TPTP Problem File: ITP047^1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ITP047^1 : TPTP v8.2.0. Released v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : Sledgehammer Determinacy problem prob_914__3357784_1
% Version : Especial.
% English :
% Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% Source : [Des21]
% Names : Determinacy/prob_914__3357784_1 [Des21]
% Status : Theorem
% Rating : 0.30 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0
% Syntax : Number of formulae : 502 ( 137 unt; 144 typ; 0 def)
% Number of atoms : 1189 ( 524 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 4447 ( 181 ~; 60 |; 118 &;3553 @)
% ( 0 <=>; 535 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 8 avg)
% Number of types : 36 ( 35 usr)
% Number of type conns : 991 ( 991 >; 0 *; 0 +; 0 <<)
% Number of symbols : 112 ( 109 usr; 28 con; 0-4 aty)
% Number of variables : 1427 ( 111 ^;1223 !; 93 ?;1427 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This file was generated by Sledgehammer 2021-02-23 15:34:36.700
%------------------------------------------------------------------------------
% Could-be-implicit typings (35)
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thf(ty_n_t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J,type,
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set_Sum_sum_l_l: $tType ).
thf(ty_n_t__Set__Oset_It__Option__Ooption_Itf__r_J_J,type,
set_option_r: $tType ).
thf(ty_n_t__Set__Oset_It__Option__Ooption_Itf__l_J_J,type,
set_option_l: $tType ).
thf(ty_n_t__Data__Ocntxt_Itf__r_Mtf__l_Mtf__v_J,type,
cntxt_r_l_v: $tType ).
thf(ty_n_t__Set__Oset_It__Set__Oset_Itf__r_J_J,type,
set_set_r: $tType ).
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thf(ty_n_t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,type,
val_r_l_v: $tType ).
thf(ty_n_t__Set__Oset_Itf__r_J,type,
set_r: $tType ).
thf(ty_n_t__Set__Oset_Itf__l_J,type,
set_l: $tType ).
thf(ty_n_t__Data__Oconst,type,
const: $tType ).
thf(ty_n_tf__v,type,
v: $tType ).
thf(ty_n_tf__r,type,
r: $tType ).
thf(ty_n_tf__l,type,
l: $tType ).
% Explicit typings (109)
thf(sy_c_Data_OLID__expression_001tf__l_001tf__r_001tf__v,type,
lID_expression_l_r_v: produc1156025366_r_l_v > expr_r_l_v ).
thf(sy_c_Data_OLID__local__store_001tf__l_001tf__r_001tf__v,type,
lID_lo1265057957_l_r_v: produc1156025366_r_l_v > l > option_val_r_l_v ).
thf(sy_c_Data_OLID__snapshot_001tf__l_001tf__r_001tf__v,type,
lID_snapshot_l_r_v: produc1156025366_r_l_v > l > option_val_r_l_v ).
thf(sy_c_Data_Ocombine_001tf__l_001t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,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(sy_c_Data_Oconst_OUnit,type,
unit: const ).
thf(sy_c_Data_Oexpr_ORef_001tf__r_001tf__l_001tf__v,type,
ref_r_l_v: expr_r_l_v > expr_r_l_v ).
thf(sy_c_Data_Oexpr_ORfork_001tf__r_001tf__l_001tf__v,type,
rfork_r_l_v: expr_r_l_v > expr_r_l_v ).
thf(sy_c_Data_Oexpr_ORjoin_001tf__r_001tf__l_001tf__v,type,
rjoin_r_l_v: expr_r_l_v > expr_r_l_v ).
thf(sy_c_Data_Oexpr_OVE_001tf__r_001tf__l_001tf__v,type,
vE_r_l_v: val_r_l_v > expr_r_l_v ).
thf(sy_c_Data_Oplug_001tf__r_001tf__l_001tf__v,type,
plug_r_l_v: cntxt_r_l_v > expr_r_l_v > expr_r_l_v ).
thf(sy_c_Data_Oval_OCV_001tf__r_001tf__l_001tf__v,type,
cV_r_l_v: const > val_r_l_v ).
thf(sy_c_Data_Oval_OLoc_001tf__l_001tf__r_001tf__v,type,
loc_l_r_v: l > val_r_l_v ).
thf(sy_c_Data_Oval_ORid_001tf__r_001tf__l_001tf__v,type,
rid_r_l_v: r > val_r_l_v ).
thf(sy_c_Executions_Osubstitution_Oexecution_001tf__r_001tf__l_001tf__v,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(sy_c_Executions_Osubstitution_Oinductive__invariant_001tf__r_001tf__l_001tf__v,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(sy_c_Executions_Osubstitution_Oreachable_001tf__r_001tf__l_001tf__v,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(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_It__Set__Oset_Itf__l_J_J,type,
finite160708696_set_l: set_option_set_l > $o ).
thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_It__Set__Oset_Itf__r_J_J,type,
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finite1036466630um_r_l: set_op865065573um_r_l > $o ).
thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_Itf__l_J,type,
finite2114249848tion_l: set_option_l > $o ).
thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_Itf__r_J,type,
finite16335230tion_r: set_option_r > $o ).
thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_Itf__l_Mtf__l_J,type,
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thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_Itf__r_Mtf__l_J,type,
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finite1507191824od_r_r: set_Product_prod_r_r > $o ).
thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_Itf__l_J,type,
finite_finite_set_l: set_set_l > $o ).
thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_Itf__r_J,type,
finite_finite_set_r: set_set_r > $o ).
thf(sy_c_Finite__Set_Ofinite_001t__Sum____Type__Osum_Itf__l_Mtf__l_J,type,
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thf(sy_c_Finite__Set_Ofinite_001t__Sum____Type__Osum_Itf__l_Mtf__r_J,type,
finite1591053314um_l_r: set_Sum_sum_l_r > $o ).
thf(sy_c_Finite__Set_Ofinite_001t__Sum____Type__Osum_Itf__r_Mtf__l_J,type,
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thf(sy_c_Finite__Set_Ofinite_001t__Sum____Type__Osum_Itf__r_Mtf__r_J,type,
finite115218812um_r_r: set_Sum_sum_r_r > $o ).
thf(sy_c_Finite__Set_Ofinite_001tf__l,type,
finite_finite_l: set_l > $o ).
thf(sy_c_Finite__Set_Ofinite_001tf__r,type,
finite_finite_r: set_r > $o ).
thf(sy_c_Fun_Obij__betw_001tf__l_001tf__l,type,
bij_betw_l_l: ( l > l ) > set_l > set_l > $o ).
thf(sy_c_Fun_Obij__betw_001tf__l_001tf__r,type,
bij_betw_l_r: ( l > r ) > set_l > set_r > $o ).
thf(sy_c_Fun_Obij__betw_001tf__r_001tf__l,type,
bij_betw_r_l: ( r > l ) > set_r > set_l > $o ).
thf(sy_c_Fun_Obij__betw_001tf__r_001tf__r,type,
bij_betw_r_r: ( r > r ) > set_r > set_r > $o ).
thf(sy_c_Fun_Ofun__upd_001tf__l_001t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J,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(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,
fun_up709272714_r_l_v: ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v > r > option1457017436_r_l_v ).
thf(sy_c_If_001t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J,type,
if_option_val_r_l_v: $o > option_val_r_l_v > option_val_r_l_v > option_val_r_l_v ).
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if_opt1153928738_r_l_v: $o > option1457017436_r_l_v > option1457017436_r_l_v > option1457017436_r_l_v ).
thf(sy_c_Occurrences_OLID_092_060_094sub_062G_001tf__r_001tf__l_001tf__v,type,
lID_G_r_l_v: ( r > option1457017436_r_l_v ) > set_l ).
thf(sy_c_Occurrences_OLID_092_060_094sub_062L_001tf__l_001tf__r_001tf__v,type,
lID_L_l_r_v: produc1156025366_r_l_v > set_l ).
thf(sy_c_Occurrences_ORID_092_060_094sub_062G_001tf__r_001tf__l_001tf__v,type,
rID_G_r_l_v: ( r > option1457017436_r_l_v ) > set_r ).
thf(sy_c_Occurrences_ORID_092_060_094sub_062L_001tf__l_001tf__r_001tf__v,type,
rID_L_l_r_v: produc1156025366_r_l_v > set_r ).
thf(sy_c_OperationalSemantics_Osubstitution_Odomains__subsume_001tf__l_001tf__r_001tf__v,type,
domain87684397_l_r_v: produc1156025366_r_l_v > $o ).
thf(sy_c_OperationalSemantics_Osubstitution_Odomains__subsume__globally_001tf__r_001tf__l_001tf__v,type,
domain1547879849_r_l_v: ( r > option1457017436_r_l_v ) > $o ).
thf(sy_c_OperationalSemantics_Osubstitution_Orevision__step_001tf__r_001tf__l_001tf__v,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(sy_c_OperationalSemantics_Osubstitution_Orevision__step__relaxed_001tf__r_001tf__l_001tf__v,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(sy_c_OperationalSemantics_Osubstitution_Osubsumes__accessible_001tf__r_001tf__l_001tf__v,type,
subsum148050133_r_l_v: r > r > ( r > option1457017436_r_l_v ) > $o ).
thf(sy_c_OperationalSemantics_Osubstitution_Osubsumes__accessible__globally_001tf__r_001tf__l_001tf__v,type,
subsum680764357_r_l_v: ( r > option1457017436_r_l_v ) > $o ).
thf(sy_c_Option_Ooption_ONone_001t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,type,
none_val_r_l_v: option_val_r_l_v ).
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,
none_P277133687_r_l_v: option1457017436_r_l_v ).
thf(sy_c_Option_Ooption_OSome_001t__Data__Oval_Itf__r_Mtf__l_Mtf__v_J,type,
some_val_r_l_v: val_r_l_v > option_val_r_l_v ).
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,
some_P1807977723_r_l_v: produc1156025366_r_l_v > option1457017436_r_l_v ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__l_J,type,
ord_less_eq_set_l: set_l > set_l > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__r_J,type,
ord_less_eq_set_r: set_r > set_r > $o ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Set__Oset_Itf__l_J_J_J,type,
top_to471808607_set_l: set_option_set_l ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Set__Oset_Itf__r_J_J_J,type,
top_to555798885_set_r: set_option_set_r ).
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thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Sum____Type__Osum_Itf__l_Mtf__r_J_J_J,type,
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top_top_set_option_l: set_option_l ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_Itf__r_J_J,type,
top_top_set_option_r: set_option_r ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_Itf__l_Mtf__l_J_J,type,
top_to320296343od_l_l: set_Product_prod_l_l ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_Itf__l_Mtf__r_J_J,type,
top_to715231133od_l_r: set_Product_prod_l_r ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_Itf__r_Mtf__l_J_J,type,
top_to1639761425od_r_l: set_Product_prod_r_l ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_Itf__r_Mtf__r_J_J,type,
top_to2034696215od_r_r: set_Product_prod_r_r ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_Itf__l_J_J,type,
top_top_set_set_l: set_set_l ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_Itf__r_J_J,type,
top_top_set_set_r: set_set_r ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Sum____Type__Osum_Itf__l_Mtf__l_J_J,type,
top_to1010946379um_l_l: set_Sum_sum_l_l ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Sum____Type__Osum_Itf__l_Mtf__r_J_J,type,
top_to1405881169um_l_r: set_Sum_sum_l_r ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Sum____Type__Osum_Itf__r_Mtf__l_J_J,type,
top_to182927813um_r_l: set_Sum_sum_r_l ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Sum____Type__Osum_Itf__r_Mtf__r_J_J,type,
top_to577862603um_r_r: set_Sum_sum_r_r ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__l_J,type,
top_top_set_l: set_l ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__r_J,type,
top_top_set_r: set_r ).
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,
produc1834103605_r_l_v: ( l > option_val_r_l_v ) > expr_r_l_v > produc1164766533_r_l_v ).
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,
produc297528454_r_l_v: ( l > option_val_r_l_v ) > produc1164766533_r_l_v > produc1156025366_r_l_v ).
thf(sy_c_Product__Type_OPair_001_062_Itf__l_Mtf__l_J_001t__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J,type,
produc2057232216_r_l_v: ( l > l ) > produc1156025366_r_l_v > produc1489027110_r_l_v ).
thf(sy_c_Product__Type_OPair_001_062_Itf__r_Mtf__r_J_001t__Product____Type__Oprod_I_062_Itf__l_Mtf__l_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Product____Type__Oprod_I_062_Itf__l_Mt__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_J_Mt__Data__Oexpr_Itf__r_Mtf__l_Mtf__v_J_J_J_J,type,
produc2111504612_r_l_v: ( r > r ) > produc1489027110_r_l_v > produc1394974636_r_l_v ).
thf(sy_c_Renaming_O_092_060R_062_092_060_094sub_062G_001tf__r_001tf__l_001tf__v,type,
r_G_r_l_v: ( r > r ) > ( l > l ) > ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v ).
thf(sy_c_Renaming_O_092_060R_062_092_060_094sub_062L_001tf__r_001tf__l_001tf__v,type,
r_L_r_l_v: ( r > r ) > ( l > l ) > produc1156025366_r_l_v > produc1156025366_r_l_v ).
thf(sy_c_Renaming_Oeq__states_001tf__r_001tf__l_001tf__v,type,
eq_states_r_l_v: ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
thf(sy_c_Renaming_Ois__global__renaming_001tf__r_001tf__l_001tf__v,type,
is_glo1871033385_r_l_v: ( r > r ) > ( l > l ) > ( r > option1457017436_r_l_v ) > ( r > option1457017436_r_l_v ) > $o ).
thf(sy_c_Set_OCollect_001t__Set__Oset_Itf__l_J,type,
collect_set_l: ( set_l > $o ) > set_set_l ).
thf(sy_c_Set_OCollect_001t__Set__Oset_Itf__r_J,type,
collect_set_r: ( set_r > $o ) > set_set_r ).
thf(sy_c_Set_OCollect_001t__Sum____Type__Osum_Itf__l_Mtf__l_J,type,
collect_Sum_sum_l_l: ( sum_sum_l_l > $o ) > set_Sum_sum_l_l ).
thf(sy_c_Set_OCollect_001t__Sum____Type__Osum_Itf__l_Mtf__r_J,type,
collect_Sum_sum_l_r: ( sum_sum_l_r > $o ) > set_Sum_sum_l_r ).
thf(sy_c_Set_OCollect_001t__Sum____Type__Osum_Itf__r_Mtf__l_J,type,
collect_Sum_sum_r_l: ( sum_sum_r_l > $o ) > set_Sum_sum_r_l ).
thf(sy_c_Set_OCollect_001tf__l,type,
collect_l: ( l > $o ) > set_l ).
thf(sy_c_Set_OCollect_001tf__r,type,
collect_r: ( r > $o ) > set_r ).
thf(sy_c_Substitution_Osubstitution_001tf__r_001tf__l_001tf__v,type,
substitution_r_l_v: ( expr_r_l_v > v > expr_r_l_v > expr_r_l_v ) > $o ).
thf(sy_c_member_001t__Set__Oset_Itf__l_J,type,
member_set_l: set_l > set_set_l > $o ).
thf(sy_c_member_001t__Set__Oset_Itf__r_J,type,
member_set_r: set_r > set_set_r > $o ).
thf(sy_c_member_001tf__l,type,
member_l: l > set_l > $o ).
thf(sy_c_member_001tf__r,type,
member_r: r > set_r > $o ).
thf(sy_v__092_060E_062____,type,
e: cntxt_r_l_v ).
thf(sy_v__092_060alpha_062,type,
alpha: r > r ).
thf(sy_v__092_060beta_062,type,
beta: l > l ).
thf(sy_v__092_060sigma_062____,type,
sigma: l > option_val_r_l_v ).
thf(sy_v__092_060tau_062____,type,
tau: l > option_val_r_l_v ).
thf(sy_v_e____,type,
e2: expr_r_l_v ).
thf(sy_v_r,type,
r2: r ).
thf(sy_v_r_H____,type,
r3: r ).
thf(sy_v_s,type,
s: r > option1457017436_r_l_v ).
thf(sy_v_s_H,type,
s2: r > option1457017436_r_l_v ).
thf(sy_v_subst,type,
subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v ).
% Relevant facts (352)
thf(fact_0_local_Ofork_I2_J,axiom,
( ( s @ r2 )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( rfork_r_l_v @ e2 ) ) ) ) ) ) ).
% local.fork(2)
thf(fact_1_expr_Oinject_I7_J,axiom,
! [X7: expr_r_l_v,Y7: expr_r_l_v] :
( ( ( rfork_r_l_v @ X7 )
= ( rfork_r_l_v @ Y7 ) )
= ( X7 = Y7 ) ) ).
% expr.inject(7)
thf(fact_2_injective__cntxt,axiom,
! [E: cntxt_r_l_v,E1: expr_r_l_v,E2: expr_r_l_v] :
( ( ( plug_r_l_v @ E @ E1 )
= ( plug_r_l_v @ E @ E2 ) )
= ( E1 = E2 ) ) ).
% injective_cntxt
thf(fact_3_fun__upd__upd,axiom,
! [F: r > option1457017436_r_l_v,X: r,Y: option1457017436_r_l_v,Z: option1457017436_r_l_v] :
( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ F @ X @ Y ) @ X @ Z )
= ( fun_up709272714_r_l_v @ F @ X @ Z ) ) ).
% fun_upd_upd
thf(fact_4_fun__upd__upd,axiom,
! [F: l > option_val_r_l_v,X: l,Y: option_val_r_l_v,Z: option_val_r_l_v] :
( ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ F @ X @ Y ) @ X @ Z )
= ( fun_up1835647912_r_l_v @ F @ X @ Z ) ) ).
% fun_upd_upd
thf(fact_5_fun__upd__triv,axiom,
! [F: r > option1457017436_r_l_v,X: r] :
( ( fun_up709272714_r_l_v @ F @ X @ ( F @ X ) )
= F ) ).
% fun_upd_triv
thf(fact_6_fun__upd__triv,axiom,
! [F: l > option_val_r_l_v,X: l] :
( ( fun_up1835647912_r_l_v @ F @ X @ ( F @ X ) )
= F ) ).
% fun_upd_triv
thf(fact_7_fun__upd__apply,axiom,
( fun_up709272714_r_l_v
= ( ^ [F2: r > option1457017436_r_l_v,X2: r,Y2: option1457017436_r_l_v,Z2: r] : ( if_opt1153928738_r_l_v @ ( Z2 = X2 ) @ Y2 @ ( F2 @ Z2 ) ) ) ) ).
% fun_upd_apply
thf(fact_8_fun__upd__apply,axiom,
( fun_up1835647912_r_l_v
= ( ^ [F2: l > option_val_r_l_v,X2: l,Y2: option_val_r_l_v,Z2: l] : ( if_option_val_r_l_v @ ( Z2 = X2 ) @ Y2 @ ( F2 @ Z2 ) ) ) ) ).
% fun_upd_apply
thf(fact_9_option_Oinject,axiom,
! [X22: produc1156025366_r_l_v,Y22: produc1156025366_r_l_v] :
( ( ( some_P1807977723_r_l_v @ X22 )
= ( some_P1807977723_r_l_v @ Y22 ) )
= ( X22 = Y22 ) ) ).
% option.inject
thf(fact_10_option_Oinject,axiom,
! [X22: val_r_l_v,Y22: val_r_l_v] :
( ( ( some_val_r_l_v @ X22 )
= ( some_val_r_l_v @ Y22 ) )
= ( X22 = Y22 ) ) ).
% option.inject
thf(fact_11_prod_Oinject,axiom,
! [X1: r > r,X22: produc1489027110_r_l_v,Y1: r > r,Y22: produc1489027110_r_l_v] :
( ( ( produc2111504612_r_l_v @ X1 @ X22 )
= ( produc2111504612_r_l_v @ Y1 @ Y22 ) )
= ( ( X1 = Y1 )
& ( X22 = Y22 ) ) ) ).
