf(func_def_51,type,
finite1182752216tion_l: set_set_option_l > $o ).
thf(func_def_52,type,
finite1577687006tion_r: set_set_option_r > $o ).
thf(func_def_53,type,
finite1619243214_r_l_v: set_se888453765_r_l_v > $o ).
thf(func_def_54,type,
finite1256628466_set_l: set_set_set_l > $o ).
thf(func_def_55,type,
finite1651563256_set_r: set_set_set_r > $o ).
thf(func_def_56,type,
finite_finite_set_l: set_set_l > $o ).
thf(func_def_57,type,
finite_finite_set_r: set_set_r > $o ).
thf(func_def_58,type,
finite_finite_l: set_l > $o ).
thf(func_def_59,type,
finite_finite_r: set_r > $o ).
thf(func_def_60,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_61,type,
fun_up709272714_r_l_v: ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v > r > option1457017436_r_l_v ).
thf(func_def_62,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_63,type,
if_opt1153928738_r_l_v: $o > option1457017436_r_l_v > option1457017436_r_l_v > option1457017436_r_l_v ).
thf(func_def_64,type,
dom_Pr939617279_r_l_v: ( produc1389397445_r_l_v > option_val_r_l_v ) > set_Pr1409704485_r_l_v ).
thf(func_def_65,type,
dom_Pr1162080227_r_l_v: ( produc1389397445_r_l_v > option1457017436_r_l_v ) > set_Pr1409704485_r_l_v ).
thf(func_def_66,type,
dom_l_val_r_l_v: ( l > option_val_r_l_v ) > set_l ).
thf(func_def_67,type,
dom_l_45837855_r_l_v: ( l > option1457017436_r_l_v ) > set_l ).
thf(func_def_68,type,
dom_r_val_r_l_v: ( r > option_val_r_l_v ) > set_r ).
thf(func_def_69,type,
dom_r_259548057_r_l_v: ( r > option1457017436_r_l_v ) > set_r ).
thf(func_def_70,type,
lID_G_r_l_v: ( r > option1457017436_r_l_v ) > set_l ).
thf(func_def_71,type,
lID_L_l_r_v: produc1156025366_r_l_v > set_l ).
thf(func_def_72,type,
rID_G_r_l_v: ( r > option1457017436_r_l_v ) > set_r ).
thf(func_def_73,type,
rID_L_l_r_v: produc1156025366_r_l_v > set_r ).
thf(func_def_74,type,
domain87684397_l_r_v: produc1156025366_r_l_v > $o ).
thf(func_def_75,type,
domain1547879849_r_l_v: ( r > option1457017436_r_l_v ) > $o ).
thf(func_def_76,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_77,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_78,type,
subsum148050133_r_l_v: r > r > ( r > option1457017436_r_l_v ) > $o ).
thf(func_def_79,type,
subsum680764357_r_l_v: ( r > option1457017436_r_l_v ) > $o ).
thf(func_def_80,type,
none_val_r_l_v: option_val_r_l_v ).
thf(func_def_81,type,
none_P277133687_r_l_v: option1457017436_r_l_v ).
thf(func_def_82,type,
some_val_r_l_v: val_r_l_v > option_val_r_l_v ).
thf(func_def_83,type,
some_P1807977723_r_l_v: produc1156025366_r_l_v > option1457017436_r_l_v ).
thf(func_def_84,type,
the_val_r_l_v: option_val_r_l_v > val_r_l_v ).
thf(func_def_85,type,
the_Pr1541010602_r_l_v: option1457017436_r_l_v > produc1156025366_r_l_v ).
thf(func_def_86,type,
ord_le1506375887tion_l: set_option_l > set_option_l > $o ).
thf(func_def_87,type,
ord_le1901310677tion_r: set_option_r > set_option_r > $o ).
thf(func_def_88,type,
ord_le803113413_r_l_v: set_Pr1409704485_r_l_v > set_Pr1409704485_r_l_v > $o ).
thf(func_def_89,type,
ord_le2116509289_set_l: set_set_l > set_set_l > $o ).
thf(func_def_90,type,
ord_le363960431_set_r: set_set_r > set_set_r > $o ).
thf(func_def_91,type,
ord_less_eq_set_l: set_l > set_l > $o ).
thf(func_def_92,type,
ord_less_eq_set_r: set_r > set_r > $o ).
thf(func_def_93,type,
top_top_set_option_l: set_option_l ).
thf(func_def_94,type,
top_top_set_option_r: set_option_r ).
thf(func_def_95,type,
top_top_set_l: set_l ).
thf(func_def_96,type,
top_top_set_r: set_r ).
thf(func_def_97,type,
produc1834103605_r_l_v: ( l > option_val_r_l_v ) > expr_r_l_v > produc1164766533_r_l_v ).
thf(func_def_98,type,
produc297528454_r_l_v: ( l > option_val_r_l_v ) > produc1164766533_r_l_v > produc1156025366_r_l_v ).
thf(func_def_99,type,
produc1175464189_r_l_v: ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > produc1389397445_r_l_v ).
thf(func_def_100,type,
eq_states_r_l_v: ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
thf(func_def_101,type,
collect_option_l: ( option_l > $o ) > set_option_l ).
thf(func_def_102,type,
collect_option_r: ( option_r > $o ) > set_option_r ).
thf(func_def_103,type,
collec1978425008_r_l_v: ( produc1389397445_r_l_v > $o ) > set_Pr1409704485_r_l_v ).
thf(func_def_104,type,
collect_set_option_l: ( set_option_l > $o ) > set_set_option_l ).
thf(func_def_105,type,
collect_set_option_r: ( set_option_r > $o ) > set_set_option_r ).
thf(func_def_106,type,
collec330370832_r_l_v: ( set_Pr1409704485_r_l_v > $o ) > set_se888453765_r_l_v ).
thf(func_def_107,type,
collect_set_set_l: ( set_set_l > $o ) > set_set_set_l ).
thf(func_def_108,type,
collect_set_set_r: ( set_set_r > $o ) > set_set_set_r ).
thf(func_def_109,type,
collect_set_l: ( set_l > $o ) > set_set_l ).
thf(func_def_110,type,
collect_set_r: ( set_r > $o ) > set_set_r ).
thf(func_def_111,type,
collect_l: ( l > $o ) > set_l ).
thf(func_def_112,type,
collect_r: ( r > $o ) > set_r ).
thf(func_def_113,type,
substitution_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > $o ).
thf(func_def_114,type,
transi1323086383_r_l_v: set_Pr1409704485_r_l_v > set_Pr1409704485_r_l_v ).
thf(func_def_115,type,
member_option_l: option_l > set_option_l > $o ).
thf(func_def_116,type,
member_option_r: option_r > set_option_r > $o ).
thf(func_def_117,type,
member1522896238_r_l_v: produc1389397445_r_l_v > set_Pr1409704485_r_l_v > $o ).
thf(func_def_118,type,
member_set_l: set_l > set_set_l > $o ).
thf(func_def_119,type,
member_set_r: set_r > set_set_r > $o ).
thf(func_def_120,type,
member_l: l > set_l > $o ).
thf(func_def_121,type,
member_r: r > set_r > $o ).
thf(func_def_122,type,
e: cntxt_r_l_v ).
thf(func_def_123,type,
sigma: l > option_val_r_l_v ).
thf(func_def_124,type,
tau: l > option_val_r_l_v ).
thf(func_def_125,type,
e2: expr_r_l_v ).
thf(func_def_126,type,
r2: r ).
thf(func_def_127,type,
r3: r ).
thf(func_def_128,type,
r4: r ).
thf(func_def_129,type,
s_1: r > option1457017436_r_l_v ).
thf(func_def_130,type,
s_2: r > option1457017436_r_l_v ).
thf(func_def_131,type,
s_22: r > option1457017436_r_l_v ).
thf(func_def_132,type,
subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v ).
thf(func_def_133,type,
x: produc1156025366_r_l_v ).
thf(func_def_149,type,
sP0: ( option1457017436_r_l_v > option_val_r_l_v > $o ) > option1457017436_r_l_v > option_val_r_l_v > $o ).
thf(func_def_150,type,
sP1: ( option_val_r_l_v > option1457017436_r_l_v > $o ) > option_val_r_l_v > option1457017436_r_l_v > $o ).
thf(func_def_151,type,
sP2: ( option1457017436_r_l_v > option1457017436_r_l_v > $o ) > option1457017436_r_l_v > option1457017436_r_l_v > $o ).
thf(func_def_152,type,
sP3: ( option_val_r_l_v > option_val_r_l_v > $o ) > option_val_r_l_v > option_val_r_l_v > $o ).
thf(func_def_153,type,
sK4: option_val_r_l_v > val_r_l_v ).
thf(func_def_154,type,
sK5: produc1156025366_r_l_v > l > option_val_r_l_v ).
thf(func_def_155,type,
sK6: produc1156025366_r_l_v > expr_r_l_v ).
thf(func_def_156,type,
sK7: produc1156025366_r_l_v > l > option_val_r_l_v ).
thf(func_def_157,type,
sK8: ( option1457017436_r_l_v > option_val_r_l_v > $o ) > option1457017436_r_l_v > option_val_r_l_v > produc1156025366_r_l_v ).
thf(func_def_158,type,
sK9: ( option1457017436_r_l_v > option_val_r_l_v > $o ) > option1457017436_r_l_v > option_val_r_l_v > val_r_l_v ).
thf(func_def_159,type,
sK10: option_val_r_l_v > val_r_l_v ).
thf(func_def_160,type,
sK11: ( option_val_r_l_v > option1457017436_r_l_v > $o ) > option_val_r_l_v > option1457017436_r_l_v > produc1156025366_r_l_v ).
thf(func_def_161,type,
sK12: ( option_val_r_l_v > option1457017436_r_l_v > $o ) > option_val_r_l_v > option1457017436_r_l_v > val_r_l_v ).
thf(func_def_162,type,
sK13: ( option1457017436_r_l_v > $o ) > produc1156025366_r_l_v ).
thf(func_def_163,type,
sK14: ( option1457017436_r_l_v > option1457017436_r_l_v > $o ) > option1457017436_r_l_v > option1457017436_r_l_v > produc1156025366_r_l_v ).
thf(func_def_164,type,
sK15: ( option1457017436_r_l_v > option1457017436_r_l_v > $o ) > option1457017436_r_l_v > option1457017436_r_l_v > produc1156025366_r_l_v ).
thf(func_def_165,type,
sK16: ( produc1156025366_r_l_v > $o ) > l > option_val_r_l_v ).
thf(func_def_166,type,
sK17: ( produc1156025366_r_l_v > $o ) > l > option_val_r_l_v ).
thf(func_def_167,type,
sK18: ( produc1156025366_r_l_v > $o ) > expr_r_l_v ).
thf(func_def_168,type,
sK19: option_val_r_l_v > val_r_l_v ).
thf(func_def_169,type,
sK20: ( option_val_r_l_v > $o ) > val_r_l_v ).
thf(func_def_170,type,
sK21: option1457017436_r_l_v > produc1156025366_r_l_v ).
thf(func_def_171,type,
sK22: option1457017436_r_l_v > produc1156025366_r_l_v ).
thf(func_def_172,type,
sK23: ( option_val_r_l_v > option_val_r_l_v > $o ) > option_val_r_l_v > option_val_r_l_v > val_r_l_v ).
thf(func_def_173,type,
sK24: ( option_val_r_l_v > option_val_r_l_v > $o ) > option_val_r_l_v > option_val_r_l_v > val_r_l_v ).
thf(func_def_174,type,
sK25: option1457017436_r_l_v > produc1156025366_r_l_v ).
thf(func_def_176,type,
ph27:
!>[X0: $tType] : X0 ).
thf(func_def_177,type,
sK28: r ).
thf(func_def_178,type,
sK29: r ).
thf(func_def_179,type,
sK30: r ).
thf(func_def_180,type,
sK31: r ).
thf(f1253,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1252,f1020]) ).
thf(f1020,plain,
r2 != r3,
inference(cnf_transformation,[status(thm)],[f3]) ).
thf(f3,axiom,
r2 != r3,
file('/export/starexec/sandbox/tmp/tmp.bnlJrUVmuy/DTF2THF_7638.p',fact_2_assms_I6_J) ).
thf(f1252,plain,
r2 = r3,
inference(trivial_inequality_removal,[status(thm)],[f1247]) ).
thf(f1247,plain,
( ( r2 = r3 )
| ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r3 @ ( 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 @ r4 ) ) ) ) ) ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [Y0: l] : none_val_r_l_v
@ e2 ) ) ) )
!= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r3 @ ( 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 @ r4 ) ) ) ) ) ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [Y0: l] : none_val_r_l_v
@ e2 ) ) ) ) ) ),
inference(superposition,[status(thm)],[f1139,f1084]) ).
thf(f1084,plain,
! [X2: r > option1457017436_r_l_v,X3: r,X0: option1457017436_r_l_v,X1: r,X4: option1457017436_r_l_v] :
( ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ X2 @ X1 @ X4 ) @ X3 @ X0 )
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ X2 @ X3 @ X0 ) @ X1 @ X4 ) )
| ( X1 = X3 ) ),
inference(cnf_transformation,[status(thm)],[f950]) ).
thf(f950,plain,
! [X0: option1457017436_r_l_v,X1: r,X2: r > option1457017436_r_l_v,X3: r,X4: option1457017436_r_l_v] :
( ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ X2 @ X1 @ X4 ) @ X3 @ X0 )
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ X2 @ X3 @ X0 ) @ X1 @ X4 ) )
| ( X1 = X3 ) ),
inference(ennf_transformation,[status(thm)],[f919]) ).
thf(f919,plain,
! [X0: option1457017436_r_l_v,X1: r,X2: r > option1457017436_r_l_v,X3: r,X4: option1457017436_r_l_v] :
( ( X1 != X3 )
=> ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ X2 @ X1 @ X4 ) @ X3 @ X0 )
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ X2 @ X3 @ X0 ) @ X1 @ X4 ) ) ),
inference(rectify,[status(thm)],[f41]) ).
thf(f41,axiom,
! [X40: option1457017436_r_l_v,X36: r,X38: r > option1457017436_r_l_v,X37: r,X39: option1457017436_r_l_v] :
( ( X36 != X37 )
=> ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ X38 @ X36 @ X39 ) @ X37 @ X40 )
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ X38 @ X37 @ X40 ) @ X36 @ X39 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bnlJrUVmuy/DTF2THF_7638.p',fact_40_fun__upd__twist) ).
thf(f1139,plain,
( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r3 @ ( 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 @ r4 ) ) ) ) ) ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [Y0: l] : none_val_r_l_v
@ e2 ) ) ) )
!= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( 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 @ r4 ) ) ) ) ) ) ) @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [Y0: l] : none_val_r_l_v
@ e2 ) ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f1136,f1045]) ).
thf(f1045,plain,
r4 != r2,
inference(cnf_transformation,[status(thm)],[f2]) ).
thf(f2,axiom,
r4 != r2,
file('/export/starexec/sandbox/tmp/tmp.bnlJrUVmuy/DTF2THF_7638.p',fact_1_assms_I7_J) ).
thf(f1136,plain,
( ( r4 = r2 )
| ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r3 @ ( 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 @ r4 ) ) ) ) ) ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [Y0: l] : none_val_r_l_v
@ e2 ) ) ) )
!= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( 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 @ r4 ) ) ) ) ) ) ) @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [Y0: l] : none_val_r_l_v
@ e2 ) ) ) ) ) ),
inference(superposition,[status(thm)],[f1021,f1084]) ).
thf(f1021,plain,
( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r3 @ ( 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 @ r4 ) ) ) ) ) ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [Y0: l] : none_val_r_l_v
@ e2 ) ) ) )
!= ( fun_up709272714_r_l_v
@ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( 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 @ r4 ) ) ) ) ) ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [Y0: l] : none_val_r_l_v
@ e2 ) ) ) )
@ r2
@ ( some_P1807977723_r_l_v @ x ) ) ),
inference(cnf_transformation,[status(thm)],[f907]) ).
thf(f907,plain,
( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r3 @ ( 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 @ r4 ) ) ) ) ) ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [Y0: l] : none_val_r_l_v
@ e2 ) ) ) )
!= ( fun_up709272714_r_l_v
@ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( 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 @ r4 ) ) ) ) ) ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [Y0: l] : none_val_r_l_v
@ e2 ) ) ) )
@ r2
@ ( some_P1807977723_r_l_v @ x ) ) ),
inference(flattening,[status(thm)],[f606]) ).
thf(f606,plain,
( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r3 @ ( 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 @ r4 ) ) ) ) ) ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [Y0: l] : none_val_r_l_v
@ e2 ) ) ) )
!= ( fun_up709272714_r_l_v
@ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( 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 @ r4 ) ) ) ) ) ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [Y0: l] : none_val_r_l_v
@ e2 ) ) ) )
@ r2
@ ( some_P1807977723_r_l_v @ x ) ) ),
inference(fool_elimination,[status(thm)],[f605]) ).
thf(f605,plain,
( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r3 @ ( 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 @ r4 ) ) ) ) ) ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [X0: l] : none_val_r_l_v
@ e2 ) ) ) )
!= ( fun_up709272714_r_l_v
@ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( 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 @ r4 ) ) ) ) ) ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [X1: l] : none_val_r_l_v
@ e2 ) ) ) )
@ r2
@ ( some_P1807977723_r_l_v @ x ) ) ),
inference(rectify,[status(thm)],[f360]) ).
thf(f360,negated_conjecture,
( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r3 @ ( 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 @ r4 ) ) ) ) ) ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [X0: l] : none_val_r_l_v
@ e2 ) ) ) )
!= ( fun_up709272714_r_l_v
@ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( 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 @ r4 ) ) ) ) ) ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [X0: l] : none_val_r_l_v
@ e2 ) ) ) )
@ r2
@ ( some_P1807977723_r_l_v @ x ) ) ),
inference(negated_conjecture,[status(cth)],[f359]) ).
thf(f359,conjecture,
( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r3 @ ( 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 @ r4 ) ) ) ) ) ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [X0: l] : none_val_r_l_v
@ e2 ) ) ) )
= ( fun_up709272714_r_l_v
@ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( 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 @ r4 ) ) ) ) ) ) ) @ r4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [X0: l] : none_val_r_l_v
@ e2 ) ) ) )
@ r2
@ ( some_P1807977723_r_l_v @ x ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bnlJrUVmuy/DTF2THF_7638.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP045^1 : 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
% 0.17/0.34 % Computer : n023.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 08:25:04 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : ITP045^1 : TPTP v9.2.1. Released v7.5.0.
% 0.31/0.46 % Domain : Interactive Theorem Proving
% 0.31/0.46 % Problem : Sledgehammer Determinacy problem prob_286__3350038_1
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English :
% 0.31/0.46
% 0.31/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.31/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Des21]
% 0.31/0.46 % Names : Determinacy/prob_286__3350038_1 [Des21]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.56 v9.1.0, 0.50 v9.0.0, 0.70 v8.2.0, 0.77 v8.1.0, 0.73 v7.5.0
% 0.31/0.46 % Syntax : Number of formulae : 493 ( 136 unt; 134 typ; 0 def)
% 0.31/0.46 % Number of atoms : 1123 ( 504 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 13 ( 3 avg)
% 0.31/0.46 % Number of connectives : 4618 ( 162 ~; 47 |; 96 &;3816 @)
% 0.31/0.46 % ( 0 <=>; 497 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 35 ( 8 avg)
% 0.31/0.46 % Number of types : 27 ( 26 usr)
% 0.31/0.46 % Number of type conns : 968 ( 968 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 111 ( 108 usr; 17 con; 0-4 aty)
% 0.31/0.46 % Number of variables : 1406 ( 110 ^;1216 !; 80 ?;1406 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:31:36.481
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % Could-be-implicit typings (26)
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_I_062_Itf__r_Mt__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_J_M_062_Itf__r_Mt__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_J_J_J_J,type,
% 0.31/0.46 set_se888453765_r_l_v: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_Itf__r_Mt__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_J_M_062_Itf__r_Mt__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_J_J_J,type,
% 0.31/0.46 set_Pr1409704485_r_l_v: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Product____Type__Oprod_I_062_Itf__r_Mt__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_J_M_062_Itf__r_Mt__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_J_J,type,
% 0.31/0.46 produc1389397445_r_l_v: $tType ).
% 0.31/0.46
% 0.31/0.46 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,
% 0.31/0.46 option1457017436_r_l_v: $tType ).
% 0.31/0.46
% 0.31/0.46 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,
% 0.31/0.46 produc1156025366_r_l_v: $tType ).
% 0.31/0.46
% 0.31/0.46 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,
% 0.31/0.46 produc1164766533_r_l_v: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Option__Ooption_Itf__r_J_J_J,type,
% 0.31/0.46 set_set_option_r: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Option__Ooption_Itf__l_J_J_J,type,
% 0.31/0.46 set_set_option_l: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J,type,
% 0.31/0.46 option_val_r_l_v: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Set__Oset_Itf__r_J_J_J,type,
% 0.31/0.46 set_set_set_r: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Set__Oset_Itf__l_J_J_J,type,
% 0.31/0.46 set_set_set_l: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__Option__Ooption_Itf__r_J_J,type,
% 0.31/0.46 set_option_r: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__Option__Ooption_Itf__l_J_J,type,
% 0.31/0.46 set_option_l: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Data__Ocntxt_Itf__r_Mtf__l_Mtf__v_J,type,
% 0.31/0.46 cntxt_r_l_v: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__Set__Oset_Itf__r_J_J,type,
% 0.31/0.46 set_set_r: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__Set__Oset_Itf__l_J_J,type,
% 0.31/0.46 set_set_l: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J,type,
% 0.31/0.46 expr_r_l_v: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,type,
% 0.31/0.46 val_r_l_v: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Option__Ooption_Itf__r_J,type,
% 0.31/0.46 option_r: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Option__Ooption_Itf__l_J,type,
% 0.31/0.46 option_l: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_Itf__r_J,type,
% 0.31/0.46 set_r: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_Itf__l_J,type,
% 0.31/0.46 set_l: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Data__Oconst,type,
% 0.31/0.46 const: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_tf__v,type,
% 0.31/0.46 v: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_tf__r,type,
% 0.31/0.46 r: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_tf__l,type,
% 0.31/0.46 l: $tType ).
% 0.31/0.46
% 0.31/0.46 % Explicit typings (108)
% 0.31/0.46 thf(sy_c_Data_Ocombine_001tf__l_001t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,type,
% 0.31/0.46 combine_l_val_r_l_v: ( l > option_val_r_l_v ) > ( l > option_val_r_l_v ) > l > option_val_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Data_Oconst_OF,type,
% 0.31/0.46 f: const ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Data_Oconst_OT,type,
% 0.31/0.46 t: const ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Data_Oconst_OUnit,type,
% 0.31/0.46 unit: const ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Data_Odoms_001tf__l_001tf__r_001tf__v,type,
% 0.31/0.46 doms_l_r_v: produc1156025366_r_l_v > set_l ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Data_Oexpr_OAssign_001tf__r_001tf__l_001tf__v,type,
% 0.31/0.46 assign_r_l_v: expr_r_l_v > expr_r_l_v > expr_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Data_Oexpr_OIte_001tf__r_001tf__l_001tf__v,type,
% 0.31/0.46 ite_r_l_v: expr_r_l_v > expr_r_l_v > expr_r_l_v > expr_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Data_Oexpr_ORead_001tf__r_001tf__l_001tf__v,type,
% 0.31/0.46 read_r_l_v: expr_r_l_v > expr_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Data_Oexpr_ORef_001tf__r_001tf__l_001tf__v,type,
% 0.31/0.46 ref_r_l_v: expr_r_l_v > expr_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Data_Oexpr_ORfork_001tf__r_001tf__l_001tf__v,type,
% 0.31/0.46 rfork_r_l_v: expr_r_l_v > expr_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Data_Oexpr_ORjoin_001tf__r_001tf__l_001tf__v,type,
% 0.31/0.46 rjoin_r_l_v: expr_r_l_v > expr_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Data_Oexpr_OVE_001tf__r_001tf__l_001tf__v,type,
% 0.31/0.46 vE_r_l_v: val_r_l_v > expr_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Data_Oplug_001tf__r_001tf__l_001tf__v,type,
% 0.31/0.46 plug_r_l_v: cntxt_r_l_v > expr_r_l_v > expr_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Data_Oval_OCV_001tf__r_001tf__l_001tf__v,type,
% 0.31/0.46 cV_r_l_v: const > val_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Data_Oval_OLoc_001tf__l_001tf__r_001tf__v,type,
% 0.31/0.46 loc_l_r_v: l > val_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Data_Oval_ORid_001tf__r_001tf__l_001tf__v,type,
% 0.31/0.46 rid_r_l_v: r > val_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Executions_Osubstitution_Oexecution_001tf__r_001tf__l_001tf__v,type,
% 0.31/0.46 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 ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Executions_Osubstitution_Oinductive__invariant_001tf__r_001tf__l_001tf__v,type,
% 0.31/0.46 induct1670415253_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( ( r > option1457017436_r_l_v ) > $o ) > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Executions_Osubstitution_Omaximal__execution_001tf__r_001tf__l_001tf__v,type,
% 0.31/0.46 maxima311842975_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 ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Executions_Osubstitution_Oreachable_001tf__r_001tf__l_001tf__v,type,
% 0.31/0.46 reachable_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Executions_Osubstitution_Osteps_001tf__r_001tf__l_001tf__v,type,
% 0.31/0.46 steps_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > set_Pr1409704485_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Executions_Osubstitution_Oterminates__in_001tf__r_001tf__l_001tf__v,type,
% 0.31/0.46 terminates_in_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 ) > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_Itf__l_J,type,
% 0.31/0.46 finite2114249848tion_l: set_option_l > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_Itf__r_J,type,
% 0.31/0.46 finite16335230tion_r: set_option_r > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_I_062_Itf__r_Mt__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_J_M_062_Itf__r_Mt__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_J_J,type,
% 0.31/0.46 finite1853159534_r_l_v: set_Pr1409704485_r_l_v > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Option__Ooption_Itf__l_J_J,type,
% 0.31/0.46 finite1182752216tion_l: set_set_option_l > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Option__Ooption_Itf__r_J_J,type,
% 0.31/0.46 finite1577687006tion_r: set_set_option_r > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Product____Type__Oprod_I_062_Itf__r_Mt__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_J_M_062_Itf__r_Mt__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_J_J_J,type,
% 0.31/0.46 finite1619243214_r_l_v: set_se888453765_r_l_v > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Set__Oset_Itf__l_J_J,type,
% 0.31/0.46 finite1256628466_set_l: set_set_set_l > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Set__Oset_Itf__r_J_J,type,
% 0.31/0.46 finite1651563256_set_r: set_set_set_r > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_Itf__l_J,type,
% 0.31/0.46 finite_finite_set_l: set_set_l > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_Itf__r_J,type,
% 0.31/0.46 finite_finite_set_r: set_set_r > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Finite__Set_Ofinite_001tf__l,type,
% 0.31/0.46 finite_finite_l: set_l > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Finite__Set_Ofinite_001tf__r,type,
% 0.31/0.46 finite_finite_r: set_r > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Fun_Ofun__upd_001tf__l_001t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J,type,
% 0.31/0.46 fun_up1835647912_r_l_v: ( l > option_val_r_l_v ) > l > option_val_r_l_v > l > option_val_r_l_v ).
% 0.31/0.46
% 0.31/0.46 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,
% 0.31/0.46 fun_up709272714_r_l_v: ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v > r > option1457017436_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_If_001t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J,type,
% 0.31/0.46 if_option_val_r_l_v: $o > option_val_r_l_v > option_val_r_l_v > option_val_r_l_v ).
% 0.31/0.46
% 0.31/0.46 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,
% 0.31/0.46 if_opt1153928738_r_l_v: $o > option1457017436_r_l_v > option1457017436_r_l_v > option1457017436_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Map_Odom_001t__Product____Type__Oprod_I_062_Itf__r_Mt__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_J_M_062_Itf__r_Mt__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_J_J_001t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,type,
% 0.31/0.46 dom_Pr939617279_r_l_v: ( produc1389397445_r_l_v > option_val_r_l_v ) > set_Pr1409704485_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Map_Odom_001t__Product____Type__Oprod_I_062_Itf__r_Mt__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_J_M_062_Itf__r_Mt__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_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__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,
% 0.31/0.46 dom_Pr1162080227_r_l_v: ( produc1389397445_r_l_v > option1457017436_r_l_v ) > set_Pr1409704485_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Map_Odom_001tf__l_001t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,type,
% 0.31/0.46 dom_l_val_r_l_v: ( l > option_val_r_l_v ) > set_l ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Map_Odom_001tf__l_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,
% 0.31/0.46 dom_l_45837855_r_l_v: ( l > option1457017436_r_l_v ) > set_l ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Map_Odom_001tf__r_001t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,type,
% 0.31/0.46 dom_r_val_r_l_v: ( r > option_val_r_l_v ) > set_r ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Map_Odom_001tf__r_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,
% 0.31/0.46 dom_r_259548057_r_l_v: ( r > option1457017436_r_l_v ) > set_r ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Occurrences_OLID_092_060_094sub_062G_001tf__r_001tf__l_001tf__v,type,
% 0.31/0.46 lID_G_r_l_v: ( r > option1457017436_r_l_v ) > set_l ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Occurrences_OLID_092_060_094sub_062L_001tf__l_001tf__r_001tf__v,type,
% 0.31/0.46 lID_L_l_r_v: produc1156025366_r_l_v > set_l ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Occurrences_ORID_092_060_094sub_062G_001tf__r_001tf__l_001tf__v,type,
% 0.31/0.46 rID_G_r_l_v: ( r > option1457017436_r_l_v ) > set_r ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Occurrences_ORID_092_060_094sub_062L_001tf__l_001tf__r_001tf__v,type,
% 0.31/0.46 rID_L_l_r_v: produc1156025366_r_l_v > set_r ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_OperationalSemantics_Osubstitution_Odomains__subsume_001tf__l_001tf__r_001tf__v,type,
% 0.31/0.46 domain87684397_l_r_v: produc1156025366_r_l_v > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_OperationalSemantics_Osubstitution_Odomains__subsume__globally_001tf__r_001tf__l_001tf__v,type,
% 0.31/0.46 domain1547879849_r_l_v: ( r > option1457017436_r_l_v ) > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_OperationalSemantics_Osubstitution_Orevision__step_001tf__r_001tf__l_001tf__v,type,
% 0.31/0.46 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 ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_OperationalSemantics_Osubstitution_Orevision__step__relaxed_001tf__r_001tf__l_001tf__v,type,
% 0.31/0.46 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 ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_OperationalSemantics_Osubstitution_Osubsumes__accessible_001tf__r_001tf__l_001tf__v,type,
% 0.31/0.46 subsum148050133_r_l_v: r > r > ( r > option1457017436_r_l_v ) > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_OperationalSemantics_Osubstitution_Osubsumes__accessible__globally_001tf__r_001tf__l_001tf__v,type,
% 0.31/0.46 subsum680764357_r_l_v: ( r > option1457017436_r_l_v ) > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Option_Ooption_ONone_001t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,type,
% 0.31/0.46 none_val_r_l_v: option_val_r_l_v ).
% 0.31/0.46
% 0.31/0.46 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,
% 0.31/0.46 none_P277133687_r_l_v: option1457017436_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Option_Ooption_OSome_001t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,type,
% 0.31/0.46 some_val_r_l_v: val_r_l_v > option_val_r_l_v ).
% 0.31/0.46
% 0.31/0.46 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,
% 0.31/0.46 some_P1807977723_r_l_v: produc1156025366_r_l_v > option1457017436_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Option_Ooption_Othe_001t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,type,
% 0.31/0.46 the_val_r_l_v: option_val_r_l_v > val_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Option_Ooption_Othe_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,
% 0.31/0.46 the_Pr1541010602_r_l_v: option1457017436_r_l_v > produc1156025366_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Option__Ooption_Itf__l_J_J,type,
% 0.31/0.46 ord_le1506375887tion_l: set_option_l > set_option_l > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Option__Ooption_Itf__r_J_J,type,
% 0.31/0.46 ord_le1901310677tion_r: set_option_r > set_option_r > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_062_Itf__r_Mt__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_J_M_062_Itf__r_Mt__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_J_J_J,type,
% 0.31/0.46 ord_le803113413_r_l_v: set_Pr1409704485_r_l_v > set_Pr1409704485_r_l_v > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_Itf__l_J_J,type,
% 0.31/0.46 ord_le2116509289_set_l: set_set_l > set_set_l > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_Itf__r_J_J,type,
% 0.31/0.46 ord_le363960431_set_r: set_set_r > set_set_r > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__l_J,type,
% 0.31/0.46 ord_less_eq_set_l: set_l > set_l > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__r_J,type,
% 0.31/0.46 ord_less_eq_set_r: set_r > set_r > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_Itf__l_J_J,type,
% 0.31/0.46 top_top_set_option_l: set_option_l ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_Itf__r_J_J,type,
% 0.31/0.46 top_top_set_option_r: set_option_r ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__l_J,type,
% 0.31/0.46 top_top_set_l: set_l ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__r_J,type,
% 0.31/0.46 top_top_set_r: set_r ).
% 0.31/0.46
% 0.31/0.46 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,
% 0.31/0.46 produc1834103605_r_l_v: ( l > option_val_r_l_v ) > expr_r_l_v > produc1164766533_r_l_v ).
% 0.31/0.46
% 0.31/0.46 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,
% 0.31/0.46 produc297528454_r_l_v: ( l > option_val_r_l_v ) > produc1164766533_r_l_v > produc1156025366_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Product__Type_OPair_001_062_Itf__r_Mt__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_J_001_062_Itf__r_Mt__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_J,type,
% 0.31/0.46 produc1175464189_r_l_v: ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > produc1389397445_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Renaming_Oeq__states_001tf__r_001tf__l_001tf__v,type,
% 0.31/0.46 eq_states_r_l_v: ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect_001t__Option__Ooption_Itf__l_J,type,
% 0.31/0.46 collect_option_l: ( option_l > $o ) > set_option_l ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect_001t__Option__Ooption_Itf__r_J,type,
% 0.31/0.46 collect_option_r: ( option_r > $o ) > set_option_r ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_I_062_Itf__r_Mt__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_J_M_062_Itf__r_Mt__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_J_J,type,
% 0.31/0.46 collec1978425008_r_l_v: ( produc1389397445_r_l_v > $o ) > set_Pr1409704485_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Option__Ooption_Itf__l_J_J,type,
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% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Option__Ooption_Itf__r_J_J,type,
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% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Product____Type__Oprod_I_062_Itf__r_Mt__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_J_M_062_Itf__r_Mt__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_J_J_J,type,
% 0.31/0.46 collec330370832_r_l_v: ( set_Pr1409704485_r_l_v > $o ) > set_se888453765_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Set__Oset_Itf__l_J_J,type,
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% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Set__Oset_Itf__r_J_J,type,
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% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect_001t__Set__Oset_Itf__l_J,type,
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% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect_001t__Set__Oset_Itf__r_J,type,
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% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect_001tf__l,type,
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% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect_001tf__r,type,
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% 0.31/0.46
% 0.31/0.46 thf(sy_c_Substitution_Osubstitution_001tf__r_001tf__l_001tf__v,type,
% 0.31/0.46 substitution_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Transitive__Closure_Ortrancl_001_062_Itf__r_Mt__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_J,type,
% 0.31/0.46 transi1323086383_r_l_v: set_Pr1409704485_r_l_v > set_Pr1409704485_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_member_001t__Option__Ooption_Itf__l_J,type,
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% 0.31/0.46
% 0.31/0.46 thf(sy_c_member_001t__Option__Ooption_Itf__r_J,type,
% 0.31/0.46 member_option_r: option_r > set_option_r > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_member_001t__Product____Type__Oprod_I_062_Itf__r_Mt__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_J_M_062_Itf__r_Mt__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_J_J,type,
% 0.31/0.46 member1522896238_r_l_v: produc1389397445_r_l_v > set_Pr1409704485_r_l_v > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_member_001t__Set__Oset_Itf__l_J,type,
% 0.31/0.46 member_set_l: set_l > set_set_l > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_member_001t__Set__Oset_Itf__r_J,type,
% 0.31/0.46 member_set_r: set_r > set_set_r > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_member_001tf__l,type,
% 0.31/0.46 member_l: l > set_l > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_member_001tf__r,type,
% 0.31/0.46 member_r: r > set_r > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v__092_060E_062,type,
% 0.31/0.46 e: cntxt_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v__092_060sigma_062,type,
% 0.31/0.46 sigma: l > option_val_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v__092_060tau_062,type,
% 0.31/0.46 tau: l > option_val_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_e,type,
% 0.31/0.46 e2: expr_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_r,type,
% 0.31/0.46 r2: r ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_r_H,type,
% 0.31/0.46 r3: r ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_r_H_H,type,
% 0.31/0.46 r4: r ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_s_092_060_094sub_0621,type,
% 0.31/0.46 s_1: r > option1457017436_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_s_092_060_094sub_0622,type,
% 0.31/0.46 s_2: r > option1457017436_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_s_092_060_094sub_0622_H,type,
% 0.31/0.46 s_22: r > option1457017436_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_subst,type,
% 0.31/0.46 subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_x,type,
% 0.31/0.46 x: produc1156025366_r_l_v ).
% 0.31/0.46
% 0.31/0.46 % Relevant facts (353)
% 0.31/0.46 thf(fact_0_assms_I4_J,axiom,
% 0.31/0.46 ~ ( member_r @ r4 @ ( rID_G_r_l_v @ s_2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % assms(4)
% 0.31/0.46 thf(fact_1_assms_I7_J,axiom,
% 0.31/0.46 r2 != r4 ).
% 0.31/0.46
% 0.31/0.46 % assms(7)
% 0.31/0.46 thf(fact_2_assms_I6_J,axiom,
% 0.31/0.46 r2 != r3 ).
% 0.31/0.46
% 0.31/0.46 % assms(6)
% 0.31/0.46 thf(fact_3_assms_I1_J,axiom,
% 0.31/0.46 ( s_2
% 0.31/0.46 = ( fun_up709272714_r_l_v @ s_1 @ r2 @ ( some_P1807977723_r_l_v @ x ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % assms(1)
% 0.31/0.46 thf(fact_4_assms_I3_J,axiom,
% 0.31/0.46 ( ( s_2 @ r3 )
% 0.31/0.46 = ( 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 ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % assms(3)
% 0.31/0.46 thf(fact_5_assms_I2_J,axiom,
% 0.31/0.46 ( s_22
% 0.31/0.46 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( 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 @ r4 ) ) ) ) ) ) ) @ r4
% 0.31/0.46 @ ( some_P1807977723_r_l_v
% 0.31/0.46 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
% 0.31/0.46 @ ( produc1834103605_r_l_v
% 0.31/0.46 @ ^ [X: l] : none_val_r_l_v
% 0.31/0.46 @ e2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % assms(2)
% 0.31/0.46 thf(fact_6_revision__step_Ofork,axiom,
% 0.31/0.46 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E2: expr_r_l_v,R2: r] :
% 0.31/0.46 ( ( ( S @ R )
% 0.31/0.46 = ( 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 ) ) ) ) ) )
% 0.31/0.46 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 0.31/0.46 => ( revision_step_r_l_v @ subst @ R @ S
% 0.31/0.46 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( 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 @ R2 ) ) ) ) ) ) ) @ R2
% 0.31/0.46 @ ( some_P1807977723_r_l_v
% 0.31/0.46 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau )
% 0.31/0.46 @ ( produc1834103605_r_l_v
% 0.31/0.46 @ ^ [X: l] : none_val_r_l_v
% 0.31/0.46 @ E2 ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % revision_step.fork
% 0.31/0.46 thf(fact_7_assms_I5_J,axiom,
% 0.31/0.46 ( revision_step_r_l_v @ subst @ r2 @ s_22
% 0.31/0.46 @ ( fun_up709272714_r_l_v
% 0.31/0.46 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( 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 @ r4 ) ) ) ) ) ) ) @ r4
% 0.31/0.46 @ ( some_P1807977723_r_l_v
% 0.31/0.46 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
% 0.31/0.46 @ ( produc1834103605_r_l_v
% 0.31/0.46 @ ^ [X: l] : none_val_r_l_v
% 0.31/0.46 @ e2 ) ) ) )
% 0.31/0.46 @ r2
% 0.31/0.46 @ ( some_P1807977723_r_l_v @ x ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % assms(5)
% 0.31/0.46 thf(fact_8_restrictions__inwards,axiom,
% 0.31/0.46 ! [X2: r,X3: r,F: r > option1457017436_r_l_v,Y: produc1156025366_r_l_v] :
% 0.31/0.46 ( ( X2 != X3 )
% 0.31/0.46 => ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ F @ X2 @ ( some_P1807977723_r_l_v @ Y ) ) @ X3 @ none_P277133687_r_l_v )
% 0.31/0.46 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ F @ X3 @ none_P277133687_r_l_v ) @ X2 @ ( some_P1807977723_r_l_v @ Y ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % restrictions_inwards
% 0.31/0.46 thf(fact_9_restrictions__inwards,axiom,
% 0.31/0.46 ! [X2: l,X3: l,F: l > option_val_r_l_v,Y: val_r_l_v] :
% 0.31/0.46 ( ( X2 != X3 )
% 0.31/0.46 => ( ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ F @ X2 @ ( some_val_r_l_v @ Y ) ) @ X3 @ none_val_r_l_v )
% 0.31/0.46 = ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ F @ X3 @ none_val_r_l_v ) @ X2 @ ( some_val_r_l_v @ Y ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % restrictions_inwards
% 0.31/0.46 thf(fact_10_empty__upd__none,axiom,
% 0.31/0.46 ! [X2: l] :
% 0.31/0.46 ( ( fun_up1835647912_r_l_v
% 0.31/0.46 @ ^ [X: l] : none_val_r_l_v
% 0.31/0.46 @ X2
% 0.31/0.46 @ none_val_r_l_v )
% 0.31/0.46 = ( ^ [X: l] : none_val_r_l_v ) ) ).
% 0.31/0.46
% 0.31/0.46 % empty_upd_none
% 0.31/0.46 thf(fact_11_empty__upd__none,axiom,
% 0.31/0.46 ! [X2: r] :
% 0.31/0.46 ( ( fun_up709272714_r_l_v
% 0.31/0.46 @ ^ [X: r] : none_P277133687_r_l_v
% 0.31/0.46 @ X2
% 0.31/0.46 @ none_P277133687_r_l_v )
% 0.31/0.46 = ( ^ [X: r] : none_P277133687_r_l_v ) ) ).
% 0.31/0.46
% 0.31/0.46 % empty_upd_none
% 0.31/0.46 thf(fact_12_not__None__eq,axiom,
% 0.31/0.46 ! [X2: option1457017436_r_l_v] :
% 0.31/0.46 ( ( X2 != none_P277133687_r_l_v )
% 0.31/0.46 = ( ? [Y2: produc1156025366_r_l_v] :
% 0.31/0.46 ( X2
% 0.31/0.46 = ( some_P1807977723_r_l_v @ Y2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % not_None_eq
% 0.31/0.46 thf(fact_13_not__None__eq,axiom,
% 0.31/0.46 ! [X2: option_val_r_l_v] :
% 0.31/0.46 ( ( X2 != none_val_r_l_v )
% 0.31/0.46 = ( ? [Y2: val_r_l_v] :
% 0.31/0.46 ( X2
% 0.31/0.46 = ( some_val_r_l_v @ Y2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % not_None_eq
% 0.31/0.46 thf(fact_14_not__Some__eq,axiom,
% 0.31/0.46 ! [X2: option1457017436_r_l_v] :
% 0.31/0.46 ( ( ! [Y2: produc1156025366_r_l_v] :
% 0.31/0.46 ( X2
% 0.31/0.46 != ( some_P1807977723_r_l_v @ Y2 ) ) )
% 0.31/0.46 = ( X2 = none_P277133687_r_l_v ) ) ).
% 0.31/0.46
% 0.31/0.46 % not_Some_eq
% 0.31/0.46 thf(fact_15_not__Some__eq,axiom,
% 0.31/0.46 ! [X2: option_val_r_l_v] :
% 0.31/0.46 ( ( ! [Y2: val_r_l_v] :
% 0.31/0.46 ( X2
% 0.31/0.46 != ( some_val_r_l_v @ Y2 ) ) )
% 0.31/0.46 = ( X2 = none_val_r_l_v ) ) ).
% 0.31/0.46
% 0.31/0.46 % not_Some_eq
% 0.31/0.46 thf(fact_16_map__upd__nonempty,axiom,
% 0.31/0.46 ! [T: r > option1457017436_r_l_v,K: r,X2: produc1156025366_r_l_v] :
% 0.31/0.46 ( ( fun_up709272714_r_l_v @ T @ K @ ( some_P1807977723_r_l_v @ X2 ) )
% 0.31/0.46 != ( ^ [X: r] : none_P277133687_r_l_v ) ) ).
% 0.31/0.46
% 0.31/0.46 % map_upd_nonempty
% 0.31/0.46 thf(fact_17_map__upd__nonempty,axiom,
% 0.31/0.46 ! [T: l > option_val_r_l_v,K: l,X2: val_r_l_v] :
% 0.31/0.46 ( ( fun_up1835647912_r_l_v @ T @ K @ ( some_val_r_l_v @ X2 ) )
% 0.31/0.46 != ( ^ [X: l] : none_val_r_l_v ) ) ).
% 0.31/0.46
% 0.31/0.46 % map_upd_nonempty
% 0.31/0.46 thf(fact_18_fork__pseudodeterministic,axiom,
% 0.31/0.46 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E2: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.31/0.46 ( ( ( S @ R )
% 0.31/0.46 = ( 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 ) ) ) ) ) )
% 0.31/0.46 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.31/0.46 = ( ? [R3: r] :
% 0.31/0.46 ( ~ ( member_r @ R3 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( 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 ) ) ) ) ) ) ) )
% 0.31/0.46 & ( S2
% 0.31/0.46 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( 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
% 0.31/0.46 @ ( some_P1807977723_r_l_v
% 0.31/0.46 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau )
% 0.31/0.46 @ ( produc1834103605_r_l_v
% 0.31/0.46 @ ^ [X: l] : none_val_r_l_v
% 0.31/0.46 @ E2 ) ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % fork_pseudodeterministic
% 0.31/0.46 thf(fact_19_revision__step__relaxed_Ofork,axiom,
% 0.31/0.46 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E2: expr_r_l_v,R2: r] :
% 0.31/0.46 ( ( ( S @ R )
% 0.31/0.46 = ( 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 ) ) ) ) ) )
% 0.31/0.46 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 0.31/0.46 => ( revisi1291188644_r_l_v @ subst @ R @ S
% 0.31/0.46 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( 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 @ R2 ) ) ) ) ) ) ) @ R2
% 0.31/0.46 @ ( some_P1807977723_r_l_v
% 0.31/0.46 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau )
% 0.31/0.46 @ ( produc1834103605_r_l_v
% 0.31/0.46 @ ^ [X: l] : none_val_r_l_v
% 0.31/0.46 @ E2 ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % revision_step_relaxed.fork
% 0.31/0.46 thf(fact_20_val_Oinject_I4_J,axiom,
% 0.31/0.46 ! [X4: r,Y4: r] :
% 0.31/0.46 ( ( ( rid_r_l_v @ X4 )
% 0.31/0.46 = ( rid_r_l_v @ Y4 ) )
% 0.31/0.46 = ( X4 = Y4 ) ) ).
% 0.31/0.46
% 0.31/0.46 % val.inject(4)
% 0.31/0.46 thf(fact_21_injective__cntxt,axiom,
% 0.31/0.46 ! [E: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 0.31/0.46 ( ( ( plug_r_l_v @ E @ E1 )
% 0.31/0.46 = ( plug_r_l_v @ E @ E22 ) )
% 0.31/0.46 = ( E1 = E22 ) ) ).
% 0.31/0.46
% 0.31/0.46 % injective_cntxt
% 0.31/0.47 thf(fact_22_expr_Oinject_I1_J,axiom,
% 0.31/0.47 ! [X1: val_r_l_v,Y1: val_r_l_v] :
% 0.31/0.47 ( ( ( vE_r_l_v @ X1 )
% 0.31/0.47 = ( vE_r_l_v @ Y1 ) )
% 0.31/0.47 = ( X1 = Y1 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.inject(1)
% 0.31/0.47 thf(fact_23_fun__upd__upd,axiom,
% 0.31/0.47 ! [F: r > option1457017436_r_l_v,X2: r,Y: option1457017436_r_l_v,Z: option1457017436_r_l_v] :
% 0.31/0.47 ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ F @ X2 @ Y ) @ X2 @ Z )
% 0.31/0.47 = ( fun_up709272714_r_l_v @ F @ X2 @ Z ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_upd
% 0.31/0.47 thf(fact_24_fun__upd__upd,axiom,
% 0.31/0.47 ! [F: l > option_val_r_l_v,X2: l,Y: option_val_r_l_v,Z: option_val_r_l_v] :
% 0.31/0.47 ( ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ F @ X2 @ Y ) @ X2 @ Z )
% 0.31/0.47 = ( fun_up1835647912_r_l_v @ F @ X2 @ Z ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_upd
% 0.31/0.47 thf(fact_25_fun__upd__triv,axiom,
% 0.31/0.47 ! [F: r > option1457017436_r_l_v,X2: r] :
% 0.31/0.47 ( ( fun_up709272714_r_l_v @ F @ X2 @ ( F @ X2 ) )
% 0.31/0.47 = F ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_triv
% 0.31/0.47 thf(fact_26_fun__upd__triv,axiom,
% 0.31/0.47 ! [F: l > option_val_r_l_v,X2: l] :
% 0.31/0.47 ( ( fun_up1835647912_r_l_v @ F @ X2 @ ( F @ X2 ) )
% 0.31/0.47 = F ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_triv
% 0.31/0.47 thf(fact_27_option_Oinject,axiom,
% 0.31/0.47 ! [X22: produc1156025366_r_l_v,Y22: produc1156025366_r_l_v] :
% 0.31/0.47 ( ( ( some_P1807977723_r_l_v @ X22 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ Y22 ) )
% 0.31/0.47 = ( X22 = Y22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.inject
% 0.31/0.47 thf(fact_28_option_Oinject,axiom,
% 0.31/0.47 ! [X22: val_r_l_v,Y22: val_r_l_v] :
% 0.31/0.47 ( ( ( some_val_r_l_v @ X22 )
% 0.31/0.47 = ( some_val_r_l_v @ Y22 ) )
% 0.31/0.47 = ( X22 = Y22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.inject
% 0.31/0.47 thf(fact_29_fun__upd__apply,axiom,
% 0.31/0.47 ( fun_up709272714_r_l_v
% 0.31/0.47 = ( ^ [F2: r > option1457017436_r_l_v,X: r,Y2: option1457017436_r_l_v,Z2: r] : ( if_opt1153928738_r_l_v @ ( Z2 = X ) @ Y2 @ ( F2 @ Z2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_apply
% 0.31/0.47 thf(fact_30_fun__upd__apply,axiom,
% 0.31/0.47 ( fun_up1835647912_r_l_v
% 0.31/0.47 = ( ^ [F2: l > option_val_r_l_v,X: l,Y2: option_val_r_l_v,Z2: l] : ( if_option_val_r_l_v @ ( Z2 = X ) @ Y2 @ ( F2 @ Z2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_apply
% 0.31/0.47 thf(fact_31_expr_Oinject_I7_J,axiom,
% 0.31/0.47 ! [X7: expr_r_l_v,Y7: expr_r_l_v] :
% 0.31/0.47 ( ( ( rfork_r_l_v @ X7 )
% 0.31/0.47 = ( rfork_r_l_v @ Y7 ) )
% 0.31/0.47 = ( X7 = Y7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.inject(7)
% 0.31/0.47 thf(fact_32_RID_092_060_094sub_062GI_I1_J,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R: r,V: produc1156025366_r_l_v] :
% 0.31/0.47 ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ V ) )
% 0.31/0.47 => ( member_r @ R @ ( rID_G_r_l_v @ S ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % RID\<^sub>GI(1)
% 0.31/0.47 thf(fact_33_in__restricted__global__in__unrestricted__global_I1_J,axiom,
% 0.31/0.47 ! [R2: r,S: r > option1457017436_r_l_v,R: r] :
% 0.31/0.47 ( ( member_r @ R2 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 0.31/0.47 => ( member_r @ R2 @ ( rID_G_r_l_v @ S ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % in_restricted_global_in_unrestricted_global(1)
% 0.31/0.47 thf(fact_34_only__fork__introduces__rids_H,axiom,
% 0.31/0.47 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v,R2: r] :
% 0.31/0.47 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.31/0.47 => ( ! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E4: expr_r_l_v] :
% 0.31/0.47 ( ( S @ R )
% 0.31/0.47 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 0.31/0.47 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 0.31/0.47 => ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % only_fork_introduces_rids'
% 0.31/0.47 thf(fact_35_in__restricted__global__in__updated__global_I1_J,axiom,
% 0.31/0.47 ! [R2: r,S: r > option1457017436_r_l_v,R: r,Ls: produc1156025366_r_l_v] :
% 0.31/0.47 ( ( member_r @ R2 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 0.31/0.47 => ( member_r @ R2 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ Ls ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % in_restricted_global_in_updated_global(1)
% 0.31/0.47 thf(fact_36_substitution__axioms,axiom,
% 0.31/0.47 substitution_r_l_v @ subst ).