% prod.inject
thf(fact_12_prod_Oinject,axiom,
! [X1: l > l,X22: produc1156025366_r_l_v,Y1: l > l,Y22: produc1156025366_r_l_v] :
( ( ( produc2057232216_r_l_v @ X1 @ X22 )
= ( produc2057232216_r_l_v @ Y1 @ Y22 ) )
= ( ( X1 = Y1 )
& ( X22 = Y22 ) ) ) ).
% prod.inject
thf(fact_13_prod_Oinject,axiom,
! [X1: l > option_val_r_l_v,X22: produc1164766533_r_l_v,Y1: l > option_val_r_l_v,Y22: produc1164766533_r_l_v] :
( ( ( produc297528454_r_l_v @ X1 @ X22 )
= ( produc297528454_r_l_v @ Y1 @ Y22 ) )
= ( ( X1 = Y1 )
& ( X22 = Y22 ) ) ) ).
% prod.inject
thf(fact_14_prod_Oinject,axiom,
! [X1: l > option_val_r_l_v,X22: expr_r_l_v,Y1: l > option_val_r_l_v,Y22: expr_r_l_v] :
( ( ( produc1834103605_r_l_v @ X1 @ X22 )
= ( produc1834103605_r_l_v @ Y1 @ Y22 ) )
= ( ( X1 = Y1 )
& ( X22 = Y22 ) ) ) ).
% prod.inject
thf(fact_15_old_Oprod_Oinject,axiom,
! [A: r > r,B: produc1489027110_r_l_v,A2: r > r,B2: produc1489027110_r_l_v] :
( ( ( produc2111504612_r_l_v @ A @ B )
= ( produc2111504612_r_l_v @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ) ).
% old.prod.inject
thf(fact_16_old_Oprod_Oinject,axiom,
! [A: l > l,B: produc1156025366_r_l_v,A2: l > l,B2: produc1156025366_r_l_v] :
( ( ( produc2057232216_r_l_v @ A @ B )
= ( produc2057232216_r_l_v @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ) ).
% old.prod.inject
thf(fact_17_old_Oprod_Oinject,axiom,
! [A: l > option_val_r_l_v,B: produc1164766533_r_l_v,A2: l > option_val_r_l_v,B2: produc1164766533_r_l_v] :
( ( ( produc297528454_r_l_v @ A @ B )
= ( produc297528454_r_l_v @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ) ).
% old.prod.inject
thf(fact_18_old_Oprod_Oinject,axiom,
! [A: l > option_val_r_l_v,B: expr_r_l_v,A2: l > option_val_r_l_v,B2: expr_r_l_v] :
( ( ( produc1834103605_r_l_v @ A @ B )
= ( produc1834103605_r_l_v @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ) ).
% old.prod.inject
thf(fact_19_LID__local__store_Ocases,axiom,
! [X: produc1156025366_r_l_v] :
~ ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E3: expr_r_l_v] :
( X
!= ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) ) ).
% LID_local_store.cases
thf(fact_20_LID__local__store_Oinduct,axiom,
! [P: produc1156025366_r_l_v > $o,A0: produc1156025366_r_l_v] :
( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E3: expr_r_l_v] : ( P @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) )
=> ( P @ A0 ) ) ).
% LID_local_store.induct
thf(fact_21__092_060R_062_092_060_094sub_062L_Oinduct,axiom,
! [P: ( r > r ) > ( l > l ) > produc1156025366_r_l_v > $o,A0: r > r,A1: l > l,A22: produc1156025366_r_l_v] :
( ! [Alpha: r > r,Beta: l > l,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E3: expr_r_l_v] : ( P @ Alpha @ Beta @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) )
=> ( P @ A0 @ A1 @ A22 ) ) ).
% \<R>\<^sub>L.induct
thf(fact_22_map__upd__eqD1,axiom,
! [M: r > option1457017436_r_l_v,A: r,X: produc1156025366_r_l_v,N: r > option1457017436_r_l_v,Y: produc1156025366_r_l_v] :
( ( ( fun_up709272714_r_l_v @ M @ A @ ( some_P1807977723_r_l_v @ X ) )
= ( fun_up709272714_r_l_v @ N @ A @ ( some_P1807977723_r_l_v @ Y ) ) )
=> ( X = Y ) ) ).
% map_upd_eqD1
thf(fact_23_map__upd__eqD1,axiom,
! [M: l > option_val_r_l_v,A: l,X: val_r_l_v,N: l > option_val_r_l_v,Y: val_r_l_v] :
( ( ( fun_up1835647912_r_l_v @ M @ A @ ( some_val_r_l_v @ X ) )
= ( fun_up1835647912_r_l_v @ N @ A @ ( some_val_r_l_v @ Y ) ) )
=> ( X = Y ) ) ).
% map_upd_eqD1
thf(fact_24__092_060R_062_092_060_094sub_062L_Ocases,axiom,
! [X: produc1394974636_r_l_v] :
~ ! [Alpha: r > r,Beta: l > l,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E3: expr_r_l_v] :
( X
!= ( produc2111504612_r_l_v @ Alpha @ ( produc2057232216_r_l_v @ Beta @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) ) ) ) ).
% \<R>\<^sub>L.cases
thf(fact_25_old_Oprod_Oinducts,axiom,
! [P: produc1394974636_r_l_v > $o,Prod: produc1394974636_r_l_v] :
( ! [A3: r > r,B3: produc1489027110_r_l_v] : ( P @ ( produc2111504612_r_l_v @ A3 @ B3 ) )
=> ( P @ Prod ) ) ).
% old.prod.inducts
thf(fact_26_old_Oprod_Oinducts,axiom,
! [P: produc1489027110_r_l_v > $o,Prod: produc1489027110_r_l_v] :
( ! [A3: l > l,B3: produc1156025366_r_l_v] : ( P @ ( produc2057232216_r_l_v @ A3 @ B3 ) )
=> ( P @ Prod ) ) ).
% old.prod.inducts
thf(fact_27_old_Oprod_Oinducts,axiom,
! [P: produc1156025366_r_l_v > $o,Prod: produc1156025366_r_l_v] :
( ! [A3: l > option_val_r_l_v,B3: produc1164766533_r_l_v] : ( P @ ( produc297528454_r_l_v @ A3 @ B3 ) )
=> ( P @ Prod ) ) ).
% old.prod.inducts
thf(fact_28_old_Oprod_Oinducts,axiom,
! [P: produc1164766533_r_l_v > $o,Prod: produc1164766533_r_l_v] :
( ! [A3: l > option_val_r_l_v,B3: expr_r_l_v] : ( P @ ( produc1834103605_r_l_v @ A3 @ B3 ) )
=> ( P @ Prod ) ) ).
% old.prod.inducts
thf(fact_29_old_Oprod_Oexhaust,axiom,
! [Y: produc1394974636_r_l_v] :
~ ! [A3: r > r,B3: produc1489027110_r_l_v] :
( Y
!= ( produc2111504612_r_l_v @ A3 @ B3 ) ) ).
% old.prod.exhaust
thf(fact_30_old_Oprod_Oexhaust,axiom,
! [Y: produc1489027110_r_l_v] :
~ ! [A3: l > l,B3: produc1156025366_r_l_v] :
( Y
!= ( produc2057232216_r_l_v @ A3 @ B3 ) ) ).
% old.prod.exhaust
thf(fact_31_old_Oprod_Oexhaust,axiom,
! [Y: produc1156025366_r_l_v] :
~ ! [A3: l > option_val_r_l_v,B3: produc1164766533_r_l_v] :
( Y
!= ( produc297528454_r_l_v @ A3 @ B3 ) ) ).
% old.prod.exhaust
thf(fact_32_old_Oprod_Oexhaust,axiom,
! [Y: produc1164766533_r_l_v] :
~ ! [A3: l > option_val_r_l_v,B3: expr_r_l_v] :
( Y
!= ( produc1834103605_r_l_v @ A3 @ B3 ) ) ).
% old.prod.exhaust
thf(fact_33_Pair__inject,axiom,
! [A: r > r,B: produc1489027110_r_l_v,A2: r > r,B2: produc1489027110_r_l_v] :
( ( ( produc2111504612_r_l_v @ A @ B )
= ( produc2111504612_r_l_v @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ) ).
% Pair_inject
thf(fact_34_Pair__inject,axiom,
! [A: l > l,B: produc1156025366_r_l_v,A2: l > l,B2: produc1156025366_r_l_v] :
( ( ( produc2057232216_r_l_v @ A @ B )
= ( produc2057232216_r_l_v @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ) ).
% Pair_inject
thf(fact_35_Pair__inject,axiom,
! [A: l > option_val_r_l_v,B: produc1164766533_r_l_v,A2: l > option_val_r_l_v,B2: produc1164766533_r_l_v] :
( ( ( produc297528454_r_l_v @ A @ B )
= ( produc297528454_r_l_v @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ) ).
% Pair_inject
thf(fact_36_Pair__inject,axiom,
! [A: l > option_val_r_l_v,B: expr_r_l_v,A2: l > option_val_r_l_v,B2: expr_r_l_v] :
( ( ( produc1834103605_r_l_v @ A @ B )
= ( produc1834103605_r_l_v @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ) ).
% Pair_inject
thf(fact_37_prod__cases,axiom,
! [P: produc1394974636_r_l_v > $o,P2: produc1394974636_r_l_v] :
( ! [A3: r > r,B3: produc1489027110_r_l_v] : ( P @ ( produc2111504612_r_l_v @ A3 @ B3 ) )
=> ( P @ P2 ) ) ).
% prod_cases
thf(fact_38_prod__cases,axiom,
! [P: produc1489027110_r_l_v > $o,P2: produc1489027110_r_l_v] :
( ! [A3: l > l,B3: produc1156025366_r_l_v] : ( P @ ( produc2057232216_r_l_v @ A3 @ B3 ) )
=> ( P @ P2 ) ) ).
% prod_cases
thf(fact_39_prod__cases,axiom,
! [P: produc1156025366_r_l_v > $o,P2: produc1156025366_r_l_v] :
( ! [A3: l > option_val_r_l_v,B3: produc1164766533_r_l_v] : ( P @ ( produc297528454_r_l_v @ A3 @ B3 ) )
=> ( P @ P2 ) ) ).
% prod_cases
thf(fact_40_prod__cases,axiom,
! [P: produc1164766533_r_l_v > $o,P2: produc1164766533_r_l_v] :
( ! [A3: l > option_val_r_l_v,B3: expr_r_l_v] : ( P @ ( produc1834103605_r_l_v @ A3 @ B3 ) )
=> ( P @ P2 ) ) ).
% prod_cases
thf(fact_41_surj__pair,axiom,
! [P2: produc1394974636_r_l_v] :
? [X3: r > r,Y3: produc1489027110_r_l_v] :
( P2
= ( produc2111504612_r_l_v @ X3 @ Y3 ) ) ).
% surj_pair
thf(fact_42_surj__pair,axiom,
! [P2: produc1489027110_r_l_v] :
? [X3: l > l,Y3: produc1156025366_r_l_v] :
( P2
= ( produc2057232216_r_l_v @ X3 @ Y3 ) ) ).
% surj_pair
thf(fact_43_surj__pair,axiom,
! [P2: produc1156025366_r_l_v] :
? [X3: l > option_val_r_l_v,Y3: produc1164766533_r_l_v] :
( P2
= ( produc297528454_r_l_v @ X3 @ Y3 ) ) ).
% surj_pair
thf(fact_44_surj__pair,axiom,
! [P2: produc1164766533_r_l_v] :
? [X3: l > option_val_r_l_v,Y3: expr_r_l_v] :
( P2
= ( produc1834103605_r_l_v @ X3 @ Y3 ) ) ).
% surj_pair
thf(fact_45_fun__upd__idem__iff,axiom,
! [F: r > option1457017436_r_l_v,X: r,Y: option1457017436_r_l_v] :
( ( ( fun_up709272714_r_l_v @ F @ X @ Y )
= F )
= ( ( F @ X )
= Y ) ) ).
% fun_upd_idem_iff
thf(fact_46_fun__upd__idem__iff,axiom,
! [F: l > option_val_r_l_v,X: l,Y: option_val_r_l_v] :
( ( ( fun_up1835647912_r_l_v @ F @ X @ Y )
= F )
= ( ( F @ X )
= Y ) ) ).
% fun_upd_idem_iff
thf(fact_47_fun__upd__twist,axiom,
! [A: r,C: r,M: r > option1457017436_r_l_v,B: option1457017436_r_l_v,D: option1457017436_r_l_v] :
( ( A != C )
=> ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ M @ A @ B ) @ C @ D )
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ M @ C @ D ) @ A @ B ) ) ) ).
% fun_upd_twist
thf(fact_48_fun__upd__twist,axiom,
! [A: l,C: l,M: l > option_val_r_l_v,B: option_val_r_l_v,D: option_val_r_l_v] :
( ( A != C )
=> ( ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ M @ A @ B ) @ C @ D )
= ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ M @ C @ D ) @ A @ B ) ) ) ).
% fun_upd_twist
thf(fact_49_fun__upd__other,axiom,
! [Z: r,X: r,F: r > option1457017436_r_l_v,Y: option1457017436_r_l_v] :
( ( Z != X )
=> ( ( fun_up709272714_r_l_v @ F @ X @ Y @ Z )
= ( F @ Z ) ) ) ).
% fun_upd_other
thf(fact_50_fun__upd__other,axiom,
! [Z: l,X: l,F: l > option_val_r_l_v,Y: option_val_r_l_v] :
( ( Z != X )
=> ( ( fun_up1835647912_r_l_v @ F @ X @ Y @ Z )
= ( F @ Z ) ) ) ).
% fun_upd_other
thf(fact_51_fun__upd__same,axiom,
! [F: r > option1457017436_r_l_v,X: r,Y: option1457017436_r_l_v] :
( ( fun_up709272714_r_l_v @ F @ X @ Y @ X )
= Y ) ).
% fun_upd_same
thf(fact_52_fun__upd__same,axiom,
! [F: l > option_val_r_l_v,X: l,Y: option_val_r_l_v] :
( ( fun_up1835647912_r_l_v @ F @ X @ Y @ X )
= Y ) ).
% fun_upd_same
thf(fact_53_fun__upd__idem,axiom,
! [F: r > option1457017436_r_l_v,X: r,Y: option1457017436_r_l_v] :
( ( ( F @ X )
= Y )
=> ( ( fun_up709272714_r_l_v @ F @ X @ Y )
= F ) ) ).
% fun_upd_idem
thf(fact_54_fun__upd__idem,axiom,
! [F: l > option_val_r_l_v,X: l,Y: option_val_r_l_v] :
( ( ( F @ X )
= Y )
=> ( ( fun_up1835647912_r_l_v @ F @ X @ Y )
= F ) ) ).
% fun_upd_idem
thf(fact_55_fun__upd__eqD,axiom,
! [F: r > option1457017436_r_l_v,X: r,Y: option1457017436_r_l_v,G: r > option1457017436_r_l_v,Z: option1457017436_r_l_v] :
( ( ( fun_up709272714_r_l_v @ F @ X @ Y )
= ( fun_up709272714_r_l_v @ G @ X @ Z ) )
=> ( Y = Z ) ) ).
% fun_upd_eqD
thf(fact_56_fun__upd__eqD,axiom,
! [F: l > option_val_r_l_v,X: l,Y: option_val_r_l_v,G: l > option_val_r_l_v,Z: option_val_r_l_v] :
( ( ( fun_up1835647912_r_l_v @ F @ X @ Y )
= ( fun_up1835647912_r_l_v @ G @ X @ Z ) )
=> ( Y = Z ) ) ).
% fun_upd_eqD
thf(fact_57_fun__upd__def,axiom,
( fun_up709272714_r_l_v
= ( ^ [F2: r > option1457017436_r_l_v,A4: r,B4: option1457017436_r_l_v,X2: r] : ( if_opt1153928738_r_l_v @ ( X2 = A4 ) @ B4 @ ( F2 @ X2 ) ) ) ) ).
% fun_upd_def
thf(fact_58_fun__upd__def,axiom,
( fun_up1835647912_r_l_v
= ( ^ [F2: l > option_val_r_l_v,A4: l,B4: option_val_r_l_v,X2: l] : ( if_option_val_r_l_v @ ( X2 = A4 ) @ B4 @ ( F2 @ X2 ) ) ) ) ).
% fun_upd_def
thf(fact_59_prod__induct5,axiom,
! [P: produc1394974636_r_l_v > $o,X: produc1394974636_r_l_v] :
( ! [A3: r > r,B3: l > l,C2: l > option_val_r_l_v,D2: l > option_val_r_l_v,E3: expr_r_l_v] : ( P @ ( produc2111504612_r_l_v @ A3 @ ( produc2057232216_r_l_v @ B3 @ ( produc297528454_r_l_v @ C2 @ ( produc1834103605_r_l_v @ D2 @ E3 ) ) ) ) )
=> ( P @ X ) ) ).
% prod_induct5
thf(fact_60_prod__induct4,axiom,
! [P: produc1394974636_r_l_v > $o,X: produc1394974636_r_l_v] :
( ! [A3: r > r,B3: l > l,C2: l > option_val_r_l_v,D2: produc1164766533_r_l_v] : ( P @ ( produc2111504612_r_l_v @ A3 @ ( produc2057232216_r_l_v @ B3 @ ( produc297528454_r_l_v @ C2 @ D2 ) ) ) )
=> ( P @ X ) ) ).
% prod_induct4
thf(fact_61_prod__induct4,axiom,
! [P: produc1489027110_r_l_v > $o,X: produc1489027110_r_l_v] :
( ! [A3: l > l,B3: l > option_val_r_l_v,C2: l > option_val_r_l_v,D2: expr_r_l_v] : ( P @ ( produc2057232216_r_l_v @ A3 @ ( produc297528454_r_l_v @ B3 @ ( produc1834103605_r_l_v @ C2 @ D2 ) ) ) )
=> ( P @ X ) ) ).
% prod_induct4
thf(fact_62_prod__induct3,axiom,
! [P: produc1394974636_r_l_v > $o,X: produc1394974636_r_l_v] :
( ! [A3: r > r,B3: l > l,C2: produc1156025366_r_l_v] : ( P @ ( produc2111504612_r_l_v @ A3 @ ( produc2057232216_r_l_v @ B3 @ C2 ) ) )
=> ( P @ X ) ) ).
% prod_induct3
thf(fact_63_prod__induct3,axiom,
! [P: produc1489027110_r_l_v > $o,X: produc1489027110_r_l_v] :
( ! [A3: l > l,B3: l > option_val_r_l_v,C2: produc1164766533_r_l_v] : ( P @ ( produc2057232216_r_l_v @ A3 @ ( produc297528454_r_l_v @ B3 @ C2 ) ) )
=> ( P @ X ) ) ).
% prod_induct3
thf(fact_64_prod__induct3,axiom,
! [P: produc1156025366_r_l_v > $o,X: produc1156025366_r_l_v] :
( ! [A3: l > option_val_r_l_v,B3: l > option_val_r_l_v,C2: expr_r_l_v] : ( P @ ( produc297528454_r_l_v @ A3 @ ( produc1834103605_r_l_v @ B3 @ C2 ) ) )
=> ( P @ X ) ) ).
% prod_induct3
thf(fact_65_prod__cases5,axiom,
! [Y: produc1394974636_r_l_v] :
~ ! [A3: r > r,B3: l > l,C2: l > option_val_r_l_v,D2: l > option_val_r_l_v,E3: expr_r_l_v] :
( Y
!= ( produc2111504612_r_l_v @ A3 @ ( produc2057232216_r_l_v @ B3 @ ( produc297528454_r_l_v @ C2 @ ( produc1834103605_r_l_v @ D2 @ E3 ) ) ) ) ) ).