% 0.31/0.47
% 0.31/0.47 % substitution_axioms
% 0.31/0.47 thf(fact_37_expr_Odistinct_I11_J,axiom,
% 0.31/0.47 ! [X1: val_r_l_v,X7: expr_r_l_v] :
% 0.31/0.47 ( ( vE_r_l_v @ X1 )
% 0.31/0.47 != ( rfork_r_l_v @ X7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(11)
% 0.31/0.47 thf(fact_38_fun__upd__idem__iff,axiom,
% 0.31/0.47 ! [F: r > option1457017436_r_l_v,X2: r,Y: option1457017436_r_l_v] :
% 0.31/0.47 ( ( ( fun_up709272714_r_l_v @ F @ X2 @ Y )
% 0.31/0.47 = F )
% 0.31/0.47 = ( ( F @ X2 )
% 0.31/0.47 = Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_idem_iff
% 0.31/0.47 thf(fact_39_fun__upd__idem__iff,axiom,
% 0.31/0.47 ! [F: l > option_val_r_l_v,X2: l,Y: option_val_r_l_v] :
% 0.31/0.47 ( ( ( fun_up1835647912_r_l_v @ F @ X2 @ Y )
% 0.31/0.47 = F )
% 0.31/0.47 = ( ( F @ X2 )
% 0.31/0.47 = Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_idem_iff
% 0.31/0.47 thf(fact_40_fun__upd__twist,axiom,
% 0.31/0.47 ! [A: r,C: r,M: r > option1457017436_r_l_v,B: option1457017436_r_l_v,D: option1457017436_r_l_v] :
% 0.31/0.47 ( ( A != C )
% 0.31/0.47 => ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ M @ A @ B ) @ C @ D )
% 0.31/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ M @ C @ D ) @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_twist
% 0.31/0.47 thf(fact_41_fun__upd__twist,axiom,
% 0.31/0.47 ! [A: l,C: l,M: l > option_val_r_l_v,B: option_val_r_l_v,D: option_val_r_l_v] :
% 0.31/0.47 ( ( A != C )
% 0.31/0.47 => ( ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ M @ A @ B ) @ C @ D )
% 0.31/0.47 = ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ M @ C @ D ) @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_twist
% 0.31/0.47 thf(fact_42_fun__upd__other,axiom,
% 0.31/0.47 ! [Z: r,X2: r,F: r > option1457017436_r_l_v,Y: option1457017436_r_l_v] :
% 0.31/0.47 ( ( Z != X2 )
% 0.31/0.47 => ( ( fun_up709272714_r_l_v @ F @ X2 @ Y @ Z )
% 0.31/0.47 = ( F @ Z ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_other
% 0.31/0.47 thf(fact_43_fun__upd__other,axiom,
% 0.31/0.47 ! [Z: l,X2: l,F: l > option_val_r_l_v,Y: option_val_r_l_v] :
% 0.31/0.47 ( ( Z != X2 )
% 0.31/0.47 => ( ( fun_up1835647912_r_l_v @ F @ X2 @ Y @ Z )
% 0.31/0.47 = ( F @ Z ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_other
% 0.31/0.47 thf(fact_44_fun__upd__same,axiom,
% 0.31/0.47 ! [F: r > option1457017436_r_l_v,X2: r,Y: option1457017436_r_l_v] :
% 0.31/0.47 ( ( fun_up709272714_r_l_v @ F @ X2 @ Y @ X2 )
% 0.31/0.47 = Y ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_same
% 0.31/0.47 thf(fact_45_fun__upd__same,axiom,
% 0.31/0.47 ! [F: l > option_val_r_l_v,X2: l,Y: option_val_r_l_v] :
% 0.31/0.47 ( ( fun_up1835647912_r_l_v @ F @ X2 @ Y @ X2 )
% 0.31/0.47 = Y ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_same
% 0.31/0.47 thf(fact_46_fun__upd__idem,axiom,
% 0.31/0.47 ! [F: r > option1457017436_r_l_v,X2: r,Y: option1457017436_r_l_v] :
% 0.31/0.47 ( ( ( F @ X2 )
% 0.31/0.47 = Y )
% 0.31/0.47 => ( ( fun_up709272714_r_l_v @ F @ X2 @ Y )
% 0.31/0.47 = F ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_idem
% 0.31/0.47 thf(fact_47_fun__upd__idem,axiom,
% 0.31/0.47 ! [F: l > option_val_r_l_v,X2: l,Y: option_val_r_l_v] :
% 0.31/0.47 ( ( ( F @ X2 )
% 0.31/0.47 = Y )
% 0.31/0.47 => ( ( fun_up1835647912_r_l_v @ F @ X2 @ Y )
% 0.31/0.47 = F ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_idem
% 0.31/0.47 thf(fact_48_fun__upd__eqD,axiom,
% 0.31/0.47 ! [F: r > option1457017436_r_l_v,X2: r,Y: option1457017436_r_l_v,G: r > option1457017436_r_l_v,Z: option1457017436_r_l_v] :
% 0.31/0.47 ( ( ( fun_up709272714_r_l_v @ F @ X2 @ Y )
% 0.31/0.47 = ( fun_up709272714_r_l_v @ G @ X2 @ Z ) )
% 0.31/0.47 => ( Y = Z ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_eqD
% 0.31/0.47 thf(fact_49_fun__upd__eqD,axiom,
% 0.31/0.47 ! [F: l > option_val_r_l_v,X2: l,Y: option_val_r_l_v,G: l > option_val_r_l_v,Z: option_val_r_l_v] :
% 0.31/0.47 ( ( ( fun_up1835647912_r_l_v @ F @ X2 @ Y )
% 0.31/0.47 = ( fun_up1835647912_r_l_v @ G @ X2 @ Z ) )
% 0.31/0.47 => ( Y = Z ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_eqD
% 0.31/0.47 thf(fact_50_fun__upd__def,axiom,
% 0.31/0.47 ( fun_up709272714_r_l_v
% 0.31/0.47 = ( ^ [F2: r > option1457017436_r_l_v,A2: r,B2: option1457017436_r_l_v,X: r] : ( if_opt1153928738_r_l_v @ ( X = A2 ) @ B2 @ ( F2 @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_def
% 0.31/0.47 thf(fact_51_fun__upd__def,axiom,
% 0.31/0.47 ( fun_up1835647912_r_l_v
% 0.31/0.47 = ( ^ [F2: l > option_val_r_l_v,A2: l,B2: option_val_r_l_v,X: l] : ( if_option_val_r_l_v @ ( X = A2 ) @ B2 @ ( F2 @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fun_upd_def
% 0.31/0.47 thf(fact_52_combine__options__cases,axiom,
% 0.31/0.47 ! [X2: option1457017436_r_l_v,P: option1457017436_r_l_v > option1457017436_r_l_v > $o,Y: option1457017436_r_l_v] :
% 0.31/0.47 ( ( ( X2 = none_P277133687_r_l_v )
% 0.31/0.47 => ( P @ X2 @ Y ) )
% 0.31/0.47 => ( ( ( Y = none_P277133687_r_l_v )
% 0.31/0.47 => ( P @ X2 @ Y ) )
% 0.31/0.47 => ( ! [A3: produc1156025366_r_l_v,B3: produc1156025366_r_l_v] :
% 0.31/0.47 ( ( X2
% 0.31/0.47 = ( some_P1807977723_r_l_v @ A3 ) )
% 0.31/0.47 => ( ( Y
% 0.31/0.47 = ( some_P1807977723_r_l_v @ B3 ) )
% 0.31/0.47 => ( P @ X2 @ Y ) ) )
% 0.31/0.47 => ( P @ X2 @ Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % combine_options_cases
% 0.31/0.47 thf(fact_53_combine__options__cases,axiom,
% 0.31/0.47 ! [X2: option1457017436_r_l_v,P: option1457017436_r_l_v > option_val_r_l_v > $o,Y: option_val_r_l_v] :
% 0.31/0.47 ( ( ( X2 = none_P277133687_r_l_v )
% 0.31/0.47 => ( P @ X2 @ Y ) )
% 0.31/0.47 => ( ( ( Y = none_val_r_l_v )
% 0.31/0.47 => ( P @ X2 @ Y ) )
% 0.31/0.47 => ( ! [A3: produc1156025366_r_l_v,B3: val_r_l_v] :
% 0.31/0.47 ( ( X2
% 0.31/0.47 = ( some_P1807977723_r_l_v @ A3 ) )
% 0.31/0.47 => ( ( Y
% 0.31/0.47 = ( some_val_r_l_v @ B3 ) )
% 0.31/0.47 => ( P @ X2 @ Y ) ) )
% 0.31/0.47 => ( P @ X2 @ Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % combine_options_cases
% 0.31/0.47 thf(fact_54_combine__options__cases,axiom,
% 0.31/0.47 ! [X2: option_val_r_l_v,P: option_val_r_l_v > option1457017436_r_l_v > $o,Y: option1457017436_r_l_v] :
% 0.31/0.47 ( ( ( X2 = none_val_r_l_v )
% 0.31/0.47 => ( P @ X2 @ Y ) )
% 0.31/0.47 => ( ( ( Y = none_P277133687_r_l_v )
% 0.31/0.47 => ( P @ X2 @ Y ) )
% 0.31/0.47 => ( ! [A3: val_r_l_v,B3: produc1156025366_r_l_v] :
% 0.31/0.47 ( ( X2
% 0.31/0.47 = ( some_val_r_l_v @ A3 ) )
% 0.31/0.47 => ( ( Y
% 0.31/0.47 = ( some_P1807977723_r_l_v @ B3 ) )
% 0.31/0.47 => ( P @ X2 @ Y ) ) )
% 0.31/0.47 => ( P @ X2 @ Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % combine_options_cases
% 0.31/0.47 thf(fact_55_combine__options__cases,axiom,
% 0.31/0.47 ! [X2: option_val_r_l_v,P: option_val_r_l_v > option_val_r_l_v > $o,Y: option_val_r_l_v] :
% 0.31/0.47 ( ( ( X2 = none_val_r_l_v )
% 0.31/0.47 => ( P @ X2 @ Y ) )
% 0.31/0.47 => ( ( ( Y = none_val_r_l_v )
% 0.31/0.47 => ( P @ X2 @ Y ) )
% 0.31/0.47 => ( ! [A3: val_r_l_v,B3: val_r_l_v] :
% 0.31/0.47 ( ( X2
% 0.31/0.47 = ( some_val_r_l_v @ A3 ) )
% 0.31/0.47 => ( ( Y
% 0.31/0.47 = ( some_val_r_l_v @ B3 ) )
% 0.31/0.47 => ( P @ X2 @ Y ) ) )
% 0.31/0.47 => ( P @ X2 @ Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % combine_options_cases
% 0.31/0.47 thf(fact_56_split__option__all,axiom,
% 0.31/0.47 ( ( ^ [P2: option1457017436_r_l_v > $o] :
% 0.31/0.47 ! [X5: option1457017436_r_l_v] : ( P2 @ X5 ) )
% 0.31/0.47 = ( ^ [P3: option1457017436_r_l_v > $o] :
% 0.31/0.47 ( ( P3 @ none_P277133687_r_l_v )
% 0.31/0.47 & ! [X: produc1156025366_r_l_v] : ( P3 @ ( some_P1807977723_r_l_v @ X ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_option_all
% 0.31/0.47 thf(fact_57_split__option__all,axiom,
% 0.31/0.47 ( ( ^ [P2: option_val_r_l_v > $o] :
% 0.31/0.47 ! [X5: option_val_r_l_v] : ( P2 @ X5 ) )
% 0.31/0.47 = ( ^ [P3: option_val_r_l_v > $o] :
% 0.31/0.47 ( ( P3 @ none_val_r_l_v )
% 0.31/0.47 & ! [X: val_r_l_v] : ( P3 @ ( some_val_r_l_v @ X ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_option_all
% 0.31/0.47 thf(fact_58_split__option__ex,axiom,
% 0.31/0.47 ( ( ^ [P2: option1457017436_r_l_v > $o] :
% 0.31/0.47 ? [X5: option1457017436_r_l_v] : ( P2 @ X5 ) )
% 0.31/0.47 = ( ^ [P3: option1457017436_r_l_v > $o] :
% 0.31/0.47 ( ( P3 @ none_P277133687_r_l_v )
% 0.31/0.47 | ? [X: produc1156025366_r_l_v] : ( P3 @ ( some_P1807977723_r_l_v @ X ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_option_ex
% 0.31/0.47 thf(fact_59_split__option__ex,axiom,
% 0.31/0.47 ( ( ^ [P2: option_val_r_l_v > $o] :
% 0.31/0.47 ? [X5: option_val_r_l_v] : ( P2 @ X5 ) )
% 0.31/0.47 = ( ^ [P3: option_val_r_l_v > $o] :
% 0.31/0.47 ( ( P3 @ none_val_r_l_v )
% 0.31/0.47 | ? [X: val_r_l_v] : ( P3 @ ( some_val_r_l_v @ X ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_option_ex
% 0.31/0.47 thf(fact_60_option_Oinducts,axiom,
% 0.31/0.47 ! [P: option1457017436_r_l_v > $o,Option: option1457017436_r_l_v] :
% 0.31/0.47 ( ( P @ none_P277133687_r_l_v )
% 0.31/0.47 => ( ! [X6: produc1156025366_r_l_v] : ( P @ ( some_P1807977723_r_l_v @ X6 ) )
% 0.31/0.47 => ( P @ Option ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.inducts
% 0.31/0.47 thf(fact_61_option_Oinducts,axiom,
% 0.31/0.47 ! [P: option_val_r_l_v > $o,Option: option_val_r_l_v] :
% 0.31/0.47 ( ( P @ none_val_r_l_v )
% 0.31/0.47 => ( ! [X6: val_r_l_v] : ( P @ ( some_val_r_l_v @ X6 ) )
% 0.31/0.47 => ( P @ Option ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.inducts
% 0.31/0.47 thf(fact_62_option_Oexhaust,axiom,
% 0.31/0.47 ! [Y: option1457017436_r_l_v] :
% 0.31/0.47 ( ( Y != none_P277133687_r_l_v )
% 0.31/0.47 => ~ ! [X23: produc1156025366_r_l_v] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( some_P1807977723_r_l_v @ X23 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.exhaust
% 0.31/0.47 thf(fact_63_option_Oexhaust,axiom,
% 0.31/0.47 ! [Y: option_val_r_l_v] :
% 0.31/0.47 ( ( Y != none_val_r_l_v )
% 0.31/0.47 => ~ ! [X23: val_r_l_v] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( some_val_r_l_v @ X23 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.exhaust
% 0.31/0.47 thf(fact_64_option_OdiscI,axiom,
% 0.31/0.47 ! [Option: option1457017436_r_l_v,X22: produc1156025366_r_l_v] :
% 0.31/0.47 ( ( Option
% 0.31/0.47 = ( some_P1807977723_r_l_v @ X22 ) )
% 0.31/0.47 => ( Option != none_P277133687_r_l_v ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.discI
% 0.31/0.47 thf(fact_65_option_OdiscI,axiom,
% 0.31/0.47 ! [Option: option_val_r_l_v,X22: val_r_l_v] :
% 0.31/0.47 ( ( Option
% 0.31/0.47 = ( some_val_r_l_v @ X22 ) )
% 0.31/0.47 => ( Option != none_val_r_l_v ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.discI
% 0.31/0.47 thf(fact_66_option_Odistinct_I1_J,axiom,
% 0.31/0.47 ! [X22: produc1156025366_r_l_v] :
% 0.31/0.47 ( none_P277133687_r_l_v
% 0.31/0.47 != ( some_P1807977723_r_l_v @ X22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.distinct(1)
% 0.31/0.47 thf(fact_67_option_Odistinct_I1_J,axiom,
% 0.31/0.47 ! [X22: val_r_l_v] :
% 0.31/0.47 ( none_val_r_l_v
% 0.31/0.47 != ( some_val_r_l_v @ X22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.distinct(1)
% 0.31/0.47 thf(fact_68_mem__Collect__eq,axiom,
% 0.31/0.47 ! [A: set_l,P: set_l > $o] :
% 0.31/0.47 ( ( member_set_l @ A @ ( collect_set_l @ P ) )
% 0.31/0.47 = ( P @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % mem_Collect_eq
% 0.31/0.47 thf(fact_69_mem__Collect__eq,axiom,
% 0.31/0.47 ! [A: set_r,P: set_r > $o] :
% 0.31/0.47 ( ( member_set_r @ A @ ( collect_set_r @ P ) )
% 0.31/0.47 = ( P @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % mem_Collect_eq
% 0.31/0.47 thf(fact_70_mem__Collect__eq,axiom,
% 0.31/0.47 ! [A: r,P: r > $o] :
% 0.31/0.47 ( ( member_r @ A @ ( collect_r @ P ) )
% 0.31/0.47 = ( P @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % mem_Collect_eq
% 0.31/0.47 thf(fact_71_mem__Collect__eq,axiom,
% 0.31/0.47 ! [A: produc1389397445_r_l_v,P: produc1389397445_r_l_v > $o] :
% 0.31/0.47 ( ( member1522896238_r_l_v @ A @ ( collec1978425008_r_l_v @ P ) )
% 0.31/0.47 = ( P @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % mem_Collect_eq
% 0.31/0.47 thf(fact_72_mem__Collect__eq,axiom,
% 0.31/0.47 ! [A: l,P: l > $o] :
% 0.31/0.47 ( ( member_l @ A @ ( collect_l @ P ) )
% 0.31/0.47 = ( P @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % mem_Collect_eq
% 0.31/0.47 thf(fact_73_Collect__mem__eq,axiom,
% 0.31/0.47 ! [A4: set_set_l] :
% 0.31/0.47 ( ( collect_set_l
% 0.31/0.47 @ ^ [X: set_l] : ( member_set_l @ X @ A4 ) )
% 0.31/0.47 = A4 ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mem_eq
% 0.31/0.47 thf(fact_74_Collect__mem__eq,axiom,
% 0.31/0.47 ! [A4: set_set_r] :
% 0.31/0.47 ( ( collect_set_r
% 0.31/0.47 @ ^ [X: set_r] : ( member_set_r @ X @ A4 ) )
% 0.31/0.47 = A4 ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mem_eq
% 0.31/0.47 thf(fact_75_Collect__mem__eq,axiom,
% 0.31/0.47 ! [A4: set_r] :
% 0.31/0.47 ( ( collect_r
% 0.31/0.47 @ ^ [X: r] : ( member_r @ X @ A4 ) )
% 0.31/0.47 = A4 ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mem_eq
% 0.31/0.47 thf(fact_76_Collect__mem__eq,axiom,
% 0.31/0.47 ! [A4: set_Pr1409704485_r_l_v] :
% 0.31/0.47 ( ( collec1978425008_r_l_v
% 0.31/0.47 @ ^ [X: produc1389397445_r_l_v] : ( member1522896238_r_l_v @ X @ A4 ) )
% 0.31/0.47 = A4 ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mem_eq
% 0.31/0.47 thf(fact_77_Collect__mem__eq,axiom,
% 0.31/0.47 ! [A4: set_l] :
% 0.31/0.47 ( ( collect_l
% 0.31/0.47 @ ^ [X: l] : ( member_l @ X @ A4 ) )
% 0.31/0.47 = A4 ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mem_eq
% 0.31/0.47 thf(fact_78_Collect__cong,axiom,
% 0.31/0.47 ! [P: l > $o,Q: l > $o] :
% 0.31/0.47 ( ! [X6: l] :
% 0.31/0.47 ( ( P @ X6 )
% 0.31/0.47 = ( Q @ X6 ) )
% 0.31/0.47 => ( ( collect_l @ P )
% 0.31/0.47 = ( collect_l @ Q ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_cong
% 0.31/0.47 thf(fact_79_Collect__cong,axiom,
% 0.31/0.47 ! [P: produc1389397445_r_l_v > $o,Q: produc1389397445_r_l_v > $o] :
% 0.31/0.47 ( ! [X6: produc1389397445_r_l_v] :
% 0.31/0.47 ( ( P @ X6 )
% 0.31/0.47 = ( Q @ X6 ) )
% 0.31/0.47 => ( ( collec1978425008_r_l_v @ P )
% 0.31/0.47 = ( collec1978425008_r_l_v @ Q ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_cong
% 0.31/0.47 thf(fact_80_Collect__cong,axiom,
% 0.31/0.47 ! [P: r > $o,Q: r > $o] :
% 0.31/0.47 ( ! [X6: r] :
% 0.31/0.47 ( ( P @ X6 )
% 0.31/0.47 = ( Q @ X6 ) )
% 0.31/0.47 => ( ( collect_r @ P )
% 0.31/0.47 = ( collect_r @ Q ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_cong
% 0.31/0.47 thf(fact_81_Collect__cong,axiom,
% 0.31/0.47 ! [P: set_l > $o,Q: set_l > $o] :
% 0.31/0.47 ( ! [X6: set_l] :
% 0.31/0.47 ( ( P @ X6 )
% 0.31/0.47 = ( Q @ X6 ) )
% 0.31/0.47 => ( ( collect_set_l @ P )
% 0.31/0.47 = ( collect_set_l @ Q ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_cong
% 0.31/0.47 thf(fact_82_Collect__cong,axiom,
% 0.31/0.47 ! [P: set_r > $o,Q: set_r > $o] :
% 0.31/0.47 ( ! [X6: set_r] :
% 0.31/0.47 ( ( P @ X6 )
% 0.31/0.47 = ( Q @ X6 ) )
% 0.31/0.47 => ( ( collect_set_r @ P )
% 0.31/0.47 = ( collect_set_r @ Q ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_cong
% 0.31/0.47 thf(fact_83_map__upd__Some__unfold,axiom,
% 0.31/0.47 ! [M: r > option1457017436_r_l_v,A: r,B: produc1156025366_r_l_v,X2: r,Y: produc1156025366_r_l_v] :
% 0.31/0.47 ( ( ( fun_up709272714_r_l_v @ M @ A @ ( some_P1807977723_r_l_v @ B ) @ X2 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ Y ) )
% 0.31/0.47 = ( ( ( X2 = A )
% 0.31/0.47 & ( B = Y ) )
% 0.31/0.47 | ( ( X2 != A )
% 0.31/0.47 & ( ( M @ X2 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ Y ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_upd_Some_unfold
% 0.31/0.47 thf(fact_84_map__upd__Some__unfold,axiom,
% 0.31/0.47 ! [M: l > option_val_r_l_v,A: l,B: val_r_l_v,X2: l,Y: val_r_l_v] :
% 0.31/0.47 ( ( ( fun_up1835647912_r_l_v @ M @ A @ ( some_val_r_l_v @ B ) @ X2 )
% 0.31/0.47 = ( some_val_r_l_v @ Y ) )
% 0.31/0.47 = ( ( ( X2 = A )
% 0.31/0.47 & ( B = Y ) )
% 0.31/0.47 | ( ( X2 != A )
% 0.31/0.47 & ( ( M @ X2 )
% 0.31/0.47 = ( some_val_r_l_v @ Y ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_upd_Some_unfold
% 0.31/0.47 thf(fact_85_map__upd__triv,axiom,
% 0.31/0.47 ! [T: r > option1457017436_r_l_v,K: r,X2: produc1156025366_r_l_v] :
% 0.31/0.47 ( ( ( T @ K )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ X2 ) )
% 0.31/0.47 => ( ( fun_up709272714_r_l_v @ T @ K @ ( some_P1807977723_r_l_v @ X2 ) )
% 0.31/0.47 = T ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_upd_triv
% 0.31/0.47 thf(fact_86_map__upd__triv,axiom,
% 0.31/0.47 ! [T: l > option_val_r_l_v,K: l,X2: val_r_l_v] :
% 0.31/0.47 ( ( ( T @ K )
% 0.31/0.47 = ( some_val_r_l_v @ X2 ) )
% 0.31/0.47 => ( ( fun_up1835647912_r_l_v @ T @ K @ ( some_val_r_l_v @ X2 ) )
% 0.31/0.47 = T ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_upd_triv
% 0.31/0.47 thf(fact_87_map__upd__eqD1,axiom,
% 0.31/0.47 ! [M: r > option1457017436_r_l_v,A: r,X2: produc1156025366_r_l_v,N: r > option1457017436_r_l_v,Y: produc1156025366_r_l_v] :
% 0.31/0.47 ( ( ( fun_up709272714_r_l_v @ M @ A @ ( some_P1807977723_r_l_v @ X2 ) )
% 0.31/0.47 = ( fun_up709272714_r_l_v @ N @ A @ ( some_P1807977723_r_l_v @ Y ) ) )
% 0.31/0.47 => ( X2 = Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_upd_eqD1
% 0.31/0.47 thf(fact_88_map__upd__eqD1,axiom,
% 0.31/0.47 ! [M: l > option_val_r_l_v,A: l,X2: val_r_l_v,N: l > option_val_r_l_v,Y: val_r_l_v] :
% 0.31/0.47 ( ( ( fun_up1835647912_r_l_v @ M @ A @ ( some_val_r_l_v @ X2 ) )
% 0.31/0.47 = ( fun_up1835647912_r_l_v @ N @ A @ ( some_val_r_l_v @ Y ) ) )
% 0.31/0.47 => ( X2 = Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_upd_eqD1
% 0.31/0.47 thf(fact_89_LID__local__store_Oinduct,axiom,
% 0.31/0.47 ! [P: produc1156025366_r_l_v > $o,A0: produc1156025366_r_l_v] :
% 0.31/0.47 ( ! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E4: expr_r_l_v] : ( P @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ E4 ) ) )
% 0.31/0.47 => ( P @ A0 ) ) ).
% 0.31/0.47
% 0.31/0.47 % LID_local_store.induct
% 0.31/0.47 thf(fact_90_LID__local__store_Ocases,axiom,
% 0.31/0.47 ! [X2: produc1156025366_r_l_v] :
% 0.31/0.47 ~ ! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E4: expr_r_l_v] :
% 0.31/0.47 ( X2
% 0.31/0.47 != ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ E4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % LID_local_store.cases
% 0.31/0.47 thf(fact_91_combine_Osimps,axiom,
% 0.31/0.47 ( combine_l_val_r_l_v
% 0.31/0.47 = ( ^ [F2: l > option_val_r_l_v,G2: l > option_val_r_l_v,X: l] :
% 0.31/0.47 ( if_option_val_r_l_v
% 0.31/0.47 @ ( ( G2 @ X )
% 0.31/0.47 = none_val_r_l_v )
% 0.31/0.47 @ ( F2 @ X )
% 0.31/0.47 @ ( G2 @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % combine.simps
% 0.31/0.47 thf(fact_92_combine_Oelims,axiom,
% 0.31/0.47 ! [X2: l > option_val_r_l_v,Xa: l > option_val_r_l_v,Xb: l,Y: option_val_r_l_v] :
% 0.31/0.47 ( ( ( combine_l_val_r_l_v @ X2 @ Xa @ Xb )
% 0.31/0.47 = Y )
% 0.31/0.47 => ( ( ( ( Xa @ Xb )
% 0.31/0.47 = none_val_r_l_v )
% 0.31/0.47 => ( Y
% 0.31/0.47 = ( X2 @ Xb ) ) )
% 0.31/0.47 & ( ( ( Xa @ Xb )
% 0.31/0.47 != none_val_r_l_v )
% 0.31/0.47 => ( Y
% 0.31/0.47 = ( Xa @ Xb ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % combine.elims
% 0.31/0.47 thf(fact_93_local__steps__commute,axiom,
% 0.31/0.47 ! [S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,X2: produc1156025366_r_l_v,S_22: r > option1457017436_r_l_v,R2: r,Y: produc1156025366_r_l_v] :
% 0.31/0.47 ( ( S_2
% 0.31/0.47 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) )
% 0.31/0.47 => ( ( S_22
% 0.31/0.47 = ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
% 0.31/0.47 => ( ( revision_step_r_l_v @ subst @ R2 @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
% 0.31/0.47 => ( ( 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 @ X2 ) ) )
% 0.31/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.31/0.47 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 0.31/0.47 | ( S_2 = S_3 ) )
% 0.31/0.47 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 0.31/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % local_steps_commute
% 0.31/0.47 thf(fact_94_revision__step__relaxed_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r] :
% 0.31/0.47 ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = none_P277133687_r_l_v )
% 0.31/0.47 => ( revisi1291188644_r_l_v @ subst @ R @ S
% 0.31/0.47 @ ^ [X: r] : none_P277133687_r_l_v ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step_relaxed.join\<^sub>\<epsilon>
% 0.31/0.47 thf(fact_95_revision__step_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r] :
% 0.31/0.47 ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = none_P277133687_r_l_v )
% 0.31/0.47 => ( revision_step_r_l_v @ subst @ R @ S
% 0.31/0.47 @ ^ [X: r] : none_P277133687_r_l_v ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step.join\<^sub>\<epsilon>
% 0.31/0.47 thf(fact_96_transition__relations__equivalent,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R: r,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( reachable_r_l_v @ subst @ S )
% 0.31/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.31/0.47 = ( revisi1291188644_r_l_v @ subst @ R @ S @ S2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % transition_relations_equivalent
% 0.31/0.47 thf(fact_97_SLC__commute,axiom,
% 0.31/0.47 ! [S_33: r > option1457017436_r_l_v,S_34: r > option1457017436_r_l_v,R2: r,S_2: r > option1457017436_r_l_v,R: r,S_22: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( S_33 = S_34 )
% 0.31/0.47 => ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_33 )
% 0.31/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_34 )
% 0.31/0.47 => ( ( eq_states_r_l_v @ S_33 @ S_34 )
% 0.31/0.47 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_33 )
% 0.31/0.47 | ( S_2 = S_33 ) )
% 0.31/0.47 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_34 )
% 0.31/0.47 | ( S_22 = S_34 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % SLC_commute
% 0.31/0.47 thf(fact_98_SLC__sym,axiom,
% 0.31/0.47 ! [R2: r,S_2: r > option1457017436_r_l_v,R: r,S_22: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ? [S_35: r > option1457017436_r_l_v,S_36: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( eq_states_r_l_v @ S_35 @ S_36 )
% 0.31/0.47 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_35 )
% 0.31/0.47 | ( S_2 = S_35 ) )
% 0.31/0.47 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_36 )
% 0.31/0.47 | ( S_22 = S_36 ) ) )
% 0.31/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.31/0.47 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_3 )
% 0.31/0.47 | ( S_22 = S_3 ) )
% 0.31/0.47 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_32 )
% 0.31/0.47 | ( S_2 = S_32 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % SLC_sym
% 0.31/0.47 thf(fact_99_local__determinism,axiom,
% 0.31/0.47 ! [R: r,S_1: r > option1457017436_r_l_v,S_2: r > option1457017436_r_l_v,S_22: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( revision_step_r_l_v @ subst @ R @ S_1 @ S_2 )
% 0.31/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S_1 @ S_22 )
% 0.31/0.47 => ( eq_states_r_l_v @ S_2 @ S_22 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % local_determinism
% 0.31/0.47 thf(fact_100_reachability__closed__under__execution__step,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R: r,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( reachable_r_l_v @ subst @ S )
% 0.31/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.31/0.47 => ( reachable_r_l_v @ subst @ S2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % reachability_closed_under_execution_step
% 0.31/0.47 thf(fact_101_only__fork__introduces__rids,axiom,
% 0.31/0.47 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.31/0.47 => ( ! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E4: expr_r_l_v] :
% 0.31/0.47 ( ( S @ R )
% 0.31/0.47 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 0.31/0.47 => ( ord_less_eq_set_r @ ( rID_G_r_l_v @ S2 ) @ ( rID_G_r_l_v @ S ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % only_fork_introduces_rids
% 0.31/0.47 thf(fact_102_substitution_Ofork__pseudodeterministic,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E2: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( ( S @ R )
% 0.31/0.47 = ( 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 ) ) ) ) ) )
% 0.31/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.31/0.47 = ( ? [R3: r] :
% 0.31/0.47 ( ~ ( member_r @ R3 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E2 ) ) ) ) ) ) ) )
% 0.31/0.47 & ( S2
% 0.31/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( 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
% 0.31/0.47 @ ( some_P1807977723_r_l_v
% 0.31/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau )
% 0.31/0.47 @ ( produc1834103605_r_l_v
% 0.31/0.47 @ ^ [X: l] : none_val_r_l_v
% 0.31/0.47 @ E2 ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.fork_pseudodeterministic
% 0.31/0.47 thf(fact_103_expr_Oinject_I8_J,axiom,
% 0.31/0.47 ! [X8: expr_r_l_v,Y8: expr_r_l_v] :
% 0.31/0.47 ( ( ( rjoin_r_l_v @ X8 )
% 0.31/0.47 = ( rjoin_r_l_v @ Y8 ) )
% 0.31/0.47 = ( X8 = Y8 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.inject(8)
% 0.31/0.47 thf(fact_104_SLC__join_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.31/0.47 ! [S_1: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: 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] :
% 0.31/0.47 ( ( ( S_1 @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( S_2
% 0.31/0.47 = ( ^ [X: r] : none_P277133687_r_l_v ) )
% 0.31/0.47 => ( ( ( S_1 @ R4 )
% 0.31/0.47 = none_P277133687_r_l_v )
% 0.31/0.47 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 0.31/0.47 => ( ( R != R2 )
% 0.31/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.31/0.47 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 0.31/0.47 | ( S_2 = S_3 ) )
% 0.31/0.47 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 0.31/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % SLC_join\<^sub>\<epsilon>
% 0.31/0.47 thf(fact_105_reachable__def,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( reachable_r_l_v @ subst @ S )
% 0.31/0.47 = ( ? [E5: expr_r_l_v,S3: r > option1457017436_r_l_v] : ( execution_r_l_v @ subst @ E5 @ S3 @ S ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % reachable_def
% 0.31/0.47 thf(fact_106_rjoin_092_060_094sub_062_092_060epsilon_062__deterministic,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = none_P277133687_r_l_v )
% 0.31/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.31/0.47 = ( S2
% 0.31/0.47 = ( ^ [X: r] : none_P277133687_r_l_v ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rjoin\<^sub>\<epsilon>_deterministic
% 0.31/0.47 thf(fact_107_substitution_Olocal__determinism,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S_1 @ S_2 )
% 0.31/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S_1 @ S_22 )
% 0.31/0.47 => ( eq_states_r_l_v @ S_2 @ S_22 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.local_determinism
% 0.31/0.47 thf(fact_108_substitution_OSLC__commute,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_33: r > option1457017436_r_l_v,S_34: r > option1457017436_r_l_v,R2: r,S_2: r > option1457017436_r_l_v,R: r,S_22: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( S_33 = S_34 )
% 0.31/0.47 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_33 )
% 0.31/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_34 )
% 0.31/0.47 => ( ( eq_states_r_l_v @ S_33 @ S_34 )
% 0.31/0.47 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_33 )
% 0.31/0.47 | ( S_2 = S_33 ) )
% 0.31/0.47 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_34 )
% 0.31/0.47 | ( S_22 = S_34 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.SLC_commute
% 0.31/0.47 thf(fact_109_substitution_OSLC__sym,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ? [S_35: r > option1457017436_r_l_v,S_36: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( eq_states_r_l_v @ S_35 @ S_36 )
% 0.31/0.47 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_35 )
% 0.31/0.47 | ( S_2 = S_35 ) )
% 0.31/0.47 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_36 )
% 0.31/0.47 | ( S_22 = S_36 ) ) )
% 0.31/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.31/0.47 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_3 )
% 0.31/0.47 | ( S_22 = S_3 ) )
% 0.31/0.47 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_32 )
% 0.31/0.47 | ( S_2 = S_32 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.SLC_sym
% 0.31/0.47 thf(fact_110_expr_Odistinct_I13_J,axiom,
% 0.31/0.47 ! [X1: val_r_l_v,X8: expr_r_l_v] :
% 0.31/0.47 ( ( vE_r_l_v @ X1 )
% 0.31/0.47 != ( rjoin_r_l_v @ X8 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(13)
% 0.31/0.47 thf(fact_111_expr_Odistinct_I55_J,axiom,
% 0.31/0.47 ! [X7: expr_r_l_v,X8: expr_r_l_v] :
% 0.31/0.47 ( ( rfork_r_l_v @ X7 )
% 0.31/0.47 != ( rjoin_r_l_v @ X8 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(55)
% 0.31/0.47 thf(fact_112_substitution_Olocal__steps__commute,axiom,
% 0.31/0.47 ! [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,X2: produc1156025366_r_l_v,S_22: r > option1457017436_r_l_v,R2: r,Y: produc1156025366_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( S_2
% 0.31/0.47 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) )
% 0.31/0.47 => ( ( S_22
% 0.31/0.47 = ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
% 0.31/0.47 => ( ( revision_step_r_l_v @ Subst @ R2 @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
% 0.31/0.47 => ( ( 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 @ X2 ) ) )
% 0.31/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.31/0.47 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 0.31/0.47 | ( S_2 = S_3 ) )
% 0.31/0.47 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 0.31/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.local_steps_commute
% 0.31/0.47 thf(fact_113_ID__restricted__global__subset__unrestricted_I2_J,axiom,
% 0.31/0.47 ! [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 ) ) ).
% 0.31/0.47
% 0.31/0.47 % ID_restricted_global_subset_unrestricted(2)
% 0.31/0.47 thf(fact_114_substitution_OSLC__join_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: 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] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( ( S_1 @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( S_2
% 0.31/0.47 = ( ^ [X: r] : none_P277133687_r_l_v ) )
% 0.31/0.47 => ( ( ( S_1 @ R4 )
% 0.31/0.47 = none_P277133687_r_l_v )
% 0.31/0.47 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
% 0.31/0.47 => ( ( R != R2 )
% 0.31/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.31/0.47 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 0.31/0.47 | ( S_2 = S_3 ) )
% 0.31/0.47 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 0.31/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.SLC_join\<^sub>\<epsilon>
% 0.31/0.47 thf(fact_115_substitution_Orjoin_092_060_094sub_062_092_060epsilon_062__deterministic,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = none_P277133687_r_l_v )
% 0.31/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.31/0.47 = ( S2
% 0.31/0.47 = ( ^ [X: r] : none_P277133687_r_l_v ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.rjoin\<^sub>\<epsilon>_deterministic
% 0.31/0.47 thf(fact_116_inductive__invariant__is__execution__invariant,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,P: ( r > option1457017436_r_l_v ) > $o] :
% 0.31/0.47 ( ( reachable_r_l_v @ subst @ S )
% 0.31/0.47 => ( ( induct1670415253_r_l_v @ subst @ P )
% 0.31/0.47 => ( P @ S ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % inductive_invariant_is_execution_invariant
% 0.31/0.47 thf(fact_117_substitution_Orevision__step__relaxed_Ofork,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E2: expr_r_l_v,R2: r] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( ( S @ R )
% 0.31/0.47 = ( 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 ) ) ) ) ) )
% 0.31/0.47 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 0.31/0.47 => ( revisi1291188644_r_l_v @ Subst @ R @ S
% 0.31/0.47 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( 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 @ R2 ) ) ) ) ) ) ) @ R2
% 0.31/0.47 @ ( some_P1807977723_r_l_v
% 0.31/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau )
% 0.31/0.47 @ ( produc1834103605_r_l_v
% 0.31/0.47 @ ^ [X: l] : none_val_r_l_v
% 0.31/0.47 @ E2 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step_relaxed.fork
% 0.31/0.47 thf(fact_118_substitution_Orevision__step_Ofork,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E2: expr_r_l_v,R2: r] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( ( S @ R )
% 0.31/0.47 = ( 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 ) ) ) ) ) )
% 0.31/0.47 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 0.31/0.47 => ( revision_step_r_l_v @ Subst @ R @ S
% 0.31/0.47 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( 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 @ R2 ) ) ) ) ) ) ) @ R2
% 0.31/0.47 @ ( some_P1807977723_r_l_v
% 0.31/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau )
% 0.31/0.47 @ ( produc1834103605_r_l_v
% 0.31/0.47 @ ^ [X: l] : none_val_r_l_v
% 0.31/0.47 @ E2 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step.fork
% 0.31/0.47 thf(fact_119_substitution_Orevision__step__relaxed_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = none_P277133687_r_l_v )
% 0.31/0.47 => ( revisi1291188644_r_l_v @ Subst @ R @ S
% 0.31/0.47 @ ^ [X: r] : none_P277133687_r_l_v ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step_relaxed.join\<^sub>\<epsilon>
% 0.31/0.47 thf(fact_120_substitution_Orevision__step_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = none_P277133687_r_l_v )
% 0.31/0.47 => ( revision_step_r_l_v @ Subst @ R @ S
% 0.31/0.47 @ ^ [X: r] : none_P277133687_r_l_v ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step.join\<^sub>\<epsilon>
% 0.31/0.47 thf(fact_121_substitution_Oonly__fork__introduces__rids,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.31/0.47 => ( ! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E4: expr_r_l_v] :
% 0.31/0.47 ( ( S @ R )
% 0.31/0.47 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 0.31/0.47 => ( ord_less_eq_set_r @ ( rID_G_r_l_v @ S2 ) @ ( rID_G_r_l_v @ S ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.only_fork_introduces_rids
% 0.31/0.47 thf(fact_122_reachable__imp___092_060S_062_092_060_094sub_062G,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( reachable_r_l_v @ subst @ S )
% 0.31/0.47 => ( domain1547879849_r_l_v @ S ) ) ).
% 0.31/0.47
% 0.31/0.47 % reachable_imp_\<S>\<^sub>G
% 0.31/0.47 thf(fact_123_domains__subsume__globally__def,axiom,
% 0.31/0.47 ( domain1547879849_r_l_v
% 0.31/0.47 = ( ^ [S4: r > option1457017436_r_l_v] :
% 0.31/0.47 ! [R5: r,Ls2: produc1156025366_r_l_v] :
% 0.31/0.47 ( ( ( S4 @ R5 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ Ls2 ) )
% 0.31/0.47 => ( domain87684397_l_r_v @ Ls2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % domains_subsume_globally_def
% 0.31/0.47 thf(fact_124_substitution_Orevision__step_Ocong,axiom,
% 0.31/0.47 revision_step_r_l_v = revision_step_r_l_v ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step.cong
% 0.31/0.47 thf(fact_125_substitution_Orevision__step__relaxed_Ocong,axiom,
% 0.31/0.47 revisi1291188644_r_l_v = revisi1291188644_r_l_v ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step_relaxed.cong
% 0.31/0.47 thf(fact_126_substitution_Oonly__fork__introduces__rids_H,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.31/0.47 => ( ! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E4: expr_r_l_v] :
% 0.31/0.47 ( ( S @ R )
% 0.31/0.47 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 0.31/0.47 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 0.31/0.47 => ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.only_fork_introduces_rids'
% 0.31/0.47 thf(fact_127_nice__ind__inv__is__inductive__invariant,axiom,
% 0.31/0.47 ( induct1670415253_r_l_v @ subst
% 0.31/0.47 @ ^ [S4: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( domain1547879849_r_l_v @ S4 )
% 0.31/0.47 & ( subsum680764357_r_l_v @ S4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % nice_ind_inv_is_inductive_invariant
% 0.31/0.47 thf(fact_128_step__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I2_J,axiom,
% 0.31/0.47 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.31/0.47 => ( ( domain1547879849_r_l_v @ S )
% 0.31/0.47 => ( ( subsum680764357_r_l_v @ S )
% 0.31/0.47 => ( subsum680764357_r_l_v @ S2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % step_preserves_\<S>\<^sub>G_and_\<A>\<^sub>G(2)
% 0.31/0.47 thf(fact_129_step__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I1_J,axiom,
% 0.31/0.47 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.31/0.47 => ( ( domain1547879849_r_l_v @ S )
% 0.31/0.47 => ( ( subsum680764357_r_l_v @ S )
% 0.31/0.47 => ( domain1547879849_r_l_v @ S2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % step_preserves_\<S>\<^sub>G_and_\<A>\<^sub>G(1)
% 0.31/0.47 thf(fact_130_valid__stepE,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S @ S2 ) @ ( steps_r_l_v @ subst ) )
% 0.31/0.47 => ? [R6: r] : ( revision_step_r_l_v @ subst @ R6 @ S @ S2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % valid_stepE
% 0.31/0.47 thf(fact_131_substitution_Odomains__subsume__globallyI,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ! [R6: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E4: expr_r_l_v] :
% 0.31/0.47 ( ( ( S @ R6 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ E4 ) ) ) )
% 0.31/0.47 => ( domain87684397_l_r_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ E4 ) ) ) )
% 0.31/0.47 => ( domain1547879849_r_l_v @ S ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.domains_subsume_globallyI
% 0.31/0.47 thf(fact_132_substitution_Otransition__relations__equivalent,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( reachable_r_l_v @ Subst @ S )
% 0.31/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.31/0.47 = ( revisi1291188644_r_l_v @ Subst @ R @ S @ S2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.transition_relations_equivalent
% 0.31/0.47 thf(fact_133_valid__stepI,axiom,
% 0.31/0.47 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.31/0.47 => ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S @ S2 ) @ ( steps_r_l_v @ subst ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % valid_stepI
% 0.31/0.47 thf(fact_134_domains__subsume__globallyI,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ! [R6: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E4: expr_r_l_v] :
% 0.31/0.47 ( ( ( S @ R6 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ E4 ) ) ) )
% 0.31/0.47 => ( domain87684397_l_r_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ E4 ) ) ) )
% 0.31/0.47 => ( domain1547879849_r_l_v @ S ) ) ).
% 0.31/0.47
% 0.31/0.47 % domains_subsume_globallyI
% 0.31/0.47 thf(fact_135_maximal__execution__def,axiom,
% 0.31/0.47 ! [E2: expr_r_l_v,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( maxima311842975_r_l_v @ subst @ E2 @ S @ S2 )
% 0.31/0.47 = ( ( execution_r_l_v @ subst @ E2 @ S @ S2 )
% 0.31/0.47 & ~ ? [S5: r > option1457017436_r_l_v] : ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S2 @ S5 ) @ ( steps_r_l_v @ subst ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % maximal_execution_def
% 0.31/0.47 thf(fact_136_substitution_Osteps_Ocong,axiom,
% 0.31/0.47 steps_r_l_v = steps_r_l_v ).
% 0.31/0.47
% 0.31/0.47 % substitution.steps.cong
% 0.31/0.47 thf(fact_137_substitution_Ovalid__stepE,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S @ S2 ) @ ( steps_r_l_v @ Subst ) )
% 0.31/0.47 => ? [R6: r] : ( revision_step_r_l_v @ Subst @ R6 @ S @ S2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.valid_stepE
% 0.31/0.47 thf(fact_138_substitution_Ovalid__stepI,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.31/0.47 => ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S @ S2 ) @ ( steps_r_l_v @ Subst ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.valid_stepI
% 0.31/0.47 thf(fact_139_substitution_Oreachable_Ocong,axiom,
% 0.31/0.47 reachable_r_l_v = reachable_r_l_v ).
% 0.31/0.47
% 0.31/0.47 % substitution.reachable.cong
% 0.31/0.47 thf(fact_140_substitution_Oinductive__invariant_Ocong,axiom,
% 0.31/0.47 induct1670415253_r_l_v = induct1670415253_r_l_v ).
% 0.31/0.47
% 0.31/0.47 % substitution.inductive_invariant.cong
% 0.31/0.47 thf(fact_141_substitution_Oexecution_Ocong,axiom,
% 0.31/0.47 execution_r_l_v = execution_r_l_v ).
% 0.31/0.47
% 0.31/0.47 % substitution.execution.cong
% 0.31/0.47 thf(fact_142_substitution_Onice__ind__inv__is__inductive__invariant,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( induct1670415253_r_l_v @ Subst
% 0.31/0.47 @ ^ [S4: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( domain1547879849_r_l_v @ S4 )
% 0.31/0.47 & ( subsum680764357_r_l_v @ S4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.nice_ind_inv_is_inductive_invariant
% 0.31/0.47 thf(fact_143_substitution_Ostep__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I2_J,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.31/0.47 => ( ( domain1547879849_r_l_v @ S )
% 0.31/0.47 => ( ( subsum680764357_r_l_v @ S )
% 0.31/0.47 => ( subsum680764357_r_l_v @ S2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.step_preserves_\<S>\<^sub>G_and_\<A>\<^sub>G(2)
% 0.31/0.47 thf(fact_144_substitution_Ostep__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I1_J,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.31/0.47 => ( ( domain1547879849_r_l_v @ S )
% 0.31/0.47 => ( ( subsum680764357_r_l_v @ S )
% 0.31/0.47 => ( domain1547879849_r_l_v @ S2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.step_preserves_\<S>\<^sub>G_and_\<A>\<^sub>G(1)
% 0.31/0.47 thf(fact_145_substitution_Odomains__subsume__globally__def,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( domain1547879849_r_l_v @ S )
% 0.31/0.47 = ( ! [R5: r,Ls2: produc1156025366_r_l_v] :
% 0.31/0.47 ( ( ( S @ R5 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ Ls2 ) )
% 0.31/0.47 => ( domain87684397_l_r_v @ Ls2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.domains_subsume_globally_def
% 0.31/0.47 thf(fact_146_substitution_Oreachability__closed__under__execution__step,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( reachable_r_l_v @ Subst @ S )
% 0.31/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.31/0.47 => ( reachable_r_l_v @ Subst @ S2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.reachability_closed_under_execution_step
% 0.31/0.47 thf(fact_147_substitution_Oreachable__imp___092_060S_062_092_060_094sub_062G,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( reachable_r_l_v @ Subst @ S )
% 0.31/0.47 => ( domain1547879849_r_l_v @ S ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.reachable_imp_\<S>\<^sub>G
% 0.31/0.47 thf(fact_148_substitution_Oinductive__invariant__is__execution__invariant,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( reachable_r_l_v @ Subst @ S )
% 0.31/0.47 => ( ( induct1670415253_r_l_v @ Subst @ P )
% 0.31/0.47 => ( P @ S ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.inductive_invariant_is_execution_invariant
% 0.31/0.47 thf(fact_149_substitution_Oreachable__def,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( reachable_r_l_v @ Subst @ S )
% 0.31/0.47 = ( ? [E5: expr_r_l_v,S3: r > option1457017436_r_l_v] : ( execution_r_l_v @ Subst @ E5 @ S3 @ S ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.reachable_def
% 0.31/0.47 thf(fact_150_SLC__join,axiom,
% 0.31/0.47 ! [S_1: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: 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] :
% 0.31/0.47 ( ( ( S_1 @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( S_2
% 0.31/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
% 0.31/0.47 => ( ( ( S_1 @ R4 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.31/0.47 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 0.31/0.47 => ( ( R != R2 )
% 0.31/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.31/0.47 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 0.31/0.47 | ( S_2 = S_3 ) )
% 0.31/0.47 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 0.31/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % SLC_join
% 0.31/0.47 thf(fact_151_join__and__local__commute,axiom,
% 0.31/0.47 ! [S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: 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] :
% 0.31/0.47 ( ( S_2
% 0.31/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
% 0.31/0.47 => ( ( S_22
% 0.31/0.47 = ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Ls ) ) )
% 0.31/0.47 => ( ( R != R2 )
% 0.31/0.47 => ( ( R2 != R4 )
% 0.31/0.47 => ( ( 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 @ Sigma @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau @ 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 ) ) )
% 0.31/0.47 => ( ( ( S_22 @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S_22 @ R4 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.31/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.31/0.47 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 0.31/0.47 | ( S_2 = S_3 ) )
% 0.31/0.47 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 0.31/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % join_and_local_commute
% 0.31/0.47 thf(fact_152_substitution_Omaximal__execution__def,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,E2: expr_r_l_v,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( maxima311842975_r_l_v @ Subst @ E2 @ S @ S2 )
% 0.31/0.47 = ( ( execution_r_l_v @ Subst @ E2 @ S @ S2 )
% 0.31/0.47 & ~ ? [S5: r > option1457017436_r_l_v] : ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S2 @ S5 ) @ ( steps_r_l_v @ Subst ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.maximal_execution_def
% 0.31/0.47 thf(fact_153_substitution_Osubsumes__accessible__globallyI,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ! [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] :
% 0.31/0.47 ( ( ( S @ R_1 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_1 @ ( produc1834103605_r_l_v @ Tau_1 @ E_1 ) ) ) )
% 0.31/0.47 => ( ( ( S @ R_2 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_2 @ ( produc1834103605_r_l_v @ Tau_2 @ E_2 ) ) ) )
% 0.31/0.47 => ( subsum148050133_r_l_v @ R_1 @ R_2 @ S ) ) )
% 0.31/0.47 => ( subsum680764357_r_l_v @ S ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.subsumes_accessible_globallyI
% 0.31/0.47 thf(fact_154_revision__step__relaxed_Ojoin,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: 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] :
% 0.31/0.47 ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.31/0.47 => ( 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 @ Sigma @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step_relaxed.join
% 0.31/0.47 thf(fact_155_val_Oinject_I1_J,axiom,
% 0.31/0.47 ! [X1: const,Y1: const] :
% 0.31/0.47 ( ( ( cV_r_l_v @ X1 )
% 0.31/0.47 = ( cV_r_l_v @ Y1 ) )
% 0.31/0.47 = ( X1 = Y1 ) ) ).
% 0.31/0.47
% 0.31/0.47 % val.inject(1)
% 0.31/0.47 thf(fact_156_terminates__in__def,axiom,
% 0.31/0.47 ! [E2: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( terminates_in_r_l_v @ subst @ E2 @ S2 )
% 0.31/0.47 = ( ? [S4: r > option1457017436_r_l_v] : ( maxima311842975_r_l_v @ subst @ E2 @ S4 @ S2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % terminates_in_def
% 0.31/0.47 thf(fact_157_revision__step_Ojoin,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: 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] :
% 0.31/0.47 ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.31/0.47 => ( 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 @ Sigma @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step.join
% 0.31/0.47 thf(fact_158_subsumes__accessible__globallyI,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ! [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] :
% 0.31/0.47 ( ( ( S @ R_1 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_1 @ ( produc1834103605_r_l_v @ Tau_1 @ E_1 ) ) ) )
% 0.31/0.47 => ( ( ( S @ R_2 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_2 @ ( produc1834103605_r_l_v @ Tau_2 @ E_2 ) ) ) )
% 0.31/0.47 => ( subsum148050133_r_l_v @ R_1 @ R_2 @ S ) ) )
% 0.31/0.47 => ( subsum680764357_r_l_v @ S ) ) ).
% 0.31/0.47
% 0.31/0.47 % subsumes_accessible_globallyI
% 0.31/0.47 thf(fact_159_rjoin__deterministic,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: 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] :
% 0.31/0.47 ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.31/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.31/0.47 = ( S2
% 0.31/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rjoin_deterministic
% 0.31/0.47 thf(fact_160_substitution_Omaximal__execution_Ocong,axiom,
% 0.31/0.47 maxima311842975_r_l_v = maxima311842975_r_l_v ).
% 0.31/0.47
% 0.31/0.47 % substitution.maximal_execution.cong
% 0.31/0.47 thf(fact_161_val_Odistinct_I5_J,axiom,
% 0.31/0.47 ! [X1: const,X4: r] :
% 0.31/0.47 ( ( cV_r_l_v @ X1 )
% 0.31/0.47 != ( rid_r_l_v @ X4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % val.distinct(5)
% 0.31/0.47 thf(fact_162_substitution_Orevision__step_Ojoin,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: 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] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.31/0.47 => ( 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 @ Sigma @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step.join
% 0.31/0.47 thf(fact_163_substitution_Orjoin__deterministic,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: 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] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.31/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.31/0.47 = ( S2
% 0.31/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.rjoin_deterministic
% 0.31/0.47 thf(fact_164_substitution_Orevision__step__relaxed_Ojoin,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: 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] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.31/0.47 => ( 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 @ Sigma @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step_relaxed.join
% 0.31/0.47 thf(fact_165_substitution_Ojoin__and__local__commute,axiom,
% 0.31/0.47 ! [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,Sigma: l > option_val_r_l_v,Tau: 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] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( S_2
% 0.31/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
% 0.31/0.47 => ( ( S_22
% 0.31/0.47 = ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Ls ) ) )
% 0.31/0.47 => ( ( R != R2 )
% 0.31/0.47 => ( ( R2 != R4 )
% 0.31/0.47 => ( ( 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 @ Sigma @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau @ 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 ) ) )
% 0.31/0.47 => ( ( ( S_22 @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( ( S_22 @ R4 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.31/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.31/0.47 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 0.31/0.47 | ( S_2 = S_3 ) )
% 0.31/0.47 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 0.31/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.join_and_local_commute
% 0.31/0.47 thf(fact_166_substitution_OSLC__join,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: 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] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( ( S_1 @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( S_2
% 0.31/0.47 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
% 0.31/0.47 => ( ( ( S_1 @ R4 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 0.31/0.47 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
% 0.31/0.47 => ( ( R != R2 )
% 0.31/0.47 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 0.31/0.47 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 0.31/0.47 | ( S_2 = S_3 ) )
% 0.31/0.47 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 0.31/0.47 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.SLC_join
% 0.31/0.47 thf(fact_167_reachable__imp__identifiers__finite_I1_J,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( reachable_r_l_v @ subst @ S )
% 0.31/0.47 => ( finite_finite_r @ ( rID_G_r_l_v @ S ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % reachable_imp_identifiers_finite(1)
% 0.31/0.47 thf(fact_168_RID_092_060_094sub_062G__finite__invariant,axiom,
% 0.31/0.47 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.31/0.47 => ( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
% 0.31/0.47 => ( finite_finite_r @ ( rID_G_r_l_v @ S2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % RID\<^sub>G_finite_invariant
% 0.31/0.47 thf(fact_169_reachability__closed__under__execution,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( reachable_r_l_v @ subst @ S )
% 0.31/0.47 => ( ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S @ S2 ) @ ( transi1323086383_r_l_v @ ( steps_r_l_v @ subst ) ) )
% 0.31/0.47 => ( reachable_r_l_v @ subst @ S2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % reachability_closed_under_execution
% 0.31/0.47 thf(fact_170_revision__step__relaxed_OifTrue,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 0.31/0.47 ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.31/0.47 => ( revisi1291188644_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ E1 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step_relaxed.ifTrue
% 0.31/0.47 thf(fact_171_empty__map__finite_I3_J,axiom,
% 0.31/0.47 ( finite_finite_r
% 0.31/0.47 @ ( rID_G_r_l_v
% 0.31/0.47 @ ^ [X: r] : none_P277133687_r_l_v ) ) ).
% 0.31/0.47
% 0.31/0.47 % empty_map_finite(3)
% 0.31/0.47 thf(fact_172_expr_Oinject_I3_J,axiom,
% 0.31/0.47 ! [X31: expr_r_l_v,X32: expr_r_l_v,X33: expr_r_l_v,Y31: expr_r_l_v,Y32: expr_r_l_v,Y33: expr_r_l_v] :
% 0.31/0.47 ( ( ( ite_r_l_v @ X31 @ X32 @ X33 )
% 0.31/0.47 = ( ite_r_l_v @ Y31 @ Y32 @ Y33 ) )
% 0.31/0.47 = ( ( X31 = Y31 )
% 0.31/0.47 & ( X32 = Y32 )
% 0.31/0.47 & ( X33 = Y33 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.inject(3)
% 0.31/0.47 thf(fact_173_revision__step_OifTrue,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 0.31/0.47 ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.31/0.47 => ( revision_step_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ E1 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step.ifTrue
% 0.31/0.47 thf(fact_174_finite__state__imp__restriction__finite_I1_J,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R: r] :
% 0.31/0.47 ( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
% 0.31/0.47 => ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_state_imp_restriction_finite(1)
% 0.31/0.47 thf(fact_175_ifTrue__deterministic,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.31/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.31/0.47 = ( S2
% 0.31/0.47 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ E1 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ifTrue_deterministic
% 0.31/0.47 thf(fact_176_expr_Odistinct_I3_J,axiom,
% 0.31/0.47 ! [X1: val_r_l_v,X31: expr_r_l_v,X32: expr_r_l_v,X33: expr_r_l_v] :
% 0.31/0.47 ( ( vE_r_l_v @ X1 )
% 0.31/0.47 != ( ite_r_l_v @ X31 @ X32 @ X33 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(3)
% 0.31/0.47 thf(fact_177_expr_Odistinct_I35_J,axiom,
% 0.31/0.47 ! [X31: expr_r_l_v,X32: expr_r_l_v,X33: expr_r_l_v,X8: expr_r_l_v] :
% 0.31/0.47 ( ( ite_r_l_v @ X31 @ X32 @ X33 )
% 0.31/0.47 != ( rjoin_r_l_v @ X8 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(35)
% 0.31/0.47 thf(fact_178_expr_Odistinct_I33_J,axiom,
% 0.31/0.47 ! [X31: expr_r_l_v,X32: expr_r_l_v,X33: expr_r_l_v,X7: expr_r_l_v] :
% 0.31/0.47 ( ( ite_r_l_v @ X31 @ X32 @ X33 )
% 0.31/0.47 != ( rfork_r_l_v @ X7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(33)
% 0.31/0.47 thf(fact_179_substitution_Oterminates__in_Ocong,axiom,
% 0.31/0.47 terminates_in_r_l_v = terminates_in_r_l_v ).
% 0.31/0.47
% 0.31/0.47 % substitution.terminates_in.cong
% 0.31/0.47 thf(fact_180_const_Odistinct_I3_J,axiom,
% 0.31/0.47 unit != t ).
% 0.31/0.47
% 0.31/0.47 % const.distinct(3)
% 0.31/0.47 thf(fact_181_substitution_ORID_092_060_094sub_062G__finite__invariant,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.31/0.47 => ( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
% 0.31/0.47 => ( finite_finite_r @ ( rID_G_r_l_v @ S2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.RID\<^sub>G_finite_invariant
% 0.31/0.47 thf(fact_182_substitution_Oreachable__imp__identifiers__finite_I1_J,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( reachable_r_l_v @ Subst @ S )
% 0.31/0.47 => ( finite_finite_r @ ( rID_G_r_l_v @ S ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.reachable_imp_identifiers_finite(1)
% 0.31/0.47 thf(fact_183_substitution_Oempty__map__finite_I3_J,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( finite_finite_r
% 0.31/0.47 @ ( rID_G_r_l_v
% 0.31/0.47 @ ^ [X: r] : none_P277133687_r_l_v ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.empty_map_finite(3)
% 0.31/0.47 thf(fact_184_substitution_Oreachability__closed__under__execution,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( reachable_r_l_v @ Subst @ S )
% 0.31/0.47 => ( ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S @ S2 ) @ ( transi1323086383_r_l_v @ ( steps_r_l_v @ Subst ) ) )
% 0.31/0.47 => ( reachable_r_l_v @ Subst @ S2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.reachability_closed_under_execution
% 0.31/0.47 thf(fact_185_substitution_Ofinite__state__imp__restriction__finite_I1_J,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
% 0.31/0.47 => ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.finite_state_imp_restriction_finite(1)
% 0.31/0.47 thf(fact_186_substitution_OifTrue__deterministic,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.31/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.31/0.47 = ( S2
% 0.31/0.47 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ E1 ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.ifTrue_deterministic
% 0.31/0.47 thf(fact_187_substitution_Orevision__step_OifTrue,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.31/0.47 => ( revision_step_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ E1 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step.ifTrue
% 0.31/0.47 thf(fact_188_substitution_Orevision__step__relaxed_OifTrue,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.31/0.47 => ( revisi1291188644_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ E1 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step_relaxed.ifTrue
% 0.31/0.47 thf(fact_189_substitution_Oterminates__in__def,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,E2: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( terminates_in_r_l_v @ Subst @ E2 @ S2 )
% 0.31/0.47 = ( ? [S4: r > option1457017436_r_l_v] : ( maxima311842975_r_l_v @ Subst @ E2 @ S4 @ S2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.terminates_in_def
% 0.31/0.47 thf(fact_190_revision__step__relaxed_OifFalse,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 0.31/0.47 ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.31/0.47 => ( revisi1291188644_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ E22 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step_relaxed.ifFalse
% 0.31/0.47 thf(fact_191_revision__step_OifFalse,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 0.31/0.47 ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.31/0.47 => ( revision_step_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ E22 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step.ifFalse
% 0.31/0.47 thf(fact_192_ifFalse__deterministic,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.31/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.31/0.47 = ( S2
% 0.31/0.47 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ E22 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ifFalse_deterministic
% 0.31/0.47 thf(fact_193_finite__Collect__subsets,axiom,
% 0.31/0.47 ! [A4: set_set_l] :
% 0.31/0.47 ( ( finite_finite_set_l @ A4 )
% 0.31/0.47 => ( finite1256628466_set_l
% 0.31/0.47 @ ( collect_set_set_l
% 0.31/0.47 @ ^ [B4: set_set_l] : ( ord_le2116509289_set_l @ B4 @ A4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_Collect_subsets
% 0.31/0.47 thf(fact_194_finite__Collect__subsets,axiom,
% 0.31/0.47 ! [A4: set_set_r] :
% 0.31/0.47 ( ( finite_finite_set_r @ A4 )
% 0.31/0.47 => ( finite1651563256_set_r
% 0.31/0.47 @ ( collect_set_set_r
% 0.31/0.47 @ ^ [B4: set_set_r] : ( ord_le363960431_set_r @ B4 @ A4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_Collect_subsets
% 0.31/0.47 thf(fact_195_finite__Collect__subsets,axiom,
% 0.31/0.47 ! [A4: set_Pr1409704485_r_l_v] :
% 0.31/0.47 ( ( finite1853159534_r_l_v @ A4 )
% 0.31/0.47 => ( finite1619243214_r_l_v
% 0.31/0.47 @ ( collec330370832_r_l_v
% 0.31/0.47 @ ^ [B4: set_Pr1409704485_r_l_v] : ( ord_le803113413_r_l_v @ B4 @ A4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_Collect_subsets
% 0.31/0.47 thf(fact_196_finite__Collect__subsets,axiom,
% 0.31/0.47 ! [A4: set_option_l] :
% 0.31/0.47 ( ( finite2114249848tion_l @ A4 )
% 0.31/0.47 => ( finite1182752216tion_l
% 0.31/0.47 @ ( collect_set_option_l
% 0.31/0.47 @ ^ [B4: set_option_l] : ( ord_le1506375887tion_l @ B4 @ A4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_Collect_subsets
% 0.31/0.47 thf(fact_197_finite__Collect__subsets,axiom,
% 0.31/0.47 ! [A4: set_option_r] :
% 0.31/0.47 ( ( finite16335230tion_r @ A4 )
% 0.31/0.47 => ( finite1577687006tion_r
% 0.31/0.47 @ ( collect_set_option_r
% 0.31/0.47 @ ^ [B4: set_option_r] : ( ord_le1901310677tion_r @ B4 @ A4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_Collect_subsets
% 0.31/0.47 thf(fact_198_finite__Collect__subsets,axiom,
% 0.31/0.47 ! [A4: set_r] :
% 0.31/0.47 ( ( finite_finite_r @ A4 )
% 0.31/0.47 => ( finite_finite_set_r
% 0.31/0.47 @ ( collect_set_r
% 0.31/0.47 @ ^ [B4: set_r] : ( ord_less_eq_set_r @ B4 @ A4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_Collect_subsets
% 0.31/0.47 thf(fact_199_finite__Collect__subsets,axiom,
% 0.31/0.47 ! [A4: set_l] :
% 0.31/0.47 ( ( finite_finite_l @ A4 )
% 0.31/0.47 => ( finite_finite_set_l
% 0.31/0.47 @ ( collect_set_l
% 0.31/0.47 @ ^ [B4: set_l] : ( ord_less_eq_set_l @ B4 @ A4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_Collect_subsets
% 0.31/0.47 thf(fact_200_finite__Collect__disjI,axiom,
% 0.31/0.47 ! [P: set_l > $o,Q: set_l > $o] :
% 0.31/0.47 ( ( finite_finite_set_l
% 0.31/0.47 @ ( collect_set_l
% 0.31/0.47 @ ^ [X: set_l] :
% 0.31/0.47 ( ( P @ X )
% 0.31/0.47 | ( Q @ X ) ) ) )
% 0.31/0.47 = ( ( finite_finite_set_l @ ( collect_set_l @ P ) )
% 0.31/0.47 & ( finite_finite_set_l @ ( collect_set_l @ Q ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_Collect_disjI
% 0.31/0.47 thf(fact_201_finite__Collect__disjI,axiom,
% 0.31/0.47 ! [P: set_r > $o,Q: set_r > $o] :
% 0.31/0.47 ( ( finite_finite_set_r
% 0.31/0.47 @ ( collect_set_r
% 0.31/0.47 @ ^ [X: set_r] :
% 0.31/0.47 ( ( P @ X )
% 0.31/0.47 | ( Q @ X ) ) ) )
% 0.31/0.47 = ( ( finite_finite_set_r @ ( collect_set_r @ P ) )
% 0.31/0.47 & ( finite_finite_set_r @ ( collect_set_r @ Q ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_Collect_disjI
% 0.31/0.47 thf(fact_202_finite__Collect__disjI,axiom,
% 0.31/0.47 ! [P: produc1389397445_r_l_v > $o,Q: produc1389397445_r_l_v > $o] :
% 0.31/0.47 ( ( finite1853159534_r_l_v
% 0.31/0.47 @ ( collec1978425008_r_l_v
% 0.31/0.47 @ ^ [X: produc1389397445_r_l_v] :
% 0.31/0.47 ( ( P @ X )
% 0.31/0.47 | ( Q @ X ) ) ) )
% 0.31/0.47 = ( ( finite1853159534_r_l_v @ ( collec1978425008_r_l_v @ P ) )
% 0.31/0.47 & ( finite1853159534_r_l_v @ ( collec1978425008_r_l_v @ Q ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_Collect_disjI
% 0.31/0.47 thf(fact_203_finite__Collect__disjI,axiom,
% 0.31/0.47 ! [P: option_l > $o,Q: option_l > $o] :
% 0.31/0.47 ( ( finite2114249848tion_l
% 0.31/0.47 @ ( collect_option_l
% 0.31/0.47 @ ^ [X: option_l] :
% 0.31/0.47 ( ( P @ X )
% 0.31/0.47 | ( Q @ X ) ) ) )
% 0.31/0.47 = ( ( finite2114249848tion_l @ ( collect_option_l @ P ) )
% 0.31/0.47 & ( finite2114249848tion_l @ ( collect_option_l @ Q ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_Collect_disjI
% 0.31/0.47 thf(fact_204_finite__Collect__disjI,axiom,
% 0.31/0.47 ! [P: option_r > $o,Q: option_r > $o] :
% 0.31/0.47 ( ( finite16335230tion_r
% 0.31/0.47 @ ( collect_option_r
% 0.31/0.47 @ ^ [X: option_r] :
% 0.31/0.47 ( ( P @ X )
% 0.31/0.47 | ( Q @ X ) ) ) )
% 0.31/0.47 = ( ( finite16335230tion_r @ ( collect_option_r @ P ) )
% 0.31/0.47 & ( finite16335230tion_r @ ( collect_option_r @ Q ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_Collect_disjI
% 0.31/0.47 thf(fact_205_finite__Collect__disjI,axiom,
% 0.31/0.47 ! [P: r > $o,Q: r > $o] :
% 0.31/0.47 ( ( finite_finite_r
% 0.31/0.47 @ ( collect_r
% 0.31/0.47 @ ^ [X: r] :
% 0.31/0.47 ( ( P @ X )
% 0.31/0.47 | ( Q @ X ) ) ) )
% 0.31/0.47 = ( ( finite_finite_r @ ( collect_r @ P ) )
% 0.31/0.47 & ( finite_finite_r @ ( collect_r @ Q ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_Collect_disjI
% 0.31/0.47 thf(fact_206_finite__Collect__disjI,axiom,
% 0.31/0.47 ! [P: l > $o,Q: l > $o] :
% 0.31/0.47 ( ( finite_finite_l
% 0.31/0.47 @ ( collect_l
% 0.31/0.47 @ ^ [X: l] :
% 0.31/0.47 ( ( P @ X )
% 0.31/0.47 | ( Q @ X ) ) ) )
% 0.31/0.47 = ( ( finite_finite_l @ ( collect_l @ P ) )
% 0.31/0.47 & ( finite_finite_l @ ( collect_l @ Q ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_Collect_disjI
% 0.31/0.47 thf(fact_207_finite__Collect__conjI,axiom,
% 0.31/0.47 ! [P: set_l > $o,Q: set_l > $o] :
% 0.31/0.47 ( ( ( finite_finite_set_l @ ( collect_set_l @ P ) )
% 0.31/0.47 | ( finite_finite_set_l @ ( collect_set_l @ Q ) ) )
% 0.31/0.47 => ( finite_finite_set_l
% 0.31/0.47 @ ( collect_set_l
% 0.31/0.47 @ ^ [X: set_l] :
% 0.31/0.47 ( ( P @ X )
% 0.31/0.47 & ( Q @ X ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_Collect_conjI
% 0.31/0.47 thf(fact_208_finite__Collect__conjI,axiom,
% 0.31/0.47 ! [P: set_r > $o,Q: set_r > $o] :
% 0.31/0.47 ( ( ( finite_finite_set_r @ ( collect_set_r @ P ) )
% 0.31/0.47 | ( finite_finite_set_r @ ( collect_set_r @ Q ) ) )
% 0.31/0.47 => ( finite_finite_set_r
% 0.31/0.47 @ ( collect_set_r
% 0.31/0.47 @ ^ [X: set_r] :
% 0.31/0.47 ( ( P @ X )
% 0.31/0.47 & ( Q @ X ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_Collect_conjI
% 0.31/0.47 thf(fact_209_finite__Collect__conjI,axiom,
% 0.31/0.47 ! [P: produc1389397445_r_l_v > $o,Q: produc1389397445_r_l_v > $o] :
% 0.31/0.47 ( ( ( finite1853159534_r_l_v @ ( collec1978425008_r_l_v @ P ) )
% 0.31/0.47 | ( finite1853159534_r_l_v @ ( collec1978425008_r_l_v @ Q ) ) )
% 0.31/0.47 => ( finite1853159534_r_l_v
% 0.31/0.47 @ ( collec1978425008_r_l_v
% 0.31/0.47 @ ^ [X: produc1389397445_r_l_v] :
% 0.31/0.47 ( ( P @ X )
% 0.31/0.47 & ( Q @ X ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_Collect_conjI
% 0.31/0.47 thf(fact_210_finite__Collect__conjI,axiom,
% 0.31/0.47 ! [P: option_l > $o,Q: option_l > $o] :
% 0.31/0.47 ( ( ( finite2114249848tion_l @ ( collect_option_l @ P ) )
% 0.31/0.47 | ( finite2114249848tion_l @ ( collect_option_l @ Q ) ) )
% 0.31/0.47 => ( finite2114249848tion_l
% 0.31/0.47 @ ( collect_option_l
% 0.31/0.47 @ ^ [X: option_l] :
% 0.31/0.47 ( ( P @ X )
% 0.31/0.47 & ( Q @ X ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_Collect_conjI
% 0.31/0.47 thf(fact_211_finite__Collect__conjI,axiom,
% 0.31/0.47 ! [P: option_r > $o,Q: option_r > $o] :
% 0.31/0.47 ( ( ( finite16335230tion_r @ ( collect_option_r @ P ) )
% 0.31/0.47 | ( finite16335230tion_r @ ( collect_option_r @ Q ) ) )
% 0.31/0.47 => ( finite16335230tion_r
% 0.31/0.47 @ ( collect_option_r
% 0.31/0.47 @ ^ [X: option_r] :
% 0.31/0.47 ( ( P @ X )
% 0.31/0.47 & ( Q @ X ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_Collect_conjI
% 0.31/0.47 thf(fact_212_finite__Collect__conjI,axiom,
% 0.31/0.47 ! [P: r > $o,Q: r > $o] :
% 0.31/0.47 ( ( ( finite_finite_r @ ( collect_r @ P ) )
% 0.31/0.47 | ( finite_finite_r @ ( collect_r @ Q ) ) )
% 0.31/0.47 => ( finite_finite_r
% 0.31/0.47 @ ( collect_r
% 0.31/0.47 @ ^ [X: r] :
% 0.31/0.47 ( ( P @ X )
% 0.31/0.47 & ( Q @ X ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_Collect_conjI
% 0.31/0.47 thf(fact_213_finite__Collect__conjI,axiom,
% 0.31/0.47 ! [P: l > $o,Q: l > $o] :
% 0.31/0.47 ( ( ( finite_finite_l @ ( collect_l @ P ) )
% 0.31/0.47 | ( finite_finite_l @ ( collect_l @ Q ) ) )
% 0.31/0.47 => ( finite_finite_l
% 0.31/0.47 @ ( collect_l
% 0.31/0.47 @ ^ [X: l] :
% 0.31/0.47 ( ( P @ X )
% 0.31/0.47 & ( Q @ X ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_Collect_conjI
% 0.31/0.47 thf(fact_214_const_Odistinct_I1_J,axiom,
% 0.31/0.47 unit != f ).
% 0.31/0.47
% 0.31/0.47 % const.distinct(1)
% 0.31/0.47 thf(fact_215_const_Odistinct_I5_J,axiom,
% 0.31/0.47 f != t ).
% 0.31/0.47
% 0.31/0.47 % const.distinct(5)
% 0.31/0.47 thf(fact_216_const_Oinduct,axiom,
% 0.31/0.47 ! [P: const > $o,Const: const] :
% 0.31/0.47 ( ( P @ unit )
% 0.31/0.47 => ( ( P @ f )
% 0.31/0.47 => ( ( P @ t )
% 0.31/0.47 => ( P @ Const ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % const.induct
% 0.31/0.47 thf(fact_217_const_Oexhaust,axiom,
% 0.31/0.47 ! [Y: const] :
% 0.31/0.47 ( ( Y != unit )
% 0.31/0.47 => ( ( Y != f )
% 0.31/0.47 => ( Y = t ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % const.exhaust
% 0.31/0.47 thf(fact_218_pigeonhole__infinite__rel,axiom,
% 0.31/0.47 ! [A4: set_option_r,B5: set_option_l,R7: option_r > option_l > $o] :
% 0.31/0.47 ( ~ ( finite16335230tion_r @ A4 )
% 0.31/0.47 => ( ( finite2114249848tion_l @ B5 )
% 0.31/0.47 => ( ! [X6: option_r] :
% 0.31/0.47 ( ( member_option_r @ X6 @ A4 )
% 0.31/0.47 => ? [Xa2: option_l] :
% 0.31/0.47 ( ( member_option_l @ Xa2 @ B5 )
% 0.31/0.47 & ( R7 @ X6 @ Xa2 ) ) )
% 0.31/0.47 => ? [X6: option_l] :
% 0.31/0.47 ( ( member_option_l @ X6 @ B5 )
% 0.31/0.47 & ~ ( finite16335230tion_r
% 0.31/0.47 @ ( collect_option_r
% 0.31/0.47 @ ^ [A2: option_r] :
% 0.31/0.47 ( ( member_option_r @ A2 @ A4 )
% 0.31/0.47 & ( R7 @ A2 @ X6 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % pigeonhole_infinite_rel
% 0.31/0.47 thf(fact_219_pigeonhole__infinite__rel,axiom,
% 0.31/0.47 ! [A4: set_option_r,B5: set_option_r,R7: option_r > option_r > $o] :
% 0.31/0.47 ( ~ ( finite16335230tion_r @ A4 )
% 0.31/0.47 => ( ( finite16335230tion_r @ B5 )
% 0.31/0.47 => ( ! [X6: option_r] :
% 0.31/0.47 ( ( member_option_r @ X6 @ A4 )
% 0.31/0.47 => ? [Xa2: option_r] :
% 0.31/0.47 ( ( member_option_r @ Xa2 @ B5 )
% 0.31/0.47 & ( R7 @ X6 @ Xa2 ) ) )
% 0.31/0.47 => ? [X6: option_r] :
% 0.31/0.47 ( ( member_option_r @ X6 @ B5 )
% 0.31/0.47 & ~ ( finite16335230tion_r
% 0.31/0.47 @ ( collect_option_r
% 0.31/0.47 @ ^ [A2: option_r] :
% 0.31/0.47 ( ( member_option_r @ A2 @ A4 )
% 0.31/0.47 & ( R7 @ A2 @ X6 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % pigeonhole_infinite_rel
% 0.31/0.47 thf(fact_220_pigeonhole__infinite__rel,axiom,
% 0.31/0.47 ! [A4: set_Pr1409704485_r_l_v,B5: set_r,R7: produc1389397445_r_l_v > r > $o] :
% 0.31/0.47 ( ~ ( finite1853159534_r_l_v @ A4 )
% 0.31/0.47 => ( ( finite_finite_r @ B5 )
% 0.31/0.47 => ( ! [X6: produc1389397445_r_l_v] :
% 0.31/0.47 ( ( member1522896238_r_l_v @ X6 @ A4 )
% 0.31/0.47 => ? [Xa2: r] :
% 0.31/0.47 ( ( member_r @ Xa2 @ B5 )
% 0.31/0.47 & ( R7 @ X6 @ Xa2 ) ) )
% 0.31/0.47 => ? [X6: r] :
% 0.31/0.47 ( ( member_r @ X6 @ B5 )
% 0.31/0.47 & ~ ( finite1853159534_r_l_v
% 0.31/0.47 @ ( collec1978425008_r_l_v
% 0.31/0.47 @ ^ [A2: produc1389397445_r_l_v] :
% 0.31/0.47 ( ( member1522896238_r_l_v @ A2 @ A4 )
% 0.31/0.47 & ( R7 @ A2 @ X6 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % pigeonhole_infinite_rel
% 0.31/0.47 thf(fact_221_pigeonhole__infinite__rel,axiom,
% 0.31/0.47 ! [A4: set_Pr1409704485_r_l_v,B5: set_l,R7: produc1389397445_r_l_v > l > $o] :
% 0.31/0.47 ( ~ ( finite1853159534_r_l_v @ A4 )
% 0.31/0.47 => ( ( finite_finite_l @ B5 )
% 0.31/0.47 => ( ! [X6: produc1389397445_r_l_v] :
% 0.31/0.47 ( ( member1522896238_r_l_v @ X6 @ A4 )
% 0.31/0.47 => ? [Xa2: l] :
% 0.31/0.47 ( ( member_l @ Xa2 @ B5 )
% 0.31/0.47 & ( R7 @ X6 @ Xa2 ) ) )
% 0.31/0.47 => ? [X6: l] :
% 0.31/0.47 ( ( member_l @ X6 @ B5 )
% 0.31/0.47 & ~ ( finite1853159534_r_l_v
% 0.31/0.47 @ ( collec1978425008_r_l_v
% 0.31/0.47 @ ^ [A2: produc1389397445_r_l_v] :
% 0.31/0.47 ( ( member1522896238_r_l_v @ A2 @ A4 )
% 0.31/0.47 & ( R7 @ A2 @ X6 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % pigeonhole_infinite_rel
% 0.31/0.47 thf(fact_222_pigeonhole__infinite__rel,axiom,
% 0.31/0.47 ! [A4: set_r,B5: set_r,R7: r > r > $o] :
% 0.31/0.47 ( ~ ( finite_finite_r @ A4 )
% 0.31/0.47 => ( ( finite_finite_r @ B5 )
% 0.31/0.47 => ( ! [X6: r] :
% 0.31/0.47 ( ( member_r @ X6 @ A4 )
% 0.31/0.47 => ? [Xa2: r] :
% 0.31/0.47 ( ( member_r @ Xa2 @ B5 )
% 0.31/0.47 & ( R7 @ X6 @ Xa2 ) ) )
% 0.31/0.47 => ? [X6: r] :
% 0.31/0.47 ( ( member_r @ X6 @ B5 )
% 0.31/0.47 & ~ ( finite_finite_r
% 0.31/0.47 @ ( collect_r
% 0.31/0.47 @ ^ [A2: r] :
% 0.31/0.47 ( ( member_r @ A2 @ A4 )
% 0.31/0.47 & ( R7 @ A2 @ X6 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % pigeonhole_infinite_rel
% 0.31/0.47 thf(fact_223_pigeonhole__infinite__rel,axiom,
% 0.31/0.47 ! [A4: set_r,B5: set_l,R7: r > l > $o] :
% 0.31/0.47 ( ~ ( finite_finite_r @ A4 )
% 0.31/0.47 => ( ( finite_finite_l @ B5 )
% 0.31/0.47 => ( ! [X6: r] :
% 0.31/0.47 ( ( member_r @ X6 @ A4 )
% 0.31/0.47 => ? [Xa2: l] :
% 0.31/0.47 ( ( member_l @ Xa2 @ B5 )
% 0.31/0.47 & ( R7 @ X6 @ Xa2 ) ) )
% 0.31/0.47 => ? [X6: l] :
% 0.31/0.47 ( ( member_l @ X6 @ B5 )
% 0.31/0.47 & ~ ( finite_finite_r
% 0.31/0.47 @ ( collect_r
% 0.31/0.47 @ ^ [A2: r] :
% 0.31/0.47 ( ( member_r @ A2 @ A4 )
% 0.31/0.47 & ( R7 @ A2 @ X6 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % pigeonhole_infinite_rel
% 0.31/0.47 thf(fact_224_pigeonhole__infinite__rel,axiom,
% 0.31/0.47 ! [A4: set_l,B5: set_r,R7: l > r > $o] :
% 0.31/0.47 ( ~ ( finite_finite_l @ A4 )
% 0.31/0.47 => ( ( finite_finite_r @ B5 )
% 0.31/0.47 => ( ! [X6: l] :
% 0.31/0.47 ( ( member_l @ X6 @ A4 )
% 0.31/0.47 => ? [Xa2: r] :
% 0.31/0.47 ( ( member_r @ Xa2 @ B5 )
% 0.31/0.47 & ( R7 @ X6 @ Xa2 ) ) )
% 0.31/0.47 => ? [X6: r] :
% 0.31/0.47 ( ( member_r @ X6 @ B5 )
% 0.31/0.47 & ~ ( finite_finite_l
% 0.31/0.47 @ ( collect_l
% 0.31/0.47 @ ^ [A2: l] :
% 0.31/0.47 ( ( member_l @ A2 @ A4 )
% 0.31/0.47 & ( R7 @ A2 @ X6 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % pigeonhole_infinite_rel
% 0.31/0.47 thf(fact_225_pigeonhole__infinite__rel,axiom,
% 0.31/0.47 ! [A4: set_l,B5: set_l,R7: l > l > $o] :
% 0.31/0.47 ( ~ ( finite_finite_l @ A4 )
% 0.31/0.47 => ( ( finite_finite_l @ B5 )
% 0.31/0.47 => ( ! [X6: l] :
% 0.31/0.47 ( ( member_l @ X6 @ A4 )
% 0.31/0.47 => ? [Xa2: l] :
% 0.31/0.47 ( ( member_l @ Xa2 @ B5 )
% 0.31/0.47 & ( R7 @ X6 @ Xa2 ) ) )
% 0.31/0.47 => ? [X6: l] :
% 0.31/0.47 ( ( member_l @ X6 @ B5 )
% 0.31/0.47 & ~ ( finite_finite_l
% 0.31/0.47 @ ( collect_l
% 0.31/0.47 @ ^ [A2: l] :
% 0.31/0.47 ( ( member_l @ A2 @ A4 )
% 0.31/0.47 & ( R7 @ A2 @ X6 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % pigeonhole_infinite_rel
% 0.31/0.47 thf(fact_226_not__finite__existsD,axiom,
% 0.31/0.47 ! [P: r > $o] :
% 0.31/0.47 ( ~ ( finite_finite_r @ ( collect_r @ P ) )
% 0.31/0.47 => ? [X_1: r] : ( P @ X_1 ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_finite_existsD
% 0.31/0.47 thf(fact_227_not__finite__existsD,axiom,
% 0.31/0.47 ! [P: l > $o] :
% 0.31/0.47 ( ~ ( finite_finite_l @ ( collect_l @ P ) )
% 0.31/0.47 => ? [X_1: l] : ( P @ X_1 ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_finite_existsD
% 0.31/0.47 thf(fact_228_finite__has__maximal2,axiom,
% 0.31/0.47 ! [A4: set_set_r,A: set_r] :
% 0.31/0.47 ( ( finite_finite_set_r @ A4 )
% 0.31/0.47 => ( ( member_set_r @ A @ A4 )
% 0.31/0.47 => ? [X6: set_r] :
% 0.31/0.47 ( ( member_set_r @ X6 @ A4 )
% 0.31/0.47 & ( ord_less_eq_set_r @ A @ X6 )
% 0.31/0.47 & ! [Xa2: set_r] :
% 0.31/0.47 ( ( member_set_r @ Xa2 @ A4 )
% 0.31/0.47 => ( ( ord_less_eq_set_r @ X6 @ Xa2 )
% 0.31/0.47 => ( X6 = Xa2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_has_maximal2
% 0.31/0.47 thf(fact_229_finite__has__maximal2,axiom,
% 0.31/0.47 ! [A4: set_set_l,A: set_l] :
% 0.31/0.47 ( ( finite_finite_set_l @ A4 )
% 0.31/0.47 => ( ( member_set_l @ A @ A4 )
% 0.31/0.47 => ? [X6: set_l] :
% 0.31/0.47 ( ( member_set_l @ X6 @ A4 )
% 0.31/0.47 & ( ord_less_eq_set_l @ A @ X6 )
% 0.31/0.47 & ! [Xa2: set_l] :
% 0.31/0.47 ( ( member_set_l @ Xa2 @ A4 )
% 0.31/0.47 => ( ( ord_less_eq_set_l @ X6 @ Xa2 )
% 0.31/0.47 => ( X6 = Xa2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_has_maximal2
% 0.31/0.47 thf(fact_230_finite__has__minimal2,axiom,
% 0.31/0.47 ! [A4: set_set_r,A: set_r] :
% 0.31/0.47 ( ( finite_finite_set_r @ A4 )
% 0.31/0.47 => ( ( member_set_r @ A @ A4 )
% 0.31/0.47 => ? [X6: set_r] :
% 0.31/0.47 ( ( member_set_r @ X6 @ A4 )
% 0.31/0.47 & ( ord_less_eq_set_r @ X6 @ A )
% 0.31/0.47 & ! [Xa2: set_r] :
% 0.31/0.47 ( ( member_set_r @ Xa2 @ A4 )
% 0.31/0.47 => ( ( ord_less_eq_set_r @ Xa2 @ X6 )
% 0.31/0.47 => ( X6 = Xa2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_has_minimal2
% 0.31/0.47 thf(fact_231_finite__has__minimal2,axiom,
% 0.31/0.47 ! [A4: set_set_l,A: set_l] :
% 0.31/0.47 ( ( finite_finite_set_l @ A4 )
% 0.31/0.47 => ( ( member_set_l @ A @ A4 )
% 0.31/0.47 => ? [X6: set_l] :
% 0.31/0.47 ( ( member_set_l @ X6 @ A4 )
% 0.31/0.47 & ( ord_less_eq_set_l @ X6 @ A )
% 0.31/0.47 & ! [Xa2: set_l] :
% 0.31/0.47 ( ( member_set_l @ Xa2 @ A4 )
% 0.31/0.47 => ( ( ord_less_eq_set_l @ Xa2 @ X6 )
% 0.31/0.47 => ( X6 = Xa2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_has_minimal2
% 0.31/0.47 thf(fact_232_finite__subset,axiom,
% 0.31/0.47 ! [A4: set_r,B5: set_r] :
% 0.31/0.47 ( ( ord_less_eq_set_r @ A4 @ B5 )
% 0.31/0.47 => ( ( finite_finite_r @ B5 )
% 0.31/0.47 => ( finite_finite_r @ A4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_subset
% 0.31/0.47 thf(fact_233_finite__subset,axiom,
% 0.31/0.47 ! [A4: set_l,B5: set_l] :
% 0.31/0.47 ( ( ord_less_eq_set_l @ A4 @ B5 )
% 0.31/0.47 => ( ( finite_finite_l @ B5 )
% 0.31/0.47 => ( finite_finite_l @ A4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_subset
% 0.31/0.47 thf(fact_234_infinite__super,axiom,
% 0.31/0.47 ! [S6: set_r,T2: set_r] :
% 0.31/0.47 ( ( ord_less_eq_set_r @ S6 @ T2 )
% 0.31/0.47 => ( ~ ( finite_finite_r @ S6 )
% 0.31/0.47 => ~ ( finite_finite_r @ T2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % infinite_super
% 0.31/0.47 thf(fact_235_infinite__super,axiom,
% 0.31/0.47 ! [S6: set_l,T2: set_l] :
% 0.31/0.47 ( ( ord_less_eq_set_l @ S6 @ T2 )
% 0.31/0.47 => ( ~ ( finite_finite_l @ S6 )
% 0.31/0.47 => ~ ( finite_finite_l @ T2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % infinite_super
% 0.31/0.47 thf(fact_236_rev__finite__subset,axiom,
% 0.31/0.47 ! [B5: set_r,A4: set_r] :
% 0.31/0.47 ( ( finite_finite_r @ B5 )
% 0.31/0.47 => ( ( ord_less_eq_set_r @ A4 @ B5 )
% 0.31/0.47 => ( finite_finite_r @ A4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rev_finite_subset
% 0.31/0.47 thf(fact_237_rev__finite__subset,axiom,
% 0.31/0.47 ! [B5: set_l,A4: set_l] :
% 0.31/0.47 ( ( finite_finite_l @ B5 )
% 0.31/0.47 => ( ( ord_less_eq_set_l @ A4 @ B5 )
% 0.31/0.47 => ( finite_finite_l @ A4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rev_finite_subset
% 0.31/0.47 thf(fact_238_finite__update__induct,axiom,
% 0.31/0.47 ! [F: r > option1457017436_r_l_v,C: option1457017436_r_l_v,P: ( r > option1457017436_r_l_v ) > $o] :
% 0.31/0.47 ( ( finite_finite_r
% 0.31/0.47 @ ( collect_r
% 0.31/0.47 @ ^ [A2: r] :
% 0.31/0.47 ( ( F @ A2 )
% 0.31/0.47 != C ) ) )
% 0.31/0.47 => ( ( P
% 0.31/0.47 @ ^ [A2: r] : C )
% 0.31/0.47 => ( ! [A3: r,B3: option1457017436_r_l_v,F3: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( finite_finite_r
% 0.31/0.47 @ ( collect_r
% 0.31/0.47 @ ^ [C2: r] :
% 0.31/0.47 ( ( F3 @ C2 )
% 0.31/0.47 != C ) ) )
% 0.31/0.47 => ( ( ( F3 @ A3 )
% 0.31/0.47 = C )
% 0.31/0.47 => ( ( B3 != C )
% 0.31/0.47 => ( ( P @ F3 )
% 0.31/0.47 => ( P @ ( fun_up709272714_r_l_v @ F3 @ A3 @ B3 ) ) ) ) ) )
% 0.31/0.47 => ( P @ F ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_update_induct
% 0.31/0.47 thf(fact_239_finite__update__induct,axiom,
% 0.31/0.47 ! [F: l > option_val_r_l_v,C: option_val_r_l_v,P: ( l > option_val_r_l_v ) > $o] :
% 0.31/0.47 ( ( finite_finite_l
% 0.31/0.47 @ ( collect_l
% 0.31/0.47 @ ^ [A2: l] :
% 0.31/0.47 ( ( F @ A2 )
% 0.31/0.47 != C ) ) )
% 0.31/0.47 => ( ( P
% 0.31/0.47 @ ^ [A2: l] : C )
% 0.31/0.47 => ( ! [A3: l,B3: option_val_r_l_v,F3: l > option_val_r_l_v] :
% 0.31/0.47 ( ( finite_finite_l
% 0.31/0.47 @ ( collect_l
% 0.31/0.47 @ ^ [C2: l] :
% 0.31/0.47 ( ( F3 @ C2 )
% 0.31/0.47 != C ) ) )
% 0.31/0.47 => ( ( ( F3 @ A3 )
% 0.31/0.47 = C )
% 0.31/0.47 => ( ( B3 != C )
% 0.31/0.47 => ( ( P @ F3 )
% 0.31/0.47 => ( P @ ( fun_up1835647912_r_l_v @ F3 @ A3 @ B3 ) ) ) ) ) )
% 0.31/0.47 => ( P @ F ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_update_induct
% 0.31/0.47 thf(fact_240_substitution_Orevision__step_OifFalse,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.31/0.47 => ( revision_step_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ E22 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step.ifFalse
% 0.31/0.47 thf(fact_241_substitution_OifFalse__deterministic,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.31/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.31/0.47 = ( S2
% 0.31/0.47 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ E22 ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.ifFalse_deterministic
% 0.31/0.47 thf(fact_242_substitution_Orevision__step__relaxed_OifFalse,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 0.31/0.47 => ( revisi1291188644_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ E22 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step_relaxed.ifFalse
% 0.31/0.47 thf(fact_243_reachable__imp__identifiers__available_I1_J,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( reachable_r_l_v @ subst @ S )
% 0.31/0.47 => ( ~ ( finite_finite_r @ top_top_set_r )
% 0.31/0.47 => ? [R6: r] :
% 0.31/0.47 ~ ( member_r @ R6 @ ( rID_G_r_l_v @ S ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % reachable_imp_identifiers_available(1)
% 0.31/0.47 thf(fact_244_local__state__of__finite__restricted__global__state__is__finite_I1_J,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ Ls ) )
% 0.31/0.47 => ( ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 0.31/0.47 => ( ( R != R2 )
% 0.31/0.47 => ( finite_finite_r @ ( rID_L_l_r_v @ Ls ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % local_state_of_finite_restricted_global_state_is_finite(1)
% 0.31/0.47 thf(fact_245_empty__map__finite_I4_J,axiom,
% 0.31/0.47 ( finite_finite_l
% 0.31/0.47 @ ( lID_G_r_l_v
% 0.31/0.47 @ ^ [X: r] : none_P277133687_r_l_v ) ) ).