% prod_cases5
thf(fact_66_prod__cases4,axiom,
! [Y: produc1394974636_r_l_v] :
~ ! [A3: r > r,B3: l > l,C2: l > option_val_r_l_v,D2: produc1164766533_r_l_v] :
( Y
!= ( produc2111504612_r_l_v @ A3 @ ( produc2057232216_r_l_v @ B3 @ ( produc297528454_r_l_v @ C2 @ D2 ) ) ) ) ).
% prod_cases4
thf(fact_67_prod__cases4,axiom,
! [Y: produc1489027110_r_l_v] :
~ ! [A3: l > l,B3: l > option_val_r_l_v,C2: l > option_val_r_l_v,D2: expr_r_l_v] :
( Y
!= ( produc2057232216_r_l_v @ A3 @ ( produc297528454_r_l_v @ B3 @ ( produc1834103605_r_l_v @ C2 @ D2 ) ) ) ) ).
% prod_cases4
thf(fact_68_prod__cases3,axiom,
! [Y: produc1394974636_r_l_v] :
~ ! [A3: r > r,B3: l > l,C2: produc1156025366_r_l_v] :
( Y
!= ( produc2111504612_r_l_v @ A3 @ ( produc2057232216_r_l_v @ B3 @ C2 ) ) ) ).
% prod_cases3
thf(fact_69_prod__cases3,axiom,
! [Y: produc1489027110_r_l_v] :
~ ! [A3: l > l,B3: l > option_val_r_l_v,C2: produc1164766533_r_l_v] :
( Y
!= ( produc2057232216_r_l_v @ A3 @ ( produc297528454_r_l_v @ B3 @ C2 ) ) ) ).
% prod_cases3
thf(fact_70_prod__cases3,axiom,
! [Y: produc1156025366_r_l_v] :
~ ! [A3: l > option_val_r_l_v,B3: l > option_val_r_l_v,C2: expr_r_l_v] :
( Y
!= ( produc297528454_r_l_v @ A3 @ ( produc1834103605_r_l_v @ B3 @ C2 ) ) ) ).
% prod_cases3
thf(fact_71_map__upd__Some__unfold,axiom,
! [M: r > option1457017436_r_l_v,A: r,B: produc1156025366_r_l_v,X: r,Y: produc1156025366_r_l_v] :
( ( ( fun_up709272714_r_l_v @ M @ A @ ( some_P1807977723_r_l_v @ B ) @ X )
= ( some_P1807977723_r_l_v @ Y ) )
= ( ( ( X = A )
& ( B = Y ) )
| ( ( X != A )
& ( ( M @ X )
= ( some_P1807977723_r_l_v @ Y ) ) ) ) ) ).
% map_upd_Some_unfold
thf(fact_72_map__upd__Some__unfold,axiom,
! [M: l > option_val_r_l_v,A: l,B: val_r_l_v,X: l,Y: val_r_l_v] :
( ( ( fun_up1835647912_r_l_v @ M @ A @ ( some_val_r_l_v @ B ) @ X )
= ( some_val_r_l_v @ Y ) )
= ( ( ( X = A )
& ( B = Y ) )
| ( ( X != A )
& ( ( M @ X )
= ( some_val_r_l_v @ Y ) ) ) ) ) ).
% map_upd_Some_unfold
thf(fact_73_map__upd__triv,axiom,
! [T: r > option1457017436_r_l_v,K: r,X: produc1156025366_r_l_v] :
( ( ( T @ K )
= ( some_P1807977723_r_l_v @ X ) )
=> ( ( fun_up709272714_r_l_v @ T @ K @ ( some_P1807977723_r_l_v @ X ) )
= T ) ) ).
% map_upd_triv
thf(fact_74_map__upd__triv,axiom,
! [T: l > option_val_r_l_v,K: l,X: val_r_l_v] :
( ( ( T @ K )
= ( some_val_r_l_v @ X ) )
=> ( ( fun_up1835647912_r_l_v @ T @ K @ ( some_val_r_l_v @ X ) )
= T ) ) ).
% map_upd_triv
thf(fact_75_LID__local__store_Osimps,axiom,
! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E4: expr_r_l_v] :
( ( lID_lo1265057957_l_r_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ E4 ) ) )
= Tau2 ) ).
% LID_local_store.simps
thf(fact_76_LID__local__store_Oelims,axiom,
! [X: produc1156025366_r_l_v,Y: l > option_val_r_l_v] :
( ( ( lID_lo1265057957_l_r_v @ X )
= Y )
=> ~ ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v] :
( ? [E3: expr_r_l_v] :
( X
= ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) )
=> ( Y != Tau ) ) ) ).
% LID_local_store.elims
thf(fact_77_LID__expression_Osimps,axiom,
! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E4: expr_r_l_v] :
( ( lID_expression_l_r_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ E4 ) ) )
= E4 ) ).
% LID_expression.simps
thf(fact_78_LID__expression_Oelims,axiom,
! [X: produc1156025366_r_l_v,Y: expr_r_l_v] :
( ( ( lID_expression_l_r_v @ X )
= Y )
=> ~ ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E3: expr_r_l_v] :
( ( X
= ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) )
=> ( Y != E3 ) ) ) ).
% LID_expression.elims
thf(fact_79_mem__Collect__eq,axiom,
! [A: set_l,P: set_l > $o] :
( ( member_set_l @ A @ ( collect_set_l @ P ) )
= ( P @ A ) ) ).
% mem_Collect_eq
thf(fact_80_mem__Collect__eq,axiom,
! [A: set_r,P: set_r > $o] :
( ( member_set_r @ A @ ( collect_set_r @ P ) )
= ( P @ A ) ) ).
% mem_Collect_eq
thf(fact_81_mem__Collect__eq,axiom,
! [A: r,P: r > $o] :
( ( member_r @ A @ ( collect_r @ P ) )
= ( P @ A ) ) ).
% mem_Collect_eq
thf(fact_82_mem__Collect__eq,axiom,
! [A: l,P: l > $o] :
( ( member_l @ A @ ( collect_l @ P ) )
= ( P @ A ) ) ).
% mem_Collect_eq
thf(fact_83_Collect__mem__eq,axiom,
! [A5: set_set_l] :
( ( collect_set_l
@ ^ [X2: set_l] : ( member_set_l @ X2 @ A5 ) )
= A5 ) ).
% Collect_mem_eq
thf(fact_84_Collect__mem__eq,axiom,
! [A5: set_set_r] :
( ( collect_set_r
@ ^ [X2: set_r] : ( member_set_r @ X2 @ A5 ) )
= A5 ) ).
% Collect_mem_eq
thf(fact_85_Collect__mem__eq,axiom,
! [A5: set_r] :
( ( collect_r
@ ^ [X2: r] : ( member_r @ X2 @ A5 ) )
= A5 ) ).
% Collect_mem_eq
thf(fact_86_Collect__mem__eq,axiom,
! [A5: set_l] :
( ( collect_l
@ ^ [X2: l] : ( member_l @ X2 @ A5 ) )
= A5 ) ).
% Collect_mem_eq
thf(fact_87_Collect__cong,axiom,
! [P: l > $o,Q: l > $o] :
( ! [X3: l] :
( ( P @ X3 )
= ( Q @ X3 ) )
=> ( ( collect_l @ P )
= ( collect_l @ Q ) ) ) ).
% Collect_cong
thf(fact_88_Collect__cong,axiom,
! [P: r > $o,Q: r > $o] :
( ! [X3: r] :
( ( P @ X3 )
= ( Q @ X3 ) )
=> ( ( collect_r @ P )
= ( collect_r @ Q ) ) ) ).
% Collect_cong
thf(fact_89_Collect__cong,axiom,
! [P: set_l > $o,Q: set_l > $o] :
( ! [X3: set_l] :
( ( P @ X3 )
= ( Q @ X3 ) )
=> ( ( collect_set_l @ P )
= ( collect_set_l @ Q ) ) ) ).
% Collect_cong
thf(fact_90_Collect__cong,axiom,
! [P: set_r > $o,Q: set_r > $o] :
( ! [X3: set_r] :
( ( P @ X3 )
= ( Q @ X3 ) )
=> ( ( collect_set_r @ P )
= ( collect_set_r @ Q ) ) ) ).
% Collect_cong
thf(fact_91_local_Ofork_I3_J,axiom,
~ ( member_r @ r3 @ ( rID_G_r_l_v @ s ) ) ).
% local.fork(3)
thf(fact_92_LID__snapshot_Osimps,axiom,
! [Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E4: expr_r_l_v] :
( ( lID_snapshot_l_r_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ E4 ) ) )
= Sigma2 ) ).
% LID_snapshot.simps
thf(fact_93_LID__snapshot_Oelims,axiom,
! [X: produc1156025366_r_l_v,Y: l > option_val_r_l_v] :
( ( ( lID_snapshot_l_r_v @ X )
= Y )
=> ~ ! [Sigma: l > option_val_r_l_v] :
( ? [Tau: l > option_val_r_l_v,E3: expr_r_l_v] :
( X
= ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) )
=> ( Y != Sigma ) ) ) ).
% LID_snapshot.elims
thf(fact_94_local_Ofork_I1_J,axiom,
( s2
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ s @ r2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( vE_r_l_v @ ( rid_r_l_v @ r3 ) ) ) ) ) ) ) @ r3
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ sigma @ tau )
@ ( produc1834103605_r_l_v
@ ^ [X2: l] : none_val_r_l_v
@ e2 ) ) ) ) ) ).
% local.fork(1)
thf(fact_95_expr_Oinject_I1_J,axiom,
! [X1: val_r_l_v,Y1: val_r_l_v] :
( ( ( vE_r_l_v @ X1 )
= ( vE_r_l_v @ Y1 ) )
= ( X1 = Y1 ) ) ).
% expr.inject(1)
thf(fact_96_val_Oinject_I4_J,axiom,
! [X4: r,Y4: r] :
( ( ( rid_r_l_v @ X4 )
= ( rid_r_l_v @ Y4 ) )
= ( X4 = Y4 ) ) ).
% val.inject(4)
thf(fact_97_not__None__eq,axiom,
! [X: option1457017436_r_l_v] :
( ( X != none_P277133687_r_l_v )
= ( ? [Y2: produc1156025366_r_l_v] :
( X
= ( some_P1807977723_r_l_v @ Y2 ) ) ) ) ).
% not_None_eq
thf(fact_98_not__None__eq,axiom,
! [X: option_val_r_l_v] :
( ( X != none_val_r_l_v )
= ( ? [Y2: val_r_l_v] :
( X
= ( some_val_r_l_v @ Y2 ) ) ) ) ).
% not_None_eq
thf(fact_99_not__Some__eq,axiom,
! [X: option1457017436_r_l_v] :
( ( ! [Y2: produc1156025366_r_l_v] :
( X
!= ( some_P1807977723_r_l_v @ Y2 ) ) )
= ( X = none_P277133687_r_l_v ) ) ).
% not_Some_eq
thf(fact_100_not__Some__eq,axiom,
! [X: option_val_r_l_v] :
( ( ! [Y2: val_r_l_v] :
( X
!= ( some_val_r_l_v @ Y2 ) ) )
= ( X = none_val_r_l_v ) ) ).
% not_Some_eq
thf(fact_101_empty__upd__none,axiom,
! [X: l] :
( ( fun_up1835647912_r_l_v
@ ^ [X2: l] : none_val_r_l_v
@ X
@ none_val_r_l_v )
= ( ^ [X2: l] : none_val_r_l_v ) ) ).
% empty_upd_none
thf(fact_102_empty__upd__none,axiom,
! [X: r] :
( ( fun_up709272714_r_l_v
@ ^ [X2: r] : none_P277133687_r_l_v
@ X
@ none_P277133687_r_l_v )
= ( ^ [X2: r] : none_P277133687_r_l_v ) ) ).
% empty_upd_none
thf(fact_103_combine_Oelims,axiom,
! [X: l > option_val_r_l_v,Xa: l > option_val_r_l_v,Xb: l,Y: option_val_r_l_v] :
( ( ( combine_l_val_r_l_v @ X @ Xa @ Xb )
= Y )
=> ( ( ( ( Xa @ Xb )
= none_val_r_l_v )
=> ( Y
= ( X @ Xb ) ) )
& ( ( ( Xa @ Xb )
!= none_val_r_l_v )
=> ( Y
= ( Xa @ Xb ) ) ) ) ) ).
% combine.elims
thf(fact_104_combine_Osimps,axiom,
( combine_l_val_r_l_v
= ( ^ [F2: l > option_val_r_l_v,G2: l > option_val_r_l_v,X2: l] :
( if_option_val_r_l_v
@ ( ( G2 @ X2 )
= none_val_r_l_v )
@ ( F2 @ X2 )
@ ( G2 @ X2 ) ) ) ) ).
% combine.simps
thf(fact_105_option_Odistinct_I1_J,axiom,
! [X22: produc1156025366_r_l_v] :
( none_P277133687_r_l_v
!= ( some_P1807977723_r_l_v @ X22 ) ) ).
% option.distinct(1)
thf(fact_106_option_Odistinct_I1_J,axiom,
! [X22: val_r_l_v] :
( none_val_r_l_v
!= ( some_val_r_l_v @ X22 ) ) ).
% option.distinct(1)
thf(fact_107_option_OdiscI,axiom,
! [Option: option1457017436_r_l_v,X22: produc1156025366_r_l_v] :
( ( Option
= ( some_P1807977723_r_l_v @ X22 ) )
=> ( Option != none_P277133687_r_l_v ) ) ).
% option.discI
thf(fact_108_option_OdiscI,axiom,
! [Option: option_val_r_l_v,X22: val_r_l_v] :
( ( Option
= ( some_val_r_l_v @ X22 ) )
=> ( Option != none_val_r_l_v ) ) ).
% option.discI
thf(fact_109_option_Oexhaust,axiom,
! [Y: option1457017436_r_l_v] :
( ( Y != none_P277133687_r_l_v )
=> ~ ! [X23: produc1156025366_r_l_v] :
( Y
!= ( some_P1807977723_r_l_v @ X23 ) ) ) ).
% option.exhaust
thf(fact_110_option_Oexhaust,axiom,
! [Y: option_val_r_l_v] :
( ( Y != none_val_r_l_v )
=> ~ ! [X23: val_r_l_v] :
( Y
!= ( some_val_r_l_v @ X23 ) ) ) ).
% option.exhaust
thf(fact_111_option_Oinducts,axiom,
! [P: option1457017436_r_l_v > $o,Option: option1457017436_r_l_v] :
( ( P @ none_P277133687_r_l_v )
=> ( ! [X3: produc1156025366_r_l_v] : ( P @ ( some_P1807977723_r_l_v @ X3 ) )
=> ( P @ Option ) ) ) ).
% option.inducts
thf(fact_112_option_Oinducts,axiom,
! [P: option_val_r_l_v > $o,Option: option_val_r_l_v] :
( ( P @ none_val_r_l_v )
=> ( ! [X3: val_r_l_v] : ( P @ ( some_val_r_l_v @ X3 ) )
=> ( P @ Option ) ) ) ).
% option.inducts
thf(fact_113_split__option__ex,axiom,
( ( ^ [P3: option1457017436_r_l_v > $o] :
? [X5: option1457017436_r_l_v] : ( P3 @ X5 ) )
= ( ^ [P4: option1457017436_r_l_v > $o] :
( ( P4 @ none_P277133687_r_l_v )
| ? [X2: produc1156025366_r_l_v] : ( P4 @ ( some_P1807977723_r_l_v @ X2 ) ) ) ) ) ).
% split_option_ex
thf(fact_114_split__option__ex,axiom,
( ( ^ [P3: option_val_r_l_v > $o] :
? [X5: option_val_r_l_v] : ( P3 @ X5 ) )
= ( ^ [P4: option_val_r_l_v > $o] :
( ( P4 @ none_val_r_l_v )
| ? [X2: val_r_l_v] : ( P4 @ ( some_val_r_l_v @ X2 ) ) ) ) ) ).
% split_option_ex
thf(fact_115_split__option__all,axiom,
( ( ^ [P3: option1457017436_r_l_v > $o] :
! [X5: option1457017436_r_l_v] : ( P3 @ X5 ) )
= ( ^ [P4: option1457017436_r_l_v > $o] :
( ( P4 @ none_P277133687_r_l_v )
& ! [X2: produc1156025366_r_l_v] : ( P4 @ ( some_P1807977723_r_l_v @ X2 ) ) ) ) ) ).
% split_option_all
thf(fact_116_split__option__all,axiom,
( ( ^ [P3: option_val_r_l_v > $o] :
! [X5: option_val_r_l_v] : ( P3 @ X5 ) )
= ( ^ [P4: option_val_r_l_v > $o] :
( ( P4 @ none_val_r_l_v )
& ! [X2: val_r_l_v] : ( P4 @ ( some_val_r_l_v @ X2 ) ) ) ) ) ).
% split_option_all
thf(fact_117_combine__options__cases,axiom,
! [X: option1457017436_r_l_v,P: option1457017436_r_l_v > option1457017436_r_l_v > $o,Y: option1457017436_r_l_v] :
( ( ( X = none_P277133687_r_l_v )
=> ( P @ X @ Y ) )
=> ( ( ( Y = none_P277133687_r_l_v )
=> ( P @ X @ Y ) )
=> ( ! [A3: produc1156025366_r_l_v,B3: produc1156025366_r_l_v] :
( ( X
= ( some_P1807977723_r_l_v @ A3 ) )
=> ( ( Y
= ( some_P1807977723_r_l_v @ B3 ) )
=> ( P @ X @ Y ) ) )
=> ( P @ X @ Y ) ) ) ) ).
% combine_options_cases
thf(fact_118_combine__options__cases,axiom,
! [X: option1457017436_r_l_v,P: option1457017436_r_l_v > option_val_r_l_v > $o,Y: option_val_r_l_v] :
( ( ( X = none_P277133687_r_l_v )
=> ( P @ X @ Y ) )
=> ( ( ( Y = none_val_r_l_v )
=> ( P @ X @ Y ) )
=> ( ! [A3: produc1156025366_r_l_v,B3: val_r_l_v] :
( ( X
= ( some_P1807977723_r_l_v @ A3 ) )
=> ( ( Y
= ( some_val_r_l_v @ B3 ) )
=> ( P @ X @ Y ) ) )
=> ( P @ X @ Y ) ) ) ) ).
% combine_options_cases
thf(fact_119_combine__options__cases,axiom,
! [X: option_val_r_l_v,P: option_val_r_l_v > option1457017436_r_l_v > $o,Y: option1457017436_r_l_v] :
( ( ( X = none_val_r_l_v )
=> ( P @ X @ Y ) )
=> ( ( ( Y = none_P277133687_r_l_v )
=> ( P @ X @ Y ) )
=> ( ! [A3: val_r_l_v,B3: produc1156025366_r_l_v] :
( ( X
= ( some_val_r_l_v @ A3 ) )
=> ( ( Y
= ( some_P1807977723_r_l_v @ B3 ) )
=> ( P @ X @ Y ) ) )
=> ( P @ X @ Y ) ) ) ) ).
% combine_options_cases
thf(fact_120_combine__options__cases,axiom,
! [X: option_val_r_l_v,P: option_val_r_l_v > option_val_r_l_v > $o,Y: option_val_r_l_v] :
( ( ( X = none_val_r_l_v )
=> ( P @ X @ Y ) )
=> ( ( ( Y = none_val_r_l_v )
=> ( P @ X @ Y ) )
=> ( ! [A3: val_r_l_v,B3: val_r_l_v] :
( ( X
= ( some_val_r_l_v @ A3 ) )
=> ( ( Y
= ( some_val_r_l_v @ B3 ) )
=> ( P @ X @ Y ) ) )
=> ( P @ X @ Y ) ) ) ) ).