% 0.31/0.47
% 0.31/0.47 % empty_map_finite(4)
% 0.31/0.47 thf(fact_246_RID_092_060_094sub_062L__finite__invariant,axiom,
% 0.31/0.47 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.31/0.47 => ( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
% 0.31/0.47 => ( finite_finite_l @ ( lID_G_r_l_v @ S2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % RID\<^sub>L_finite_invariant
% 0.31/0.47 thf(fact_247_reachable__imp__identifiers__finite_I2_J,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( reachable_r_l_v @ subst @ S )
% 0.31/0.47 => ( finite_finite_l @ ( lID_G_r_l_v @ S ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % reachable_imp_identifiers_finite(2)
% 0.31/0.47 thf(fact_248_finite__option__UNIV,axiom,
% 0.31/0.47 ( ( finite16335230tion_r @ top_top_set_option_r )
% 0.31/0.47 = ( finite_finite_r @ top_top_set_r ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_option_UNIV
% 0.31/0.47 thf(fact_249_finite__option__UNIV,axiom,
% 0.31/0.47 ( ( finite2114249848tion_l @ top_top_set_option_l )
% 0.31/0.47 = ( finite_finite_l @ top_top_set_l ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_option_UNIV
% 0.31/0.47 thf(fact_250_finite__Collect__not,axiom,
% 0.31/0.47 ! [P: r > $o] :
% 0.31/0.47 ( ( finite_finite_r @ ( collect_r @ P ) )
% 0.31/0.47 => ( ( finite_finite_r
% 0.31/0.47 @ ( collect_r
% 0.31/0.47 @ ^ [X: r] :
% 0.31/0.47 ~ ( P @ X ) ) )
% 0.31/0.47 = ( finite_finite_r @ top_top_set_r ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_Collect_not
% 0.31/0.47 thf(fact_251_finite__Collect__not,axiom,
% 0.31/0.47 ! [P: l > $o] :
% 0.31/0.47 ( ( finite_finite_l @ ( collect_l @ P ) )
% 0.31/0.47 => ( ( finite_finite_l
% 0.31/0.47 @ ( collect_l
% 0.31/0.47 @ ^ [X: l] :
% 0.31/0.47 ~ ( P @ X ) ) )
% 0.31/0.47 = ( finite_finite_l @ top_top_set_l ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_Collect_not
% 0.31/0.47 thf(fact_252_in__restricted__global__in__unrestricted__global_I2_J,axiom,
% 0.31/0.47 ! [L: l,S: r > option1457017436_r_l_v,R: r] :
% 0.31/0.47 ( ( member_l @ L @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 0.31/0.47 => ( member_l @ L @ ( lID_G_r_l_v @ S ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % in_restricted_global_in_unrestricted_global(2)
% 0.31/0.47 thf(fact_253_RID_092_060_094sub_062GI_I2_J,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ Ls ) )
% 0.31/0.47 => ( ( member_r @ R @ ( rID_L_l_r_v @ Ls ) )
% 0.31/0.47 => ( member_r @ R @ ( rID_G_r_l_v @ S ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % RID\<^sub>GI(2)
% 0.31/0.47 thf(fact_254_finite__state__imp__restriction__finite_I2_J,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R: r] :
% 0.31/0.47 ( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
% 0.31/0.47 => ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_state_imp_restriction_finite(2)
% 0.31/0.47 thf(fact_255_in__restricted__global__in__updated__global_I2_J,axiom,
% 0.31/0.47 ! [L: l,S: r > option1457017436_r_l_v,R: r,Ls: produc1156025366_r_l_v] :
% 0.31/0.47 ( ( member_l @ L @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 0.31/0.47 => ( member_l @ L @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ Ls ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % in_restricted_global_in_updated_global(2)
% 0.31/0.47 thf(fact_256_substitution_Oreachable__imp__identifiers__available_I2_J,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( reachable_r_l_v @ Subst @ S )
% 0.31/0.47 => ( ~ ( finite_finite_l @ top_top_set_l )
% 0.31/0.47 => ? [L2: l] :
% 0.31/0.47 ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.reachable_imp_identifiers_available(2)
% 0.31/0.47 thf(fact_257_substitution_ORID_092_060_094sub_062L__finite__invariant,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.31/0.47 => ( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
% 0.31/0.47 => ( finite_finite_l @ ( lID_G_r_l_v @ S2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.RID\<^sub>L_finite_invariant
% 0.31/0.47 thf(fact_258_ID__restricted__global__subset__unrestricted_I1_J,axiom,
% 0.31/0.47 ! [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 ) ) ).
% 0.31/0.47
% 0.31/0.47 % ID_restricted_global_subset_unrestricted(1)
% 0.31/0.47 thf(fact_259_substitution_Oreachable__imp__identifiers__finite_I2_J,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( reachable_r_l_v @ Subst @ S )
% 0.31/0.47 => ( finite_finite_l @ ( lID_G_r_l_v @ S ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.reachable_imp_identifiers_finite(2)
% 0.31/0.47 thf(fact_260_substitution_Oempty__map__finite_I4_J,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( finite_finite_l
% 0.31/0.47 @ ( lID_G_r_l_v
% 0.31/0.47 @ ^ [X: r] : none_P277133687_r_l_v ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.empty_map_finite(4)
% 0.31/0.47 thf(fact_261_substitution_Oreachable__imp__identifiers__available_I1_J,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( reachable_r_l_v @ Subst @ S )
% 0.31/0.47 => ( ~ ( finite_finite_r @ top_top_set_r )
% 0.31/0.47 => ? [R6: r] :
% 0.31/0.47 ~ ( member_r @ R6 @ ( rID_G_r_l_v @ S ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.reachable_imp_identifiers_available(1)
% 0.31/0.47 thf(fact_262_substitution_Ofinite__state__imp__restriction__finite_I2_J,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
% 0.31/0.47 => ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.finite_state_imp_restriction_finite(2)
% 0.31/0.47 thf(fact_263_substitution_Olocal__state__of__finite__restricted__global__state__is__finite_I1_J,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ Ls ) )
% 0.31/0.47 => ( ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 0.31/0.47 => ( ( R != R2 )
% 0.31/0.47 => ( finite_finite_r @ ( rID_L_l_r_v @ Ls ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.local_state_of_finite_restricted_global_state_is_finite(1)
% 0.31/0.47 thf(fact_264_only__new__introduces__lids_H,axiom,
% 0.31/0.47 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v,L: l] :
% 0.31/0.47 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.31/0.47 => ( ! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,V2: val_r_l_v] :
% 0.31/0.47 ( ( S @ R )
% 0.31/0.47 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ref_r_l_v @ ( vE_r_l_v @ V2 ) ) ) ) ) ) )
% 0.31/0.47 => ( ~ ( member_l @ L @ ( lID_G_r_l_v @ S ) )
% 0.31/0.47 => ~ ( member_l @ L @ ( lID_G_r_l_v @ S2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % only_new_introduces_lids'
% 0.31/0.47 thf(fact_265_local__state__of__finite__restricted__global__state__is__finite_I2_J,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
% 0.31/0.47 ( ( ( S @ R2 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ Ls ) )
% 0.31/0.47 => ( ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 0.31/0.47 => ( ( R != R2 )
% 0.31/0.47 => ( finite_finite_l @ ( lID_L_l_r_v @ Ls ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % local_state_of_finite_restricted_global_state_is_finite(2)
% 0.31/0.47 thf(fact_266_only__new__introduces__lids,axiom,
% 0.31/0.47 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.31/0.47 => ( ! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,V2: val_r_l_v] :
% 0.31/0.47 ( ( S @ R )
% 0.31/0.47 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ref_r_l_v @ ( vE_r_l_v @ V2 ) ) ) ) ) ) )
% 0.31/0.47 => ( ord_less_eq_set_l @ ( lID_G_r_l_v @ S2 ) @ ( lID_G_r_l_v @ S ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % only_new_introduces_lids
% 0.31/0.47 thf(fact_267_expr_Oinject_I4_J,axiom,
% 0.31/0.47 ! [X4: expr_r_l_v,Y4: expr_r_l_v] :
% 0.31/0.47 ( ( ( ref_r_l_v @ X4 )
% 0.31/0.47 = ( ref_r_l_v @ Y4 ) )
% 0.31/0.47 = ( X4 = Y4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.inject(4)
% 0.31/0.47 thf(fact_268_reachable__imp__identifiers__available_I2_J,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( reachable_r_l_v @ subst @ S )
% 0.31/0.47 => ( ~ ( finite_finite_l @ top_top_set_l )
% 0.31/0.47 => ? [L2: l] :
% 0.31/0.47 ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % reachable_imp_identifiers_available(2)
% 0.31/0.47 thf(fact_269_LID_092_060_094sub_062GI,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R: r,Ls: produc1156025366_r_l_v,L: l] :
% 0.31/0.47 ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ Ls ) )
% 0.31/0.47 => ( ( member_l @ L @ ( lID_L_l_r_v @ Ls ) )
% 0.31/0.47 => ( member_l @ L @ ( lID_G_r_l_v @ S ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % LID\<^sub>GI
% 0.31/0.47 thf(fact_270_expr_Odistinct_I41_J,axiom,
% 0.31/0.47 ! [X4: expr_r_l_v,X7: expr_r_l_v] :
% 0.31/0.47 ( ( ref_r_l_v @ X4 )
% 0.31/0.47 != ( rfork_r_l_v @ X7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(41)
% 0.31/0.47 thf(fact_271_expr_Odistinct_I43_J,axiom,
% 0.31/0.47 ! [X4: expr_r_l_v,X8: expr_r_l_v] :
% 0.31/0.47 ( ( ref_r_l_v @ X4 )
% 0.31/0.47 != ( rjoin_r_l_v @ X8 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(43)
% 0.31/0.47 thf(fact_272_expr_Odistinct_I5_J,axiom,
% 0.31/0.47 ! [X1: val_r_l_v,X4: expr_r_l_v] :
% 0.31/0.47 ( ( vE_r_l_v @ X1 )
% 0.31/0.47 != ( ref_r_l_v @ X4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(5)
% 0.31/0.47 thf(fact_273_expr_Odistinct_I27_J,axiom,
% 0.31/0.47 ! [X31: expr_r_l_v,X32: expr_r_l_v,X33: expr_r_l_v,X4: expr_r_l_v] :
% 0.31/0.47 ( ( ite_r_l_v @ X31 @ X32 @ X33 )
% 0.31/0.47 != ( ref_r_l_v @ X4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(27)
% 0.31/0.47 thf(fact_274_LID_092_060_094sub_062GE,axiom,
% 0.31/0.47 ! [L: l,S: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( member_l @ L @ ( lID_G_r_l_v @ S ) )
% 0.31/0.47 => ~ ! [R6: r,Ls3: produc1156025366_r_l_v] :
% 0.31/0.47 ( ( ( S @ R6 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ Ls3 ) )
% 0.31/0.47 => ~ ( member_l @ L @ ( lID_L_l_r_v @ Ls3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % LID\<^sub>GE
% 0.31/0.47 thf(fact_275_substitution_Oonly__new__introduces__lids_H,axiom,
% 0.31/0.47 ! [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,L: l] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.31/0.47 => ( ! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,V2: val_r_l_v] :
% 0.31/0.47 ( ( S @ R )
% 0.31/0.47 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ref_r_l_v @ ( vE_r_l_v @ V2 ) ) ) ) ) ) )
% 0.31/0.47 => ( ~ ( member_l @ L @ ( lID_G_r_l_v @ S ) )
% 0.31/0.47 => ~ ( member_l @ L @ ( lID_G_r_l_v @ S2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.only_new_introduces_lids'
% 0.31/0.47 thf(fact_276_substitution_Oonly__new__introduces__lids,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.31/0.47 => ( ! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,V2: val_r_l_v] :
% 0.31/0.47 ( ( S @ R )
% 0.31/0.47 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ref_r_l_v @ ( vE_r_l_v @ V2 ) ) ) ) ) ) )
% 0.31/0.47 => ( ord_less_eq_set_l @ ( lID_G_r_l_v @ S2 ) @ ( lID_G_r_l_v @ S ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.only_new_introduces_lids
% 0.31/0.47 thf(fact_277_substitution_Olocal__state__of__finite__restricted__global__state__is__finite_I2_J,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( ( S @ R2 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ Ls ) )
% 0.31/0.47 => ( ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 0.31/0.47 => ( ( R != R2 )
% 0.31/0.47 => ( finite_finite_l @ ( lID_L_l_r_v @ Ls ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.local_state_of_finite_restricted_global_state_is_finite(2)
% 0.31/0.47 thf(fact_278_domains__subsume__def,axiom,
% 0.31/0.47 ( domain87684397_l_r_v
% 0.31/0.47 = ( ^ [Ls2: produc1156025366_r_l_v] : ( ord_less_eq_set_l @ ( lID_L_l_r_v @ Ls2 ) @ ( doms_l_r_v @ Ls2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % domains_subsume_def
% 0.31/0.47 thf(fact_279_revision__step_Onew,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,V: val_r_l_v,L: l] :
% 0.31/0.47 ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.31/0.47 => ( ~ ( member_l @ L @ ( lID_G_r_l_v @ S ) )
% 0.31/0.47 => ( revision_step_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau @ L @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step.new
% 0.31/0.47 thf(fact_280_val_Oinject_I3_J,axiom,
% 0.31/0.47 ! [X34: l,Y3: l] :
% 0.31/0.47 ( ( ( loc_l_r_v @ X34 )
% 0.31/0.47 = ( loc_l_r_v @ Y3 ) )
% 0.31/0.47 = ( X34 = Y3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % val.inject(3)
% 0.31/0.47 thf(fact_281_new__pseudodeterministic,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.31/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.31/0.47 = ( ? [L3: l] :
% 0.31/0.47 ( ~ ( member_l @ L3 @ ( lID_G_r_l_v @ S ) )
% 0.31/0.47 & ( S2
% 0.31/0.47 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau @ L3 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( loc_l_r_v @ L3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % new_pseudodeterministic
% 0.31/0.47 thf(fact_282_val_Odistinct_I15_J,axiom,
% 0.31/0.47 ! [X34: l,X4: r] :
% 0.31/0.47 ( ( loc_l_r_v @ X34 )
% 0.31/0.47 != ( rid_r_l_v @ X4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % val.distinct(15)
% 0.31/0.47 thf(fact_283_val_Odistinct_I3_J,axiom,
% 0.31/0.47 ! [X1: const,X34: l] :
% 0.31/0.47 ( ( cV_r_l_v @ X1 )
% 0.31/0.47 != ( loc_l_r_v @ X34 ) ) ).
% 0.31/0.47
% 0.31/0.47 % val.distinct(3)
% 0.31/0.47 thf(fact_284_substitution_Odomains__subsume__def,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,Ls: produc1156025366_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( domain87684397_l_r_v @ Ls )
% 0.31/0.47 = ( ord_less_eq_set_l @ ( lID_L_l_r_v @ Ls ) @ ( doms_l_r_v @ Ls ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.domains_subsume_def
% 0.31/0.47 thf(fact_285_substitution_Onew__pseudodeterministic,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.31/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.31/0.47 = ( ? [L3: l] :
% 0.31/0.47 ( ~ ( member_l @ L3 @ ( lID_G_r_l_v @ S ) )
% 0.31/0.47 & ( S2
% 0.31/0.47 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau @ L3 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( loc_l_r_v @ L3 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.new_pseudodeterministic
% 0.31/0.47 thf(fact_286_substitution_Orevision__step_Onew,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,V: val_r_l_v,L: l] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.31/0.47 => ( ~ ( member_l @ L @ ( lID_G_r_l_v @ S ) )
% 0.31/0.47 => ( revision_step_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau @ L @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step.new
% 0.31/0.47 thf(fact_287_revision__step__relaxed_Oset,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,L: l,V: val_r_l_v] :
% 0.31/0.47 ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.31/0.47 => ( revisi1291188644_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau @ L @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step_relaxed.set
% 0.31/0.47 thf(fact_288_substitution_Orevision__step__relaxed_Oset,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,L: l,V: val_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.31/0.47 => ( revisi1291188644_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau @ L @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step_relaxed.set
% 0.31/0.47 thf(fact_289_expr_Oinject_I6_J,axiom,
% 0.31/0.47 ! [X61: expr_r_l_v,X62: expr_r_l_v,Y61: expr_r_l_v,Y62: expr_r_l_v] :
% 0.31/0.47 ( ( ( assign_r_l_v @ X61 @ X62 )
% 0.31/0.47 = ( assign_r_l_v @ Y61 @ Y62 ) )
% 0.31/0.47 = ( ( X61 = Y61 )
% 0.31/0.47 & ( X62 = Y62 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.inject(6)
% 0.31/0.47 thf(fact_290_expr_Odistinct_I39_J,axiom,
% 0.31/0.47 ! [X4: expr_r_l_v,X61: expr_r_l_v,X62: expr_r_l_v] :
% 0.31/0.47 ( ( ref_r_l_v @ X4 )
% 0.31/0.47 != ( assign_r_l_v @ X61 @ X62 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(39)
% 0.31/0.47 thf(fact_291_expr_Odistinct_I51_J,axiom,
% 0.31/0.47 ! [X61: expr_r_l_v,X62: expr_r_l_v,X7: expr_r_l_v] :
% 0.31/0.47 ( ( assign_r_l_v @ X61 @ X62 )
% 0.31/0.47 != ( rfork_r_l_v @ X7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(51)
% 0.31/0.47 thf(fact_292_expr_Odistinct_I53_J,axiom,
% 0.31/0.47 ! [X61: expr_r_l_v,X62: expr_r_l_v,X8: expr_r_l_v] :
% 0.31/0.47 ( ( assign_r_l_v @ X61 @ X62 )
% 0.31/0.47 != ( rjoin_r_l_v @ X8 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(53)
% 0.31/0.47 thf(fact_293_expr_Odistinct_I9_J,axiom,
% 0.31/0.47 ! [X1: val_r_l_v,X61: expr_r_l_v,X62: expr_r_l_v] :
% 0.31/0.47 ( ( vE_r_l_v @ X1 )
% 0.31/0.47 != ( assign_r_l_v @ X61 @ X62 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(9)
% 0.31/0.47 thf(fact_294_expr_Odistinct_I31_J,axiom,
% 0.31/0.47 ! [X31: expr_r_l_v,X32: expr_r_l_v,X33: expr_r_l_v,X61: expr_r_l_v,X62: expr_r_l_v] :
% 0.31/0.47 ( ( ite_r_l_v @ X31 @ X32 @ X33 )
% 0.31/0.47 != ( assign_r_l_v @ X61 @ X62 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(31)
% 0.31/0.47 thf(fact_295_revision__step_Oset,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,L: l,V: val_r_l_v] :
% 0.31/0.47 ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.31/0.47 => ( ( member_l @ L @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau ) ) )
% 0.31/0.47 => ( revision_step_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau @ L @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step.set
% 0.31/0.47 thf(fact_296_set__deterministic,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,L: l,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.31/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.31/0.47 = ( ( member_l @ L @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau ) ) )
% 0.31/0.47 & ( S2
% 0.31/0.47 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau @ L @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % set_deterministic
% 0.31/0.47 thf(fact_297_dom__const,axiom,
% 0.31/0.47 ! [F: r > produc1156025366_r_l_v] :
% 0.31/0.47 ( ( dom_r_259548057_r_l_v
% 0.31/0.47 @ ^ [X: r] : ( some_P1807977723_r_l_v @ ( F @ X ) ) )
% 0.31/0.47 = top_top_set_r ) ).
% 0.31/0.47
% 0.31/0.47 % dom_const
% 0.31/0.47 thf(fact_298_dom__const,axiom,
% 0.31/0.47 ! [F: r > val_r_l_v] :
% 0.31/0.47 ( ( dom_r_val_r_l_v
% 0.31/0.47 @ ^ [X: r] : ( some_val_r_l_v @ ( F @ X ) ) )
% 0.31/0.47 = top_top_set_r ) ).
% 0.31/0.47
% 0.31/0.47 % dom_const
% 0.31/0.47 thf(fact_299_dom__const,axiom,
% 0.31/0.47 ! [F: l > produc1156025366_r_l_v] :
% 0.31/0.47 ( ( dom_l_45837855_r_l_v
% 0.31/0.47 @ ^ [X: l] : ( some_P1807977723_r_l_v @ ( F @ X ) ) )
% 0.31/0.47 = top_top_set_l ) ).
% 0.31/0.47
% 0.31/0.47 % dom_const
% 0.31/0.47 thf(fact_300_dom__const,axiom,
% 0.31/0.47 ! [F: l > val_r_l_v] :
% 0.31/0.47 ( ( dom_l_val_r_l_v
% 0.31/0.47 @ ^ [X: l] : ( some_val_r_l_v @ ( F @ X ) ) )
% 0.31/0.47 = top_top_set_l ) ).
% 0.31/0.47
% 0.31/0.47 % dom_const
% 0.31/0.47 thf(fact_301_domI,axiom,
% 0.31/0.47 ! [M: r > option1457017436_r_l_v,A: r,B: produc1156025366_r_l_v] :
% 0.31/0.47 ( ( ( M @ A )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ B ) )
% 0.31/0.47 => ( member_r @ A @ ( dom_r_259548057_r_l_v @ M ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % domI
% 0.31/0.47 thf(fact_302_domI,axiom,
% 0.31/0.47 ! [M: produc1389397445_r_l_v > option1457017436_r_l_v,A: produc1389397445_r_l_v,B: produc1156025366_r_l_v] :
% 0.31/0.47 ( ( ( M @ A )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ B ) )
% 0.31/0.47 => ( member1522896238_r_l_v @ A @ ( dom_Pr1162080227_r_l_v @ M ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % domI
% 0.31/0.47 thf(fact_303_domI,axiom,
% 0.31/0.47 ! [M: l > option1457017436_r_l_v,A: l,B: produc1156025366_r_l_v] :
% 0.31/0.47 ( ( ( M @ A )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ B ) )
% 0.31/0.47 => ( member_l @ A @ ( dom_l_45837855_r_l_v @ M ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % domI
% 0.31/0.47 thf(fact_304_domI,axiom,
% 0.31/0.47 ! [M: r > option_val_r_l_v,A: r,B: val_r_l_v] :
% 0.31/0.47 ( ( ( M @ A )
% 0.31/0.47 = ( some_val_r_l_v @ B ) )
% 0.31/0.47 => ( member_r @ A @ ( dom_r_val_r_l_v @ M ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % domI
% 0.31/0.47 thf(fact_305_domI,axiom,
% 0.31/0.47 ! [M: produc1389397445_r_l_v > option_val_r_l_v,A: produc1389397445_r_l_v,B: val_r_l_v] :
% 0.31/0.47 ( ( ( M @ A )
% 0.31/0.47 = ( some_val_r_l_v @ B ) )
% 0.31/0.47 => ( member1522896238_r_l_v @ A @ ( dom_Pr939617279_r_l_v @ M ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % domI
% 0.31/0.47 thf(fact_306_domI,axiom,
% 0.31/0.47 ! [M: l > option_val_r_l_v,A: l,B: val_r_l_v] :
% 0.31/0.47 ( ( ( M @ A )
% 0.31/0.47 = ( some_val_r_l_v @ B ) )
% 0.31/0.47 => ( member_l @ A @ ( dom_l_val_r_l_v @ M ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % domI
% 0.31/0.47 thf(fact_307_domD,axiom,
% 0.31/0.47 ! [A: r,M: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( member_r @ A @ ( dom_r_259548057_r_l_v @ M ) )
% 0.31/0.47 => ? [B3: produc1156025366_r_l_v] :
% 0.31/0.47 ( ( M @ A )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % domD
% 0.31/0.47 thf(fact_308_domD,axiom,
% 0.31/0.47 ! [A: produc1389397445_r_l_v,M: produc1389397445_r_l_v > option1457017436_r_l_v] :
% 0.31/0.47 ( ( member1522896238_r_l_v @ A @ ( dom_Pr1162080227_r_l_v @ M ) )
% 0.31/0.47 => ? [B3: produc1156025366_r_l_v] :
% 0.31/0.47 ( ( M @ A )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % domD
% 0.31/0.47 thf(fact_309_domD,axiom,
% 0.31/0.47 ! [A: l,M: l > option1457017436_r_l_v] :
% 0.31/0.47 ( ( member_l @ A @ ( dom_l_45837855_r_l_v @ M ) )
% 0.31/0.47 => ? [B3: produc1156025366_r_l_v] :
% 0.31/0.47 ( ( M @ A )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % domD
% 0.31/0.47 thf(fact_310_domD,axiom,
% 0.31/0.47 ! [A: r,M: r > option_val_r_l_v] :
% 0.31/0.47 ( ( member_r @ A @ ( dom_r_val_r_l_v @ M ) )
% 0.31/0.47 => ? [B3: val_r_l_v] :
% 0.31/0.47 ( ( M @ A )
% 0.31/0.47 = ( some_val_r_l_v @ B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % domD
% 0.31/0.47 thf(fact_311_domD,axiom,
% 0.31/0.47 ! [A: produc1389397445_r_l_v,M: produc1389397445_r_l_v > option_val_r_l_v] :
% 0.31/0.47 ( ( member1522896238_r_l_v @ A @ ( dom_Pr939617279_r_l_v @ M ) )
% 0.31/0.47 => ? [B3: val_r_l_v] :
% 0.31/0.47 ( ( M @ A )
% 0.31/0.47 = ( some_val_r_l_v @ B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % domD
% 0.31/0.47 thf(fact_312_domD,axiom,
% 0.31/0.47 ! [A: l,M: l > option_val_r_l_v] :
% 0.31/0.47 ( ( member_l @ A @ ( dom_l_val_r_l_v @ M ) )
% 0.31/0.47 => ? [B3: val_r_l_v] :
% 0.31/0.47 ( ( M @ A )
% 0.31/0.47 = ( some_val_r_l_v @ B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % domD
% 0.31/0.47 thf(fact_313_dom__def,axiom,
% 0.31/0.47 ( dom_l_val_r_l_v
% 0.31/0.47 = ( ^ [M2: l > option_val_r_l_v] :
% 0.31/0.47 ( collect_l
% 0.31/0.47 @ ^ [A2: l] :
% 0.31/0.47 ( ( M2 @ A2 )
% 0.31/0.47 != none_val_r_l_v ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dom_def
% 0.31/0.47 thf(fact_314_dom__def,axiom,
% 0.31/0.47 ( dom_r_259548057_r_l_v
% 0.31/0.47 = ( ^ [M2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( collect_r
% 0.31/0.47 @ ^ [A2: r] :
% 0.31/0.47 ( ( M2 @ A2 )
% 0.31/0.47 != none_P277133687_r_l_v ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dom_def
% 0.31/0.47 thf(fact_315_domIff,axiom,
% 0.31/0.47 ! [A: r,M: r > option_val_r_l_v] :
% 0.31/0.47 ( ( member_r @ A @ ( dom_r_val_r_l_v @ M ) )
% 0.31/0.47 = ( ( M @ A )
% 0.31/0.47 != none_val_r_l_v ) ) ).
% 0.31/0.47
% 0.31/0.47 % domIff
% 0.31/0.47 thf(fact_316_domIff,axiom,
% 0.31/0.47 ! [A: produc1389397445_r_l_v,M: produc1389397445_r_l_v > option_val_r_l_v] :
% 0.31/0.47 ( ( member1522896238_r_l_v @ A @ ( dom_Pr939617279_r_l_v @ M ) )
% 0.31/0.47 = ( ( M @ A )
% 0.31/0.47 != none_val_r_l_v ) ) ).
% 0.31/0.47
% 0.31/0.47 % domIff
% 0.31/0.47 thf(fact_317_domIff,axiom,
% 0.31/0.47 ! [A: l,M: l > option_val_r_l_v] :
% 0.31/0.47 ( ( member_l @ A @ ( dom_l_val_r_l_v @ M ) )
% 0.31/0.47 = ( ( M @ A )
% 0.31/0.47 != none_val_r_l_v ) ) ).
% 0.31/0.47
% 0.31/0.47 % domIff
% 0.31/0.47 thf(fact_318_domIff,axiom,
% 0.31/0.47 ! [A: r,M: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( member_r @ A @ ( dom_r_259548057_r_l_v @ M ) )
% 0.31/0.47 = ( ( M @ A )
% 0.31/0.47 != none_P277133687_r_l_v ) ) ).
% 0.31/0.47
% 0.31/0.47 % domIff
% 0.31/0.47 thf(fact_319_domIff,axiom,
% 0.31/0.47 ! [A: produc1389397445_r_l_v,M: produc1389397445_r_l_v > option1457017436_r_l_v] :
% 0.31/0.47 ( ( member1522896238_r_l_v @ A @ ( dom_Pr1162080227_r_l_v @ M ) )
% 0.31/0.47 = ( ( M @ A )
% 0.31/0.47 != none_P277133687_r_l_v ) ) ).
% 0.31/0.47
% 0.31/0.47 % domIff
% 0.31/0.47 thf(fact_320_domIff,axiom,
% 0.31/0.47 ! [A: l,M: l > option1457017436_r_l_v] :
% 0.31/0.47 ( ( member_l @ A @ ( dom_l_45837855_r_l_v @ M ) )
% 0.31/0.47 = ( ( M @ A )
% 0.31/0.47 != none_P277133687_r_l_v ) ) ).
% 0.31/0.47
% 0.31/0.47 % domIff
% 0.31/0.47 thf(fact_321_finite__map__freshness,axiom,
% 0.31/0.47 ! [F: r > option_val_r_l_v] :
% 0.31/0.47 ( ( finite_finite_r @ ( dom_r_val_r_l_v @ F ) )
% 0.31/0.47 => ( ~ ( finite_finite_r @ top_top_set_r )
% 0.31/0.47 => ? [X6: r] :
% 0.31/0.47 ( ( F @ X6 )
% 0.31/0.47 = none_val_r_l_v ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_map_freshness
% 0.31/0.47 thf(fact_322_finite__map__freshness,axiom,
% 0.31/0.47 ! [F: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( finite_finite_r @ ( dom_r_259548057_r_l_v @ F ) )
% 0.31/0.47 => ( ~ ( finite_finite_r @ top_top_set_r )
% 0.31/0.47 => ? [X6: r] :
% 0.31/0.47 ( ( F @ X6 )
% 0.31/0.47 = none_P277133687_r_l_v ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_map_freshness
% 0.31/0.47 thf(fact_323_finite__map__freshness,axiom,
% 0.31/0.47 ! [F: l > option_val_r_l_v] :
% 0.31/0.47 ( ( finite_finite_l @ ( dom_l_val_r_l_v @ F ) )
% 0.31/0.47 => ( ~ ( finite_finite_l @ top_top_set_l )
% 0.31/0.47 => ? [X6: l] :
% 0.31/0.47 ( ( F @ X6 )
% 0.31/0.47 = none_val_r_l_v ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_map_freshness
% 0.31/0.47 thf(fact_324_finite__map__freshness,axiom,
% 0.31/0.47 ! [F: l > option1457017436_r_l_v] :
% 0.31/0.47 ( ( finite_finite_l @ ( dom_l_45837855_r_l_v @ F ) )
% 0.31/0.47 => ( ~ ( finite_finite_l @ top_top_set_l )
% 0.31/0.47 => ? [X6: l] :
% 0.31/0.47 ( ( F @ X6 )
% 0.31/0.47 = none_P277133687_r_l_v ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % finite_map_freshness
% 0.31/0.47 thf(fact_325_substitution_Oset__deterministic,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,L: l,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.31/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.31/0.47 = ( ( member_l @ L @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau ) ) )
% 0.31/0.47 & ( S2
% 0.31/0.47 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau @ L @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.set_deterministic
% 0.31/0.47 thf(fact_326_substitution_Orevision__step_Oset,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,L: l,V: val_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 0.31/0.47 => ( ( member_l @ L @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau ) ) )
% 0.31/0.47 => ( revision_step_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau @ L @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step.set
% 0.31/0.47 thf(fact_327_revision__step_Oget,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,L: l] :
% 0.31/0.47 ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( read_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( member_l @ L @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau ) ) )
% 0.31/0.47 => ( revision_step_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( the_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau @ L ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step.get
% 0.31/0.47 thf(fact_328_revision__step__relaxed_Oget,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,L: l] :
% 0.31/0.47 ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( read_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) ) ) ) ) ) )
% 0.31/0.47 => ( revisi1291188644_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( the_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau @ L ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revision_step_relaxed.get
% 0.31/0.47 thf(fact_329__092_060S_062_092_060_094sub_062G__imp___092_060A_062__refl,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R: r] :
% 0.31/0.47 ( ( domain1547879849_r_l_v @ S )
% 0.31/0.47 => ( ( member_r @ R @ ( dom_r_259548057_r_l_v @ S ) )
% 0.31/0.47 => ( subsum148050133_r_l_v @ R @ R @ S ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % \<S>\<^sub>G_imp_\<A>_refl
% 0.31/0.47 thf(fact_330_subsumes__accessible__globally__def,axiom,
% 0.31/0.47 ( subsum680764357_r_l_v
% 0.31/0.47 = ( ^ [S4: r > option1457017436_r_l_v] :
% 0.31/0.47 ! [R_12: r,R_22: r] :
% 0.31/0.47 ( ( member_r @ R_12 @ ( dom_r_259548057_r_l_v @ S4 ) )
% 0.31/0.47 => ( ( member_r @ R_22 @ ( dom_r_259548057_r_l_v @ S4 ) )
% 0.31/0.47 => ( subsum148050133_r_l_v @ R_12 @ R_22 @ S4 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subsumes_accessible_globally_def
% 0.31/0.47 thf(fact_331_expr_Oinject_I5_J,axiom,
% 0.31/0.47 ! [X52: expr_r_l_v,Y5: expr_r_l_v] :
% 0.31/0.47 ( ( ( read_r_l_v @ X52 )
% 0.31/0.47 = ( read_r_l_v @ Y5 ) )
% 0.31/0.47 = ( X52 = Y5 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.inject(5)
% 0.31/0.47 thf(fact_332_option_Ocollapse,axiom,
% 0.31/0.47 ! [Option: option1457017436_r_l_v] :
% 0.31/0.47 ( ( Option != none_P277133687_r_l_v )
% 0.31/0.47 => ( ( some_P1807977723_r_l_v @ ( the_Pr1541010602_r_l_v @ Option ) )
% 0.31/0.47 = Option ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.collapse
% 0.31/0.47 thf(fact_333_option_Ocollapse,axiom,
% 0.31/0.47 ! [Option: option_val_r_l_v] :
% 0.31/0.47 ( ( Option != none_val_r_l_v )
% 0.31/0.47 => ( ( some_val_r_l_v @ ( the_val_r_l_v @ Option ) )
% 0.31/0.47 = Option ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.collapse
% 0.31/0.47 thf(fact_334_get__deterministic,axiom,
% 0.31/0.47 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,L: l,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( read_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 0.31/0.47 = ( ( member_l @ L @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau ) ) )
% 0.31/0.47 & ( S2
% 0.31/0.47 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( the_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau @ L ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % get_deterministic
% 0.31/0.47 thf(fact_335_expr_Odistinct_I37_J,axiom,
% 0.31/0.47 ! [X4: expr_r_l_v,X52: expr_r_l_v] :
% 0.31/0.47 ( ( ref_r_l_v @ X4 )
% 0.31/0.47 != ( read_r_l_v @ X52 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(37)
% 0.31/0.47 thf(fact_336_option_Oexpand,axiom,
% 0.31/0.47 ! [Option: option_val_r_l_v,Option2: option_val_r_l_v] :
% 0.31/0.47 ( ( ( Option = none_val_r_l_v )
% 0.31/0.47 = ( Option2 = none_val_r_l_v ) )
% 0.31/0.47 => ( ( ( Option != none_val_r_l_v )
% 0.31/0.47 => ( ( Option2 != none_val_r_l_v )
% 0.31/0.47 => ( ( the_val_r_l_v @ Option )
% 0.31/0.47 = ( the_val_r_l_v @ Option2 ) ) ) )
% 0.31/0.47 => ( Option = Option2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.expand
% 0.31/0.47 thf(fact_337_option_Oexpand,axiom,
% 0.31/0.47 ! [Option: option1457017436_r_l_v,Option2: option1457017436_r_l_v] :
% 0.31/0.47 ( ( ( Option = none_P277133687_r_l_v )
% 0.31/0.47 = ( Option2 = none_P277133687_r_l_v ) )
% 0.31/0.47 => ( ( ( Option != none_P277133687_r_l_v )
% 0.31/0.47 => ( ( Option2 != none_P277133687_r_l_v )
% 0.31/0.47 => ( ( the_Pr1541010602_r_l_v @ Option )
% 0.31/0.47 = ( the_Pr1541010602_r_l_v @ Option2 ) ) ) )
% 0.31/0.47 => ( Option = Option2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.expand
% 0.31/0.47 thf(fact_338_expr_Odistinct_I47_J,axiom,
% 0.31/0.47 ! [X52: expr_r_l_v,X7: expr_r_l_v] :
% 0.31/0.47 ( ( read_r_l_v @ X52 )
% 0.31/0.47 != ( rfork_r_l_v @ X7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(47)
% 0.31/0.47 thf(fact_339_expr_Odistinct_I49_J,axiom,
% 0.31/0.47 ! [X52: expr_r_l_v,X8: expr_r_l_v] :
% 0.31/0.47 ( ( read_r_l_v @ X52 )
% 0.31/0.47 != ( rjoin_r_l_v @ X8 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(49)
% 0.31/0.47 thf(fact_340_expr_Odistinct_I7_J,axiom,
% 0.31/0.47 ! [X1: val_r_l_v,X52: expr_r_l_v] :
% 0.31/0.47 ( ( vE_r_l_v @ X1 )
% 0.31/0.47 != ( read_r_l_v @ X52 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(7)
% 0.31/0.47 thf(fact_341_expr_Odistinct_I29_J,axiom,
% 0.31/0.47 ! [X31: expr_r_l_v,X32: expr_r_l_v,X33: expr_r_l_v,X52: expr_r_l_v] :
% 0.31/0.47 ( ( ite_r_l_v @ X31 @ X32 @ X33 )
% 0.31/0.47 != ( read_r_l_v @ X52 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(29)
% 0.31/0.47 thf(fact_342_expr_Odistinct_I45_J,axiom,
% 0.31/0.47 ! [X52: expr_r_l_v,X61: expr_r_l_v,X62: expr_r_l_v] :
% 0.31/0.47 ( ( read_r_l_v @ X52 )
% 0.31/0.47 != ( assign_r_l_v @ X61 @ X62 ) ) ).
% 0.31/0.47
% 0.31/0.47 % expr.distinct(45)
% 0.31/0.47 thf(fact_343_option_Oexhaust__sel,axiom,
% 0.31/0.47 ! [Option: option1457017436_r_l_v] :
% 0.31/0.47 ( ( Option != none_P277133687_r_l_v )
% 0.31/0.47 => ( Option
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( the_Pr1541010602_r_l_v @ Option ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.exhaust_sel
% 0.31/0.47 thf(fact_344_option_Oexhaust__sel,axiom,
% 0.31/0.47 ! [Option: option_val_r_l_v] :
% 0.31/0.47 ( ( Option != none_val_r_l_v )
% 0.31/0.47 => ( Option
% 0.31/0.47 = ( some_val_r_l_v @ ( the_val_r_l_v @ Option ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % option.exhaust_sel
% 0.31/0.47 thf(fact_345_option_Osel,axiom,
% 0.31/0.47 ! [X22: produc1156025366_r_l_v] :
% 0.31/0.47 ( ( the_Pr1541010602_r_l_v @ ( some_P1807977723_r_l_v @ X22 ) )
% 0.31/0.47 = X22 ) ).
% 0.31/0.47
% 0.31/0.47 % option.sel
% 0.31/0.47 thf(fact_346_option_Osel,axiom,
% 0.31/0.47 ! [X22: val_r_l_v] :
% 0.31/0.47 ( ( the_val_r_l_v @ ( some_val_r_l_v @ X22 ) )
% 0.31/0.47 = X22 ) ).
% 0.31/0.47
% 0.31/0.47 % option.sel
% 0.31/0.47 thf(fact_347_RID_092_060_094sub_062GE,axiom,
% 0.31/0.47 ! [R: r,S: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( member_r @ R @ ( rID_G_r_l_v @ S ) )
% 0.31/0.47 => ( ~ ( member_r @ R @ ( dom_r_259548057_r_l_v @ S ) )
% 0.31/0.47 => ~ ! [R8: r,Ls3: produc1156025366_r_l_v] :
% 0.31/0.47 ( ( ( S @ R8 )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ Ls3 ) )
% 0.31/0.47 => ~ ( member_r @ R @ ( rID_L_l_r_v @ Ls3 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % RID\<^sub>GE
% 0.31/0.47 thf(fact_348_substitution_O_092_060S_062_092_060_094sub_062G__imp___092_060A_062__refl,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( domain1547879849_r_l_v @ S )
% 0.31/0.47 => ( ( member_r @ R @ ( dom_r_259548057_r_l_v @ S ) )
% 0.31/0.47 => ( subsum148050133_r_l_v @ R @ R @ S ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.\<S>\<^sub>G_imp_\<A>_refl
% 0.31/0.47 thf(fact_349_substitution_Osubsumes__accessible__globally__def,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( subsum680764357_r_l_v @ S )
% 0.31/0.47 = ( ! [R_12: r,R_22: r] :
% 0.31/0.47 ( ( member_r @ R_12 @ ( dom_r_259548057_r_l_v @ S ) )
% 0.31/0.47 => ( ( member_r @ R_22 @ ( dom_r_259548057_r_l_v @ S ) )
% 0.31/0.47 => ( subsum148050133_r_l_v @ R_12 @ R_22 @ S ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.subsumes_accessible_globally_def
% 0.31/0.47 thf(fact_350_substitution_Orevision__step__relaxed_Oget,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,L: l] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( read_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) ) ) ) ) ) )
% 0.31/0.47 => ( revisi1291188644_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( the_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau @ L ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step_relaxed.get
% 0.31/0.47 thf(fact_351_substitution_Oget__deterministic,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,L: l,S2: r > option1457017436_r_l_v] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( read_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 0.31/0.47 = ( ( member_l @ L @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau ) ) )
% 0.31/0.47 & ( S2
% 0.31/0.47 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( the_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau @ L ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.get_deterministic
% 0.31/0.47 thf(fact_352_substitution_Orevision__step_Oget,axiom,
% 0.31/0.47 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,L: l] :
% 0.31/0.47 ( ( substitution_r_l_v @ Subst )
% 0.31/0.47 => ( ( ( S @ R )
% 0.31/0.47 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( read_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) ) ) ) ) ) )
% 0.31/0.47 => ( ( member_l @ L @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau ) ) )
% 0.31/0.47 => ( revision_step_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( the_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau @ L ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % substitution.revision_step.get
% 0.31/0.47
% 0.31/0.47 % Helper facts (5)
% 0.31/0.47 thf(help_If_2_1_If_001t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_T,axiom,
% 0.31/0.47 ! [X2: option_val_r_l_v,Y: option_val_r_l_v] :
% 0.31/0.47 ( ( if_option_val_r_l_v @ $false @ X2 @ Y )
% 0.31/0.47 = Y ) ).
% 0.31/0.47
% 0.31/0.47 thf(help_If_1_1_If_001t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_T,axiom,
% 0.31/0.47 ! [X2: option_val_r_l_v,Y: option_val_r_l_v] :
% 0.31/0.47 ( ( if_option_val_r_l_v @ $true @ X2 @ Y )
% 0.31/0.47 = X2 ) ).
% 0.31/0.47
% 0.31/0.47 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,
% 0.31/0.47 ! [P: $o] :
% 0.31/0.47 ( ( P = $true )
% 0.31/0.47 | ( P = $false ) ) ).
% 0.31/0.47
% 0.31/0.47 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,
% 0.31/0.47 ! [X2: option1457017436_r_l_v,Y: option1457017436_r_l_v] :
% 0.31/0.47 ( ( if_opt1153928738_r_l_v @ $false @ X2 @ Y )
% 0.31/0.47 = Y ) ).
% 0.31/0.47
% 0.31/0.47 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,
% 0.31/0.47 ! [X2: option1457017436_r_l_v,Y: option1457017436_r_l_v] :
% 0.31/0.47 ( ( if_opt1153928738_r_l_v @ $true @ X2 @ Y )
% 0.31/0.47 = X2 ) ).
% 0.31/0.47
% 0.31/0.47 % Conjectures (1)
% 0.31/0.47 thf(conj_0,conjecture,
% 0.31/0.47 ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r3 @ ( 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 @ r4 ) ) ) ) ) ) ) @ r4
% 0.31/0.47 @ ( some_P1807977723_r_l_v
% 0.31/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
% 0.31/0.47 @ ( produc1834103605_r_l_v
% 0.31/0.47 @ ^ [X: l] : none_val_r_l_v
% 0.31/0.47 @ e2 ) ) ) )
% 0.31/0.47 = ( fun_up709272714_r_l_v
% 0.31/0.47 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( 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 @ r4 ) ) ) ) ) ) ) @ r4
% 0.31/0.47 @ ( some_P1807977723_r_l_v
% 0.31/0.47 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
% 0.31/0.47 @ ( produc1834103605_r_l_v
% 0.31/0.47 @ ^ [X: l] : none_val_r_l_v
% 0.31/0.47 @ e2 ) ) ) )
% 0.31/0.47 @ r2
% 0.31/0.47 @ ( some_P1807977723_r_l_v @ x ) ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 3.03/1.54 ---- Embedded in THF ---
% 3.03/1.54 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.03/1.54 %%% Generated on Tue Feb 24 08:25:05 EST 2026
% 3.03/1.54 %%% using '$$dhol' embedding, version 1.3.0.
% 3.03/1.54 %%% Logic specification used:
% 3.03/1.54 %%% thf(spec, logic, $$dhol).
% 3.03/1.54
% 3.03/1.54 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.bnlJrUVmuy/DTF2DTF7638.p
% See solution above
% 3.03/1.54 ------------------------
% 3.03/1.58 ---- Cleaned THF ---
% 3.03/1.58 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_I_062_Itf__r_Mt__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_J_M_062_Itf__r_Mt__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_J_J_J_J,type,
% 3.03/1.58 set_se888453765_r_l_v: $tType ).
% 3.03/1.58
% 3.03/1.58 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_Itf__r_Mt__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_J_M_062_Itf__r_Mt__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_J_J_J,type,
% 3.03/1.58 set_Pr1409704485_r_l_v: $tType ).
% 3.03/1.58
% 3.03/1.58 thf(ty_n_t__Product____Type__Oprod_I_062_Itf__r_Mt__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_J_M_062_Itf__r_Mt__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_J_J,type,
% 3.03/1.58 produc1389397445_r_l_v: $tType ).
% 3.03/1.58
% 3.03/1.58 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,
% 3.03/1.58 option1457017436_r_l_v: $tType ).
% 3.03/1.58
% 3.03/1.58 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,
% 3.03/1.58 produc1156025366_r_l_v: $tType ).
% 3.03/1.58
% 3.03/1.58 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,
% 3.03/1.58 produc1164766533_r_l_v: $tType ).
% 3.03/1.58
% 3.03/1.58 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Option__Ooption_Itf__r_J_J_J,type,
% 3.03/1.58 set_set_option_r: $tType ).
% 3.03/1.58
% 3.03/1.58 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Option__Ooption_Itf__l_J_J_J,type,
% 3.03/1.58 set_set_option_l: $tType ).
% 3.03/1.58
% 3.03/1.58 thf(ty_n_t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J,type,
% 3.03/1.58 option_val_r_l_v: $tType ).
% 3.03/1.58
% 3.03/1.58 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Set__Oset_Itf__r_J_J_J,type,
% 3.03/1.58 set_set_set_r: $tType ).
% 3.03/1.58
% 3.03/1.58 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Set__Oset_Itf__l_J_J_J,type,
% 3.03/1.58 set_set_set_l: $tType ).
% 3.03/1.58
% 3.03/1.58 thf(ty_n_t__Set__Oset_It__Option__Ooption_Itf__r_J_J,type,
% 3.03/1.58 set_option_r: $tType ).
% 3.03/1.58
% 3.03/1.58 thf(ty_n_t__Set__Oset_It__Option__Ooption_Itf__l_J_J,type,
% 3.03/1.58 set_option_l: $tType ).
% 3.03/1.58
% 3.03/1.58 thf(ty_n_t__Data__Ocntxt_Itf__r_Mtf__l_Mtf__v_J,type,
% 3.03/1.58 cntxt_r_l_v: $tType ).
% 3.03/1.58
% 3.03/1.58 thf(ty_n_t__Set__Oset_It__Set__Oset_Itf__r_J_J,type,
% 3.03/1.58 set_set_r: $tType ).
% 3.03/1.58
% 3.03/1.58 thf(ty_n_t__Set__Oset_It__Set__Oset_Itf__l_J_J,type,
% 3.03/1.58 set_set_l: $tType ).
% 3.03/1.58
% 3.03/1.58 thf(ty_n_t__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J,type,
% 3.03/1.58 expr_r_l_v: $tType ).
% 3.03/1.58
% 3.03/1.58 thf(ty_n_t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,type,
% 3.03/1.58 val_r_l_v: $tType ).
% 3.03/1.58
% 3.03/1.58 thf(ty_n_t__Option__Ooption_Itf__r_J,type,
% 3.03/1.58 option_r: $tType ).
% 3.03/1.58
% 3.03/1.58 thf(ty_n_t__Option__Ooption_Itf__l_J,type,
% 3.03/1.58 option_l: $tType ).
% 3.03/1.58
% 3.03/1.58 thf(ty_n_t__Set__Oset_Itf__r_J,type,
% 3.03/1.58 set_r: $tType ).
% 3.03/1.58
% 3.03/1.58 thf(ty_n_t__Set__Oset_Itf__l_J,type,
% 3.03/1.58 set_l: $tType ).
% 3.03/1.58
% 3.03/1.58 thf(ty_n_t__Data__Oconst,type,
% 3.03/1.58 const: $tType ).
% 3.03/1.58
% 3.03/1.58 thf(ty_n_tf__v,type,
% 3.03/1.58 v: $tType ).
% 3.03/1.58
% 3.03/1.58 thf(ty_n_tf__r,type,
% 3.03/1.58 r: $tType ).
% 3.03/1.58
% 3.03/1.58 thf(ty_n_tf__l,type,
% 3.03/1.58 l: $tType ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Data_Ocombine_001tf__l_001t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,type,
% 3.03/1.58 combine_l_val_r_l_v: ( l > option_val_r_l_v ) > ( l > option_val_r_l_v ) > l > option_val_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Data_Oconst_OF,type,
% 3.03/1.58 f: const ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Data_Oconst_OT,type,
% 3.03/1.58 t: const ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Data_Oconst_OUnit,type,
% 3.03/1.58 unit: const ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Data_Odoms_001tf__l_001tf__r_001tf__v,type,
% 3.03/1.58 doms_l_r_v: produc1156025366_r_l_v > set_l ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Data_Oexpr_OAssign_001tf__r_001tf__l_001tf__v,type,
% 3.03/1.58 assign_r_l_v: expr_r_l_v > expr_r_l_v > expr_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Data_Oexpr_OIte_001tf__r_001tf__l_001tf__v,type,
% 3.03/1.58 ite_r_l_v: expr_r_l_v > expr_r_l_v > expr_r_l_v > expr_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Data_Oexpr_ORead_001tf__r_001tf__l_001tf__v,type,
% 3.03/1.58 read_r_l_v: expr_r_l_v > expr_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Data_Oexpr_ORef_001tf__r_001tf__l_001tf__v,type,
% 3.03/1.58 ref_r_l_v: expr_r_l_v > expr_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Data_Oexpr_ORfork_001tf__r_001tf__l_001tf__v,type,
% 3.03/1.58 rfork_r_l_v: expr_r_l_v > expr_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Data_Oexpr_ORjoin_001tf__r_001tf__l_001tf__v,type,
% 3.03/1.58 rjoin_r_l_v: expr_r_l_v > expr_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Data_Oexpr_OVE_001tf__r_001tf__l_001tf__v,type,
% 3.03/1.58 vE_r_l_v: val_r_l_v > expr_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Data_Oplug_001tf__r_001tf__l_001tf__v,type,
% 3.03/1.58 plug_r_l_v: cntxt_r_l_v > expr_r_l_v > expr_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Data_Oval_OCV_001tf__r_001tf__l_001tf__v,type,
% 3.03/1.58 cV_r_l_v: const > val_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Data_Oval_OLoc_001tf__l_001tf__r_001tf__v,type,
% 3.03/1.58 loc_l_r_v: l > val_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Data_Oval_ORid_001tf__r_001tf__l_001tf__v,type,
% 3.03/1.58 rid_r_l_v: r > val_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Executions_Osubstitution_Oexecution_001tf__r_001tf__l_001tf__v,type,
% 3.03/1.58 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 ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Executions_Osubstitution_Oinductive__invariant_001tf__r_001tf__l_001tf__v,type,
% 3.03/1.58 induct1670415253_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( ( r > option1457017436_r_l_v ) > $o ) > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Executions_Osubstitution_Omaximal__execution_001tf__r_001tf__l_001tf__v,type,
% 3.03/1.58 maxima311842975_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 ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Executions_Osubstitution_Oreachable_001tf__r_001tf__l_001tf__v,type,
% 3.03/1.58 reachable_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Executions_Osubstitution_Osteps_001tf__r_001tf__l_001tf__v,type,
% 3.03/1.58 steps_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > set_Pr1409704485_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Executions_Osubstitution_Oterminates__in_001tf__r_001tf__l_001tf__v,type,
% 3.03/1.58 terminates_in_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 ) > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_Itf__l_J,type,
% 3.03/1.58 finite2114249848tion_l: set_option_l > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_Itf__r_J,type,
% 3.03/1.58 finite16335230tion_r: set_option_r > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_I_062_Itf__r_Mt__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_J_M_062_Itf__r_Mt__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_J_J,type,
% 3.03/1.58 finite1853159534_r_l_v: set_Pr1409704485_r_l_v > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Option__Ooption_Itf__l_J_J,type,
% 3.03/1.58 finite1182752216tion_l: set_set_option_l > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Option__Ooption_Itf__r_J_J,type,
% 3.03/1.58 finite1577687006tion_r: set_set_option_r > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Product____Type__Oprod_I_062_Itf__r_Mt__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_J_M_062_Itf__r_Mt__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_J_J_J,type,
% 3.03/1.58 finite1619243214_r_l_v: set_se888453765_r_l_v > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Set__Oset_Itf__l_J_J,type,
% 3.03/1.58 finite1256628466_set_l: set_set_set_l > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Set__Oset_Itf__r_J_J,type,
% 3.03/1.58 finite1651563256_set_r: set_set_set_r > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_Itf__l_J,type,
% 3.03/1.58 finite_finite_set_l: set_set_l > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_Itf__r_J,type,
% 3.03/1.58 finite_finite_set_r: set_set_r > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Finite__Set_Ofinite_001tf__l,type,
% 3.03/1.58 finite_finite_l: set_l > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Finite__Set_Ofinite_001tf__r,type,
% 3.03/1.58 finite_finite_r: set_r > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Fun_Ofun__upd_001tf__l_001t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J,type,
% 3.03/1.58 fun_up1835647912_r_l_v: ( l > option_val_r_l_v ) > l > option_val_r_l_v > l > option_val_r_l_v ).
% 3.03/1.58
% 3.03/1.58 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,
% 3.03/1.58 fun_up709272714_r_l_v: ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v > r > option1457017436_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_If_001t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J,type,
% 3.03/1.58 if_option_val_r_l_v: $o > option_val_r_l_v > option_val_r_l_v > option_val_r_l_v ).
% 3.03/1.58
% 3.03/1.58 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,
% 3.03/1.58 if_opt1153928738_r_l_v: $o > option1457017436_r_l_v > option1457017436_r_l_v > option1457017436_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Map_Odom_001t__Product____Type__Oprod_I_062_Itf__r_Mt__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_J_M_062_Itf__r_Mt__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_J_J_001t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,type,
% 3.03/1.58 dom_Pr939617279_r_l_v: ( produc1389397445_r_l_v > option_val_r_l_v ) > set_Pr1409704485_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Map_Odom_001t__Product____Type__Oprod_I_062_Itf__r_Mt__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_J_M_062_Itf__r_Mt__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_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__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,
% 3.03/1.58 dom_Pr1162080227_r_l_v: ( produc1389397445_r_l_v > option1457017436_r_l_v ) > set_Pr1409704485_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Map_Odom_001tf__l_001t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,type,
% 3.03/1.58 dom_l_val_r_l_v: ( l > option_val_r_l_v ) > set_l ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Map_Odom_001tf__l_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,
% 3.03/1.58 dom_l_45837855_r_l_v: ( l > option1457017436_r_l_v ) > set_l ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Map_Odom_001tf__r_001t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,type,
% 3.03/1.58 dom_r_val_r_l_v: ( r > option_val_r_l_v ) > set_r ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Map_Odom_001tf__r_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,
% 3.03/1.58 dom_r_259548057_r_l_v: ( r > option1457017436_r_l_v ) > set_r ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Occurrences_OLID_092_060_094sub_062G_001tf__r_001tf__l_001tf__v,type,
% 3.03/1.58 lID_G_r_l_v: ( r > option1457017436_r_l_v ) > set_l ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Occurrences_OLID_092_060_094sub_062L_001tf__l_001tf__r_001tf__v,type,
% 3.03/1.58 lID_L_l_r_v: produc1156025366_r_l_v > set_l ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Occurrences_ORID_092_060_094sub_062G_001tf__r_001tf__l_001tf__v,type,
% 3.03/1.58 rID_G_r_l_v: ( r > option1457017436_r_l_v ) > set_r ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Occurrences_ORID_092_060_094sub_062L_001tf__l_001tf__r_001tf__v,type,
% 3.03/1.58 rID_L_l_r_v: produc1156025366_r_l_v > set_r ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_OperationalSemantics_Osubstitution_Odomains__subsume_001tf__l_001tf__r_001tf__v,type,
% 3.03/1.58 domain87684397_l_r_v: produc1156025366_r_l_v > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_OperationalSemantics_Osubstitution_Odomains__subsume__globally_001tf__r_001tf__l_001tf__v,type,
% 3.03/1.58 domain1547879849_r_l_v: ( r > option1457017436_r_l_v ) > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_OperationalSemantics_Osubstitution_Orevision__step_001tf__r_001tf__l_001tf__v,type,
% 3.03/1.58 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 ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_OperationalSemantics_Osubstitution_Orevision__step__relaxed_001tf__r_001tf__l_001tf__v,type,
% 3.03/1.58 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 ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_OperationalSemantics_Osubstitution_Osubsumes__accessible_001tf__r_001tf__l_001tf__v,type,
% 3.03/1.58 subsum148050133_r_l_v: r > r > ( r > option1457017436_r_l_v ) > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_OperationalSemantics_Osubstitution_Osubsumes__accessible__globally_001tf__r_001tf__l_001tf__v,type,
% 3.03/1.58 subsum680764357_r_l_v: ( r > option1457017436_r_l_v ) > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Option_Ooption_ONone_001t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,type,
% 3.03/1.58 none_val_r_l_v: option_val_r_l_v ).
% 3.03/1.58
% 3.03/1.58 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,
% 3.03/1.58 none_P277133687_r_l_v: option1457017436_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Option_Ooption_OSome_001t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,type,
% 3.03/1.58 some_val_r_l_v: val_r_l_v > option_val_r_l_v ).
% 3.03/1.58
% 3.03/1.58 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,
% 3.03/1.58 some_P1807977723_r_l_v: produc1156025366_r_l_v > option1457017436_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Option_Ooption_Othe_001t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,type,
% 3.03/1.58 the_val_r_l_v: option_val_r_l_v > val_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Option_Ooption_Othe_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,
% 3.03/1.58 the_Pr1541010602_r_l_v: option1457017436_r_l_v > produc1156025366_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Option__Ooption_Itf__l_J_J,type,
% 3.03/1.58 ord_le1506375887tion_l: set_option_l > set_option_l > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Option__Ooption_Itf__r_J_J,type,
% 3.03/1.58 ord_le1901310677tion_r: set_option_r > set_option_r > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_062_Itf__r_Mt__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_J_M_062_Itf__r_Mt__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_J_J_J,type,
% 3.03/1.58 ord_le803113413_r_l_v: set_Pr1409704485_r_l_v > set_Pr1409704485_r_l_v > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_Itf__l_J_J,type,
% 3.03/1.58 ord_le2116509289_set_l: set_set_l > set_set_l > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_Itf__r_J_J,type,
% 3.03/1.58 ord_le363960431_set_r: set_set_r > set_set_r > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__l_J,type,
% 3.03/1.58 ord_less_eq_set_l: set_l > set_l > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__r_J,type,
% 3.03/1.58 ord_less_eq_set_r: set_r > set_r > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_Itf__l_J_J,type,
% 3.03/1.58 top_top_set_option_l: set_option_l ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_Itf__r_J_J,type,
% 3.03/1.58 top_top_set_option_r: set_option_r ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__l_J,type,
% 3.03/1.58 top_top_set_l: set_l ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__r_J,type,
% 3.03/1.58 top_top_set_r: set_r ).
% 3.03/1.58
% 3.03/1.58 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,
% 3.03/1.58 produc1834103605_r_l_v: ( l > option_val_r_l_v ) > expr_r_l_v > produc1164766533_r_l_v ).
% 3.03/1.58
% 3.03/1.58 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,
% 3.03/1.58 produc297528454_r_l_v: ( l > option_val_r_l_v ) > produc1164766533_r_l_v > produc1156025366_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Product__Type_OPair_001_062_Itf__r_Mt__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_J_001_062_Itf__r_Mt__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_J,type,
% 3.03/1.58 produc1175464189_r_l_v: ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > produc1389397445_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Renaming_Oeq__states_001tf__r_001tf__l_001tf__v,type,
% 3.03/1.58 eq_states_r_l_v: ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Set_OCollect_001t__Option__Ooption_Itf__l_J,type,
% 3.03/1.58 collect_option_l: ( option_l > $o ) > set_option_l ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Set_OCollect_001t__Option__Ooption_Itf__r_J,type,
% 3.03/1.58 collect_option_r: ( option_r > $o ) > set_option_r ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_I_062_Itf__r_Mt__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_J_M_062_Itf__r_Mt__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_J_J,type,
% 3.03/1.58 collec1978425008_r_l_v: ( produc1389397445_r_l_v > $o ) > set_Pr1409704485_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Option__Ooption_Itf__l_J_J,type,
% 3.03/1.58 collect_set_option_l: ( set_option_l > $o ) > set_set_option_l ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Option__Ooption_Itf__r_J_J,type,
% 3.03/1.58 collect_set_option_r: ( set_option_r > $o ) > set_set_option_r ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Product____Type__Oprod_I_062_Itf__r_Mt__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_J_M_062_Itf__r_Mt__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_J_J_J,type,
% 3.03/1.58 collec330370832_r_l_v: ( set_Pr1409704485_r_l_v > $o ) > set_se888453765_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Set__Oset_Itf__l_J_J,type,
% 3.03/1.58 collect_set_set_l: ( set_set_l > $o ) > set_set_set_l ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Set__Oset_Itf__r_J_J,type,
% 3.03/1.58 collect_set_set_r: ( set_set_r > $o ) > set_set_set_r ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Set_OCollect_001t__Set__Oset_Itf__l_J,type,
% 3.03/1.58 collect_set_l: ( set_l > $o ) > set_set_l ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Set_OCollect_001t__Set__Oset_Itf__r_J,type,
% 3.03/1.58 collect_set_r: ( set_r > $o ) > set_set_r ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Set_OCollect_001tf__l,type,
% 3.03/1.58 collect_l: ( l > $o ) > set_l ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Set_OCollect_001tf__r,type,
% 3.03/1.58 collect_r: ( r > $o ) > set_r ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Substitution_Osubstitution_001tf__r_001tf__l_001tf__v,type,
% 3.03/1.58 substitution_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_Transitive__Closure_Ortrancl_001_062_Itf__r_Mt__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_J,type,
% 3.03/1.58 transi1323086383_r_l_v: set_Pr1409704485_r_l_v > set_Pr1409704485_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_member_001t__Option__Ooption_Itf__l_J,type,
% 3.03/1.58 member_option_l: option_l > set_option_l > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_member_001t__Option__Ooption_Itf__r_J,type,
% 3.03/1.58 member_option_r: option_r > set_option_r > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_member_001t__Product____Type__Oprod_I_062_Itf__r_Mt__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_J_M_062_Itf__r_Mt__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_J_J,type,
% 3.03/1.58 member1522896238_r_l_v: produc1389397445_r_l_v > set_Pr1409704485_r_l_v > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_member_001t__Set__Oset_Itf__l_J,type,
% 3.03/1.58 member_set_l: set_l > set_set_l > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_member_001t__Set__Oset_Itf__r_J,type,
% 3.03/1.58 member_set_r: set_r > set_set_r > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_member_001tf__l,type,
% 3.03/1.58 member_l: l > set_l > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_c_member_001tf__r,type,
% 3.03/1.58 member_r: r > set_r > $o ).
% 3.03/1.58
% 3.03/1.58 thf(sy_v__092_060E_062,type,
% 3.03/1.58 e: cntxt_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_v__092_060sigma_062,type,
% 3.03/1.58 sigma: l > option_val_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_v__092_060tau_062,type,
% 3.03/1.58 tau: l > option_val_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_v_e,type,
% 3.03/1.58 e2: expr_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_v_r,type,
% 3.03/1.58 r2: r ).
% 3.03/1.58
% 3.03/1.58 thf(sy_v_r_H,type,
% 3.03/1.58 r3: r ).
% 3.03/1.58
% 3.03/1.58 thf(sy_v_r_H_H,type,
% 3.03/1.58 r4: r ).
% 3.03/1.58
% 3.03/1.58 thf(sy_v_s_092_060_094sub_0621,type,
% 3.03/1.58 s_1: r > option1457017436_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_v_s_092_060_094sub_0622,type,
% 3.03/1.58 s_2: r > option1457017436_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_v_s_092_060_094sub_0622_H,type,
% 3.03/1.58 s_22: r > option1457017436_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_v_subst,type,
% 3.03/1.58 subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(sy_v_x,type,
% 3.03/1.58 x: produc1156025366_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(fact_0_assms_I4_J,axiom,
% 3.03/1.58 ~ ( member_r @ r4 @ ( rID_G_r_l_v @ s_2 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_1_assms_I7_J,axiom,
% 3.03/1.58 r2 != r4 ).
% 3.03/1.58
% 3.03/1.58 thf(fact_2_assms_I6_J,axiom,
% 3.03/1.58 r2 != r3 ).
% 3.03/1.58
% 3.03/1.58 thf(fact_3_assms_I1_J,axiom,
% 3.03/1.58 ( s_2
% 3.03/1.58 = ( fun_up709272714_r_l_v @ s_1 @ r2 @ ( some_P1807977723_r_l_v @ x ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_4_assms_I3_J,axiom,
% 3.03/1.58 ( ( s_2 @ r3 )
% 3.03/1.58 = ( 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 ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_5_assms_I2_J,axiom,
% 3.03/1.58 ( s_22
% 3.03/1.58 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( 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 @ r4 ) ) ) ) ) ) ) @ r4
% 3.03/1.58 @ ( some_P1807977723_r_l_v
% 3.03/1.58 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
% 3.03/1.58 @ ( produc1834103605_r_l_v
% 3.03/1.58 @ ^ [X: l] : none_val_r_l_v
% 3.03/1.58 @ e2 ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_6_revision__step_Ofork,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E2: expr_r_l_v,R2: r] :
% 3.03/1.58 ( ( ( S @ R )
% 3.03/1.58 = ( 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 ) ) ) ) ) )
% 3.03/1.58 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 3.03/1.58 => ( revision_step_r_l_v @ subst @ R @ S
% 3.03/1.58 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( 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 @ R2 ) ) ) ) ) ) ) @ R2
% 3.03/1.58 @ ( some_P1807977723_r_l_v
% 3.03/1.58 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau )
% 3.03/1.58 @ ( produc1834103605_r_l_v
% 3.03/1.58 @ ^ [X: l] : none_val_r_l_v
% 3.03/1.58 @ E2 ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_7_assms_I5_J,axiom,
% 3.03/1.58 ( revision_step_r_l_v @ subst @ r2 @ s_22
% 3.03/1.58 @ ( fun_up709272714_r_l_v
% 3.03/1.58 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( 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 @ r4 ) ) ) ) ) ) ) @ r4
% 3.03/1.58 @ ( some_P1807977723_r_l_v
% 3.03/1.58 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
% 3.03/1.58 @ ( produc1834103605_r_l_v
% 3.03/1.58 @ ^ [X: l] : none_val_r_l_v
% 3.03/1.58 @ e2 ) ) ) )
% 3.03/1.58 @ r2
% 3.03/1.58 @ ( some_P1807977723_r_l_v @ x ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_8_restrictions__inwards,axiom,
% 3.03/1.58 ! [X2: r,X3: r,F: r > option1457017436_r_l_v,Y: produc1156025366_r_l_v] :
% 3.03/1.58 ( ( X2 != X3 )
% 3.03/1.58 => ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ F @ X2 @ ( some_P1807977723_r_l_v @ Y ) ) @ X3 @ none_P277133687_r_l_v )
% 3.03/1.58 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ F @ X3 @ none_P277133687_r_l_v ) @ X2 @ ( some_P1807977723_r_l_v @ Y ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_9_restrictions__inwards,axiom,
% 3.03/1.58 ! [X2: l,X3: l,F: l > option_val_r_l_v,Y: val_r_l_v] :
% 3.03/1.58 ( ( X2 != X3 )
% 3.03/1.58 => ( ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ F @ X2 @ ( some_val_r_l_v @ Y ) ) @ X3 @ none_val_r_l_v )
% 3.03/1.58 = ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ F @ X3 @ none_val_r_l_v ) @ X2 @ ( some_val_r_l_v @ Y ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_10_empty__upd__none,axiom,
% 3.03/1.58 ! [X2: l] :
% 3.03/1.58 ( ( fun_up1835647912_r_l_v
% 3.03/1.58 @ ^ [X: l] : none_val_r_l_v
% 3.03/1.58 @ X2
% 3.03/1.58 @ none_val_r_l_v )
% 3.03/1.58 = ( ^ [X: l] : none_val_r_l_v ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_11_empty__upd__none,axiom,
% 3.03/1.58 ! [X2: r] :
% 3.03/1.58 ( ( fun_up709272714_r_l_v
% 3.03/1.58 @ ^ [X: r] : none_P277133687_r_l_v
% 3.03/1.58 @ X2
% 3.03/1.58 @ none_P277133687_r_l_v )
% 3.03/1.58 = ( ^ [X: r] : none_P277133687_r_l_v ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_12_not__None__eq,axiom,
% 3.03/1.58 ! [X2: option1457017436_r_l_v] :
% 3.03/1.58 ( ( X2 != none_P277133687_r_l_v )
% 3.03/1.58 = ( ? [Y2: produc1156025366_r_l_v] :
% 3.03/1.58 ( X2
% 3.03/1.58 = ( some_P1807977723_r_l_v @ Y2 ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_13_not__None__eq,axiom,
% 3.03/1.58 ! [X2: option_val_r_l_v] :
% 3.03/1.58 ( ( X2 != none_val_r_l_v )
% 3.03/1.58 = ( ? [Y2: val_r_l_v] :
% 3.03/1.58 ( X2
% 3.03/1.58 = ( some_val_r_l_v @ Y2 ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_14_not__Some__eq,axiom,
% 3.03/1.58 ! [X2: option1457017436_r_l_v] :
% 3.03/1.58 ( ( ! [Y2: produc1156025366_r_l_v] :
% 3.03/1.58 ( X2
% 3.03/1.58 != ( some_P1807977723_r_l_v @ Y2 ) ) )
% 3.03/1.58 = ( X2 = none_P277133687_r_l_v ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_15_not__Some__eq,axiom,
% 3.03/1.58 ! [X2: option_val_r_l_v] :
% 3.03/1.58 ( ( ! [Y2: val_r_l_v] :
% 3.03/1.58 ( X2
% 3.03/1.58 != ( some_val_r_l_v @ Y2 ) ) )
% 3.03/1.58 = ( X2 = none_val_r_l_v ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_16_map__upd__nonempty,axiom,
% 3.03/1.58 ! [T: r > option1457017436_r_l_v,K: r,X2: produc1156025366_r_l_v] :
% 3.03/1.58 ( ( fun_up709272714_r_l_v @ T @ K @ ( some_P1807977723_r_l_v @ X2 ) )
% 3.03/1.58 != ( ^ [X: r] : none_P277133687_r_l_v ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_17_map__upd__nonempty,axiom,
% 3.03/1.58 ! [T: l > option_val_r_l_v,K: l,X2: val_r_l_v] :
% 3.03/1.58 ( ( fun_up1835647912_r_l_v @ T @ K @ ( some_val_r_l_v @ X2 ) )
% 3.03/1.58 != ( ^ [X: l] : none_val_r_l_v ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_18_fork__pseudodeterministic,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E2: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( ( S @ R )
% 3.03/1.58 = ( 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 ) ) ) ) ) )
% 3.03/1.58 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.03/1.58 = ( ? [R3: r] :
% 3.03/1.58 ( ~ ( member_r @ R3 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( 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 ) ) ) ) ) ) ) )
% 3.03/1.58 & ( S2
% 3.03/1.58 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( 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
% 3.03/1.58 @ ( some_P1807977723_r_l_v
% 3.03/1.58 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau )
% 3.03/1.58 @ ( produc1834103605_r_l_v
% 3.03/1.58 @ ^ [X: l] : none_val_r_l_v
% 3.03/1.58 @ E2 ) ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_19_revision__step__relaxed_Ofork,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E2: expr_r_l_v,R2: r] :
% 3.03/1.58 ( ( ( S @ R )
% 3.03/1.58 = ( 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 ) ) ) ) ) )
% 3.03/1.58 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 3.03/1.58 => ( revisi1291188644_r_l_v @ subst @ R @ S
% 3.03/1.58 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( 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 @ R2 ) ) ) ) ) ) ) @ R2
% 3.03/1.58 @ ( some_P1807977723_r_l_v
% 3.03/1.58 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau )
% 3.03/1.58 @ ( produc1834103605_r_l_v
% 3.03/1.58 @ ^ [X: l] : none_val_r_l_v
% 3.03/1.58 @ E2 ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_20_val_Oinject_I4_J,axiom,
% 3.03/1.58 ! [X4: r,Y4: r] :
% 3.03/1.58 ( ( ( rid_r_l_v @ X4 )
% 3.03/1.58 = ( rid_r_l_v @ Y4 ) )
% 3.03/1.58 = ( X4 = Y4 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_21_injective__cntxt,axiom,
% 3.03/1.58 ! [E: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 3.03/1.58 ( ( ( plug_r_l_v @ E @ E1 )
% 3.03/1.58 = ( plug_r_l_v @ E @ E22 ) )
% 3.03/1.58 = ( E1 = E22 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_22_expr_Oinject_I1_J,axiom,
% 3.03/1.58 ! [X1: val_r_l_v,Y1: val_r_l_v] :
% 3.03/1.58 ( ( ( vE_r_l_v @ X1 )
% 3.03/1.58 = ( vE_r_l_v @ Y1 ) )
% 3.03/1.58 = ( X1 = Y1 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_23_fun__upd__upd,axiom,
% 3.03/1.58 ! [F: r > option1457017436_r_l_v,X2: r,Y: option1457017436_r_l_v,Z: option1457017436_r_l_v] :
% 3.03/1.58 ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ F @ X2 @ Y ) @ X2 @ Z )
% 3.03/1.58 = ( fun_up709272714_r_l_v @ F @ X2 @ Z ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_24_fun__upd__upd,axiom,
% 3.03/1.58 ! [F: l > option_val_r_l_v,X2: l,Y: option_val_r_l_v,Z: option_val_r_l_v] :
% 3.03/1.58 ( ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ F @ X2 @ Y ) @ X2 @ Z )
% 3.03/1.58 = ( fun_up1835647912_r_l_v @ F @ X2 @ Z ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_25_fun__upd__triv,axiom,
% 3.03/1.58 ! [F: r > option1457017436_r_l_v,X2: r] :
% 3.03/1.58 ( ( fun_up709272714_r_l_v @ F @ X2 @ ( F @ X2 ) )
% 3.03/1.58 = F ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_26_fun__upd__triv,axiom,
% 3.03/1.58 ! [F: l > option_val_r_l_v,X2: l] :
% 3.03/1.58 ( ( fun_up1835647912_r_l_v @ F @ X2 @ ( F @ X2 ) )
% 3.03/1.58 = F ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_27_option_Oinject,axiom,
% 3.03/1.58 ! [X22: produc1156025366_r_l_v,Y22: produc1156025366_r_l_v] :
% 3.03/1.58 ( ( ( some_P1807977723_r_l_v @ X22 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ Y22 ) )
% 3.03/1.58 = ( X22 = Y22 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_28_option_Oinject,axiom,
% 3.03/1.58 ! [X22: val_r_l_v,Y22: val_r_l_v] :
% 3.03/1.58 ( ( ( some_val_r_l_v @ X22 )
% 3.03/1.58 = ( some_val_r_l_v @ Y22 ) )
% 3.03/1.58 = ( X22 = Y22 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_29_fun__upd__apply,axiom,
% 3.03/1.58 ( fun_up709272714_r_l_v
% 3.03/1.58 = ( ^ [F2: r > option1457017436_r_l_v,X: r,Y2: option1457017436_r_l_v,Z2: r] : ( if_opt1153928738_r_l_v @ ( Z2 = X ) @ Y2 @ ( F2 @ Z2 ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_30_fun__upd__apply,axiom,
% 3.03/1.58 ( fun_up1835647912_r_l_v
% 3.03/1.58 = ( ^ [F2: l > option_val_r_l_v,X: l,Y2: option_val_r_l_v,Z2: l] : ( if_option_val_r_l_v @ ( Z2 = X ) @ Y2 @ ( F2 @ Z2 ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_31_expr_Oinject_I7_J,axiom,
% 3.03/1.58 ! [X7: expr_r_l_v,Y7: expr_r_l_v] :
% 3.03/1.58 ( ( ( rfork_r_l_v @ X7 )
% 3.03/1.58 = ( rfork_r_l_v @ Y7 ) )
% 3.03/1.58 = ( X7 = Y7 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_32_RID_092_060_094sub_062GI_I1_J,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r,V: produc1156025366_r_l_v] :
% 3.03/1.58 ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ V ) )
% 3.03/1.58 => ( member_r @ R @ ( rID_G_r_l_v @ S ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_33_in__restricted__global__in__unrestricted__global_I1_J,axiom,
% 3.03/1.58 ! [R2: r,S: r > option1457017436_r_l_v,R: r] :
% 3.03/1.58 ( ( member_r @ R2 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 3.03/1.58 => ( member_r @ R2 @ ( rID_G_r_l_v @ S ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_34_only__fork__introduces__rids_H,axiom,
% 3.03/1.58 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v,R2: r] :
% 3.03/1.58 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.03/1.58 => ( ! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E4: expr_r_l_v] :
% 3.03/1.58 ( ( S @ R )
% 3.03/1.58 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 3.03/1.58 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 3.03/1.58 => ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S2 ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_35_in__restricted__global__in__updated__global_I1_J,axiom,
% 3.03/1.58 ! [R2: r,S: r > option1457017436_r_l_v,R: r,Ls: produc1156025366_r_l_v] :
% 3.03/1.58 ( ( member_r @ R2 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 3.03/1.58 => ( member_r @ R2 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ Ls ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_36_substitution__axioms,axiom,
% 3.03/1.58 substitution_r_l_v @ subst ).
% 3.03/1.58
% 3.03/1.58 thf(fact_37_expr_Odistinct_I11_J,axiom,
% 3.03/1.58 ! [X1: val_r_l_v,X7: expr_r_l_v] :
% 3.03/1.58 ( ( vE_r_l_v @ X1 )
% 3.03/1.58 != ( rfork_r_l_v @ X7 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_38_fun__upd__idem__iff,axiom,
% 3.03/1.58 ! [F: r > option1457017436_r_l_v,X2: r,Y: option1457017436_r_l_v] :
% 3.03/1.58 ( ( ( fun_up709272714_r_l_v @ F @ X2 @ Y )
% 3.03/1.58 = F )
% 3.03/1.58 = ( ( F @ X2 )
% 3.03/1.58 = Y ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_39_fun__upd__idem__iff,axiom,
% 3.03/1.58 ! [F: l > option_val_r_l_v,X2: l,Y: option_val_r_l_v] :
% 3.03/1.58 ( ( ( fun_up1835647912_r_l_v @ F @ X2 @ Y )
% 3.03/1.58 = F )
% 3.03/1.58 = ( ( F @ X2 )
% 3.03/1.58 = Y ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_40_fun__upd__twist,axiom,
% 3.03/1.58 ! [A: r,C: r,M: r > option1457017436_r_l_v,B: option1457017436_r_l_v,D: option1457017436_r_l_v] :
% 3.03/1.58 ( ( A != C )
% 3.03/1.58 => ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ M @ A @ B ) @ C @ D )
% 3.03/1.58 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ M @ C @ D ) @ A @ B ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_41_fun__upd__twist,axiom,
% 3.03/1.58 ! [A: l,C: l,M: l > option_val_r_l_v,B: option_val_r_l_v,D: option_val_r_l_v] :
% 3.03/1.58 ( ( A != C )
% 3.03/1.58 => ( ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ M @ A @ B ) @ C @ D )
% 3.03/1.58 = ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ M @ C @ D ) @ A @ B ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_42_fun__upd__other,axiom,
% 3.03/1.58 ! [Z: r,X2: r,F: r > option1457017436_r_l_v,Y: option1457017436_r_l_v] :
% 3.03/1.58 ( ( Z != X2 )
% 3.03/1.58 => ( ( fun_up709272714_r_l_v @ F @ X2 @ Y @ Z )
% 3.03/1.58 = ( F @ Z ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_43_fun__upd__other,axiom,
% 3.03/1.58 ! [Z: l,X2: l,F: l > option_val_r_l_v,Y: option_val_r_l_v] :
% 3.03/1.58 ( ( Z != X2 )
% 3.03/1.58 => ( ( fun_up1835647912_r_l_v @ F @ X2 @ Y @ Z )
% 3.03/1.58 = ( F @ Z ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_44_fun__upd__same,axiom,
% 3.03/1.58 ! [F: r > option1457017436_r_l_v,X2: r,Y: option1457017436_r_l_v] :
% 3.03/1.58 ( ( fun_up709272714_r_l_v @ F @ X2 @ Y @ X2 )
% 3.03/1.58 = Y ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_45_fun__upd__same,axiom,
% 3.03/1.58 ! [F: l > option_val_r_l_v,X2: l,Y: option_val_r_l_v] :
% 3.03/1.58 ( ( fun_up1835647912_r_l_v @ F @ X2 @ Y @ X2 )
% 3.03/1.58 = Y ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_46_fun__upd__idem,axiom,
% 3.03/1.58 ! [F: r > option1457017436_r_l_v,X2: r,Y: option1457017436_r_l_v] :
% 3.03/1.58 ( ( ( F @ X2 )
% 3.03/1.58 = Y )
% 3.03/1.58 => ( ( fun_up709272714_r_l_v @ F @ X2 @ Y )
% 3.03/1.58 = F ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_47_fun__upd__idem,axiom,
% 3.03/1.58 ! [F: l > option_val_r_l_v,X2: l,Y: option_val_r_l_v] :
% 3.03/1.58 ( ( ( F @ X2 )
% 3.03/1.58 = Y )
% 3.03/1.58 => ( ( fun_up1835647912_r_l_v @ F @ X2 @ Y )
% 3.03/1.58 = F ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_48_fun__upd__eqD,axiom,
% 3.03/1.58 ! [F: r > option1457017436_r_l_v,X2: r,Y: option1457017436_r_l_v,G: r > option1457017436_r_l_v,Z: option1457017436_r_l_v] :
% 3.03/1.58 ( ( ( fun_up709272714_r_l_v @ F @ X2 @ Y )
% 3.03/1.58 = ( fun_up709272714_r_l_v @ G @ X2 @ Z ) )
% 3.03/1.58 => ( Y = Z ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_49_fun__upd__eqD,axiom,
% 3.03/1.58 ! [F: l > option_val_r_l_v,X2: l,Y: option_val_r_l_v,G: l > option_val_r_l_v,Z: option_val_r_l_v] :
% 3.03/1.58 ( ( ( fun_up1835647912_r_l_v @ F @ X2 @ Y )
% 3.03/1.58 = ( fun_up1835647912_r_l_v @ G @ X2 @ Z ) )
% 3.03/1.58 => ( Y = Z ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_50_fun__upd__def,axiom,
% 3.03/1.58 ( fun_up709272714_r_l_v
% 3.03/1.58 = ( ^ [F2: r > option1457017436_r_l_v,A2: r,B2: option1457017436_r_l_v,X: r] : ( if_opt1153928738_r_l_v @ ( X = A2 ) @ B2 @ ( F2 @ X ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_51_fun__upd__def,axiom,
% 3.03/1.58 ( fun_up1835647912_r_l_v
% 3.03/1.58 = ( ^ [F2: l > option_val_r_l_v,A2: l,B2: option_val_r_l_v,X: l] : ( if_option_val_r_l_v @ ( X = A2 ) @ B2 @ ( F2 @ X ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_52_combine__options__cases,axiom,
% 3.03/1.58 ! [X2: option1457017436_r_l_v,P: option1457017436_r_l_v > option1457017436_r_l_v > $o,Y: option1457017436_r_l_v] :
% 3.03/1.58 ( ( ( X2 = none_P277133687_r_l_v )
% 3.03/1.58 => ( P @ X2 @ Y ) )
% 3.03/1.58 => ( ( ( Y = none_P277133687_r_l_v )
% 3.03/1.58 => ( P @ X2 @ Y ) )
% 3.03/1.58 => ( ! [A3: produc1156025366_r_l_v,B3: produc1156025366_r_l_v] :
% 3.03/1.58 ( ( X2
% 3.03/1.58 = ( some_P1807977723_r_l_v @ A3 ) )
% 3.03/1.58 => ( ( Y
% 3.03/1.58 = ( some_P1807977723_r_l_v @ B3 ) )
% 3.03/1.58 => ( P @ X2 @ Y ) ) )
% 3.03/1.58 => ( P @ X2 @ Y ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_53_combine__options__cases,axiom,
% 3.03/1.58 ! [X2: option1457017436_r_l_v,P: option1457017436_r_l_v > option_val_r_l_v > $o,Y: option_val_r_l_v] :
% 3.03/1.58 ( ( ( X2 = none_P277133687_r_l_v )
% 3.03/1.58 => ( P @ X2 @ Y ) )
% 3.03/1.58 => ( ( ( Y = none_val_r_l_v )
% 3.03/1.58 => ( P @ X2 @ Y ) )
% 3.03/1.58 => ( ! [A3: produc1156025366_r_l_v,B3: val_r_l_v] :
% 3.03/1.58 ( ( X2
% 3.03/1.58 = ( some_P1807977723_r_l_v @ A3 ) )
% 3.03/1.58 => ( ( Y
% 3.03/1.58 = ( some_val_r_l_v @ B3 ) )
% 3.03/1.58 => ( P @ X2 @ Y ) ) )
% 3.03/1.58 => ( P @ X2 @ Y ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_54_combine__options__cases,axiom,
% 3.03/1.58 ! [X2: option_val_r_l_v,P: option_val_r_l_v > option1457017436_r_l_v > $o,Y: option1457017436_r_l_v] :
% 3.03/1.58 ( ( ( X2 = none_val_r_l_v )
% 3.03/1.58 => ( P @ X2 @ Y ) )
% 3.03/1.58 => ( ( ( Y = none_P277133687_r_l_v )
% 3.03/1.58 => ( P @ X2 @ Y ) )
% 3.03/1.58 => ( ! [A3: val_r_l_v,B3: produc1156025366_r_l_v] :
% 3.03/1.58 ( ( X2
% 3.03/1.58 = ( some_val_r_l_v @ A3 ) )
% 3.03/1.58 => ( ( Y
% 3.03/1.58 = ( some_P1807977723_r_l_v @ B3 ) )
% 3.03/1.58 => ( P @ X2 @ Y ) ) )
% 3.03/1.58 => ( P @ X2 @ Y ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_55_combine__options__cases,axiom,
% 3.03/1.58 ! [X2: option_val_r_l_v,P: option_val_r_l_v > option_val_r_l_v > $o,Y: option_val_r_l_v] :
% 3.03/1.58 ( ( ( X2 = none_val_r_l_v )
% 3.03/1.58 => ( P @ X2 @ Y ) )
% 3.03/1.58 => ( ( ( Y = none_val_r_l_v )
% 3.03/1.58 => ( P @ X2 @ Y ) )
% 3.03/1.58 => ( ! [A3: val_r_l_v,B3: val_r_l_v] :
% 3.03/1.58 ( ( X2
% 3.03/1.58 = ( some_val_r_l_v @ A3 ) )
% 3.03/1.58 => ( ( Y
% 3.03/1.58 = ( some_val_r_l_v @ B3 ) )
% 3.03/1.58 => ( P @ X2 @ Y ) ) )
% 3.03/1.58 => ( P @ X2 @ Y ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_56_split__option__all,axiom,
% 3.03/1.58 ( ( ^ [P2: option1457017436_r_l_v > $o] :
% 3.03/1.58 ! [X5: option1457017436_r_l_v] : ( P2 @ X5 ) )
% 3.03/1.58 = ( ^ [P3: option1457017436_r_l_v > $o] :
% 3.03/1.58 ( ( P3 @ none_P277133687_r_l_v )
% 3.03/1.58 & ! [X: produc1156025366_r_l_v] : ( P3 @ ( some_P1807977723_r_l_v @ X ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_57_split__option__all,axiom,
% 3.03/1.58 ( ( ^ [P2: option_val_r_l_v > $o] :
% 3.03/1.58 ! [X5: option_val_r_l_v] : ( P2 @ X5 ) )
% 3.03/1.58 = ( ^ [P3: option_val_r_l_v > $o] :
% 3.03/1.58 ( ( P3 @ none_val_r_l_v )
% 3.03/1.58 & ! [X: val_r_l_v] : ( P3 @ ( some_val_r_l_v @ X ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_58_split__option__ex,axiom,
% 3.03/1.58 ( ( ^ [P2: option1457017436_r_l_v > $o] :
% 3.03/1.58 ? [X5: option1457017436_r_l_v] : ( P2 @ X5 ) )
% 3.03/1.58 = ( ^ [P3: option1457017436_r_l_v > $o] :
% 3.03/1.58 ( ( P3 @ none_P277133687_r_l_v )
% 3.03/1.58 | ? [X: produc1156025366_r_l_v] : ( P3 @ ( some_P1807977723_r_l_v @ X ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_59_split__option__ex,axiom,
% 3.03/1.58 ( ( ^ [P2: option_val_r_l_v > $o] :
% 3.03/1.58 ? [X5: option_val_r_l_v] : ( P2 @ X5 ) )
% 3.03/1.58 = ( ^ [P3: option_val_r_l_v > $o] :
% 3.03/1.58 ( ( P3 @ none_val_r_l_v )
% 3.03/1.58 | ? [X: val_r_l_v] : ( P3 @ ( some_val_r_l_v @ X ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_60_option_Oinducts,axiom,
% 3.03/1.58 ! [P: option1457017436_r_l_v > $o,Option: option1457017436_r_l_v] :
% 3.03/1.58 ( ( P @ none_P277133687_r_l_v )
% 3.03/1.58 => ( ! [X6: produc1156025366_r_l_v] : ( P @ ( some_P1807977723_r_l_v @ X6 ) )
% 3.03/1.58 => ( P @ Option ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_61_option_Oinducts,axiom,
% 3.03/1.58 ! [P: option_val_r_l_v > $o,Option: option_val_r_l_v] :
% 3.03/1.58 ( ( P @ none_val_r_l_v )
% 3.03/1.58 => ( ! [X6: val_r_l_v] : ( P @ ( some_val_r_l_v @ X6 ) )
% 3.03/1.58 => ( P @ Option ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_62_option_Oexhaust,axiom,
% 3.03/1.58 ! [Y: option1457017436_r_l_v] :
% 3.03/1.58 ( ( Y != none_P277133687_r_l_v )
% 3.03/1.58 => ~ ! [X23: produc1156025366_r_l_v] :
% 3.03/1.58 ( Y
% 3.03/1.58 != ( some_P1807977723_r_l_v @ X23 ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_63_option_Oexhaust,axiom,
% 3.03/1.58 ! [Y: option_val_r_l_v] :
% 3.03/1.58 ( ( Y != none_val_r_l_v )
% 3.03/1.58 => ~ ! [X23: val_r_l_v] :
% 3.03/1.58 ( Y
% 3.03/1.58 != ( some_val_r_l_v @ X23 ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_64_option_OdiscI,axiom,
% 3.03/1.58 ! [Option: option1457017436_r_l_v,X22: produc1156025366_r_l_v] :
% 3.03/1.58 ( ( Option
% 3.03/1.58 = ( some_P1807977723_r_l_v @ X22 ) )
% 3.03/1.58 => ( Option != none_P277133687_r_l_v ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_65_option_OdiscI,axiom,
% 3.03/1.58 ! [Option: option_val_r_l_v,X22: val_r_l_v] :
% 3.03/1.58 ( ( Option
% 3.03/1.58 = ( some_val_r_l_v @ X22 ) )
% 3.03/1.58 => ( Option != none_val_r_l_v ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_66_option_Odistinct_I1_J,axiom,
% 3.03/1.58 ! [X22: produc1156025366_r_l_v] :
% 3.03/1.58 ( none_P277133687_r_l_v
% 3.03/1.58 != ( some_P1807977723_r_l_v @ X22 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_67_option_Odistinct_I1_J,axiom,
% 3.03/1.58 ! [X22: val_r_l_v] :
% 3.03/1.58 ( none_val_r_l_v
% 3.03/1.58 != ( some_val_r_l_v @ X22 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_68_mem__Collect__eq,axiom,
% 3.03/1.58 ! [A: set_l,P: set_l > $o] :
% 3.03/1.58 ( ( member_set_l @ A @ ( collect_set_l @ P ) )
% 3.03/1.58 = ( P @ A ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_69_mem__Collect__eq,axiom,
% 3.03/1.58 ! [A: set_r,P: set_r > $o] :
% 3.03/1.58 ( ( member_set_r @ A @ ( collect_set_r @ P ) )
% 3.03/1.58 = ( P @ A ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_70_mem__Collect__eq,axiom,
% 3.03/1.58 ! [A: r,P: r > $o] :
% 3.03/1.58 ( ( member_r @ A @ ( collect_r @ P ) )
% 3.03/1.58 = ( P @ A ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_71_mem__Collect__eq,axiom,
% 3.03/1.58 ! [A: produc1389397445_r_l_v,P: produc1389397445_r_l_v > $o] :
% 3.03/1.58 ( ( member1522896238_r_l_v @ A @ ( collec1978425008_r_l_v @ P ) )
% 3.03/1.58 = ( P @ A ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_72_mem__Collect__eq,axiom,
% 3.03/1.58 ! [A: l,P: l > $o] :
% 3.03/1.58 ( ( member_l @ A @ ( collect_l @ P ) )
% 3.03/1.58 = ( P @ A ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_73_Collect__mem__eq,axiom,
% 3.03/1.58 ! [A4: set_set_l] :
% 3.03/1.58 ( ( collect_set_l
% 3.03/1.58 @ ^ [X: set_l] : ( member_set_l @ X @ A4 ) )
% 3.03/1.58 = A4 ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_74_Collect__mem__eq,axiom,
% 3.03/1.58 ! [A4: set_set_r] :
% 3.03/1.58 ( ( collect_set_r
% 3.03/1.58 @ ^ [X: set_r] : ( member_set_r @ X @ A4 ) )
% 3.03/1.58 = A4 ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_75_Collect__mem__eq,axiom,
% 3.03/1.58 ! [A4: set_r] :
% 3.03/1.58 ( ( collect_r
% 3.03/1.58 @ ^ [X: r] : ( member_r @ X @ A4 ) )
% 3.03/1.58 = A4 ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_76_Collect__mem__eq,axiom,
% 3.03/1.58 ! [A4: set_Pr1409704485_r_l_v] :
% 3.03/1.58 ( ( collec1978425008_r_l_v
% 3.03/1.58 @ ^ [X: produc1389397445_r_l_v] : ( member1522896238_r_l_v @ X @ A4 ) )
% 3.03/1.58 = A4 ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_77_Collect__mem__eq,axiom,
% 3.03/1.58 ! [A4: set_l] :
% 3.03/1.58 ( ( collect_l
% 3.03/1.58 @ ^ [X: l] : ( member_l @ X @ A4 ) )
% 3.03/1.58 = A4 ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_78_Collect__cong,axiom,
% 3.03/1.58 ! [P: l > $o,Q: l > $o] :
% 3.03/1.58 ( ! [X6: l] :
% 3.03/1.58 ( ( P @ X6 )
% 3.03/1.58 = ( Q @ X6 ) )
% 3.03/1.58 => ( ( collect_l @ P )
% 3.03/1.58 = ( collect_l @ Q ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_79_Collect__cong,axiom,
% 3.03/1.58 ! [P: produc1389397445_r_l_v > $o,Q: produc1389397445_r_l_v > $o] :
% 3.03/1.58 ( ! [X6: produc1389397445_r_l_v] :
% 3.03/1.58 ( ( P @ X6 )
% 3.03/1.58 = ( Q @ X6 ) )
% 3.03/1.58 => ( ( collec1978425008_r_l_v @ P )
% 3.03/1.58 = ( collec1978425008_r_l_v @ Q ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_80_Collect__cong,axiom,
% 3.03/1.58 ! [P: r > $o,Q: r > $o] :
% 3.03/1.58 ( ! [X6: r] :
% 3.03/1.58 ( ( P @ X6 )
% 3.03/1.58 = ( Q @ X6 ) )
% 3.03/1.58 => ( ( collect_r @ P )
% 3.03/1.58 = ( collect_r @ Q ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_81_Collect__cong,axiom,
% 3.03/1.58 ! [P: set_l > $o,Q: set_l > $o] :
% 3.03/1.58 ( ! [X6: set_l] :
% 3.03/1.58 ( ( P @ X6 )
% 3.03/1.58 = ( Q @ X6 ) )
% 3.03/1.58 => ( ( collect_set_l @ P )
% 3.03/1.58 = ( collect_set_l @ Q ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_82_Collect__cong,axiom,
% 3.03/1.58 ! [P: set_r > $o,Q: set_r > $o] :
% 3.03/1.58 ( ! [X6: set_r] :
% 3.03/1.58 ( ( P @ X6 )
% 3.03/1.58 = ( Q @ X6 ) )
% 3.03/1.58 => ( ( collect_set_r @ P )
% 3.03/1.58 = ( collect_set_r @ Q ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_83_map__upd__Some__unfold,axiom,
% 3.03/1.58 ! [M: r > option1457017436_r_l_v,A: r,B: produc1156025366_r_l_v,X2: r,Y: produc1156025366_r_l_v] :
% 3.03/1.58 ( ( ( fun_up709272714_r_l_v @ M @ A @ ( some_P1807977723_r_l_v @ B ) @ X2 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ Y ) )
% 3.03/1.58 = ( ( ( X2 = A )
% 3.03/1.58 & ( B = Y ) )
% 3.03/1.58 | ( ( X2 != A )
% 3.03/1.58 & ( ( M @ X2 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ Y ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_84_map__upd__Some__unfold,axiom,
% 3.03/1.58 ! [M: l > option_val_r_l_v,A: l,B: val_r_l_v,X2: l,Y: val_r_l_v] :
% 3.03/1.58 ( ( ( fun_up1835647912_r_l_v @ M @ A @ ( some_val_r_l_v @ B ) @ X2 )
% 3.03/1.58 = ( some_val_r_l_v @ Y ) )
% 3.03/1.58 = ( ( ( X2 = A )
% 3.03/1.58 & ( B = Y ) )
% 3.03/1.58 | ( ( X2 != A )
% 3.03/1.58 & ( ( M @ X2 )
% 3.03/1.58 = ( some_val_r_l_v @ Y ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_85_map__upd__triv,axiom,
% 3.03/1.58 ! [T: r > option1457017436_r_l_v,K: r,X2: produc1156025366_r_l_v] :
% 3.03/1.58 ( ( ( T @ K )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ X2 ) )
% 3.03/1.58 => ( ( fun_up709272714_r_l_v @ T @ K @ ( some_P1807977723_r_l_v @ X2 ) )
% 3.03/1.58 = T ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_86_map__upd__triv,axiom,
% 3.03/1.58 ! [T: l > option_val_r_l_v,K: l,X2: val_r_l_v] :
% 3.03/1.58 ( ( ( T @ K )
% 3.03/1.58 = ( some_val_r_l_v @ X2 ) )
% 3.03/1.58 => ( ( fun_up1835647912_r_l_v @ T @ K @ ( some_val_r_l_v @ X2 ) )
% 3.03/1.58 = T ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_87_map__upd__eqD1,axiom,
% 3.03/1.58 ! [M: r > option1457017436_r_l_v,A: r,X2: produc1156025366_r_l_v,N: r > option1457017436_r_l_v,Y: produc1156025366_r_l_v] :
% 3.03/1.58 ( ( ( fun_up709272714_r_l_v @ M @ A @ ( some_P1807977723_r_l_v @ X2 ) )
% 3.03/1.58 = ( fun_up709272714_r_l_v @ N @ A @ ( some_P1807977723_r_l_v @ Y ) ) )
% 3.03/1.58 => ( X2 = Y ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_88_map__upd__eqD1,axiom,
% 3.03/1.58 ! [M: l > option_val_r_l_v,A: l,X2: val_r_l_v,N: l > option_val_r_l_v,Y: val_r_l_v] :
% 3.03/1.58 ( ( ( fun_up1835647912_r_l_v @ M @ A @ ( some_val_r_l_v @ X2 ) )
% 3.03/1.58 = ( fun_up1835647912_r_l_v @ N @ A @ ( some_val_r_l_v @ Y ) ) )
% 3.03/1.58 => ( X2 = Y ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_89_LID__local__store_Oinduct,axiom,
% 3.03/1.58 ! [P: produc1156025366_r_l_v > $o,A0: produc1156025366_r_l_v] :
% 3.03/1.58 ( ! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E4: expr_r_l_v] : ( P @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ E4 ) ) )
% 3.03/1.58 => ( P @ A0 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_90_LID__local__store_Ocases,axiom,
% 3.03/1.58 ! [X2: produc1156025366_r_l_v] :
% 3.03/1.58 ~ ! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E4: expr_r_l_v] :
% 3.03/1.58 ( X2
% 3.03/1.58 != ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ E4 ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_91_combine_Osimps,axiom,
% 3.03/1.58 ( combine_l_val_r_l_v
% 3.03/1.58 = ( ^ [F2: l > option_val_r_l_v,G2: l > option_val_r_l_v,X: l] :
% 3.03/1.58 ( if_option_val_r_l_v
% 3.03/1.58 @ ( ( G2 @ X )
% 3.03/1.58 = none_val_r_l_v )
% 3.03/1.58 @ ( F2 @ X )
% 3.03/1.58 @ ( G2 @ X ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_92_combine_Oelims,axiom,
% 3.03/1.58 ! [X2: l > option_val_r_l_v,Xa: l > option_val_r_l_v,Xb: l,Y: option_val_r_l_v] :
% 3.03/1.58 ( ( ( combine_l_val_r_l_v @ X2 @ Xa @ Xb )
% 3.03/1.58 = Y )
% 3.03/1.58 => ( ( ( ( Xa @ Xb )
% 3.03/1.58 = none_val_r_l_v )
% 3.03/1.58 => ( Y
% 3.03/1.58 = ( X2 @ Xb ) ) )
% 3.03/1.58 & ( ( ( Xa @ Xb )
% 3.03/1.58 != none_val_r_l_v )