% combine_options_cases
thf(fact_121_expr_Odistinct_I11_J,axiom,
! [X1: val_r_l_v,X7: expr_r_l_v] :
( ( vE_r_l_v @ X1 )
!= ( rfork_r_l_v @ X7 ) ) ).
% expr.distinct(11)
thf(fact_122_map__upd__nonempty,axiom,
! [T: r > option1457017436_r_l_v,K: r,X: produc1156025366_r_l_v] :
( ( fun_up709272714_r_l_v @ T @ K @ ( some_P1807977723_r_l_v @ X ) )
!= ( ^ [X2: r] : none_P277133687_r_l_v ) ) ).
% map_upd_nonempty
thf(fact_123_map__upd__nonempty,axiom,
! [T: l > option_val_r_l_v,K: l,X: val_r_l_v] :
( ( fun_up1835647912_r_l_v @ T @ K @ ( some_val_r_l_v @ X ) )
!= ( ^ [X2: l] : none_val_r_l_v ) ) ).
% map_upd_nonempty
thf(fact_124_restrictions__inwards,axiom,
! [X: r,X6: r,F: r > option1457017436_r_l_v,Y: produc1156025366_r_l_v] :
( ( X != X6 )
=> ( ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ F @ X @ ( some_P1807977723_r_l_v @ Y ) ) @ X6 @ none_P277133687_r_l_v )
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ F @ X6 @ none_P277133687_r_l_v ) @ X @ ( some_P1807977723_r_l_v @ Y ) ) ) ) ).
% restrictions_inwards
thf(fact_125_restrictions__inwards,axiom,
! [X: l,X6: l,F: l > option_val_r_l_v,Y: val_r_l_v] :
( ( X != X6 )
=> ( ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ F @ X @ ( some_val_r_l_v @ Y ) ) @ X6 @ none_val_r_l_v )
= ( fun_up1835647912_r_l_v @ ( fun_up1835647912_r_l_v @ F @ X6 @ none_val_r_l_v ) @ X @ ( some_val_r_l_v @ Y ) ) ) ) ).
% restrictions_inwards
thf(fact_126_RID_092_060_094sub_062GI_I1_J,axiom,
! [S: r > option1457017436_r_l_v,R: r,V: produc1156025366_r_l_v] :
( ( ( S @ R )
= ( some_P1807977723_r_l_v @ V ) )
=> ( member_r @ R @ ( rID_G_r_l_v @ S ) ) ) ).
% RID\<^sub>GI(1)
thf(fact_127_revision__step__relaxed_Ofork,axiom,
! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,E4: expr_r_l_v,R2: r] :
( ( ( S @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
=> ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
=> ( revisi1291188644_r_l_v @ subst @ R @ S
@ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) @ R2
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
@ ( produc1834103605_r_l_v
@ ^ [X2: l] : none_val_r_l_v
@ E4 ) ) ) ) ) ) ) ).
% revision_step_relaxed.fork
thf(fact_128_revision__step_Ofork,axiom,
! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,E4: expr_r_l_v,R2: r] :
( ( ( S @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
=> ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
=> ( revision_step_r_l_v @ subst @ R @ S
@ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) @ R2
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
@ ( produc1834103605_r_l_v
@ ^ [X2: l] : none_val_r_l_v
@ E4 ) ) ) ) ) ) ) ).
% revision_step.fork
thf(fact_129__092_060alpha_062r_H__fresh,axiom,
~ ( member_r @ ( alpha @ r3 ) @ ( rID_G_r_l_v @ ( r_G_r_l_v @ alpha @ beta @ s ) ) ) ).
% \<alpha>r'_fresh
thf(fact_130_substitution_Orevision__step__relaxed_Ofork,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,E4: expr_r_l_v,R2: r] :
( ( substitution_r_l_v @ Subst )
=> ( ( ( S @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
=> ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
=> ( revisi1291188644_r_l_v @ Subst @ R @ S
@ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) @ R2
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
@ ( produc1834103605_r_l_v
@ ^ [X2: l] : none_val_r_l_v
@ E4 ) ) ) ) ) ) ) ) ).
% substitution.revision_step_relaxed.fork
thf(fact_131_substitution_Ofork__pseudodeterministic,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,E4: expr_r_l_v,S2: r > option1457017436_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( ( ( S @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
=> ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
= ( ? [R3: r] :
( ~ ( member_r @ R3 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) ) ) )
& ( S2
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R3 ) ) ) ) ) ) ) @ R3
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
@ ( produc1834103605_r_l_v
@ ^ [X2: l] : none_val_r_l_v
@ E4 ) ) ) ) ) ) ) ) ) ) ).
% substitution.fork_pseudodeterministic
thf(fact_132_local_Ostep,axiom,
revision_step_r_l_v @ subst @ r2 @ s @ s2 ).
% local.step
thf(fact_133_substitution__axioms,axiom,
substitution_r_l_v @ subst ).
% substitution_axioms
thf(fact_134_rename__empty_I2_J,axiom,
! [Alpha2: r > r,Beta2: l > l] :
( ( r_G_r_l_v @ Alpha2 @ Beta2
@ ^ [X2: r] : none_P277133687_r_l_v )
= ( ^ [X2: r] : none_P277133687_r_l_v ) ) ).
% rename_empty(2)
thf(fact_135_in__restricted__global__in__unrestricted__global_I1_J,axiom,
! [R2: r,S: r > option1457017436_r_l_v,R: r] :
( ( member_r @ R2 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
=> ( member_r @ R2 @ ( rID_G_r_l_v @ S ) ) ) ).
% in_restricted_global_in_unrestricted_global(1)
thf(fact_136_only__fork__introduces__rids_H,axiom,
! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v,R2: r] :
( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
=> ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E5: cntxt_r_l_v,E3: expr_r_l_v] :
( ( S @ R )
!= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E5 @ ( rfork_r_l_v @ E3 ) ) ) ) ) )
=> ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
=> ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S2 ) ) ) ) ) ).
% only_fork_introduces_rids'
thf(fact_137_in__restricted__global__in__updated__global_I1_J,axiom,
! [R2: r,S: r > option1457017436_r_l_v,R: r,Ls: produc1156025366_r_l_v] :
( ( member_r @ R2 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
=> ( member_r @ R2 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ Ls ) ) ) ) ) ).
% in_restricted_global_in_updated_global(1)
thf(fact_138_fork__pseudodeterministic,axiom,
! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,E4: expr_r_l_v,S2: r > option1457017436_r_l_v] :
( ( ( S @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
=> ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
= ( ? [R3: r] :
( ~ ( member_r @ R3 @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) ) ) )
& ( S2
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R3 ) ) ) ) ) ) ) @ R3
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
@ ( produc1834103605_r_l_v
@ ^ [X2: l] : none_val_r_l_v
@ E4 ) ) ) ) ) ) ) ) ) ).
% fork_pseudodeterministic
thf(fact_139_substitution_Orevision__step_Ocong,axiom,
revision_step_r_l_v = revision_step_r_l_v ).
% substitution.revision_step.cong
thf(fact_140_substitution_Orevision__step__relaxed_Ocong,axiom,
revisi1291188644_r_l_v = revisi1291188644_r_l_v ).
% substitution.revision_step_relaxed.cong
thf(fact_141_substitution_Oonly__fork__introduces__rids_H,axiom,
! [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] :
( ( substitution_r_l_v @ Subst )
=> ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
=> ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E5: cntxt_r_l_v,E3: expr_r_l_v] :
( ( S @ R )
!= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E5 @ ( rfork_r_l_v @ E3 ) ) ) ) ) )
=> ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
=> ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S2 ) ) ) ) ) ) ).
% substitution.only_fork_introduces_rids'
thf(fact_142_substitution_Orevision__step_Ofork,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,E4: expr_r_l_v,R2: r] :
( ( substitution_r_l_v @ Subst )
=> ( ( ( S @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
=> ( ~ ( member_r @ R2 @ ( rID_G_r_l_v @ S ) )
=> ( revision_step_r_l_v @ Subst @ R @ S
@ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) @ R2
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
@ ( produc1834103605_r_l_v
@ ^ [X2: l] : none_val_r_l_v
@ E4 ) ) ) ) ) ) ) ) ).
% substitution.revision_step.fork
thf(fact_143_local__and__fork__commute,axiom,
! [S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,X: produc1156025366_r_l_v,S_22: r > option1457017436_r_l_v,R2: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R4: r,E4: expr_r_l_v] :
( ( S_2
= ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X ) ) )
=> ( ( S_22
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) @ R4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
@ ( produc1834103605_r_l_v
@ ^ [X2: l] : none_val_r_l_v
@ E4 ) ) ) ) )
=> ( ( ( S_2 @ R2 )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
=> ( ~ ( member_r @ R4 @ ( rID_G_r_l_v @ S_2 ) )
=> ( ( revision_step_r_l_v @ subst @ R @ S_22
@ ( fun_up709272714_r_l_v
@ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) @ R4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
@ ( produc1834103605_r_l_v
@ ^ [X2: l] : none_val_r_l_v
@ E4 ) ) ) )
@ R
@ ( some_P1807977723_r_l_v @ X ) ) )
=> ( ( R != R2 )
=> ( ( R != R4 )
=> ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
( ( eq_states_r_l_v @ S_3 @ S_32 )
& ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
| ( S_2 = S_3 ) )
& ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
| ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% local_and_fork_commute
thf(fact_144_revision__step__relaxed_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r] :
( ( ( S @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
=> ( ( ( S @ R2 )
= none_P277133687_r_l_v )
=> ( revisi1291188644_r_l_v @ subst @ R @ S
@ ^ [X2: r] : none_P277133687_r_l_v ) ) ) ).
% revision_step_relaxed.join\<^sub>\<epsilon>
thf(fact_145_revision__step_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r] :
( ( ( S @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
=> ( ( ( S @ R2 )
= none_P277133687_r_l_v )
=> ( revision_step_r_l_v @ subst @ R @ S
@ ^ [X2: r] : none_P277133687_r_l_v ) ) ) ).
% revision_step.join\<^sub>\<epsilon>
thf(fact_146_substitution_Olocal__and__fork__commute,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,X: produc1156025366_r_l_v,S_22: r > option1457017436_r_l_v,R2: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R4: r,E4: expr_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( ( S_2
= ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X ) ) )
=> ( ( S_22
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) @ R4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
@ ( produc1834103605_r_l_v
@ ^ [X2: l] : none_val_r_l_v
@ E4 ) ) ) ) )
=> ( ( ( S_2 @ R2 )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
=> ( ~ ( member_r @ R4 @ ( rID_G_r_l_v @ S_2 ) )
=> ( ( revision_step_r_l_v @ Subst @ R @ S_22
@ ( fun_up709272714_r_l_v
@ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) @ R4
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
@ ( produc1834103605_r_l_v
@ ^ [X2: l] : none_val_r_l_v
@ E4 ) ) ) )
@ R
@ ( some_P1807977723_r_l_v @ X ) ) )
=> ( ( R != R2 )
=> ( ( R != R4 )
=> ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
( ( eq_states_r_l_v @ S_3 @ S_32 )
& ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
| ( S_2 = S_3 ) )
& ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
| ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% substitution.local_and_fork_commute
thf(fact_147_local__steps__commute,axiom,
! [S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,X: produc1156025366_r_l_v,S_22: r > option1457017436_r_l_v,R2: r,Y: produc1156025366_r_l_v] :
( ( S_2
= ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X ) ) )
=> ( ( S_22
= ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
=> ( ( revision_step_r_l_v @ subst @ R2 @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X ) ) @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X ) ) @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
=> ( ( revision_step_r_l_v @ subst @ R @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) @ R @ ( some_P1807977723_r_l_v @ X ) ) )
=> ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
( ( eq_states_r_l_v @ S_3 @ S_32 )
& ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
| ( S_2 = S_3 ) )
& ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
| ( S_22 = S_32 ) ) ) ) ) ) ) ).
% local_steps_commute
thf(fact_148_transition__relations__equivalent,axiom,
! [S: r > option1457017436_r_l_v,R: r,S2: r > option1457017436_r_l_v] :
( ( reachable_r_l_v @ subst @ S )
=> ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
= ( revisi1291188644_r_l_v @ subst @ R @ S @ S2 ) ) ) ).
% transition_relations_equivalent
thf(fact_149_local__determinism,axiom,
! [R: r,S_1: r > option1457017436_r_l_v,S_2: r > option1457017436_r_l_v,S_22: r > option1457017436_r_l_v] :
( ( revision_step_r_l_v @ subst @ R @ S_1 @ S_2 )
=> ( ( revision_step_r_l_v @ subst @ R @ S_1 @ S_22 )
=> ( eq_states_r_l_v @ S_2 @ S_22 ) ) ) ).
% local_determinism
thf(fact_150_SLC__sym,axiom,
! [R2: r,S_2: r > option1457017436_r_l_v,R: r,S_22: r > option1457017436_r_l_v] :
( ? [S_33: r > option1457017436_r_l_v,S_34: r > option1457017436_r_l_v] :
( ( eq_states_r_l_v @ S_33 @ S_34 )
& ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_33 )
| ( S_2 = S_33 ) )
& ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_34 )
| ( S_22 = S_34 ) ) )
=> ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
( ( eq_states_r_l_v @ S_3 @ S_32 )
& ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_3 )
| ( S_22 = S_3 ) )
& ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_32 )
| ( S_2 = S_32 ) ) ) ) ).
% SLC_sym
thf(fact_151_SLC__commute,axiom,
! [S_35: r > option1457017436_r_l_v,S_36: r > option1457017436_r_l_v,R2: r,S_2: r > option1457017436_r_l_v,R: r,S_22: r > option1457017436_r_l_v] :
( ( S_35 = S_36 )
=> ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_35 )
=> ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_36 )
=> ( ( eq_states_r_l_v @ S_35 @ S_36 )
& ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_35 )
| ( S_2 = S_35 ) )
& ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_36 )
| ( S_22 = S_36 ) ) ) ) ) ) ).
% SLC_commute
thf(fact_152_reachability__closed__under__execution__step,axiom,
! [S: r > option1457017436_r_l_v,R: r,S2: r > option1457017436_r_l_v] :
( ( reachable_r_l_v @ subst @ S )
=> ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
=> ( reachable_r_l_v @ subst @ S2 ) ) ) ).
% reachability_closed_under_execution_step
thf(fact_153_expr_Oinject_I8_J,axiom,
! [X8: expr_r_l_v,Y8: expr_r_l_v] :
( ( ( rjoin_r_l_v @ X8 )
= ( rjoin_r_l_v @ Y8 ) )
= ( X8 = Y8 ) ) ).
% expr.inject(8)
thf(fact_154_SLC__join_092_060_094sub_062_092_060epsilon_062,axiom,
! [S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R4: r,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
( ( ( S_1 @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
=> ( ( S_2
= ( ^ [X2: r] : none_P277133687_r_l_v ) )
=> ( ( ( S_1 @ R4 )
= none_P277133687_r_l_v )
=> ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
=> ( ( R != R2 )
=> ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
( ( eq_states_r_l_v @ S_3 @ S_32 )
& ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
| ( S_2 = S_3 ) )
& ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
| ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% SLC_join\<^sub>\<epsilon>
thf(fact_155_reachable__def,axiom,
! [S: r > option1457017436_r_l_v] :
( ( reachable_r_l_v @ subst @ S )
= ( ? [E6: expr_r_l_v,S3: r > option1457017436_r_l_v] : ( execution_r_l_v @ subst @ E6 @ S3 @ S ) ) ) ).
% reachable_def
thf(fact_156_rjoin_092_060_094sub_062_092_060epsilon_062__deterministic,axiom,
! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,S2: r > option1457017436_r_l_v] :
( ( ( S @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
=> ( ( ( S @ R2 )
= none_P277133687_r_l_v )
=> ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
= ( S2
= ( ^ [X2: r] : none_P277133687_r_l_v ) ) ) ) ) ).
% rjoin\<^sub>\<epsilon>_deterministic
thf(fact_157__092_060alpha_062_092_060beta_062__sym,axiom,
! [S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
( ( eq_states_r_l_v @ S @ S2 )
=> ( eq_states_r_l_v @ S2 @ S ) ) ).
% \<alpha>\<beta>_sym
thf(fact_158__092_060alpha_062_092_060beta_062__refl,axiom,
! [S: r > option1457017436_r_l_v] : ( eq_states_r_l_v @ S @ S ) ).
% \<alpha>\<beta>_refl
thf(fact_159__092_060alpha_062_092_060beta_062__trans,axiom,
! [S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v,S4: r > option1457017436_r_l_v] :
( ( eq_states_r_l_v @ S @ S2 )
=> ( ( eq_states_r_l_v @ S2 @ S4 )
=> ( eq_states_r_l_v @ S @ S4 ) ) ) ).
% \<alpha>\<beta>_trans
thf(fact_160_expr_Odistinct_I13_J,axiom,
! [X1: val_r_l_v,X8: expr_r_l_v] :
( ( vE_r_l_v @ X1 )
!= ( rjoin_r_l_v @ X8 ) ) ).
% expr.distinct(13)
thf(fact_161_expr_Odistinct_I55_J,axiom,
! [X7: expr_r_l_v,X8: expr_r_l_v] :
( ( rfork_r_l_v @ X7 )
!= ( rjoin_r_l_v @ X8 ) ) ).
% expr.distinct(55)
thf(fact_162_substitution_Olocal__determinism,axiom,
! [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] :
( ( substitution_r_l_v @ Subst )
=> ( ( revision_step_r_l_v @ Subst @ R @ S_1 @ S_2 )
=> ( ( revision_step_r_l_v @ Subst @ R @ S_1 @ S_22 )
=> ( eq_states_r_l_v @ S_2 @ S_22 ) ) ) ) ).
% substitution.local_determinism
thf(fact_163_substitution_OSLC__commute,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_35: r > option1457017436_r_l_v,S_36: r > option1457017436_r_l_v,R2: r,S_2: r > option1457017436_r_l_v,R: r,S_22: r > option1457017436_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( ( S_35 = S_36 )
=> ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_35 )
=> ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_36 )
=> ( ( eq_states_r_l_v @ S_35 @ S_36 )
& ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_35 )
| ( S_2 = S_35 ) )
& ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_36 )
| ( S_22 = S_36 ) ) ) ) ) ) ) ).
% substitution.SLC_commute
thf(fact_164_substitution_OSLC__sym,axiom,
! [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] :
( ( substitution_r_l_v @ Subst )
=> ( ? [S_33: r > option1457017436_r_l_v,S_34: r > option1457017436_r_l_v] :
( ( eq_states_r_l_v @ S_33 @ S_34 )
& ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_33 )
| ( S_2 = S_33 ) )
& ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_34 )
| ( S_22 = S_34 ) ) )
=> ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
( ( eq_states_r_l_v @ S_3 @ S_32 )
& ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_3 )
| ( S_22 = S_3 ) )
& ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_32 )
| ( S_2 = S_32 ) ) ) ) ) ).
% substitution.SLC_sym
thf(fact_165_substitution_OSLC__join_092_060_094sub_062_092_060epsilon_062,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R4: r,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( ( ( S_1 @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
=> ( ( S_2
= ( ^ [X2: r] : none_P277133687_r_l_v ) )
=> ( ( ( S_1 @ R4 )
= none_P277133687_r_l_v )
=> ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
=> ( ( R != R2 )
=> ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
( ( eq_states_r_l_v @ S_3 @ S_32 )
& ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
| ( S_2 = S_3 ) )
& ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
| ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% substitution.SLC_join\<^sub>\<epsilon>
thf(fact_166_substitution_Olocal__steps__commute,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,X: produc1156025366_r_l_v,S_22: r > option1457017436_r_l_v,R2: r,Y: produc1156025366_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( ( S_2
= ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X ) ) )
=> ( ( S_22
= ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
=> ( ( revision_step_r_l_v @ Subst @ R2 @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X ) ) @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ X ) ) @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) )
=> ( ( revision_step_r_l_v @ Subst @ R @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Y ) ) @ R @ ( some_P1807977723_r_l_v @ X ) ) )
=> ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
( ( eq_states_r_l_v @ S_3 @ S_32 )
& ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
| ( S_2 = S_3 ) )
& ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
| ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% substitution.local_steps_commute
thf(fact_167_substitution_Orjoin_092_060_094sub_062_092_060epsilon_062__deterministic,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,S2: r > option1457017436_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( ( ( S @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
=> ( ( ( S @ R2 )
= none_P277133687_r_l_v )
=> ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
= ( S2
= ( ^ [X2: r] : none_P277133687_r_l_v ) ) ) ) ) ) ).