% 3.03/1.58 => ( Y
% 3.03/1.58 = ( Xa @ Xb ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_93_local__steps__commute,axiom,
% 3.03/1.58 ! [S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,X2: produc1156025366_r_l_v,S_22: r > option1457017436_r_l_v,R2: r,Y: produc1156025366_r_l_v] :
% 3.03/1.58 ( ( S_2
% 3.03/1.58 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) )
% 3.03/1.58 => ( ( S_22
% 3.03/1.58 = ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
% 3.03/1.58 => ( ( revision_step_r_l_v @ subst @ R2 @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
% 3.03/1.58 => ( ( 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 @ X2 ) ) )
% 3.03/1.58 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.03/1.58 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 3.03/1.58 | ( S_2 = S_3 ) )
% 3.03/1.58 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 3.03/1.58 | ( S_22 = S_32 ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_94_revision__step__relaxed_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r] :
% 3.03/1.58 ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 3.03/1.58 => ( ( ( S @ R2 )
% 3.03/1.58 = none_P277133687_r_l_v )
% 3.03/1.58 => ( revisi1291188644_r_l_v @ subst @ R @ S
% 3.03/1.58 @ ^ [X: r] : none_P277133687_r_l_v ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_95_revision__step_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r] :
% 3.03/1.58 ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 3.03/1.58 => ( ( ( S @ R2 )
% 3.03/1.58 = none_P277133687_r_l_v )
% 3.03/1.58 => ( revision_step_r_l_v @ subst @ R @ S
% 3.03/1.58 @ ^ [X: r] : none_P277133687_r_l_v ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_96_transition__relations__equivalent,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( reachable_r_l_v @ subst @ S )
% 3.03/1.58 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.03/1.58 = ( revisi1291188644_r_l_v @ subst @ R @ S @ S2 ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_97_SLC__commute,axiom,
% 3.03/1.58 ! [S_33: r > option1457017436_r_l_v,S_34: r > option1457017436_r_l_v,R2: r,S_2: r > option1457017436_r_l_v,R: r,S_22: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( S_33 = S_34 )
% 3.03/1.58 => ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_33 )
% 3.03/1.58 => ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_34 )
% 3.03/1.58 => ( ( eq_states_r_l_v @ S_33 @ S_34 )
% 3.03/1.58 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_33 )
% 3.03/1.58 | ( S_2 = S_33 ) )
% 3.03/1.58 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_34 )
% 3.03/1.58 | ( S_22 = S_34 ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_98_SLC__sym,axiom,
% 3.03/1.58 ! [R2: r,S_2: r > option1457017436_r_l_v,R: r,S_22: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ? [S_35: r > option1457017436_r_l_v,S_36: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( eq_states_r_l_v @ S_35 @ S_36 )
% 3.03/1.58 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_35 )
% 3.03/1.58 | ( S_2 = S_35 ) )
% 3.03/1.58 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_36 )
% 3.03/1.58 | ( S_22 = S_36 ) ) )
% 3.03/1.58 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.03/1.58 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_3 )
% 3.03/1.58 | ( S_22 = S_3 ) )
% 3.03/1.58 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_32 )
% 3.03/1.58 | ( S_2 = S_32 ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_99_local__determinism,axiom,
% 3.03/1.58 ! [R: r,S_1: r > option1457017436_r_l_v,S_2: r > option1457017436_r_l_v,S_22: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( revision_step_r_l_v @ subst @ R @ S_1 @ S_2 )
% 3.03/1.58 => ( ( revision_step_r_l_v @ subst @ R @ S_1 @ S_22 )
% 3.03/1.58 => ( eq_states_r_l_v @ S_2 @ S_22 ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_100_reachability__closed__under__execution__step,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( reachable_r_l_v @ subst @ S )
% 3.03/1.58 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.03/1.58 => ( reachable_r_l_v @ subst @ S2 ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_101_only__fork__introduces__rids,axiom,
% 3.03/1.58 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.03/1.58 => ( ! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E4: expr_r_l_v] :
% 3.03/1.58 ( ( S @ R )
% 3.03/1.58 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 3.03/1.58 => ( ord_less_eq_set_r @ ( rID_G_r_l_v @ S2 ) @ ( rID_G_r_l_v @ S ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_102_substitution_Ofork__pseudodeterministic,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E2: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( ( S @ R )
% 3.03/1.58 = ( 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 ) ) ) ) ) )
% 3.03/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.03/1.58 = ( ? [R3: r] :
% 3.03/1.58 ( ~ ( member_r @ R3 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( 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 ) ) ) ) ) ) ) )
% 3.03/1.58 & ( S2
% 3.03/1.58 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( 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
% 3.03/1.58 @ ( some_P1807977723_r_l_v
% 3.03/1.58 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau )
% 3.03/1.58 @ ( produc1834103605_r_l_v
% 3.03/1.58 @ ^ [X: l] : none_val_r_l_v
% 3.03/1.58 @ E2 ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_103_expr_Oinject_I8_J,axiom,
% 3.03/1.58 ! [X8: expr_r_l_v,Y8: expr_r_l_v] :
% 3.03/1.58 ( ( ( rjoin_r_l_v @ X8 )
% 3.03/1.58 = ( rjoin_r_l_v @ Y8 ) )
% 3.03/1.58 = ( X8 = Y8 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_104_SLC__join_092_060_094sub_062_092_060epsilon_062,axiom,
% 3.03/1.58 ! [S_1: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: 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] :
% 3.03/1.58 ( ( ( S_1 @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 3.03/1.58 => ( ( S_2
% 3.03/1.58 = ( ^ [X: r] : none_P277133687_r_l_v ) )
% 3.03/1.58 => ( ( ( S_1 @ R4 )
% 3.03/1.58 = none_P277133687_r_l_v )
% 3.03/1.58 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 3.03/1.58 => ( ( R != R2 )
% 3.03/1.58 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.03/1.58 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 3.03/1.58 | ( S_2 = S_3 ) )
% 3.03/1.58 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 3.03/1.58 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_105_reachable__def,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( reachable_r_l_v @ subst @ S )
% 3.03/1.58 = ( ? [E5: expr_r_l_v,S3: r > option1457017436_r_l_v] : ( execution_r_l_v @ subst @ E5 @ S3 @ S ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_106_rjoin_092_060_094sub_062_092_060epsilon_062__deterministic,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 3.03/1.58 => ( ( ( S @ R2 )
% 3.03/1.58 = none_P277133687_r_l_v )
% 3.03/1.58 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.03/1.58 = ( S2
% 3.03/1.58 = ( ^ [X: r] : none_P277133687_r_l_v ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_107_substitution_Olocal__determinism,axiom,
% 3.03/1.58 ! [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] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S_1 @ S_2 )
% 3.03/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S_1 @ S_22 )
% 3.03/1.58 => ( eq_states_r_l_v @ S_2 @ S_22 ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_108_substitution_OSLC__commute,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_33: r > option1457017436_r_l_v,S_34: r > option1457017436_r_l_v,R2: r,S_2: r > option1457017436_r_l_v,R: r,S_22: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( S_33 = S_34 )
% 3.03/1.58 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_33 )
% 3.03/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_34 )
% 3.03/1.58 => ( ( eq_states_r_l_v @ S_33 @ S_34 )
% 3.03/1.58 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_33 )
% 3.03/1.58 | ( S_2 = S_33 ) )
% 3.03/1.58 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_34 )
% 3.03/1.58 | ( S_22 = S_34 ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_109_substitution_OSLC__sym,axiom,
% 3.03/1.58 ! [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] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ? [S_35: r > option1457017436_r_l_v,S_36: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( eq_states_r_l_v @ S_35 @ S_36 )
% 3.03/1.58 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_35 )
% 3.03/1.58 | ( S_2 = S_35 ) )
% 3.03/1.58 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_36 )
% 3.03/1.58 | ( S_22 = S_36 ) ) )
% 3.03/1.58 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.03/1.58 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_3 )
% 3.03/1.58 | ( S_22 = S_3 ) )
% 3.03/1.58 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_32 )
% 3.03/1.58 | ( S_2 = S_32 ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_110_expr_Odistinct_I13_J,axiom,
% 3.03/1.58 ! [X1: val_r_l_v,X8: expr_r_l_v] :
% 3.03/1.58 ( ( vE_r_l_v @ X1 )
% 3.03/1.58 != ( rjoin_r_l_v @ X8 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_111_expr_Odistinct_I55_J,axiom,
% 3.03/1.58 ! [X7: expr_r_l_v,X8: expr_r_l_v] :
% 3.03/1.58 ( ( rfork_r_l_v @ X7 )
% 3.03/1.58 != ( rjoin_r_l_v @ X8 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_112_substitution_Olocal__steps__commute,axiom,
% 3.03/1.58 ! [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,X2: produc1156025366_r_l_v,S_22: r > option1457017436_r_l_v,R2: r,Y: produc1156025366_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( S_2
% 3.03/1.58 = ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) )
% 3.03/1.58 => ( ( S_22
% 3.03/1.58 = ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
% 3.03/1.58 => ( ( revision_step_r_l_v @ Subst @ R2 @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X2 ) ) @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
% 3.03/1.58 => ( ( 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 @ X2 ) ) )
% 3.03/1.58 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.03/1.58 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 3.03/1.58 | ( S_2 = S_3 ) )
% 3.03/1.58 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 3.03/1.58 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_113_ID__restricted__global__subset__unrestricted_I2_J,axiom,
% 3.03/1.58 ! [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 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_114_substitution_OSLC__join_092_060_094sub_062_092_060epsilon_062,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: 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] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( ( S_1 @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 3.03/1.58 => ( ( S_2
% 3.03/1.58 = ( ^ [X: r] : none_P277133687_r_l_v ) )
% 3.03/1.58 => ( ( ( S_1 @ R4 )
% 3.03/1.58 = none_P277133687_r_l_v )
% 3.03/1.58 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
% 3.03/1.58 => ( ( R != R2 )
% 3.03/1.58 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.03/1.58 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 3.03/1.58 | ( S_2 = S_3 ) )
% 3.03/1.58 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 3.03/1.58 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_115_substitution_Orjoin_092_060_094sub_062_092_060epsilon_062__deterministic,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 3.03/1.58 => ( ( ( S @ R2 )
% 3.03/1.58 = none_P277133687_r_l_v )
% 3.03/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.03/1.58 = ( S2
% 3.03/1.58 = ( ^ [X: r] : none_P277133687_r_l_v ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_116_inductive__invariant__is__execution__invariant,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,P: ( r > option1457017436_r_l_v ) > $o] :
% 3.03/1.58 ( ( reachable_r_l_v @ subst @ S )
% 3.03/1.58 => ( ( induct1670415253_r_l_v @ subst @ P )
% 3.03/1.58 => ( P @ S ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_117_substitution_Orevision__step__relaxed_Ofork,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E2: expr_r_l_v,R2: r] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( ( S @ R )
% 3.03/1.58 = ( 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 ) ) ) ) ) )
% 3.03/1.58 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 3.03/1.58 => ( revisi1291188644_r_l_v @ Subst @ R @ S
% 3.03/1.58 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( 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 @ R2 ) ) ) ) ) ) ) @ R2
% 3.03/1.58 @ ( some_P1807977723_r_l_v
% 3.03/1.58 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau )
% 3.03/1.58 @ ( produc1834103605_r_l_v
% 3.03/1.58 @ ^ [X: l] : none_val_r_l_v
% 3.03/1.58 @ E2 ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_118_substitution_Orevision__step_Ofork,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E2: expr_r_l_v,R2: r] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( ( S @ R )
% 3.03/1.58 = ( 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 ) ) ) ) ) )
% 3.03/1.58 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 3.03/1.58 => ( revision_step_r_l_v @ Subst @ R @ S
% 3.03/1.58 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( 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 @ R2 ) ) ) ) ) ) ) @ R2
% 3.03/1.58 @ ( some_P1807977723_r_l_v
% 3.03/1.58 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau )
% 3.03/1.58 @ ( produc1834103605_r_l_v
% 3.03/1.58 @ ^ [X: l] : none_val_r_l_v
% 3.03/1.58 @ E2 ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_119_substitution_Orevision__step__relaxed_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 3.03/1.58 => ( ( ( S @ R2 )
% 3.03/1.58 = none_P277133687_r_l_v )
% 3.03/1.58 => ( revisi1291188644_r_l_v @ Subst @ R @ S
% 3.03/1.58 @ ^ [X: r] : none_P277133687_r_l_v ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_120_substitution_Orevision__step_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 3.03/1.58 => ( ( ( S @ R2 )
% 3.03/1.58 = none_P277133687_r_l_v )
% 3.03/1.58 => ( revision_step_r_l_v @ Subst @ R @ S
% 3.03/1.58 @ ^ [X: r] : none_P277133687_r_l_v ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_121_substitution_Oonly__fork__introduces__rids,axiom,
% 3.03/1.58 ! [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] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.03/1.58 => ( ! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E4: expr_r_l_v] :
% 3.03/1.58 ( ( S @ R )
% 3.03/1.58 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 3.03/1.58 => ( ord_less_eq_set_r @ ( rID_G_r_l_v @ S2 ) @ ( rID_G_r_l_v @ S ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_122_reachable__imp___092_060S_062_092_060_094sub_062G,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( reachable_r_l_v @ subst @ S )
% 3.03/1.58 => ( domain1547879849_r_l_v @ S ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_123_domains__subsume__globally__def,axiom,
% 3.03/1.58 ( domain1547879849_r_l_v
% 3.03/1.58 = ( ^ [S4: r > option1457017436_r_l_v] :
% 3.03/1.58 ! [R5: r,Ls2: produc1156025366_r_l_v] :
% 3.03/1.58 ( ( ( S4 @ R5 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ Ls2 ) )
% 3.03/1.58 => ( domain87684397_l_r_v @ Ls2 ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_124_substitution_Orevision__step_Ocong,axiom,
% 3.03/1.58 revision_step_r_l_v = revision_step_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(fact_125_substitution_Orevision__step__relaxed_Ocong,axiom,
% 3.03/1.58 revisi1291188644_r_l_v = revisi1291188644_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(fact_126_substitution_Oonly__fork__introduces__rids_H,axiom,
% 3.03/1.58 ! [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] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.03/1.58 => ( ! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,E4: expr_r_l_v] :
% 3.03/1.58 ( ( S @ R )
% 3.03/1.58 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
% 3.03/1.58 => ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
% 3.03/1.58 => ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S2 ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_127_nice__ind__inv__is__inductive__invariant,axiom,
% 3.03/1.58 ( induct1670415253_r_l_v @ subst
% 3.03/1.58 @ ^ [S4: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( domain1547879849_r_l_v @ S4 )
% 3.03/1.58 & ( subsum680764357_r_l_v @ S4 ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_128_step__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I2_J,axiom,
% 3.03/1.58 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.03/1.58 => ( ( domain1547879849_r_l_v @ S )
% 3.03/1.58 => ( ( subsum680764357_r_l_v @ S )
% 3.03/1.58 => ( subsum680764357_r_l_v @ S2 ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_129_step__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I1_J,axiom,
% 3.03/1.58 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.03/1.58 => ( ( domain1547879849_r_l_v @ S )
% 3.03/1.58 => ( ( subsum680764357_r_l_v @ S )
% 3.03/1.58 => ( domain1547879849_r_l_v @ S2 ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_130_valid__stepE,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S @ S2 ) @ ( steps_r_l_v @ subst ) )
% 3.03/1.58 => ? [R6: r] : ( revision_step_r_l_v @ subst @ R6 @ S @ S2 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_131_substitution_Odomains__subsume__globallyI,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ! [R6: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E4: expr_r_l_v] :
% 3.03/1.58 ( ( ( S @ R6 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ E4 ) ) ) )
% 3.03/1.58 => ( domain87684397_l_r_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ E4 ) ) ) )
% 3.03/1.58 => ( domain1547879849_r_l_v @ S ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_132_substitution_Otransition__relations__equivalent,axiom,
% 3.03/1.58 ! [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] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( reachable_r_l_v @ Subst @ S )
% 3.03/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.03/1.58 = ( revisi1291188644_r_l_v @ Subst @ R @ S @ S2 ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_133_valid__stepI,axiom,
% 3.03/1.58 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.03/1.58 => ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S @ S2 ) @ ( steps_r_l_v @ subst ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_134_domains__subsume__globallyI,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ! [R6: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E4: expr_r_l_v] :
% 3.03/1.58 ( ( ( S @ R6 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ E4 ) ) ) )
% 3.03/1.58 => ( domain87684397_l_r_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ E4 ) ) ) )
% 3.03/1.58 => ( domain1547879849_r_l_v @ S ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_135_maximal__execution__def,axiom,
% 3.03/1.58 ! [E2: expr_r_l_v,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( maxima311842975_r_l_v @ subst @ E2 @ S @ S2 )
% 3.03/1.58 = ( ( execution_r_l_v @ subst @ E2 @ S @ S2 )
% 3.03/1.58 & ~ ? [S5: r > option1457017436_r_l_v] : ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S2 @ S5 ) @ ( steps_r_l_v @ subst ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_136_substitution_Osteps_Ocong,axiom,
% 3.03/1.58 steps_r_l_v = steps_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(fact_137_substitution_Ovalid__stepE,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S @ S2 ) @ ( steps_r_l_v @ Subst ) )
% 3.03/1.58 => ? [R6: r] : ( revision_step_r_l_v @ Subst @ R6 @ S @ S2 ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_138_substitution_Ovalid__stepI,axiom,
% 3.03/1.58 ! [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] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.03/1.58 => ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S @ S2 ) @ ( steps_r_l_v @ Subst ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_139_substitution_Oreachable_Ocong,axiom,
% 3.03/1.58 reachable_r_l_v = reachable_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(fact_140_substitution_Oinductive__invariant_Ocong,axiom,
% 3.03/1.58 induct1670415253_r_l_v = induct1670415253_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(fact_141_substitution_Oexecution_Ocong,axiom,
% 3.03/1.58 execution_r_l_v = execution_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(fact_142_substitution_Onice__ind__inv__is__inductive__invariant,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( induct1670415253_r_l_v @ Subst
% 3.03/1.58 @ ^ [S4: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( domain1547879849_r_l_v @ S4 )
% 3.03/1.58 & ( subsum680764357_r_l_v @ S4 ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_143_substitution_Ostep__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I2_J,axiom,
% 3.03/1.58 ! [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] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.03/1.58 => ( ( domain1547879849_r_l_v @ S )
% 3.03/1.58 => ( ( subsum680764357_r_l_v @ S )
% 3.03/1.58 => ( subsum680764357_r_l_v @ S2 ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_144_substitution_Ostep__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I1_J,axiom,
% 3.03/1.58 ! [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] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.03/1.58 => ( ( domain1547879849_r_l_v @ S )
% 3.03/1.58 => ( ( subsum680764357_r_l_v @ S )
% 3.03/1.58 => ( domain1547879849_r_l_v @ S2 ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_145_substitution_Odomains__subsume__globally__def,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( domain1547879849_r_l_v @ S )
% 3.03/1.58 = ( ! [R5: r,Ls2: produc1156025366_r_l_v] :
% 3.03/1.58 ( ( ( S @ R5 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ Ls2 ) )
% 3.03/1.58 => ( domain87684397_l_r_v @ Ls2 ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_146_substitution_Oreachability__closed__under__execution__step,axiom,
% 3.03/1.58 ! [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] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( reachable_r_l_v @ Subst @ S )
% 3.03/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.03/1.58 => ( reachable_r_l_v @ Subst @ S2 ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_147_substitution_Oreachable__imp___092_060S_062_092_060_094sub_062G,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( reachable_r_l_v @ Subst @ S )
% 3.03/1.58 => ( domain1547879849_r_l_v @ S ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_148_substitution_Oinductive__invariant__is__execution__invariant,axiom,
% 3.03/1.58 ! [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] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( reachable_r_l_v @ Subst @ S )
% 3.03/1.58 => ( ( induct1670415253_r_l_v @ Subst @ P )
% 3.03/1.58 => ( P @ S ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_149_substitution_Oreachable__def,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( reachable_r_l_v @ Subst @ S )
% 3.03/1.58 = ( ? [E5: expr_r_l_v,S3: r > option1457017436_r_l_v] : ( execution_r_l_v @ Subst @ E5 @ S3 @ S ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_150_SLC__join,axiom,
% 3.03/1.58 ! [S_1: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: 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] :
% 3.03/1.58 ( ( ( S_1 @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 3.03/1.58 => ( ( S_2
% 3.03/1.58 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
% 3.03/1.58 => ( ( ( S_1 @ R4 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 3.03/1.58 => ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
% 3.03/1.58 => ( ( R != R2 )
% 3.03/1.58 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.03/1.58 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 3.03/1.58 | ( S_2 = S_3 ) )
% 3.03/1.58 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 3.03/1.58 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_151_join__and__local__commute,axiom,
% 3.03/1.58 ! [S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: 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] :
% 3.03/1.58 ( ( S_2
% 3.03/1.58 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
% 3.03/1.58 => ( ( S_22
% 3.03/1.58 = ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Ls ) ) )
% 3.03/1.58 => ( ( R != R2 )
% 3.03/1.58 => ( ( R2 != R4 )
% 3.03/1.58 => ( ( 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 @ Sigma @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau @ 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 ) ) )
% 3.03/1.58 => ( ( ( S_22 @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 3.03/1.58 => ( ( ( S_22 @ R4 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 3.03/1.58 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.03/1.58 & ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
% 3.03/1.58 | ( S_2 = S_3 ) )
% 3.03/1.58 & ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
% 3.03/1.58 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_152_substitution_Omaximal__execution__def,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,E2: expr_r_l_v,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( maxima311842975_r_l_v @ Subst @ E2 @ S @ S2 )
% 3.03/1.58 = ( ( execution_r_l_v @ Subst @ E2 @ S @ S2 )
% 3.03/1.58 & ~ ? [S5: r > option1457017436_r_l_v] : ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S2 @ S5 ) @ ( steps_r_l_v @ Subst ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_153_substitution_Osubsumes__accessible__globallyI,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ! [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] :
% 3.03/1.58 ( ( ( S @ R_1 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_1 @ ( produc1834103605_r_l_v @ Tau_1 @ E_1 ) ) ) )
% 3.03/1.58 => ( ( ( S @ R_2 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_2 @ ( produc1834103605_r_l_v @ Tau_2 @ E_2 ) ) ) )
% 3.03/1.58 => ( subsum148050133_r_l_v @ R_1 @ R_2 @ S ) ) )
% 3.03/1.58 => ( subsum680764357_r_l_v @ S ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_154_revision__step__relaxed_Ojoin,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: 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] :
% 3.03/1.58 ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 3.03/1.58 => ( ( ( S @ R2 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 3.03/1.58 => ( 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 @ Sigma @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_155_val_Oinject_I1_J,axiom,
% 3.03/1.58 ! [X1: const,Y1: const] :
% 3.03/1.58 ( ( ( cV_r_l_v @ X1 )
% 3.03/1.58 = ( cV_r_l_v @ Y1 ) )
% 3.03/1.58 = ( X1 = Y1 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_156_terminates__in__def,axiom,
% 3.03/1.58 ! [E2: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( terminates_in_r_l_v @ subst @ E2 @ S2 )
% 3.03/1.58 = ( ? [S4: r > option1457017436_r_l_v] : ( maxima311842975_r_l_v @ subst @ E2 @ S4 @ S2 ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_157_revision__step_Ojoin,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: 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] :
% 3.03/1.58 ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 3.03/1.58 => ( ( ( S @ R2 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 3.03/1.58 => ( 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 @ Sigma @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_158_subsumes__accessible__globallyI,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ! [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] :
% 3.03/1.58 ( ( ( S @ R_1 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_1 @ ( produc1834103605_r_l_v @ Tau_1 @ E_1 ) ) ) )
% 3.03/1.58 => ( ( ( S @ R_2 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_2 @ ( produc1834103605_r_l_v @ Tau_2 @ E_2 ) ) ) )
% 3.03/1.58 => ( subsum148050133_r_l_v @ R_1 @ R_2 @ S ) ) )
% 3.03/1.58 => ( subsum680764357_r_l_v @ S ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_159_rjoin__deterministic,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: 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] :
% 3.03/1.58 ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 3.03/1.58 => ( ( ( S @ R2 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 3.03/1.58 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.03/1.58 = ( S2
% 3.03/1.58 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_160_substitution_Omaximal__execution_Ocong,axiom,
% 3.03/1.58 maxima311842975_r_l_v = maxima311842975_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(fact_161_val_Odistinct_I5_J,axiom,
% 3.03/1.58 ! [X1: const,X4: r] :
% 3.03/1.58 ( ( cV_r_l_v @ X1 )
% 3.03/1.58 != ( rid_r_l_v @ X4 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_162_substitution_Orevision__step_Ojoin,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: 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] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 3.03/1.58 => ( ( ( S @ R2 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 3.03/1.58 => ( 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 @ Sigma @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_163_substitution_Orjoin__deterministic,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: 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] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 3.03/1.58 => ( ( ( S @ R2 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 3.03/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.03/1.58 = ( S2
% 3.03/1.58 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_164_substitution_Orevision__step__relaxed_Ojoin,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: 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] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
% 3.03/1.58 => ( ( ( S @ R2 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 3.03/1.58 => ( 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 @ Sigma @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_165_substitution_Ojoin__and__local__commute,axiom,
% 3.03/1.58 ! [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,Sigma: l > option_val_r_l_v,Tau: 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] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( S_2
% 3.03/1.58 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
% 3.03/1.58 => ( ( S_22
% 3.03/1.58 = ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Ls ) ) )
% 3.03/1.58 => ( ( R != R2 )
% 3.03/1.58 => ( ( R2 != R4 )
% 3.03/1.58 => ( ( 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 @ Sigma @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau @ 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 ) ) )
% 3.03/1.58 => ( ( ( S_22 @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 3.03/1.58 => ( ( ( S_22 @ R4 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 3.03/1.58 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.03/1.58 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 3.03/1.58 | ( S_2 = S_3 ) )
% 3.03/1.58 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 3.03/1.58 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_166_substitution_OSLC__join,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: 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] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( ( S_1 @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
% 3.03/1.58 => ( ( S_2
% 3.03/1.58 = ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
% 3.03/1.58 => ( ( ( S_1 @ R4 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
% 3.03/1.58 => ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
% 3.03/1.58 => ( ( R != R2 )
% 3.03/1.58 => ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( eq_states_r_l_v @ S_3 @ S_32 )
% 3.03/1.58 & ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
% 3.03/1.58 | ( S_2 = S_3 ) )
% 3.03/1.58 & ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
% 3.03/1.58 | ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_167_reachable__imp__identifiers__finite_I1_J,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( reachable_r_l_v @ subst @ S )
% 3.03/1.58 => ( finite_finite_r @ ( rID_G_r_l_v @ S ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_168_RID_092_060_094sub_062G__finite__invariant,axiom,
% 3.03/1.58 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.03/1.58 => ( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
% 3.03/1.58 => ( finite_finite_r @ ( rID_G_r_l_v @ S2 ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_169_reachability__closed__under__execution,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( reachable_r_l_v @ subst @ S )
% 3.03/1.58 => ( ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S @ S2 ) @ ( transi1323086383_r_l_v @ ( steps_r_l_v @ subst ) ) )
% 3.03/1.58 => ( reachable_r_l_v @ subst @ S2 ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_170_revision__step__relaxed_OifTrue,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 3.03/1.58 ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.03/1.58 => ( revisi1291188644_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ E1 ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_171_empty__map__finite_I3_J,axiom,
% 3.03/1.58 ( finite_finite_r
% 3.03/1.58 @ ( rID_G_r_l_v
% 3.03/1.58 @ ^ [X: r] : none_P277133687_r_l_v ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_172_expr_Oinject_I3_J,axiom,
% 3.03/1.58 ! [X31: expr_r_l_v,X32: expr_r_l_v,X33: expr_r_l_v,Y31: expr_r_l_v,Y32: expr_r_l_v,Y33: expr_r_l_v] :
% 3.03/1.58 ( ( ( ite_r_l_v @ X31 @ X32 @ X33 )
% 3.03/1.58 = ( ite_r_l_v @ Y31 @ Y32 @ Y33 ) )
% 3.03/1.58 = ( ( X31 = Y31 )
% 3.03/1.58 & ( X32 = Y32 )
% 3.03/1.58 & ( X33 = Y33 ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_173_revision__step_OifTrue,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 3.03/1.58 ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.03/1.58 => ( revision_step_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ E1 ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_174_finite__state__imp__restriction__finite_I1_J,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r] :
% 3.03/1.58 ( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
% 3.03/1.58 => ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_175_ifTrue__deterministic,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.03/1.58 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.03/1.58 = ( S2
% 3.03/1.58 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ E1 ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_176_expr_Odistinct_I3_J,axiom,
% 3.03/1.58 ! [X1: val_r_l_v,X31: expr_r_l_v,X32: expr_r_l_v,X33: expr_r_l_v] :
% 3.03/1.58 ( ( vE_r_l_v @ X1 )
% 3.03/1.58 != ( ite_r_l_v @ X31 @ X32 @ X33 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_177_expr_Odistinct_I35_J,axiom,
% 3.03/1.58 ! [X31: expr_r_l_v,X32: expr_r_l_v,X33: expr_r_l_v,X8: expr_r_l_v] :
% 3.03/1.58 ( ( ite_r_l_v @ X31 @ X32 @ X33 )
% 3.03/1.58 != ( rjoin_r_l_v @ X8 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_178_expr_Odistinct_I33_J,axiom,
% 3.03/1.58 ! [X31: expr_r_l_v,X32: expr_r_l_v,X33: expr_r_l_v,X7: expr_r_l_v] :
% 3.03/1.58 ( ( ite_r_l_v @ X31 @ X32 @ X33 )
% 3.03/1.58 != ( rfork_r_l_v @ X7 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_179_substitution_Oterminates__in_Ocong,axiom,
% 3.03/1.58 terminates_in_r_l_v = terminates_in_r_l_v ).
% 3.03/1.58
% 3.03/1.58 thf(fact_180_const_Odistinct_I3_J,axiom,
% 3.03/1.58 unit != t ).
% 3.03/1.58
% 3.03/1.58 thf(fact_181_substitution_ORID_092_060_094sub_062G__finite__invariant,axiom,
% 3.03/1.58 ! [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] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.03/1.58 => ( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
% 3.03/1.58 => ( finite_finite_r @ ( rID_G_r_l_v @ S2 ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_182_substitution_Oreachable__imp__identifiers__finite_I1_J,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( reachable_r_l_v @ Subst @ S )
% 3.03/1.58 => ( finite_finite_r @ ( rID_G_r_l_v @ S ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_183_substitution_Oempty__map__finite_I3_J,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( finite_finite_r
% 3.03/1.58 @ ( rID_G_r_l_v
% 3.03/1.58 @ ^ [X: r] : none_P277133687_r_l_v ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_184_substitution_Oreachability__closed__under__execution,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( reachable_r_l_v @ Subst @ S )
% 3.03/1.58 => ( ( member1522896238_r_l_v @ ( produc1175464189_r_l_v @ S @ S2 ) @ ( transi1323086383_r_l_v @ ( steps_r_l_v @ Subst ) ) )
% 3.03/1.58 => ( reachable_r_l_v @ Subst @ S2 ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_185_substitution_Ofinite__state__imp__restriction__finite_I1_J,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
% 3.03/1.58 => ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_186_substitution_OifTrue__deterministic,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.03/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.03/1.58 = ( S2
% 3.03/1.58 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ E1 ) ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_187_substitution_Orevision__step_OifTrue,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.03/1.58 => ( revision_step_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ E1 ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_188_substitution_Orevision__step__relaxed_OifTrue,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ t ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.03/1.58 => ( revisi1291188644_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ E1 ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_189_substitution_Oterminates__in__def,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,E2: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( terminates_in_r_l_v @ Subst @ E2 @ S2 )
% 3.03/1.58 = ( ? [S4: r > option1457017436_r_l_v] : ( maxima311842975_r_l_v @ Subst @ E2 @ S4 @ S2 ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_190_revision__step__relaxed_OifFalse,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 3.03/1.58 ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.03/1.58 => ( revisi1291188644_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ E22 ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_191_revision__step_OifFalse,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 3.03/1.58 ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.03/1.58 => ( revision_step_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ E22 ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_192_ifFalse__deterministic,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.03/1.58 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.03/1.58 = ( S2
% 3.03/1.58 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ E22 ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_193_finite__Collect__subsets,axiom,
% 3.03/1.58 ! [A4: set_set_l] :
% 3.03/1.58 ( ( finite_finite_set_l @ A4 )
% 3.03/1.58 => ( finite1256628466_set_l
% 3.03/1.58 @ ( collect_set_set_l
% 3.03/1.58 @ ^ [B4: set_set_l] : ( ord_le2116509289_set_l @ B4 @ A4 ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_194_finite__Collect__subsets,axiom,
% 3.03/1.58 ! [A4: set_set_r] :
% 3.03/1.58 ( ( finite_finite_set_r @ A4 )
% 3.03/1.58 => ( finite1651563256_set_r
% 3.03/1.58 @ ( collect_set_set_r
% 3.03/1.58 @ ^ [B4: set_set_r] : ( ord_le363960431_set_r @ B4 @ A4 ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_195_finite__Collect__subsets,axiom,
% 3.03/1.58 ! [A4: set_Pr1409704485_r_l_v] :
% 3.03/1.58 ( ( finite1853159534_r_l_v @ A4 )
% 3.03/1.58 => ( finite1619243214_r_l_v
% 3.03/1.58 @ ( collec330370832_r_l_v
% 3.03/1.58 @ ^ [B4: set_Pr1409704485_r_l_v] : ( ord_le803113413_r_l_v @ B4 @ A4 ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_196_finite__Collect__subsets,axiom,
% 3.03/1.58 ! [A4: set_option_l] :
% 3.03/1.58 ( ( finite2114249848tion_l @ A4 )
% 3.03/1.58 => ( finite1182752216tion_l
% 3.03/1.58 @ ( collect_set_option_l
% 3.03/1.58 @ ^ [B4: set_option_l] : ( ord_le1506375887tion_l @ B4 @ A4 ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_197_finite__Collect__subsets,axiom,
% 3.03/1.58 ! [A4: set_option_r] :
% 3.03/1.58 ( ( finite16335230tion_r @ A4 )
% 3.03/1.58 => ( finite1577687006tion_r
% 3.03/1.58 @ ( collect_set_option_r
% 3.03/1.58 @ ^ [B4: set_option_r] : ( ord_le1901310677tion_r @ B4 @ A4 ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_198_finite__Collect__subsets,axiom,
% 3.03/1.58 ! [A4: set_r] :
% 3.03/1.58 ( ( finite_finite_r @ A4 )
% 3.03/1.58 => ( finite_finite_set_r
% 3.03/1.58 @ ( collect_set_r
% 3.03/1.58 @ ^ [B4: set_r] : ( ord_less_eq_set_r @ B4 @ A4 ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_199_finite__Collect__subsets,axiom,
% 3.03/1.58 ! [A4: set_l] :
% 3.03/1.58 ( ( finite_finite_l @ A4 )
% 3.03/1.58 => ( finite_finite_set_l
% 3.03/1.58 @ ( collect_set_l
% 3.03/1.58 @ ^ [B4: set_l] : ( ord_less_eq_set_l @ B4 @ A4 ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_200_finite__Collect__disjI,axiom,
% 3.03/1.58 ! [P: set_l > $o,Q: set_l > $o] :
% 3.03/1.58 ( ( finite_finite_set_l
% 3.03/1.58 @ ( collect_set_l
% 3.03/1.58 @ ^ [X: set_l] :
% 3.03/1.58 ( ( P @ X )
% 3.03/1.58 | ( Q @ X ) ) ) )
% 3.03/1.58 = ( ( finite_finite_set_l @ ( collect_set_l @ P ) )
% 3.03/1.58 & ( finite_finite_set_l @ ( collect_set_l @ Q ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_201_finite__Collect__disjI,axiom,
% 3.03/1.58 ! [P: set_r > $o,Q: set_r > $o] :
% 3.03/1.58 ( ( finite_finite_set_r
% 3.03/1.58 @ ( collect_set_r
% 3.03/1.58 @ ^ [X: set_r] :
% 3.03/1.58 ( ( P @ X )
% 3.03/1.58 | ( Q @ X ) ) ) )
% 3.03/1.58 = ( ( finite_finite_set_r @ ( collect_set_r @ P ) )
% 3.03/1.58 & ( finite_finite_set_r @ ( collect_set_r @ Q ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_202_finite__Collect__disjI,axiom,
% 3.03/1.58 ! [P: produc1389397445_r_l_v > $o,Q: produc1389397445_r_l_v > $o] :
% 3.03/1.58 ( ( finite1853159534_r_l_v
% 3.03/1.58 @ ( collec1978425008_r_l_v
% 3.03/1.58 @ ^ [X: produc1389397445_r_l_v] :
% 3.03/1.58 ( ( P @ X )
% 3.03/1.58 | ( Q @ X ) ) ) )
% 3.03/1.58 = ( ( finite1853159534_r_l_v @ ( collec1978425008_r_l_v @ P ) )
% 3.03/1.58 & ( finite1853159534_r_l_v @ ( collec1978425008_r_l_v @ Q ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_203_finite__Collect__disjI,axiom,
% 3.03/1.58 ! [P: option_l > $o,Q: option_l > $o] :
% 3.03/1.58 ( ( finite2114249848tion_l
% 3.03/1.58 @ ( collect_option_l
% 3.03/1.58 @ ^ [X: option_l] :
% 3.03/1.58 ( ( P @ X )
% 3.03/1.58 | ( Q @ X ) ) ) )
% 3.03/1.58 = ( ( finite2114249848tion_l @ ( collect_option_l @ P ) )
% 3.03/1.58 & ( finite2114249848tion_l @ ( collect_option_l @ Q ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_204_finite__Collect__disjI,axiom,
% 3.03/1.58 ! [P: option_r > $o,Q: option_r > $o] :
% 3.03/1.58 ( ( finite16335230tion_r
% 3.03/1.58 @ ( collect_option_r
% 3.03/1.58 @ ^ [X: option_r] :
% 3.03/1.58 ( ( P @ X )
% 3.03/1.58 | ( Q @ X ) ) ) )
% 3.03/1.58 = ( ( finite16335230tion_r @ ( collect_option_r @ P ) )
% 3.03/1.58 & ( finite16335230tion_r @ ( collect_option_r @ Q ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_205_finite__Collect__disjI,axiom,
% 3.03/1.58 ! [P: r > $o,Q: r > $o] :
% 3.03/1.58 ( ( finite_finite_r
% 3.03/1.58 @ ( collect_r
% 3.03/1.58 @ ^ [X: r] :
% 3.03/1.58 ( ( P @ X )
% 3.03/1.58 | ( Q @ X ) ) ) )
% 3.03/1.58 = ( ( finite_finite_r @ ( collect_r @ P ) )
% 3.03/1.58 & ( finite_finite_r @ ( collect_r @ Q ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_206_finite__Collect__disjI,axiom,
% 3.03/1.58 ! [P: l > $o,Q: l > $o] :
% 3.03/1.58 ( ( finite_finite_l
% 3.03/1.58 @ ( collect_l
% 3.03/1.58 @ ^ [X: l] :
% 3.03/1.58 ( ( P @ X )
% 3.03/1.58 | ( Q @ X ) ) ) )
% 3.03/1.58 = ( ( finite_finite_l @ ( collect_l @ P ) )
% 3.03/1.58 & ( finite_finite_l @ ( collect_l @ Q ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_207_finite__Collect__conjI,axiom,
% 3.03/1.58 ! [P: set_l > $o,Q: set_l > $o] :
% 3.03/1.58 ( ( ( finite_finite_set_l @ ( collect_set_l @ P ) )
% 3.03/1.58 | ( finite_finite_set_l @ ( collect_set_l @ Q ) ) )
% 3.03/1.58 => ( finite_finite_set_l
% 3.03/1.58 @ ( collect_set_l
% 3.03/1.58 @ ^ [X: set_l] :
% 3.03/1.58 ( ( P @ X )
% 3.03/1.58 & ( Q @ X ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_208_finite__Collect__conjI,axiom,
% 3.03/1.58 ! [P: set_r > $o,Q: set_r > $o] :
% 3.03/1.58 ( ( ( finite_finite_set_r @ ( collect_set_r @ P ) )
% 3.03/1.58 | ( finite_finite_set_r @ ( collect_set_r @ Q ) ) )
% 3.03/1.58 => ( finite_finite_set_r
% 3.03/1.58 @ ( collect_set_r
% 3.03/1.58 @ ^ [X: set_r] :
% 3.03/1.58 ( ( P @ X )
% 3.03/1.58 & ( Q @ X ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_209_finite__Collect__conjI,axiom,
% 3.03/1.58 ! [P: produc1389397445_r_l_v > $o,Q: produc1389397445_r_l_v > $o] :
% 3.03/1.58 ( ( ( finite1853159534_r_l_v @ ( collec1978425008_r_l_v @ P ) )
% 3.03/1.58 | ( finite1853159534_r_l_v @ ( collec1978425008_r_l_v @ Q ) ) )
% 3.03/1.58 => ( finite1853159534_r_l_v
% 3.03/1.58 @ ( collec1978425008_r_l_v
% 3.03/1.58 @ ^ [X: produc1389397445_r_l_v] :
% 3.03/1.58 ( ( P @ X )
% 3.03/1.58 & ( Q @ X ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_210_finite__Collect__conjI,axiom,
% 3.03/1.58 ! [P: option_l > $o,Q: option_l > $o] :
% 3.03/1.58 ( ( ( finite2114249848tion_l @ ( collect_option_l @ P ) )
% 3.03/1.58 | ( finite2114249848tion_l @ ( collect_option_l @ Q ) ) )
% 3.03/1.58 => ( finite2114249848tion_l
% 3.03/1.58 @ ( collect_option_l
% 3.03/1.58 @ ^ [X: option_l] :
% 3.03/1.58 ( ( P @ X )
% 3.03/1.58 & ( Q @ X ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_211_finite__Collect__conjI,axiom,
% 3.03/1.58 ! [P: option_r > $o,Q: option_r > $o] :
% 3.03/1.58 ( ( ( finite16335230tion_r @ ( collect_option_r @ P ) )
% 3.03/1.58 | ( finite16335230tion_r @ ( collect_option_r @ Q ) ) )
% 3.03/1.58 => ( finite16335230tion_r
% 3.03/1.58 @ ( collect_option_r
% 3.03/1.58 @ ^ [X: option_r] :
% 3.03/1.58 ( ( P @ X )
% 3.03/1.58 & ( Q @ X ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_212_finite__Collect__conjI,axiom,
% 3.03/1.58 ! [P: r > $o,Q: r > $o] :
% 3.03/1.58 ( ( ( finite_finite_r @ ( collect_r @ P ) )
% 3.03/1.58 | ( finite_finite_r @ ( collect_r @ Q ) ) )
% 3.03/1.58 => ( finite_finite_r
% 3.03/1.58 @ ( collect_r
% 3.03/1.58 @ ^ [X: r] :
% 3.03/1.58 ( ( P @ X )
% 3.03/1.58 & ( Q @ X ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_213_finite__Collect__conjI,axiom,
% 3.03/1.58 ! [P: l > $o,Q: l > $o] :
% 3.03/1.58 ( ( ( finite_finite_l @ ( collect_l @ P ) )
% 3.03/1.58 | ( finite_finite_l @ ( collect_l @ Q ) ) )
% 3.03/1.58 => ( finite_finite_l
% 3.03/1.58 @ ( collect_l
% 3.03/1.58 @ ^ [X: l] :
% 3.03/1.58 ( ( P @ X )
% 3.03/1.58 & ( Q @ X ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_214_const_Odistinct_I1_J,axiom,
% 3.03/1.58 unit != f ).
% 3.03/1.58
% 3.03/1.58 thf(fact_215_const_Odistinct_I5_J,axiom,
% 3.03/1.58 f != t ).