% substitution.rjoin\<^sub>\<epsilon>_deterministic
thf(fact_168_substitution_Orevision__step_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r] :
( ( substitution_r_l_v @ Subst )
=> ( ( ( S @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
=> ( ( ( S @ R2 )
= none_P277133687_r_l_v )
=> ( revision_step_r_l_v @ Subst @ R @ S
@ ^ [X2: r] : none_P277133687_r_l_v ) ) ) ) ).
% substitution.revision_step.join\<^sub>\<epsilon>
thf(fact_169_substitution_Orevision__step__relaxed_Ojoin_092_060_094sub_062_092_060epsilon_062,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r] :
( ( substitution_r_l_v @ Subst )
=> ( ( ( S @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
=> ( ( ( S @ R2 )
= none_P277133687_r_l_v )
=> ( revisi1291188644_r_l_v @ Subst @ R @ S
@ ^ [X2: r] : none_P277133687_r_l_v ) ) ) ) ).
% substitution.revision_step_relaxed.join\<^sub>\<epsilon>
thf(fact_170_inductive__invariant__is__execution__invariant,axiom,
! [S: r > option1457017436_r_l_v,P: ( r > option1457017436_r_l_v ) > $o] :
( ( reachable_r_l_v @ subst @ S )
=> ( ( induct1670415253_r_l_v @ subst @ P )
=> ( P @ S ) ) ) ).
% inductive_invariant_is_execution_invariant
thf(fact_171_reachable__imp___092_060S_062_092_060_094sub_062G,axiom,
! [S: r > option1457017436_r_l_v] :
( ( reachable_r_l_v @ subst @ S )
=> ( domain1547879849_r_l_v @ S ) ) ).
% reachable_imp_\<S>\<^sub>G
thf(fact_172_substitution_Otransition__relations__equivalent,axiom,
! [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] :
( ( substitution_r_l_v @ Subst )
=> ( ( reachable_r_l_v @ Subst @ S )
=> ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
= ( revisi1291188644_r_l_v @ Subst @ R @ S @ S2 ) ) ) ) ).
% substitution.transition_relations_equivalent
thf(fact_173_SLC__fork,axiom,
! [S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,E4: expr_r_l_v,S_2: r > option1457017436_r_l_v,Left_forkee: r,R2: r,S_22: r > option1457017436_r_l_v] :
( ( ( S_1 @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
=> ( ( S_2
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ Left_forkee ) ) ) ) ) ) ) @ Left_forkee
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
@ ( produc1834103605_r_l_v
@ ^ [X2: l] : none_val_r_l_v
@ E4 ) ) ) ) )
=> ( ~ ( member_r @ Left_forkee @ ( rID_G_r_l_v @ S_1 ) )
=> ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
=> ( ( R != R2 )
=> ( ( reachable_r_l_v @ subst @ S_1 )
=> ( ~ ( finite_finite_r @ top_top_set_r )
=> ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
( ( eq_states_r_l_v @ S_3 @ S_32 )
& ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
| ( S_2 = S_3 ) )
& ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
| ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% SLC_fork
thf(fact_174_join__and__local__commute,axiom,
! [S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,E: cntxt_r_l_v,R4: r,S_22: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,Sigma3: l > option_val_r_l_v,V: val_r_l_v] :
( ( S_2
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
=> ( ( S_22
= ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Ls ) ) )
=> ( ( R != R2 )
=> ( ( R2 != R4 )
=> ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) @ R2 @ ( some_P1807977723_r_l_v @ Ls ) ) )
=> ( ( ( S_22 @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
=> ( ( ( S_22 @ R4 )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
=> ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
( ( eq_states_r_l_v @ S_3 @ S_32 )
& ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
| ( S_2 = S_3 ) )
& ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
| ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% join_and_local_commute
thf(fact_175_empty__map__finite_I3_J,axiom,
( finite_finite_r
@ ( rID_G_r_l_v
@ ^ [X2: r] : none_P277133687_r_l_v ) ) ).
% empty_map_finite(3)
thf(fact_176_val_Oinject_I1_J,axiom,
! [X1: const,Y1: const] :
( ( ( cV_r_l_v @ X1 )
= ( cV_r_l_v @ Y1 ) )
= ( X1 = Y1 ) ) ).
% val.inject(1)
thf(fact_177_RID_092_060_094sub_062G__finite__invariant,axiom,
! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
=> ( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
=> ( finite_finite_r @ ( rID_G_r_l_v @ S2 ) ) ) ) ).
% RID\<^sub>G_finite_invariant
thf(fact_178_reachable__imp__identifiers__finite_I1_J,axiom,
! [S: r > option1457017436_r_l_v] :
( ( reachable_r_l_v @ subst @ S )
=> ( finite_finite_r @ ( rID_G_r_l_v @ S ) ) ) ).
% reachable_imp_identifiers_finite(1)
thf(fact_179_reachable__imp__identifiers__available_I1_J,axiom,
! [S: r > option1457017436_r_l_v] :
( ( reachable_r_l_v @ subst @ S )
=> ( ~ ( finite_finite_r @ top_top_set_r )
=> ? [R5: r] :
~ ( member_r @ R5 @ ( rID_G_r_l_v @ S ) ) ) ) ).
% reachable_imp_identifiers_available(1)
thf(fact_180_finite__option__UNIV,axiom,
( ( finite1036466630um_r_l @ top_to1855148309um_r_l )
= ( finite65649782um_r_l @ top_to182927813um_r_l ) ) ).
% finite_option_UNIV
thf(fact_181_finite__option__UNIV,axiom,
( ( finite111936338um_l_r @ top_to1150555297um_l_r )
= ( finite1591053314um_l_r @ top_to1405881169um_l_r ) ) ).
% finite_option_UNIV
thf(fact_182_finite__option__UNIV,axiom,
( ( finite1864485196um_l_l @ top_to1066565019um_l_l )
= ( finite1541484284um_l_l @ top_to1010946379um_l_l ) ) ).
% finite_option_UNIV
thf(fact_183_finite__option__UNIV,axiom,
( ( finite555643486_set_r @ top_to555798885_set_r )
= ( finite_finite_set_r @ top_top_set_set_r ) ) ).
% finite_option_UNIV
thf(fact_184_finite__option__UNIV,axiom,
( ( finite160708696_set_l @ top_to471808607_set_l )
= ( finite_finite_set_l @ top_top_set_set_l ) ) ).
% finite_option_UNIV
thf(fact_185_finite__option__UNIV,axiom,
( ( finite16335230tion_r @ top_top_set_option_r )
= ( finite_finite_r @ top_top_set_r ) ) ).
% finite_option_UNIV
thf(fact_186_finite__option__UNIV,axiom,
( ( finite2114249848tion_l @ top_top_set_option_l )
= ( finite_finite_l @ top_top_set_l ) ) ).
% finite_option_UNIV
thf(fact_187_domains__subsume__globally__def,axiom,
( domain1547879849_r_l_v
= ( ^ [S5: r > option1457017436_r_l_v] :
! [R6: r,Ls2: produc1156025366_r_l_v] :
( ( ( S5 @ R6 )
= ( some_P1807977723_r_l_v @ Ls2 ) )
=> ( domain87684397_l_r_v @ Ls2 ) ) ) ) ).
% domains_subsume_globally_def
thf(fact_188_finite__state__imp__restriction__finite_I1_J,axiom,
! [S: r > option1457017436_r_l_v,R: r] :
( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
=> ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ).
% finite_state_imp_restriction_finite(1)
thf(fact_189_revision__step_Ojoin,axiom,
! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v] :
( ( ( S @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
=> ( ( ( S @ R2 )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
=> ( revision_step_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ).
% revision_step.join
thf(fact_190_revision__step__relaxed_Ojoin,axiom,
! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v] :
( ( ( S @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
=> ( ( ( S @ R2 )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
=> ( revisi1291188644_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ).
% revision_step_relaxed.join
thf(fact_191_SLC__join,axiom,
! [S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R4: r,S_2: r > option1457017436_r_l_v,Tau3: l > option_val_r_l_v,Sigma3: l > option_val_r_l_v,V: val_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
( ( ( S_1 @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
=> ( ( S_2
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
=> ( ( ( S_1 @ R4 )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
=> ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
=> ( ( R != R2 )
=> ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
( ( eq_states_r_l_v @ S_3 @ S_32 )
& ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
| ( S_2 = S_3 ) )
& ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
| ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% SLC_join
thf(fact_192_bij___092_060alpha_062,axiom,
bij_betw_r_r @ alpha @ top_top_set_r @ top_top_set_r ).
% bij_\<alpha>
thf(fact_193_rjoin__deterministic,axiom,
! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
( ( ( S @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
=> ( ( ( S @ R2 )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
=> ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
= ( S2
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ).
% rjoin_deterministic
thf(fact_194_substitution_Oexecution_Ocong,axiom,
execution_r_l_v = execution_r_l_v ).
% substitution.execution.cong
thf(fact_195_substitution_Oinductive__invariant_Ocong,axiom,
induct1670415253_r_l_v = induct1670415253_r_l_v ).
% substitution.inductive_invariant.cong
thf(fact_196_val_Odistinct_I5_J,axiom,
! [X1: const,X4: r] :
( ( cV_r_l_v @ X1 )
!= ( rid_r_l_v @ X4 ) ) ).
% val.distinct(5)
thf(fact_197_substitution_Oreachable__imp__identifiers__available_I1_J,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( ( reachable_r_l_v @ Subst @ S )
=> ( ~ ( finite_finite_r @ top_top_set_r )
=> ? [R5: r] :
~ ( member_r @ R5 @ ( rID_G_r_l_v @ S ) ) ) ) ) ).
% substitution.reachable_imp_identifiers_available(1)
thf(fact_198_substitution_Ostrong__local__confluence,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,R: r,S_1: r > option1457017436_r_l_v,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( ( revision_step_r_l_v @ Subst @ R @ S_1 @ S_2 )
=> ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
=> ( ( reachable_r_l_v @ Subst @ S_1 )
=> ( ~ ( finite_finite_l @ top_top_set_l )
=> ( ~ ( finite_finite_r @ top_top_set_r )
=> ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
( ( eq_states_r_l_v @ S_3 @ S_32 )
& ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
| ( S_2 = S_3 ) )
& ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
| ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% substitution.strong_local_confluence
thf(fact_199_substitution_ORID_092_060_094sub_062G__finite__invariant,axiom,
! [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] :
( ( substitution_r_l_v @ Subst )
=> ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
=> ( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
=> ( finite_finite_r @ ( rID_G_r_l_v @ S2 ) ) ) ) ) ).
% substitution.RID\<^sub>G_finite_invariant
thf(fact_200_substitution_Oreachable__imp__identifiers__finite_I1_J,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( ( reachable_r_l_v @ Subst @ S )
=> ( finite_finite_r @ ( rID_G_r_l_v @ S ) ) ) ) ).
% substitution.reachable_imp_identifiers_finite(1)
thf(fact_201_substitution_Oreachable__imp___092_060S_062_092_060_094sub_062G,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( ( reachable_r_l_v @ Subst @ S )
=> ( domain1547879849_r_l_v @ S ) ) ) ).
% substitution.reachable_imp_\<S>\<^sub>G
thf(fact_202_substitution_Oinductive__invariant__is__execution__invariant,axiom,
! [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] :
( ( substitution_r_l_v @ Subst )
=> ( ( reachable_r_l_v @ Subst @ S )
=> ( ( induct1670415253_r_l_v @ Subst @ P )
=> ( P @ S ) ) ) ) ).
% substitution.inductive_invariant_is_execution_invariant
thf(fact_203_substitution_Oempty__map__finite_I3_J,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( finite_finite_r
@ ( rID_G_r_l_v
@ ^ [X2: r] : none_P277133687_r_l_v ) ) ) ).
% substitution.empty_map_finite(3)
thf(fact_204_substitution_Oreachable__def,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( ( reachable_r_l_v @ Subst @ S )
= ( ? [E6: expr_r_l_v,S3: r > option1457017436_r_l_v] : ( execution_r_l_v @ Subst @ E6 @ S3 @ S ) ) ) ) ).
% substitution.reachable_def
thf(fact_205_substitution_Ofinite__state__imp__restriction__finite_I1_J,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r] :
( ( substitution_r_l_v @ Subst )
=> ( ( finite_finite_r @ ( rID_G_r_l_v @ S ) )
=> ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ) ).
% substitution.finite_state_imp_restriction_finite(1)
thf(fact_206_substitution_Oreachable_Ocong,axiom,
reachable_r_l_v = reachable_r_l_v ).
% substitution.reachable.cong
thf(fact_207_substitution_Orevision__step_Ojoin,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( ( ( S @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
=> ( ( ( S @ R2 )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
=> ( revision_step_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ).
% substitution.revision_step.join
thf(fact_208_substitution_Orjoin__deterministic,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( ( ( S @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
=> ( ( ( S @ R2 )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
=> ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
= ( S2
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ) ).
% substitution.rjoin_deterministic
thf(fact_209_substitution_Orevision__step__relaxed_Ojoin,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R2: r,Sigma3: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,V: val_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( ( ( S @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R2 ) ) ) ) ) ) ) )
=> ( ( ( S @ R2 )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
=> ( revisi1291188644_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R2 @ none_P277133687_r_l_v ) ) ) ) ) ).
% substitution.revision_step_relaxed.join
thf(fact_210_substitution_Ojoin__and__local__commute,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_2: r > option1457017436_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,Tau3: l > option_val_r_l_v,E: cntxt_r_l_v,R4: r,S_22: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,Sigma3: l > option_val_r_l_v,V: val_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( ( S_2
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
=> ( ( S_22
= ( fun_up709272714_r_l_v @ S_1 @ R2 @ ( some_P1807977723_r_l_v @ Ls ) ) )
=> ( ( R != R2 )
=> ( ( R2 != R4 )
=> ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) @ R2 @ ( some_P1807977723_r_l_v @ Ls ) ) )
=> ( ( ( S_22 @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
=> ( ( ( S_22 @ R4 )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
=> ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
( ( eq_states_r_l_v @ S_3 @ S_32 )
& ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
| ( S_2 = S_3 ) )
& ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
| ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% substitution.join_and_local_commute
thf(fact_211_substitution_OSLC__join,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,R4: r,S_2: r > option1457017436_r_l_v,Tau3: l > option_val_r_l_v,Sigma3: l > option_val_r_l_v,V: val_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( ( ( S_1 @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rjoin_r_l_v @ ( vE_r_l_v @ ( rid_r_l_v @ R4 ) ) ) ) ) ) ) )
=> ( ( S_2
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( combine_l_val_r_l_v @ Tau2 @ Tau3 ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( cV_r_l_v @ unit ) ) ) ) ) ) ) @ R4 @ none_P277133687_r_l_v ) )
=> ( ( ( S_1 @ R4 )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma3 @ ( produc1834103605_r_l_v @ Tau3 @ ( vE_r_l_v @ V ) ) ) ) )
=> ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
=> ( ( R != R2 )
=> ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
( ( eq_states_r_l_v @ S_3 @ S_32 )
& ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
| ( S_2 = S_3 ) )
& ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
| ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ).
% substitution.SLC_join
thf(fact_212_substitution_OSLC__fork,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,E4: expr_r_l_v,S_2: r > option1457017436_r_l_v,Left_forkee: r,R2: r,S_22: r > option1457017436_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( ( ( S_1 @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( rfork_r_l_v @ E4 ) ) ) ) ) )
=> ( ( S_2
= ( fun_up709272714_r_l_v @ ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( rid_r_l_v @ Left_forkee ) ) ) ) ) ) ) @ Left_forkee
@ ( some_P1807977723_r_l_v
@ ( produc297528454_r_l_v @ ( combine_l_val_r_l_v @ Sigma2 @ Tau2 )
@ ( produc1834103605_r_l_v
@ ^ [X2: l] : none_val_r_l_v
@ E4 ) ) ) ) )
=> ( ~ ( member_r @ Left_forkee @ ( rID_G_r_l_v @ S_1 ) )
=> ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
=> ( ( R != R2 )
=> ( ( reachable_r_l_v @ Subst @ S_1 )
=> ( ~ ( finite_finite_r @ top_top_set_r )
=> ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
( ( eq_states_r_l_v @ S_3 @ S_32 )
& ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
| ( S_2 = S_3 ) )
& ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
| ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% substitution.SLC_fork
thf(fact_213_substitution_Oreachability__closed__under__execution__step,axiom,
! [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] :
( ( substitution_r_l_v @ Subst )
=> ( ( reachable_r_l_v @ Subst @ S )
=> ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
=> ( reachable_r_l_v @ Subst @ S2 ) ) ) ) ).
% substitution.reachability_closed_under_execution_step
thf(fact_214_nice__ind__inv__is__inductive__invariant,axiom,
( induct1670415253_r_l_v @ subst
@ ^ [S5: r > option1457017436_r_l_v] :
( ( domain1547879849_r_l_v @ S5 )
& ( subsum680764357_r_l_v @ S5 ) ) ) ).
% nice_ind_inv_is_inductive_invariant
thf(fact_215_step__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I2_J,axiom,
! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
=> ( ( domain1547879849_r_l_v @ S )
=> ( ( subsum680764357_r_l_v @ S )
=> ( subsum680764357_r_l_v @ S2 ) ) ) ) ).
% step_preserves_\<S>\<^sub>G_and_\<A>\<^sub>G(2)
thf(fact_216_step__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I1_J,axiom,
! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
=> ( ( domain1547879849_r_l_v @ S )
=> ( ( subsum680764357_r_l_v @ S )
=> ( domain1547879849_r_l_v @ S2 ) ) ) ) ).
% step_preserves_\<S>\<^sub>G_and_\<A>\<^sub>G(1)
thf(fact_217_finite__Collect__not,axiom,
! [P: sum_sum_r_l > $o] :
( ( finite65649782um_r_l @ ( collect_Sum_sum_r_l @ P ) )
=> ( ( finite65649782um_r_l
@ ( collect_Sum_sum_r_l
@ ^ [X2: sum_sum_r_l] :
~ ( P @ X2 ) ) )
= ( finite65649782um_r_l @ top_to182927813um_r_l ) ) ) ).
% finite_Collect_not
thf(fact_218_finite__Collect__not,axiom,
! [P: sum_sum_l_r > $o] :
( ( finite1591053314um_l_r @ ( collect_Sum_sum_l_r @ P ) )
=> ( ( finite1591053314um_l_r
@ ( collect_Sum_sum_l_r
@ ^ [X2: sum_sum_l_r] :
~ ( P @ X2 ) ) )
= ( finite1591053314um_l_r @ top_to1405881169um_l_r ) ) ) ).
% finite_Collect_not
thf(fact_219_finite__Collect__not,axiom,
! [P: sum_sum_l_l > $o] :
( ( finite1541484284um_l_l @ ( collect_Sum_sum_l_l @ P ) )
=> ( ( finite1541484284um_l_l
@ ( collect_Sum_sum_l_l
@ ^ [X2: sum_sum_l_l] :
~ ( P @ X2 ) ) )
= ( finite1541484284um_l_l @ top_to1010946379um_l_l ) ) ) ).
% finite_Collect_not
thf(fact_220_finite__Collect__not,axiom,
! [P: set_r > $o] :
( ( finite_finite_set_r @ ( collect_set_r @ P ) )
=> ( ( finite_finite_set_r
@ ( collect_set_r
@ ^ [X2: set_r] :
~ ( P @ X2 ) ) )
= ( finite_finite_set_r @ top_top_set_set_r ) ) ) ).
% finite_Collect_not
thf(fact_221_finite__Collect__not,axiom,
! [P: set_l > $o] :
( ( finite_finite_set_l @ ( collect_set_l @ P ) )
=> ( ( finite_finite_set_l
@ ( collect_set_l
@ ^ [X2: set_l] :
~ ( P @ X2 ) ) )
= ( finite_finite_set_l @ top_top_set_set_l ) ) ) ).
% finite_Collect_not
thf(fact_222_finite__Collect__not,axiom,
! [P: r > $o] :
( ( finite_finite_r @ ( collect_r @ P ) )
=> ( ( finite_finite_r
@ ( collect_r
@ ^ [X2: r] :
~ ( P @ X2 ) ) )
= ( finite_finite_r @ top_top_set_r ) ) ) ).
% finite_Collect_not
thf(fact_223_finite__Collect__not,axiom,
! [P: l > $o] :
( ( finite_finite_l @ ( collect_l @ P ) )
=> ( ( finite_finite_l
@ ( collect_l
@ ^ [X2: l] :
~ ( P @ X2 ) ) )
= ( finite_finite_l @ top_top_set_l ) ) ) ).
% finite_Collect_not
thf(fact_224_in__renamed__in__unlabelled__global_I1_J,axiom,
! [Alpha2: r > r,Beta2: l > l,R: r,S: r > option1457017436_r_l_v] :
( ( bij_betw_r_r @ Alpha2 @ top_top_set_r @ top_top_set_r )
=> ( ( bij_betw_l_l @ Beta2 @ top_top_set_l @ top_top_set_l )
=> ( ( member_r @ ( Alpha2 @ R ) @ ( rID_G_r_l_v @ ( r_G_r_l_v @ Alpha2 @ Beta2 @ S ) ) )
= ( member_r @ R @ ( rID_G_r_l_v @ S ) ) ) ) ) ).
% in_renamed_in_unlabelled_global(1)
thf(fact_225_finite__Collect__conjI,axiom,
! [P: sum_sum_r_l > $o,Q: sum_sum_r_l > $o] :
( ( ( finite65649782um_r_l @ ( collect_Sum_sum_r_l @ P ) )
| ( finite65649782um_r_l @ ( collect_Sum_sum_r_l @ Q ) ) )
=> ( finite65649782um_r_l
@ ( collect_Sum_sum_r_l
@ ^ [X2: sum_sum_r_l] :
( ( P @ X2 )
& ( Q @ X2 ) ) ) ) ) ).
% finite_Collect_conjI
thf(fact_226_finite__Collect__conjI,axiom,
! [P: sum_sum_l_r > $o,Q: sum_sum_l_r > $o] :
( ( ( finite1591053314um_l_r @ ( collect_Sum_sum_l_r @ P ) )
| ( finite1591053314um_l_r @ ( collect_Sum_sum_l_r @ Q ) ) )
=> ( finite1591053314um_l_r
@ ( collect_Sum_sum_l_r
@ ^ [X2: sum_sum_l_r] :
( ( P @ X2 )
& ( Q @ X2 ) ) ) ) ) ).
% finite_Collect_conjI
thf(fact_227_finite__Collect__conjI,axiom,
! [P: sum_sum_l_l > $o,Q: sum_sum_l_l > $o] :
( ( ( finite1541484284um_l_l @ ( collect_Sum_sum_l_l @ P ) )
| ( finite1541484284um_l_l @ ( collect_Sum_sum_l_l @ Q ) ) )
=> ( finite1541484284um_l_l
@ ( collect_Sum_sum_l_l
@ ^ [X2: sum_sum_l_l] :
( ( P @ X2 )
& ( Q @ X2 ) ) ) ) ) ).
% finite_Collect_conjI
thf(fact_228_finite__Collect__conjI,axiom,
! [P: set_r > $o,Q: set_r > $o] :
( ( ( finite_finite_set_r @ ( collect_set_r @ P ) )
| ( finite_finite_set_r @ ( collect_set_r @ Q ) ) )
=> ( finite_finite_set_r
@ ( collect_set_r
@ ^ [X2: set_r] :
( ( P @ X2 )
& ( Q @ X2 ) ) ) ) ) ).
% finite_Collect_conjI
thf(fact_229_finite__Collect__conjI,axiom,
! [P: set_l > $o,Q: set_l > $o] :
( ( ( finite_finite_set_l @ ( collect_set_l @ P ) )
| ( finite_finite_set_l @ ( collect_set_l @ Q ) ) )
=> ( finite_finite_set_l
@ ( collect_set_l
@ ^ [X2: set_l] :
( ( P @ X2 )
& ( Q @ X2 ) ) ) ) ) ).
% finite_Collect_conjI
thf(fact_230_finite__Collect__conjI,axiom,
! [P: r > $o,Q: r > $o] :
( ( ( finite_finite_r @ ( collect_r @ P ) )
| ( finite_finite_r @ ( collect_r @ Q ) ) )
=> ( finite_finite_r
@ ( collect_r
@ ^ [X2: r] :
( ( P @ X2 )
& ( Q @ X2 ) ) ) ) ) ).
% finite_Collect_conjI
thf(fact_231_finite__Collect__conjI,axiom,
! [P: l > $o,Q: l > $o] :
( ( ( finite_finite_l @ ( collect_l @ P ) )
| ( finite_finite_l @ ( collect_l @ Q ) ) )
=> ( finite_finite_l
@ ( collect_l
@ ^ [X2: l] :
( ( P @ X2 )
& ( Q @ X2 ) ) ) ) ) ).
% finite_Collect_conjI
thf(fact_232_finite__Collect__disjI,axiom,
! [P: set_r > $o,Q: set_r > $o] :
( ( finite_finite_set_r
@ ( collect_set_r
@ ^ [X2: set_r] :
( ( P @ X2 )
| ( Q @ X2 ) ) ) )
= ( ( finite_finite_set_r @ ( collect_set_r @ P ) )
& ( finite_finite_set_r @ ( collect_set_r @ Q ) ) ) ) ).
% finite_Collect_disjI
thf(fact_233_finite__Collect__disjI,axiom,
! [P: set_l > $o,Q: set_l > $o] :
( ( finite_finite_set_l
@ ( collect_set_l
@ ^ [X2: set_l] :
( ( P @ X2 )
| ( Q @ X2 ) ) ) )
= ( ( finite_finite_set_l @ ( collect_set_l @ P ) )
& ( finite_finite_set_l @ ( collect_set_l @ Q ) ) ) ) ).
% finite_Collect_disjI
thf(fact_234_finite__Collect__disjI,axiom,
! [P: r > $o,Q: r > $o] :
( ( finite_finite_r
@ ( collect_r
@ ^ [X2: r] :
( ( P @ X2 )
| ( Q @ X2 ) ) ) )
= ( ( finite_finite_r @ ( collect_r @ P ) )
& ( finite_finite_r @ ( collect_r @ Q ) ) ) ) ).
% finite_Collect_disjI
thf(fact_235_finite__Collect__disjI,axiom,
! [P: l > $o,Q: l > $o] :
( ( finite_finite_l
@ ( collect_l
@ ^ [X2: l] :
( ( P @ X2 )
| ( Q @ X2 ) ) ) )
= ( ( finite_finite_l @ ( collect_l @ P ) )
& ( finite_finite_l @ ( collect_l @ Q ) ) ) ) ).
% finite_Collect_disjI
thf(fact_236_strong__local__confluence,axiom,
! [R: r,S_1: r > option1457017436_r_l_v,S_2: r > option1457017436_r_l_v,R2: r,S_22: r > option1457017436_r_l_v] :
( ( revision_step_r_l_v @ subst @ R @ S_1 @ S_2 )
=> ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
=> ( ( reachable_r_l_v @ subst @ S_1 )
=> ( ~ ( finite_finite_l @ top_top_set_l )
=> ( ~ ( finite_finite_r @ top_top_set_r )
=> ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
( ( eq_states_r_l_v @ S_3 @ S_32 )
& ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
| ( S_2 = S_3 ) )
& ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
| ( S_22 = S_32 ) ) ) ) ) ) ) ) ).
% strong_local_confluence
thf(fact_237_finite__Plus__UNIV__iff,axiom,
( ( finite115218812um_r_r @ top_to577862603um_r_r )
= ( ( finite_finite_r @ top_top_set_r )
& ( finite_finite_r @ top_top_set_r ) ) ) ).
% finite_Plus_UNIV_iff
thf(fact_238_finite__Plus__UNIV__iff,axiom,
( ( finite65649782um_r_l @ top_to182927813um_r_l )
= ( ( finite_finite_r @ top_top_set_r )
& ( finite_finite_l @ top_top_set_l ) ) ) ).
% finite_Plus_UNIV_iff
thf(fact_239_finite__Plus__UNIV__iff,axiom,
( ( finite1591053314um_l_r @ top_to1405881169um_l_r )
= ( ( finite_finite_l @ top_top_set_l )
& ( finite_finite_r @ top_top_set_r ) ) ) ).
% finite_Plus_UNIV_iff
thf(fact_240_finite__Plus__UNIV__iff,axiom,
( ( finite1541484284um_l_l @ top_to1010946379um_l_l )
= ( ( finite_finite_l @ top_top_set_l )
& ( finite_finite_l @ top_top_set_l ) ) ) ).
% finite_Plus_UNIV_iff
thf(fact_241_eq__statesI,axiom,
! [Alpha2: r > r,Beta2: l > l,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
( ( ( r_G_r_l_v @ Alpha2 @ Beta2 @ S )
= S2 )
=> ( ( bij_betw_r_r @ Alpha2 @ top_top_set_r @ top_top_set_r )
=> ( ( bij_betw_l_l @ Beta2 @ top_top_set_l @ top_top_set_l )
=> ( eq_states_r_l_v @ S @ S2 ) ) ) ) ).
% eq_statesI
thf(fact_242_renaming__distr__global_I2_J,axiom,
! [Alpha2: r > r,Beta2: l > l,S: r > option1457017436_r_l_v,R: r] :
( ( bij_betw_r_r @ Alpha2 @ top_top_set_r @ top_top_set_r )
=> ( ( r_G_r_l_v @ Alpha2 @ Beta2 @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) )
= ( fun_up709272714_r_l_v @ ( r_G_r_l_v @ Alpha2 @ Beta2 @ S ) @ ( Alpha2 @ R ) @ none_P277133687_r_l_v ) ) ) ).
% renaming_distr_global(2)
thf(fact_243_domains__subsume__globallyI,axiom,
! [S: r > option1457017436_r_l_v] :
( ! [R5: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E3: expr_r_l_v] :
( ( ( S @ R5 )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) ) )
=> ( domain87684397_l_r_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) ) )
=> ( domain1547879849_r_l_v @ S ) ) ).
% domains_subsume_globallyI
thf(fact_244_bij___092_060beta_062,axiom,
bij_betw_l_l @ beta @ top_top_set_l @ top_top_set_l ).
% bij_\<beta>
thf(fact_245_bij__betw__finite,axiom,
! [F: r > r,A5: set_r,B5: set_r] :
( ( bij_betw_r_r @ F @ A5 @ B5 )
=> ( ( finite_finite_r @ A5 )
= ( finite_finite_r @ B5 ) ) ) ).
% bij_betw_finite
thf(fact_246_bij__betw__finite,axiom,
! [F: r > l,A5: set_r,B5: set_l] :
( ( bij_betw_r_l @ F @ A5 @ B5 )
=> ( ( finite_finite_r @ A5 )
= ( finite_finite_l @ B5 ) ) ) ).
% bij_betw_finite
thf(fact_247_bij__betw__finite,axiom,
! [F: l > r,A5: set_l,B5: set_r] :
( ( bij_betw_l_r @ F @ A5 @ B5 )
=> ( ( finite_finite_l @ A5 )
= ( finite_finite_r @ B5 ) ) ) ).
% bij_betw_finite
thf(fact_248_bij__betw__finite,axiom,
! [F: l > l,A5: set_l,B5: set_l] :
( ( bij_betw_l_l @ F @ A5 @ B5 )
=> ( ( finite_finite_l @ A5 )
= ( finite_finite_l @ B5 ) ) ) ).
% bij_betw_finite
thf(fact_249_bij__pointE,axiom,
! [F: r > r,Y: r] :
( ( bij_betw_r_r @ F @ top_top_set_r @ top_top_set_r )
=> ~ ! [X3: r] :
( ( Y
= ( F @ X3 ) )
=> ~ ! [X9: r] :
( ( Y
= ( F @ X9 ) )
=> ( X9 = X3 ) ) ) ) ).
% bij_pointE
thf(fact_250_bij__pointE,axiom,
! [F: r > l,Y: l] :
( ( bij_betw_r_l @ F @ top_top_set_r @ top_top_set_l )
=> ~ ! [X3: r] :
( ( Y
= ( F @ X3 ) )
=> ~ ! [X9: r] :
( ( Y
= ( F @ X9 ) )
=> ( X9 = X3 ) ) ) ) ).
% bij_pointE
thf(fact_251_bij__pointE,axiom,
! [F: l > r,Y: r] :
( ( bij_betw_l_r @ F @ top_top_set_l @ top_top_set_r )
=> ~ ! [X3: l] :
( ( Y
= ( F @ X3 ) )
=> ~ ! [X9: l] :
( ( Y
= ( F @ X9 ) )
=> ( X9 = X3 ) ) ) ) ).
% bij_pointE
thf(fact_252_bij__pointE,axiom,
! [F: l > l,Y: l] :
( ( bij_betw_l_l @ F @ top_top_set_l @ top_top_set_l )
=> ~ ! [X3: l] :
( ( Y
= ( F @ X3 ) )
=> ~ ! [X9: l] :
( ( Y
= ( F @ X9 ) )
=> ( X9 = X3 ) ) ) ) ).
% bij_pointE
thf(fact_253_bij__betwE,axiom,
! [F: r > r,A5: set_r,B5: set_r] :
( ( bij_betw_r_r @ F @ A5 @ B5 )
=> ! [X10: r] :
( ( member_r @ X10 @ A5 )
=> ( member_r @ ( F @ X10 ) @ B5 ) ) ) ).
% bij_betwE
thf(fact_254_bij__betwE,axiom,
! [F: l > l,A5: set_l,B5: set_l] :
( ( bij_betw_l_l @ F @ A5 @ B5 )
=> ! [X10: l] :
( ( member_l @ X10 @ A5 )
=> ( member_l @ ( F @ X10 ) @ B5 ) ) ) ).
% bij_betwE
thf(fact_255_bij__betw__inv,axiom,
! [F: r > r,A5: set_r,B5: set_r] :
( ( bij_betw_r_r @ F @ A5 @ B5 )
=> ? [G3: r > r] : ( bij_betw_r_r @ G3 @ B5 @ A5 ) ) ).
% bij_betw_inv
thf(fact_256_bij__betw__inv,axiom,
! [F: l > l,A5: set_l,B5: set_l] :
( ( bij_betw_l_l @ F @ A5 @ B5 )
=> ? [G3: l > l] : ( bij_betw_l_l @ G3 @ B5 @ A5 ) ) ).
% bij_betw_inv
thf(fact_257_bij__betw__cong,axiom,
! [A5: set_r,F: r > r,G: r > r,A6: set_r] :
( ! [A3: r] :
( ( member_r @ A3 @ A5 )
=> ( ( F @ A3 )
= ( G @ A3 ) ) )
=> ( ( bij_betw_r_r @ F @ A5 @ A6 )
= ( bij_betw_r_r @ G @ A5 @ A6 ) ) ) ).
% bij_betw_cong
thf(fact_258_bij__betw__cong,axiom,
! [A5: set_l,F: l > l,G: l > l,A6: set_l] :
( ! [A3: l] :
( ( member_l @ A3 @ A5 )
=> ( ( F @ A3 )
= ( G @ A3 ) ) )
=> ( ( bij_betw_l_l @ F @ A5 @ A6 )
= ( bij_betw_l_l @ G @ A5 @ A6 ) ) ) ).
% bij_betw_cong
thf(fact_259_bij__betw__apply,axiom,
! [F: r > l,A5: set_r,B5: set_l,A: r] :
( ( bij_betw_r_l @ F @ A5 @ B5 )
=> ( ( member_r @ A @ A5 )
=> ( member_l @ ( F @ A ) @ B5 ) ) ) ).
% bij_betw_apply
thf(fact_260_bij__betw__apply,axiom,
! [F: l > r,A5: set_l,B5: set_r,A: l] :
( ( bij_betw_l_r @ F @ A5 @ B5 )
=> ( ( member_l @ A @ A5 )
=> ( member_r @ ( F @ A ) @ B5 ) ) ) ).
% bij_betw_apply
thf(fact_261_bij__betw__apply,axiom,
! [F: r > r,A5: set_r,B5: set_r,A: r] :
( ( bij_betw_r_r @ F @ A5 @ B5 )
=> ( ( member_r @ A @ A5 )
=> ( member_r @ ( F @ A ) @ B5 ) ) ) ).
% bij_betw_apply
thf(fact_262_bij__betw__apply,axiom,
! [F: l > l,A5: set_l,B5: set_l,A: l] :
( ( bij_betw_l_l @ F @ A5 @ B5 )
=> ( ( member_l @ A @ A5 )
=> ( member_l @ ( F @ A ) @ B5 ) ) ) ).
% bij_betw_apply
thf(fact_263_bij__betw__iff__bijections,axiom,
( bij_betw_l_r
= ( ^ [F2: l > r,A7: set_l,B6: set_r] :
? [G2: r > l] :
( ! [X2: l] :
( ( member_l @ X2 @ A7 )
=> ( ( member_r @ ( F2 @ X2 ) @ B6 )
& ( ( G2 @ ( F2 @ X2 ) )
= X2 ) ) )
& ! [X2: r] :
( ( member_r @ X2 @ B6 )
=> ( ( member_l @ ( G2 @ X2 ) @ A7 )
& ( ( F2 @ ( G2 @ X2 ) )
= X2 ) ) ) ) ) ) ).
% bij_betw_iff_bijections
thf(fact_264_bij__betw__iff__bijections,axiom,
( bij_betw_r_l
= ( ^ [F2: r > l,A7: set_r,B6: set_l] :
? [G2: l > r] :
( ! [X2: r] :
( ( member_r @ X2 @ A7 )
=> ( ( member_l @ ( F2 @ X2 ) @ B6 )
& ( ( G2 @ ( F2 @ X2 ) )
= X2 ) ) )
& ! [X2: l] :
( ( member_l @ X2 @ B6 )
=> ( ( member_r @ ( G2 @ X2 ) @ A7 )
& ( ( F2 @ ( G2 @ X2 ) )
= X2 ) ) ) ) ) ) ).
% bij_betw_iff_bijections
thf(fact_265_bij__betw__iff__bijections,axiom,
( bij_betw_r_r
= ( ^ [F2: r > r,A7: set_r,B6: set_r] :
? [G2: r > r] :
( ! [X2: r] :
( ( member_r @ X2 @ A7 )
=> ( ( member_r @ ( F2 @ X2 ) @ B6 )
& ( ( G2 @ ( F2 @ X2 ) )
= X2 ) ) )
& ! [X2: r] :
( ( member_r @ X2 @ B6 )
=> ( ( member_r @ ( G2 @ X2 ) @ A7 )
& ( ( F2 @ ( G2 @ X2 ) )
= X2 ) ) ) ) ) ) ).