% 3.03/1.58
% 3.03/1.58 thf(fact_216_const_Oinduct,axiom,
% 3.03/1.58 ! [P: const > $o,Const: const] :
% 3.03/1.58 ( ( P @ unit )
% 3.03/1.58 => ( ( P @ f )
% 3.03/1.58 => ( ( P @ t )
% 3.03/1.58 => ( P @ Const ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_217_const_Oexhaust,axiom,
% 3.03/1.58 ! [Y: const] :
% 3.03/1.58 ( ( Y != unit )
% 3.03/1.58 => ( ( Y != f )
% 3.03/1.58 => ( Y = t ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_218_pigeonhole__infinite__rel,axiom,
% 3.03/1.58 ! [A4: set_option_r,B5: set_option_l,R7: option_r > option_l > $o] :
% 3.03/1.58 ( ~ ( finite16335230tion_r @ A4 )
% 3.03/1.58 => ( ( finite2114249848tion_l @ B5 )
% 3.03/1.58 => ( ! [X6: option_r] :
% 3.03/1.58 ( ( member_option_r @ X6 @ A4 )
% 3.03/1.58 => ? [Xa2: option_l] :
% 3.03/1.58 ( ( member_option_l @ Xa2 @ B5 )
% 3.03/1.58 & ( R7 @ X6 @ Xa2 ) ) )
% 3.03/1.58 => ? [X6: option_l] :
% 3.03/1.58 ( ( member_option_l @ X6 @ B5 )
% 3.03/1.58 & ~ ( finite16335230tion_r
% 3.03/1.58 @ ( collect_option_r
% 3.03/1.58 @ ^ [A2: option_r] :
% 3.03/1.58 ( ( member_option_r @ A2 @ A4 )
% 3.03/1.58 & ( R7 @ A2 @ X6 ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_219_pigeonhole__infinite__rel,axiom,
% 3.03/1.58 ! [A4: set_option_r,B5: set_option_r,R7: option_r > option_r > $o] :
% 3.03/1.58 ( ~ ( finite16335230tion_r @ A4 )
% 3.03/1.58 => ( ( finite16335230tion_r @ B5 )
% 3.03/1.58 => ( ! [X6: option_r] :
% 3.03/1.58 ( ( member_option_r @ X6 @ A4 )
% 3.03/1.58 => ? [Xa2: option_r] :
% 3.03/1.58 ( ( member_option_r @ Xa2 @ B5 )
% 3.03/1.58 & ( R7 @ X6 @ Xa2 ) ) )
% 3.03/1.58 => ? [X6: option_r] :
% 3.03/1.58 ( ( member_option_r @ X6 @ B5 )
% 3.03/1.58 & ~ ( finite16335230tion_r
% 3.03/1.58 @ ( collect_option_r
% 3.03/1.58 @ ^ [A2: option_r] :
% 3.03/1.58 ( ( member_option_r @ A2 @ A4 )
% 3.03/1.58 & ( R7 @ A2 @ X6 ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_220_pigeonhole__infinite__rel,axiom,
% 3.03/1.58 ! [A4: set_Pr1409704485_r_l_v,B5: set_r,R7: produc1389397445_r_l_v > r > $o] :
% 3.03/1.58 ( ~ ( finite1853159534_r_l_v @ A4 )
% 3.03/1.58 => ( ( finite_finite_r @ B5 )
% 3.03/1.58 => ( ! [X6: produc1389397445_r_l_v] :
% 3.03/1.58 ( ( member1522896238_r_l_v @ X6 @ A4 )
% 3.03/1.58 => ? [Xa2: r] :
% 3.03/1.58 ( ( member_r @ Xa2 @ B5 )
% 3.03/1.58 & ( R7 @ X6 @ Xa2 ) ) )
% 3.03/1.58 => ? [X6: r] :
% 3.03/1.58 ( ( member_r @ X6 @ B5 )
% 3.03/1.58 & ~ ( finite1853159534_r_l_v
% 3.03/1.58 @ ( collec1978425008_r_l_v
% 3.03/1.58 @ ^ [A2: produc1389397445_r_l_v] :
% 3.03/1.58 ( ( member1522896238_r_l_v @ A2 @ A4 )
% 3.03/1.58 & ( R7 @ A2 @ X6 ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_221_pigeonhole__infinite__rel,axiom,
% 3.03/1.58 ! [A4: set_Pr1409704485_r_l_v,B5: set_l,R7: produc1389397445_r_l_v > l > $o] :
% 3.03/1.58 ( ~ ( finite1853159534_r_l_v @ A4 )
% 3.03/1.58 => ( ( finite_finite_l @ B5 )
% 3.03/1.58 => ( ! [X6: produc1389397445_r_l_v] :
% 3.03/1.58 ( ( member1522896238_r_l_v @ X6 @ A4 )
% 3.03/1.58 => ? [Xa2: l] :
% 3.03/1.58 ( ( member_l @ Xa2 @ B5 )
% 3.03/1.58 & ( R7 @ X6 @ Xa2 ) ) )
% 3.03/1.58 => ? [X6: l] :
% 3.03/1.58 ( ( member_l @ X6 @ B5 )
% 3.03/1.58 & ~ ( finite1853159534_r_l_v
% 3.03/1.58 @ ( collec1978425008_r_l_v
% 3.03/1.58 @ ^ [A2: produc1389397445_r_l_v] :
% 3.03/1.58 ( ( member1522896238_r_l_v @ A2 @ A4 )
% 3.03/1.58 & ( R7 @ A2 @ X6 ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_222_pigeonhole__infinite__rel,axiom,
% 3.03/1.58 ! [A4: set_r,B5: set_r,R7: r > r > $o] :
% 3.03/1.58 ( ~ ( finite_finite_r @ A4 )
% 3.03/1.58 => ( ( finite_finite_r @ B5 )
% 3.03/1.58 => ( ! [X6: r] :
% 3.03/1.58 ( ( member_r @ X6 @ A4 )
% 3.03/1.58 => ? [Xa2: r] :
% 3.03/1.58 ( ( member_r @ Xa2 @ B5 )
% 3.03/1.58 & ( R7 @ X6 @ Xa2 ) ) )
% 3.03/1.58 => ? [X6: r] :
% 3.03/1.58 ( ( member_r @ X6 @ B5 )
% 3.03/1.58 & ~ ( finite_finite_r
% 3.03/1.58 @ ( collect_r
% 3.03/1.58 @ ^ [A2: r] :
% 3.03/1.58 ( ( member_r @ A2 @ A4 )
% 3.03/1.58 & ( R7 @ A2 @ X6 ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_223_pigeonhole__infinite__rel,axiom,
% 3.03/1.58 ! [A4: set_r,B5: set_l,R7: r > l > $o] :
% 3.03/1.58 ( ~ ( finite_finite_r @ A4 )
% 3.03/1.58 => ( ( finite_finite_l @ B5 )
% 3.03/1.58 => ( ! [X6: r] :
% 3.03/1.58 ( ( member_r @ X6 @ A4 )
% 3.03/1.58 => ? [Xa2: l] :
% 3.03/1.58 ( ( member_l @ Xa2 @ B5 )
% 3.03/1.58 & ( R7 @ X6 @ Xa2 ) ) )
% 3.03/1.58 => ? [X6: l] :
% 3.03/1.58 ( ( member_l @ X6 @ B5 )
% 3.03/1.58 & ~ ( finite_finite_r
% 3.03/1.58 @ ( collect_r
% 3.03/1.58 @ ^ [A2: r] :
% 3.03/1.58 ( ( member_r @ A2 @ A4 )
% 3.03/1.58 & ( R7 @ A2 @ X6 ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_224_pigeonhole__infinite__rel,axiom,
% 3.03/1.58 ! [A4: set_l,B5: set_r,R7: l > r > $o] :
% 3.03/1.58 ( ~ ( finite_finite_l @ A4 )
% 3.03/1.58 => ( ( finite_finite_r @ B5 )
% 3.03/1.58 => ( ! [X6: l] :
% 3.03/1.58 ( ( member_l @ X6 @ A4 )
% 3.03/1.58 => ? [Xa2: r] :
% 3.03/1.58 ( ( member_r @ Xa2 @ B5 )
% 3.03/1.58 & ( R7 @ X6 @ Xa2 ) ) )
% 3.03/1.58 => ? [X6: r] :
% 3.03/1.58 ( ( member_r @ X6 @ B5 )
% 3.03/1.58 & ~ ( finite_finite_l
% 3.03/1.58 @ ( collect_l
% 3.03/1.58 @ ^ [A2: l] :
% 3.03/1.58 ( ( member_l @ A2 @ A4 )
% 3.03/1.58 & ( R7 @ A2 @ X6 ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_225_pigeonhole__infinite__rel,axiom,
% 3.03/1.58 ! [A4: set_l,B5: set_l,R7: l > l > $o] :
% 3.03/1.58 ( ~ ( finite_finite_l @ A4 )
% 3.03/1.58 => ( ( finite_finite_l @ B5 )
% 3.03/1.58 => ( ! [X6: l] :
% 3.03/1.58 ( ( member_l @ X6 @ A4 )
% 3.03/1.58 => ? [Xa2: l] :
% 3.03/1.58 ( ( member_l @ Xa2 @ B5 )
% 3.03/1.58 & ( R7 @ X6 @ Xa2 ) ) )
% 3.03/1.58 => ? [X6: l] :
% 3.03/1.58 ( ( member_l @ X6 @ B5 )
% 3.03/1.58 & ~ ( finite_finite_l
% 3.03/1.58 @ ( collect_l
% 3.03/1.58 @ ^ [A2: l] :
% 3.03/1.58 ( ( member_l @ A2 @ A4 )
% 3.03/1.58 & ( R7 @ A2 @ X6 ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_226_not__finite__existsD,axiom,
% 3.03/1.58 ! [P: r > $o] :
% 3.03/1.58 ( ~ ( finite_finite_r @ ( collect_r @ P ) )
% 3.03/1.58 => ? [X_1: r] : ( P @ X_1 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_227_not__finite__existsD,axiom,
% 3.03/1.58 ! [P: l > $o] :
% 3.03/1.58 ( ~ ( finite_finite_l @ ( collect_l @ P ) )
% 3.03/1.58 => ? [X_1: l] : ( P @ X_1 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_228_finite__has__maximal2,axiom,
% 3.03/1.58 ! [A4: set_set_r,A: set_r] :
% 3.03/1.58 ( ( finite_finite_set_r @ A4 )
% 3.03/1.58 => ( ( member_set_r @ A @ A4 )
% 3.03/1.58 => ? [X6: set_r] :
% 3.03/1.58 ( ( member_set_r @ X6 @ A4 )
% 3.03/1.58 & ( ord_less_eq_set_r @ A @ X6 )
% 3.03/1.58 & ! [Xa2: set_r] :
% 3.03/1.58 ( ( member_set_r @ Xa2 @ A4 )
% 3.03/1.58 => ( ( ord_less_eq_set_r @ X6 @ Xa2 )
% 3.03/1.58 => ( X6 = Xa2 ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_229_finite__has__maximal2,axiom,
% 3.03/1.58 ! [A4: set_set_l,A: set_l] :
% 3.03/1.58 ( ( finite_finite_set_l @ A4 )
% 3.03/1.58 => ( ( member_set_l @ A @ A4 )
% 3.03/1.58 => ? [X6: set_l] :
% 3.03/1.58 ( ( member_set_l @ X6 @ A4 )
% 3.03/1.58 & ( ord_less_eq_set_l @ A @ X6 )
% 3.03/1.58 & ! [Xa2: set_l] :
% 3.03/1.58 ( ( member_set_l @ Xa2 @ A4 )
% 3.03/1.58 => ( ( ord_less_eq_set_l @ X6 @ Xa2 )
% 3.03/1.58 => ( X6 = Xa2 ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_230_finite__has__minimal2,axiom,
% 3.03/1.58 ! [A4: set_set_r,A: set_r] :
% 3.03/1.58 ( ( finite_finite_set_r @ A4 )
% 3.03/1.58 => ( ( member_set_r @ A @ A4 )
% 3.03/1.58 => ? [X6: set_r] :
% 3.03/1.58 ( ( member_set_r @ X6 @ A4 )
% 3.03/1.58 & ( ord_less_eq_set_r @ X6 @ A )
% 3.03/1.58 & ! [Xa2: set_r] :
% 3.03/1.58 ( ( member_set_r @ Xa2 @ A4 )
% 3.03/1.58 => ( ( ord_less_eq_set_r @ Xa2 @ X6 )
% 3.03/1.58 => ( X6 = Xa2 ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_231_finite__has__minimal2,axiom,
% 3.03/1.58 ! [A4: set_set_l,A: set_l] :
% 3.03/1.58 ( ( finite_finite_set_l @ A4 )
% 3.03/1.58 => ( ( member_set_l @ A @ A4 )
% 3.03/1.58 => ? [X6: set_l] :
% 3.03/1.58 ( ( member_set_l @ X6 @ A4 )
% 3.03/1.58 & ( ord_less_eq_set_l @ X6 @ A )
% 3.03/1.58 & ! [Xa2: set_l] :
% 3.03/1.58 ( ( member_set_l @ Xa2 @ A4 )
% 3.03/1.58 => ( ( ord_less_eq_set_l @ Xa2 @ X6 )
% 3.03/1.58 => ( X6 = Xa2 ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_232_finite__subset,axiom,
% 3.03/1.58 ! [A4: set_r,B5: set_r] :
% 3.03/1.58 ( ( ord_less_eq_set_r @ A4 @ B5 )
% 3.03/1.58 => ( ( finite_finite_r @ B5 )
% 3.03/1.58 => ( finite_finite_r @ A4 ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_233_finite__subset,axiom,
% 3.03/1.58 ! [A4: set_l,B5: set_l] :
% 3.03/1.58 ( ( ord_less_eq_set_l @ A4 @ B5 )
% 3.03/1.58 => ( ( finite_finite_l @ B5 )
% 3.03/1.58 => ( finite_finite_l @ A4 ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_234_infinite__super,axiom,
% 3.03/1.58 ! [S6: set_r,T2: set_r] :
% 3.03/1.58 ( ( ord_less_eq_set_r @ S6 @ T2 )
% 3.03/1.58 => ( ~ ( finite_finite_r @ S6 )
% 3.03/1.58 => ~ ( finite_finite_r @ T2 ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_235_infinite__super,axiom,
% 3.03/1.58 ! [S6: set_l,T2: set_l] :
% 3.03/1.58 ( ( ord_less_eq_set_l @ S6 @ T2 )
% 3.03/1.58 => ( ~ ( finite_finite_l @ S6 )
% 3.03/1.58 => ~ ( finite_finite_l @ T2 ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_236_rev__finite__subset,axiom,
% 3.03/1.58 ! [B5: set_r,A4: set_r] :
% 3.03/1.58 ( ( finite_finite_r @ B5 )
% 3.03/1.58 => ( ( ord_less_eq_set_r @ A4 @ B5 )
% 3.03/1.58 => ( finite_finite_r @ A4 ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_237_rev__finite__subset,axiom,
% 3.03/1.58 ! [B5: set_l,A4: set_l] :
% 3.03/1.58 ( ( finite_finite_l @ B5 )
% 3.03/1.58 => ( ( ord_less_eq_set_l @ A4 @ B5 )
% 3.03/1.58 => ( finite_finite_l @ A4 ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_238_finite__update__induct,axiom,
% 3.03/1.58 ! [F: r > option1457017436_r_l_v,C: option1457017436_r_l_v,P: ( r > option1457017436_r_l_v ) > $o] :
% 3.03/1.58 ( ( finite_finite_r
% 3.03/1.58 @ ( collect_r
% 3.03/1.58 @ ^ [A2: r] :
% 3.03/1.58 ( ( F @ A2 )
% 3.03/1.58 != C ) ) )
% 3.03/1.58 => ( ( P
% 3.03/1.58 @ ^ [A2: r] : C )
% 3.03/1.58 => ( ! [A3: r,B3: option1457017436_r_l_v,F3: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( finite_finite_r
% 3.03/1.58 @ ( collect_r
% 3.03/1.58 @ ^ [C2: r] :
% 3.03/1.58 ( ( F3 @ C2 )
% 3.03/1.58 != C ) ) )
% 3.03/1.58 => ( ( ( F3 @ A3 )
% 3.03/1.58 = C )
% 3.03/1.58 => ( ( B3 != C )
% 3.03/1.58 => ( ( P @ F3 )
% 3.03/1.58 => ( P @ ( fun_up709272714_r_l_v @ F3 @ A3 @ B3 ) ) ) ) ) )
% 3.03/1.58 => ( P @ F ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_239_finite__update__induct,axiom,
% 3.03/1.58 ! [F: l > option_val_r_l_v,C: option_val_r_l_v,P: ( l > option_val_r_l_v ) > $o] :
% 3.03/1.58 ( ( finite_finite_l
% 3.03/1.58 @ ( collect_l
% 3.03/1.58 @ ^ [A2: l] :
% 3.03/1.58 ( ( F @ A2 )
% 3.03/1.58 != C ) ) )
% 3.03/1.58 => ( ( P
% 3.03/1.58 @ ^ [A2: l] : C )
% 3.03/1.58 => ( ! [A3: l,B3: option_val_r_l_v,F3: l > option_val_r_l_v] :
% 3.03/1.58 ( ( finite_finite_l
% 3.03/1.58 @ ( collect_l
% 3.03/1.58 @ ^ [C2: l] :
% 3.03/1.58 ( ( F3 @ C2 )
% 3.03/1.58 != C ) ) )
% 3.03/1.58 => ( ( ( F3 @ A3 )
% 3.03/1.58 = C )
% 3.03/1.58 => ( ( B3 != C )
% 3.03/1.58 => ( ( P @ F3 )
% 3.03/1.58 => ( P @ ( fun_up1835647912_r_l_v @ F3 @ A3 @ B3 ) ) ) ) ) )
% 3.03/1.58 => ( P @ F ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_240_substitution_Orevision__step_OifFalse,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.03/1.58 => ( revision_step_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ E22 ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_241_substitution_OifFalse__deterministic,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.03/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.03/1.58 = ( S2
% 3.03/1.58 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ E22 ) ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_242_substitution_Orevision__step__relaxed_OifFalse,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,E1: expr_r_l_v,E22: expr_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ite_r_l_v @ ( vE_r_l_v @ ( cV_r_l_v @ f ) ) @ E1 @ E22 ) ) ) ) ) )
% 3.03/1.58 => ( revisi1291188644_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ E22 ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_243_reachable__imp__identifiers__available_I1_J,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( reachable_r_l_v @ subst @ S )
% 3.03/1.58 => ( ~ ( finite_finite_r @ top_top_set_r )
% 3.03/1.58 => ? [R6: r] :
% 3.03/1.58 ~ ( member_r @ R6 @ ( rID_G_r_l_v @ S ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_244_local__state__of__finite__restricted__global__state__is__finite_I1_J,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
% 3.03/1.58 ( ( ( S @ R2 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ Ls ) )
% 3.03/1.58 => ( ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 3.03/1.58 => ( ( R != R2 )
% 3.03/1.58 => ( finite_finite_r @ ( rID_L_l_r_v @ Ls ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_245_empty__map__finite_I4_J,axiom,
% 3.03/1.58 ( finite_finite_l
% 3.03/1.58 @ ( lID_G_r_l_v
% 3.03/1.58 @ ^ [X: r] : none_P277133687_r_l_v ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_246_RID_092_060_094sub_062L__finite__invariant,axiom,
% 3.03/1.58 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.03/1.58 => ( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
% 3.03/1.58 => ( finite_finite_l @ ( lID_G_r_l_v @ S2 ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_247_reachable__imp__identifiers__finite_I2_J,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( reachable_r_l_v @ subst @ S )
% 3.03/1.58 => ( finite_finite_l @ ( lID_G_r_l_v @ S ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_248_finite__option__UNIV,axiom,
% 3.03/1.58 ( ( finite16335230tion_r @ top_top_set_option_r )
% 3.03/1.58 = ( finite_finite_r @ top_top_set_r ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_249_finite__option__UNIV,axiom,
% 3.03/1.58 ( ( finite2114249848tion_l @ top_top_set_option_l )
% 3.03/1.58 = ( finite_finite_l @ top_top_set_l ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_250_finite__Collect__not,axiom,
% 3.03/1.58 ! [P: r > $o] :
% 3.03/1.58 ( ( finite_finite_r @ ( collect_r @ P ) )
% 3.03/1.58 => ( ( finite_finite_r
% 3.03/1.58 @ ( collect_r
% 3.03/1.58 @ ^ [X: r] :
% 3.03/1.58 ~ ( P @ X ) ) )
% 3.03/1.58 = ( finite_finite_r @ top_top_set_r ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_251_finite__Collect__not,axiom,
% 3.03/1.58 ! [P: l > $o] :
% 3.03/1.58 ( ( finite_finite_l @ ( collect_l @ P ) )
% 3.03/1.58 => ( ( finite_finite_l
% 3.03/1.58 @ ( collect_l
% 3.03/1.58 @ ^ [X: l] :
% 3.03/1.58 ~ ( P @ X ) ) )
% 3.03/1.58 = ( finite_finite_l @ top_top_set_l ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_252_in__restricted__global__in__unrestricted__global_I2_J,axiom,
% 3.03/1.58 ! [L: l,S: r > option1457017436_r_l_v,R: r] :
% 3.03/1.58 ( ( member_l @ L @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 3.03/1.58 => ( member_l @ L @ ( lID_G_r_l_v @ S ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_253_RID_092_060_094sub_062GI_I2_J,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
% 3.03/1.58 ( ( ( S @ R2 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ Ls ) )
% 3.03/1.58 => ( ( member_r @ R @ ( rID_L_l_r_v @ Ls ) )
% 3.03/1.58 => ( member_r @ R @ ( rID_G_r_l_v @ S ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_254_finite__state__imp__restriction__finite_I2_J,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r] :
% 3.03/1.58 ( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
% 3.03/1.58 => ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_255_in__restricted__global__in__updated__global_I2_J,axiom,
% 3.03/1.58 ! [L: l,S: r > option1457017436_r_l_v,R: r,Ls: produc1156025366_r_l_v] :
% 3.03/1.58 ( ( member_l @ L @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 3.03/1.58 => ( member_l @ L @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ Ls ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_256_substitution_Oreachable__imp__identifiers__available_I2_J,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( reachable_r_l_v @ Subst @ S )
% 3.03/1.58 => ( ~ ( finite_finite_l @ top_top_set_l )
% 3.03/1.58 => ? [L2: l] :
% 3.03/1.58 ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_257_substitution_ORID_092_060_094sub_062L__finite__invariant,axiom,
% 3.03/1.58 ! [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] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.03/1.58 => ( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
% 3.03/1.58 => ( finite_finite_l @ ( lID_G_r_l_v @ S2 ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_258_ID__restricted__global__subset__unrestricted_I1_J,axiom,
% 3.03/1.58 ! [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 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_259_substitution_Oreachable__imp__identifiers__finite_I2_J,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( reachable_r_l_v @ Subst @ S )
% 3.03/1.58 => ( finite_finite_l @ ( lID_G_r_l_v @ S ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_260_substitution_Oempty__map__finite_I4_J,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( finite_finite_l
% 3.03/1.58 @ ( lID_G_r_l_v
% 3.03/1.58 @ ^ [X: r] : none_P277133687_r_l_v ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_261_substitution_Oreachable__imp__identifiers__available_I1_J,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( reachable_r_l_v @ Subst @ S )
% 3.03/1.58 => ( ~ ( finite_finite_r @ top_top_set_r )
% 3.03/1.58 => ? [R6: r] :
% 3.03/1.58 ~ ( member_r @ R6 @ ( rID_G_r_l_v @ S ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_262_substitution_Ofinite__state__imp__restriction__finite_I2_J,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
% 3.03/1.58 => ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_263_substitution_Olocal__state__of__finite__restricted__global__state__is__finite_I1_J,axiom,
% 3.03/1.58 ! [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] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( ( S @ R2 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ Ls ) )
% 3.03/1.58 => ( ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 3.03/1.58 => ( ( R != R2 )
% 3.03/1.58 => ( finite_finite_r @ ( rID_L_l_r_v @ Ls ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_264_only__new__introduces__lids_H,axiom,
% 3.03/1.58 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v,L: l] :
% 3.03/1.58 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.03/1.58 => ( ! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,V2: val_r_l_v] :
% 3.03/1.58 ( ( S @ R )
% 3.03/1.58 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ref_r_l_v @ ( vE_r_l_v @ V2 ) ) ) ) ) ) )
% 3.03/1.58 => ( ~ ( member_l @ L @ ( lID_G_r_l_v @ S ) )
% 3.03/1.58 => ~ ( member_l @ L @ ( lID_G_r_l_v @ S2 ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_265_local__state__of__finite__restricted__global__state__is__finite_I2_J,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
% 3.03/1.58 ( ( ( S @ R2 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ Ls ) )
% 3.03/1.58 => ( ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 3.03/1.58 => ( ( R != R2 )
% 3.03/1.58 => ( finite_finite_l @ ( lID_L_l_r_v @ Ls ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_266_only__new__introduces__lids,axiom,
% 3.03/1.58 ! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.03/1.58 => ( ! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,V2: val_r_l_v] :
% 3.03/1.58 ( ( S @ R )
% 3.03/1.58 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ref_r_l_v @ ( vE_r_l_v @ V2 ) ) ) ) ) ) )
% 3.03/1.58 => ( ord_less_eq_set_l @ ( lID_G_r_l_v @ S2 ) @ ( lID_G_r_l_v @ S ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_267_expr_Oinject_I4_J,axiom,
% 3.03/1.58 ! [X4: expr_r_l_v,Y4: expr_r_l_v] :
% 3.03/1.58 ( ( ( ref_r_l_v @ X4 )
% 3.03/1.58 = ( ref_r_l_v @ Y4 ) )
% 3.03/1.58 = ( X4 = Y4 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_268_reachable__imp__identifiers__available_I2_J,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( reachable_r_l_v @ subst @ S )
% 3.03/1.58 => ( ~ ( finite_finite_l @ top_top_set_l )
% 3.03/1.58 => ? [L2: l] :
% 3.03/1.58 ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_269_LID_092_060_094sub_062GI,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r,Ls: produc1156025366_r_l_v,L: l] :
% 3.03/1.58 ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ Ls ) )
% 3.03/1.58 => ( ( member_l @ L @ ( lID_L_l_r_v @ Ls ) )
% 3.03/1.58 => ( member_l @ L @ ( lID_G_r_l_v @ S ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_270_expr_Odistinct_I41_J,axiom,
% 3.03/1.58 ! [X4: expr_r_l_v,X7: expr_r_l_v] :
% 3.03/1.58 ( ( ref_r_l_v @ X4 )
% 3.03/1.58 != ( rfork_r_l_v @ X7 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_271_expr_Odistinct_I43_J,axiom,
% 3.03/1.58 ! [X4: expr_r_l_v,X8: expr_r_l_v] :
% 3.03/1.58 ( ( ref_r_l_v @ X4 )
% 3.03/1.58 != ( rjoin_r_l_v @ X8 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_272_expr_Odistinct_I5_J,axiom,
% 3.03/1.58 ! [X1: val_r_l_v,X4: expr_r_l_v] :
% 3.03/1.58 ( ( vE_r_l_v @ X1 )
% 3.03/1.58 != ( ref_r_l_v @ X4 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_273_expr_Odistinct_I27_J,axiom,
% 3.03/1.58 ! [X31: expr_r_l_v,X32: expr_r_l_v,X33: expr_r_l_v,X4: expr_r_l_v] :
% 3.03/1.58 ( ( ite_r_l_v @ X31 @ X32 @ X33 )
% 3.03/1.58 != ( ref_r_l_v @ X4 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_274_LID_092_060_094sub_062GE,axiom,
% 3.03/1.58 ! [L: l,S: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( member_l @ L @ ( lID_G_r_l_v @ S ) )
% 3.03/1.58 => ~ ! [R6: r,Ls3: produc1156025366_r_l_v] :
% 3.03/1.58 ( ( ( S @ R6 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ Ls3 ) )
% 3.03/1.58 => ~ ( member_l @ L @ ( lID_L_l_r_v @ Ls3 ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_275_substitution_Oonly__new__introduces__lids_H,axiom,
% 3.03/1.58 ! [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,L: l] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.03/1.58 => ( ! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,V2: val_r_l_v] :
% 3.03/1.58 ( ( S @ R )
% 3.03/1.58 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ref_r_l_v @ ( vE_r_l_v @ V2 ) ) ) ) ) ) )
% 3.03/1.58 => ( ~ ( member_l @ L @ ( lID_G_r_l_v @ S ) )
% 3.03/1.58 => ~ ( member_l @ L @ ( lID_G_r_l_v @ S2 ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_276_substitution_Oonly__new__introduces__lids,axiom,
% 3.03/1.58 ! [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] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.03/1.58 => ( ! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E3: cntxt_r_l_v,V2: val_r_l_v] :
% 3.03/1.58 ( ( S @ R )
% 3.03/1.58 != ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E3 @ ( ref_r_l_v @ ( vE_r_l_v @ V2 ) ) ) ) ) ) )
% 3.03/1.58 => ( ord_less_eq_set_l @ ( lID_G_r_l_v @ S2 ) @ ( lID_G_r_l_v @ S ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_277_substitution_Olocal__state__of__finite__restricted__global__state__is__finite_I2_J,axiom,
% 3.03/1.58 ! [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] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( ( S @ R2 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ Ls ) )
% 3.03/1.58 => ( ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
% 3.03/1.58 => ( ( R != R2 )
% 3.03/1.58 => ( finite_finite_l @ ( lID_L_l_r_v @ Ls ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_278_domains__subsume__def,axiom,
% 3.03/1.58 ( domain87684397_l_r_v
% 3.03/1.58 = ( ^ [Ls2: produc1156025366_r_l_v] : ( ord_less_eq_set_l @ ( lID_L_l_r_v @ Ls2 ) @ ( doms_l_r_v @ Ls2 ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_279_revision__step_Onew,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,V: val_r_l_v,L: l] :
% 3.03/1.58 ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 3.03/1.58 => ( ~ ( member_l @ L @ ( lID_G_r_l_v @ S ) )
% 3.03/1.58 => ( revision_step_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau @ L @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_280_val_Oinject_I3_J,axiom,
% 3.03/1.58 ! [X34: l,Y3: l] :
% 3.03/1.58 ( ( ( loc_l_r_v @ X34 )
% 3.03/1.58 = ( loc_l_r_v @ Y3 ) )
% 3.03/1.58 = ( X34 = Y3 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_281_new__pseudodeterministic,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 3.03/1.58 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.03/1.58 = ( ? [L3: l] :
% 3.03/1.58 ( ~ ( member_l @ L3 @ ( lID_G_r_l_v @ S ) )
% 3.03/1.58 & ( S2
% 3.03/1.58 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau @ L3 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( loc_l_r_v @ L3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_282_val_Odistinct_I15_J,axiom,
% 3.03/1.58 ! [X34: l,X4: r] :
% 3.03/1.58 ( ( loc_l_r_v @ X34 )
% 3.03/1.58 != ( rid_r_l_v @ X4 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_283_val_Odistinct_I3_J,axiom,
% 3.03/1.58 ! [X1: const,X34: l] :
% 3.03/1.58 ( ( cV_r_l_v @ X1 )
% 3.03/1.58 != ( loc_l_r_v @ X34 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_284_substitution_Odomains__subsume__def,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,Ls: produc1156025366_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( domain87684397_l_r_v @ Ls )
% 3.03/1.58 = ( ord_less_eq_set_l @ ( lID_L_l_r_v @ Ls ) @ ( doms_l_r_v @ Ls ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_285_substitution_Onew__pseudodeterministic,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 3.03/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.03/1.58 = ( ? [L3: l] :
% 3.03/1.58 ( ~ ( member_l @ L3 @ ( lID_G_r_l_v @ S ) )
% 3.03/1.58 & ( S2
% 3.03/1.58 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau @ L3 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( loc_l_r_v @ L3 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_286_substitution_Orevision__step_Onew,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,V: val_r_l_v,L: l] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 3.03/1.58 => ( ~ ( member_l @ L @ ( lID_G_r_l_v @ S ) )
% 3.03/1.58 => ( revision_step_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau @ L @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_287_revision__step__relaxed_Oset,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,L: l,V: val_r_l_v] :
% 3.03/1.58 ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 3.03/1.58 => ( revisi1291188644_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau @ L @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_288_substitution_Orevision__step__relaxed_Oset,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,L: l,V: val_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 3.03/1.58 => ( revisi1291188644_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau @ L @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_289_expr_Oinject_I6_J,axiom,
% 3.03/1.58 ! [X61: expr_r_l_v,X62: expr_r_l_v,Y61: expr_r_l_v,Y62: expr_r_l_v] :
% 3.03/1.58 ( ( ( assign_r_l_v @ X61 @ X62 )
% 3.03/1.58 = ( assign_r_l_v @ Y61 @ Y62 ) )
% 3.03/1.58 = ( ( X61 = Y61 )
% 3.03/1.58 & ( X62 = Y62 ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_290_expr_Odistinct_I39_J,axiom,
% 3.03/1.58 ! [X4: expr_r_l_v,X61: expr_r_l_v,X62: expr_r_l_v] :
% 3.03/1.58 ( ( ref_r_l_v @ X4 )
% 3.03/1.58 != ( assign_r_l_v @ X61 @ X62 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_291_expr_Odistinct_I51_J,axiom,
% 3.03/1.58 ! [X61: expr_r_l_v,X62: expr_r_l_v,X7: expr_r_l_v] :
% 3.03/1.58 ( ( assign_r_l_v @ X61 @ X62 )
% 3.03/1.58 != ( rfork_r_l_v @ X7 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_292_expr_Odistinct_I53_J,axiom,
% 3.03/1.58 ! [X61: expr_r_l_v,X62: expr_r_l_v,X8: expr_r_l_v] :
% 3.03/1.58 ( ( assign_r_l_v @ X61 @ X62 )
% 3.03/1.58 != ( rjoin_r_l_v @ X8 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_293_expr_Odistinct_I9_J,axiom,
% 3.03/1.58 ! [X1: val_r_l_v,X61: expr_r_l_v,X62: expr_r_l_v] :
% 3.03/1.58 ( ( vE_r_l_v @ X1 )
% 3.03/1.58 != ( assign_r_l_v @ X61 @ X62 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_294_expr_Odistinct_I31_J,axiom,
% 3.03/1.58 ! [X31: expr_r_l_v,X32: expr_r_l_v,X33: expr_r_l_v,X61: expr_r_l_v,X62: expr_r_l_v] :
% 3.03/1.58 ( ( ite_r_l_v @ X31 @ X32 @ X33 )
% 3.03/1.58 != ( assign_r_l_v @ X61 @ X62 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_295_revision__step_Oset,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,L: l,V: val_r_l_v] :
% 3.03/1.58 ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 3.03/1.58 => ( ( member_l @ L @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau ) ) )
% 3.03/1.58 => ( revision_step_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau @ L @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_296_set__deterministic,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,L: l,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 3.03/1.58 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.03/1.58 = ( ( member_l @ L @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau ) ) )
% 3.03/1.58 & ( S2
% 3.03/1.58 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau @ L @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_297_dom__const,axiom,
% 3.03/1.58 ! [F: r > produc1156025366_r_l_v] :
% 3.03/1.58 ( ( dom_r_259548057_r_l_v
% 3.03/1.58 @ ^ [X: r] : ( some_P1807977723_r_l_v @ ( F @ X ) ) )
% 3.03/1.58 = top_top_set_r ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_298_dom__const,axiom,
% 3.03/1.58 ! [F: r > val_r_l_v] :
% 3.03/1.58 ( ( dom_r_val_r_l_v
% 3.03/1.58 @ ^ [X: r] : ( some_val_r_l_v @ ( F @ X ) ) )
% 3.03/1.58 = top_top_set_r ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_299_dom__const,axiom,
% 3.03/1.58 ! [F: l > produc1156025366_r_l_v] :
% 3.03/1.58 ( ( dom_l_45837855_r_l_v
% 3.03/1.58 @ ^ [X: l] : ( some_P1807977723_r_l_v @ ( F @ X ) ) )
% 3.03/1.58 = top_top_set_l ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_300_dom__const,axiom,
% 3.03/1.58 ! [F: l > val_r_l_v] :
% 3.03/1.58 ( ( dom_l_val_r_l_v
% 3.03/1.58 @ ^ [X: l] : ( some_val_r_l_v @ ( F @ X ) ) )
% 3.03/1.58 = top_top_set_l ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_301_domI,axiom,
% 3.03/1.58 ! [M: r > option1457017436_r_l_v,A: r,B: produc1156025366_r_l_v] :
% 3.03/1.58 ( ( ( M @ A )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ B ) )
% 3.03/1.58 => ( member_r @ A @ ( dom_r_259548057_r_l_v @ M ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_302_domI,axiom,
% 3.03/1.58 ! [M: produc1389397445_r_l_v > option1457017436_r_l_v,A: produc1389397445_r_l_v,B: produc1156025366_r_l_v] :
% 3.03/1.58 ( ( ( M @ A )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ B ) )
% 3.03/1.58 => ( member1522896238_r_l_v @ A @ ( dom_Pr1162080227_r_l_v @ M ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_303_domI,axiom,
% 3.03/1.58 ! [M: l > option1457017436_r_l_v,A: l,B: produc1156025366_r_l_v] :
% 3.03/1.58 ( ( ( M @ A )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ B ) )
% 3.03/1.58 => ( member_l @ A @ ( dom_l_45837855_r_l_v @ M ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_304_domI,axiom,
% 3.03/1.58 ! [M: r > option_val_r_l_v,A: r,B: val_r_l_v] :
% 3.03/1.58 ( ( ( M @ A )
% 3.03/1.58 = ( some_val_r_l_v @ B ) )
% 3.03/1.58 => ( member_r @ A @ ( dom_r_val_r_l_v @ M ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_305_domI,axiom,
% 3.03/1.58 ! [M: produc1389397445_r_l_v > option_val_r_l_v,A: produc1389397445_r_l_v,B: val_r_l_v] :
% 3.03/1.58 ( ( ( M @ A )
% 3.03/1.58 = ( some_val_r_l_v @ B ) )
% 3.03/1.58 => ( member1522896238_r_l_v @ A @ ( dom_Pr939617279_r_l_v @ M ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_306_domI,axiom,
% 3.03/1.58 ! [M: l > option_val_r_l_v,A: l,B: val_r_l_v] :
% 3.03/1.58 ( ( ( M @ A )
% 3.03/1.58 = ( some_val_r_l_v @ B ) )
% 3.03/1.58 => ( member_l @ A @ ( dom_l_val_r_l_v @ M ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_307_domD,axiom,
% 3.03/1.58 ! [A: r,M: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( member_r @ A @ ( dom_r_259548057_r_l_v @ M ) )
% 3.03/1.58 => ? [B3: produc1156025366_r_l_v] :
% 3.03/1.58 ( ( M @ A )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ B3 ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_308_domD,axiom,
% 3.03/1.58 ! [A: produc1389397445_r_l_v,M: produc1389397445_r_l_v > option1457017436_r_l_v] :
% 3.03/1.58 ( ( member1522896238_r_l_v @ A @ ( dom_Pr1162080227_r_l_v @ M ) )
% 3.03/1.58 => ? [B3: produc1156025366_r_l_v] :
% 3.03/1.58 ( ( M @ A )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ B3 ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_309_domD,axiom,
% 3.03/1.58 ! [A: l,M: l > option1457017436_r_l_v] :
% 3.03/1.58 ( ( member_l @ A @ ( dom_l_45837855_r_l_v @ M ) )
% 3.03/1.58 => ? [B3: produc1156025366_r_l_v] :
% 3.03/1.58 ( ( M @ A )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ B3 ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_310_domD,axiom,
% 3.03/1.58 ! [A: r,M: r > option_val_r_l_v] :
% 3.03/1.58 ( ( member_r @ A @ ( dom_r_val_r_l_v @ M ) )
% 3.03/1.58 => ? [B3: val_r_l_v] :
% 3.03/1.58 ( ( M @ A )
% 3.03/1.58 = ( some_val_r_l_v @ B3 ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_311_domD,axiom,
% 3.03/1.58 ! [A: produc1389397445_r_l_v,M: produc1389397445_r_l_v > option_val_r_l_v] :
% 3.03/1.58 ( ( member1522896238_r_l_v @ A @ ( dom_Pr939617279_r_l_v @ M ) )
% 3.03/1.58 => ? [B3: val_r_l_v] :
% 3.03/1.58 ( ( M @ A )
% 3.03/1.58 = ( some_val_r_l_v @ B3 ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_312_domD,axiom,
% 3.03/1.58 ! [A: l,M: l > option_val_r_l_v] :
% 3.03/1.58 ( ( member_l @ A @ ( dom_l_val_r_l_v @ M ) )
% 3.03/1.58 => ? [B3: val_r_l_v] :
% 3.03/1.58 ( ( M @ A )
% 3.03/1.58 = ( some_val_r_l_v @ B3 ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_313_dom__def,axiom,
% 3.03/1.58 ( dom_l_val_r_l_v
% 3.03/1.58 = ( ^ [M2: l > option_val_r_l_v] :
% 3.03/1.58 ( collect_l
% 3.03/1.58 @ ^ [A2: l] :
% 3.03/1.58 ( ( M2 @ A2 )
% 3.03/1.58 != none_val_r_l_v ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_314_dom__def,axiom,
% 3.03/1.58 ( dom_r_259548057_r_l_v
% 3.03/1.58 = ( ^ [M2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( collect_r
% 3.03/1.58 @ ^ [A2: r] :
% 3.03/1.58 ( ( M2 @ A2 )
% 3.03/1.58 != none_P277133687_r_l_v ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_315_domIff,axiom,
% 3.03/1.58 ! [A: r,M: r > option_val_r_l_v] :
% 3.03/1.58 ( ( member_r @ A @ ( dom_r_val_r_l_v @ M ) )
% 3.03/1.58 = ( ( M @ A )
% 3.03/1.58 != none_val_r_l_v ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_316_domIff,axiom,
% 3.03/1.58 ! [A: produc1389397445_r_l_v,M: produc1389397445_r_l_v > option_val_r_l_v] :
% 3.03/1.58 ( ( member1522896238_r_l_v @ A @ ( dom_Pr939617279_r_l_v @ M ) )
% 3.03/1.58 = ( ( M @ A )
% 3.03/1.58 != none_val_r_l_v ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_317_domIff,axiom,
% 3.03/1.58 ! [A: l,M: l > option_val_r_l_v] :
% 3.03/1.58 ( ( member_l @ A @ ( dom_l_val_r_l_v @ M ) )
% 3.03/1.58 = ( ( M @ A )
% 3.03/1.58 != none_val_r_l_v ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_318_domIff,axiom,
% 3.03/1.58 ! [A: r,M: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( member_r @ A @ ( dom_r_259548057_r_l_v @ M ) )
% 3.03/1.58 = ( ( M @ A )
% 3.03/1.58 != none_P277133687_r_l_v ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_319_domIff,axiom,
% 3.03/1.58 ! [A: produc1389397445_r_l_v,M: produc1389397445_r_l_v > option1457017436_r_l_v] :
% 3.03/1.58 ( ( member1522896238_r_l_v @ A @ ( dom_Pr1162080227_r_l_v @ M ) )
% 3.03/1.58 = ( ( M @ A )
% 3.03/1.58 != none_P277133687_r_l_v ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_320_domIff,axiom,
% 3.03/1.58 ! [A: l,M: l > option1457017436_r_l_v] :
% 3.03/1.58 ( ( member_l @ A @ ( dom_l_45837855_r_l_v @ M ) )
% 3.03/1.58 = ( ( M @ A )
% 3.03/1.58 != none_P277133687_r_l_v ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_321_finite__map__freshness,axiom,
% 3.03/1.58 ! [F: r > option_val_r_l_v] :
% 3.03/1.58 ( ( finite_finite_r @ ( dom_r_val_r_l_v @ F ) )
% 3.03/1.58 => ( ~ ( finite_finite_r @ top_top_set_r )
% 3.03/1.58 => ? [X6: r] :
% 3.03/1.58 ( ( F @ X6 )
% 3.03/1.58 = none_val_r_l_v ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_322_finite__map__freshness,axiom,
% 3.03/1.58 ! [F: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( finite_finite_r @ ( dom_r_259548057_r_l_v @ F ) )
% 3.03/1.58 => ( ~ ( finite_finite_r @ top_top_set_r )
% 3.03/1.58 => ? [X6: r] :
% 3.03/1.58 ( ( F @ X6 )
% 3.03/1.58 = none_P277133687_r_l_v ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_323_finite__map__freshness,axiom,
% 3.03/1.58 ! [F: l > option_val_r_l_v] :
% 3.03/1.58 ( ( finite_finite_l @ ( dom_l_val_r_l_v @ F ) )
% 3.03/1.58 => ( ~ ( finite_finite_l @ top_top_set_l )
% 3.03/1.58 => ? [X6: l] :
% 3.03/1.58 ( ( F @ X6 )
% 3.03/1.58 = none_val_r_l_v ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_324_finite__map__freshness,axiom,
% 3.03/1.58 ! [F: l > option1457017436_r_l_v] :
% 3.03/1.58 ( ( finite_finite_l @ ( dom_l_45837855_r_l_v @ F ) )
% 3.03/1.58 => ( ~ ( finite_finite_l @ top_top_set_l )
% 3.03/1.58 => ? [X6: l] :
% 3.03/1.58 ( ( F @ X6 )
% 3.03/1.58 = none_P277133687_r_l_v ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_325_substitution_Oset__deterministic,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,L: l,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 3.03/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.03/1.58 = ( ( member_l @ L @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau ) ) )
% 3.03/1.58 & ( S2
% 3.03/1.58 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau @ L @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_326_substitution_Orevision__step_Oset,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,L: l,V: val_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( assign_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) @ ( vE_r_l_v @ V ) ) ) ) ) ) )
% 3.03/1.58 => ( ( member_l @ L @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau ) ) )
% 3.03/1.58 => ( revision_step_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau @ L @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_327_revision__step_Oget,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,L: l] :
% 3.03/1.58 ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( read_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) ) ) ) ) ) )
% 3.03/1.58 => ( ( member_l @ L @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau ) ) )
% 3.03/1.58 => ( revision_step_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( the_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau @ L ) ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_328_revision__step__relaxed_Oget,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,L: l] :
% 3.03/1.58 ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( read_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) ) ) ) ) ) )
% 3.03/1.58 => ( revisi1291188644_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( the_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau @ L ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_329__092_060S_062_092_060_094sub_062G__imp___092_060A_062__refl,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r] :
% 3.03/1.58 ( ( domain1547879849_r_l_v @ S )
% 3.03/1.58 => ( ( member_r @ R @ ( dom_r_259548057_r_l_v @ S ) )
% 3.03/1.58 => ( subsum148050133_r_l_v @ R @ R @ S ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_330_subsumes__accessible__globally__def,axiom,
% 3.03/1.58 ( subsum680764357_r_l_v
% 3.03/1.58 = ( ^ [S4: r > option1457017436_r_l_v] :
% 3.03/1.58 ! [R_12: r,R_22: r] :
% 3.03/1.58 ( ( member_r @ R_12 @ ( dom_r_259548057_r_l_v @ S4 ) )
% 3.03/1.58 => ( ( member_r @ R_22 @ ( dom_r_259548057_r_l_v @ S4 ) )
% 3.03/1.58 => ( subsum148050133_r_l_v @ R_12 @ R_22 @ S4 ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_331_expr_Oinject_I5_J,axiom,
% 3.03/1.58 ! [X52: expr_r_l_v,Y5: expr_r_l_v] :
% 3.03/1.58 ( ( ( read_r_l_v @ X52 )
% 3.03/1.58 = ( read_r_l_v @ Y5 ) )
% 3.03/1.58 = ( X52 = Y5 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_332_option_Ocollapse,axiom,
% 3.03/1.58 ! [Option: option1457017436_r_l_v] :
% 3.03/1.58 ( ( Option != none_P277133687_r_l_v )
% 3.03/1.58 => ( ( some_P1807977723_r_l_v @ ( the_Pr1541010602_r_l_v @ Option ) )
% 3.03/1.58 = Option ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_333_option_Ocollapse,axiom,
% 3.03/1.58 ! [Option: option_val_r_l_v] :
% 3.03/1.58 ( ( Option != none_val_r_l_v )
% 3.03/1.58 => ( ( some_val_r_l_v @ ( the_val_r_l_v @ Option ) )
% 3.03/1.58 = Option ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_334_get__deterministic,axiom,
% 3.03/1.58 ! [S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,L: l,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( read_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) ) ) ) ) ) )
% 3.03/1.58 => ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
% 3.03/1.58 = ( ( member_l @ L @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau ) ) )
% 3.03/1.58 & ( S2
% 3.03/1.58 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( the_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau @ L ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_335_expr_Odistinct_I37_J,axiom,
% 3.03/1.58 ! [X4: expr_r_l_v,X52: expr_r_l_v] :
% 3.03/1.58 ( ( ref_r_l_v @ X4 )
% 3.03/1.58 != ( read_r_l_v @ X52 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_336_option_Oexpand,axiom,
% 3.03/1.58 ! [Option: option_val_r_l_v,Option2: option_val_r_l_v] :
% 3.03/1.58 ( ( ( Option = none_val_r_l_v )
% 3.03/1.58 = ( Option2 = none_val_r_l_v ) )
% 3.03/1.58 => ( ( ( Option != none_val_r_l_v )
% 3.03/1.58 => ( ( Option2 != none_val_r_l_v )
% 3.03/1.58 => ( ( the_val_r_l_v @ Option )
% 3.03/1.58 = ( the_val_r_l_v @ Option2 ) ) ) )
% 3.03/1.58 => ( Option = Option2 ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_337_option_Oexpand,axiom,
% 3.03/1.58 ! [Option: option1457017436_r_l_v,Option2: option1457017436_r_l_v] :
% 3.03/1.58 ( ( ( Option = none_P277133687_r_l_v )
% 3.03/1.58 = ( Option2 = none_P277133687_r_l_v ) )
% 3.03/1.58 => ( ( ( Option != none_P277133687_r_l_v )
% 3.03/1.58 => ( ( Option2 != none_P277133687_r_l_v )
% 3.03/1.58 => ( ( the_Pr1541010602_r_l_v @ Option )
% 3.03/1.58 = ( the_Pr1541010602_r_l_v @ Option2 ) ) ) )
% 3.03/1.58 => ( Option = Option2 ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_338_expr_Odistinct_I47_J,axiom,
% 3.03/1.58 ! [X52: expr_r_l_v,X7: expr_r_l_v] :
% 3.03/1.58 ( ( read_r_l_v @ X52 )
% 3.03/1.58 != ( rfork_r_l_v @ X7 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_339_expr_Odistinct_I49_J,axiom,
% 3.03/1.58 ! [X52: expr_r_l_v,X8: expr_r_l_v] :
% 3.03/1.58 ( ( read_r_l_v @ X52 )
% 3.03/1.58 != ( rjoin_r_l_v @ X8 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_340_expr_Odistinct_I7_J,axiom,
% 3.03/1.58 ! [X1: val_r_l_v,X52: expr_r_l_v] :
% 3.03/1.58 ( ( vE_r_l_v @ X1 )
% 3.03/1.58 != ( read_r_l_v @ X52 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_341_expr_Odistinct_I29_J,axiom,
% 3.03/1.58 ! [X31: expr_r_l_v,X32: expr_r_l_v,X33: expr_r_l_v,X52: expr_r_l_v] :
% 3.03/1.58 ( ( ite_r_l_v @ X31 @ X32 @ X33 )
% 3.03/1.58 != ( read_r_l_v @ X52 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_342_expr_Odistinct_I45_J,axiom,
% 3.03/1.58 ! [X52: expr_r_l_v,X61: expr_r_l_v,X62: expr_r_l_v] :
% 3.03/1.58 ( ( read_r_l_v @ X52 )
% 3.03/1.58 != ( assign_r_l_v @ X61 @ X62 ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_343_option_Oexhaust__sel,axiom,
% 3.03/1.58 ! [Option: option1457017436_r_l_v] :
% 3.03/1.58 ( ( Option != none_P277133687_r_l_v )
% 3.03/1.58 => ( Option
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( the_Pr1541010602_r_l_v @ Option ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_344_option_Oexhaust__sel,axiom,
% 3.03/1.58 ! [Option: option_val_r_l_v] :
% 3.03/1.58 ( ( Option != none_val_r_l_v )
% 3.03/1.58 => ( Option
% 3.03/1.58 = ( some_val_r_l_v @ ( the_val_r_l_v @ Option ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_345_option_Osel,axiom,
% 3.03/1.58 ! [X22: produc1156025366_r_l_v] :
% 3.03/1.58 ( ( the_Pr1541010602_r_l_v @ ( some_P1807977723_r_l_v @ X22 ) )
% 3.03/1.58 = X22 ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_346_option_Osel,axiom,
% 3.03/1.58 ! [X22: val_r_l_v] :
% 3.03/1.58 ( ( the_val_r_l_v @ ( some_val_r_l_v @ X22 ) )
% 3.03/1.58 = X22 ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_347_RID_092_060_094sub_062GE,axiom,
% 3.03/1.58 ! [R: r,S: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( member_r @ R @ ( rID_G_r_l_v @ S ) )
% 3.03/1.58 => ( ~ ( member_r @ R @ ( dom_r_259548057_r_l_v @ S ) )
% 3.03/1.58 => ~ ! [R8: r,Ls3: produc1156025366_r_l_v] :
% 3.03/1.58 ( ( ( S @ R8 )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ Ls3 ) )
% 3.03/1.58 => ~ ( member_r @ R @ ( rID_L_l_r_v @ Ls3 ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_348_substitution_O_092_060S_062_092_060_094sub_062G__imp___092_060A_062__refl,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( domain1547879849_r_l_v @ S )
% 3.03/1.58 => ( ( member_r @ R @ ( dom_r_259548057_r_l_v @ S ) )
% 3.03/1.58 => ( subsum148050133_r_l_v @ R @ R @ S ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_349_substitution_Osubsumes__accessible__globally__def,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( subsum680764357_r_l_v @ S )
% 3.03/1.58 = ( ! [R_12: r,R_22: r] :
% 3.03/1.58 ( ( member_r @ R_12 @ ( dom_r_259548057_r_l_v @ S ) )
% 3.03/1.58 => ( ( member_r @ R_22 @ ( dom_r_259548057_r_l_v @ S ) )
% 3.03/1.58 => ( subsum148050133_r_l_v @ R_12 @ R_22 @ S ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_350_substitution_Orevision__step__relaxed_Oget,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,L: l] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( read_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) ) ) ) ) ) )
% 3.03/1.58 => ( revisi1291188644_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( the_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau @ L ) ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_351_substitution_Oget__deterministic,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,L: l,S2: r > option1457017436_r_l_v] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( read_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) ) ) ) ) ) )
% 3.03/1.58 => ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
% 3.03/1.58 = ( ( member_l @ L @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau ) ) )
% 3.03/1.58 & ( S2
% 3.03/1.58 = ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( the_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau @ L ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(fact_352_substitution_Orevision__step_Oget,axiom,
% 3.03/1.58 ! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E: cntxt_r_l_v,L: l] :
% 3.03/1.58 ( ( substitution_r_l_v @ Subst )
% 3.03/1.58 => ( ( ( S @ R )
% 3.03/1.58 = ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( read_r_l_v @ ( vE_r_l_v @ ( loc_l_r_v @ L ) ) ) ) ) ) ) )
% 3.03/1.58 => ( ( member_l @ L @ ( dom_l_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau ) ) )
% 3.03/1.58 => ( revision_step_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( the_val_r_l_v @ ( combine_l_val_r_l_v @ Sigma @ Tau @ L ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(help_If_2_1_If_001t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_T,axiom,
% 3.03/1.58 ! [X2: option_val_r_l_v,Y: option_val_r_l_v] :
% 3.03/1.58 ( ( if_option_val_r_l_v @ $false @ X2 @ Y )
% 3.03/1.58 = Y ) ).
% 3.03/1.58
% 3.03/1.58 thf(help_If_1_1_If_001t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_T,axiom,
% 3.03/1.58 ! [X2: option_val_r_l_v,Y: option_val_r_l_v] :
% 3.03/1.58 ( ( if_option_val_r_l_v @ $true @ X2 @ Y )
% 3.03/1.58 = X2 ) ).