% bij_betw_iff_bijections
thf(fact_266_bij__betw__iff__bijections,axiom,
( bij_betw_l_l
= ( ^ [F2: l > l,A7: set_l,B6: set_l] :
? [G2: l > l] :
( ! [X2: l] :
( ( member_l @ X2 @ A7 )
=> ( ( member_l @ ( F2 @ X2 ) @ B6 )
& ( ( G2 @ ( F2 @ X2 ) )
= X2 ) ) )
& ! [X2: l] :
( ( member_l @ X2 @ B6 )
=> ( ( member_l @ ( G2 @ X2 ) @ A7 )
& ( ( F2 @ ( G2 @ X2 ) )
= X2 ) ) ) ) ) ) ).
% bij_betw_iff_bijections
thf(fact_267_eq__statesE,axiom,
! [S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
( ( eq_states_r_l_v @ S @ S2 )
=> ~ ! [Alpha: r > r,Beta: l > l] :
( ( ( r_G_r_l_v @ Alpha @ Beta @ S )
= S2 )
=> ( ( bij_betw_r_r @ Alpha @ top_top_set_r @ top_top_set_r )
=> ~ ( bij_betw_l_l @ Beta @ top_top_set_l @ top_top_set_l ) ) ) ) ).
% eq_statesE
thf(fact_268_eq__states__def,axiom,
( eq_states_r_l_v
= ( ^ [S5: r > option1457017436_r_l_v,S3: r > option1457017436_r_l_v] :
? [Alpha3: r > r,Beta3: l > l] :
( ( bij_betw_r_r @ Alpha3 @ top_top_set_r @ top_top_set_r )
& ( bij_betw_l_l @ Beta3 @ top_top_set_l @ top_top_set_l )
& ( ( r_G_r_l_v @ Alpha3 @ Beta3 @ S5 )
= S3 ) ) ) ) ).
% eq_states_def
thf(fact_269_substitution_Oin__renamed__in__unlabelled__global_I1_J,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,Alpha2: r > r,Beta2: l > l,R: r,S: r > option1457017436_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( ( bij_betw_r_r @ Alpha2 @ top_top_set_r @ top_top_set_r )
=> ( ( bij_betw_l_l @ Beta2 @ top_top_set_l @ top_top_set_l )
=> ( ( member_r @ ( Alpha2 @ R ) @ ( rID_G_r_l_v @ ( r_G_r_l_v @ Alpha2 @ Beta2 @ S ) ) )
= ( member_r @ R @ ( rID_G_r_l_v @ S ) ) ) ) ) ) ).
% substitution.in_renamed_in_unlabelled_global(1)
thf(fact_270_not__finite__existsD,axiom,
! [P: r > $o] :
( ~ ( finite_finite_r @ ( collect_r @ P ) )
=> ? [X_1: r] : ( P @ X_1 ) ) ).
% not_finite_existsD
thf(fact_271_not__finite__existsD,axiom,
! [P: l > $o] :
( ~ ( finite_finite_l @ ( collect_l @ P ) )
=> ? [X_1: l] : ( P @ X_1 ) ) ).
% not_finite_existsD
thf(fact_272_pigeonhole__infinite__rel,axiom,
! [A5: set_r,B5: set_r,R7: r > r > $o] :
( ~ ( finite_finite_r @ A5 )
=> ( ( finite_finite_r @ B5 )
=> ( ! [X3: r] :
( ( member_r @ X3 @ A5 )
=> ? [Xa2: r] :
( ( member_r @ Xa2 @ B5 )
& ( R7 @ X3 @ Xa2 ) ) )
=> ? [X3: r] :
( ( member_r @ X3 @ B5 )
& ~ ( finite_finite_r
@ ( collect_r
@ ^ [A4: r] :
( ( member_r @ A4 @ A5 )
& ( R7 @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% pigeonhole_infinite_rel
thf(fact_273_pigeonhole__infinite__rel,axiom,
! [A5: set_r,B5: set_l,R7: r > l > $o] :
( ~ ( finite_finite_r @ A5 )
=> ( ( finite_finite_l @ B5 )
=> ( ! [X3: r] :
( ( member_r @ X3 @ A5 )
=> ? [Xa2: l] :
( ( member_l @ Xa2 @ B5 )
& ( R7 @ X3 @ Xa2 ) ) )
=> ? [X3: l] :
( ( member_l @ X3 @ B5 )
& ~ ( finite_finite_r
@ ( collect_r
@ ^ [A4: r] :
( ( member_r @ A4 @ A5 )
& ( R7 @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% pigeonhole_infinite_rel
thf(fact_274_pigeonhole__infinite__rel,axiom,
! [A5: set_l,B5: set_r,R7: l > r > $o] :
( ~ ( finite_finite_l @ A5 )
=> ( ( finite_finite_r @ B5 )
=> ( ! [X3: l] :
( ( member_l @ X3 @ A5 )
=> ? [Xa2: r] :
( ( member_r @ Xa2 @ B5 )
& ( R7 @ X3 @ Xa2 ) ) )
=> ? [X3: r] :
( ( member_r @ X3 @ B5 )
& ~ ( finite_finite_l
@ ( collect_l
@ ^ [A4: l] :
( ( member_l @ A4 @ A5 )
& ( R7 @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% pigeonhole_infinite_rel
thf(fact_275_pigeonhole__infinite__rel,axiom,
! [A5: set_l,B5: set_l,R7: l > l > $o] :
( ~ ( finite_finite_l @ A5 )
=> ( ( finite_finite_l @ B5 )
=> ( ! [X3: l] :
( ( member_l @ X3 @ A5 )
=> ? [Xa2: l] :
( ( member_l @ Xa2 @ B5 )
& ( R7 @ X3 @ Xa2 ) ) )
=> ? [X3: l] :
( ( member_l @ X3 @ B5 )
& ~ ( finite_finite_l
@ ( collect_l
@ ^ [A4: l] :
( ( member_l @ A4 @ A5 )
& ( R7 @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% pigeonhole_infinite_rel
thf(fact_276_finite__Prod__UNIV,axiom,
( ( finite_finite_r @ top_top_set_r )
=> ( ( finite_finite_r @ top_top_set_r )
=> ( finite1507191824od_r_r @ top_to2034696215od_r_r ) ) ) ).
% finite_Prod_UNIV
thf(fact_277_finite__Prod__UNIV,axiom,
( ( finite_finite_r @ top_top_set_r )
=> ( ( finite_finite_l @ top_top_set_l )
=> ( finite1457622794od_r_l @ top_to1639761425od_r_l ) ) ) ).
% finite_Prod_UNIV
thf(fact_278_finite__Prod__UNIV,axiom,
( ( finite_finite_l @ top_top_set_l )
=> ( ( finite_finite_r @ top_top_set_r )
=> ( finite835542678od_l_r @ top_to715231133od_l_r ) ) ) ).
% finite_Prod_UNIV
thf(fact_279_finite__Prod__UNIV,axiom,
( ( finite_finite_l @ top_top_set_l )
=> ( ( finite_finite_l @ top_top_set_l )
=> ( finite785973648od_l_l @ top_to320296343od_l_l ) ) ) ).
% finite_Prod_UNIV
thf(fact_280_ex__new__if__finite,axiom,
! [A5: set_r] :
( ~ ( finite_finite_r @ top_top_set_r )
=> ( ( finite_finite_r @ A5 )
=> ? [A3: r] :
~ ( member_r @ A3 @ A5 ) ) ) ).
% ex_new_if_finite
thf(fact_281_ex__new__if__finite,axiom,
! [A5: set_l] :
( ~ ( finite_finite_l @ top_top_set_l )
=> ( ( finite_finite_l @ A5 )
=> ? [A3: l] :
~ ( member_l @ A3 @ A5 ) ) ) ).
% ex_new_if_finite
thf(fact_282_finite__prod,axiom,
( ( finite1507191824od_r_r @ top_to2034696215od_r_r )
= ( ( finite_finite_r @ top_top_set_r )
& ( finite_finite_r @ top_top_set_r ) ) ) ).
% finite_prod
thf(fact_283_finite__prod,axiom,
( ( finite1457622794od_r_l @ top_to1639761425od_r_l )
= ( ( finite_finite_r @ top_top_set_r )
& ( finite_finite_l @ top_top_set_l ) ) ) ).
% finite_prod
thf(fact_284_finite__prod,axiom,
( ( finite835542678od_l_r @ top_to715231133od_l_r )
= ( ( finite_finite_l @ top_top_set_l )
& ( finite_finite_r @ top_top_set_r ) ) ) ).
% finite_prod
thf(fact_285_finite__prod,axiom,
( ( finite785973648od_l_l @ top_to320296343od_l_l )
= ( ( finite_finite_l @ top_top_set_l )
& ( finite_finite_l @ top_top_set_l ) ) ) ).
% finite_prod
thf(fact_286_Finite__Set_Ofinite__set,axiom,
( ( finite_finite_set_r @ top_top_set_set_r )
= ( finite_finite_r @ top_top_set_r ) ) ).
% Finite_Set.finite_set
thf(fact_287_Finite__Set_Ofinite__set,axiom,
( ( finite_finite_set_l @ top_top_set_set_l )
= ( finite_finite_l @ top_top_set_l ) ) ).
% Finite_Set.finite_set
thf(fact_288_substitution_Ostep__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I1_J,axiom,
! [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] :
( ( substitution_r_l_v @ Subst )
=> ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
=> ( ( domain1547879849_r_l_v @ S )
=> ( ( subsum680764357_r_l_v @ S )
=> ( domain1547879849_r_l_v @ S2 ) ) ) ) ) ).
% substitution.step_preserves_\<S>\<^sub>G_and_\<A>\<^sub>G(1)
thf(fact_289_substitution_Ostep__preserves___092_060S_062_092_060_094sub_062G__and___092_060A_062_092_060_094sub_062G_I2_J,axiom,
! [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] :
( ( substitution_r_l_v @ Subst )
=> ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
=> ( ( domain1547879849_r_l_v @ S )
=> ( ( subsum680764357_r_l_v @ S )
=> ( subsum680764357_r_l_v @ S2 ) ) ) ) ) ).
% substitution.step_preserves_\<S>\<^sub>G_and_\<A>\<^sub>G(2)
thf(fact_290_finite__update__induct,axiom,
! [F: r > option1457017436_r_l_v,C: option1457017436_r_l_v,P: ( r > option1457017436_r_l_v ) > $o] :
( ( finite_finite_r
@ ( collect_r
@ ^ [A4: r] :
( ( F @ A4 )
!= C ) ) )
=> ( ( P
@ ^ [A4: r] : C )
=> ( ! [A3: r,B3: option1457017436_r_l_v,F3: r > option1457017436_r_l_v] :
( ( finite_finite_r
@ ( collect_r
@ ^ [C3: r] :
( ( F3 @ C3 )
!= C ) ) )
=> ( ( ( F3 @ A3 )
= C )
=> ( ( B3 != C )
=> ( ( P @ F3 )
=> ( P @ ( fun_up709272714_r_l_v @ F3 @ A3 @ B3 ) ) ) ) ) )
=> ( P @ F ) ) ) ) ).
% finite_update_induct
thf(fact_291_finite__update__induct,axiom,
! [F: l > option_val_r_l_v,C: option_val_r_l_v,P: ( l > option_val_r_l_v ) > $o] :
( ( finite_finite_l
@ ( collect_l
@ ^ [A4: l] :
( ( F @ A4 )
!= C ) ) )
=> ( ( P
@ ^ [A4: l] : C )
=> ( ! [A3: l,B3: option_val_r_l_v,F3: l > option_val_r_l_v] :
( ( finite_finite_l
@ ( collect_l
@ ^ [C3: l] :
( ( F3 @ C3 )
!= C ) ) )
=> ( ( ( F3 @ A3 )
= C )
=> ( ( B3 != C )
=> ( ( P @ F3 )
=> ( P @ ( fun_up1835647912_r_l_v @ F3 @ A3 @ B3 ) ) ) ) ) )
=> ( P @ F ) ) ) ) ).
% finite_update_induct
thf(fact_292_substitution_Onice__ind__inv__is__inductive__invariant,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( induct1670415253_r_l_v @ Subst
@ ^ [S5: r > option1457017436_r_l_v] :
( ( domain1547879849_r_l_v @ S5 )
& ( subsum680764357_r_l_v @ S5 ) ) ) ) ).
% substitution.nice_ind_inv_is_inductive_invariant
thf(fact_293_substitution_Odomains__subsume__globally__def,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( ( domain1547879849_r_l_v @ S )
= ( ! [R6: r,Ls2: produc1156025366_r_l_v] :
( ( ( S @ R6 )
= ( some_P1807977723_r_l_v @ Ls2 ) )
=> ( domain87684397_l_r_v @ Ls2 ) ) ) ) ) ).
% substitution.domains_subsume_globally_def
thf(fact_294_substitution_Odomains__subsume__globallyI,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( ! [R5: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E3: expr_r_l_v] :
( ( ( S @ R5 )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) ) )
=> ( domain87684397_l_r_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) ) )
=> ( domain1547879849_r_l_v @ S ) ) ) ).
% substitution.domains_subsume_globallyI
thf(fact_295__092_060R_062_092_060_094sub_062GI,axiom,
! [Alpha2: r > r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v,Beta2: l > l] :
( ( bij_betw_r_r @ Alpha2 @ top_top_set_r @ top_top_set_r )
=> ( ! [R5: r] :
( ( ( S @ R5 )
= none_P277133687_r_l_v )
=> ( ( S2 @ ( Alpha2 @ R5 ) )
= none_P277133687_r_l_v ) )
=> ( ! [R5: r,Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E3: expr_r_l_v] :
( ( ( S @ R5 )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) ) )
=> ( ( S2 @ ( Alpha2 @ R5 ) )
= ( some_P1807977723_r_l_v @ ( r_L_r_l_v @ Alpha2 @ Beta2 @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ E3 ) ) ) ) ) )
=> ( ( r_G_r_l_v @ Alpha2 @ Beta2 @ S )
= S2 ) ) ) ) ).
% \<R>\<^sub>GI
thf(fact_296_substitution_Osubsumes__accessible__globallyI,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( ! [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] :
( ( ( S @ R_1 )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_1 @ ( produc1834103605_r_l_v @ Tau_1 @ E_1 ) ) ) )
=> ( ( ( S @ R_2 )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_2 @ ( produc1834103605_r_l_v @ Tau_2 @ E_2 ) ) ) )
=> ( subsum148050133_r_l_v @ R_1 @ R_2 @ S ) ) )
=> ( subsum680764357_r_l_v @ S ) ) ) ).
% substitution.subsumes_accessible_globallyI
thf(fact_297__092_060R_062_092_060_094sub_062G__implements__renaming,axiom,
! [Alpha2: r > r,Beta2: l > l,S: r > option1457017436_r_l_v] :
( ( bij_betw_r_r @ Alpha2 @ top_top_set_r @ top_top_set_r )
=> ( is_glo1871033385_r_l_v @ Alpha2 @ Beta2 @ S @ ( r_G_r_l_v @ Alpha2 @ Beta2 @ S ) ) ) ).
% \<R>\<^sub>G_implements_renaming
thf(fact_298_subsumes__accessible__globallyI,axiom,
! [S: r > option1457017436_r_l_v] :
( ! [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] :
( ( ( S @ R_1 )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_1 @ ( produc1834103605_r_l_v @ Tau_1 @ E_1 ) ) ) )
=> ( ( ( S @ R_2 )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma_2 @ ( produc1834103605_r_l_v @ Tau_2 @ E_2 ) ) ) )
=> ( subsum148050133_r_l_v @ R_1 @ R_2 @ S ) ) )
=> ( subsum680764357_r_l_v @ S ) ) ).
% subsumes_accessible_globallyI
thf(fact_299_renaming__distr__global_I1_J,axiom,
! [Alpha2: r > r,Beta2: l > l,S: r > option1457017436_r_l_v,R: r,Ls: produc1156025366_r_l_v] :
( ( bij_betw_r_r @ Alpha2 @ top_top_set_r @ top_top_set_r )
=> ( ( r_G_r_l_v @ Alpha2 @ Beta2 @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ Ls ) ) )
= ( fun_up709272714_r_l_v @ ( r_G_r_l_v @ Alpha2 @ Beta2 @ S ) @ ( Alpha2 @ R ) @ ( some_P1807977723_r_l_v @ ( r_L_r_l_v @ Alpha2 @ Beta2 @ Ls ) ) ) ) ) ).
% renaming_distr_global(1)
thf(fact_300_RID_092_060_094sub_062GI_I2_J,axiom,
! [S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
( ( ( S @ R2 )
= ( some_P1807977723_r_l_v @ Ls ) )
=> ( ( member_r @ R @ ( rID_L_l_r_v @ Ls ) )
=> ( member_r @ R @ ( rID_G_r_l_v @ S ) ) ) ) ).
% RID\<^sub>GI(2)
thf(fact_301_local__state__of__finite__restricted__global__state__is__finite_I1_J,axiom,
! [S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
( ( ( S @ R2 )
= ( some_P1807977723_r_l_v @ Ls ) )
=> ( ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
=> ( ( R != R2 )
=> ( finite_finite_r @ ( rID_L_l_r_v @ Ls ) ) ) ) ) ).
% local_state_of_finite_restricted_global_state_is_finite(1)
thf(fact_302_substitution_Olocal__state__of__finite__restricted__global__state__is__finite_I1_J,axiom,
! [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] :
( ( substitution_r_l_v @ Subst )
=> ( ( ( S @ R2 )
= ( some_P1807977723_r_l_v @ Ls ) )
=> ( ( finite_finite_r @ ( rID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
=> ( ( R != R2 )
=> ( finite_finite_r @ ( rID_L_l_r_v @ Ls ) ) ) ) ) ) ).
% substitution.local_state_of_finite_restricted_global_state_is_finite(1)
thf(fact_303_reachable__imp__identifiers__available_I2_J,axiom,
! [S: r > option1457017436_r_l_v] :
( ( reachable_r_l_v @ subst @ S )
=> ( ~ ( finite_finite_l @ top_top_set_l )
=> ? [L: l] :
~ ( member_l @ L @ ( lID_G_r_l_v @ S ) ) ) ) ).
% reachable_imp_identifiers_available(2)
thf(fact_304_only__fork__introduces__rids,axiom,
! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
=> ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E5: cntxt_r_l_v,E3: expr_r_l_v] :
( ( S @ R )
!= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E5 @ ( rfork_r_l_v @ E3 ) ) ) ) ) )
=> ( ord_less_eq_set_r @ ( rID_G_r_l_v @ S2 ) @ ( rID_G_r_l_v @ S ) ) ) ) ).
% only_fork_introduces_rids
thf(fact_305_empty__map__finite_I4_J,axiom,
( finite_finite_l
@ ( lID_G_r_l_v
@ ^ [X2: r] : none_P277133687_r_l_v ) ) ).
% empty_map_finite(4)
thf(fact_306_in__renamed__in__unlabelled__global_I2_J,axiom,
! [Alpha2: r > r,Beta2: l > l,L2: l,S: r > option1457017436_r_l_v] :
( ( bij_betw_r_r @ Alpha2 @ top_top_set_r @ top_top_set_r )
=> ( ( bij_betw_l_l @ Beta2 @ top_top_set_l @ top_top_set_l )
=> ( ( member_l @ ( Beta2 @ L2 ) @ ( lID_G_r_l_v @ ( r_G_r_l_v @ Alpha2 @ Beta2 @ S ) ) )
= ( member_l @ L2 @ ( lID_G_r_l_v @ S ) ) ) ) ) ).
% in_renamed_in_unlabelled_global(2)
thf(fact_307_RID_092_060_094sub_062L__finite__invariant,axiom,
! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
=> ( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
=> ( finite_finite_l @ ( lID_G_r_l_v @ S2 ) ) ) ) ).
% RID\<^sub>L_finite_invariant
thf(fact_308_reachable__imp__identifiers__finite_I2_J,axiom,
! [S: r > option1457017436_r_l_v] :
( ( reachable_r_l_v @ subst @ S )
=> ( finite_finite_l @ ( lID_G_r_l_v @ S ) ) ) ).
% reachable_imp_identifiers_finite(2)
thf(fact_309_in__restricted__global__in__unrestricted__global_I2_J,axiom,
! [L2: l,S: r > option1457017436_r_l_v,R: r] :
( ( member_l @ L2 @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
=> ( member_l @ L2 @ ( lID_G_r_l_v @ S ) ) ) ).
% in_restricted_global_in_unrestricted_global(2)
thf(fact_310_LID_092_060_094sub_062GI,axiom,
! [S: r > option1457017436_r_l_v,R: r,Ls: produc1156025366_r_l_v,L2: l] :
( ( ( S @ R )
= ( some_P1807977723_r_l_v @ Ls ) )
=> ( ( member_l @ L2 @ ( lID_L_l_r_v @ Ls ) )
=> ( member_l @ L2 @ ( lID_G_r_l_v @ S ) ) ) ) ).
% LID\<^sub>GI
thf(fact_311_finite__Collect__subsets,axiom,
! [A5: set_r] :
( ( finite_finite_r @ A5 )
=> ( finite_finite_set_r
@ ( collect_set_r
@ ^ [B6: set_r] : ( ord_less_eq_set_r @ B6 @ A5 ) ) ) ) ).
% finite_Collect_subsets
thf(fact_312_finite__Collect__subsets,axiom,
! [A5: set_l] :
( ( finite_finite_l @ A5 )
=> ( finite_finite_set_l
@ ( collect_set_l
@ ^ [B6: set_l] : ( ord_less_eq_set_l @ B6 @ A5 ) ) ) ) ).
% finite_Collect_subsets
thf(fact_313_finite__state__imp__restriction__finite_I2_J,axiom,
! [S: r > option1457017436_r_l_v,R: r] :
( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
=> ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ).
% finite_state_imp_restriction_finite(2)
thf(fact_314_in__restricted__global__in__updated__global_I2_J,axiom,
! [L2: l,S: r > option1457017436_r_l_v,R: r,Ls: produc1156025366_r_l_v] :
( ( member_l @ L2 @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
=> ( member_l @ L2 @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ Ls ) ) ) ) ) ).
% in_restricted_global_in_updated_global(2)
thf(fact_315_local__state__of__finite__restricted__global__state__is__finite_I2_J,axiom,
! [S: r > option1457017436_r_l_v,R2: r,Ls: produc1156025366_r_l_v,R: r] :
( ( ( S @ R2 )
= ( some_P1807977723_r_l_v @ Ls ) )
=> ( ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
=> ( ( R != R2 )
=> ( finite_finite_l @ ( lID_L_l_r_v @ Ls ) ) ) ) ) ).
% local_state_of_finite_restricted_global_state_is_finite(2)
thf(fact_316_ID__restricted__global__subset__unrestricted_I1_J,axiom,
! [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 ) ) ).
% ID_restricted_global_subset_unrestricted(1)
thf(fact_317_finite__has__minimal2,axiom,
! [A5: set_set_r,A: set_r] :
( ( finite_finite_set_r @ A5 )
=> ( ( member_set_r @ A @ A5 )
=> ? [X3: set_r] :
( ( member_set_r @ X3 @ A5 )
& ( ord_less_eq_set_r @ X3 @ A )
& ! [Xa2: set_r] :
( ( member_set_r @ Xa2 @ A5 )
=> ( ( ord_less_eq_set_r @ Xa2 @ X3 )
=> ( X3 = Xa2 ) ) ) ) ) ) ).
% finite_has_minimal2
thf(fact_318_finite__has__minimal2,axiom,
! [A5: set_set_l,A: set_l] :
( ( finite_finite_set_l @ A5 )
=> ( ( member_set_l @ A @ A5 )
=> ? [X3: set_l] :
( ( member_set_l @ X3 @ A5 )
& ( ord_less_eq_set_l @ X3 @ A )
& ! [Xa2: set_l] :
( ( member_set_l @ Xa2 @ A5 )
=> ( ( ord_less_eq_set_l @ Xa2 @ X3 )
=> ( X3 = Xa2 ) ) ) ) ) ) ).
% finite_has_minimal2
thf(fact_319_finite__has__maximal2,axiom,
! [A5: set_set_r,A: set_r] :
( ( finite_finite_set_r @ A5 )
=> ( ( member_set_r @ A @ A5 )
=> ? [X3: set_r] :
( ( member_set_r @ X3 @ A5 )
& ( ord_less_eq_set_r @ A @ X3 )
& ! [Xa2: set_r] :
( ( member_set_r @ Xa2 @ A5 )
=> ( ( ord_less_eq_set_r @ X3 @ Xa2 )
=> ( X3 = Xa2 ) ) ) ) ) ) ).
% finite_has_maximal2
thf(fact_320_finite__has__maximal2,axiom,
! [A5: set_set_l,A: set_l] :
( ( finite_finite_set_l @ A5 )
=> ( ( member_set_l @ A @ A5 )
=> ? [X3: set_l] :
( ( member_set_l @ X3 @ A5 )
& ( ord_less_eq_set_l @ A @ X3 )
& ! [Xa2: set_l] :
( ( member_set_l @ Xa2 @ A5 )
=> ( ( ord_less_eq_set_l @ X3 @ Xa2 )
=> ( X3 = Xa2 ) ) ) ) ) ) ).
% finite_has_maximal2
thf(fact_321_rev__finite__subset,axiom,
! [B5: set_r,A5: set_r] :
( ( finite_finite_r @ B5 )
=> ( ( ord_less_eq_set_r @ A5 @ B5 )
=> ( finite_finite_r @ A5 ) ) ) ).
% rev_finite_subset
thf(fact_322_rev__finite__subset,axiom,
! [B5: set_l,A5: set_l] :
( ( finite_finite_l @ B5 )
=> ( ( ord_less_eq_set_l @ A5 @ B5 )
=> ( finite_finite_l @ A5 ) ) ) ).
% rev_finite_subset
thf(fact_323_infinite__super,axiom,
! [S6: set_r,T2: set_r] :
( ( ord_less_eq_set_r @ S6 @ T2 )
=> ( ~ ( finite_finite_r @ S6 )
=> ~ ( finite_finite_r @ T2 ) ) ) ).
% infinite_super
thf(fact_324_infinite__super,axiom,
! [S6: set_l,T2: set_l] :
( ( ord_less_eq_set_l @ S6 @ T2 )
=> ( ~ ( finite_finite_l @ S6 )
=> ~ ( finite_finite_l @ T2 ) ) ) ).
% infinite_super
thf(fact_325_finite__subset,axiom,
! [A5: set_r,B5: set_r] :
( ( ord_less_eq_set_r @ A5 @ B5 )
=> ( ( finite_finite_r @ B5 )
=> ( finite_finite_r @ A5 ) ) ) ).
% finite_subset
thf(fact_326_finite__subset,axiom,
! [A5: set_l,B5: set_l] :
( ( ord_less_eq_set_l @ A5 @ B5 )
=> ( ( finite_finite_l @ B5 )
=> ( finite_finite_l @ A5 ) ) ) ).
% finite_subset
thf(fact_327_LID_092_060_094sub_062GE,axiom,
! [L2: l,S: r > option1457017436_r_l_v] :
( ( member_l @ L2 @ ( lID_G_r_l_v @ S ) )
=> ~ ! [R5: r,Ls3: produc1156025366_r_l_v] :
( ( ( S @ R5 )
= ( some_P1807977723_r_l_v @ Ls3 ) )
=> ~ ( member_l @ L2 @ ( lID_L_l_r_v @ Ls3 ) ) ) ) ).
% LID\<^sub>GE
thf(fact_328_substitution_ORID_092_060_094sub_062L__finite__invariant,axiom,
! [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] :
( ( substitution_r_l_v @ Subst )
=> ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
=> ( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
=> ( finite_finite_l @ ( lID_G_r_l_v @ S2 ) ) ) ) ) ).
% substitution.RID\<^sub>L_finite_invariant
thf(fact_329_ID__restricted__global__subset__unrestricted_I2_J,axiom,
! [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 ) ) ).
% ID_restricted_global_subset_unrestricted(2)
thf(fact_330_substitution_Oreachable__imp__identifiers__finite_I2_J,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( ( reachable_r_l_v @ Subst @ S )
=> ( finite_finite_l @ ( lID_G_r_l_v @ S ) ) ) ) ).
% substitution.reachable_imp_identifiers_finite(2)
thf(fact_331_substitution_Oempty__map__finite_I4_J,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( finite_finite_l
@ ( lID_G_r_l_v
@ ^ [X2: r] : none_P277133687_r_l_v ) ) ) ).
% substitution.empty_map_finite(4)
thf(fact_332_substitution_Oreachable__imp__identifiers__available_I2_J,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( ( reachable_r_l_v @ Subst @ S )
=> ( ~ ( finite_finite_l @ top_top_set_l )
=> ? [L: l] :
~ ( member_l @ L @ ( lID_G_r_l_v @ S ) ) ) ) ) ).
% substitution.reachable_imp_identifiers_available(2)
thf(fact_333_substitution_Ofinite__state__imp__restriction__finite_I2_J,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r] :
( ( substitution_r_l_v @ Subst )
=> ( ( finite_finite_l @ ( lID_G_r_l_v @ S ) )
=> ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) ) ) ) ).
% substitution.finite_state_imp_restriction_finite(2)
thf(fact_334_substitution_Oin__renamed__in__unlabelled__global_I2_J,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,Alpha2: r > r,Beta2: l > l,L2: l,S: r > option1457017436_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( ( bij_betw_r_r @ Alpha2 @ top_top_set_r @ top_top_set_r )
=> ( ( bij_betw_l_l @ Beta2 @ top_top_set_l @ top_top_set_l )
=> ( ( member_l @ ( Beta2 @ L2 ) @ ( lID_G_r_l_v @ ( r_G_r_l_v @ Alpha2 @ Beta2 @ S ) ) )
= ( member_l @ L2 @ ( lID_G_r_l_v @ S ) ) ) ) ) ) ).
% substitution.in_renamed_in_unlabelled_global(2)
thf(fact_335_substitution_Olocal__state__of__finite__restricted__global__state__is__finite_I2_J,axiom,
! [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] :
( ( substitution_r_l_v @ Subst )
=> ( ( ( S @ R2 )
= ( some_P1807977723_r_l_v @ Ls ) )
=> ( ( finite_finite_l @ ( lID_G_r_l_v @ ( fun_up709272714_r_l_v @ S @ R @ none_P277133687_r_l_v ) ) )
=> ( ( R != R2 )
=> ( finite_finite_l @ ( lID_L_l_r_v @ Ls ) ) ) ) ) ) ).
% substitution.local_state_of_finite_restricted_global_state_is_finite(2)
thf(fact_336_substitution_Oonly__fork__introduces__rids,axiom,
! [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] :
( ( substitution_r_l_v @ Subst )
=> ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
=> ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E5: cntxt_r_l_v,E3: expr_r_l_v] :
( ( S @ R )
!= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E5 @ ( rfork_r_l_v @ E3 ) ) ) ) ) )
=> ( ord_less_eq_set_r @ ( rID_G_r_l_v @ S2 ) @ ( rID_G_r_l_v @ S ) ) ) ) ) ).
% substitution.only_fork_introduces_rids
thf(fact_337_only__new__introduces__lids_H,axiom,
! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v,L2: l] :
( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
=> ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E5: cntxt_r_l_v,V2: val_r_l_v] :
( ( S @ R )
!= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E5 @ ( ref_r_l_v @ ( vE_r_l_v @ V2 ) ) ) ) ) ) )
=> ( ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S ) )
=> ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S2 ) ) ) ) ) ).
% only_new_introduces_lids'
thf(fact_338_SLC__new,axiom,
! [S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,V: val_r_l_v,S_2: r > option1457017436_r_l_v,L2: l,R2: r,S_22: r > option1457017436_r_l_v] :
( ( ( S_1 @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
=> ( ( S_2
= ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) ) ) ) ) ) )
=> ( ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S_1 ) )
=> ( ( revision_step_r_l_v @ subst @ R2 @ S_1 @ S_22 )
=> ( ( R != R2 )
=> ( ( reachable_r_l_v @ subst @ S_1 )
=> ( ~ ( finite_finite_l @ top_top_set_l )
=> ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
( ( eq_states_r_l_v @ S_3 @ S_32 )
& ( ( revision_step_r_l_v @ subst @ R2 @ S_2 @ S_3 )
| ( S_2 = S_3 ) )
& ( ( revision_step_r_l_v @ subst @ R @ S_22 @ S_32 )
| ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ).
% SLC_new
thf(fact_339_val_Oinject_I3_J,axiom,
! [X32: l,Y32: l] :
( ( ( loc_l_r_v @ X32 )
= ( loc_l_r_v @ Y32 ) )
= ( X32 = Y32 ) ) ).
% val.inject(3)
thf(fact_340_expr_Oinject_I4_J,axiom,
! [X4: expr_r_l_v,Y4: expr_r_l_v] :
( ( ( ref_r_l_v @ X4 )
= ( ref_r_l_v @ Y4 ) )
= ( X4 = Y4 ) ) ).
% expr.inject(4)
thf(fact_341_revision__step_Onew,axiom,
! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,V: val_r_l_v,L2: l] :
( ( ( S @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
=> ( ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S ) )
=> ( revision_step_r_l_v @ subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) ) ) ) ) ) ) ) ) ).
% revision_step.new
thf(fact_342_only__new__introduces__lids,axiom,
! [R: r,S: r > option1457017436_r_l_v,S2: r > option1457017436_r_l_v] :
( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
=> ( ! [Sigma: l > option_val_r_l_v,Tau: l > option_val_r_l_v,E5: cntxt_r_l_v,V2: val_r_l_v] :
( ( S @ R )
!= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma @ ( produc1834103605_r_l_v @ Tau @ ( plug_r_l_v @ E5 @ ( ref_r_l_v @ ( vE_r_l_v @ V2 ) ) ) ) ) ) )
=> ( ord_less_eq_set_l @ ( lID_G_r_l_v @ S2 ) @ ( lID_G_r_l_v @ S ) ) ) ) ).
% only_new_introduces_lids
thf(fact_343_new__pseudodeterministic,axiom,
! [S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
( ( ( S @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
=> ( ( revision_step_r_l_v @ subst @ R @ S @ S2 )
= ( ? [L3: l] :
( ~ ( member_l @ L3 @ ( lID_G_r_l_v @ S ) )
& ( S2
= ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L3 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( loc_l_r_v @ L3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% new_pseudodeterministic
thf(fact_344_expr_Odistinct_I5_J,axiom,
! [X1: val_r_l_v,X4: expr_r_l_v] :
( ( vE_r_l_v @ X1 )
!= ( ref_r_l_v @ X4 ) ) ).
% expr.distinct(5)
thf(fact_345_val_Odistinct_I15_J,axiom,
! [X32: l,X4: r] :
( ( loc_l_r_v @ X32 )
!= ( rid_r_l_v @ X4 ) ) ).
% val.distinct(15)
thf(fact_346_expr_Odistinct_I43_J,axiom,
! [X4: expr_r_l_v,X8: expr_r_l_v] :
( ( ref_r_l_v @ X4 )
!= ( rjoin_r_l_v @ X8 ) ) ).
% expr.distinct(43)
thf(fact_347_expr_Odistinct_I41_J,axiom,
! [X4: expr_r_l_v,X7: expr_r_l_v] :
( ( ref_r_l_v @ X4 )
!= ( rfork_r_l_v @ X7 ) ) ).
% expr.distinct(41)
thf(fact_348_val_Odistinct_I3_J,axiom,
! [X1: const,X32: l] :
( ( cV_r_l_v @ X1 )
!= ( loc_l_r_v @ X32 ) ) ).
% val.distinct(3)
thf(fact_349_substitution_Onew__pseudodeterministic,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,V: val_r_l_v,S2: r > option1457017436_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( ( ( S @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
=> ( ( revision_step_r_l_v @ Subst @ R @ S @ S2 )
= ( ? [L3: l] :
( ~ ( member_l @ L3 @ ( lID_G_r_l_v @ S ) )
& ( S2
= ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L3 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( loc_l_r_v @ L3 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% substitution.new_pseudodeterministic
thf(fact_350_substitution_Orevision__step_Onew,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,V: val_r_l_v,L2: l] :
( ( substitution_r_l_v @ Subst )
=> ( ( ( S @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
=> ( ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S ) )
=> ( revision_step_r_l_v @ Subst @ R @ S @ ( fun_up709272714_r_l_v @ S @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) ) ) ) ) ) ) ) ) ) ).
% substitution.revision_step.new
thf(fact_351_substitution_OSLC__new,axiom,
! [Subst: expr_r_l_v > v > expr_r_l_v > expr_r_l_v,S_1: r > option1457017436_r_l_v,R: r,Sigma2: l > option_val_r_l_v,Tau2: l > option_val_r_l_v,E: cntxt_r_l_v,V: val_r_l_v,S_2: r > option1457017436_r_l_v,L2: l,R2: r,S_22: r > option1457017436_r_l_v] :
( ( substitution_r_l_v @ Subst )
=> ( ( ( S_1 @ R )
= ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ Tau2 @ ( plug_r_l_v @ E @ ( ref_r_l_v @ ( vE_r_l_v @ V ) ) ) ) ) ) )
=> ( ( S_2
= ( fun_up709272714_r_l_v @ S_1 @ R @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ Sigma2 @ ( produc1834103605_r_l_v @ ( fun_up1835647912_r_l_v @ Tau2 @ L2 @ ( some_val_r_l_v @ V ) ) @ ( plug_r_l_v @ E @ ( vE_r_l_v @ ( loc_l_r_v @ L2 ) ) ) ) ) ) ) )
=> ( ~ ( member_l @ L2 @ ( lID_G_r_l_v @ S_1 ) )
=> ( ( revision_step_r_l_v @ Subst @ R2 @ S_1 @ S_22 )
=> ( ( R != R2 )
=> ( ( reachable_r_l_v @ Subst @ S_1 )
=> ( ~ ( finite_finite_l @ top_top_set_l )
=> ? [S_3: r > option1457017436_r_l_v,S_32: r > option1457017436_r_l_v] :
( ( eq_states_r_l_v @ S_3 @ S_32 )
& ( ( revision_step_r_l_v @ Subst @ R2 @ S_2 @ S_3 )
| ( S_2 = S_3 ) )
& ( ( revision_step_r_l_v @ Subst @ R @ S_22 @ S_32 )
| ( S_22 = S_32 ) ) ) ) ) ) ) ) ) ) ) ).
% substitution.SLC_new
% Helper facts (5)
thf(help_If_2_1_If_001t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_T,axiom,
! [X: option_val_r_l_v,Y: option_val_r_l_v] :
( ( if_option_val_r_l_v @ $false @ X @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__Option__Ooption_It__Data__Oval_Itf__r_Mtf__l_Mtf__v_J_J_T,axiom,
! [X: option_val_r_l_v,Y: option_val_r_l_v] :
( ( if_option_val_r_l_v @ $true @ X @ Y )
= X ) ).
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,
! [P: $o] :
( ( P = $true )
| ( P = $false ) ) ).
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,
! [X: option1457017436_r_l_v,Y: option1457017436_r_l_v] :
( ( if_opt1153928738_r_l_v @ $false @ X @ Y )
= Y ) ).
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,
! [X: option1457017436_r_l_v,Y: option1457017436_r_l_v] :
( ( if_opt1153928738_r_l_v @ $true @ X @ Y )
= X ) ).
% Conjectures (1)
thf(conj_0,conjecture,
( s
= ( fun_up709272714_r_l_v @ s @ r2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( rfork_r_l_v @ e2 ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------