% 3.03/1.58
% 3.03/1.58 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,
% 3.03/1.58 ! [P: $o] :
% 3.03/1.58 ( ( P = $true )
% 3.03/1.58 | ( P = $false ) ) ).
% 3.03/1.58
% 3.03/1.58 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,
% 3.03/1.58 ! [X2: option1457017436_r_l_v,Y: option1457017436_r_l_v] :
% 3.03/1.58 ( ( if_opt1153928738_r_l_v @ $false @ X2 @ Y )
% 3.03/1.59 = Y ) ).
% 3.03/1.59
% 3.03/1.59 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,
% 3.03/1.59 ! [X2: option1457017436_r_l_v,Y: option1457017436_r_l_v] :
% 3.03/1.59 ( ( if_opt1153928738_r_l_v @ $true @ X2 @ Y )
% 3.03/1.59 = X2 ) ).
% 3.03/1.59
% 3.03/1.59 thf(conj_0,conjecture,
% 3.03/1.59 ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r2 @ ( some_P1807977723_r_l_v @ x ) ) @ r3 @ ( 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 @ r4 ) ) ) ) ) ) ) @ r4
% 3.03/1.59 @ ( some_P1807977723_r_l_v
% 3.03/1.59 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
% 3.03/1.59 @ ( produc1834103605_r_l_v
% 3.03/1.59 @ ^ [X: l] : none_val_r_l_v
% 3.03/1.59 @ e2 ) ) ) )
% 3.03/1.59 = ( fun_up709272714_r_l_v
% 3.03/1.59 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s_1 @ r3 @ ( 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 @ r4 ) ) ) ) ) ) ) @ r4
% 3.03/1.59 @ ( some_P1807977723_r_l_v
% 3.03/1.59 @ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
% 3.03/1.59 @ ( produc1834103605_r_l_v
% 3.03/1.59 @ ^ [X: l] : none_val_r_l_v
% 3.03/1.59 @ e2 ) ) ) )
% 3.03/1.59 @ r2
% 3.03/1.59 @ ( some_P1807977723_r_l_v @ x ) ) ) ).
% 3.03/1.59 ------------------------
% 3.16/1.61 % (7760)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7638 for (2999ds/18Mi)
% 3.16/1.61 % (7754)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7638 for (2999ds/183Mi)
% 3.16/1.61 % (7755)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_7638 for (2999ds/4Mi)
% 3.16/1.61 % (7756)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_7638 for (2999ds/27Mi)
% 3.16/1.61 % (7755)Instruction limit reached!
% 3.16/1.61 % (7755)------------------------------
% 3.16/1.61 % (7755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.61 % (7755)Termination reason: Unknown
% 3.16/1.61 % (7755)Termination phase: shuffling
% 3.16/1.61
% 3.16/1.61 % (7755)Memory used [KB]: 1535
% 3.16/1.61 % (7755)Time elapsed: 0.003 s
% 3.16/1.61 % (7755)Instructions burned: 4 (million)
% 3.16/1.61 % (7755)------------------------------
% 3.16/1.61 % (7755)------------------------------
% 3.16/1.62 % (7760)Instruction limit reached!
% 3.16/1.62 % (7760)------------------------------
% 3.16/1.62 % (7760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.62 % (7760)Termination reason: Unknown
% 3.16/1.62 % (7760)Termination phase: shuffling
% 3.16/1.62
% 3.16/1.62 % (7760)Memory used [KB]: 1918
% 3.16/1.62 % (7760)Time elapsed: 0.008 s
% 3.16/1.62 % (7760)Instructions burned: 20 (million)
% 3.16/1.62 % (7760)------------------------------
% 3.16/1.62 % (7760)------------------------------
% 3.16/1.62 % (7757)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7638 for (2999ds/2Mi)
% 3.16/1.62 % (7758)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_7638 for (2999ds/2Mi)
% 3.16/1.62 % (7759)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_7638 for (2999ds/275Mi)
% 3.16/1.62 % (7757)Instruction limit reached!
% 3.16/1.62 % (7757)------------------------------
% 3.16/1.62 % (7757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.62 % (7757)Termination reason: Unknown
% 3.16/1.62 % (7758)Instruction limit reached!
% 3.16/1.62 % (7758)------------------------------
% 3.16/1.62 % (7758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.62 % (7757)Termination phase: shuffling
% 3.16/1.62
% 3.16/1.62 % (7757)Memory used [KB]: 1535
% 3.16/1.62 % (7757)Time elapsed: 0.004 s
% 3.16/1.62 % (7757)Instructions burned: 3 (million)
% 3.16/1.62 % (7757)------------------------------
% 3.16/1.62 % (7757)------------------------------
% 3.16/1.62 % (7758)Termination reason: Unknown
% 3.16/1.62 % (7758)Termination phase: shuffling
% 3.16/1.62
% 3.16/1.62 % (7758)Memory used [KB]: 1535
% 3.16/1.62 % (7758)Time elapsed: 0.004 s
% 3.16/1.62 % (7758)Instructions burned: 3 (million)
% 3.16/1.62 % (7758)------------------------------
% 3.16/1.62 % (7758)------------------------------
% 3.16/1.62 % (7756)Instruction limit reached!
% 3.16/1.62 % (7756)------------------------------
% 3.16/1.62 % (7756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.62 % (7756)Termination reason: Unknown
% 3.16/1.62 % (7756)Termination phase: shuffling
% 3.16/1.62
% 3.16/1.62 % (7756)Memory used [KB]: 1918
% 3.16/1.62 % (7756)Time elapsed: 0.011 s
% 3.16/1.62 % (7756)Instructions burned: 27 (million)
% 3.16/1.62 % (7756)------------------------------
% 3.16/1.62 % (7756)------------------------------
% 3.16/1.62 % (7761)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7638 for (2999ds/3Mi)
% 3.16/1.63 % (7761)Instruction limit reached!
% 3.16/1.63 % (7761)------------------------------
% 3.16/1.63 % (7761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.63 % (7761)Termination reason: Unknown
% 3.16/1.63 % (7761)Termination phase: shuffling
% 3.16/1.63
% 3.16/1.63 % (7761)Memory used [KB]: 1663
% 3.16/1.63 % (7761)Time elapsed: 0.003 s
% 3.16/1.63 % (7761)Instructions burned: 5 (million)
% 3.16/1.63 % (7761)------------------------------
% 3.16/1.63 % (7761)------------------------------
% 3.16/1.63 % (7762)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_7638 for (2999ds/37Mi)
% 3.16/1.63 % (7765)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_7638 for (2999ds/1041Mi)
% 3.16/1.64 % (7766)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_7638 for (2999ds/7Mi)
% 3.16/1.64 % (7762)Instruction limit reached!
% 3.16/1.64 % (7762)------------------------------
% 3.16/1.64 % (7762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.64 % (7762)Termination reason: Unknown
% 3.16/1.64 % (7762)Termination phase: shuffling
% 3.16/1.64
% 3.16/1.64 % (7762)Memory used [KB]: 2302
% 3.16/1.64 % (7762)Time elapsed: 0.012 s
% 3.16/1.64 % (7766)Instruction limit reached!
% 3.16/1.64 % (7766)------------------------------
% 3.16/1.64 % (7766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.64 % (7766)Termination reason: Unknown
% 3.16/1.64 % (7766)Termination phase: shuffling
% 3.16/1.64
% 3.16/1.64 % (7766)Memory used [KB]: 1663
% 3.16/1.64 % (7766)Time elapsed: 0.004 s
% 3.16/1.64 % (7766)Instructions burned: 8 (million)
% 3.16/1.64 % (7766)------------------------------
% 3.16/1.64 % (7766)------------------------------
% 3.16/1.64 % (7762)Instructions burned: 40 (million)
% 3.16/1.64 % (7762)------------------------------
% 3.16/1.64 % (7762)------------------------------
% 3.16/1.64 % (7763)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_7638 for (2999ds/15Mi)
% 3.16/1.64 % (7764)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_7638 for (2999ds/3Mi)
% 3.16/1.64 % (7764)Instruction limit reached!
% 3.16/1.64 % (7764)------------------------------
% 3.16/1.64 % (7764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.64 % (7764)Termination reason: Unknown
% 3.16/1.64 % (7764)Termination phase: shuffling
% 3.16/1.64
% 3.16/1.64 % (7764)Memory used [KB]: 1535
% 3.16/1.64 % (7764)Time elapsed: 0.004 s
% 3.16/1.64 % (7764)Instructions burned: 3 (million)
% 3.16/1.64 % (7764)------------------------------
% 3.16/1.64 % (7764)------------------------------
% 3.16/1.65 % (7767)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_7638 for (2999ds/16Mi)
% 3.16/1.65 % (7768)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_7638 for (2999ds/3Mi)
% 3.16/1.65 % (7763)Instruction limit reached!
% 3.16/1.65 % (7763)------------------------------
% 3.16/1.65 % (7763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.65 % (7763)Termination reason: Unknown
% 3.16/1.65 % (7763)Termination phase: shuffling
% 3.16/1.65
% 3.16/1.65 % (7763)Memory used [KB]: 1791
% 3.16/1.65 % (7763)Time elapsed: 0.012 s
% 3.16/1.65 % (7763)Instructions burned: 16 (million)
% 3.16/1.65 % (7763)------------------------------
% 3.16/1.65 % (7763)------------------------------
% 3.16/1.65 % (7768)Instruction limit reached!
% 3.16/1.65 % (7768)------------------------------
% 3.16/1.65 % (7768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.65 % (7768)Termination reason: Unknown
% 3.16/1.65 % (7768)Termination phase: shuffling
% 3.16/1.65
% 3.16/1.65 % (7768)Memory used [KB]: 1535
% 3.16/1.65 % (7768)Time elapsed: 0.003 s
% 3.16/1.65 % (7768)Instructions burned: 5 (million)
% 3.16/1.65 % (7768)------------------------------
% 3.16/1.65 % (7768)------------------------------
% 3.16/1.65 % (7767)Instruction limit reached!
% 3.16/1.65 % (7767)------------------------------
% 3.16/1.65 % (7767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.65 % (7767)Termination reason: Unknown
% 3.16/1.65 % (7767)Termination phase: shuffling
% 3.16/1.65
% 3.16/1.65 % (7767)Memory used [KB]: 1918
% 3.16/1.65 % (7767)Time elapsed: 0.007 s
% 3.16/1.65 % (7767)Instructions burned: 17 (million)
% 3.16/1.65 % (7767)------------------------------
% 3.16/1.65 % (7767)------------------------------
% 3.16/1.66 % (7769)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_7638 for (2999ds/3Mi)
% 3.16/1.66 % (7771)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_7638 for (2999ds/3Mi)
% 3.16/1.66 % (7771)Instruction limit reached!
% 3.16/1.66 % (7771)------------------------------
% 3.16/1.66 % (7771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.66 % (7771)Termination reason: Unknown
% 3.16/1.66 % (7771)Termination phase: shuffling
% 3.16/1.66
% 3.16/1.66 % (7771)Memory used [KB]: 1535
% 3.16/1.66 % (7771)Time elapsed: 0.002 s
% 3.16/1.66 % (7771)Instructions burned: 3 (million)
% 3.16/1.66 % (7771)------------------------------
% 3.16/1.66 % (7771)------------------------------
% 3.16/1.66 % (7769)Instruction limit reached!
% 3.16/1.66 % (7769)------------------------------
% 3.16/1.66 % (7769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.66 % (7769)Termination reason: Unknown
% 3.16/1.66 % (7769)Termination phase: shuffling
% 3.16/1.66
% 3.16/1.66 % (7769)Memory used [KB]: 1535
% 3.16/1.66 % (7769)Time elapsed: 0.005 s
% 3.16/1.66 % (7769)Instructions burned: 4 (million)
% 3.16/1.66 % (7769)------------------------------
% 3.16/1.66 % (7769)------------------------------
% 3.16/1.66 % (7754)Instruction limit reached!
% 3.16/1.66 % (7754)------------------------------
% 3.16/1.66 % (7754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.66 % (7754)Termination reason: Unknown
% 3.16/1.66 % (7754)Termination phase: Property scanning
% 3.16/1.66
% 3.16/1.66 % (7754)Memory used [KB]: 3070
% 3.16/1.66 % (7754)Time elapsed: 0.052 s
% 3.16/1.66 % (7754)Instructions burned: 183 (million)
% 3.16/1.66 % (7754)------------------------------
% 3.16/1.66 % (7754)------------------------------
% 3.16/1.66 % (7772)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_7638 for (2999ds/4Mi)
% 3.16/1.67 % (7770)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_7638 for (2999ds/7Mi)
% 3.16/1.67 % (7772)Instruction limit reached!
% 3.16/1.67 % (7772)------------------------------
% 3.16/1.67 % (7772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.67 % (7772)Termination reason: Unknown
% 3.16/1.67 % (7772)Termination phase: shuffling
% 3.16/1.67
% 3.16/1.67 % (7772)Memory used [KB]: 1663
% 3.16/1.67 % (7772)Time elapsed: 0.003 s
% 3.16/1.67 % (7772)Instructions burned: 6 (million)
% 3.16/1.67 % (7772)------------------------------
% 3.16/1.67 % (7772)------------------------------
% 3.16/1.67 % (7770)Instruction limit reached!
% 3.16/1.67 % (7770)------------------------------
% 3.16/1.67 % (7770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.67 % (7770)Termination reason: Unknown
% 3.16/1.67 % (7770)Termination phase: shuffling
% 3.16/1.67
% 3.16/1.67 % (7770)Memory used [KB]: 1663
% 3.16/1.67 % (7770)Time elapsed: 0.004 s
% 3.16/1.67 % (7770)Instructions burned: 8 (million)
% 3.16/1.67 % (7770)------------------------------
% 3.16/1.67 % (7770)------------------------------
% 3.16/1.67 % (7773)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_7638 for (2999ds/18Mi)
% 3.16/1.67 % (7775)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7638 for (2999ds/6Mi)
% 3.16/1.68 % (7776)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_7638 for (2999ds/902Mi)
% 3.16/1.68 % (7775)Instruction limit reached!
% 3.16/1.68 % (7775)------------------------------
% 3.16/1.68 % (7775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.68 % (7775)Termination reason: Unknown
% 3.16/1.68 % (7775)Termination phase: shuffling
% 3.16/1.68
% 3.16/1.68 % (7775)Memory used [KB]: 1663
% 3.16/1.68 % (7775)Time elapsed: 0.004 s
% 3.16/1.68 % (7775)Instructions burned: 8 (million)
% 3.16/1.68 % (7775)------------------------------
% 3.16/1.68 % (7775)------------------------------
% 3.16/1.68 % (7773)Instruction limit reached!
% 3.16/1.68 % (7773)------------------------------
% 3.16/1.68 % (7773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.68 % (7773)Termination reason: Unknown
% 3.16/1.68 % (7773)Termination phase: shuffling
% 3.16/1.68
% 3.16/1.68 % (7773)Memory used [KB]: 1918
% 3.16/1.68 % (7773)Time elapsed: 0.007 s
% 3.16/1.68 % (7773)Instructions burned: 19 (million)
% 3.16/1.68 % (7773)------------------------------
% 3.16/1.68 % (7773)------------------------------
% 3.16/1.68 % (7777)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_7638 for (2999ds/21Mi)
% 3.16/1.68 % (7774)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_7638 for (2999ds/710Mi)
% 3.16/1.69 % (7778)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_7638 for (2999ds/5Mi)
% 3.16/1.69 % (7779)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_7638 for (2999ds/6Mi)
% 3.16/1.69 % (7777)Instruction limit reached!
% 3.16/1.69 % (7777)------------------------------
% 3.16/1.69 % (7777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.69 % (7777)Termination reason: Unknown
% 3.16/1.69 % (7777)Termination phase: shuffling
% 3.16/1.69
% 3.16/1.69 % (7777)Memory used [KB]: 1918
% 3.16/1.69 % (7777)Time elapsed: 0.009 s
% 3.16/1.69 % (7777)Instructions burned: 23 (million)
% 3.16/1.69 % (7777)------------------------------
% 3.16/1.69 % (7777)------------------------------
% 3.16/1.69 % (7759)First to succeed.
% 3.16/1.69 % (7778)Instruction limit reached!
% 3.16/1.69 % (7778)------------------------------
% 3.16/1.69 % (7778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.69 % (7778)Termination reason: Unknown
% 3.16/1.69 % (7778)Termination phase: shuffling
% 3.16/1.69
% 3.16/1.69 % (7778)Memory used [KB]: 1663
% 3.16/1.69 % (7778)Time elapsed: 0.003 s
% 3.16/1.69 % (7778)Instructions burned: 6 (million)
% 3.16/1.69 % (7778)------------------------------
% 3.16/1.69 % (7778)------------------------------
% 3.16/1.69 % (7779)Instruction limit reached!
% 3.16/1.69 % (7779)------------------------------
% 3.16/1.69 % (7779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.69 % (7779)Termination reason: Unknown
% 3.16/1.69 % (7779)Termination phase: shuffling
% 3.16/1.69
% 3.16/1.69 % (7779)Memory used [KB]: 1663
% 3.16/1.69 % (7779)Time elapsed: 0.003 s
% 3.16/1.69 % (7779)Instructions burned: 6 (million)
% 3.16/1.69 % (7779)------------------------------
% 3.16/1.69 % (7779)------------------------------
% 3.16/1.69 % (7759)Refutation found. Thanks to Tanya!
% 3.16/1.69 % SZS status Theorem for DTF2THF_7638
% 3.16/1.69 % SZS output start Proof for DTF2THF_7638
% 3.16/1.69 thf(type_def_5, type, l: $tType).
% 3.16/1.69 thf(type_def_6, type, option_val_r_l_v: $tType).
% 3.16/1.69 thf(type_def_8, type, const: $tType).
% 3.16/1.69 thf(type_def_9, type, produc1156025366_r_l_v: $tType).
% 3.16/1.69 thf(type_def_10, type, set_l: $tType).
% 3.16/1.69 thf(type_def_11, type, expr_r_l_v: $tType).
% 3.16/1.69 thf(type_def_12, type, val_r_l_v: $tType).
% 3.16/1.69 thf(type_def_13, type, cntxt_r_l_v: $tType).
% 3.16/1.69 thf(type_def_14, type, r: $tType).
% 3.16/1.69 thf(type_def_15, type, v: $tType).
% 3.16/1.69 thf(type_def_16, type, option1457017436_r_l_v: $tType).
% 3.16/1.69 thf(type_def_17, type, set_Pr1409704485_r_l_v: $tType).
% 3.16/1.69 thf(type_def_18, type, set_option_l: $tType).
% 3.16/1.69 thf(type_def_19, type, set_option_r: $tType).
% 3.16/1.69 thf(type_def_20, type, set_set_option_l: $tType).
% 3.16/1.69 thf(type_def_21, type, set_set_option_r: $tType).
% 3.16/1.69 thf(type_def_22, type, set_se888453765_r_l_v: $tType).
% 3.16/1.69 thf(type_def_23, type, set_set_set_l: $tType).
% 3.16/1.69 thf(type_def_24, type, set_set_set_r: $tType).
% 3.16/1.69 thf(type_def_25, type, set_set_l: $tType).
% 3.16/1.69 thf(type_def_26, type, set_set_r: $tType).
% 3.16/1.69 thf(type_def_27, type, set_r: $tType).
% 3.16/1.69 thf(type_def_28, type, produc1389397445_r_l_v: $tType).
% 3.16/1.69 thf(type_def_29, type, produc1164766533_r_l_v: $tType).
% 3.16/1.69 thf(type_def_30, type, option_l: $tType).
% 3.16/1.69 thf(type_def_31, type, option_r: $tType).
% 3.16/1.69 thf(func_def_0, type, set_se888453765_r_l_v: $tType).
% 3.16/1.69 thf(func_def_1, type, set_Pr1409704485_r_l_v: $tType).
% 3.16/1.69 thf(func_def_2, type, produc1389397445_r_l_v: $tType).
% 3.16/1.69 thf(func_def_3, type, option1457017436_r_l_v: $tType).
% 3.16/1.69 thf(func_def_4, type, produc1156025366_r_l_v: $tType).
% 3.16/1.69 thf(func_def_5, type, produc1164766533_r_l_v: $tType).
% 3.16/1.69 thf(func_def_6, type, set_set_option_r: $tType).
% 3.16/1.69 thf(func_def_7, type, set_set_option_l: $tType).
% 3.16/1.69 thf(func_def_8, type, option_val_r_l_v: $tType).
% 3.16/1.69 thf(func_def_9, type, set_set_set_r: $tType).
% 3.16/1.69 thf(func_def_10, type, set_set_set_l: $tType).
% 3.16/1.69 thf(func_def_11, type, set_option_r: $tType).
% 3.16/1.69 thf(func_def_12, type, set_option_l: $tType).
% 3.16/1.69 thf(func_def_13, type, cntxt_r_l_v: $tType).
% 3.16/1.69 thf(func_def_14, type, set_set_r: $tType).
% 3.16/1.69 thf(func_def_15, type, set_set_l: $tType).
% 3.16/1.69 thf(func_def_16, type, expr_r_l_v: $tType).
% 3.16/1.69 thf(func_def_17, type, val_r_l_v: $tType).
% 3.16/1.69 thf(func_def_18, type, option_r: $tType).
% 3.16/1.69 thf(func_def_19, type, option_l: $tType).
% 3.16/1.69 thf(func_def_20, type, set_r: $tType).
% 3.16/1.69 thf(func_def_21, type, set_l: $tType).
% 3.16/1.69 thf(func_def_22, type, const: $tType).
% 3.16/1.69 thf(func_def_23, type, v: $tType).
% 3.16/1.69 thf(func_def_24, type, r: $tType).
% 3.16/1.69 thf(func_def_25, type, l: $tType).
% 3.16/1.69 thf(func_def_26, 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).
% 3.16/1.69 thf(func_def_27, type, f: const).
% 3.16/1.69 thf(func_def_28, type, t: const).
% 3.16/1.69 thf(func_def_29, type, unit: const).
% 3.16/1.69 thf(func_def_30, type, doms_l_r_v: produc1156025366_r_l_v > set_l).
% 3.16/1.69 thf(func_def_31, type, assign_r_l_v: expr_r_l_v > expr_r_l_v > expr_r_l_v).
% 3.16/1.69 thf(func_def_32, type, ite_r_l_v: expr_r_l_v > expr_r_l_v > expr_r_l_v > expr_r_l_v).
% 3.16/1.69 thf(func_def_33, type, read_r_l_v: expr_r_l_v > expr_r_l_v).
% 3.16/1.69 thf(func_def_34, type, ref_r_l_v: expr_r_l_v > expr_r_l_v).
% 3.16/1.69 thf(func_def_35, type, rfork_r_l_v: expr_r_l_v > expr_r_l_v).
% 3.16/1.69 thf(func_def_36, type, rjoin_r_l_v: expr_r_l_v > expr_r_l_v).
% 3.16/1.69 thf(func_def_37, type, vE_r_l_v: val_r_l_v > expr_r_l_v).
% 3.16/1.69 thf(func_def_38, type, plug_r_l_v: cntxt_r_l_v > expr_r_l_v > expr_r_l_v).
% 3.16/1.69 thf(func_def_39, type, cV_r_l_v: const > val_r_l_v).
% 3.16/1.69 thf(func_def_40, type, loc_l_r_v: l > val_r_l_v).
% 3.16/1.69 thf(func_def_41, type, rid_r_l_v: r > val_r_l_v).
% 3.16/1.69 thf(func_def_42, 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).
% 3.16/1.69 thf(func_def_43, 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).
% 3.16/1.69 thf(func_def_44, type, maxima311842975_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).
% 3.16/1.69 thf(func_def_45, type, reachable_r_l_v: (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > (r > option1457017436_r_l_v) > $o).
% 3.16/1.69 thf(func_def_46, type, steps_r_l_v: (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > set_Pr1409704485_r_l_v).
% 3.16/1.69 thf(func_def_47, type, terminates_in_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) > $o).
% 3.16/1.69 thf(func_def_48, type, finite2114249848tion_l: set_option_l > $o).
% 3.16/1.69 thf(func_def_49, type, finite16335230tion_r: set_option_r > $o).
% 3.16/1.69 thf(func_def_50, type, finite1853159534_r_l_v: set_Pr1409704485_r_l_v > $o).
% 3.16/1.69 thf(func_def_51, type, finite1182752216tion_l: set_set_option_l > $o).
% 3.16/1.69 thf(func_def_52, type, finite1577687006tion_r: set_set_option_r > $o).
% 3.16/1.69 thf(func_def_53, type, finite1619243214_r_l_v: set_se888453765_r_l_v > $o).
% 3.16/1.69 thf(func_def_54, type, finite1256628466_set_l: set_set_set_l > $o).
% 3.16/1.69 thf(func_def_55, type, finite1651563256_set_r: set_set_set_r > $o).
% 3.16/1.69 thf(func_def_56, type, finite_finite_set_l: set_set_l > $o).
% 3.16/1.69 thf(func_def_57, type, finite_finite_set_r: set_set_r > $o).
% 3.16/1.69 thf(func_def_58, type, finite_finite_l: set_l > $o).
% 3.16/1.69 thf(func_def_59, type, finite_finite_r: set_r > $o).
% 3.16/1.69 thf(func_def_60, type, fun_up1835647912_r_l_v: (l > option_val_r_l_v) > l > option_val_r_l_v > l > option_val_r_l_v).
% 3.16/1.69 thf(func_def_61, type, fun_up709272714_r_l_v: (r > option1457017436_r_l_v) > r > option1457017436_r_l_v > r > option1457017436_r_l_v).
% 3.16/1.69 thf(func_def_62, type, if_option_val_r_l_v: $o > option_val_r_l_v > option_val_r_l_v > option_val_r_l_v).
% 3.16/1.69 thf(func_def_63, type, if_opt1153928738_r_l_v: $o > option1457017436_r_l_v > option1457017436_r_l_v > option1457017436_r_l_v).
% 3.16/1.69 thf(func_def_64, type, dom_Pr939617279_r_l_v: (produc1389397445_r_l_v > option_val_r_l_v) > set_Pr1409704485_r_l_v).
% 3.16/1.69 thf(func_def_65, type, dom_Pr1162080227_r_l_v: (produc1389397445_r_l_v > option1457017436_r_l_v) > set_Pr1409704485_r_l_v).
% 3.16/1.69 thf(func_def_66, type, dom_l_val_r_l_v: (l > option_val_r_l_v) > set_l).
% 3.16/1.69 thf(func_def_67, type, dom_l_45837855_r_l_v: (l > option1457017436_r_l_v) > set_l).
% 3.16/1.69 thf(func_def_68, type, dom_r_val_r_l_v: (r > option_val_r_l_v) > set_r).
% 3.16/1.69 thf(func_def_69, type, dom_r_259548057_r_l_v: (r > option1457017436_r_l_v) > set_r).
% 3.16/1.69 thf(func_def_70, type, lID_G_r_l_v: (r > option1457017436_r_l_v) > set_l).
% 3.16/1.69 thf(func_def_71, type, lID_L_l_r_v: produc1156025366_r_l_v > set_l).
% 3.16/1.69 thf(func_def_72, type, rID_G_r_l_v: (r > option1457017436_r_l_v) > set_r).
% 3.16/1.69 thf(func_def_73, type, rID_L_l_r_v: produc1156025366_r_l_v > set_r).
% 3.16/1.69 thf(func_def_74, type, domain87684397_l_r_v: produc1156025366_r_l_v > $o).
% 3.16/1.69 thf(func_def_75, type, domain1547879849_r_l_v: (r > option1457017436_r_l_v) > $o).
% 3.16/1.69 thf(func_def_76, 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).
% 3.16/1.69 thf(func_def_77, 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).
% 3.16/1.69 thf(func_def_78, type, subsum148050133_r_l_v: r > r > (r > option1457017436_r_l_v) > $o).
% 3.16/1.69 thf(func_def_79, type, subsum680764357_r_l_v: (r > option1457017436_r_l_v) > $o).
% 3.16/1.69 thf(func_def_80, type, none_val_r_l_v: option_val_r_l_v).
% 3.16/1.69 thf(func_def_81, type, none_P277133687_r_l_v: option1457017436_r_l_v).
% 3.16/1.69 thf(func_def_82, type, some_val_r_l_v: val_r_l_v > option_val_r_l_v).
% 3.16/1.69 thf(func_def_83, type, some_P1807977723_r_l_v: produc1156025366_r_l_v > option1457017436_r_l_v).
% 3.16/1.69 thf(func_def_84, type, the_val_r_l_v: option_val_r_l_v > val_r_l_v).
% 3.16/1.69 thf(func_def_85, type, the_Pr1541010602_r_l_v: option1457017436_r_l_v > produc1156025366_r_l_v).
% 3.16/1.69 thf(func_def_86, type, ord_le1506375887tion_l: set_option_l > set_option_l > $o).
% 3.16/1.69 thf(func_def_87, type, ord_le1901310677tion_r: set_option_r > set_option_r > $o).
% 3.16/1.69 thf(func_def_88, type, ord_le803113413_r_l_v: set_Pr1409704485_r_l_v > set_Pr1409704485_r_l_v > $o).
% 3.16/1.69 thf(func_def_89, type, ord_le2116509289_set_l: set_set_l > set_set_l > $o).
% 3.16/1.69 thf(func_def_90, type, ord_le363960431_set_r: set_set_r > set_set_r > $o).
% 3.16/1.69 thf(func_def_91, type, ord_less_eq_set_l: set_l > set_l > $o).
% 3.16/1.69 thf(func_def_92, type, ord_less_eq_set_r: set_r > set_r > $o).
% 3.16/1.69 thf(func_def_93, type, top_top_set_option_l: set_option_l).
% 3.16/1.69 thf(func_def_94, type, top_top_set_option_r: set_option_r).
% 3.16/1.69 thf(func_def_95, type, top_top_set_l: set_l).
% 3.16/1.69 thf(func_def_96, type, top_top_set_r: set_r).
% 3.16/1.69 thf(func_def_97, type, produc1834103605_r_l_v: (l > option_val_r_l_v) > expr_r_l_v > produc1164766533_r_l_v).
% 3.16/1.69 thf(func_def_98, type, produc297528454_r_l_v: (l > option_val_r_l_v) > produc1164766533_r_l_v > produc1156025366_r_l_v).
% 3.16/1.69 thf(func_def_99, type, produc1175464189_r_l_v: (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > produc1389397445_r_l_v).
% 3.16/1.69 thf(func_def_100, type, eq_states_r_l_v: (r > option1457017436_r_l_v) > (r > option1457017436_r_l_v) > $o).
% 3.16/1.69 thf(func_def_101, type, collect_option_l: (option_l > $o) > set_option_l).
% 3.16/1.69 thf(func_def_102, type, collect_option_r: (option_r > $o) > set_option_r).
% 3.16/1.69 thf(func_def_103, type, collec1978425008_r_l_v: (produc1389397445_r_l_v > $o) > set_Pr1409704485_r_l_v).
% 3.16/1.69 thf(func_def_104, type, collect_set_option_l: (set_option_l > $o) > set_set_option_l).
% 3.16/1.69 thf(func_def_105, type, collect_set_option_r: (set_option_r > $o) > set_set_option_r).
% 3.16/1.69 thf(func_def_106, type, collec330370832_r_l_v: (set_Pr1409704485_r_l_v > $o) > set_se888453765_r_l_v).
% 3.16/1.69 thf(func_def_107, type, collect_set_set_l: (set_set_l > $o) > set_set_set_l).
% 3.16/1.69 thf(func_def_108, type, collect_set_set_r: (set_set_r > $o) > set_set_set_r).
% 3.16/1.69 thf(func_def_109, type, collect_set_l: (set_l > $o) > set_set_l).
% 3.16/1.69 thf(func_def_110, type, collect_set_r: (set_r > $o) > set_set_r).
% 3.16/1.69 thf(func_def_111, type, collect_l: (l > $o) > set_l).
% 3.16/1.69 thf(func_def_112, type, collect_r: (r > $o) > set_r).
% 3.16/1.69 thf(func_def_113, type, substitution_r_l_v: (expr_r_l_v > v > expr_r_l_v > expr_r_l_v) > $o).
% 3.16/1.69 thf(func_def_114, type, transi1323086383_r_l_v: set_Pr1409704485_r_l_v > set_Pr1409704485_r_l_v).
% 3.16/1.69 thf(func_def_115, type, member_option_l: option_l > set_option_l > $o).
% 3.16/1.69 thf(func_def_116, type, member_option_r: option_r > set_option_r > $o).
% 3.16/1.69 thf(func_def_117, type, member1522896238_r_l_v: produc1389397445_r_l_v > set_Pr1409704485_r_l_v > $o).
% 3.16/1.69 thf(func_def_118, type, member_set_l: set_l > set_set_l > $o).
% 3.16/1.69 thf(func_def_119, type, member_set_r: set_r > set_set_r > $o).
% 3.16/1.69 thf(func_def_120, type, member_l: l > set_l > $o).
% 3.16/1.69 thf(func_def_121, type, member_r: r > set_r > $o).
% 3.16/1.69 thf(func_def_122, type, e: cntxt_r_l_v).
% 3.16/1.69 thf(func_def_123, type, sigma: l > option_val_r_l_v).
% 3.16/1.69 thf(func_def_124, type, tau: l > option_val_r_l_v).
% 3.16/1.69 thf(func_def_125, type, e2: expr_r_l_v).
% 3.16/1.69 thf(func_def_126, type, r2: r).
% 3.16/1.69 thf(func_def_127, type, r3: r).
% 3.16/1.69 thf(func_def_128, type, r4: r).
% 3.16/1.69 thf(func_def_129, type, s_1: r > option1457017436_r_l_v).
% 3.16/1.69 thf(func_def_130, type, s_2: r > option1457017436_r_l_v).
% 3.16/1.69 thf(func_def_131, type, s_22: r > option1457017436_r_l_v).
% 3.16/1.69 thf(func_def_132, type, subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v).
% 3.16/1.69 thf(func_def_133, type, x: produc1156025366_r_l_v).
% 3.16/1.69 thf(func_def_149, type, sP0: (option1457017436_r_l_v > option_val_r_l_v > $o) > option1457017436_r_l_v > option_val_r_l_v > $o).
% 3.16/1.69 thf(func_def_150, type, sP1: (option_val_r_l_v > option1457017436_r_l_v > $o) > option_val_r_l_v > option1457017436_r_l_v > $o).
% 3.16/1.69 thf(func_def_151, type, sP2: (option1457017436_r_l_v > option1457017436_r_l_v > $o) > option1457017436_r_l_v > option1457017436_r_l_v > $o).
% 3.16/1.69 thf(func_def_152, type, sP3: (option_val_r_l_v > option_val_r_l_v > $o) > option_val_r_l_v > option_val_r_l_v > $o).
% 3.16/1.69 thf(func_def_153, type, sK4: option_val_r_l_v > val_r_l_v).
% 3.16/1.69 thf(func_def_154, type, sK5: produc1156025366_r_l_v > l > option_val_r_l_v).
% 3.16/1.69 thf(func_def_155, type, sK6: produc1156025366_r_l_v > expr_r_l_v).
% 3.16/1.69 thf(func_def_156, type, sK7: produc1156025366_r_l_v > l > option_val_r_l_v).
% 3.16/1.69 thf(func_def_157, type, sK8: (option1457017436_r_l_v > option_val_r_l_v > $o) > option1457017436_r_l_v > option_val_r_l_v > produc1156025366_r_l_v).
% 3.16/1.69 thf(func_def_158, type, sK9: (option1457017436_r_l_v > option_val_r_l_v > $o) > option1457017436_r_l_v > option_val_r_l_v > val_r_l_v).
% 3.16/1.69 thf(func_def_159, type, sK10: option_val_r_l_v > val_r_l_v).
% 3.16/1.69 thf(func_def_160, type, sK11: (option_val_r_l_v > option1457017436_r_l_v > $o) > option_val_r_l_v > option1457017436_r_l_v > produc1156025366_r_l_v).
% 3.16/1.69 thf(func_def_161, type, sK12: (option_val_r_l_v > option1457017436_r_l_v > $o) > option_val_r_l_v > option1457017436_r_l_v > val_r_l_v).
% 3.16/1.69 thf(func_def_162, type, sK13: (option1457017436_r_l_v > $o) > produc1156025366_r_l_v).
% 3.16/1.69 thf(func_def_163, type, sK14: (option1457017436_r_l_v > option1457017436_r_l_v > $o) > option1457017436_r_l_v > option1457017436_r_l_v > produc1156025366_r_l_v).
% 3.16/1.69 thf(func_def_164, type, sK15: (option1457017436_r_l_v > option1457017436_r_l_v > $o) > option1457017436_r_l_v > option1457017436_r_l_v > produc1156025366_r_l_v).
% 3.16/1.69 thf(func_def_165, type, sK16: (produc1156025366_r_l_v > $o) > l > option_val_r_l_v).
% 3.16/1.69 thf(func_def_166, type, sK17: (produc1156025366_r_l_v > $o) > l > option_val_r_l_v).
% 3.16/1.69 thf(func_def_167, type, sK18: (produc1156025366_r_l_v > $o) > expr_r_l_v).
% 3.16/1.69 thf(func_def_168, type, sK19: option_val_r_l_v > val_r_l_v).
% 3.16/1.69 thf(func_def_169, type, sK20: (option_val_r_l_v > $o) > val_r_l_v).
% 3.16/1.69 thf(func_def_170, type, sK21: option1457017436_r_l_v > produc1156025366_r_l_v).
% 3.16/1.69 thf(func_def_171, type, sK22: option1457017436_r_l_v > produc1156025366_r_l_v).
% 3.16/1.69 thf(func_def_172, type, sK23: (option_val_r_l_v > option_val_r_l_v > $o) > option_val_r_l_v > option_val_r_l_v > val_r_l_v).
% 3.16/1.69 thf(func_def_173, type, sK24: (option_val_r_l_v > option_val_r_l_v > $o) > option_val_r_l_v > option_val_r_l_v > val_r_l_v).
% 3.16/1.69 thf(func_def_174, type, sK25: option1457017436_r_l_v > produc1156025366_r_l_v).
% 3.16/1.69 thf(func_def_176, type, ph27: !>[X0: $tType]:(X0)).
% 3.16/1.69 thf(func_def_177, type, sK28: r).
% 3.16/1.69 thf(func_def_178, type, sK29: r).
% 3.16/1.69 thf(func_def_179, type, sK30: r).
% 3.16/1.69 thf(func_def_180, type, sK31: r).
% 3.16/1.69 thf(f1253,plain,(
% 3.16/1.69 $false),
% 3.16/1.69 inference(subsumption_resolution,[status(thm)],[f1252,f1020])).
% 3.16/1.69 thf(f1020,plain,(
% 3.16/1.69 (r2 != r3)),
% 3.16/1.69 inference(cnf_transformation,[status(thm)],[f3])).
% 3.16/1.69 thf(f3,axiom,(
% 3.16/1.69 (r2 != r3)),
% 3.16/1.69 file('/export/starexec/sandbox/tmp/tmp.bnlJrUVmuy/DTF2THF_7638.p',fact_2_assms_I6_J)).
% 3.16/1.69 thf(f1252,plain,(
% 3.16/1.69 (r2 = r3)),
% 3.16/1.69 inference(trivial_inequality_removal,[status(thm)],[f1247])).
% 3.16/1.69 thf(f1247,plain,(
% 3.16/1.69 (r2 = r3) | ((fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ s_1 @ r2 @ (some_P1807977723_r_l_v @ x)) @ r3 @ (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 @ r4))))))) @ r4 @ (some_P1807977723_r_l_v @ (produc297528454_r_l_v @ (combine_l_val_r_l_v @ sigma @ tau) @ (produc1834103605_r_l_v @ (^[Y0 : l]: (none_val_r_l_v)) @ e2)))) != (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ s_1 @ r2 @ (some_P1807977723_r_l_v @ x)) @ r3 @ (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 @ r4))))))) @ r4 @ (some_P1807977723_r_l_v @ (produc297528454_r_l_v @ (combine_l_val_r_l_v @ sigma @ tau) @ (produc1834103605_r_l_v @ (^[Y0 : l]: (none_val_r_l_v)) @ e2)))))),
% 3.16/1.69 inference(superposition,[status(thm)],[f1139,f1084])).
% 3.16/1.69 thf(f1084,plain,(
% 3.16/1.69 ( ! [X2 : r > option1457017436_r_l_v,X3 : r,X0 : option1457017436_r_l_v,X1 : r,X4 : option1457017436_r_l_v] : (((fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ X2 @ X1 @ X4) @ X3 @ X0) = (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ X2 @ X3 @ X0) @ X1 @ X4)) | (X1 = X3)) )),
% 3.16/1.69 inference(cnf_transformation,[status(thm)],[f950])).
% 3.16/1.69 thf(f950,plain,(
% 3.16/1.69 ! [X0 : option1457017436_r_l_v,X1 : r,X2 : r > option1457017436_r_l_v,X3 : r,X4 : option1457017436_r_l_v] : (((fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ X2 @ X1 @ X4) @ X3 @ X0) = (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ X2 @ X3 @ X0) @ X1 @ X4)) | (X1 = X3))),
% 3.16/1.69 inference(ennf_transformation,[status(thm)],[f919])).
% 3.16/1.69 thf(f919,plain,(
% 3.16/1.69 ! [X0 : option1457017436_r_l_v,X1 : r,X2 : r > option1457017436_r_l_v,X3 : r,X4 : option1457017436_r_l_v] : ((X1 != X3) => ((fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ X2 @ X1 @ X4) @ X3 @ X0) = (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ X2 @ X3 @ X0) @ X1 @ X4)))),
% 3.16/1.69 inference(rectify,[status(thm)],[f41])).
% 3.16/1.69 thf(f41,axiom,(
% 3.16/1.69 ! [X40 : option1457017436_r_l_v,X36 : r,X38 : r > option1457017436_r_l_v,X37 : r,X39 : option1457017436_r_l_v] : ((X36 != X37) => ((fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ X38 @ X36 @ X39) @ X37 @ X40) = (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ X38 @ X37 @ X40) @ X36 @ X39)))),
% 3.16/1.69 file('/export/starexec/sandbox/tmp/tmp.bnlJrUVmuy/DTF2THF_7638.p',fact_40_fun__upd__twist)).
% 3.16/1.69 thf(f1139,plain,(
% 3.16/1.69 ((fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ s_1 @ r2 @ (some_P1807977723_r_l_v @ x)) @ r3 @ (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 @ r4))))))) @ r4 @ (some_P1807977723_r_l_v @ (produc297528454_r_l_v @ (combine_l_val_r_l_v @ sigma @ tau) @ (produc1834103605_r_l_v @ (^[Y0 : l]: (none_val_r_l_v)) @ e2)))) != (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ s_1 @ r3 @ (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 @ r4))))))) @ r2 @ (some_P1807977723_r_l_v @ x)) @ r4 @ (some_P1807977723_r_l_v @ (produc297528454_r_l_v @ (combine_l_val_r_l_v @ sigma @ tau) @ (produc1834103605_r_l_v @ (^[Y0 : l]: (none_val_r_l_v)) @ e2)))))),
% 3.16/1.69 inference(subsumption_resolution,[status(thm)],[f1136,f1045])).
% 3.16/1.69 thf(f1045,plain,(
% 3.16/1.69 (r4 != r2)),
% 3.16/1.69 inference(cnf_transformation,[status(thm)],[f2])).
% 3.16/1.69 thf(f2,axiom,(
% 3.16/1.69 (r4 != r2)),
% 3.16/1.69 file('/export/starexec/sandbox/tmp/tmp.bnlJrUVmuy/DTF2THF_7638.p',fact_1_assms_I7_J)).
% 3.16/1.69 thf(f1136,plain,(
% 3.16/1.69 (r4 = r2) | ((fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ s_1 @ r2 @ (some_P1807977723_r_l_v @ x)) @ r3 @ (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 @ r4))))))) @ r4 @ (some_P1807977723_r_l_v @ (produc297528454_r_l_v @ (combine_l_val_r_l_v @ sigma @ tau) @ (produc1834103605_r_l_v @ (^[Y0 : l]: (none_val_r_l_v)) @ e2)))) != (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ s_1 @ r3 @ (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 @ r4))))))) @ r2 @ (some_P1807977723_r_l_v @ x)) @ r4 @ (some_P1807977723_r_l_v @ (produc297528454_r_l_v @ (combine_l_val_r_l_v @ sigma @ tau) @ (produc1834103605_r_l_v @ (^[Y0 : l]: (none_val_r_l_v)) @ e2)))))),
% 3.16/1.69 inference(superposition,[status(thm)],[f1021,f1084])).
% 3.16/1.69 thf(f1021,plain,(
% 3.16/1.69 ((fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ s_1 @ r2 @ (some_P1807977723_r_l_v @ x)) @ r3 @ (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 @ r4))))))) @ r4 @ (some_P1807977723_r_l_v @ (produc297528454_r_l_v @ (combine_l_val_r_l_v @ sigma @ tau) @ (produc1834103605_r_l_v @ (^[Y0 : l]: (none_val_r_l_v)) @ e2)))) != (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ s_1 @ r3 @ (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 @ r4))))))) @ r4 @ (some_P1807977723_r_l_v @ (produc297528454_r_l_v @ (combine_l_val_r_l_v @ sigma @ tau) @ (produc1834103605_r_l_v @ (^[Y0 : l]: (none_val_r_l_v)) @ e2)))) @ r2 @ (some_P1807977723_r_l_v @ x)))),
% 3.16/1.69 inference(cnf_transformation,[status(thm)],[f907])).
% 3.16/1.69 thf(f907,plain,(
% 3.16/1.69 ((fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ s_1 @ r2 @ (some_P1807977723_r_l_v @ x)) @ r3 @ (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 @ r4))))))) @ r4 @ (some_P1807977723_r_l_v @ (produc297528454_r_l_v @ (combine_l_val_r_l_v @ sigma @ tau) @ (produc1834103605_r_l_v @ (^[Y0 : l]: (none_val_r_l_v)) @ e2)))) != (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ s_1 @ r3 @ (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 @ r4))))))) @ r4 @ (some_P1807977723_r_l_v @ (produc297528454_r_l_v @ (combine_l_val_r_l_v @ sigma @ tau) @ (produc1834103605_r_l_v @ (^[Y0 : l]: (none_val_r_l_v)) @ e2)))) @ r2 @ (some_P1807977723_r_l_v @ x)))),
% 3.16/1.69 inference(flattening,[status(thm)],[f606])).
% 3.16/1.69 thf(f606,plain,(
% 3.16/1.69 ~((fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ s_1 @ r2 @ (some_P1807977723_r_l_v @ x)) @ r3 @ (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 @ r4))))))) @ r4 @ (some_P1807977723_r_l_v @ (produc297528454_r_l_v @ (combine_l_val_r_l_v @ sigma @ tau) @ (produc1834103605_r_l_v @ (^[Y0 : l]: (none_val_r_l_v)) @ e2)))) = (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ s_1 @ r3 @ (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 @ r4))))))) @ r4 @ (some_P1807977723_r_l_v @ (produc297528454_r_l_v @ (combine_l_val_r_l_v @ sigma @ tau) @ (produc1834103605_r_l_v @ (^[Y0 : l]: (none_val_r_l_v)) @ e2)))) @ r2 @ (some_P1807977723_r_l_v @ x)))),
% 3.16/1.69 inference(fool_elimination,[status(thm)],[f605])).
% 3.16/1.69 thf(f605,plain,(
% 3.16/1.69 ~((fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ s_1 @ r2 @ (some_P1807977723_r_l_v @ x)) @ r3 @ (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 @ r4))))))) @ r4 @ (some_P1807977723_r_l_v @ (produc297528454_r_l_v @ (combine_l_val_r_l_v @ sigma @ tau) @ (produc1834103605_r_l_v @ (^[X0 : l] : (none_val_r_l_v)) @ e2)))) = (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ s_1 @ r3 @ (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 @ r4))))))) @ r4 @ (some_P1807977723_r_l_v @ (produc297528454_r_l_v @ (combine_l_val_r_l_v @ sigma @ tau) @ (produc1834103605_r_l_v @ (^[X1 : l] : (none_val_r_l_v)) @ e2)))) @ r2 @ (some_P1807977723_r_l_v @ x)))),
% 3.16/1.69 inference(rectify,[status(thm)],[f360])).
% 3.16/1.69 thf(f360,negated_conjecture,(
% 3.16/1.69 ~((fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ s_1 @ r2 @ (some_P1807977723_r_l_v @ x)) @ r3 @ (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 @ r4))))))) @ r4 @ (some_P1807977723_r_l_v @ (produc297528454_r_l_v @ (combine_l_val_r_l_v @ sigma @ tau) @ (produc1834103605_r_l_v @ (^[X0 : l] : (none_val_r_l_v)) @ e2)))) = (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ s_1 @ r3 @ (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 @ r4))))))) @ r4 @ (some_P1807977723_r_l_v @ (produc297528454_r_l_v @ (combine_l_val_r_l_v @ sigma @ tau) @ (produc1834103605_r_l_v @ (^[X0 : l] : (none_val_r_l_v)) @ e2)))) @ r2 @ (some_P1807977723_r_l_v @ x)))),
% 3.16/1.69 inference(negated_conjecture,[status(cth)],[f359])).
% 3.16/1.69 thf(f359,conjecture,(
% 3.16/1.69 ((fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ s_1 @ r2 @ (some_P1807977723_r_l_v @ x)) @ r3 @ (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 @ r4))))))) @ r4 @ (some_P1807977723_r_l_v @ (produc297528454_r_l_v @ (combine_l_val_r_l_v @ sigma @ tau) @ (produc1834103605_r_l_v @ (^[X0 : l] : (none_val_r_l_v)) @ e2)))) = (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ (fun_up709272714_r_l_v @ s_1 @ r3 @ (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 @ r4))))))) @ r4 @ (some_P1807977723_r_l_v @ (produc297528454_r_l_v @ (combine_l_val_r_l_v @ sigma @ tau) @ (produc1834103605_r_l_v @ (^[X0 : l] : (none_val_r_l_v)) @ e2)))) @ r2 @ (some_P1807977723_r_l_v @ x)))),
% 3.16/1.69 file('/export/starexec/sandbox/tmp/tmp.bnlJrUVmuy/DTF2THF_7638.p',conj_0)).
% 3.16/1.69 % SZS output end Proof for DTF2THF_7638
% 3.16/1.69 % (7759)------------------------------
% 3.16/1.69 % (7759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.69 % (7759)Termination reason: Refutation
% 3.16/1.69
% 3.16/1.69 % (7759)Memory used [KB]: 7291
% 3.16/1.69 % (7759)Time elapsed: 0.070 s
% 3.16/1.69 % (7759)Instructions burned: 164 (million)
% 3.16/1.69 % (7759)------------------------------
% 3.16/1.69 % (7759)------------------------------
% 3.16/1.69 % (7753)Success in time 0.099 s
%------------------------------------------------------------------------------